<?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_25.out</source>

<heading><![CDATA[
Prover9 (64) version 2022-12A (+ restricted para), January 2023.
Process 2610354 was started by veroff on b146-19,
Sat Jan 17 08:41:51 2026
The command was "prover9 -f nil3_23_32_to_25.in".
]]></heading>

<proof number="1" length="18659" max_count="65">

<comments><![CDATA[
% Proof 1 at 4668.22 (+ 271.21) seconds: "nil3 25, aa2-Nl".
% Length of proof: 18659 (0 new hints)
% Level of proof: 932
% Maximum clause weight: 65.000
% Given clauses in run: 18647
% Given clauses in proof: 18647 (0 new hints)
]]></comments>

  <clause id="1" type="goal">
    <literal><![CDATA[
      a(a(x,a(y,z,u),w),v5,v6) = 1
    ]]></literal>
    <attribute><![CDATA[
      label("nil3 25, aa2-Nl")
    ]]></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(a(c1,a(c2,c3,c4),c5),c6,c7) != 1
    ]]></literal>
    <attribute><![CDATA[
      label("nil3 25, aa2-Nl")
    ]]></attribute>
    <attribute><![CDATA[
      answer("nil3 25, aa2-Nl")
    ]]></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[
      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="182">
    <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="183">
    <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="184">
    <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="185">
    <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="186">
    <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="187">
    <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="188">
    <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="189">
    <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="190">
    <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="191">
    <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="192">
    <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="193">
    <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="194">
    <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="195">
    <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="196">
    <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="197">
    <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="198">
    <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="199">
    <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="200">
    <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="201">
    <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="202">
    <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="203">
    <literal><![CDATA[
      K(x,1) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,202,a)].">
      <j1 rule="hyper" parents="50 202"/>
    </justification>
  </clause>

  <clause id="204">
    <literal><![CDATA[
      T(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(49,a,202,a)].">
      <j1 rule="hyper" parents="49 202"/>
    </justification>
  </clause>

  <clause id="205">
    <literal><![CDATA[
      K(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,204,a)].">
      <j1 rule="hyper" parents="50 204"/>
    </justification>
  </clause>

  <clause id="206">
    <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="207">
    <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="208">
    <literal><![CDATA[
      K(x,1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(203(a,2),120(a,1,1))].">
      <j1 rule="para" parents="203 120"/>
    </justification>
  </clause>

  <clause id="209">
    <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="210">
    <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="211">
    <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="212">
    <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="213">
    <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="214">
    <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="215">
    <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="216">
    <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="217">
    <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="218">
    <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="219">
    <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="220">
    <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="221">
    <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="222">
    <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="223">
    <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="224">
    <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="225">
    <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="226">
    <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="227">
    <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="228">
    <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="229">
    <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="230">
    <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="231">
    <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="232">
    <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="233">
    <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="234">
    <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="235">
    <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="236">
    <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="237">
    <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="238">
    <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="239">
    <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="240">
    <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="241">
    <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="242">
    <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="243">
    <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="244">
    <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="245">
    <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="246">
    <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="247">
    <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="248">
    <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="249">
    <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="250">
    <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="251">
    <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="252">
    <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="253">
    <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="254">
    <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="255">
    <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="256">
    <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="257">
    <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="258">
    <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="259">
    <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="260">
    <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="261">
    <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="262">
    <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="263">
    <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="264">
    <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="265">
    <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="266">
    <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="267">
    <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="268">
    <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="269">
    <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="270">
    <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="271">
    <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="272">
    <literal><![CDATA[
      K(x \ y,y / x) = 1
    ]]></literal>
    <justification jstring="[para(107(a,1),271(a,1,1))].">
      <j1 rule="para" parents="107 271"/>
    </justification>
  </clause>

  <clause id="273">
    <literal><![CDATA[
      x / T(y,y \ x) = y \ x
    ]]></literal>
    <justification jstring="[para(5(a,1),191(a,1,1))].">
      <j1 rule="para" parents="5 191"/>
    </justification>
  </clause>

  <clause id="274">
    <literal><![CDATA[
      (x * y) / z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(191(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="191 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="275">
    <literal><![CDATA[
      (x * y) / T(y,T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(105(a,1),191(a,1,1))].">
      <j1 rule="para" parents="105 191"/>
    </justification>
  </clause>

  <clause id="276">
    <literal><![CDATA[
      (x / y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(195(a,2),174(a,1))].">
      <j1 rule="para" parents="195 174"/>
    </justification>
  </clause>

  <clause id="277">
    <literal><![CDATA[
      (x / y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(195(a,2),175(a,1))].">
      <j1 rule="para" parents="195 175"/>
    </justification>
  </clause>

  <clause id="278">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      T(z / x,x) = y
    ]]></literal>
    <justification jstring="[para(226(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="226 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="279">
    <literal><![CDATA[
      (x * T(T(y,x),z)) / x = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,18,a,b,230,a),flip(a)].">
      <j1 rule="hyper" parents="35 18 230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="280">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(230(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="230 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="281">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * z) / y = x
    ]]></literal>
    <justification jstring="[para(230(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="230 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="282">
    <literal><![CDATA[
      K(x,(y * x) / y) = 1
    ]]></literal>
    <justification jstring="[para(230(a,1),271(a,1,1))].">
      <j1 rule="para" parents="230 271"/>
    </justification>
  </clause>

  <clause id="283">
    <literal><![CDATA[
      L(x,y,z) \ (u * L(T(x,u),y,z)) = u
    ]]></literal>
    <justification jstring="[para(20(a,2),232(a,1,2,2))].">
      <j1 rule="para" parents="20 232"/>
    </justification>
  </clause>

  <clause id="284">
    <literal><![CDATA[
      T(x \ y,y / x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(51,a,272,a)].">
      <j1 rule="hyper" parents="51 272"/>
    </justification>
  </clause>

  <clause id="285">
    <literal><![CDATA[
      T(x,(y * x) / y) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,282,a)].">
      <j1 rule="hyper" parents="51 282"/>
    </justification>
  </clause>

  <clause id="286">
    <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="287">
    <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="288">
    <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="289">
    <literal><![CDATA[
      1 != x
    ]]></literal>
    <literal><![CDATA[
      x \ y = y
    ]]></literal>
    <justification jstring="[para(69(a,1),192(a,1))].">
      <j1 rule="para" parents="69 192"/>
    </justification>
  </clause>

  <clause id="290">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      x * (y \ z) = z
    ]]></literal>
    <justification jstring="[para(6(a,1),193(a,1)),flip(b)].">
      <j1 rule="para" parents="6 193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="291">
    <literal><![CDATA[
      x / L(y,z,u) != u * z
    ]]></literal>
    <literal><![CDATA[
      u * (z * y) = x
    ]]></literal>
    <justification jstring="[para(13(a,2),193(a,1,2))].">
      <j1 rule="para" parents="13 193"/>
    </justification>
  </clause>

  <clause id="292">
    <literal><![CDATA[
      T(x / y,L(y \ x,z,u)) = x / y
    ]]></literal>
    <justification jstring="[para(107(a,1),218(a,1,2,1))].">
      <j1 rule="para" parents="107 218"/>
    </justification>
  </clause>

  <clause id="293">
    <literal><![CDATA[
      R(x,y,z) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(15(a,2),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="15 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="294">
    <literal><![CDATA[
      x * T(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(191(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="191 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="295">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      y * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(231(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="231 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="296">
    <literal><![CDATA[
      (x * y) * L(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(13(a,2),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="297">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(6(a,1),276(a,1,1))].">
      <j1 rule="para" parents="6 276"/>
    </justification>
  </clause>

  <clause id="298">
    <literal><![CDATA[
      x \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(191(a,1),276(a,1,1)),flip(b)].">
      <j1 rule="para" parents="191 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="299">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(6(a,1),277(a,1,1))].">
      <j1 rule="para" parents="6 277"/>
    </justification>
  </clause>

  <clause id="300">
    <literal><![CDATA[
      ((x / y) \ x) * (y \ z) = z
    ]]></literal>
    <justification jstring="[hyper(290,a,75,a)].">
      <j1 rule="hyper" parents="290 75"/>
    </justification>
  </clause>

  <clause id="301">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * (L(L(x,u,w),y,z) \ v5) = v5
    ]]></literal>
    <justification jstring="[hyper(290,a,25,a)].">
      <j1 rule="hyper" parents="290 25"/>
    </justification>
  </clause>

  <clause id="302">
    <literal><![CDATA[
      ((x / y) * y) * (x \ z) = z
    ]]></literal>
    <justification jstring="[hyper(290,a,7,a)].">
      <j1 rule="hyper" parents="290 7"/>
    </justification>
  </clause>

  <clause id="303">
    <literal><![CDATA[
      T((x * y) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(107(a,2),297(a,1))].">
      <j1 rule="para" parents="107 297"/>
    </justification>
  </clause>

  <clause id="304">
    <literal><![CDATA[
      x \ (y * 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(162(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="162 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="305">
    <literal><![CDATA[
      T(x,x) != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(17(a,2),299(a,1))].">
      <j1 rule="para" parents="17 299"/>
    </justification>
  </clause>

  <clause id="306">
    <literal><![CDATA[
      T((x * y) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(107(a,2),299(a,1))].">
      <j1 rule="para" parents="107 299"/>
    </justification>
  </clause>

  <clause id="307">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      x * (u \ (u * y)) = z
    ]]></literal>
    <justification jstring="[para(63(a,1),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="63 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="308">
    <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="309">
    <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="310">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * (z \ x) = y
    ]]></literal>
    <justification jstring="[para(67(a,1),263(a,1)),flip(b)].">
      <j1 rule="para" parents="67 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="311">
    <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="312">
    <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="313">
    <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="314">
    <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="315">
    <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="316">
    <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="317">
    <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="318">
    <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="319">
    <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="320">
    <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="321">
    <literal><![CDATA[
      (x * y) \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(84(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="84 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="322">
    <literal><![CDATA[
      (x \ y) \ y = z * (z \ T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(310,a,106,a),flip(a)].">
      <j1 rule="hyper" parents="310 106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="323">
    <literal><![CDATA[
      T(x,x \ y) * (((x \ y) \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(290,a,106,a)].">
      <j1 rule="hyper" parents="290 106"/>
    </justification>
  </clause>

  <clause id="324">
    <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="325">
    <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="326">
    <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="327">
    <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="328">
    <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="329">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,x \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(290,a,106,a(flip))].">
      <j1 rule="hyper" parents="290 106"/>
    </justification>
  </clause>

  <clause id="330">
    <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="331">
    <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="332">
    <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="333">
    <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="334">
    <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="335">
    <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="336">
    <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="337">
    <literal><![CDATA[
      (x / (y * (y \ z))) * z = x
    ]]></literal>
    <justification jstring="[hyper(260,a,151,a),flip(a)].">
      <j1 rule="hyper" parents="260 151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="338">
    <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="339">
    <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="340">
    <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="341">
    <literal><![CDATA[
      ((x / y) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(157(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="157 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="342">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(157(a,2),259(a,1))].">
      <j1 rule="para" parents="157 259"/>
    </justification>
  </clause>

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

  <clause id="344">
    <literal><![CDATA[
      x / x != y
    ]]></literal>
    <literal><![CDATA[
      1 = y
    ]]></literal>
    <justification jstring="[para(2(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="345">
    <literal><![CDATA[
      x / (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(5(a,1),342(a,1,1))].">
      <j1 rule="para" parents="5 342"/>
    </justification>
  </clause>

  <clause id="346">
    <literal><![CDATA[
      (x * T(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(105(a,2),342(a,1,1))].">
      <j1 rule="para" parents="105 342"/>
    </justification>
  </clause>

  <clause id="347">
    <literal><![CDATA[
      x / (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(5(a,1),343(a,1,1))].">
      <j1 rule="para" parents="5 343"/>
    </justification>
  </clause>

  <clause id="348">
    <literal><![CDATA[
      (x * T(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(105(a,2),343(a,1,1))].">
      <j1 rule="para" parents="105 343"/>
    </justification>
  </clause>

  <clause id="349">
    <literal><![CDATA[
      (x * (y * z)) / L(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      x * y = u
    ]]></literal>
    <justification jstring="[para(13(a,2),345(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13 345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="350">
    <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="351">
    <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="352">
    <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="353">
    <literal><![CDATA[
      (x * (x \ y)) / z != u
    ]]></literal>
    <literal><![CDATA[
      y / z = u
    ]]></literal>
    <justification jstring="[para(158(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="158 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="354">
    <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="355">
    <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="356">
    <literal><![CDATA[
      x * (y * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(161(a,1),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="161 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="357">
    <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="358">
    <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="359">
    <literal><![CDATA[
      (x / (y \ x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(184(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="184 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="360">
    <literal><![CDATA[
      x / y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      u \ x = y
    ]]></literal>
    <justification jstring="[para(185(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="185 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="361">
    <literal><![CDATA[
      (x * (x \ y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      y \ z = u
    ]]></literal>
    <justification jstring="[para(185(a,1),276(a,1,1)),flip(b)].">
      <j1 rule="para" parents="185 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="362">
    <literal><![CDATA[
      (x / y) \ x != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(196(a,2),38(a,1))].">
      <j1 rule="para" parents="196 38"/>
    </justification>
  </clause>

  <clause id="363">
    <literal><![CDATA[
      x \ y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      y / u = x
    ]]></literal>
    <justification jstring="[para(196(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="196 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="364">
    <literal><![CDATA[
      (x / y) * ((z / y) \ z) = x
    ]]></literal>
    <justification jstring="[hyper(334,a,7,a(flip),b,197,a),flip(a)].">
      <j1 rule="hyper" parents="334 7 197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="365">
    <literal><![CDATA[
      x * ((y / z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      u / z = x
    ]]></literal>
    <justification jstring="[para(197(a,2),130(a,1))].">
      <j1 rule="para" parents="197 130"/>
    </justification>
  </clause>

  <clause id="366">
    <literal><![CDATA[
      (x \ y) * z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) = z
    ]]></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="367">
    <literal><![CDATA[
      (x \ y) \ y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(227(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="227 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="368">
    <literal><![CDATA[
      T(x / (x / y),(z / (x / y)) \ z) = y
    ]]></literal>
    <justification jstring="[para(75(a,2),252(a,1,2))].">
      <j1 rule="para" parents="75 252"/>
    </justification>
  </clause>

  <clause id="369">
    <literal><![CDATA[
      x * T(x \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,105,a,b,266,a)].">
      <j1 rule="hyper" parents="334 105 266"/>
    </justification>
  </clause>

  <clause id="370">
    <literal><![CDATA[
      K(x \ 1,x) / x = x \ 1
    ]]></literal>
    <justification jstring="[hyper(130,a,266,a(flip))].">
      <j1 rule="hyper" parents="130 266"/>
    </justification>
  </clause>

  <clause id="371">
    <literal><![CDATA[
      (x \ 1) \ K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(123,a,266,a(flip))].">
      <j1 rule="hyper" parents="123 266"/>
    </justification>
  </clause>

  <clause id="372">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ ((x * (y \ 1)) * y) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(266(a,2),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="266 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="373">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / (x * y) = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(266(a,2),15(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="266 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="374">
    <literal><![CDATA[
      x \ K(x \ 1,x) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(266(a,2),17(a,2,2)),flip(a)].">
      <j1 rule="para" parents="266 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="375">
    <literal><![CDATA[
      K(x,1 / x) \ (x * ((1 / x) * y)) = L(y,1 / x,x)
    ]]></literal>
    <justification jstring="[para(268(a,2),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="268 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="376">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      (z / x) \ z = y
    ]]></literal>
    <justification jstring="[para(300(a,1),211(a,1))].">
      <j1 rule="para" parents="300 211"/>
    </justification>
  </clause>

  <clause id="377">
    <literal><![CDATA[
      R(x / y,y,x \ z) = z / (y * (x \ z))
    ]]></literal>
    <justification jstring="[para(302(a,1),15(a,2,1))].">
      <j1 rule="para" parents="302 15"/>
    </justification>
  </clause>

  <clause id="378">
    <literal><![CDATA[
      x \ (y * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      z / u = x
    ]]></literal>
    <justification jstring="[para(308(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="308 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="379">
    <literal><![CDATA[
      R(x,y,(x * y) \ z) \ z = y * ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(15(a,2),313(a,1,1))].">
      <j1 rule="para" parents="15 313"/>
    </justification>
  </clause>

  <clause id="380">
    <literal><![CDATA[
      R(x,y,y \ z) * z = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(15(a,2),337(a,1,1))].">
      <j1 rule="para" parents="15 337"/>
    </justification>
  </clause>

  <clause id="381">
    <literal><![CDATA[
      (x / T(y,y \ z)) * ((y \ z) \ z) = x
    ]]></literal>
    <justification jstring="[para(273(a,1),364(a,1,2,1))].">
      <j1 rule="para" parents="273 364"/>
    </justification>
  </clause>

  <clause id="382">
    <literal><![CDATA[
      (x \ 1) * x != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(370(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="370 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="383">
    <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="384">
    <literal><![CDATA[
      L(x,1,y) = x
    ]]></literal>
    <justification jstring="[hyper(299,a,383,a),flip(a)].">
      <j1 rule="hyper" parents="299 383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="385">
    <literal><![CDATA[
      L(x,1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(383(a,1),297(a,1))].">
      <j1 rule="para" parents="383 297"/>
    </justification>
  </clause>

  <clause id="387">
    <literal><![CDATA[
      a(x,1,y) = 1
    ]]></literal>
    <justification jstring="[hyper(48,a,384,a)].">
      <j1 rule="hyper" parents="48 384"/>
    </justification>
  </clause>

  <clause id="388">
    <literal><![CDATA[
      R(1,x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(344,a,95,a),flip(a)].">
      <j1 rule="hyper" parents="344 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="390">
    <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="391">
    <literal><![CDATA[
      R(x,1,y) = x
    ]]></literal>
    <justification jstring="[hyper(343,a,390,a),flip(a)].">
      <j1 rule="hyper" parents="343 390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="392">
    <literal><![CDATA[
      R(x,1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(390(a,1),342(a,1))].">
      <j1 rule="para" parents="390 342"/>
    </justification>
  </clause>

  <clause id="394">
    <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="395">
    <literal><![CDATA[
      R(x,y,1) = x
    ]]></literal>
    <justification jstring="[hyper(343,a,394,a),flip(a)].">
      <j1 rule="hyper" parents="343 394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="396">
    <literal><![CDATA[
      R(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(394(a,1),342(a,1))].">
      <j1 rule="para" parents="394 342"/>
    </justification>
  </clause>

  <clause id="398">
    <literal><![CDATA[
      K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(11(a,2),213(a,1))].">
      <j1 rule="para" parents="11 213"/>
    </justification>
  </clause>

  <clause id="399">
    <literal><![CDATA[
      L(x,y,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * (y * x) = z
    ]]></literal>
    <justification jstring="[para(13(a,2),213(a,1))].">
      <j1 rule="para" parents="13 213"/>
    </justification>
  </clause>

  <clause id="400">
    <literal><![CDATA[
      L(x \ 1,x,1 / x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(334,a,165,a(flip),b,221,a),flip(a)].">
      <j1 rule="hyper" parents="334 165 221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="401">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(334,a,156,a(flip),b,221,a),flip(a)].">
      <j1 rule="hyper" parents="334 156 221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="402">
    <literal><![CDATA[
      L(x \ 1,x,y) * (((y * x) \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(290,a,221,a)].">
      <j1 rule="hyper" parents="290 221"/>
    </justification>
  </clause>

  <clause id="403">
    <literal><![CDATA[
      x \ L(y \ 1,y,z) = x \ ((z * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(57,a,221,a)].">
      <j1 rule="hyper" parents="57 221"/>
    </justification>
  </clause>

  <clause id="404">
    <literal><![CDATA[
      L(x \ 1,x,y) \ z = ((y * x) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(56,a,221,a)].">
      <j1 rule="hyper" parents="56 221"/>
    </justification>
  </clause>

  <clause id="405">
    <literal><![CDATA[
      x * L(y \ 1,y,z) = x * ((z * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(53,a,221,a)].">
      <j1 rule="hyper" parents="53 221"/>
    </justification>
  </clause>

  <clause id="406">
    <literal><![CDATA[
      L(x \ 1,x,y) * z = ((y * x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(52,a,221,a)].">
      <j1 rule="hyper" parents="52 221"/>
    </justification>
  </clause>

  <clause id="407">
    <literal><![CDATA[
      x / L(y \ 1,y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(201,a,221,a(flip))].">
      <j1 rule="hyper" parents="201 221"/>
    </justification>
  </clause>

  <clause id="408">
    <literal><![CDATA[
      (x * y) * L(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(134,a,221,a(flip))].">
      <j1 rule="hyper" parents="134 221"/>
    </justification>
  </clause>

  <clause id="409">
    <literal><![CDATA[
      L(x \ 1,x,y / x) = y \ (y / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),221(a,2,1))].">
      <j1 rule="para" parents="7 221"/>
    </justification>
  </clause>

  <clause id="410">
    <literal><![CDATA[
      T((x * y) \ x,z) = L(T(y \ 1,z),y,x)
    ]]></literal>
    <justification jstring="[para(221(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="221 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="411">
    <literal><![CDATA[
      R((x * y) \ x,z,u) = L(R(y \ 1,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(221(a,1),24(a,1,1))].">
      <j1 rule="para" parents="221 24"/>
    </justification>
  </clause>

  <clause id="412">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,u) = L((u * x) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(221(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="221 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="413">
    <literal><![CDATA[
      R(1 / x,x,x \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(334,a,172,a(flip),b,223,a),flip(a)].">
      <j1 rule="hyper" parents="334 172 223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="414">
    <literal><![CDATA[
      x * R(1 / y,y,z) = x * (z / (y * z))
    ]]></literal>
    <justification jstring="[hyper(53,a,223,a)].">
      <j1 rule="hyper" parents="53 223"/>
    </justification>
  </clause>

  <clause id="415">
    <literal><![CDATA[
      (x / (y * x)) * (R(1 / y,y,x) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(290,a,223,a(flip))].">
      <j1 rule="hyper" parents="290 223"/>
    </justification>
  </clause>

  <clause id="416">
    <literal><![CDATA[
      R(1 / x,x,y) \ y = x * y
    ]]></literal>
    <justification jstring="[hyper(192,a,223,a(flip))].">
      <j1 rule="hyper" parents="192 223"/>
    </justification>
  </clause>

  <clause id="417">
    <literal><![CDATA[
      R(1 / x,x,x \ y) = (x \ y) / y
    ]]></literal>
    <justification jstring="[para(5(a,1),223(a,2,2))].">
      <j1 rule="para" parents="5 223"/>
    </justification>
  </clause>

  <clause id="418">
    <literal><![CDATA[
      R(1 / (x / y),x / y,y) = y / x
    ]]></literal>
    <justification jstring="[para(7(a,1),223(a,2,2))].">
      <j1 rule="para" parents="7 223"/>
    </justification>
  </clause>

  <clause id="419">
    <literal><![CDATA[
      T(x / (y * x),z) = R(T(1 / y,z),y,x)
    ]]></literal>
    <justification jstring="[para(223(a,1),22(a,2,1)),flip(a)].">
      <j1 rule="para" parents="223 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="420">
    <literal><![CDATA[
      R(R(1 / x,y,z),x,u) = R(u / (x * u),y,z)
    ]]></literal>
    <justification jstring="[para(223(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="223 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="421">
    <literal><![CDATA[
      T(x,y) * z != x * y
    ]]></literal>
    <literal><![CDATA[
      T(y,T(x,y)) = z
    ]]></literal>
    <justification jstring="[para(105(a,1),247(a,2))].">
      <j1 rule="para" parents="105 247"/>
    </justification>
  </clause>

  <clause id="422">
    <literal><![CDATA[
      x * T(T(y,x),z) != u * x
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(18(a,1),249(a,1,2))].">
      <j1 rule="para" parents="18 249"/>
    </justification>
  </clause>

  <clause id="423">
    <literal><![CDATA[
      x * ((1 / y) * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(7(a,2),258(a,1,2))].">
      <j1 rule="para" parents="7 258"/>
    </justification>
  </clause>

  <clause id="424">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(159(a,2),258(a,1))].">
      <j1 rule="para" parents="159 258"/>
    </justification>
  </clause>

  <clause id="425">
    <literal><![CDATA[
      ((1 / x) * x) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(7(a,2),261(a,1,1))].">
      <j1 rule="para" parents="7 261"/>
    </justification>
  </clause>

  <clause id="426">
    <literal><![CDATA[
      x * (y * (y \ 1)) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(5(a,2),262(a,1,2))].">
      <j1 rule="para" parents="5 262"/>
    </justification>
  </clause>

  <clause id="427">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(162(a,2),262(a,1))].">
      <j1 rule="para" parents="162 262"/>
    </justification>
  </clause>

  <clause id="428">
    <literal><![CDATA[
      x * T(T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(18(a,1),294(a,1,2))].">
      <j1 rule="para" parents="18 294"/>
    </justification>
  </clause>

  <clause id="429">
    <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),294(a,1,2))].">
      <j1 rule="para" parents="20 294"/>
    </justification>
  </clause>

  <clause id="430">
    <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),294(a,1,2))].">
      <j1 rule="para" parents="22 294"/>
    </justification>
  </clause>

  <clause id="431">
    <literal><![CDATA[
      T(x / y,y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(5(a,1),303(a,1,1,1)),flip(b)].">
      <j1 rule="para" parents="5 303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="432">
    <literal><![CDATA[
      L(T(x \ 1,y),x,1 / x) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(400(a,1),20(a,2,1))].">
      <j1 rule="para" parents="400 20"/>
    </justification>
  </clause>

  <clause id="433">
    <literal><![CDATA[
      x / L(y,1 / y,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),407(a,1,2,1))].">
      <j1 rule="para" parents="75 407"/>
    </justification>
  </clause>

  <clause id="434">
    <literal><![CDATA[
      (x * y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(407(a,1),276(a,1,1)),flip(b)].">
      <j1 rule="para" parents="407 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="435">
    <literal><![CDATA[
      L(L(x \ 1,x,y),y * x,z) = (z * (y * x)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(408(a,1),13(a,2,2,2))].">
      <j1 rule="para" parents="408 13"/>
    </justification>
  </clause>

  <clause id="436">
    <literal><![CDATA[
      R(x,x \ 1,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(72(a,1),416(a,1,1,1))].">
      <j1 rule="para" parents="72 416"/>
    </justification>
  </clause>

  <clause id="437">
    <literal><![CDATA[
      x / (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,y,x) = z
    ]]></literal>
    <justification jstring="[para(416(a,1),345(a,1,2)),flip(b)].">
      <j1 rule="para" parents="416 345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="438">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ (x * y) = z
    ]]></literal>
    <justification jstring="[para(6(a,1),431(a,1,1))].">
      <j1 rule="para" parents="6 431"/>
    </justification>
  </clause>

  <clause id="439">
    <literal><![CDATA[
      T(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(72(a,1),431(a,1,1))].">
      <j1 rule="para" parents="72 431"/>
    </justification>
  </clause>

  <clause id="440">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ (y * x) = z
    ]]></literal>
    <justification jstring="[para(191(a,1),431(a,1,1))].">
      <j1 rule="para" parents="191 431"/>
    </justification>
  </clause>

  <clause id="441">
    <literal><![CDATA[
      T(x * y,K(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ (y * x) = z
    ]]></literal>
    <justification jstring="[para(189(a,1),431(a,1,1))].">
      <j1 rule="para" parents="189 431"/>
    </justification>
  </clause>

  <clause id="442">
    <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="443">
    <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="444">
    <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="445">
    <literal><![CDATA[
      K(x \ 1,x) \ 1 = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(266(a,2),86(a,1,1))].">
      <j1 rule="para" parents="266 86"/>
    </justification>
  </clause>

  <clause id="446">
    <literal><![CDATA[
      K(x,1 / x) \ 1 = K(1 / x,x)
    ]]></literal>
    <justification jstring="[para(268(a,2),88(a,1,1))].">
      <j1 rule="para" parents="268 88"/>
    </justification>
  </clause>

  <clause id="447">
    <literal><![CDATA[
      T(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(108(a,1),298(a,1))].">
      <j1 rule="para" parents="108 298"/>
    </justification>
  </clause>

  <clause id="448">
    <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="449">
    <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="450">
    <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="451">
    <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="452">
    <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="453">
    <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="454">
    <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="455">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = z
    ]]></literal>
    <justification jstring="[para(191(a,1),118(b,1)),flip(c)].">
      <j1 rule="para" parents="191 118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="456">
    <literal><![CDATA[
      (x / ((y * z) \ y)) * L(z \ 1,z,y) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,221,a,b,75,a)].">
      <j1 rule="hyper" parents="119 221 75"/>
    </justification>
  </clause>

  <clause id="457">
    <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="458">
    <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="459">
    <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="460">
    <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="461">
    <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="462">
    <literal><![CDATA[
      L(x \ T(y,z),x,z) = (z * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(233(a,1),13(a,2,2))].">
      <j1 rule="para" parents="233 13"/>
    </justification>
  </clause>

  <clause id="463">
    <literal><![CDATA[
      x * T(x \ (y * x),z) = T(y,z) * x
    ]]></literal>
    <justification jstring="[para(17(a,1),243(a,1,2,1))].">
      <j1 rule="para" parents="17 243"/>
    </justification>
  </clause>

  <clause id="464">
    <literal><![CDATA[
      x * T(T(T(y,x),z),u) = T(T(y,z),u) * x
    ]]></literal>
    <justification jstring="[para(18(a,1),243(a,1,2,1))].">
      <j1 rule="para" parents="18 243"/>
    </justification>
  </clause>

  <clause id="465">
    <literal><![CDATA[
      T(x / y,z) * y = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="466">
    <literal><![CDATA[
      T((x * y) / x,z) * x = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(230(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="230 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="467">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(106(a,1),243(a,1,2,1))].">
      <j1 rule="para" parents="106 243"/>
    </justification>
  </clause>

  <clause id="468">
    <literal><![CDATA[
      T(x / (x / y),z) * (x / y) = (x / y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(252(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="252 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="469">
    <literal><![CDATA[
      (x * T(x \ y,z)) / x = T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(281,a,254,a)].">
      <j1 rule="hyper" parents="281 254"/>
    </justification>
  </clause>

  <clause id="470">
    <literal><![CDATA[
      T(x \ y,z) != T(u,x)
    ]]></literal>
    <literal><![CDATA[
      T(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(254(a,1),44(a,1))].">
      <j1 rule="para" parents="254 44"/>
    </justification>
  </clause>

  <clause id="471">
    <literal><![CDATA[
      x * T(x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,z) * x = u
    ]]></literal>
    <justification jstring="[para(254(a,1),294(a,1,2))].">
      <j1 rule="para" parents="254 294"/>
    </justification>
  </clause>

  <clause id="472">
    <literal><![CDATA[
      (x * T(y,z)) / x = T((x * y) / x,z)
    ]]></literal>
    <justification jstring="[para(230(a,1),279(a,1,1,2,1))].">
      <j1 rule="para" parents="230 279"/>
    </justification>
  </clause>

  <clause id="473">
    <literal><![CDATA[
      T(x,y) != T(z,u)
    ]]></literal>
    <literal><![CDATA[
      T((y * z) / y,u) = x
    ]]></literal>
    <justification jstring="[para(280(a,1),44(a,2)),flip(b)].">
      <j1 rule="para" parents="280 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="474">
    <literal><![CDATA[
      (x * T(y,z)) / x != u
    ]]></literal>
    <literal><![CDATA[
      T((x * y) / x,z) = u
    ]]></literal>
    <justification jstring="[para(280(a,1),346(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="280 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="475">
    <literal><![CDATA[
      (x * y) \ (x * ((z \ y) * z)) = L(K(z \ y,z),y,x)
    ]]></literal>
    <justification jstring="[para(315(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="315 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="476">
    <literal><![CDATA[
      (x \ y) * x != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,x) = z
    ]]></literal>
    <justification jstring="[para(315(a,1),38(a,1))].">
      <j1 rule="para" parents="315 38"/>
    </justification>
  </clause>

  <clause id="477">
    <literal><![CDATA[
      x \ ((y \ x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,y) = z
    ]]></literal>
    <justification jstring="[para(315(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="315 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="478">
    <literal><![CDATA[
      K(x \ y,x) * z != (x \ y) * x
    ]]></literal>
    <literal><![CDATA[
      T(y,K(x \ y,x)) = z
    ]]></literal>
    <justification jstring="[para(315(a,1),247(a,2))].">
      <j1 rule="para" parents="315 247"/>
    </justification>
  </clause>

  <clause id="479">
    <literal><![CDATA[
      x \ (y * (x / y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x / y) = z
    ]]></literal>
    <justification jstring="[para(316(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="316 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="480">
    <literal><![CDATA[
      1 / K(x,x \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,266,a,b,350,a),flip(a)].">
      <j1 rule="hyper" parents="334 266 350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="481">
    <literal><![CDATA[
      (x * (y * z)) / T(x * y,L(z,y,x)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(288,a,90,a)].">
      <j1 rule="hyper" parents="288 90"/>
    </justification>
  </clause>

  <clause id="482">
    <literal><![CDATA[
      L(x,y,z) \ (z * (y * x)) = T(z * y,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(286,a,90,a),flip(a)].">
      <j1 rule="hyper" parents="286 90"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="483">
    <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="484">
    <literal><![CDATA[
      (x * y) * L(z,T(x,y),y) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,229,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="58 229 90"/>
    </justification>
  </clause>

  <clause id="485">
    <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="486">
    <literal><![CDATA[
      L(x \ T(y * x,y),x,y) = y
    ]]></literal>
    <justification jstring="[hyper(29,a,233,a(flip),b,90,a),flip(a)].">
      <j1 rule="hyper" parents="29 233 90"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="487">
    <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="488">
    <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="489">
    <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="490">
    <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="491">
    <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="492">
    <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="493">
    <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="494">
    <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="495">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(90(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="90 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="496">
    <literal><![CDATA[
      K(x \ 1,x) * L(y,x,x \ 1) = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(266(a,2),90(a,1,1))].">
      <j1 rule="para" parents="266 90"/>
    </justification>
  </clause>

  <clause id="497">
    <literal><![CDATA[
      x * ((x \ 1) * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(90(a,1),206(a,1))].">
      <j1 rule="para" parents="90 206"/>
    </justification>
  </clause>

  <clause id="498">
    <literal><![CDATA[
      (1 / x) * (x * 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[
      (x * y) * L(K(z \ y,z),y,x) = x * ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(315(a,1),90(a,2,2))].">
      <j1 rule="para" parents="315 90"/>
    </justification>
  </clause>

  <clause id="500">
    <literal><![CDATA[
      L(x \ y,x,1 / x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(334,a,165,a(flip),b,92,a),flip(a)].">
      <j1 rule="hyper" parents="334 165 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="501">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(334,a,164,a(flip),b,92,a),flip(a)].">
      <j1 rule="hyper" parents="334 164 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="502">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(334,a,156,a(flip),b,92,a),flip(a)].">
      <j1 rule="hyper" parents="334 156 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="503">
    <literal><![CDATA[
      L(x \ ((y * x) / y),x,y) = K(y,(y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(334,a,87,a(flip),b,92,a),flip(a)].">
      <j1 rule="hyper" parents="334 87 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="504">
    <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="505">
    <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="506">
    <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="507">
    <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="508">
    <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="509">
    <literal><![CDATA[
      L(x \ (1 / y),x,y) = (y * x) \ K(y,1 / y)
    ]]></literal>
    <justification jstring="[para(268(a,2),92(a,2,2))].">
      <j1 rule="para" parents="268 92"/>
    </justification>
  </clause>

  <clause id="510">
    <literal><![CDATA[
      x / L(y \ z,y,x / z) = (x / z) * y
    ]]></literal>
    <justification jstring="[para(92(a,2),338(a,1,2))].">
      <j1 rule="para" parents="92 338"/>
    </justification>
  </clause>

  <clause id="511">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(92(a,2),212(a,1))].">
      <j1 rule="para" parents="92 212"/>
    </justification>
  </clause>

  <clause id="512">
    <literal><![CDATA[
      L(x \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) \ y = z
    ]]></literal>
    <justification jstring="[para(92(a,2),304(a,1))].">
      <j1 rule="para" parents="92 304"/>
    </justification>
  </clause>

  <clause id="513">
    <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="514">
    <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="515">
    <literal><![CDATA[
      R(x / y,y,x \ z) \ z = y * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,302,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="116 302 101"/>
    </justification>
  </clause>

  <clause id="516">
    <literal><![CDATA[
      R(x,T(y,x),z) \ ((y * x) * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(116,a,229,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="116 229 101"/>
    </justification>
  </clause>

  <clause id="517">
    <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="518">
    <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="519">
    <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="520">
    <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="521">
    <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="522">
    <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="523">
    <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="524">
    <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="525">
    <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="526">
    <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="527">
    <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="528">
    <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="529">
    <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="530">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(101(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="101 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="531">
    <literal><![CDATA[
      (R(x,y,z) * (y * z)) / z != u
    ]]></literal>
    <literal><![CDATA[
      x * y = u
    ]]></literal>
    <justification jstring="[para(101(a,2),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="101 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="532">
    <literal><![CDATA[
      R(x,y \ 1,y) * K(y \ 1,y) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[para(266(a,2),101(a,1,2))].">
      <j1 rule="para" parents="266 101"/>
    </justification>
  </clause>

  <clause id="533">
    <literal><![CDATA[
      (x * y) * (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(101(a,1),209(a,1)),flip(b)].">
      <j1 rule="para" parents="101 209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="534">
    <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="535">
    <literal><![CDATA[
      R(x / (1 / y),1 / y,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(334,a,173,a(flip),b,102,a),flip(a)].">
      <j1 rule="hyper" parents="334 173 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="536">
    <literal><![CDATA[
      R(x / y,y,y \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,172,a(flip),b,102,a),flip(a)].">
      <j1 rule="hyper" parents="334 172 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="537">
    <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="538">
    <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="539">
    <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="540">
    <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="541">
    <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="542">
    <literal><![CDATA[
      R(x / T(y,z),T(y,z),y) = (x * y) / (y * T(y,z))
    ]]></literal>
    <justification jstring="[para(251(a,1),102(a,2,2))].">
      <j1 rule="para" parents="251 102"/>
    </justification>
  </clause>

  <clause id="543">
    <literal><![CDATA[
      R(x / y,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * (y \ 1) = z
    ]]></literal>
    <justification jstring="[para(102(a,2),215(a,1)),flip(b)].">
      <j1 rule="para" parents="102 215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="544">
    <literal><![CDATA[
      R(R(1 / x,x,y),x * y,z) = (y * z) / ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(223(a,2),102(a,1,1))].">
      <j1 rule="para" parents="223 102"/>
    </justification>
  </clause>

  <clause id="545">
    <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="546">
    <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="547">
    <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="548">
    <literal><![CDATA[
      x \ (y * x) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(y,x) = u
    ]]></literal>
    <justification jstring="[para(233(a,1),122(a,1,2)),flip(b)].">
      <j1 rule="para" parents="233 122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="549">
    <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="550">
    <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="551">
    <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="552">
    <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="553">
    <literal><![CDATA[
      x * y != 1
    ]]></literal>
    <literal><![CDATA[
      (z * x) * y = R(z,x,y)
    ]]></literal>
    <justification jstring="[para(187(a,1),169(a,1))].">
      <j1 rule="para" parents="187 169"/>
    </justification>
  </clause>

  <clause id="554">
    <literal><![CDATA[
      R(x * y,K(y,x),z) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(84(a,1),187(a,1,2,1))].">
      <j1 rule="para" parents="84 187"/>
    </justification>
  </clause>

  <clause id="555">
    <literal><![CDATA[
      R(x,K(y \ x,y),z) \ (((y \ x) * y) * z) = K(y \ x,y) * z
    ]]></literal>
    <justification jstring="[para(315(a,1),187(a,1,2,1))].">
      <j1 rule="para" parents="315 187"/>
    </justification>
  </clause>

  <clause id="556">
    <literal><![CDATA[
      (x * y) / L(z,y / z,x) = x * (y / z)
    ]]></literal>
    <justification jstring="[para(7(a,1),190(a,1,1,2))].">
      <j1 rule="para" parents="7 190"/>
    </justification>
  </clause>

  <clause id="557">
    <literal><![CDATA[
      (x * (y * z)) / L(T(y,z),z,x) = x * z
    ]]></literal>
    <justification jstring="[para(105(a,1),190(a,1,1,2))].">
      <j1 rule="para" parents="105 190"/>
    </justification>
  </clause>

  <clause id="558">
    <literal><![CDATA[
      (x * (y * z)) / L(K(y,z),z * y,x) = x * (z * y)
    ]]></literal>
    <justification jstring="[para(84(a,1),190(a,1,1,2))].">
      <j1 rule="para" parents="84 190"/>
    </justification>
  </clause>

  <clause id="559">
    <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(190(a,1),431(a,1,1))].">
      <j1 rule="para" parents="190 431"/>
    </justification>
  </clause>

  <clause id="560">
    <literal><![CDATA[
      K(x,1 / x) \ x = L(x,1 / x,x)
    ]]></literal>
    <justification jstring="[para(268(a,2),225(a,2,1)),flip(a)].">
      <j1 rule="para" parents="268 225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="561">
    <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,265,a)].">
      <j1 rule="hyper" parents="116 25 265"/>
    </justification>
  </clause>

  <clause id="562">
    <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,265,a)].">
      <j1 rule="hyper" parents="116 20 265"/>
    </justification>
  </clause>

  <clause id="563">
    <literal><![CDATA[
      L(x,y \ 1,y) != y * z
    ]]></literal>
    <literal><![CDATA[
      (y \ 1) * x = z
    ]]></literal>
    <justification jstring="[para(265(a,1),38(a,1))].">
      <j1 rule="para" parents="265 38"/>
    </justification>
  </clause>

  <clause id="564">
    <literal><![CDATA[
      L(T(x,y \ 1),y \ 1,y) = y * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(105(a,1),265(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="565">
    <literal><![CDATA[
      x \ L(y,x \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(265(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="265 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="566">
    <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,267,a)].">
      <j1 rule="hyper" parents="116 25 267"/>
    </justification>
  </clause>

  <clause id="567">
    <literal><![CDATA[
      L(T(x,y),y,1 / y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[para(105(a,1),267(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="568">
    <literal><![CDATA[
      (1 / x) \ L(y,x,1 / x) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(267(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="267 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="569">
    <literal><![CDATA[
      (x \ 1) \ R(y,x,x \ 1) = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(286,a,269,a),flip(a)].">
      <j1 rule="hyper" parents="286 269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="570">
    <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,269,a)].">
      <j1 rule="hyper" parents="117 24 269"/>
    </justification>
  </clause>

  <clause id="571">
    <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,269,a)].">
      <j1 rule="hyper" parents="117 22 269"/>
    </justification>
  </clause>

  <clause id="572">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(269(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="269 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="573">
    <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),269(a,1,1)),flip(a)].">
      <j1 rule="para" parents="101 269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="574">
    <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,270,a)].">
      <j1 rule="hyper" parents="117 26 270"/>
    </justification>
  </clause>

  <clause id="575">
    <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,270,a)].">
      <j1 rule="hyper" parents="117 24 270"/>
    </justification>
  </clause>

  <clause id="576">
    <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,270,a)].">
      <j1 rule="hyper" parents="117 22 270"/>
    </justification>
  </clause>

  <clause id="577">
    <literal><![CDATA[
      L(T(x \ (y \ z),u),x,y) = T((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(311(a,1),20(a,2,1))].">
      <j1 rule="para" parents="311 20"/>
    </justification>
  </clause>

  <clause id="578">
    <literal><![CDATA[
      L(R(x \ (y \ z),u,w),x,y) = R((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(311(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="311 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="579">
    <literal><![CDATA[
      L(L(x \ (y \ z),u,w),x,y) = L((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(311(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="311 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="580">
    <literal><![CDATA[
      L(x,(y \ z) / x,y) = (y * ((y \ z) / x)) \ z
    ]]></literal>
    <justification jstring="[para(75(a,1),311(a,1,1))].">
      <j1 rule="para" parents="75 311"/>
    </justification>
  </clause>

  <clause id="581">
    <literal><![CDATA[
      (x * (x \ y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(72(a,1),341(a,1,1,1))].">
      <j1 rule="para" parents="72 341"/>
    </justification>
  </clause>

  <clause id="582">
    <literal><![CDATA[
      (x * T(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) * z = u
    ]]></literal>
    <justification jstring="[para(191(a,1),341(a,1,1,1))].">
      <j1 rule="para" parents="191 341"/>
    </justification>
  </clause>

  <clause id="583">
    <literal><![CDATA[
      ((x \ 1) * x) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) * y = z
    ]]></literal>
    <justification jstring="[para(370(a,1),341(a,1,1,1))].">
      <j1 rule="para" parents="370 341"/>
    </justification>
  </clause>

  <clause id="584">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(157(a,1),351(a,1,1))].">
      <j1 rule="para" parents="157 351"/>
    </justification>
  </clause>

  <clause id="585">
    <literal><![CDATA[
      (x * y) / y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(157(a,2),351(a,1))].">
      <j1 rule="para" parents="157 351"/>
    </justification>
  </clause>

  <clause id="586">
    <literal><![CDATA[
      x * (y \ (y * (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      z / w = u
    ]]></literal>
    <justification jstring="[para(4(a,2),352(a,1,2))].">
      <j1 rule="para" parents="4 352"/>
    </justification>
  </clause>

  <clause id="587">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(161(a,1),352(a,1,2))].">
      <j1 rule="para" parents="161 352"/>
    </justification>
  </clause>

  <clause id="588">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(161(a,2),352(a,1))].">
      <j1 rule="para" parents="161 352"/>
    </justification>
  </clause>

  <clause id="589">
    <literal><![CDATA[
      ((x / y) * y) / z != u
    ]]></literal>
    <literal><![CDATA[
      x / z = u
    ]]></literal>
    <justification jstring="[para(75(a,1),353(a,1,1,2))].">
      <j1 rule="para" parents="75 353"/>
    </justification>
  </clause>

  <clause id="590">
    <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),354(a,1,2))].">
      <j1 rule="para" parents="90 354"/>
    </justification>
  </clause>

  <clause id="591">
    <literal><![CDATA[
      x \ y != z * (u \ (u * (z \ w)))
    ]]></literal>
    <literal><![CDATA[
      x * w = y
    ]]></literal>
    <justification jstring="[para(4(a,2),355(a,2,2))].">
      <j1 rule="para" parents="4 355"/>
    </justification>
  </clause>

  <clause id="592">
    <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),355(a,2,2))].">
      <j1 rule="para" parents="13 355"/>
    </justification>
  </clause>

  <clause id="593">
    <literal><![CDATA[
      x \ y != z * T(u,z)
    ]]></literal>
    <literal><![CDATA[
      x * (u * z) = y
    ]]></literal>
    <justification jstring="[para(17(a,2),355(a,2,2))].">
      <j1 rule="para" parents="17 355"/>
    </justification>
  </clause>

  <clause id="594">
    <literal><![CDATA[
      x \ y != (z / u) * u
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></literal>
    <justification jstring="[para(75(a,1),355(a,2,2))].">
      <j1 rule="para" parents="75 355"/>
    </justification>
  </clause>

  <clause id="595">
    <literal><![CDATA[
      (x / y) \ x != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * y = u
    ]]></literal>
    <justification jstring="[para(196(a,2),355(a,2)),flip(a)].">
      <j1 rule="para" parents="196 355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="596">
    <literal><![CDATA[
      x \ y != (z \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      x * K(z \ 1,z) = y
    ]]></literal>
    <justification jstring="[para(371(a,1),355(a,2,2))].">
      <j1 rule="para" parents="371 355"/>
    </justification>
  </clause>

  <clause id="597">
    <literal><![CDATA[
      x * (y \ (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(161(a,2),356(a,1,2))].">
      <j1 rule="para" parents="161 356"/>
    </justification>
  </clause>

  <clause id="598">
    <literal><![CDATA[
      x * ((y / z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(196(a,2),356(a,1,2))].">
      <j1 rule="para" parents="196 356"/>
    </justification>
  </clause>

  <clause id="599">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) != u
    ]]></literal>
    <literal><![CDATA[
      y \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(92(a,2),361(a,1))].">
      <j1 rule="para" parents="92 361"/>
    </justification>
  </clause>

  <clause id="600">
    <literal><![CDATA[
      (x * (x \ y)) \ z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y \ z) = w
    ]]></literal>
    <justification jstring="[para(185(a,1),362(a,1,1))].">
      <j1 rule="para" parents="185 362"/>
    </justification>
  </clause>

  <clause id="601">
    <literal><![CDATA[
      T((x \ y) \ 1,y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(401(a,1),177(a,1,2))].">
      <j1 rule="para" parents="401 177"/>
    </justification>
  </clause>

  <clause id="602">
    <literal><![CDATA[
      T(1 / (x \ y),y \ x) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[para(401(a,1),292(a,1,2))].">
      <j1 rule="para" parents="401 292"/>
    </justification>
  </clause>

  <clause id="603">
    <literal><![CDATA[
      T(x \ (x / y),z) = L(T(y \ 1,z),y,x / y)
    ]]></literal>
    <justification jstring="[para(409(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="409 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="604">
    <literal><![CDATA[
      x * R(1 / y,y,y \ z) = x * ((y \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(119,a,417,a,b,4,a)].">
      <j1 rule="hyper" parents="119 417 4"/>
    </justification>
  </clause>

  <clause id="605">
    <literal><![CDATA[
      ((x \ y) / y) * (R(1 / x,x,x \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(290,a,417,a(flip))].">
      <j1 rule="hyper" parents="290 417"/>
    </justification>
  </clause>

  <clause id="606">
    <literal><![CDATA[
      T((x \ y) / y,z) = R(T(1 / x,z),x,x \ y)
    ]]></literal>
    <justification jstring="[para(417(a,1),22(a,2,1)),flip(a)].">
      <j1 rule="para" parents="417 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="607">
    <literal><![CDATA[
      T(1 / (x / y),y / x) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[para(418(a,1),176(a,1,2))].">
      <j1 rule="para" parents="418 176"/>
    </justification>
  </clause>

  <clause id="608">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(157(a,1),424(a,1,1))].">
      <j1 rule="para" parents="157 424"/>
    </justification>
  </clause>

  <clause id="609">
    <literal><![CDATA[
      x * (y \ (y * (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ z = w
    ]]></literal>
    <justification jstring="[para(4(a,2),427(a,1,2))].">
      <j1 rule="para" parents="4 427"/>
    </justification>
  </clause>

  <clause id="610">
    <literal><![CDATA[
      x * (y * (y \ (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ z = w
    ]]></literal>
    <justification jstring="[para(5(a,2),427(a,1,2))].">
      <j1 rule="para" parents="5 427"/>
    </justification>
  </clause>

  <clause id="611">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(161(a,1),427(a,1,2))].">
      <j1 rule="para" parents="161 427"/>
    </justification>
  </clause>

  <clause id="612">
    <literal><![CDATA[
      x / y != x * (1 / z)
    ]]></literal>
    <literal><![CDATA[
      L(z,1 / z,x) = y
    ]]></literal>
    <justification jstring="[para(433(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="433 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="613">
    <literal><![CDATA[
      x \ y != (z \ 1) * y
    ]]></literal>
    <literal><![CDATA[
      R(z,z \ 1,y) = x
    ]]></literal>
    <justification jstring="[para(436(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="436 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="614">
    <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),439(a,1))].">
      <j1 rule="para" parents="22 439"/>
    </justification>
  </clause>

  <clause id="615">
    <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),439(a,1,2))].">
      <j1 rule="para" parents="106 439"/>
    </justification>
  </clause>

  <clause id="616">
    <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),447(a,1,1))].">
      <j1 rule="para" parents="106 447"/>
    </justification>
  </clause>

  <clause id="617">
    <literal><![CDATA[
      x \ L(y,x \ 1,x) != (x \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(450(a,2),38(a,1))].">
      <j1 rule="para" parents="450 38"/>
    </justification>
  </clause>

  <clause id="618">
    <literal><![CDATA[
      (x * y) / z != x * u
    ]]></literal>
    <literal><![CDATA[
      L(u \ y,u,x) = z
    ]]></literal>
    <justification jstring="[para(483(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="483 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="619">
    <literal><![CDATA[
      (x * y) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ z,y,x) = u
    ]]></literal>
    <justification jstring="[para(483(a,1),276(a,1,1)),flip(b)].">
      <j1 rule="para" parents="483 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="620">
    <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(483(a,1),431(a,1,1))].">
      <j1 rule="para" parents="483 431"/>
    </justification>
  </clause>

  <clause id="621">
    <literal><![CDATA[
      L(T(x \ y,z),x,1 / x) = T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(500(a,1),20(a,2,1))].">
      <j1 rule="para" parents="500 20"/>
    </justification>
  </clause>

  <clause id="622">
    <literal><![CDATA[
      L(R(x \ y,z,u),x,1 / x) = R((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(500(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="500 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="623">
    <literal><![CDATA[
      L(L(x \ y,z,u),x,1 / x) = L((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(500(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="500 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="624">
    <literal><![CDATA[
      L(T((x \ 1) \ y,z),x \ 1,x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(501(a,1),20(a,2,1))].">
      <j1 rule="para" parents="501 20"/>
    </justification>
  </clause>

  <clause id="625">
    <literal><![CDATA[
      L(R((x \ 1) \ y,z,u),x \ 1,x) = R(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="626">
    <literal><![CDATA[
      L(L((x \ 1) \ y,z,u),x \ 1,x) = L(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="627">
    <literal><![CDATA[
      T((x \ 1) \ y,x * y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(501(a,1),177(a,1,2))].">
      <j1 rule="para" parents="501 177"/>
    </justification>
  </clause>

  <clause id="628">
    <literal><![CDATA[
      R(T(x / (1 / y),z),1 / y,y) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(535(a,1),22(a,2,1))].">
      <j1 rule="para" parents="535 22"/>
    </justification>
  </clause>

  <clause id="629">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ 1) = T(x * (y \ 1),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[
      (x * (x \ y)) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y * z) = w
    ]]></literal>
    <justification jstring="[para(149(a,2),549(a,1))].">
      <j1 rule="para" parents="149 549"/>
    </justification>
  </clause>

  <clause id="631">
    <literal><![CDATA[
      x * (y \ (y * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(152(a,2),549(a,1))].">
      <j1 rule="para" parents="152 549"/>
    </justification>
  </clause>

  <clause id="632">
    <literal><![CDATA[
      (x * (x \ y)) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      (y * z) / w = u
    ]]></literal>
    <justification jstring="[para(149(a,2),550(a,1))].">
      <j1 rule="para" parents="149 550"/>
    </justification>
  </clause>

  <clause id="633">
    <literal><![CDATA[
      x * (y \ (y * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(152(a,2),550(a,1))].">
      <j1 rule="para" parents="152 550"/>
    </justification>
  </clause>

  <clause id="634">
    <literal><![CDATA[
      R(x,y,z) \ ((x * y) * z) != u * w
    ]]></literal>
    <literal><![CDATA[
      (y * z) / w = u
    ]]></literal>
    <justification jstring="[para(187(a,2),550(a,1))].">
      <j1 rule="para" parents="187 550"/>
    </justification>
  </clause>

  <clause id="635">
    <literal><![CDATA[
      x \ (y * (y \ (x * z))) != u \ w
    ]]></literal>
    <literal><![CDATA[
      u * z = w
    ]]></literal>
    <justification jstring="[para(5(a,2),551(a,1,2))].">
      <j1 rule="para" parents="5 551"/>
    </justification>
  </clause>

  <clause id="636">
    <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),551(a,1,2))].">
      <j1 rule="para" parents="90 551"/>
    </justification>
  </clause>

  <clause id="637">
    <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),551(a,1,2))].">
      <j1 rule="para" parents="90 551"/>
    </justification>
  </clause>

  <clause id="638">
    <literal><![CDATA[
      ((x / y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(196(a,2),581(a,1,1))].">
      <j1 rule="para" parents="196 581"/>
    </justification>
  </clause>

  <clause id="639">
    <literal><![CDATA[
      (x * (x \ y)) / z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y / z) = w
    ]]></literal>
    <justification jstring="[para(158(a,1),585(a,1,1))].">
      <j1 rule="para" parents="158 585"/>
    </justification>
  </clause>

  <clause id="640">
    <literal><![CDATA[
      (x * y) \ x != z * u
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) / u = z
    ]]></literal>
    <justification jstring="[para(408(a,1),588(a,1,2))].">
      <j1 rule="para" parents="408 588"/>
    </justification>
  </clause>

  <clause id="641">
    <literal><![CDATA[
      R((x / y) / z,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / (z * y) = u
    ]]></literal>
    <justification jstring="[para(102(a,2),589(a,1))].">
      <j1 rule="para" parents="102 589"/>
    </justification>
  </clause>

  <clause id="642">
    <literal><![CDATA[
      x \ y != (z * u) / u
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></literal>
    <justification jstring="[para(157(a,2),594(a,2))].">
      <j1 rule="para" parents="157 594"/>
    </justification>
  </clause>

  <clause id="643">
    <literal><![CDATA[
      x \ y != (z / (u \ z)) * w
    ]]></literal>
    <literal><![CDATA[
      x * (u * w) = y
    ]]></literal>
    <justification jstring="[para(184(a,1),594(a,2,1))].">
      <j1 rule="para" parents="184 594"/>
    </justification>
  </clause>

  <clause id="644">
    <literal><![CDATA[
      x * ((y \ z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,y \ z) = u
    ]]></literal>
    <justification jstring="[para(227(a,1),597(a,1,2,2))].">
      <j1 rule="para" parents="227 597"/>
    </justification>
  </clause>

  <clause id="645">
    <literal><![CDATA[
      x * ((y * z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      x * L(z \ 1,z,y) = u
    ]]></literal>
    <justification jstring="[para(408(a,1),597(a,1,2,2))].">
      <j1 rule="para" parents="408 597"/>
    </justification>
  </clause>

  <clause id="646">
    <literal><![CDATA[
      x \ y != (z * T(u,z)) / z
    ]]></literal>
    <literal><![CDATA[
      x * u = y
    ]]></literal>
    <justification jstring="[para(105(a,2),642(a,2,1))].">
      <j1 rule="para" parents="105 642"/>
    </justification>
  </clause>

  <clause id="647">
    <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),298(a,1))].">
      <j1 rule="para" parents="110 298"/>
    </justification>
  </clause>

  <clause id="648">
    <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="649">
    <literal><![CDATA[
      x * (y * T(z,x * y)) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,90,a(flip),b,244,a)].">
      <j1 rule="hyper" parents="58 90 244"/>
    </justification>
  </clause>

  <clause id="650">
    <literal><![CDATA[
      x \ (L(y,z,x) * (x * z)) = z * T(y,x * z)
    ]]></literal>
    <justification jstring="[hyper(116,a,244,a(flip),b,90,a(flip))].">
      <j1 rule="hyper" parents="116 244 90"/>
    </justification>
  </clause>

  <clause id="651">
    <literal><![CDATA[
      x * L(x \ (y * x),z,u) = L(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(17(a,1),244(a,1,2,1))].">
      <j1 rule="para" parents="17 244"/>
    </justification>
  </clause>

  <clause id="652">
    <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),244(a,1,2,1))].">
      <j1 rule="para" parents="22 244"/>
    </justification>
  </clause>

  <clause id="653">
    <literal><![CDATA[
      L(x / y,z,u) * y = y * L(y \ x,z,u)
    ]]></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="654">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(230(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="230 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="655">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ y,z,u) = L(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(106(a,1),244(a,1,2,1))].">
      <j1 rule="para" parents="106 244"/>
    </justification>
  </clause>

  <clause id="656">
    <literal><![CDATA[
      (x * y) * R(T(z,x * y),x,y) = (z * x) * y
    ]]></literal>
    <justification jstring="[hyper(334,a,101,a(flip),b,245,a),flip(a)].">
      <j1 rule="hyper" parents="334 101 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="657">
    <literal><![CDATA[
      R(x / y,z,u) * y = y * R(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="658">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(230(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="230 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="659">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ y,z,u) = R(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="660">
    <literal><![CDATA[
      R(x / (x / y),z,u) * (x / y) = (x / y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(252(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="252 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="661">
    <literal><![CDATA[
      T(x / y,(z / y) \ z) = y \ x
    ]]></literal>
    <justification jstring="[hyper(246,a,364,a,b,300,a)].">
      <j1 rule="hyper" parents="246 364 300"/>
    </justification>
  </clause>

  <clause id="662">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) / x = L(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(281,a,255,a)].">
      <j1 rule="hyper" parents="281 255"/>
    </justification>
  </clause>

  <clause id="663">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) / x = R(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(281,a,256,a)].">
      <j1 rule="hyper" parents="281 256"/>
    </justification>
  </clause>

  <clause id="664">
    <literal><![CDATA[
      T(x / (y * x),y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(223(a,1),256(a,1,1))].">
      <j1 rule="para" parents="223 256"/>
    </justification>
  </clause>

  <clause id="665">
    <literal><![CDATA[
      x * R(x \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(y / x,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(256(a,1),294(a,1,2))].">
      <j1 rule="para" parents="256 294"/>
    </justification>
  </clause>

  <clause id="666">
    <literal><![CDATA[
      T((x * y) / (z * y),z) = R(z \ x,z,y)
    ]]></literal>
    <justification jstring="[para(102(a,1),256(a,1,1))].">
      <j1 rule="para" parents="102 256"/>
    </justification>
  </clause>

  <clause id="667">
    <literal><![CDATA[
      R(x \ (y / z),x,z) = T(y / (x * z),x)
    ]]></literal>
    <justification jstring="[para(314(a,1),256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="314 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="668">
    <literal><![CDATA[
      R((x / y) \ 1,x / y,y) = T(y / x,x / y)
    ]]></literal>
    <justification jstring="[para(418(a,1),256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="418 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="669">
    <literal><![CDATA[
      R(x \ y,x,x \ 1) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[para(536(a,1),256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="536 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="670">
    <literal><![CDATA[
      (x / (y * x)) * y = y * R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,664,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 664 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="671">
    <literal><![CDATA[
      x * R(x \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y / (x * y)) * x = z
    ]]></literal>
    <justification jstring="[para(664(a,1),294(a,1,2))].">
      <j1 rule="para" parents="664 294"/>
    </justification>
  </clause>

  <clause id="672">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      T(u,w) = w \ (x * z)
    ]]></literal>
    <justification jstring="[para(312(a,1),247(a,1))].">
      <j1 rule="para" parents="312 247"/>
    </justification>
  </clause>

  <clause id="673">
    <literal><![CDATA[
      x * (y \ T(z,z \ u)) = x * (y \ ((z \ u) \ u))
    ]]></literal>
    <justification jstring="[para(322(a,2),152(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="322 152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="674">
    <literal><![CDATA[
      T(x,x \ y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) \ z = u
    ]]></literal>
    <justification jstring="[para(323(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="323 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="675">
    <literal><![CDATA[
      T(x \ T(y,y \ z),x \ ((y \ z) \ z)) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(455,a,324,a,b,xx)].">
      <j1 rule="hyper" parents="455 324"/>
    </justification>
  </clause>

  <clause id="676">
    <literal><![CDATA[
      (x \ T(y,y \ z)) \ u = (x \ ((y \ z) \ z)) \ u
    ]]></literal>
    <justification jstring="[hyper(56,a,324,a)].">
      <j1 rule="hyper" parents="56 324"/>
    </justification>
  </clause>

  <clause id="677">
    <literal><![CDATA[
      (x * T(y,y \ z)) / ((y \ z) \ z) = x
    ]]></literal>
    <justification jstring="[hyper(343,a,326,a),flip(a)].">
      <j1 rule="hyper" parents="343 326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="678">
    <literal><![CDATA[
      x / ((y \ z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      u * T(y,y \ z) = x
    ]]></literal>
    <justification jstring="[para(326(a,1),133(a,1))].">
      <j1 rule="para" parents="326 133"/>
    </justification>
  </clause>

  <clause id="679">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) = K(z,T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(116,a,327,a(flip),b,84,a)].">
      <j1 rule="hyper" parents="116 327 84"/>
    </justification>
  </clause>

  <clause id="680">
    <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(327(a,1),321(a,1,2))].">
      <j1 rule="para" parents="327 321"/>
    </justification>
  </clause>

  <clause id="681">
    <literal><![CDATA[
      T(T(x,x \ y),z) = T((x \ y) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(246,a,328,a,b,105,a)].">
      <j1 rule="hyper" parents="246 328 105"/>
    </justification>
  </clause>

  <clause id="682">
    <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,328,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="116 328 90"/>
    </justification>
  </clause>

  <clause id="683">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) = K(z,(x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(328(a,2),11(a,2,1)),flip(a)].">
      <j1 rule="para" parents="328 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="684">
    <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(328(a,2),321(a,1,1))].">
      <j1 rule="para" parents="328 321"/>
    </justification>
  </clause>

  <clause id="685">
    <literal><![CDATA[
      T(x,x \ y) * z != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) * z = u
    ]]></literal>
    <justification jstring="[para(329(a,1),597(a,1))].">
      <j1 rule="para" parents="329 597"/>
    </justification>
  </clause>

  <clause id="686">
    <literal><![CDATA[
      (x \ y) * L(T((x \ y) \ y,z),u,w) = L(T(x,z),u,w) * (x \ y)
    ]]></literal>
    <justification jstring="[para(330(a,1),244(a,1,2,1))].">
      <j1 rule="para" parents="330 244"/>
    </justification>
  </clause>

  <clause id="687">
    <literal><![CDATA[
      x \ (x / y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x / y) = z
    ]]></literal>
    <justification jstring="[para(7(a,1),434(a,1,1))].">
      <j1 rule="para" parents="7 434"/>
    </justification>
  </clause>

  <clause id="688">
    <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),437(a,1,2))].">
      <j1 rule="para" parents="105 437"/>
    </justification>
  </clause>

  <clause id="689">
    <literal><![CDATA[
      (1 / x) / K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      R(1 / x,x,1 / x) = y
    ]]></literal>
    <justification jstring="[para(268(a,2),437(a,1,2))].">
      <j1 rule="para" parents="268 437"/>
    </justification>
  </clause>

  <clause id="690">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,85,a(flip),b,442,a)].">
      <j1 rule="hyper" parents="334 85 442"/>
    </justification>
  </clause>

  <clause id="691">
    <literal><![CDATA[
      K(x \ (x * y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(63(a,1),690(a,1,1)),flip(a)].">
      <j1 rule="para" parents="63 690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="692">
    <literal><![CDATA[
      K((x / y) \ x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),691(a,1,1,2))].">
      <j1 rule="para" parents="7 691"/>
    </justification>
  </clause>

  <clause id="693">
    <literal><![CDATA[
      x / T(y,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x / ((y \ z) \ z) = u
    ]]></literal>
    <justification jstring="[para(457(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="457 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="694">
    <literal><![CDATA[
      T((x * y) / x,z) * x != x * u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(466(a,2),38(a,1))].">
      <j1 rule="para" parents="466 38"/>
    </justification>
  </clause>

  <clause id="695">
    <literal><![CDATA[
      T(x / y,z) * y != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(469(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="469 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="696">
    <literal><![CDATA[
      T(T(x / y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(469(a,1),303(a,1,1)),flip(b)].">
      <j1 rule="para" parents="469 303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="697">
    <literal><![CDATA[
      T((x * (y / z)) / x,z) = (x * (z \ y)) / x
    ]]></literal>
    <justification jstring="[para(107(a,1),472(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="698">
    <literal><![CDATA[
      T((x * y) / x,z) * x != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(472(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="472 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="699">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(472(a,1),303(a,1,1)),flip(b)].">
      <j1 rule="para" parents="472 303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="700">
    <literal><![CDATA[
      T(1 / ((x * y) \ x),y) = 1 / ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),602(a,1,2))].">
      <j1 rule="para" parents="4 602"/>
    </justification>
  </clause>

  <clause id="701">
    <literal><![CDATA[
      T(x * y,(x \ 1) \ y) = x * y
    ]]></literal>
    <justification jstring="[hyper(49,a,627,a)].">
      <j1 rule="hyper" parents="49 627"/>
    </justification>
  </clause>

  <clause id="702">
    <literal><![CDATA[
      T(x * (y * z),a(x,y,z)) = a(x,y,z) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(451,a,xx,b,80,a)].">
      <j1 rule="hyper" parents="451 80"/>
    </justification>
  </clause>

  <clause id="703">
    <literal><![CDATA[
      ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(288,a,80,a)].">
      <j1 rule="hyper" parents="288 80"/>
    </justification>
  </clause>

  <clause id="704">
    <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="705">
    <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="706">
    <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="707">
    <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="708">
    <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="709">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(80(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="80 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="710">
    <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="711">
    <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="712">
    <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),551(a,1,2))].">
      <j1 rule="para" parents="80 551"/>
    </justification>
  </clause>

  <clause id="713">
    <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="714">
    <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="715">
    <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="716">
    <literal><![CDATA[
      x * L(y,z,x / z) != u
    ]]></literal>
    <literal><![CDATA[
      (x / z) * (z * y) = u
    ]]></literal>
    <justification jstring="[para(93(a,1),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="93 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="717">
    <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="718">
    <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="719">
    <literal><![CDATA[
      R(x,x \ y,y \ z) \ z = (x \ y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(98(a,2),313(a,1,1))].">
      <j1 rule="para" parents="98 313"/>
    </justification>
  </clause>

  <clause id="720">
    <literal><![CDATA[
      R(x,x \ (y / z),z) \ y = (x \ (y / z)) * z
    ]]></literal>
    <justification jstring="[para(98(a,2),339(a,1,1))].">
      <j1 rule="para" parents="98 339"/>
    </justification>
  </clause>

  <clause id="721">
    <literal><![CDATA[
      R(x,y,y \ z) * z != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * (y \ z) = u
    ]]></literal>
    <justification jstring="[para(100(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="100 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="722">
    <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="723">
    <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="724">
    <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="725">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(269(a,1),220(a,1,2))].">
      <j1 rule="para" parents="269 220"/>
    </justification>
  </clause>

  <clause id="726">
    <literal><![CDATA[
      x * a(x,y,y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,725,a)].">
      <j1 rule="hyper" parents="134 725"/>
    </justification>
  </clause>

  <clause id="727">
    <literal><![CDATA[
      L(x \ a(y,z,z \ 1),x,y) = (y * x) \ R(y,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(725(a,1),311(a,1,1,2))].">
      <j1 rule="para" parents="725 311"/>
    </justification>
  </clause>

  <clause id="728">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(726(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="726 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="729">
    <literal><![CDATA[
      x \ R(x,1 / y,y) = a(x,1 / y,y)
    ]]></literal>
    <justification jstring="[para(270(a,1),224(a,1,2))].">
      <j1 rule="para" parents="270 224"/>
    </justification>
  </clause>

  <clause id="730">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) = T(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,20,a(flip),b,239,a),flip(a)].">
      <j1 rule="hyper" parents="334 20 239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="731">
    <literal><![CDATA[
      L(T(x,y),y,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(298,a,239,a),flip(a)].">
      <j1 rule="hyper" parents="298 239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="732">
    <literal><![CDATA[
      L(T(x,y),y,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * (x * y) = z
    ]]></literal>
    <justification jstring="[para(239(a,1),213(a,1))].">
      <j1 rule="para" parents="239 213"/>
    </justification>
  </clause>

  <clause id="733">
    <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),239(a,1,2))].">
      <j1 rule="para" parents="101 239"/>
    </justification>
  </clause>

  <clause id="734">
    <literal><![CDATA[
      L(T(x,y \ z),y \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      z \ (y * (x * (y \ z))) = u
    ]]></literal>
    <justification jstring="[para(239(a,1),361(a,1))].">
      <j1 rule="para" parents="239 361"/>
    </justification>
  </clause>

  <clause id="735">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,20,a(flip),b,731,a)].">
      <j1 rule="hyper" parents="58 20 731"/>
    </justification>
  </clause>

  <clause id="736">
    <literal><![CDATA[
      L(T(T(x,y),z),y,x) = T(T(x,x * y),z)
    ]]></literal>
    <justification jstring="[para(731(a,1),20(a,2,1))].">
      <j1 rule="para" parents="731 20"/>
    </justification>
  </clause>

  <clause id="737">
    <literal><![CDATA[
      L(R(T(x,y),z,u),y,x) = R(T(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(731(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="731 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="738">
    <literal><![CDATA[
      x * T(y,y * x) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[para(731(a,1),244(a,1,2))].">
      <j1 rule="para" parents="731 244"/>
    </justification>
  </clause>

  <clause id="739">
    <literal><![CDATA[
      (x * y) * R(L(T(x,y),y,x),z,u) = R(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[para(731(a,2),245(a,1,2,1))].">
      <j1 rule="para" parents="731 245"/>
    </justification>
  </clause>

  <clause id="740">
    <literal><![CDATA[
      (x * T(y,y * x)) / x = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(281,a,735,a)].">
      <j1 rule="hyper" parents="281 735"/>
    </justification>
  </clause>

  <clause id="741">
    <literal><![CDATA[
      T((x * y) / x,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,280,a,b,735,a)].">
      <j1 rule="hyper" parents="35 280 735"/>
    </justification>
  </clause>

  <clause id="742">
    <literal><![CDATA[
      T(L(L(x,y,x),z,u),y) = L(T(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(735(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="735 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="743">
    <literal><![CDATA[
      x * L(T(y,y * x),z,u) = L(L(y,x,y),z,u) * x
    ]]></literal>
    <justification jstring="[para(735(a,1),244(a,1,2,1))].">
      <j1 rule="para" parents="735 244"/>
    </justification>
  </clause>

  <clause id="744">
    <literal><![CDATA[
      L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),738(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="745">
    <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),738(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="105 738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="746">
    <literal><![CDATA[
      ((x \ y) * T(x,y)) / (x \ y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),740(a,1,1,2,2))].">
      <j1 rule="para" parents="5 740"/>
    </justification>
  </clause>

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

  <clause id="748">
    <literal><![CDATA[
      T(T((x * y) / x,z),y * x) = T(L(y,x,y),z)
    ]]></literal>
    <justification jstring="[para(741(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="741 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="749">
    <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(318(a,1),465(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="318 465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="750">
    <literal><![CDATA[
      T(R(x / y,y,y \ z),z) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(451,a,148,a(flip),b,380,a)].">
      <j1 rule="hyper" parents="451 148 380"/>
    </justification>
  </clause>

  <clause id="751">
    <literal><![CDATA[
      x * R(T(y,x),z,z \ x) = (y * z) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,245,a,b,380,a)].">
      <j1 rule="hyper" parents="58 245 380"/>
    </justification>
  </clause>

  <clause id="752">
    <literal><![CDATA[
      x \ ((y * z) * (z \ x)) = R(T(y,x),z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(116,a,380,a(flip),b,245,a)].">
      <j1 rule="hyper" parents="116 380 245"/>
    </justification>
  </clause>

  <clause id="753">
    <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),380(a,1,1))].">
      <j1 rule="para" parents="24 380"/>
    </justification>
  </clause>

  <clause id="754">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (z * ((y * x) \ y)) = T(z,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(246,a,67,a(flip),b,402,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="246 67 402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="755">
    <literal><![CDATA[
      L(x \ 1,x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      ((y * x) \ y) \ u = z
    ]]></literal>
    <justification jstring="[para(402(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="402 38"/>
      <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(404(a,2),134(a,1))].">
      <j1 rule="para" parents="404 134"/>
    </justification>
  </clause>

  <clause id="757">
    <literal><![CDATA[
      x * (y * L(z \ 1,z,u)) = x * (y * ((u * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(119,a,405,a,b,4,a)].">
      <j1 rule="hyper" parents="119 405 4"/>
    </justification>
  </clause>

  <clause id="758">
    <literal><![CDATA[
      x * L(y \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      u / ((z * y) \ z) = x
    ]]></literal>
    <justification jstring="[para(405(a,2),130(a,1))].">
      <j1 rule="para" parents="405 130"/>
    </justification>
  </clause>

  <clause id="759">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,410,a,b,13,a(flip))].">
      <j1 rule="hyper" parents="119 410 13"/>
    </justification>
  </clause>

  <clause id="760">
    <literal><![CDATA[
      R(1 / x,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      y / (x * y) = z
    ]]></literal>
    <justification jstring="[para(415(a,1),211(a,1))].">
      <j1 rule="para" parents="415 211"/>
    </justification>
  </clause>

  <clause id="761">
    <literal><![CDATA[
      R(T(1 / x,x * y),x,y) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(431,a,419,a),flip(a)].">
      <j1 rule="hyper" parents="431 419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="762">
    <literal><![CDATA[
      T(x / (y * x),z) * (y * x) = (T(1 / y,z) * y) * x
    ]]></literal>
    <justification jstring="[para(419(a,2),101(a,1,1))].">
      <j1 rule="para" parents="419 101"/>
    </justification>
  </clause>

  <clause id="763">
    <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),422(a,1,2))].">
      <j1 rule="para" parents="106 422"/>
    </justification>
  </clause>

  <clause id="764">
    <literal><![CDATA[
      x * T(x \ (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(17(a,1),428(a,1,2,1))].">
      <j1 rule="para" parents="17 428"/>
    </justification>
  </clause>

  <clause id="765">
    <literal><![CDATA[
      L(T(x \ 1,x),x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(334,a,107,a(flip),b,432,a),flip(a)].">
      <j1 rule="hyper" parents="334 107 432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="766">
    <literal><![CDATA[
      (1 / x) \ T(1 / x,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,432,a(flip),b,267,a)].">
      <j1 rule="hyper" parents="116 432 267"/>
    </justification>
  </clause>

  <clause id="767">
    <literal><![CDATA[
      x / L(y \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x / ((z * y) \ z) = u
    ]]></literal>
    <justification jstring="[para(456(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="456 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="768">
    <literal><![CDATA[
      x * ((x \ y) * T(z,y)) = L(z,x \ y,x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,244,a(flip),b,460,a),flip(a)].">
      <j1 rule="hyper" parents="58 244 460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="769">
    <literal><![CDATA[
      x \ (L(y,x \ z,x) * z) = (x \ z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,244,a(flip),b,460,a(flip))].">
      <j1 rule="hyper" parents="116 244 460"/>
    </justification>
  </clause>

  <clause id="770">
    <literal><![CDATA[
      x \ (y * ((y \ x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y \ x,y) = u
    ]]></literal>
    <justification jstring="[para(460(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="460 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="771">
    <literal><![CDATA[
      x * L(y,T(z,z \ x),z \ x) = (z \ x) * (((z \ x) \ x) * y)
    ]]></literal>
    <justification jstring="[para(106(a,2),460(a,1,2,2))].">
      <j1 rule="para" parents="106 460"/>
    </justification>
  </clause>

  <clause id="772">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,11,a,b,462,a)].">
      <j1 rule="hyper" parents="334 11 462"/>
    </justification>
  </clause>

  <clause id="773">
    <literal><![CDATA[
      L(T(x \ T(y,z),u),x,z) = T((z * x) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(462(a,1),20(a,2,1))].">
      <j1 rule="para" parents="462 20"/>
    </justification>
  </clause>

  <clause id="774">
    <literal><![CDATA[
      L(x \ T(x,y),x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(462(a,2),321(a,1))].">
      <j1 rule="para" parents="462 321"/>
    </justification>
  </clause>

  <clause id="775">
    <literal><![CDATA[
      L(x \ y,x,y / x) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(246,a,151,a(flip),b,485,a),flip(a)].">
      <j1 rule="hyper" parents="246 151 485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="776">
    <literal><![CDATA[
      (x / y) \ (L(z,y,x / y) * x) = y * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,244,a(flip),b,485,a(flip))].">
      <j1 rule="hyper" parents="116 244 485"/>
    </justification>
  </clause>

  <clause id="777">
    <literal><![CDATA[
      x \ (y * L(z,x \ y,x)) != (x \ y) * u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(487(a,2),38(a,1))].">
      <j1 rule="para" parents="487 38"/>
    </justification>
  </clause>

  <clause id="778">
    <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),487(a,1,2,2))].">
      <j1 rule="para" parents="147 487"/>
    </justification>
  </clause>

  <clause id="779">
    <literal><![CDATA[
      L(T((x \ y) \ z,u),x \ y,x) = T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(502(a,1),20(a,2,1))].">
      <j1 rule="para" parents="502 20"/>
    </justification>
  </clause>

  <clause id="780">
    <literal><![CDATA[
      L(R((x \ y) \ z,u,w),x \ y,x) = R(y \ (x * z),u,w)
    ]]></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="781">
    <literal><![CDATA[
      L(L((x \ y) \ z,u,w),x \ y,x) = L(y \ (x * z),u,w)
    ]]></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="782">
    <literal><![CDATA[
      L(x,y \ z,y) != z \ (y * u)
    ]]></literal>
    <literal><![CDATA[
      (y \ z) \ u = x
    ]]></literal>
    <justification jstring="[para(502(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="502 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="783">
    <literal><![CDATA[
      L(x \ y,x,y / x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y / x,y) = z
    ]]></literal>
    <justification jstring="[para(505(a,2),298(a,1))].">
      <j1 rule="para" parents="505 298"/>
    </justification>
  </clause>

  <clause id="784">
    <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(188(a,1),515(a,1,1,1))].">
      <j1 rule="para" parents="188 515"/>
    </justification>
  </clause>

  <clause id="785">
    <literal><![CDATA[
      (x * y) / ((z \ x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      R(z,z \ x,y) = u
    ]]></literal>
    <justification jstring="[para(517(a,1),345(a,1,2)),flip(b)].">
      <j1 rule="para" parents="517 345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="786">
    <literal><![CDATA[
      R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(538(a,1),22(a,2,1))].">
      <j1 rule="para" parents="538 22"/>
    </justification>
  </clause>

  <clause id="787">
    <literal><![CDATA[
      R(R(x / (y / z),u,w),y / z,z) = R((x * z) / y,u,w)
    ]]></literal>
    <justification jstring="[para(538(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="538 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="788">
    <literal><![CDATA[
      R(x / R(1 / y,y,z),z / (y * z),y * z) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[para(223(a,2),538(a,1,1,2))].">
      <j1 rule="para" parents="223 538"/>
    </justification>
  </clause>

  <clause id="789">
    <literal><![CDATA[
      R(x / (y / (z * y)),R(1 / z,z,y),z * y) = (x * (z * y)) / y
    ]]></literal>
    <justification jstring="[para(223(a,2),538(a,1,2))].">
      <j1 rule="para" parents="223 538"/>
    </justification>
  </clause>

  <clause id="790">
    <literal><![CDATA[
      R((x / y) \ z,x / y,y) = T((z * y) / x,x / y)
    ]]></literal>
    <justification jstring="[para(538(a,1),256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="538 256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="791">
    <literal><![CDATA[
      T(x,y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(x,y) = u
    ]]></literal>
    <justification jstring="[para(17(a,2),548(a,1))].">
      <j1 rule="para" parents="17 548"/>
    </justification>
  </clause>

  <clause id="792">
    <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(556(a,1),431(a,1,1))].">
      <j1 rule="para" parents="556 431"/>
    </justification>
  </clause>

  <clause id="793">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(z,y),y,x) = u
    ]]></literal>
    <justification jstring="[para(557(a,1),276(a,1,1)),flip(b)].">
      <j1 rule="para" parents="557 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="794">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) * x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,765,a(flip),b,567,a),flip(a)].">
      <j1 rule="hyper" parents="58 765 567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="795">
    <literal><![CDATA[
      T(L(x,y,1 / y),y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,20,a(flip),b,567,a)].">
      <j1 rule="hyper" parents="58 20 567"/>
    </justification>
  </clause>

  <clause id="796">
    <literal><![CDATA[
      (1 / x) \ (x \ 1) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(116,a,765,a(flip),b,567,a(flip))].">
      <j1 rule="hyper" parents="116 765 567"/>
    </justification>
  </clause>

  <clause id="797">
    <literal><![CDATA[
      (1 / x) \ T(L(y,x,1 / x),x) = y * x
    ]]></literal>
    <justification jstring="[hyper(116,a,20,a(flip),b,567,a(flip))].">
      <j1 rule="hyper" parents="116 20 567"/>
    </justification>
  </clause>

  <clause id="798">
    <literal><![CDATA[
      (1 / (1 / x)) * (x * (1 / x)) = (1 / x) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),794(a,1,2,1))].">
      <j1 rule="para" parents="75 794"/>
    </justification>
  </clause>

  <clause id="799">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,x) = x \ 1
    ]]></literal>
    <justification jstring="[para(266(a,2),794(a,1,2))].">
      <j1 rule="para" parents="266 794"/>
    </justification>
  </clause>

  <clause id="800">
    <literal><![CDATA[
      (1 / x) \ (x \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,266,a,b,796,a),flip(a)].">
      <j1 rule="hyper" parents="334 266 796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="801">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = x \ ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,799,a(flip),b,186,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 799 186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="802">
    <literal><![CDATA[
      (x \ 1) \ ((1 / x) * (K(x \ 1,x) * y)) = L(y,K(x \ 1,x),1 / x)
    ]]></literal>
    <justification jstring="[para(799(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="799 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="803">
    <literal><![CDATA[
      K(x \ 1,x) * y != x \ 1
    ]]></literal>
    <literal><![CDATA[
      T(1 / x,K(x \ 1,x)) = y
    ]]></literal>
    <justification jstring="[para(799(a,1),247(a,2))].">
      <j1 rule="para" parents="799 247"/>
    </justification>
  </clause>

  <clause id="804">
    <literal><![CDATA[
      (x * (y \ 1)) / L(K(y \ 1,y),1 / y,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(799(a,1),190(a,1,1,2))].">
      <j1 rule="para" parents="799 190"/>
    </justification>
  </clause>

  <clause id="805">
    <literal><![CDATA[
      x / L(K(y \ 1,y),1 / y,x / (y \ 1)) = (x / (y \ 1)) * (1 / y)
    ]]></literal>
    <justification jstring="[para(800(a,1),510(a,1,2,1))].">
      <j1 rule="para" parents="800 510"/>
    </justification>
  </clause>

  <clause id="806">
    <literal><![CDATA[
      T(x / y,y) != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * (y \ x) = u
    ]]></literal>
    <justification jstring="[para(469(a,1),646(a,2)),flip(a)].">
      <j1 rule="para" parents="469 646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="807">
    <literal><![CDATA[
      R(x,y,z) = T(((y * x) * z) / (y * z),y)
    ]]></literal>
    <justification jstring="[para(4(a,1),666(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4 666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="808">
    <literal><![CDATA[
      T(x / (y * z),y) * (y * z) = ((y \ (x / z)) * y) * z
    ]]></literal>
    <justification jstring="[para(667(a,1),101(a,1,1))].">
      <j1 rule="para" parents="667 101"/>
    </justification>
  </clause>

  <clause id="809">
    <literal><![CDATA[
      ((x \ y) * x) * (x \ 1) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,269,a,b,669,a)].">
      <j1 rule="hyper" parents="58 269 669"/>
    </justification>
  </clause>

  <clause id="810">
    <literal><![CDATA[
      T((x * y) * (x \ 1),x) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),669(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="811">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,x / y,y) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),670(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="812">
    <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(666(a,1),696(a,1,1))].">
      <j1 rule="para" parents="666 696"/>
    </justification>
  </clause>

  <clause id="813">
    <literal><![CDATA[
      (x * y) * (y \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(707(a,1),38(a,1))].">
      <j1 rule="para" parents="707 38"/>
    </justification>
  </clause>

  <clause id="814">
    <literal><![CDATA[
      T(L(x,y \ z,y),y \ z) = z \ (y * (x * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(361,a,730,a),flip(a)].">
      <j1 rule="hyper" parents="361 730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="815">
    <literal><![CDATA[
      T(L(x,y,z / y),y) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[para(7(a,1),730(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="816">
    <literal><![CDATA[
      (x * y) * T(T(x,x * y),z) = x * (y * T(T(x,y),z))
    ]]></literal>
    <justification jstring="[hyper(119,a,736,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 736 13"/>
    </justification>
  </clause>

  <clause id="817">
    <literal><![CDATA[
      T((1 / x) * (x * y),x) = (1 / x) * (y * x)
    ]]></literal>
    <justification jstring="[para(267(a,2),795(a,1,1))].">
      <j1 rule="para" parents="267 795"/>
    </justification>
  </clause>

  <clause id="818">
    <literal><![CDATA[
      (1 / x) * ((x \ y) * x) = T((1 / x) * y,x)
    ]]></literal>
    <justification jstring="[para(500(a,1),795(a,1,1)),flip(a)].">
      <j1 rule="para" parents="500 795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="819">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) * y,x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(500(a,1),797(a,1,2,1))].">
      <j1 rule="para" parents="500 797"/>
    </justification>
  </clause>

  <clause id="820">
    <literal><![CDATA[
      (((x * y) * z) / (x * z)) * x = x * R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,807,a,b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 807 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="821">
    <literal><![CDATA[
      T(x,y) != R(z,y,u)
    ]]></literal>
    <literal><![CDATA[
      ((y * z) * u) / (y * u) = x
    ]]></literal>
    <justification jstring="[para(807(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="807 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="822">
    <literal><![CDATA[
      T(((1 / x) * y) * x,1 / x) = R(y,1 / x,x)
    ]]></literal>
    <justification jstring="[para(173(a,1),807(a,2,1)),flip(a)].">
      <j1 rule="para" parents="173 807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="823">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = T(R(z,x,y),x * y)
    ]]></literal>
    <justification jstring="[para(807(a,2),254(a,1,1)),flip(a)].">
      <j1 rule="para" parents="807 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="824">
    <literal><![CDATA[
      T(R(x,y,x),y * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(807(a,2),280(a,1,1))].">
      <j1 rule="para" parents="807 280"/>
    </justification>
  </clause>

  <clause id="825">
    <literal><![CDATA[
      R(T(x,y * x),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,22,a,b,824,a)].">
      <j1 rule="hyper" parents="58 22 824"/>
    </justification>
  </clause>

  <clause id="826">
    <literal><![CDATA[
      L(R(x,y,x),z,u) * (y * x) = (y * x) * L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(824(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="824 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="827">
    <literal><![CDATA[
      R(R(x,y,x),z,u) * (y * x) = (y * x) * R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(824(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="824 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="828">
    <literal><![CDATA[
      R(x,y,z) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      T(z,y * z) = x
    ]]></literal>
    <justification jstring="[para(824(a,1),144(a,1)),flip(a)].">
      <j1 rule="para" parents="824 144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="829">
    <literal><![CDATA[
      ((x * T(y,x * y)) * y) / (x * y) = y
    ]]></literal>
    <justification jstring="[hyper(35,a,807,a(flip),b,825,a(flip))].">
      <j1 rule="hyper" parents="35 807 825"/>
    </justification>
  </clause>

  <clause id="830">
    <literal><![CDATA[
      R(T(x,y),y / x,x) = T(x,y / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),825(a,1,1,2))].">
      <j1 rule="para" parents="7 825"/>
    </justification>
  </clause>

  <clause id="831">
    <literal><![CDATA[
      R(x,y / z,z) != T(z,y / z)
    ]]></literal>
    <literal><![CDATA[
      T(z,y) = x
    ]]></literal>
    <justification jstring="[para(830(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="830 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="832">
    <literal><![CDATA[
      R(x,1 / x,x) = T(x,1 / x)
    ]]></literal>
    <justification jstring="[para(202(a,1),830(a,1,1))].">
      <j1 rule="para" parents="202 830"/>
    </justification>
  </clause>

  <clause id="833">
    <literal><![CDATA[
      T(x,1 / x) / x = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,832,a(flip),b,270,a)].">
      <j1 rule="hyper" parents="117 832 270"/>
    </justification>
  </clause>

  <clause id="834">
    <literal><![CDATA[
      R(R(x,y,z),1 / x,x) = R(T(x,1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(832(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="832 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="835">
    <literal><![CDATA[
      T(x,1 / x) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(334,a,268,a,b,833,a),flip(a)].">
      <j1 rule="hyper" parents="334 268 833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="836">
    <literal><![CDATA[
      K(x,1 / x) * x = T(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(133,a,835,a)].">
      <j1 rule="hyper" parents="133 835"/>
    </justification>
  </clause>

  <clause id="837">
    <literal><![CDATA[
      T(x * T(y,x * y),y) = x * y
    ]]></literal>
    <justification jstring="[hyper(274,a,829,a)].">
      <j1 rule="hyper" parents="274 829"/>
    </justification>
  </clause>

  <clause id="838">
    <literal><![CDATA[
      T((x / y) * T(y,(x / y) * y),y) = x
    ]]></literal>
    <justification jstring="[hyper(334,a,7,a(flip),b,837,a),flip(a)].">
      <j1 rule="hyper" parents="334 7 837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="839">
    <literal><![CDATA[
      T((x / y) * T(y,x),y) = x
    ]]></literal>
    <justification jstring="[para(7(a,1),838(a,1,1,2,2))].">
      <j1 rule="para" parents="7 838"/>
    </justification>
  </clause>

  <clause id="840">
    <literal><![CDATA[
      (x / y) * T(y,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(281,a,839,a),flip(a)].">
      <j1 rule="hyper" parents="281 839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="841">
    <literal><![CDATA[
      T(x * T(T(y,x),y * x),T(y,x)) = y * x
    ]]></literal>
    <justification jstring="[para(191(a,1),839(a,1,1,1))].">
      <j1 rule="para" parents="191 839"/>
    </justification>
  </clause>

  <clause id="842">
    <literal><![CDATA[
      T(x,y) \ ((x * y) / x) = T(y / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(451,a,xx,b,840,a),flip(a)].">
      <j1 rule="hyper" parents="451 840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="843">
    <literal><![CDATA[
      ((x \ y) * y) / (x \ y) = x * T(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(359,a,840,a),flip(a)].">
      <j1 rule="hyper" parents="359 840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="844">
    <literal><![CDATA[
      ((x * y) / x) / T(x,y) = y / x
    ]]></literal>
    <justification jstring="[hyper(130,a,840,a)].">
      <j1 rule="hyper" parents="130 840"/>
    </justification>
  </clause>

  <clause id="845">
    <literal><![CDATA[
      T(x,y) = (y / x) \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(123,a,840,a),flip(a)].">
      <j1 rule="hyper" parents="123 840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="846">
    <literal><![CDATA[
      T(x,y) \ ((x * y) / x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y / x,T(x,y)) = z
    ]]></literal>
    <justification jstring="[para(840(a,1),298(a,1,2))].">
      <j1 rule="para" parents="840 298"/>
    </justification>
  </clause>

  <clause id="847">
    <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(407(a,1),840(a,1,1)),flip(a)].">
      <j1 rule="para" parents="407 840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="848">
    <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(433(a,1),840(a,1,1)),flip(a)].">
      <j1 rule="para" parents="433 840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="849">
    <literal><![CDATA[
      (x * R(y,x,x \ 1)) / x = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(281,a,810,a)].">
      <j1 rule="hyper" parents="281 810"/>
    </justification>
  </clause>

  <clause id="850">
    <literal><![CDATA[
      R(T(T(x,y),z),u,w) = T(T(R(x,u,w),z),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,22,a,b,111,a)].">
      <j1 rule="hyper" parents="334 22 111"/>
    </justification>
  </clause>

  <clause id="851">
    <literal><![CDATA[
      x * y != 1
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(69(a,1),291(a,1)),flip(a)].">
      <j1 rule="para" parents="69 291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="852">
    <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),293(a,1,2))].">
      <j1 rule="para" parents="105 293"/>
    </justification>
  </clause>

  <clause id="853">
    <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),296(a,1,2))].">
      <j1 rule="para" parents="24 296"/>
    </justification>
  </clause>

  <clause id="854">
    <literal><![CDATA[
      L(T(x,x \ y),z,u) = L((x \ y) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,20,a,b,331,a)].">
      <j1 rule="hyper" parents="58 20 331"/>
    </justification>
  </clause>

  <clause id="855">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = R((x \ y) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,22,a,b,332,a)].">
      <j1 rule="hyper" parents="58 22 332"/>
    </justification>
  </clause>

  <clause id="856">
    <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),349(a,1,1))].">
      <j1 rule="para" parents="7 349"/>
    </justification>
  </clause>

  <clause id="857">
    <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),493(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="858">
    <literal><![CDATA[
      K(x \ 1,x) * y != (x \ 1) * (x * z)
    ]]></literal>
    <literal><![CDATA[
      L(z,x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(266(a,2),493(a,1,1))].">
      <j1 rule="para" parents="266 493"/>
    </justification>
  </clause>

  <clause id="859">
    <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),494(a,1,2))].">
      <j1 rule="para" parents="147 494"/>
    </justification>
  </clause>

  <clause id="860">
    <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),495(a,1,1))].">
      <j1 rule="para" parents="105 495"/>
    </justification>
  </clause>

  <clause id="861">
    <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),495(a,1,2,2))].">
      <j1 rule="para" parents="90 495"/>
    </justification>
  </clause>

  <clause id="862">
    <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(328(a,2),495(a,1,1))].">
      <j1 rule="para" parents="328 495"/>
    </justification>
  </clause>

  <clause id="863">
    <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),495(a,1,2,2))].">
      <j1 rule="para" parents="80 495"/>
    </justification>
  </clause>

  <clause id="864">
    <literal><![CDATA[
      x * K(x \ 1,x) != y
    ]]></literal>
    <literal><![CDATA[
      L(x,x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(266(a,2),497(a,1,2))].">
      <j1 rule="para" parents="266 497"/>
    </justification>
  </clause>

  <clause id="865">
    <literal><![CDATA[
      L(x,x \ 1,x) != y
    ]]></literal>
    <literal><![CDATA[
      x * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(371(a,1),511(a,1,1))].">
      <j1 rule="para" parents="371 511"/>
    </justification>
  </clause>

  <clause id="866">
    <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),527(a,2,2))].">
      <j1 rule="para" parents="84 527"/>
    </justification>
  </clause>

  <clause id="867">
    <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(799(a,1),527(a,2,2))].">
      <j1 rule="para" parents="799 527"/>
    </justification>
  </clause>

  <clause id="868">
    <literal><![CDATA[
      x / (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      R((x / z) / y,y,z) = u
    ]]></literal>
    <justification jstring="[para(79(a,1),530(a,1,1))].">
      <j1 rule="para" parents="79 530"/>
    </justification>
  </clause>

  <clause id="869">
    <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),565(a,1,2))].">
      <j1 rule="para" parents="20 565"/>
    </justification>
  </clause>

  <clause id="870">
    <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),617(a,1,2))].">
      <j1 rule="para" parents="25 617"/>
    </justification>
  </clause>

  <clause id="871">
    <literal><![CDATA[
      R(x / y,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) / (y * z) = u
    ]]></literal>
    <justification jstring="[para(6(a,1),641(a,1,1,1))].">
      <j1 rule="para" parents="6 641"/>
    </justification>
  </clause>

  <clause id="872">
    <literal><![CDATA[
      (x * ((y * x) \ y)) / x = L(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,405,a(flip),b,653,a)].">
      <j1 rule="hyper" parents="117 405 653"/>
    </justification>
  </clause>

  <clause id="873">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) * (x \ y) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(401(a,1),653(a,2,2))].">
      <j1 rule="para" parents="401 653"/>
    </justification>
  </clause>

  <clause id="874">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) / (x \ y) = L(1 / (x \ y),x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),872(a,1,1,2,1))].">
      <j1 rule="para" parents="5 872"/>
    </justification>
  </clause>

  <clause id="875">
    <literal><![CDATA[
      L((x * y) / x,z,u) = (x * L(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(130,a,654,a),flip(a)].">
      <j1 rule="hyper" parents="130 654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="876">
    <literal><![CDATA[
      L((x * (y \ 1)) / x,y,z) = (x * ((z * y) \ z)) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,405,a(flip),b,654,a),flip(a)].">
      <j1 rule="hyper" parents="117 405 654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="877">
    <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,654,a),flip(a)].">
      <j1 rule="hyper" parents="117 90 654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="878">
    <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(318(a,1),657(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="318 657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="879">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,x,y) != u
    ]]></literal>
    <literal><![CDATA[
      ((z / (x * y)) * x) * y = u
    ]]></literal>
    <justification jstring="[para(657(a,1),293(a,1))].">
      <j1 rule="para" parents="657 293"/>
    </justification>
  </clause>

  <clause id="880">
    <literal><![CDATA[
      ((((x * y) * z) / (x * y)) * x) * y = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(293,a,658,a)].">
      <j1 rule="hyper" parents="293 658"/>
    </justification>
  </clause>

  <clause id="881">
    <literal><![CDATA[
      R((x * y) / x,z,u) = (x * R(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(130,a,658,a),flip(a)].">
      <j1 rule="hyper" parents="130 658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="882">
    <literal><![CDATA[
      R((x * y) / x,z,u) \ (x * R(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(123,a,658,a)].">
      <j1 rule="hyper" parents="123 658"/>
    </justification>
  </clause>

  <clause id="883">
    <literal><![CDATA[
      R((x * (1 / y)) / x,y,z) = (x * (z / (y * z))) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,414,a(flip),b,658,a),flip(a)].">
      <j1 rule="hyper" parents="117 414 658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="884">
    <literal><![CDATA[
      (((x * y) / x) * z) * (z \ x) = x * R(y,z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,380,a(flip),b,658,a)].">
      <j1 rule="hyper" parents="58 380 658"/>
    </justification>
  </clause>

  <clause id="885">
    <literal><![CDATA[
      ((x * y) * R(z,x,y)) / y = (((x * y) * z) / (x * y)) * x
    ]]></literal>
    <justification jstring="[hyper(117,a,658,a(flip),b,101,a(flip))].">
      <j1 rule="hyper" parents="117 658 101"/>
    </justification>
  </clause>

  <clause id="886">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) / (x / y) = L(x / (x / y),z,u)
    ]]></literal>
    <justification jstring="[para(75(a,1),662(a,1,1,2,1))].">
      <j1 rule="para" parents="75 662"/>
    </justification>
  </clause>

  <clause id="887">
    <literal><![CDATA[
      L(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(662(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="662 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="888">
    <literal><![CDATA[
      T(L(x / y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(662(a,1),303(a,1,1)),flip(b)].">
      <j1 rule="para" parents="662 303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="889">
    <literal><![CDATA[
      (x * ((y * x) \ (y * z))) / x = L(z / x,x,y)
    ]]></literal>
    <justification jstring="[para(92(a,1),662(a,1,1,2))].">
      <j1 rule="para" parents="92 662"/>
    </justification>
  </clause>

  <clause id="890">
    <literal><![CDATA[
      L((x \ y) / z,z,x) = (z * ((x * z) \ y)) / z
    ]]></literal>
    <justification jstring="[para(311(a,1),662(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="311 662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="891">
    <literal><![CDATA[
      (x * ((1 / x) * y)) / x = L(y / x,x,1 / x)
    ]]></literal>
    <justification jstring="[para(500(a,1),662(a,1,1,2))].">
      <j1 rule="para" parents="500 662"/>
    </justification>
  </clause>

  <clause id="892">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) / (x \ 1) = L(y / (x \ 1),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(501(a,1),662(a,1,1,2))].">
      <j1 rule="para" parents="501 662"/>
    </justification>
  </clause>

  <clause id="893">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[para(772(a,2),662(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="772 662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="894">
    <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),663(a,1,1,2,1))].">
      <j1 rule="para" parents="13 663"/>
    </justification>
  </clause>

  <clause id="895">
    <literal><![CDATA[
      ((x / y) * R(y,z,u)) / (x / y) = R(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="896">
    <literal><![CDATA[
      R(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * R(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(663(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="663 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="897">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / x = (y * (z / x)) / y
    ]]></literal>
    <justification jstring="[hyper(281,a,697,a)].">
      <j1 rule="hyper" parents="281 697"/>
    </justification>
  </clause>

  <clause id="898">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,697,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 697 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="899">
    <literal><![CDATA[
      ((x * (y / z)) / x) \ (z * ((x * (z \ y)) / x)) = z
    ]]></literal>
    <justification jstring="[para(697(a,1),232(a,1,2,2))].">
      <j1 rule="para" parents="697 232"/>
    </justification>
  </clause>

  <clause id="900">
    <literal><![CDATA[
      x * ((y * (x \ z)) / y) != u
    ]]></literal>
    <literal><![CDATA[
      ((y * (z / x)) / y) * x = u
    ]]></literal>
    <justification jstring="[para(697(a,1),294(a,1,2))].">
      <j1 rule="para" parents="697 294"/>
    </justification>
  </clause>

  <clause id="901">
    <literal><![CDATA[
      T(T(1 / ((x * y) \ x),z),y) = T(1 / ((x * y) \ x),z)
    ]]></literal>
    <justification jstring="[para(700(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="700 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="902">
    <literal><![CDATA[
      (1 / (1 / x)) * (x * (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(334,a,75,a(flip),b,798,a),flip(a)].">
      <j1 rule="hyper" parents="334 75 798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="904">
    <literal><![CDATA[
      (1 / (1 / x)) * K(x,1 / x) = x
    ]]></literal>
    <justification jstring="[para(268(a,2),902(a,1,2))].">
      <j1 rule="para" parents="268 902"/>
    </justification>
  </clause>

  <clause id="905">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) * x = (1 / x) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),819(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="906">
    <literal><![CDATA[
      T(T(x,x * y) * y,T(x,y)) = x * y
    ]]></literal>
    <justification jstring="[para(243(a,1),841(a,1,1))].">
      <j1 rule="para" parents="243 841"/>
    </justification>
  </clause>

  <clause id="907">
    <literal><![CDATA[
      T(T(x / y,(x / y) * y) * y,T(x / y,y)) = x
    ]]></literal>
    <justification jstring="[hyper(334,a,7,a(flip),b,906,a),flip(a)].">
      <j1 rule="hyper" parents="334 7 906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="908">
    <literal><![CDATA[
      T(x,y * T(y \ x,x)) = x
    ]]></literal>
    <justification jstring="[para(843(a,1),285(a,1,2))].">
      <j1 rule="para" parents="843 285"/>
    </justification>
  </clause>

  <clause id="909">
    <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),850(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="107 850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="910">
    <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,855,a,b,323,a)].">
      <j1 rule="hyper" parents="116 855 323"/>
    </justification>
  </clause>

  <clause id="911">
    <literal><![CDATA[
      x \ R(T(y,y \ z),u,w) = x \ R((y \ z) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(116,a,855,a,b,5,a)].">
      <j1 rule="hyper" parents="116 855 5"/>
    </justification>
  </clause>

  <clause id="912">
    <literal><![CDATA[
      R(x,x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * z) / ((x \ y) * z) = u
    ]]></literal>
    <justification jstring="[para(72(a,1),871(a,1,1))].">
      <j1 rule="para" parents="72 871"/>
    </justification>
  </clause>

  <clause id="913">
    <literal><![CDATA[
      (x * y) * ((z * L(u,y,x)) / z) = x * (y * ((z * u) / z))
    ]]></literal>
    <justification jstring="[hyper(119,a,875,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 875 13"/>
    </justification>
  </clause>

  <clause id="914">
    <literal><![CDATA[
      L((x * y) / x,z,u) != w / x
    ]]></literal>
    <literal><![CDATA[
      x * L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(875(a,2),41(a,1))].">
      <j1 rule="para" parents="875 41"/>
    </justification>
  </clause>

  <clause id="915">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x != w
    ]]></literal>
    <literal><![CDATA[
      x * L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(875(a,2),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="875 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="916">
    <literal><![CDATA[
      L((x * (y \ z)) / x,y,u) = (x * ((u * y) \ (u * z))) / x
    ]]></literal>
    <justification jstring="[para(92(a,1),875(a,2,1,2))].">
      <j1 rule="para" parents="92 875"/>
    </justification>
  </clause>

  <clause id="917">
    <literal><![CDATA[
      L((x * (y \ (z \ u))) / x,y,z) = (x * ((z * y) \ u)) / x
    ]]></literal>
    <justification jstring="[para(311(a,1),875(a,2,1,2))].">
      <j1 rule="para" parents="311 875"/>
    </justification>
  </clause>

  <clause id="918">
    <literal><![CDATA[
      L((x * (y \ 1)) / x,y,z / y) = (x * (z \ (z / y))) / x
    ]]></literal>
    <justification jstring="[para(409(a,1),875(a,2,1,2))].">
      <j1 rule="para" parents="409 875"/>
    </justification>
  </clause>

  <clause id="919">
    <literal><![CDATA[
      L((x * (y \ z)) / x,y,1 / y) = (x * ((1 / y) * z)) / x
    ]]></literal>
    <justification jstring="[para(500(a,1),875(a,2,1,2))].">
      <j1 rule="para" parents="500 875"/>
    </justification>
  </clause>

  <clause id="920">
    <literal><![CDATA[
      L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x
    ]]></literal>
    <justification jstring="[para(502(a,1),875(a,2,1,2))].">
      <j1 rule="para" parents="502 875"/>
    </justification>
  </clause>

  <clause id="921">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x != w
    ]]></literal>
    <literal><![CDATA[
      x * R(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(881(a,2),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="881 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="922">
    <literal><![CDATA[
      R((x * ((y / z) / u)) / x,u,z) = (x * (y / (u * z))) / x
    ]]></literal>
    <justification jstring="[para(314(a,1),881(a,2,1,2))].">
      <j1 rule="para" parents="314 881"/>
    </justification>
  </clause>

  <clause id="923">
    <literal><![CDATA[
      R((x * (y / (1 / z))) / x,1 / z,z) = (x * (y * z)) / x
    ]]></literal>
    <justification jstring="[para(535(a,1),881(a,2,1,2))].">
      <j1 rule="para" parents="535 881"/>
    </justification>
  </clause>

  <clause id="924">
    <literal><![CDATA[
      R((x * (y / z)) / x,z,z \ 1) = (x * (y * (z \ 1))) / x
    ]]></literal>
    <justification jstring="[para(536(a,1),881(a,2,1,2))].">
      <j1 rule="para" parents="536 881"/>
    </justification>
  </clause>

  <clause id="925">
    <literal><![CDATA[
      ((x * R(y,z,u)) / x) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      (((x * y) / x) * z) * u = w
    ]]></literal>
    <justification jstring="[para(881(a,1),293(a,1,1))].">
      <j1 rule="para" parents="881 293"/>
    </justification>
  </clause>

  <clause id="926">
    <literal><![CDATA[
      ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((1 / x) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(116,a,905,a(flip),b,315,a)].">
      <j1 rule="hyper" parents="116 905 315"/>
    </justification>
  </clause>

  <clause id="927">
    <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="928">
    <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="929">
    <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),345(a,1,2)),flip(b)].">
      <j1 rule="para" parents="83 345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="930">
    <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),276(a,1,1)),flip(b)].">
      <j1 rule="para" parents="99 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="931">
    <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="932">
    <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),487(a,1,2,2))].">
      <j1 rule="para" parents="146 487"/>
    </justification>
  </clause>

  <clause id="933">
    <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),494(a,1,2))].">
      <j1 rule="para" parents="146 494"/>
    </justification>
  </clause>

  <clause id="934">
    <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,238,a)].">
      <j1 rule="hyper" parents="119 25 238"/>
    </justification>
  </clause>

  <clause id="935">
    <literal><![CDATA[
      T(((x * y) * x) / (x * y),y) = R(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,472,a(flip),b,241,a)].">
      <j1 rule="hyper" parents="58 472 241"/>
    </justification>
  </clause>

  <clause id="936">
    <literal><![CDATA[
      T(R(x,y,T(x,y)),x * y) = T(x,y)
    ]]></literal>
    <justification jstring="[para(241(a,1),230(a,1,1))].">
      <j1 rule="para" parents="241 230"/>
    </justification>
  </clause>

  <clause id="937">
    <literal><![CDATA[
      T(R(x,y,T(x,y)),z) * (x * y) = (x * y) * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(241(a,1),466(a,1,1,1))].">
      <j1 rule="para" parents="241 466"/>
    </justification>
  </clause>

  <clause id="938">
    <literal><![CDATA[
      T(x,y * z) != T(y,z)
    ]]></literal>
    <literal><![CDATA[
      R(y,z,T(y,z)) = x
    ]]></literal>
    <justification jstring="[para(936(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="936 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="939">
    <literal><![CDATA[
      (x * y) * T(y,x) = (y * x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,824,a(flip),b,253,a)].">
      <j1 rule="hyper" parents="119 824 253"/>
    </justification>
  </clause>

  <clause id="940">
    <literal><![CDATA[
      (x * (y / x)) * x = y * T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(341,a,939,a),flip(a)].">
      <j1 rule="hyper" parents="341 939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="941">
    <literal><![CDATA[
      (x * (y / x)) \ (y * (y / x)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,148,a(flip),b,939,a)].">
      <j1 rule="hyper" parents="116 148 939"/>
    </justification>
  </clause>

  <clause id="942">
    <literal><![CDATA[
      ((x \ 1) * x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,64,a(flip),b,939,a)].">
      <j1 rule="hyper" parents="116 64 939"/>
    </justification>
  </clause>

  <clause id="943">
    <literal><![CDATA[
      (T(x,y) * (y * x)) \ ((x * y) * x) = K(y * x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,939,a(flip),b,84,a)].">
      <j1 rule="hyper" parents="116 939 84"/>
    </justification>
  </clause>

  <clause id="944">
    <literal><![CDATA[
      K(x \ 1,x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(266(a,2),942(a,1,1))].">
      <j1 rule="para" parents="266 942"/>
    </justification>
  </clause>

  <clause id="945">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,106,a(flip),b,944,a)].">
      <j1 rule="hyper" parents="119 106 944"/>
    </justification>
  </clause>

  <clause id="946">
    <literal><![CDATA[
      (x * y) \ (y * T(x,y / x)) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[para(940(a,1),82(a,1,2))].">
      <j1 rule="para" parents="940 82"/>
    </justification>
  </clause>

  <clause id="947">
    <literal><![CDATA[
      ((x / y) * (x / (x / y))) * y = x * (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(119,a,252,a(flip),b,941,a)].">
      <j1 rule="hyper" parents="119 252 941"/>
    </justification>
  </clause>

  <clause id="948">
    <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,411,a,b,238,a)].">
      <j1 rule="hyper" parents="119 411 238"/>
    </justification>
  </clause>

  <clause id="949">
    <literal><![CDATA[
      (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,411,a,b,13,a(flip))].">
      <j1 rule="hyper" parents="119 411 13"/>
    </justification>
  </clause>

  <clause id="950">
    <literal><![CDATA[
      L(L(x \ 1,y * x,z),x,y) = (z * (y * x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,92,a(flip),b,412,a),flip(a)].">
      <j1 rule="hyper" parents="334 92 412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="951">
    <literal><![CDATA[
      (x * y) * L((x * y) \ x,z,u) = x * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,412,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 412 13"/>
    </justification>
  </clause>

  <clause id="952">
    <literal><![CDATA[
      L((x * (y \ z)) \ x,y \ z,y) = L(z \ y,y \ z,x)
    ]]></literal>
    <justification jstring="[para(401(a,1),412(a,1,1)),flip(a)].">
      <j1 rule="para" parents="401 412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="953">
    <literal><![CDATA[
      R(x / (y * x),z,u) * (y * x) = (R(1 / y,z,u) * y) * x
    ]]></literal>
    <justification jstring="[para(420(a,1),101(a,1,1))].">
      <j1 rule="para" parents="420 101"/>
    </justification>
  </clause>

  <clause id="954">
    <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),429(a,1,2,1))].">
      <j1 rule="para" parents="17 429"/>
    </justification>
  </clause>

  <clause id="955">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(92(a,1),461(a,1,2,1))].">
      <j1 rule="para" parents="92 461"/>
    </justification>
  </clause>

  <clause id="956">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,u) = x * (y * T(y \ (x \ z),u))
    ]]></literal>
    <justification jstring="[para(311(a,1),461(a,1,2,1))].">
      <j1 rule="para" parents="311 461"/>
    </justification>
  </clause>

  <clause id="957">
    <literal><![CDATA[
      x * (T(y,x) * T(z,y * x)) = L(z,T(y,x),x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(429,a,484,a),flip(a)].">
      <j1 rule="hyper" parents="429 484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="958">
    <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,504,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="116 504 90"/>
    </justification>
  </clause>

  <clause id="959">
    <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(504(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="504 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="960">
    <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(504(a,2),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="504 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="961">
    <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),507(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="105 507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="962">
    <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(507(a,2),296(a,1,2))].">
      <j1 rule="para" parents="507 296"/>
    </justification>
  </clause>

  <clause id="963">
    <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(508(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="508 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="964">
    <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(508(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="508 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="965">
    <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,228,a(flip),b,516,a)].">
      <j1 rule="hyper" parents="58 228 516"/>
    </justification>
  </clause>

  <clause id="966">
    <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),524(a,1,2))].">
      <j1 rule="para" parents="105 524"/>
    </justification>
  </clause>

  <clause id="967">
    <literal><![CDATA[
      T((x * y) / (z * y),u) * (z * y) = (T(x / z,u) * z) * y
    ]]></literal>
    <justification jstring="[para(102(a,1),524(a,1,1,1))].">
      <j1 rule="para" parents="102 524"/>
    </justification>
  </clause>

  <clause id="968">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = T(x / (z * y),u) * (z * y)
    ]]></literal>
    <justification jstring="[para(314(a,1),524(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="314 524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="969">
    <literal><![CDATA[
      R(T(x / y,y * z),y,z) = (y * z) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(431,a,539,a),flip(a)].">
      <j1 rule="hyper" parents="431 539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="970">
    <literal><![CDATA[
      R(T(T(x / y,z),y * u),y,u) = T((y * u) \ (x * u),z)
    ]]></literal>
    <justification jstring="[para(541(a,1),850(a,2,1))].">
      <j1 rule="para" parents="541 850"/>
    </justification>
  </clause>

  <clause id="971">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(501(a,1),562(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="501 562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="972">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) = T(1 / x,y) * x
    ]]></literal>
    <justification jstring="[para(413(a,1),571(a,1,1,1))].">
      <j1 rule="para" parents="413 571"/>
    </justification>
  </clause>

  <clause id="973">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = T(x / y,z) * y
    ]]></literal>
    <justification jstring="[para(536(a,1),571(a,1,1,1))].">
      <j1 rule="para" parents="536 571"/>
    </justification>
  </clause>

  <clause id="974">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,465,a(flip),b,972,a),flip(a)].">
      <j1 rule="hyper" parents="334 465 972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="975">
    <literal><![CDATA[
      T(x * T(x \ 1,y),x \ 1) = (x \ 1) \ T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(974(a,1),107(a,1,1))].">
      <j1 rule="para" parents="974 107"/>
    </justification>
  </clause>

  <clause id="976">
    <literal><![CDATA[
      T(x / (1 / y),z) * (1 / y) = T(x * y,z) / y
    ]]></literal>
    <justification jstring="[para(535(a,1),576(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="535 576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="977">
    <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(577(a,1),296(a,1,2))].">
      <j1 rule="para" parents="577 296"/>
    </justification>
  </clause>

  <clause id="978">
    <literal><![CDATA[
      x \ y != z * (u \ (u * w))
    ]]></literal>
    <literal><![CDATA[
      x * (z * w) = y
    ]]></literal>
    <justification jstring="[para(4(a,1),591(a,2,2,2,2))].">
      <j1 rule="para" parents="4 591"/>
    </justification>
  </clause>

  <clause id="979">
    <literal><![CDATA[
      (x / y) * (y * T(y \ 1,z)) = x * T(x \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,603,a,b,93,a),flip(a)].">
      <j1 rule="hyper" parents="119 603 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="980">
    <literal><![CDATA[
      R(1 / x,x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) / y = z
    ]]></literal>
    <justification jstring="[para(605(a,1),211(a,1))].">
      <j1 rule="para" parents="605 211"/>
    </justification>
  </clause>

  <clause id="981">
    <literal><![CDATA[
      R(T(1 / x,y),x,x \ y) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(431,a,606,a),flip(a)].">
      <j1 rule="hyper" parents="431 606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="982">
    <literal><![CDATA[
      T((x \ y) / y,z) * y = (T(1 / x,z) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(606(a,2),380(a,1,1))].">
      <j1 rule="para" parents="606 380"/>
    </justification>
  </clause>

  <clause id="983">
    <literal><![CDATA[
      (1 / x) * (x * T(x \ y,z)) = T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[hyper(399,a,621,a)].">
      <j1 rule="hyper" parents="399 621"/>
    </justification>
  </clause>

  <clause id="984">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) * y,z) = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,621,a(flip),b,267,a)].">
      <j1 rule="hyper" parents="116 621 267"/>
    </justification>
  </clause>

  <clause id="985">
    <literal><![CDATA[
      x * (((x \ 1) \ y) * (x \ 1)) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,564,a(flip),b,624,a)].">
      <j1 rule="hyper" parents="58 564 624"/>
    </justification>
  </clause>

  <clause id="986">
    <literal><![CDATA[
      x \ T(x * y,x \ 1) = ((x \ 1) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,624,a(flip),b,564,a(flip))].">
      <j1 rule="hyper" parents="116 624 564"/>
    </justification>
  </clause>

  <clause id="987">
    <literal><![CDATA[
      ((x / y) * y) / z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x / z) = w
    ]]></literal>
    <justification jstring="[para(75(a,1),639(a,1,1,2))].">
      <j1 rule="para" parents="75 639"/>
    </justification>
  </clause>

  <clause id="988">
    <literal><![CDATA[
      R(T(x,y * z),y,z) != (y * z) \ u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(648(a,1),42(a,1))].">
      <j1 rule="para" parents="648 42"/>
    </justification>
  </clause>

  <clause id="989">
    <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),648(a,1,2)),flip(a)].">
      <j1 rule="para" parents="80 648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="990">
    <literal><![CDATA[
      x \ (((x * y) \ x) * (x * y)) = y * T(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(116,a,406,a(flip),b,649,a)].">
      <j1 rule="hyper" parents="116 406 649"/>
    </justification>
  </clause>

  <clause id="991">
    <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),694(a,1,1))].">
      <j1 rule="para" parents="106 694"/>
    </justification>
  </clause>

  <clause id="992">
    <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),695(a,1,1,1))].">
      <j1 rule="para" parents="72 695"/>
    </justification>
  </clause>

  <clause id="993">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * T(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(972(a,2),695(a,1))].">
      <j1 rule="para" parents="972 695"/>
    </justification>
  </clause>

  <clause id="994">
    <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),698(a,1,1,1,1))].">
      <j1 rule="para" parents="7 698"/>
    </justification>
  </clause>

  <clause id="995">
    <literal><![CDATA[
      (x * y) / a(z,z \ y,T(x,y)) = z * ((z \ y) * T(x,y))
    ]]></literal>
    <justification jstring="[para(105(a,1),704(a,1,1))].">
      <j1 rule="para" parents="105 704"/>
    </justification>
  </clause>

  <clause id="996">
    <literal><![CDATA[
      ((x * y) * (y \ z)) / T(x * z,a(x,y,y \ z)) = a(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(288,a,706,a)].">
      <j1 rule="hyper" parents="288 706"/>
    </justification>
  </clause>

  <clause id="997">
    <literal><![CDATA[
      (x / y) * ((y \ 1) * y) = x * T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[hyper(119,a,603,a,b,715,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 603 715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="998">
    <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),737(a,1,1))].">
      <j1 rule="para" parents="22 737"/>
    </justification>
  </clause>

  <clause id="999">
    <literal><![CDATA[
      T(L(L(x,y,x),z,u),y) = T(L(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,20,a(flip),b,742,a),flip(a)].">
      <j1 rule="hyper" parents="334 20 742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1000">
    <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),746(a,1,1,2))].">
      <j1 rule="para" parents="178 746"/>
    </justification>
  </clause>

  <clause id="1001">
    <literal><![CDATA[
      L(x,x \ y,x) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(746(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="746 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1002">
    <literal><![CDATA[
      T(T((x * y) / x,z),y * x) = L(T(y,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,20,a,b,748,a),flip(a)].">
      <j1 rule="hyper" parents="334 20 748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1003">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ z) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,22,a,b,750,a)].">
      <j1 rule="hyper" parents="58 22 750"/>
    </justification>
  </clause>

  <clause id="1004">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,y) = x \ ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(401(a,1),769(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="401 769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1005">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ z,y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[para(502(a,1),769(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="502 769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1006">
    <literal><![CDATA[
      (x / y) \ ((x \ (x / y)) * x) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(409(a,1),776(a,1,2,1))].">
      <j1 rule="para" parents="409 776"/>
    </justification>
  </clause>

  <clause id="1007">
    <literal><![CDATA[
      x \ ((x / y) * ((y \ z) * y)) = T(x \ ((x / y) * z),y)
    ]]></literal>
    <justification jstring="[para(505(a,1),815(a,1,1)),flip(a)].">
      <j1 rule="para" parents="505 815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1008">
    <literal><![CDATA[
      (x * y) * ((y * ((x * y) \ z)) / y) = x * (y * ((x \ z) / y))
    ]]></literal>
    <justification jstring="[hyper(119,a,890,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 890 13"/>
    </justification>
  </clause>

  <clause id="1009">
    <literal><![CDATA[
      L((x \ (y * (x * z))) / z,z,x) = (z * T(y,x * z)) / z
    ]]></literal>
    <justification jstring="[para(17(a,2),890(a,2,1,2))].">
      <j1 rule="para" parents="17 890"/>
    </justification>
  </clause>

  <clause id="1010">
    <literal><![CDATA[
      L((x \ (T(x,y) * y)) / y,y,x) = (y * K(T(x,y),y)) / y
    ]]></literal>
    <justification jstring="[para(237(a,1),890(a,2,1,2))].">
      <j1 rule="para" parents="237 890"/>
    </justification>
  </clause>

  <clause id="1011">
    <literal><![CDATA[
      (x * y) * ((y * ((x * y) \ z)) / y) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * ((x \ z) / y)) = u
    ]]></literal>
    <justification jstring="[para(890(a,1),296(a,1,2))].">
      <j1 rule="para" parents="890 296"/>
    </justification>
  </clause>

  <clause id="1012">
    <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(998(a,2),46(a,1)),flip(a)].">
      <j1 rule="para" parents="998 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1013">
    <literal><![CDATA[
      x * R(T(y,y * x),z,u) = L(R(y,z,u),x,y) * x
    ]]></literal>
    <justification jstring="[para(998(a,1),244(a,1,2))].">
      <j1 rule="para" parents="998 244"/>
    </justification>
  </clause>

  <clause id="1014">
    <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),999(a,1,1))].">
      <j1 rule="para" parents="25 999"/>
    </justification>
  </clause>

  <clause id="1015">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (T(y / z,x) * z) * (z \ x)
    ]]></literal>
    <justification jstring="[para(1003(a,1),380(a,1,1))].">
      <j1 rule="para" parents="1003 380"/>
    </justification>
  </clause>

  <clause id="1016">
    <literal><![CDATA[
      (x * y) * T(L(x,z,u),x * y) = x * (y * T(L(x,z,u),y))
    ]]></literal>
    <justification jstring="[para(1014(a,1),461(a,1,2))].">
      <j1 rule="para" parents="1014 461"/>
    </justification>
  </clause>

  <clause id="1017">
    <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(301(a,1),211(a,1))].">
      <j1 rule="para" parents="301 211"/>
    </justification>
  </clause>

  <clause id="1018">
    <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(504(a,2),709(a,1,1))].">
      <j1 rule="para" parents="504 709"/>
    </justification>
  </clause>

  <clause id="1019">
    <literal><![CDATA[
      (x * ((y * z) / y)) / x = (y * ((x * z) / x)) / y
    ]]></literal>
    <justification jstring="[para(4(a,1),897(a,1,1,2,1,2))].">
      <j1 rule="para" parents="4 897"/>
    </justification>
  </clause>

  <clause id="1020">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x * (z \ y)) / x) = u
    ]]></literal>
    <justification jstring="[para(897(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="897 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1021">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ y)) / z) = ((z * x) / z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(72(a,1),898(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1022">
    <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),898(a,1,1,1,2))].">
      <j1 rule="para" parents="102 898"/>
    </justification>
  </clause>

  <clause id="1023">
    <literal><![CDATA[
      ((x * (y / (y / z))) / x) \ ((y / z) * ((x * z) / x)) = y / z
    ]]></literal>
    <justification jstring="[para(75(a,1),899(a,1,2,2,1,2))].">
      <j1 rule="para" parents="75 899"/>
    </justification>
  </clause>

  <clause id="1024">
    <literal><![CDATA[
      T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y)
    ]]></literal>
    <justification jstring="[para(102(a,1),909(a,1,1,1))].">
      <j1 rule="para" parents="102 909"/>
    </justification>
  </clause>

  <clause id="1025">
    <literal><![CDATA[
      R(T(x \ y,z),x,x \ z) = T(z \ (y * (x \ z)),x)
    ]]></literal>
    <justification jstring="[para(750(a,1),909(a,1,1)),flip(a)].">
      <j1 rule="para" parents="750 909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1026">
    <literal><![CDATA[
      x \ T(x * (y * (x \ 1)),z) = T(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(764,a,971,a),flip(a)].">
      <j1 rule="hyper" parents="764 971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1027">
    <literal><![CDATA[
      (x \ 1) \ (x \ T(x * y,z)) = T((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,971,a)].">
      <j1 rule="hyper" parents="123 971"/>
    </justification>
  </clause>

  <clause id="1028">
    <literal><![CDATA[
      T(x * (y * (x \ 1)),z) = x * (T(y,z) * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(119,a,463,a(flip),b,971,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 463 971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1029">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3(a,1),971(a,2,2,1))].">
      <j1 rule="para" parents="3 971"/>
    </justification>
  </clause>

  <clause id="1030">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),971(a,2,2,1))].">
      <j1 rule="para" parents="5 971"/>
    </justification>
  </clause>

  <clause id="1031">
    <literal><![CDATA[
      x \ T(x * y,x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = z
    ]]></literal>
    <justification jstring="[para(971(a,1),294(a,1))].">
      <j1 rule="para" parents="971 294"/>
    </justification>
  </clause>

  <clause id="1032">
    <literal><![CDATA[
      T(1 / (x \ 1),y) * (x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(471,a,1029,a)].">
      <j1 rule="hyper" parents="471 1029"/>
    </justification>
  </clause>

  <clause id="1033">
    <literal><![CDATA[
      T(x,y) * (x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,467,a(flip),b,1029,a)].">
      <j1 rule="hyper" parents="58 467 1029"/>
    </justification>
  </clause>

  <clause id="1034">
    <literal><![CDATA[
      T(x,y) \ (x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,1029,a(flip),b,467,a(flip))].">
      <j1 rule="hyper" parents="116 1029 467"/>
    </justification>
  </clause>

  <clause id="1035">
    <literal><![CDATA[
      (x * y) \ (y * (x \ T(x,y))) = L(x \ 1,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(1033(a,1),238(a,1,2,2))].">
      <j1 rule="para" parents="1033 238"/>
    </justification>
  </clause>

  <clause id="1036">
    <literal><![CDATA[
      T(x,y) * (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(1034(a,1),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1034 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1037">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(467(a,2),1036(a,1))].">
      <j1 rule="para" parents="467 1036"/>
    </justification>
  </clause>

  <clause id="1039">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,465,a(flip),b,973,a),flip(a)].">
      <j1 rule="hyper" parents="334 465 973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1040">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(973(a,2),695(a,1))].">
      <j1 rule="para" parents="973 695"/>
    </justification>
  </clause>

  <clause id="1041">
    <literal><![CDATA[
      T(((1 / x) * y) * x,z) / x = (1 / x) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(698,a,976,a),flip(a)].">
      <j1 rule="hyper" parents="698 976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1042">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(695,a,976,a)].">
      <j1 rule="hyper" parents="695 976"/>
    </justification>
  </clause>

  <clause id="1043">
    <literal><![CDATA[
      (1 / x) \ (T(y * x,z) / x) = T((1 / x) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,976,a(flip),b,465,a(flip))].">
      <j1 rule="hyper" parents="116 976 465"/>
    </justification>
  </clause>

  <clause id="1044">
    <literal><![CDATA[
      T(1 / (1 / x),y) * (1 / x) = T(x,y) / x
    ]]></literal>
    <justification jstring="[para(2(a,1),976(a,2,1,1))].">
      <j1 rule="para" parents="2 976"/>
    </justification>
  </clause>

  <clause id="1045">
    <literal><![CDATA[
      x / y != T(z / (1 / y),u) * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      T(z * y,u) = x
    ]]></literal>
    <justification jstring="[para(976(a,2),41(a,1)),flip(a)].">
      <j1 rule="para" parents="976 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1046">
    <literal><![CDATA[
      T(x * y,1 / y) / y = ((1 / y) \ x) * (1 / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),976(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1047">
    <literal><![CDATA[
      T(x * y,z) / y != u
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * T((1 / y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(976(a,1),695(a,1))].">
      <j1 rule="para" parents="976 695"/>
    </justification>
  </clause>

  <clause id="1048">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(695,a,1044,a)].">
      <j1 rule="hyper" parents="695 1044"/>
    </justification>
  </clause>

  <clause id="1049">
    <literal><![CDATA[
      (1 / x) * T(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,468,a(flip),b,1044,a)].">
      <j1 rule="hyper" parents="58 468 1044"/>
    </justification>
  </clause>

  <clause id="1050">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) / x) = T(1 / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(451,a,1044,a(flip),b,468,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="451 1044 468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1051">
    <literal><![CDATA[
      (T(x,y) / x) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(117,a,1044,a(flip),b,468,a(flip))].">
      <j1 rule="hyper" parents="117 1044 468"/>
    </justification>
  </clause>

  <clause id="1052">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(1044(a,1),695(a,1))].">
      <j1 rule="para" parents="1044 695"/>
    </justification>
  </clause>

  <clause id="1053">
    <literal><![CDATA[
      T(x,x \ y) / x = (1 / x) * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,327,a(flip),b,1049,a),flip(a)].">
      <j1 rule="hyper" parents="58 327 1049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1054">
    <literal><![CDATA[
      T(x / y,y) / (x / y) = (1 / (x / y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),1049(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1055">
    <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(1049(a,1),741(a,1,2))].">
      <j1 rule="para" parents="1049 741"/>
    </justification>
  </clause>

  <clause id="1056">
    <literal><![CDATA[
      L(x \ 1,x,T(x,y) / x) = T(1 / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(687,a,1050,a)].">
      <j1 rule="hyper" parents="687 1050"/>
    </justification>
  </clause>

  <clause id="1057">
    <literal><![CDATA[
      (1 / x) * ((x \ y) \ y) = ((x \ y) \ y) / x
    ]]></literal>
    <justification jstring="[para(106(a,1),1053(a,1,1)),flip(a)].">
      <j1 rule="para" parents="106 1053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1058">
    <literal><![CDATA[
      ((x \ 1) \ (x \ y)) * (x \ 1) = x \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(5(a,1),986(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1059">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x * T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[para(266(a,2),997(a,1,2))].">
      <j1 rule="para" parents="266 997"/>
    </justification>
  </clause>

  <clause id="1060">
    <literal><![CDATA[
      K(x,y) = ((y * x) \ y) * T(((y * x) \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,442,a,b,1004,a)].">
      <j1 rule="hyper" parents="334 442 1004"/>
    </justification>
  </clause>

  <clause id="1061">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,85,a(flip),b,1004,a),flip(a)].">
      <j1 rule="hyper" parents="334 85 1004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1062">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,x) = ((x * y) \ x) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,442,a,b,1004,a),flip(a)].">
      <j1 rule="hyper" parents="116 442 1004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1063">
    <literal><![CDATA[
      K(x \ (x / y),x) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(477,a,1006,a)].">
      <j1 rule="hyper" parents="477 1006"/>
    </justification>
  </clause>

  <clause id="1064">
    <literal><![CDATA[
      x \ K(y \ (y / x),y) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,85,a(flip),b,1006,a(flip))].">
      <j1 rule="hyper" parents="116 85 1006"/>
    </justification>
  </clause>

  <clause id="1065">
    <literal><![CDATA[
      K(x \ (x / (1 / y)),x) = T(y,x) / y
    ]]></literal>
    <justification jstring="[hyper(334,a,1048,a(flip),b,1063,a),flip(a)].">
      <j1 rule="hyper" parents="334 1048 1063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1066">
    <literal><![CDATA[
      K(x \ (x / (y \ 1)),x) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,1029,a(flip),b,1063,a),flip(a)].">
      <j1 rule="hyper" parents="334 1029 1063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1067">
    <literal><![CDATA[
      T(x,y) = x * K(y \ (y / (x \ 1)),y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1063,a,b,1029,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1063 1029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1068">
    <literal><![CDATA[
      K(x \ (x / y),x) / y = T(1 / y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,1063,a,b,465,a)].">
      <j1 rule="hyper" parents="117 1063 465"/>
    </justification>
  </clause>

  <clause id="1069">
    <literal><![CDATA[
      K(T(1 / x,T(x,y)),T(x,y)) = x * T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(1050(a,1),1063(a,1,1))].">
      <j1 rule="para" parents="1050 1063"/>
    </justification>
  </clause>

  <clause id="1070">
    <literal><![CDATA[
      T(x,y) = K(y \ (y / (1 / x)),y) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,1065,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 1065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1071">
    <literal><![CDATA[
      K(x \ (x / (1 / (y / (x * y)))),x) = R(x \ 1,x,y) / (y / (x * y))
    ]]></literal>
    <justification jstring="[para(664(a,1),1065(a,2,1))].">
      <j1 rule="para" parents="664 1065"/>
    </justification>
  </clause>

  <clause id="1072">
    <literal><![CDATA[
      K(x \ (x / (((x * y) / x) \ 1)),x) = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[para(230(a,1),1066(a,2,2))].">
      <j1 rule="para" parents="230 1066"/>
    </justification>
  </clause>

  <clause id="1073">
    <literal><![CDATA[
      K((x * y) \ x,x * y) / y = T(1 / y,x * y)
    ]]></literal>
    <justification jstring="[para(6(a,1),1068(a,1,1,1,2))].">
      <j1 rule="para" parents="6 1068"/>
    </justification>
  </clause>

  <clause id="1074">
    <literal><![CDATA[
      T((x \ 1) \ (x \ y),z) = (x \ 1) \ (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),1027(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1075">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(1027(a,1),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1027 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1076">
    <literal><![CDATA[
      (x \ T(y,z)) / (x \ 1) = T((x \ y) / (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(117,a,1030,a(flip),b,465,a)].">
      <j1 rule="hyper" parents="117 1030 465"/>
    </justification>
  </clause>

  <clause id="1077">
    <literal><![CDATA[
      (x * T(x \ y,z)) * (x \ 1) = T(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(133,a,1039,a)].">
      <j1 rule="hyper" parents="133 1039"/>
    </justification>
  </clause>

  <clause id="1078">
    <literal><![CDATA[
      T(x * y,1 / y) / y != z
    ]]></literal>
    <literal><![CDATA[
      ((1 / y) \ x) * (1 / y) = z
    ]]></literal>
    <justification jstring="[para(1042(a,1),294(a,1))].">
      <j1 rule="para" parents="1042 294"/>
    </justification>
  </clause>

  <clause id="1079">
    <literal><![CDATA[
      T((1 / x) \ (y / x),z) = (1 / x) \ (T(y,z) / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),1043(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 1043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1080">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y * x,z) / x = u
    ]]></literal>
    <justification jstring="[para(1043(a,1),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1043 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1081">
    <literal><![CDATA[
      ((1 / x) \ (y / x)) * (1 / x) = T(y,1 / x) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),1046(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7 1046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1082">
    <literal><![CDATA[
      (1 / (x / y)) * (y \ x) = (y \ x) / (x / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),1054(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 1054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1083">
    <literal><![CDATA[
      ((x / y) \ x) / (x / (x / y)) = (1 / (x / (x / y))) * y
    ]]></literal>
    <justification jstring="[hyper(598,a,1082,a),flip(a)].">
      <j1 rule="hyper" parents="598 1082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1084">
    <literal><![CDATA[
      (x \ y) \ ((x \ y) / (y / x)) = T(1 / (y / x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(451,a,xx,b,1082,a),flip(a)].">
      <j1 rule="hyper" parents="451 1082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1085">
    <literal><![CDATA[
      (x \ y) / (y / x) != (x \ y) * z
    ]]></literal>
    <literal><![CDATA[
      T(1 / (y / x),x \ y) = z
    ]]></literal>
    <justification jstring="[para(1082(a,1),247(a,2)),flip(a)].">
      <j1 rule="para" parents="1082 247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1086">
    <literal><![CDATA[
      ((x * y) \ x) * T(((x * y) \ x) \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(1062(a,2),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1062 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1087">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,y) = ((y * x) \ y) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(221(a,2),1062(a,1,1,1))].">
      <j1 rule="para" parents="221 1062"/>
    </justification>
  </clause>

  <clause id="1088">
    <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(1062(a,1),974(a,1,1))].">
      <j1 rule="para" parents="1062 974"/>
    </justification>
  </clause>

  <clause id="1089">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(1074(a,2),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1074 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1090">
    <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(1074(a,2),355(a,2,2))].">
      <j1 rule="para" parents="1074 355"/>
    </justification>
  </clause>

  <clause id="1091">
    <literal><![CDATA[
      T((x * y) * (x \ 1),z) = (x * T(y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),1077(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1092">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ (y / x)) = (T(y,1 / x) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[para(1081(a,1),86(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1081 86"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1093">
    <literal><![CDATA[
      T((x * y) * (x \ 1),y) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(104(a,1),1091(a,2,1,2))].">
      <j1 rule="para" parents="104 1091"/>
    </justification>
  </clause>

  <clause id="1094">
    <literal><![CDATA[
      K((x * y) * (x \ 1),y) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,1093,a)].">
      <j1 rule="hyper" parents="50 1093"/>
    </justification>
  </clause>

  <clause id="1095">
    <literal><![CDATA[
      K(((1 / x) * y) * x,y) = 1
    ]]></literal>
    <justification jstring="[para(75(a,1),1094(a,1,1,2))].">
      <j1 rule="para" parents="75 1094"/>
    </justification>
  </clause>

  <clause id="1096">
    <literal><![CDATA[
      K(x * y,(1 / y) \ x) = 1
    ]]></literal>
    <justification jstring="[para(5(a,1),1095(a,1,1,1))].">
      <j1 rule="para" parents="5 1095"/>
    </justification>
  </clause>

  <clause id="1097">
    <literal><![CDATA[
      T(x * y,(1 / y) \ x) = x * y
    ]]></literal>
    <justification jstring="[hyper(51,a,1096,a)].">
      <j1 rule="hyper" parents="51 1096"/>
    </justification>
  </clause>

  <clause id="1098">
    <literal><![CDATA[
      K(x,1 / x) \ (x * (T(x,y) / x)) = L(T(x,y),1 / x,x)
    ]]></literal>
    <justification jstring="[para(1049(a,1),375(a,1,2,2))].">
      <j1 rule="para" parents="1049 375"/>
    </justification>
  </clause>

  <clause id="1099">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(311(a,1),458(a,1,2,1))].">
      <j1 rule="para" parents="311 458"/>
    </justification>
  </clause>

  <clause id="1100">
    <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),459(a,1,2,1))].">
      <j1 rule="para" parents="92 459"/>
    </justification>
  </clause>

  <clause id="1101">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(311(a,1),459(a,1,2,1))].">
      <j1 rule="para" parents="311 459"/>
    </justification>
  </clause>

  <clause id="1102">
    <literal><![CDATA[
      K(x \ 1,x) * L(x \ y,x,x \ 1) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(334,a,151,a(flip),b,496,a),flip(a)].">
      <j1 rule="hyper" parents="334 151 496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1103">
    <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(577(a,1),496(a,1,2))].">
      <j1 rule="para" parents="577 496"/>
    </justification>
  </clause>

  <clause id="1104">
    <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),525(a,1,1,1))].">
      <j1 rule="para" parents="102 525"/>
    </justification>
  </clause>

  <clause id="1105">
    <literal><![CDATA[
      (L((x / y) / z,u,w) * z) * y = L(x / (z * y),u,w) * (z * y)
    ]]></literal>
    <justification jstring="[para(314(a,1),525(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="314 525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1106">
    <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),526(a,1,1,1))].">
      <j1 rule="para" parents="102 526"/>
    </justification>
  </clause>

  <clause id="1107">
    <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,532,a(flip),b,245,a)].">
      <j1 rule="hyper" parents="116 532 245"/>
    </justification>
  </clause>

  <clause id="1108">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(501(a,1),561(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="501 561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1109">
    <literal><![CDATA[
      (1 / x) \ L(1 / x,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(400(a,1),566(a,1,2,1))].">
      <j1 rule="para" parents="400 566"/>
    </justification>
  </clause>

  <clause id="1110">
    <literal><![CDATA[
      (1 / x) \ L((1 / x) * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(500(a,1),566(a,1,2,1))].">
      <j1 rule="para" parents="500 566"/>
    </justification>
  </clause>

  <clause id="1111">
    <literal><![CDATA[
      (1 / x) \ L(x \ 1,y,z) = x * L(T(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(765(a,1),566(a,1,2,1))].">
      <j1 rule="para" parents="765 566"/>
    </justification>
  </clause>

  <clause id="1112">
    <literal><![CDATA[
      L(x \ 1,y,z) / (x \ 1) = L(1 / x,y,z) * x
    ]]></literal>
    <justification jstring="[para(413(a,1),570(a,1,1,1))].">
      <j1 rule="para" parents="413 570"/>
    </justification>
  </clause>

  <clause id="1113">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = L(x / y,z,u) * y
    ]]></literal>
    <justification jstring="[para(536(a,1),570(a,1,1,1))].">
      <j1 rule="para" parents="536 570"/>
    </justification>
  </clause>

  <clause id="1114">
    <literal><![CDATA[
      L(x \ 1,y,z) / (x \ 1) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,653,a(flip),b,1112,a),flip(a)].">
      <j1 rule="hyper" parents="334 653 1112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1115">
    <literal><![CDATA[
      L(x \ 1,x,y) / (x \ 1) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,405,a(flip),b,1114,a),flip(a)].">
      <j1 rule="hyper" parents="334 405 1114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1116">
    <literal><![CDATA[
      ((x * y) \ x) / (y \ 1) = y * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(221(a,1),1115(a,1,1))].">
      <j1 rule="para" parents="221 1115"/>
    </justification>
  </clause>

  <clause id="1117">
    <literal><![CDATA[
      (x \ y) * ((x * (x \ y)) \ x) = (y \ x) / ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(401(a,1),1115(a,1,1)),flip(a)].">
      <j1 rule="para" parents="401 1115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1118">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * (x \ 1) = (y * x) \ y
    ]]></literal>
    <justification jstring="[hyper(133,a,1116,a)].">
      <j1 rule="hyper" parents="133 1116"/>
    </justification>
  </clause>

  <clause id="1119">
    <literal><![CDATA[
      ((x * y) \ x) * K(y \ 1,y * ((x * y) \ x)) = (y \ 1) * (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(1118(a,1),84(a,1,1))].">
      <j1 rule="para" parents="1118 84"/>
    </justification>
  </clause>

  <clause id="1120">
    <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(574(a,2),39(a,1))].">
      <j1 rule="para" parents="574 39"/>
    </justification>
  </clause>

  <clause id="1121">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) * (1 / x) = R(x / 1,y,z) / x
    ]]></literal>
    <justification jstring="[para(418(a,1),574(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="418 574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1122">
    <literal><![CDATA[
      L(T(x,1 / x),y,z) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(832(a,1),575(a,1,1,1))].">
      <j1 rule="para" parents="832 575"/>
    </justification>
  </clause>

  <clause id="1123">
    <literal><![CDATA[
      T(L(x,y,z),1 / x) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(20(a,1),1122(a,1,1))].">
      <j1 rule="para" parents="20 1122"/>
    </justification>
  </clause>

  <clause id="1124">
    <literal><![CDATA[
      (1 / x) \ (L(x,y,z) / x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,1081,a,b,1123,a(flip))].">
      <j1 rule="hyper" parents="30 1081 1123"/>
    </justification>
  </clause>

  <clause id="1125">
    <literal><![CDATA[
      (L(x,y,z) / x) / L(x,y,z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(201,a,1124,a)].">
      <j1 rule="hyper" parents="201 1124"/>
    </justification>
  </clause>

  <clause id="1126">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(134,a,1124,a)].">
      <j1 rule="hyper" parents="134 1124"/>
    </justification>
  </clause>

  <clause id="1127">
    <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(1126(a,1),741(a,1,2))].">
      <j1 rule="para" parents="1126 741"/>
    </justification>
  </clause>

  <clause id="1128">
    <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(578(a,1),496(a,1,2))].">
      <j1 rule="para" parents="578 496"/>
    </justification>
  </clause>

  <clause id="1129">
    <literal><![CDATA[
      L((x * (y \ z)) \ u,y \ z,y) = L(z \ (y * (x \ u)),y \ z,x)
    ]]></literal>
    <justification jstring="[para(502(a,1),579(a,1,1)),flip(a)].">
      <j1 rule="para" parents="502 579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1130">
    <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(579(a,1),296(a,1,2))].">
      <j1 rule="para" parents="579 296"/>
    </justification>
  </clause>

  <clause id="1131">
    <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(579(a,1),496(a,1,2))].">
      <j1 rule="para" parents="579 496"/>
    </justification>
  </clause>

  <clause id="1132">
    <literal><![CDATA[
      (1 / x) * (x * R(x \ y,z,u)) = R((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(399,a,622,a)].">
      <j1 rule="hyper" parents="399 622"/>
    </justification>
  </clause>

  <clause id="1133">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,625,a(flip),b,265,a),flip(a)].">
      <j1 rule="hyper" parents="116 625 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1134">
    <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(745(a,2),38(a,1)),flip(a)].">
      <j1 rule="para" parents="745 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1135">
    <literal><![CDATA[
      x * ((x \ y) * T((x \ y) \ z,u)) = y * T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(119,a,779,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="119 779 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1136">
    <literal><![CDATA[
      (T(x / (y / z),u) * (y / z)) * z = T((x * z) / y,u) * y
    ]]></literal>
    <justification jstring="[para(786(a,1),520(a,1,1)),flip(a)].">
      <j1 rule="para" parents="786 520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1137">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,22,a,b,823,a),flip(a)].">
      <j1 rule="hyper" parents="334 22 823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1138">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * (y * ((z * (y \ 1)) / 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="1139">
    <literal><![CDATA[
      ((x * (y / (z * y))) / x) * (z * y) = (((x * (1 / z)) / x) * z) * y
    ]]></literal>
    <justification jstring="[para(883(a,1),101(a,1,1))].">
      <j1 rule="para" parents="883 101"/>
    </justification>
  </clause>

  <clause id="1140">
    <literal><![CDATA[
      ((x * ((y \ z) / (y * (y \ z)))) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(883(a,1),380(a,1,1))].">
      <j1 rule="para" parents="883 380"/>
    </justification>
  </clause>

  <clause id="1141">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = ((x * (1 / y)) / x) * y
    ]]></literal>
    <justification jstring="[hyper(117,a,604,a(flip),b,884,a)].">
      <j1 rule="hyper" parents="117 604 884"/>
    </justification>
  </clause>

  <clause id="1142">
    <literal><![CDATA[
      ((x \ y) * x) * (x \ z) = z * T(z \ (y * (x \ z)),x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1025,a(flip),b,752,a),flip(a)].">
      <j1 rule="hyper" parents="119 1025 752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1143">
    <literal><![CDATA[
      K(x,y) = L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1087,a,b,404,a),flip(a)].">
      <j1 rule="hyper" parents="119 1087 404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1144">
    <literal><![CDATA[
      K(x \ 1,x) * y != (x \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      L(x \ z,x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(1102(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="1102 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1145">
    <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,358,a(flip))].">
      <j1 rule="hyper" parents="116 80 358"/>
    </justification>
  </clause>

  <clause id="1146">
    <literal><![CDATA[
      T(x,x * (y * T(y \ 1,x))) = x
    ]]></literal>
    <justification jstring="[para(759(a,1),908(a,1,2))].">
      <j1 rule="para" parents="759 908"/>
    </justification>
  </clause>

  <clause id="1147">
    <literal><![CDATA[
      T(x,x * K(y,x)) = x
    ]]></literal>
    <justification jstring="[para(1060(a,2),1146(a,1,2,2))].">
      <j1 rule="para" parents="1060 1146"/>
    </justification>
  </clause>

  <clause id="1148">
    <literal><![CDATA[
      T(x * K(y,x),x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(49,a,1147,a)].">
      <j1 rule="hyper" parents="49 1147"/>
    </justification>
  </clause>

  <clause id="1149">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = (T(1 / x,z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(695,a,762,a)].">
      <j1 rule="hyper" parents="695 762"/>
    </justification>
  </clause>

  <clause id="1150">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[hyper(695,a,808,a)].">
      <j1 rule="hyper" parents="695 808"/>
    </justification>
  </clause>

  <clause id="1151">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) * T((x * z) \ y,x) = u
    ]]></literal>
    <justification jstring="[para(808(a,1),695(a,1))].">
      <j1 rule="para" parents="808 695"/>
    </justification>
  </clause>

  <clause id="1152">
    <literal><![CDATA[
      x * (y * T(T(x,y),z)) = T(x,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(428,a,816,a),flip(a)].">
      <j1 rule="hyper" parents="428 816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1153">
    <literal><![CDATA[
      T(x,y) * (x * z) = x * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(243(a,1),1152(a,1,2)),flip(a)].">
      <j1 rule="para" parents="243 1152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1154">
    <literal><![CDATA[
      x \ (T(x,y) * z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(611,a,1153,a)].">
      <j1 rule="hyper" parents="611 1153"/>
    </justification>
  </clause>

  <clause id="1155">
    <literal><![CDATA[
      T(x,y) * (x \ (T(x,y) \ z)) = x \ z
    ]]></literal>
    <justification jstring="[hyper(610,a,1153,a),flip(a)].">
      <j1 rule="hyper" parents="610 1153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1156">
    <literal><![CDATA[
      (T(x,y) * z) / (T(x,y) * (x \ z)) = x
    ]]></literal>
    <justification jstring="[hyper(587,a,1153,a)].">
      <j1 rule="hyper" parents="587 1153"/>
    </justification>
  </clause>

  <clause id="1157">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,y) \ z)) = (x * (T(x,y) \ z)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(451,a,151,a(flip),b,1153,a)].">
      <j1 rule="hyper" parents="451 151 1153"/>
    </justification>
  </clause>

  <clause id="1158">
    <literal><![CDATA[
      x * (T(x,y) * (x \ z)) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(356,a,1153,a),flip(a)].">
      <j1 rule="hyper" parents="356 1153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1159">
    <literal><![CDATA[
      T(x,y) * (x * (T(x,y) \ z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(334,a,151,a(flip),b,1153,a),flip(a)].">
      <j1 rule="hyper" parents="334 151 1153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1160">
    <literal><![CDATA[
      (x * (T(x,y) * z)) / (x * z) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,1153,a)].">
      <j1 rule="hyper" parents="130 1153"/>
    </justification>
  </clause>

  <clause id="1161">
    <literal><![CDATA[
      T(x,y) \ (x * z) = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,1153,a)].">
      <j1 rule="hyper" parents="116 151 1153"/>
    </justification>
  </clause>

  <clause id="1162">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,68,a(flip),b,1153,a),flip(a)].">
      <j1 rule="hyper" parents="116 68 1153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1163">
    <literal><![CDATA[
      x * (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,65,a(flip),b,1153,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 1153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1164">
    <literal><![CDATA[
      (x / y) * (T(x / y,z) * y) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(7(a,1),1153(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 1153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1165">
    <literal><![CDATA[
      x * (T(x,y) * T(z,x)) = T(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(105(a,1),1153(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 1153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1166">
    <literal><![CDATA[
      (x / y) * (T(x / y,y) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),1153(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 1153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1167">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(278,a,1163,a)].">
      <j1 rule="hyper" parents="278 1163"/>
    </justification>
  </clause>

  <clause id="1168">
    <literal><![CDATA[
      (T(x,y) \ x) / (T(x,y) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(130,a,1163,a)].">
      <j1 rule="hyper" parents="130 1163"/>
    </justification>
  </clause>

  <clause id="1169">
    <literal><![CDATA[
      x \ (T(x,y) \ x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,1163,a)].">
      <j1 rule="hyper" parents="123 1163"/>
    </justification>
  </clause>

  <clause id="1170">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,1 / x) = (1 / x) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1163,a(flip),b,449,a),flip(a)].">
      <j1 rule="hyper" parents="119 1163 449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1171">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ 1 = z
    ]]></literal>
    <justification jstring="[para(1163(a,1),303(a,1,1,1)),flip(b)].">
      <j1 rule="para" parents="1163 303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1172">
    <literal><![CDATA[
      T((1 / x) * (T(x,y) \ x),x) = (1 / x) * ((T(x,y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(1163(a,1),817(a,1,1,2))].">
      <j1 rule="para" parents="1163 817"/>
    </justification>
  </clause>

  <clause id="1173">
    <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(1168(a,1),431(a,1,1))].">
      <j1 rule="para" parents="1168 431"/>
    </justification>
  </clause>

  <clause id="1174">
    <literal><![CDATA[
      (T(x,y) \ T(x,z)) / (T(x,y) \ 1) = T(x,z)
    ]]></literal>
    <justification jstring="[para(1168(a,1),1076(a,2,1))].">
      <j1 rule="para" parents="1168 1076"/>
    </justification>
  </clause>

  <clause id="1175">
    <literal><![CDATA[
      x \ (T(x,x \ y) * z) = ((x \ y) \ y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(334,a,328,a(flip),b,1154,a),flip(a)].">
      <j1 rule="hyper" parents="334 328 1154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1176">
    <literal><![CDATA[
      T(x,y) \ (x \ z) = x \ (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(123,a,1155,a)].">
      <j1 rule="hyper" parents="123 1155"/>
    </justification>
  </clause>

  <clause id="1177">
    <literal><![CDATA[
      x \ (T(x,y) \ (z * x)) = T(x,y) \ T(z,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,17,a,b,1155,a),flip(a)].">
      <j1 rule="hyper" parents="116 17 1155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1178">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (T(x,y) \ z) = w
    ]]></literal>
    <justification jstring="[para(1155(a,1),609(a,1,2,2))].">
      <j1 rule="para" parents="1155 609"/>
    </justification>
  </clause>

  <clause id="1179">
    <literal><![CDATA[
      (T(x,y) * z) / u != x
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(1156(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="1156 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1180">
    <literal><![CDATA[
      T(x,y) * z != x * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(1156(a,1),125(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1156 125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1181">
    <literal><![CDATA[
      x \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(1156(a,1),276(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1156 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1182">
    <literal><![CDATA[
      x * (T(x,y) \ y) = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(421,a,1159,a),flip(a)].">
      <j1 rule="hyper" parents="421 1159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1183">
    <literal><![CDATA[
      T(x,y) \ K(x,1 / x) = x * (T(x,y) \ (1 / x))
    ]]></literal>
    <justification jstring="[hyper(116,a,268,a,b,1159,a)].">
      <j1 rule="hyper" parents="116 268 1159"/>
    </justification>
  </clause>

  <clause id="1184">
    <literal><![CDATA[
      x * (T(x,y) \ ((x \ T(x,y)) * z)) = L(z,x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(29,a,460,a,b,1159,a),flip(a)].">
      <j1 rule="hyper" parents="29 460 1159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1185">
    <literal><![CDATA[
      x * (T(x,y) \ (T(x,y) / x)) = K(x,T(x,y) / x)
    ]]></literal>
    <justification jstring="[hyper(29,a,316,a,b,1159,a),flip(a)].">
      <j1 rule="hyper" parents="29 316 1159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1186">
    <literal><![CDATA[
      T(x,y) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(1159(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1159 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1187">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ y) = T(y,T(x / y,y))
    ]]></literal>
    <justification jstring="[para(107(a,1),1182(a,1,2,1))].">
      <j1 rule="para" parents="107 1182"/>
    </justification>
  </clause>

  <clause id="1188">
    <literal><![CDATA[
      x \ y != T(z,u) * (z \ (T(z,u) \ w))
    ]]></literal>
    <literal><![CDATA[
      x * (z \ w) = y
    ]]></literal>
    <justification jstring="[para(1162(a,1),591(a,2,2,2))].">
      <j1 rule="para" parents="1162 591"/>
    </justification>
  </clause>

  <clause id="1189">
    <literal><![CDATA[
      T(x,y) * (x \ (T(x,y) \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x \ z) = w
    ]]></literal>
    <justification jstring="[para(1162(a,1),609(a,1,2,2))].">
      <j1 rule="para" parents="1162 609"/>
    </justification>
  </clause>

  <clause id="1190">
    <literal><![CDATA[
      T(x,y) * (x \ (T(x,y) \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      x \ z = u
    ]]></literal>
    <justification jstring="[para(1176(a,1),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1176 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1191">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(1176(a,2),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1176 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1192">
    <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,460,a,b,1165,a),flip(a)].">
      <j1 rule="hyper" parents="29 460 1165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1193">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * x) = x * K(x \ (x / T(x,y)),x)
    ]]></literal>
    <justification jstring="[para(1063(a,2),1165(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1063 1165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1194">
    <literal><![CDATA[
      T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,1174,a)].">
      <j1 rule="hyper" parents="133 1174"/>
    </justification>
  </clause>

  <clause id="1195">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ y) = T(y,y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),1187(a,2,2))].">
      <j1 rule="para" parents="107 1187"/>
    </justification>
  </clause>

  <clause id="1196">
    <literal><![CDATA[
      ((x * y) / x) * (y \ x) = T(x,x \ (x * y))
    ]]></literal>
    <justification jstring="[para(4(a,1),1195(a,1,2,1))].">
      <j1 rule="para" parents="4 1195"/>
    </justification>
  </clause>

  <clause id="1197">
    <literal><![CDATA[
      T(x / y,z) \ T(x / y,y) = (y \ x) * (T(x / y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,1),1194(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 1194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1198">
    <literal><![CDATA[
      T(x,y) = ((x * y) / x) * (y \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1196(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4 1196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1199">
    <literal><![CDATA[
      ((x * y) / x) \ T(x,y) = y \ x
    ]]></literal>
    <justification jstring="[hyper(791,a,1198,a)].">
      <j1 rule="hyper" parents="791 1198"/>
    </justification>
  </clause>

  <clause id="1200">
    <literal><![CDATA[
      T((x * y) / x,y \ x) = (y \ x) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(451,a,1198,a,b,xx)].">
      <j1 rule="hyper" parents="451 1198"/>
    </justification>
  </clause>

  <clause id="1201">
    <literal><![CDATA[
      ((x * (x / y)) / x) * y = T(x,x / y)
    ]]></literal>
    <justification jstring="[hyper(334,a,197,a(flip),b,1198,a)].">
      <j1 rule="hyper" parents="334 197 1198"/>
    </justification>
  </clause>

  <clause id="1202">
    <literal><![CDATA[
      T(x,x / y) / y = (x * (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,1198,a,b,197,a(flip))].">
      <j1 rule="hyper" parents="117 1198 197"/>
    </justification>
  </clause>

  <clause id="1203">
    <literal><![CDATA[
      ((x * y) * x) / (x * y) = T(x * y,x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,1198,a,b,152,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="117 1198 152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1204">
    <literal><![CDATA[
      T(x,y) / (y \ x) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,1198,a,b,xx)].">
      <j1 rule="hyper" parents="117 1198"/>
    </justification>
  </clause>

  <clause id="1205">
    <literal><![CDATA[
      (x / (x / y)) * (y \ (x / y)) = T(x / y,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),1198(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 1198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1206">
    <literal><![CDATA[
      ((x * R(y,y \ 1,x)) / x) * ((y \ 1) * x) = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[para(436(a,1),1198(a,2,2)),flip(a)].">
      <j1 rule="para" parents="436 1198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1207">
    <literal><![CDATA[
      T(T(x,y) / (y \ x),x) = y
    ]]></literal>
    <justification jstring="[para(1204(a,2),230(a,1,1))].">
      <j1 rule="para" parents="1204 230"/>
    </justification>
  </clause>

  <clause id="1208">
    <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(1204(a,1),1064(a,1,2,1,2))].">
      <j1 rule="para" parents="1204 1064"/>
    </justification>
  </clause>

  <clause id="1209">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(1207(a,1),254(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1207 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1210">
    <literal><![CDATA[
      T(T(R(x,y,y \ 1),x * y) / (y \ 1),R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(448(a,1),1207(a,1,1,2))].">
      <j1 rule="para" parents="448 1207"/>
    </justification>
  </clause>

  <clause id="1211">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) = T(y,y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,898,a(flip),b,1201,a)].">
      <j1 rule="hyper" parents="58 898 1201"/>
    </justification>
  </clause>

  <clause id="1212">
    <literal><![CDATA[
      x \ T(y,y / x) = (y * (x \ y)) / y
    ]]></literal>
    <justification jstring="[hyper(116,a,1201,a(flip),b,898,a(flip))].">
      <j1 rule="hyper" parents="116 1201 898"/>
    </justification>
  </clause>

  <clause id="1213">
    <literal><![CDATA[
      ((x * (x / y)) / x) * y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x / y) = z
    ]]></literal>
    <justification jstring="[para(1202(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1202 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1214">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),y) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(334,a,106,a(flip),b,1209,a),flip(a)].">
      <j1 rule="hyper" parents="334 106 1209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1215">
    <literal><![CDATA[
      (x / y) * ((x * y) / x) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[para(75(a,1),1211(a,1,2,1,2))].">
      <j1 rule="para" parents="75 1211"/>
    </justification>
  </clause>

  <clause id="1216">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(y,y / x) = u
    ]]></literal>
    <justification jstring="[para(1211(a,2),791(a,1))].">
      <j1 rule="para" parents="1211 791"/>
    </justification>
  </clause>

  <clause id="1217">
    <literal><![CDATA[
      (x * y) * L((x \ y) / y,y,x) = T(y,y / (x * y))
    ]]></literal>
    <justification jstring="[para(890(a,2),1211(a,1,2))].">
      <j1 rule="para" parents="890 1211"/>
    </justification>
  </clause>

  <clause id="1218">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,y / x) = z
    ]]></literal>
    <justification jstring="[para(1212(a,1),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1212 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1219">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),x * y) = L(T(x,x \ y),y,x)
    ]]></literal>
    <justification jstring="[para(1200(a,1),1002(a,1,1))].">
      <j1 rule="para" parents="1200 1002"/>
    </justification>
  </clause>

  <clause id="1220">
    <literal><![CDATA[
      T(T(x * y,x) / y,y) = R(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[para(1203(a,1),935(a,1,1))].">
      <j1 rule="para" parents="1203 935"/>
    </justification>
  </clause>

  <clause id="1221">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(431,a,1220,a)].">
      <j1 rule="hyper" parents="431 1220"/>
    </justification>
  </clause>

  <clause id="1222">
    <literal><![CDATA[
      R(x,y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      y \ T(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(1220(a,1),431(a,1))].">
      <j1 rule="para" parents="1220 431"/>
    </justification>
  </clause>

  <clause id="1223">
    <literal><![CDATA[
      L(R(x,y,T(x,y)),y,x) = x
    ]]></literal>
    <justification jstring="[para(1221(a,1),486(a,1,1))].">
      <j1 rule="para" parents="1221 486"/>
    </justification>
  </clause>

  <clause id="1224">
    <literal><![CDATA[
      (x * y) / ((x * y) / x) = y / (x \ ((x * y) / x))
    ]]></literal>
    <justification jstring="[hyper(117,a,230,a(flip),b,1205,a),flip(a)].">
      <j1 rule="hyper" parents="117 230 1205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1225">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(231(a,1),1215(a,1,2)),flip(a)].">
      <j1 rule="para" parents="231 1215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1226">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      y * (T(y,x) \ x) = z
    ]]></literal>
    <justification jstring="[para(242(a,1),1186(a,1))].">
      <j1 rule="para" parents="242 1186"/>
    </justification>
  </clause>

  <clause id="1227">
    <literal><![CDATA[
      x * (T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(4(a,1),1191(a,1,2,2))].">
      <j1 rule="para" parents="4 1191"/>
    </justification>
  </clause>

  <clause id="1228">
    <literal><![CDATA[
      (x / y) * (y * T(y \ x,z)) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(465(a,1),1164(a,1,2))].">
      <j1 rule="para" parents="465 1164"/>
    </justification>
  </clause>

  <clause id="1229">
    <literal><![CDATA[
      x \ (((x \ y) \ y) * z) = ((x \ y) \ y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(106(a,1),1175(a,1,2,1))].">
      <j1 rule="para" parents="106 1175"/>
    </justification>
  </clause>

  <clause id="1230">
    <literal><![CDATA[
      x * T(1 / x,T(x,y)) = K(x,T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(1050(a,1),1185(a,1,2))].">
      <j1 rule="para" parents="1050 1185"/>
    </justification>
  </clause>

  <clause id="1231">
    <literal><![CDATA[
      x * (y * ((x \ y) / y)) = T(y,y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(296,a,1217,a)].">
      <j1 rule="hyper" parents="296 1217"/>
    </justification>
  </clause>

  <clause id="1232">
    <literal><![CDATA[
      T(x,x / (y * x)) != z
    ]]></literal>
    <literal><![CDATA[
      y * (x * ((y \ x) / x)) = z
    ]]></literal>
    <justification jstring="[para(1217(a,1),296(a,1))].">
      <j1 rule="para" parents="1217 296"/>
    </justification>
  </clause>

  <clause id="1233">
    <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(911(a,2),674(a,1))].">
      <j1 rule="para" parents="911 674"/>
    </justification>
  </clause>

  <clause id="1234">
    <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(952(a,1),45(a,1))].">
      <j1 rule="para" parents="952 45"/>
    </justification>
  </clause>

  <clause id="1235">
    <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,975,a(flip),b,983,a)].">
      <j1 rule="hyper" parents="116 975 983"/>
    </justification>
  </clause>

  <clause id="1236">
    <literal><![CDATA[
      (T(1 / x,y) * x) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(695,a,982,a),flip(a)].">
      <j1 rule="hyper" parents="695 982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1237">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (z * T(z \ y,x)) * (z \ x)
    ]]></literal>
    <justification jstring="[para(465(a,1),1015(a,2,1))].">
      <j1 rule="para" parents="465 1015"/>
    </justification>
  </clause>

  <clause id="1238">
    <literal><![CDATA[
      T((x * y) / x,K(x \ (x / (((x * y) / x) \ 1)),x)) = (((x * y) / x) \ y) \ y
    ]]></literal>
    <justification jstring="[para(1072(a,2),106(a,1,2))].">
      <j1 rule="para" parents="1072 106"/>
    </justification>
  </clause>

  <clause id="1239">
    <literal><![CDATA[
      (1 / (x / (x / y))) * y = y / (x / (x / y))
    ]]></literal>
    <justification jstring="[para(75(a,1),1083(a,1,1)),flip(a)].">
      <j1 rule="para" parents="75 1083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1240">
    <literal><![CDATA[
      K(T(1 / (1 / x),x \ 1),x \ 1) = T(x,x \ 1) / x
    ]]></literal>
    <justification jstring="[para(1084(a,1),1065(a,1,1))].">
      <j1 rule="para" parents="1084 1065"/>
    </justification>
  </clause>

  <clause id="1241">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3(a,1),1108(a,2,2,1))].">
      <j1 rule="para" parents="3 1108"/>
    </justification>
  </clause>

  <clause id="1242">
    <literal><![CDATA[
      L(x,y,z) * (x \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,655,a(flip),b,1241,a)].">
      <j1 rule="hyper" parents="58 655 1241"/>
    </justification>
  </clause>

  <clause id="1243">
    <literal><![CDATA[
      L(x,y,z) \ (x \ L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,1241,a(flip),b,655,a(flip))].">
      <j1 rule="hyper" parents="116 1241 655"/>
    </justification>
  </clause>

  <clause id="1244">
    <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(1242(a,1),670(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1242 670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1245">
    <literal><![CDATA[
      x \ T(x * (x \ L(x,y,z)),u) = T(L(x,y,z),u) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1242(a,1),1026(a,1,2,1,2))].">
      <j1 rule="para" parents="1242 1026"/>
    </justification>
  </clause>

  <clause id="1246">
    <literal><![CDATA[
      L((1 / x) * (y * x),z,u) = (1 / x) * (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,651,a(flip),b,1110,a),flip(a)].">
      <j1 rule="hyper" parents="119 651 1110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1247">
    <literal><![CDATA[
      x * L(x \ ((1 / x) \ y),z,u) = (1 / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),1110(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1248">
    <literal><![CDATA[
      (1 / x) \ L(x \ 1,y,z) = L(x \ 1,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(334,a,244,a(flip),b,1111,a),flip(a)].">
      <j1 rule="hyper" parents="334 244 1111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1249">
    <literal><![CDATA[
      (x * y) \ x = (1 / y) * (L(y \ 1,y,x) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1248,a(flip),b,403,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1248 403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1250">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) * (x \ y) = (1 / (x \ y)) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(401(a,1),1248(a,1,2)),flip(a)].">
      <j1 rule="para" parents="401 1248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1251">
    <literal><![CDATA[
      (1 / x) * (((y * x) \ y) * x) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(221(a,1),1249(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="221 1249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1252">
    <literal><![CDATA[
      x * L(x \ (((y * x) \ y) * x),z,u) = (1 / x) \ L((y * x) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(1251(a,1),1110(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1251 1110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1253">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,653,a(flip),b,1113,a),flip(a)].">
      <j1 rule="hyper" parents="334 653 1113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1254">
    <literal><![CDATA[
      (x \ y) / ((y \ x) \ 1) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),1117(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1256">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) * (1 / x) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(70(a,1),1121(a,2,1,1))].">
      <j1 rule="para" parents="70 1121"/>
    </justification>
  </clause>

  <clause id="1257">
    <literal><![CDATA[
      (1 / x) * R((1 / x) \ 1,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(896,a,1256,a)].">
      <j1 rule="hyper" parents="896 1256"/>
    </justification>
  </clause>

  <clause id="1258">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,660,a(flip),b,1256,a)].">
      <j1 rule="hyper" parents="58 660 1256"/>
    </justification>
  </clause>

  <clause id="1259">
    <literal><![CDATA[
      R(x,y,z) \ (R(x,y,z) / x) = T(1 / x,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(451,a,1256,a(flip),b,660,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="451 1256 660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1260">
    <literal><![CDATA[
      (R(x,y,z) / x) / R(x,y,z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(117,a,1256,a(flip),b,660,a(flip))].">
      <j1 rule="hyper" parents="117 1256 660"/>
    </justification>
  </clause>

  <clause id="1261">
    <literal><![CDATA[
      R(x \ 1,y,z) / (x \ 1) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(359,a,1258,a),flip(a)].">
      <j1 rule="hyper" parents="359 1258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1262">
    <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(1258(a,1),247(a,2)),flip(a)].">
      <j1 rule="para" parents="1258 247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1263">
    <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(1258(a,1),92(a,2,1))].">
      <j1 rule="para" parents="1258 92"/>
    </justification>
  </clause>

  <clause id="1264">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) / x = u
    ]]></literal>
    <justification jstring="[para(1260(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1260 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1265">
    <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(1259(a,1),720(a,1,1,2))].">
      <j1 rule="para" parents="1259 720"/>
    </justification>
  </clause>

  <clause id="1266">
    <literal><![CDATA[
      (1 / x) * (x * R(x \ 1,y,z)) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(3(a,1),1132(a,2,1))].">
      <j1 rule="para" parents="3 1132"/>
    </justification>
  </clause>

  <clause id="1267">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,1266,a)].">
      <j1 rule="hyper" parents="123 1266"/>
    </justification>
  </clause>

  <clause id="1268">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,x / y,y) = (1 / (x / y)) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,418,a(flip),b,1266,a),flip(a)].">
      <j1 rule="hyper" parents="116 418 1266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1269">
    <literal><![CDATA[
      (1 / x) * ((y / (x * y)) * x) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(670(a,2),1266(a,1,2))].">
      <j1 rule="para" parents="670 1266"/>
    </justification>
  </clause>

  <clause id="1270">
    <literal><![CDATA[
      ((x / (y * x)) * y) \ (x / (y * x)) = T(1 / y,(x / (y * x)) * y)
    ]]></literal>
    <justification jstring="[hyper(451,a,223,a(flip),b,1269,a),flip(a)].">
      <j1 rule="hyper" parents="451 223 1269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1271">
    <literal><![CDATA[
      x * R(x \ 1,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(1 / x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(1267(a,1),728(a,1))].">
      <j1 rule="para" parents="1267 728"/>
    </justification>
  </clause>

  <clause id="1272">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3(a,1),1133(a,2,2,1))].">
      <j1 rule="para" parents="3 1133"/>
    </justification>
  </clause>

  <clause id="1273">
    <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),1133(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="17 1133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1274">
    <literal><![CDATA[
      R(x,y,z) * (x \ 1) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,659,a(flip),b,1272,a)].">
      <j1 rule="hyper" parents="58 659 1272"/>
    </justification>
  </clause>

  <clause id="1275">
    <literal><![CDATA[
      (x \ R(x,y,z)) / (x \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,1272,a(flip),b,659,a(flip))].">
      <j1 rule="hyper" parents="117 1272 659"/>
    </justification>
  </clause>

  <clause id="1276">
    <literal><![CDATA[
      R(x,y,z) \ (x \ R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,1272,a(flip),b,659,a(flip))].">
      <j1 rule="hyper" parents="116 1272 659"/>
    </justification>
  </clause>

  <clause id="1277">
    <literal><![CDATA[
      (x \ R(x,y,z)) / R(T(x,x \ 1),y,z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(117,a,1274,a(flip),b,245,a)].">
      <j1 rule="hyper" parents="117 1274 245"/>
    </justification>
  </clause>

  <clause id="1278">
    <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(1274(a,1),320(a,1,1))].">
      <j1 rule="para" parents="1274 320"/>
    </justification>
  </clause>

  <clause id="1279">
    <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(1274(a,1),670(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1274 670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1280">
    <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(1274(a,1),697(a,2,1))].">
      <j1 rule="para" parents="1274 697"/>
    </justification>
  </clause>

  <clause id="1281">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(334,a,898,a(flip),b,1141,a),flip(a)].">
      <j1 rule="hyper" parents="334 898 1141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1282">
    <literal><![CDATA[
      ((x \ 1) * x) * (x \ y) = y * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(2(a,1),1142(a,2,2,1,2))].">
      <j1 rule="para" parents="2 1142"/>
    </justification>
  </clause>

  <clause id="1283">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(583,a,1282,a)].">
      <j1 rule="hyper" parents="583 1282"/>
    </justification>
  </clause>

  <clause id="1284">
    <literal><![CDATA[
      (x * T(x \ (y \ x),y)) / (y \ x) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,1283,a)].">
      <j1 rule="hyper" parents="130 1283"/>
    </justification>
  </clause>

  <clause id="1285">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ (x \ y),x) = z
    ]]></literal>
    <justification jstring="[para(1284(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1284 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1286">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[para(465(a,1),1149(a,2,1))].">
      <j1 rule="para" parents="465 1149"/>
    </justification>
  </clause>

  <clause id="1287">
    <literal><![CDATA[
      ((x \ (x / y)) * x) * y = x * (y * T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,759,a(flip),b,1150,a),flip(a)].">
      <j1 rule="hyper" parents="58 759 1150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1288">
    <literal><![CDATA[
      x * ((y \ x) * T((y \ x) \ 1,x)) = ((x \ y) * x) * (y \ x)
    ]]></literal>
    <justification jstring="[para(72(a,1),1287(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 1287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1289">
    <literal><![CDATA[
      (x / y) * ((y \ x) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),1166(a,1,2,1))].">
      <j1 rule="para" parents="107 1166"/>
    </justification>
  </clause>

  <clause id="1290">
    <literal><![CDATA[
      (x \ (x * y)) * (((x * y) / x) * z) = ((x * y) / x) * (y * z)
    ]]></literal>
    <justification jstring="[para(230(a,1),1166(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="230 1166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1291">
    <literal><![CDATA[
      ((x / y) \ x) * ((x / (x / y)) * z) = (x / (x / y)) * (y * z)
    ]]></literal>
    <justification jstring="[para(252(a,1),1166(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="252 1166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1292">
    <literal><![CDATA[
      (x \ y) \ ((y / x) * z) = (y / x) * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(611,a,1289,a)].">
      <j1 rule="hyper" parents="611 1289"/>
    </justification>
  </clause>

  <clause id="1293">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ 1) = (y \ x) \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(426,a,1289,a),flip(a)].">
      <j1 rule="hyper" parents="426 1289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1294">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = (x \ 1) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1057,a(flip),b,1293,a)].">
      <j1 rule="hyper" parents="58 1057 1293"/>
    </justification>
  </clause>

  <clause id="1295">
    <literal><![CDATA[
      (x \ (x * y)) \ ((x * y) / x) = ((x * y) / x) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),1293(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1296">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(465(a,1),1236(a,1,1))].">
      <j1 rule="para" parents="465 1236"/>
    </justification>
  </clause>

  <clause id="1297">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ z) = z * T(z \ ((x \ 1) \ z),y)
    ]]></literal>
    <justification jstring="[para(1032(a,1),1236(a,1,1))].">
      <j1 rule="para" parents="1032 1236"/>
    </justification>
  </clause>

  <clause id="1298">
    <literal><![CDATA[
      (x \ (y \ x)) * x = (y * T(y \ 1,x)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(2(a,1),1237(a,1,1,2))].">
      <j1 rule="para" parents="2 1237"/>
    </justification>
  </clause>

  <clause id="1299">
    <literal><![CDATA[
      T(x * T(x \ 1,y),x \ y) = K(y \ (x \ y),y)
    ]]></literal>
    <justification jstring="[hyper(246,a,1298,a(flip),b,315,a)].">
      <j1 rule="hyper" parents="246 1298 315"/>
    </justification>
  </clause>

  <clause id="1300">
    <literal><![CDATA[
      L(x \ ((1 / x) \ y),z,u) = x \ ((1 / x) \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(123,a,1247,a),flip(a)].">
      <j1 rule="hyper" parents="123 1247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1301">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) * (x \ 1) = L(y * (x \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,1253,a)].">
      <j1 rule="hyper" parents="133 1253"/>
    </justification>
  </clause>

  <clause id="1302">
    <literal><![CDATA[
      x * L(x \ (y / (x \ 1)),z,u) = L(y,z,u) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),1253(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7 1253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1303">
    <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),1253(a,1,1,1,2))].">
      <j1 rule="para" parents="75 1253"/>
    </justification>
  </clause>

  <clause id="1304">
    <literal><![CDATA[
      T(x,x * T(x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(246,a,759,a(flip),b,1286,a(flip))].">
      <j1 rule="hyper" parents="246 759 1286"/>
    </justification>
  </clause>

  <clause id="1305">
    <literal><![CDATA[
      T(x,(x \ 1) * x) = x
    ]]></literal>
    <justification jstring="[para(105(a,1),1304(a,1,2))].">
      <j1 rule="para" parents="105 1304"/>
    </justification>
  </clause>

  <clause id="1306">
    <literal><![CDATA[
      T(x,K(x \ 1,x)) = x
    ]]></literal>
    <justification jstring="[para(369(a,1),1304(a,1,2))].">
      <j1 rule="para" parents="369 1304"/>
    </justification>
  </clause>

  <clause id="1307">
    <literal><![CDATA[
      R(x,(x * T(x \ 1,y)) / x,x) = T(x,(x * T(x \ 1,y)) / x)
    ]]></literal>
    <justification jstring="[para(1304(a,1),830(a,1,1))].">
      <j1 rule="para" parents="1304 830"/>
    </justification>
  </clause>

  <clause id="1308">
    <literal><![CDATA[
      T(x \ 1,T(x,y) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(467(a,1),1304(a,1,2))].">
      <j1 rule="para" parents="467 1304"/>
    </justification>
  </clause>

  <clause id="1309">
    <literal><![CDATA[
      T(x \ 1,x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1029(a,1),1304(a,1,2))].">
      <j1 rule="para" parents="1029 1304"/>
    </justification>
  </clause>

  <clause id="1310">
    <literal><![CDATA[
      T(1 / x,T(x,y) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(1048(a,1),1304(a,1,2))].">
      <j1 rule="para" parents="1048 1304"/>
    </justification>
  </clause>

  <clause id="1311">
    <literal><![CDATA[
      R(x,x \ 1,x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1305(a,1),825(a,1,1))].">
      <j1 rule="para" parents="1305 825"/>
    </justification>
  </clause>

  <clause id="1312">
    <literal><![CDATA[
      T(x,x \ 1) \ x = (x \ 1) * x
    ]]></literal>
    <justification jstring="[para(1311(a,1),436(a,1,1))].">
      <j1 rule="para" parents="1311 436"/>
    </justification>
  </clause>

  <clause id="1313">
    <literal><![CDATA[
      T(x \ T(x,y),x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,1309,a)].">
      <j1 rule="hyper" parents="49 1309"/>
    </justification>
  </clause>

  <clause id="1314">
    <literal><![CDATA[
      (x \ T(x,y)) * (x \ 1) = (x \ 1) * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,1309,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 1309 17"/>
    </justification>
  </clause>

  <clause id="1315">
    <literal><![CDATA[
      T((x * (1 / y)) / x,T(y,z) / y) = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(1310(a,1),472(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1310 472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1316">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ x = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(674,a,1312,a)].">
      <j1 rule="hyper" parents="674 1312"/>
    </justification>
  </clause>

  <clause id="1317">
    <literal><![CDATA[
      T(x,x \ 1) \ 1 = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(246,a,1312,a(flip),b,1163,a),flip(a)].">
      <j1 rule="hyper" parents="246 1312 1163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1318">
    <literal><![CDATA[
      ((x \ 1) \ 1) * K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(596,a,1316,a)].">
      <j1 rule="hyper" parents="596 1316"/>
    </justification>
  </clause>

  <clause id="1319">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ x != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(1316(a,2),382(a,1))].">
      <j1 rule="para" parents="1316 382"/>
    </justification>
  </clause>

  <clause id="1320">
    <literal><![CDATA[
      T((1 / x) \ 1,1 / x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(661(a,1),1317(a,1,1)),flip(a)].">
      <j1 rule="para" parents="661 1317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1321">
    <literal><![CDATA[
      R(x \ 1,T(x,y),x \ 1) = T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(1308(a,1),825(a,1,1))].">
      <j1 rule="para" parents="1308 825"/>
    </justification>
  </clause>

  <clause id="1322">
    <literal><![CDATA[
      T((x * y) \ (y * x),y \ 1) = L(y \ T(y,x),y,x)
    ]]></literal>
    <justification jstring="[para(1313(a,1),773(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1313 773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1323">
    <literal><![CDATA[
      T(x,1 / x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),1320(a,1,1))].">
      <j1 rule="para" parents="75 1320"/>
    </justification>
  </clause>

  <clause id="1324">
    <literal><![CDATA[
      T(x,1 / x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,106,a,b,1323,a),flip(a)].">
      <j1 rule="hyper" parents="334 106 1323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1325">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,1323,a(flip),b,836,a)].">
      <j1 rule="hyper" parents="117 1323 836"/>
    </justification>
  </clause>

  <clause id="1326">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(1323(a,1),1122(a,1,1,1))].">
      <j1 rule="para" parents="1323 1122"/>
    </justification>
  </clause>

  <clause id="1327">
    <literal><![CDATA[
      K(x,1 / x) * x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,836,a,b,1324,a)].">
      <j1 rule="hyper" parents="58 836 1324"/>
    </justification>
  </clause>

  <clause id="1328">
    <literal><![CDATA[
      (x * T(y,y \ 1)) / x = T((x * y) / x,1 / y)
    ]]></literal>
    <justification jstring="[para(1324(a,1),472(a,1,1,2))].">
      <j1 rule="para" parents="1324 472"/>
    </justification>
  </clause>

  <clause id="1329">
    <literal><![CDATA[
      R(R(x,y,z),1 / x,x) = R(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1324(a,1),834(a,2,1))].">
      <j1 rule="para" parents="1324 834"/>
    </justification>
  </clause>

  <clause id="1330">
    <literal><![CDATA[
      (x \ 1) \ (1 / x) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1294,a(flip),b,1325,a)].">
      <j1 rule="hyper" parents="58 1294 1325"/>
    </justification>
  </clause>

  <clause id="1331">
    <literal><![CDATA[
      T(x,x \ 1) / x != y
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / x) = y
    ]]></literal>
    <justification jstring="[para(1327(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1327 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1332">
    <literal><![CDATA[
      (1 / x) / K(x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(201,a,1330,a)].">
      <j1 rule="hyper" parents="201 1330"/>
    </justification>
  </clause>

  <clause id="1333">
    <literal><![CDATA[
      R(1 / x,x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(689,a,1332,a)].">
      <j1 rule="hyper" parents="689 1332"/>
    </justification>
  </clause>

  <clause id="1334">
    <literal><![CDATA[
      R(x / (y * x),y,1 / y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(1333(a,1),420(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1333 420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1335">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x != y
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / x) = y
    ]]></literal>
    <justification jstring="[para(106(a,1),1331(a,1,1))].">
      <j1 rule="para" parents="106 1331"/>
    </justification>
  </clause>

  <clause id="1336">
    <literal><![CDATA[
      (x \ 1) / (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) = y
    ]]></literal>
    <justification jstring="[para(661(a,1),1331(a,1,1))].">
      <j1 rule="para" parents="661 1331"/>
    </justification>
  </clause>

  <clause id="1337">
    <literal><![CDATA[
      R(x \ 1,x,y) \ (((y / (x * y)) * x) * (1 / x)) = x * (1 / x)
    ]]></literal>
    <justification jstring="[para(1334(a,1),187(a,1,1))].">
      <j1 rule="para" parents="1334 187"/>
    </justification>
  </clause>

  <clause id="1338">
    <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(1329(a,1),729(a,1,2))].">
      <j1 rule="para" parents="1329 729"/>
    </justification>
  </clause>

  <clause id="1339">
    <literal><![CDATA[
      L(1 / x,y,z) * (1 / (1 / x)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(75(a,1),1326(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 1326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1340">
    <literal><![CDATA[
      T(L(x,y,z) * (1 / x),x) = x \ L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1326(a,1),107(a,1,1))].">
      <j1 rule="para" parents="1326 107"/>
    </justification>
  </clause>

  <clause id="1341">
    <literal><![CDATA[
      T((x * y) / x,1 / y) = T((x * y) / x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(474,a,1328,a),flip(a)].">
      <j1 rule="hyper" parents="474 1328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1342">
    <literal><![CDATA[
      T((x * T(y,x)) / x,T(y,x) \ 1) = T(y,1 / T(y,x))
    ]]></literal>
    <justification jstring="[para(231(a,1),1341(a,1,1)),flip(a)].">
      <j1 rule="para" parents="231 1341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1343">
    <literal><![CDATA[
      K(x,y) = T((y * x) \ (x * y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,772,a,b,1322,a)].">
      <j1 rule="hyper" parents="334 772 1322"/>
    </justification>
  </clause>

  <clause id="1344">
    <literal><![CDATA[
      T(K(x,y),x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,2),1343(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11 1343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1345">
    <literal><![CDATA[
      T(x \ 1,K(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(49,a,1344,a)].">
      <j1 rule="hyper" parents="49 1344"/>
    </justification>
  </clause>

  <clause id="1346">
    <literal><![CDATA[
      K(x,y) * (x \ 1) = (x \ 1) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1344,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1344 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1347">
    <literal><![CDATA[
      (x \ 1) * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ 1) = z
    ]]></literal>
    <justification jstring="[para(1344(a,1),294(a,1,2))].">
      <j1 rule="para" parents="1344 294"/>
    </justification>
  </clause>

  <clause id="1348">
    <literal><![CDATA[
      T((x * y) \ x,K(y,z)) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(1345(a,1),410(a,2,1))].">
      <j1 rule="para" parents="1345 410"/>
    </justification>
  </clause>

  <clause id="1349">
    <literal><![CDATA[
      T((x * y) \ x,K(y,z)) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(334,a,221,a(flip),b,1348,a),flip(a)].">
      <j1 rule="hyper" parents="334 221 1348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1350">
    <literal><![CDATA[
      T(K(x,y),(z * x) \ z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,1349,a)].">
      <j1 rule="hyper" parents="49 1349"/>
    </justification>
  </clause>

  <clause id="1351">
    <literal><![CDATA[
      T(K(x \ 1,y),x) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(164(a,1),1350(a,1,2))].">
      <j1 rule="para" parents="164 1350"/>
    </justification>
  </clause>

  <clause id="1352">
    <literal><![CDATA[
      T(K(x,y),1 / x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(165(a,1),1350(a,1,2))].">
      <j1 rule="para" parents="165 1350"/>
    </justification>
  </clause>

  <clause id="1353">
    <literal><![CDATA[
      T(1 / x,K(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(49,a,1352,a)].">
      <j1 rule="hyper" parents="49 1352"/>
    </justification>
  </clause>

  <clause id="1354">
    <literal><![CDATA[
      T((1 * x) / y,K(y / x,z)) = R(1 / (y / x),y / x,x)
    ]]></literal>
    <justification jstring="[para(1353(a,1),786(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1353 786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1356">
    <literal><![CDATA[
      K(x \ 1,y) * x = x * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1351,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1351 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1357">
    <literal><![CDATA[
      x * K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) * x = z
    ]]></literal>
    <justification jstring="[para(1351(a,1),294(a,1,2))].">
      <j1 rule="para" parents="1351 294"/>
    </justification>
  </clause>

  <clause id="1358">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1295(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 1295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1359">
    <literal><![CDATA[
      (x * T(x \ (y \ x),z)) / (y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(1296(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1296 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1360">
    <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),1300(a,2,2,1))].">
      <j1 rule="para" parents="72 1300"/>
    </justification>
  </clause>

  <clause id="1361">
    <literal><![CDATA[
      T(x,1 / T(x,y)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(231(a,1),1342(a,1,1)),flip(a)].">
      <j1 rule="para" parents="231 1342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1362">
    <literal><![CDATA[
      (x / y) * (y * L(y \ z,u,w)) = x * L(x \ ((x / y) * z),u,w)
    ]]></literal>
    <justification jstring="[para(505(a,1),714(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="505 714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1363">
    <literal><![CDATA[
      x * (y * R(T(x,y),z,u)) = R(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,459,a(flip),b,739,a)].">
      <j1 rule="hyper" parents="58 459 739"/>
    </justification>
  </clause>

  <clause id="1364">
    <literal><![CDATA[
      R(x,y,z) * (x * u) = x * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(245(a,1),1363(a,1,2)),flip(a)].">
      <j1 rule="para" parents="245 1363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1365">
    <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(672,a,1364,a),flip(a)].">
      <j1 rule="hyper" parents="672 1364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1366">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(611,a,1364,a)].">
      <j1 rule="hyper" parents="611 1364"/>
    </justification>
  </clause>

  <clause id="1367">
    <literal><![CDATA[
      R(x,y,z) * (x \ (R(x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(610,a,1364,a),flip(a)].">
      <j1 rule="hyper" parents="610 1364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1368">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(x,y,z) * (x \ u)) = x
    ]]></literal>
    <justification jstring="[hyper(587,a,1364,a)].">
      <j1 rule="hyper" parents="587 1364"/>
    </justification>
  </clause>

  <clause id="1369">
    <literal><![CDATA[
      x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(356,a,1364,a),flip(a)].">
      <j1 rule="hyper" parents="356 1364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1370">
    <literal><![CDATA[
      R(x,y,z) \ (x * (R(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(123,a,1364,a)].">
      <j1 rule="hyper" parents="123 1364"/>
    </justification>
  </clause>

  <clause id="1371">
    <literal><![CDATA[
      x * (R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,65,a(flip),b,1364,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 1364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1372">
    <literal><![CDATA[
      x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x)
    ]]></literal>
    <justification jstring="[para(105(a,1),1364(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 1364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1373">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * T(x,R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(295,a,1371,a)].">
      <j1 rule="hyper" parents="295 1371"/>
    </justification>
  </clause>

  <clause id="1374">
    <literal><![CDATA[
      L(R(x,y,z) \ 1,x,1 / x) = (1 / x) * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1371,a(flip),b,449,a),flip(a)].">
      <j1 rule="hyper" parents="119 1371 449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1375">
    <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(1371(a,1),1026(a,1,2,1,2))].">
      <j1 rule="para" parents="1371 1026"/>
    </justification>
  </clause>

  <clause id="1376">
    <literal><![CDATA[
      R(x,y,z) * (x \ (y * z)) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(101(a,1),1366(a,1,2)),flip(a)].">
      <j1 rule="para" parents="101 1366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1377">
    <literal><![CDATA[
      R(x,y,y \ z) * (x \ z) = x \ ((x * y) * (y \ z))
    ]]></literal>
    <justification jstring="[para(380(a,1),1366(a,1,2)),flip(a)].">
      <j1 rule="para" parents="380 1366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1378">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) * (x \ u) = w
    ]]></literal>
    <justification jstring="[para(1368(a,1),276(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1368 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1379">
    <literal><![CDATA[
      R(x,y,x) * (x \ (y * x)) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(246,a,101,a(flip),b,1369,a),flip(a)].">
      <j1 rule="hyper" parents="246 101 1369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1380">
    <literal><![CDATA[
      R(x,y,x) * T(y,x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(17(a,2),1379(a,1,2))].">
      <j1 rule="para" parents="17 1379"/>
    </justification>
  </clause>

  <clause id="1381">
    <literal><![CDATA[
      R(x,y,x) \ T(x * y,x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,1380,a)].">
      <j1 rule="hyper" parents="123 1380"/>
    </justification>
  </clause>

  <clause id="1382">
    <literal><![CDATA[
      x \ T(y * z,y) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      R(y,z,y) = x
    ]]></literal>
    <justification jstring="[para(1381(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="1381 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1383">
    <literal><![CDATA[
      R(x,y,z) = (x \ ((x * y) * z)) / (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(130,a,1376,a),flip(a)].">
      <j1 rule="hyper" parents="130 1376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1384">
    <literal><![CDATA[
      x \ ((x * (x \ y)) * ((x \ y) \ z)) = ((y * ((x \ y) \ z)) / z) * (x \ z)
    ]]></literal>
    <justification jstring="[para(718(a,1),1377(a,1,1)),flip(a)].">
      <j1 rule="para" parents="718 1377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1385">
    <literal><![CDATA[
      L((x \ y) / y,z,u) * y = (L(1 / x,z,u) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(417(a,1),753(a,1,1,1))].">
      <j1 rule="para" parents="417 753"/>
    </justification>
  </clause>

  <clause id="1386">
    <literal><![CDATA[
      x * ((x \ y) * R((x \ y) \ z,u,w)) = y * R(y \ (x * z),u,w)
    ]]></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="1387">
    <literal><![CDATA[
      x \ (y * R(y \ (x * z),u,w)) = (x \ y) * R((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(780(a,1),487(a,1,2,2))].">
      <j1 rule="para" parents="780 487"/>
    </justification>
  </clause>

  <clause id="1388">
    <literal><![CDATA[
      x \ (y * L(y \ (x * z),u,w)) = (x \ y) * L((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(781(a,1),487(a,1,2,2))].">
      <j1 rule="para" parents="781 487"/>
    </justification>
  </clause>

  <clause id="1389">
    <literal><![CDATA[
      (R(x / (y / z),u,w) * (y / z)) * z = R((x * z) / y,u,w) * y
    ]]></literal>
    <justification jstring="[para(787(a,1),520(a,1,1)),flip(a)].">
      <j1 rule="para" parents="787 520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1390">
    <literal><![CDATA[
      (x * y) * L(T(y,x),z,u) = (L(y,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,525,a(flip),b,826,a),flip(a)].">
      <j1 rule="hyper" parents="58 525 826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1391">
    <literal><![CDATA[
      (x * y) * R(T(y,x),z,u) = (R(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[
      L(((x * y) * z) / (x * y),y,x) != u / (x * y)
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(877(a,2),41(a,1))].">
      <j1 rule="para" parents="877 41"/>
    </justification>
  </clause>

  <clause id="1393">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (x * u))) / z) = x * (y * ((z * (y \ u)) / z))
    ]]></literal>
    <justification jstring="[para(92(a,1),913(a,1,2,1,2))].">
      <j1 rule="para" parents="92 913"/>
    </justification>
  </clause>

  <clause id="1394">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ u)) / z) = x * (y * ((z * (y \ (x \ u))) / z))
    ]]></literal>
    <justification jstring="[para(311(a,1),913(a,1,2,1,2))].">
      <j1 rule="para" parents="311 913"/>
    </justification>
  </clause>

  <clause id="1395">
    <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(916(a,1),296(a,1,2))].">
      <j1 rule="para" parents="916 296"/>
    </justification>
  </clause>

  <clause id="1396">
    <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(917(a,1),296(a,1,2))].">
      <j1 rule="para" parents="917 296"/>
    </justification>
  </clause>

  <clause id="1397">
    <literal><![CDATA[
      (x / y) * (y * ((z * (y \ 1)) / z)) = x * ((z * (x \ (x / y))) / z)
    ]]></literal>
    <justification jstring="[hyper(119,a,918,a(flip),b,93,a),flip(a)].">
      <j1 rule="hyper" parents="119 918 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1398">
    <literal><![CDATA[
      (1 / x) \ ((y * ((1 / x) * z)) / y) = x * ((y * (x \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(116,a,919,a(flip),b,267,a)].">
      <j1 rule="hyper" parents="116 919 267"/>
    </justification>
  </clause>

  <clause id="1399">
    <literal><![CDATA[
      ((x * (y / (1 / z))) / x) * (1 / z) = ((x * (y * z)) / x) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,923,a(flip),b,270,a),flip(a)].">
      <j1 rule="hyper" parents="117 923 270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1400">
    <literal><![CDATA[
      ((x * (y * (z \ 1))) / x) / (z \ 1) = ((x * (y / z)) / x) * z
    ]]></literal>
    <justification jstring="[hyper(117,a,924,a(flip),b,269,a)].">
      <j1 rule="hyper" parents="117 924 269"/>
    </justification>
  </clause>

  <clause id="1401">
    <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,961,a(flip),b,238,a)].">
      <j1 rule="hyper" parents="119 961 238"/>
    </justification>
  </clause>

  <clause id="1402">
    <literal><![CDATA[
      (T(x,y) * z) * T(x,z) = (x * z) * T(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,937,a(flip),b,966,a),flip(a)].">
      <j1 rule="hyper" parents="58 937 966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1403">
    <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,1402,a)].">
      <j1 rule="hyper" parents="117 64 1402"/>
    </justification>
  </clause>

  <clause id="1404">
    <literal><![CDATA[
      T(T(x,x \ 1),y) / T(x,x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,1033,a(flip),b,1403,a),flip(a)].">
      <j1 rule="hyper" parents="334 1033 1403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1405">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (T(z / x,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,970,a(flip),b,648,a)].">
      <j1 rule="hyper" parents="119 970 648"/>
    </justification>
  </clause>

  <clause id="1406">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(1044(a,1),994(a,1))].">
      <j1 rule="para" parents="1044 994"/>
    </justification>
  </clause>

  <clause id="1407">
    <literal><![CDATA[
      (x * y) / a(z,z \ y,T(x,y)) = L(x,z \ y,z) * y
    ]]></literal>
    <justification jstring="[hyper(334,a,768,a(flip),b,995,a),flip(a)].">
      <j1 rule="hyper" parents="334 768 995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1408">
    <literal><![CDATA[
      (L(x,y \ z,y) * z) \ (x * z) = a(y,y \ z,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(192,a,1407,a)].">
      <j1 rule="hyper" parents="192 1407"/>
    </justification>
  </clause>

  <clause id="1409">
    <literal><![CDATA[
      L((x \ (y * (x * z))) / z,z,x) = T((z * y) / z,x * z)
    ]]></literal>
    <justification jstring="[hyper(334,a,472,a(flip),b,1009,a),flip(a)].">
      <j1 rule="hyper" parents="334 472 1009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1410">
    <literal><![CDATA[
      L((T(x,y) * (x \ y)) / y,y,x) = (y * K(T(x,y),y)) / y
    ]]></literal>
    <justification jstring="[para(1154(a,1),1010(a,1,1,1))].">
      <j1 rule="para" parents="1154 1010"/>
    </justification>
  </clause>

  <clause id="1411">
    <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),1020(a,1,1,1,2))].">
      <j1 rule="para" parents="72 1020"/>
    </justification>
  </clause>

  <clause id="1412">
    <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),1031(a,1,2,1))].">
      <j1 rule="para" parents="7 1031"/>
    </justification>
  </clause>

  <clause id="1413">
    <literal><![CDATA[
      K(x \ (x * y),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(1061(a,1),1086(a,1))].">
      <j1 rule="para" parents="1061 1086"/>
    </justification>
  </clause>

  <clause id="1414">
    <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),1145(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1415">
    <literal><![CDATA[
      T((1 * x) / y,K(y / x,z)) = x / y
    ]]></literal>
    <justification jstring="[hyper(334,a,418,a(flip),b,1354,a),flip(a)].">
      <j1 rule="hyper" parents="334 418 1354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1416">
    <literal><![CDATA[
      T(x / y,K(y / x,z)) = x / y
    ]]></literal>
    <justification jstring="[para(2(a,1),1415(a,1,1,1))].">
      <j1 rule="para" parents="2 1415"/>
    </justification>
  </clause>

  <clause id="1417">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(1416(a,1),254(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1416 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1418">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(334,a,107,a(flip),b,1417,a),flip(a)].">
      <j1 rule="hyper" parents="334 107 1417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1419">
    <literal><![CDATA[
      R(x,y,a(z,u,a(w,v5,v6))) = x
    ]]></literal>
    <justification jstring="[hyper(527,a,357,a)].">
      <j1 rule="hyper" parents="527 357"/>
    </justification>
  </clause>

  <clause id="1420">
    <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,357,a(flip))].">
      <j1 rule="hyper" parents="116 80 357"/>
    </justification>
  </clause>

  <clause id="1421">
    <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(357(a,1),538(a,2,1))].">
      <j1 rule="para" parents="357 538"/>
    </justification>
  </clause>

  <clause id="1422">
    <literal><![CDATA[
      R(x,y,a(z,u,a(w,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      x = v7
    ]]></literal>
    <justification jstring="[para(1419(a,1),46(a,2))].">
      <j1 rule="para" parents="1419 46"/>
    </justification>
  </clause>

  <clause id="1423">
    <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),521(a,1,1,1))].">
      <j1 rule="para" parents="7 521"/>
    </justification>
  </clause>

  <clause id="1424">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = K(x,(y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,679,a(flip),b,683,a)].">
      <j1 rule="hyper" parents="58 679 683"/>
    </justification>
  </clause>

  <clause id="1425">
    <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),853(a,1,2,1))].">
      <j1 rule="para" parents="92 853"/>
    </justification>
  </clause>

  <clause id="1426">
    <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,357,a(flip),b,927,a)].">
      <j1 rule="hyper" parents="116 357 927"/>
    </justification>
  </clause>

  <clause id="1427">
    <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,927,a),flip(a)].">
      <j1 rule="hyper" parents="29 80 927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1428">
    <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),949(a,1,1))].">
      <j1 rule="para" parents="90 949"/>
    </justification>
  </clause>

  <clause id="1429">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (R(1 / x,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(896,a,953,a)].">
      <j1 rule="hyper" parents="896 953"/>
    </justification>
  </clause>

  <clause id="1430">
    <literal><![CDATA[
      ((x \ ((x * y) / z)) * x) * z = x * (z * T(z \ y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,1150,a(flip),b,955,a)].">
      <j1 rule="hyper" parents="58 1150 955"/>
    </justification>
  </clause>

  <clause id="1431">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[para(5(a,1),1430(a,1,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1432">
    <literal><![CDATA[
      x * (x * T(x \ T(y,x),x)) = ((x \ y) * x) * x
    ]]></literal>
    <justification jstring="[para(231(a,1),1430(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="231 1430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1433">
    <literal><![CDATA[
      x * T(x \ T(y,x),x) = T((x \ y) * x,x)
    ]]></literal>
    <justification jstring="[hyper(247,a,1432,a),flip(a)].">
      <j1 rule="hyper" parents="247 1432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1434">
    <literal><![CDATA[
      T((x \ y) * x,x) = (x \ T(y,x)) * x
    ]]></literal>
    <justification jstring="[hyper(294,a,1433,a),flip(a)].">
      <j1 rule="hyper" parents="294 1433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1435">
    <literal><![CDATA[
      T((x \ y) * x,x) / x = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,1433,a(flip),b,105,a(flip))].">
      <j1 rule="hyper" parents="117 1433 105"/>
    </justification>
  </clause>

  <clause id="1436">
    <literal><![CDATA[
      T(x,y) \ T((y \ x) * y,y) = K(y \ T(x,y),y)
    ]]></literal>
    <justification jstring="[para(1433(a,1),444(a,1,2))].">
      <j1 rule="para" parents="1433 444"/>
    </justification>
  </clause>

  <clause id="1437">
    <literal><![CDATA[
      x * (T((x \ y) * x,x) / x) = T(y,x)
    ]]></literal>
    <justification jstring="[para(1434(a,2),71(a,1,2,1))].">
      <j1 rule="para" parents="1434 71"/>
    </justification>
  </clause>

  <clause id="1438">
    <literal><![CDATA[
      T(x * y,y) / y = y \ T(y * x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1435(a,1,1,1,1))].">
      <j1 rule="para" parents="4 1435"/>
    </justification>
  </clause>

  <clause id="1439">
    <literal><![CDATA[
      (x \ T(y,x)) * x != z
    ]]></literal>
    <literal><![CDATA[
      T((x \ y) * x,x) = z
    ]]></literal>
    <justification jstring="[para(1435(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1435 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1440">
    <literal><![CDATA[
      x \ T(x * (y / x),x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(76(a,1),1435(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 1435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1441">
    <literal><![CDATA[
      x * (T(y * x,x) / x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1437(a,1,2,1,1,1))].">
      <j1 rule="para" parents="4 1437"/>
    </justification>
  </clause>

  <clause id="1442">
    <literal><![CDATA[
      T(x * (y / x),x) = x * (T(y,x) / x)
    ]]></literal>
    <justification jstring="[para(76(a,1),1437(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="76 1437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1443">
    <literal><![CDATA[
      T(x * ((1 / x) * y),x) = x * ((1 / x) * T(y,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,1041,a(flip),b,1438,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1041 1438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1444">
    <literal><![CDATA[
      x \ T(x * T((x * y) / x,z),x) = T(x * T(y,z),x) / x
    ]]></literal>
    <justification jstring="[para(466(a,1),1438(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="466 1438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1445">
    <literal><![CDATA[
      x \ T(x * L((x * y) / x,z,u),x) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[para(654(a,1),1438(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="654 1438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1446">
    <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(1274(a,1),1441(a,1,2,1,1))].">
      <j1 rule="para" parents="1274 1441"/>
    </justification>
  </clause>

  <clause id="1447">
    <literal><![CDATA[
      T(x * y,x) \ T(y * x,x) = K(x \ T(x * y,x),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1436(a,1,2,1,1))].">
      <j1 rule="para" parents="4 1436"/>
    </justification>
  </clause>

  <clause id="1448">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = x * (T((x \ y) * z,x) / z)
    ]]></literal>
    <justification jstring="[para(1042(a,1),1431(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1042 1431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1449">
    <literal><![CDATA[
      ((x \ (y / y)) * x) * y = x * (K(x \ 1,x) * (x \ y))
    ]]></literal>
    <justification jstring="[para(1283(a,2),1431(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1283 1431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1450">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) = ((x \ 1) * x) * y
    ]]></literal>
    <justification jstring="[para(69(a,1),1449(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="69 1449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1451">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(583,a,1450,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="583 1450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1453">
    <literal><![CDATA[
      K(x \ 1,x) * (x * y) = x * (K(x \ 1,x) * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1451(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 1451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1454">
    <literal><![CDATA[
      x * (K(x \ 1,x) * T(y,x)) = K(x \ 1,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(17(a,2),1451(a,1,2,2))].">
      <j1 rule="para" parents="17 1451"/>
    </justification>
  </clause>

  <clause id="1455">
    <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(1453(a,1),239(a,1,2))].">
      <j1 rule="para" parents="1453 239"/>
    </justification>
  </clause>

  <clause id="1456">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1286,a(flip),b,956,a),flip(a)].">
      <j1 rule="hyper" parents="58 1286 956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1457">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * y = x * ((y \ (x \ y)) * y)
    ]]></literal>
    <justification jstring="[para(105(a,1),1456(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 1456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1458">
    <literal><![CDATA[
      x * T(y * T(y \ 1,x),x) = y * ((x \ (y \ x)) * x)
    ]]></literal>
    <justification jstring="[hyper(295,a,1457,a)].">
      <j1 rule="hyper" parents="295 1457"/>
    </justification>
  </clause>

  <clause id="1459">
    <literal><![CDATA[
      (x * ((y \ (x \ y)) * y)) / y = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,1457,a)].">
      <j1 rule="hyper" parents="130 1457"/>
    </justification>
  </clause>

  <clause id="1460">
    <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(1276(a,1),1459(a,1,1,2,1))].">
      <j1 rule="para" parents="1276 1459"/>
    </justification>
  </clause>

  <clause id="1461">
    <literal><![CDATA[
      (T((x * y) / x,z) * x) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(698,a,967,a),flip(a)].">
      <j1 rule="hyper" parents="698 967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1462">
    <literal><![CDATA[
      (x * T(y,z)) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(466(a,1),1461(a,1,1))].">
      <j1 rule="para" parents="466 1461"/>
    </justification>
  </clause>

  <clause id="1463">
    <literal><![CDATA[
      (x * y) / T(y,z) = (x / T(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(608,a,1462,a)].">
      <j1 rule="hyper" parents="608 1462"/>
    </justification>
  </clause>

  <clause id="1464">
    <literal><![CDATA[
      T((x / y) * T(y,z),y) = y \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(451,a,148,a(flip),b,1462,a)].">
      <j1 rule="hyper" parents="451 148 1462"/>
    </justification>
  </clause>

  <clause id="1465">
    <literal><![CDATA[
      (1 / T(x,y)) * x = x / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(425,a,1462,a),flip(a)].">
      <j1 rule="hyper" parents="425 1462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1466">
    <literal><![CDATA[
      ((x / T(y,z)) * y) * T(y,z) = x * y
    ]]></literal>
    <justification jstring="[hyper(341,a,1462,a),flip(a)].">
      <j1 rule="hyper" parents="341 1462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1467">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * y) * T(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,1462,a)].">
      <j1 rule="hyper" parents="123 1462"/>
    </justification>
  </clause>

  <clause id="1468">
    <literal><![CDATA[
      (x * T(y,z)) / y = (x / y) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,148,a(flip),b,1462,a)].">
      <j1 rule="hyper" parents="117 148 1462"/>
    </justification>
  </clause>

  <clause id="1469">
    <literal><![CDATA[
      ((x / T(y,z)) / y) * T(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(117,a,79,a(flip),b,1462,a),flip(a)].">
      <j1 rule="hyper" parents="117 79 1462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1470">
    <literal><![CDATA[
      (x * (y / z)) * T(y / z,z) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(107(a,1),1462(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1471">
    <literal><![CDATA[
      (x / T(x,y)) / x = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,1465,a)].">
      <j1 rule="hyper" parents="130 1465"/>
    </justification>
  </clause>

  <clause id="1472">
    <literal><![CDATA[
      (1 / T(x,y)) \ (x / T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(123,a,1465,a)].">
      <j1 rule="hyper" parents="123 1465"/>
    </justification>
  </clause>

  <clause id="1473">
    <literal><![CDATA[
      (1 / T(x,y)) \ (T(x,z) / T(x,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(1472(a,1),1079(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1472 1079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1474">
    <literal><![CDATA[
      T(x,1 / T(x,y)) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1472(a,1),1081(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1472 1081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1475">
    <literal><![CDATA[
      (x / T(y,z)) / y = (x / y) / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,153,a(flip),b,1463,a(flip))].">
      <j1 rule="hyper" parents="117 153 1463"/>
    </justification>
  </clause>

  <clause id="1476">
    <literal><![CDATA[
      (x * y) / T(y,z) != y * u
    ]]></literal>
    <literal><![CDATA[
      T(x / T(y,z),y) = u
    ]]></literal>
    <justification jstring="[para(1463(a,2),247(a,2)),flip(a)].">
      <j1 rule="para" parents="1463 247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1477">
    <literal><![CDATA[
      x * T(y,z) != u * y
    ]]></literal>
    <literal><![CDATA[
      (u / T(y,z)) * y = x
    ]]></literal>
    <justification jstring="[para(1466(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="1466 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1478">
    <literal><![CDATA[
      (x * y) / T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (x / T(y,z)) * y = u
    ]]></literal>
    <justification jstring="[para(1466(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1466 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1479">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[para(1225(a,2),1466(a,1,1))].">
      <j1 rule="para" parents="1225 1466"/>
    </justification>
  </clause>

  <clause id="1480">
    <literal><![CDATA[
      R(T(x,y * T(x,z)),y,T(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1467(a,1),1137(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1467 1137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1481">
    <literal><![CDATA[
      ((x / T(y,z)) / y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x / y = u
    ]]></literal>
    <justification jstring="[para(1468(a,1),589(a,1))].">
      <j1 rule="para" parents="1468 589"/>
    </justification>
  </clause>

  <clause id="1482">
    <literal><![CDATA[
      R(T(x,L(x,y,x) * y),y,T(x,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(738(a,1),1480(a,1,1,2))].">
      <j1 rule="para" parents="738 1480"/>
    </justification>
  </clause>

  <clause id="1483">
    <literal><![CDATA[
      (T(x,y) / T(x,z)) / T(x,y) = 1 / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(201,a,1473,a)].">
      <j1 rule="hyper" parents="201 1473"/>
    </justification>
  </clause>

  <clause id="1484">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(1479(a,1),1165(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1479 1165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1485">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) / T(x,z)) = T(1 / T(x,z),T(x,y))
    ]]></literal>
    <justification jstring="[para(1483(a,1),107(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1483 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1486">
    <literal><![CDATA[
      (x / y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * T(y,z)) / y = u
    ]]></literal>
    <justification jstring="[para(6(a,1),1481(a,1,1,1))].">
      <j1 rule="para" parents="6 1481"/>
    </justification>
  </clause>

  <clause id="1487">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1361(a,1),1474(a,1,1))].">
      <j1 rule="para" parents="1361 1474"/>
    </justification>
  </clause>

  <clause id="1488">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x * (x * y)) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(130,a,1484,a),flip(a)].">
      <j1 rule="hyper" parents="130 1484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1489">
    <literal><![CDATA[
      ((x * (1 / T(x,y))) / x) * T(x,y) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(1487(a,1),1469(a,1,1,1))].">
      <j1 rule="para" parents="1487 1469"/>
    </justification>
  </clause>

  <clause id="1490">
    <literal><![CDATA[
      (x * (x * y)) / (y * x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1225,a(flip),b,1488,a),flip(a)].">
      <j1 rule="hyper" parents="58 1225 1488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1491">
    <literal><![CDATA[
      R(((x * (x * y)) / x) / y,y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(868,a,1490,a)].">
      <j1 rule="hyper" parents="868 1490"/>
    </justification>
  </clause>

  <clause id="1492">
    <literal><![CDATA[
      (x * (y / z)) * (z \ y) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(107(a,1),1470(a,1,2))].">
      <j1 rule="para" parents="107 1470"/>
    </justification>
  </clause>

  <clause id="1493">
    <literal><![CDATA[
      (x * (y \ (y * z))) * ((y * z) / y) = (x * ((y * z) / y)) * z
    ]]></literal>
    <justification jstring="[para(230(a,1),1470(a,1,2)),flip(a)].">
      <j1 rule="para" parents="230 1470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1494">
    <literal><![CDATA[
      (x * (y \ z)) / (z / y) = (x / (z / y)) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(608,a,1492,a)].">
      <j1 rule="hyper" parents="608 1492"/>
    </justification>
  </clause>

  <clause id="1495">
    <literal><![CDATA[
      (x * (y / z)) / (z \ y) = (x / (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(117,a,148,a(flip),b,1492,a)].">
      <j1 rule="hyper" parents="117 148 1492"/>
    </justification>
  </clause>

  <clause id="1496">
    <literal><![CDATA[
      ((x / (y \ z)) / (z / y)) * (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x / (z / y) = u
    ]]></literal>
    <justification jstring="[para(1494(a,1),589(a,1))].">
      <j1 rule="para" parents="1494 589"/>
    </justification>
  </clause>

  <clause id="1497">
    <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(1485(a,1),1068(a,1,1,1))].">
      <j1 rule="para" parents="1485 1068"/>
    </justification>
  </clause>

  <clause id="1498">
    <literal><![CDATA[
      (x / (y / z)) * (z \ y) != u
    ]]></literal>
    <literal><![CDATA[
      (x * (z \ y)) / (y / z) = u
    ]]></literal>
    <justification jstring="[para(6(a,1),1496(a,1,1,1))].">
      <j1 rule="para" parents="6 1496"/>
    </justification>
  </clause>

  <clause id="1499">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = (z * y) * T((z * y) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,465,a(flip),b,968,a),flip(a)].">
      <j1 rule="hyper" parents="334 465 968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1500">
    <literal><![CDATA[
      x * (y * T(L(x,z,u),y)) = L(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(294,a,1016,a),flip(a)].">
      <j1 rule="hyper" parents="294 1016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1501">
    <literal><![CDATA[
      L(x,y,z) * (x * u) = x * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(105(a,1),1500(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 1500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1502">
    <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(672,a,1501,a),flip(a)].">
      <j1 rule="hyper" parents="672 1501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1503">
    <literal><![CDATA[
      x \ (L(x,y,z) * u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(611,a,1501,a)].">
      <j1 rule="hyper" parents="611 1501"/>
    </justification>
  </clause>

  <clause id="1504">
    <literal><![CDATA[
      L(x,y,z) * (x \ (L(x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(610,a,1501,a),flip(a)].">
      <j1 rule="hyper" parents="610 1501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1505">
    <literal><![CDATA[
      x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(356,a,1501,a),flip(a)].">
      <j1 rule="hyper" parents="356 1501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1506">
    <literal><![CDATA[
      (x * (L(x,y,z) * u)) / (x * u) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,1501,a)].">
      <j1 rule="hyper" parents="130 1501"/>
    </justification>
  </clause>

  <clause id="1507">
    <literal><![CDATA[
      L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(123,a,1501,a)].">
      <j1 rule="hyper" parents="123 1501"/>
    </justification>
  </clause>

  <clause id="1508">
    <literal><![CDATA[
      (x * y) / (x * (L(x,z,u) \ y)) = L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,151,a(flip),b,1501,a)].">
      <j1 rule="hyper" parents="117 151 1501"/>
    </justification>
  </clause>

  <clause id="1509">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,1501,a)].">
      <j1 rule="hyper" parents="116 151 1501"/>
    </justification>
  </clause>

  <clause id="1510">
    <literal><![CDATA[
      x * (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,65,a(flip),b,1501,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 1501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1511">
    <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,1501,a(flip),b,84,a)].">
      <j1 rule="hyper" parents="116 1501 84"/>
    </justification>
  </clause>

  <clause id="1512">
    <literal><![CDATA[
      x \ (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,1510,a)].">
      <j1 rule="hyper" parents="123 1510"/>
    </justification>
  </clause>

  <clause id="1513">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,1 / x) = (1 / x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1510,a(flip),b,449,a),flip(a)].">
      <j1 rule="hyper" parents="119 1510 449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1514">
    <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(1510(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1510 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1515">
    <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(1510(a,1),321(a,1,1))].">
      <j1 rule="para" parents="1510 321"/>
    </justification>
  </clause>

  <clause id="1516">
    <literal><![CDATA[
      T((1 / x) * (L(x,y,z) \ x),x) = (1 / x) * ((L(x,y,z) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(1510(a,1),817(a,1,1,2))].">
      <j1 rule="para" parents="1510 817"/>
    </justification>
  </clause>

  <clause id="1517">
    <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(1510(a,2),1299(a,1,2))].">
      <j1 rule="para" parents="1510 1299"/>
    </justification>
  </clause>

  <clause id="1518">
    <literal><![CDATA[
      x \ (L(x,y,z) * (u * x)) = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[para(17(a,2),1503(a,2,2))].">
      <j1 rule="para" parents="17 1503"/>
    </justification>
  </clause>

  <clause id="1519">
    <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,1504,a),flip(a)].">
      <j1 rule="hyper" parents="116 17 1504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1520">
    <literal><![CDATA[
      T((x * y) / x,L(y,z,u) * x) = L((y * x) / x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1507(a,1),1409(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1507 1409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1521">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (L(x,y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(1508(a,1),276(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1508 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1522">
    <literal><![CDATA[
      ((x * y) \ x) * ((y \ 1) * (L(y \ 1,y,x) \ z)) = (y \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(756,a,1509,a)].">
      <j1 rule="hyper" parents="756 1509"/>
    </justification>
  </clause>

  <clause id="1523">
    <literal><![CDATA[
      (x \ 1) * ((y * ((x \ 1) \ 1)) / y) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(334,a,1358,a(flip),b,1021,a),flip(a)].">
      <j1 rule="hyper" parents="334 1358 1021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1524">
    <literal><![CDATA[
      ((x * (y / (y / T(z,x)))) / x) \ ((y / T(z,x)) * z) = y / T(z,x)
    ]]></literal>
    <justification jstring="[para(231(a,1),1023(a,1,2,2))].">
      <j1 rule="para" parents="231 1023"/>
    </justification>
  </clause>

  <clause id="1525">
    <literal><![CDATA[
      x * ((x \ y) * T((x \ y) \ 1,z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(3(a,1),1135(a,2,2,1,2))].">
      <j1 rule="para" parents="3 1135"/>
    </justification>
  </clause>

  <clause id="1526">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(123,a,1525,a),flip(a)].">
      <j1 rule="hyper" parents="123 1525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1527">
    <literal><![CDATA[
      x * T(x \ y,y \ x) = y * K((y \ x) \ 1,y \ x)
    ]]></literal>
    <justification jstring="[para(369(a,1),1525(a,1,2)),flip(a)].">
      <j1 rule="para" parents="369 1525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1528">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(z \ (z / (y \ x)),z)
    ]]></literal>
    <justification jstring="[para(1063(a,2),1525(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1063 1525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1529">
    <literal><![CDATA[
      (x \ y) * K(z \ (z / ((x \ y) \ (x \ 1))),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(1089,a,1528,a),flip(a)].">
      <j1 rule="hyper" parents="1089 1528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1530">
    <literal><![CDATA[
      T(x * y,z) / y = x * K(z \ (z / (x \ (1 / y))),z)
    ]]></literal>
    <justification jstring="[hyper(1080,a,1528,a)].">
      <j1 rule="hyper" parents="1080 1528"/>
    </justification>
  </clause>

  <clause id="1531">
    <literal><![CDATA[
      K(x \ (x / (y \ z)),x) = y \ (z * T(z \ y,x))
    ]]></literal>
    <justification jstring="[hyper(549,a,1528,a),flip(a)].">
      <j1 rule="hyper" parents="549 1528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1532">
    <literal><![CDATA[
      (x * y) * K(z \ (z / ((x * y) \ x)),z) = x * T(y,z)
    ]]></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="1533">
    <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),1528(a,2,2,1,2,2))].">
      <j1 rule="para" parents="13 1528"/>
    </justification>
  </clause>

  <clause id="1534">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),x) = z \ ((y * z) * T((y * z) \ z,x))
    ]]></literal>
    <justification jstring="[para(17(a,2),1531(a,1,1,2,2))].">
      <j1 rule="para" parents="17 1531"/>
    </justification>
  </clause>

  <clause id="1535">
    <literal><![CDATA[
      K(x \ (x / (y \ (y / z))),x) = y \ ((y / z) * T(z,x))
    ]]></literal>
    <justification jstring="[para(75(a,1),1531(a,2,2,2,1))].">
      <j1 rule="para" parents="75 1531"/>
    </justification>
  </clause>

  <clause id="1536">
    <literal><![CDATA[
      T(x,x * (y \ (z * T(z \ y,x)))) = x
    ]]></literal>
    <justification jstring="[para(1531(a,1),1147(a,1,2,2))].">
      <j1 rule="para" parents="1531 1147"/>
    </justification>
  </clause>

  <clause id="1537">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ ((y \ x) * ((y \ x) \ x)))) = x
    ]]></literal>
    <justification jstring="[para(1214(a,1),1536(a,1,2,2,2,2))].">
      <j1 rule="para" parents="1214 1536"/>
    </justification>
  </clause>

  <clause id="1538">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ x)) = x
    ]]></literal>
    <justification jstring="[para(5(a,1),1537(a,1,2,2,2))].">
      <j1 rule="para" parents="5 1537"/>
    </justification>
  </clause>

  <clause id="1539">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,z) \ x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1538(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1538 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1540">
    <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,1526,a)].">
      <j1 rule="hyper" parents="116 92 1526"/>
    </justification>
  </clause>

  <clause id="1541">
    <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),1527(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1542">
    <literal><![CDATA[
      (x / y) * K(z \ (z / ((x / y) \ (1 / y))),z) = T(x,z) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),1530(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7 1530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1543">
    <literal><![CDATA[
      K(x \ (x / (x \ (x / y))),x) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(840(a,1),1535(a,2,2))].">
      <j1 rule="para" parents="840 1535"/>
    </justification>
  </clause>

  <clause id="1544">
    <literal><![CDATA[
      (T(x / (y / z),u) * (y / z)) * z = y * T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,465,a(flip),b,1136,a),flip(a)].">
      <j1 rule="hyper" parents="334 465 1136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1545">
    <literal><![CDATA[
      (x * (T(x,y) \ x)) \ (x * x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1539,a(flip),b,1157,a),flip(a)].">
      <j1 rule="hyper" parents="58 1539 1157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1546">
    <literal><![CDATA[
      (x * x) / T(x,y) = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(201,a,1545,a)].">
      <j1 rule="hyper" parents="201 1545"/>
    </justification>
  </clause>

  <clause id="1547">
    <literal><![CDATA[
      (x / T(x,y)) * x = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(1478,a,1546,a)].">
      <j1 rule="hyper" parents="1478 1546"/>
    </justification>
  </clause>

  <clause id="1548">
    <literal><![CDATA[
      T(x / T(x,y),x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(1476,a,1546,a)].">
      <j1 rule="hyper" parents="1476 1546"/>
    </justification>
  </clause>

  <clause id="1549">
    <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(1546(a,2),741(a,1,2))].">
      <j1 rule="para" parents="1546 741"/>
    </justification>
  </clause>

  <clause id="1550">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(1548(a,1),465(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1548 465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1551">
    <literal><![CDATA[
      (x \ y) * (T(y / x,z) \ 1) = T(y / x,z) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),1197(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1552">
    <literal><![CDATA[
      T(x / (y \ x),z) \ ((y \ x) \ x) = ((y \ x) \ x) * (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),1551(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="72 1551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1553">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),1245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1555">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(20(a,2),1553(a,2,2))].">
      <j1 rule="para" parents="20 1553"/>
    </justification>
  </clause>

  <clause id="1556">
    <literal><![CDATA[
      L(T(x,y),z,u) * (x \ 1) = x \ L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(20(a,2),1555(a,1,1))].">
      <j1 rule="para" parents="20 1555"/>
    </justification>
  </clause>

  <clause id="1557">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ x) = x * K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(1061(a,1),1288(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1061 1288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1558">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(y \ (y * x),y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1557(a,1,1,1))].">
      <j1 rule="para" parents="4 1557"/>
    </justification>
  </clause>

  <clause id="1559">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1558(a,2,2,1))].">
      <j1 rule="para" parents="4 1558"/>
    </justification>
  </clause>

  <clause id="1560">
    <literal><![CDATA[
      (x * y) * L(x \ 1,x,y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(645,a,1559,a)].">
      <j1 rule="hyper" parents="645 1559"/>
    </justification>
  </clause>

  <clause id="1561">
    <literal><![CDATA[
      x \ (y * K(x / y,y)) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[hyper(335,a,1559,a)].">
      <j1 rule="hyper" parents="335 1559"/>
    </justification>
  </clause>

  <clause id="1563">
    <literal><![CDATA[
      ((x * y) / x) * (y * z) = y * (((x * y) / x) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),1290(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 1290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1564">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = ((y * x) / y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(611,a,1563,a)].">
      <j1 rule="hyper" parents="611 1563"/>
    </justification>
  </clause>

  <clause id="1565">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = y * (((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,1563,a)].">
      <j1 rule="hyper" parents="116 151 1563"/>
    </justification>
  </clause>

  <clause id="1566">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((((x * y) / x) \ y) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(770,a,1564,a),flip(a)].">
      <j1 rule="hyper" parents="770 1564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1567">
    <literal><![CDATA[
      (x / (x / y)) * (y * z) = y * ((x / (x / y)) * z)
    ]]></literal>
    <justification jstring="[hyper(638,a,1291,a),flip(a)].">
      <j1 rule="hyper" parents="638 1291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1568">
    <literal><![CDATA[
      (x / (x / y)) * (y \ 1) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(426,a,1567,a),flip(a)].">
      <j1 rule="hyper" parents="426 1567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1570">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = x \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,1082,a(flip),b,1568,a)].">
      <j1 rule="hyper" parents="58 1082 1568"/>
    </justification>
  </clause>

  <clause id="1571">
    <literal><![CDATA[
      (L(1 / x,y,z) * x) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[hyper(887,a,1385,a),flip(a)].">
      <j1 rule="hyper" parents="887 1385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1572">
    <literal><![CDATA[
      (1 / x) \ ((y * (1 / x)) / y) = x * ((y * (x \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(3(a,1),1398(a,1,2,1,2))].">
      <j1 rule="para" parents="3 1398"/>
    </justification>
  </clause>

  <clause id="1573">
    <literal><![CDATA[
      ((x * (x * y)) / x) / y = T(x,x / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(1213,a,1399,a),flip(a)].">
      <j1 rule="hyper" parents="1213 1399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1574">
    <literal><![CDATA[
      (1 / x) * ((y * ((1 / x) \ z)) / y) = ((y * (z * x)) / y) / x
    ]]></literal>
    <justification jstring="[hyper(1020,a,1399,a)].">
      <j1 rule="hyper" parents="1020 1399"/>
    </justification>
  </clause>

  <clause id="1575">
    <literal><![CDATA[
      ((x * (1 / (1 / y))) / x) * (1 / y) = ((x * y) / x) / y
    ]]></literal>
    <justification jstring="[para(2(a,1),1399(a,2,1,1,2))].">
      <j1 rule="para" parents="2 1399"/>
    </justification>
  </clause>

  <clause id="1576">
    <literal><![CDATA[
      T(x,x / (1 / (x \ y))) = ((x * y) / x) / (x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),1573(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 1573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1577">
    <literal><![CDATA[
      R(T(x,x / (1 / y)),y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(1573(a,1),1491(a,1,1))].">
      <j1 rule="para" parents="1573 1491"/>
    </justification>
  </clause>

  <clause id="1578">
    <literal><![CDATA[
      (1 / x) * ((y * ((1 / x) \ 1)) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(1020,a,1575,a)].">
      <j1 rule="hyper" parents="1020 1575"/>
    </justification>
  </clause>

  <clause id="1579">
    <literal><![CDATA[
      (1 / x) * ((y * x) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[para(75(a,1),1578(a,1,2,1,2))].">
      <j1 rule="para" parents="75 1578"/>
    </justification>
  </clause>

  <clause id="1581">
    <literal><![CDATA[
      x \ y != ((z * (u \ 1)) / z) / (u \ 1)
    ]]></literal>
    <literal><![CDATA[
      x * (u * ((z * (u \ 1)) / z)) = y
    ]]></literal>
    <justification jstring="[para(1579(a,1),643(a,2))].">
      <j1 rule="para" parents="1579 643"/>
    </justification>
  </clause>

  <clause id="1582">
    <literal><![CDATA[
      ((x * (y * (z \ 1))) / x) / (z \ 1) = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(334,a,898,a(flip),b,1400,a),flip(a)].">
      <j1 rule="hyper" parents="334 898 1400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1583">
    <literal><![CDATA[
      x * (y * T(y \ (x \ (z * y)),u)) = (T(z / x,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,956,a(flip),b,1405,a)].">
      <j1 rule="hyper" parents="58 956 1405"/>
    </justification>
  </clause>

  <clause id="1584">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[para(465(a,1),1405(a,2,1))].">
      <j1 rule="para" parents="465 1405"/>
    </justification>
  </clause>

  <clause id="1585">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(657(a,1),1429(a,2,1))].">
      <j1 rule="para" parents="657 1429"/>
    </justification>
  </clause>

  <clause id="1586">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(1020,a,1489,a)].">
      <j1 rule="hyper" parents="1020 1489"/>
    </justification>
  </clause>

  <clause id="1587">
    <literal><![CDATA[
      (x * ((y * z) / y)) * z = (x * z) * ((y * z) / y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1493(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 1493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1588">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / ((z * y) / z)) * y
    ]]></literal>
    <justification jstring="[hyper(608,a,1587,a)].">
      <j1 rule="hyper" parents="608 1587"/>
    </justification>
  </clause>

  <clause id="1589">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * y = y / ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(425,a,1587,a),flip(a)].">
      <j1 rule="hyper" parents="425 1587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1591">
    <literal><![CDATA[
      ((x / y) * y) * ((x * y) / x) = T(x,x / (x / y)) * y
    ]]></literal>
    <justification jstring="[para(1215(a,1),1587(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1215 1587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1592">
    <literal><![CDATA[
      T(x,x / (x / y)) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(341,a,1591,a),flip(a)].">
      <j1 rule="hyper" parents="341 1591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1593">
    <literal><![CDATA[
      T(x,x / (x / y)) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1180,a,1592,a)].">
      <j1 rule="hyper" parents="1180 1592"/>
    </justification>
  </clause>

  <clause id="1595">
    <literal><![CDATA[
      ((x * y) / x) / (x \ y) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(130,a,1593,a)].">
      <j1 rule="hyper" parents="130 1593"/>
    </justification>
  </clause>

  <clause id="1596">
    <literal><![CDATA[
      T(x,x / (1 / (x \ y))) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1576,a,b,1595,a)].">
      <j1 rule="hyper" parents="58 1576 1595"/>
    </justification>
  </clause>

  <clause id="1597">
    <literal><![CDATA[
      T(x,x / (x / (x * y))) = T(x,x / (1 / y))
    ]]></literal>
    <justification jstring="[para(4(a,1),1596(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4 1596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1598">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = (x * z) * T((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(465(a,1),1499(a,1,1))].">
      <j1 rule="para" parents="465 1499"/>
    </justification>
  </clause>

  <clause id="1599">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),x) = z \ ((y * T(y \ 1,x)) * z)
    ]]></literal>
    <justification jstring="[para(1286(a,1),1534(a,2,2))].">
      <j1 rule="para" parents="1286 1534"/>
    </justification>
  </clause>

  <clause id="1600">
    <literal><![CDATA[
      T(x * T(x \ 1,y),z) = K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,17,a,b,1599,a)].">
      <j1 rule="hyper" parents="334 17 1599"/>
    </justification>
  </clause>

  <clause id="1601">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * z = z * K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1599,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="119 1599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1602">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ 1,z) = T(x * T(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,1063,a(flip),b,1600,a)].">
      <j1 rule="hyper" parents="334 1063 1600"/>
    </justification>
  </clause>

  <clause id="1603">
    <literal><![CDATA[
      T(x,y) \ T(x * T(x \ 1,z),y) = T(T(x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,1600,a,b,1063,a(flip))].">
      <j1 rule="hyper" parents="116 1600 1063"/>
    </justification>
  </clause>

  <clause id="1604">
    <literal><![CDATA[
      K(x \ (x / T(x,y)),x) = T(K(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(369(a,1),1600(a,1,1)),flip(a)].">
      <j1 rule="para" parents="369 1600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1605">
    <literal><![CDATA[
      K(x \ (x / T(y \ x,z)),x) = T(K(x \ y,x),z)
    ]]></literal>
    <justification jstring="[para(1061(a,1),1600(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1061 1600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1606">
    <literal><![CDATA[
      K(x \ (x / T(L(y \ 1,y,x),z)),x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(1143(a,2),1600(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1143 1600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1607">
    <literal><![CDATA[
      T(K(x \ 1,x),y) / T(x,y) = T(1 / T(x,y),x)
    ]]></literal>
    <justification jstring="[para(1604(a,1),1068(a,1,1))].">
      <j1 rule="para" parents="1604 1068"/>
    </justification>
  </clause>

  <clause id="1608">
    <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),1605(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="106 1605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1609">
    <literal><![CDATA[
      T(x * T(x \ 1,T(x,y)),y) = (T(x,y) \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(294,a,1602,a),flip(a)].">
      <j1 rule="hyper" parents="294 1602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1610">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(x * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1309(a,1),1603(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1309 1603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1611">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ z,u)) * y = x * T(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(465(a,1),1544(a,1,1))].">
      <j1 rule="para" parents="465 1544"/>
    </justification>
  </clause>

  <clause id="1612">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(653(a,1),1571(a,1,1))].">
      <j1 rule="para" parents="653 1571"/>
    </justification>
  </clause>

  <clause id="1613">
    <literal><![CDATA[
      x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[para(465(a,1),1583(a,2,1))].">
      <j1 rule="para" parents="465 1583"/>
    </justification>
  </clause>

  <clause id="1614">
    <literal><![CDATA[
      (x * y) \ ((x * T(x \ z,u)) * y) = T((x * y) \ (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(123,a,1584,a)].">
      <j1 rule="hyper" parents="123 1584"/>
    </justification>
  </clause>

  <clause id="1615">
    <literal><![CDATA[
      ((x * y) * T((x * y) \ x,z)) * y = (x * y) * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,759,a(flip),b,1584,a),flip(a)].">
      <j1 rule="hyper" parents="58 759 1584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1616">
    <literal><![CDATA[
      x * T(x \ (x \ (y * x)),z) = T(x * T(x \ y,z),x)
    ]]></literal>
    <justification jstring="[hyper(246,a,1584,a(flip),b,956,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="246 1584 956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1617">
    <literal><![CDATA[
      T(x * T(x \ y,z),x) = x * T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[para(17(a,2),1616(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 1616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1618">
    <literal><![CDATA[
      x \ T(x * T(x \ y,z),x) = T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(791,a,1617,a)].">
      <j1 rule="hyper" parents="791 1617"/>
    </justification>
  </clause>

  <clause id="1619">
    <literal><![CDATA[
      T(x \ T(x * y,x),z) = x \ T(x * T(y,z),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1618(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1620">
    <literal><![CDATA[
      x \ T(x * T(y / x,z),x) = T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[para(1440(a,1),1619(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1440 1619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1621">
    <literal><![CDATA[
      T(x * T(y / x,z),x) = x * T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,1620,a),flip(a)].">
      <j1 rule="hyper" parents="134 1620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1622">
    <literal><![CDATA[
      T(x * T(y,z),x) / x = T(T(x * y,x) / x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1444,a(flip),b,1620,a)].">
      <j1 rule="hyper" parents="58 1444 1620"/>
    </justification>
  </clause>

  <clause id="1623">
    <literal><![CDATA[
      T(x * T(1 / x,y),x) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(204(a,1),1621(a,2,2,1,1))].">
      <j1 rule="para" parents="204 1621"/>
    </justification>
  </clause>

  <clause id="1624">
    <literal><![CDATA[
      T(x,x * R(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(246,a,949,a(flip),b,1585,a(flip))].">
      <j1 rule="hyper" parents="246 949 1585"/>
    </justification>
  </clause>

  <clause id="1625">
    <literal><![CDATA[
      T(x * R(x \ 1,y,z),x) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(246,a,1585,a(flip),b,949,a(flip))].">
      <j1 rule="hyper" parents="246 1585 949"/>
    </justification>
  </clause>

  <clause id="1626">
    <literal><![CDATA[
      T(1 / x,(1 / x) * R(x,y,z)) = 1 / x
    ]]></literal>
    <justification jstring="[para(75(a,1),1624(a,1,2,2,1))].">
      <j1 rule="para" parents="75 1624"/>
    </justification>
  </clause>

  <clause id="1627">
    <literal><![CDATA[
      T(x \ 1,R(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(659(a,1),1624(a,1,2))].">
      <j1 rule="para" parents="659 1624"/>
    </justification>
  </clause>

  <clause id="1628">
    <literal><![CDATA[
      T(x \ 1,x \ R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1272(a,1),1624(a,1,2))].">
      <j1 rule="para" parents="1272 1624"/>
    </justification>
  </clause>

  <clause id="1629">
    <literal><![CDATA[
      T(x \ R(x,y,z),x \ 1) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(49,a,1628,a)].">
      <j1 rule="hyper" parents="49 1628"/>
    </justification>
  </clause>

  <clause id="1630">
    <literal><![CDATA[
      T(T(x \ 1,y),x \ R(x,z,u)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1628(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1628 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1631">
    <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(1626(a,1),740(a,1,1,2))].">
      <j1 rule="para" parents="1626 740"/>
    </justification>
  </clause>

  <clause id="1632">
    <literal><![CDATA[
      R(x \ 1,R(x,y,z),x \ 1) = T(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1627(a,1),825(a,1,1))].">
      <j1 rule="para" parents="1627 825"/>
    </justification>
  </clause>

  <clause id="1633">
    <literal><![CDATA[
      T(x * ((x * R(x \ 1,y,z)) / x),x) = x * ((x * R(x \ 1,y,z)) / x)
    ]]></literal>
    <justification jstring="[para(1625(a,1),1442(a,2,2,1))].">
      <j1 rule="para" parents="1625 1442"/>
    </justification>
  </clause>

  <clause id="1634">
    <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(1632(a,1),1381(a,1,1))].">
      <j1 rule="para" parents="1632 1381"/>
    </justification>
  </clause>

  <clause id="1635">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(1163(a,1),1586(a,1,2,1))].">
      <j1 rule="para" parents="1163 1586"/>
    </justification>
  </clause>

  <clause id="1636">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u))
    ]]></literal>
    <justification jstring="[hyper(334,a,956,a(flip),b,1598,a),flip(a)].">
      <j1 rule="hyper" parents="334 956 1598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1637">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (z / y)) * x) * y = u
    ]]></literal>
    <justification jstring="[para(1598(a,1),582(a,1))].">
      <j1 rule="para" parents="1598 582"/>
    </justification>
  </clause>

  <clause id="1638">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(1,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),1610(a,2,2,1))].">
      <j1 rule="para" parents="5 1610"/>
    </justification>
  </clause>

  <clause id="1640">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(204(a,1),1638(a,2,2))].">
      <j1 rule="para" parents="204 1638"/>
    </justification>
  </clause>

  <clause id="1642">
    <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,956,a(flip),b,1611,a)].">
      <j1 rule="hyper" parents="117 956 1611"/>
    </justification>
  </clause>

  <clause id="1643">
    <literal><![CDATA[
      ((x * y) / z) * T(((x * y) / z) \ x,u) = (x * (y * T(y \ z,u))) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,955,a(flip),b,1611,a),flip(a)].">
      <j1 rule="hyper" parents="117 955 1611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1644">
    <literal><![CDATA[
      (x / y) * T((x / y) \ z,x) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,105,a(flip),b,1611,a),flip(a)].">
      <j1 rule="hyper" parents="117 105 1611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1645">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ 1,z)) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2(a,1),1611(a,2,2,1,2))].">
      <j1 rule="para" parents="2 1611"/>
    </justification>
  </clause>

  <clause id="1646">
    <literal><![CDATA[
      (x / y) * T((x / y) \ 1,z) = (x * T(x \ y,z)) / y
    ]]></literal>
    <justification jstring="[hyper(130,a,1645,a),flip(a)].">
      <j1 rule="hyper" parents="130 1645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1647">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) * y = x * T(x \ y,x / y)
    ]]></literal>
    <justification jstring="[para(369(a,1),1645(a,1,1))].">
      <j1 rule="para" parents="369 1645"/>
    </justification>
  </clause>

  <clause id="1648">
    <literal><![CDATA[
      K(x \ (x / (y / z)),x) * z = y * T(y \ z,x)
    ]]></literal>
    <justification jstring="[para(1063(a,2),1645(a,1,1))].">
      <j1 rule="para" parents="1063 1645"/>
    </justification>
  </clause>

  <clause id="1649">
    <literal><![CDATA[
      K(x \ (x / (y / z)),x) = (y * T(y \ z,x)) / z
    ]]></literal>
    <justification jstring="[hyper(130,a,1648,a),flip(a)].">
      <j1 rule="hyper" parents="130 1648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1650">
    <literal><![CDATA[
      K(x \ (x / ((y * z) / y)),x) = (y * (z * T(z \ 1,x))) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,759,a(flip),b,1648,a),flip(a)].">
      <j1 rule="hyper" parents="117 759 1648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1651">
    <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),1649(a,1,1,2))].">
      <j1 rule="para" parents="6 1649"/>
    </justification>
  </clause>

  <clause id="1652">
    <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),1649(a,1,1,2,2))].">
      <j1 rule="para" parents="15 1649"/>
    </justification>
  </clause>

  <clause id="1653">
    <literal><![CDATA[
      K(x \ (x / ((y \ x) / T(x,y))),x) = ((y \ x) * ((y \ x) \ x)) / T(x,y)
    ]]></literal>
    <justification jstring="[para(1214(a,1),1649(a,2,1,2))].">
      <j1 rule="para" parents="1214 1649"/>
    </justification>
  </clause>

  <clause id="1654">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,x / (y * x)) * x
    ]]></literal>
    <justification jstring="[hyper(334,a,463,a(flip),b,1647,a),flip(a)].">
      <j1 rule="hyper" parents="334 463 1647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1655">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((x \ 1) \ u) = u * L(u \ ((x \ 1) \ u),y,z)
    ]]></literal>
    <justification jstring="[para(1241(a,1),1612(a,1,1))].">
      <j1 rule="para" parents="1241 1612"/>
    </justification>
  </clause>

  <clause id="1656">
    <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,1443,a,b,1613,a)].">
      <j1 rule="hyper" parents="58 1443 1613"/>
    </justification>
  </clause>

  <clause id="1657">
    <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),1613(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="92 1613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1658">
    <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(1614(a,1),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1614 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1659">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (z / y)) * x) * y = u
    ]]></literal>
    <justification jstring="[para(1636(a,1),582(a,1))].">
      <j1 rule="para" parents="1636 582"/>
    </justification>
  </clause>

  <clause id="1660">
    <literal><![CDATA[
      (x \ 1) * (y * T(y \ ((x \ 1) \ z),u)) = (x \ T(x * (z / y),u)) * y
    ]]></literal>
    <justification jstring="[para(971(a,1),1636(a,1,1)),flip(a)].">
      <j1 rule="para" parents="971 1636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1661">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ (x \ x),y))
    ]]></literal>
    <justification jstring="[para(1059(a,2),1636(a,1,1))].">
      <j1 rule="para" parents="1059 1636"/>
    </justification>
  </clause>

  <clause id="1662">
    <literal><![CDATA[
      K(x \ (x / ((y * x) / y)),x) = (y * K(x \ 1,x)) / y
    ]]></literal>
    <justification jstring="[para(369(a,1),1650(a,2,1,2))].">
      <j1 rule="para" parents="369 1650"/>
    </justification>
  </clause>

  <clause id="1663">
    <literal><![CDATA[
      ((x * y) / x) \ ((x * K(y \ 1,y)) / x) = T(((x * y) / x) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,1662,a(flip),b,1063,a(flip))].">
      <j1 rule="hyper" parents="116 1662 1063"/>
    </justification>
  </clause>

  <clause id="1664">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(61(a,1),1661(a,2,2,2,1,2))].">
      <j1 rule="para" parents="61 1661"/>
    </justification>
  </clause>

  <clause id="1666">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * ((y \ 1) * y)
    ]]></literal>
    <justification jstring="[para(105(a,1),1664(a,2,2))].">
      <j1 rule="para" parents="105 1664"/>
    </justification>
  </clause>

  <clause id="1667">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(369(a,1),1664(a,2,2))].">
      <j1 rule="para" parents="369 1664"/>
    </justification>
  </clause>

  <clause id="1668">
    <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,1666,a),flip(a)].">
      <j1 rule="hyper" parents="30 101 1666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1669">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * y = (x * y) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),1667(a,1,1,1))].">
      <j1 rule="para" parents="6 1667"/>
    </justification>
  </clause>

  <clause id="1670">
    <literal><![CDATA[
      (L(1 / x,x,y) * K(x \ 1,x)) * x = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(872(a,1),1667(a,1,1,1))].">
      <j1 rule="para" parents="872 1667"/>
    </justification>
  </clause>

  <clause id="1671">
    <literal><![CDATA[
      ((x / K(y \ 1,y)) * y) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(341,a,1669,a),flip(a)].">
      <j1 rule="hyper" parents="341 1669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1672">
    <literal><![CDATA[
      ((x * (y \ 1)) / K(y \ 1,y)) * y = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,532,a,b,1671,a),flip(a)].">
      <j1 rule="hyper" parents="30 532 1671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1673">
    <literal><![CDATA[
      (x * (y \ 1)) / K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ 1,y) / y = z
    ]]></literal>
    <justification jstring="[para(1668(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1668 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1674">
    <literal><![CDATA[
      (L(x,y,z) * (z * y)) \ (x * (z * y)) = a(z,y,T(x,z * y))
    ]]></literal>
    <justification jstring="[para(649(a,1),236(a,1,1))].">
      <j1 rule="para" parents="649 236"/>
    </justification>
  </clause>

  <clause id="1675">
    <literal><![CDATA[
      L(x,T(y,y \ z),y \ z) = L(x,(y \ z) \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(29,a,460,a,b,771,a),flip(a)].">
      <j1 rule="hyper" parents="29 460 771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1676">
    <literal><![CDATA[
      x * ((x \ y) * ((z * ((x \ y) \ u)) / z)) = y * ((z * (y \ (x * u))) / z)
    ]]></literal>
    <justification jstring="[hyper(119,a,920,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="119 920 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1677">
    <literal><![CDATA[
      x \ (y * ((z * (y \ (x * u))) / z)) = (x \ y) * ((z * ((x \ y) \ u)) / z)
    ]]></literal>
    <justification jstring="[para(920(a,1),487(a,1,2,2))].">
      <j1 rule="para" parents="920 487"/>
    </justification>
  </clause>

  <clause id="1678">
    <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(508(a,1),934(a,1,2,1))].">
      <j1 rule="para" parents="508 934"/>
    </justification>
  </clause>

  <clause id="1679">
    <literal><![CDATA[
      (1 / (x \ y)) \ (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(401(a,1),1250(a,1,1)),flip(a)].">
      <j1 rule="para" parents="401 1250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1680">
    <literal><![CDATA[
      (x \ (x * y)) * ((x * y) \ x) = (1 / ((x * y) \ x)) \ y
    ]]></literal>
    <justification jstring="[para(4(a,1),1679(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 1679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1681">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) \ y = y * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1680(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 1680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1682">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * (y * ((x * y) \ x)) = y
    ]]></literal>
    <justification jstring="[hyper(134,a,1681,a)].">
      <j1 rule="hyper" parents="134 1681"/>
    </justification>
  </clause>

  <clause id="1683">
    <literal><![CDATA[
      (1 / (x / y)) * ((y / x) * (x / y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(119,a,811,a(flip),b,1268,a(flip))].">
      <j1 rule="hyper" parents="119 811 1268"/>
    </justification>
  </clause>

  <clause id="1684">
    <literal><![CDATA[
      T(1 / (x / y),(y / x) * (x / y)) = ((y / x) * (x / y)) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(451,a,xx,b,1683,a)].">
      <j1 rule="hyper" parents="451 1683"/>
    </justification>
  </clause>

  <clause id="1685">
    <literal><![CDATA[
      T(x,(x * T(x \ 1,y)) / x) = R(x,T(1 / x,y),x)
    ]]></literal>
    <justification jstring="[para(469(a,1),1307(a,1,2)),flip(a)].">
      <j1 rule="para" parents="469 1307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1686">
    <literal><![CDATA[
      R(x,T(1 / x,y),x) = T(x,T(1 / x,y))
    ]]></literal>
    <justification jstring="[para(469(a,1),1685(a,1,2)),flip(a)].">
      <j1 rule="para" parents="469 1685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1687">
    <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(1686(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1686 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1688">
    <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(1686(a,1),1380(a,1,1))].">
      <j1 rule="para" parents="1686 1380"/>
    </justification>
  </clause>

  <clause id="1689">
    <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),1520(a,2,1))].">
      <j1 rule="para" parents="6 1520"/>
    </justification>
  </clause>

  <clause id="1690">
    <literal><![CDATA[
      x * T(y,L(y,z,u) * x) = L(y,x,L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(1689(a,1),466(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1689 466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1691">
    <literal><![CDATA[
      L(T(x,y),y,L(x,z,u)) = T(x,L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(29,a,244,a,b,1690,a)].">
      <j1 rule="hyper" parents="29 244 1690"/>
    </justification>
  </clause>

  <clause id="1692">
    <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(971(a,1),1659(a,1,2))].">
      <j1 rule="para" parents="971 1659"/>
    </justification>
  </clause>

  <clause id="1693">
    <literal><![CDATA[
      R((x * y) / (x * z),u,w) * (x * z) = x * (z * R(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(665,a,1100,a)].">
      <j1 rule="hyper" parents="665 1100"/>
    </justification>
  </clause>

  <clause id="1694">
    <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,1585,a(flip),b,1100,a),flip(a)].">
      <j1 rule="hyper" parents="58 1585 1100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1695">
    <literal><![CDATA[
      x * (y * R(y \ (x \ z),x,y)) = ((z / (x * y)) * x) * y
    ]]></literal>
    <justification jstring="[hyper(879,a,1101,a),flip(a)].">
      <j1 rule="hyper" parents="879 1101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1696">
    <literal><![CDATA[
      x * (y * R(y \ (x \ y),z,u)) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1585,a(flip),b,1101,a),flip(a)].">
      <j1 rule="hyper" parents="58 1585 1101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1697">
    <literal><![CDATA[
      (((x * (y * z)) / (x * y)) * x) * y = x * (y * R(z,x,y))
    ]]></literal>
    <justification jstring="[para(62(a,1),1695(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="62 1695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1698">
    <literal><![CDATA[
      (((x * (y * z)) / (x * z)) * x) * z = x * (z * R(T(y,z),x,z))
    ]]></literal>
    <justification jstring="[para(105(a,1),1697(a,1,1,1,1,2))].">
      <j1 rule="para" parents="105 1697"/>
    </justification>
  </clause>

  <clause id="1699">
    <literal><![CDATA[
      (((x * (y * z)) / (x * z)) * x) * z = x * (R(y,x,z) * z)
    ]]></literal>
    <justification jstring="[para(245(a,1),1698(a,2,2))].">
      <j1 rule="para" parents="245 1698"/>
    </justification>
  </clause>

  <clause id="1700">
    <literal><![CDATA[
      (L((x * y) / x,z,u) * x) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(915,a,1104,a),flip(a)].">
      <j1 rule="hyper" parents="915 1104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1701">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (L(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(887,a,1104,a)].">
      <j1 rule="hyper" parents="887 1104"/>
    </justification>
  </clause>

  <clause id="1702">
    <literal><![CDATA[
      (x * L(y,z,u)) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(654(a,1),1700(a,1,1))].">
      <j1 rule="para" parents="654 1700"/>
    </justification>
  </clause>

  <clause id="1703">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = (x / L(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(608,a,1702,a)].">
      <j1 rule="hyper" parents="608 1702"/>
    </justification>
  </clause>

  <clause id="1704">
    <literal><![CDATA[
      ((x / L(y,z,u)) * y) \ (x * y) = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(584,a,1702,a)].">
      <j1 rule="hyper" parents="584 1702"/>
    </justification>
  </clause>

  <clause id="1705">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = x / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(425,a,1702,a),flip(a)].">
      <j1 rule="hyper" parents="425 1702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1706">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) * y = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,148,a(flip),b,1702,a),flip(a)].">
      <j1 rule="hyper" parents="334 148 1702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1707">
    <literal><![CDATA[
      ((1 / L(x,y,z)) * x) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(207,a,1702,a),flip(a)].">
      <j1 rule="hyper" parents="207 1702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1708">
    <literal><![CDATA[
      (x * L(y,z,u)) \ ((x * y) * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,1702,a)].">
      <j1 rule="hyper" parents="123 1702"/>
    </justification>
  </clause>

  <clause id="1709">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) \ (x * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,148,a(flip),b,1702,a)].">
      <j1 rule="hyper" parents="116 148 1702"/>
    </justification>
  </clause>

  <clause id="1710">
    <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(1702(a,1),321(a,1,1))].">
      <j1 rule="para" parents="1702 321"/>
    </justification>
  </clause>

  <clause id="1711">
    <literal><![CDATA[
      (x / L(y,z,u)) / y = (x / y) / L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,153,a(flip),b,1703,a(flip))].">
      <j1 rule="hyper" parents="117 153 1703"/>
    </justification>
  </clause>

  <clause id="1712">
    <literal><![CDATA[
      (x * y) / L(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / L(y,z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(1704(a,1),345(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1704 345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1713">
    <literal><![CDATA[
      ((x * y) / z) * L(z,y,x) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,90,a(flip),b,1706,a),flip(a)].">
      <j1 rule="hyper" parents="117 90 1706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1714">
    <literal><![CDATA[
      R(T(x,y * L(x,z,u)),y,L(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1708(a,1),1137(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1708 1137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1715">
    <literal><![CDATA[
      ((x * (y * z)) / z) / L(z,y,x) = (x * y) / z
    ]]></literal>
    <justification jstring="[para(190(a,1),1711(a,1,1)),flip(a)].">
      <j1 rule="para" parents="190 1711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1716">
    <literal><![CDATA[
      L(x,y,z) \ ((z * (y * x)) / x) = T((z * y) / x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(451,a,xx,b,1713,a),flip(a)].">
      <j1 rule="hyper" parents="451 1713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1717">
    <literal><![CDATA[
      L(x,y,z) = ((z * y) / x) \ ((z * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(123,a,1713,a),flip(a)].">
      <j1 rule="hyper" parents="123 1713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1718">
    <literal><![CDATA[
      (x * L(y,z,u)) * T(y,x) = (y * x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,1714,a(flip),b,648,a)].">
      <j1 rule="hyper" parents="119 1714 648"/>
    </justification>
  </clause>

  <clause id="1719">
    <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(1715(a,1),431(a,1,1))].">
      <j1 rule="para" parents="1715 431"/>
    </justification>
  </clause>

  <clause id="1720">
    <literal><![CDATA[
      ((x * (y / z)) / z) \ ((x * y) / z) = L(z,y / z,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),1717(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 1717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1721">
    <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,1718,a)].">
      <j1 rule="hyper" parents="117 149 1718"/>
    </justification>
  </clause>

  <clause id="1722">
    <literal><![CDATA[
      (L((x / y) / z,u,w) * z) * y = (z * y) * L((z * y) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(334,a,653,a(flip),b,1105,a),flip(a)].">
      <j1 rule="hyper" parents="334 653 1105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1723">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(896,a,1106,a)].">
      <j1 rule="hyper" parents="896 1106"/>
    </justification>
  </clause>

  <clause id="1724">
    <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(1242(a,1),1129(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1242 1129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1725">
    <literal><![CDATA[
      x * (y * ((x * (y \ 1)) / x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(1218,a,1138,a),flip(a)].">
      <j1 rule="hyper" parents="1218 1138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1726">
    <literal><![CDATA[
      x \ T(x,x / (x * y)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(1216,a,1138,a)].">
      <j1 rule="hyper" parents="1216 1138"/>
    </justification>
  </clause>

  <clause id="1727">
    <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),1138(a,1,1))].">
      <j1 rule="para" parents="90 1138"/>
    </justification>
  </clause>

  <clause id="1728">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(1586(a,1),1725(a,1,2))].">
      <j1 rule="para" parents="1586 1725"/>
    </justification>
  </clause>

  <clause id="1729">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) / (y \ 1) = T(y,y / (y * x))
    ]]></literal>
    <justification jstring="[hyper(117,a,1726,a(flip),b,1033,a)].">
      <j1 rule="hyper" parents="117 1726 1033"/>
    </justification>
  </clause>

  <clause id="1730">
    <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(1274(a,1),1729(a,1,1,2,1))].">
      <j1 rule="para" parents="1274 1729"/>
    </justification>
  </clause>

  <clause id="1731">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = (((z * (1 / x)) / z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(1020,a,1139,a)].">
      <j1 rule="hyper" parents="1020 1139"/>
    </justification>
  </clause>

  <clause id="1732">
    <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),1139(a,1,2))].">
      <j1 rule="para" parents="101 1139"/>
    </justification>
  </clause>

  <clause id="1733">
    <literal><![CDATA[
      (((x * y) / x) * (y \ 1)) * x = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(925,a,1206,a)].">
      <j1 rule="hyper" parents="925 1206"/>
    </justification>
  </clause>

  <clause id="1734">
    <literal><![CDATA[
      (x \ ((y * x) / y)) * y = T(y,R(x,x \ 1,y))
    ]]></literal>
    <justification jstring="[para(1358(a,1),1733(a,1,1))].">
      <j1 rule="para" parents="1358 1733"/>
    </justification>
  </clause>

  <clause id="1735">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) / x = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(130,a,1734,a)].">
      <j1 rule="hyper" parents="130 1734"/>
    </justification>
  </clause>

  <clause id="1736">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) = (T(y,x) \ y) * x
    ]]></literal>
    <justification jstring="[para(231(a,1),1734(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="231 1734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1737">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      y \ ((x * y) / x) = z
    ]]></literal>
    <justification jstring="[para(1734(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1734 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1738">
    <literal><![CDATA[
      (1 / x) \ ((y * (1 / x)) / y) = T(y,R(1 / x,x,y)) / y
    ]]></literal>
    <justification jstring="[para(75(a,1),1735(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 1735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1739">
    <literal><![CDATA[
      T(1 / x,T(x,R(y,y \ 1,x))) = L(x \ 1,x,y \ ((x * y) / x))
    ]]></literal>
    <justification jstring="[para(1735(a,1),1056(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1735 1056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1740">
    <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(1736(a,1),1169(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1736 1169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1741">
    <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(1736(a,1),1545(a,1,1,2,1))].">
      <j1 rule="para" parents="1736 1545"/>
    </justification>
  </clause>

  <clause id="1742">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) / x = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1572,a(flip),b,1738,a),flip(a)].">
      <j1 rule="hyper" parents="58 1572 1738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1743">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * y = T(y,R(1 / x,x,y))
    ]]></literal>
    <justification jstring="[hyper(133,a,1742,a)].">
      <j1 rule="hyper" parents="133 1742"/>
    </justification>
  </clause>

  <clause id="1744">
    <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(1163(a,1),1743(a,1,1,2,1))].">
      <j1 rule="para" parents="1163 1743"/>
    </justification>
  </clause>

  <clause id="1745">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) = (x \ T(x,x / (x * y))) * x
    ]]></literal>
    <justification jstring="[para(1726(a,2),1743(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1726 1743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1746">
    <literal><![CDATA[
      T(T(x,x * y) * y,R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(571(a,1),1210(a,1,1))].">
      <j1 rule="para" parents="571 1210"/>
    </justification>
  </clause>

  <clause id="1747">
    <literal><![CDATA[
      T(T(T(x,x * y) * y,z),R(x,y,y \ 1)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(1746(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1746 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1748">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,R(x / y,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(907(a,1),1747(a,1,1)),flip(a)].">
      <j1 rule="para" parents="907 1747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1749">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(536(a,1),1748(a,2,2))].">
      <j1 rule="para" parents="536 1748"/>
    </justification>
  </clause>

  <clause id="1750">
    <literal><![CDATA[
      T(x,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(7(a,1),1749(a,1,1))].">
      <j1 rule="para" parents="7 1749"/>
    </justification>
  </clause>

  <clause id="1751">
    <literal><![CDATA[
      T(x,x * (y \ 1)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),1750(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1752">
    <literal><![CDATA[
      T(x,(1 / y) \ x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[para(75(a,1),1751(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 1751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1753">
    <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(1270(a,1),434(a,1))].">
      <j1 rule="para" parents="1270 434"/>
    </justification>
  </clause>

  <clause id="1754">
    <literal><![CDATA[
      x \ R(x * (y * (x \ 1)),z,u) = R(y,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,245,a(flip),b,1273,a),flip(a)].">
      <j1 rule="hyper" parents="334 245 1273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1755">
    <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(1163(a,1),1754(a,1,2,1,2))].">
      <j1 rule="para" parents="1163 1754"/>
    </justification>
  </clause>

  <clause id="1756">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ y,z,u) = L(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[para(75(a,1),1303(a,1,2)),flip(a)].">
      <j1 rule="para" parents="75 1303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1757">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ 1,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(2(a,1),1756(a,2,1,1))].">
      <j1 rule="para" parents="2 1756"/>
    </justification>
  </clause>

  <clause id="1758">
    <literal><![CDATA[
      L((x \ 1) \ (x \ y),z,u) = (x \ 1) \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),1360(a,1,1,2,1))].">
      <j1 rule="para" parents="72 1360"/>
    </justification>
  </clause>

  <clause id="1760">
    <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),1362(a,2,2,1,2))].">
      <j1 rule="para" parents="5 1362"/>
    </justification>
  </clause>

  <clause id="1761">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ 1,z,u) = x \ (y * R(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(3(a,1),1387(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3 1387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1762">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ 1,z,u) = x \ (y * L(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) \ (x \ z),u,w) = x \ (y * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),1388(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5 1388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1764">
    <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),1762(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13 1762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1765">
    <literal><![CDATA[
      (R(1 / (x / y),z,u) * (x / y)) * y = R(y / x,z,u) * x
    ]]></literal>
    <justification jstring="[para(2(a,1),1389(a,2,1,1,1))].">
      <j1 rule="para" parents="2 1389"/>
    </justification>
  </clause>

  <clause id="1766">
    <literal><![CDATA[
      (R(1 / (x / y),z,u) * (x / y)) * y = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,657,a(flip),b,1765,a),flip(a)].">
      <j1 rule="hyper" parents="334 657 1765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1767">
    <literal><![CDATA[
      ((x / y) * R((x / y) \ 1,z,u)) * y = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(657(a,1),1766(a,1,1))].">
      <j1 rule="para" parents="657 1766"/>
    </justification>
  </clause>

  <clause id="1768">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,z,u) = (x * R(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(130,a,1767,a),flip(a)].">
      <j1 rule="hyper" parents="130 1767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1769">
    <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),1768(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15 1768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1770">
    <literal><![CDATA[
      (x / y) \ (x * ((z * (x \ (x / y))) / z)) = y * ((z * (y \ 1)) / z)
    ]]></literal>
    <justification jstring="[hyper(123,a,1397,a)].">
      <j1 rule="hyper" parents="123 1397"/>
    </justification>
  </clause>

  <clause id="1771">
    <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(334,a,357,a(flip),b,1420,a),flip(a)].">
      <j1 rule="hyper" parents="334 357 1420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1772">
    <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),1427(a,1,1))].">
      <j1 rule="para" parents="13 1427"/>
    </justification>
  </clause>

  <clause id="1773">
    <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,1772,a)].">
      <j1 rule="hyper" parents="123 1772"/>
    </justification>
  </clause>

  <clause id="1774">
    <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(1772(a,1),491(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1772 491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1775">
    <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(1773(a,1),1003(a,1,3))].">
      <j1 rule="para" parents="1773 1003"/>
    </justification>
  </clause>

  <clause id="1776">
    <literal><![CDATA[
      (x \ (y / (1 / x))) * x = T(y,x) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,1437,a(flip),b,1448,a),flip(a)].">
      <j1 rule="hyper" parents="117 1437 1448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1777">
    <literal><![CDATA[
      ((x * (1 / (1 / T(y,x)))) / x) \ (y / T(y,x)) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[para(1465(a,1),1524(a,1,2))].">
      <j1 rule="para" parents="1465 1524"/>
    </justification>
  </clause>

  <clause id="1778">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,z) \ 1) = T(x,z) \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(72(a,1),1552(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 1552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1780">
    <literal><![CDATA[
      (x * (y * T(y \ 1,z))) * y = (x * y) * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(759(a,1),1615(a,1,1))].">
      <j1 rule="para" parents="759 1615"/>
    </justification>
  </clause>

  <clause id="1781">
    <literal><![CDATA[
      T(x,T(1 / x,y)) * T(x \ 1,y) = T(x * T(1 / x,y),x)
    ]]></literal>
    <justification jstring="[para(254(a,1),1688(a,1,2))].">
      <j1 rule="para" parents="254 1688"/>
    </justification>
  </clause>

  <clause id="1782">
    <literal><![CDATA[
      T(x,T(1 / x,y)) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,1623,a(flip),b,1781,a),flip(a)].">
      <j1 rule="hyper" parents="334 1623 1781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1783">
    <literal><![CDATA[
      R((x * y) / (x * z),u,w) * (x * z) = x * (R(y / z,u,w) * z)
    ]]></literal>
    <justification jstring="[para(657(a,2),1693(a,2,2))].">
      <j1 rule="para" parents="657 1693"/>
    </justification>
  </clause>

  <clause id="1784">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(653(a,1),1701(a,2,1))].">
      <j1 rule="para" parents="653 1701"/>
    </justification>
  </clause>

  <clause id="1785">
    <literal><![CDATA[
      (x * L(x \ (y / z),u,w)) * z = (x * z) * L((x * z) \ y,u,w)
    ]]></literal>
    <justification jstring="[para(653(a,1),1722(a,1,1))].">
      <j1 rule="para" parents="653 1722"/>
    </justification>
  </clause>

  <clause id="1786">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(657(a,1),1723(a,2,1))].">
      <j1 rule="para" parents="657 1723"/>
    </justification>
  </clause>

  <clause id="1787">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y
    ]]></literal>
    <justification jstring="[para(898(a,1),1731(a,2,1))].">
      <j1 rule="para" parents="898 1731"/>
    </justification>
  </clause>

  <clause id="1788">
    <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(1763(a,1),141(a,2,2))].">
      <j1 rule="para" parents="1763 141"/>
    </justification>
  </clause>

  <clause id="1789">
    <literal><![CDATA[
      (x / y) \ (x * ((x / y) / x)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[para(5(a,1),1770(a,1,2,2,1))].">
      <j1 rule="para" parents="5 1770"/>
    </justification>
  </clause>

  <clause id="1790">
    <literal><![CDATA[
      K(x,(x / y) / x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(479,a,1789,a)].">
      <j1 rule="hyper" parents="479 1789"/>
    </justification>
  </clause>

  <clause id="1791">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,(y / x) / y) = z
    ]]></literal>
    <justification jstring="[para(1789(a,1),479(a,1))].">
      <j1 rule="para" parents="1789 479"/>
    </justification>
  </clause>

  <clause id="1792">
    <literal><![CDATA[
      K(x,(x / (y \ 1)) / x) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(334,a,1523,a(flip),b,1790,a),flip(a)].">
      <j1 rule="hyper" parents="334 1523 1790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1793">
    <literal><![CDATA[
      x * K(x,(x / y) / x) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(119,a,1790,a,b,1726,a)].">
      <j1 rule="hyper" parents="119 1790 1726"/>
    </justification>
  </clause>

  <clause id="1794">
    <literal><![CDATA[
      (x \ y) * ((y * ((x \ y) \ 1)) / y) = K(y,x / y)
    ]]></literal>
    <justification jstring="[para(72(a,1),1790(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 1790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1795">
    <literal><![CDATA[
      x * ((T(x,y) * (x \ 1)) / T(x,y)) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(1051(a,1),1790(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1051 1790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1796">
    <literal><![CDATA[
      x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) = K(L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[para(1125(a,1),1790(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1125 1790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1797">
    <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(1254(a,1),1790(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1254 1790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1798">
    <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(1274(a,1),1792(a,2,2,1))].">
      <j1 rule="para" parents="1274 1792"/>
    </justification>
  </clause>

  <clause id="1799">
    <literal><![CDATA[
      T(x,x / (x * (y \ x))) = x * K(x,y / x)
    ]]></literal>
    <justification jstring="[para(72(a,1),1793(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="72 1793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1800">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) = x * K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(99(a,2),1799(a,1,2))].">
      <j1 rule="para" parents="99 1799"/>
    </justification>
  </clause>

  <clause id="1801">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),1800(a,2,2,2))].">
      <j1 rule="para" parents="6 1800"/>
    </justification>
  </clause>

  <clause id="1802">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) * (x \ z) = x \ ((x * K(x,y)) * z)
    ]]></literal>
    <justification jstring="[para(1801(a,1),1154(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1801 1154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1803">
    <literal><![CDATA[
      x \ ((x * K(x,y)) * z) = (x * K(x,y)) * (x \ z)
    ]]></literal>
    <justification jstring="[para(1801(a,1),1802(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1801 1802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1804">
    <literal><![CDATA[
      (x * K(x,y)) * (x \ 1) = x \ (x * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(304,a,1803,a),flip(a)].">
      <j1 rule="hyper" parents="304 1803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1805">
    <literal><![CDATA[
      (x * K(x,y)) * (x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,4,a(flip),b,1804,a),flip(a)].">
      <j1 rule="hyper" parents="334 4 1804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1806">
    <literal><![CDATA[
      K(x,y) / (x \ 1) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,4,a(flip),b,1804,a)].">
      <j1 rule="hyper" parents="117 4 1804"/>
    </justification>
  </clause>

  <clause id="1808">
    <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),1783(a,2,2,1,1))].">
      <j1 rule="para" parents="6 1783"/>
    </justification>
  </clause>

  <clause id="1809">
    <literal><![CDATA[
      x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1099,a(flip),b,1784,a)].">
      <j1 rule="hyper" parents="58 1099 1784"/>
    </justification>
  </clause>

  <clause id="1810">
    <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,951,a(flip),b,1784,a),flip(a)].">
      <j1 rule="hyper" parents="58 951 1784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1811">
    <literal><![CDATA[
      x * L(x \ (x \ (y * x)),z,u) = T(x * L(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(246,a,1784,a(flip),b,1099,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="246 1784 1099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1812">
    <literal><![CDATA[
      (x * y) * L((x * y) \ y,z,u) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(2(a,1),1784(a,1,2,1,2))].">
      <j1 rule="para" parents="2 1784"/>
    </justification>
  </clause>

  <clause id="1813">
    <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),1811(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 1811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1814">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,u),x) = L(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(791,a,1813,a)].">
      <j1 rule="hyper" parents="791 1813"/>
    </justification>
  </clause>

  <clause id="1815">
    <literal><![CDATA[
      T(x * L(x \ 1,y,z),x) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(204(a,1),1813(a,2,2,1,2))].">
      <j1 rule="para" parents="204 1813"/>
    </justification>
  </clause>

  <clause id="1816">
    <literal><![CDATA[
      T(x,x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,1815,a)].">
      <j1 rule="hyper" parents="49 1815"/>
    </justification>
  </clause>

  <clause id="1817">
    <literal><![CDATA[
      K(x,x * L(x \ 1,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,1816,a)].">
      <j1 rule="hyper" parents="50 1816"/>
    </justification>
  </clause>

  <clause id="1818">
    <literal><![CDATA[
      T(x \ y,(x \ y) * (y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[para(401(a,1),1816(a,1,2,2))].">
      <j1 rule="para" parents="401 1816"/>
    </justification>
  </clause>

  <clause id="1819">
    <literal><![CDATA[
      T(x \ 1,L(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(655(a,1),1816(a,1,2))].">
      <j1 rule="para" parents="655 1816"/>
    </justification>
  </clause>

  <clause id="1820">
    <literal><![CDATA[
      T(1 / x,L(x,y,z) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(1757(a,1),1816(a,1,2))].">
      <j1 rule="para" parents="1757 1816"/>
    </justification>
  </clause>

  <clause id="1821">
    <literal><![CDATA[
      T((x * (1 / y)) / x,L(y,z,u) / y) = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(1820(a,1),472(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1820 472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1822">
    <literal><![CDATA[
      T(x \ (x / y),(x \ (x / y)) * y) = x \ (x / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),1818(a,1,2,2))].">
      <j1 rule="para" parents="75 1818"/>
    </justification>
  </clause>

  <clause id="1823">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) * (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(1818(a,1),738(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1818 738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1824">
    <literal><![CDATA[
      R(x \ 1,L(x,y,z),x \ 1) = T(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1819(a,1),825(a,1,1))].">
      <j1 rule="para" parents="1819 825"/>
    </justification>
  </clause>

  <clause id="1825">
    <literal><![CDATA[
      T((x \ (x / y)) * y,x \ (x / y)) = (x \ (x / y)) * y
    ]]></literal>
    <justification jstring="[hyper(49,a,1822,a)].">
      <j1 rule="hyper" parents="49 1822"/>
    </justification>
  </clause>

  <clause id="1826">
    <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),1814(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1827">
    <literal><![CDATA[
      x \ T(x * L(y / x,z,u),x) = L(T(y,x) / x,z,u)
    ]]></literal>
    <justification jstring="[para(1440(a,1),1826(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1440 1826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1828">
    <literal><![CDATA[
      L(T(x * y,x) / x,z,u) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,1445,a(flip),b,1827,a),flip(a)].">
      <j1 rule="hyper" parents="58 1445 1827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1829">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) = L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,873,a,b,1823,a),flip(a)].">
      <j1 rule="hyper" parents="30 873 1823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1830">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (x \ y) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(1234,a,1829,a)].">
      <j1 rule="hyper" parents="1234 1829"/>
    </justification>
  </clause>

  <clause id="1831">
    <literal><![CDATA[
      x * L(x \ y,y \ x,x \ y) = y * ((y \ x) * (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(119,a,1829,a,b,91,a)].">
      <j1 rule="hyper" parents="119 1829 91"/>
    </justification>
  </clause>

  <clause id="1832">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,y \ x) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(434,a,1830,a)].">
      <j1 rule="hyper" parents="434 1830"/>
    </justification>
  </clause>

  <clause id="1833">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / (x \ (x * y))
    ]]></literal>
    <justification jstring="[para(4(a,1),1830(a,1,1,2))].">
      <j1 rule="para" parents="4 1830"/>
    </justification>
  </clause>

  <clause id="1834">
    <literal><![CDATA[
      L(((x * y) \ x) \ 1,(x * y) \ x,y) = 1 / ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1832(a,1,3))].">
      <j1 rule="para" parents="4 1832"/>
    </justification>
  </clause>

  <clause id="1835">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / y
    ]]></literal>
    <justification jstring="[para(4(a,1),1833(a,2,2))].">
      <j1 rule="para" parents="4 1833"/>
    </justification>
  </clause>

  <clause id="1836">
    <literal><![CDATA[
      L(x \ 1,x,(y * x) \ y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(434,a,1835,a)].">
      <j1 rule="hyper" parents="434 1835"/>
    </justification>
  </clause>

  <clause id="1837">
    <literal><![CDATA[
      ((x * y) \ x) / (1 / y) = ((x * y) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(201,a,1835,a)].">
      <j1 rule="hyper" parents="201 1835"/>
    </justification>
  </clause>

  <clause id="1838">
    <literal><![CDATA[
      (((x * y) \ x) * y) * (1 / y) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(134,a,1835,a)].">
      <j1 rule="hyper" parents="134 1835"/>
    </justification>
  </clause>

  <clause id="1839">
    <literal><![CDATA[
      L(x \ 1,x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[para(2(a,1),1836(a,1,3,1))].">
      <j1 rule="para" parents="2 1836"/>
    </justification>
  </clause>

  <clause id="1840">
    <literal><![CDATA[
      L(T(x \ 1,y),x,x \ 1) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(1839(a,1),20(a,2,1))].">
      <j1 rule="para" parents="1839 20"/>
    </justification>
  </clause>

  <clause id="1841">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,x \ 1) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1839(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1839 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1842">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[para(1839(a,1),407(a,1,2))].">
      <j1 rule="para" parents="1839 407"/>
    </justification>
  </clause>

  <clause id="1843">
    <literal><![CDATA[
      x * L(x \ (y \ x),y,y \ 1) = (y * (1 / y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(1839(a,1),1612(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1839 1612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1844">
    <literal><![CDATA[
      T(1 / (1 / x),x \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(1085,a,1842,a)].">
      <j1 rule="hyper" parents="1085 1842"/>
    </justification>
  </clause>

  <clause id="1845">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,266,a,b,1842,a),flip(a)].">
      <j1 rule="hyper" parents="334 266 1842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1846">
    <literal><![CDATA[
      T(T(1 / (1 / x),y),x \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1844(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1844 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1847">
    <literal><![CDATA[
      T(1 / (1 / (1 / x)),x) = 1 / x
    ]]></literal>
    <justification jstring="[para(75(a,1),1844(a,1,2))].">
      <j1 rule="para" parents="75 1844"/>
    </justification>
  </clause>

  <clause id="1848">
    <literal><![CDATA[
      T(x,y \ 1) != T(y,z)
    ]]></literal>
    <literal><![CDATA[
      T(1 / (1 / y),z) = x
    ]]></literal>
    <justification jstring="[para(1844(a,1),138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1844 138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1849">
    <literal><![CDATA[
      T(x,x \ 1) / x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1844(a,1),1240(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1844 1240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1850">
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1336,a,1845,a)].">
      <j1 rule="hyper" parents="1336 1845"/>
    </justification>
  </clause>

  <clause id="1851">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,1845,a)].">
      <j1 rule="hyper" parents="133 1845"/>
    </justification>
  </clause>

  <clause id="1852">
    <literal><![CDATA[
      x \ (1 / (1 / x)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1570,a(flip),b,1845,a)].">
      <j1 rule="hyper" parents="58 1570 1845"/>
    </justification>
  </clause>

  <clause id="1853">
    <literal><![CDATA[
      x * K(x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1845,a(flip),b,1570,a(flip))].">
      <j1 rule="hyper" parents="119 1845 1570"/>
    </justification>
  </clause>

  <clause id="1854">
    <literal><![CDATA[
      (1 / (1 / (1 / x))) * x = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1847,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1847 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1855">
    <literal><![CDATA[
      K(x,1 / x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1331,a,1849,a)].">
      <j1 rule="hyper" parents="1331 1849"/>
    </justification>
  </clause>

  <clause id="1856">
    <literal><![CDATA[
      K(x,x \ 1) * x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,1849,a)].">
      <j1 rule="hyper" parents="133 1849"/>
    </justification>
  </clause>

  <clause id="1857">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(106(a,1),1849(a,1,1))].">
      <j1 rule="para" parents="106 1849"/>
    </justification>
  </clause>

  <clause id="1858">
    <literal><![CDATA[
      K(x,x \ 1) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(398,a,1855,a),flip(a)].">
      <j1 rule="hyper" parents="398 1855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1859">
    <literal><![CDATA[
      K((x / y) \ x,1 / y) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,692,a,b,1855,a)].">
      <j1 rule="hyper" parents="58 692 1855"/>
    </justification>
  </clause>

  <clause id="1860">
    <literal><![CDATA[
      (x \ 1) * K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(119,a,1855,a(flip),b,1330,a)].">
      <j1 rule="hyper" parents="119 1855 1330"/>
    </justification>
  </clause>

  <clause id="1861">
    <literal><![CDATA[
      x \ K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(116,a,1855,a(flip),b,268,a(flip))].">
      <j1 rule="hyper" parents="116 1855 268"/>
    </justification>
  </clause>

  <clause id="1862">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),1855(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 1855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1863">
    <literal><![CDATA[
      K(x,x \ 1) \ 1 = K(1 / x,x)
    ]]></literal>
    <justification jstring="[para(1855(a,1),446(a,1,1))].">
      <j1 rule="para" parents="1855 446"/>
    </justification>
  </clause>

  <clause id="1864">
    <literal><![CDATA[
      K(x,x \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(1855(a,1),398(a,1))].">
      <j1 rule="para" parents="1855 398"/>
    </justification>
  </clause>

  <clause id="1865">
    <literal><![CDATA[
      (1 / (1 / x)) * K(x,x \ 1) = x
    ]]></literal>
    <justification jstring="[para(1855(a,1),904(a,1,2))].">
      <j1 rule="para" parents="1855 904"/>
    </justification>
  </clause>

  <clause id="1866">
    <literal><![CDATA[
      R(x \ 1,x,y) \ (((y / (x * y)) * x) * (1 / x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,1337,a,b,1858,a)].">
      <j1 rule="hyper" parents="334 1337 1858"/>
    </justification>
  </clause>

  <clause id="1867">
    <literal><![CDATA[
      L(x,y,z) * K(x,x \ 1) = x * (L(x,y,z) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(119,a,1858,a,b,1507,a)].">
      <j1 rule="hyper" parents="119 1858 1507"/>
    </justification>
  </clause>

  <clause id="1868">
    <literal><![CDATA[
      R(x,y,1 / y) * K(y,y \ 1) = (x * y) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1858,a,b,187,a)].">
      <j1 rule="hyper" parents="119 1858 187"/>
    </justification>
  </clause>

  <clause id="1869">
    <literal><![CDATA[
      K(x \ 1,x) \ 1 = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,445,a,b,1858,a)].">
      <j1 rule="hyper" parents="58 445 1858"/>
    </justification>
  </clause>

  <clause id="1870">
    <literal><![CDATA[
      T((x * y) \ (K(x,x \ 1) * y),x) = R(T(1 / x,x * y),x,y)
    ]]></literal>
    <justification jstring="[para(1858(a,2),1137(a,1,1,2,1))].">
      <j1 rule="para" parents="1858 1137"/>
    </justification>
  </clause>

  <clause id="1871">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ (1 / x)) = z
    ]]></literal>
    <justification jstring="[para(1858(a,2),1186(a,1,2))].">
      <j1 rule="para" parents="1858 1186"/>
    </justification>
  </clause>

  <clause id="1872">
    <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(1858(a,2),956(a,1,1))].">
      <j1 rule="para" parents="1858 956"/>
    </justification>
  </clause>

  <clause id="1873">
    <literal><![CDATA[
      x * (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(1861(a,1),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1861 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1874">
    <literal><![CDATA[
      T(x \ (K(y,y \ 1) * (y \ x)),y) = R(T(1 / y,x),y,y \ x)
    ]]></literal>
    <justification jstring="[para(1861(a,1),1025(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1861 1025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1875">
    <literal><![CDATA[
      T(1 / x,K(x \ 1,x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(803,a,1851,a)].">
      <j1 rule="hyper" parents="803 1851"/>
    </justification>
  </clause>

  <clause id="1876">
    <literal><![CDATA[
      (x \ 1) * L(y,1 / x,K(x \ 1,x)) = K(x \ 1,x) * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(1851(a,1),90(a,1,1))].">
      <j1 rule="para" parents="1851 90"/>
    </justification>
  </clause>

  <clause id="1877">
    <literal><![CDATA[
      x * (T(x,y) \ K(x \ 1,x)) = T(x,y) \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(1852(a,1),1162(a,1,2,2))].">
      <j1 rule="para" parents="1852 1162"/>
    </justification>
  </clause>

  <clause id="1878">
    <literal><![CDATA[
      K(x \ 1,x) * x = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1357,a,1853,a)].">
      <j1 rule="hyper" parents="1357 1853"/>
    </justification>
  </clause>

  <clause id="1879">
    <literal><![CDATA[
      L(x,x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(864,a,1853,a)].">
      <j1 rule="hyper" parents="864 1853"/>
    </justification>
  </clause>

  <clause id="1880">
    <literal><![CDATA[
      L(R(x,y,z),x \ 1,x) = R(1 / (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(1879(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1879 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1881">
    <literal><![CDATA[
      1 / (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      x * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(1879(a,1),865(a,1))].">
      <j1 rule="para" parents="1879 865"/>
    </justification>
  </clause>

  <clause id="1882">
    <literal><![CDATA[
      T(x,x \ 1) * L(y,x,K(x,x \ 1)) = K(x,x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(1856(a,1),90(a,1,1))].">
      <j1 rule="para" parents="1856 90"/>
    </justification>
  </clause>

  <clause id="1883">
    <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(1856(a,1),495(a,1,2,2))].">
      <j1 rule="para" parents="1856 495"/>
    </justification>
  </clause>

  <clause id="1884">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(1347,a,1860,a)].">
      <j1 rule="hyper" parents="1347 1860"/>
    </justification>
  </clause>

  <clause id="1885">
    <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,1865,a(flip),b,187,a)].">
      <j1 rule="hyper" parents="119 1865 187"/>
    </justification>
  </clause>

  <clause id="1886">
    <literal><![CDATA[
      R(x / (1 / (1 / y)),1 / (1 / y),K(y,y \ 1)) = (x * K(y,y \ 1)) / y
    ]]></literal>
    <justification jstring="[para(1865(a,1),102(a,2,2))].">
      <j1 rule="para" parents="1865 102"/>
    </justification>
  </clause>

  <clause id="1887">
    <literal><![CDATA[
      L(1 / x,y,z) * K(x \ 1,x) = K(x \ 1,x) * L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1875(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1875 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1888">
    <literal><![CDATA[
      (1 / (1 / x)) / (x * x) = R(x \ 1,x,x)
    ]]></literal>
    <justification jstring="[para(1878(a,1),373(a,1,1))].">
      <j1 rule="para" parents="1878 373"/>
    </justification>
  </clause>

  <clause id="1889">
    <literal><![CDATA[
      (1 / x) / L(y,(x \ 1) / y,K(x,x \ 1)) = K(x,x \ 1) * ((x \ 1) / y)
    ]]></literal>
    <justification jstring="[para(1884(a,1),556(a,1,1))].">
      <j1 rule="para" parents="1884 556"/>
    </justification>
  </clause>

  <clause id="1890">
    <literal><![CDATA[
      K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(268(a,2),1873(a,1))].">
      <j1 rule="para" parents="268 1873"/>
    </justification>
  </clause>

  <clause id="1891">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1890,a,1850,a)].">
      <j1 rule="hyper" parents="1890 1850"/>
    </justification>
  </clause>

  <clause id="1892">
    <literal><![CDATA[
      x / (1 / (1 / x)) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1239,a(flip),b,1854,a)].">
      <j1 rule="hyper" parents="58 1239 1854"/>
    </justification>
  </clause>

  <clause id="1893">
    <literal><![CDATA[
      L(x,1 / x,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(612,a,1892,a)].">
      <j1 rule="hyper" parents="612 1892"/>
    </justification>
  </clause>

  <clause id="1894">
    <literal><![CDATA[
      K(x,1 / x) * (1 / (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,1893,a(flip),b,560,a)].">
      <j1 rule="hyper" parents="119 1893 560"/>
    </justification>
  </clause>

  <clause id="1895">
    <literal><![CDATA[
      L(T(x,y),1 / x,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1893(a,1),20(a,2,1))].">
      <j1 rule="para" parents="1893 20"/>
    </justification>
  </clause>

  <clause id="1896">
    <literal><![CDATA[
      K(x,x \ 1) * (1 / (1 / x)) = x
    ]]></literal>
    <justification jstring="[para(1855(a,1),1894(a,1,1))].">
      <j1 rule="para" parents="1855 1894"/>
    </justification>
  </clause>

  <clause id="1897">
    <literal><![CDATA[
      K(x,x \ 1) \ x = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(123,a,1896,a)].">
      <j1 rule="hyper" parents="123 1896"/>
    </justification>
  </clause>

  <clause id="1898">
    <literal><![CDATA[
      K(1 / x,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(75(a,1),1891(a,1,2))].">
      <j1 rule="para" parents="75 1891"/>
    </justification>
  </clause>

  <clause id="1899">
    <literal><![CDATA[
      K(x,x \ 1) \ 1 = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1863,a,b,1898,a)].">
      <j1 rule="hyper" parents="58 1863 1898"/>
    </justification>
  </clause>

  <clause id="1900">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),1898(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 1898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1901">
    <literal><![CDATA[
      x \ ((x \ 1) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,801,a(flip),b,1900,a)].">
      <j1 rule="hyper" parents="58 801 1900"/>
    </justification>
  </clause>

  <clause id="1902">
    <literal><![CDATA[
      x * K(x,x \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,1900,a(flip),b,801,a(flip))].">
      <j1 rule="hyper" parents="119 1900 801"/>
    </justification>
  </clause>

  <clause id="1903">
    <literal><![CDATA[
      x \ ((x \ 1) \ 1) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(334,a,1855,a,b,1901,a),flip(a)].">
      <j1 rule="hyper" parents="334 1855 1901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1904">
    <literal><![CDATA[
      x * K(x,x \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,1901,a(flip),b,324,a)].">
      <j1 rule="hyper" parents="119 1901 324"/>
    </justification>
  </clause>

  <clause id="1905">
    <literal><![CDATA[
      x \ ((x \ 1) \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(1902(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1902 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1906">
    <literal><![CDATA[
      x \ (T(x,y) \ ((x \ 1) \ 1)) = T(x,y) \ K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,1903,a(flip),b,1155,a),flip(a)].">
      <j1 rule="hyper" parents="116 1903 1155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1907">
    <literal><![CDATA[
      T(x,x \ 1) * L(y,K(x,x \ 1),x) = x * (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(1904(a,1),90(a,1,1))].">
      <j1 rule="para" parents="1904 90"/>
    </justification>
  </clause>

  <clause id="1908">
    <literal><![CDATA[
      K(x \ 1,x) * T(1 / x,y) = (x \ 1) * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(1840(a,1),496(a,1,2))].">
      <j1 rule="para" parents="1840 496"/>
    </justification>
  </clause>

  <clause id="1909">
    <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(1888(a,1),653(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1888 653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1910">
    <literal><![CDATA[
      K(x,1 / x) * T(1 / (1 / x),y) = x * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1895,a(flip),b,1098,a)].">
      <j1 rule="hyper" parents="119 1895 1098"/>
    </justification>
  </clause>

  <clause id="1911">
    <literal><![CDATA[
      K(((x * y) \ x) \ (((x * y) \ x) * y),(x * y) \ x) * y = T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(1837(a,1),1070(a,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1837 1070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1912">
    <literal><![CDATA[
      (x * y) \ x = (L(y \ 1,y,x) * y) * (1 / y)
    ]]></literal>
    <justification jstring="[para(221(a,2),1838(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="221 1838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1913">
    <literal><![CDATA[
      K(x \ 1,x) * L(1 / x,y,z) = (x \ 1) * (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(1841(a,1),496(a,1,2))].">
      <j1 rule="para" parents="1841 496"/>
    </justification>
  </clause>

  <clause id="1914">
    <literal><![CDATA[
      L(x \ 1,x,y) / (1 / x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(640,a,1912,a)].">
      <j1 rule="hyper" parents="640 1912"/>
    </justification>
  </clause>

  <clause id="1915">
    <literal><![CDATA[
      x \ (T(x,y) \ ((x \ 1) \ 1)) = x * (T(x,y) \ (1 / x))
    ]]></literal>
    <justification jstring="[hyper(334,a,1183,a(flip),b,1906,a),flip(a)].">
      <j1 rule="hyper" parents="334 1183 1906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1916">
    <literal><![CDATA[
      K(x,x \ 1) * T(1 / (1 / x),y) = x * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(1855(a,1),1910(a,1,1))].">
      <j1 rule="para" parents="1855 1910"/>
    </justification>
  </clause>

  <clause id="1917">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ x,y) = x * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(1897(a,2),1916(a,1,2,1))].">
      <j1 rule="para" parents="1897 1916"/>
    </justification>
  </clause>

  <clause id="1918">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ x = 1 / ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(512,a,1834,a)].">
      <j1 rule="hyper" parents="512 1834"/>
    </justification>
  </clause>

  <clause id="1919">
    <literal><![CDATA[
      x * L(x \ (y \ x),y,y \ 1) = K(y,y \ 1) * (y \ x)
    ]]></literal>
    <justification jstring="[para(1858(a,2),1843(a,2,1))].">
      <j1 rule="para" parents="1858 1843"/>
    </justification>
  </clause>

  <clause id="1920">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1099,a(flip),b,1812,a)].">
      <j1 rule="hyper" parents="58 1099 1812"/>
    </justification>
  </clause>

  <clause id="1921">
    <literal><![CDATA[
      T(x * L(x \ 1,T(x,y),y),y) = T(x,y) * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(246,a,1812,a(flip),b,484,a(flip))].">
      <j1 rule="hyper" parents="246 1812 484"/>
    </justification>
  </clause>

  <clause id="1922">
    <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,1908,a(flip),b,650,a)].">
      <j1 rule="hyper" parents="119 1908 650"/>
    </justification>
  </clause>

  <clause id="1923">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * (K(x,x \ 1) \ 1) = T(x * (K(x,x \ 1) \ 1),y)
    ]]></literal>
    <justification jstring="[para(1917(a,1),1077(a,1,1))].">
      <j1 rule="para" parents="1917 1077"/>
    </justification>
  </clause>

  <clause id="1924">
    <literal><![CDATA[
      (x / y) * L((x / y) \ 1,z,u) = (x * L(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,1760,a(flip),b,1920,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="117 1760 1920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1925">
    <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),1920(a,1,2,2,1,2))].">
      <j1 rule="para" parents="4 1920"/>
    </justification>
  </clause>

  <clause id="1926">
    <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(1655(a,2),1920(a,1,2))].">
      <j1 rule="para" parents="1655 1920"/>
    </justification>
  </clause>

  <clause id="1927">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),x,x \ 1)) = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1839(a,1),1920(a,2,1,2))].">
      <j1 rule="para" parents="1839 1920"/>
    </justification>
  </clause>

  <clause id="1928">
    <literal><![CDATA[
      x * (K(x,x \ 1) * (x \ y)) = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1919(a,1),1927(a,1,2))].">
      <j1 rule="para" parents="1919 1927"/>
    </justification>
  </clause>

  <clause id="1929">
    <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,1928,a),flip(a)].">
      <j1 rule="hyper" parents="29 90 1928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1930">
    <literal><![CDATA[
      x * (K(x,x \ 1) * (x \ y)) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1858(a,2),1928(a,2,1))].">
      <j1 rule="para" parents="1858 1928"/>
    </justification>
  </clause>

  <clause id="1931">
    <literal><![CDATA[
      x \ (K(x,x \ 1) * y) = K(x,x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(123,a,1930,a)].">
      <j1 rule="hyper" parents="123 1930"/>
    </justification>
  </clause>

  <clause id="1932">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = x * (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1930(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 1930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1933">
    <literal><![CDATA[
      x * (K(x,x \ 1) * T(y,x)) = K(x,x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(17(a,2),1930(a,1,2,2))].">
      <j1 rule="para" parents="17 1930"/>
    </justification>
  </clause>

  <clause id="1934">
    <literal><![CDATA[
      K(x,x \ 1) * y != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * (x \ y) = z
    ]]></literal>
    <justification jstring="[para(1930(a,1),38(a,1))].">
      <j1 rule="para" parents="1930 38"/>
    </justification>
  </clause>

  <clause id="1935">
    <literal><![CDATA[
      (1 / x) * (K(x \ 1,x) * ((1 / x) \ y)) = K(1 / x,(1 / x) \ 1) * y
    ]]></literal>
    <justification jstring="[para(1891(a,1),1930(a,1,2,1))].">
      <j1 rule="para" parents="1891 1930"/>
    </justification>
  </clause>

  <clause id="1936">
    <literal><![CDATA[
      K(x,x \ 1) * y != (1 / x) * z
    ]]></literal>
    <literal><![CDATA[
      x \ L(z,1 / x,x) = y
    ]]></literal>
    <justification jstring="[para(1929(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="1929 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1937">
    <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),1924(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15 1924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1938">
    <literal><![CDATA[
      T((x * y) \ (K(x,x \ 1) * y),x) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(334,a,761,a(flip),b,1870,a),flip(a)].">
      <j1 rule="hyper" parents="334 761 1870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1939">
    <literal><![CDATA[
      T(x \ (K(y,y \ 1) * (y \ x)),y) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,981,a(flip),b,1874,a),flip(a)].">
      <j1 rule="hyper" parents="334 981 1874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1940">
    <literal><![CDATA[
      T(x,x \ 1) * L(y,x,K(x,x \ 1)) = x * (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,1932,a(flip),b,1882,a),flip(a)].">
      <j1 rule="hyper" parents="334 1932 1882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1941">
    <literal><![CDATA[
      L(x,K(y,y \ 1),y) = L(x,y,K(y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(29,a,1907,a,b,1940,a)].">
      <j1 rule="hyper" parents="29 1907 1940"/>
    </justification>
  </clause>

  <clause id="1942">
    <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(1940(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="1940 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1943">
    <literal><![CDATA[
      L(x,1 / y,K(1 / y,(1 / y) \ 1)) = L(x,K(y \ 1,y),1 / y)
    ]]></literal>
    <justification jstring="[para(1891(a,1),1941(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1891 1941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1944">
    <literal><![CDATA[
      (x * L(x \ (y / z),u,w)) * z = x * (z * L(z \ (x \ y),u,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,1099,a(flip),b,1785,a),flip(a)].">
      <j1 rule="hyper" parents="334 1099 1785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1945">
    <literal><![CDATA[
      x * (y * R(y \ (x \ (z * y)),u,w)) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1101,a(flip),b,1786,a)].">
      <j1 rule="hyper" parents="58 1101 1786"/>
    </justification>
  </clause>

  <clause id="1946">
    <literal><![CDATA[
      (x \ (y * x)) * R((x \ (y * x)) \ x,z,u) = T(y * R(y \ x,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(246,a,1786,a(flip),b,1386,a),flip(a)].">
      <j1 rule="hyper" parents="246 1786 1386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1947">
    <literal><![CDATA[
      x * R(x \ (x \ (y * x)),z,u) = T(x * R(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(246,a,1786,a(flip),b,1101,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="246 1786 1101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1948">
    <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,1786,a(flip),b,1386,a),flip(a)].">
      <j1 rule="hyper" parents="116 1786 1386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1949">
    <literal><![CDATA[
      x \ ((x * R(x \ y,z,u)) * w) = w * R(w \ (x \ (y * w)),z,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,1786,a(flip),b,1101,a(flip))].">
      <j1 rule="hyper" parents="116 1786 1101"/>
    </justification>
  </clause>

  <clause id="1950">
    <literal><![CDATA[
      (x * R(x \ (x * y),z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),1786(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1951">
    <literal><![CDATA[
      (x * R(y,z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),1950(a,1,1,2,1))].">
      <j1 rule="para" parents="4 1950"/>
    </justification>
  </clause>

  <clause id="1952">
    <literal><![CDATA[
      ((x / R(y,z,u)) * y) \ (x * y) = R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(584,a,1951,a)].">
      <j1 rule="hyper" parents="584 1951"/>
    </justification>
  </clause>

  <clause id="1953">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = x / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(425,a,1951,a),flip(a)].">
      <j1 rule="hyper" parents="425 1951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1954">
    <literal><![CDATA[
      ((x / R(y,z,u)) * y) * R(y,z,u) = x * y
    ]]></literal>
    <justification jstring="[hyper(341,a,1951,a),flip(a)].">
      <j1 rule="hyper" parents="341 1951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1955">
    <literal><![CDATA[
      (x * R(y,z,u)) \ ((x * y) * R(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,1951,a)].">
      <j1 rule="hyper" parents="123 1951"/>
    </justification>
  </clause>

  <clause id="1956">
    <literal><![CDATA[
      (x * R(y,z,u)) / y = (x / y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,148,a(flip),b,1951,a)].">
      <j1 rule="hyper" parents="117 148 1951"/>
    </justification>
  </clause>

  <clause id="1957">
    <literal><![CDATA[
      ((x / y) * R(y,z,u)) \ (x * R(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,148,a(flip),b,1951,a)].">
      <j1 rule="hyper" parents="116 148 1951"/>
    </justification>
  </clause>

  <clause id="1958">
    <literal><![CDATA[
      (x / R(x,y,z)) / x = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,1953,a)].">
      <j1 rule="hyper" parents="130 1953"/>
    </justification>
  </clause>

  <clause id="1959">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x != u
    ]]></literal>
    <literal><![CDATA[
      x / R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1958(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1958 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1960">
    <literal><![CDATA[
      (x * y) / R(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / R(y,z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(1952(a,1),345(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1952 345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1961">
    <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(1954(a,1),822(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1954 822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1962">
    <literal><![CDATA[
      T(R(x,y,R(x,z,u)),y * R(x,z,u)) = T(x,y)
    ]]></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[
      (x * R(y / x,z,u)) \ (y * R(y / x,z,u)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,541,a(flip),b,1962,a)].">
      <j1 rule="hyper" parents="58 541 1962"/>
    </justification>
  </clause>

  <clause id="1964">
    <literal><![CDATA[
      (x * R(y,z,u)) * T(y,x) = (y * x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,1962,a(flip),b,253,a)].">
      <j1 rule="hyper" parents="119 1962 253"/>
    </justification>
  </clause>

  <clause id="1965">
    <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(1962(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="1962 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1966">
    <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,1964,a)].">
      <j1 rule="hyper" parents="117 64 1964"/>
    </justification>
  </clause>

  <clause id="1967">
    <literal><![CDATA[
      R(x,y,z) / ((x \ 1) \ 1) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(693,a,1966,a)].">
      <j1 rule="hyper" parents="693 1966"/>
    </justification>
  </clause>

  <clause id="1968">
    <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),1947(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 1947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1969">
    <literal><![CDATA[
      x \ T(x * R(x \ y,z,u),x) = R(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(791,a,1968,a)].">
      <j1 rule="hyper" parents="791 1968"/>
    </justification>
  </clause>

  <clause id="1970">
    <literal><![CDATA[
      T(x * R(x \ y,z,u),x) / x = R(T(y,x) / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,1968,a,b,657,a)].">
      <j1 rule="hyper" parents="117 1968 657"/>
    </justification>
  </clause>

  <clause id="1971">
    <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),1970(a,1,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1972">
    <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),1961(a,2,1))].">
      <j1 rule="para" parents="2 1961"/>
    </justification>
  </clause>

  <clause id="1973">
    <literal><![CDATA[
      (x * R(y / x,z,u)) \ (y * R(y / x,z,u)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(334,a,107,a(flip),b,1963,a),flip(a)].">
      <j1 rule="hyper" parents="334 107 1963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1974">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * x = x * (x * ((y * (x \ 1)) / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1138,a(flip),b,1787,a),flip(a)].">
      <j1 rule="hyper" parents="58 1138 1787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1975">
    <literal><![CDATA[
      (x * (((x * y) * (x \ 1)) / (x * y))) * y = (x * y) * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(5(a,1),1787(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1976">
    <literal><![CDATA[
      (1 / x) * ((1 / x) * ((y * ((1 / x) \ 1)) / y)) = (((y * x) / y) / x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(1578(a,1),1974(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1578 1974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1977">
    <literal><![CDATA[
      R(T(x,y),z,u) * (x * w) = x * (R(T(x,y),z,u) * w)
    ]]></literal>
    <justification jstring="[para(1160(a,1),1808(a,1,1,1))].">
      <j1 rule="para" parents="1160 1808"/>
    </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="[hyper(116,a,151,a(flip),b,1977,a)].">
      <j1 rule="hyper" parents="116 151 1977"/>
    </justification>
  </clause>

  <clause id="1979">
    <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,1887,a,b,1913,a)].">
      <j1 rule="hyper" parents="58 1887 1913"/>
    </justification>
  </clause>

  <clause id="1980">
    <literal><![CDATA[
      (x / y) * L((x / y) \ (z / y),u,w) = (x * L(x \ z,u,w)) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,1760,a(flip),b,1944,a),flip(a)].">
      <j1 rule="hyper" parents="117 1760 1944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1981">
    <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(187(a,1),1945(a,1,2,2,1,2))].">
      <j1 rule="para" parents="187 1945"/>
    </justification>
  </clause>

  <clause id="1982">
    <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(1949(a,1),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1949 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1983">
    <literal><![CDATA[
      (x * L(x \ (y * x),z,u)) / y = (x / y) * L(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(845(a,2),1980(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="845 1980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1984">
    <literal><![CDATA[
      (x / y) * L(T(y,x),z,u) = (L(y,z,u) * x) / y
    ]]></literal>
    <justification jstring="[para(651(a,1),1983(a,1,1)),flip(a)].">
      <j1 rule="para" parents="651 1983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1985">
    <literal><![CDATA[
      (L(x,y,z) * (u * x)) / x = u * L(T(x,u * x),y,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),1984(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 1984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1986">
    <literal><![CDATA[
      T(x * L(T(y,x * y),z,u),y) = y \ (L(y,z,u) * (x * y))
    ]]></literal>
    <justification jstring="[para(1985(a,1),107(a,1,1))].">
      <j1 rule="para" parents="1985 107"/>
    </justification>
  </clause>

  <clause id="1987">
    <literal><![CDATA[
      T(x * L(T(y,x * y),z,u),y) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,1518,a(flip),b,1986,a),flip(a)].">
      <j1 rule="hyper" parents="334 1518 1986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1988">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,9,a,b,513,a)].">
      <j1 rule="hyper" parents="334 9 513"/>
    </justification>
  </clause>

  <clause id="1989">
    <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(513(a,1),412(a,1,1)),flip(a)].">
      <j1 rule="para" parents="513 412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1990">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(x,y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(724,a,1988,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="724 1988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1991">
    <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),1988(a,2,2))].">
      <j1 rule="para" parents="13 1988"/>
    </justification>
  </clause>

  <clause id="1992">
    <literal><![CDATA[
      L(K(x,y),z,u) * a(u,z,K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,1990,a)].">
      <j1 rule="hyper" parents="134 1990"/>
    </justification>
  </clause>

  <clause id="1993">
    <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(1990(a,1),355(a,2,2))].">
      <j1 rule="para" parents="1990 355"/>
    </justification>
  </clause>

  <clause id="1994">
    <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(1991(a,2),814(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1991 814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1995">
    <literal><![CDATA[
      K(x,(y \ z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,y \ z)) = u
    ]]></literal>
    <justification jstring="[para(683(a,1),680(a,1))].">
      <j1 rule="para" parents="683 680"/>
    </justification>
  </clause>

  <clause id="1996">
    <literal><![CDATA[
      K(x,T(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ z) \ z) = u
    ]]></literal>
    <justification jstring="[para(679(a,1),684(a,1))].">
      <j1 rule="para" parents="679 684"/>
    </justification>
  </clause>

  <clause id="1997">
    <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,1292,a(flip),b,802,a)].">
      <j1 rule="hyper" parents="58 1292 802"/>
    </justification>
  </clause>

  <clause id="1998">
    <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(265(a,1),1460(a,1,1))].">
      <j1 rule="para" parents="265 1460"/>
    </justification>
  </clause>

  <clause id="1999">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) / R(x,y,z) = x * T(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1880(a,1),1998(a,1,1))].">
      <j1 rule="para" parents="1880 1998"/>
    </justification>
  </clause>

  <clause id="2000">
    <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(956(a,1),1658(a,1))].">
      <j1 rule="para" parents="956 1658"/>
    </justification>
  </clause>

  <clause id="2001">
    <literal><![CDATA[
      x \ (((T(y,x) \ y) * x) \ x) = ((T(y,x) \ y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(1736(a,1),1740(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1736 1740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2002">
    <literal><![CDATA[
      (T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,(1 * x) / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(542(a,1),1744(a,2,2))].">
      <j1 rule="para" parents="542 1744"/>
    </justification>
  </clause>

  <clause id="2003">
    <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),2002(a,2,2,1))].">
      <j1 rule="para" parents="2 2002"/>
    </justification>
  </clause>

  <clause id="2004">
    <literal><![CDATA[
      (T(x,T(x,y) \ 1) / x) * x = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(1635(a,1),2003(a,1,1))].">
      <j1 rule="para" parents="1635 2003"/>
    </justification>
  </clause>

  <clause id="2005">
    <literal><![CDATA[
      T(x,x / (x * T(x,y))) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(260,a,2004,a),flip(a)].">
      <j1 rule="hyper" parents="260 2004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2007">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,1728,a,b,2005,a)].">
      <j1 rule="hyper" parents="58 1728 2005"/>
    </justification>
  </clause>

  <clause id="2008">
    <literal><![CDATA[
      x * (T(x,y) * ((T(x,y) \ x) / x)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(1635(a,2),2007(a,1,2))].">
      <j1 rule="para" parents="1635 2007"/>
    </justification>
  </clause>

  <clause id="2009">
    <literal><![CDATA[
      L(x \ L(y,1 / x,K(x \ 1,x)),x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(1144,a,1876,a(flip))].">
      <j1 rule="hyper" parents="1144 1876"/>
    </justification>
  </clause>

  <clause id="2010">
    <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(496(a,1),1997(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="496 1997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2011">
    <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),2000(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="5 2000"/>
    </justification>
  </clause>

  <clause id="2012">
    <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(842(a,1),1208(a,1,2,1))].">
      <j1 rule="para" parents="842 1208"/>
    </justification>
  </clause>

  <clause id="2013">
    <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,2012,a)].">
      <j1 rule="hyper" parents="134 2012"/>
    </justification>
  </clause>

  <clause id="2014">
    <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,1526,a(flip),b,2013,a),flip(a)].">
      <j1 rule="hyper" parents="58 1526 2013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2015">
    <literal><![CDATA[
      (1 / x) \ L((y * x) \ y,z,u) = L((y * x) \ y,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(954,a,1252,a),flip(a)].">
      <j1 rule="hyper" parents="954 1252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2016">
    <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(1631(a,1),1280(a,1,1))].">
      <j1 rule="para" parents="1631 1280"/>
    </justification>
  </clause>

  <clause id="2017">
    <literal><![CDATA[
      L(x \ 1,R(x,y,z),1 / x) = (x \ R(x,y,z)) / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(888,a,2016,a)].">
      <j1 rule="hyper" parents="888 2016"/>
    </justification>
  </clause>

  <clause id="2018">
    <literal><![CDATA[
      ((x * ((y \ x) \ z)) / z) * (y \ z) = y \ (x * ((y \ x) \ z))
    ]]></literal>
    <justification jstring="[para(5(a,1),1384(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2020">
    <literal><![CDATA[
      x * ((x * y) * ((z * ((x * y) \ y)) / z)) = (x * ((z * (x \ 1)) / z)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1787,a(flip),b,1393,a),flip(a)].">
      <j1 rule="hyper" parents="58 1787 1393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2021">
    <literal><![CDATA[
      T(x * T(x \ ((y * z) / y),u),y) = T(x,y) * T(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(246,a,1598,a,b,1401,a(flip))].">
      <j1 rule="hyper" parents="246 1598 1401"/>
    </justification>
  </clause>

  <clause id="2022">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(x * T(x \ y,z),y)
    ]]></literal>
    <justification jstring="[hyper(246,a,1584,a(flip),b,1401,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="246 1584 1401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2023">
    <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),1401(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 1401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2024">
    <literal><![CDATA[
      x * L(y,T(y,x) \ y,T(y,x)) = (y * x) * T(K(x,y),y)
    ]]></literal>
    <justification jstring="[para(1192(a,1),2023(a,1,2))].">
      <j1 rule="para" parents="1192 2023"/>
    </justification>
  </clause>

  <clause id="2025">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ T(z,y),u) = T(x * T(x \ z,u),y)
    ]]></literal>
    <justification jstring="[para(231(a,1),2021(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="231 2021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2026">
    <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(1514(a,1),502(a,1,1))].">
      <j1 rule="para" parents="1514 502"/>
    </justification>
  </clause>

  <clause id="2027">
    <literal><![CDATA[
      T(x * ((x * R(x \ 1,y,z)) / x),x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(663(a,1),1633(a,2,2))].">
      <j1 rule="para" parents="663 1633"/>
    </justification>
  </clause>

  <clause id="2028">
    <literal><![CDATA[
      T(x * R(1 / x,y,z),x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(663(a,1),2027(a,1,1,2))].">
      <j1 rule="para" parents="663 2027"/>
    </justification>
  </clause>

  <clause id="2029">
    <literal><![CDATA[
      T(x * (y / (x * y)),x) = x * R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(223(a,1),2028(a,1,1,2))].">
      <j1 rule="para" parents="223 2028"/>
    </justification>
  </clause>

  <clause id="2030">
    <literal><![CDATA[
      T(x * (y / (x * y)),x) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(334,a,414,a(flip),b,2029,a),flip(a)].">
      <j1 rule="hyper" parents="334 414 2029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2031">
    <literal><![CDATA[
      T(x,x * (y / (x * y))) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,2030,a)].">
      <j1 rule="hyper" parents="49 2030"/>
    </justification>
  </clause>

  <clause id="2032">
    <literal><![CDATA[
      T(x / y,(x / y) * (y / x)) = x / y
    ]]></literal>
    <justification jstring="[para(7(a,1),2031(a,1,2,2,2))].">
      <j1 rule="para" parents="7 2031"/>
    </justification>
  </clause>

  <clause id="2033">
    <literal><![CDATA[
      T(x \ y,(y / x) * (x / y)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(2032(a,1),254(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2032 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2034">
    <literal><![CDATA[
      T(x \ y,(y / x) * (x / y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(334,a,107,a(flip),b,2033,a),flip(a)].">
      <j1 rule="hyper" parents="334 107 2033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2035">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = (y * (y \ x)) / x
    ]]></literal>
    <justification jstring="[para(2034(a,1),1651(a,2,1,2))].">
      <j1 rule="para" parents="2034 1651"/>
    </justification>
  </clause>

  <clause id="2036">
    <literal><![CDATA[
      K(x \ (x / ((y \ x) / T(x,y))),x) = x / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,154,a(flip),b,1653,a),flip(a)].">
      <j1 rule="hyper" parents="334 154 1653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2038">
    <literal><![CDATA[
      (x \ T(x * (y / z),z)) * z = (x \ 1) * ((z \ ((x \ 1) \ y)) * z)
    ]]></literal>
    <justification jstring="[para(105(a,1),1660(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 1660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2039">
    <literal><![CDATA[
      (x \ T(x * (y / y),z)) * y = (x \ 1) * ((x \ T(x,z)) * ((x \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(1297(a,2),1660(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1297 1660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2040">
    <literal><![CDATA[
      T((x \ (x * (y / x))) * x,x) = (x \ 1) * ((x \ ((x \ 1) \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(1439,a,2038,a)].">
      <j1 rule="hyper" parents="1439 2038"/>
    </justification>
  </clause>

  <clause id="2041">
    <literal><![CDATA[
      T(x,y) = (y \ 1) * ((y \ ((y \ 1) \ x)) * y)
    ]]></literal>
    <justification jstring="[para(76(a,1),2040(a,1,1))].">
      <j1 rule="para" parents="76 2040"/>
    </justification>
  </clause>

  <clause id="2042">
    <literal><![CDATA[
      (x \ ((x \ 1) \ y)) * x = (x \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(791,a,2041,a),flip(a)].">
      <j1 rule="hyper" parents="791 2041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2043">
    <literal><![CDATA[
      (x \ 1) * ((x \ y) * x) = T((x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2041(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4 2041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2044">
    <literal><![CDATA[
      T((x \ 1) * (x * y),x) = (x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(62(a,1),2041(a,2,2,1))].">
      <j1 rule="para" parents="62 2041"/>
    </justification>
  </clause>

  <clause id="2045">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = L(K(x \ y,x),y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,2043,a(flip),b,499,a)].">
      <j1 rule="hyper" parents="116 2043 499"/>
    </justification>
  </clause>

  <clause id="2046">
    <literal><![CDATA[
      T(((x / y) \ 1) * x,x / y) = ((x / y) \ 1) * (y * (x / y))
    ]]></literal>
    <justification jstring="[para(75(a,1),2043(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 2043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2047">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * (K(y \ x,y) * x)
    ]]></literal>
    <justification jstring="[para(85(a,1),2043(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="85 2043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2048">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * x = x * ((x \ 1) * (y * x))
    ]]></literal>
    <justification jstring="[hyper(119,a,2044,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 2044 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2049">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * x = L(y * x,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,265,a(flip),b,2048,a),flip(a)].">
      <j1 rule="hyper" parents="334 265 2048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2050">
    <literal><![CDATA[
      x * ((x \ y) * ((z * ((x \ y) \ 1)) / z)) = y * ((z * (y \ x)) / z)
    ]]></literal>
    <justification jstring="[para(3(a,1),1676(a,2,2,1,2,2))].">
      <j1 rule="para" parents="3 1676"/>
    </justification>
  </clause>

  <clause id="2051">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ 1)) / z) = x \ (y * ((z * (y \ x)) / z))
    ]]></literal>
    <justification jstring="[hyper(123,a,2050,a),flip(a)].">
      <j1 rule="hyper" parents="123 2050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2052">
    <literal><![CDATA[
      x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[para(1790(a,2),2050(a,1,2))].">
      <j1 rule="para" parents="1790 2050"/>
    </justification>
  </clause>

  <clause id="2053">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = y * K(z,(z / T(x,y)) / z)
    ]]></literal>
    <justification jstring="[para(17(a,2),2052(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 2052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2054">
    <literal><![CDATA[
      T(x * ((y * (x \ 1)) / y),z) = K(y,(y / T(x,z)) / y)
    ]]></literal>
    <justification jstring="[hyper(246,a,1787,a(flip),b,2053,a(flip))].">
      <j1 rule="hyper" parents="246 1787 2053"/>
    </justification>
  </clause>

  <clause id="2055">
    <literal><![CDATA[
      T(x,y) * ((z * (T(x,y) \ 1)) / z) = T(x * ((z * (x \ 1)) / z),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,1790,a(flip),b,2054,a)].">
      <j1 rule="hyper" parents="334 1790 2054"/>
    </justification>
  </clause>

  <clause id="2056">
    <literal><![CDATA[
      K(x,(x / T(y \ x,z)) / x) = T(K(x,y / x),z)
    ]]></literal>
    <justification jstring="[para(1794(a,1),2054(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1794 2054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2057">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,(x / (y \ x)) / x)
    ]]></literal>
    <justification jstring="[para(1418(a,1),2056(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1418 2056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2058">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(72(a,1),2057(a,2,2,1))].">
      <j1 rule="para" parents="72 2057"/>
    </justification>
  </clause>

  <clause id="2060">
    <literal><![CDATA[
      T(K(x,y),K((y * x) / x,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(6(a,1),2058(a,1,1,2))].">
      <j1 rule="para" parents="6 2058"/>
    </justification>
  </clause>

  <clause id="2061">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(6(a,1),2060(a,1,2,1))].">
      <j1 rule="para" parents="6 2060"/>
    </justification>
  </clause>

  <clause id="2062">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),2061(a,2,2))].">
      <j1 rule="para" parents="6 2061"/>
    </justification>
  </clause>

  <clause id="2063">
    <literal><![CDATA[
      K(K(x,y),K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,2062,a)].">
      <j1 rule="hyper" parents="50 2062"/>
    </justification>
  </clause>

  <clause id="2064">
    <literal><![CDATA[
      T(K(x,y),K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,2062,a)].">
      <j1 rule="hyper" parents="49 2062"/>
    </justification>
  </clause>

  <clause id="2065">
    <literal><![CDATA[
      K(x,y) * K(z,x) = K(z,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,2062,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2062 17"/>
    </justification>
  </clause>

  <clause id="2066">
    <literal><![CDATA[
      T(x,K(y,z)) != K(u,y)
    ]]></literal>
    <literal><![CDATA[
      K(u,y) = x
    ]]></literal>
    <justification jstring="[para(2062(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2062 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2067">
    <literal><![CDATA[
      K(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2062(a,1),294(a,1,2))].">
      <j1 rule="para" parents="2062 294"/>
    </justification>
  </clause>

  <clause id="2068">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,w) = K(y,w) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2062(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2062 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2069">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(y,w) = K(y,w) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2062(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2062 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2070">
    <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(2062(a,1),593(a,2,2))].">
      <j1 rule="para" parents="2062 593"/>
    </justification>
  </clause>

  <clause id="2071">
    <literal><![CDATA[
      T((x * y) \ (y * x),K(z,y)) = K(y,x)
    ]]></literal>
    <justification jstring="[para(11(a,1),2064(a,1,1))].">
      <j1 rule="para" parents="11 2064"/>
    </justification>
  </clause>

  <clause id="2072">
    <literal><![CDATA[
      T(x,K(y,z)) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = x
    ]]></literal>
    <justification jstring="[para(2064(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2064 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2073">
    <literal><![CDATA[
      K(x,y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2064(a,1),294(a,1,2))].">
      <j1 rule="para" parents="2064 294"/>
    </justification>
  </clause>

  <clause id="2074">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(w,x) = K(w,x) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2064(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2064 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2075">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(w,x) = K(w,x) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2064(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2064 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2076">
    <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(2064(a,1),593(a,2,2))].">
      <j1 rule="para" parents="2064 593"/>
    </justification>
  </clause>

  <clause id="2077">
    <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(2064(a,1),430(a,1,2,1))].">
      <j1 rule="para" parents="2064 430"/>
    </justification>
  </clause>

  <clause id="2078">
    <literal><![CDATA[
      T((x * y) \ (y * x),K(z,y)) = L(y \ T(y,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,772,a(flip),b,2071,a),flip(a)].">
      <j1 rule="hyper" parents="334 772 2071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2079">
    <literal><![CDATA[
      T(x \ T(x,y),K(z,x)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,773,a,b,2078,a(flip))].">
      <j1 rule="hyper" parents="36 773 2078"/>
    </justification>
  </clause>

  <clause id="2080">
    <literal><![CDATA[
      T(K(x,y),y \ T(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,2079,a)].">
      <j1 rule="hyper" parents="49 2079"/>
    </justification>
  </clause>

  <clause id="2081">
    <literal><![CDATA[
      K(K(x,y),y \ T(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,2080,a)].">
      <j1 rule="hyper" parents="50 2080"/>
    </justification>
  </clause>

  <clause id="2082">
    <literal><![CDATA[
      K(K(x,y),y \ ((T(z,y) \ z) * y)) = 1
    ]]></literal>
    <justification jstring="[para(1736(a,1),2081(a,1,2,2))].">
      <j1 rule="para" parents="1736 2081"/>
    </justification>
  </clause>

  <clause id="2083">
    <literal><![CDATA[
      K(K(x,y),T(T(z,y) \ z,y)) = 1
    ]]></literal>
    <justification jstring="[para(17(a,2),2082(a,1,2))].">
      <j1 rule="para" parents="17 2082"/>
    </justification>
  </clause>

  <clause id="2084">
    <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),2055(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 2055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2085">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(5(a,1),2055(a,2,1,2,1))].">
      <j1 rule="para" parents="5 2055"/>
    </justification>
  </clause>

  <clause id="2086">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1163(a,1),2085(a,1,2,1))].">
      <j1 rule="para" parents="1163 2085"/>
    </justification>
  </clause>

  <clause id="2087">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(K(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1858(a,2),2086(a,2,1))].">
      <j1 rule="para" parents="1858 2086"/>
    </justification>
  </clause>

  <clause id="2088">
    <literal><![CDATA[
      x * T(K(x,x \ 1),y) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(2087(a,1),2008(a,1,2))].">
      <j1 rule="para" parents="2087 2008"/>
    </justification>
  </clause>

  <clause id="2089">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      T(K(x,x \ 1),y) = z
    ]]></literal>
    <justification jstring="[para(2088(a,1),38(a,1))].">
      <j1 rule="para" parents="2088 38"/>
    </justification>
  </clause>

  <clause id="2090">
    <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(334,a,1858,a,b,2084,a),flip(a)].">
      <j1 rule="hyper" parents="334 1858 2084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2091">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = T(K(T(x,y),1 / x),y)
    ]]></literal>
    <justification jstring="[para(1795(a,1),2090(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1795 2090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2092">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ (x \ u))) / z) = x \ (y * ((z * (y \ u)) / z))
    ]]></literal>
    <justification jstring="[para(5(a,1),1677(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 1677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2093">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) * (x * u) = x * ((x * R(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1585(a,1),1694(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1585 1694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2094">
    <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(1272(a,1),2093(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1272 2093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2095">
    <literal><![CDATA[
      R(x,y,z) * (T(x,u) \ 1) = T(x,u) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),1755(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2096">
    <literal><![CDATA[
      (x * (y * L(y \ 1,z,u))) * y = (x * y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(951(a,1),1810(a,1,1))].">
      <j1 rule="para" parents="951 1810"/>
    </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="[hyper(117,a,148,a(flip),b,2096,a)].">
      <j1 rule="hyper" parents="117 148 2096"/>
    </justification>
  </clause>

  <clause id="2098">
    <literal><![CDATA[
      (x * y) * (y * L(y \ 1,y,1 / y)) = (x * (y * (1 / y))) * y
    ]]></literal>
    <justification jstring="[para(400(a,1),2096(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="400 2096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2099">
    <literal><![CDATA[
      (x * (y * (1 / y))) * y = (x * y) * (y * (1 / y))
    ]]></literal>
    <justification jstring="[para(400(a,1),2098(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="400 2098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2100">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = (x * y) * (y * (1 / y))
    ]]></literal>
    <justification jstring="[para(1858(a,2),2099(a,1,1,2))].">
      <j1 rule="para" parents="1858 2099"/>
    </justification>
  </clause>

  <clause id="2101">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = (x * y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(1858(a,2),2100(a,2,2))].">
      <j1 rule="para" parents="1858 2100"/>
    </justification>
  </clause>

  <clause id="2102">
    <literal><![CDATA[
      T((x / y) * K(y,y \ 1),y) = y \ (x * K(y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(451,a,148,a(flip),b,2101,a)].">
      <j1 rule="hyper" parents="451 148 2101"/>
    </justification>
  </clause>

  <clause id="2103">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ ((x * y) * K(y,y \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,2101,a)].">
      <j1 rule="hyper" parents="123 2101"/>
    </justification>
  </clause>

  <clause id="2104">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / y = (x / y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,148,a(flip),b,2101,a)].">
      <j1 rule="hyper" parents="117 148 2101"/>
    </justification>
  </clause>

  <clause id="2105">
    <literal><![CDATA[
      R(T(x,y * K(x,x \ 1)),y,K(x,x \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2103(a,1),1137(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2103 1137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2106">
    <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(2104(a,1),431(a,1,1))].">
      <j1 rule="para" parents="2104 431"/>
    </justification>
  </clause>

  <clause id="2107">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * (K(x,x \ 1) \ 1),y)
    ]]></literal>
    <justification jstring="[para(1899(a,1),1923(a,1,2))].">
      <j1 rule="para" parents="1899 1923"/>
    </justification>
  </clause>

  <clause id="2108">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * K(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(1899(a,1),2107(a,2,1,2))].">
      <j1 rule="para" parents="1899 2107"/>
    </justification>
  </clause>

  <clause id="2109">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1853(a,1),2108(a,2,1))].">
      <j1 rule="para" parents="1853 2108"/>
    </justification>
  </clause>

  <clause id="2110">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x * u) = x * ((x * L(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1812(a,1),1925(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1812 1925"/>
      <j2 rule="flip"/>
    </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="[hyper(116,a,151,a(flip),b,2110,a)].">
      <j1 rule="hyper" parents="116 151 2110"/>
    </justification>
  </clause>

  <clause id="2112">
    <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(619,a,2111,a)].">
      <j1 rule="hyper" parents="619 2111"/>
    </justification>
  </clause>

  <clause id="2113">
    <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(449(a,1),1935(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="449 1935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2114">
    <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),1946(a,1,1))].">
      <j1 rule="para" parents="17 1946"/>
    </justification>
  </clause>

  <clause id="2115">
    <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),2114(a,1,2,1,1))].">
      <j1 rule="para" parents="17 2114"/>
    </justification>
  </clause>

  <clause id="2116">
    <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),2115(a,2,1,2,1))].">
      <j1 rule="para" parents="4 2115"/>
    </justification>
  </clause>

  <clause id="2117">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = x / x
    ]]></literal>
    <justification jstring="[hyper(334,a,154,a(flip),b,2035,a),flip(a)].">
      <j1 rule="hyper" parents="334 154 2035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2119">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = 1
    ]]></literal>
    <justification jstring="[hyper(334,a,69,a(flip),b,2117,a),flip(a)].">
      <j1 rule="hyper" parents="334 69 2117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2121">
    <literal><![CDATA[
      T(1 / (x / y),(y / x) * (x / y)) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[para(2119(a,1),1073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2119 1073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2122">
    <literal><![CDATA[
      ((x / y) * (y / x)) \ (x / y) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1684,a(flip),b,2121,a)].">
      <j1 rule="hyper" parents="58 1684 2121"/>
    </justification>
  </clause>

  <clause id="2123">
    <literal><![CDATA[
      K(1 / (x / y),(y / x) * (x / y)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,2121,a)].">
      <j1 rule="hyper" parents="50 2121"/>
    </justification>
  </clause>

  <clause id="2124">
    <literal><![CDATA[
      ((x / y) * (y / x)) * (1 / (y / x)) = x / y
    ]]></literal>
    <justification jstring="[hyper(119,a,2121,a(flip),b,1684,a(flip))].">
      <j1 rule="hyper" parents="119 2121 1684"/>
    </justification>
  </clause>

  <clause id="2125">
    <literal><![CDATA[
      K(1 / x,(y / (x * y)) * ((x * y) / y)) = 1
    ]]></literal>
    <justification jstring="[para(6(a,1),2123(a,1,1,2))].">
      <j1 rule="para" parents="6 2123"/>
    </justification>
  </clause>

  <clause id="2126">
    <literal><![CDATA[
      ((x * y) / y) * (y / (x * y)) = x / (1 / (y / (x * y)))
    ]]></literal>
    <justification jstring="[hyper(117,a,6,a(flip),b,2124,a),flip(a)].">
      <j1 rule="hyper" parents="117 6 2124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2127">
    <literal><![CDATA[
      K(1 / x,(y / (x * y)) * x) = 1
    ]]></literal>
    <justification jstring="[para(6(a,1),2125(a,1,2,2))].">
      <j1 rule="para" parents="6 2125"/>
    </justification>
  </clause>

  <clause id="2128">
    <literal><![CDATA[
      T(1 / x,(y / (x * y)) * x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(51,a,2127,a)].">
      <j1 rule="hyper" parents="51 2127"/>
    </justification>
  </clause>

  <clause id="2129">
    <literal><![CDATA[
      L(x \ 1,x,y / (x * y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(1753,a,2128,a)].">
      <j1 rule="hyper" parents="1753 2128"/>
    </justification>
  </clause>

  <clause id="2130">
    <literal><![CDATA[
      ((x / (y * x)) * y) * (1 / y) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2128,a(flip),b,1270,a)].">
      <j1 rule="hyper" parents="119 2128 1270"/>
    </justification>
  </clause>

  <clause id="2131">
    <literal><![CDATA[
      L(x \ 1,x,R(1 / x,x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[para(223(a,2),2129(a,1,3))].">
      <j1 rule="para" parents="223 2129"/>
    </justification>
  </clause>

  <clause id="2132">
    <literal><![CDATA[
      R(1 / x,x,y) / (1 / x) = R(1 / x,x,y) * x
    ]]></literal>
    <justification jstring="[para(2131(a,1),407(a,1,2))].">
      <j1 rule="para" parents="2131 407"/>
    </justification>
  </clause>

  <clause id="2133">
    <literal><![CDATA[
      R(x \ 1,x,y) \ (y / (x * y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2130(a,1),1866(a,1,2))].">
      <j1 rule="para" parents="2130 1866"/>
    </justification>
  </clause>

  <clause id="2134">
    <literal><![CDATA[
      x / (y * x) = R(y \ 1,y,x) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,2133,a),flip(a)].">
      <j1 rule="hyper" parents="134 2133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2135">
    <literal><![CDATA[
      T(1 / (1 / x),R(1 / x,x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(1262,a,2132,a)].">
      <j1 rule="hyper" parents="1262 2132"/>
    </justification>
  </clause>

  <clause id="2136">
    <literal><![CDATA[
      T(1 / (1 / x),y / (x * y)) = x
    ]]></literal>
    <justification jstring="[para(223(a,1),2135(a,1,2))].">
      <j1 rule="para" parents="223 2135"/>
    </justification>
  </clause>

  <clause id="2137">
    <literal><![CDATA[
      T(x,y / (x * y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2136(a,1),1846(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2136 1846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2138">
    <literal><![CDATA[
      T(x,y / (x * y)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(334,a,106,a(flip),b,2137,a),flip(a)].">
      <j1 rule="hyper" parents="334 106 2137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2139">
    <literal><![CDATA[
      x \ T(x,y / (x * y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,2137,a,b,1904,a)].">
      <j1 rule="hyper" parents="116 2137 1904"/>
    </justification>
  </clause>

  <clause id="2140">
    <literal><![CDATA[
      T(x,y / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) \ 1 = z
    ]]></literal>
    <justification jstring="[para(2137(a,2),439(a,1))].">
      <j1 rule="para" parents="2137 439"/>
    </justification>
  </clause>

  <clause id="2141">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,y \ 1) * x
    ]]></literal>
    <justification jstring="[para(2137(a,1),1654(a,2,1))].">
      <j1 rule="para" parents="2137 1654"/>
    </justification>
  </clause>

  <clause id="2142">
    <literal><![CDATA[
      T(x / y,y / x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(7(a,1),2138(a,1,2,2))].">
      <j1 rule="para" parents="7 2138"/>
    </justification>
  </clause>

  <clause id="2143">
    <literal><![CDATA[
      x \ T(x,y / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2138(a,2),1905(a,1,2))].">
      <j1 rule="para" parents="2138 1905"/>
    </justification>
  </clause>

  <clause id="2144">
    <literal><![CDATA[
      T(x / (y * x),y) = ((x / (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(6(a,1),2142(a,1,2))].">
      <j1 rule="para" parents="6 2142"/>
    </justification>
  </clause>

  <clause id="2145">
    <literal><![CDATA[
      ((((x * y) / x) \ 1) \ 1) * x = x * T(y,x / (x * y))
    ]]></literal>
    <justification jstring="[para(2142(a,1),466(a,1,1))].">
      <j1 rule="para" parents="2142 466"/>
    </justification>
  </clause>

  <clause id="2146">
    <literal><![CDATA[
      T(x / y,y / x) != z
    ]]></literal>
    <literal><![CDATA[
      ((x / y) \ 1) \ 1 = z
    ]]></literal>
    <justification jstring="[para(7(a,1),2140(a,1,2,2))].">
      <j1 rule="para" parents="7 2140"/>
    </justification>
  </clause>

  <clause id="2147">
    <literal><![CDATA[
      R(x \ 1,x,y) = ((y / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,664,a(flip),b,2144,a)].">
      <j1 rule="hyper" parents="58 664 2144"/>
    </justification>
  </clause>

  <clause id="2148">
    <literal><![CDATA[
      (R(1 / x,x,y) \ 1) \ 1 = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(223(a,2),2147(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="223 2147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2149">
    <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),2147(a,2,1,1,2))].">
      <j1 rule="para" parents="101 2147"/>
    </justification>
  </clause>

  <clause id="2150">
    <literal><![CDATA[
      x / (1 / (y / (x * y))) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(6(a,1),2126(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 2126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2151">
    <literal><![CDATA[
      K(x \ (x * (y / (x * y))),x) = R(x \ 1,x,y) / (y / (x * y))
    ]]></literal>
    <justification jstring="[para(2150(a,1),1071(a,1,1,2))].">
      <j1 rule="para" parents="2150 1071"/>
    </justification>
  </clause>

  <clause id="2152">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = T(x,y / (y * x))
    ]]></literal>
    <justification jstring="[hyper(991,a,2145,a)].">
      <j1 rule="hyper" parents="991 2145"/>
    </justification>
  </clause>

  <clause id="2153">
    <literal><![CDATA[
      R(x \ 1,x,y) / (y / (x * y)) = K(y / (x * y),x)
    ]]></literal>
    <justification jstring="[hyper(1413,a,2151,a),flip(a)].">
      <j1 rule="hyper" parents="1413 2151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2155">
    <literal><![CDATA[
      K(x / (y * x),y) * (x / (y * x)) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,2153,a)].">
      <j1 rule="hyper" parents="133 2153"/>
    </justification>
  </clause>

  <clause id="2157">
    <literal><![CDATA[
      (x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)) = (x \ T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(170(a,1),2039(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="170 2039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2158">
    <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,2157,a),flip(a)].">
      <j1 rule="hyper" parents="115 5 2157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2159">
    <literal><![CDATA[
      (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = y * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,461,a(flip),b,847,a),flip(a)].">
      <j1 rule="hyper" parents="334 461 847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2160">
    <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(2159(a,1),1358(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2159 1358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2161">
    <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(2159(a,1),1579(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2159 1579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2162">
    <literal><![CDATA[
      R((x * (y * z)) / (x * y),u,w) = (x * (y * R(z,u,w))) / (x * y)
    ]]></literal>
    <justification jstring="[para(459(a,1),894(a,1,1)),flip(a)].">
      <j1 rule="para" parents="459 894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2163">
    <literal><![CDATA[
      (T(x,y) * (1 / x)) / T(x,y) = L(1 / x,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1315,a(flip),b,1055,a)].">
      <j1 rule="hyper" parents="58 1315 1055"/>
    </justification>
  </clause>

  <clause id="2165">
    <literal><![CDATA[
      T(L(1 / x,T(x,y),1 / x),x) = (T(x,y) * (x \ 1)) / T(x,y)
    ]]></literal>
    <justification jstring="[para(2163(a,1),697(a,1,1))].">
      <j1 rule="para" parents="2163 697"/>
    </justification>
  </clause>

  <clause id="2166">
    <literal><![CDATA[
      (T(x,y) * (x \ 1)) / T(x,y) = L(x \ 1,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(888,a,2165,a),flip(a)].">
      <j1 rule="hyper" parents="888 2165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2167">
    <literal><![CDATA[
      x * L(x \ 1,T(x,y),1 / x) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(2166(a,1),1795(a,1,2))].">
      <j1 rule="para" parents="2166 1795"/>
    </justification>
  </clause>

  <clause id="2168">
    <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(1455(a,1),298(a,1))].">
      <j1 rule="para" parents="1455 298"/>
    </justification>
  </clause>

  <clause id="2169">
    <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),1540(a,1,2,1,2,1))].">
      <j1 rule="para" parents="4 1540"/>
    </justification>
  </clause>

  <clause id="2170">
    <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,374,a,b,2169,a),flip(a)].">
      <j1 rule="hyper" parents="33 374 2169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2171">
    <literal><![CDATA[
      ((x \ 1) * (x * L(x \ 1,x,y))) * x = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(1979(a,1),1670(a,1,1))].">
      <j1 rule="para" parents="1979 1670"/>
    </justification>
  </clause>

  <clause id="2172">
    <literal><![CDATA[
      (x * (((T(y,x) \ y) * x) \ x)) \ (x * x) = (T(y,x) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(334,a,1736,a(flip),b,1741,a),flip(a)].">
      <j1 rule="hyper" parents="334 1736 1741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2173">
    <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(1101(a,2),1982(a,1))].">
      <j1 rule="para" parents="1101 1982"/>
    </justification>
  </clause>

  <clause id="2174">
    <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(2149(a,1),534(a,1,1))].">
      <j1 rule="para" parents="2149 534"/>
    </justification>
  </clause>

  <clause id="2175">
    <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(2171(a,1),39(a,1))].">
      <j1 rule="para" parents="2171 39"/>
    </justification>
  </clause>

  <clause id="2176">
    <literal><![CDATA[
      L(x,y,T(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z \ u) \ u) = w
    ]]></literal>
    <justification jstring="[para(682(a,1),862(a,1))].">
      <j1 rule="para" parents="682 862"/>
    </justification>
  </clause>

  <clause id="2177">
    <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),948(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="105 948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2178">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ 1,z,u) = T(x * R(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(246,a,1585,a(flip),b,2177,a),flip(a)].">
      <j1 rule="hyper" parents="246 1585 2177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2179">
    <literal><![CDATA[
      T(x * R(x \ 1,T(x,y),z),y) = (z / (T(x,y) * z)) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(671,a,2178,a),flip(a)].">
      <j1 rule="hyper" parents="671 2178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2180">
    <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(1033(a,1),2179(a,2,1,2))].">
      <j1 rule="para" parents="1033 2179"/>
    </justification>
  </clause>

  <clause id="2181">
    <literal><![CDATA[
      ((x \ 1) / (x \ T(x,y))) * T(x,y) = T(x * T(x \ 1,T(x,y)),y)
    ]]></literal>
    <justification jstring="[para(1321(a,1),2180(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1321 2180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2182">
    <literal><![CDATA[
      (x \ 1) / (x \ T(x,y)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(30,a,1609,a(flip),b,2181,a),flip(a)].">
      <j1 rule="hyper" parents="30 1609 2181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2183">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,y)) = (x \ T(x,y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(2182(a,1),107(a,1,1))].">
      <j1 rule="para" parents="2182 107"/>
    </justification>
  </clause>

  <clause id="2184">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,1640,a(flip),b,2183,a),flip(a)].">
      <j1 rule="hyper" parents="58 1640 2183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2186">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ (T(x,y) \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(2184(a,1),2158(a,1,2,2))].">
      <j1 rule="para" parents="2184 2158"/>
    </justification>
  </clause>

  <clause id="2187">
    <literal><![CDATA[
      (x \ 1) \ (T(x,y) \ 1) = (x \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,2186,a),flip(a)].">
      <j1 rule="hyper" parents="123 2186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2188">
    <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,1522,a,b,1119,a)].">
      <j1 rule="hyper" parents="29 1522 1119"/>
    </justification>
  </clause>

  <clause id="2189">
    <literal><![CDATA[
      ((x * ((y \ z) / z)) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),1140(a,1,1,1,2,2))].">
      <j1 rule="para" parents="5 1140"/>
    </justification>
  </clause>

  <clause id="2190">
    <literal><![CDATA[
      (((x * ((y \ z) / z)) / x) * z) / (y \ z) = ((x * (1 / y)) / x) * y
    ]]></literal>
    <justification jstring="[hyper(550,a,2189,a)].">
      <j1 rule="hyper" parents="550 2189"/>
    </justification>
  </clause>

  <clause id="2191">
    <literal><![CDATA[
      (((x * ((y \ z) / z)) / x) * z) / (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      ((x * (1 / y)) / x) * y = u
    ]]></literal>
    <justification jstring="[para(2189(a,2),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2189 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2192">
    <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(334,a,1956,a,b,2190,a),flip(a)].">
      <j1 rule="hyper" parents="334 1956 2190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2193">
    <literal><![CDATA[
      T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),1375(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2194">
    <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(246,a,1785,a,b,1678,a(flip))].">
      <j1 rule="hyper" parents="246 1785 1678"/>
    </justification>
  </clause>

  <clause id="2195">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ y,z,u) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(246,a,1784,a(flip),b,1678,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="246 1784 1678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2196">
    <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),2195(a,2,1,2,1))].">
      <j1 rule="para" parents="4 2195"/>
    </justification>
  </clause>

  <clause id="2197">
    <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(231(a,1),2194(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="231 2194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2198">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[para(204(a,1),2197(a,1,2,1,2))].">
      <j1 rule="para" parents="204 2197"/>
    </justification>
  </clause>

  <clause id="2199">
    <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(2197(a,2),791(a,1))].">
      <j1 rule="para" parents="2197 791"/>
    </justification>
  </clause>

  <clause id="2200">
    <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,2198,a)].">
      <j1 rule="hyper" parents="123 2198"/>
    </justification>
  </clause>

  <clause id="2201">
    <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,405,a(flip),b,2198,a),flip(a)].">
      <j1 rule="hyper" parents="58 405 2198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2202">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,x,1 / x) = T(x * T(1 / x,1),y)
    ]]></literal>
    <justification jstring="[para(775(a,1),2198(a,2,1,2))].">
      <j1 rule="para" parents="775 2198"/>
    </justification>
  </clause>

  <clause id="2203">
    <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(401(a,1),2200(a,1,2,1,2))].">
      <j1 rule="para" parents="401 2200"/>
    </justification>
  </clause>

  <clause id="2204">
    <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(1049(a,1),2201(a,2,2,1))].">
      <j1 rule="para" parents="1049 2201"/>
    </justification>
  </clause>

  <clause id="2205">
    <literal><![CDATA[
      T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * T(1 / x,1),y)
    ]]></literal>
    <justification jstring="[para(1170(a,1),2202(a,1,2))].">
      <j1 rule="para" parents="1170 2202"/>
    </justification>
  </clause>

  <clause id="2206">
    <literal><![CDATA[
      T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(202(a,1),2205(a,2,1,2))].">
      <j1 rule="para" parents="202 2205"/>
    </justification>
  </clause>

  <clause id="2207">
    <literal><![CDATA[
      (1 / x) * (T(x,y) \ x) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(29,a,2086,a,b,2206,a),flip(a)].">
      <j1 rule="hyper" parents="29 2086 2206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2208">
    <literal><![CDATA[
      T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(K(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1858(a,2),2206(a,2,1))].">
      <j1 rule="para" parents="1858 2206"/>
    </justification>
  </clause>

  <clause id="2209">
    <literal><![CDATA[
      (T(x,y) \ x) \ ((T(x,y) \ x) / x) = T(1 / x,T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(451,a,xx,b,2207,a),flip(a)].">
      <j1 rule="hyper" parents="451 2207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2210">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) = (1 / x) * ((T(x,y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(2207(a,1),1172(a,1,1))].">
      <j1 rule="para" parents="2207 1172"/>
    </justification>
  </clause>

  <clause id="2211">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(1171,a,2210,a),flip(a)].">
      <j1 rule="hyper" parents="1171 2210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2212">
    <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(2209(a,1),1059(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2209 1059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2213">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = T(K(T(x,y),1 / x),y)
    ]]></literal>
    <justification jstring="[para(2167(a,1),2204(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2167 2204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2214">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = K(T(x,y),T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,2091,a,b,2213,a),flip(a)].">
      <j1 rule="hyper" parents="334 2091 2213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2215">
    <literal><![CDATA[
      (T(x,y) / x) \ (1 / x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,1858,a(flip),b,2214,a),flip(a)].">
      <j1 rule="hyper" parents="29 1858 2214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2216">
    <literal><![CDATA[
      (T(x,y) / x) * (1 / T(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(134,a,2215,a)].">
      <j1 rule="hyper" parents="134 2215"/>
    </justification>
  </clause>

  <clause id="2217">
    <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(273(a,1),2215(a,1,2))].">
      <j1 rule="para" parents="273 2215"/>
    </justification>
  </clause>

  <clause id="2218">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = 1 / T(T(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1404(a,1),2217(a,1,1))].">
      <j1 rule="para" parents="1404 2217"/>
    </justification>
  </clause>

  <clause id="2219">
    <literal><![CDATA[
      1 / T(T(x,x \ 1),y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2184,a(flip),b,2218,a),flip(a)].">
      <j1 rule="hyper" parents="58 2184 2218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2220">
    <literal><![CDATA[
      T(T(x,x \ 1),y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(192,a,2219,a),flip(a)].">
      <j1 rule="hyper" parents="192 2219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2221">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ 1 = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(368(a,1),2219(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="368 2219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2222">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,681,a(flip),b,2220,a)].">
      <j1 rule="hyper" parents="58 681 2220"/>
    </justification>
  </clause>

  <clause id="2223">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) \ 1 = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(661(a,1),2220(a,1,1)),flip(a)].">
      <j1 rule="para" parents="661 2220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2224">
    <literal><![CDATA[
      1 / (1 / T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(201,a,2221,a)].">
      <j1 rule="hyper" parents="201 2221"/>
    </justification>
  </clause>

  <clause id="2225">
    <literal><![CDATA[
      x * ((T(y,x) \ 1) \ 1) = ((y \ 1) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,2222,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2222 17"/>
    </justification>
  </clause>

  <clause id="2226">
    <literal><![CDATA[
      T(((x / y) \ 1) \ 1,y) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(107(a,1),2222(a,2,1,1))].">
      <j1 rule="para" parents="107 2222"/>
    </justification>
  </clause>

  <clause id="2227">
    <literal><![CDATA[
      T(x,y) * K(T(x,y) \ 1,T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(1881,a,2224,a)].">
      <j1 rule="hyper" parents="1881 2224"/>
    </justification>
  </clause>

  <clause id="2228">
    <literal><![CDATA[
      T(1 / (1 / (x / y)),y) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[para(107(a,1),2224(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 2224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2229">
    <literal><![CDATA[
      ((x * T(1 / (1 / y),x)) / x) \ (y / T(y,x)) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[para(2224(a,1),1777(a,1,1,1,2))].">
      <j1 rule="para" parents="2224 1777"/>
    </justification>
  </clause>

  <clause id="2230">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(763,a,2225,a)].">
      <j1 rule="hyper" parents="763 2225"/>
    </justification>
  </clause>

  <clause id="2231">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) * y = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,1),2225(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="107 2225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2232">
    <literal><![CDATA[
      (T(x,y) \ 1) \ (T(x,y) \ x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(1173,a,2230,a)].">
      <j1 rule="hyper" parents="1173 2230"/>
    </justification>
  </clause>

  <clause id="2233">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = x * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,1902,a,b,2230,a),flip(a)].">
      <j1 rule="hyper" parents="334 1902 2230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2234">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,106,a,b,2230,a),flip(a)].">
      <j1 rule="hyper" parents="334 106 2230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2235">
    <literal><![CDATA[
      T(K(x,x \ 1),y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2089,a,2233,a)].">
      <j1 rule="hyper" parents="2089 2233"/>
    </justification>
  </clause>

  <clause id="2236">
    <literal><![CDATA[
      T(x,K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,2235,a)].">
      <j1 rule="hyper" parents="49 2235"/>
    </justification>
  </clause>

  <clause id="2237">
    <literal><![CDATA[
      K(x,x \ 1) * y = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,2235,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 2235 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2238">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = (1 / x) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(116,a,2235,a(flip),b,2208,a)].">
      <j1 rule="hyper" parents="116 2235 2208"/>
    </justification>
  </clause>

  <clause id="2239">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,2235,a(flip),b,2087,a)].">
      <j1 rule="hyper" parents="116 2235 2087"/>
    </justification>
  </clause>

  <clause id="2240">
    <literal><![CDATA[
      K(x,x \ 1) * y != z * K(x,x \ 1)
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(2235(a,1),248(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2235 248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2241">
    <literal><![CDATA[
      x * K(y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,y \ 1) * x = z
    ]]></literal>
    <justification jstring="[para(2235(a,1),294(a,1,2))].">
      <j1 rule="para" parents="2235 294"/>
    </justification>
  </clause>

  <clause id="2242">
    <literal><![CDATA[
      x \ y != z * K(u,u \ 1)
    ]]></literal>
    <literal><![CDATA[
      x * (K(u,u \ 1) * z) = y
    ]]></literal>
    <justification jstring="[para(2235(a,1),593(a,2,2))].">
      <j1 rule="para" parents="2235 593"/>
    </justification>
  </clause>

  <clause id="2244">
    <literal><![CDATA[
      T(x,K(y,y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(2236(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2236 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2245">
    <literal><![CDATA[
      T(x,K(1 / y,y)) = x
    ]]></literal>
    <justification jstring="[para(75(a,1),2236(a,1,2,2))].">
      <j1 rule="para" parents="75 2236"/>
    </justification>
  </clause>

  <clause id="2246">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2236(a,1),294(a,1,2))].">
      <j1 rule="para" parents="2236 294"/>
    </justification>
  </clause>

  <clause id="2247">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      (y * K(x,x \ 1)) * z = u
    ]]></literal>
    <justification jstring="[para(2236(a,1),582(a,1,1,2))].">
      <j1 rule="para" parents="2236 582"/>
    </justification>
  </clause>

  <clause id="2248">
    <literal><![CDATA[
      T(x,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(1862(a,1),2236(a,1,2))].">
      <j1 rule="para" parents="1862 2236"/>
    </justification>
  </clause>

  <clause id="2249">
    <literal><![CDATA[
      T(K(x \ 1,x),y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(49,a,2248,a)].">
      <j1 rule="hyper" parents="49 2248"/>
    </justification>
  </clause>

  <clause id="2250">
    <literal><![CDATA[
      K(x \ 1,x) * y = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2248,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2248 17"/>
    </justification>
  </clause>

  <clause id="2251">
    <literal><![CDATA[
      (x * K(y \ 1,y)) / x = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2248(a,1),191(a,1,2))].">
      <j1 rule="para" parents="2248 191"/>
    </justification>
  </clause>

  <clause id="2252">
    <literal><![CDATA[
      T(x,(y \ 1) * y) = x
    ]]></literal>
    <justification jstring="[para(266(a,1),2248(a,1,2))].">
      <j1 rule="para" parents="266 2248"/>
    </justification>
  </clause>

  <clause id="2253">
    <literal><![CDATA[
      K(x \ 1,x) * y != z * K(x \ 1,x)
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(2248(a,1),249(a,1,2))].">
      <j1 rule="para" parents="2248 249"/>
    </justification>
  </clause>

  <clause id="2254">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(2248(a,1),294(a,1,2))].">
      <j1 rule="para" parents="2248 294"/>
    </justification>
  </clause>

  <clause id="2256">
    <literal><![CDATA[
      K(x \ 1,x) \ ((y * (x \ 1)) * x) = R(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2248(a,1),1107(a,2,1))].">
      <j1 rule="para" parents="2248 1107"/>
    </justification>
  </clause>

  <clause id="2257">
    <literal><![CDATA[
      ((x \ 1) * x) * y = y * ((x \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2252,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2252 17"/>
    </justification>
  </clause>

  <clause id="2258">
    <literal><![CDATA[
      K(x \ (x / T(x,y)),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1604,a,b,2249,a)].">
      <j1 rule="hyper" parents="58 1604 2249"/>
    </justification>
  </clause>

  <clause id="2259">
    <literal><![CDATA[
      T((x \ 1) * x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(266(a,1),2249(a,1,1))].">
      <j1 rule="para" parents="266 2249"/>
    </justification>
  </clause>

  <clause id="2260">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,y) * x = z
    ]]></literal>
    <justification jstring="[para(2249(a,1),294(a,1,2))].">
      <j1 rule="para" parents="2249 294"/>
    </justification>
  </clause>

  <clause id="2261">
    <literal><![CDATA[
      K(x \ 1,x) / T(x,y) = T(1 / T(x,y),x)
    ]]></literal>
    <justification jstring="[para(2249(a,1),1607(a,1,1))].">
      <j1 rule="para" parents="2249 1607"/>
    </justification>
  </clause>

  <clause id="2262">
    <literal><![CDATA[
      K(x,x \ 1) * L(x,y,z) = x * (L(x,y,z) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(334,a,1867,a(flip),b,2237,a),flip(a)].">
      <j1 rule="hyper" parents="334 1867 2237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2263">
    <literal><![CDATA[
      (K(x,x \ 1) * y) / z = (y * K(x,x \ 1)) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,2237,a,b,7,a)].">
      <j1 rule="hyper" parents="117 2237 7"/>
    </justification>
  </clause>

  <clause id="2264">
    <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,2237,a(flip),b,484,a)].">
      <j1 rule="hyper" parents="116 2237 484"/>
    </justification>
  </clause>

  <clause id="2265">
    <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(2237(a,2),517(a,1,2))].">
      <j1 rule="para" parents="2237 517"/>
    </justification>
  </clause>

  <clause id="2266">
    <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(2237(a,2),648(a,1,1))].">
      <j1 rule="para" parents="2237 648"/>
    </justification>
  </clause>

  <clause id="2267">
    <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(2237(a,1),793(a,1,2))].">
      <j1 rule="para" parents="2237 793"/>
    </justification>
  </clause>

  <clause id="2268">
    <literal><![CDATA[
      K(x \ 1,x) * (y / x) = y * T(y \ (y / x),x)
    ]]></literal>
    <justification jstring="[hyper(334,a,1059,a(flip),b,2250,a),flip(a)].">
      <j1 rule="hyper" parents="334 1059 2250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2269">
    <literal><![CDATA[
      x * (K(y \ 1,y) * z) = x * (z * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,2250,a,b,4,a)].">
      <j1 rule="hyper" parents="119 2250 4"/>
    </justification>
  </clause>

  <clause id="2270">
    <literal><![CDATA[
      R(K(x \ 1,x),y,z) * (y * z) = (y * K(x \ 1,x)) * z
    ]]></literal>
    <justification jstring="[para(2250(a,1),101(a,2,1))].">
      <j1 rule="para" parents="2250 101"/>
    </justification>
  </clause>

  <clause id="2271">
    <literal><![CDATA[
      L(x \ (K(y \ 1,y) \ z),x,K(y \ 1,y)) = (x * K(y \ 1,y)) \ z
    ]]></literal>
    <justification jstring="[para(2250(a,1),311(a,2,1))].">
      <j1 rule="para" parents="2250 311"/>
    </justification>
  </clause>

  <clause id="2272">
    <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(2250(a,2),517(a,1,2))].">
      <j1 rule="para" parents="2250 517"/>
    </justification>
  </clause>

  <clause id="2273">
    <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(2250(a,2),648(a,1,1))].">
      <j1 rule="para" parents="2250 648"/>
    </justification>
  </clause>

  <clause id="2274">
    <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(2250(a,1),793(a,1,2))].">
      <j1 rule="para" parents="2250 793"/>
    </justification>
  </clause>

  <clause id="2275">
    <literal><![CDATA[
      T(K(x \ 1,x),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(2251(a,1),303(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2251 303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2276">
    <literal><![CDATA[
      ((x * y) / x) \ K(y \ 1,y) = T(((x * y) / x) \ 1,y)
    ]]></literal>
    <justification jstring="[para(2251(a,1),1663(a,1,2))].">
      <j1 rule="para" parents="2251 1663"/>
    </justification>
  </clause>

  <clause id="2277">
    <literal><![CDATA[
      a(x \ 1,x,x \ 1) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(813,a,2257,a)].">
      <j1 rule="hyper" parents="813 2257"/>
    </justification>
  </clause>

  <clause id="2279">
    <literal><![CDATA[
      x * K(x \ (x / T(x,y)),x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2258,a,b,1852,a)].">
      <j1 rule="hyper" parents="119 2258 1852"/>
    </justification>
  </clause>

  <clause id="2280">
    <literal><![CDATA[
      (x * (((x \ y) \ 1) \ 1)) / x = ((y / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(281,a,2226,a)].">
      <j1 rule="hyper" parents="281 2226"/>
    </justification>
  </clause>

  <clause id="2281">
    <literal><![CDATA[
      T(T(x / y,y / x),y) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2142(a,2),2226(a,1,1))].">
      <j1 rule="para" parents="2142 2226"/>
    </justification>
  </clause>

  <clause id="2282">
    <literal><![CDATA[
      (x * (1 / (1 / (x \ y)))) / x = 1 / (1 / (y / x))
    ]]></literal>
    <justification jstring="[hyper(281,a,2228,a)].">
      <j1 rule="hyper" parents="281 2228"/>
    </justification>
  </clause>

  <clause id="2283">
    <literal><![CDATA[
      (1 / (1 / (x / y))) * y = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(119,a,2228,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 2228 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2284">
    <literal><![CDATA[
      (T(x,y) \ 1) * ((x \ 1) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(134,a,2232,a)].">
      <j1 rule="hyper" parents="134 2232"/>
    </justification>
  </clause>

  <clause id="2286">
    <literal><![CDATA[
      T(x,y) \ (1 / (1 / x)) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(116,a,2279,a(flip),b,1193,a)].">
      <j1 rule="hyper" parents="116 2279 1193"/>
    </justification>
  </clause>

  <clause id="2287">
    <literal><![CDATA[
      T(x,y / (y * x)) = ((y \ (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(699,a,2281,a)].">
      <j1 rule="hyper" parents="699 2281"/>
    </justification>
  </clause>

  <clause id="2288">
    <literal><![CDATA[
      T(x \ y,x / y) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(696,a,2281,a)].">
      <j1 rule="hyper" parents="696 2281"/>
    </justification>
  </clause>

  <clause id="2289">
    <literal><![CDATA[
      T((x * y) \ y,x) = (((x * y) \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(6(a,1),2288(a,1,2))].">
      <j1 rule="para" parents="6 2288"/>
    </justification>
  </clause>

  <clause id="2290">
    <literal><![CDATA[
      T(x \ (y \ x),y) = ((x \ (y \ x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(72(a,1),2288(a,1,2))].">
      <j1 rule="para" parents="72 2288"/>
    </justification>
  </clause>

  <clause id="2291">
    <literal><![CDATA[
      T(x,y / (y * x)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),2287(a,2,1,1))].">
      <j1 rule="para" parents="4 2287"/>
    </justification>
  </clause>

  <clause id="2292">
    <literal><![CDATA[
      T(x,y / (y * x)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,106,a,b,2291,a),flip(a)].">
      <j1 rule="hyper" parents="334 106 2291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2293">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2152,a,b,2291,a)].">
      <j1 rule="hyper" parents="58 2152 2291"/>
    </justification>
  </clause>

  <clause id="2294">
    <literal><![CDATA[
      T(1 / (1 / x),y / (y * x)) = x
    ]]></literal>
    <justification jstring="[hyper(1848,a,2292,a(flip))].">
      <j1 rule="hyper" parents="1848 2292"/>
    </justification>
  </clause>

  <clause id="2295">
    <literal><![CDATA[
      T(1 / (1 / x),(y / x) / y) = x
    ]]></literal>
    <justification jstring="[para(7(a,1),2294(a,1,2,2))].">
      <j1 rule="para" parents="7 2294"/>
    </justification>
  </clause>

  <clause id="2296">
    <literal><![CDATA[
      (1 / (1 / x)) \ (((y / x) / y) * x) = (y / x) / y
    ]]></literal>
    <justification jstring="[para(2295(a,1),232(a,1,2,2))].">
      <j1 rule="para" parents="2295 232"/>
    </justification>
  </clause>

  <clause id="2298">
    <literal><![CDATA[
      1 / T((x * y) \ y,x) = ((x * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(201,a,2289,a(flip))].">
      <j1 rule="hyper" parents="201 2289"/>
    </justification>
  </clause>

  <clause id="2299">
    <literal><![CDATA[
      T(1 / (1 / ((x * y) \ y)),x) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(34,a,2221,a,b,2298,a(flip))].">
      <j1 rule="hyper" parents="34 2221 2298"/>
    </justification>
  </clause>

  <clause id="2300">
    <literal><![CDATA[
      (x * y) \ (K(x,x \ 1) * y) = 1 / (1 / ((x * y) \ y))
    ]]></literal>
    <justification jstring="[hyper(35,a,1938,a,b,2299,a)].">
      <j1 rule="hyper" parents="35 1938 2299"/>
    </justification>
  </clause>

  <clause id="2301">
    <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(757(a,2),2254(a,1))].">
      <j1 rule="para" parents="757 2254"/>
    </justification>
  </clause>

  <clause id="2302">
    <literal><![CDATA[
      x * T(x \ (x / y),y) != z
    ]]></literal>
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2268(a,1),2254(a,1))].">
      <j1 rule="para" parents="2268 2254"/>
    </justification>
  </clause>

  <clause id="2303">
    <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(2269(a,2),709(a,1,2))].">
      <j1 rule="para" parents="2269 709"/>
    </justification>
  </clause>

  <clause id="2304">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) / x = (((x * y) / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),2280(a,1,1,2,1,1))].">
      <j1 rule="para" parents="4 2280"/>
    </justification>
  </clause>

  <clause id="2305">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * (((y \ x) \ 1) \ 1) = z
    ]]></literal>
    <justification jstring="[para(2280(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2280 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2306">
    <literal><![CDATA[
      (x * (1 / (1 / y))) / x = 1 / (1 / ((x * y) / x))
    ]]></literal>
    <justification jstring="[para(4(a,1),2282(a,1,1,2,2,2))].">
      <j1 rule="para" parents="4 2282"/>
    </justification>
  </clause>

  <clause id="2307">
    <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(2097(a,2),2296(a,1,2))].">
      <j1 rule="para" parents="2097 2296"/>
    </justification>
  </clause>

  <clause id="2308">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ L(x,y,z)) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1934,a,2262,a)].">
      <j1 rule="hyper" parents="1934 2262"/>
    </justification>
  </clause>

  <clause id="2309">
    <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(2276(a,2),1299(a,1,1,2))].">
      <j1 rule="para" parents="2276 1299"/>
    </justification>
  </clause>

  <clause id="2311">
    <literal><![CDATA[
      (x * y) * (1 / (1 / ((x * y) \ y))) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(134,a,2300,a)].">
      <j1 rule="hyper" parents="134 2300"/>
    </justification>
  </clause>

  <clause id="2312">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K(x,x \ 1) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(2246,a,2308,a)].">
      <j1 rule="hyper" parents="2246 2308"/>
    </justification>
  </clause>

  <clause id="2313">
    <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(334,a,1339,a(flip),b,2308,a),flip(a)].">
      <j1 rule="hyper" parents="334 1339 2308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2314">
    <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),2305(a,1,1,1,1))].">
      <j1 rule="para" parents="102 2305"/>
    </justification>
  </clause>

  <clause id="2315">
    <literal><![CDATA[
      (1 / (1 / x)) \ (x / T(x,y)) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(231(a,1),2229(a,1,1))].">
      <j1 rule="para" parents="231 2229"/>
    </justification>
  </clause>

  <clause id="2317">
    <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(334,a,372,a(flip),b,2271,a),flip(a)].">
      <j1 rule="hyper" parents="334 372 2271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2318">
    <literal><![CDATA[
      K(x,(y * x) \ y) * x = T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1911(a,1,1,1))].">
      <j1 rule="para" parents="4 1911"/>
    </justification>
  </clause>

  <clause id="2319">
    <literal><![CDATA[
      T(K(x,(y * x) \ y),x) = x \ T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(451,a,xx,b,2318,a)].">
      <j1 rule="hyper" parents="451 2318"/>
    </justification>
  </clause>

  <clause id="2321">
    <literal><![CDATA[
      L(T(K(x,(y * x) \ y),x),x,y) = K(((y * x) \ y) \ 1,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(2319(a,2),2170(a,1,1))].">
      <j1 rule="para" parents="2319 2170"/>
    </justification>
  </clause>

  <clause id="2322">
    <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(659(a,1),1948(a,2,2,1))].">
      <j1 rule="para" parents="659 1948"/>
    </justification>
  </clause>

  <clause id="2323">
    <literal><![CDATA[
      (((x * y) / x) / y) * (1 / y) = (1 / y) * (((x * y) / x) / y)
    ]]></literal>
    <justification jstring="[para(1578(a,1),1976(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1578 1976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2324">
    <literal><![CDATA[
      ((1 / x) * (((y * x) / y) / x)) / (1 / x) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(130,a,2323,a)].">
      <j1 rule="hyper" parents="130 2323"/>
    </justification>
  </clause>

  <clause id="2325">
    <literal><![CDATA[
      R(((x * y) / x) / y,y,x) = ((1 / y) * ((x * y) / (y * x))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(2324(a,1),922(a,1,1))].">
      <j1 rule="para" parents="2324 922"/>
    </justification>
  </clause>

  <clause id="2326">
    <literal><![CDATA[
      ((1 / x) * ((y * x) / (x * y))) / (1 / x) = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(641,a,2325,a),flip(a)].">
      <j1 rule="hyper" parents="641 2325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2327">
    <literal><![CDATA[
      T((x * y) / (y * x),y * x) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(2326(a,1),697(a,1,1))].">
      <j1 rule="para" parents="2326 697"/>
    </justification>
  </clause>

  <clause id="2328">
    <literal><![CDATA[
      ((1 / x) * ((x * y) \ (y * x))) / (1 / x) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(431,a,2327,a),flip(a)].">
      <j1 rule="hyper" parents="431 2327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2329">
    <literal><![CDATA[
      K(x,y) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(334,a,11,a,b,2328,a)].">
      <j1 rule="hyper" parents="334 11 2328"/>
    </justification>
  </clause>

  <clause id="2330">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) / (1 / x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(11(a,2),2329(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 2329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2331">
    <literal><![CDATA[
      T(1 / x,K(y,x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(274,a,2330,a)].">
      <j1 rule="hyper" parents="274 2330"/>
    </justification>
  </clause>

  <clause id="2332">
    <literal><![CDATA[
      K(x,y) * (1 / y) = (1 / y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,2330,a)].">
      <j1 rule="hyper" parents="133 2330"/>
    </justification>
  </clause>

  <clause id="2333">
    <literal><![CDATA[
      (K(x,y) * (1 / y)) / K(x,y) = 1 / y
    ]]></literal>
    <justification jstring="[para(2330(a,1),78(a,1,1,1))].">
      <j1 rule="para" parents="2330 78"/>
    </justification>
  </clause>

  <clause id="2334">
    <literal><![CDATA[
      K(1 / x,K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,2331,a)].">
      <j1 rule="hyper" parents="50 2331"/>
    </justification>
  </clause>

  <clause id="2335">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = T(1 / x,x)
    ]]></literal>
    <justification jstring="[para(2331(a,1),254(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2331 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2337">
    <literal><![CDATA[
      K(x,K(y,x \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(72(a,1),2334(a,1,1))].">
      <j1 rule="para" parents="72 2334"/>
    </justification>
  </clause>

  <clause id="2338">
    <literal><![CDATA[
      K(x,y \ 1) * y = y * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(552,a,2337,a)].">
      <j1 rule="hyper" parents="552 2337"/>
    </justification>
  </clause>

  <clause id="2339">
    <literal><![CDATA[
      T(x,K(y,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,2337,a)].">
      <j1 rule="hyper" parents="51 2337"/>
    </justification>
  </clause>

  <clause id="2340">
    <literal><![CDATA[
      L(x,y,z) * K(u,x \ 1) = K(u,x \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2339(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2339 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2341">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(334,a,107,a(flip),b,2335,a),flip(a)].">
      <j1 rule="hyper" parents="334 107 2335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2342">
    <literal><![CDATA[
      T((x * y) \ x,K(z,y)) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(2341(a,1),410(a,2,1))].">
      <j1 rule="para" parents="2341 410"/>
    </justification>
  </clause>

  <clause id="2343">
    <literal><![CDATA[
      R(1 / x,y,z) \ (K(u,x) * R(1 / x,y,z)) = K(u,x)
    ]]></literal>
    <justification jstring="[para(2333(a,1),882(a,1,1,1))].">
      <j1 rule="para" parents="2333 882"/>
    </justification>
  </clause>

  <clause id="2344">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = L((y \ x) \ 1,y \ x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),2342(a,1,1,1))].">
      <j1 rule="para" parents="5 2342"/>
    </justification>
  </clause>

  <clause id="2345">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(334,a,401,a(flip),b,2344,a),flip(a)].">
      <j1 rule="hyper" parents="334 401 2344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2346">
    <literal><![CDATA[
      K(x,y \ z) * (z \ y) = (z \ y) * K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,2345,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2345 17"/>
    </justification>
  </clause>

  <clause id="2347">
    <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(2340(a,2),39(a,1))].">
      <j1 rule="para" parents="2340 39"/>
    </justification>
  </clause>

  <clause id="2348">
    <literal><![CDATA[
      T(K(x,y),R(1 / y,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(298,a,2343,a)].">
      <j1 rule="hyper" parents="298 2343"/>
    </justification>
  </clause>

  <clause id="2349">
    <literal><![CDATA[
      T(K(x,y),z / (y * z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(223(a,1),2348(a,1,2))].">
      <j1 rule="para" parents="223 2348"/>
    </justification>
  </clause>

  <clause id="2350">
    <literal><![CDATA[
      K(x,y) * (z / (y * z)) = (z / (y * z)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,2349,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 2349 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2351">
    <literal><![CDATA[
      (x / (y * x)) * K(x / (y * x),y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2155,a(flip),b,2350,a),flip(a)].">
      <j1 rule="hyper" parents="58 2155 2350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2352">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * (x * z) = x * ((x * ((y * (x \ 1)) / y)) * z)
    ]]></literal>
    <justification jstring="[para(1787(a,1),2020(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1787 2020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2353">
    <literal><![CDATA[
      L(x \ R(x,y \ 1,y),x,K(y \ 1,y)) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2256(a,1),2317(a,1,1,2))].">
      <j1 rule="para" parents="2256 2317"/>
    </justification>
  </clause>

  <clause id="2354">
    <literal><![CDATA[
      (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * ((1 / x) * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,461,a(flip),b,848,a),flip(a)].">
      <j1 rule="hyper" parents="334 461 848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2355">
    <literal><![CDATA[
      (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(1049(a,1),2354(a,2,2))].">
      <j1 rule="para" parents="1049 2354"/>
    </justification>
  </clause>

  <clause id="2356">
    <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(2355(a,1),1565(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2355 1565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2357">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (((z * (u / x)) / z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(925,a,1022,a),flip(a)].">
      <j1 rule="hyper" parents="925 1022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2358">
    <literal><![CDATA[
      (((x * ((y / z) / u)) / x) * u) * z = (u * z) * ((x * ((u * z) \ y)) / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),2357(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 2357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2359">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (x * ((z * (x \ u)) / z)) * y
    ]]></literal>
    <justification jstring="[para(898(a,1),2357(a,2,1))].">
      <j1 rule="para" parents="898 2357"/>
    </justification>
  </clause>

  <clause id="2360">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(341,a,2358,a),flip(a)].">
      <j1 rule="hyper" parents="341 2358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2361">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) != u
    ]]></literal>
    <literal><![CDATA[
      (x * ((z / y) / x)) * y = u
    ]]></literal>
    <justification jstring="[para(2358(a,1),341(a,1))].">
      <j1 rule="para" parents="2358 341"/>
    </justification>
  </clause>

  <clause id="2362">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(1218,a,2360,a),flip(a)].">
      <j1 rule="hyper" parents="1218 2360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2363">
    <literal><![CDATA[
      x * (y * ((x * (y \ (x \ z))) / x)) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1394,a(flip),b,2360,a)].">
      <j1 rule="hyper" parents="58 1394 2360"/>
    </justification>
  </clause>

  <clause id="2364">
    <literal><![CDATA[
      T(x,x / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x * ((x / y) / x),y) = y \ z
    ]]></literal>
    <justification jstring="[para(2362(a,1),286(a,1))].">
      <j1 rule="para" parents="2362 286"/>
    </justification>
  </clause>

  <clause id="2365">
    <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(377(a,2),2363(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="377 2363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2366">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((z * ((x * (z \ 1)) / x)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(1787(a,1),2363(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1787 2363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2367">
    <literal><![CDATA[
      T(x,x / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = z
    ]]></literal>
    <justification jstring="[para(1211(a,1),2361(a,1))].">
      <j1 rule="para" parents="1211 2361"/>
    </justification>
  </clause>

  <clause id="2368">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (((x / y) * y) \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[hyper(341,a,2359,a),flip(a)].">
      <j1 rule="hyper" parents="341 2359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2369">
    <literal><![CDATA[
      (x \ (y * x)) * ((z * ((x \ (y * x)) \ x)) / z) = T(y * ((z * (y \ x)) / z),x)
    ]]></literal>
    <justification jstring="[hyper(246,a,2359,a(flip),b,1676,a),flip(a)].">
      <j1 rule="hyper" parents="246 2359 1676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2370">
    <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),2369(a,1,1))].">
      <j1 rule="para" parents="17 2369"/>
    </justification>
  </clause>

  <clause id="2371">
    <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),2370(a,1,2,1,2,1))].">
      <j1 rule="para" parents="17 2370"/>
    </justification>
  </clause>

  <clause id="2372">
    <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(843(a,1),1549(a,1,1))].">
      <j1 rule="para" parents="843 1549"/>
    </justification>
  </clause>

  <clause id="2373">
    <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(1192(a,1),2372(a,1,1))].">
      <j1 rule="para" parents="1192 2372"/>
    </justification>
  </clause>

  <clause id="2374">
    <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(1546(a,1),2373(a,1,2))].">
      <j1 rule="para" parents="1546 2373"/>
    </justification>
  </clause>

  <clause id="2375">
    <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,2374,a)].">
      <j1 rule="hyper" parents="58 20 2374"/>
    </justification>
  </clause>

  <clause id="2376">
    <literal><![CDATA[
      L(x,T(x,y) \ x,T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(1538(a,1),2375(a,1,1))].">
      <j1 rule="para" parents="1538 2375"/>
    </justification>
  </clause>

  <clause id="2377">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1192,a,b,2376,a)].">
      <j1 rule="hyper" parents="58 1192 2376"/>
    </justification>
  </clause>

  <clause id="2378">
    <literal><![CDATA[
      x * L(y,T(y,x) \ y,y) = (y * x) * T(K(x,y),y)
    ]]></literal>
    <justification jstring="[para(2376(a,1),2024(a,1,2))].">
      <j1 rule="para" parents="2376 2024"/>
    </justification>
  </clause>

  <clause id="2379">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1550,a(flip),b,2377,a),flip(a)].">
      <j1 rule="hyper" parents="58 1550 2377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2380">
    <literal><![CDATA[
      (x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * (y * T(y \ 1,u))) * z
    ]]></literal>
    <justification jstring="[para(759(a,1),1657(a,1,1)),flip(a)].">
      <j1 rule="para" parents="759 1657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2381">
    <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),2380(a,1,2))].">
      <j1 rule="para" parents="105 2380"/>
    </justification>
  </clause>

  <clause id="2382">
    <literal><![CDATA[
      (x * x) * L((x * x) \ (1 / (1 / x)),y,z) = (L(x \ 1,y,z) * x) * x
    ]]></literal>
    <justification jstring="[hyper(334,a,525,a(flip),b,1909,a),flip(a)].">
      <j1 rule="hyper" parents="334 525 1909"/>
      <j2 rule="flip"/>
    </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(1130,a,2382,a)].">
      <j1 rule="hyper" parents="1130 2382"/>
    </justification>
  </clause>

  <clause id="2384">
    <literal><![CDATA[
      x * (x * L(x \ K(x \ 1,x),y,z)) = (L(x \ 1,y,z) * x) * x
    ]]></literal>
    <justification jstring="[para(1852(a,1),2383(a,1,2,2,1,2))].">
      <j1 rule="para" parents="1852 2383"/>
    </justification>
  </clause>

  <clause id="2385">
    <literal><![CDATA[
      x * (x * L(T(x \ 1,x),y,z)) = (L(x \ 1,y,z) * x) * x
    ]]></literal>
    <justification jstring="[para(374(a,1),2384(a,1,2,2,1))].">
      <j1 rule="para" parents="374 2384"/>
    </justification>
  </clause>

  <clause id="2386">
    <literal><![CDATA[
      (L(x \ 1,y,z) * x) * x = x * (L(x \ 1,y,z) * x)
    ]]></literal>
    <justification jstring="[para(244(a,1),2385(a,1,2)),flip(a)].">
      <j1 rule="para" parents="244 2385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2387">
    <literal><![CDATA[
      T(x,L(x \ 1,y,z) * x) = x
    ]]></literal>
    <justification jstring="[hyper(247,a,2386,a)].">
      <j1 rule="hyper" parents="247 2386"/>
    </justification>
  </clause>

  <clause id="2388">
    <literal><![CDATA[
      T(x \ y,(y \ x) * (x \ y)) = x \ y
    ]]></literal>
    <justification jstring="[para(401(a,1),2387(a,1,2,1))].">
      <j1 rule="para" parents="401 2387"/>
    </justification>
  </clause>

  <clause id="2389">
    <literal><![CDATA[
      T(x \ (x / y),y * (x \ (x / y))) = x \ (x / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),2388(a,1,2,1))].">
      <j1 rule="para" parents="75 2388"/>
    </justification>
  </clause>

  <clause id="2390">
    <literal><![CDATA[
      R(x \ (x / y),y,x \ (x / y)) = T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[para(2389(a,1),825(a,1,1))].">
      <j1 rule="para" parents="2389 825"/>
    </justification>
  </clause>

  <clause id="2391">
    <literal><![CDATA[
      T(x \ (x / y),y) \ T((x \ (x / y)) * y,x \ (x / y)) = T(y,x \ (x / y))
    ]]></literal>
    <justification jstring="[para(2390(a,1),1381(a,1,1))].">
      <j1 rule="para" parents="2390 1381"/>
    </justification>
  </clause>

  <clause id="2392">
    <literal><![CDATA[
      T(x \ (x / y),y) \ ((x \ (x / y)) * y) = T(y,x \ (x / y))
    ]]></literal>
    <justification jstring="[para(1825(a,1),2391(a,1,2))].">
      <j1 rule="para" parents="1825 2391"/>
    </justification>
  </clause>

  <clause id="2393">
    <literal><![CDATA[
      T(x,T(y \ (y / x),x)) = T(x,y \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,242,a(flip),b,2392,a)].">
      <j1 rule="hyper" parents="58 242 2392"/>
    </justification>
  </clause>

  <clause id="2394">
    <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(1259(a,1),2393(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1259 2393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2395">
    <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(254(a,1),2394(a,2,2))].">
      <j1 rule="para" parents="254 2394"/>
    </justification>
  </clause>

  <clause id="2396">
    <literal><![CDATA[
      T(x,T(1 / x,R(x,y,z))) = T(x,T(x \ 1,R(x,y,z)))
    ]]></literal>
    <justification jstring="[para(1259(a,1),2395(a,1,2))].">
      <j1 rule="para" parents="1259 2395"/>
    </justification>
  </clause>

  <clause id="2397">
    <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(1453(a,1),2113(a,2,2))].">
      <j1 rule="para" parents="1453 2113"/>
    </justification>
  </clause>

  <clause id="2398">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = (x \ 1) * T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(754(a,1),2188(a,1,2)),flip(a)].">
      <j1 rule="para" parents="754 2188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2399">
    <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(334,a,267,a(flip),b,2397,a),flip(a)].">
      <j1 rule="hyper" parents="334 267 2397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2400">
    <literal><![CDATA[
      L(K(x \ 1,x) * y,x,1 / x) = K(x \ 1,x) * L(y,x,1 / x)
    ]]></literal>
    <justification jstring="[para(1891(a,1),2399(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1891 2399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2401">
    <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),2400(a,1,1)),flip(a)].">
      <j1 rule="para" parents="105 2400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2402">
    <literal><![CDATA[
      L(x,y,L(z \ u,z,w)) = L(x,y,(w * z) \ (w * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,958,a(flip),b,960,a)].">
      <j1 rule="hyper" parents="58 958 960"/>
    </justification>
  </clause>

  <clause id="2403">
    <literal><![CDATA[
      L(x,y,L(z \ 1,z,u)) = L(x,y,(u * z) \ u)
    ]]></literal>
    <justification jstring="[para(3(a,1),2402(a,2,3,2))].">
      <j1 rule="para" parents="3 2402"/>
    </justification>
  </clause>

  <clause id="2404">
    <literal><![CDATA[
      L((x * y) \ x,((x * y) \ x) \ 1,L(y \ 1,y,x)) = 1 / (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(334,a,1879,a(flip),b,2403,a),flip(a)].">
      <j1 rule="hyper" parents="334 1879 2403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2405">
    <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(2404(a,1),951(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2404 951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2406">
    <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(266(a,2),1103(a,1,2,1,1))].">
      <j1 rule="para" parents="266 1103"/>
    </justification>
  </clause>

  <clause id="2407">
    <literal><![CDATA[
      (x \ 1) * ((x \ R(x,y,z)) / (x \ 1)) = T((x \ 1) * R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[para(1629(a,1),1446(a,1,2,1))].">
      <j1 rule="para" parents="1629 1446"/>
    </justification>
  </clause>

  <clause id="2408">
    <literal><![CDATA[
      T((x \ 1) * R(x,y,z),x \ 1) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1275(a,1),2407(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1275 2407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2409">
    <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(2408(a,1),1634(a,1,2))].">
      <j1 rule="para" parents="2408 1634"/>
    </justification>
  </clause>

  <clause id="2410">
    <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,242,a(flip),b,2409,a)].">
      <j1 rule="hyper" parents="58 242 2409"/>
    </justification>
  </clause>

  <clause id="2411">
    <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,2410,a)].">
      <j1 rule="hyper" parents="58 22 2410"/>
    </justification>
  </clause>

  <clause id="2412">
    <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(334,a,22,a,b,2411,a),flip(a)].">
      <j1 rule="hyper" parents="334 22 2411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2413">
    <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(2396(a,2),2412(a,1,1))].">
      <j1 rule="para" parents="2396 2412"/>
    </justification>
  </clause>

  <clause id="2414">
    <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),1642(a,1,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 1642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2415">
    <literal><![CDATA[
      (x * T(x \ y,x)) * (1 / x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(68(a,1),1656(a,1,1)),flip(a)].">
      <j1 rule="para" parents="68 1656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2416">
    <literal><![CDATA[
      ((x \ y) * x) * (1 / x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(582,a,2415,a)].">
      <j1 rule="hyper" parents="582 2415"/>
    </justification>
  </clause>

  <clause id="2418">
    <literal><![CDATA[
      T((x * y) * (1 / x),x) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2416(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2419">
    <literal><![CDATA[
      T(x * (1 / y),y) != z * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      (y \ x) * y = z
    ]]></literal>
    <justification jstring="[para(2416(a,1),39(a,1))].">
      <j1 rule="para" parents="2416 39"/>
    </justification>
  </clause>

  <clause id="2420">
    <literal><![CDATA[
      T((x * y) * (1 / x),x) != z * (1 / x)
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(2418(a,2),39(a,1))].">
      <j1 rule="para" parents="2418 39"/>
    </justification>
  </clause>

  <clause id="2421">
    <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(1858(a,2),1872(a,1,2,1,1))].">
      <j1 rule="para" parents="1858 1872"/>
    </justification>
  </clause>

  <clause id="2422">
    <literal><![CDATA[
      (x \ 1) * ((x \ L(x,y,z)) * ((x \ 1) \ u)) = (x \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[para(1241(a,1),1926(a,2,1))].">
      <j1 rule="para" parents="1241 1926"/>
    </justification>
  </clause>

  <clause id="2423">
    <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),2422(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 2422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2424">
    <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,2423,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 2423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2425">
    <literal><![CDATA[
      L(L(x,y,y \ 1),K(y \ 1,y),1 / y) = (1 / y) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(334,a,152,a(flip),b,2010,a),flip(a)].">
      <j1 rule="hyper" parents="334 152 2010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2426">
    <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(2010(a,2),597(a,1))].">
      <j1 rule="para" parents="2010 597"/>
    </justification>
  </clause>

  <clause id="2428">
    <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(2425(a,2),498(a,1))].">
      <j1 rule="para" parents="2425 498"/>
    </justification>
  </clause>

  <clause id="2429">
    <literal><![CDATA[
      (x \ R(x,y,z)) * ((x \ 1) * u) = (x \ 1) * ((x \ R(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1272(a,1),2094(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1272 2094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2430">
    <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,2429,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 2429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2431">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) * (x \ 1) = x \ (x * (y * T(y \ 1,x)))
    ]]></literal>
    <justification jstring="[para(2159(a,1),2160(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2159 2160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2432">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) * (x \ 1) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,4,a(flip),b,2431,a),flip(a)].">
      <j1 rule="hyper" parents="334 4 2431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2434">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = (y * (x \ T(x,y))) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(1029(a,1),2432(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1029 2432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2435">
    <literal><![CDATA[
      ((x * y) \ x) * T(((x * y) \ x) \ 1,x) = (x * K(y,x)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1060(a,2),2432(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1060 2432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2436">
    <literal><![CDATA[
      (x * (y \ T(y,x))) * (x \ 1) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(1037,a,2434,a),flip(a)].">
      <j1 rule="hyper" parents="1037 2434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2437">
    <literal><![CDATA[
      (x * K(y,x)) * (x \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(1086,a,2435,a),flip(a)].">
      <j1 rule="hyper" parents="1086 2435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2438">
    <literal><![CDATA[
      K(x,y) / (y \ 1) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,1060,a,b,2435,a(flip))].">
      <j1 rule="hyper" parents="117 1060 2435"/>
    </justification>
  </clause>

  <clause id="2439">
    <literal><![CDATA[
      (1 / x) * K(y,1 / x) = K(y,1 / x) / x
    ]]></literal>
    <justification jstring="[hyper(365,a,2437,a),flip(a)].">
      <j1 rule="hyper" parents="365 2437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2440">
    <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(2438(a,1),979(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2438 979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2441">
    <literal><![CDATA[
      (1 / x) * (x * (y * T(y \ 1,x))) = (x * (y * T(y \ 1,x))) / x
    ]]></literal>
    <justification jstring="[para(2159(a,1),2161(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2159 2161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2442">
    <literal><![CDATA[
      L(x * T(x \ 1,y),y,1 / y) = (y * (x * T(x \ 1,y))) / y
    ]]></literal>
    <justification jstring="[hyper(498,a,2441,a)].">
      <j1 rule="hyper" parents="498 2441"/>
    </justification>
  </clause>

  <clause id="2443">
    <literal><![CDATA[
      (x * (((x * y) \ x) * T(((x * y) \ x) \ 1,x))) / x = L(K(y,x),x,1 / x)
    ]]></literal>
    <justification jstring="[para(1060(a,2),2442(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1060 2442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2444">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = (y * K(x,y)) / y
    ]]></literal>
    <justification jstring="[para(1060(a,2),2443(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1060 2443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2445">
    <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(254(a,1),2212(a,1,2))].">
      <j1 rule="para" parents="254 2212"/>
    </justification>
  </clause>

  <clause id="2446">
    <literal><![CDATA[
      ((T(x,y) \ x) / x) * K(x \ 1,x) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(294,a,2445,a),flip(a)].">
      <j1 rule="hyper" parents="294 2445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2447">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) \ L(1 / x,y,z)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(1891(a,1),2313(a,1,1))].">
      <j1 rule="para" parents="1891 2313"/>
    </justification>
  </clause>

  <clause id="2448">
    <literal><![CDATA[
      K(x \ 1,x) * (x * L(x \ 1,y,z)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(1109(a,1),2447(a,1,2))].">
      <j1 rule="para" parents="1109 2447"/>
    </justification>
  </clause>

  <clause id="2449">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(2301,a,2448,a)].">
      <j1 rule="hyper" parents="2301 2448"/>
    </justification>
  </clause>

  <clause id="2450">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(334,a,1914,a(flip),b,2449,a),flip(a)].">
      <j1 rule="hyper" parents="334 1914 2449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2451">
    <literal><![CDATA[
      (x \ 1) * (x * L(x \ 1,x,y)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(2175,a,2450,a)].">
      <j1 rule="hyper" parents="2175 2450"/>
    </justification>
  </clause>

  <clause id="2452">
    <literal><![CDATA[
      (x * y) \ x = (y \ 1) * (y * L(y \ 1,y,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,221,a(flip),b,2451,a)].">
      <j1 rule="hyper" parents="334 221 2451"/>
    </justification>
  </clause>

  <clause id="2453">
    <literal><![CDATA[
      (x \ 1) * (x * ((y * x) \ y)) = (y * x) \ y
    ]]></literal>
    <justification jstring="[hyper(334,a,757,a(flip),b,2452,a)].">
      <j1 rule="hyper" parents="334 757 2452"/>
    </justification>
  </clause>

  <clause id="2454">
    <literal><![CDATA[
      (x \ 1) \ ((y * x) \ y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,2452,a,b,757,a(flip))].">
      <j1 rule="hyper" parents="116 2452 757"/>
    </justification>
  </clause>

  <clause id="2455">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,2453,a(flip),b,1119,a),flip(a)].">
      <j1 rule="hyper" parents="115 2453 1119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2456">
    <literal><![CDATA[
      T(x,(y * x) \ y) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,2455,a(flip),b,2398,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 2455 2398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2457">
    <literal><![CDATA[
      T(x,(y * x) \ y) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,106,a,b,2456,a),flip(a)].">
      <j1 rule="hyper" parents="334 106 2456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2458">
    <literal><![CDATA[
      K(x,(y * x) \ y) = ((x \ 1) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,2456,a(flip),b,2318,a),flip(a)].">
      <j1 rule="hyper" parents="117 2456 2318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2459">
    <literal><![CDATA[
      T(x \ y,y \ x) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(5(a,1),2456(a,1,2,1))].">
      <j1 rule="para" parents="5 2456"/>
    </justification>
  </clause>

  <clause id="2460">
    <literal><![CDATA[
      T(1 / (1 / x),(y * x) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(1848,a,2457,a(flip))].">
      <j1 rule="hyper" parents="1848 2457"/>
    </justification>
  </clause>

  <clause id="2461">
    <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),2457(a,1,2,1))].">
      <j1 rule="para" parents="84 2457"/>
    </justification>
  </clause>

  <clause id="2462">
    <literal><![CDATA[
      T(1 / (1 / (x \ y)),y \ x) = x \ y
    ]]></literal>
    <justification jstring="[para(5(a,1),2460(a,1,2,1))].">
      <j1 rule="para" parents="5 2460"/>
    </justification>
  </clause>

  <clause id="2463">
    <literal><![CDATA[
      K(x,(y * x) \ y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,1857,a(flip),b,2458,a),flip(a)].">
      <j1 rule="hyper" parents="334 1857 2458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2464">
    <literal><![CDATA[
      K(x,(y * x) \ y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / x) = z
    ]]></literal>
    <justification jstring="[para(2458(a,2),1335(a,1))].">
      <j1 rule="para" parents="2458 1335"/>
    </justification>
  </clause>

  <clause id="2465">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ 1) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(5(a,1),2463(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 2463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2466">
    <literal><![CDATA[
      K(x,y \ (y / x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),2463(a,1,2,1))].">
      <j1 rule="para" parents="7 2463"/>
    </justification>
  </clause>

  <clause id="2467">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(T(x,y),(x * y) \ y)
    ]]></literal>
    <justification jstring="[para(105(a,1),2463(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="105 2463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2468">
    <literal><![CDATA[
      K(x \ y,T(y,x) \ ((y * x) / y)) = K(x \ y,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1198(a,2),2463(a,1,2,1))].">
      <j1 rule="para" parents="1198 2463"/>
    </justification>
  </clause>

  <clause id="2469">
    <literal><![CDATA[
      K(x,(y * x) \ y) \ 1 = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2463(a,2),1899(a,1,1))].">
      <j1 rule="para" parents="2463 1899"/>
    </justification>
  </clause>

  <clause id="2470">
    <literal><![CDATA[
      T(K(x,(y * x) \ y),z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2463(a,2),2235(a,1,1))].">
      <j1 rule="para" parents="2463 2235"/>
    </justification>
  </clause>

  <clause id="2471">
    <literal><![CDATA[
      K((x / y) \ x,z \ (z / y)) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,692,a,b,2466,a)].">
      <j1 rule="hyper" parents="58 692 2466"/>
    </justification>
  </clause>

  <clause id="2472">
    <literal><![CDATA[
      T(x \ y,x / y) = T(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,2288,a,b,2459,a)].">
      <j1 rule="hyper" parents="334 2288 2459"/>
    </justification>
  </clause>

  <clause id="2473">
    <literal><![CDATA[
      1 / T(x \ y,y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(201,a,2459,a(flip))].">
      <j1 rule="hyper" parents="201 2459"/>
    </justification>
  </clause>

  <clause id="2474">
    <literal><![CDATA[
      x * K((x \ y) \ 1,x \ y) = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2459(a,1),1527(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2459 1527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2475">
    <literal><![CDATA[
      K(x \ (x / T(y \ x,x \ y)),x) = T(K(x \ y,x),(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(2459(a,2),1608(a,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2459 1608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2476">
    <literal><![CDATA[
      (1 / (1 / (x \ y))) * (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,2462,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 2462 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2477">
    <literal><![CDATA[
      L(K(x,x \ 1),x,y) = K(((y * x) \ y) \ 1,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(2470(a,1),2321(a,1,1))].">
      <j1 rule="para" parents="2470 2321"/>
    </justification>
  </clause>

  <clause id="2478">
    <literal><![CDATA[
      T(T(x / y,x \ y),y) = T(y \ x,y / x)
    ]]></literal>
    <justification jstring="[hyper(334,a,254,a,b,2472,a)].">
      <j1 rule="hyper" parents="334 254 2472"/>
    </justification>
  </clause>

  <clause id="2479">
    <literal><![CDATA[
      1 / T(x \ (x / y),y) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),2473(a,1,2,2))].">
      <j1 rule="para" parents="75 2473"/>
    </justification>
  </clause>

  <clause id="2480">
    <literal><![CDATA[
      L(x * ((y * x) \ y),x \ 1,y * x) = ((y * x) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(2454(a,1),311(a,1,1))].">
      <j1 rule="para" parents="2454 311"/>
    </justification>
  </clause>

  <clause id="2481">
    <literal><![CDATA[
      (x \ y) * (1 / (x \ y)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(1864,a,2465,a)].">
      <j1 rule="hyper" parents="1864 2465"/>
    </justification>
  </clause>

  <clause id="2482">
    <literal><![CDATA[
      K((x * y) \ x,((x * y) \ x) \ 1) = K((x * y) \ x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),2465(a,2,2))].">
      <j1 rule="para" parents="4 2465"/>
    </justification>
  </clause>

  <clause id="2483">
    <literal><![CDATA[
      T(x,K(y \ z,z \ y)) = x
    ]]></literal>
    <justification jstring="[para(2465(a,1),2236(a,1,2))].">
      <j1 rule="para" parents="2465 2236"/>
    </justification>
  </clause>

  <clause id="2484">
    <literal><![CDATA[
      K(x \ y,y \ x) * z = z * K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(2420,a,2483,a),flip(a)].">
      <j1 rule="hyper" parents="2420 2483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2485">
    <literal><![CDATA[
      T(x / y,y / x) = T(x / y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(35,a,254,a,b,2478,a)].">
      <j1 rule="hyper" parents="35 254 2478"/>
    </justification>
  </clause>

  <clause id="2486">
    <literal><![CDATA[
      T(x / y,x \ y) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(2146,a,2485,a),flip(a)].">
      <j1 rule="hyper" parents="2146 2485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2487">
    <literal><![CDATA[
      T(x / (x * y),y) = ((x / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),2486(a,1,2))].">
      <j1 rule="para" parents="4 2486"/>
    </justification>
  </clause>

  <clause id="2488">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(30,a,1823,a,b,2476,a)].">
      <j1 rule="hyper" parents="30 1823 2476"/>
    </justification>
  </clause>

  <clause id="2489">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(30,a,873,a,b,2476,a)].">
      <j1 rule="hyper" parents="30 873 2476"/>
    </justification>
  </clause>

  <clause id="2490">
    <literal><![CDATA[
      x * ((x \ y) * (1 / (x \ y))) = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(2488(a,1),1831(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2488 1831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2491">
    <literal><![CDATA[
      T(K(x,y),K(x,y) \ 1) = T(K(x,y),K(y,x))
    ]]></literal>
    <justification jstring="[para(11(a,2),2461(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11 2461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2492">
    <literal><![CDATA[
      T(K(x,y),K(y,x)) = (K(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(439,a,2491,a),flip(a)].">
      <j1 rule="hyper" parents="439 2491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2493">
    <literal><![CDATA[
      (K(x,y) \ 1) \ 1 = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2064,a(flip),b,2492,a),flip(a)].">
      <j1 rule="hyper" parents="58 2064 2492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2496">
    <literal><![CDATA[
      K(x,y) != z \ 1
    ]]></literal>
    <literal><![CDATA[
      K(x,y) \ 1 = z
    ]]></literal>
    <justification jstring="[para(2493(a,1),43(a,1))].">
      <j1 rule="para" parents="2493 43"/>
    </justification>
  </clause>

  <clause id="2497">
    <literal><![CDATA[
      1 / (1 / K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2493(a,1),194(a,1,2,2))].">
      <j1 rule="para" parents="2493 194"/>
    </justification>
  </clause>

  <clause id="2498">
    <literal><![CDATA[
      K(x,y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      1 / K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2497(a,1),276(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2497 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2499">
    <literal><![CDATA[
      x * K(x \ y,y \ x) = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(2481(a,1),2490(a,1,2))].">
      <j1 rule="para" parents="2481 2490"/>
    </justification>
  </clause>

  <clause id="2500">
    <literal><![CDATA[
      K(x \ y,y \ x) * x = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,2484,a,b,2499,a)].">
      <j1 rule="hyper" parents="58 2484 2499"/>
    </justification>
  </clause>

  <clause id="2501">
    <literal><![CDATA[
      (x / y) * K(y,y \ 1) = x * (1 / (1 / (x \ (x / y))))
    ]]></literal>
    <justification jstring="[para(2471(a,1),2499(a,1,2))].">
      <j1 rule="para" parents="2471 2499"/>
    </justification>
  </clause>

  <clause id="2502">
    <literal><![CDATA[
      K(x \ (y * x),(y * x) \ x) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(30,a,2311,a(flip),b,2500,a),flip(a)].">
      <j1 rule="hyper" parents="30 2311 2500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2503">
    <literal><![CDATA[
      K(T(x,y),(x * y) \ y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(17(a,2),2502(a,1,1))].">
      <j1 rule="para" parents="17 2502"/>
    </justification>
  </clause>

  <clause id="2504">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2467,a,b,2503,a)].">
      <j1 rule="hyper" parents="58 2467 2503"/>
    </justification>
  </clause>

  <clause id="2506">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,2504,a(flip),b,1858,a(flip))].">
      <j1 rule="hyper" parents="116 2504 1858"/>
    </justification>
  </clause>

  <clause id="2507">
    <literal><![CDATA[
      x * (T(x,y) \ (1 / x)) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1871,a,2506,a)].">
      <j1 rule="hyper" parents="1871 2506"/>
    </justification>
  </clause>

  <clause id="2508">
    <literal><![CDATA[
      (T(x,y) \ x) / x = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2239,a(flip),b,2506,a)].">
      <j1 rule="hyper" parents="58 2239 2506"/>
    </justification>
  </clause>

  <clause id="2509">
    <literal><![CDATA[
      (1 / x) \ (1 / T(x,y)) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,2506,a(flip),b,2238,a(flip))].">
      <j1 rule="hyper" parents="116 2506 2238"/>
    </justification>
  </clause>

  <clause id="2510">
    <literal><![CDATA[
      (1 / T(x,y)) * x = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(133,a,2508,a)].">
      <j1 rule="hyper" parents="133 2508"/>
    </justification>
  </clause>

  <clause id="2511">
    <literal><![CDATA[
      x / T(x,y) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(32,a,1471,a,b,2508,a)].">
      <j1 rule="hyper" parents="32 1471 2508"/>
    </justification>
  </clause>

  <clause id="2512">
    <literal><![CDATA[
      T(1 / T(x,y),x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(2508(a,1),1167(a,1,1))].">
      <j1 rule="para" parents="2508 1167"/>
    </justification>
  </clause>

  <clause id="2513">
    <literal><![CDATA[
      (T(x,y) \ x) \ x = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(192,a,2511,a)].">
      <j1 rule="hyper" parents="192 2511"/>
    </justification>
  </clause>

  <clause id="2514">
    <literal><![CDATA[
      (T(x,y) \ x) * T(x,y) = x
    ]]></literal>
    <justification jstring="[hyper(133,a,2511,a)].">
      <j1 rule="hyper" parents="133 2511"/>
    </justification>
  </clause>

  <clause id="2515">
    <literal><![CDATA[
      K(x \ (x / ((y \ x) / T(x,y))),x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,2036,a,b,2511,a)].">
      <j1 rule="hyper" parents="58 2036 2511"/>
    </justification>
  </clause>

  <clause id="2516">
    <literal><![CDATA[
      (T(x,y) \ x) * x = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(2511(a,1),1547(a,1,1))].">
      <j1 rule="para" parents="2511 1547"/>
    </justification>
  </clause>

  <clause id="2517">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,2379,a,b,2514,a)].">
      <j1 rule="hyper" parents="58 2379 2514"/>
    </justification>
  </clause>

  <clause id="2519">
    <literal><![CDATA[
      (x * y) * T(K(y,x),x) = y * x
    ]]></literal>
    <justification jstring="[para(2517(a,1),2378(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2517 2378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2520">
    <literal><![CDATA[
      K(x \ 1,x) / T(x,y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2261,a,b,2512,a)].">
      <j1 rule="hyper" parents="58 2261 2512"/>
    </justification>
  </clause>

  <clause id="2521">
    <literal><![CDATA[
      T(K(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2519,a),flip(a)].">
      <j1 rule="hyper" parents="320 2519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2522">
    <literal><![CDATA[
      (x * K(y,x)) / x = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(281,a,2521,a)].">
      <j1 rule="hyper" parents="281 2521"/>
    </justification>
  </clause>

  <clause id="2523">
    <literal><![CDATA[
      T(x,K(y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,2521,a)].">
      <j1 rule="hyper" parents="49 2521"/>
    </justification>
  </clause>

  <clause id="2524">
    <literal><![CDATA[
      K(x,y) * y = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,2521,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 2521 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2525">
    <literal><![CDATA[
      T(L(K(x,y),z,u),y) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2521(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2521 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2526">
    <literal><![CDATA[
      (x * K(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2521(a,1),346(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="2521 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2527">
    <literal><![CDATA[
      T(x,K(y,R(x,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(144,a,2523,a)].">
      <j1 rule="hyper" parents="144 2523"/>
    </justification>
  </clause>

  <clause id="2528">
    <literal><![CDATA[
      T(x,K(y,T(x,z))) = x
    ]]></literal>
    <justification jstring="[hyper(138,a,2523,a)].">
      <j1 rule="hyper" parents="138 2523"/>
    </justification>
  </clause>

  <clause id="2529">
    <literal><![CDATA[
      T(T(x,y),K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2523(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2523 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2530">
    <literal><![CDATA[
      T(x,y) * K(z,x) = K(z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(2523(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2523 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2531">
    <literal><![CDATA[
      L(x,y,z) * K(u,x) = K(u,x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2523(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2523 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2532">
    <literal><![CDATA[
      R(x,y,z) * K(u,x) = K(u,x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2523(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2523 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2533">
    <literal><![CDATA[
      K(x,y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2523(a,1),428(a,1,2,1))].">
      <j1 rule="para" parents="2523 428"/>
    </justification>
  </clause>

  <clause id="2534">
    <literal><![CDATA[
      L(x \ y,x,K(z,y)) = (K(z,y) * x) \ (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(2523(a,1),462(a,1,1,2))].">
      <j1 rule="para" parents="2523 462"/>
    </justification>
  </clause>

  <clause id="2535">
    <literal><![CDATA[
      T(T(x,y),z) * K(u,x) = K(u,x) * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(2523(a,1),464(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2523 464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2536">
    <literal><![CDATA[
      T(x,y * T(y \ 1,x)) = x
    ]]></literal>
    <justification jstring="[para(1063(a,1),2523(a,1,2))].">
      <j1 rule="para" parents="1063 2523"/>
    </justification>
  </clause>

  <clause id="2537">
    <literal><![CDATA[
      T(x,y \ T(y,x)) = x
    ]]></literal>
    <justification jstring="[para(1066(a,1),2523(a,1,2))].">
      <j1 rule="para" parents="1066 2523"/>
    </justification>
  </clause>

  <clause id="2538">
    <literal><![CDATA[
      T(x,x \ ((y * x) / y)) = x
    ]]></literal>
    <justification jstring="[para(1543(a,1),2523(a,1,2))].">
      <j1 rule="para" parents="1543 2523"/>
    </justification>
  </clause>

  <clause id="2539">
    <literal><![CDATA[
      K(x,T(y,z)) * y = y * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,2528,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2528 17"/>
    </justification>
  </clause>

  <clause id="2540">
    <literal><![CDATA[
      T(x / y,K(z,y \ x)) = x / y
    ]]></literal>
    <justification jstring="[para(107(a,1),2528(a,1,2,2))].">
      <j1 rule="para" parents="107 2528"/>
    </justification>
  </clause>

  <clause id="2541">
    <literal><![CDATA[
      T(x \ T(x,y),y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,2537,a)].">
      <j1 rule="hyper" parents="49 2537"/>
    </justification>
  </clause>

  <clause id="2542">
    <literal><![CDATA[
      (x \ T(x,y)) * y = y * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,2537,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2537 17"/>
    </justification>
  </clause>

  <clause id="2543">
    <literal><![CDATA[
      T(x,y) * (z \ T(z,x)) = (z \ T(z,x)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(2537(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2537 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2544">
    <literal><![CDATA[
      T(T(x,y),K(z,R(x,u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2527(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2527 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2545">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2444,a,b,2522,a)].">
      <j1 rule="hyper" parents="58 2444 2522"/>
    </justification>
  </clause>

  <clause id="2546">
    <literal><![CDATA[
      L((T(x,y) * (x \ y)) / y,y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1410,a,b,2522,a)].">
      <j1 rule="hyper" parents="58 1410 2522"/>
    </justification>
  </clause>

  <clause id="2547">
    <literal><![CDATA[
      T(K(x,y),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2522(a,1),303(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2522 303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2548">
    <literal><![CDATA[
      R(K(x,y),y,(y * K(x,y)) \ z) \ z = y * ((y * K(x,y)) \ z)
    ]]></literal>
    <justification jstring="[para(2522(a,1),515(a,1,1,1))].">
      <j1 rule="para" parents="2522 515"/>
    </justification>
  </clause>

  <clause id="2549">
    <literal><![CDATA[
      R(x,K(y,z),z) * (z * K(y,z)) = (x * K(y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,2524,a(flip),b,187,a)].">
      <j1 rule="hyper" parents="119 2524 187"/>
    </justification>
  </clause>

  <clause id="2550">
    <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(2524(a,1),527(a,2,2))].">
      <j1 rule="para" parents="2524 527"/>
    </justification>
  </clause>

  <clause id="2551">
    <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(2524(a,1),530(a,1,2))].">
      <j1 rule="para" parents="2524 530"/>
    </justification>
  </clause>

  <clause id="2552">
    <literal><![CDATA[
      T(K(x,y),T(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,2529,a)].">
      <j1 rule="hyper" parents="49 2529"/>
    </justification>
  </clause>

  <clause id="2553">
    <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(2529(a,1),428(a,1,2,1))].">
      <j1 rule="para" parents="2529 428"/>
    </justification>
  </clause>

  <clause id="2554">
    <literal><![CDATA[
      T(x * T(x \ 1,y),y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,2536,a)].">
      <j1 rule="hyper" parents="49 2536"/>
    </justification>
  </clause>

  <clause id="2555">
    <literal><![CDATA[
      ((x * y) / x) / y = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(2538(a,1),273(a,1,2))].">
      <j1 rule="para" parents="2538 273"/>
    </justification>
  </clause>

  <clause id="2556">
    <literal><![CDATA[
      K(K(x,y),T(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,2552,a)].">
      <j1 rule="hyper" parents="50 2552"/>
    </justification>
  </clause>

  <clause id="2557">
    <literal><![CDATA[
      T(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(2552(a,1),294(a,1,2))].">
      <j1 rule="para" parents="2552 294"/>
    </justification>
  </clause>

  <clause id="2558">
    <literal><![CDATA[
      K(x \ T(x,y),T(y,z)) = 1
    ]]></literal>
    <justification jstring="[para(1066(a,1),2556(a,1,1))].">
      <j1 rule="para" parents="1066 2556"/>
    </justification>
  </clause>

  <clause id="2559">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(51,a,2558,a)].">
      <j1 rule="hyper" parents="51 2558"/>
    </justification>
  </clause>

  <clause id="2560">
    <literal><![CDATA[
      (1 / x) * (x * K(y,x)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(399,a,2545,a)].">
      <j1 rule="hyper" parents="399 2545"/>
    </justification>
  </clause>

  <clause id="2561">
    <literal><![CDATA[
      (1 / x) \ K(y,x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,2545,a(flip),b,267,a)].">
      <j1 rule="hyper" parents="116 2545 267"/>
    </justification>
  </clause>

  <clause id="2562">
    <literal><![CDATA[
      x * (y \ T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      (y \ T(y,x)) * x = z
    ]]></literal>
    <justification jstring="[para(2541(a,1),294(a,1,2))].">
      <j1 rule="para" parents="2541 294"/>
    </justification>
  </clause>

  <clause id="2563">
    <literal><![CDATA[
      (x \ 1) * K(y,x \ 1) = x \ K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,2560,a(flip),b,186,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 2560 186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2564">
    <literal><![CDATA[
      T(x,y) \ ((x \ 1) \ 1) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,2507,a(flip),b,1915,a),flip(a)].">
      <j1 rule="hyper" parents="119 2507 1915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2565">
    <literal><![CDATA[
      (T(x,y) \ 1) * T(x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,2520,a)].">
      <j1 rule="hyper" parents="133 2520"/>
    </justification>
  </clause>

  <clause id="2566">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(32,a,370,a,b,2520,a)].">
      <j1 rule="hyper" parents="32 370 2520"/>
    </justification>
  </clause>

  <clause id="2567">
    <literal><![CDATA[
      T(x,L(K(y,x),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,2525,a)].">
      <j1 rule="hyper" parents="49 2525"/>
    </justification>
  </clause>

  <clause id="2568">
    <literal><![CDATA[
      x * (T(x,y) \ (y * (x \ T(x,y)))) = L(y,x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[para(2542(a,1),1184(a,1,2,2))].">
      <j1 rule="para" parents="2542 1184"/>
    </justification>
  </clause>

  <clause id="2569">
    <literal><![CDATA[
      x * (((y * x) / y) / x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(119,a,2555,a,b,xx)].">
      <j1 rule="hyper" parents="119 2555"/>
    </justification>
  </clause>

  <clause id="2570">
    <literal><![CDATA[
      (1 / x) * ((y * x) / y) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1579,a,b,2555,a)].">
      <j1 rule="hyper" parents="58 1579 2555"/>
    </justification>
  </clause>

  <clause id="2571">
    <literal><![CDATA[
      (x \ 1) * (x * ((y * (x \ 1)) / y)) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(1581,a,2555,a(flip))].">
      <j1 rule="hyper" parents="1581 2555"/>
    </justification>
  </clause>

  <clause id="2572">
    <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(895(a,1),2555(a,1,1)),flip(a)].">
      <j1 rule="para" parents="895 2555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2573">
    <literal><![CDATA[
      (1 / T(x,y)) * K(x \ 1,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,2565,a(flip),b,796,a)].">
      <j1 rule="hyper" parents="119 2565 796"/>
    </justification>
  </clause>

  <clause id="2574">
    <literal><![CDATA[
      T(x,y) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(2566(a,1),2227(a,1,2))].">
      <j1 rule="para" parents="2566 2227"/>
    </justification>
  </clause>

  <clause id="2575">
    <literal><![CDATA[
      T(K(x,y),L(y,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(247,a,2531,a)].">
      <j1 rule="hyper" parents="247 2531"/>
    </justification>
  </clause>

  <clause id="2576">
    <literal><![CDATA[
      x * ((y \ (x \ y)) * y) = y * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(2554(a,1),1458(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2554 1458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2577">
    <literal><![CDATA[
      T(1 / x,(y * x) / y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(246,a,2570,a,b,1358,a)].">
      <j1 rule="hyper" parents="246 2570 1358"/>
    </justification>
  </clause>

  <clause id="2578">
    <literal><![CDATA[
      x * ((1 / T(x,y)) * K(x \ 1,x)) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,2573,a,b,1169,a)].">
      <j1 rule="hyper" parents="119 2573 1169"/>
    </justification>
  </clause>

  <clause id="2579">
    <literal><![CDATA[
      x * (T(x,y) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,2109,a,b,2574,a)].">
      <j1 rule="hyper" parents="30 2109 2574"/>
    </justification>
  </clause>

  <clause id="2581">
    <literal><![CDATA[
      T(x,y) / x = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,2579,a),flip(a)].">
      <j1 rule="hyper" parents="123 2579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2582">
    <literal><![CDATA[
      K(x,T(x,y) / x) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,2579,a(flip),b,316,a),flip(a)].">
      <j1 rule="hyper" parents="115 2579 316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2583">
    <literal><![CDATA[
      (x \ T(x,y)) * x = T(x,y)
    ]]></literal>
    <justification jstring="[para(2579(a,1),76(a,1,1,2))].">
      <j1 rule="para" parents="2579 76"/>
    </justification>
  </clause>

  <clause id="2584">
    <literal><![CDATA[
      T(1 / x,T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,2582,a(flip),b,1230,a),flip(a)].">
      <j1 rule="hyper" parents="116 2582 1230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2585">
    <literal><![CDATA[
      x \ T(x,R(y,y \ 1,x)) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(1737,a,2581,a),flip(a)].">
      <j1 rule="hyper" parents="1737 2581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2586">
    <literal><![CDATA[
      (1 / x) * T(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1406,a,2581,a)].">
      <j1 rule="hyper" parents="1406 2581"/>
    </justification>
  </clause>

  <clause id="2587">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1052,a,2581,a)].">
      <j1 rule="hyper" parents="1052 2581"/>
    </justification>
  </clause>

  <clause id="2588">
    <literal><![CDATA[
      (x \ 1) \ T(x \ 1,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(993,a,2581,a),flip(a)].">
      <j1 rule="hyper" parents="993 2581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2589">
    <literal><![CDATA[
      T(x,x \ T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(31,a,273,a,b,2581,a)].">
      <j1 rule="hyper" parents="31 273 2581"/>
    </justification>
  </clause>

  <clause id="2590">
    <literal><![CDATA[
      (x \ T(x,y)) * x != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2581(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2581 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2591">
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = (T(x,y) * z) / (x * z)
    ]]></literal>
    <justification jstring="[para(2581(a,1),102(a,1,1))].">
      <j1 rule="para" parents="2581 102"/>
    </justification>
  </clause>

  <clause id="2592">
    <literal><![CDATA[
      R((x / y) \ T(x / y,z),x / y,y) = (T(x / y,z) * y) / x
    ]]></literal>
    <justification jstring="[para(2581(a,1),538(a,1,1))].">
      <j1 rule="para" parents="2581 538"/>
    </justification>
  </clause>

  <clause id="2593">
    <literal><![CDATA[
      (x \ T(x,y)) * (1 / T(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[para(2581(a,1),2216(a,1,1))].">
      <j1 rule="para" parents="2581 2216"/>
    </justification>
  </clause>

  <clause id="2594">
    <literal><![CDATA[
      T(x,K(y \ (y / (x \ 1)),y)) = x
    ]]></literal>
    <justification jstring="[para(1066(a,2),2589(a,1,2))].">
      <j1 rule="para" parents="1066 2589"/>
    </justification>
  </clause>

  <clause id="2595">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1745,a,b,2583,a)].">
      <j1 rule="hyper" parents="58 1745 2583"/>
    </justification>
  </clause>

  <clause id="2596">
    <literal><![CDATA[
      T(x,y) \ ((x \ T(x,y)) * (x * z)) = L(z,x,x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(2583(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2583 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2597">
    <literal><![CDATA[
      T(x,y) * L(z,x,x \ T(x,y)) = (x \ T(x,y)) * (x * z)
    ]]></literal>
    <justification jstring="[para(2583(a,1),90(a,1,1))].">
      <j1 rule="para" parents="2583 90"/>
    </justification>
  </clause>

  <clause id="2598">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = u
    ]]></literal>
    <justification jstring="[para(2583(a,1),530(a,1,1,1))].">
      <j1 rule="para" parents="2583 530"/>
    </justification>
  </clause>

  <clause id="2599">
    <literal><![CDATA[
      L(x,x \ T(x,y),x) = T(x,y) / (x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(2583(a,1),1000(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2583 1000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2600">
    <literal><![CDATA[
      T(1 / (1 / x),T(1 / x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(334,a,75,a(flip),b,2584,a),flip(a)].">
      <j1 rule="hyper" parents="334 75 2584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2601">
    <literal><![CDATA[
      L(x \ 1,x,y \ ((x * y) / x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,1739,a(flip),b,2584,a)].">
      <j1 rule="hyper" parents="58 1739 2584"/>
    </justification>
  </clause>

  <clause id="2602">
    <literal><![CDATA[
      T(x \ 1,T(x,y)) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2584(a,1),254(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2584 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2603">
    <literal><![CDATA[
      T(x / (y * x),T(y,z)) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(2584(a,1),419(a,2,1))].">
      <j1 rule="para" parents="2584 419"/>
    </justification>
  </clause>

  <clause id="2604">
    <literal><![CDATA[
      x * T(x \ 1,T(x,y)) = K(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(2584(a,1),1069(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2584 1069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2605">
    <literal><![CDATA[
      (((x * y) / x) \ y) \ y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,1238,a(flip),b,2594,a)].">
      <j1 rule="hyper" parents="58 1238 2594"/>
    </justification>
  </clause>

  <clause id="2606">
    <literal><![CDATA[
      (((x * y) / x) \ y) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[hyper(119,a,2594,a(flip),b,1238,a(flip))].">
      <j1 rule="hyper" parents="119 2594 1238"/>
    </justification>
  </clause>

  <clause id="2607">
    <literal><![CDATA[
      T(x,T(1 / x,y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2600(a,1),1846(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2600 1846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2608">
    <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(2602(a,1),1600(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2602 1600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2609">
    <literal><![CDATA[
      T(x,x \ 1) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(2607(a,1),1782(a,1,1))].">
      <j1 rule="para" parents="2607 1782"/>
    </justification>
  </clause>

  <clause id="2611">
    <literal><![CDATA[
      x / ((y * x) / y) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(201,a,2605,a)].">
      <j1 rule="hyper" parents="201 2605"/>
    </justification>
  </clause>

  <clause id="2612">
    <literal><![CDATA[
      (((x * y) / x) \ y) / y = 1 / ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,2611,a(flip),b,1589,a)].">
      <j1 rule="hyper" parents="117 2611 1589"/>
    </justification>
  </clause>

  <clause id="2613">
    <literal><![CDATA[
      T(x,x / (y * x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[para(223(a,1),2595(a,1,2))].">
      <j1 rule="para" parents="223 2595"/>
    </justification>
  </clause>

  <clause id="2615">
    <literal><![CDATA[
      L(x \ 1,x,T(y,x) \ y) = x \ 1
    ]]></literal>
    <justification jstring="[para(231(a,1),2601(a,1,3,2))].">
      <j1 rule="para" parents="231 2601"/>
    </justification>
  </clause>

  <clause id="2616">
    <literal><![CDATA[
      L(x * T(x \ 1,y),x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2588(a,1),774(a,1,1))].">
      <j1 rule="para" parents="2588 774"/>
    </justification>
  </clause>

  <clause id="2618">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = x * T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2602(a,1),2604(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2602 2604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2619">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,369,a(flip),b,2618,a),flip(a)].">
      <j1 rule="hyper" parents="334 369 2618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2622">
    <literal><![CDATA[
      x \ ((y * x) / y) != y \ z
    ]]></literal>
    <literal><![CDATA[
      T(y,R(x,x \ 1,y)) = z
    ]]></literal>
    <justification jstring="[para(2585(a,1),42(a,1))].">
      <j1 rule="para" parents="2585 42"/>
    </justification>
  </clause>

  <clause id="2623">
    <literal><![CDATA[
      T(x,y \ ((x * y) / x)) = x
    ]]></literal>
    <justification jstring="[para(2585(a,1),2589(a,1,2))].">
      <j1 rule="para" parents="2585 2589"/>
    </justification>
  </clause>

  <clause id="2624">
    <literal><![CDATA[
      T(x,T(y,x) \ y) = x
    ]]></literal>
    <justification jstring="[para(231(a,1),2623(a,1,2,2))].">
      <j1 rule="para" parents="231 2623"/>
    </justification>
  </clause>

  <clause id="2625">
    <literal><![CDATA[
      T(T(x,y) \ x,y) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(49,a,2624,a)].">
      <j1 rule="hyper" parents="49 2624"/>
    </justification>
  </clause>

  <clause id="2626">
    <literal><![CDATA[
      (T(x,y) \ x) * y = y * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2624,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2624 17"/>
    </justification>
  </clause>

  <clause id="2627">
    <literal><![CDATA[
      K(K(x,y),T(z,y) \ z) = 1
    ]]></literal>
    <justification jstring="[para(2625(a,1),2083(a,1,2))].">
      <j1 rule="para" parents="2625 2083"/>
    </justification>
  </clause>

  <clause id="2628">
    <literal><![CDATA[
      K(x \ T(x,y),T(z,y) \ z) = 1
    ]]></literal>
    <justification jstring="[para(1066(a,1),2627(a,1,1))].">
      <j1 rule="para" parents="1066 2627"/>
    </justification>
  </clause>

  <clause id="2629">
    <literal><![CDATA[
      1 / (x \ T(x,y)) = (x \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,2628,a(flip),b,2481,a),flip(a)].">
      <j1 rule="hyper" parents="116 2628 2481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2630">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1736,a,b,2626,a)].">
      <j1 rule="hyper" parents="58 1736 2626"/>
    </justification>
  </clause>

  <clause id="2631">
    <literal><![CDATA[
      x \ ((x * (T(y,x) \ y)) \ x) = ((T(y,x) \ y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(2626(a,1),2001(a,1,2,1))].">
      <j1 rule="para" parents="2626 2001"/>
    </justification>
  </clause>

  <clause id="2632">
    <literal><![CDATA[
      (x * ((x * (T(y,x) \ y)) \ x)) \ (x * x) = (T(y,x) \ y) * x
    ]]></literal>
    <justification jstring="[para(2626(a,1),2172(a,1,1,2,1))].">
      <j1 rule="para" parents="2626 2172"/>
    </justification>
  </clause>

  <clause id="2634">
    <literal><![CDATA[
      L(x,x \ T(x,y),x) = x
    ]]></literal>
    <justification jstring="[hyper(334,a,72,a(flip),b,2599,a),flip(a)].">
      <j1 rule="hyper" parents="334 72 2599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2635">
    <literal><![CDATA[
      T(x \ 1,T(x,y) \ x) = x \ 1
    ]]></literal>
    <justification jstring="[para(2515(a,1),2341(a,1,2))].">
      <j1 rule="para" parents="2515 2341"/>
    </justification>
  </clause>

  <clause id="2636">
    <literal><![CDATA[
      T(T(x,y) \ x,x \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(49,a,2635,a)].">
      <j1 rule="hyper" parents="49 2635"/>
    </justification>
  </clause>

  <clause id="2637">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(685,a,2609,a)].">
      <j1 rule="hyper" parents="685 2609"/>
    </justification>
  </clause>

  <clause id="2639">
    <literal><![CDATA[
      x \ ((x * (T(y,x) \ y)) \ x) = (x * (T(y,x) \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(2626(a,1),2631(a,2,1))].">
      <j1 rule="para" parents="2626 2631"/>
    </justification>
  </clause>

  <clause id="2640">
    <literal><![CDATA[
      K((x * y) \ x,((x * y) \ x) \ 1) = L(K(y,y \ 1),y,x) \ 1
    ]]></literal>
    <justification jstring="[para(2477(a,2),445(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2477 445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2642">
    <literal><![CDATA[
      L(x * y,x \ T(x,z),x) = x * L(y,x,x \ T(x,z))
    ]]></literal>
    <justification jstring="[para(2596(a,1),1184(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2596 1184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2643">
    <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),2642(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 2642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2644">
    <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,2194,a,b,2597,a)].">
      <j1 rule="hyper" parents="58 2194 2597"/>
    </justification>
  </clause>

  <clause id="2645">
    <literal><![CDATA[
      K(x \ y,T(x / y,T(y,x))) = K(x \ y,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(842(a,1),2468(a,1,2))].">
      <j1 rule="para" parents="842 2468"/>
    </justification>
  </clause>

  <clause id="2646">
    <literal><![CDATA[
      K(x \ y,T(x / y,T(y,x))) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,2465,a(flip),b,2645,a),flip(a)].">
      <j1 rule="hyper" parents="334 2465 2645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2647">
    <literal><![CDATA[
      (x * ((x * (T(y,x) \ y)) \ x)) \ (x * x) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,2626,a(flip),b,2632,a),flip(a)].">
      <j1 rule="hyper" parents="334 2626 2632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2648">
    <literal><![CDATA[
      L(x * ((y * x) \ y),x \ 1,y * x) = R(y,x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(269(a,1),2480(a,2,1))].">
      <j1 rule="para" parents="269 2480"/>
    </justification>
  </clause>

  <clause id="2649">
    <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(2548(a,2),1028(a,1,1,2))].">
      <j1 rule="para" parents="2548 1028"/>
    </justification>
  </clause>

  <clause id="2650">
    <literal><![CDATA[
      R((x / y) \ T(x / y,z),x / y,y) = (y * T(y \ x,z)) / x
    ]]></literal>
    <justification jstring="[para(465(a,1),2592(a,2,1))].">
      <j1 rule="para" parents="465 2592"/>
    </justification>
  </clause>

  <clause id="2651">
    <literal><![CDATA[
      K((x * y) \ x,y) = L(K(y,y \ 1),y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2482,a(flip),b,2640,a)].">
      <j1 rule="hyper" parents="58 2482 2640"/>
    </justification>
  </clause>

  <clause id="2652">
    <literal><![CDATA[
      T(K(x \ y,x),(y \ x) \ 1) = T(K(x \ y,x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1605,a(flip),b,2475,a),flip(a)].">
      <j1 rule="hyper" parents="58 1605 2475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2653">
    <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),2652(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2654">
    <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(1485(a,1),2608(a,1,1))].">
      <j1 rule="para" parents="1485 2608"/>
    </justification>
  </clause>

  <clause id="2655">
    <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),2654(a,2,1))].">
      <j1 rule="para" parents="105 2654"/>
    </justification>
  </clause>

  <clause id="2656">
    <literal><![CDATA[
      K(T(1 / T(x,y),T(x,z)),T(x,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,2259,a(flip),b,2655,a),flip(a)].">
      <j1 rule="hyper" parents="334 2259 2655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2658">
    <literal><![CDATA[
      T(1 / T(x,y),T(x,z)) = K(x \ 1,x) / T(x,y)
    ]]></literal>
    <justification jstring="[para(2656(a,1),1497(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2656 1497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2659">
    <literal><![CDATA[
      T(1 / T(x,y),T(x,z)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(334,a,2520,a(flip),b,2658,a),flip(a)].">
      <j1 rule="hyper" parents="334 2520 2658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2661">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2659(a,1),2656(a,1,1))].">
      <j1 rule="para" parents="2659 2656"/>
    </justification>
  </clause>

  <clause id="2664">
    <literal><![CDATA[
      T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),y \ (y * x))
    ]]></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="2665">
    <literal><![CDATA[
      T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2664(a,2,2))].">
      <j1 rule="para" parents="4 2664"/>
    </justification>
  </clause>

  <clause id="2667">
    <literal><![CDATA[
      (x * (T(y,x) / y)) \ (x * z) = x * ((x * (T(y,x) / y)) \ z)
    ]]></literal>
    <justification jstring="[para(2355(a,1),2356(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2355 2356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2668">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * z) = x * ((x * (T(y,x) / y)) \ z)
    ]]></literal>
    <justification jstring="[para(2581(a,1),2667(a,1,1,2))].">
      <j1 rule="para" parents="2581 2667"/>
    </justification>
  </clause>

  <clause id="2669">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * z) = x * ((x * (y \ T(y,x))) \ z)
    ]]></literal>
    <justification jstring="[para(2581(a,1),2668(a,2,2,1,2))].">
      <j1 rule="para" parents="2581 2668"/>
    </justification>
  </clause>

  <clause id="2670">
    <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(2669(a,2),38(a,1))].">
      <j1 rule="para" parents="2669 38"/>
    </justification>
  </clause>

  <clause id="2671">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (x \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[para(7(a,1),2368(a,2,2,1,2,1))].">
      <j1 rule="para" parents="7 2368"/>
    </justification>
  </clause>

  <clause id="2672">
    <literal><![CDATA[
      (x * ((y * (x \ (z * u))) / y)) / u = (x / u) * ((y * ((x / u) \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(130,a,2671,a)].">
      <j1 rule="hyper" parents="130 2671"/>
    </justification>
  </clause>

  <clause id="2673">
    <literal><![CDATA[
      (x / y) * ((z * ((x / y) \ 1)) / z) = (x * ((z * (x \ y)) / z)) / y
    ]]></literal>
    <justification jstring="[para(2(a,1),2672(a,1,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2 2672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2674">
    <literal><![CDATA[
      L(x * K(y \ 1,y),y,1 / y) = L(x,y,1 / y) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(429,a,2401,a),flip(a)].">
      <j1 rule="hyper" parents="429 2401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2675">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[hyper(334,a,1660,a(flip),b,2406,a),flip(a)].">
      <j1 rule="hyper" parents="334 1660 2406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2676">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,z) = x * (T((x \ y) * x,z) / x)
    ]]></literal>
    <justification jstring="[para(1042(a,1),2421(a,2,2))].">
      <j1 rule="para" parents="1042 2421"/>
    </justification>
  </clause>

  <clause id="2677">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,1437,a(flip),b,2676,a),flip(a)].">
      <j1 rule="hyper" parents="334 1437 2676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2678">
    <literal><![CDATA[
      T(x * K(y,y \ 1),y) = T(x,y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(764,a,2677,a),flip(a)].">
      <j1 rule="hyper" parents="764 2677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2679">
    <literal><![CDATA[
      T((1 / K(x,x \ 1)) * y,x) = (1 / K(x,x \ 1)) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2677,a(flip),b,984,a),flip(a)].">
      <j1 rule="hyper" parents="119 2677 984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2680">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,x) = K(x,x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2677(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 2677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2681">
    <literal><![CDATA[
      T((x / y) * K(y,y \ 1),y) = (y \ x) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,1),2678(a,2,1))].">
      <j1 rule="para" parents="107 2678"/>
    </justification>
  </clause>

  <clause id="2682">
    <literal><![CDATA[
      x * T(K(x,x \ 1) * y,x) = K(x,x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(2680(a,2),1933(a,1,2))].">
      <j1 rule="para" parents="2680 1933"/>
    </justification>
  </clause>

  <clause id="2683">
    <literal><![CDATA[
      x \ (y * K(x,x \ 1)) = (x \ y) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2106,a,2681,a)].">
      <j1 rule="hyper" parents="2106 2681"/>
    </justification>
  </clause>

  <clause id="2684">
    <literal><![CDATA[
      x * ((x \ y) * K(x,x \ 1)) = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,2681,a(flip),b,2102,a(flip))].">
      <j1 rule="hyper" parents="119 2681 2102"/>
    </justification>
  </clause>

  <clause id="2685">
    <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(2681(a,2),39(a,1))].">
      <j1 rule="para" parents="2681 39"/>
    </justification>
  </clause>

  <clause id="2686">
    <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),2683(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="75 2683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2687">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = x * (y * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(4(a,1),2684(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 2684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2688">
    <literal><![CDATA[
      R(x,y,K(x,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(527,a,2687,a)].">
      <j1 rule="hyper" parents="527 2687"/>
    </justification>
  </clause>

  <clause id="2689">
    <literal><![CDATA[
      (1 / x) * (y * K(1 / x,(1 / x) \ 1)) = ((1 / x) * y) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(1891(a,1),2687(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1891 2687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2690">
    <literal><![CDATA[
      R(T(x,y),z,K(x,x \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2688(a,1),22(a,2,1))].">
      <j1 rule="para" parents="2688 22"/>
    </justification>
  </clause>

  <clause id="2691">
    <literal><![CDATA[
      T(x,y * K(x,x \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2105,a(flip),b,2690,a),flip(a)].">
      <j1 rule="hyper" parents="58 2105 2690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2693">
    <literal><![CDATA[
      T(x \ 1,y * K(x \ 1,x)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1862(a,1),2691(a,1,2,2))].">
      <j1 rule="para" parents="1862 2691"/>
    </justification>
  </clause>

  <clause id="2694">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = K(x,x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(294,a,2682,a)].">
      <j1 rule="hyper" parents="294 2682"/>
    </justification>
  </clause>

  <clause id="2695">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = z
    ]]></literal>
    <justification jstring="[para(2682(a,1),294(a,1))].">
      <j1 rule="para" parents="2682 294"/>
    </justification>
  </clause>

  <clause id="2696">
    <literal><![CDATA[
      L(x,y,K(x,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(493,a,2694,a)].">
      <j1 rule="hyper" parents="493 2694"/>
    </justification>
  </clause>

  <clause id="2697">
    <literal><![CDATA[
      L(1 / x,y,K(x \ 1,x)) = 1 / x
    ]]></literal>
    <justification jstring="[para(1891(a,1),2696(a,1,3))].">
      <j1 rule="para" parents="1891 2696"/>
    </justification>
  </clause>

  <clause id="2698">
    <literal><![CDATA[
      L(T(1 / x,y),z,K(x \ 1,x)) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(2697(a,1),20(a,2,1))].">
      <j1 rule="para" parents="2697 20"/>
    </justification>
  </clause>

  <clause id="2699">
    <literal><![CDATA[
      (1 / K(x,x \ 1)) * T(y,x) = T(K(x \ 1,x) * y,x)
    ]]></literal>
    <justification jstring="[para(480(a,1),2679(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="480 2679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2700">
    <literal><![CDATA[
      T(K(x \ 1,x) * y,x) = K(x \ 1,x) * T(y,x)
    ]]></literal>
    <justification jstring="[para(480(a,1),2699(a,1,1)),flip(a)].">
      <j1 rule="para" parents="480 2699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2701">
    <literal><![CDATA[
      x * T(K(x \ 1,x) * y,x) = K(x \ 1,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(2700(a,2),1454(a,1,2))].">
      <j1 rule="para" parents="2700 1454"/>
    </justification>
  </clause>

  <clause id="2702">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * x = K(x \ 1,x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(294,a,2701,a)].">
      <j1 rule="hyper" parents="294 2701"/>
    </justification>
  </clause>

  <clause id="2703">
    <literal><![CDATA[
      L(x,y,K(x \ 1,x)) = x
    ]]></literal>
    <justification jstring="[hyper(493,a,2702,a)].">
      <j1 rule="hyper" parents="493 2702"/>
    </justification>
  </clause>

  <clause id="2704">
    <literal><![CDATA[
      L(T(x,y),z,K(x \ 1,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2703(a,1),20(a,2,1))].">
      <j1 rule="para" parents="2703 20"/>
    </justification>
  </clause>

  <clause id="2705">
    <literal><![CDATA[
      T(x,K(x \ 1,x) * y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2168,a,2704,a)].">
      <j1 rule="hyper" parents="2168 2704"/>
    </justification>
  </clause>

  <clause id="2706">
    <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(449(a,1),2686(a,1,1)),flip(a)].">
      <j1 rule="para" parents="449 2686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2707">
    <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(2207(a,1),2689(a,2,1))].">
      <j1 rule="para" parents="2207 2689"/>
    </justification>
  </clause>

  <clause id="2708">
    <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(1898(a,1),2706(a,1,2,2))].">
      <j1 rule="para" parents="1898 2706"/>
    </justification>
  </clause>

  <clause id="2709">
    <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(2674(a,2),2708(a,1,2))].">
      <j1 rule="para" parents="2674 2708"/>
    </justification>
  </clause>

  <clause id="2710">
    <literal><![CDATA[
      (x * y) * K(1 / x,(1 / x) \ 1) = x * (y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(568,a,2709,a),flip(a)].">
      <j1 rule="hyper" parents="568 2709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2711">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x) = x * (y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(1891(a,1),2710(a,1,2))].">
      <j1 rule="para" parents="1891 2710"/>
    </justification>
  </clause>

  <clause id="2712">
    <literal><![CDATA[
      R(x,y,K(x \ 1,x)) = x
    ]]></literal>
    <justification jstring="[hyper(527,a,2711,a)].">
      <j1 rule="hyper" parents="527 2711"/>
    </justification>
  </clause>

  <clause id="2713">
    <literal><![CDATA[
      (x * (1 / T(x,y))) * K(x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(334,a,2578,a(flip),b,2711,a),flip(a)].">
      <j1 rule="hyper" parents="334 2578 2711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2714">
    <literal><![CDATA[
      x * ((T(x,y) \ 1) * K(x \ 1,x)) = (T(x,y) \ x) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(1163(a,1),2711(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1163 2711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2715">
    <literal><![CDATA[
      R(T(x,y),z,K(x \ 1,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2712(a,1),22(a,2,1))].">
      <j1 rule="para" parents="2712 22"/>
    </justification>
  </clause>

  <clause id="2716">
    <literal><![CDATA[
      R(1 / x,y,K(x,x \ 1)) = 1 / x
    ]]></literal>
    <justification jstring="[para(1859(a,1),2712(a,1,3))].">
      <j1 rule="para" parents="1859 2712"/>
    </justification>
  </clause>

  <clause id="2717">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x \ 1,x) = T(x,y) \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2715(a,1),436(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2715 436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2718">
    <literal><![CDATA[
      R(R(1 / x,y,z),u,K(x,x \ 1)) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(2716(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2716 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2719">
    <literal><![CDATA[
      (T(x,y) \ x) * K(x \ 1,x) = x * (T(x,y) \ K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(2717(a,1),2714(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2717 2714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2720">
    <literal><![CDATA[
      (T(x,y) \ x) * K(x \ 1,x) = T(x,y) \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(334,a,1877,a(flip),b,2719,a),flip(a)].">
      <j1 rule="hyper" parents="334 1877 2719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2721">
    <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(895(a,1),2572(a,1,2)),flip(a)].">
      <j1 rule="para" parents="895 2572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2722">
    <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,1999,a(flip),b,2721,a),flip(a)].">
      <j1 rule="hyper" parents="58 1999 2721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2723">
    <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(334,a,524,a(flip),b,749,a),flip(a)].">
      <j1 rule="hyper" parents="334 524 749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2724">
    <literal><![CDATA[
      x * (K(x,y) * T(K(x,y) \ y,z)) = (T(y,z) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(962,a,2723,a)].">
      <j1 rule="hyper" parents="962 2723"/>
    </justification>
  </clause>

  <clause id="2725">
    <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),2724(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 2724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2726">
    <literal><![CDATA[
      x * ((K(x,y) \ y) * K(x,y)) = (y * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(2523(a,1),2725(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2523 2725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2727">
    <literal><![CDATA[
      (K(x,y) \ y) * K(x,y) = y
    ]]></literal>
    <justification jstring="[hyper(29,a,84,a(flip),b,2726,a),flip(a)].">
      <j1 rule="hyper" parents="29 84 2726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2728">
    <literal><![CDATA[
      x / K(y,x) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(130,a,2727,a)].">
      <j1 rule="hyper" parents="130 2727"/>
    </justification>
  </clause>

  <clause id="2729">
    <literal><![CDATA[
      (K(x,y) \ y) \ y = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,2727,a)].">
      <j1 rule="hyper" parents="123 2727"/>
    </justification>
  </clause>

  <clause id="2730">
    <literal><![CDATA[
      K(x,y) != z \ y
    ]]></literal>
    <literal><![CDATA[
      K(x,y) \ y = z
    ]]></literal>
    <justification jstring="[para(2729(a,1),43(a,1))].">
      <j1 rule="para" parents="2729 43"/>
    </justification>
  </clause>

  <clause id="2731">
    <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,1821,a(flip),b,1127,a)].">
      <j1 rule="hyper" parents="58 1821 1127"/>
    </justification>
  </clause>

  <clause id="2733">
    <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(2731(a,1),898(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2731 898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2734">
    <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(334,a,653,a(flip),b,2733,a),flip(a)].">
      <j1 rule="hyper" parents="334 653 2733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2735">
    <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,1796,a(flip),b,2734,a),flip(a)].">
      <j1 rule="hyper" parents="58 1796 2734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2736">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * ((y * u) * T((y * u) \ y,z))
    ]]></literal>
    <justification jstring="[hyper(962,a,1533,a),flip(a)].">
      <j1 rule="hyper" parents="962 1533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2737">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * (y * (u * T(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(759(a,1),2736(a,2,2))].">
      <j1 rule="para" parents="759 2736"/>
    </justification>
  </clause>

  <clause id="2738">
    <literal><![CDATA[
      L(x * T(x \ 1,y),z,u) = K(y \ (y / L(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(493,a,2737,a)].">
      <j1 rule="hyper" parents="493 2737"/>
    </justification>
  </clause>

  <clause id="2739">
    <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(334,a,1063,a(flip),b,2738,a)].">
      <j1 rule="hyper" parents="334 1063 2738"/>
    </justification>
  </clause>

  <clause id="2740">
    <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),2738(a,2,1,2))].">
      <j1 rule="para" parents="69 2738"/>
    </justification>
  </clause>

  <clause id="2741">
    <literal><![CDATA[
      L(x \ T(x,y),z,u) = K(y \ (y / L(x \ 1,z,u)),y)
    ]]></literal>
    <justification jstring="[para(1029(a,1),2738(a,1,1))].">
      <j1 rule="para" parents="1029 2738"/>
    </justification>
  </clause>

  <clause id="2742">
    <literal><![CDATA[
      L(T(x,y) / x,z,u) = K(y \ (y / L(1 / x,z,u)),y)
    ]]></literal>
    <justification jstring="[para(1048(a,1),2738(a,1,1))].">
      <j1 rule="para" parents="1048 2738"/>
    </justification>
  </clause>

  <clause id="2743">
    <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),2741(a,2,1,2))].">
      <j1 rule="para" parents="6 2741"/>
    </justification>
  </clause>

  <clause id="2744">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * z) * T((y * z) \ z,x)) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(1584(a,1),1652(a,2,1))].">
      <j1 rule="para" parents="1584 1652"/>
    </justification>
  </clause>

  <clause id="2745">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * T(y \ 1,x)) * z) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(1286(a,1),2744(a,2,1,1))].">
      <j1 rule="para" parents="1286 2744"/>
    </justification>
  </clause>

  <clause id="2746">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(y \ (y / R(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,15,a,b,2745,a)].">
      <j1 rule="hyper" parents="334 15 2745"/>
    </justification>
  </clause>

  <clause id="2747">
    <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(2745(a,2),530(a,1))].">
      <j1 rule="para" parents="2745 530"/>
    </justification>
  </clause>

  <clause id="2748">
    <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(334,a,1063,a(flip),b,2746,a)].">
      <j1 rule="hyper" parents="334 1063 2746"/>
    </justification>
  </clause>

  <clause id="2749">
    <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(1277(a,1),2746(a,2,1,2))].">
      <j1 rule="para" parents="1277 2746"/>
    </justification>
  </clause>

  <clause id="2750">
    <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(1063(a,1),2747(a,1))].">
      <j1 rule="para" parents="1063 2747"/>
    </justification>
  </clause>

  <clause id="2751">
    <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(294,a,2748,a),flip(a)].">
      <j1 rule="hyper" parents="294 2748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2752">
    <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),1724(a,1,1))].">
      <j1 rule="para" parents="60 1724"/>
    </justification>
  </clause>

  <clause id="2753">
    <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(2643(a,1),2644(a,1,1))].">
      <j1 rule="para" parents="2643 2644"/>
    </justification>
  </clause>

  <clause id="2754">
    <literal><![CDATA[
      L(x \ (x * y),z \ T(z,x),z) = (z \ T(z,x)) * (z * (T(z,x) \ y))
    ]]></literal>
    <justification jstring="[hyper(888,a,2753,a)].">
      <j1 rule="hyper" parents="888 2753"/>
    </justification>
  </clause>

  <clause id="2755">
    <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),2754(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2756">
    <literal><![CDATA[
      (x \ T(x,y)) \ x = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(116,a,2634,a(flip),b,2755,a)].">
      <j1 rule="hyper" parents="116 2634 2755"/>
    </justification>
  </clause>

  <clause id="2757">
    <literal><![CDATA[
      (x \ T(x,y)) * T(y,T(x,y)) = L(y,x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[para(1182(a,1),2755(a,1,2))].">
      <j1 rule="para" parents="1182 2755"/>
    </justification>
  </clause>

  <clause id="2758">
    <literal><![CDATA[
      L(1 / x,x \ T(x,y),x) = (x \ T(x,y)) * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(2507(a,1),2755(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2507 2755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2759">
    <literal><![CDATA[
      x * (T(x,R(y,x,(y * x) \ x)) \ x) = (x \ (x * K(x,y))) \ x
    ]]></literal>
    <justification jstring="[para(1801(a,1),2756(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1801 2756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2760">
    <literal><![CDATA[
      x * (T(x,R(y,y \ 1,x)) \ x) = (y \ ((x * y) / x)) \ x
    ]]></literal>
    <justification jstring="[para(2585(a,1),2756(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2585 2756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2761">
    <literal><![CDATA[
      T(x,T(y,x)) * (y \ T(y,x)) = L(x,y \ T(y,x),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2543,a,b,2757,a)].">
      <j1 rule="hyper" parents="58 2543 2757"/>
    </justification>
  </clause>

  <clause id="2762">
    <literal><![CDATA[
      L(1 / x,x \ T(x,y),x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(334,a,2593,a(flip),b,2758,a),flip(a)].">
      <j1 rule="hyper" parents="334 2593 2758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2764">
    <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(2762(a,1),649(a,2,1))].">
      <j1 rule="para" parents="2762 649"/>
    </justification>
  </clause>

  <clause id="2765">
    <literal><![CDATA[
      x * (T(x,R(y,x,(y * x) \ x)) \ x) = K(x,y) \ x
    ]]></literal>
    <justification jstring="[para(4(a,1),2759(a,2,1))].">
      <j1 rule="para" parents="4 2759"/>
    </justification>
  </clause>

  <clause id="2767">
    <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),2764(a,1,2,2,2))].">
      <j1 rule="para" parents="5 2764"/>
    </justification>
  </clause>

  <clause id="2769">
    <literal><![CDATA[
      (1 / x) * (x * (x \ T(x,y))) = x * ((x \ T(x,y)) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(2584(a,1),2767(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2584 2767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2770">
    <literal><![CDATA[
      (1 / x) * (x * (x \ T(x,y))) = x * ((x \ 1) * (x \ T(x,y)))
    ]]></literal>
    <justification jstring="[para(1314(a,1),2769(a,2,2))].">
      <j1 rule="para" parents="1314 2769"/>
    </justification>
  </clause>

  <clause id="2772">
    <literal><![CDATA[
      (1 / x) * (x * (x \ T(x,y))) = L(x \ T(x,y),x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,265,a(flip),b,2770,a),flip(a)].">
      <j1 rule="hyper" parents="334 265 2770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2773">
    <literal><![CDATA[
      L(x \ T(x,y),x \ 1,x) = (1 / x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(356,a,2772,a),flip(a)].">
      <j1 rule="hyper" parents="356 2772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2775">
    <literal><![CDATA[
      L(x \ T(x,y),x \ 1,x) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,2586,a(flip),b,2773,a),flip(a)].">
      <j1 rule="hyper" parents="334 2586 2773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2776">
    <literal><![CDATA[
      L(x \ (x * K(x,y)),x \ 1,x) = x \ T(x,R(y,x,(y * x) \ x))
    ]]></literal>
    <justification jstring="[para(1801(a,1),2775(a,1,1,2))].">
      <j1 rule="para" parents="1801 2775"/>
    </justification>
  </clause>

  <clause id="2777">
    <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),2776(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2779">
    <literal><![CDATA[
      L(K(x,y),x \ 1,x) = x \ (x * K(x,y))
    ]]></literal>
    <justification jstring="[para(1801(a,1),2777(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1801 2777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2780">
    <literal><![CDATA[
      L(K(x,y),x \ 1,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,4,a(flip),b,2779,a),flip(a)].">
      <j1 rule="hyper" parents="334 4 2779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2782">
    <literal><![CDATA[
      (x \ 1) * K(x,y) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,2780,a(flip),b,265,a),flip(a)].">
      <j1 rule="hyper" parents="116 2780 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2783">
    <literal><![CDATA[
      K(x,y) * (x \ 1) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1347,a,2782,a)].">
      <j1 rule="hyper" parents="1347 2782"/>
    </justification>
  </clause>

  <clause id="2784">
    <literal><![CDATA[
      K(x,y) \ (x \ K(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,2782,a(flip),b,1346,a)].">
      <j1 rule="hyper" parents="116 2782 1346"/>
    </justification>
  </clause>

  <clause id="2785">
    <literal><![CDATA[
      x \ K(x,y) != z * K(x,y)
    ]]></literal>
    <literal><![CDATA[
      x \ 1 = z
    ]]></literal>
    <justification jstring="[para(2782(a,1),39(a,1))].">
      <j1 rule="para" parents="2782 39"/>
    </justification>
  </clause>

  <clause id="2786">
    <literal><![CDATA[
      K(x,y) \ (x \ K(x,y)) != z * u
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) / u = z
    ]]></literal>
    <justification jstring="[para(2783(a,1),588(a,1,2))].">
      <j1 rule="para" parents="2783 588"/>
    </justification>
  </clause>

  <clause id="2787">
    <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(2783(a,1),493(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2783 493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2788">
    <literal><![CDATA[
      x \ y != K(z,u) * (z \ 1)
    ]]></literal>
    <literal><![CDATA[
      x * (z \ K(z,u)) = y
    ]]></literal>
    <justification jstring="[para(2784(a,1),355(a,2,2))].">
      <j1 rule="para" parents="2784 355"/>
    </justification>
  </clause>

  <clause id="2789">
    <literal><![CDATA[
      (((x * y) \ x) \ K(y,x)) / (((x * y) \ x) \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,1060,a,b,1088,a),flip(a)].">
      <j1 rule="hyper" parents="334 1060 1088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2790">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = T(K(y,x),((x * y) \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(2789(a,1),107(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2789 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2791">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = T(K(y,x),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,2665,a(flip),b,2790,a),flip(a)].">
      <j1 rule="hyper" parents="334 2665 2790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2792">
    <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(266(a,2),1128(a,1,2,1,1))].">
      <j1 rule="para" parents="266 1128"/>
    </justification>
  </clause>

  <clause id="2793">
    <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(266(a,2),1131(a,1,2,1,1))].">
      <j1 rule="para" parents="266 1131"/>
    </justification>
  </clause>

  <clause id="2794">
    <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(1687(a,1),1265(a,1,1))].">
      <j1 rule="para" parents="1687 1265"/>
    </justification>
  </clause>

  <clause id="2795">
    <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(2413(a,1),2794(a,1,1))].">
      <j1 rule="para" parents="2413 2794"/>
    </justification>
  </clause>

  <clause id="2796">
    <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(1259(a,1),2795(a,2,1))].">
      <j1 rule="para" parents="1259 2795"/>
    </justification>
  </clause>

  <clause id="2798">
    <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(2796(a,2),695(a,1))].">
      <j1 rule="para" parents="2796 695"/>
    </justification>
  </clause>

  <clause id="2799">
    <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(2739(a,1),1517(a,1,1))].">
      <j1 rule="para" parents="2739 1517"/>
    </justification>
  </clause>

  <clause id="2800">
    <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(369(a,1),2799(a,1,1,1))].">
      <j1 rule="para" parents="369 2799"/>
    </justification>
  </clause>

  <clause id="2801">
    <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(1510(a,1),2800(a,1,2))].">
      <j1 rule="para" parents="1510 2800"/>
    </justification>
  </clause>

  <clause id="2802">
    <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,2801,a)].">
      <j1 rule="hyper" parents="58 20 2801"/>
    </justification>
  </clause>

  <clause id="2803">
    <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(1512(a,1),2802(a,2,1))].">
      <j1 rule="para" parents="1512 2802"/>
    </justification>
  </clause>

  <clause id="2804">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(2249(a,1),2803(a,1,1))].">
      <j1 rule="para" parents="2249 2803"/>
    </justification>
  </clause>

  <clause id="2805">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x) \ 1,z) = x * (y * K(z \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,2804,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 2804 13"/>
    </justification>
  </clause>

  <clause id="2807">
    <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),2322(a,1,1))].">
      <j1 rule="para" parents="85 2322"/>
    </justification>
  </clause>

  <clause id="2808">
    <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),2807(a,1,2,1,1))].">
      <j1 rule="para" parents="85 2807"/>
    </justification>
  </clause>

  <clause id="2809">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ x) * K(1 / x,(1 / x) \ 1)) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,2446,a(flip),b,2707,a),flip(a)].">
      <j1 rule="hyper" parents="334 2446 2707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2810">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ x) * K(x \ 1,x)) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(1891(a,1),2809(a,1,2,2))].">
      <j1 rule="para" parents="1891 2809"/>
    </justification>
  </clause>

  <clause id="2811">
    <literal><![CDATA[
      (1 / x) * (T(x,y) \ (1 / (1 / x))) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(2720(a,1),2810(a,1,2))].">
      <j1 rule="para" parents="2720 2810"/>
    </justification>
  </clause>

  <clause id="2812">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(2286(a,1),2811(a,1,2))].">
      <j1 rule="para" parents="2286 2811"/>
    </justification>
  </clause>

  <clause id="2813">
    <literal><![CDATA[
      (x \ 1) \ (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,2211,a(flip),b,2812,a(flip))].">
      <j1 rule="hyper" parents="116 2211 2812"/>
    </justification>
  </clause>

  <clause id="2814">
    <literal><![CDATA[
      (x \ T(x,y)) \ 1 = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,2187,a(flip),b,2813,a)].">
      <j1 rule="hyper" parents="58 2187 2813"/>
    </justification>
  </clause>

  <clause id="2815">
    <literal><![CDATA[
      1 / (x \ T(x,y)) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,2629,a,b,2814,a)].">
      <j1 rule="hyper" parents="58 2629 2814"/>
    </justification>
  </clause>

  <clause id="2816">
    <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),2814(a,1,1,2))].">
      <j1 rule="para" parents="22 2814"/>
    </justification>
  </clause>

  <clause id="2817">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = ((x / y) \ (y \ x)) \ 1
    ]]></literal>
    <justification jstring="[para(107(a,1),2814(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 2814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2818">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) \ x = (x \ (x * K(x,y))) \ 1
    ]]></literal>
    <justification jstring="[para(1801(a,1),2814(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1801 2814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2819">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ 1 = T(x \ 1,y) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(2588(a,1),2814(a,1,1))].">
      <j1 rule="para" parents="2588 2814"/>
    </justification>
  </clause>

  <clause id="2820">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ x = 1 / (y \ ((x * y) / x))
    ]]></literal>
    <justification jstring="[para(2585(a,1),2815(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2585 2815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2821">
    <literal><![CDATA[
      ((x / y) \ (y \ x)) \ 1 = (y \ x) \ (x / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),2817(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 2817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2822">
    <literal><![CDATA[
      (x \ (x * y)) \ ((x * y) / x) = (((x * y) / x) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),2821(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 2821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2823">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1) = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(1143(a,2),2819(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1143 2819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2824">
    <literal><![CDATA[
      T((x \ y) \ 1,z) \ ((x \ y) \ 1) = (x \ (y * T(y \ x,z))) \ 1
    ]]></literal>
    <justification jstring="[para(1526(a,1),2819(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1526 2819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2825">
    <literal><![CDATA[
      (((x * y) / x) \ y) \ 1 = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2822(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2826">
    <literal><![CDATA[
      1 / (x \ ((y * x) / y)) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(201,a,2825,a)].">
      <j1 rule="hyper" parents="201 2825"/>
    </justification>
  </clause>

  <clause id="2827">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ x = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,2820,a,b,2826,a)].">
      <j1 rule="hyper" parents="58 2820 2826"/>
    </justification>
  </clause>

  <clause id="2828">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ 1 = x \ (((x * y) / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,2827,a(flip),b,1163,a),flip(a)].">
      <j1 rule="hyper" parents="116 2827 1163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2829">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(231(a,1),2827(a,2,1))].">
      <j1 rule="para" parents="231 2827"/>
    </justification>
  </clause>

  <clause id="2830">
    <literal><![CDATA[
      (x \ ((y * x) / y)) \ y = y * (((y * x) / y) \ x)
    ]]></literal>
    <justification jstring="[para(2827(a,1),2760(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2827 2760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2831">
    <literal><![CDATA[
      x * (((x * T(y,x)) / x) \ T(y,x)) = (T(y,x) \ y) \ x
    ]]></literal>
    <justification jstring="[para(231(a,1),2830(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="231 2830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2832">
    <literal><![CDATA[
      T(x,x \ (((x * y) / x) \ y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2828(a,1),2234(a,1,2))].">
      <j1 rule="para" parents="2828 2234"/>
    </justification>
  </clause>

  <clause id="2833">
    <literal><![CDATA[
      T(x,x \ (y \ T(y,x))) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(231(a,1),2832(a,1,2,2,1))].">
      <j1 rule="para" parents="231 2832"/>
    </justification>
  </clause>

  <clause id="2834">
    <literal><![CDATA[
      T(x,x \ ((((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)))) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1062(a,1),2833(a,1,2,2,2))].">
      <j1 rule="para" parents="1062 2833"/>
    </justification>
  </clause>

  <clause id="2835">
    <literal><![CDATA[
      (x * (T(y,x) \ y)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(2630(a,1),2829(a,1,1))].">
      <j1 rule="para" parents="2630 2829"/>
    </justification>
  </clause>

  <clause id="2836">
    <literal><![CDATA[
      x / (y \ T(y,x)) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(201,a,2835,a)].">
      <j1 rule="hyper" parents="201 2835"/>
    </justification>
  </clause>

  <clause id="2837">
    <literal><![CDATA[
      (x * (T(y,x) \ y)) \ 1 = x \ (y \ T(y,x))
    ]]></literal>
    <justification jstring="[para(2835(a,1),2639(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2835 2639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2838">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * x) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[para(2835(a,1),2647(a,1,1,2))].">
      <j1 rule="para" parents="2835 2647"/>
    </justification>
  </clause>

  <clause id="2839">
    <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(1062(a,1),2836(a,1,2,2))].">
      <j1 rule="para" parents="1062 2836"/>
    </justification>
  </clause>

  <clause id="2840">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ x = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(2670,a,2838,a)].">
      <j1 rule="hyper" parents="2670 2838"/>
    </justification>
  </clause>

  <clause id="2841">
    <literal><![CDATA[
      (T(x,y) \ x) \ y = y * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(231(a,1),2831(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="231 2831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2842">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) \ x = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),2818(a,2,1))].">
      <j1 rule="para" parents="4 2818"/>
    </justification>
  </clause>

  <clause id="2844">
    <literal><![CDATA[
      x * (K(x,y) \ 1) = K(x,y) \ x
    ]]></literal>
    <justification jstring="[para(2842(a,1),2765(a,1,2))].">
      <j1 rule="para" parents="2842 2765"/>
    </justification>
  </clause>

  <clause id="2845">
    <literal><![CDATA[
      x \ (K(x,y) \ x) = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,2844,a)].">
      <j1 rule="hyper" parents="123 2844"/>
    </justification>
  </clause>

  <clause id="2846">
    <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),2816(a,2,1))].">
      <j1 rule="para" parents="22 2816"/>
    </justification>
  </clause>

  <clause id="2847">
    <literal><![CDATA[
      L(x \ 1,x,K(y,x) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[para(2823(a,1),2615(a,1,3))].">
      <j1 rule="para" parents="2823 2615"/>
    </justification>
  </clause>

  <clause id="2848">
    <literal><![CDATA[
      T(x,K(y,x) \ 1) = x
    ]]></literal>
    <justification jstring="[para(2823(a,1),2624(a,1,2))].">
      <j1 rule="para" parents="2823 2624"/>
    </justification>
  </clause>

  <clause id="2849">
    <literal><![CDATA[
      (K(x,y) \ 1) * y = y * (K(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,2848,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2848 17"/>
    </justification>
  </clause>

  <clause id="2850">
    <literal><![CDATA[
      (x * (K(y,x) \ 1)) \ (K(y,x) \ 1) = L(x \ 1,x,K(y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(2849(a,1),221(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2849 221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2851">
    <literal><![CDATA[
      (x * (K(y,x) \ 1)) \ (K(y,x) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(334,a,2847,a(flip),b,2850,a),flip(a)].">
      <j1 rule="hyper" parents="334 2847 2850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2853">
    <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(334,a,1945,a(flip),b,2792,a),flip(a)].">
      <j1 rule="hyper" parents="334 1945 2792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2854">
    <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(334,a,1809,a(flip),b,2793,a),flip(a)].">
      <j1 rule="hyper" parents="334 1809 2793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2855">
    <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(1133(a,1),2853(a,2,1))].">
      <j1 rule="para" parents="1133 2853"/>
    </justification>
  </clause>

  <clause id="2856">
    <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(1108(a,1),2854(a,2,1))].">
      <j1 rule="para" parents="1108 2854"/>
    </justification>
  </clause>

  <clause id="2857">
    <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(334,a,526,a(flip),b,878,a),flip(a)].">
      <j1 rule="hyper" parents="334 526 878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2858">
    <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(1425,a,2857,a)].">
      <j1 rule="hyper" parents="1425 2857"/>
    </justification>
  </clause>

  <clause id="2859">
    <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(1311(a,1),2858(a,2,1,1))].">
      <j1 rule="para" parents="1311 2858"/>
    </justification>
  </clause>

  <clause id="2860">
    <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),1981(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="17 1981"/>
      <j2 rule="flip"/>
    </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) * (R(y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(245(a,1),2860(a,2,2))].">
      <j1 rule="para" parents="245 2860"/>
    </justification>
  </clause>

  <clause id="2862">
    <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),1989(a,2,1,2))].">
      <j1 rule="para" parents="3 1989"/>
    </justification>
  </clause>

  <clause id="2863">
    <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(2267,a,2266,a),flip(a)].">
      <j1 rule="hyper" parents="2267 2266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2864">
    <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(2274,a,2273,a),flip(a)].">
      <j1 rule="hyper" parents="2274 2273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2865">
    <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),1235(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 1235"/>
      <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(x,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),2865(a,2,2,2,1))].">
      <j1 rule="para" parents="75 2865"/>
    </justification>
  </clause>

  <clause id="2867">
    <literal><![CDATA[
      x * T(x \ T(x,y),(1 / x) \ 1) = (1 / x) \ (x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),2866(a,1,2,1,2,1))].">
      <j1 rule="para" parents="75 2866"/>
    </justification>
  </clause>

  <clause id="2868">
    <literal><![CDATA[
      (1 / x) \ (x \ T(x,y)) = x * T(x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[para(75(a,1),2867(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 2867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2869">
    <literal><![CDATA[
      (1 / x) \ (x \ T(x,y)) = (x \ T(x,y)) * x
    ]]></literal>
    <justification jstring="[hyper(334,a,105,a(flip),b,2868,a),flip(a)].">
      <j1 rule="hyper" parents="334 105 2868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2870">
    <literal><![CDATA[
      (x \ T(x,R(y,x,(y * x) \ x))) * x = (1 / x) \ (x \ (x * K(x,y)))
    ]]></literal>
    <justification jstring="[para(1801(a,1),2869(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1801 2869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2871">
    <literal><![CDATA[
      (x \ T(x,R(y,x,(y * x) \ x))) * x = (1 / x) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),2870(a,2,2))].">
      <j1 rule="para" parents="4 2870"/>
    </justification>
  </clause>

  <clause id="2873">
    <literal><![CDATA[
      (x \ (x * K(x,y))) * x = (1 / x) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(1801(a,1),2871(a,1,1,2))].">
      <j1 rule="para" parents="1801 2871"/>
    </justification>
  </clause>

  <clause id="2874">
    <literal><![CDATA[
      (1 / x) \ K(x,y) = K(x,y) * x
    ]]></literal>
    <justification jstring="[para(4(a,1),2873(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2876">
    <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(2305,a,2174,a)].">
      <j1 rule="hyper" parents="2305 2174"/>
    </justification>
  </clause>

  <clause id="2877">
    <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(2405(a,1),38(a,1))].">
      <j1 rule="para" parents="2405 38"/>
    </justification>
  </clause>

  <clause id="2878">
    <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(1029(a,1),2440(a,2,2))].">
      <j1 rule="para" parents="1029 2440"/>
    </justification>
  </clause>

  <clause id="2879">
    <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(2438(a,1),2878(a,1,2,1,2))].">
      <j1 rule="para" parents="2438 2878"/>
    </justification>
  </clause>

  <clause id="2880">
    <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),2879(a,1,2,1))].">
      <j1 rule="para" parents="17 2879"/>
    </justification>
  </clause>

  <clause id="2881">
    <literal><![CDATA[
      (x * K(y,x)) * (x \ T(x,z)) = K(y,x) * T(x,z)
    ]]></literal>
    <justification jstring="[para(2523(a,1),2880(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2523 2880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2882">
    <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(1816(a,1),2743(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1816 2743"/>
      <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(1,y,z)
    ]]></literal>
    <justification jstring="[para(61(a,1),2882(a,2,1))].">
      <j1 rule="para" parents="61 2882"/>
    </justification>
  </clause>

  <clause id="2884">
    <literal><![CDATA[
      K((x * L(x \ 1,y,z)) \ x,x * L(x \ 1,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(334,a,182,a(flip),b,2883,a),flip(a)].">
      <j1 rule="hyper" parents="334 182 2883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2886">
    <literal><![CDATA[
      ((x * L(x \ 1,y,z)) \ x) * (x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(443,a,2884,a)].">
      <j1 rule="hyper" parents="443 2884"/>
    </justification>
  </clause>

  <clause id="2888">
    <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(2886(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="2886 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2889">
    <literal><![CDATA[
      a(L(x \ y,x,z),u,w) = a((z * x) \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(1018,a,959,a),flip(a)].">
      <j1 rule="hyper" parents="1018 959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2890">
    <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(1967(a,1),1798(a,1,2,1))].">
      <j1 rule="para" parents="1967 1798"/>
    </justification>
  </clause>

  <clause id="2891">
    <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),2890(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 2890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2892">
    <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,2891,a),flip(a)].">
      <j1 rule="hyper" parents="134 2891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2894">
    <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,2892,a,b,2563,a(flip))].">
      <j1 rule="hyper" parents="119 2892 2563"/>
    </justification>
  </clause>

  <clause id="2895">
    <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(2894(a,1),1730(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2894 1730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2896">
    <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(334,a,1806,a(flip),b,2895,a),flip(a)].">
      <j1 rule="hyper" parents="334 1806 2895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2897">
    <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,2613,a,b,2896,a)].">
      <j1 rule="hyper" parents="58 2613 2896"/>
    </justification>
  </clause>

  <clause id="2898">
    <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,2897,a)].">
      <j1 rule="hyper" parents="58 22 2897"/>
    </justification>
  </clause>

  <clause id="2899">
    <literal><![CDATA[
      R(x,y,z) * K(R(x,y,z),x \ 1) = R((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(2138(a,1),2898(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2138 2898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2900">
    <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,855,a,b,2899,a)].">
      <j1 rule="hyper" parents="116 855 2899"/>
    </justification>
  </clause>

  <clause id="2902">
    <literal><![CDATA[
      a(R(x,y,z),1 / x,x) = K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,1338,a(flip),b,2900,a)].">
      <j1 rule="hyper" parents="58 1338 2900"/>
    </justification>
  </clause>

  <clause id="2903">
    <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(2900(a,1),2846(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2900 2846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2904">
    <literal><![CDATA[
      x * ((x \ R(x,y,z)) / R(x,y,z)) = a(R(x,y,z),1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,2894,a,b,2902,a)].">
      <j1 rule="hyper" parents="334 2894 2902"/>
    </justification>
  </clause>

  <clause id="2905">
    <literal><![CDATA[
      x * L(x \ 1,R(x,y,z),1 / x) = a(R(x,y,z),1 / x,x)
    ]]></literal>
    <justification jstring="[para(2017(a,2),2904(a,1,2))].">
      <j1 rule="para" parents="2017 2904"/>
    </justification>
  </clause>

  <clause id="2906">
    <literal><![CDATA[
      K(R(x,y,z),x \ 1) \ 1 = x * T(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(2798,a,2903,a),flip(a)].">
      <j1 rule="hyper" parents="2798 2903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2907">
    <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),1797(a,2,2))].">
      <j1 rule="para" parents="6 1797"/>
    </justification>
  </clause>

  <clause id="2908">
    <literal><![CDATA[
      (((x \ y) * (y \ x)) / (x \ y)) * ((y \ x) \ 1) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1021,a(flip),b,2907,a)].">
      <j1 rule="hyper" parents="58 1021 2907"/>
    </justification>
  </clause>

  <clause id="2910">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) * ((y \ x) \ 1) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(874(a,1),2908(a,1,1))].">
      <j1 rule="para" parents="874 2908"/>
    </justification>
  </clause>

  <clause id="2911">
    <literal><![CDATA[
      (x \ y) * K(y \ x,x \ y) = L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,2437,a,b,2910,a)].">
      <j1 rule="hyper" parents="30 2437 2910"/>
    </justification>
  </clause>

  <clause id="2912">
    <literal><![CDATA[
      (x \ y) * K(y \ x,x \ y) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(334,a,2489,a(flip),b,2911,a),flip(a)].">
      <j1 rule="hyper" parents="334 2489 2911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2913">
    <literal><![CDATA[
      K((x \ y) \ 1,x \ y) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(29,a,1853,a,b,2912,a)].">
      <j1 rule="hyper" parents="29 1853 2912"/>
    </justification>
  </clause>

  <clause id="2914">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,(x * y) \ x) = K(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,691,a(flip),b,2913,a),flip(a)].">
      <j1 rule="hyper" parents="334 691 2913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2915">
    <literal><![CDATA[
      K(1 / (x \ y),x \ y) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1898,a,b,2913,a)].">
      <j1 rule="hyper" parents="58 1898 2913"/>
    </justification>
  </clause>

  <clause id="2916">
    <literal><![CDATA[
      x * K(y \ x,x \ y) = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2913(a,1),2474(a,1,2))].">
      <j1 rule="para" parents="2913 2474"/>
    </justification>
  </clause>

  <clause id="2917">
    <literal><![CDATA[
      K(1 / ((x * y) \ x),(x * y) \ x) = K(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,691,a(flip),b,2915,a),flip(a)].">
      <j1 rule="hyper" parents="334 691 2915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2918">
    <literal><![CDATA[
      L(K(x,x \ 1),x,y) = K(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2477,a,b,2914,a)].">
      <j1 rule="hyper" parents="58 2477 2914"/>
    </justification>
  </clause>

  <clause id="2919">
    <literal><![CDATA[
      (x * y) * K(y,(x * y) \ x) = x * T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(2914(a,1),1541(a,1,2))].">
      <j1 rule="para" parents="2914 1541"/>
    </justification>
  </clause>

  <clause id="2920">
    <literal><![CDATA[
      L(K(x,x \ 1),x,y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,2463,a(flip),b,2918,a),flip(a)].">
      <j1 rule="hyper" parents="334 2463 2918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2921">
    <literal><![CDATA[
      K(x,(y * x) \ y) \ 1 = K((y * x) \ y,x)
    ]]></literal>
    <justification jstring="[para(2918(a,1),2651(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2918 2651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2923">
    <literal><![CDATA[
      L(K(x \ 1,x),1 / x,y) = K(1 / x,(1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(1891(a,1),2920(a,1,1))].">
      <j1 rule="para" parents="1891 2920"/>
    </justification>
  </clause>

  <clause id="2924">
    <literal><![CDATA[
      K((x * y) \ x,y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2469,a(flip),b,2921,a),flip(a)].">
      <j1 rule="hyper" parents="58 2469 2921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2926">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) = K((x * y) \ y,T(x,y))
    ]]></literal>
    <justification jstring="[para(105(a,1),2924(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="105 2924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2927">
    <literal><![CDATA[
      K((x * y) \ y,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2661,a(flip),b,2926,a),flip(a)].">
      <j1 rule="hyper" parents="58 2661 2926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2928">
    <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(840(a,1),2926(a,2,1,1))].">
      <j1 rule="para" parents="840 2926"/>
    </justification>
  </clause>

  <clause id="2930">
    <literal><![CDATA[
      K((x * y) \ y,y \ (x * y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(17(a,1),2927(a,1,2))].">
      <j1 rule="para" parents="17 2927"/>
    </justification>
  </clause>

  <clause id="2931">
    <literal><![CDATA[
      (x * y) * ((((x * y) \ y) \ 1) \ 1) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2930(a,1),2916(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2930 2916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2932">
    <literal><![CDATA[
      L(K(x \ 1,x),1 / x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,1891,a(flip),b,2923,a),flip(a)].">
      <j1 rule="hyper" parents="334 1891 2923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2933">
    <literal><![CDATA[
      (x * (y \ 1)) / K(y \ 1,y) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(2932(a,1),804(a,1,2))].">
      <j1 rule="para" parents="2932 804"/>
    </justification>
  </clause>

  <clause id="2934">
    <literal><![CDATA[
      (x / (y \ 1)) * (1 / y) = x / K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2932(a,1),805(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2932 805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2935">
    <literal><![CDATA[
      R(x,y \ 1,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(1673,a,2933,a)].">
      <j1 rule="hyper" parents="1673 2933"/>
    </justification>
  </clause>

  <clause id="2936">
    <literal><![CDATA[
      (x / (1 / y)) * (y \ 1) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(340,a,2933,a),flip(a)].">
      <j1 rule="hyper" parents="340 2933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2937">
    <literal><![CDATA[
      (x * (1 / y)) * K(y \ 1,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,2933,a)].">
      <j1 rule="hyper" parents="133 2933"/>
    </justification>
  </clause>

  <clause id="2938">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2933(a,1),1672(a,1,1))].">
      <j1 rule="para" parents="2933 1672"/>
    </justification>
  </clause>

  <clause id="2940">
    <literal><![CDATA[
      R(x,1 / y,y) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1120,a,2935,a),flip(a)].">
      <j1 rule="hyper" parents="1120 2935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2941">
    <literal><![CDATA[
      R(T(x / (1 / y),z),y \ 1,y) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(1045,a,2935,a),flip(a)].">
      <j1 rule="hyper" parents="1045 2935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2942">
    <literal><![CDATA[
      R(x / (1 / y),y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(340,a,2935,a),flip(a)].">
      <j1 rule="hyper" parents="340 2935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2943">
    <literal><![CDATA[
      x / y != z * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      R(z,y \ 1,y) = x
    ]]></literal>
    <justification jstring="[para(2935(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="2935 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2944">
    <literal><![CDATA[
      x \ R(y,x \ 1,x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(2935(a,1),107(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2935 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2945">
    <literal><![CDATA[
      (x * (1 / y)) * y != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2935(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2935 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2946">
    <literal><![CDATA[
      R(x,(y \ 1) \ 1,y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),2940(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 2940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2947">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) * x = R(K(y,x),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2332(a,1),2938(a,1,1))].">
      <j1 rule="para" parents="2332 2938"/>
    </justification>
  </clause>

  <clause id="2948">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * R(y / (1 / x),x \ 1,x)) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(2942(a,1),1973(a,1,1,2))].">
      <j1 rule="para" parents="2942 1973"/>
    </justification>
  </clause>

  <clause id="2950">
    <literal><![CDATA[
      (x * (y \ 1)) / (1 / y) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1498,a,2936,a)].">
      <j1 rule="hyper" parents="1498 2936"/>
    </justification>
  </clause>

  <clause id="2951">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y \ 1,y) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(1496,a,2936,a),flip(a)].">
      <j1 rule="hyper" parents="1496 2936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2952">
    <literal><![CDATA[
      R(x,1 / y,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(867,a,2937,a)].">
      <j1 rule="hyper" parents="867 2937"/>
    </justification>
  </clause>

  <clause id="2953">
    <literal><![CDATA[
      R(x,1 / (1 / y),K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1859(a,1),2952(a,1,3))].">
      <j1 rule="para" parents="1859 2952"/>
    </justification>
  </clause>

  <clause id="2954">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / y = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1886,a(flip),b,2953,a)].">
      <j1 rule="hyper" parents="58 1886 2953"/>
    </justification>
  </clause>

  <clause id="2955">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * K(y,y \ 1) = x * y
    ]]></literal>
    <justification jstring="[para(2953(a,1),1885(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2953 1885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2956">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * (1 / y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,2950,a)].">
      <j1 rule="hyper" parents="133 2950"/>
    </justification>
  </clause>

  <clause id="2957">
    <literal><![CDATA[
      R(x * K(y \ 1,y),y \ 1,y) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[para(2950(a,1),2942(a,1,1))].">
      <j1 rule="para" parents="2950 2942"/>
    </justification>
  </clause>

  <clause id="2958">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (x \ 1)) = y / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(2260,a,2951,a)].">
      <j1 rule="hyper" parents="2260 2951"/>
    </justification>
  </clause>

  <clause id="2960">
    <literal><![CDATA[
      (x / y) * K(y,y \ 1) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,2104,a(flip),b,2954,a)].">
      <j1 rule="hyper" parents="58 2104 2954"/>
    </justification>
  </clause>

  <clause id="2961">
    <literal><![CDATA[
      x * K(y,y \ 1) != z * y
    ]]></literal>
    <literal><![CDATA[
      z * (1 / (1 / y)) = x
    ]]></literal>
    <justification jstring="[para(2955(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="2955 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2962">
    <literal><![CDATA[
      K(x,x \ 1) * (y / x) = y / (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(2241,a,2960,a)].">
      <j1 rule="hyper" parents="2241 2960"/>
    </justification>
  </clause>

  <clause id="2963">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (x / y)))) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,2501,a(flip),b,2960,a)].">
      <j1 rule="hyper" parents="58 2501 2960"/>
    </justification>
  </clause>

  <clause id="2964">
    <literal><![CDATA[
      1 / (1 / (x \ (x / y))) = x \ (x / (1 / (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(116,a,2960,a(flip),b,2501,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 2960 2501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2965">
    <literal><![CDATA[
      K(x,1 / x) * (y / x) = y / (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(1855(a,2),2962(a,1,1))].">
      <j1 rule="para" parents="1855 2962"/>
    </justification>
  </clause>

  <clause id="2966">
    <literal><![CDATA[
      T(x * y,x \ (1 / y)) = R(((x / (1 / y)) \ 1) \ 1,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2486(a,1),2941(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2486 2941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2967">
    <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(2515(a,1),2947(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2515 2947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2968">
    <literal><![CDATA[
      (x / (1 / (1 / y))) / x = 1 / (1 / ((x / y) / x))
    ]]></literal>
    <justification jstring="[hyper(117,a,2963,a(flip),b,2283,a)].">
      <j1 rule="hyper" parents="117 2963 2283"/>
    </justification>
  </clause>

  <clause id="2969">
    <literal><![CDATA[
      x / (1 / (1 / (y \ x))) = x * (1 / (1 / (x \ y)))
    ]]></literal>
    <justification jstring="[para(72(a,1),2963(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="72 2963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2970">
    <literal><![CDATA[
      (x \ (x / (1 / (1 / y)))) \ 1 = 1 / (x \ (x / y))
    ]]></literal>
    <justification jstring="[hyper(192,a,2964,a)].">
      <j1 rule="hyper" parents="192 2964"/>
    </justification>
  </clause>

  <clause id="2971">
    <literal><![CDATA[
      1 / (1 / (x \ (x / (y \ 1)))) = x \ (x / (1 / y))
    ]]></literal>
    <justification jstring="[para(72(a,1),2964(a,2,2,2,2))].">
      <j1 rule="para" parents="72 2964"/>
    </justification>
  </clause>

  <clause id="2972">
    <literal><![CDATA[
      1 / (1 / ((x / (y \ 1)) / x)) = (x / (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(72(a,1),2968(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 2968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2973">
    <literal><![CDATA[
      (x * (1 / (1 / (x \ y)))) \ x = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(192,a,2969,a)].">
      <j1 rule="hyper" parents="192 2969"/>
    </justification>
  </clause>

  <clause id="2974">
    <literal><![CDATA[
      x / (1 / (1 / ((x * y) \ x))) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(4(a,1),2969(a,2,2,2,2))].">
      <j1 rule="para" parents="4 2969"/>
    </justification>
  </clause>

  <clause id="2975">
    <literal><![CDATA[
      1 / (x \ (x / (y \ 1))) = (x \ (x / (1 / y))) \ 1
    ]]></literal>
    <justification jstring="[para(72(a,1),2970(a,1,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="72 2970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2976">
    <literal><![CDATA[
      1 / (x \ (x / ((y \ 1) \ 1))) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[para(194(a,1),2970(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="194 2970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2977">
    <literal><![CDATA[
      1 / ((x / (y \ 1)) / x) = ((x / (1 / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(192,a,2972,a),flip(a)].">
      <j1 rule="hyper" parents="192 2972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2978">
    <literal><![CDATA[
      1 / (1 / ((x * y) \ x)) = (x * (1 / (1 / y))) \ x
    ]]></literal>
    <justification jstring="[para(4(a,1),2973(a,1,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4 2973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2979">
    <literal><![CDATA[
      (x * (1 / (1 / T(y,x)))) \ x = 1 / (1 / ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(17(a,2),2973(a,1,1,2,2,2))].">
      <j1 rule="para" parents="17 2973"/>
    </justification>
  </clause>

  <clause id="2980">
    <literal><![CDATA[
      (x * K(x \ y,y \ x)) \ y = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(2499(a,2),2973(a,1,1))].">
      <j1 rule="para" parents="2499 2973"/>
    </justification>
  </clause>

  <clause id="2981">
    <literal><![CDATA[
      T(x \ (x / (1 / y)),1 / y) = x \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(31,a,2479,a,b,2975,a)].">
      <j1 rule="hyper" parents="31 2479 2975"/>
    </justification>
  </clause>

  <clause id="2982">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ 1 = x \ (x / ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(192,a,2976,a)].">
      <j1 rule="hyper" parents="192 2976"/>
    </justification>
  </clause>

  <clause id="2983">
    <literal><![CDATA[
      T(x \ (x / y),y) = x \ (x / ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(31,a,2479,a,b,2976,a)].">
      <j1 rule="hyper" parents="31 2479 2976"/>
    </justification>
  </clause>

  <clause id="2984">
    <literal><![CDATA[
      x * (((x \ (x / y)) \ 1) \ 1) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2976(a,1),199(a,1,2,1))].">
      <j1 rule="para" parents="2976 199"/>
    </justification>
  </clause>

  <clause id="2985">
    <literal><![CDATA[
      x * T(x \ (x / y),y) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,2983,a,b,xx)].">
      <j1 rule="hyper" parents="119 2983"/>
    </justification>
  </clause>

  <clause id="2986">
    <literal><![CDATA[
      x * (y \ (y / ((x \ 1) \ 1))) = (y \ (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,2983,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2983 17"/>
    </justification>
  </clause>

  <clause id="2987">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2302,a,2985,a)].">
      <j1 rule="hyper" parents="2302 2985"/>
    </justification>
  </clause>

  <clause id="2988">
    <literal><![CDATA[
      (x * y) / ((y \ 1) \ 1) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),2987(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 2987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2989">
    <literal><![CDATA[
      (x / ((y \ 1) \ 1)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2987(a,1),1667(a,1,1))].">
      <j1 rule="para" parents="2987 1667"/>
    </justification>
  </clause>

  <clause id="2990">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * ((y \ 1) \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(133,a,2988,a)].">
      <j1 rule="hyper" parents="133 2988"/>
    </justification>
  </clause>

  <clause id="2991">
    <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(2220(a,2),2988(a,1,2))].">
      <j1 rule="para" parents="2220 2988"/>
    </justification>
  </clause>

  <clause id="2992">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),2989(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 2989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2993">
    <literal><![CDATA[
      (x / T(y,y \ 1)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(106(a,2),2989(a,1,1,2))].">
      <j1 rule="para" parents="106 2989"/>
    </justification>
  </clause>

  <clause id="2994">
    <literal><![CDATA[
      (x * T(y,y \ 1)) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[para(677(a,1),2989(a,1,1)),flip(a)].">
      <j1 rule="para" parents="677 2989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2995">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * ((x \ 1) \ 1) = y * x
    ]]></literal>
    <justification jstring="[para(2250(a,2),2990(a,1,1))].">
      <j1 rule="para" parents="2250 2990"/>
    </justification>
  </clause>

  <clause id="2996">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ 1) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,532,a,b,2992,a),flip(a)].">
      <j1 rule="hyper" parents="30 532 2992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2997">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T(x,x \ 1)) = y * x
    ]]></literal>
    <justification jstring="[hyper(2260,a,2994,a)].">
      <j1 rule="hyper" parents="2260 2994"/>
    </justification>
  </clause>

  <clause id="2998">
    <literal><![CDATA[
      K(x \ 1,x) \ (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,2994,a(flip),b,2250,a)].">
      <j1 rule="hyper" parents="116 2994 2250"/>
    </justification>
  </clause>

  <clause id="2999">
    <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(2998(a,1),2855(a,1,2,1))].">
      <j1 rule="para" parents="2998 2855"/>
    </justification>
  </clause>

  <clause id="3000">
    <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(2998(a,1),2856(a,1,2,1))].">
      <j1 rule="para" parents="2998 2856"/>
    </justification>
  </clause>

  <clause id="3001">
    <literal><![CDATA[
      R(x,y \ 1,(y \ 1) \ 1) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(533,a,2996,a)].">
      <j1 rule="hyper" parents="533 2996"/>
    </justification>
  </clause>

  <clause id="3002">
    <literal><![CDATA[
      T(x * ((y \ 1) \ 1),y \ 1) = R((y \ 1) \ x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,809,a(flip),b,2996,a)].">
      <j1 rule="hyper" parents="58 809 2996"/>
    </justification>
  </clause>

  <clause id="3003">
    <literal><![CDATA[
      ((x * y) * K(x \ 1,x)) \ y = 1 / (1 / ((x * y) \ y))
    ]]></literal>
    <justification jstring="[para(2930(a,1),2980(a,1,1,2))].">
      <j1 rule="para" parents="2930 2980"/>
    </justification>
  </clause>

  <clause id="3004">
    <literal><![CDATA[
      x / (((y \ x) \ 1) \ 1) = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),2984(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 2984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3005">
    <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(1287(a,1),2957(a,2,1))].">
      <j1 rule="para" parents="1287 2957"/>
    </justification>
  </clause>

  <clause id="3006">
    <literal><![CDATA[
      K(1 / ((x * y) \ x),(x * y) \ x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,1 / y) = z
    ]]></literal>
    <justification jstring="[para(2917(a,2),2464(a,1))].">
      <j1 rule="para" parents="2917 2464"/>
    </justification>
  </clause>

  <clause id="3007">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(2463(a,1),2919(a,1,2))].">
      <j1 rule="para" parents="2463 2919"/>
    </justification>
  </clause>

  <clause id="3008">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2456(a,1),3007(a,2,2))].">
      <j1 rule="para" parents="2456 3007"/>
    </justification>
  </clause>

  <clause id="3009">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(2457(a,1),3007(a,2,2))].">
      <j1 rule="para" parents="2457 3007"/>
    </justification>
  </clause>

  <clause id="3011">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2241,a,3008,a)].">
      <j1 rule="hyper" parents="2241 3008"/>
    </justification>
  </clause>

  <clause id="3012">
    <literal><![CDATA[
      (x / y) * ((y \ 1) \ 1) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(341,a,3008,a),flip(a)].">
      <j1 rule="hyper" parents="341 3008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3013">
    <literal><![CDATA[
      (x / ((y \ 1) \ 1)) * y = x / K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,3008,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 3008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3014">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2101,a,b,3008,a)].">
      <j1 rule="hyper" parents="58 2101 3008"/>
    </justification>
  </clause>

  <clause id="3016">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2241,a,3009,a)].">
      <j1 rule="hyper" parents="2241 3009"/>
    </justification>
  </clause>

  <clause id="3017">
    <literal><![CDATA[
      (x / y) * T(y,y \ 1) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(341,a,3009,a),flip(a)].">
      <j1 rule="hyper" parents="341 3009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3018">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (x * T(y,y \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,3009,a(flip),b,2101,a)].">
      <j1 rule="hyper" parents="116 3009 2101"/>
    </justification>
  </clause>

  <clause id="3019">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2695,a,3011,a)].">
      <j1 rule="hyper" parents="2695 3011"/>
    </justification>
  </clause>

  <clause id="3020">
    <literal><![CDATA[
      (x / y) * ((y \ 1) \ 1) = K(y,y \ 1) * x
    ]]></literal>
    <justification jstring="[para(7(a,1),3011(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 3011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3021">
    <literal><![CDATA[
      x / K(y,y \ 1) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2989,a(flip),b,3013,a),flip(a)].">
      <j1 rule="hyper" parents="58 2989 3013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3022">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * K(y \ 1,y) = x
    ]]></literal>
    <justification jstring="[hyper(343,a,3021,a),flip(a)].">
      <j1 rule="hyper" parents="343 3021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3023">
    <literal><![CDATA[
      x / K(y \ 1,y) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(340,a,3021,a),flip(a)].">
      <j1 rule="hyper" parents="340 3021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3024">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * K(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(133,a,3021,a)].">
      <j1 rule="hyper" parents="133 3021"/>
    </justification>
  </clause>

  <clause id="3025">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z * K(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[para(3021(a,1),133(a,1))].">
      <j1 rule="para" parents="3021 133"/>
    </justification>
  </clause>

  <clause id="3026">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * K(y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(3021(a,1),260(a,1,1))].">
      <j1 rule="para" parents="3021 260"/>
    </justification>
  </clause>

  <clause id="3027">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(3021(a,1),342(a,1))].">
      <j1 rule="para" parents="3021 342"/>
    </justification>
  </clause>

  <clause id="3028">
    <literal><![CDATA[
      K(x \ 1,x) * (y * K(x,x \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(2260,a,3022,a)].">
      <j1 rule="hyper" parents="2260 3022"/>
    </justification>
  </clause>

  <clause id="3029">
    <literal><![CDATA[
      (x / (1 / y)) * K(y,y \ 1) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(30,a,2951,a,b,3022,a),flip(a)].">
      <j1 rule="hyper" parents="30 2951 3022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3030">
    <literal><![CDATA[
      (x * (y \ 1)) * K(y,y \ 1) = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(30,a,2937,a,b,3022,a),flip(a)].">
      <j1 rule="hyper" parents="30 2937 3022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3031">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(30,a,2250,a(flip),b,3022,a),flip(a)].">
      <j1 rule="hyper" parents="30 2250 3022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3032">
    <literal><![CDATA[
      (x / (y * x)) * K(y \ 1,y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(2134(a,2),3022(a,1,1))].">
      <j1 rule="para" parents="2134 3022"/>
    </justification>
  </clause>

  <clause id="3033">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(2237(a,2),3022(a,1,1))].">
      <j1 rule="para" parents="2237 3022"/>
    </justification>
  </clause>

  <clause id="3034">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      z * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(3022(a,1),2253(a,2)),flip(b)].">
      <j1 rule="para" parents="3022 2253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3035">
    <literal><![CDATA[
      (x * y) * K(y \ 1,y) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(2955(a,1),3022(a,1,1))].">
      <j1 rule="para" parents="2955 3022"/>
    </justification>
  </clause>

  <clause id="3036">
    <literal><![CDATA[
      (x / (1 / (1 / y))) * K(y \ 1,y) = x / y
    ]]></literal>
    <justification jstring="[para(2960(a,1),3022(a,1,1))].">
      <j1 rule="para" parents="2960 3022"/>
    </justification>
  </clause>

  <clause id="3037">
    <literal><![CDATA[
      (x / (y \ 1)) * (1 / y) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2934,a,b,3023,a)].">
      <j1 rule="hyper" parents="58 2934 3023"/>
    </justification>
  </clause>

  <clause id="3038">
    <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(3023(a,1),641(a,1,1,1))].">
      <j1 rule="para" parents="3023 641"/>
    </justification>
  </clause>

  <clause id="3039">
    <literal><![CDATA[
      K(x,x \ 1) * (y * K(x \ 1,x)) = y
    ]]></literal>
    <justification jstring="[hyper(2241,a,3024,a)].">
      <j1 rule="hyper" parents="2241 3024"/>
    </justification>
  </clause>

  <clause id="3040">
    <literal><![CDATA[
      K(x,x \ 1) \ y = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3024,a(flip),b,2237,a)].">
      <j1 rule="hyper" parents="116 3024 2237"/>
    </justification>
  </clause>

  <clause id="3041">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      z * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(3024(a,1),2240(a,2)),flip(b)].">
      <j1 rule="para" parents="3024 2240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3042">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * K(x,x \ 1) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(858,a,3028,a),flip(a)].">
      <j1 rule="hyper" parents="858 3028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3043">
    <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(3028(a,1),92(a,2,1))].">
      <j1 rule="para" parents="3028 92"/>
    </justification>
  </clause>

  <clause id="3044">
    <literal><![CDATA[
      K(x \ 1,x) * (K(x,x \ 1) * y) = y
    ]]></literal>
    <justification jstring="[para(2237(a,2),3028(a,1,2))].">
      <j1 rule="para" parents="2237 3028"/>
    </justification>
  </clause>

  <clause id="3045">
    <literal><![CDATA[
      K(x \ 1,x) * (y * x) = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(2955(a,1),3028(a,1,2))].">
      <j1 rule="para" parents="2955 3028"/>
    </justification>
  </clause>

  <clause id="3046">
    <literal><![CDATA[
      K(x,x \ 1) * (K(x \ 1,x) * y) = y
    ]]></literal>
    <justification jstring="[hyper(2241,a,3031,a)].">
      <j1 rule="hyper" parents="2241 3031"/>
    </justification>
  </clause>

  <clause id="3047">
    <literal><![CDATA[
      x * K(y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,y) * z = x
    ]]></literal>
    <justification jstring="[para(3031(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="3031 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3048">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) * z = y
    ]]></literal>
    <justification jstring="[para(3031(a,1),2240(a,2)),flip(b)].">
      <j1 rule="para" parents="3031 2240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3049">
    <literal><![CDATA[
      K(x,x \ 1) * (y / (1 / x)) = y / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(30,a,2951,a,b,3033,a),flip(a)].">
      <j1 rule="hyper" parents="30 2951 3033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3050">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (x \ 1)) = y * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(30,a,2937,a,b,3033,a),flip(a)].">
      <j1 rule="hyper" parents="30 2937 3033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3051">
    <literal><![CDATA[
      K(x \ 1,x) \ y = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(116,a,3033,a(flip),b,2250,a)].">
      <j1 rule="hyper" parents="116 3033 2250"/>
    </justification>
  </clause>

  <clause id="3052">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,y \ 1) * z = x
    ]]></literal>
    <justification jstring="[para(3033(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="3033 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3053">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * z = y
    ]]></literal>
    <justification jstring="[para(3033(a,1),2253(a,2)),flip(b)].">
      <j1 rule="para" parents="3033 2253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3054">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) * y) = L(x \ y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1144,a,3044,a),flip(a)].">
      <j1 rule="hyper" parents="1144 3044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3055">
    <literal><![CDATA[
      K(x,x \ 1) * (K(x \ 1,x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(3051(a,1),299(a,1))].">
      <j1 rule="para" parents="3051 299"/>
    </justification>
  </clause>

  <clause id="3056">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[para(3051(a,1),2675(a,1,2,1))].">
      <j1 rule="para" parents="3051 2675"/>
    </justification>
  </clause>

  <clause id="3057">
    <literal><![CDATA[
      (x / T(y,y \ 1)) * K(y,y \ 1) = x / y
    ]]></literal>
    <justification jstring="[hyper(117,a,381,a(flip),b,3014,a),flip(a)].">
      <j1 rule="hyper" parents="117 381 3014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3058">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2695,a,3016,a)].">
      <j1 rule="hyper" parents="2695 3016"/>
    </justification>
  </clause>

  <clause id="3059">
    <literal><![CDATA[
      L(x,K(x,x \ 1),y) = x
    ]]></literal>
    <justification jstring="[hyper(1883,a,3018,a)].">
      <j1 rule="hyper" parents="1883 3018"/>
    </justification>
  </clause>

  <clause id="3060">
    <literal><![CDATA[
      L(1 / x,K(x \ 1,x),y) = 1 / x
    ]]></literal>
    <justification jstring="[para(1891(a,1),3059(a,1,2))].">
      <j1 rule="para" parents="1891 3059"/>
    </justification>
  </clause>

  <clause id="3061">
    <literal><![CDATA[
      (R(x,y,y \ 1) / (1 / y)) * K(y,y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(334,a,452,a(flip),b,3029,a),flip(a)].">
      <j1 rule="hyper" parents="334 452 3029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3062">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(30,a,1868,a,b,3030,a),flip(a)].">
      <j1 rule="hyper" parents="30 1868 3030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3063">
    <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(3030(a,1),522(a,1,1))].">
      <j1 rule="para" parents="3030 522"/>
    </justification>
  </clause>

  <clause id="3064">
    <literal><![CDATA[
      R(x,y,1 / y) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(130,a,3062,a)].">
      <j1 rule="hyper" parents="130 3062"/>
    </justification>
  </clause>

  <clause id="3065">
    <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,3062,a)].">
      <j1 rule="hyper" parents="117 22 3062"/>
    </justification>
  </clause>

  <clause id="3066">
    <literal><![CDATA[
      R(x \ y,x,1 / x) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,809,a(flip),b,3062,a),flip(a)].">
      <j1 rule="hyper" parents="58 809 3062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3067">
    <literal><![CDATA[
      R(1 / L(x,y,z),x,1 / x) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1705(a,1),3062(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1705 3062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3068">
    <literal><![CDATA[
      (x / (1 / (1 / y))) / (1 / y) = (x / y) / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,3036,a(flip),b,2936,a),flip(a)].">
      <j1 rule="hyper" parents="117 3036 2936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3069">
    <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(2224(a,1),3049(a,1,2,2))].">
      <j1 rule="para" parents="2224 3049"/>
    </justification>
  </clause>

  <clause id="3070">
    <literal><![CDATA[
      K(x / (y * x),y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,2351,a,b,3032,a)].">
      <j1 rule="hyper" parents="29 2351 3032"/>
    </justification>
  </clause>

  <clause id="3071">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) = K(y / x,x / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),3070(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 3070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3073">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) = K(y,x / (y * x))
    ]]></literal>
    <justification jstring="[para(6(a,1),3071(a,2,1))].">
      <j1 rule="para" parents="6 3071"/>
    </justification>
  </clause>

  <clause id="3074">
    <literal><![CDATA[
      R(x,y,y \ 1) / (1 / y) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(2961,a,3061,a),flip(a)].">
      <j1 rule="hyper" parents="2961 3061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3075">
    <literal><![CDATA[
      x / (1 / y) != z * (1 / (1 / y))
    ]]></literal>
    <literal><![CDATA[
      R(z,y,y \ 1) = x
    ]]></literal>
    <justification jstring="[para(3074(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="3074 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3076">
    <literal><![CDATA[
      (x * T(1 / (1 / y),x)) \ x = 1 / (1 / ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(2224(a,1),2979(a,1,1,2))].">
      <j1 rule="para" parents="2224 2979"/>
    </justification>
  </clause>

  <clause id="3077">
    <literal><![CDATA[
      1 / (1 / ((x * y) \ y)) = ((1 / (1 / x)) * y) \ y
    ]]></literal>
    <justification jstring="[para(105(a,1),3076(a,1,1)),flip(a)].">
      <j1 rule="para" parents="105 3076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3078">
    <literal><![CDATA[
      (((1 / (1 / x)) * y) \ y) \ 1 = 1 / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(192,a,3077,a)].">
      <j1 rule="hyper" parents="192 3077"/>
    </justification>
  </clause>

  <clause id="3079">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(34,a,3003,a,b,3077,a(flip))].">
      <j1 rule="hyper" parents="34 3003 3077"/>
    </justification>
  </clause>

  <clause id="3080">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / (1 / x)) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(3052,a,3079,a)].">
      <j1 rule="hyper" parents="3052 3079"/>
    </justification>
  </clause>

  <clause id="3081">
    <literal><![CDATA[
      (1 / (1 / x)) * (x \ y) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(581,a,3079,a),flip(a)].">
      <j1 rule="hyper" parents="581 3079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3082">
    <literal><![CDATA[
      x * (y * K(x \ 1,x)) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,2711,a(flip),b,3079,a)].">
      <j1 rule="hyper" parents="58 2711 3079"/>
    </justification>
  </clause>

  <clause id="3083">
    <literal><![CDATA[
      ((x \ y) * z) * K(y \ x,x \ y) = (1 / (1 / (x \ y))) * z
    ]]></literal>
    <justification jstring="[para(2913(a,1),3079(a,1,2))].">
      <j1 rule="para" parents="2913 3079"/>
    </justification>
  </clause>

  <clause id="3084">
    <literal><![CDATA[
      ((1 / (1 / x)) * y) * (1 / x) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(3079(a,1),2956(a,1,1))].">
      <j1 rule="para" parents="3079 2956"/>
    </justification>
  </clause>

  <clause id="3085">
    <literal><![CDATA[
      x \ (K(x,x \ 1) * y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(611,a,3080,a)].">
      <j1 rule="hyper" parents="611 3080"/>
    </justification>
  </clause>

  <clause id="3086">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ (1 / (1 / x))) * y) = x * K(y \ (1 / (1 / x)),y)
    ]]></literal>
    <justification jstring="[para(315(a,1),3080(a,1,2))].">
      <j1 rule="para" parents="315 3080"/>
    </justification>
  </clause>

  <clause id="3087">
    <literal><![CDATA[
      (1 / (1 / x)) * (x \ (y * x)) = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(334,a,3035,a(flip),b,3081,a),flip(a)].">
      <j1 rule="hyper" parents="334 3035 3081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3088">
    <literal><![CDATA[
      x * (K(x \ 1,x) * y) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,2269,a,b,3082,a)].">
      <j1 rule="hyper" parents="58 2269 3082"/>
    </justification>
  </clause>

  <clause id="3089">
    <literal><![CDATA[
      (1 / (1 / x)) * (y / (1 / (1 / x))) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(3036(a,1),3082(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3036 3082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3090">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,1931,a(flip),b,3085,a)].">
      <j1 rule="hyper" parents="58 1931 3085"/>
    </justification>
  </clause>

  <clause id="3091">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / (1 / x)) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,3088,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 3088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3092">
    <literal><![CDATA[
      T(x,y) * (K(x \ 1,x) * z) = (1 / (1 / T(x,y))) * z
    ]]></literal>
    <justification jstring="[para(2566(a,1),3088(a,1,2,1))].">
      <j1 rule="para" parents="2566 3088"/>
    </justification>
  </clause>

  <clause id="3093">
    <literal><![CDATA[
      (x \ y) * K(x,x \ 1) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(2246,a,3090,a)].">
      <j1 rule="hyper" parents="2246 3090"/>
    </justification>
  </clause>

  <clause id="3094">
    <literal><![CDATA[
      (1 / (1 / x)) \ L(y,1 / x,x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1929,a(flip),b,3090,a),flip(a)].">
      <j1 rule="hyper" parents="58 1929 3090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3095">
    <literal><![CDATA[
      K(x,1 / x) * (x \ y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(1855(a,2),3090(a,1,1))].">
      <j1 rule="para" parents="1855 3090"/>
    </justification>
  </clause>

  <clause id="3096">
    <literal><![CDATA[
      T(x \ ((1 / (1 / y)) \ x),y) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[para(3090(a,1),1939(a,1,1,2))].">
      <j1 rule="para" parents="3090 1939"/>
    </justification>
  </clause>

  <clause id="3097">
    <literal><![CDATA[
      ((1 / (1 / x)) \ y) * x = (x \ y) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3090(a,1),3019(a,1,1))].">
      <j1 rule="para" parents="3090 3019"/>
    </justification>
  </clause>

  <clause id="3098">
    <literal><![CDATA[
      K(x \ 1,x) * (K(1 / x,y) * (1 / x)) = x \ K(1 / x,y)
    ]]></literal>
    <justification jstring="[para(2874(a,1),3091(a,1,2))].">
      <j1 rule="para" parents="2874 3091"/>
    </justification>
  </clause>

  <clause id="3099">
    <literal><![CDATA[
      ((1 / (1 / x)) \ y) / (1 / x) = (x \ y) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,3093,a(flip),b,3037,a)].">
      <j1 rule="hyper" parents="117 3093 3037"/>
    </justification>
  </clause>

  <clause id="3100">
    <literal><![CDATA[
      (x \ y) * K(x,1 / x) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(1855(a,2),3093(a,1,2))].">
      <j1 rule="para" parents="1855 3093"/>
    </justification>
  </clause>

  <clause id="3101">
    <literal><![CDATA[
      1 / (((x \ 1) * y) \ y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(72(a,1),3078(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 3078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3102">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 / (1 / x))) * y) * (1 / x)
    ]]></literal>
    <justification jstring="[para(315(a,1),3084(a,1,1)),flip(a)].">
      <j1 rule="para" parents="315 3084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3103">
    <literal><![CDATA[
      (1 / (1 / x)) * T(y,x) = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(17(a,2),3087(a,1,2))].">
      <j1 rule="para" parents="17 3087"/>
    </justification>
  </clause>

  <clause id="3104">
    <literal><![CDATA[
      T(x,1 / (1 / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(422,a,3103,a),flip(a)].">
      <j1 rule="hyper" parents="422 3103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3105">
    <literal><![CDATA[
      T(x,1 / y) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),3104(a,1,2,2))].">
      <j1 rule="para" parents="72 3104"/>
    </justification>
  </clause>

  <clause id="3106">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(194(a,1),3104(a,1,2)),flip(a)].">
      <j1 rule="para" parents="194 3104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3107">
    <literal><![CDATA[
      (1 / x) \ (y * (1 / x)) = T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(438,a,3105,a)].">
      <j1 rule="hyper" parents="438 3105"/>
    </justification>
  </clause>

  <clause id="3109">
    <literal><![CDATA[
      T(T(x,y),K(z,z \ 1)) = T(x,(y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,2236,a,b,3106,a)].">
      <j1 rule="hyper" parents="334 2236 3106"/>
    </justification>
  </clause>

  <clause id="3110">
    <literal><![CDATA[
      T((x \ 1) * y,(x \ 1) \ 1) = (x \ 1) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(334,a,2043,a,b,3106,a),flip(a)].">
      <j1 rule="hyper" parents="334 2043 3106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3111">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(y,x) = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,3106,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 3106 17"/>
    </justification>
  </clause>

  <clause id="3112">
    <literal><![CDATA[
      T(x,T(y,y \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(106(a,2),3106(a,1,2))].">
      <j1 rule="para" parents="106 3106"/>
    </justification>
  </clause>

  <clause id="3113">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z)) = T(x,z / (y * z))
    ]]></literal>
    <justification jstring="[para(2147(a,2),3106(a,1,2))].">
      <j1 rule="para" parents="2147 3106"/>
    </justification>
  </clause>

  <clause id="3114">
    <literal><![CDATA[
      T(x,R(1 / y,y,z)) = T(x,R(y \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(2148(a,1),3106(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2148 3106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3116">
    <literal><![CDATA[
      T(x,x \ 1) * T(y,x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,3112,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 3112 17"/>
    </justification>
  </clause>

  <clause id="3117">
    <literal><![CDATA[
      T(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,1 / y) = z
    ]]></literal>
    <justification jstring="[para(3107(a,1),298(a,1))].">
      <j1 rule="para" parents="3107 298"/>
    </justification>
  </clause>

  <clause id="3118">
    <literal><![CDATA[
      T(x,R(y \ 1,y,x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(334,a,2613,a(flip),b,3113,a),flip(a)].">
      <j1 rule="hyper" parents="334 2613 3113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3119">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(3109(a,1),2244(a,1)),flip(b)].">
      <j1 rule="para" parents="3109 2244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3120">
    <literal><![CDATA[
      T(x,T(y,y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(106(a,2),3119(a,1,2))].">
      <j1 rule="para" parents="106 3119"/>
    </justification>
  </clause>

  <clause id="3121">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / (y * z)) = u
    ]]></literal>
    <justification jstring="[para(2147(a,2),3119(a,1,2))].">
      <j1 rule="para" parents="2147 3119"/>
    </justification>
  </clause>

  <clause id="3122">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (x \ y) = (y / x) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,1),3111(a,1,2))].">
      <j1 rule="para" parents="107 3111"/>
    </justification>
  </clause>

  <clause id="3123">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * y = T(y,R(x \ 1,x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1743,a,b,3114,a)].">
      <j1 rule="hyper" parents="58 1743 3114"/>
    </justification>
  </clause>

  <clause id="3124">
    <literal><![CDATA[
      T(x / (1 / (1 / y)),1 / (1 / y)) / (1 / y) = (y \ x) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,2),3099(a,1,1))].">
      <j1 rule="para" parents="107 3099"/>
    </justification>
  </clause>

  <clause id="3125">
    <literal><![CDATA[
      ((((1 / x) * y) \ y) \ 1) \ 1 = ((x \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(192,a,3101,a)].">
      <j1 rule="hyper" parents="192 3101"/>
    </justification>
  </clause>

  <clause id="3126">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (x \ y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(334,a,3020,a(flip),b,3122,a),flip(a)].">
      <j1 rule="hyper" parents="334 3020 3122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3127">
    <literal><![CDATA[
      x * (((x \ 1) \ 1) \ y) = K(x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(609,a,3126,a),flip(a)].">
      <j1 rule="hyper" parents="609 3126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3128">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(597,a,3126,a),flip(a)].">
      <j1 rule="hyper" parents="597 3126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3129">
    <literal><![CDATA[
      x \ (K(x \ 1,x) * y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,3046,a(flip),b,3126,a),flip(a)].">
      <j1 rule="hyper" parents="116 3046 3126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3130">
    <literal><![CDATA[
      T(x,x \ 1) * (x \ y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,328,a,b,3126,a)].">
      <j1 rule="hyper" parents="58 328 3126"/>
    </justification>
  </clause>

  <clause id="3131">
    <literal><![CDATA[
      x * (K(x,x \ 1) * y) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,3126,a(flip),b,1229,a)].">
      <j1 rule="hyper" parents="119 3126 1229"/>
    </justification>
  </clause>

  <clause id="3132">
    <literal><![CDATA[
      x * (K(x,x \ 1) * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,3126,a(flip),b,1175,a)].">
      <j1 rule="hyper" parents="119 3126 1175"/>
    </justification>
  </clause>

  <clause id="3133">
    <literal><![CDATA[
      x * (((x \ 1) \ 1) \ y) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,3040,a(flip),b,3127,a),flip(a)].">
      <j1 rule="hyper" parents="334 3040 3127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3134">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(2246,a,3128,a)].">
      <j1 rule="hyper" parents="2246 3128"/>
    </justification>
  </clause>

  <clause id="3135">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(334,a,328,a,b,3128,a),flip(a)].">
      <j1 rule="hyper" parents="334 328 3128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3136">
    <literal><![CDATA[
      x * (((x \ 1) \ 1) \ y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(134,a,3129,a)].">
      <j1 rule="hyper" parents="134 3129"/>
    </justification>
  </clause>

  <clause id="3137">
    <literal><![CDATA[
      K(x,x \ 1) * (T(x,x \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(1190,a,3130,a),flip(a)].">
      <j1 rule="hyper" parents="1190 3130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3138">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,3131,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 3131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3139">
    <literal><![CDATA[
      K(x,x \ 1) * T(x \ 1,y) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,2637,a(flip),b,3131,a),flip(a)].">
      <j1 rule="hyper" parents="29 2637 3131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3140">
    <literal><![CDATA[
      x * (y * K(x,x \ 1)) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(2237(a,1),3131(a,1,2))].">
      <j1 rule="para" parents="2237 3131"/>
    </justification>
  </clause>

  <clause id="3141">
    <literal><![CDATA[
      L(x,y,K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(1942,a,3132,a(flip))].">
      <j1 rule="hyper" parents="1942 3132"/>
    </justification>
  </clause>

  <clause id="3142">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ ((K(x,x \ 1) * y) * x) = K(K(x,x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(3132(a,1),11(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3132 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3143">
    <literal><![CDATA[
      L(x,K(y \ 1,y),1 / y) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,1943,a(flip),b,3141,a)].">
      <j1 rule="hyper" parents="58 1943 3141"/>
    </justification>
  </clause>

  <clause id="3144">
    <literal><![CDATA[
      L(x,1 / y,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(1891(a,1),3141(a,1,3))].">
      <j1 rule="para" parents="1891 3141"/>
    </justification>
  </clause>

  <clause id="3145">
    <literal><![CDATA[
      L(x,y,1 / y) = L(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2428,a,3143,a)].">
      <j1 rule="hyper" parents="2428 3143"/>
    </justification>
  </clause>

  <clause id="3146">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2426,a,3143,a)].">
      <j1 rule="hyper" parents="2426 3143"/>
    </justification>
  </clause>

  <clause id="3148">
    <literal><![CDATA[
      (1 / x) * (K(x \ 1,x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,3143,a(flip),b,802,a),flip(a)].">
      <j1 rule="hyper" parents="119 3143 802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3149">
    <literal><![CDATA[
      L(x,y,y \ 1) / (y * x) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(117,a,3143,a(flip),b,2425,a(flip))].">
      <j1 rule="hyper" parents="117 3143 2425"/>
    </justification>
  </clause>

  <clause id="3150">
    <literal><![CDATA[
      (x \ 1) \ (K(x \ 1,x) * y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,3143,a(flip),b,1997,a),flip(a)].">
      <j1 rule="hyper" parents="116 3143 1997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3151">
    <literal><![CDATA[
      (1 / x) \ L(y,x,x \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(116,a,3143,a(flip),b,2425,a(flip))].">
      <j1 rule="hyper" parents="116 3143 2425"/>
    </justification>
  </clause>

  <clause id="3152">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(3144(a,1),1876(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3144 1876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3153">
    <literal><![CDATA[
      L(x \ y,x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(3144(a,1),2009(a,1,1,2))].">
      <j1 rule="para" parents="3144 2009"/>
    </justification>
  </clause>

  <clause id="3154">
    <literal><![CDATA[
      L(T(x,y),y,y \ 1) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(732,a,3145,a),flip(a)].">
      <j1 rule="hyper" parents="732 3145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3155">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,x \ 1) = (1 / x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1513,a(flip),b,3145,a),flip(a)].">
      <j1 rule="hyper" parents="58 1513 3145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3156">
    <literal><![CDATA[
      L(L(x \ y,z,u),x,x \ 1) = L((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,623,a(flip),b,3145,a),flip(a)].">
      <j1 rule="hyper" parents="58 623 3145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3157">
    <literal><![CDATA[
      L(T(x \ y,z),x,x \ 1) = T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,621,a(flip),b,3145,a),flip(a)].">
      <j1 rule="hyper" parents="58 621 3145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3158">
    <literal><![CDATA[
      L(x,y \ 1,(y \ 1) \ 1) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),3145(a,1,3)),flip(a)].">
      <j1 rule="para" parents="72 3145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3160">
    <literal><![CDATA[
      x * ((1 / x) * (y * x)) = L(y,x,x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(29,a,1246,a(flip),b,3146,a),flip(a)].">
      <j1 rule="hyper" parents="29 1246 3146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3161">
    <literal><![CDATA[
      L(x \ 1,x,x \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      1 / x = y
    ]]></literal>
    <justification jstring="[para(3146(a,1),209(a,1)),flip(b)].">
      <j1 rule="para" parents="3146 209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3162">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x = a(1 / y,y,x)
    ]]></literal>
    <justification jstring="[para(3146(a,1),222(a,1,1))].">
      <j1 rule="para" parents="3146 222"/>
    </justification>
  </clause>

  <clause id="3163">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = L(K(x,y),y * x,1 / y)
    ]]></literal>
    <justification jstring="[para(3146(a,1),317(a,1,1))].">
      <j1 rule="para" parents="3146 317"/>
    </justification>
  </clause>

  <clause id="3164">
    <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(3146(a,1),491(a,1,1))].">
      <j1 rule="para" parents="3146 491"/>
    </justification>
  </clause>

  <clause id="3165">
    <literal><![CDATA[
      (1 / x) * (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(3149(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3149 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3166">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,(x \ 1) \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(334,a,186,a(flip),b,3153,a),flip(a)].">
      <j1 rule="hyper" parents="334 186 3153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3167">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,3054,a,b,3153,a)].">
      <j1 rule="hyper" parents="58 3054 3153"/>
    </justification>
  </clause>

  <clause id="3168">
    <literal><![CDATA[
      ((x \ 1) * x) \ ((x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,92,a(flip),b,3153,a)].">
      <j1 rule="hyper" parents="58 92 3153"/>
    </justification>
  </clause>

  <clause id="3169">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (x * y) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,2711,a(flip),b,3133,a),flip(a)].">
      <j1 rule="hyper" parents="29 2711 3133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3170">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(334,a,328,a,b,3134,a),flip(a)].">
      <j1 rule="hyper" parents="334 328 3134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3171">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(30,a,2141,a,b,3135,a)].">
      <j1 rule="hyper" parents="30 2141 3135"/>
    </justification>
  </clause>

  <clause id="3172">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(29,a,1451,a,b,3136,a)].">
      <j1 rule="hyper" parents="29 1451 3136"/>
    </justification>
  </clause>

  <clause id="3173">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (x * y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(29,a,1453,a(flip),b,3136,a),flip(a)].">
      <j1 rule="hyper" parents="29 1453 3136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3174">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = T(x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(3048,a,3137,a)].">
      <j1 rule="hyper" parents="3048 3137"/>
    </justification>
  </clause>

  <clause id="3175">
    <literal><![CDATA[
      (x \ y) * K(x \ 1,x) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(3041,a,3138,a)].">
      <j1 rule="hyper" parents="3041 3138"/>
    </justification>
  </clause>

  <clause id="3176">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * K(x,x \ 1) = x \ y
    ]]></literal>
    <justification jstring="[hyper(2246,a,3138,a)].">
      <j1 rule="hyper" parents="2246 3138"/>
    </justification>
  </clause>

  <clause id="3177">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(3138(a,1),3019(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3138 3019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3179">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,3148,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 3148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3180">
    <literal><![CDATA[
      (1 / x) * (y * K(x \ 1,x)) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,2269,a(flip),b,3148,a)].">
      <j1 rule="hyper" parents="58 2269 3148"/>
    </justification>
  </clause>

  <clause id="3181">
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = (x \ 1) * (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(2958(a,1),3148(a,1,2))].">
      <j1 rule="para" parents="2958 3148"/>
    </justification>
  </clause>

  <clause id="3182">
    <literal><![CDATA[
      (x \ 1) * (y * T(x,x \ 1)) = (1 / x) * (y * x)
    ]]></literal>
    <justification jstring="[para(2997(a,1),3148(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2997 3148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3183">
    <literal><![CDATA[
      (x \ 1) * (K(x,x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(3044(a,1),3148(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3044 3148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3184">
    <literal><![CDATA[
      (x \ 1) * ((1 / x) \ y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(134,a,3150,a)].">
      <j1 rule="hyper" parents="134 3150"/>
    </justification>
  </clause>

  <clause id="3185">
    <literal><![CDATA[
      ((x \ 1) * y) * K(x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(3034,a,3152,a)].">
      <j1 rule="hyper" parents="3034 3152"/>
    </justification>
  </clause>

  <clause id="3186">
    <literal><![CDATA[
      ((1 / x) * y) * K(x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(2254,a,3152,a)].">
      <j1 rule="hyper" parents="2254 3152"/>
    </justification>
  </clause>

  <clause id="3187">
    <literal><![CDATA[
      K(x \ 1,x) * y != (x \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * z = y
    ]]></literal>
    <justification jstring="[para(3152(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="3152 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3188">
    <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(3152(a,1),92(a,2,1))].">
      <j1 rule="para" parents="3152 92"/>
    </justification>
  </clause>

  <clause id="3189">
    <literal><![CDATA[
      ((x \ 1) * y) / L(T(1 / x,y),y,K(x \ 1,x)) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(3152(a,1),557(a,1,1))].">
      <j1 rule="para" parents="3152 557"/>
    </justification>
  </clause>

  <clause id="3190">
    <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(3152(a,1),491(a,1,1))].">
      <j1 rule="para" parents="3152 491"/>
    </justification>
  </clause>

  <clause id="3191">
    <literal><![CDATA[
      T(x,(1 / x) * y) = T(x,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(3152(a,1),2705(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3152 2705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3192">
    <literal><![CDATA[
      ((x \ 1) * y) * ((x \ 1) \ 1) = ((1 / x) * y) * x
    ]]></literal>
    <justification jstring="[para(3152(a,1),2995(a,1,1))].">
      <j1 rule="para" parents="3152 2995"/>
    </justification>
  </clause>

  <clause id="3193">
    <literal><![CDATA[
      x \ L(y,1 / x,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(1936,a,3167,a)].">
      <j1 rule="hyper" parents="1936 3167"/>
    </justification>
  </clause>

  <clause id="3194">
    <literal><![CDATA[
      L(x,1 / y,y) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(870,a,3193,a)].">
      <j1 rule="hyper" parents="870 3193"/>
    </justification>
  </clause>

  <clause id="3195">
    <literal><![CDATA[
      (x \ 1) \ L(y,x,x \ 1) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(72(a,1),3193(a,1,2,2))].">
      <j1 rule="para" parents="72 3193"/>
    </justification>
  </clause>

  <clause id="3196">
    <literal><![CDATA[
      L(x,(y \ 1) \ 1,y \ 1) = L(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),3194(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 3194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3197">
    <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(326(a,2),3194(a,1,2)),flip(a)].">
      <j1 rule="para" parents="326 3194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3198">
    <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(3194(a,1),2176(a,1))].">
      <j1 rule="para" parents="3194 2176"/>
    </justification>
  </clause>

  <clause id="3199">
    <literal><![CDATA[
      (1 / (1 / x)) \ L(y,x \ 1,x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(3194(a,1),3094(a,1,2))].">
      <j1 rule="para" parents="3194 3094"/>
    </justification>
  </clause>

  <clause id="3200">
    <literal><![CDATA[
      x * T(x \ (y \ x),y) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(1285,a,3172,a)].">
      <j1 rule="hyper" parents="1285 3172"/>
    </justification>
  </clause>

  <clause id="3201">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) \ 1) \ y = z
    ]]></literal>
    <justification jstring="[para(3174(a,2),674(a,1))].">
      <j1 rule="para" parents="3174 674"/>
    </justification>
  </clause>

  <clause id="3202">
    <literal><![CDATA[
      ((1 / x) \ y) * K(x,x \ 1) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(3034,a,3179,a)].">
      <j1 rule="hyper" parents="3034 3179"/>
    </justification>
  </clause>

  <clause id="3203">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(2254,a,3179,a)].">
      <j1 rule="hyper" parents="2254 3179"/>
    </justification>
  </clause>

  <clause id="3204">
    <literal><![CDATA[
      T((x \ 1) * y,K(z \ 1,z)) = (1 / x) * (y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,2248,a,b,3180,a)].">
      <j1 rule="hyper" parents="334 2248 3180"/>
    </justification>
  </clause>

  <clause id="3205">
    <literal><![CDATA[
      (x \ 1) * (x * (1 / T(x,y))) = (1 / x) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(2713(a,1),3180(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2713 3180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3206">
    <literal><![CDATA[
      (x \ 1) \ ((1 / x) * y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(123,a,3183,a)].">
      <j1 rule="hyper" parents="123 3183"/>
    </justification>
  </clause>

  <clause id="3207">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,x \ 1,x) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,3183,a(flip),b,450,a),flip(a)].">
      <j1 rule="hyper" parents="119 3183 450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3208">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(3184(a,1),597(a,1))].">
      <j1 rule="para" parents="3184 597"/>
    </justification>
  </clause>

  <clause id="3209">
    <literal><![CDATA[
      L(((x \ 1) \ 1) \ y,x,x \ 1) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(511,a,3196,a),flip(a)].">
      <j1 rule="hyper" parents="511 3196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3210">
    <literal><![CDATA[
      x * (((x \ (y \ x)) \ 1) \ 1) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(2290(a,1),3200(a,1,2))].">
      <j1 rule="para" parents="2290 3200"/>
    </justification>
  </clause>

  <clause id="3211">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) \ y = z
    ]]></literal>
    <justification jstring="[para(3202(a,1),3027(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3202 3027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3212">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) * K(x \ 1,x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,2561,a(flip),b,3203,a),flip(a)].">
      <j1 rule="hyper" parents="334 2561 3203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3213">
    <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(3160(a,1),2606(a,1,1,1,1))].">
      <j1 rule="para" parents="3160 2606"/>
    </justification>
  </clause>

  <clause id="3214">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ L(y,x \ 1,x) = (((x \ 1) \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(3158(a,1),3195(a,1,2))].">
      <j1 rule="para" parents="3158 3195"/>
    </justification>
  </clause>

  <clause id="3215">
    <literal><![CDATA[
      K(x,x \ 1) * L(y,x \ 1,x) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,3199,a(flip),b,3085,a),flip(a)].">
      <j1 rule="hyper" parents="119 3199 3085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3216">
    <literal><![CDATA[
      L(x * K(y \ 1,y),y,y \ 1) = (y \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(3169(a,1),3209(a,1,1))].">
      <j1 rule="para" parents="3169 3209"/>
    </justification>
  </clause>

  <clause id="3217">
    <literal><![CDATA[
      (((x * y) \ y) \ 1) \ 1 = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[para(72(a,1),3125(a,1,1,1,1,1))].">
      <j1 rule="para" parents="72 3125"/>
    </justification>
  </clause>

  <clause id="3218">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = ((y \ 1) * (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(3146(a,1),3125(a,1,1,1,1))].">
      <j1 rule="para" parents="3146 3125"/>
    </justification>
  </clause>

  <clause id="3219">
    <literal><![CDATA[
      K(x,y / (x * y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3073,a(flip),b,3171,a)].">
      <j1 rule="hyper" parents="58 3073 3171"/>
    </justification>
  </clause>

  <clause id="3222">
    <literal><![CDATA[
      K(x,y / (x * y)) = x \ T(x,z / (x * z))
    ]]></literal>
    <justification jstring="[hyper(334,a,2139,a,b,3219,a),flip(a)].">
      <j1 rule="hyper" parents="334 2139 3219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3223">
    <literal><![CDATA[
      K(x,y / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(3222(a,2),2143(a,1))].">
      <j1 rule="para" parents="3222 2143"/>
    </justification>
  </clause>

  <clause id="3224">
    <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),3223(a,1,2,2))].">
      <j1 rule="para" parents="7 3223"/>
    </justification>
  </clause>

  <clause id="3225">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) = y * K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,315,a,b,3177,a),flip(a)].">
      <j1 rule="hyper" parents="334 315 3177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3226">
    <literal><![CDATA[
      T((x \ 1) * (y / (x \ 1)),K(z \ 1,z)) = (1 / x) * (y / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(334,a,2248,a,b,3181,a)].">
      <j1 rule="hyper" parents="334 2248 3181"/>
    </justification>
  </clause>

  <clause id="3227">
    <literal><![CDATA[
      (1 / x) * K(y,x \ 1) = K(y,x \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,2437,a(flip),b,3192,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="117 2437 3192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3228">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) / y = (((x \ y) / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(117,a,3210,a(flip),b,2231,a)].">
      <j1 rule="hyper" parents="117 3210 2231"/>
    </justification>
  </clause>

  <clause id="3229">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) \ x = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),3210(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 3210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3230">
    <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(187(a,1),3210(a,1,2,1,1,2))].">
      <j1 rule="para" parents="187 3210"/>
    </justification>
  </clause>

  <clause id="3231">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ ((x \ 1) \ K(y,x)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,3133,a,b,3212,a(flip))].">
      <j1 rule="hyper" parents="29 3133 3212"/>
    </justification>
  </clause>

  <clause id="3232">
    <literal><![CDATA[
      ((x \ 1) \ 1) * K(y,x) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,3231,a)].">
      <j1 rule="hyper" parents="134 3231"/>
    </justification>
  </clause>

  <clause id="3233">
    <literal><![CDATA[
      x * (K(y,x) * K(x,x \ 1)) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3140,a,b,3232,a)].">
      <j1 rule="hyper" parents="58 3140 3232"/>
    </justification>
  </clause>

  <clause id="3234">
    <literal><![CDATA[
      T((x * y) \ y,x) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,2289,a,b,3217,a)].">
      <j1 rule="hyper" parents="58 2289 3217"/>
    </justification>
  </clause>

  <clause id="3235">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ y = T((x * y) \ y,x)
    ]]></literal>
    <justification jstring="[para(106(a,2),3234(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="106 3234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3236">
    <literal><![CDATA[
      ((((1 / x) \ y) / y) \ 1) \ 1 = ((x \ 1) \ y) / y
    ]]></literal>
    <justification jstring="[para(75(a,1),3228(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 3228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3237">
    <literal><![CDATA[
      x / (x * (((x \ y) \ 1) \ 1)) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(201,a,3229,a)].">
      <j1 rule="hyper" parents="201 3229"/>
    </justification>
  </clause>

  <clause id="3238">
    <literal><![CDATA[
      x / (x * ((y \ 1) \ 1)) = ((x / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),3237(a,1,2,2,1,1))].">
      <j1 rule="para" parents="4 3237"/>
    </justification>
  </clause>

  <clause id="3239">
    <literal><![CDATA[
      x / ((((y / x) \ 1) \ 1) * x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2231(a,2),3237(a,1,2))].">
      <j1 rule="para" parents="2231 3237"/>
    </justification>
  </clause>

  <clause id="3240">
    <literal><![CDATA[
      T(x / (x * y),y) = x / (x * ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(334,a,2487,a,b,3238,a)].">
      <j1 rule="hyper" parents="334 2487 3238"/>
    </justification>
  </clause>

  <clause id="3241">
    <literal><![CDATA[
      x / (x * T(y,y \ 1)) = T(x / (x * y),y)
    ]]></literal>
    <justification jstring="[para(106(a,2),3240(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="106 3240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3242">
    <literal><![CDATA[
      T(x / (x * y),y) \ x = x * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(192,a,3241,a)].">
      <j1 rule="hyper" parents="192 3241"/>
    </justification>
  </clause>

  <clause id="3243">
    <literal><![CDATA[
      x / (((y \ 1) \ 1) * x) = ((x / (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(6(a,1),3239(a,1,2,1,1,1))].">
      <j1 rule="para" parents="6 3239"/>
    </justification>
  </clause>

  <clause id="3244">
    <literal><![CDATA[
      R(x \ 1,x,y) = y / (((x \ 1) \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,2147,a,b,3243,a)].">
      <j1 rule="hyper" parents="334 2147 3243"/>
    </justification>
  </clause>

  <clause id="3245">
    <literal><![CDATA[
      R(x \ 1,(x \ 1) \ 1,y) = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,219,a,b,3244,a)].">
      <j1 rule="hyper" parents="334 219 3244"/>
    </justification>
  </clause>

  <clause id="3246">
    <literal><![CDATA[
      R(x \ 1,x,y) \ y = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(118,a,3244,a,b,154,a)].">
      <j1 rule="hyper" parents="118 3244 154"/>
    </justification>
  </clause>

  <clause id="3247">
    <literal><![CDATA[
      x / (T(y,y \ 1) * x) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(106(a,2),3244(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="106 3244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3248">
    <literal><![CDATA[
      R(x,1 / x,y) \ y = (((1 / x) \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),3246(a,1,1,1))].">
      <j1 rule="para" parents="75 3246"/>
    </justification>
  </clause>

  <clause id="3249">
    <literal><![CDATA[
      R(x,1 / x,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),3248(a,2,1,1))].">
      <j1 rule="para" parents="75 3248"/>
    </justification>
  </clause>

  <clause id="3250">
    <literal><![CDATA[
      R(x,1 / x,y) = R(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(613,a,3249,a),flip(a)].">
      <j1 rule="hyper" parents="613 3249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3251">
    <literal><![CDATA[
      L(R(x,x \ 1,y),x \ 1,x) = R(1 / (1 / x),1 / x,y)
    ]]></literal>
    <justification jstring="[para(3250(a,1),1880(a,1,1))].">
      <j1 rule="para" parents="3250 1880"/>
    </justification>
  </clause>

  <clause id="3252">
    <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,2352,a(flip),b,3123,a)].">
      <j1 rule="hyper" parents="58 2352 3123"/>
    </justification>
  </clause>

  <clause id="3253">
    <literal><![CDATA[
      K(x \ 1,x) * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * (x * K(y,x)) = z
    ]]></literal>
    <justification jstring="[para(2560(a,1),3208(a,1,2))].">
      <j1 rule="para" parents="2560 3208"/>
    </justification>
  </clause>

  <clause id="3254">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y / x,(y / x) \ 1) = z
    ]]></literal>
    <justification jstring="[para(3071(a,2),3224(a,1))].">
      <j1 rule="para" parents="3071 3224"/>
    </justification>
  </clause>

  <clause id="3255">
    <literal><![CDATA[
      T(x,y) * (K(x \ 1,x) * z) = T(1 / (1 / x),y) * z
    ]]></literal>
    <justification jstring="[para(2224(a,1),3092(a,2,1))].">
      <j1 rule="para" parents="2224 3092"/>
    </justification>
  </clause>

  <clause id="3256">
    <literal><![CDATA[
      L((1 / T(x,y)) * x,x \ 1,x) = ((1 / x) * (T(x,y) \ x)) * x
    ]]></literal>
    <justification jstring="[para(3205(a,1),2049(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3205 2049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3257">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,(x \ 1) \ 1) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(476,a,3225,a)].">
      <j1 rule="hyper" parents="476 3225"/>
    </justification>
  </clause>

  <clause id="3258">
    <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,3255,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 3255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3259">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (T(x,y) \ z) = x * (T(1 / (1 / x),y) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,3258,a(flip),b,3173,a)].">
      <j1 rule="hyper" parents="119 3258 3173"/>
    </justification>
  </clause>

  <clause id="3260">
    <literal><![CDATA[
      R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(T(x,y) \ x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2284(a,1),3002(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2284 3002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3261">
    <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,663,a,b,3067,a)].">
      <j1 rule="hyper" parents="58 663 3067"/>
    </justification>
  </clause>

  <clause id="3262">
    <literal><![CDATA[
      R(1 / (1 / x),1 / x,y) = R(1 / (1 / x),x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1880,a(flip),b,3251,a),flip(a)].">
      <j1 rule="hyper" parents="58 1880 3251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3263">
    <literal><![CDATA[
      R(1 / (1 / x),x \ 1,(1 / x) \ y) = ((1 / x) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(980,a,3262,a),flip(a)].">
      <j1 rule="hyper" parents="980 3262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3264">
    <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(3263(a,2),87(a,1,2,2))].">
      <j1 rule="para" parents="3263 87"/>
    </justification>
  </clause>

  <clause id="3265">
    <literal><![CDATA[
      ((x \ (x / y)) * z) * K(y,y \ 1) = (1 / (1 / (x \ (x / y)))) * z
    ]]></literal>
    <justification jstring="[para(2471(a,1),3083(a,1,2))].">
      <j1 rule="para" parents="2471 3083"/>
    </justification>
  </clause>

  <clause id="3266">
    <literal><![CDATA[
      ((1 / x) * (T(x,y) \ x)) * x = L(T(x,y) \ x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2510(a,1),3256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2510 3256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3267">
    <literal><![CDATA[
      R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(334,a,2636,a(flip),b,3260,a),flip(a)].">
      <j1 rule="hyper" parents="334 2636 3260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3268">
    <literal><![CDATA[
      R(T(x,y) \ x,x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[para(2813(a,1),3267(a,1,1))].">
      <j1 rule="para" parents="2813 3267"/>
    </justification>
  </clause>

  <clause id="3269">
    <literal><![CDATA[
      (x * T(y,z)) / T(T(y,y \ 1),z) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2566(a,1),2991(a,2,2))].">
      <j1 rule="para" parents="2566 2991"/>
    </justification>
  </clause>

  <clause id="3270">
    <literal><![CDATA[
      (x * T(y,z)) / T((y \ 1) \ 1,z) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(106(a,1),3269(a,1,2,1))].">
      <j1 rule="para" parents="106 3269"/>
    </justification>
  </clause>

  <clause id="3273">
    <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(3270(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3270 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3274">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (1 / (1 / (x \ (x / (y \ 1))))) * z
    ]]></literal>
    <justification jstring="[para(1862(a,1),3265(a,1,2))].">
      <j1 rule="para" parents="1862 3265"/>
    </justification>
  </clause>

  <clause id="3275">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * (y * x)) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(2942(a,1),2948(a,1,2,2))].">
      <j1 rule="para" parents="2942 2948"/>
    </justification>
  </clause>

  <clause id="3276">
    <literal><![CDATA[
      ((x \ 1) * y) / T(1 / x,y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(2698(a,1),3189(a,1,2))].">
      <j1 rule="para" parents="2698 3189"/>
    </justification>
  </clause>

  <clause id="3277">
    <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(3276(a,1),1601(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3276 1601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3279">
    <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(3017(a,1),3000(a,1,2,1))].">
      <j1 rule="para" parents="3017 3000"/>
    </justification>
  </clause>

  <clause id="3280">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ (y * T(x,x \ 1)) = K(K(x,x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(3058(a,1),3142(a,1,2))].">
      <j1 rule="para" parents="3058 3142"/>
    </justification>
  </clause>

  <clause id="3281">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,x) = K(y,T(x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(321,a,3280,a),flip(a)].">
      <j1 rule="hyper" parents="321 3280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3282">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,x) = K(y,(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,1424,a(flip),b,3281,a),flip(a)].">
      <j1 rule="hyper" parents="334 1424 3281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3283">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,(x \ 1) \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[para(3046(a,1),3282(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3046 3282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3284">
    <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(3146(a,1),3164(a,1,2))].">
      <j1 rule="para" parents="3146 3164"/>
    </justification>
  </clause>

  <clause id="3285">
    <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(334,a,452,a,b,3102,a)].">
      <j1 rule="hyper" parents="334 452 3102"/>
    </justification>
  </clause>

  <clause id="3286">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (x \ (x / (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(2971(a,1),3274(a,2,1))].">
      <j1 rule="para" parents="2971 3274"/>
    </justification>
  </clause>

  <clause id="3287">
    <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(334,a,3266,a(flip),b,2967,a),flip(a)].">
      <j1 rule="hyper" parents="334 3266 2967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3288">
    <literal><![CDATA[
      R(T(x,y) \ x,x \ 1,x) = L(T(x,y) \ x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2515(a,1),3287(a,1,1))].">
      <j1 rule="para" parents="2515 3287"/>
    </justification>
  </clause>

  <clause id="3289">
    <literal><![CDATA[
      L(T(x,y) \ x,x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,3268,a(flip),b,3288,a),flip(a)].">
      <j1 rule="hyper" parents="58 3268 3288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3290">
    <literal><![CDATA[
      L(T(x,y) \ x,T(x,y),y) = L((x * y) \ (y * x),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3289(a,1),964(a,1,1))].">
      <j1 rule="para" parents="3289 964"/>
    </justification>
  </clause>

  <clause id="3291">
    <literal><![CDATA[
      L((x * y) \ (y * x),x \ 1,x) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,508,a(flip),b,3290,a),flip(a)].">
      <j1 rule="hyper" parents="58 508 3290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3292">
    <literal><![CDATA[
      K(x,y) = L((y * x) \ (x * y),y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,11,a,b,3291,a)].">
      <j1 rule="hyper" parents="334 11 3291"/>
    </justification>
  </clause>

  <clause id="3293">
    <literal><![CDATA[
      L(K(x,y),y \ 1,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,2),3292(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11 3292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3294">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3293,a(flip),b,265,a),flip(a)].">
      <j1 rule="hyper" parents="116 3293 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3295">
    <literal><![CDATA[
      T(x * y,R(x \ 1,x,x * y)) = x * ((x * y) * (y / (x * y)))
    ]]></literal>
    <justification jstring="[para(1975(a,1),3252(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1975 3252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3296">
    <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(1891(a,1),3069(a,1,1))].">
      <j1 rule="para" parents="1891 3069"/>
    </justification>
  </clause>

  <clause id="3297">
    <literal><![CDATA[
      K(x \ 1,x) * (y / T(1 / (1 / x),z)) = y / ((1 / T(x,z)) \ 1)
    ]]></literal>
    <justification jstring="[para(2566(a,1),3296(a,1,1))].">
      <j1 rule="para" parents="2566 3296"/>
    </justification>
  </clause>

  <clause id="3298">
    <literal><![CDATA[
      K(x \ 1,x) * (y / T(1 / (1 / x),z)) = y / T(x,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),3297(a,2,2))].">
      <j1 rule="para" parents="75 3297"/>
    </justification>
  </clause>

  <clause id="3301">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (y / T(x,z)) = x * (y / T(1 / (1 / x),z))
    ]]></literal>
    <justification jstring="[hyper(119,a,3298,a(flip),b,3173,a)].">
      <j1 rule="hyper" parents="119 3298 3173"/>
    </justification>
  </clause>

  <clause id="3303">
    <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(1199(a,1),2928(a,2,1))].">
      <j1 rule="para" parents="1199 2928"/>
    </justification>
  </clause>

  <clause id="3304">
    <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(334,a,2646,a(flip),b,3303,a),flip(a)].">
      <j1 rule="hyper" parents="334 2646 3303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3305">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2661,a(flip),b,3304,a)].">
      <j1 rule="hyper" parents="58 2661 3304"/>
    </justification>
  </clause>

  <clause id="3306">
    <literal><![CDATA[
      K(x / y,(x / y) \ 1) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(3254,a,3305,a)].">
      <j1 rule="hyper" parents="3254 3305"/>
    </justification>
  </clause>

  <clause id="3308">
    <literal><![CDATA[
      K(x / y,y / x) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3071,a(flip),b,3305,a)].">
      <j1 rule="hyper" parents="58 3071 3305"/>
    </justification>
  </clause>

  <clause id="3309">
    <literal><![CDATA[
      K(1 / (x \ y),x \ y) = K(x / y,y / x)
    ]]></literal>
    <justification jstring="[hyper(334,a,2915,a,b,3308,a)].">
      <j1 rule="hyper" parents="334 2915 3308"/>
    </justification>
  </clause>

  <clause id="3310">
    <literal><![CDATA[
      x * K(x / y,(x / y) \ 1) = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3306(a,2),2916(a,1,2))].">
      <j1 rule="para" parents="3306 2916"/>
    </justification>
  </clause>

  <clause id="3311">
    <literal><![CDATA[
      K((x * y) / x,x / (x * y)) = K(y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(3006,a,3309,a),flip(a)].">
      <j1 rule="hyper" parents="3006 3309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3312">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y
    ]]></literal>
    <justification jstring="[para(3286(a,1),3005(a,1,1))].">
      <j1 rule="para" parents="3286 3005"/>
    </justification>
  </clause>

  <clause id="3313">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[para(1029(a,1),3312(a,2,1,2))].">
      <j1 rule="para" parents="1029 3312"/>
    </justification>
  </clause>

  <clause id="3314">
    <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(270(a,1),2192(a,2,1))].">
      <j1 rule="para" parents="270 2192"/>
    </justification>
  </clause>

  <clause id="3315">
    <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(1972(a,1),3314(a,2,1))].">
      <j1 rule="para" parents="1972 3314"/>
    </justification>
  </clause>

  <clause id="3316">
    <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(2191,a,3315,a)].">
      <j1 rule="hyper" parents="2191 3315"/>
    </justification>
  </clause>

  <clause id="3317">
    <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),2309(a,1,1))].">
      <j1 rule="para" parents="5 2309"/>
    </justification>
  </clause>

  <clause id="3318">
    <literal><![CDATA[
      K(x \ (((y * x) / y) \ x),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(2275,a,3317,a),flip(a)].">
      <j1 rule="hyper" parents="2275 3317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3321">
    <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(3030(a,1),3063(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3030 3063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3322">
    <literal><![CDATA[
      R(R(x,y,z \ 1),y * (z \ 1),K(z,z \ 1)) = R(x,y,1 / z)
    ]]></literal>
    <justification jstring="[hyper(334,a,15,a,b,3321,a),flip(a)].">
      <j1 rule="hyper" parents="334 15 3321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3323">
    <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(3321(a,2),530(a,1))].">
      <j1 rule="para" parents="3321 530"/>
    </justification>
  </clause>

  <clause id="3324">
    <literal><![CDATA[
      R(1 / x,y,1 / x) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2718,a(flip),b,3322,a),flip(a)].">
      <j1 rule="hyper" parents="58 2718 3322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3325">
    <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),3322(a,1,2,2))].">
      <j1 rule="para" parents="106 3322"/>
    </justification>
  </clause>

  <clause id="3327">
    <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(1862(a,1),3325(a,1,3))].">
      <j1 rule="para" parents="1862 3325"/>
    </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,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),3327(a,2,3))].">
      <j1 rule="para" parents="72 3327"/>
    </justification>
  </clause>

  <clause id="3330">
    <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(3152(a,1),3190(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3152 3190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3331">
    <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(3330(a,2),495(a,1))].">
      <j1 rule="para" parents="3330 495"/>
    </justification>
  </clause>

  <clause id="3332">
    <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(2693(a,1),1922(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2693 1922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3333">
    <literal><![CDATA[
      x * ((y \ 1) * (y * T(y \ 1,x))) = (1 / y) * (x * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(3060(a,1),3332(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3060 3332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3334">
    <literal><![CDATA[
      T((x \ 1) * y,K(z \ 1,z)) = y * ((x \ 1) * (x * T(x \ 1,y)))
    ]]></literal>
    <justification jstring="[hyper(334,a,3204,a,b,3333,a)].">
      <j1 rule="hyper" parents="334 3204 3333"/>
    </justification>
  </clause>

  <clause id="3336">
    <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(1501(a,1),2026(a,2,2))].">
      <j1 rule="para" parents="1501 2026"/>
    </justification>
  </clause>

  <clause id="3337">
    <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(2236(a,1),2264(a,1,2,1,1))].">
      <j1 rule="para" parents="2236 2264"/>
    </justification>
  </clause>

  <clause id="3338">
    <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),3213(a,1,1,1))].">
      <j1 rule="para" parents="6 3213"/>
    </justification>
  </clause>

  <clause id="3340">
    <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(3338(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="3338 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3341">
    <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(265(a,1),3336(a,2,2,2))].">
      <j1 rule="para" parents="265 3336"/>
    </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)) = L(x,L(y,z,u) \ 1,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,4,a(flip),b,3341,a),flip(a)].">
      <j1 rule="hyper" parents="334 4 3341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3343">
    <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(1017,a,3342,a)].">
      <j1 rule="hyper" parents="1017 3342"/>
    </justification>
  </clause>

  <clause id="3345">
    <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(2587(a,1),3277(a,2,1))].">
      <j1 rule="para" parents="2587 3277"/>
    </justification>
  </clause>

  <clause id="3346">
    <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),1428(a,1,2,1,1))].">
      <j1 rule="para" parents="90 1428"/>
    </justification>
  </clause>

  <clause id="3347">
    <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(1425,a,3346,a),flip(a)].">
      <j1 rule="hyper" parents="1425 3346"/>
      <j2 rule="flip"/>
    </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(z \ 1,u,w)))
    ]]></literal>
    <justification jstring="[para(949(a,1),3347(a,2,2))].">
      <j1 rule="para" parents="949 3347"/>
    </justification>
  </clause>

  <clause id="3349">
    <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(493,a,3348,a),flip(a)].">
      <j1 rule="hyper" parents="493 3348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3350">
    <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,3348,a)].">
      <j1 rule="hyper" parents="123 3348"/>
    </justification>
  </clause>

  <clause id="3351">
    <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,1244,a(flip),b,3349,a),flip(a)].">
      <j1 rule="hyper" parents="58 1244 3349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3352">
    <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(3349(a,1),3261(a,1,1))].">
      <j1 rule="para" parents="3349 3261"/>
    </justification>
  </clause>

  <clause id="3353">
    <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(3066(a,1),3352(a,1,1,1,2))].">
      <j1 rule="para" parents="3066 3352"/>
    </justification>
  </clause>

  <clause id="3354">
    <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),3353(a,1,1,1,2,1))].">
      <j1 rule="para" parents="2 3353"/>
    </justification>
  </clause>

  <clause id="3355">
    <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(3350(a,1),495(a,1))].">
      <j1 rule="para" parents="3350 495"/>
    </justification>
  </clause>

  <clause id="3356">
    <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(1824(a,1),3351(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1824 3351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3357">
    <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(334,a,2740,a(flip),b,3356,a),flip(a)].">
      <j1 rule="hyper" parents="334 2740 3356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3358">
    <literal><![CDATA[
      (x \ 1) / (x \ L(x,y,z)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(30,a,266,a(flip),b,3357,a),flip(a)].">
      <j1 rule="hyper" parents="30 266 3357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3359">
    <literal><![CDATA[
      x / ((1 / x) \ L(1 / x,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),3358(a,1,1))].">
      <j1 rule="para" parents="75 3358"/>
    </justification>
  </clause>

  <clause id="3360">
    <literal><![CDATA[
      x / (x * L(x \ 1,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1109(a,1),3359(a,1,2))].">
      <j1 rule="para" parents="1109 3359"/>
    </justification>
  </clause>

  <clause id="3361">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) * (x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(133,a,3360,a)].">
      <j1 rule="hyper" parents="133 3360"/>
    </justification>
  </clause>

  <clause id="3362">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ x = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(2888,a,3361,a)].">
      <j1 rule="hyper" parents="2888 3361"/>
    </justification>
  </clause>

  <clause id="3363">
    <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(434,a,3362,a)].">
      <j1 rule="hyper" parents="434 3362"/>
    </justification>
  </clause>

  <clause id="3364">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 = (L(x,y,z) / x) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(1757(a,1),3362(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1757 3362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3365">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ 1 = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,3363,a(flip),b,2112,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 3363 2112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3366">
    <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(334,a,2363,a(flip),b,2365,a),flip(a)].">
      <j1 rule="hyper" parents="334 2363 2365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3367">
    <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),3285(a,1,1,3))].">
      <j1 rule="para" parents="75 3285"/>
    </justification>
  </clause>

  <clause id="3368">
    <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(2940(a,1),3367(a,1,1))].">
      <j1 rule="para" parents="2940 3367"/>
    </justification>
  </clause>

  <clause id="3369">
    <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),1994(a,1,2,2,2))].">
      <j1 rule="para" parents="13 1994"/>
    </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),L(z,y,x))
    ]]></literal>
    <justification jstring="[para(13(a,2),3369(a,2,2))].">
      <j1 rule="para" parents="13 3369"/>
    </justification>
  </clause>

  <clause id="3371">
    <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(1317(a,1),2749(a,1,1,2,1))].">
      <j1 rule="para" parents="1317 2749"/>
    </justification>
  </clause>

  <clause id="3372">
    <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(1630(a,1),3371(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1630 3371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3374">
    <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(3116(a,1),3372(a,2,1))].">
      <j1 rule="para" parents="3116 3372"/>
    </justification>
  </clause>

  <clause id="3375">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = R(1,y,z)
    ]]></literal>
    <justification jstring="[para(227(a,1),3374(a,2,1))].">
      <j1 rule="para" parents="227 3374"/>
    </justification>
  </clause>

  <clause id="3376">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(334,a,388,a(flip),b,3375,a),flip(a)].">
      <j1 rule="hyper" parents="334 388 3375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3378">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ (x \ 1)) * (x \ R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(443,a,3376,a)].">
      <j1 rule="hyper" parents="443 3376"/>
    </justification>
  </clause>

  <clause id="3380">
    <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(3378(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3378 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3381">
    <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),1727(a,1,2,1,2,1))].">
      <j1 rule="para" parents="90 1727"/>
    </justification>
  </clause>

  <clause id="3382">
    <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(1395,a,3381,a),flip(a)].">
      <j1 rule="hyper" parents="1395 3381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3383">
    <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(1138(a,1),3382(a,2,2))].">
      <j1 rule="para" parents="1138 3382"/>
    </justification>
  </clause>

  <clause id="3384">
    <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(493,a,3383,a),flip(a)].">
      <j1 rule="hyper" parents="493 3383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3385">
    <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),3384(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 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) = K(L(x,y,z),L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,1858,a,b,3385,a),flip(a)].">
      <j1 rule="hyper" parents="334 1858 3385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3387">
    <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(1796(a,1),3386(a,1,1))].">
      <j1 rule="para" parents="1796 3386"/>
    </justification>
  </clause>

  <clause id="3388">
    <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),1732(a,1,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="101 1732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3389">
    <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(334,a,898,a(flip),b,3388,a),flip(a)].">
      <j1 rule="hyper" parents="334 898 3388"/>
      <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) * ((x * ((y * z) \ z)) / x)) * u
    ]]></literal>
    <justification jstring="[hyper(334,a,2359,a(flip),b,3389,a),flip(a)].">
      <j1 rule="hyper" parents="334 2359 3389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3391">
    <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,2357,a(flip),b,3389,a)].">
      <j1 rule="hyper" parents="117 2357 3389"/>
    </justification>
  </clause>

  <clause id="3392">
    <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(898(a,1),3390(a,1,1))].">
      <j1 rule="para" parents="898 3390"/>
    </justification>
  </clause>

  <clause id="3393">
    <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(1139(a,1),3391(a,1,1,1))].">
      <j1 rule="para" parents="1139 3391"/>
    </justification>
  </clause>

  <clause id="3394">
    <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(530,a,3393,a),flip(a)].">
      <j1 rule="hyper" parents="530 3393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3395">
    <literal><![CDATA[
      R(((x * (1 / x)) / x) * x,y,z) = T(x,1 / R(x,y,z)) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,3316,a(flip),b,3394,a),flip(a)].">
      <j1 rule="hyper" parents="58 3316 3394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3396">
    <literal><![CDATA[
      R((K(x,1 / x) / x) * x,y,z) = T(x,1 / R(x,y,z)) / x
    ]]></literal>
    <justification jstring="[para(268(a,2),3395(a,1,1,1,1))].">
      <j1 rule="para" parents="268 3395"/>
    </justification>
  </clause>

  <clause id="3397">
    <literal><![CDATA[
      T(x,1 / R(x,y,z)) / x = R(K(x,1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),3396(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 3396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3399">
    <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(1787(a,1),3392(a,2,1))].">
      <j1 rule="para" parents="1787 3392"/>
    </justification>
  </clause>

  <clause id="3400">
    <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,3399,a),flip(a)].">
      <j1 rule="hyper" parents="30 101 3399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3401">
    <literal><![CDATA[
      R(x * ((y * (x \ 1)) / y),z,u) = K(y,(y / R(x,z,u)) / y)
    ]]></literal>
    <justification jstring="[hyper(1791,a,3400,a),flip(a)].">
      <j1 rule="hyper" parents="1791 3400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3402">
    <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),3400(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 3400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3403">
    <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(334,a,1858,a,b,3402,a),flip(a)].">
      <j1 rule="hyper" parents="334 1858 3402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3404">
    <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(1274(a,1),3403(a,1,1,2,1))].">
      <j1 rule="para" parents="1274 3403"/>
    </justification>
  </clause>

  <clause id="3405">
    <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(2894(a,1),3404(a,1,1))].">
      <j1 rule="para" parents="2894 3404"/>
    </justification>
  </clause>

  <clause id="3406">
    <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),1764(a,2,2,1,1))].">
      <j1 rule="para" parents="13 1764"/>
    </justification>
  </clause>

  <clause id="3407">
    <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(1099(a,1),3406(a,1,2))].">
      <j1 rule="para" parents="1099 3406"/>
    </justification>
  </clause>

  <clause id="3408">
    <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),3407(a,1,2,2,2,1,2))].">
      <j1 rule="para" parents="4 3407"/>
    </justification>
  </clause>

  <clause id="3409">
    <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(951(a,1),3408(a,1,2,2))].">
      <j1 rule="para" parents="951 3408"/>
    </justification>
  </clause>

  <clause id="3410">
    <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(590,a,3409,a)].">
      <j1 rule="hyper" parents="590 3409"/>
    </justification>
  </clause>

  <clause id="3411">
    <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(495,a,3409,a),flip(a)].">
      <j1 rule="hyper" parents="495 3409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3412">
    <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,221,a(flip),b,3410,a),flip(a)].">
      <j1 rule="hyper" parents="119 221 3410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3413">
    <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(1839(a,1),3410(a,1,2,1,2))].">
      <j1 rule="para" parents="1839 3410"/>
    </justification>
  </clause>

  <clause id="3414">
    <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(1858(a,2),3413(a,1,2,1))].">
      <j1 rule="para" parents="1858 3413"/>
    </justification>
  </clause>

  <clause id="3415">
    <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(1126(a,1),3412(a,2,2,1))].">
      <j1 rule="para" parents="1126 3412"/>
    </justification>
  </clause>

  <clause id="3416">
    <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(2735(a,1),3415(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2735 3415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3417">
    <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(334,a,3387,a(flip),b,3416,a),flip(a)].">
      <j1 rule="hyper" parents="334 3387 3416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3418">
    <literal><![CDATA[
      (L(x,y,z) / x) \ (1 / x) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,1858,a(flip),b,3417,a),flip(a)].">
      <j1 rule="hyper" parents="29 1858 3417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3419">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3364,a,b,3418,a)].">
      <j1 rule="hyper" parents="58 3364 3418"/>
    </justification>
  </clause>

  <clause id="3420">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) = 1 / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(201,a,3419,a),flip(a)].">
      <j1 rule="hyper" parents="201 3419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3421">
    <literal><![CDATA[
      1 / L(x \ 1,y,z) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(72(a,1),3419(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 3419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3422">
    <literal><![CDATA[
      1 / L((x \ 1) \ 1,y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(194(a,1),3419(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="194 3419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3423">
    <literal><![CDATA[
      1 / (1 / L(x \ 1,y,z)) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),3420(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 3420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3424">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      1 / L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3420(a,2),276(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3420 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3425">
    <literal><![CDATA[
      L(1 / (1 / (x \ y)),x,1 / x) = 1 / (1 / ((1 / x) * y))
    ]]></literal>
    <justification jstring="[para(500(a,1),3420(a,2,2,2))].">
      <j1 rule="para" parents="500 3420"/>
    </justification>
  </clause>

  <clause id="3426">
    <literal><![CDATA[
      T(1 / (1 / L(x,y,z)),1 / x) = L((1 / x) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(3420(a,1),255(a,1,1))].">
      <j1 rule="para" parents="3420 255"/>
    </justification>
  </clause>

  <clause id="3427">
    <literal><![CDATA[
      L(1 / x,x,y) \ 1 = 1 / ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(767,a,3421,a),flip(a)].">
      <j1 rule="hyper" parents="767 3421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3428">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) \ 1 = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(192,a,3421,a)].">
      <j1 rule="hyper" parents="192 3421"/>
    </justification>
  </clause>

  <clause id="3429">
    <literal><![CDATA[
      L(1 / x,x,y) = 1 / (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(201,a,3427,a),flip(a)].">
      <j1 rule="hyper" parents="201 3427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3430">
    <literal><![CDATA[
      L(x,x \ 1,y) = 1 / (1 / ((y * (x \ 1)) \ y))
    ]]></literal>
    <justification jstring="[para(72(a,1),3429(a,1,1))].">
      <j1 rule="para" parents="72 3429"/>
    </justification>
  </clause>

  <clause id="3431">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) = (L(x,y,z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(192,a,3422,a),flip(a)].">
      <j1 rule="hyper" parents="192 3422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3432">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * L((x \ 1) \ 1,y,z) = 1
    ]]></literal>
    <justification jstring="[hyper(133,a,3422,a)].">
      <j1 rule="hyper" parents="133 3422"/>
    </justification>
  </clause>

  <clause id="3433">
    <literal><![CDATA[
      1 / (1 / L(L(x \ 1,y,z),u,w)) = L(L(1 / x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(3423(a,1),3420(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3423 3420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3434">
    <literal><![CDATA[
      L(((x \ y) \ 1) \ 1,x,1 / x) = (((1 / x) * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(500(a,1),3431(a,2,1,1))].">
      <j1 rule="para" parents="500 3431"/>
    </justification>
  </clause>

  <clause id="3435">
    <literal><![CDATA[
      L((((x \ y) \ z) \ 1) \ 1,x \ y,x) = ((y \ (x * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(502(a,1),3431(a,2,1,1))].">
      <j1 rule="para" parents="502 3431"/>
    </justification>
  </clause>

  <clause id="3436">
    <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,450,a,b,3432,a(flip))].">
      <j1 rule="hyper" parents="168 450 3432"/>
    </justification>
  </clause>

  <clause id="3437">
    <literal><![CDATA[
      x / L(y,y \ 1,x) = x * (1 / (1 / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(3430(a,2),2974(a,1,2))].">
      <j1 rule="para" parents="3430 2974"/>
    </justification>
  </clause>

  <clause id="3438">
    <literal><![CDATA[
      x / L(y,y \ 1,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(72(a,1),3437(a,2,2,2))].">
      <j1 rule="para" parents="72 3437"/>
    </justification>
  </clause>

  <clause id="3440">
    <literal><![CDATA[
      K(x \ (x / L(y,y \ 1,x)),z) = K(1 / y,z)
    ]]></literal>
    <justification jstring="[para(3438(a,2),691(a,1,1,2))].">
      <j1 rule="para" parents="3438 691"/>
    </justification>
  </clause>

  <clause id="3441">
    <literal><![CDATA[
      L(x * T(x \ 1,y),x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2738,a,b,3440,a)].">
      <j1 rule="hyper" parents="58 2738 3440"/>
    </justification>
  </clause>

  <clause id="3442">
    <literal><![CDATA[
      K(1 / x,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2616,a,3441,a),flip(a)].">
      <j1 rule="hyper" parents="2616 3441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3443">
    <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,3441,a)].">
      <j1 rule="hyper" parents="58 93 3441"/>
    </justification>
  </clause>

  <clause id="3444">
    <literal><![CDATA[
      L((1 / x) * T((1 / x) \ 1,y),x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(75(a,1),3441(a,1,2))].">
      <j1 rule="para" parents="75 3441"/>
    </justification>
  </clause>

  <clause id="3445">
    <literal><![CDATA[
      K(1 / x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(3441(a,1),2616(a,1))].">
      <j1 rule="para" parents="3441 2616"/>
    </justification>
  </clause>

  <clause id="3446">
    <literal><![CDATA[
      K(1 / (1 / x),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,692,a(flip),b,3442,a),flip(a)].">
      <j1 rule="hyper" parents="334 692 3442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3447">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = (T(y,1 / x) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1092,a(flip),b,3442,a),flip(a)].">
      <j1 rule="hyper" parents="58 1092 3442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3448">
    <literal><![CDATA[
      K((x \ 1) \ 1,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),3442(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 3442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3449">
    <literal><![CDATA[
      K(L(x,x \ 1,y),z) = K((y * (x \ 1)) \ y,z)
    ]]></literal>
    <justification jstring="[para(3430(a,2),3446(a,1,1))].">
      <j1 rule="para" parents="3430 3446"/>
    </justification>
  </clause>

  <clause id="3450">
    <literal><![CDATA[
      K(T(x,x \ 1),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(106(a,2),3448(a,1,1))].">
      <j1 rule="para" parents="106 3448"/>
    </justification>
  </clause>

  <clause id="3451">
    <literal><![CDATA[
      K(T(1 / x,y),z) = K(T(x \ 1,y),z)
    ]]></literal>
    <justification jstring="[para(2223(a,1),3448(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2223 3448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3452">
    <literal><![CDATA[
      K(((1 / x) * y) \ y,z) = K(((x \ 1) * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(3125(a,1),3448(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3125 3448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3453">
    <literal><![CDATA[
      T(1 / (1 / L(x,y,z)),1 / x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),3426(a,2,1))].">
      <j1 rule="para" parents="75 3426"/>
    </justification>
  </clause>

  <clause id="3454">
    <literal><![CDATA[
      T(T(1 / (1 / L(x,y,z)),u),1 / x) = T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(3453(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3453 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3455">
    <literal><![CDATA[
      1 / T(L(x,y,z),1 / x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(3453(a,1),2221(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3453 2221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3456">
    <literal><![CDATA[
      (1 / x) \ (1 / (1 / ((1 / x) * y))) = x * (1 / (1 / (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(116,a,3425,a(flip),b,267,a)].">
      <j1 rule="hyper" parents="116 3425 267"/>
    </justification>
  </clause>

  <clause id="3457">
    <literal><![CDATA[
      (1 / x) \ ((((1 / x) * y) \ 1) \ 1) = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,3434,a(flip),b,267,a)].">
      <j1 rule="hyper" parents="116 3434 267"/>
    </justification>
  </clause>

  <clause id="3458">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1048(a,1),3444(a,1,1))].">
      <j1 rule="para" parents="1048 3444"/>
    </justification>
  </clause>

  <clause id="3459">
    <literal><![CDATA[
      K(1 / (1 / x),y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,893,a(flip),b,3458,a),flip(a)].">
      <j1 rule="hyper" parents="58 893 3458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3460">
    <literal><![CDATA[
      T(K(1 / (1 / x),y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3459(a,2),230(a,1,1))].">
      <j1 rule="para" parents="3459 230"/>
    </justification>
  </clause>

  <clause id="3461">
    <literal><![CDATA[
      T(K(x,y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3446(a,1),3460(a,1,1))].">
      <j1 rule="para" parents="3446 3460"/>
    </justification>
  </clause>

  <clause id="3462">
    <literal><![CDATA[
      K(T(x,x \ 1),y) = T(K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(334,a,3450,a,b,3461,a)].">
      <j1 rule="hyper" parents="334 3450 3461"/>
    </justification>
  </clause>

  <clause id="3463">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2791,a,b,3461,a)].">
      <j1 rule="hyper" parents="58 2791 3461"/>
    </justification>
  </clause>

  <clause id="3464">
    <literal><![CDATA[
      T(x,K(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,3461,a)].">
      <j1 rule="hyper" parents="49 3461"/>
    </justification>
  </clause>

  <clause id="3465">
    <literal><![CDATA[
      K(x,y) * x = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,3461,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 3461 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3466">
    <literal><![CDATA[
      x * K(x,y) != z * x
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3461(a,1),249(a,1,2))].">
      <j1 rule="para" parents="3461 249"/>
    </justification>
  </clause>

  <clause id="3467">
    <literal><![CDATA[
      R(K(x,y),z,u) * x = x * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3461(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3461 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3468">
    <literal><![CDATA[
      T(T(x,y),K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3464(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3464 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3469">
    <literal><![CDATA[
      K(x,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3464(a,1),294(a,1,2))].">
      <j1 rule="para" parents="3464 294"/>
    </justification>
  </clause>

  <clause id="3470">
    <literal><![CDATA[
      T(x,y) * K(x,z) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3464(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3464 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3471">
    <literal><![CDATA[
      T(T(T(x,y),z),K(x,u)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(3464(a,1),109(a,2,1,1))].">
      <j1 rule="para" parents="3464 109"/>
    </justification>
  </clause>

  <clause id="3472">
    <literal><![CDATA[
      L(x,y,z) * K(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3464(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3464 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3473">
    <literal><![CDATA[
      R(x,y,z) * K(x,u) = K(x,u) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3464(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3464 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3474">
    <literal><![CDATA[
      T((x \ y) \ y,K(x,z)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(3464(a,1),330(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3464 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3475">
    <literal><![CDATA[
      T((x * y) / x,K(y,z)) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(3464(a,1),472(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3464 472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3477">
    <literal><![CDATA[
      K(1 / x,y) * (1 / x) = (1 / x) * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(3442(a,1),3465(a,2,2))].">
      <j1 rule="para" parents="3442 3465"/>
    </justification>
  </clause>

  <clause id="3478">
    <literal><![CDATA[
      T(K(x,y),T(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,3468,a)].">
      <j1 rule="hyper" parents="49 3468"/>
    </justification>
  </clause>

  <clause id="3479">
    <literal><![CDATA[
      T(x,y) * z != K(x,u) * T(x,y)
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = z
    ]]></literal>
    <justification jstring="[para(3468(a,1),248(a,1,2)),flip(a),flip(b)].">
      <j1 rule="para" parents="3468 248"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3480">
    <literal><![CDATA[
      T(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(3478(a,1),294(a,1,2))].">
      <j1 rule="para" parents="3478 294"/>
    </justification>
  </clause>

  <clause id="3481">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),x) = z
    ]]></literal>
    <justification jstring="[para(3478(a,1),3120(a,1))].">
      <j1 rule="para" parents="3478 3120"/>
    </justification>
  </clause>

  <clause id="3482">
    <literal><![CDATA[
      T(K(x,y),T(T(x,z),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,3471,a)].">
      <j1 rule="hyper" parents="49 3471"/>
    </justification>
  </clause>

  <clause id="3483">
    <literal><![CDATA[
      T(K(x,y),(z * x) / z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,3475,a)].">
      <j1 rule="hyper" parents="49 3475"/>
    </justification>
  </clause>

  <clause id="3484">
    <literal><![CDATA[
      T(K(x \ y,z),y / x) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),3483(a,1,2,1))].">
      <j1 rule="para" parents="5 3483"/>
    </justification>
  </clause>

  <clause id="3486">
    <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(852,a,3467,a),flip(a)].">
      <j1 rule="hyper" parents="852 3467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3487">
    <literal><![CDATA[
      T(x,R(K(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(247,a,3467,a)].">
      <j1 rule="hyper" parents="247 3467"/>
    </justification>
  </clause>

  <clause id="3488">
    <literal><![CDATA[
      K(x,R(K(x,y),z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,3467,a,b,84,a),flip(a)].">
      <j1 rule="hyper" parents="115 3467 84"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3489">
    <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(3487(a,1),244(a,1,2,1))].">
      <j1 rule="para" parents="3487 244"/>
    </justification>
  </clause>

  <clause id="3490">
    <literal><![CDATA[
      T(K(x,y),L(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(247,a,3472,a)].">
      <j1 rule="hyper" parents="247 3472"/>
    </justification>
  </clause>

  <clause id="3491">
    <literal><![CDATA[
      T(K(x,y),R(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(247,a,3473,a)].">
      <j1 rule="hyper" parents="247 3473"/>
    </justification>
  </clause>

  <clause id="3492">
    <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(3491(a,1),294(a,1,2))].">
      <j1 rule="para" parents="3491 294"/>
    </justification>
  </clause>

  <clause id="3493">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * K(x \ 1,y)) = x \ K(1 / x,y)
    ]]></literal>
    <justification jstring="[para(3477(a,1),3098(a,1,2))].">
      <j1 rule="para" parents="3477 3098"/>
    </justification>
  </clause>

  <clause id="3494">
    <literal><![CDATA[
      T(x,x \ K(y,x)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3463(a,1),2834(a,1,2,2))].">
      <j1 rule="para" parents="3463 2834"/>
    </justification>
  </clause>

  <clause id="3495">
    <literal><![CDATA[
      x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(3463(a,1),2839(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3463 2839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3496">
    <literal><![CDATA[
      K(x,y) / T(y,y \ 1) = y \ K(x,y)
    ]]></literal>
    <justification jstring="[para(3494(a,1),273(a,1,2))].">
      <j1 rule="para" parents="3494 273"/>
    </justification>
  </clause>

  <clause id="3497">
    <literal><![CDATA[
      K(x,y) * K(y \ 1,y) = (y \ K(x,y)) * y
    ]]></literal>
    <justification jstring="[para(3496(a,1),2993(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3496 2993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3498">
    <literal><![CDATA[
      (x \ K(y,x)) * K(x,x \ 1) = K(y,x) / x
    ]]></literal>
    <justification jstring="[para(3496(a,1),3057(a,1,1))].">
      <j1 rule="para" parents="3496 3057"/>
    </justification>
  </clause>

  <clause id="3499">
    <literal><![CDATA[
      K(x,y) * K(y,y \ 1) = y * (K(x,y) / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,3498,a(flip),b,2683,a),flip(a)].">
      <j1 rule="hyper" parents="119 3498 2683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3500">
    <literal><![CDATA[
      x * (x * (K(y,x) / x)) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(3499(a,1),3233(a,1,2))].">
      <j1 rule="para" parents="3499 3233"/>
    </justification>
  </clause>

  <clause id="3501">
    <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,3500,a(flip),b,1159,a),flip(a)].">
      <j1 rule="hyper" parents="116 3500 1159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3502">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = (T(y,x \ 1) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[para(3105(a,1),3447(a,2,1,1))].">
      <j1 rule="para" parents="3105 3447"/>
    </justification>
  </clause>

  <clause id="3503">
    <literal><![CDATA[
      (1 / x) \ ((((1 / x) * y) \ 1) \ 1) = y * K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,2916,a,b,3457,a),flip(a)].">
      <j1 rule="hyper" parents="334 2916 3457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3504">
    <literal><![CDATA[
      (x \ 1) * K(x \ 1,y) = x \ K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(3208,a,3493,a)].">
      <j1 rule="hyper" parents="3208 3493"/>
    </justification>
  </clause>

  <clause id="3505">
    <literal><![CDATA[
      (x \ K(1 / x,y)) * ((x \ 1) \ 1) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(3504(a,1),1805(a,1,1))].">
      <j1 rule="para" parents="3504 1805"/>
    </justification>
  </clause>

  <clause id="3506">
    <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),3505(a,1,1,2))].">
      <j1 rule="para" parents="87 3505"/>
    </justification>
  </clause>

  <clause id="3507">
    <literal><![CDATA[
      L(T((x \ y) \ z,z \ (x \ y)),x \ y,x) = ((y \ (x * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2459(a,2),3435(a,1,1))].">
      <j1 rule="para" parents="2459 3435"/>
    </justification>
  </clause>

  <clause id="3508">
    <literal><![CDATA[
      L((x \ 1) \ 1,L(x,y,z) \ 1,L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(143,a,3436,a)].">
      <j1 rule="hyper" parents="143 3436"/>
    </justification>
  </clause>

  <clause id="3509">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * ((x \ 1) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,3508,a(flip),b,265,a),flip(a)].">
      <j1 rule="hyper" parents="116 3508 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3511">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * T(x,x \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(644,a,3509,a)].">
      <j1 rule="hyper" parents="644 3509"/>
    </justification>
  </clause>

  <clause id="3512">
    <literal><![CDATA[
      T(x,L(x,y,z) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(246,a,1510,a,b,3509,a)].">
      <j1 rule="hyper" parents="246 1510 3509"/>
    </justification>
  </clause>

  <clause id="3513">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(x \ 1,x) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(3509(a,1),2992(a,1,1))].">
      <j1 rule="para" parents="3509 2992"/>
    </justification>
  </clause>

  <clause id="3514">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ ((L(x,y,z) \ 1) * x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,3513,a)].">
      <j1 rule="hyper" parents="123 3513"/>
    </justification>
  </clause>

  <clause id="3515">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1515,a,3514,a)].">
      <j1 rule="hyper" parents="1515 3514"/>
    </justification>
  </clause>

  <clause id="3516">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2804,a,b,3515,a)].">
      <j1 rule="hyper" parents="58 2804 3515"/>
    </justification>
  </clause>

  <clause id="3517">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) = x * (y * K(z \ 1,z))
    ]]></literal>
    <justification jstring="[para(3515(a,1),2805(a,1,2))].">
      <j1 rule="para" parents="3515 2805"/>
    </justification>
  </clause>

  <clause id="3520">
    <literal><![CDATA[
      a(x,y,K(z \ 1,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,3516,a,b,1992,a),flip(a)].">
      <j1 rule="hyper" parents="115 3516 1992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3521">
    <literal><![CDATA[
      (x \ 1) * K(y \ 1,y) = x \ K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,3516,a(flip),b,265,a),flip(a)].">
      <j1 rule="hyper" parents="116 3516 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3522">
    <literal><![CDATA[
      x \ (y * K(z \ 1,z)) = (x \ y) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(3516(a,1),487(a,1,2,2))].">
      <j1 rule="para" parents="3516 487"/>
    </justification>
  </clause>

  <clause id="3525">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(1859(a,1),3520(a,1,3))].">
      <j1 rule="para" parents="1859 3520"/>
    </justification>
  </clause>

  <clause id="3526">
    <literal><![CDATA[
      a(x,y,K(1 / z,z)) = 1
    ]]></literal>
    <justification jstring="[para(1898(a,2),3520(a,1,3))].">
      <j1 rule="para" parents="1898 3520"/>
    </justification>
  </clause>

  <clause id="3528">
    <literal><![CDATA[
      (x * y) * K(z,z \ 1) = x * (y * K(z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(214,a,3525,a)].">
      <j1 rule="hyper" parents="214 3525"/>
    </justification>
  </clause>

  <clause id="3529">
    <literal><![CDATA[
      L(K(x,x \ 1),y,z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(47,a,3525,a)].">
      <j1 rule="hyper" parents="47 3525"/>
    </justification>
  </clause>

  <clause id="3530">
    <literal><![CDATA[
      L(K(1 / x,x),y,z) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(47,a,3526,a)].">
      <j1 rule="hyper" parents="47 3526"/>
    </justification>
  </clause>

  <clause id="3532">
    <literal><![CDATA[
      (x \ 1) * K(y,y \ 1) = x \ K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,3529,a(flip),b,265,a),flip(a)].">
      <j1 rule="hyper" parents="116 3529 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3533">
    <literal><![CDATA[
      x \ (y * K(z,z \ 1)) = (x \ y) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(3529(a,1),487(a,1,2,2))].">
      <j1 rule="para" parents="3529 487"/>
    </justification>
  </clause>

  <clause id="3534">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,x \ 1) = L(x,y,z) \ K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3529(a,1),3414(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3529 3414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3535">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ 1) = y \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(2260,a,3521,a)].">
      <j1 rule="hyper" parents="2260 3521"/>
    </justification>
  </clause>

  <clause id="3536">
    <literal><![CDATA[
      (x \ K(y,y \ 1)) * y = (x \ 1) * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3532(a,1),3014(a,1,1))].">
      <j1 rule="para" parents="3532 3014"/>
    </justification>
  </clause>

  <clause id="3537">
    <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(3431(a,2),3535(a,1,2))].">
      <j1 rule="para" parents="3431 3535"/>
    </justification>
  </clause>

  <clause id="3538">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * K(x \ 1,x))) = y * z
    ]]></literal>
    <justification jstring="[hyper(3052,a,3517,a)].">
      <j1 rule="hyper" parents="3052 3517"/>
    </justification>
  </clause>

  <clause id="3539">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(2260,a,3517,a)].">
      <j1 rule="hyper" parents="2260 3517"/>
    </justification>
  </clause>

  <clause id="3540">
    <literal><![CDATA[
      R(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(527,a,3517,a)].">
      <j1 rule="hyper" parents="527 3517"/>
    </justification>
  </clause>

  <clause id="3541">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) = x * (K(z \ 1,z) * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,2269,a,b,3517,a),flip(a)].">
      <j1 rule="hyper" parents="334 2269 3517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3546">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / z = x / (z * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(3038,a,3540,a),flip(a)].">
      <j1 rule="hyper" parents="3038 3540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3547">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3328,a(flip),b,3540,a),flip(a)].">
      <j1 rule="hyper" parents="58 3328 3540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3548">
    <literal><![CDATA[
      R(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[para(75(a,1),3540(a,1,3,1))].">
      <j1 rule="para" parents="75 3540"/>
    </justification>
  </clause>

  <clause id="3549">
    <literal><![CDATA[
      R(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1859(a,1),3540(a,1,3))].">
      <j1 rule="para" parents="1859 3540"/>
    </justification>
  </clause>

  <clause id="3550">
    <literal><![CDATA[
      R(x,y,K(1 / z,z)) = x
    ]]></literal>
    <justification jstring="[para(1898(a,2),3540(a,1,3))].">
      <j1 rule="para" parents="1898 3540"/>
    </justification>
  </clause>

  <clause id="3551">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = (x \ z) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(3540(a,1),2272(a,1,1))].">
      <j1 rule="para" parents="3540 2272"/>
    </justification>
  </clause>

  <clause id="3552">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / z != u
    ]]></literal>
    <literal><![CDATA[
      x / (z * K(y \ 1,y)) = u
    ]]></literal>
    <justification jstring="[para(3540(a,1),3038(a,1))].">
      <j1 rule="para" parents="3540 3038"/>
    </justification>
  </clause>

  <clause id="3553">
    <literal><![CDATA[
      R(x,y,K(z,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3548(a,1),46(a,2))].">
      <j1 rule="para" parents="3548 46"/>
    </justification>
  </clause>

  <clause id="3554">
    <literal><![CDATA[
      (x * y) * K(z,1 / z) = x * (y * K(z,1 / z))
    ]]></literal>
    <justification jstring="[para(3548(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3548 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3555">
    <literal><![CDATA[
      R(x,y,1 / z) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(3323,a,3549,a)].">
      <j1 rule="hyper" parents="3323 3549"/>
    </justification>
  </clause>

  <clause id="3558">
    <literal><![CDATA[
      R(x,y,K(z,z \ 1)) != 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="3559">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * z) = (x \ z) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3549(a,1),2265(a,1,1))].">
      <j1 rule="para" parents="3549 2265"/>
    </justification>
  </clause>

  <clause id="3561">
    <literal><![CDATA[
      R(x,y,z) * (y * ((z \ 1) \ 1)) = (x * y) * ((z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3547(a,1),101(a,1,1))].">
      <j1 rule="para" parents="3547 101"/>
    </justification>
  </clause>

  <clause id="3565">
    <literal><![CDATA[
      x \ (y * K(z \ 1,z)) = K(z \ 1,z) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,2250,a,b,3522,a),flip(a)].">
      <j1 rule="hyper" parents="334 2250 3522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3566">
    <literal><![CDATA[
      (x \ (1 / y)) * K(y \ 1,y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(799(a,1),3522(a,1,2)),flip(a)].">
      <j1 rule="para" parents="799 3522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3567">
    <literal><![CDATA[
      (x \ ((y \ 1) \ 1)) * K(y \ 1,y) = x \ y
    ]]></literal>
    <justification jstring="[para(1318(a,1),3522(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1318 3522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3568">
    <literal><![CDATA[
      (x \ y) * K(y \ 1,y) = x \ (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(1853(a,1),3522(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1853 3522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3569">
    <literal><![CDATA[
      (x \ (y / (z \ 1))) * K(z \ 1,z) = x \ (y / (1 / z))
    ]]></literal>
    <justification jstring="[para(2951(a,1),3522(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2951 3522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3570">
    <literal><![CDATA[
      (x \ ((y \ 1) \ z)) * K(y \ 1,y) = x \ ((1 / y) \ z)
    ]]></literal>
    <justification jstring="[para(3203(a,1),3522(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3203 3522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3571">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ x) = y \ ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(3052,a,3567,a)].">
      <j1 rule="hyper" parents="3052 3567"/>
    </justification>
  </clause>

  <clause id="3572">
    <literal><![CDATA[
      (x \ y) * K(y,y \ 1) = x \ ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(3025,a,3567,a)].">
      <j1 rule="hyper" parents="3025 3567"/>
    </justification>
  </clause>

  <clause id="3573">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ x) = y \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(2260,a,3568,a)].">
      <j1 rule="hyper" parents="2260 3568"/>
    </justification>
  </clause>

  <clause id="3575">
    <literal><![CDATA[
      (x \ y) * K(y,y \ 1) = x \ T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,324,a,b,3572,a),flip(a)].">
      <j1 rule="hyper" parents="334 324 3572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3576">
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) = y * (z * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(2241,a,3528,a)].">
      <j1 rule="hyper" parents="2241 3528"/>
    </justification>
  </clause>

  <clause id="3577">
    <literal><![CDATA[
      x \ (y * K(z,z \ 1)) = K(z,z \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,2237,a,b,3533,a),flip(a)].">
      <j1 rule="hyper" parents="334 2237 3533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3579">
    <literal><![CDATA[
      (L(x,y,z) \ K(x,x \ 1)) * x = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(334,a,3509,a(flip),b,3536,a),flip(a)].">
      <j1 rule="hyper" parents="334 3509 3536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3580">
    <literal><![CDATA[
      1 / (x * K(y \ 1,y)) = K(y,y \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(423,a,3538,a),flip(a)].">
      <j1 rule="hyper" parents="423 3538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3581">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (K(x \ 1,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[para(2250(a,2),3538(a,1,2,2))].">
      <j1 rule="para" parents="2250 3538"/>
    </justification>
  </clause>

  <clause id="3582">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * (x \ 1))) = y * (z * (1 / x))
    ]]></literal>
    <justification jstring="[para(2937(a,1),3538(a,1,2,2))].">
      <j1 rule="para" parents="2937 3538"/>
    </justification>
  </clause>

  <clause id="3583">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z / (1 / x))) = y * (z / (x \ 1))
    ]]></literal>
    <justification jstring="[para(2951(a,1),3538(a,1,2,2))].">
      <j1 rule="para" parents="2951 3538"/>
    </justification>
  </clause>

  <clause id="3584">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z / ((x \ 1) \ 1))) = y * (z / x)
    ]]></literal>
    <justification jstring="[para(2987(a,1),3538(a,1,2,2))].">
      <j1 rule="para" parents="2987 3538"/>
    </justification>
  </clause>

  <clause id="3585">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * x)) = y * (z * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(2992(a,1),3538(a,1,2,2))].">
      <j1 rule="para" parents="2992 3538"/>
    </justification>
  </clause>

  <clause id="3586">
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) = y * (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3033(a,1),3538(a,1,2,2))].">
      <j1 rule="para" parents="3033 3538"/>
    </justification>
  </clause>

  <clause id="3587">
    <literal><![CDATA[
      K(x,x \ 1) * (y * ((x \ 1) * z)) = y * ((1 / x) * z)
    ]]></literal>
    <justification jstring="[para(3186(a,1),3538(a,1,2,2))].">
      <j1 rule="para" parents="3186 3538"/>
    </justification>
  </clause>

  <clause id="3588">
    <literal><![CDATA[
      K(x,x \ 1) * (y * ((1 / x) \ z)) = y * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(3203(a,1),3538(a,1,2,2))].">
      <j1 rule="para" parents="3203 3538"/>
    </justification>
  </clause>

  <clause id="3589">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[hyper(334,a,2269,a,b,3539,a),flip(a)].">
      <j1 rule="hyper" parents="334 2269 3539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3590">
    <literal><![CDATA[
      (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(u * K(z \ 1,z),y,x)
    ]]></literal>
    <justification jstring="[para(3539(a,2),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3539 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3591">
    <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(3539(a,1),506(a,1,1))].">
      <j1 rule="para" parents="3539 506"/>
    </justification>
  </clause>

  <clause id="3592">
    <literal><![CDATA[
      x \ (y * (K(z \ 1,z) * u)) = (x \ (y * u)) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(3541(a,1),3522(a,1,2))].">
      <j1 rule="para" parents="3541 3522"/>
    </justification>
  </clause>

  <clause id="3593">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / (z * ((y \ 1) \ 1)) = x / (z * y)
    ]]></literal>
    <justification jstring="[para(2992(a,1),3546(a,2,2))].">
      <j1 rule="para" parents="2992 3546"/>
    </justification>
  </clause>

  <clause id="3594">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = K(y \ 1,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(334,a,2250,a,b,3551,a),flip(a)].">
      <j1 rule="hyper" parents="334 2250 3551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3596">
    <literal><![CDATA[
      x * (K(y,y \ 1) * (x \ z)) = K(y,y \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(2242,a,3559,a)].">
      <j1 rule="hyper" parents="2242 3559"/>
    </justification>
  </clause>

  <clause id="3597">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * z) = K(y,y \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(334,a,2237,a,b,3559,a),flip(a)].">
      <j1 rule="hyper" parents="334 2237 3559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3598">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ (z * (1 / x))) = y \ (z * (x \ 1))
    ]]></literal>
    <justification jstring="[para(2937(a,1),3565(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2937 3565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3599">
    <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),3577(a,2,2))].">
      <j1 rule="para" parents="13 3577"/>
    </justification>
  </clause>

  <clause id="3600">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ ((x \ 1) * z)) = y \ ((1 / x) * z)
    ]]></literal>
    <justification jstring="[para(3185(a,1),3577(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3185 3577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3601">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ ((1 / x) \ z)) = y \ ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(3202(a,1),3577(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3202 3577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3603">
    <literal><![CDATA[
      x \ (y * (K(z,z \ 1) * u)) = (x \ (y * u)) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(3586(a,1),3559(a,1,2))].">
      <j1 rule="para" parents="3586 3559"/>
    </justification>
  </clause>

  <clause id="3604">
    <literal><![CDATA[
      (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(K(z \ 1,z) * u,y,x)
    ]]></literal>
    <justification jstring="[para(3589(a,2),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3589 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3607">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ z) * K(y \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(3594(a,2),2254(a,1))].">
      <j1 rule="para" parents="3594 2254"/>
    </justification>
  </clause>

  <clause id="3611">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ z) * K(y,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(3597(a,2),2246(a,1))].">
      <j1 rule="para" parents="3597 2246"/>
    </justification>
  </clause>

  <clause id="3612">
    <literal><![CDATA[
      (1 / x) * (y * ((1 / x) \ z)) = (x \ 1) * (y * ((x \ 1) \ z))
    ]]></literal>
    <justification jstring="[hyper(119,a,3588,a(flip),b,3206,a),flip(a)].">
      <j1 rule="hyper" parents="119 3588 3206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3613">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ (z * ((1 / x) \ u))) = y \ (z * ((x \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(116,a,3588,a(flip),b,3596,a),flip(a)].">
      <j1 rule="hyper" parents="116 3588 3596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3614">
    <literal><![CDATA[
      (1 / (1 / x)) / (y * x) = x / (y * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(1865(a,1),3593(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1865 3593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3617">
    <literal><![CDATA[
      (x * y) * ((z \ 1) \ 1) != u * (y * ((z \ 1) \ 1))
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3561(a,1),39(a,1))].">
      <j1 rule="para" parents="3561 39"/>
    </justification>
  </clause>

  <clause id="3618">
    <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),3592(a,2,1))].">
      <j1 rule="para" parents="13 3592"/>
    </justification>
  </clause>

  <clause id="3619">
    <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(3592(a,1),2303(a,1))].">
      <j1 rule="para" parents="3592 2303"/>
    </justification>
  </clause>

  <clause id="3620">
    <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(709,a,3603,a),flip(a)].">
      <j1 rule="hyper" parents="709 3603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3621">
    <literal><![CDATA[
      x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(334,a,2728,a(flip),b,3495,a),flip(a)].">
      <j1 rule="hyper" parents="334 2728 3495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3622">
    <literal><![CDATA[
      x * (((x * y) \ (x * T(x \ (x * y),x))) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(2824(a,1),3495(a,1,2))].">
      <j1 rule="para" parents="2824 3495"/>
    </justification>
  </clause>

  <clause id="3623">
    <literal><![CDATA[
      x * (((x * y) \ (x * T(y,x))) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),3622(a,1,2,1,2,2,1))].">
      <j1 rule="para" parents="4 3622"/>
    </justification>
  </clause>

  <clause id="3624">
    <literal><![CDATA[
      x * (((x * y) \ (y * x)) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(105(a,1),3623(a,1,2,1,2))].">
      <j1 rule="para" parents="105 3623"/>
    </justification>
  </clause>

  <clause id="3625">
    <literal><![CDATA[
      x * (K(y,x) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(11(a,2),3624(a,1,2,1))].">
      <j1 rule="para" parents="11 3624"/>
    </justification>
  </clause>

  <clause id="3626">
    <literal><![CDATA[
      x * (K(y,x) \ 1) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(334,a,2728,a(flip),b,3625,a),flip(a)].">
      <j1 rule="hyper" parents="334 2728 3625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3627">
    <literal><![CDATA[
      (K(x,y) \ 1) \ (K(x,y) \ y) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,3626,a(flip),b,2849,a)].">
      <j1 rule="hyper" parents="116 3626 2849"/>
    </justification>
  </clause>

  <clause id="3628">
    <literal><![CDATA[
      K(x,y) \ y != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) \ 1 = z
    ]]></literal>
    <justification jstring="[para(3626(a,1),38(a,1))].">
      <j1 rule="para" parents="3626 38"/>
    </justification>
  </clause>

  <clause id="3629">
    <literal><![CDATA[
      (K(x,y) \ y) \ (K(x,y) \ 1) = y \ 1
    ]]></literal>
    <justification jstring="[para(3626(a,1),2851(a,1,1))].">
      <j1 rule="para" parents="3626 2851"/>
    </justification>
  </clause>

  <clause id="3630">
    <literal><![CDATA[
      (K(x,y) \ 1) * T(y,z) = K(x,y) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(3627(a,1),1030(a,1,2,1))].">
      <j1 rule="para" parents="3627 1030"/>
    </justification>
  </clause>

  <clause id="3631">
    <literal><![CDATA[
      (K(x,y) \ y) * (y \ 1) = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(134,a,3629,a)].">
      <j1 rule="hyper" parents="134 3629"/>
    </justification>
  </clause>

  <clause id="3632">
    <literal><![CDATA[
      R(K(x,y) \ y,y \ 1,y) = (K(x,y) \ 1) * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3631(a,1),2996(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3631 2996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3633">
    <literal><![CDATA[
      K(x,y) \ T(y,y \ z) = (K(x,y) \ 1) * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,327,a(flip),b,3630,a),flip(a)].">
      <j1 rule="hyper" parents="58 327 3630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3634">
    <literal><![CDATA[
      (K(x,y) \ 1) * ((y \ z) \ z) = K(x,y) \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,324,a(flip),b,3633,a),flip(a)].">
      <j1 rule="hyper" parents="58 324 3633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3635">
    <literal><![CDATA[
      R(K(x,y) \ y,y \ 1,y) = K(x,y) \ ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,3634,a(flip),b,3632,a),flip(a)].">
      <j1 rule="hyper" parents="334 3634 3632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3636">
    <literal><![CDATA[
      x * (K(x,y) * (K(x,y) \ ((y \ 1) \ 1))) = (T(y,y \ 1) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(3635(a,1),2859(a,1,2,2))].">
      <j1 rule="para" parents="3635 2859"/>
    </justification>
  </clause>

  <clause id="3637">
    <literal><![CDATA[
      x * (x * (T(x,y) \ (K(z,x) / x))) = T(x,y) \ ((x \ 1) \ K(z,x))
    ]]></literal>
    <justification jstring="[para(1161(a,1),3501(a,1,2))].">
      <j1 rule="para" parents="1161 3501"/>
    </justification>
  </clause>

  <clause id="3638">
    <literal><![CDATA[
      x \ ((((x * y) \ x) \ 1) \ T(((x * y) \ x) \ 1,x)) = (K(y,x) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(3621(a,1),2837(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3621 2837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3639">
    <literal><![CDATA[
      T(x \ (y * z),z \ (y \ x)) = ((x \ (y * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,779,a(flip),b,3507,a)].">
      <j1 rule="hyper" parents="58 779 3507"/>
    </justification>
  </clause>

  <clause id="3640">
    <literal><![CDATA[
      L(K(x \ 1,x) * y,z,u) = L(y,z,u) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3604,a(flip),b,3618,a)].">
      <j1 rule="hyper" parents="58 3604 3618"/>
    </justification>
  </clause>

  <clause id="3641">
    <literal><![CDATA[
      L(x * K(y \ 1,y),z,u) = L(x,z,u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3590,a(flip),b,3618,a)].">
      <j1 rule="hyper" parents="58 3590 3618"/>
    </justification>
  </clause>

  <clause id="3642">
    <literal><![CDATA[
      L(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,2250,a,b,3640,a),flip(a)].">
      <j1 rule="hyper" parents="334 2250 3640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3643">
    <literal><![CDATA[
      L(x,y,z) * K(x \ 1,x) = L(1 / (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(1878(a,1),3640(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1878 3640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3645">
    <literal><![CDATA[
      K(x \ 1,x) * L((x \ 1) \ 1,y,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(945(a,1),3642(a,1,1)),flip(a)].">
      <j1 rule="para" parents="945 3642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3646">
    <literal><![CDATA[
      K(x \ 1,x) * L(1 / x,y,z) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1851(a,1),3642(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1851 3642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3648">
    <literal><![CDATA[
      K(x \ 1,x) * L(y * K(x,x \ 1),z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[para(3028(a,1),3642(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3028 3642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3649">
    <literal><![CDATA[
      K(x,x \ 1) * L(x,y,z) = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(3053,a,3645,a)].">
      <j1 rule="hyper" parents="3053 3645"/>
    </justification>
  </clause>

  <clause id="3650">
    <literal><![CDATA[
      L(x,y,z) * K(x,x \ 1) = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(3034,a,3645,a)].">
      <j1 rule="hyper" parents="3034 3645"/>
    </justification>
  </clause>

  <clause id="3651">
    <literal><![CDATA[
      K(x \ 1,x) * ((y * (x \ 1)) \ y) = L(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,405,a(flip),b,3645,a)].">
      <j1 rule="hyper" parents="58 405 3645"/>
    </justification>
  </clause>

  <clause id="3652">
    <literal><![CDATA[
      L(x \ 1,y,z) * K(x,x \ 1) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3034,a,3646,a)].">
      <j1 rule="hyper" parents="3034 3646"/>
    </justification>
  </clause>

  <clause id="3654">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,3646,a(flip),b,1913,a(flip))].">
      <j1 rule="hyper" parents="116 3646 1913"/>
    </justification>
  </clause>

  <clause id="3655">
    <literal><![CDATA[
      K(x,x \ 1) * L(x,y,z) = L(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,854,a,b,3649,a),flip(a)].">
      <j1 rule="hyper" parents="334 854 3649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3656">
    <literal><![CDATA[
      x \ L((x \ 1) \ 1,y,z) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3649,a(flip),b,2262,a(flip))].">
      <j1 rule="hyper" parents="116 3649 2262"/>
    </justification>
  </clause>

  <clause id="3657">
    <literal><![CDATA[
      L(x,y,z) * K(x,1 / x) = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1855(a,2),3650(a,1,2))].">
      <j1 rule="para" parents="1855 3650"/>
    </justification>
  </clause>

  <clause id="3658">
    <literal><![CDATA[
      ((x * y) \ x) \ L(1 / y,y,x) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(755,a,3652,a)].">
      <j1 rule="hyper" parents="755 3652"/>
    </justification>
  </clause>

  <clause id="3659">
    <literal><![CDATA[
      x \ L(T(x,x \ 1),y,z) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3655,a(flip),b,2262,a(flip))].">
      <j1 rule="hyper" parents="116 3655 2262"/>
    </justification>
  </clause>

  <clause id="3660">
    <literal><![CDATA[
      T(L(x,y,z) * (1 / x),x) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1340,a,b,3656,a)].">
      <j1 rule="hyper" parents="58 1340 3656"/>
    </justification>
  </clause>

  <clause id="3661">
    <literal><![CDATA[
      (x \ L(x,y,z)) * x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2419,a,3660,a)].">
      <j1 rule="hyper" parents="2419 3660"/>
    </justification>
  </clause>

  <clause id="3662">
    <literal><![CDATA[
      T(x,x \ L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(366,a,3661,a)].">
      <j1 rule="hyper" parents="366 3661"/>
    </justification>
  </clause>

  <clause id="3663">
    <literal><![CDATA[
      L(x,y,z) / x = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,3661,a)].">
      <j1 rule="hyper" parents="130 3661"/>
    </justification>
  </clause>

  <clause id="3664">
    <literal><![CDATA[
      K(x \ L(x,y,z),x) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,3661,a(flip),b,315,a),flip(a)].">
      <j1 rule="hyper" parents="115 3661 315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3665">
    <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(3661(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3661 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3666">
    <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(3661(a,1),434(a,1,1))].">
      <j1 rule="para" parents="3661 434"/>
    </justification>
  </clause>

  <clause id="3667">
    <literal><![CDATA[
      T(x,y) * (x \ L(x,z,u)) = (x \ L(x,z,u)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3662(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3662 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3668">
    <literal><![CDATA[
      L(x * K(y,y \ 1),z,u) = K(y,y \ 1) * L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(3053,a,3648,a),flip(a)].">
      <j1 rule="hyper" parents="3053 3648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3669">
    <literal><![CDATA[
      L(x * K(y,y \ 1),z,u) = L(x,z,u) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3034,a,3648,a),flip(a)].">
      <j1 rule="hyper" parents="3034 3648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3670">
    <literal><![CDATA[
      (x \ L(x * (y / x),z,u)) * x = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,3279,a(flip),b,3648,a)].">
      <j1 rule="hyper" parents="58 3279 3648"/>
    </justification>
  </clause>

  <clause id="3672">
    <literal><![CDATA[
      (x \ L(x * y,z,u)) * x = L(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(6(a,1),3670(a,1,1,2,1,2))].">
      <j1 rule="para" parents="6 3670"/>
    </justification>
  </clause>

  <clause id="3673">
    <literal><![CDATA[
      L(x * (y / x),z,u) = x * (L(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(3670(a,1),71(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3670 71"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3674">
    <literal><![CDATA[
      L((x \ y) * x,z,u) = (x \ L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(71(a,1),3670(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="71 3670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3675">
    <literal><![CDATA[
      (x \ 1) \ L((x \ 1) * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(30,a,1301,a,b,3672,a),flip(a)].">
      <j1 rule="hyper" parents="30 1301 3672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3676">
    <literal><![CDATA[
      L(x * ((y \ (z \ u)) / x),y,z) = x * (((z * y) \ u) / x)
    ]]></literal>
    <justification jstring="[para(311(a,1),3673(a,2,2,1))].">
      <j1 rule="para" parents="311 3673"/>
    </justification>
  </clause>

  <clause id="3677">
    <literal><![CDATA[
      L(x * (y / x),y \ 1,y) = x * ((1 / (1 / y)) / x)
    ]]></literal>
    <justification jstring="[para(1879(a,1),3673(a,2,2,1))].">
      <j1 rule="para" parents="1879 3673"/>
    </justification>
  </clause>

  <clause id="3678">
    <literal><![CDATA[
      (x * y) * ((z \ L(u,y,x)) * z) = x * (y * ((z \ u) * z))
    ]]></literal>
    <justification jstring="[hyper(119,a,3674,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 3674 13"/>
    </justification>
  </clause>

  <clause id="3679">
    <literal><![CDATA[
      L((x \ y) * x,z,u) != w * x
    ]]></literal>
    <literal><![CDATA[
      x \ L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(3674(a,2),39(a,1))].">
      <j1 rule="para" parents="3674 39"/>
    </justification>
  </clause>

  <clause id="3680">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ z)) * x,y \ 1,y) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(501(a,1),3674(a,2,1,2))].">
      <j1 rule="para" parents="501 3674"/>
    </justification>
  </clause>

  <clause id="3681">
    <literal><![CDATA[
      L((x \ ((y \ z) \ u)) * x,y \ z,y) = (x \ (z \ (y * u))) * x
    ]]></literal>
    <justification jstring="[para(502(a,1),3674(a,2,1,2))].">
      <j1 rule="para" parents="502 3674"/>
    </justification>
  </clause>

  <clause id="3682">
    <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,3667,a(flip),b,1158,a)].">
      <j1 rule="hyper" parents="116 3667 1158"/>
    </justification>
  </clause>

  <clause id="3683">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,z,u) = K(x,x \ 1) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(2237(a,2),3668(a,1,1))].">
      <j1 rule="para" parents="2237 3668"/>
    </justification>
  </clause>

  <clause id="3684">
    <literal><![CDATA[
      x \ L(y * K(z,z \ 1),u,w) = (x \ L(y,u,w)) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(3668(a,2),3559(a,1,2))].">
      <j1 rule="para" parents="3668 3559"/>
    </justification>
  </clause>

  <clause id="3685">
    <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(2465(a,1),3669(a,2,2))].">
      <j1 rule="para" parents="2465 3669"/>
    </justification>
  </clause>

  <clause id="3686">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ u) / z)) = x * (y * (z * ((y \ (x \ u)) / z)))
    ]]></literal>
    <justification jstring="[hyper(119,a,3676,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 3676 13"/>
    </justification>
  </clause>

  <clause id="3687">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ u)) * z) = x * (y * ((z \ (y \ (x \ u))) * z))
    ]]></literal>
    <justification jstring="[para(311(a,1),3678(a,1,2,1,2))].">
      <j1 rule="para" parents="311 3678"/>
    </justification>
  </clause>

  <clause id="3688">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(116,a,3680,a(flip),b,265,a),flip(a)].">
      <j1 rule="hyper" parents="116 3680 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3689">
    <literal><![CDATA[
      L(x \ 1,x,x \ L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(3666,a,1243,a)].">
      <j1 rule="hyper" parents="3666 1243"/>
    </justification>
  </clause>

  <clause id="3690">
    <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(3689(a,1),3410(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3689 3410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3691">
    <literal><![CDATA[
      (L(x,y,z) \ 1) \ K(x \ 1,x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3645,a(flip),b,3537,a),flip(a)].">
      <j1 rule="hyper" parents="58 3645 3537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3692">
    <literal><![CDATA[
      K(x \ 1,x) / L(x,y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(201,a,3691,a)].">
      <j1 rule="hyper" parents="201 3691"/>
    </justification>
  </clause>

  <clause id="3693">
    <literal><![CDATA[
      K(1 / x,x) / L(x,y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1898(a,2),3692(a,1,1))].">
      <j1 rule="para" parents="1898 3692"/>
    </justification>
  </clause>

  <clause id="3694">
    <literal><![CDATA[
      K(1 / x,x) / L(x,y,z) = 1 / T(L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[hyper(334,a,3455,a,b,3693,a),flip(a)].">
      <j1 rule="hyper" parents="334 3455 3693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3695">
    <literal><![CDATA[
      K(x,y) = (T(y,y \ 1) * x) \ (x * ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(611,a,3636,a),flip(a)].">
      <j1 rule="hyper" parents="611 3636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3696">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,683,a(flip),b,3695,a)].">
      <j1 rule="hyper" parents="334 683 3695"/>
    </justification>
  </clause>

  <clause id="3698">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = z
    ]]></literal>
    <justification jstring="[para(3695(a,2),684(a,1))].">
      <j1 rule="para" parents="3695 684"/>
    </justification>
  </clause>

  <clause id="3699">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3282,a,b,3696,a)].">
      <j1 rule="hyper" parents="58 3282 3696"/>
    </justification>
  </clause>

  <clause id="3700">
    <literal><![CDATA[
      K(x,1 / y) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),3696(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 3696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3701">
    <literal><![CDATA[
      K(x,1 / (1 / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(200(a,1),3696(a,1,2)),flip(a)].">
      <j1 rule="para" parents="200 3696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3702">
    <literal><![CDATA[
      K(x,T(y,1 / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1323(a,2),3696(a,1,2))].">
      <j1 rule="para" parents="1323 3696"/>
    </justification>
  </clause>

  <clause id="3703">
    <literal><![CDATA[
      K(x,T(y / z,z / y)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(2142(a,2),3696(a,1,2))].">
      <j1 rule="para" parents="2142 3696"/>
    </justification>
  </clause>

  <clause id="3704">
    <literal><![CDATA[
      K(x,T(1 / y,z)) = K(x,T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(2223(a,1),3696(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2223 3696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3705">
    <literal><![CDATA[
      K(x,T(y / z,y \ z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(2486(a,2),3696(a,1,2))].">
      <j1 rule="para" parents="2486 3696"/>
    </justification>
  </clause>

  <clause id="3706">
    <literal><![CDATA[
      K(x,((1 / y) \ z) / z) = K(x,((y \ 1) \ z) / z)
    ]]></literal>
    <justification jstring="[para(3236(a,1),3696(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3236 3696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3708">
    <literal><![CDATA[
      (1 / x) * K(y,1 / x) = K(y,x \ 1) / x
    ]]></literal>
    <justification jstring="[para(3700(a,1),2439(a,2,1))].">
      <j1 rule="para" parents="3700 2439"/>
    </justification>
  </clause>

  <clause id="3709">
    <literal><![CDATA[
      (x \ 1) * K(y,x \ 1) = x \ K(y,1 / x)
    ]]></literal>
    <justification jstring="[para(3700(a,2),2563(a,2,2))].">
      <j1 rule="para" parents="3700 2563"/>
    </justification>
  </clause>

  <clause id="3711">
    <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(3433(a,1),3701(a,1,2))].">
      <j1 rule="para" parents="3433 3701"/>
    </justification>
  </clause>

  <clause id="3712">
    <literal><![CDATA[
      K((1 / x) * y,x) = K((x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(3167(a,1),3699(a,1,1))].">
      <j1 rule="para" parents="3167 3699"/>
    </justification>
  </clause>

  <clause id="3713">
    <literal><![CDATA[
      K(x \ ((1 / y) \ z),y) = K(x \ ((y \ 1) \ z),y)
    ]]></literal>
    <justification jstring="[para(3601(a,1),3699(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3601 3699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3714">
    <literal><![CDATA[
      K((1 / (1 / x)) * y,1 / x) = K(x * y,1 / x)
    ]]></literal>
    <justification jstring="[para(75(a,1),3712(a,2,1,1))].">
      <j1 rule="para" parents="75 3712"/>
    </justification>
  </clause>

  <clause id="3715">
    <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,3264,a,b,3706,a)].">
      <j1 rule="hyper" parents="58 3264 3706"/>
    </justification>
  </clause>

  <clause id="3716">
    <literal><![CDATA[
      ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((x \ 1) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,926,a,b,3713,a)].">
      <j1 rule="hyper" parents="58 926 3713"/>
    </justification>
  </clause>

  <clause id="3717">
    <literal><![CDATA[
      x \ (((x * y) \ x) * T(((x * y) \ x) \ 1,x)) = (K(y,x) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(2588(a,1),3638(a,1,2))].">
      <j1 rule="para" parents="2588 3638"/>
    </justification>
  </clause>

  <clause id="3718">
    <literal><![CDATA[
      (K(x,y) \ y) \ 1 = y \ K(x,y)
    ]]></literal>
    <justification jstring="[para(1060(a,2),3717(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1060 3717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3719">
    <literal><![CDATA[
      1 / (x \ K(y,x)) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(201,a,3718,a)].">
      <j1 rule="hyper" parents="201 3718"/>
    </justification>
  </clause>

  <clause id="3720">
    <literal><![CDATA[
      L(x * K(y \ z,z \ y),u,w) = L(x,u,w) * K(y \ z,z \ y)
    ]]></literal>
    <justification jstring="[para(2465(a,1),3685(a,1,1,2))].">
      <j1 rule="para" parents="2465 3685"/>
    </justification>
  </clause>

  <clause id="3721">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ x) / z)) = x * (y * (z * ((y \ 1) / z)))
    ]]></literal>
    <justification jstring="[para(61(a,1),3686(a,2,2,2,2,1,2))].">
      <j1 rule="para" parents="61 3686"/>
    </justification>
  </clause>

  <clause id="3722">
    <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),3690(a,2,2,1))].">
      <j1 rule="para" parents="5 3690"/>
    </justification>
  </clause>

  <clause id="3724">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,x \ L(x,u,w)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(182(a,1),3722(a,2,2))].">
      <j1 rule="para" parents="182 3722"/>
    </justification>
  </clause>

  <clause id="3725">
    <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,3724,a(flip),b,3665,a),flip(a)].">
      <j1 rule="hyper" parents="119 3724 3665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3727">
    <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(1510(a,1),3725(a,1,2))].">
      <j1 rule="para" parents="1510 3725"/>
    </justification>
  </clause>

  <clause id="3728">
    <literal><![CDATA[
      1 / (L(x,y,z) \ x) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,5,a(flip),b,3727,a)].">
      <j1 rule="hyper" parents="117 5 3727"/>
    </justification>
  </clause>

  <clause id="3729">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,3727,a)].">
      <j1 rule="hyper" parents="116 5 3727"/>
    </justification>
  </clause>

  <clause id="3730">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) = (x \ 1) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(3729(a,1),2424(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3729 2424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3731">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ 1 = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(3654(a,1),3729(a,1,1))].">
      <j1 rule="para" parents="3654 3729"/>
    </justification>
  </clause>

  <clause id="3732">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ 1) = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3365,a(flip),b,3731,a),flip(a)].">
      <j1 rule="hyper" parents="58 3365 3731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3733">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) \ ((x \ 1) \ 1) = (x \ L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(1241(a,1),3731(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1241 3731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3734">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) \ ((x \ 1) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(334,a,3729,a(flip),b,3733,a),flip(a)].">
      <j1 rule="hyper" parents="334 3729 3733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3735">
    <literal><![CDATA[
      x \ T((y \ 1) * (x / (y \ 1)),K(z \ 1,z)) = K(1 / y,x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(3334(a,2),3443(a,1,2))].">
      <j1 rule="para" parents="3334 3443"/>
    </justification>
  </clause>

  <clause id="3736">
    <literal><![CDATA[
      x \ ((1 / y) * (x / (1 / y))) = K(1 / y,x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(3226(a,1),3735(a,1,2))].">
      <j1 rule="para" parents="3226 3735"/>
    </justification>
  </clause>

  <clause id="3737">
    <literal><![CDATA[
      (x \ K(1 / x,y / (x \ 1))) * ((x \ 1) \ 1) = K(x \ 1,y / (1 / x))
    ]]></literal>
    <justification jstring="[para(3736(a,1),3506(a,1,1,2))].">
      <j1 rule="para" parents="3736 3506"/>
    </justification>
  </clause>

  <clause id="3738">
    <literal><![CDATA[
      K(x \ 1,y / (1 / x)) = K(x \ 1,y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,3505,a(flip),b,3737,a),flip(a)].">
      <j1 rule="hyper" parents="58 3505 3737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3739">
    <literal><![CDATA[
      K(x \ 1,(y * (1 / x)) / (x \ 1)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),3738(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 3738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3740">
    <literal><![CDATA[
      K(x \ 1,(y / (x \ 1)) * (1 / x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1495(a,1),3739(a,1,2))].">
      <j1 rule="para" parents="1495 3739"/>
    </justification>
  </clause>

  <clause id="3741">
    <literal><![CDATA[
      K(x \ 1,y * K(x,x \ 1)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(3037(a,1),3740(a,1,2))].">
      <j1 rule="para" parents="3037 3740"/>
    </justification>
  </clause>

  <clause id="3742">
    <literal><![CDATA[
      K(x \ 1,((x \ 1) \ 1) * y) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(3134(a,1),3741(a,1,2))].">
      <j1 rule="para" parents="3134 3741"/>
    </justification>
  </clause>

  <clause id="3743">
    <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(3517(a,1),3591(a,1,1,2))].">
      <j1 rule="para" parents="3517 3591"/>
    </justification>
  </clause>

  <clause id="3744">
    <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(3607,a,3743,a)].">
      <j1 rule="hyper" parents="3607 3743"/>
    </justification>
  </clause>

  <clause id="3745">
    <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(3619,a,3744,a),flip(a)].">
      <j1 rule="hyper" parents="3619 3744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3746">
    <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),1769(a,2,2,1,1))].">
      <j1 rule="para" parents="15 1769"/>
    </justification>
  </clause>

  <clause id="3747">
    <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(1786(a,1),3746(a,1,1))].">
      <j1 rule="para" parents="1786 3746"/>
    </justification>
  </clause>

  <clause id="3748">
    <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(1585(a,1),3747(a,1,1,1))].">
      <j1 rule="para" parents="1585 3747"/>
    </justification>
  </clause>

  <clause id="3749">
    <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(530,a,3748,a),flip(a)].">
      <j1 rule="hyper" parents="530 3748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3750">
    <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,1279,a(flip),b,3749,a),flip(a)].">
      <j1 rule="hyper" parents="58 1279 3749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3751">
    <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(669(a,1),3749(a,2,1,2))].">
      <j1 rule="para" parents="669 3749"/>
    </justification>
  </clause>

  <clause id="3752">
    <literal><![CDATA[
      R(x * T(1 * (x \ 1),x),y,z) = a(1 / R(x,y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1271,a,3751,a),flip(a)].">
      <j1 rule="hyper" parents="1271 3751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3753">
    <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),3752(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2 3752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3754">
    <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(1632(a,1),3750(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1632 3750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3755">
    <literal><![CDATA[
      (x \ 1) / (x \ R(x,y,z)) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(30,a,2751,a(flip),b,3754,a),flip(a)].">
      <j1 rule="hyper" parents="30 2751 3754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3756">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(3380,a,3755,a)].">
      <j1 rule="hyper" parents="3380 3755"/>
    </justification>
  </clause>

  <clause id="3757">
    <literal><![CDATA[
      (x \ 1) \ (R(x,y,z) \ 1) = (x \ R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,3756,a(flip),b,2430,a)].">
      <j1 rule="hyper" parents="116 3756 2430"/>
    </justification>
  </clause>

  <clause id="3758">
    <literal><![CDATA[
      ((1 / x) \ R(1 / x,y,z)) \ x = R(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),3756(a,1,2))].">
      <j1 rule="para" parents="75 3756"/>
    </justification>
  </clause>

  <clause id="3759">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) \ x = R(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1267(a,1),3758(a,1,1))].">
      <j1 rule="para" parents="1267 3758"/>
    </justification>
  </clause>

  <clause id="3760">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) \ 1 = (R(x,y,z) / x) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(1257(a,1),3759(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1257 3759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3761">
    <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),1937(a,2,2,1,1))].">
      <j1 rule="para" parents="15 1937"/>
    </justification>
  </clause>

  <clause id="3762">
    <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(1784(a,1),3761(a,1,1))].">
      <j1 rule="para" parents="1784 3761"/>
    </justification>
  </clause>

  <clause id="3763">
    <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(1812(a,1),3762(a,1,1,1))].">
      <j1 rule="para" parents="1812 3762"/>
    </justification>
  </clause>

  <clause id="3764">
    <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(530,a,3763,a),flip(a)].">
      <j1 rule="hyper" parents="530 3763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3765">
    <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(775(a,1),3764(a,2,1,2))].">
      <j1 rule="para" parents="775 3764"/>
    </justification>
  </clause>

  <clause id="3766">
    <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(1263(a,1),3764(a,1,2))].">
      <j1 rule="para" parents="1263 3764"/>
    </justification>
  </clause>

  <clause id="3767">
    <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(1374(a,1),3765(a,1,2))].">
      <j1 rule="para" parents="1374 3765"/>
    </justification>
  </clause>

  <clause id="3768">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(x * (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(202(a,1),3767(a,2,1,2))].">
      <j1 rule="para" parents="202 3767"/>
    </justification>
  </clause>

  <clause id="3769">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(K(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1858(a,2),3768(a,2,1))].">
      <j1 rule="para" parents="1858 3768"/>
    </justification>
  </clause>

  <clause id="3770">
    <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),3766(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3 3766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3771">
    <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(2905(a,1),3770(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2905 3770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3772">
    <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(2902(a,1),3771(a,2,1))].">
      <j1 rule="para" parents="2902 3771"/>
    </justification>
  </clause>

  <clause id="3773">
    <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(334,a,3405,a(flip),b,3772,a),flip(a)].">
      <j1 rule="hyper" parents="334 3405 3772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3774">
    <literal><![CDATA[
      (R(x,y,z) / x) \ (1 / x) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,1858,a(flip),b,3773,a),flip(a)].">
      <j1 rule="hyper" parents="29 1858 3773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3775">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) \ 1 = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3760,a,b,3774,a)].">
      <j1 rule="hyper" parents="58 3760 3774"/>
    </justification>
  </clause>

  <clause id="3776">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) = 1 / (1 / R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(201,a,3775,a),flip(a)].">
      <j1 rule="hyper" parents="201 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(118,a,3775,a,b,154,a)].">
      <j1 rule="hyper" parents="118 3775 154"/>
    </justification>
  </clause>

  <clause id="3778">
    <literal><![CDATA[
      R(T(1 / (1 / x),y),z,u) \ 1 = 1 / R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2224(a,1),3775(a,1,1,1))].">
      <j1 rule="para" parents="2224 3775"/>
    </justification>
  </clause>

  <clause id="3779">
    <literal><![CDATA[
      1 / (1 / R(x \ 1,y,z)) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),3776(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 3776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3780">
    <literal><![CDATA[
      (R(1 / x,y,z) \ 1) \ 1 = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),3777(a,1,1,1,1,2))].">
      <j1 rule="para" parents="72 3777"/>
    </justification>
  </clause>

  <clause id="3781">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) = (R(x,y,z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(194(a,1),3777(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="194 3777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3782">
    <literal><![CDATA[
      T(x,R(1 / y,z,u)) = T(x,R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(3779(a,1),3104(a,1,2))].">
      <j1 rule="para" parents="3779 3104"/>
    </justification>
  </clause>

  <clause id="3783">
    <literal><![CDATA[
      T(x,R(x,y,z) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(722,a,3781,a)].">
      <j1 rule="hyper" parents="722 3781"/>
    </justification>
  </clause>

  <clause id="3784">
    <literal><![CDATA[
      ((R(x,y,z) \ 1) \ 1) * (y * z) = (((x \ 1) \ 1) * y) * z
    ]]></literal>
    <justification jstring="[para(3781(a,1),101(a,1,1))].">
      <j1 rule="para" parents="3781 101"/>
    </justification>
  </clause>

  <clause id="3785">
    <literal><![CDATA[
      R(((x / y) \ 1) \ 1,y,y \ 1) = ((x * (y \ 1)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(536(a,1),3781(a,2,1,1))].">
      <j1 rule="para" parents="536 3781"/>
    </justification>
  </clause>

  <clause id="3786">
    <literal><![CDATA[
      R(((x / (1 / y)) \ 1) \ 1,y \ 1,y) = ((x * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2942(a,1),3781(a,2,1,1))].">
      <j1 rule="para" parents="2942 3781"/>
    </justification>
  </clause>

  <clause id="3787">
    <literal><![CDATA[
      T(x,R((y \ 1) \ 1,z,u)) = T(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(3781(a,2),3106(a,1,2))].">
      <j1 rule="para" parents="3781 3106"/>
    </justification>
  </clause>

  <clause id="3788">
    <literal><![CDATA[
      T(x,1 / R(x,y,z)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(3117,a,3783,a)].">
      <j1 rule="hyper" parents="3117 3783"/>
    </justification>
  </clause>

  <clause id="3789">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * ((x \ 1) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(3783(a,1),1373(a,1,2))].">
      <j1 rule="para" parents="3783 1373"/>
    </justification>
  </clause>

  <clause id="3790">
    <literal><![CDATA[
      R(K(x,1 / x),y,z) = ((x \ 1) \ 1) / x
    ]]></literal>
    <justification jstring="[para(3788(a,1),3397(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3788 3397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3791">
    <literal><![CDATA[
      R(K(x,1 / x),y,z) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(334,a,1325,a(flip),b,3790,a),flip(a)].">
      <j1 rule="hyper" parents="334 1325 3790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3793">
    <literal><![CDATA[
      K(x,1 / x) * (1 / y) = K(x,1 / x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,3791,a(flip),b,2938,a),flip(a)].">
      <j1 rule="hyper" parents="117 3791 2938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3794">
    <literal><![CDATA[
      R(K(x \ 1,x),y,z) = K(x \ 1,1 / (x \ 1))
    ]]></literal>
    <justification jstring="[para(72(a,1),3791(a,1,1,2))].">
      <j1 rule="para" parents="72 3791"/>
    </justification>
  </clause>

  <clause id="3795">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = K(x,1 / x) * (y * z)
    ]]></literal>
    <justification jstring="[para(3791(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3791 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3796">
    <literal><![CDATA[
      K(x,1 / x) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = u
    ]]></literal>
    <justification jstring="[para(3791(a,1),293(a,1,1))].">
      <j1 rule="para" parents="3791 293"/>
    </justification>
  </clause>

  <clause id="3797">
    <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(3580(a,1),3782(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3580 3782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3798">
    <literal><![CDATA[
      R(K(x \ 1,x),y,z) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),3794(a,2,2))].">
      <j1 rule="para" parents="72 3794"/>
    </justification>
  </clause>

  <clause id="3800">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / y) = K(x \ 1,x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,3798,a(flip),b,2938,a),flip(a)].">
      <j1 rule="hyper" parents="117 3798 2938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3801">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * z = K(x \ 1,x) * (y * z)
    ]]></literal>
    <justification jstring="[para(3798(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3798 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3802">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(3798(a,1),2270(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3798 2270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3803">
    <literal><![CDATA[
      (1 / x) * K(y \ 1,y) = K(y \ 1,y) / x
    ]]></literal>
    <justification jstring="[hyper(2254,a,3800,a)].">
      <j1 rule="hyper" parents="2254 3800"/>
    </justification>
  </clause>

  <clause id="3804">
    <literal><![CDATA[
      (R(x,y,z) \ 1) \ (R(x,y,z) \ x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,3789,a)].">
      <j1 rule="hyper" parents="123 3789"/>
    </justification>
  </clause>

  <clause id="3806">
    <literal><![CDATA[
      L(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[hyper(493,a,3795,a)].">
      <j1 rule="hyper" parents="493 3795"/>
    </justification>
  </clause>

  <clause id="3807">
    <literal><![CDATA[
      K(x,1 / x) * ((x \ y) * z) = ((1 / (1 / x)) \ y) * z
    ]]></literal>
    <justification jstring="[para(3095(a,1),3795(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3095 3795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3808">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[para(72(a,1),3806(a,1,3,2))].">
      <j1 rule="para" parents="72 3806"/>
    </justification>
  </clause>

  <clause id="3809">
    <literal><![CDATA[
      L(x,y,1) = x
    ]]></literal>
    <justification jstring="[para(205(a,1),3806(a,1,3))].">
      <j1 rule="para" parents="205 3806"/>
    </justification>
  </clause>

  <clause id="3810">
    <literal><![CDATA[
      L(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1855(a,1),3806(a,1,3))].">
      <j1 rule="para" parents="1855 3806"/>
    </justification>
  </clause>

  <clause id="3811">
    <literal><![CDATA[
      L(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(3809(a,1),45(a,2))].">
      <j1 rule="para" parents="3809 45"/>
    </justification>
  </clause>

  <clause id="3812">
    <literal><![CDATA[
      L(x,y,1 / z) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(3331,a,3808,a),flip(a)].">
      <j1 rule="hyper" parents="3331 3808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3813">
    <literal><![CDATA[
      a(x,y,z * K(u \ 1,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3745,a(flip),b,3808,a)].">
      <j1 rule="hyper" parents="58 3745 3808"/>
    </justification>
  </clause>

  <clause id="3814">
    <literal><![CDATA[
      ((x \ 1) * y) \ (K(x \ 1,x) * z) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,3188,a(flip),b,3808,a)].">
      <j1 rule="hyper" parents="58 3188 3808"/>
    </justification>
  </clause>

  <clause id="3815">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ z = x \ (K(y \ 1,y) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3043,a(flip),b,3808,a),flip(a)].">
      <j1 rule="hyper" parents="58 3043 3808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3816">
    <literal><![CDATA[
      x \ R(x,y \ 1,y) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2353,a(flip),b,3808,a),flip(a)].">
      <j1 rule="hyper" parents="58 2353 3808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3817">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ (K(x \ 1,x) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,92,a(flip),b,3808,a)].">
      <j1 rule="hyper" parents="58 92 3808"/>
    </justification>
  </clause>

  <clause id="3818">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(3808(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="3808 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3819">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3808(a,1),45(a,2))].">
      <j1 rule="para" parents="3808 45"/>
    </justification>
  </clause>

  <clause id="3820">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / z = K(x \ 1,x) * (y / z)
    ]]></literal>
    <justification jstring="[para(3808(a,1),556(a,1,2))].">
      <j1 rule="para" parents="3808 556"/>
    </justification>
  </clause>

  <clause id="3821">
    <literal><![CDATA[
      L(x,y,K(z \ u,u \ z)) = x
    ]]></literal>
    <justification jstring="[para(2913(a,1),3808(a,1,3))].">
      <j1 rule="para" parents="2913 3808"/>
    </justification>
  </clause>

  <clause id="3823">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z = K(x,x \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1392,a,3810,a),flip(a)].">
      <j1 rule="hyper" parents="1392 3810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3825">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ ((x * z) * K(y,y \ 1)) = z
    ]]></literal>
    <justification jstring="[hyper(58,a,3337,a,b,3810,a)].">
      <j1 rule="hyper" parents="58 3337 3810"/>
    </justification>
  </clause>

  <clause id="3826">
    <literal><![CDATA[
      R(T(x,y * K(z,z \ 1)),y,K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2863,a,b,3810,a)].">
      <j1 rule="hyper" parents="58 2863 3810"/>
    </justification>
  </clause>

  <clause id="3827">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ (K(x,x \ 1) * 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="3829">
    <literal><![CDATA[
      L(x,y,K(z,z \ 1)) != 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="3830">
    <literal><![CDATA[
      K(x,x \ 1) * (1 / y) = K(x,x \ 1) / y
    ]]></literal>
    <justification jstring="[para(3810(a,1),433(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3810 433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3831">
    <literal><![CDATA[
      (K(x,x \ 1) * y) / z = K(x,x \ 1) * (y / z)
    ]]></literal>
    <justification jstring="[para(3810(a,1),556(a,1,2))].">
      <j1 rule="para" parents="3810 556"/>
    </justification>
  </clause>

  <clause id="3832">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) / y) = (1 / x) / y
    ]]></literal>
    <justification jstring="[para(3810(a,1),1889(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3810 1889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3833">
    <literal><![CDATA[
      (K(x \ y,y \ x) * z) * u = K(x \ y,y \ x) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(1392,a,3821,a),flip(a)].">
      <j1 rule="hyper" parents="1392 3821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3834">
    <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,3284,a,b,3812,a)].">
      <j1 rule="hyper" parents="58 3284 3812"/>
    </justification>
  </clause>

  <clause id="3835">
    <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,3163,a,b,3812,a)].">
      <j1 rule="hyper" parents="58 3163 3812"/>
    </justification>
  </clause>

  <clause id="3836">
    <literal><![CDATA[
      ((1 / x) * y) * L(z,y,x \ 1) = (1 / x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,3812,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 3812 13"/>
    </justification>
  </clause>

  <clause id="3837">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),3812(a,1,3)),flip(a)].">
      <j1 rule="para" parents="72 3812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3838">
    <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(2864(a,2),3818(a,1)),flip(b)].">
      <j1 rule="para" parents="2864 3818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3839">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ 1),u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(2220(a,2),3837(a,1,3))].">
      <j1 rule="para" parents="2220 3837"/>
    </justification>
  </clause>

  <clause id="3840">
    <literal><![CDATA[
      L(x,y,R(1 / z,u,w)) = L(x,y,R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(3780(a,1),3837(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3780 3837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3842">
    <literal><![CDATA[
      a(x,y,1 / z) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(799(a,1),3813(a,1,3)),flip(a)].">
      <j1 rule="para" parents="799 3813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3843">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(1318(a,1),3813(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1318 3813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3844">
    <literal><![CDATA[
      a(x,y,K(z \ 1,z) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(2250(a,2),3813(a,1,3))].">
      <j1 rule="para" parents="2250 3813"/>
    </justification>
  </clause>

  <clause id="3845">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(3033(a,1),3813(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3033 3813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3847">
    <literal><![CDATA[
      a(x,y,L(z,z \ 1,u)) = a(x,y,(u * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(3651(a,1),3844(a,1,3))].">
      <j1 rule="para" parents="3651 3844"/>
    </justification>
  </clause>

  <clause id="3848">
    <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(334,a,3024,a,b,3845,a),flip(a)].">
      <j1 rule="hyper" parents="334 3024 3845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3849">
    <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,3620,a,b,3845,a)].">
      <j1 rule="hyper" parents="58 3620 3845"/>
    </justification>
  </clause>

  <clause id="3850">
    <literal><![CDATA[
      K(x,x \ 1) / y != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(3830(a,1),2246(a,1))].">
      <j1 rule="para" parents="3830 2246"/>
    </justification>
  </clause>

  <clause id="3851">
    <literal><![CDATA[
      ((x \ 1) / y) * K(x,x \ 1) = (1 / x) / y
    ]]></literal>
    <justification jstring="[hyper(2246,a,3832,a)].">
      <j1 rule="hyper" parents="2246 3832"/>
    </justification>
  </clause>

  <clause id="3852">
    <literal><![CDATA[
      (1 / x) / (y \ (x \ 1)) = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(359,a,3851,a),flip(a)].">
      <j1 rule="hyper" parents="359 3851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3853">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (1 / y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(192,a,3852,a)].">
      <j1 rule="hyper" parents="192 3852"/>
    </justification>
  </clause>

  <clause id="3854">
    <literal><![CDATA[
      L(1 / x,y,z) \ (1 / x) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(3652(a,1),3853(a,1,1))].">
      <j1 rule="para" parents="3652 3853"/>
    </justification>
  </clause>

  <clause id="3856">
    <literal><![CDATA[
      K(x,x \ 1) * ((K(x \ 1,x) * y) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(3053,a,3801,a(flip))].">
      <j1 rule="hyper" parents="3053 3801"/>
    </justification>
  </clause>

  <clause id="3857">
    <literal><![CDATA[
      ((K(x \ 1,x) * (y * z)) * u) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(3801(a,1),15(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3801 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3858">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) * u = K(z \ 1,z) * ((x * y) * u)
    ]]></literal>
    <justification jstring="[para(3539(a,1),3801(a,1,1))].">
      <j1 rule="para" parents="3539 3801"/>
    </justification>
  </clause>

  <clause id="3859">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T((x \ 1) \ 1,z)) = y * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(3273,a,3802,a),flip(a)].">
      <j1 rule="hyper" parents="3273 3802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3861">
    <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(3802(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3802 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3862">
    <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(3802(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3802 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3863">
    <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(3802(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3802 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3864">
    <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(3802(a,1),321(a,1,2))].">
      <j1 rule="para" parents="3802 321"/>
    </justification>
  </clause>

  <clause id="3866">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * ((x \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(3804(a,1),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3804 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3867">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ z = K(y \ 1,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(334,a,3594,a(flip),b,3815,a),flip(a)].">
      <j1 rule="hyper" parents="334 3594 3815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3869">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = y \ (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[para(2237(a,2),3815(a,1,1))].">
      <j1 rule="para" parents="2237 3815"/>
    </justification>
  </clause>

  <clause id="3870">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = y \ (z * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(3028(a,1),3817(a,1,2))].">
      <j1 rule="para" parents="3028 3817"/>
    </justification>
  </clause>

  <clause id="3871">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ (K(z \ 1,z) * u) = (x * y) \ u
    ]]></literal>
    <justification jstring="[para(3539(a,1),3817(a,1,1))].">
      <j1 rule="para" parents="3539 3817"/>
    </justification>
  </clause>

  <clause id="3872">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / z = (y / z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,2250,a(flip),b,3820,a),flip(a)].">
      <j1 rule="hyper" parents="334 2250 3820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3873">
    <literal><![CDATA[
      R(K(x,x \ 1),y,z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(3617,a,3823,a)].">
      <j1 rule="hyper" parents="3617 3823"/>
    </justification>
  </clause>

  <clause id="3874">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = K(y,y \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(2247,a,3823,a)].">
      <j1 rule="hyper" parents="2247 3823"/>
    </justification>
  </clause>

  <clause id="3875">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * (z * x)) = T(K(y,y \ 1) * z,x)
    ]]></literal>
    <justification jstring="[hyper(451,a,xx,b,3823,a),flip(a)].">
      <j1 rule="hyper" parents="451 3823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3876">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z = y * (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(334,a,3586,a(flip),b,3823,a),flip(a)].">
      <j1 rule="hyper" parents="334 3586 3823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3878">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ x) * z) = (y \ ((x \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(3571(a,1),3823(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3571 3823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3879">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3769,a,b,3873,a)].">
      <j1 rule="hyper" parents="58 3769 3873"/>
    </justification>
  </clause>

  <clause id="3882">
    <literal><![CDATA[
      L(x,K(y,y \ 1),z) = x
    ]]></literal>
    <justification jstring="[hyper(29,a,3599,a(flip),b,3825,a(flip))].">
      <j1 rule="hyper" parents="29 3599 3825"/>
    </justification>
  </clause>

  <clause id="3883">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ K(y,y \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[para(64(a,1),3825(a,1,2))].">
      <j1 rule="para" parents="64 3825"/>
    </justification>
  </clause>

  <clause id="3884">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = x * (K(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(1392,a,3882,a),flip(a)].">
      <j1 rule="hyper" parents="1392 3882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3887">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ 1 = x \ K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3024(a,1),3883(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3024 3883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3888">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ 1 = y \ K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3031(a,1),3883(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3031 3883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3889">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 = L(x,y,z) \ K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3643(a,1),3887(a,1,1))].">
      <j1 rule="para" parents="3643 3887"/>
    </justification>
  </clause>

  <clause id="3890">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ z = x \ (K(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3039(a,1),3827(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3039 3827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3891">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ u = (x * y) \ (K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(3538(a,1),3827(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3538 3827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3892">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / z = K(y,y \ 1) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,2263,a(flip),b,3831,a)].">
      <j1 rule="hyper" parents="58 2263 3831"/>
    </justification>
  </clause>

  <clause id="3893">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ (1 / (1 / x))) * z) = (y \ x) * z
    ]]></literal>
    <justification jstring="[para(3573(a,1),3856(a,1,2,1))].">
      <j1 rule="para" parents="3573 3856"/>
    </justification>
  </clause>

  <clause id="3894">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = K(x \ 1,x) * (y \ z)
    ]]></literal>
    <justification jstring="[para(2237(a,2),3867(a,1,1))].">
      <j1 rule="para" parents="2237 3867"/>
    </justification>
  </clause>

  <clause id="3895">
    <literal><![CDATA[
      K(x \ 1,x) * ((y * x) \ z) = (y * ((x \ 1) \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(3008(a,1),3867(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3008 3867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3896">
    <literal><![CDATA[
      K(x \ 1,x) * ((x * y) \ z) = (((x \ 1) \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(3134(a,1),3867(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3134 3867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3897">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = (y \ z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,3551,a(flip),b,3869,a),flip(a)].">
      <j1 rule="hyper" parents="334 3551 3869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3898">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = K(x,x \ 1) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(334,a,3577,a(flip),b,3870,a),flip(a)].">
      <j1 rule="hyper" parents="334 3577 3870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3899">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = (y \ z) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,3533,a(flip),b,3870,a),flip(a)].">
      <j1 rule="hyper" parents="334 3533 3870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3900">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / z != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) * (y / z) = u
    ]]></literal>
    <justification jstring="[para(3872(a,2),2260(a,1))].">
      <j1 rule="para" parents="3872 2260"/>
    </justification>
  </clause>

  <clause id="3901">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ x) * z) = (y \ T(x,x \ 1)) * z
    ]]></literal>
    <justification jstring="[para(3575(a,1),3874(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3575 3874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3902">
    <literal><![CDATA[
      (x * (y * K(z,z \ 1))) * u = (x * y) * (K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(3576(a,1),3876(a,1,1))].">
      <j1 rule="para" parents="3576 3876"/>
    </justification>
  </clause>

  <clause id="3903">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ (z * K(y \ 1,y)) = x \ z
    ]]></literal>
    <justification jstring="[para(3039(a,1),3890(a,2,2))].">
      <j1 rule="para" parents="3039 3890"/>
    </justification>
  </clause>

  <clause id="3904">
    <literal><![CDATA[
      x / (y * K(z \ 1,z)) = K(z,z \ 1) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(3552,a,3892,a)].">
      <j1 rule="hyper" parents="3552 3892"/>
    </justification>
  </clause>

  <clause id="3906">
    <literal><![CDATA[
      (((x \ 1) * y) \ z) * K(x \ 1,x) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[para(3167(a,1),3897(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3167 3897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3907">
    <literal><![CDATA[
      (x * (K(y,y \ 1) * z)) \ u = ((x * z) \ u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(3586(a,1),3897(a,1,1))].">
      <j1 rule="para" parents="3586 3897"/>
    </justification>
  </clause>

  <clause id="3908">
    <literal><![CDATA[
      K(x,x \ 1) * ((y * x) \ z) = (y * (1 / (1 / x))) \ z
    ]]></literal>
    <justification jstring="[para(3045(a,1),3898(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3045 3898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3909">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) \ y) \ z) = ((1 / x) \ y) \ z
    ]]></literal>
    <justification jstring="[para(3179(a,1),3898(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3179 3898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3910">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ u = K(z,z \ 1) * ((x * y) \ u)
    ]]></literal>
    <justification jstring="[para(3539(a,1),3898(a,1,1))].">
      <j1 rule="para" parents="3539 3898"/>
    </justification>
  </clause>

  <clause id="3911">
    <literal><![CDATA[
      K(x,x \ 1) * (L(1 / x,y,z) \ u) = L(x \ 1,y,z) \ u
    ]]></literal>
    <justification jstring="[para(3646(a,1),3898(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3646 3898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3912">
    <literal><![CDATA[
      (((1 / x) * y) \ z) * K(x,x \ 1) = ((x \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(3152(a,1),3899(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3152 3899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3914">
    <literal><![CDATA[
      x / (K(y \ 1,y) * z) = K(y,y \ 1) * (x / z)
    ]]></literal>
    <justification jstring="[para(2250(a,2),3904(a,1,2))].">
      <j1 rule="para" parents="2250 3904"/>
    </justification>
  </clause>

  <clause id="3915">
    <literal><![CDATA[
      x / (y * (z * K(u \ 1,u))) = K(u,u \ 1) * (x / (y * z))
    ]]></literal>
    <justification jstring="[para(3517(a,1),3904(a,1,2))].">
      <j1 rule="para" parents="3517 3904"/>
    </justification>
  </clause>

  <clause id="3916">
    <literal><![CDATA[
      T(x,y * K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3558,a,3826,a)].">
      <j1 rule="hyper" parents="3558 3826"/>
    </justification>
  </clause>

  <clause id="3918">
    <literal><![CDATA[
      T(x,R(1 / y,z,u) * K(w,w \ 1)) = T(x,R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,3782,a(flip),b,3916,a),flip(a)].">
      <j1 rule="hyper" parents="334 3782 3916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3920">
    <literal><![CDATA[
      T(x,y * K(z \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1862(a,1),3916(a,1,2,2))].">
      <j1 rule="para" parents="1862 3916"/>
    </justification>
  </clause>

  <clause id="3921">
    <literal><![CDATA[
      T(x,K(y,y \ 1) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2237(a,2),3916(a,1,2))].">
      <j1 rule="para" parents="2237 3916"/>
    </justification>
  </clause>

  <clause id="3922">
    <literal><![CDATA[
      T(x,L(y,z,u) * (1 / y)) = T(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(2312(a,1),3916(a,1,2))].">
      <j1 rule="para" parents="2312 3916"/>
    </justification>
  </clause>

  <clause id="3923">
    <literal><![CDATA[
      T(x,K(y \ 1,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(3031(a,1),3916(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3031 3916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3924">
    <literal><![CDATA[
      T(x,y * (1 / z)) = T(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(3030(a,1),3916(a,1,2))].">
      <j1 rule="para" parents="3030 3916"/>
    </justification>
  </clause>

  <clause id="3925">
    <literal><![CDATA[
      T(x,T(y,y \ 1) * z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(3170(a,1),3916(a,1,2))].">
      <j1 rule="para" parents="3170 3916"/>
    </justification>
  </clause>

  <clause id="3926">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) \ z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(3176(a,1),3916(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3176 3916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3927">
    <literal><![CDATA[
      T(x,(1 / y) * z) = T(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3185(a,1),3916(a,1,2))].">
      <j1 rule="para" parents="3185 3916"/>
    </justification>
  </clause>

  <clause id="3928">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(3202(a,1),3916(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3202 3916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3929">
    <literal><![CDATA[
      T(x,y * (((y \ z) \ 1) \ 1)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(3310(a,1),3916(a,1,2))].">
      <j1 rule="para" parents="3310 3916"/>
    </justification>
  </clause>

  <clause id="3930">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ 1)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(3572(a,1),3916(a,1,2))].">
      <j1 rule="para" parents="3572 3916"/>
    </justification>
  </clause>

  <clause id="3931">
    <literal><![CDATA[
      T(x,(1 / (1 / y)) * z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(3079(a,1),3920(a,1,2))].">
      <j1 rule="para" parents="3079 3920"/>
    </justification>
  </clause>

  <clause id="3932">
    <literal><![CDATA[
      T(x,(y \ 1) \ K(z,y)) = T(x,y * K(z,y))
    ]]></literal>
    <justification jstring="[para(3212(a,1),3920(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3212 3920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3934">
    <literal><![CDATA[
      T(x,y \ (1 / z)) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(3566(a,1),3920(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3566 3920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3935">
    <literal><![CDATA[
      T(x,(K(y,y \ 1) * z) \ u) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(3897(a,2),3920(a,1,2))].">
      <j1 rule="para" parents="3897 3920"/>
    </justification>
  </clause>

  <clause id="3936">
    <literal><![CDATA[
      T(x,y * ((1 / z) * u)) = T(x,y * ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(3587(a,1),3921(a,1,2))].">
      <j1 rule="para" parents="3587 3921"/>
    </justification>
  </clause>

  <clause id="3937">
    <literal><![CDATA[
      T(x,L(K(y,y \ 1) * z,u,w)) = T(x,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(3683(a,2),3921(a,1,2))].">
      <j1 rule="para" parents="3683 3921"/>
    </justification>
  </clause>

  <clause id="3938">
    <literal><![CDATA[
      T(x,y \ (z * (1 / u))) = T(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3598(a,1),3923(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3598 3923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3939">
    <literal><![CDATA[
      T((x \ 1) * y,x \ y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,701,a(flip),b,3926,a),flip(a)].">
      <j1 rule="hyper" parents="58 701 3926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3940">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ u) = T(x,(z / (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(2147(a,2),3926(a,1,2,1))].">
      <j1 rule="para" parents="2147 3926"/>
    </justification>
  </clause>

  <clause id="3941">
    <literal><![CDATA[
      T(x,(1 / y) * K(z,y \ 1)) = T(x,y \ K(z,y \ 1))
    ]]></literal>
    <justification jstring="[para(2563(a,1),3927(a,2,2))].">
      <j1 rule="para" parents="2563 3927"/>
    </justification>
  </clause>

  <clause id="3942">
    <literal><![CDATA[
      T(x,y \ (L(1 / z,u,w) \ 1)) = T(x,y \ (L(z \ 1,u,w) \ 1))
    ]]></literal>
    <justification jstring="[para(3428(a,1),3930(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3428 3930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3943">
    <literal><![CDATA[
      (1 / x) / T(y,y \ (x \ 1)) = y \ (1 / x)
    ]]></literal>
    <justification jstring="[para(3934(a,1),273(a,1,2))].">
      <j1 rule="para" parents="3934 273"/>
    </justification>
  </clause>

  <clause id="3944">
    <literal><![CDATA[
      K((x \ 1) * y,x \ y) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,3939,a)].">
      <j1 rule="hyper" parents="50 3939"/>
    </justification>
  </clause>

  <clause id="3945">
    <literal><![CDATA[
      T(x,(((y \ 1) \ 1) \ z) \ u) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(3138(a,1),3935(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3138 3935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3946">
    <literal><![CDATA[
      T(x,L(y * (z * (1 / u)),w,v5)) = T(x,L(y * (z * (u \ 1)),w,v5))
    ]]></literal>
    <justification jstring="[para(3582(a,1),3937(a,1,2,1))].">
      <j1 rule="para" parents="3582 3937"/>
    </justification>
  </clause>

  <clause id="3947">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),1 / x,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(761(a,1),3778(a,1,1)),flip(a)].">
      <j1 rule="para" parents="761 3778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3949">
    <literal><![CDATA[
      (x \ T(x,(x \ 1) * y)) * y = y * K(((1 / x) * y) \ y,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(3814(a,1),3345(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3814 3345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3950">
    <literal><![CDATA[
      L(1 / x,y,z) \ (1 / x) = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,3732,a(flip),b,3854,a),flip(a)].">
      <j1 rule="hyper" parents="334 3732 3854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3951">
    <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),3875(a,1,2,2))].">
      <j1 rule="para" parents="105 3875"/>
    </justification>
  </clause>

  <clause id="3952">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ 1)) * z,y \ 1,y) = y * ((1 / y) * ((x \ y) * z))
    ]]></literal>
    <justification jstring="[para(3878(a,1),3207(a,1,1))].">
      <j1 rule="para" parents="3878 3207"/>
    </justification>
  </clause>

  <clause id="3954">
    <literal><![CDATA[
      L(x,y,z) \ K(x,x \ 1) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3424,a,3889,a),flip(a)].">
      <j1 rule="hyper" parents="3424 3889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3955">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,x \ 1) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3534,a,b,3954,a)].">
      <j1 rule="hyper" parents="58 3534 3954"/>
    </justification>
  </clause>

  <clause id="3956">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(3954(a,1),3579(a,1,1))].">
      <j1 rule="para" parents="3954 3579"/>
    </justification>
  </clause>

  <clause id="3957">
    <literal><![CDATA[
      T(1 / L(x,y,z),x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(246,a,3956,a,b,1510,a)].">
      <j1 rule="hyper" parents="246 3956 1510"/>
    </justification>
  </clause>

  <clause id="3958">
    <literal><![CDATA[
      x / L(x,y,z) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,1705,a(flip),b,3956,a)].">
      <j1 rule="hyper" parents="58 1705 3956"/>
    </justification>
  </clause>

  <clause id="3959">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[para(3956(a,1),1707(a,1,1))].">
      <j1 rule="para" parents="3956 1707"/>
    </justification>
  </clause>

  <clause id="3960">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(192,a,3958,a)].">
      <j1 rule="hyper" parents="192 3958"/>
    </justification>
  </clause>

  <clause id="3961">
    <literal><![CDATA[
      T(L(x,y,z),L(x,y,z) \ x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(31,a,273,a,b,3958,a)].">
      <j1 rule="hyper" parents="31 273 3958"/>
    </justification>
  </clause>

  <clause id="3962">
    <literal><![CDATA[
      L(x / L(x,y,z),L(x,y,z),z * y) = (z * (y * x)) \ ((z * y) * x)
    ]]></literal>
    <justification jstring="[para(3958(a,2),513(a,1,1))].">
      <j1 rule="para" parents="3958 513"/>
    </justification>
  </clause>

  <clause id="3963">
    <literal><![CDATA[
      x / L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(3959(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3959 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3964">
    <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(3959(a,1),92(a,2,2))].">
      <j1 rule="para" parents="3959 92"/>
    </justification>
  </clause>

  <clause id="3965">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * L(a(z,u,w),y,x) = a(z,u,w)
    ]]></literal>
    <justification jstring="[para(1773(a,1),3959(a,1,1))].">
      <j1 rule="para" parents="1773 3959"/>
    </justification>
  </clause>

  <clause id="3966">
    <literal><![CDATA[
      a(x,y,K(z,u)) * L(K(z,u),y,x) = K(z,u)
    ]]></literal>
    <justification jstring="[para(1990(a,1),3959(a,1,1))].">
      <j1 rule="para" parents="1990 3959"/>
    </justification>
  </clause>

  <clause id="3967">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = T(a(x,y,z),L(z,y,x))
    ]]></literal>
    <justification jstring="[para(3959(a,1),3370(a,1,2,2))].">
      <j1 rule="para" parents="3959 3370"/>
    </justification>
  </clause>

  <clause id="3968">
    <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(3966(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="3966 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3969">
    <literal><![CDATA[
      (1 / x) * (L(x,y,z) \ x) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3155,a(flip),b,3955,a)].">
      <j1 rule="hyper" parents="58 3155 3955"/>
    </justification>
  </clause>

  <clause id="3970">
    <literal><![CDATA[
      (1 / x) * ((L(x,y,z) \ 1) * x) = T(1 / L(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(3969(a,1),1516(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3969 1516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3971">
    <literal><![CDATA[
      x * K(y \ (1 / (1 / x)),y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,3086,a(flip),b,3893,a)].">
      <j1 rule="hyper" parents="58 3086 3893"/>
    </justification>
  </clause>

  <clause id="3972">
    <literal><![CDATA[
      (x \ 1) * ((y \ T(x,x \ 1)) * z) = (1 / x) * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,3901,a(flip),b,3206,a)].">
      <j1 rule="hyper" parents="119 3901 3206"/>
    </justification>
  </clause>

  <clause id="3973">
    <literal><![CDATA[
      K(x,x \ 1) * ((y * x) \ y) = 1 / (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(334,a,2978,a,b,3908,a),flip(a)].">
      <j1 rule="hyper" parents="334 2978 3908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3974">
    <literal><![CDATA[
      T(x,K(y,z \ 1) / z) = T(x,z \ K(y,z \ 1))
    ]]></literal>
    <justification jstring="[para(3227(a,1),3941(a,1,2))].">
      <j1 rule="para" parents="3227 3941"/>
    </justification>
  </clause>

  <clause id="3975">
    <literal><![CDATA[
      T(a(x,y,z),L(z,y,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(709,a,3967,a),flip(a)].">
      <j1 rule="hyper" parents="709 3967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3976">
    <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,3970,a(flip),b,3182,a)].">
      <j1 rule="hyper" parents="116 3970 3182"/>
    </justification>
  </clause>

  <clause id="3977">
    <literal><![CDATA[
      (x * y) * (1 / (1 / ((x * y) \ x))) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,3973,a(flip),b,3577,a)].">
      <j1 rule="hyper" parents="119 3973 3577"/>
    </justification>
  </clause>

  <clause id="3978">
    <literal><![CDATA[
      x * L(x \ 1,((y * x) \ y) \ 1,L(x \ 1,x,y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2877,a,3977,a)].">
      <j1 rule="hyper" parents="2877 3977"/>
    </justification>
  </clause>

  <clause id="3979">
    <literal><![CDATA[
      (x * y) * ((((x * y) \ (z * y)) \ 1) \ 1) = ((((z / x) \ 1) \ 1) * x) * y
    ]]></literal>
    <justification jstring="[hyper(2314,a,3784,a)].">
      <j1 rule="hyper" parents="2314 3784"/>
    </justification>
  </clause>

  <clause id="3980">
    <literal><![CDATA[
      T(x * y,x \ (1 / y)) = ((x * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2966,a,b,3786,a)].">
      <j1 rule="hyper" parents="58 2966 3786"/>
    </justification>
  </clause>

  <clause id="3981">
    <literal><![CDATA[
      T(x * y,x \ (y \ 1)) = ((x * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,3934,a(flip),b,3980,a)].">
      <j1 rule="hyper" parents="58 3934 3980"/>
    </justification>
  </clause>

  <clause id="3982">
    <literal><![CDATA[
      (x * K(y \ z,z \ y)) * u = K(y \ z,z \ y) * (x * u)
    ]]></literal>
    <justification jstring="[para(2484(a,1),3833(a,1,1))].">
      <j1 rule="para" parents="2484 3833"/>
    </justification>
  </clause>

  <clause id="3983">
    <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(2951(a,1),3838(a,1,1,2))].">
      <j1 rule="para" parents="2951 3838"/>
    </justification>
  </clause>

  <clause id="3984">
    <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,3858,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="117 3858 101"/>
    </justification>
  </clause>

  <clause id="3985">
    <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,3902,a(flip),b,80,a)].">
      <j1 rule="hyper" parents="116 3902 80"/>
    </justification>
  </clause>

  <clause id="3986">
    <literal><![CDATA[
      K(x,x \ 1) * ((y * (z / (x \ 1))) \ u) = (y * (z / (1 / x))) \ u
    ]]></literal>
    <justification jstring="[para(2951(a,1),3910(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2951 3910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3987">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (z * (u * K(x \ 1,x)))) = y / (z * u)
    ]]></literal>
    <justification jstring="[hyper(119,a,3915,a,b,3051,a)].">
      <j1 rule="hyper" parents="119 3915 3051"/>
    </justification>
  </clause>

  <clause id="3988">
    <literal><![CDATA[
      (x * K(y \ z,z \ y)) * (x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ z,z \ y) = u
    ]]></literal>
    <justification jstring="[para(3982(a,2),209(a,1)),flip(b)].">
      <j1 rule="para" parents="3982 209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3989">
    <literal><![CDATA[
      x / (K(y,y \ 1) * z) = K(y \ 1,y) * (x / z)
    ]]></literal>
    <justification jstring="[para(3039(a,1),3987(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3039 3987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3990">
    <literal><![CDATA[
      x / (K(y,y \ 1) * z) = (x / z) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,2250,a(flip),b,3989,a),flip(a)].">
      <j1 rule="hyper" parents="334 2250 3989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3991">
    <literal><![CDATA[
      (x / T(y \ 1,z)) * K(y \ 1,y) = x / T(1 / y,z)
    ]]></literal>
    <justification jstring="[para(3139(a,1),3990(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3139 3990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3992">
    <literal><![CDATA[
      (x / T(y \ 1,z)) \ K(y,y \ 1) = (x / T(1 / y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(3991(a,1),3887(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3991 3887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3993">
    <literal><![CDATA[
      T(x,y / T(1 / z,u)) = T(x,y / T(z \ 1,u))
    ]]></literal>
    <justification jstring="[para(3991(a,1),3920(a,1,2))].">
      <j1 rule="para" parents="3991 3920"/>
    </justification>
  </clause>

  <clause id="3994">
    <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(3942(a,1),273(a,1,2))].">
      <j1 rule="para" parents="3942 273"/>
    </justification>
  </clause>

  <clause id="3995">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * T(x,x \ 1) = (x \ 1) \ (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(3957(a,1),3976(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3957 3976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3996">
    <literal><![CDATA[
      (x \ 1) * (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,3511,a(flip),b,3995,a(flip))].">
      <j1 rule="hyper" parents="119 3511 3995"/>
    </justification>
  </clause>

  <clause id="3997">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,3730,a,b,3996,a)].">
      <j1 rule="hyper" parents="58 3730 3996"/>
    </justification>
  </clause>

  <clause id="3998">
    <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(3997(a,1),1763(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3997 1763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3999">
    <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(3997(a,1),3675(a,2,2,1))].">
      <j1 rule="para" parents="3997 3675"/>
    </justification>
  </clause>

  <clause id="4000">
    <literal><![CDATA[
      L(x \ 1,((y * x) \ y) \ 1,L(x \ 1,x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(29,a,1858,a(flip),b,3978,a),flip(a)].">
      <j1 rule="hyper" parents="29 1858 3978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4002">
    <literal><![CDATA[
      L(x \ 1,((y * x) \ y) \ 1,(y * x) \ y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(58,a,2403,a(flip),b,4000,a)].">
      <j1 rule="hyper" parents="58 2403 4000"/>
    </justification>
  </clause>

  <clause id="4003">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) * L(y \ 1,z,u) = ((x * y) \ x) \ L(1 / y,z,u)
    ]]></literal>
    <justification jstring="[para(4002(a,1),561(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4002 561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4004">
    <literal><![CDATA[
      (K(x \ 1,x) * ((y * z) * u)) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(3801(a,1),3857(a,1,1))].">
      <j1 rule="para" parents="3801 3857"/>
    </justification>
  </clause>

  <clause id="4005">
    <literal><![CDATA[
      K(x \ 1,x) * (((y * z) * u) / (z * u)) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(3900,a,4004,a)].">
      <j1 rule="hyper" parents="3900 4004"/>
    </justification>
  </clause>

  <clause id="4006">
    <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),4005(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15 4005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4007">
    <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(334,a,2999,a(flip),b,4006,a),flip(a)].">
      <j1 rule="hyper" parents="334 2999 4006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4008">
    <literal><![CDATA[
      K(x,x \ 1) * R(K(x \ 1,x) * y,z,u) = R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(3053,a,4006,a(flip))].">
      <j1 rule="hyper" parents="3053 4006"/>
    </justification>
  </clause>

  <clause id="4009">
    <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(4006(a,2),3055(a,1,2))].">
      <j1 rule="para" parents="4006 3055"/>
    </justification>
  </clause>

  <clause id="4010">
    <literal><![CDATA[
      K(x,x \ 1) * R(x \ 1,y,z) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1851(a,1),4008(a,1,2,1))].">
      <j1 rule="para" parents="1851 4008"/>
    </justification>
  </clause>

  <clause id="4011">
    <literal><![CDATA[
      R(K(x,x \ 1) * y,z,u) = K(x,x \ 1) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(3044(a,1),4008(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3044 4008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4012">
    <literal><![CDATA[
      K(x \ 1,x) * (R(x \ 1,y,z) \ u) = R(1 / x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(4010(a,1),3894(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4010 3894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4013">
    <literal><![CDATA[
      R(K(x,x \ 1) * y,z,u) = R(y,z,u) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,2237,a(flip),b,4011,a),flip(a)].">
      <j1 rule="hyper" parents="334 2237 4011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4014">
    <literal><![CDATA[
      T(x,R(K(y,y \ 1) * (1 / z),u,w)) = T(x,R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(4013(a,2),3918(a,1,2))].">
      <j1 rule="para" parents="4013 3918"/>
    </justification>
  </clause>

  <clause id="4015">
    <literal><![CDATA[
      T(x,R(K(y,y \ 1) / z,u,w)) = T(x,R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(3830(a,1),4014(a,1,2,1))].">
      <j1 rule="para" parents="3830 4014"/>
    </justification>
  </clause>

  <clause id="4016">
    <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(3887(a,1),3797(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3887 3797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4017">
    <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,4015,a(flip),b,4016,a),flip(a)].">
      <j1 rule="hyper" parents="58 4015 4016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4019">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(3848(a,2),3026(a,1))].">
      <j1 rule="para" parents="3848 3026"/>
    </justification>
  </clause>

  <clause id="4020">
    <literal><![CDATA[
      (x \ T(x,(x \ 1) * y)) * y = y * K(((x \ 1) * y) \ y,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(3452(a,1),3949(a,2,2))].">
      <j1 rule="para" parents="3452 3949"/>
    </justification>
  </clause>

  <clause id="4021">
    <literal><![CDATA[
      (x * y) * ((((x * y) \ (z * y)) \ 1) \ 1) = (x * (((x \ z) \ 1) \ 1)) * y
    ]]></literal>
    <justification jstring="[para(2231(a,1),3979(a,2,1))].">
      <j1 rule="para" parents="2231 3979"/>
    </justification>
  </clause>

  <clause id="4022">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) * L(y \ 1,y,x) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,3658,a(flip),b,4003,a),flip(a)].">
      <j1 rule="hyper" parents="334 3658 4003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4023">
    <literal><![CDATA[
      K(x,x \ 1) / ((y * x) \ y) = ((y * x) \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(758,a,4022,a)].">
      <j1 rule="hyper" parents="758 4022"/>
    </justification>
  </clause>

  <clause id="4024">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * K(y,y \ 1) = ((x * y) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(3850,a,4023,a)].">
      <j1 rule="hyper" parents="3850 4023"/>
    </justification>
  </clause>

  <clause id="4025">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) / ((y \ 1) \ 1) = (1 / ((x * y) \ x)) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,4024,a(flip),b,3012,a)].">
      <j1 rule="hyper" parents="117 4024 3012"/>
    </justification>
  </clause>

  <clause id="4026">
    <literal><![CDATA[
      (x \ R(x * y,z,u)) * x = R(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(2997(a,1),4007(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2997 4007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4027">
    <literal><![CDATA[
      R(x * y,z,u) / y = y \ R(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(130,a,4026,a)].">
      <j1 rule="hyper" parents="130 4026"/>
    </justification>
  </clause>

  <clause id="4028">
    <literal><![CDATA[
      R((x \ y) * x,z,u) = (x \ R(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(5(a,1),4026(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 4026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4029">
    <literal><![CDATA[
      x * (R(y * x,z,u) / x) = R(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(4026(a,1),71(a,1,2,1))].">
      <j1 rule="para" parents="4026 71"/>
    </justification>
  </clause>

  <clause id="4030">
    <literal><![CDATA[
      x \ R(x * (y / x),z,u) = R(y,z,u) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),4027(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7 4027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4031">
    <literal><![CDATA[
      R((x \ y) * x,z,u) != w * x
    ]]></literal>
    <literal><![CDATA[
      x \ R(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(4028(a,2),39(a,1))].">
      <j1 rule="para" parents="4028 39"/>
    </justification>
  </clause>

  <clause id="4032">
    <literal><![CDATA[
      R((x \ (y / z)) * x,z,z \ 1) = (x \ (y * (z \ 1))) * x
    ]]></literal>
    <justification jstring="[para(536(a,1),4028(a,2,1,2))].">
      <j1 rule="para" parents="536 4028"/>
    </justification>
  </clause>

  <clause id="4033">
    <literal><![CDATA[
      R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(2942(a,1),4028(a,2,1,2))].">
      <j1 rule="para" parents="2942 4028"/>
    </justification>
  </clause>

  <clause id="4034">
    <literal><![CDATA[
      R(x * (y / x),z,u) = x * (R(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),4029(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 4029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4035">
    <literal><![CDATA[
      R(x,y,z) / x = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(170(a,1),4030(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="170 4030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4036">
    <literal><![CDATA[
      (x \ R(x,y,z)) * x = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,4035,a)].">
      <j1 rule="hyper" parents="133 4035"/>
    </justification>
  </clause>

  <clause id="4037">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1258,a,b,4035,a)].">
      <j1 rule="hyper" parents="58 1258 4035"/>
    </justification>
  </clause>

  <clause id="4038">
    <literal><![CDATA[
      T(x,x \ R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(31,a,273,a,b,4035,a)].">
      <j1 rule="hyper" parents="31 273 4035"/>
    </justification>
  </clause>

  <clause id="4039">
    <literal><![CDATA[
      (x \ 1) * (x * R(x \ 1,y,z)) = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,1261,a(flip),b,4035,a(flip))].">
      <j1 rule="hyper" parents="119 1261 4035"/>
    </justification>
  </clause>

  <clause id="4040">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,y * z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(4035(a,1),545(a,1,1))].">
      <j1 rule="para" parents="4035 545"/>
    </justification>
  </clause>

  <clause id="4041">
    <literal><![CDATA[
      x \ R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) / x = u
    ]]></literal>
    <justification jstring="[para(4037(a,1),1264(a,1))].">
      <j1 rule="para" parents="4037 1264"/>
    </justification>
  </clause>

  <clause id="4042">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(x \ 1,x) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(4037(a,1),3186(a,1,1))].">
      <j1 rule="para" parents="4037 3186"/>
    </justification>
  </clause>

  <clause id="4043">
    <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(4034(a,2),3366(a,1,1))].">
      <j1 rule="para" parents="4034 3366"/>
    </justification>
  </clause>

  <clause id="4044">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1278,a,4042,a)].">
      <j1 rule="hyper" parents="1278 4042"/>
    </justification>
  </clause>

  <clause id="4045">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) * (u * w) = (u * K(x \ 1,x)) * w
    ]]></literal>
    <justification jstring="[para(4044(a,2),3802(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4044 3802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4046">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = ((x \ (y / z)) * x) * z
    ]]></literal>
    <justification jstring="[hyper(117,a,4032,a(flip),b,269,a)].">
      <j1 rule="hyper" parents="117 4032 269"/>
    </justification>
  </clause>

  <clause id="4047">
    <literal><![CDATA[
      (x \ (x * y)) * x = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,3313,a(flip),b,4033,a),flip(a)].">
      <j1 rule="hyper" parents="58 3313 4033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4048">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,4033,a(flip),b,2938,a),flip(a)].">
      <j1 rule="hyper" parents="117 4033 2938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4049">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 * x)) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(4033(a,1),3368(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4033 3368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4050">
    <literal><![CDATA[
      (x * (y \ T(y,x))) * y = y * x
    ]]></literal>
    <justification jstring="[para(4(a,1),4047(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 4047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4051">
    <literal><![CDATA[
      x * (y \ T(y,x)) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(130,a,4050,a),flip(a)].">
      <j1 rule="hyper" parents="130 4050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4052">
    <literal><![CDATA[
      (x \ y) * (x \ T(x,x \ y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(117,a,5,a(flip),b,4050,a),flip(a)].">
      <j1 rule="hyper" parents="117 5 4050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4053">
    <literal><![CDATA[
      T(x,y) * (y \ T(y,T(x,y))) = x
    ]]></literal>
    <justification jstring="[hyper(30,a,105,a(flip),b,4050,a),flip(a)].">
      <j1 rule="hyper" parents="30 105 4050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4054">
    <literal><![CDATA[
      (x \ T(x,y)) * y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(2562,a,4051,a)].">
      <j1 rule="hyper" parents="2562 4051"/>
    </justification>
  </clause>

  <clause id="4055">
    <literal><![CDATA[
      x \ ((y * x) / y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,4051,a)].">
      <j1 rule="hyper" parents="123 4051"/>
    </justification>
  </clause>

  <clause id="4056">
    <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,849,a(flip),b,4051,a)].">
      <j1 rule="hyper" parents="116 849 4051"/>
    </justification>
  </clause>

  <clause id="4057">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,231,a(flip),b,4051,a)].">
      <j1 rule="hyper" parents="116 231 4051"/>
    </justification>
  </clause>

  <clause id="4058">
    <literal><![CDATA[
      (x / y) \ T(x / y,y) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(116,a,153,a(flip),b,4051,a),flip(a)].">
      <j1 rule="hyper" parents="116 153 4051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4059">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = y \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(29,a,2571,a,b,4051,a)].">
      <j1 rule="hyper" parents="29 2571 4051"/>
    </justification>
  </clause>

  <clause id="4060">
    <literal><![CDATA[
      ((x * y) / x) / y = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,2569,a,b,4051,a)].">
      <j1 rule="hyper" parents="29 2569 4051"/>
    </justification>
  </clause>

  <clause id="4061">
    <literal><![CDATA[
      (T(x,y) \ x) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[hyper(119,a,4051,a(flip),b,2841,a)].">
      <j1 rule="hyper" parents="119 4051 2841"/>
    </justification>
  </clause>

  <clause id="4062">
    <literal><![CDATA[
      (x * y) \ ((x * y) / x) = L(x \ 1,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4051(a,1),1035(a,1,2))].">
      <j1 rule="para" parents="4051 1035"/>
    </justification>
  </clause>

  <clause id="4063">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(4051(a,1),2436(a,1,1))].">
      <j1 rule="para" parents="4051 2436"/>
    </justification>
  </clause>

  <clause id="4064">
    <literal><![CDATA[
      ((x * y) / x) \ y = T(x,y) \ x
    ]]></literal>
    <justification jstring="[para(4051(a,1),2840(a,1,1))].">
      <j1 rule="para" parents="4051 2840"/>
    </justification>
  </clause>

  <clause id="4065">
    <literal><![CDATA[
      T(x,T(y,x)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4053(a,1),2840(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4053 2840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4066">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(4054(a,1),187(a,1,2,1))].">
      <j1 rule="para" parents="4054 187"/>
    </justification>
  </clause>

  <clause id="4067">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2622,a,4055,a)].">
      <j1 rule="hyper" parents="2622 4055"/>
    </justification>
  </clause>

  <clause id="4068">
    <literal><![CDATA[
      L(x \ T(x,y),y,x) = K(x,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(4055(a,1),503(a,1,1))].">
      <j1 rule="para" parents="4055 503"/>
    </justification>
  </clause>

  <clause id="4069">
    <literal><![CDATA[
      T(x,R(y \ 1,y,x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(3245(a,1),4067(a,1,2))].">
      <j1 rule="para" parents="3245 4067"/>
    </justification>
  </clause>

  <clause id="4070">
    <literal><![CDATA[
      R(T(x,y) \ x,y,z) = (T(y,T(x,y)) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(4057(a,2),2591(a,1,1))].">
      <j1 rule="para" parents="4057 2591"/>
    </justification>
  </clause>

  <clause id="4071">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = y * (((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[para(4060(a,1),515(a,1,1,1))].">
      <j1 rule="para" parents="4060 515"/>
    </justification>
  </clause>

  <clause id="4072">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(3340,a,4061,a)].">
      <j1 rule="hyper" parents="3340 4061"/>
    </justification>
  </clause>

  <clause id="4073">
    <literal><![CDATA[
      T(x,x \ y) \ x = (y / x) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),4064(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 4064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4074">
    <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(4064(a,1),1237(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4064 1237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4075">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(4064(a,1),1566(a,1,2,2,1))].">
      <j1 rule="para" parents="4064 1566"/>
    </justification>
  </clause>

  <clause id="4076">
    <literal><![CDATA[
      T(x,T(y,x)) * (y \ T(y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(134,a,4065,a)].">
      <j1 rule="hyper" parents="134 4065"/>
    </justification>
  </clause>

  <clause id="4077">
    <literal><![CDATA[
      (x \ T(x,y)) \ y = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[para(4065(a,1),2513(a,1,1))].">
      <j1 rule="para" parents="4065 2513"/>
    </justification>
  </clause>

  <clause id="4078">
    <literal><![CDATA[
      (x * (T(x,T(y,x)) \ x)) * y = y * x
    ]]></literal>
    <justification jstring="[para(4065(a,2),4050(a,1,1,2))].">
      <j1 rule="para" parents="4065 4050"/>
    </justification>
  </clause>

  <clause id="4079">
    <literal><![CDATA[
      L(x,y \ T(y,x),y) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,2761,a(flip),b,4076,a)].">
      <j1 rule="hyper" parents="58 2761 4076"/>
    </justification>
  </clause>

  <clause id="4080">
    <literal><![CDATA[
      T(x,T(y,x)) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y \ T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4076(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4076 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4082">
    <literal><![CDATA[
      T(x,y) \ (y * (x \ T(x,y))) = x \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,4079,a(flip),b,2568,a),flip(a)].">
      <j1 rule="hyper" parents="116 4079 2568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4083">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ y = T(y,T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(2588(a,1),4077(a,1,1))].">
      <j1 rule="para" parents="2588 4077"/>
    </justification>
  </clause>

  <clause id="4084">
    <literal><![CDATA[
      T(x,x / (y * x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3121,a,4069,a)].">
      <j1 rule="hyper" parents="3121 4069"/>
    </justification>
  </clause>

  <clause id="4085">
    <literal><![CDATA[
      x * ((x * y) * (y / (x * y))) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3295,a(flip),b,4069,a)].">
      <j1 rule="hyper" parents="58 3295 4069"/>
    </justification>
  </clause>

  <clause id="4086">
    <literal><![CDATA[
      T(x,x / (x * y)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3118,a(flip),b,4069,a)].">
      <j1 rule="hyper" parents="58 3118 4069"/>
    </justification>
  </clause>

  <clause id="4087">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = T(y,x \ 1) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,4069,a(flip),b,3123,a),flip(a)].">
      <j1 rule="hyper" parents="117 4069 3123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4088">
    <literal><![CDATA[
      x * (y * ((x \ y) / y)) = T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1232,a,4084,a)].">
      <j1 rule="hyper" parents="1232 4084"/>
    </justification>
  </clause>

  <clause id="4089">
    <literal><![CDATA[
      x \ T(y,x \ 1) = y * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(116,a,4084,a(flip),b,1231,a)].">
      <j1 rule="hyper" parents="116 4084 1231"/>
    </justification>
  </clause>

  <clause id="4090">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2367,a,4086,a)].">
      <j1 rule="hyper" parents="2367 4086"/>
    </justification>
  </clause>

  <clause id="4091">
    <literal><![CDATA[
      T(x * ((x / y) / x),y) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2364,a,4086,a)].">
      <j1 rule="hyper" parents="2364 4086"/>
    </justification>
  </clause>

  <clause id="4094">
    <literal><![CDATA[
      x * K(x,(x / y) / x) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,1793,a,b,4086,a)].">
      <j1 rule="hyper" parents="58 1793 4086"/>
    </justification>
  </clause>

  <clause id="4095">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) = x * K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1799,a(flip),b,4086,a),flip(a)].">
      <j1 rule="hyper" parents="58 1799 4086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4096">
    <literal><![CDATA[
      T(x,y \ 1) / y = x * ((x / y) / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,4086,a(flip),b,2362,a)].">
      <j1 rule="hyper" parents="117 4086 2362"/>
    </justification>
  </clause>

  <clause id="4097">
    <literal><![CDATA[
      (x * ((x / y) / x)) \ T(x,y \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,4086,a(flip),b,2362,a)].">
      <j1 rule="hyper" parents="116 4086 2362"/>
    </justification>
  </clause>

  <clause id="4098">
    <literal><![CDATA[
      K(x,(x / y) / x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,4086,a(flip),b,1793,a),flip(a)].">
      <j1 rule="hyper" parents="116 4086 1793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4099">
    <literal><![CDATA[
      (x \ y) \ (y / x) = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,4052,a(flip),b,673,a(flip))].">
      <j1 rule="hyper" parents="116 4052 673"/>
    </justification>
  </clause>

  <clause id="4100">
    <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(4063(a,1),495(a,1,1))].">
      <j1 rule="para" parents="4063 495"/>
    </justification>
  </clause>

  <clause id="4101">
    <literal><![CDATA[
      T(x * (T(x,T(y,x)) \ x),y) = x
    ]]></literal>
    <justification jstring="[hyper(246,a,4078,a,b,xx)].">
      <j1 rule="hyper" parents="246 4078"/>
    </justification>
  </clause>

  <clause id="4102">
    <literal><![CDATA[
      T(x,y) \ ((x * y) / x) = x \ y
    ]]></literal>
    <justification jstring="[para(4051(a,1),4082(a,1,2))].">
      <j1 rule="para" parents="4051 4082"/>
    </justification>
  </clause>

  <clause id="4103">
    <literal><![CDATA[
      T(x,x \ y) \ (y / x) = x \ (x \ y)
    ]]></literal>
    <justification jstring="[para(4052(a,1),4082(a,1,2))].">
      <j1 rule="para" parents="4052 4082"/>
    </justification>
  </clause>

  <clause id="4104">
    <literal><![CDATA[
      T(x / y,T(y,x)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(846,a,4102,a)].">
      <j1 rule="hyper" parents="846 4102"/>
    </justification>
  </clause>

  <clause id="4105">
    <literal><![CDATA[
      T(x,y) = ((x * y) / x) / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(201,a,4102,a),flip(a)].">
      <j1 rule="hyper" parents="201 4102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4106">
    <literal><![CDATA[
      T(x,y) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(134,a,4102,a)].">
      <j1 rule="hyper" parents="134 4102"/>
    </justification>
  </clause>

  <clause id="4107">
    <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,4102,a)].">
      <j1 rule="hyper" parents="119 85 4102"/>
    </justification>
  </clause>

  <clause id="4108">
    <literal><![CDATA[
      (x * (x * y)) / x = T(x,x * y) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,4,a(flip),b,4102,a),flip(a)].">
      <j1 rule="hyper" parents="119 4 4102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4109">
    <literal><![CDATA[
      T(x,T(y,x * y)) = y \ (x * y)
    ]]></literal>
    <justification jstring="[para(6(a,1),4104(a,1,1))].">
      <j1 rule="para" parents="6 4104"/>
    </justification>
  </clause>

  <clause id="4110">
    <literal><![CDATA[
      T(x \ y,T(x,y)) = T(x \ y,x)
    ]]></literal>
    <justification jstring="[para(4104(a,1),254(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4104 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4111">
    <literal><![CDATA[
      x \ (y * T(y \ x,T(y,x))) = K(y \ x,T(y,x))
    ]]></literal>
    <justification jstring="[para(4104(a,1),2014(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4104 2014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4112">
    <literal><![CDATA[
      T(x,x / (x / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,1595,a(flip),b,4105,a)].">
      <j1 rule="hyper" parents="334 1595 4105"/>
    </justification>
  </clause>

  <clause id="4113">
    <literal><![CDATA[
      T(x,x / (1 / y)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1597,a(flip),b,4112,a)].">
      <j1 rule="hyper" parents="58 1597 4112"/>
    </justification>
  </clause>

  <clause id="4114">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,1225,a(flip),b,4112,a)].">
      <j1 rule="hyper" parents="58 1225 4112"/>
    </justification>
  </clause>

  <clause id="4115">
    <literal><![CDATA[
      T(x,y) / ((x * y) / x) = x / y
    ]]></literal>
    <justification jstring="[hyper(117,a,4112,a(flip),b,1215,a)].">
      <j1 rule="hyper" parents="117 4112 1215"/>
    </justification>
  </clause>

  <clause id="4116">
    <literal><![CDATA[
      (x / y) \ T(x,y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,4112,a(flip),b,1215,a)].">
      <j1 rule="hyper" parents="116 4112 1215"/>
    </justification>
  </clause>

  <clause id="4117">
    <literal><![CDATA[
      T(x * y,(x * y) / x) = T(x * y,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),4112(a,1,2,2))].">
      <j1 rule="para" parents="6 4112"/>
    </justification>
  </clause>

  <clause id="4118">
    <literal><![CDATA[
      T(x,x / y) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(72(a,1),4112(a,1,2,2))].">
      <j1 rule="para" parents="72 4112"/>
    </justification>
  </clause>

  <clause id="4119">
    <literal><![CDATA[
      T(x,(y \ x) \ x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(194(a,1),4112(a,1,2)),flip(a)].">
      <j1 rule="para" parents="194 4112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4120">
    <literal><![CDATA[
      T(x,T(y,x)) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(4112(a,1),1484(a,1,1))].">
      <j1 rule="para" parents="4112 1484"/>
    </justification>
  </clause>

  <clause id="4121">
    <literal><![CDATA[
      T(x,y) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(4112(a,1),1592(a,1,1))].">
      <j1 rule="para" parents="4112 1592"/>
    </justification>
  </clause>

  <clause id="4122">
    <literal><![CDATA[
      T(x,T(y,y \ x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(106(a,2),4119(a,1,2))].">
      <j1 rule="para" parents="106 4119"/>
    </justification>
  </clause>

  <clause id="4123">
    <literal><![CDATA[
      T(x * y,T(x,y)) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),4122(a,1,2,2))].">
      <j1 rule="para" parents="4 4122"/>
    </justification>
  </clause>

  <clause id="4124">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,T(x,y)) = ((x * y) / x) \ (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4106(a,1),92(a,2,1))].">
      <j1 rule="para" parents="4106 92"/>
    </justification>
  </clause>

  <clause id="4125">
    <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(4106(a,1),495(a,1,1))].">
      <j1 rule="para" parents="4106 495"/>
    </justification>
  </clause>

  <clause id="4126">
    <literal><![CDATA[
      L(((x * y) / x) / y,y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4106(a,1),2546(a,1,1,1))].">
      <j1 rule="para" parents="4106 2546"/>
    </justification>
  </clause>

  <clause id="4127">
    <literal><![CDATA[
      T(x,T(y,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,17,a,b,4109,a),flip(a)].">
      <j1 rule="hyper" parents="334 17 4109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4128">
    <literal><![CDATA[
      T(x,y) * T(x \ y,x) = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4110,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4110 17"/>
    </justification>
  </clause>

  <clause id="4129">
    <literal><![CDATA[
      x \ (y * T(y \ x,T(y,x))) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4110(a,2),444(a,1,2,2))].">
      <j1 rule="para" parents="4110 444"/>
    </justification>
  </clause>

  <clause id="4130">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(4113(a,1),1577(a,1,1))].">
      <j1 rule="para" parents="4113 1577"/>
    </justification>
  </clause>

  <clause id="4131">
    <literal><![CDATA[
      T(x / T(y,x),y) = T(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(246,a,4114,a,b,1182,a)].">
      <j1 rule="hyper" parents="246 4114 1182"/>
    </justification>
  </clause>

  <clause id="4132">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x / T(y,x),y) = y \ z
    ]]></literal>
    <justification jstring="[para(4114(a,1),286(a,1))].">
      <j1 rule="para" parents="4114 286"/>
    </justification>
  </clause>

  <clause id="4133">
    <literal><![CDATA[
      ((x * y) * y) / (x * y) = x \ T(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(31,a,184,a(flip),b,4115,a),flip(a)].">
      <j1 rule="hyper" parents="31 184 4115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4134">
    <literal><![CDATA[
      T(x,x \ y) * (x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(5(a,1),4121(a,2,2,1))].">
      <j1 rule="para" parents="5 4121"/>
    </justification>
  </clause>

  <clause id="4135">
    <literal><![CDATA[
      ((T(x,y) * y) / x) \ ((x * (x * y)) / x) = L(x,(x * y) / x,x)
    ]]></literal>
    <justification jstring="[para(4121(a,2),1720(a,1,1,1))].">
      <j1 rule="para" parents="4121 1720"/>
    </justification>
  </clause>

  <clause id="4136">
    <literal><![CDATA[
      T(x / T(y,x),z) * y = y * T(T(y,x) \ x,z)
    ]]></literal>
    <justification jstring="[para(4131(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4131 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4137">
    <literal><![CDATA[
      (x \ 1) \ T(y,x) = y * (((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(116,a,3106,a(flip),b,4088,a)].">
      <j1 rule="hyper" parents="116 3106 4088"/>
    </justification>
  </clause>

  <clause id="4138">
    <literal><![CDATA[
      x * R(1 / y,y,y \ x) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,604,a,b,4089,a)].">
      <j1 rule="hyper" parents="334 604 4089"/>
    </justification>
  </clause>

  <clause id="4139">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(75(a,1),4089(a,2,2,1))].">
      <j1 rule="para" parents="75 4089"/>
    </justification>
  </clause>

  <clause id="4140">
    <literal><![CDATA[
      R(x,(y \ x) / x,x) = ((y \ T(x,y \ 1)) * x) / (y \ x)
    ]]></literal>
    <justification jstring="[para(4089(a,2),103(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4089 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4141">
    <literal><![CDATA[
      T(x,y) / (y \ 1) = x * ((x / (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,3106,a(flip),b,4090,a)].">
      <j1 rule="hyper" parents="117 3106 4090"/>
    </justification>
  </clause>

  <clause id="4142">
    <literal><![CDATA[
      x \ T(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,(x / y) / x) = z
    ]]></literal>
    <justification jstring="[para(4094(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4094 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4143">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) = x * K(x,(y \ x) / x)
    ]]></literal>
    <justification jstring="[para(273(a,1),4094(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="273 4094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4144">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(72(a,1),4096(a,2,2,1))].">
      <j1 rule="para" parents="72 4096"/>
    </justification>
  </clause>

  <clause id="4145">
    <literal><![CDATA[
      T(x,y) / (1 / y) = x * ((x / (1 / y)) / x)
    ]]></literal>
    <justification jstring="[para(75(a,1),4096(a,1,1,2))].">
      <j1 rule="para" parents="75 4096"/>
    </justification>
  </clause>

  <clause id="4146">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = (T(x,y \ 1) / y) \ x
    ]]></literal>
    <justification jstring="[para(4096(a,2),221(a,2,1))].">
      <j1 rule="para" parents="4096 221"/>
    </justification>
  </clause>

  <clause id="4147">
    <literal><![CDATA[
      x * (x * T(T(x,x \ (y * x)) \ ((y * x) / x),z)) = (x * T(x \ y,z)) * x
    ]]></literal>
    <justification jstring="[para(4103(a,2),1613(a,1,2,2,1))].">
      <j1 rule="para" parents="4103 1613"/>
    </justification>
  </clause>

  <clause id="4148">
    <literal><![CDATA[
      (T(x,x * y) * y) * x = x * (x * y)
    ]]></literal>
    <justification jstring="[hyper(133,a,4108,a)].">
      <j1 rule="hyper" parents="133 4108"/>
    </justification>
  </clause>

  <clause id="4149">
    <literal><![CDATA[
      T(T(x,x * y) * y,x) = x * y
    ]]></literal>
    <justification jstring="[para(4108(a,1),230(a,1,1))].">
      <j1 rule="para" parents="4108 230"/>
    </justification>
  </clause>

  <clause id="4150">
    <literal><![CDATA[
      ((x \ y) \ y) * (x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(685,a,4134,a)].">
      <j1 rule="hyper" parents="685 4134"/>
    </justification>
  </clause>

  <clause id="4151">
    <literal><![CDATA[
      T(x,x \ (y \ x)) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4089,a,b,4134,a)].">
      <j1 rule="hyper" parents="116 4089 4134"/>
    </justification>
  </clause>

  <clause id="4152">
    <literal><![CDATA[
      (x * (y / x)) \ (T(x,x \ y) * ((x \ y) * z)) = L(z,x \ y,T(x,x \ y))
    ]]></literal>
    <justification jstring="[para(4134(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4134 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4153">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[para(231(a,1),4068(a,2,2)),flip(a)].">
      <j1 rule="para" parents="231 4068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4154">
    <literal><![CDATA[
      L(x \ T(x,y),y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4060(a,1),4126(a,1,1))].">
      <j1 rule="para" parents="4060 4126"/>
    </justification>
  </clause>

  <clause id="4155">
    <literal><![CDATA[
      K(T(x,y),y) = K(x,(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4068,a(flip),b,4154,a),flip(a)].">
      <j1 rule="hyper" parents="58 4068 4154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4156">
    <literal><![CDATA[
      K(T(x,y),y) * (K(x,(x * y) / x) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(290,a,4155,a)].">
      <j1 rule="hyper" parents="290 4155"/>
    </justification>
  </clause>

  <clause id="4157">
    <literal><![CDATA[
      K(T(x,T(y,x)),T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(231(a,1),4155(a,2,2))].">
      <j1 rule="para" parents="231 4155"/>
    </justification>
  </clause>

  <clause id="4158">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,4114,a(flip),b,4130,a),flip(a)].">
      <j1 rule="hyper" parents="334 4114 4130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4159">
    <literal><![CDATA[
      L(R(x,y,x),y,x) * y = y * T(x,T(y,x))
    ]]></literal>
    <justification jstring="[para(4158(a,1),1013(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4158 1013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4160">
    <literal><![CDATA[
      (x / y) \ (y \ x) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[para(107(a,1),4058(a,1,2))].">
      <j1 rule="para" parents="107 4058"/>
    </justification>
  </clause>

  <clause id="4161">
    <literal><![CDATA[
      T(x,x \ y) \ x = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4073,a,b,4160,a)].">
      <j1 rule="hyper" parents="58 4073 4160"/>
    </justification>
  </clause>

  <clause id="4162">
    <literal><![CDATA[
      x / (x / y) = y * (T(y,y \ x) \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4073,a,b,4160,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 4073 4160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4163">
    <literal><![CDATA[
      (x * y) / ((x * y) / x) = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),4162(a,2,2,1,2))].">
      <j1 rule="para" parents="4 4162"/>
    </justification>
  </clause>

  <clause id="4164">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,1281,a,b,4059,a)].">
      <j1 rule="hyper" parents="58 1281 4059"/>
    </justification>
  </clause>

  <clause id="4165">
    <literal><![CDATA[
      L(x * ((y * (x \ 1)) / y),z,u) = y \ T(y,L(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3384,a(flip),b,4059,a)].">
      <j1 rule="hyper" parents="58 3384 4059"/>
    </justification>
  </clause>

  <clause id="4166">
    <literal><![CDATA[
      x \ (y * ((z * (y \ x)) / z)) = z \ T(z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2051,a(flip),b,4059,a)].">
      <j1 rule="hyper" parents="58 2051 4059"/>
    </justification>
  </clause>

  <clause id="4167">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,(x / T(y,z)) / x)
    ]]></literal>
    <justification jstring="[para(4059(a,1),2054(a,1,1))].">
      <j1 rule="para" parents="4059 2054"/>
    </justification>
  </clause>

  <clause id="4168">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((x \ T(x,z \ 1)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(4059(a,1),2366(a,2,2,1))].">
      <j1 rule="para" parents="4059 2366"/>
    </justification>
  </clause>

  <clause id="4169">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = K(x,(x / R(y,z,u)) / x)
    ]]></literal>
    <justification jstring="[para(4059(a,1),3401(a,1,1))].">
      <j1 rule="para" parents="4059 3401"/>
    </justification>
  </clause>

  <clause id="4170">
    <literal><![CDATA[
      ((x * (1 / y)) / x) * y = T(x,y \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(900,a,4087,a)].">
      <j1 rule="hyper" parents="900 4087"/>
    </justification>
  </clause>

  <clause id="4171">
    <literal><![CDATA[
      T(x \ T(x * y,y),x * y) = y
    ]]></literal>
    <justification jstring="[para(4133(a,1),230(a,1,1))].">
      <j1 rule="para" parents="4133 230"/>
    </justification>
  </clause>

  <clause id="4172">
    <literal><![CDATA[
      T(x \ T(x * y,y),x) = R(y,x,y)
    ]]></literal>
    <justification jstring="[para(4133(a,1),807(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4133 807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4173">
    <literal><![CDATA[
      (x \ T(x * y,y)) * x = x * R(y,x,y)
    ]]></literal>
    <justification jstring="[para(4133(a,1),820(a,1,1))].">
      <j1 rule="para" parents="4133 820"/>
    </justification>
  </clause>

  <clause id="4174">
    <literal><![CDATA[
      x * R(y,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ T(x * y,y)) * x = z
    ]]></literal>
    <justification jstring="[para(4172(a,1),294(a,1,2))].">
      <j1 rule="para" parents="4172 294"/>
    </justification>
  </clause>

  <clause id="4175">
    <literal><![CDATA[
      (x * R(y,x,y)) \ T(x * y,y) = K(x,x \ T(x * y,y))
    ]]></literal>
    <justification jstring="[para(4173(a,1),86(a,1,1))].">
      <j1 rule="para" parents="4173 86"/>
    </justification>
  </clause>

  <clause id="4176">
    <literal><![CDATA[
      (((x / y) \ 1) \ y) * ((x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(1412,a,4139,a)].">
      <j1 rule="hyper" parents="1412 4139"/>
    </justification>
  </clause>

  <clause id="4177">
    <literal><![CDATA[
      x \ (T(x,y) / (1 / y)) = (x / (1 / y)) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,4145,a,b,xx)].">
      <j1 rule="hyper" parents="116 4145"/>
    </justification>
  </clause>

  <clause id="4178">
    <literal><![CDATA[
      K(x,(x * y) / x) != z
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),y) = z
    ]]></literal>
    <justification jstring="[para(4156(a,1),211(a,1))].">
      <j1 rule="para" parents="4156 211"/>
    </justification>
  </clause>

  <clause id="4179">
    <literal><![CDATA[
      T((x * y) / x,T(x,y)) = L(R(y,x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,466,a,b,4159,a)].">
      <j1 rule="hyper" parents="30 466 4159"/>
    </justification>
  </clause>

  <clause id="4180">
    <literal><![CDATA[
      x / (y \ ((y * x) / y)) = y * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1224,a(flip),b,4163,a)].">
      <j1 rule="hyper" parents="58 1224 4163"/>
    </justification>
  </clause>

  <clause id="4182">
    <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(4133(a,1),4179(a,1,1))].">
      <j1 rule="para" parents="4133 4179"/>
    </justification>
  </clause>

  <clause id="4183">
    <literal><![CDATA[
      (x * (T(x,y) \ x)) \ y = x \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(192,a,4180,a)].">
      <j1 rule="hyper" parents="192 4180"/>
    </justification>
  </clause>

  <clause id="4184">
    <literal><![CDATA[
      ((x * y) / x) * T(((x * y) / x) \ x,y) = x * K(y \ (x * (T(x,y) \ x)),y)
    ]]></literal>
    <justification jstring="[para(4180(a,1),1528(a,2,2,1,2))].">
      <j1 rule="para" parents="4180 1528"/>
    </justification>
  </clause>

  <clause id="4185">
    <literal><![CDATA[
      x * R(1 / (1 / y),1 / y,(1 / y) \ x) = (1 / y) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),4138(a,2,2,2))].">
      <j1 rule="para" parents="75 4138"/>
    </justification>
  </clause>

  <clause id="4186">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = (x * y) * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(29,a,985,a,b,4085,a)].">
      <j1 rule="hyper" parents="29 985 4085"/>
    </justification>
  </clause>

  <clause id="4187">
    <literal><![CDATA[
      ((x \ 1) * y) * (y / ((x \ 1) * y)) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(29,a,3110,a(flip),b,4085,a),flip(a)].">
      <j1 rule="hyper" parents="29 3110 4085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4188">
    <literal><![CDATA[
      K(x \ y,T(x,y)) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4129,a(flip),b,4111,a),flip(a)].">
      <j1 rule="hyper" parents="58 4129 4111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4189">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(y,T(x,x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,691,a(flip),b,4188,a),flip(a)].">
      <j1 rule="hyper" parents="58 691 4188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4190">
    <literal><![CDATA[
      K(x,T(y,y * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1413,a,4189,a),flip(a)].">
      <j1 rule="hyper" parents="1413 4189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4192">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ x) / x) = z
    ]]></literal>
    <justification jstring="[para(4143(a,2),38(a,1))].">
      <j1 rule="para" parents="4143 38"/>
    </justification>
  </clause>

  <clause id="4193">
    <literal><![CDATA[
      x \ y != (x * ((z \ x) / x)) / (z \ x)
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ 1) = y
    ]]></literal>
    <justification jstring="[para(4164(a,2),42(a,1)),flip(a)].">
      <j1 rule="para" parents="4164 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4194">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = x \ T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,4098,a(flip),b,4167,a),flip(a)].">
      <j1 rule="hyper" parents="334 4098 4167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4195">
    <literal><![CDATA[
      x \ (y * (x / y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(((y / x) \ 1) \ x,(y / x) \ 1) = z
    ]]></literal>
    <justification jstring="[para(4176(a,1),477(a,1,2))].">
      <j1 rule="para" parents="4176 477"/>
    </justification>
  </clause>

  <clause id="4196">
    <literal><![CDATA[
      ((x \ 1) * y) * R(x,x \ 1,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(219(a,2),4187(a,1,2))].">
      <j1 rule="para" parents="219 4187"/>
    </justification>
  </clause>

  <clause id="4197">
    <literal><![CDATA[
      ((((x \ 1) * y) * x) / ((x \ 1) * y)) * (x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,4196,a(flip),b,880,a),flip(a)].">
      <j1 rule="hyper" parents="117 4196 880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4198">
    <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(2603(a,1),4194(a,2,2,2,1))].">
      <j1 rule="para" parents="2603 4194"/>
    </justification>
  </clause>

  <clause id="4199">
    <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(4070(a,1),963(a,1,1))].">
      <j1 rule="para" parents="4070 963"/>
    </justification>
  </clause>

  <clause id="4200">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = x \ T(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,4098,a(flip),b,4169,a),flip(a)].">
      <j1 rule="hyper" parents="334 4098 4169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4201">
    <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(4040(a,2),2226(a,1,1,1,1))].">
      <j1 rule="para" parents="4040 2226"/>
    </justification>
  </clause>

  <clause id="4202">
    <literal><![CDATA[
      x * (T((x \ y) * z,x) / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(58,a,1448,a(flip),b,4048,a)].">
      <j1 rule="hyper" parents="58 1448 4048"/>
    </justification>
  </clause>

  <clause id="4203">
    <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(4107(a,1),39(a,1))].">
      <j1 rule="para" parents="4107 39"/>
    </justification>
  </clause>

  <clause id="4204">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = x \ T(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(4059(a,1),4165(a,1,1))].">
      <j1 rule="para" parents="4059 4165"/>
    </justification>
  </clause>

  <clause id="4205">
    <literal><![CDATA[
      x * R(1 / (1 / y),y \ 1,(1 / y) \ x) = (1 / y) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3262(a,1),4185(a,1,2))].">
      <j1 rule="para" parents="3262 4185"/>
    </justification>
  </clause>

  <clause id="4206">
    <literal><![CDATA[
      K(x,((y \ 1) \ x) / x) = ((1 / y) \ x) \ ((1 / y) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(4205(a,1),3715(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4205 3715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4207">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(334,a,3716,a(flip),b,4206,a)].">
      <j1 rule="hyper" parents="334 3716 4206"/>
    </justification>
  </clause>

  <clause id="4208">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(58,a,4063,a(flip),b,4197,a)].">
      <j1 rule="hyper" parents="58 4063 4197"/>
    </justification>
  </clause>

  <clause id="4209">
    <literal><![CDATA[
      L(K(x \ y,x),y,x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(58,a,2045,a(flip),b,4208,a)].">
      <j1 rule="hyper" parents="58 2045 4208"/>
    </justification>
  </clause>

  <clause id="4210">
    <literal><![CDATA[
      ((x \ (x * y)) * x) / (x * y) = L(K(y,x),x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),4209(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 4209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4211">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = (x * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(4(a,1),4210(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 4210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4212">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,3835,a(flip),b,4072,a)].">
      <j1 rule="hyper" parents="58 3835 4072"/>
    </justification>
  </clause>

  <clause id="4213">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(y \ 1) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[para(3191(a,1),4212(a,2,1))].">
      <j1 rule="para" parents="3191 4212"/>
    </justification>
  </clause>

  <clause id="4214">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) \ x = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4211,a(flip),b,4213,a),flip(a)].">
      <j1 rule="hyper" parents="58 4211 4213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4215">
    <literal><![CDATA[
      x \ y != (z * y) / (y * z)
    ]]></literal>
    <literal><![CDATA[
      T(y,(y \ 1) * (z * y)) = x
    ]]></literal>
    <justification jstring="[para(4214(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="4214 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4216">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = (x \ T(x,(x \ 1) * y)) * y
    ]]></literal>
    <justification jstring="[hyper(334,a,315,a(flip),b,4020,a)].">
      <j1 rule="hyper" parents="334 315 4020"/>
    </justification>
  </clause>

  <clause id="4217">
    <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,3230,a(flip),b,4021,a)].">
      <j1 rule="hyper" parents="58 3230 4021"/>
    </justification>
  </clause>

  <clause id="4218">
    <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,2876,a(flip),b,4021,a)].">
      <j1 rule="hyper" parents="58 2876 4021"/>
    </justification>
  </clause>

  <clause id="4219">
    <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),4199(a,2,1))].">
      <j1 rule="para" parents="11 4199"/>
    </justification>
  </clause>

  <clause id="4221">
    <literal><![CDATA[
      ((x * (y * (z * K(u,u \ 1)))) \ ((x * y) * z)) * K(u,u \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(2237(a,1),3849(a,1,1,1,2,2))].">
      <j1 rule="para" parents="2237 3849"/>
    </justification>
  </clause>

  <clause id="4222">
    <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(334,a,4200,a,b,4198,a),flip(a)].">
      <j1 rule="hyper" parents="334 4200 4198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4223">
    <literal><![CDATA[
      T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = R(x \ T(x,z),z,y)
    ]]></literal>
    <justification jstring="[para(3106(a,1),4222(a,2,1,2))].">
      <j1 rule="para" parents="3106 4222"/>
    </justification>
  </clause>

  <clause id="4224">
    <literal><![CDATA[
      T(x,y / (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y / (z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(3540(a,1),3983(a,1))].">
      <j1 rule="para" parents="3540 3983"/>
    </justification>
  </clause>

  <clause id="4226">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(2(a,1),4049(a,2,1,1,2))].">
      <j1 rule="para" parents="2 4049"/>
    </justification>
  </clause>

  <clause id="4227">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / x
    ]]></literal>
    <justification jstring="[para(75(a,1),4226(a,2,2))].">
      <j1 rule="para" parents="75 4226"/>
    </justification>
  </clause>

  <clause id="4228">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[para(3971(a,1),4227(a,1,1))].">
      <j1 rule="para" parents="3971 4227"/>
    </justification>
  </clause>

  <clause id="4229">
    <literal><![CDATA[
      ((x \ y) * x) / y != ((x \ y) * x) * z
    ]]></literal>
    <literal><![CDATA[
      y \ 1 = z
    ]]></literal>
    <justification jstring="[para(4228(a,1),38(a,1))].">
      <j1 rule="para" parents="4228 38"/>
    </justification>
  </clause>

  <clause id="4230">
    <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),4147(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="17 4147"/>
    </justification>
  </clause>

  <clause id="4231">
    <literal><![CDATA[
      x * K(y \ (x * (T(x,y) \ x)),y) = (x * (y * T(y \ x,y))) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,1643,a(flip),b,4184,a),flip(a)].">
      <j1 rule="hyper" parents="58 1643 4184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4232">
    <literal><![CDATA[
      x * K(y \ (x * (T(x,y) \ x)),y) = (x * ((y \ x) * y)) / x
    ]]></literal>
    <justification jstring="[para(105(a,1),4231(a,2,1,2))].">
      <j1 rule="para" parents="105 4231"/>
    </justification>
  </clause>

  <clause id="4233">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,T(x,y) \ x,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(4064(a,1),4075(a,2,2))].">
      <j1 rule="para" parents="4064 4075"/>
    </justification>
  </clause>

  <clause id="4234">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) \ ((x * y) * z) = ((x * y) * ((((x * y) \ y) \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(3781(a,2),4217(a,1,1))].">
      <j1 rule="para" parents="3781 4217"/>
    </justification>
  </clause>

  <clause id="4235">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) \ ((x * y) * z) = (y * K(x \ 1,x)) * z
    ]]></literal>
    <justification jstring="[para(2931(a,1),4234(a,2,1))].">
      <j1 rule="para" parents="2931 4234"/>
    </justification>
  </clause>

  <clause id="4236">
    <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(3785(a,1),4235(a,1,1))].">
      <j1 rule="para" parents="3785 4235"/>
    </justification>
  </clause>

  <clause id="4237">
    <literal><![CDATA[
      ((R(x,y,z) \ 1) * R(x,y,z)) * (y * z) = (y * K(x \ 1,x)) * z
    ]]></literal>
    <justification jstring="[para(2931(a,1),4218(a,2,1))].">
      <j1 rule="para" parents="2931 4218"/>
    </justification>
  </clause>

  <clause id="4238">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) = (R(x,u,w) \ 1) * R(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(30,a,4045,a,b,4237,a)].">
      <j1 rule="hyper" parents="30 4045 4237"/>
    </justification>
  </clause>

  <clause id="4239">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,266,a,b,4238,a)].">
      <j1 rule="hyper" parents="334 266 4238"/>
    </justification>
  </clause>

  <clause id="4241">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,4044,a(flip),b,4239,a),flip(a)].">
      <j1 rule="hyper" parents="334 4044 4239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4242">
    <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,4239,a(flip),b,1852,a)].">
      <j1 rule="hyper" parents="119 4239 1852"/>
    </justification>
  </clause>

  <clause id="4243">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) \ 1 = R(x,u,w) * (1 / R(x,u,w))
    ]]></literal>
    <justification jstring="[para(4239(a,1),1869(a,1,1))].">
      <j1 rule="para" parents="4239 1869"/>
    </justification>
  </clause>

  <clause id="4244">
    <literal><![CDATA[
      (x \ (1 / R(y,z,u))) * K(y \ 1,y) = x \ (R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(4241(a,1),3566(a,1,2))].">
      <j1 rule="para" parents="4241 3566"/>
    </justification>
  </clause>

  <clause id="4245">
    <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,3776,a,b,4242,a),flip(a)].">
      <j1 rule="hyper" parents="116 3776 4242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4246">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) = x * T(x \ 1,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,2722,a(flip),b,4245,a),flip(a)].">
      <j1 rule="hyper" parents="334 2722 4245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4247">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) = K(R(x,u,w),x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(334,a,2906,a,b,4246,a),flip(a)].">
      <j1 rule="hyper" parents="334 2906 4246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4249">
    <literal><![CDATA[
      K(R(x,y,z),x \ 1) = K(x \ 1,R(x,u,w)) \ 1
    ]]></literal>
    <justification jstring="[hyper(2496,a,4247,a),flip(a)].">
      <j1 rule="hyper" parents="2496 4247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4251">
    <literal><![CDATA[
      K(R(x,y,z),x \ 1) = R(x,u,w) * (1 / R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,4243,a(flip),b,4249,a),flip(a)].">
      <j1 rule="hyper" parents="334 4243 4249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4252">
    <literal><![CDATA[
      R(x,y,z) * (1 / R(x,y,z)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(391(a,1),4251(a,1,1)),flip(a)].">
      <j1 rule="para" parents="391 4251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4253">
    <literal><![CDATA[
      R(x,y,z) \ K(x,x \ 1) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,4252,a)].">
      <j1 rule="hyper" parents="123 4252"/>
    </justification>
  </clause>

  <clause id="4254">
    <literal><![CDATA[
      (1 / x) * (R(x,y,z) \ x) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,3879,a,b,4252,a)].">
      <j1 rule="hyper" parents="29 3879 4252"/>
    </justification>
  </clause>

  <clause id="4255">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * ((x \ 1) \ 1) = (1 / R(x,y,z)) * x
    ]]></literal>
    <justification jstring="[para(4253(a,1),3536(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4253 3536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4256">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(123,a,4254,a)].">
      <j1 rule="hyper" parents="123 4254"/>
    </justification>
  </clause>

  <clause id="4257">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(4254(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4254 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4258">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(3866,a,4255,a),flip(a)].">
      <j1 rule="hyper" parents="3866 4255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4259">
    <literal><![CDATA[
      x / R(x,y,z) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(1959,a,4258,a)].">
      <j1 rule="hyper" parents="1959 4258"/>
    </justification>
  </clause>

  <clause id="4260">
    <literal><![CDATA[
      T(1 / R(x,y,z),x) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(246,a,4258,a,b,1371,a)].">
      <j1 rule="hyper" parents="246 4258 1371"/>
    </justification>
  </clause>

  <clause id="4261">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ x = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(192,a,4259,a)].">
      <j1 rule="hyper" parents="192 4259"/>
    </justification>
  </clause>

  <clause id="4262">
    <literal><![CDATA[
      (R(x,y,z) \ x) * R(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(133,a,4259,a)].">
      <j1 rule="hyper" parents="133 4259"/>
    </justification>
  </clause>

  <clause id="4263">
    <literal><![CDATA[
      (x / R(x,y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      (R(x,y,z) \ x) * u = w
    ]]></literal>
    <justification jstring="[para(4261(a,1),359(a,1,1,2))].">
      <j1 rule="para" parents="4261 359"/>
    </justification>
  </clause>

  <clause id="4264">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = (x \ 1) \ (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(3211,a,4244,a)].">
      <j1 rule="hyper" parents="3211 4244"/>
    </justification>
  </clause>

  <clause id="4265">
    <literal><![CDATA[
      (x \ 1) \ (R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(4257,a,4264,a),flip(a)].">
      <j1 rule="hyper" parents="4257 4264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4266">
    <literal><![CDATA[
      (x \ 1) * (R(x,y,z) \ x) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,4256,a(flip),b,4264,a(flip))].">
      <j1 rule="hyper" parents="119 4256 4264"/>
    </justification>
  </clause>

  <clause id="4267">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,3757,a(flip),b,4265,a)].">
      <j1 rule="hyper" parents="58 3757 4265"/>
    </justification>
  </clause>

  <clause id="4268">
    <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(3802(a,1),3862(a,1,2))].">
      <j1 rule="para" parents="3802 3862"/>
    </justification>
  </clause>

  <clause id="4269">
    <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,3891,a(flip),b,3863,a)].">
      <j1 rule="hyper" parents="58 3891 3863"/>
    </justification>
  </clause>

  <clause id="4270">
    <literal><![CDATA[
      K(x * K(y \ 1,y),z) = (z * x) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(3864,a,3871,a)].">
      <j1 rule="hyper" parents="3864 3871"/>
    </justification>
  </clause>

  <clause id="4271">
    <literal><![CDATA[
      K(x * K(y \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,11,a,b,4270,a),flip(a)].">
      <j1 rule="hyper" parents="334 11 4270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4272">
    <literal><![CDATA[
      K(x * K(y,y \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1859(a,1),4271(a,1,1,2))].">
      <j1 rule="para" parents="1859 4271"/>
    </justification>
  </clause>

  <clause id="4273">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(2250(a,2),4271(a,1,1))].">
      <j1 rule="para" parents="2250 4271"/>
    </justification>
  </clause>

  <clause id="4274">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2937(a,1),4271(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2937 4271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4275">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x / (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2951(a,1),4271(a,1,1))].">
      <j1 rule="para" parents="2951 4271"/>
    </justification>
  </clause>

  <clause id="4276">
    <literal><![CDATA[
      K(x * ((y \ 1) \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(2992(a,1),4271(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2992 4271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4277">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(3033(a,1),4271(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3033 4271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4278">
    <literal><![CDATA[
      K(x * (1 / (1 / y)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(3035(a,1),4271(a,1,1))].">
      <j1 rule="para" parents="3035 4271"/>
    </justification>
  </clause>

  <clause id="4280">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(3175(a,1),4271(a,1,1))].">
      <j1 rule="para" parents="3175 4271"/>
    </justification>
  </clause>

  <clause id="4281">
    <literal><![CDATA[
      K((1 / x) * y,z) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(3186(a,1),4271(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3186 4271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4282">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(3203(a,1),4271(a,1,1))].">
      <j1 rule="para" parents="3203 4271"/>
    </justification>
  </clause>

  <clause id="4283">
    <literal><![CDATA[
      K(x \ K(y \ 1,y),z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(3521(a,1),4271(a,1,1))].">
      <j1 rule="para" parents="3521 4271"/>
    </justification>
  </clause>

  <clause id="4284">
    <literal><![CDATA[
      K(x \ (1 / y),z) = K(x \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(3566(a,1),4271(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3566 4271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4285">
    <literal><![CDATA[
      K(x \ ((y \ 1) \ 1),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(3567(a,1),4271(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3567 4271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4286">
    <literal><![CDATA[
      K(x \ ((1 / y) \ z),u) = K(x \ ((y \ 1) \ z),u)
    ]]></literal>
    <justification jstring="[para(3570(a,1),4271(a,1,1))].">
      <j1 rule="para" parents="3570 4271"/>
    </justification>
  </clause>

  <clause id="4287">
    <literal><![CDATA[
      K((K(x,x \ 1) * y) \ z,u) = K(y \ z,u)
    ]]></literal>
    <justification jstring="[para(3897(a,2),4271(a,1,1))].">
      <j1 rule="para" parents="3897 4271"/>
    </justification>
  </clause>

  <clause id="4288">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,u) = K(((x \ 1) * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(3906(a,1),4271(a,1,1))].">
      <j1 rule="para" parents="3906 4271"/>
    </justification>
  </clause>

  <clause id="4289">
    <literal><![CDATA[
      K((x * (K(y,y \ 1) * z)) \ u,w) = K((x * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(3907(a,2),4271(a,1,1))].">
      <j1 rule="para" parents="3907 4271"/>
    </justification>
  </clause>

  <clause id="4290">
    <literal><![CDATA[
      K(((x \ 1) \ 1) * y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(3134(a,1),4272(a,1,1))].">
      <j1 rule="para" parents="3134 4272"/>
    </justification>
  </clause>

  <clause id="4291">
    <literal><![CDATA[
      K(x \ (y * K(z,z \ 1)),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(3533(a,2),4272(a,1,1))].">
      <j1 rule="para" parents="3533 4272"/>
    </justification>
  </clause>

  <clause id="4293">
    <literal><![CDATA[
      K(x \ (y * (1 / z)),u) = K(x \ (y * (z \ 1)),u)
    ]]></literal>
    <justification jstring="[para(3598(a,1),4273(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3598 4273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4294">
    <literal><![CDATA[
      K((x * ((y \ 1) \ 1)) \ z,u) = K((x * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(3895(a,1),4273(a,1,1))].">
      <j1 rule="para" parents="3895 4273"/>
    </justification>
  </clause>

  <clause id="4296">
    <literal><![CDATA[
      K(T(K(x,x \ 1) * y,x),z) = K(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(2680(a,2),4277(a,1,1))].">
      <j1 rule="para" parents="2680 4277"/>
    </justification>
  </clause>

  <clause id="4297">
    <literal><![CDATA[
      K(L(1 / x,y,z) \ u,w) = K(L(x \ 1,y,z) \ u,w)
    ]]></literal>
    <justification jstring="[para(3911(a,1),4277(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3911 4277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4298">
    <literal><![CDATA[
      K(x * T((y * z) \ z,y),u) = K(x * ((y * z) \ z),u)
    ]]></literal>
    <justification jstring="[para(2289(a,2),4276(a,1,1,2))].">
      <j1 rule="para" parents="2289 4276"/>
    </justification>
  </clause>

  <clause id="4299">
    <literal><![CDATA[
      K(x * R(1 / y,z,u),w) = K(x * R(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(3780(a,1),4276(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3780 4276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4301">
    <literal><![CDATA[
      K(x \ ((y \ 1) * y),z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(266(a,1),4283(a,1,1,2))].">
      <j1 rule="para" parents="266 4283"/>
    </justification>
  </clause>

  <clause id="4302">
    <literal><![CDATA[
      K(x \ R(1 / y,z,u),w) = K(x \ R(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(3780(a,1),4285(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3780 4285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4303">
    <literal><![CDATA[
      K((((x \ 1) \ 1) \ y) \ z,u) = K((x \ y) \ z,u)
    ]]></literal>
    <justification jstring="[para(3138(a,1),4287(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3138 4287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4304">
    <literal><![CDATA[
      K(((1 / x) / y) \ z,u) = K(((x \ 1) / y) \ z,u)
    ]]></literal>
    <justification jstring="[para(3832(a,1),4287(a,1,1,1))].">
      <j1 rule="para" parents="3832 4287"/>
    </justification>
  </clause>

  <clause id="4305">
    <literal><![CDATA[
      K((((1 / x) \ y) \ z) \ u,w) = K((((x \ 1) \ y) \ z) \ u,w)
    ]]></literal>
    <justification jstring="[para(3909(a,1),4287(a,1,1,1))].">
      <j1 rule="para" parents="3909 4287"/>
    </justification>
  </clause>

  <clause id="4306">
    <literal><![CDATA[
      K(x \ (y * (((y \ z) \ 1) \ 1)),u) = K(x \ z,u)
    ]]></literal>
    <justification jstring="[para(3310(a,1),4291(a,1,1,2))].">
      <j1 rule="para" parents="3310 4291"/>
    </justification>
  </clause>

  <clause id="4307">
    <literal><![CDATA[
      K(T((1 / x) * y,x),z) = K(T((x \ 1) * y,x),z)
    ]]></literal>
    <justification jstring="[para(3167(a,1),4296(a,1,1,1))].">
      <j1 rule="para" parents="3167 4296"/>
    </justification>
  </clause>

  <clause id="4308">
    <literal><![CDATA[
      K(((x \ 1) * (x * y)) \ z,u) = K(L(y,x,x \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[para(3146(a,1),4288(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3146 4288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4309">
    <literal><![CDATA[
      K((x * ((1 / y) / z)) \ u,w) = K((x * ((y \ 1) / z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(3832(a,1),4289(a,1,1,1,2))].">
      <j1 rule="para" parents="3832 4289"/>
    </justification>
  </clause>

  <clause id="4310">
    <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(3802(a,1),3984(a,1,2))].">
      <j1 rule="para" parents="3802 3984"/>
    </justification>
  </clause>

  <clause id="4311">
    <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(861,a,4268,a)].">
      <j1 rule="hyper" parents="861 4268"/>
    </justification>
  </clause>

  <clause id="4312">
    <literal><![CDATA[
      L(x,y,z * K(u \ 1,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3819,a,4311,a),flip(a)].">
      <j1 rule="hyper" parents="3819 4311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4313">
    <literal><![CDATA[
      L(x,y,z * K(u \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(4311(a,1),3818(a,1)),flip(b)].">
      <j1 rule="para" parents="4311 3818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4315">
    <literal><![CDATA[
      L(x,y,z * K(u,u \ 1)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1859(a,1),4312(a,1,3,2))].">
      <j1 rule="para" parents="1859 4312"/>
    </justification>
  </clause>

  <clause id="4316">
    <literal><![CDATA[
      L(x,y,((z \ 1) \ 1) * u) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(3134(a,1),4315(a,1,3))].">
      <j1 rule="para" parents="3134 4315"/>
    </justification>
  </clause>

  <clause id="4317">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = (u * y) \ (u * (y * x))
    ]]></literal>
    <justification jstring="[para(3581(a,1),4269(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3581 4269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4318">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,13,a,b,4317,a),flip(a)].">
      <j1 rule="hyper" parents="334 13 4317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4320">
    <literal><![CDATA[
      L(x,1 / y,z) = L(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(799(a,1),4318(a,1,2)),flip(a)].">
      <j1 rule="para" parents="799 4318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4321">
    <literal><![CDATA[
      L(x,(y \ 1) \ 1,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1318(a,1),4318(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1318 4318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4322">
    <literal><![CDATA[
      L(x,1 / (1 / y),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1853(a,1),4318(a,1,2))].">
      <j1 rule="para" parents="1853 4318"/>
    </justification>
  </clause>

  <clause id="4323">
    <literal><![CDATA[
      L(x,K(y \ 1,y) * z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(2250(a,2),4318(a,1,2))].">
      <j1 rule="para" parents="2250 4318"/>
    </justification>
  </clause>

  <clause id="4324">
    <literal><![CDATA[
      L(x,y * (1 / z),u) = L(x,y * (z \ 1),u)
    ]]></literal>
    <justification jstring="[para(2937(a,1),4318(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2937 4318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4325">
    <literal><![CDATA[
      L(x,y / T(1 / z,u),w) = L(x,y / T(z \ 1,u),w)
    ]]></literal>
    <justification jstring="[para(3991(a,1),4318(a,1,2))].">
      <j1 rule="para" parents="3991 4318"/>
    </justification>
  </clause>

  <clause id="4328">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * L(z,y,x) = x * ((1 / (1 / y)) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4322,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 4322 13"/>
    </justification>
  </clause>

  <clause id="4329">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * z != x * ((1 / (1 / y)) * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,y,x) = z
    ]]></literal>
    <justification jstring="[para(4328(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="4328 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4330">
    <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,3914,a(flip),b,4310,a)].">
      <j1 rule="hyper" parents="58 3914 4310"/>
    </justification>
  </clause>

  <clause id="4331">
    <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(4004(a,1),4330(a,1,2))].">
      <j1 rule="para" parents="4004 4330"/>
    </justification>
  </clause>

  <clause id="4332">
    <literal><![CDATA[
      R(x,y * K(z \ 1,z),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(4009,a,4331,a),flip(a)].">
      <j1 rule="hyper" parents="4009 4331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4334">
    <literal><![CDATA[
      R(x,1 / y,z) = R(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(799(a,1),4332(a,1,2)),flip(a)].">
      <j1 rule="para" parents="799 4332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4335">
    <literal><![CDATA[
      R(x,(y \ 1) \ 1,z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1318(a,1),4332(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1318 4332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4337">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(4334(a,1),3947(a,1,2))].">
      <j1 rule="para" parents="4334 3947"/>
    </justification>
  </clause>

  <clause id="4338">
    <literal><![CDATA[
      R(x,y,z) * (((y \ 1) \ 1) * z) = (x * ((y \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(4335(a,1),101(a,1,1))].">
      <j1 rule="para" parents="4335 101"/>
    </justification>
  </clause>

  <clause id="4339">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * z != u * (((y \ 1) \ 1) * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4338(a,1),39(a,1))].">
      <j1 rule="para" parents="4338 39"/>
    </justification>
  </clause>

  <clause id="4340">
    <literal><![CDATA[
      1 / R(T(x,(x \ 1) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(3191(a,1),4337(a,1,2,1))].">
      <j1 rule="para" parents="3191 4337"/>
    </justification>
  </clause>

  <clause id="4341">
    <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(3411(a,1),3998(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3411 3998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4342">
    <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(3802(a,1),3861(a,1,2,1))].">
      <j1 rule="para" parents="3802 3861"/>
    </justification>
  </clause>

  <clause id="4343">
    <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(3884(a,1),3985(a,1,1,2))].">
      <j1 rule="para" parents="3884 3985"/>
    </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(3801(a,1),4342(a,1,2))].">
      <j1 rule="para" parents="3801 4342"/>
    </justification>
  </clause>

  <clause id="4345">
    <literal><![CDATA[
      a(x,y * K(z,z \ 1),u) = a(x,y,K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(709,a,4343,a),flip(a)].">
      <j1 rule="hyper" parents="709 4343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4346">
    <literal><![CDATA[
      a(x,y * K(z,z \ 1),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,3845,a(flip),b,4345,a),flip(a)].">
      <j1 rule="hyper" parents="334 3845 4345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4347">
    <literal><![CDATA[
      a(x,y * K(z,z \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(4345(a,2),4019(a,1))].">
      <j1 rule="para" parents="4345 4019"/>
    </justification>
  </clause>

  <clause id="4349">
    <literal><![CDATA[
      a(x,1 / y,z) = a(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(1860(a,1),4346(a,1,2))].">
      <j1 rule="para" parents="1860 4346"/>
    </justification>
  </clause>

  <clause id="4350">
    <literal><![CDATA[
      a(x,(y \ 1) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1902(a,1),4347(a,1,2))].">
      <j1 rule="para" parents="1902 4347"/>
    </justification>
  </clause>

  <clause id="4351">
    <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(863,a,4344,a)].">
      <j1 rule="hyper" parents="863 4344"/>
    </justification>
  </clause>

  <clause id="4352">
    <literal><![CDATA[
      a(x * K(y \ 1,y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(3819,a,4351,a),flip(a)].">
      <j1 rule="hyper" parents="3819 4351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4354">
    <literal><![CDATA[
      a(1 / x,y,z) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(799(a,1),4352(a,1,1)),flip(a)].">
      <j1 rule="para" parents="799 4352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4355">
    <literal><![CDATA[
      a((x \ 1) \ 1,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(1318(a,1),4352(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1318 4352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4356">
    <literal><![CDATA[
      a((1 / x) \ y,z,u) = a((x \ 1) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(3203(a,1),4352(a,1,1))].">
      <j1 rule="para" parents="3203 4352"/>
    </justification>
  </clause>

  <clause id="4357">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x = a(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3162,a,b,4354,a)].">
      <j1 rule="hyper" parents="58 3162 4354"/>
    </justification>
  </clause>

  <clause id="4358">
    <literal><![CDATA[
      L(x,y,y \ 1) * a(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,4354,a(flip),b,3162,a)].">
      <j1 rule="hyper" parents="119 4354 3162"/>
    </justification>
  </clause>

  <clause id="4359">
    <literal><![CDATA[
      L(x,y,y \ 1) \ 1 = x \ a(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4357,a(flip),b,1510,a),flip(a)].">
      <j1 rule="hyper" parents="116 4357 1510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4360">
    <literal><![CDATA[
      a(x \ 1,x,y) * L(y,x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(4357(a,1),3959(a,1,1))].">
      <j1 rule="para" parents="4357 3959"/>
    </justification>
  </clause>

  <clause id="4361">
    <literal><![CDATA[
      a(x \ 1,x,y) \ y = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(4357(a,1),3960(a,1,1))].">
      <j1 rule="para" parents="4357 3960"/>
    </justification>
  </clause>

  <clause id="4362">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x != z
    ]]></literal>
    <literal><![CDATA[
      a(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(4358(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4358 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4363">
    <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(4358(a,1),90(a,1,1))].">
      <j1 rule="para" parents="4358 90"/>
    </justification>
  </clause>

  <clause id="4364">
    <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,1505,a,b,4363,a)].">
      <j1 rule="hyper" parents="29 1505 4363"/>
    </justification>
  </clause>

  <clause id="4365">
    <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),4364(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 4364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4366">
    <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(2414(a,1),4074(a,1,1))].">
      <j1 rule="para" parents="2414 4074"/>
    </justification>
  </clause>

  <clause id="4367">
    <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),4366(a,1,1,1,2))].">
      <j1 rule="para" parents="105 4366"/>
    </justification>
  </clause>

  <clause id="4368">
    <literal><![CDATA[
      ((x * ((y \ T(z,x)) * y)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(4064(a,1),4367(a,1,2))].">
      <j1 rule="para" parents="4064 4367"/>
    </justification>
  </clause>

  <clause id="4369">
    <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),4236(a,1,2,1))].">
      <j1 rule="para" parents="7 4236"/>
    </justification>
  </clause>

  <clause id="4370">
    <literal><![CDATA[
      (x * K((y / x) \ 1,y / x)) * (x \ 1) = K((y * (x \ 1)) \ 1,y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(1319,a,4369,a),flip(a)].">
      <j1 rule="hyper" parents="1319 4369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4372">
    <literal><![CDATA[
      (x * ((y / (z * (u \ y))) / x)) * (z * (u \ y)) = ((x * ((u / z) / x)) * z) * (u \ y)
    ]]></literal>
    <justification jstring="[hyper(293,a,4043,a),flip(a)].">
      <j1 rule="hyper" parents="293 4043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4373">
    <literal><![CDATA[
      ((x * ((x / y) / x)) * y) * (x \ z) = x * ((x \ T(x,y \ 1)) * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,4168,a(flip),b,4372,a),flip(a)].">
      <j1 rule="hyper" parents="58 4168 4372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4374">
    <literal><![CDATA[
      x * ((x \ T(x,y \ 1)) * (x \ z)) = T(x,y \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[para(4090(a,1),4373(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4090 4373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4375">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) * (x \ z) = x * ((x \ T(x,y)) * (x \ z))
    ]]></literal>
    <justification jstring="[para(3106(a,1),4374(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3106 4374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4376">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * (x \ z)) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(3106(a,1),4375(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3106 4375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4377">
    <literal><![CDATA[
      T(x,y) * (x \ (x * z)) = x * ((x \ T(x,y)) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),4376(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 4376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4378">
    <literal><![CDATA[
      (T(x,y) * z) / ((x \ T(x,y)) * z) = x
    ]]></literal>
    <justification jstring="[hyper(633,a,4377,a)].">
      <j1 rule="hyper" parents="633 4377"/>
    </justification>
  </clause>

  <clause id="4379">
    <literal><![CDATA[
      x \ (T(x,y) * z) = (x \ T(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(631,a,4377,a)].">
      <j1 rule="hyper" parents="631 4377"/>
    </justification>
  </clause>

  <clause id="4380">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(597,a,4377,a),flip(a)].">
      <j1 rule="hyper" parents="597 4377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4381">
    <literal><![CDATA[
      (x \ T(x,y)) * z = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(1179,a,4378,a),flip(a)].">
      <j1 rule="hyper" parents="1179 4378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4382">
    <literal><![CDATA[
      R(x,x \ T(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(785,a,4378,a)].">
      <j1 rule="hyper" parents="785 4378"/>
    </justification>
  </clause>

  <clause id="4383">
    <literal><![CDATA[
      R(x,T(y,x) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(4057(a,2),4382(a,1,2))].">
      <j1 rule="para" parents="4057 4382"/>
    </justification>
  </clause>

  <clause id="4384">
    <literal><![CDATA[
      R(x,K(y,x) \ 1,z) = x
    ]]></literal>
    <justification jstring="[para(2823(a,1),4383(a,1,2))].">
      <j1 rule="para" parents="2823 4383"/>
    </justification>
  </clause>

  <clause id="4386">
    <literal><![CDATA[
      L(x,y \ T(y,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(777,a,4379,a),flip(a)].">
      <j1 rule="hyper" parents="777 4379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4387">
    <literal><![CDATA[
      (x \ T(x,y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(4379(a,1),1181(a,1))].">
      <j1 rule="para" parents="4379 1181"/>
    </justification>
  </clause>

  <clause id="4391">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,4386,a(flip),b,2755,a)].">
      <j1 rule="hyper" parents="116 4386 2755"/>
    </justification>
  </clause>

  <clause id="4393">
    <literal><![CDATA[
      L(x,T(y,T(z,y)) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(4065(a,2),4386(a,1,2))].">
      <j1 rule="para" parents="4065 4386"/>
    </justification>
  </clause>

  <clause id="4394">
    <literal><![CDATA[
      L(x,T(y,z) \ y,(y * z) / y) = x
    ]]></literal>
    <justification jstring="[para(230(a,1),4393(a,1,2,1,2))].">
      <j1 rule="para" parents="230 4393"/>
    </justification>
  </clause>

  <clause id="4395">
    <literal><![CDATA[
      x \ ((T(y,x) \ y) * z) = ((y * x) / y) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,4394,a(flip),b,4233,a),flip(a)].">
      <j1 rule="hyper" parents="116 4394 4233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4397">
    <literal><![CDATA[
      (x \ T(x,y)) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(29,a,1153,a(flip),b,4380,a),flip(a)].">
      <j1 rule="hyper" parents="29 1153 4380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4400">
    <literal><![CDATA[
      (x \ T(x,x \ y)) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(334,a,4134,a(flip),b,4381,a),flip(a)].">
      <j1 rule="hyper" parents="334 4134 4381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4401">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,152,a(flip),b,4381,a)].">
      <j1 rule="hyper" parents="117 152 4381"/>
    </justification>
  </clause>

  <clause id="4402">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(116,a,152,a(flip),b,4381,a)].">
      <j1 rule="hyper" parents="116 152 4381"/>
    </justification>
  </clause>

  <clause id="4403">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(4391(a,2),597(a,1))].">
      <j1 rule="para" parents="4391 597"/>
    </justification>
  </clause>

  <clause id="4404">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(4391(a,2),1191(a,1))].">
      <j1 rule="para" parents="4391 1191"/>
    </justification>
  </clause>

  <clause id="4407">
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2598,a,4401,a)].">
      <j1 rule="hyper" parents="2598 4401"/>
    </justification>
  </clause>

  <clause id="4408">
    <literal><![CDATA[
      R(K(x,y),x,z) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4401(a,1),4219(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4401 4219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4410">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = (y / x) \ T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,2650,a(flip),b,4407,a)].">
      <j1 rule="hyper" parents="58 2650 4407"/>
    </justification>
  </clause>

  <clause id="4411">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(134,a,4395,a)].">
      <j1 rule="hyper" parents="134 4395"/>
    </justification>
  </clause>

  <clause id="4412">
    <literal><![CDATA[
      (T(x,y) \ x) * (x * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(119,a,75,a(flip),b,4395,a),flip(a)].">
      <j1 rule="hyper" parents="119 75 4395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4413">
    <literal><![CDATA[
      x \ (y * (T(y,x) \ y)) = ((y * x) / y) \ y
    ]]></literal>
    <justification jstring="[para(2516(a,1),4395(a,1,2))].">
      <j1 rule="para" parents="2516 4395"/>
    </justification>
  </clause>

  <clause id="4414">
    <literal><![CDATA[
      K(x,y) = T(T(y,x) \ y,y * x)
    ]]></literal>
    <justification jstring="[hyper(246,a,4412,a,b,84,a),flip(a)].">
      <j1 rule="hyper" parents="246 4412 84"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4415">
    <literal><![CDATA[
      (x * y) / (y * x) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(130,a,4412,a)].">
      <j1 rule="hyper" parents="130 4412"/>
    </justification>
  </clause>

  <clause id="4416">
    <literal><![CDATA[
      T(x,y * z) != K(z,y)
    ]]></literal>
    <literal><![CDATA[
      T(y,z) \ y = x
    ]]></literal>
    <justification jstring="[para(4414(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="4414 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4417">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4215,a,4415,a(flip))].">
      <j1 rule="hyper" parents="4215 4415"/>
    </justification>
  </clause>

  <clause id="4418">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = (y * (x / y)) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),4415(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 4415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4419">
    <literal><![CDATA[
      T(x,y / x) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y / (x * (y / x)) = z
    ]]></literal>
    <justification jstring="[para(4415(a,1),589(a,1))].">
      <j1 rule="para" parents="4415 589"/>
    </justification>
  </clause>

  <clause id="4420">
    <literal><![CDATA[
      T(x,T((x \ 1) * y,x)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(2043(a,1),4417(a,1,2))].">
      <j1 rule="para" parents="2043 4417"/>
    </justification>
  </clause>

  <clause id="4421">
    <literal><![CDATA[
      (((1 / x) * (y * x)) \ (y * x)) \ 1 = 1 / R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(4417(a,1),4340(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4417 4340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4422">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,4071,a,b,4411,a)].">
      <j1 rule="hyper" parents="58 4071 4411"/>
    </justification>
  </clause>

  <clause id="4423">
    <literal><![CDATA[
      x * K(((x * y) / x) \ x,y) = (x * ((y \ x) * y)) / x
    ]]></literal>
    <justification jstring="[para(4413(a,1),4232(a,1,2,1))].">
      <j1 rule="para" parents="4413 4232"/>
    </justification>
  </clause>

  <clause id="4424">
    <literal><![CDATA[
      (x * (y / x)) / y = (x \ y) \ (y / x)
    ]]></literal>
    <justification jstring="[para(107(a,1),4418(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 4418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4425">
    <literal><![CDATA[
      (x * (y / x)) / y = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,4099,a(flip),b,4424,a),flip(a)].">
      <j1 rule="hyper" parents="334 4099 4424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4426">
    <literal><![CDATA[
      (x \ (y \ x)) \ (y \ x) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4193,a,4425,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="4193 4425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4427">
    <literal><![CDATA[
      T(x,x \ (y \ x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(367,a,4426,a)].">
      <j1 rule="hyper" parents="367 4426"/>
    </justification>
  </clause>

  <clause id="4428">
    <literal><![CDATA[
      (x \ y) / T(y,x \ 1) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(201,a,4426,a)].">
      <j1 rule="hyper" parents="201 4426"/>
    </justification>
  </clause>

  <clause id="4429">
    <literal><![CDATA[
      (x \ (y \ x)) * T(x,y \ 1) = y \ x
    ]]></literal>
    <justification jstring="[hyper(134,a,4426,a)].">
      <j1 rule="hyper" parents="134 4426"/>
    </justification>
  </clause>

  <clause id="4430">
    <literal><![CDATA[
      T(x * y,(x * y) \ y) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),4427(a,1,2,2))].">
      <j1 rule="para" parents="4 4427"/>
    </justification>
  </clause>

  <clause id="4431">
    <literal><![CDATA[
      T(x,(x / y) \ 1) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(75(a,1),4427(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 4427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4432">
    <literal><![CDATA[
      x \ ((y \ x) / ((y \ x) / x)) = T(x,y \ 1) \ x
    ]]></literal>
    <justification jstring="[para(4427(a,1),4161(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4427 4161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4433">
    <literal><![CDATA[
      T(x,y \ 1) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[para(4427(a,1),4151(a,1,1))].">
      <j1 rule="para" parents="4427 4151"/>
    </justification>
  </clause>

  <clause id="4434">
    <literal><![CDATA[
      (x / y) \ T(x,x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4431(a,1),4139(a,1,2))].">
      <j1 rule="para" parents="4431 4139"/>
    </justification>
  </clause>

  <clause id="4435">
    <literal><![CDATA[
      ((x \ 1) \ y) / T(y,x) = y \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(3106(a,1),4428(a,1,2))].">
      <j1 rule="para" parents="3106 4428"/>
    </justification>
  </clause>

  <clause id="4436">
    <literal><![CDATA[
      ((x * y) \ (y \ (x * y))) * T(x * y,y \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,17,a,b,4429,a),flip(a)].">
      <j1 rule="hyper" parents="334 17 4429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4437">
    <literal><![CDATA[
      (x \ ((1 / y) \ x)) * T(x,y) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[para(75(a,1),4429(a,1,2,2))].">
      <j1 rule="para" parents="75 4429"/>
    </justification>
  </clause>

  <clause id="4438">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,x \ (y * x)) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),4434(a,2,2))].">
      <j1 rule="para" parents="6 4434"/>
    </justification>
  </clause>

  <clause id="4439">
    <literal><![CDATA[
      T(x * y,x \ 1) = ((x * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(439,a,4430,a),flip(a)].">
      <j1 rule="hyper" parents="439 4430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4440">
    <literal><![CDATA[
      T((x \ 1) * y,x) = (((x \ 1) * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(3119,a,4439,a)].">
      <j1 rule="hyper" parents="3119 4439"/>
    </justification>
  </clause>

  <clause id="4441">
    <literal><![CDATA[
      x * ((x * y) * (y / (x * y))) = ((x * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,4085,a,b,4439,a)].">
      <j1 rule="hyper" parents="58 4085 4439"/>
    </justification>
  </clause>

  <clause id="4442">
    <literal><![CDATA[
      (x \ 1) * (((x * y) \ y) \ y) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,4439,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4439 17"/>
    </justification>
  </clause>

  <clause id="4443">
    <literal><![CDATA[
      T((1 / x) * y,x) = (((1 / x) * y) \ y) \ y
    ]]></literal>
    <justification jstring="[para(75(a,1),4439(a,1,2))].">
      <j1 rule="para" parents="75 4439"/>
    </justification>
  </clause>

  <clause id="4444">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,T(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(17(a,2),4438(a,1,2,2))].">
      <j1 rule="para" parents="17 4438"/>
    </justification>
  </clause>

  <clause id="4445">
    <literal><![CDATA[
      (x \ T(x,y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(5(a,1),4403(a,1,2))].">
      <j1 rule="para" parents="5 4403"/>
    </justification>
  </clause>

  <clause id="4446">
    <literal><![CDATA[
      R(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,4153,a,b,4408,a),flip(a)].">
      <j1 rule="hyper" parents="334 4153 4408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4447">
    <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(4408(a,1),396(a,1)),flip(b)].">
      <j1 rule="para" parents="4408 396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4449">
    <literal><![CDATA[
      (K(x,y) * x) * z = K(x,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(4446(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4446 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4450">
    <literal><![CDATA[
      L(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(493,a,4449,a)].">
      <j1 rule="hyper" parents="493 4449"/>
    </justification>
  </clause>

  <clause id="4454">
    <literal><![CDATA[
      L(x,y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(4450(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="4450 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4455">
    <literal><![CDATA[
      L(x,y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(4450(a,1),45(a,2))].">
      <j1 rule="para" parents="4450 45"/>
    </justification>
  </clause>

  <clause id="4457">
    <literal><![CDATA[
      ((x \ y) / y) \ T((x \ y) / y,z) = x * T(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(1359,a,4410,a),flip(a)].">
      <j1 rule="hyper" parents="1359 4410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4459">
    <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(3151(a,1),4433(a,2,2))].">
      <j1 rule="para" parents="3151 4433"/>
    </justification>
  </clause>

  <clause id="4460">
    <literal><![CDATA[
      K(T(x,T(y,x)),T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4154(a,1),4447(a,1))].">
      <j1 rule="para" parents="4154 4447"/>
    </justification>
  </clause>

  <clause id="4461">
    <literal><![CDATA[
      R(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(4408(a,2),4447(a,1))].">
      <j1 rule="para" parents="4408 4447"/>
    </justification>
  </clause>

  <clause id="4462">
    <literal><![CDATA[
      ((x * y) \ T(x,y)) * T(x * y,y \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(17(a,2),4436(a,1,1,2))].">
      <j1 rule="para" parents="17 4436"/>
    </justification>
  </clause>

  <clause id="4463">
    <literal><![CDATA[
      x \ ((y \ x) / ((y \ x) / x)) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4058,a(flip),b,4457,a)].">
      <j1 rule="hyper" parents="58 4058 4457"/>
    </justification>
  </clause>

  <clause id="4464">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = (y * T(y \ 1,x)) \ x
    ]]></literal>
    <justification jstring="[para(4457(a,1),4077(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4457 4077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4465">
    <literal><![CDATA[
      T(x,y \ 1) \ x = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4432,a(flip),b,4463,a)].">
      <j1 rule="hyper" parents="58 4432 4463"/>
    </justification>
  </clause>

  <clause id="4466">
    <literal><![CDATA[
      K(x \ (x / y),x) = T(x,y \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(334,a,1063,a,b,4465,a)].">
      <j1 rule="hyper" parents="334 1063 4465"/>
    </justification>
  </clause>

  <clause id="4467">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,1029,a(flip),b,4465,a),flip(a)].">
      <j1 rule="hyper" parents="334 1029 4465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4468">
    <literal><![CDATA[
      K(x \ (x / y),x) \ x = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2730,a,4466,a)].">
      <j1 rule="hyper" parents="2730 4466"/>
    </justification>
  </clause>

  <clause id="4469">
    <literal><![CDATA[
      K(x \ (x / y),x) != z \ x
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(4466(a,2),43(a,1))].">
      <j1 rule="para" parents="4466 43"/>
    </justification>
  </clause>

  <clause id="4470">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(3106(a,1),4467(a,1,1))].">
      <j1 rule="para" parents="3106 4467"/>
    </justification>
  </clause>

  <clause id="4471">
    <literal><![CDATA[
      T(x,y / x) \ x = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(334,a,4058,a(flip),b,4470,a),flip(a)].">
      <j1 rule="hyper" parents="334 4058 4470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4472">
    <literal><![CDATA[
      (x * y) / x = y * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4470,a,b,4055,a),flip(a)].">
      <j1 rule="hyper" parents="119 4470 4055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4473">
    <literal><![CDATA[
      T(x,T(y,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,4065,a,b,4470,a)].">
      <j1 rule="hyper" parents="34 4065 4470"/>
    </justification>
  </clause>

  <clause id="4474">
    <literal><![CDATA[
      x * ((T(y,x) \ y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(4470(a,2),4380(a,1,2,1))].">
      <j1 rule="para" parents="4470 4380"/>
    </justification>
  </clause>

  <clause id="4475">
    <literal><![CDATA[
      T(x,y) * (x \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[para(4470(a,2),4381(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4470 4381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4476">
    <literal><![CDATA[
      K(x,y) = T(x \ T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(4470(a,1),4414(a,2,1))].">
      <j1 rule="para" parents="4470 4414"/>
    </justification>
  </clause>

  <clause id="4477">
    <literal><![CDATA[
      (T(x,y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) * (y \ z) = u
    ]]></literal>
    <justification jstring="[para(4470(a,2),4387(a,1,1))].">
      <j1 rule="para" parents="4470 4387"/>
    </justification>
  </clause>

  <clause id="4478">
    <literal><![CDATA[
      T(x / T(y,x),y) = y \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4132,a,4473,a)].">
      <j1 rule="hyper" parents="4132 4473"/>
    </justification>
  </clause>

  <clause id="4479">
    <literal><![CDATA[
      x * (T(x,y) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(1226,a,4473,a)].">
      <j1 rule="hyper" parents="1226 4473"/>
    </justification>
  </clause>

  <clause id="4480">
    <literal><![CDATA[
      T(x \ y,x) = ((x \ y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(615,a,4473,a),flip(a)].">
      <j1 rule="hyper" parents="615 4473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4481">
    <literal><![CDATA[
      T((T(x,y) * y) / T(x,y),x) = y
    ]]></literal>
    <justification jstring="[hyper(473,a,4473,a)].">
      <j1 rule="hyper" parents="473 4473"/>
    </justification>
  </clause>

  <clause id="4482">
    <literal><![CDATA[
      T(x,y) \ (x * y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(440,a,4473,a)].">
      <j1 rule="hyper" parents="440 4473"/>
    </justification>
  </clause>

  <clause id="4483">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4158,a,b,4473,a)].">
      <j1 rule="hyper" parents="58 4158 4473"/>
    </justification>
  </clause>

  <clause id="4484">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4114,a,b,4473,a)].">
      <j1 rule="hyper" parents="58 4114 4473"/>
    </justification>
  </clause>

  <clause id="4486">
    <literal><![CDATA[
      T(x,(x \ 1) * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4420,a(flip),b,4473,a),flip(a)].">
      <j1 rule="hyper" parents="58 4420 4473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4487">
    <literal><![CDATA[
      T(x,y) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(119,a,4473,a(flip),b,242,a)].">
      <j1 rule="hyper" parents="119 4473 242"/>
    </justification>
  </clause>

  <clause id="4488">
    <literal><![CDATA[
      T(x,y) / y = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,4473,a(flip),b,4114,a)].">
      <j1 rule="hyper" parents="117 4473 4114"/>
    </justification>
  </clause>

  <clause id="4489">
    <literal><![CDATA[
      T(x,y) / (T(y,x) \ x) = y
    ]]></literal>
    <justification jstring="[hyper(117,a,4473,a(flip),b,1182,a)].">
      <j1 rule="hyper" parents="117 4473 1182"/>
    </justification>
  </clause>

  <clause id="4490">
    <literal><![CDATA[
      T(x,y) \ y = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4473,a(flip),b,1182,a),flip(a)].">
      <j1 rule="hyper" parents="116 4473 1182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4491">
    <literal><![CDATA[
      T(T(x,y),T(z,x)) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(4473(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4473 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4492">
    <literal><![CDATA[
      T(x,T(T(y,x),z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(18(a,1),4473(a,1,2))].">
      <j1 rule="para" parents="18 4473"/>
    </justification>
  </clause>

  <clause id="4493">
    <literal><![CDATA[
      T(L(x,y,z),T(u,x)) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(4473(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4473 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4494">
    <literal><![CDATA[
      T(x,L(T(y,x),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(20(a,2),4473(a,1,2))].">
      <j1 rule="para" parents="20 4473"/>
    </justification>
  </clause>

  <clause id="4495">
    <literal><![CDATA[
      T(x,y / x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),4473(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 4473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4496">
    <literal><![CDATA[
      T(x,y) * T(T(y,x),z) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4473(a,1),243(a,1,2,1))].">
      <j1 rule="para" parents="4473 243"/>
    </justification>
  </clause>

  <clause id="4498">
    <literal><![CDATA[
      (x * y) / T(y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4473(a,1),275(a,1,2))].">
      <j1 rule="para" parents="4473 275"/>
    </justification>
  </clause>

  <clause id="4499">
    <literal><![CDATA[
      T(x,y) * L(T(y,x),z,u) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4473(a,1),244(a,1,2,1))].">
      <j1 rule="para" parents="4473 244"/>
    </justification>
  </clause>

  <clause id="4500">
    <literal><![CDATA[
      T(x,y) * R(T(y,x),z,u) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4473(a,1),245(a,1,2,1))].">
      <j1 rule="para" parents="4473 245"/>
    </justification>
  </clause>

  <clause id="4501">
    <literal><![CDATA[
      T(x,T(y,y * x)) = T(x,L(y,x,y))
    ]]></literal>
    <justification jstring="[para(735(a,1),4473(a,1,2))].">
      <j1 rule="para" parents="735 4473"/>
    </justification>
  </clause>

  <clause id="4502">
    <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(4473(a,1),428(a,1,2,1))].">
      <j1 rule="para" parents="4473 428"/>
    </justification>
  </clause>

  <clause id="4503">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,T(z,y)) = T(K(x,x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(3921(a,1),4473(a,1,2))].">
      <j1 rule="para" parents="3921 4473"/>
    </justification>
  </clause>

  <clause id="4504">
    <literal><![CDATA[
      T(x * (T(x,y) \ x),y) = x
    ]]></literal>
    <justification jstring="[para(4473(a,1),4101(a,1,1,2,1))].">
      <j1 rule="para" parents="4473 4101"/>
    </justification>
  </clause>

  <clause id="4505">
    <literal><![CDATA[
      T(x,y) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(4473(a,1),4120(a,1,1))].">
      <j1 rule="para" parents="4473 4120"/>
    </justification>
  </clause>

  <clause id="4506">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y \ T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4473(a,1),4080(a,1,1))].">
      <j1 rule="para" parents="4473 4080"/>
    </justification>
  </clause>

  <clause id="4507">
    <literal><![CDATA[
      K(T(x,y),T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4473(a,1),4157(a,1,1))].">
      <j1 rule="para" parents="4473 4157"/>
    </justification>
  </clause>

  <clause id="4508">
    <literal><![CDATA[
      x * (x * T(T(x,y) \ ((y * x) / x),z)) = (x * T(x \ y,z)) * x
    ]]></literal>
    <justification jstring="[para(4473(a,1),4230(a,1,2,2,1,1))].">
      <j1 rule="para" parents="4473 4230"/>
    </justification>
  </clause>

  <clause id="4509">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,y) = x * y
    ]]></literal>
    <justification jstring="[para(4473(a,1),4444(a,1,2))].">
      <j1 rule="para" parents="4473 4444"/>
    </justification>
  </clause>

  <clause id="4511">
    <literal><![CDATA[
      T(x,y) * (x \ T(y,x)) = y
    ]]></literal>
    <justification jstring="[para(4479(a,1),67(a,1,2,2))].">
      <j1 rule="para" parents="4479 67"/>
    </justification>
  </clause>

  <clause id="4513">
    <literal><![CDATA[
      T(x,y) = (x \ (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(17(a,1),4482(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17 4482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4514">
    <literal><![CDATA[
      T(x,y) / T(y,x) = x / T(T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(117,a,4473,a(flip),b,4484,a)].">
      <j1 rule="hyper" parents="117 4473 4484"/>
    </justification>
  </clause>

  <clause id="4515">
    <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(4484(a,1),619(a,1,2))].">
      <j1 rule="para" parents="4484 619"/>
    </justification>
  </clause>

  <clause id="4516">
    <literal><![CDATA[
      T(T(x,y),T(y,x)) = T(y,x) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(451,a,xx,b,4487,a)].">
      <j1 rule="hyper" parents="451 4487"/>
    </justification>
  </clause>

  <clause id="4517">
    <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,4487,a(flip),b,187,a)].">
      <j1 rule="hyper" parents="119 4487 187"/>
    </justification>
  </clause>

  <clause id="4518">
    <literal><![CDATA[
      (T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4487(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4487 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4519">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * (T(y,x) * z)) = L(z,T(y,x),T(x,y))
    ]]></literal>
    <justification jstring="[para(4487(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4487 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4520">
    <literal><![CDATA[
      (x * (y * z)) * a(x,T(y,z),T(z,y)) = (x * T(y,z)) * T(z,y)
    ]]></literal>
    <justification jstring="[para(4487(a,1),80(a,1,1,2))].">
      <j1 rule="para" parents="4487 80"/>
    </justification>
  </clause>

  <clause id="4521">
    <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(4487(a,1),530(a,1,1,1))].">
      <j1 rule="para" parents="4487 530"/>
    </justification>
  </clause>

  <clause id="4522">
    <literal><![CDATA[
      (T(x,y) / y) \ x = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(118,a,4488,a,b,154,a)].">
      <j1 rule="hyper" parents="118 4488 154"/>
    </justification>
  </clause>

  <clause id="4523">
    <literal><![CDATA[
      (T(x,y) / y) * z = (x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[hyper(52,a,4488,a)].">
      <j1 rule="hyper" parents="52 4488"/>
    </justification>
  </clause>

  <clause id="4524">
    <literal><![CDATA[
      T(x * (y / x),x) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,4488,a(flip),b,1440,a),flip(a)].">
      <j1 rule="hyper" parents="119 4488 1440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4525">
    <literal><![CDATA[
      T(x,T(y,z)) / (T(T(y,x),z) \ x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(18(a,1),4489(a,1,2,1))].">
      <j1 rule="para" parents="18 4489"/>
    </justification>
  </clause>

  <clause id="4526">
    <literal><![CDATA[
      (T(x,y) \ y) * z = (x \ T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(4489(a,1),198(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4489 198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4527">
    <literal><![CDATA[
      (x \ T(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      (T(x,y) \ y) * z = u
    ]]></literal>
    <justification jstring="[para(4489(a,1),638(a,1,1,1))].">
      <j1 rule="para" parents="4489 638"/>
    </justification>
  </clause>

  <clause id="4528">
    <literal><![CDATA[
      (T(x,y) \ y) \ z = (x \ T(y,x)) \ z
    ]]></literal>
    <justification jstring="[hyper(56,a,4490,a)].">
      <j1 rule="hyper" parents="56 4490"/>
    </justification>
  </clause>

  <clause id="4529">
    <literal><![CDATA[
      T(x,y) \ ((T(y,x) \ x) * y) = K(y \ T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4490(a,2),85(a,1,2,1))].">
      <j1 rule="para" parents="4490 85"/>
    </justification>
  </clause>

  <clause id="4530">
    <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(4490(a,1),81(a,1,1,2,1))].">
      <j1 rule="para" parents="4490 81"/>
    </justification>
  </clause>

  <clause id="4531">
    <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(4490(a,1),2116(a,1,2,1))].">
      <j1 rule="para" parents="4490 2116"/>
    </justification>
  </clause>

  <clause id="4532">
    <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(4490(a,1),2196(a,1,2,1))].">
      <j1 rule="para" parents="4490 2196"/>
    </justification>
  </clause>

  <clause id="4533">
    <literal><![CDATA[
      T(x,y / x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(334,a,106,a(flip),b,4495,a),flip(a)].">
      <j1 rule="hyper" parents="334 106 4495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4534">
    <literal><![CDATA[
      (x / y) * T(y,y \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4495,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4495 17"/>
    </justification>
  </clause>

  <clause id="4535">
    <literal><![CDATA[
      x / T(y,x / y) = y \ x
    ]]></literal>
    <justification jstring="[para(4495(a,2),273(a,1,2))].">
      <j1 rule="para" parents="4495 273"/>
    </justification>
  </clause>

  <clause id="4536">
    <literal><![CDATA[
      T(x,y / x) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(4495(a,2),439(a,1))].">
      <j1 rule="para" parents="4495 439"/>
    </justification>
  </clause>

  <clause id="4538">
    <literal><![CDATA[
      (x * (y / x)) * x = y * T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4495(a,1),940(a,2,2))].">
      <j1 rule="para" parents="4495 940"/>
    </justification>
  </clause>

  <clause id="4539">
    <literal><![CDATA[
      (x * y) \ (y * T(x,x \ y)) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[para(4495(a,1),946(a,1,2,2))].">
      <j1 rule="para" parents="4495 946"/>
    </justification>
  </clause>

  <clause id="4540">
    <literal><![CDATA[
      T(x,T(y,x / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4495(a,2),4122(a,1,2))].">
      <j1 rule="para" parents="4495 4122"/>
    </justification>
  </clause>

  <clause id="4541">
    <literal><![CDATA[
      x \ (T(x,y / x) / (1 / (x \ y))) = (x / (1 / (x \ y))) / x
    ]]></literal>
    <justification jstring="[para(4495(a,2),4177(a,1,2,1))].">
      <j1 rule="para" parents="4495 4177"/>
    </justification>
  </clause>

  <clause id="4542">
    <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),4498(a,1,2))].">
      <j1 rule="para" parents="22 4498"/>
    </justification>
  </clause>

  <clause id="4543">
    <literal><![CDATA[
      (T(x,y) * (y * x)) / T(x,y) = T(y,x) * T(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(4498(a,1),840(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4498 840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4544">
    <literal><![CDATA[
      T(x / (x / y),y \ x) = y
    ]]></literal>
    <justification jstring="[para(4162(a,2),4504(a,1,1))].">
      <j1 rule="para" parents="4162 4504"/>
    </justification>
  </clause>

  <clause id="4545">
    <literal><![CDATA[
      T(x,y) * z != y
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4511(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="4511 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4546">
    <literal><![CDATA[
      (x * (y / x)) * x = y * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(4533(a,1),940(a,2,2))].">
      <j1 rule="para" parents="4533 940"/>
    </justification>
  </clause>

  <clause id="4547">
    <literal><![CDATA[
      x / T(y \ x,y) = (y \ x) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),4535(a,1,2,2))].">
      <j1 rule="para" parents="72 4535"/>
    </justification>
  </clause>

  <clause id="4548">
    <literal><![CDATA[
      ((x \ y) * x) / (x \ y) = y / (y / x)
    ]]></literal>
    <justification jstring="[hyper(281,a,4544,a)].">
      <j1 rule="hyper" parents="281 4544"/>
    </justification>
  </clause>

  <clause id="4550">
    <literal><![CDATA[
      T(x / (x / (x / y)),y) = x / y
    ]]></literal>
    <justification jstring="[para(75(a,1),4544(a,1,2))].">
      <j1 rule="para" parents="75 4544"/>
    </justification>
  </clause>

  <clause id="4552">
    <literal><![CDATA[
      T(x,x * (y / x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(831,a,4483,a),flip(a)].">
      <j1 rule="hyper" parents="831 4483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4553">
    <literal><![CDATA[
      T(x,y * x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(828,a,4483,a)].">
      <j1 rule="hyper" parents="828 4483"/>
    </justification>
  </clause>

  <clause id="4554">
    <literal><![CDATA[
      T(R(x,y,x),x * y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(647,a,4483,a)].">
      <j1 rule="hyper" parents="647 4483"/>
    </justification>
  </clause>

  <clause id="4555">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),4483(a,1,1,2))].">
      <j1 rule="para" parents="5 4483"/>
    </justification>
  </clause>

  <clause id="4556">
    <literal><![CDATA[
      T(x,y * z) != T(y,z)
    ]]></literal>
    <literal><![CDATA[
      R(y,z,y) = x
    ]]></literal>
    <justification jstring="[para(4483(a,1),140(a,2))].">
      <j1 rule="para" parents="4483 140"/>
    </justification>
  </clause>

  <clause id="4557">
    <literal><![CDATA[
      T(x,(x \ y) * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(71(a,1),4552(a,1,2)),flip(a)].">
      <j1 rule="para" parents="71 4552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4558">
    <literal><![CDATA[
      T(x,x * T(y / x,z)) = T(x,x * T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(469(a,1),4552(a,1,2,2))].">
      <j1 rule="para" parents="469 4552"/>
    </justification>
  </clause>

  <clause id="4559">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * (y / x),x)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4552(a,1),4511(a,1,1))].">
      <j1 rule="para" parents="4552 4511"/>
    </justification>
  </clause>

  <clause id="4560">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(334,a,735,a,b,4553,a)].">
      <j1 rule="hyper" parents="334 735 4553"/>
    </justification>
  </clause>

  <clause id="4561">
    <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,4553,a)].">
      <j1 rule="hyper" parents="58 22 4553"/>
    </justification>
  </clause>

  <clause id="4562">
    <literal><![CDATA[
      T(T(x,x * y),z) = T(T(x,z),y * x)
    ]]></literal>
    <justification jstring="[para(4553(a,1),18(a,1,1))].">
      <j1 rule="para" parents="4553 18"/>
    </justification>
  </clause>

  <clause id="4563">
    <literal><![CDATA[
      T(T(x,y * x),z) = T(T(x,z),x * y)
    ]]></literal>
    <justification jstring="[para(4553(a,2),18(a,1,1))].">
      <j1 rule="para" parents="4553 18"/>
    </justification>
  </clause>

  <clause id="4564">
    <literal><![CDATA[
      x * T(y,x * y) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[para(4553(a,2),738(a,1,2))].">
      <j1 rule="para" parents="4553 738"/>
    </justification>
  </clause>

  <clause id="4565">
    <literal><![CDATA[
      x * L(T(y,x * y),z,u) = L(L(y,x,y),z,u) * x
    ]]></literal>
    <justification jstring="[para(4553(a,2),743(a,1,2,1))].">
      <j1 rule="para" parents="4553 743"/>
    </justification>
  </clause>

  <clause id="4566">
    <literal><![CDATA[
      T(x,T(y,y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4553(a,1),4127(a,1,2))].">
      <j1 rule="para" parents="4553 4127"/>
    </justification>
  </clause>

  <clause id="4567">
    <literal><![CDATA[
      (T(x,y * x) * y) * x = x * (x * y)
    ]]></literal>
    <justification jstring="[para(4553(a,2),4148(a,1,1,1))].">
      <j1 rule="para" parents="4553 4148"/>
    </justification>
  </clause>

  <clause id="4568">
    <literal><![CDATA[
      K(x,T(y,x * y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4553(a,2),4190(a,1,2))].">
      <j1 rule="para" parents="4553 4190"/>
    </justification>
  </clause>

  <clause id="4569">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) = x * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,4557,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4557 17"/>
    </justification>
  </clause>

  <clause id="4570">
    <literal><![CDATA[
      (((x \ y) * x) / T(x,y)) * x = T((x \ y) * x,x)
    ]]></literal>
    <justification jstring="[para(4557(a,1),4484(a,1,1,2))].">
      <j1 rule="para" parents="4557 4484"/>
    </justification>
  </clause>

  <clause id="4571">
    <literal><![CDATA[
      T(x,x * y) * L(T(y,x),z,u) = L(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[para(4566(a,1),244(a,1,2,1))].">
      <j1 rule="para" parents="4566 244"/>
    </justification>
  </clause>

  <clause id="4572">
    <literal><![CDATA[
      T(x,x * y) * R(T(y,x),z,u) = R(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[para(4566(a,1),245(a,1,2,1))].">
      <j1 rule="para" parents="4566 245"/>
    </justification>
  </clause>

  <clause id="4573">
    <literal><![CDATA[
      K(x,T(x \ y,y)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),4568(a,1,2,2))].">
      <j1 rule="para" parents="5 4568"/>
    </justification>
  </clause>

  <clause id="4574">
    <literal><![CDATA[
      R(x,y,T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(938,a,4554,a)].">
      <j1 rule="hyper" parents="938 4554"/>
    </justification>
  </clause>

  <clause id="4575">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(1222,a,4574,a)].">
      <j1 rule="hyper" parents="1222 4574"/>
    </justification>
  </clause>

  <clause id="4576">
    <literal><![CDATA[
      x * R(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4574,a(flip),b,1221,a)].">
      <j1 rule="hyper" parents="119 4574 1221"/>
    </justification>
  </clause>

  <clause id="4577">
    <literal><![CDATA[
      L(R(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[para(4574(a,1),1223(a,1,1))].">
      <j1 rule="para" parents="4574 1223"/>
    </justification>
  </clause>

  <clause id="4578">
    <literal><![CDATA[
      R(x,T(y,x),T(x,y)) = R(x,T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4473(a,1),4574(a,1,3))].">
      <j1 rule="para" parents="4473 4574"/>
    </justification>
  </clause>

  <clause id="4579">
    <literal><![CDATA[
      T(x \ T(x * y,y),T(x * y,y)) = y
    ]]></literal>
    <justification jstring="[hyper(58,a,4182,a,b,4577,a)].">
      <j1 rule="hyper" parents="58 4182 4577"/>
    </justification>
  </clause>

  <clause id="4580">
    <literal><![CDATA[
      T((x * y) / x,x * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(473,a,4560,a)].">
      <j1 rule="hyper" parents="473 4560"/>
    </justification>
  </clause>

  <clause id="4581">
    <literal><![CDATA[
      R(x,x \ y,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),4575(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 4575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4582">
    <literal><![CDATA[
      R(x / y,y,x / y) = y \ T(x,x / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),4575(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 4575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4583">
    <literal><![CDATA[
      (x * y) \ (x * T(z * y,z)) = L(R(z,y,z),y,x)
    ]]></literal>
    <justification jstring="[para(4575(a,1),92(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4575 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4584">
    <literal><![CDATA[
      (x \ T(x * y,y)) * x = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(4174,a,4576,a)].">
      <j1 rule="hyper" parents="4174 4576"/>
    </justification>
  </clause>

  <clause id="4585">
    <literal><![CDATA[
      T(x * y,x) != y * z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(4576(a,1),38(a,1))].">
      <j1 rule="para" parents="4576 38"/>
    </justification>
  </clause>

  <clause id="4586">
    <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(4576(a,1),495(a,1,2,2))].">
      <j1 rule="para" parents="4576 495"/>
    </justification>
  </clause>

  <clause id="4587">
    <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(4576(a,1),1099(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4576 1099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4588">
    <literal><![CDATA[
      T(x * y,x) * T(x,y) = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4576(a,1),1964(a,1,1))].">
      <j1 rule="para" parents="4576 1964"/>
    </justification>
  </clause>

  <clause id="4589">
    <literal><![CDATA[
      ((x * y) / x) \ x = y \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(4472(a,2),4183(a,1,1))].">
      <j1 rule="para" parents="4472 4183"/>
    </justification>
  </clause>

  <clause id="4590">
    <literal><![CDATA[
      x \ T(x,T(y,(y \ 1) * x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,4194,a(flip),b,4476,a)].">
      <j1 rule="hyper" parents="334 4194 4476"/>
    </justification>
  </clause>

  <clause id="4591">
    <literal><![CDATA[
      T(x,y * z) != K(z,y)
    ]]></literal>
    <literal><![CDATA[
      z \ T(z,y) = x
    ]]></literal>
    <justification jstring="[para(4476(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="4476 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4592">
    <literal><![CDATA[
      T(T(x \ y,z),x) = T(((x \ y) \ y) \ y,z)
    ]]></literal>
    <justification jstring="[para(4480(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4480 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4594">
    <literal><![CDATA[
      L((((x \ y) \ z) \ z) \ z,x \ y,x) = T(y \ (x * z),x \ y)
    ]]></literal>
    <justification jstring="[para(4480(a,1),779(a,1,1))].">
      <j1 rule="para" parents="4480 779"/>
    </justification>
  </clause>

  <clause id="4595">
    <literal><![CDATA[
      T(x \ (y \ x),x) = T(x,y \ 1) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(4426(a,1),4480(a,2,1))].">
      <j1 rule="para" parents="4426 4480"/>
    </justification>
  </clause>

  <clause id="4596">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (T(y,z) * z) / T(y,z) = x
    ]]></literal>
    <justification jstring="[para(4481(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="4481 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4597">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4481(a,1),699(a,1,1))].">
      <j1 rule="para" parents="4481 699"/>
    </justification>
  </clause>

  <clause id="4598">
    <literal><![CDATA[
      T(x,(1 / x) * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3927,a,b,4486,a)].">
      <j1 rule="hyper" parents="58 3927 4486"/>
    </justification>
  </clause>

  <clause id="4599">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = (x \ T(x,x \ y)) * y
    ]]></literal>
    <justification jstring="[para(4486(a,1),4216(a,2,1,2))].">
      <j1 rule="para" parents="4486 4216"/>
    </justification>
  </clause>

  <clause id="4600">
    <literal><![CDATA[
      T(T(x,y),T(z,x)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,18,a,b,4491,a),flip(a)].">
      <j1 rule="hyper" parents="334 18 4491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4601">
    <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),4491(a,1,2))].">
      <j1 rule="para" parents="20 4491"/>
    </justification>
  </clause>

  <clause id="4602">
    <literal><![CDATA[
      T(x,T(y,T(z,T(y,x)))) = T(x,T(T(y,x),z))
    ]]></literal>
    <justification jstring="[para(4473(a,1),4492(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4473 4492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4603">
    <literal><![CDATA[
      (x * (x * y)) \ ((x * y) * x) = K(y * x,T(x,y))
    ]]></literal>
    <justification jstring="[para(4505(a,1),943(a,1,1))].">
      <j1 rule="para" parents="4505 943"/>
    </justification>
  </clause>

  <clause id="4604">
    <literal><![CDATA[
      ((T(x,y) * y) / x) \ ((x * (x * y)) / x) = L(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[para(4505(a,1),1717(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4505 1717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4605">
    <literal><![CDATA[
      T(x,x \ y) / y = x / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(363,a,4509,a)].">
      <j1 rule="hyper" parents="363 4509"/>
    </justification>
  </clause>

  <clause id="4606">
    <literal><![CDATA[
      T(x,y) / (x * y) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(201,a,4509,a)].">
      <j1 rule="hyper" parents="201 4509"/>
    </justification>
  </clause>

  <clause id="4607">
    <literal><![CDATA[
      (x * (y / x)) / x = y / (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(281,a,4550,a)].">
      <j1 rule="hyper" parents="281 4550"/>
    </justification>
  </clause>

  <clause id="4609">
    <literal><![CDATA[
      x / T(y,(1 / y) * x) = y \ x
    ]]></literal>
    <justification jstring="[para(4598(a,2),273(a,1,2))].">
      <j1 rule="para" parents="4598 273"/>
    </justification>
  </clause>

  <clause id="4610">
    <literal><![CDATA[
      T(x,y) * T(T(y,z),x) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4600,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4600 17"/>
    </justification>
  </clause>

  <clause id="4611">
    <literal><![CDATA[
      T(T(x,y),z / x) = T(T(x,y),x \ z)
    ]]></literal>
    <justification jstring="[para(107(a,1),4600(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 4600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4612">
    <literal><![CDATA[
      T(x,y) / (x * y) = R(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,223,a,b,4606,a),flip(a)].">
      <j1 rule="hyper" parents="334 223 4606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4613">
    <literal><![CDATA[
      x / T(y \ 1,y * x) = (y \ 1) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),4609(a,1,2,2,1))].">
      <j1 rule="para" parents="72 4609"/>
    </justification>
  </clause>

  <clause id="4614">
    <literal><![CDATA[
      T(x,L(y,x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4566,a(flip),b,4501,a),flip(a)].">
      <j1 rule="hyper" parents="58 4566 4501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4615">
    <literal><![CDATA[
      T((x * y) / x,L(x,y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(473,a,4614,a(flip))].">
      <j1 rule="hyper" parents="473 4614"/>
    </justification>
  </clause>

  <clause id="4616">
    <literal><![CDATA[
      L(x,y,x) * T(y,x) = y * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,4614,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4614 17"/>
    </justification>
  </clause>

  <clause id="4617">
    <literal><![CDATA[
      L(x,y,x) \ ((x * (y * x)) / x) = y
    ]]></literal>
    <justification jstring="[hyper(1719,a,4615,a)].">
      <j1 rule="hyper" parents="1719 4615"/>
    </justification>
  </clause>

  <clause id="4618">
    <literal><![CDATA[
      (x * (y * x)) / x = L(x,y,x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,4615,a(flip),b,1716,a),flip(a)].">
      <j1 rule="hyper" parents="119 4615 1716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4619">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(334,a,106,a(flip),b,4555,a),flip(a)].">
      <j1 rule="hyper" parents="334 106 4555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4620">
    <literal><![CDATA[
      T(L(x,y,x) * y,x) = y * x
    ]]></literal>
    <justification jstring="[para(4564(a,1),837(a,1,1))].">
      <j1 rule="para" parents="4564 837"/>
    </justification>
  </clause>

  <clause id="4621">
    <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(4136(a,1),4564(a,1,2,2))].">
      <j1 rule="para" parents="4136 4564"/>
    </justification>
  </clause>

  <clause id="4622">
    <literal><![CDATA[
      T(x,L(x,y,x) * y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[para(4620(a,1),4473(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4620 4473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4623">
    <literal><![CDATA[
      R(1 / x,x,T(y,x)) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(688,a,4612,a)].">
      <j1 rule="hyper" parents="688 4612"/>
    </justification>
  </clause>

  <clause id="4624">
    <literal><![CDATA[
      (x * ((x \ y) * x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4618(a,2),1001(a,1))].">
      <j1 rule="para" parents="4618 1001"/>
    </justification>
  </clause>

  <clause id="4625">
    <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(4136(a,1),4618(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4136 4618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4626">
    <literal><![CDATA[
      R(x,x \ y,x) * y = y * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4619,a(flip),b,110,a),flip(a)].">
      <j1 rule="hyper" parents="119 4619 110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4627">
    <literal><![CDATA[
      T(x,L(x,y,x) * y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,4553,a(flip),b,4622,a),flip(a)].">
      <j1 rule="hyper" parents="334 4553 4622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4628">
    <literal><![CDATA[
      T(x,(x \ y) * T(x,y)) = T(x,(x \ y) * x)
    ]]></literal>
    <justification jstring="[para(744(a,1),4622(a,1,2))].">
      <j1 rule="para" parents="744 4622"/>
    </justification>
  </clause>

  <clause id="4629">
    <literal><![CDATA[
      R(T(x,x * y),y,T(x,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4627(a,1),1482(a,1,1))].">
      <j1 rule="para" parents="4627 1482"/>
    </justification>
  </clause>

  <clause id="4630">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) = K(x \ y,x) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),4468(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 4468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4631">
    <literal><![CDATA[
      x / (y * (x / y)) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(4419,a,4471,a)].">
      <j1 rule="hyper" parents="4419 4471"/>
    </justification>
  </clause>

  <clause id="4632">
    <literal><![CDATA[
      x \ (y / (y / x)) != z
    ]]></literal>
    <literal><![CDATA[
      y / (x * (y / x)) = z
    ]]></literal>
    <justification jstring="[para(4471(a,1),4419(a,1))].">
      <j1 rule="para" parents="4471 4419"/>
    </justification>
  </clause>

  <clause id="4633">
    <literal><![CDATA[
      (T(x,y / z) \ x) * y = z * T(z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,1228,a,b,4474,a),flip(a)].">
      <j1 rule="hyper" parents="29 1228 4474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4634">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(334,a,4411,a,b,4475,a)].">
      <j1 rule="hyper" parents="334 4411 4475"/>
    </justification>
  </clause>

  <clause id="4635">
    <literal><![CDATA[
      T(x,y) \ (y * x) = T(T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4600,a(flip),b,4516,a),flip(a)].">
      <j1 rule="hyper" parents="58 4600 4516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4636">
    <literal><![CDATA[
      (x * y) / T(T(x,y),y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(201,a,4635,a)].">
      <j1 rule="hyper" parents="201 4635"/>
    </justification>
  </clause>

  <clause id="4637">
    <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),4635(a,1,1))].">
      <j1 rule="para" parents="20 4635"/>
    </justification>
  </clause>

  <clause id="4638">
    <literal><![CDATA[
      T(T(x,y) / y,z) = T(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(246,a,4523,a,b,105,a)].">
      <j1 rule="hyper" parents="246 4523 105"/>
    </justification>
  </clause>

  <clause id="4639">
    <literal><![CDATA[
      T(T(x,y) \ y,z) = T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(246,a,4526,a,b,105,a)].">
      <j1 rule="hyper" parents="246 4526 105"/>
    </justification>
  </clause>

  <clause id="4640">
    <literal><![CDATA[
      x \ ((T(y,z) \ z) \ u) = x \ ((y \ T(z,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(116,a,4528,a,b,5,a)].">
      <j1 rule="hyper" parents="116 4528 5"/>
    </justification>
  </clause>

  <clause id="4641">
    <literal><![CDATA[
      (x / (x / y)) * (y \ x) = (x / y) * (x / (x / y))
    ]]></literal>
    <justification jstring="[para(661(a,1),4534(a,1,2))].">
      <j1 rule="para" parents="661 4534"/>
    </justification>
  </clause>

  <clause id="4642">
    <literal><![CDATA[
      T(x * (y / x),x) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(451,a,327,a(flip),b,4538,a)].">
      <j1 rule="hyper" parents="451 327 4538"/>
    </justification>
  </clause>

  <clause id="4643">
    <literal><![CDATA[
      (x \ y) * T(y,y \ (x \ y)) = (x \ T(y,x \ 1)) * y
    ]]></literal>
    <justification jstring="[para(4089(a,2),4538(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4089 4538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4644">
    <literal><![CDATA[
      (x / (x / y)) * (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      (y \ x) * y = z
    ]]></literal>
    <justification jstring="[para(4548(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4548 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4645">
    <literal><![CDATA[
      T(x / (x / y),x) = L(y,y \ x,y)
    ]]></literal>
    <justification jstring="[para(4548(a,1),747(a,1,1))].">
      <j1 rule="para" parents="4548 747"/>
    </justification>
  </clause>

  <clause id="4646">
    <literal><![CDATA[
      x * T(x / (x / y),x) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4645,a,b,91,a)].">
      <j1 rule="hyper" parents="119 4645 91"/>
    </justification>
  </clause>

  <clause id="4647">
    <literal><![CDATA[
      T(T(x / (x / y),x),z) = L(T(y,z),y \ x,y)
    ]]></literal>
    <justification jstring="[para(4645(a,2),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4645 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4648">
    <literal><![CDATA[
      L(x \ y,(x \ y) \ y,x \ y) = T(y / x,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),4645(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 4645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4649">
    <literal><![CDATA[
      T(T(x,y),z * x) = T(T(x,y),x * z)
    ]]></literal>
    <justification jstring="[hyper(447,a,4562,a),flip(a)].">
      <j1 rule="hyper" parents="447 4562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4650">
    <literal><![CDATA[
      T(T(x,y),x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,y),z * x) = u
    ]]></literal>
    <justification jstring="[para(4563(a,1),447(a,1))].">
      <j1 rule="para" parents="4563 447"/>
    </justification>
  </clause>

  <clause id="4652">
    <literal><![CDATA[
      K(x,x \ T(x * y,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4579(a,1),4573(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4579 4573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4653">
    <literal><![CDATA[
      K(x,y) = (x * R(y,x,y)) \ T(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4175,a,b,4652,a),flip(a)].">
      <j1 rule="hyper" parents="58 4175 4652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4654">
    <literal><![CDATA[
      (T(x,x \ y) / y) \ x = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(118,a,4605,a,b,154,a)].">
      <j1 rule="hyper" parents="118 4605 154"/>
    </justification>
  </clause>

  <clause id="4655">
    <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(4605(a,2),705(a,1,2,1))].">
      <j1 rule="para" parents="4605 705"/>
    </justification>
  </clause>

  <clause id="4656">
    <literal><![CDATA[
      T(x,y \ 1) / (y \ x) = x / ((x \ (y \ x)) * x)
    ]]></literal>
    <justification jstring="[para(4427(a,1),4605(a,1,1))].">
      <j1 rule="para" parents="4427 4605"/>
    </justification>
  </clause>

  <clause id="4657">
    <literal><![CDATA[
      R(1 / (1 / (1 / x)),x,y) = (x * (y / (x * y))) / x
    ]]></literal>
    <justification jstring="[para(4607(a,1),883(a,1,1))].">
      <j1 rule="para" parents="4607 883"/>
    </justification>
  </clause>

  <clause id="4658">
    <literal><![CDATA[
      T(x \ 1,x * y) = ((x \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(192,a,4613,a),flip(a)].">
      <j1 rule="hyper" parents="192 4613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4659">
    <literal><![CDATA[
      R(1 / x,x,y / x) = R(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),4623(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 4623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4660">
    <literal><![CDATA[
      K(x \ y,x) \ x = x * K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4095,a(flip),b,4630,a),flip(a)].">
      <j1 rule="hyper" parents="58 4095 4630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4661">
    <literal><![CDATA[
      T(T(x,y),z * x) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,x * z),y) = u
    ]]></literal>
    <justification jstring="[para(4649(a,2),447(a,1))].">
      <j1 rule="para" parents="4649 447"/>
    </justification>
  </clause>

  <clause id="4662">
    <literal><![CDATA[
      (T(x,y \ 1) / (y \ x)) \ x = (x \ (y \ x)) * x
    ]]></literal>
    <justification jstring="[para(4427(a,1),4654(a,1,1,1))].">
      <j1 rule="para" parents="4427 4654"/>
    </justification>
  </clause>

  <clause id="4663">
    <literal><![CDATA[
      T((x / y) \ 1,x) = (((x / y) \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[para(7(a,1),4658(a,1,2))].">
      <j1 rule="para" parents="7 4658"/>
    </justification>
  </clause>

  <clause id="4664">
    <literal><![CDATA[
      K(x \ y,x) \ 1 = K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(3628,a,4660,a)].">
      <j1 rule="hyper" parents="3628 4660"/>
    </justification>
  </clause>

  <clause id="4665">
    <literal><![CDATA[
      K(x,(x * y) / x) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),4664(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 4664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4666">
    <literal><![CDATA[
      K(T(x,y),y) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(4178,a,4665,a)].">
      <j1 rule="hyper" parents="4178 4665"/>
    </justification>
  </clause>

  <clause id="4667">
    <literal><![CDATA[
      K(T(x,y),y) \ 1 = K(y,x)
    ]]></literal>
    <justification jstring="[para(231(a,1),4665(a,1,2)),flip(a)].">
      <j1 rule="para" parents="231 4665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4669">
    <literal><![CDATA[
      x * K(T(y,x),x) = K(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,4666,a,b,2845,a)].">
      <j1 rule="hyper" parents="119 4666 2845"/>
    </justification>
  </clause>

  <clause id="4670">
    <literal><![CDATA[
      K(T(x,y),y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4666(a,1),4460(a,1))].">
      <j1 rule="para" parents="4666 4460"/>
    </justification>
  </clause>

  <clause id="4671">
    <literal><![CDATA[
      R(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[para(4667(a,1),4384(a,1,2))].">
      <j1 rule="para" parents="4667 4384"/>
    </justification>
  </clause>

  <clause id="4672">
    <literal><![CDATA[
      R(T(x,y),K(x,z),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4671(a,1),22(a,2,1))].">
      <j1 rule="para" parents="4671 22"/>
    </justification>
  </clause>

  <clause id="4673">
    <literal><![CDATA[
      (L(x,y,z) * K(x,u)) * w = L(x,y,z) * (K(x,u) * w)
    ]]></literal>
    <justification jstring="[para(4671(a,1),525(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4671 525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4674">
    <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(4672(a,1),526(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4672 526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4675">
    <literal><![CDATA[
      R(x / y,y,x / y) = y \ T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(4118(a,1),4582(a,2,2))].">
      <j1 rule="para" parents="4118 4582"/>
    </justification>
  </clause>

  <clause id="4676">
    <literal><![CDATA[
      R(x,x \ y,x) * y = (x * (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(334,a,4546,a,b,4626,a),flip(a)].">
      <j1 rule="hyper" parents="334 4546 4626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4677">
    <literal><![CDATA[
      K(x,y) = T(y * x,y) \ T(x * y,y)
    ]]></literal>
    <justification jstring="[para(4576(a,1),4653(a,2,1))].">
      <j1 rule="para" parents="4576 4653"/>
    </justification>
  </clause>

  <clause id="4678">
    <literal><![CDATA[
      K(x \ T(x * y,x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,1447,a(flip),b,4677,a)].">
      <j1 rule="hyper" parents="334 1447 4677"/>
    </justification>
  </clause>

  <clause id="4679">
    <literal><![CDATA[
      K(x \ T(y,x),x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),4678(a,1,1,2,1))].">
      <j1 rule="para" parents="5 4678"/>
    </justification>
  </clause>

  <clause id="4680">
    <literal><![CDATA[
      K(x \ ((x * y) / x),x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(230(a,1),4679(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="230 4679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4681">
    <literal><![CDATA[
      K(((x * y) / x) \ x,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4589(a,2),4680(a,1,1))].">
      <j1 rule="para" parents="4589 4680"/>
    </justification>
  </clause>

  <clause id="4682">
    <literal><![CDATA[
      (x * ((y \ x) * y)) / x = x * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4681(a,1),4423(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4681 4423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4683">
    <literal><![CDATA[
      R(x,y / x,x) = R(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,520,a,b,4676,a)].">
      <j1 rule="hyper" parents="30 520 4676"/>
    </justification>
  </clause>

  <clause id="4684">
    <literal><![CDATA[
      R(x,y / x,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,4581,a(flip),b,4683,a),flip(a)].">
      <j1 rule="hyper" parents="334 4581 4683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4685">
    <literal><![CDATA[
      R(x,x \ (y \ x),x) = ((y \ T(x,y \ 1)) * x) / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4140,a(flip),b,4683,a),flip(a)].">
      <j1 rule="hyper" parents="58 4140 4683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4686">
    <literal><![CDATA[
      R(x,(x * y) / x,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),4683(a,2,2))].">
      <j1 rule="para" parents="4 4683"/>
    </justification>
  </clause>

  <clause id="4687">
    <literal><![CDATA[
      R(x,T(y,x),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(231(a,1),4686(a,1,2)),flip(a)].">
      <j1 rule="para" parents="231 4686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4688">
    <literal><![CDATA[
      R(x,T(y,x),T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4578,a,b,4687,a)].">
      <j1 rule="hyper" parents="58 4578 4687"/>
    </justification>
  </clause>

  <clause id="4689">
    <literal><![CDATA[
      R(R(x,y,z),T(u,x),T(x,u)) = R(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(4688(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4688 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4690">
    <literal><![CDATA[
      (x \ (y * x)) \ T(y * x,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(6(a,1),4684(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 4684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4691">
    <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(4473(a,1),4525(a,1,2,1))].">
      <j1 rule="para" parents="4473 4525"/>
    </justification>
  </clause>

  <clause id="4692">
    <literal><![CDATA[
      T(x,T(y,T(z,T(y,x)))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,4492,a(flip),b,4602,a),flip(a)].">
      <j1 rule="hyper" parents="334 4492 4602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4693">
    <literal><![CDATA[
      T(x,y) * (T(y,z) * x) = x * (T(y,z) * T(x,y))
    ]]></literal>
    <justification jstring="[para(4610(a,1),1165(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4610 1165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4694">
    <literal><![CDATA[
      T(x,(x \ y) * T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,4557,a(flip),b,4628,a),flip(a)].">
      <j1 rule="hyper" parents="334 4557 4628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4695">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,y)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4694(a,1),1480(a,1,1))].">
      <j1 rule="para" parents="4694 1480"/>
    </justification>
  </clause>

  <clause id="4696">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = T(x,y) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(631,a,4634,a),flip(a)].">
      <j1 rule="hyper" parents="631 4634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4697">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = T(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1565,a,b,4634,a)].">
      <j1 rule="hyper" parents="58 1565 4634"/>
    </justification>
  </clause>

  <clause id="4698">
    <literal><![CDATA[
      T(x,y) * z != x * (((y * x) / y) \ u)
    ]]></literal>
    <literal><![CDATA[
      x \ u = z
    ]]></literal>
    <justification jstring="[para(4634(a,2),38(a,1)),flip(a)].">
      <j1 rule="para" parents="4634 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4699">
    <literal><![CDATA[
      ((x / y) \ T((x / y) * y,y)) * (x / y) = y \ (x * ((y \ x) \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4584,a,b,4642,a)].">
      <j1 rule="hyper" parents="58 4584 4642"/>
    </justification>
  </clause>

  <clause id="4700">
    <literal><![CDATA[
      x \ (y * ((x \ y) \ y)) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,4524,a(flip),b,4642,a),flip(a)].">
      <j1 rule="hyper" parents="58 4524 4642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4701">
    <literal><![CDATA[
      (x / (x / y)) * x = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(294,a,4646,a)].">
      <j1 rule="hyper" parents="294 4646"/>
    </justification>
  </clause>

  <clause id="4702">
    <literal><![CDATA[
      R(1 / x,x,y / x) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(334,a,417,a(flip),b,4659,a),flip(a)].">
      <j1 rule="hyper" parents="334 417 4659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4703">
    <literal><![CDATA[
      (x / y) / (y * (x / y)) = (y \ x) / x
    ]]></literal>
    <justification jstring="[hyper(760,a,4702,a)].">
      <j1 rule="hyper" parents="760 4702"/>
    </justification>
  </clause>

  <clause id="4704">
    <literal><![CDATA[
      ((x \ y) / y) * (x * (y / x)) = y / x
    ]]></literal>
    <justification jstring="[hyper(133,a,4703,a)].">
      <j1 rule="hyper" parents="133 4703"/>
    </justification>
  </clause>

  <clause id="4705">
    <literal><![CDATA[
      T(x,(y \ x) * y) = x
    ]]></literal>
    <justification jstring="[hyper(4203,a,4682,a)].">
      <j1 rule="hyper" parents="4203 4682"/>
    </justification>
  </clause>

  <clause id="4706">
    <literal><![CDATA[
      T((x \ y) * x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(49,a,4705,a)].">
      <j1 rule="hyper" parents="49 4705"/>
    </justification>
  </clause>

  <clause id="4707">
    <literal><![CDATA[
      T(x * (y / x),y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(76(a,1),4705(a,1,2))].">
      <j1 rule="para" parents="76 4705"/>
    </justification>
  </clause>

  <clause id="4708">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(334,a,1161,a(flip),b,4696,a),flip(a)].">
      <j1 rule="hyper" parents="334 1161 4696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4709">
    <literal><![CDATA[
      ((x * y) / x) * (y \ z) = y * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(1188,a,4697,a)].">
      <j1 rule="hyper" parents="1188 4697"/>
    </justification>
  </clause>

  <clause id="4710">
    <literal><![CDATA[
      x * (T(x,y) \ x) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) / y = z
    ]]></literal>
    <justification jstring="[para(4709(a,1),211(a,1))].">
      <j1 rule="para" parents="4709 211"/>
    </justification>
  </clause>

  <clause id="4711">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = T(x,T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,4083,a(flip),b,4464,a),flip(a)].">
      <j1 rule="hyper" parents="334 4083 4464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4712">
    <literal><![CDATA[
      T(x,T(y \ 1,x)) = T(x,(y \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(4597,a,4711,a),flip(a)].">
      <j1 rule="hyper" parents="4597 4711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4713">
    <literal><![CDATA[
      T(x,(y \ z) / z) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4597,a,4712,a),flip(a)].">
      <j1 rule="hyper" parents="4597 4712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4714">
    <literal><![CDATA[
      T(x,(y \ z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(4712(a,1),4597(a,1))].">
      <j1 rule="para" parents="4712 4597"/>
    </justification>
  </clause>

  <clause id="4715">
    <literal><![CDATA[
      T(x,y / (z * y)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),4713(a,1,2,1))].">
      <j1 rule="para" parents="4 4713"/>
    </justification>
  </clause>

  <clause id="4716">
    <literal><![CDATA[
      T(x,(y / z) \ 1) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),4713(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 4713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4719">
    <literal><![CDATA[
      T(x / (y * x),y \ 1) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(305,a,4715,a),flip(a)].">
      <j1 rule="hyper" parents="305 4715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4722">
    <literal><![CDATA[
      T(x \ T(x,(y * z) / z),T(y,u)) = R(x \ T(x,y),y,z)
    ]]></literal>
    <justification jstring="[para(4716(a,1),4223(a,1,1,2))].">
      <j1 rule="para" parents="4716 4223"/>
    </justification>
  </clause>

  <clause id="4723">
    <literal><![CDATA[
      T(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(z / y) \ 1) = u
    ]]></literal>
    <justification jstring="[para(75(a,1),4714(a,1,2,1))].">
      <j1 rule="para" parents="75 4714"/>
    </justification>
  </clause>

  <clause id="4724">
    <literal><![CDATA[
      L(T(x,y),T(y,x),x) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(1134,a,4499,a),flip(a)].">
      <j1 rule="hyper" parents="1134 4499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4725">
    <literal><![CDATA[
      L(x,T(y,x),x) * y = y * T(x,y * x)
    ]]></literal>
    <justification jstring="[para(4724(a,1),244(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4724 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4726">
    <literal><![CDATA[
      L(x,T(y,x),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,4564,a(flip),b,4725,a),flip(a)].">
      <j1 rule="hyper" parents="30 4564 4725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4727">
    <literal><![CDATA[
      L(x,(x * y) / x,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(230(a,1),4726(a,1,2)),flip(a)].">
      <j1 rule="para" parents="230 4726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4728">
    <literal><![CDATA[
      L(x,T(y,x),x) * T(y,x) = y * L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4726(a,2),4616(a,1,1))].">
      <j1 rule="para" parents="4726 4616"/>
    </justification>
  </clause>

  <clause id="4729">
    <literal><![CDATA[
      T(x,y) * T(y,x * y) = x * L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,745,a(flip),b,4728,a)].">
      <j1 rule="hyper" parents="58 745 4728"/>
    </justification>
  </clause>

  <clause id="4730">
    <literal><![CDATA[
      T(x,y) * T(y,y * x) = x * L(y,x,y)
    ]]></literal>
    <justification jstring="[para(4553(a,1),4729(a,1,2))].">
      <j1 rule="para" parents="4553 4729"/>
    </justification>
  </clause>

  <clause id="4731">
    <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(4500(a,1),235(a,1,1,2))].">
      <j1 rule="para" parents="4500 235"/>
    </justification>
  </clause>

  <clause id="4732">
    <literal><![CDATA[
      R(x,y,x) * T(x * y,x) = T(x * y,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4483(a,1),4500(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4483 4500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4733">
    <literal><![CDATA[
      T(x,y) * K(y \ x,y) = (T(y,x) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,4679,a(flip),b,4529,a)].">
      <j1 rule="hyper" parents="119 4679 4529"/>
    </justification>
  </clause>

  <clause id="4734">
    <literal><![CDATA[
      T(x,x * T(T(x,y) \ y,z)) = T(x,x * T(T(y,x) / x,z))
    ]]></literal>
    <justification jstring="[para(4490(a,2),4558(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4490 4558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4735">
    <literal><![CDATA[
      T(x,y) * (T(y,x) / x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(1440(a,1),4559(a,1,2))].">
      <j1 rule="para" parents="1440 4559"/>
    </justification>
  </clause>

  <clause id="4736">
    <literal><![CDATA[
      T(x,y) * z != x * (y / x)
    ]]></literal>
    <literal><![CDATA[
      T(y,x) / x = z
    ]]></literal>
    <justification jstring="[para(4735(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="4735 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4737">
    <literal><![CDATA[
      T(x,y) * (y / T(x,y)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4488(a,1),4735(a,1,2))].">
      <j1 rule="para" parents="4488 4735"/>
    </justification>
  </clause>

  <clause id="4738">
    <literal><![CDATA[
      T(x,y) * z != x * (y / x)
    ]]></literal>
    <literal><![CDATA[
      y / T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4737(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="4737 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4739">
    <literal><![CDATA[
      ((x \ y) * x) / T(x,y) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,1434,a(flip),b,4570,a),flip(a)].">
      <j1 rule="hyper" parents="30 1434 4570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4740">
    <literal><![CDATA[
      (x \ T(y,x)) * T(x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,4739,a)].">
      <j1 rule="hyper" parents="133 4739"/>
    </justification>
  </clause>

  <clause id="4741">
    <literal><![CDATA[
      (T(x,y) \ y) * T(x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(4527,a,4740,a)].">
      <j1 rule="hyper" parents="4527 4740"/>
    </justification>
  </clause>

  <clause id="4742">
    <literal><![CDATA[
      x \ T(x,T(y,y \ x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(4486(a,1),4590(a,1,2,2,1))].">
      <j1 rule="para" parents="4486 4590"/>
    </justification>
  </clause>

  <clause id="4743">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) = x * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,4742,a),flip(a)].">
      <j1 rule="hyper" parents="134 4742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4744">
    <literal><![CDATA[
      K(x,(y \ x) / x) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4192,a,4743,a)].">
      <j1 rule="hyper" parents="4192 4743"/>
    </justification>
  </clause>

  <clause id="4745">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,4207,a,b,4744,a)].">
      <j1 rule="hyper" parents="58 4207 4744"/>
    </justification>
  </clause>

  <clause id="4746">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,3696,a(flip),b,4745,a),flip(a)].">
      <j1 rule="hyper" parents="334 3696 4745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4747">
    <literal><![CDATA[
      K(x \ ((1 / x) \ y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4286,a,b,4746,a)].">
      <j1 rule="hyper" parents="58 4286 4746"/>
    </justification>
  </clause>

  <clause id="4748">
    <literal><![CDATA[
      K((x \ 1) * y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),4746(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 4746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4749">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),4747(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 4747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4750">
    <literal><![CDATA[
      K((x \ 1) \ y,x \ 1) = K(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,4290,a(flip),b,4748,a),flip(a)].">
      <j1 rule="hyper" parents="58 4290 4748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4751">
    <literal><![CDATA[
      K((1 / x) * (y * x),x) = K(T(y,x),x)
    ]]></literal>
    <justification jstring="[para(17(a,2),4749(a,2,1))].">
      <j1 rule="para" parents="17 4749"/>
    </justification>
  </clause>

  <clause id="4752">
    <literal><![CDATA[
      K(T((1 / x) * y,x),x) = K(T(x \ y,x),x)
    ]]></literal>
    <justification jstring="[para(818(a,1),4751(a,1,1))].">
      <j1 rule="para" parents="818 4751"/>
    </justification>
  </clause>

  <clause id="4753">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = y * K(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,4750,a(flip),b,85,a),flip(a)].">
      <j1 rule="hyper" parents="119 4750 85"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4754">
    <literal><![CDATA[
      K(T((x \ 1) * y,x),x) = K(T(x \ y,x),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4307,a(flip),b,4752,a)].">
      <j1 rule="hyper" parents="58 4307 4752"/>
    </justification>
  </clause>

  <clause id="4755">
    <literal><![CDATA[
      K(T(x \ y,x),x) \ 1 = K(x,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(4754(a,1),4667(a,1,1))].">
      <j1 rule="para" parents="4754 4667"/>
    </justification>
  </clause>

  <clause id="4756">
    <literal><![CDATA[
      K(x,(x \ 1) * y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(4670,a,4755,a),flip(a)].">
      <j1 rule="hyper" parents="4670 4755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4757">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3742,a(flip),b,4756,a),flip(a)].">
      <j1 rule="hyper" parents="58 3742 4756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4758">
    <literal><![CDATA[
      K(x * y,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y * x,y) = z
    ]]></literal>
    <justification jstring="[para(4603(a,1),321(a,1))].">
      <j1 rule="para" parents="4603 321"/>
    </justification>
  </clause>

  <clause id="4759">
    <literal><![CDATA[
      (x / y) * (x / (x / y)) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(4644,a,4641,a),flip(a)].">
      <j1 rule="hyper" parents="4644 4641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4760">
    <literal><![CDATA[
      ((x \ y) * x) * x = y * (y / (y / x))
    ]]></literal>
    <justification jstring="[para(4759(a,1),947(a,1,1))].">
      <j1 rule="para" parents="4759 947"/>
    </justification>
  </clause>

  <clause id="4761">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) = y * (y / (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(4741(a,1),4760(a,1,1))].">
      <j1 rule="para" parents="4741 4760"/>
    </justification>
  </clause>

  <clause id="4762">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = x / ((x \ ((y \ 1) \ x)) * x)
    ]]></literal>
    <justification jstring="[para(3106(a,1),4656(a,1,1))].">
      <j1 rule="para" parents="3106 4656"/>
    </justification>
  </clause>

  <clause id="4763">
    <literal><![CDATA[
      (T(x,y) / ((y \ 1) \ x)) \ x = (x \ ((y \ 1) \ x)) * x
    ]]></literal>
    <justification jstring="[para(3106(a,1),4662(a,1,1,1))].">
      <j1 rule="para" parents="3106 4662"/>
    </justification>
  </clause>

  <clause id="4764">
    <literal><![CDATA[
      x * (x / (x / T(y,x))) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4569,a(flip),b,4761,a),flip(a)].">
      <j1 rule="hyper" parents="58 4569 4761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4765">
    <literal><![CDATA[
      x / (x / T(y,x)) = T(x / (x / y),x)
    ]]></literal>
    <justification jstring="[hyper(246,a,4701,a,b,4764,a),flip(a)].">
      <j1 rule="hyper" parents="246 4701 4764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4766">
    <literal><![CDATA[
      T(x / (x / y),x) \ x = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(192,a,4765,a)].">
      <j1 rule="hyper" parents="192 4765"/>
    </justification>
  </clause>

  <clause id="4767">
    <literal><![CDATA[
      x / T(y \ x,x) = T(x / y,x) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),4766(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 4766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4768">
    <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(1148(a,1),4542(a,1,2,1))].">
      <j1 rule="para" parents="1148 4542"/>
    </justification>
  </clause>

  <clause id="4769">
    <literal><![CDATA[
      T(L(L(x,y,x),z,u) * y,x) = L(x,z,u) * T(y,x)
    ]]></literal>
    <justification jstring="[para(4565(a,1),1987(a,1,1))].">
      <j1 rule="para" parents="4565 1987"/>
    </justification>
  </clause>

  <clause id="4770">
    <literal><![CDATA[
      R(x,y,x) * T(x * y,x) = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,4588,a(flip),b,4732,a),flip(a)].">
      <j1 rule="hyper" parents="334 4588 4732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4771">
    <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(4770(a,1),4583(a,1,2))].">
      <j1 rule="para" parents="4770 4583"/>
    </justification>
  </clause>

  <clause id="4772">
    <literal><![CDATA[
      T(x,y) \ (K(z,z \ 1) * (x * y)) = T(K(z,z \ 1) * y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3951,a,b,4503,a)].">
      <j1 rule="hyper" parents="58 3951 4503"/>
    </justification>
  </clause>

  <clause id="4773">
    <literal><![CDATA[
      (x \ T(y,x \ 1)) * y = (x \ y) * T(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(4427(a,1),4643(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4427 4643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4774">
    <literal><![CDATA[
      L(x,K(y,z),L(y,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(493,a,4673,a)].">
      <j1 rule="hyper" parents="493 4673"/>
    </justification>
  </clause>

  <clause id="4775">
    <literal><![CDATA[
      (K(x,y) * L(x,z,u)) * w = L(x,z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(3472(a,1),4673(a,1,1))].">
      <j1 rule="para" parents="3472 4673"/>
    </justification>
  </clause>

  <clause id="4776">
    <literal><![CDATA[
      L(x,K(y,z),L(y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(4774(a,1),45(a,2))].">
      <j1 rule="para" parents="4774 45"/>
    </justification>
  </clause>

  <clause id="4777">
    <literal><![CDATA[
      L(x,K(y,z),y) = x
    ]]></literal>
    <justification jstring="[para(384(a,1),4774(a,1,3))].">
      <j1 rule="para" parents="384 4774"/>
    </justification>
  </clause>

  <clause id="4781">
    <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(4689(a,1),4517(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4689 4517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4782">
    <literal><![CDATA[
      L(x,(x * y) / x,x) = L(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,4135,a(flip),b,4604,a)].">
      <j1 rule="hyper" parents="58 4135 4604"/>
    </justification>
  </clause>

  <clause id="4783">
    <literal><![CDATA[
      L(x,y,T(x,y)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4727,a(flip),b,4782,a),flip(a)].">
      <j1 rule="hyper" parents="58 4727 4782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4784">
    <literal><![CDATA[
      R(x,x \ (y \ x),x) = ((y \ x) * T(x,y \ 1)) / (y \ x)
    ]]></literal>
    <justification jstring="[para(4773(a,1),4685(a,2,1))].">
      <j1 rule="para" parents="4773 4685"/>
    </justification>
  </clause>

  <clause id="4785">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) = R(x \ T(x,y),y,u)
    ]]></literal>
    <justification jstring="[para(6(a,1),4722(a,1,1,2,2))].">
      <j1 rule="para" parents="6 4722"/>
    </justification>
  </clause>

  <clause id="4786">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2559,a(flip),b,4785,a),flip(a)].">
      <j1 rule="hyper" parents="58 2559 4785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4787">
    <literal><![CDATA[
      (x \ T(x,y)) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(4786(a,1),4066(a,1,1))].">
      <j1 rule="para" parents="4786 4066"/>
    </justification>
  </clause>

  <clause id="4788">
    <literal><![CDATA[
      L(x,y \ 1,(z * y) / z) = y * ((y \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(4100,a,4787,a)].">
      <j1 rule="hyper" parents="4100 4787"/>
    </justification>
  </clause>

  <clause id="4789">
    <literal><![CDATA[
      (x \ T(x,x \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(77(a,1),4787(a,1,2))].">
      <j1 rule="para" parents="77 4787"/>
    </justification>
  </clause>

  <clause id="4791">
    <literal><![CDATA[
      (x \ ((x \ y) \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,676,a(flip),b,4789,a)].">
      <j1 rule="hyper" parents="58 676 4789"/>
    </justification>
  </clause>

  <clause id="4792">
    <literal><![CDATA[
      x / ((y \ x) * y) = y \ ((y \ x) \ x)
    ]]></literal>
    <justification jstring="[hyper(201,a,4791,a)].">
      <j1 rule="hyper" parents="201 4791"/>
    </justification>
  </clause>

  <clause id="4793">
    <literal><![CDATA[
      (x * (y / x)) / y = y / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(334,a,4425,a,b,4792,a)].">
      <j1 rule="hyper" parents="334 4425 4792"/>
    </justification>
  </clause>

  <clause id="4794">
    <literal><![CDATA[
      T(x * (y / x),y) / y = y / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(4707(a,2),4793(a,1,1))].">
      <j1 rule="para" parents="4707 4793"/>
    </justification>
  </clause>

  <clause id="4795">
    <literal><![CDATA[
      x / ((((y \ 1) * x) \ x) * ((y \ 1) * x)) = T((y \ x) * y,x) / x
    ]]></literal>
    <justification jstring="[para(4187(a,1),4794(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4187 4794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4796">
    <literal><![CDATA[
      L(x,y \ 1,(z * y) / z) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,265,a(flip),b,4788,a),flip(a)].">
      <j1 rule="hyper" parents="334 265 4788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4797">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * z) = L(z,T(x,y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(231(a,1),4788(a,1,3)),flip(a)].">
      <j1 rule="para" parents="231 4788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4798">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,T(y,z)) = L(x,T(y,z) \ 1,y)
    ]]></literal>
    <justification jstring="[para(231(a,1),4796(a,1,3)),flip(a)].">
      <j1 rule="para" parents="231 4796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4799">
    <literal><![CDATA[
      L(x,1 / T(y,y \ z),(y \ z) \ z) = L(x,T(y,y \ z) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(3198,a,4798,a)].">
      <j1 rule="hyper" parents="3198 4798"/>
    </justification>
  </clause>

  <clause id="4800">
    <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(4543(a,2),4502(a,1))].">
      <j1 rule="para" parents="4543 4502"/>
    </justification>
  </clause>

  <clause id="4801">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(334,a,4400,a(flip),b,4599,a),flip(a)].">
      <j1 rule="hyper" parents="334 4400 4599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4802">
    <literal><![CDATA[
      T(x,T(x * T(y / x,z),x)) = T(x,x * T(T(x,y) \ y,z))
    ]]></literal>
    <justification jstring="[para(1621(a,2),4734(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1621 4734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4803">
    <literal><![CDATA[
      (T(x,y) \ (x * y)) * K(z,z \ 1) = T(K(z,z \ 1) * y,x)
    ]]></literal>
    <justification jstring="[hyper(3611,a,4772,a)].">
      <j1 rule="hyper" parents="3611 4772"/>
    </justification>
  </clause>

  <clause id="4804">
    <literal><![CDATA[
      T(x,x * T(T(x,y) \ y,z)) = T(x,x * T(y / x,z))
    ]]></literal>
    <justification jstring="[hyper(4597,a,4802,a),flip(a)].">
      <j1 rule="hyper" parents="4597 4802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4805">
    <literal><![CDATA[
      T(x,x * T(T(x,y) \ y,z)) = T(x,x * T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,4558,a(flip),b,4804,a),flip(a)].">
      <j1 rule="hyper" parents="334 4558 4804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4806">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,z) = T(y,z) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(4482(a,1),4803(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4482 4803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4807">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,z) = K(x,x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,2237,a,b,4806,a),flip(a)].">
      <j1 rule="hyper" parents="334 2237 4806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4808">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(3047,a,4806,a(flip))].">
      <j1 rule="hyper" parents="3047 4806"/>
    </justification>
  </clause>

  <clause id="4810">
    <literal><![CDATA[
      T(x,T(K(y,y \ 1) * z,u)) = T(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(4806(a,2),3916(a,1,2))].">
      <j1 rule="para" parents="4806 3916"/>
    </justification>
  </clause>

  <clause id="4812">
    <literal><![CDATA[
      T(x,T((1 / y) * z,u)) = T(x,T((y \ 1) * z,u))
    ]]></literal>
    <justification jstring="[para(3167(a,1),4810(a,1,2,1))].">
      <j1 rule="para" parents="3167 4810"/>
    </justification>
  </clause>

  <clause id="4814">
    <literal><![CDATA[
      T(x * K(y,y \ 1),z) = K(y,y \ 1) * T(x,z)
    ]]></literal>
    <justification jstring="[para(2237(a,1),4807(a,1,1))].">
      <j1 rule="para" parents="2237 4807"/>
    </justification>
  </clause>

  <clause id="4815">
    <literal><![CDATA[
      (x \ T(x * (y / x),z)) * x = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3056,a(flip),b,4808,a)].">
      <j1 rule="hyper" parents="58 3056 4808"/>
    </justification>
  </clause>

  <clause id="4816">
    <literal><![CDATA[
      x \ T(x * (y / x),z) = T(y,z) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,4808,a(flip),b,3056,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="117 4808 3056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4817">
    <literal><![CDATA[
      T(x * K(y \ 1,y),z) = K(y \ 1,y) * T(x,z)
    ]]></literal>
    <justification jstring="[para(3039(a,1),4808(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3039 4808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4820">
    <literal><![CDATA[
      (x \ T(x * y,z)) * x = T(y * x,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),4815(a,1,1,2,1,2))].">
      <j1 rule="para" parents="6 4815"/>
    </justification>
  </clause>

  <clause id="4821">
    <literal><![CDATA[
      T(x * (y / x),z) = x * (T(y,z) / x)
    ]]></literal>
    <justification jstring="[para(4815(a,1),71(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4815 71"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4822">
    <literal><![CDATA[
      T((x \ y) * x,z) = (x \ T(y,z)) * x
    ]]></literal>
    <justification jstring="[para(71(a,1),4815(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="71 4815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4823">
    <literal><![CDATA[
      T(x * y,z) / y = y \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),4816(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6 4816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4824">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,z) = T(y,z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(72(a,1),4816(a,1,2,1,2))].">
      <j1 rule="para" parents="72 4816"/>
    </justification>
  </clause>

  <clause id="4825">
    <literal><![CDATA[
      T((x \ y) * x,z) / x = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(71(a,1),4816(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="71 4816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4826">
    <literal><![CDATA[
      x * (y * (T(z,x) / y)) = (y * (z / y)) * x
    ]]></literal>
    <justification jstring="[para(4816(a,1),233(a,1,2,2))].">
      <j1 rule="para" parents="4816 233"/>
    </justification>
  </clause>

  <clause id="4829">
    <literal><![CDATA[
      x \ T(T(x,y) * y,z) = T(x * y,z) / x
    ]]></literal>
    <justification jstring="[para(4121(a,2),4816(a,1,2,1))].">
      <j1 rule="para" parents="4121 4816"/>
    </justification>
  </clause>

  <clause id="4830">
    <literal><![CDATA[
      T(x \ T(x * y,z),x) = x \ T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(451,a,xx,b,4820,a)].">
      <j1 rule="hyper" parents="451 4820"/>
    </justification>
  </clause>

  <clause id="4832">
    <literal><![CDATA[
      x * (T(y * x,z) / x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(4820(a,1),71(a,1,2,1))].">
      <j1 rule="para" parents="4820 71"/>
    </justification>
  </clause>

  <clause id="4834">
    <literal><![CDATA[
      T(x,T(y * x,z)) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[para(4820(a,1),4557(a,1,2))].">
      <j1 rule="para" parents="4820 4557"/>
    </justification>
  </clause>

  <clause id="4835">
    <literal><![CDATA[
      T(x * (y / x),z) != x * u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) / x = u
    ]]></literal>
    <justification jstring="[para(4821(a,2),38(a,1))].">
      <j1 rule="para" parents="4821 38"/>
    </justification>
  </clause>

  <clause id="4836">
    <literal><![CDATA[
      (x \ y) * (T(y,z) / (x \ y)) = T((x \ y) * x,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),4821(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 4821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4837">
    <literal><![CDATA[
      T(x * ((y / z) / x),z) = x * ((z \ y) / x)
    ]]></literal>
    <justification jstring="[para(107(a,1),4821(a,2,2,1))].">
      <j1 rule="para" parents="107 4821"/>
    </justification>
  </clause>

  <clause id="4841">
    <literal><![CDATA[
      T(x * (y / x),K(z,y)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(2523(a,1),4821(a,2,2,1))].">
      <j1 rule="para" parents="2523 4821"/>
    </justification>
  </clause>

  <clause id="4842">
    <literal><![CDATA[
      T(x * (y / x),K(y,z)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(3464(a,1),4821(a,2,2,1))].">
      <j1 rule="para" parents="3464 4821"/>
    </justification>
  </clause>

  <clause id="4843">
    <literal><![CDATA[
      T(x * (y / x),z / y) = x * (T(y,y \ z) / x)
    ]]></literal>
    <justification jstring="[para(4495(a,1),4821(a,2,2,1))].">
      <j1 rule="para" parents="4495 4821"/>
    </justification>
  </clause>

  <clause id="4844">
    <literal><![CDATA[
      x \ T((x \ y) * x,z) = T(x \ T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(451,a,4822,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="451 4822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4847">
    <literal><![CDATA[
      x * ((y \ T(z,x)) * y) = ((y \ z) * y) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,4822,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4822 17"/>
    </justification>
  </clause>

  <clause id="4848">
    <literal><![CDATA[
      T((x \ y) * x,z) != u * x
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(4822(a,2),39(a,1))].">
      <j1 rule="para" parents="4822 39"/>
    </justification>
  </clause>

  <clause id="4849">
    <literal><![CDATA[
      T((x \ (y / z)) * x,z) = (x \ (z \ y)) * x
    ]]></literal>
    <justification jstring="[para(107(a,1),4822(a,2,1,2))].">
      <j1 rule="para" parents="107 4822"/>
    </justification>
  </clause>

  <clause id="4850">
    <literal><![CDATA[
      ((x * T((y \ z) * y,x)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(4822(a,2),4368(a,1,1,1,2))].">
      <j1 rule="para" parents="4822 4368"/>
    </justification>
  </clause>

  <clause id="4851">
    <literal><![CDATA[
      x \ T(x * y,1 / x) = ((1 / x) \ y) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1078,a,4823,a),flip(a)].">
      <j1 rule="hyper" parents="1078 4823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4852">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(1047,a,4823,a)].">
      <j1 rule="hyper" parents="1047 4823"/>
    </justification>
  </clause>

  <clause id="4853">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(334,a,971,a,b,4823,a)].">
      <j1 rule="hyper" parents="334 971 4823"/>
    </justification>
  </clause>

  <clause id="4855">
    <literal><![CDATA[
      (x \ T(x * y,z)) * x != u
    ]]></literal>
    <literal><![CDATA[
      T(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(4823(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4823 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4856">
    <literal><![CDATA[
      T(K(x,y) * (y * x),z) / (y * x) = (y * x) \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(84(a,1),4823(a,2,2,1))].">
      <j1 rule="para" parents="84 4823"/>
    </justification>
  </clause>

  <clause id="4857">
    <literal><![CDATA[
      x * (T(y * x,z) / x) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ T(x * y,z) = w
    ]]></literal>
    <justification jstring="[para(4823(a,2),427(a,1,2))].">
      <j1 rule="para" parents="4823 427"/>
    </justification>
  </clause>

  <clause id="4858">
    <literal><![CDATA[
      x * (y \ T(y * (x \ z),x)) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[para(4823(a,1),4202(a,1,2))].">
      <j1 rule="para" parents="4823 4202"/>
    </justification>
  </clause>

  <clause id="4860">
    <literal><![CDATA[
      T(x,y) / R(x,z,u) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(4262(a,1),4825(a,1,1,1))].">
      <j1 rule="para" parents="4262 4825"/>
    </justification>
  </clause>

  <clause id="4861">
    <literal><![CDATA[
      x \ T(x * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y * x,z) / x = u
    ]]></literal>
    <justification jstring="[para(4832(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4832 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4862">
    <literal><![CDATA[
      T(x * ((1 / (1 / y)) / x),K(z,y)) = x * ((1 / (1 / y)) / x)
    ]]></literal>
    <justification jstring="[para(3701(a,1),4841(a,1,2))].">
      <j1 rule="para" parents="3701 4841"/>
    </justification>
  </clause>

  <clause id="4863">
    <literal><![CDATA[
      T(K(x,y),z * (x / z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,4842,a)].">
      <j1 rule="hyper" parents="49 4842"/>
    </justification>
  </clause>

  <clause id="4864">
    <literal><![CDATA[
      T(K(x * y,z),y * x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),4863(a,1,2,2))].">
      <j1 rule="para" parents="6 4863"/>
    </justification>
  </clause>

  <clause id="4865">
    <literal><![CDATA[
      K(x * y,z) * (y * x) = (y * x) * K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4864,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 4864 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4866">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = z * (x * ((z \ y) / x))
    ]]></literal>
    <justification jstring="[para(107(a,1),4826(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="107 4826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4867">
    <literal><![CDATA[
      (x * (((y * z) / y) / x)) * y = y * (x * (z / x))
    ]]></literal>
    <justification jstring="[para(230(a,1),4826(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="230 4826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4869">
    <literal><![CDATA[
      T(1 / x,(y \ x) * y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(246,a,3972,a(flip),b,4847,a(flip))].">
      <j1 rule="hyper" parents="246 3972 4847"/>
    </justification>
  </clause>

  <clause id="4870">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[para(107(a,1),4847(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="107 4847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4871">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * ((x \ y) * x) = z
    ]]></literal>
    <justification jstring="[para(4869(a,1),294(a,1,2))].">
      <j1 rule="para" parents="4869 294"/>
    </justification>
  </clause>

  <clause id="4872">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) / x = (y \ (z / x)) * y
    ]]></literal>
    <justification jstring="[hyper(281,a,4849,a)].">
      <j1 rule="hyper" parents="281 4849"/>
    </justification>
  </clause>

  <clause id="4873">
    <literal><![CDATA[
      (R(x,y,z) \ T(x,u)) \ T(x,u) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(192,a,4860,a)].">
      <j1 rule="hyper" parents="192 4860"/>
    </justification>
  </clause>

  <clause id="4874">
    <literal><![CDATA[
      x \ T(y * K(z \ 1,z),u) = (x \ T(y,u)) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(4817(a,2),3551(a,1,2))].">
      <j1 rule="para" parents="4817 3551"/>
    </justification>
  </clause>

  <clause id="4875">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(334,a,1204,a(flip),b,4824,a),flip(a)].">
      <j1 rule="hyper" parents="334 1204 4824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4876">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) / (x \ y) = u
    ]]></literal>
    <justification jstring="[para(4836(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4836 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4877">
    <literal><![CDATA[
      T(x * (y / x),z / y) = T(x * (y / x),y \ z)
    ]]></literal>
    <justification jstring="[hyper(334,a,4821,a,b,4843,a),flip(a)].">
      <j1 rule="hyper" parents="334 4821 4843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4878">
    <literal><![CDATA[
      ((1 / x) / y) * T(((1 / x) / y) \ z,u) = (x \ T(x * (z * y),u)) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,4852,a(flip),b,1611,a),flip(a)].">
      <j1 rule="hyper" parents="117 4852 1611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4879">
    <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(1682(a,1),4853(a,2,1,1))].">
      <j1 rule="para" parents="1682 4853"/>
    </justification>
  </clause>

  <clause id="4880">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = ((u * ((y / x) / u)) * x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4372,a(flip),b,4866,a),flip(a)].">
      <j1 rule="hyper" parents="58 4372 4866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4881">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = y * ((x \ (y \ z)) * x)
    ]]></literal>
    <justification jstring="[hyper(1151,a,4870,a)].">
      <j1 rule="hyper" parents="1151 4870"/>
    </justification>
  </clause>

  <clause id="4882">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4046,a,b,4870,a)].">
      <j1 rule="hyper" parents="58 4046 4870"/>
    </justification>
  </clause>

  <clause id="4883">
    <literal><![CDATA[
      ((x \ R(1 / y,y,z)) * x) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(223(a,2),4870(a,1,1,1,2))].">
      <j1 rule="para" parents="223 4870"/>
    </justification>
  </clause>

  <clause id="4884">
    <literal><![CDATA[
      (x * ((y \ z) * y)) / x = (y \ ((x * z) / x)) * y
    ]]></literal>
    <justification jstring="[para(4(a,1),4872(a,1,1,2,1,2))].">
      <j1 rule="para" parents="4 4872"/>
    </justification>
  </clause>

  <clause id="4885">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x \ (z \ y)) * x) = u
    ]]></literal>
    <justification jstring="[para(4872(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4872 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4886">
    <literal><![CDATA[
      (x \ ((y * (x * z)) / y)) * x = (y * (z * x)) / y
    ]]></literal>
    <justification jstring="[para(62(a,1),4872(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="62 4872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4887">
    <literal><![CDATA[
      T(x * (y / x),(y / z) \ 1) = T(x * (y / x),y \ z)
    ]]></literal>
    <justification jstring="[hyper(4723,a,4877,a)].">
      <j1 rule="hyper" parents="4723 4877"/>
    </justification>
  </clause>

  <clause id="4888">
    <literal><![CDATA[
      (x \ ((x * y) / x)) * x = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4624,a,4884,a),flip(a)].">
      <j1 rule="hyper" parents="4624 4884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4889">
    <literal><![CDATA[
      ((x \ (y / (z \ 1))) * x) * (z \ 1) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(1692,a,4858,a)].">
      <j1 rule="hyper" parents="1692 4858"/>
    </justification>
  </clause>

  <clause id="4890">
    <literal><![CDATA[
      ((x \ y) * x) / y != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * ((x \ y) * x) = z
    ]]></literal>
    <justification jstring="[para(4228(a,1),4871(a,1))].">
      <j1 rule="para" parents="4228 4871"/>
    </justification>
  </clause>

  <clause id="4891">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      y * ((x \ (y \ z)) * x) = u
    ]]></literal>
    <justification jstring="[para(1150(a,2),4885(a,1))].">
      <j1 rule="para" parents="1150 4885"/>
    </justification>
  </clause>

  <clause id="4892">
    <literal><![CDATA[
      T(x * ((1 / (1 / y)) / x),K(z,y)) = L(x * (y / x),y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,3677,a,b,4862,a),flip(a)].">
      <j1 rule="hyper" parents="334 3677 4862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4893">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = ((y \ (z * x)) * y) / x
    ]]></literal>
    <justification jstring="[hyper(4885,a,4889,a)].">
      <j1 rule="hyper" parents="4885 4889"/>
    </justification>
  </clause>

  <clause id="4894">
    <literal><![CDATA[
      ((x \ (y * z)) * x) / z = z \ ((x \ (z * y)) * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3688,a(flip),b,4893,a),flip(a)].">
      <j1 rule="hyper" parents="58 3688 4893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4895">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * x = (y \ (z * x)) * y
    ]]></literal>
    <justification jstring="[hyper(133,a,4894,a)].">
      <j1 rule="hyper" parents="133 4894"/>
    </justification>
  </clause>

  <clause id="4896">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * x != u
    ]]></literal>
    <literal><![CDATA[
      (y \ (z * x)) * y = u
    ]]></literal>
    <justification jstring="[para(4894(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4894 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4897">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[para(4786(a,1),4422(a,1,1))].">
      <j1 rule="para" parents="4786 4422"/>
    </justification>
  </clause>

  <clause id="4898">
    <literal><![CDATA[
      (T(x,y) \ x) * z = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(4445,a,4897,a),flip(a)].">
      <j1 rule="hyper" parents="4445 4897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4899">
    <literal><![CDATA[
      (T(x,y) \ x) * (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(4403,a,4897,a),flip(a)].">
      <j1 rule="hyper" parents="4403 4897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4900">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = T(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(334,a,4475,a,b,4897,a),flip(a)].">
      <j1 rule="hyper" parents="334 4475 4897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4901">
    <literal><![CDATA[
      (T(x,y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(4897(a,1),4445(a,1))].">
      <j1 rule="para" parents="4897 4445"/>
    </justification>
  </clause>

  <clause id="4903">
    <literal><![CDATA[
      T(x,y) * (x \ z) = y * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(4477,a,4898,a)].">
      <j1 rule="hyper" parents="4477 4898"/>
    </justification>
  </clause>

  <clause id="4904">
    <literal><![CDATA[
      x * T(x \ y,z) = z * (T(z,y / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4633,a(flip),b,4898,a)].">
      <j1 rule="hyper" parents="58 4633 4898"/>
    </justification>
  </clause>

  <clause id="4907">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(4477,a,4899,a)].">
      <j1 rule="hyper" parents="4477 4899"/>
    </justification>
  </clause>

  <clause id="4908">
    <literal><![CDATA[
      ((x * y) / x) \ (T(x,y) * z) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(116,a,4899,a(flip),b,4411,a),flip(a)].">
      <j1 rule="hyper" parents="116 4899 4411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4909">
    <literal><![CDATA[
      T(x,y) * (T(y,x) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(4899(a,1),4474(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4899 4474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4910">
    <literal><![CDATA[
      T(x,y) \ (T(y,x) \ z) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(1189,a,4903,a),flip(a)].">
      <j1 rule="hyper" parents="1189 4903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4911">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y * z) = w
    ]]></literal>
    <justification jstring="[para(4903(a,2),631(a,1))].">
      <j1 rule="para" parents="4903 631"/>
    </justification>
  </clause>

  <clause id="4912">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (y * z) / w = u
    ]]></literal>
    <justification jstring="[para(4903(a,2),633(a,1))].">
      <j1 rule="para" parents="4903 633"/>
    </justification>
  </clause>

  <clause id="4913">
    <literal><![CDATA[
      ((x * y) / x) * (x * z) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4907,a(flip),b,4697,a)].">
      <j1 rule="hyper" parents="119 4907 4697"/>
    </justification>
  </clause>

  <clause id="4914">
    <literal><![CDATA[
      T(x,y) * ((x \ T(y,x)) * z) = y * L(z,x \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(487(a,1),4907(a,1,2))].">
      <j1 rule="para" parents="487 4907"/>
    </justification>
  </clause>

  <clause id="4915">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y))
    ]]></literal>
    <justification jstring="[para(4909(a,1),4519(a,1,2))].">
      <j1 rule="para" parents="4909 4519"/>
    </justification>
  </clause>

  <clause id="4916">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,(y * x) / y) \ z) = ((y * x) / y) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(741(a,1),4910(a,1,1))].">
      <j1 rule="para" parents="741 4910"/>
    </justification>
  </clause>

  <clause id="4917">
    <literal><![CDATA[
      x \ T(x * y,z) = z * (T(z,y / (x \ 1)) \ y)
    ]]></literal>
    <justification jstring="[hyper(1075,a,4904,a)].">
      <j1 rule="hyper" parents="1075 4904"/>
    </justification>
  </clause>

  <clause id="4918">
    <literal><![CDATA[
      x \ (y * ((y \ x) * z)) = L(z,y \ x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(4125,a,4908,a),flip(a)].">
      <j1 rule="hyper" parents="4125 4908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4919">
    <literal><![CDATA[
      (x \ y) * (T(x,x \ y) * z) = (y / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),4913(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 4913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4920">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,z \ 1) = y * (T(x,y) * a(x,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(726(a,1),4913(a,1,2))].">
      <j1 rule="para" parents="726 4913"/>
    </justification>
  </clause>

  <clause id="4921">
    <literal><![CDATA[
      a((x * y) / x,x,z) = (y * (T(x,y) * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(4913(a,1),83(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4913 83"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4922">
    <literal><![CDATA[
      L(x,T(y,z),T(z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(495,a,4915,a),flip(a)].">
      <j1 rule="hyper" parents="495 4915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4923">
    <literal><![CDATA[
      L(x,T(y,z),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4915(a,1),495(a,1))].">
      <j1 rule="para" parents="4915 495"/>
    </justification>
  </clause>

  <clause id="4924">
    <literal><![CDATA[
      L(x,y \ z,T(y,z / y)) = L(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(107(a,1),4922(a,1,2))].">
      <j1 rule="para" parents="107 4922"/>
    </justification>
  </clause>

  <clause id="4925">
    <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(4431(a,1),4923(a,1,2))].">
      <j1 rule="para" parents="4431 4923"/>
    </justification>
  </clause>

  <clause id="4926">
    <literal><![CDATA[
      L(x,y \ z,T(y,y \ z)) = L(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(4495(a,1),4924(a,1,3))].">
      <j1 rule="para" parents="4495 4924"/>
    </justification>
  </clause>

  <clause id="4927">
    <literal><![CDATA[
      x * (T(x,(y / z) / (z \ 1)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(58,a,4816,a(flip),b,4917,a),flip(a)].">
      <j1 rule="hyper" parents="58 4816 4917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4928">
    <literal><![CDATA[
      a((x * y) / x,x,z) = a(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,235,a(flip),b,4921,a),flip(a)].">
      <j1 rule="hyper" parents="334 235 4921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4929">
    <literal><![CDATA[
      a(x \ y,T(x,x \ y),z) = a(y / x,x,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),4928(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 4928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4930">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4909(a,1),4518(a,1,1))].">
      <j1 rule="para" parents="4909 4518"/>
    </justification>
  </clause>

  <clause id="4931">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(709,a,4930,a),flip(a)].">
      <j1 rule="hyper" parents="709 4930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4932">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4930(a,1),709(a,1))].">
      <j1 rule="para" parents="4930 709"/>
    </justification>
  </clause>

  <clause id="4933">
    <literal><![CDATA[
      a(T(x,y),T(T(y,x),x),z) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4473(a,1),4931(a,1,1))].">
      <j1 rule="para" parents="4473 4931"/>
    </justification>
  </clause>

  <clause id="4934">
    <literal><![CDATA[
      (R(x,y,z) * T(u,x)) * T(x,u) = (R(x,y,z) * u) * x
    ]]></literal>
    <justification jstring="[hyper(334,a,526,a(flip),b,4781,a),flip(a)].">
      <j1 rule="hyper" parents="334 526 4781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4935">
    <literal><![CDATA[
      T(x * y,x) * T(x,y) = (R(x,y,x) * y) * x
    ]]></literal>
    <justification jstring="[para(1380(a,1),4934(a,1,1))].">
      <j1 rule="para" parents="1380 4934"/>
    </justification>
  </clause>

  <clause id="4936">
    <literal><![CDATA[
      (R(x,y,x) * y) * x = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4588,a(flip),b,4935,a),flip(a)].">
      <j1 rule="hyper" parents="58 4588 4935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4937">
    <literal><![CDATA[
      (R(x,y,x) * y) \ (R(x,y,x) * T(x * y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(116,a,4732,a,b,4935,a(flip))].">
      <j1 rule="hyper" parents="116 4732 4935"/>
    </justification>
  </clause>

  <clause id="4938">
    <literal><![CDATA[
      (R(x,y,x) * y) \ ((x * y) * R(x,y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(4936(a,1),299(a,1,2))].">
      <j1 rule="para" parents="4936 299"/>
    </justification>
  </clause>

  <clause id="4939">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(4586,a,4937,a)].">
      <j1 rule="hyper" parents="4586 4937"/>
    </justification>
  </clause>

  <clause id="4940">
    <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(4892(a,2),563(a,1))].">
      <j1 rule="para" parents="4892 563"/>
    </justification>
  </clause>

  <clause id="4941">
    <literal><![CDATA[
      x * (x * T(T(x,y) \ y,z)) = (x * T(x \ y,z)) * x
    ]]></literal>
    <justification jstring="[para(6(a,1),4508(a,1,2,2,1,2))].">
      <j1 rule="para" parents="6 4508"/>
    </justification>
  </clause>

  <clause id="4942">
    <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(4637(a,2),447(a,1))].">
      <j1 rule="para" parents="4637 447"/>
    </justification>
  </clause>

  <clause id="4943">
    <literal><![CDATA[
      T(x,T(y,z)) / (T(T(y,x),z) \ x) = T(y,T(z,T(y,x)))
    ]]></literal>
    <justification jstring="[para(4692(a,1),4691(a,1,1))].">
      <j1 rule="para" parents="4692 4691"/>
    </justification>
  </clause>

  <clause id="4944">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4525,a(flip),b,4943,a),flip(a)].">
      <j1 rule="hyper" parents="58 4525 4943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4946">
    <literal><![CDATA[
      T(x,T(y,z)) * T(y,x) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,4944,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4944 17"/>
    </justification>
  </clause>

  <clause id="4948">
    <literal><![CDATA[
      T(x / (x / y),T(z,y)) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[para(252(a,1),4944(a,1,2,2))].">
      <j1 rule="para" parents="252 4944"/>
    </justification>
  </clause>

  <clause id="4951">
    <literal><![CDATA[
      T(x,y) \ (x * T(y,T(x,z))) = T(T(y,x),T(x,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,4946,a(flip),b,4496,a)].">
      <j1 rule="hyper" parents="116 4946 4496"/>
    </justification>
  </clause>

  <clause id="4952">
    <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(4948(a,1),4647(a,1,1))].">
      <j1 rule="para" parents="4948 4647"/>
    </justification>
  </clause>

  <clause id="4953">
    <literal><![CDATA[
      ((x / y) \ T(x,y)) * (x / y) = y \ (x * ((y \ x) \ x))
    ]]></literal>
    <justification jstring="[para(7(a,1),4699(a,1,1,2,1))].">
      <j1 rule="para" parents="7 4699"/>
    </justification>
  </clause>

  <clause id="4954">
    <literal><![CDATA[
      x \ (y * ((x \ y) \ y)) = ((y * x) / y) * (y / x)
    ]]></literal>
    <justification jstring="[para(4116(a,1),4953(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4116 4953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4955">
    <literal><![CDATA[
      ((x * y) / x) * (x / y) = y * (x / T(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4700,a(flip),b,4954,a),flip(a)].">
      <j1 rule="hyper" parents="58 4700 4954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4956">
    <literal><![CDATA[
      (x \ y) * (y / T(x \ y,y)) = ((y * (x \ y)) / y) * x
    ]]></literal>
    <justification jstring="[para(72(a,1),4955(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 4955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4957">
    <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),4956(a,1,2,2,1))].">
      <j1 rule="para" parents="106 4956"/>
    </justification>
  </clause>

  <clause id="4958">
    <literal><![CDATA[
      T((x \ y) * x,y) / y = y / (x * (y / x))
    ]]></literal>
    <justification jstring="[para(4801(a,1),4795(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4801 4795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4959">
    <literal><![CDATA[
      ((x \ y) * x) / y = y / (x * (y / x))
    ]]></literal>
    <justification jstring="[para(4706(a,1),4958(a,1,1))].">
      <j1 rule="para" parents="4706 4958"/>
    </justification>
  </clause>

  <clause id="4960">
    <literal><![CDATA[
      ((x \ y) * x) / y = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(334,a,4631,a(flip),b,4959,a),flip(a)].">
      <j1 rule="hyper" parents="334 4631 4959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4961">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(4890,a,4960,a)].">
      <j1 rule="hyper" parents="4890 4960"/>
    </justification>
  </clause>

  <clause id="4962">
    <literal><![CDATA[
      x \ (y / (y / x)) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * ((x \ y) * x) = z
    ]]></literal>
    <justification jstring="[para(4960(a,1),4890(a,1))].">
      <j1 rule="para" parents="4960 4890"/>
    </justification>
  </clause>

  <clause id="4963">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ 1)) * x,y \ 1,y) = y * (x \ (y / (y / x)))
    ]]></literal>
    <justification jstring="[para(4961(a,1),3952(a,2,2))].">
      <j1 rule="para" parents="4961 3952"/>
    </justification>
  </clause>

  <clause id="4964">
    <literal><![CDATA[
      (x \ (1 \ (y * 1))) * x = y * (x \ (y / (y / x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,3681,a(flip),b,4963,a)].">
      <j1 rule="hyper" parents="58 3681 4963"/>
    </justification>
  </clause>

  <clause id="4965">
    <literal><![CDATA[
      x * (y \ (x / (x / y))) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(163(a,1),4964(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="163 4964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4966">
    <literal><![CDATA[
      x \ (y / (y / x)) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,315,a,b,4965,a),flip(a)].">
      <j1 rule="hyper" parents="29 315 4965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4967">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(4962,a,4966,a)].">
      <j1 rule="hyper" parents="4962 4966"/>
    </justification>
  </clause>

  <clause id="4968">
    <literal><![CDATA[
      x / (y * (x / y)) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(4632,a,4966,a)].">
      <j1 rule="hyper" parents="4632 4966"/>
    </justification>
  </clause>

  <clause id="4969">
    <literal><![CDATA[
      x / (x / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,4966,a),flip(a)].">
      <j1 rule="hyper" parents="134 4966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4970">
    <literal><![CDATA[
      T(x,y) / (T(x,y) / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4679,a(flip),b,4966,a),flip(a)].">
      <j1 rule="hyper" parents="119 4679 4966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4971">
    <literal><![CDATA[
      ((x \ y) * x) / y = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4960,a,b,4966,a)].">
      <j1 rule="hyper" parents="58 4960 4966"/>
    </justification>
  </clause>

  <clause id="4976">
    <literal><![CDATA[
      K(x \ y,x) * (x * (y / x)) = y
    ]]></literal>
    <justification jstring="[hyper(133,a,4968,a)].">
      <j1 rule="hyper" parents="133 4968"/>
    </justification>
  </clause>

  <clause id="4978">
    <literal><![CDATA[
      x \ K((x \ 1) \ y,x \ 1) = y / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(334,a,2563,a(flip),b,4969,a)].">
      <j1 rule="hyper" parents="334 2563 4969"/>
    </justification>
  </clause>

  <clause id="4979">
    <literal><![CDATA[
      (x * y) * K((x * y) \ y,x * y) = y / R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(223(a,2),4969(a,1,2)),flip(a)].">
      <j1 rule="para" parents="223 4969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4980">
    <literal><![CDATA[
      T(x * K(x \ y,x),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(4969(a,1),4645(a,1,1))].">
      <j1 rule="para" parents="4969 4645"/>
    </justification>
  </clause>

  <clause id="4981">
    <literal><![CDATA[
      K(x \ y,x) * y = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,4971,a)].">
      <j1 rule="hyper" parents="133 4971"/>
    </justification>
  </clause>

  <clause id="4982">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4228,a,b,4971,a)].">
      <j1 rule="hyper" parents="58 4228 4971"/>
    </justification>
  </clause>

  <clause id="4983">
    <literal><![CDATA[
      R(K(x \ y,x),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (((x \ y) * x) * z) / (y * z) = u
    ]]></literal>
    <justification jstring="[para(4971(a,1),871(a,1,1))].">
      <j1 rule="para" parents="4971 871"/>
    </justification>
  </clause>

  <clause id="4984">
    <literal><![CDATA[
      T(x,K(y \ x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(478,a,4981,a)].">
      <j1 rule="hyper" parents="478 4981"/>
    </justification>
  </clause>

  <clause id="4985">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(4981(a,1),2047(a,2,2))].">
      <j1 rule="para" parents="4981 2047"/>
    </justification>
  </clause>

  <clause id="4986">
    <literal><![CDATA[
      T(x * y,K(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(4(a,1),4984(a,1,2,1))].">
      <j1 rule="para" parents="4 4984"/>
    </justification>
  </clause>

  <clause id="4987">
    <literal><![CDATA[
      T(x,K(y,x / y)) = x
    ]]></literal>
    <justification jstring="[para(75(a,1),4984(a,1,2,1))].">
      <j1 rule="para" parents="75 4984"/>
    </justification>
  </clause>

  <clause id="4988">
    <literal><![CDATA[
      K(x,y) \ (x * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(441,a,4986,a)].">
      <j1 rule="hyper" parents="441 4986"/>
    </justification>
  </clause>

  <clause id="4989">
    <literal><![CDATA[
      T(K(x,y),y * x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,4986,a)].">
      <j1 rule="hyper" parents="49 4986"/>
    </justification>
  </clause>

  <clause id="4990">
    <literal><![CDATA[
      K(x,y) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[hyper(119,a,4986,a(flip),b,319,a(flip))].">
      <j1 rule="hyper" parents="119 4986 319"/>
    </justification>
  </clause>

  <clause id="4991">
    <literal><![CDATA[
      K(x,y / x) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(594,a,4988,a)].">
      <j1 rule="hyper" parents="594 4988"/>
    </justification>
  </clause>

  <clause id="4992">
    <literal><![CDATA[
      K(L(x,y,z),z * y) * (z * (y * x)) = L(x,y,z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(592,a,4988,a)].">
      <j1 rule="hyper" parents="592 4988"/>
    </justification>
  </clause>

  <clause id="4993">
    <literal><![CDATA[
      x * (y * z) != z * y
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = x
    ]]></literal>
    <justification jstring="[para(4988(a,1),129(a,1,2))].">
      <j1 rule="para" parents="4988 129"/>
    </justification>
  </clause>

  <clause id="4994">
    <literal><![CDATA[
      L(x \ (y * z),x,K(z,y)) = (K(z,y) * x) \ (z * y)
    ]]></literal>
    <justification jstring="[para(4988(a,1),311(a,1,1,2))].">
      <j1 rule="para" parents="4988 311"/>
    </justification>
  </clause>

  <clause id="4995">
    <literal><![CDATA[
      K(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4591,a,4989,a),flip(a)].">
      <j1 rule="hyper" parents="4591 4989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4996">
    <literal><![CDATA[
      K(x,y) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(4416,a,4989,a),flip(a)].">
      <j1 rule="hyper" parents="4416 4989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4997">
    <literal><![CDATA[
      T(K(x,y),x) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3481,a,4995,a)].">
      <j1 rule="hyper" parents="3481 4995"/>
    </justification>
  </clause>

  <clause id="4998">
    <literal><![CDATA[
      T(T(x,y),x \ 1) = (x \ 1) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(451,a,4995,a,b,1033,a)].">
      <j1 rule="hyper" parents="451 4995 1033"/>
    </justification>
  </clause>

  <clause id="4999">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,4410,a,b,4995,a)].">
      <j1 rule="hyper" parents="334 4410 4995"/>
    </justification>
  </clause>

  <clause id="5000">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,4401,a,b,4995,a)].">
      <j1 rule="hyper" parents="334 4401 4995"/>
    </justification>
  </clause>

  <clause id="5001">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,4204,a,b,4995,a)].">
      <j1 rule="hyper" parents="334 4204 4995"/>
    </justification>
  </clause>

  <clause id="5002">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,4194,a,b,4995,a)].">
      <j1 rule="hyper" parents="334 4194 4995"/>
    </justification>
  </clause>

  <clause id="5004">
    <literal><![CDATA[
      K(x,y) = ((x * y) / x) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,4063,a,b,4995,a),flip(a)].">
      <j1 rule="hyper" parents="334 4063 4995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5005">
    <literal><![CDATA[
      K(x,y) = ((x * y) / x) / y
    ]]></literal>
    <justification jstring="[hyper(334,a,4060,a,b,4995,a),flip(a)].">
      <j1 rule="hyper" parents="334 4060 4995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5006">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,4059,a,b,4995,a)].">
      <j1 rule="hyper" parents="334 4059 4995"/>
    </justification>
  </clause>

  <clause id="5007">
    <literal><![CDATA[
      K(x,y) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(334,a,4055,a,b,4995,a),flip(a)].">
      <j1 rule="hyper" parents="334 4055 4995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5008">
    <literal><![CDATA[
      K(x,y) = (1 / x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,2586,a,b,4995,a),flip(a)].">
      <j1 rule="hyper" parents="334 2586 4995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5009">
    <literal><![CDATA[
      K(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(334,a,2581,a,b,4995,a),flip(a)].">
      <j1 rule="hyper" parents="334 2581 4995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5010">
    <literal><![CDATA[
      K(x,y) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,1033,a,b,4995,a),flip(a)].">
      <j1 rule="hyper" parents="334 1033 4995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5011">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,2588,a(flip),b,4995,a)].">
      <j1 rule="hyper" parents="334 2588 4995"/>
    </justification>
  </clause>

  <clause id="5012">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,766,a(flip),b,4995,a)].">
      <j1 rule="hyper" parents="334 766 4995"/>
    </justification>
  </clause>

  <clause id="5014">
    <literal><![CDATA[
      T(x,y) * K(y,x) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,4995,a,b,4470,a)].">
      <j1 rule="hyper" parents="119 4995 4470"/>
    </justification>
  </clause>

  <clause id="5015">
    <literal><![CDATA[
      x * K(y,(x \ z) \ 1) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4995,a,b,4166,a)].">
      <j1 rule="hyper" parents="119 4995 4166"/>
    </justification>
  </clause>

  <clause id="5016">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,4995,a,b,4057,a)].">
      <j1 rule="hyper" parents="119 4995 4057"/>
    </justification>
  </clause>

  <clause id="5017">
    <literal><![CDATA[
      (x * y) / x = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4995,a,b,4055,a),flip(a)].">
      <j1 rule="hyper" parents="119 4995 4055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5018">
    <literal><![CDATA[
      x / (x / y) = y * K(x / y,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4995,a,b,4058,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 4995 4058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5020">
    <literal><![CDATA[
      T(x,y) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4995,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="119 4995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5021">
    <literal><![CDATA[
      K(x,y) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(117,a,4995,a,b,2586,a)].">
      <j1 rule="hyper" parents="117 4995 2586"/>
    </justification>
  </clause>

  <clause id="5022">
    <literal><![CDATA[
      T(x,y) = K(x,y) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,4995,a,b,1033,a),flip(a)].">
      <j1 rule="hyper" parents="117 4995 1033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5023">
    <literal><![CDATA[
      ((x * y) / x) \ K(x,y) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,4995,a,b,4063,a)].">
      <j1 rule="hyper" parents="116 4995 4063"/>
    </justification>
  </clause>

  <clause id="5024">
    <literal><![CDATA[
      T(x,y) \ K(x,y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,4995,a,b,1033,a)].">
      <j1 rule="hyper" parents="116 4995 1033"/>
    </justification>
  </clause>

  <clause id="5026">
    <literal><![CDATA[
      x \ T(x,y \ 1) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3700,a,b,4995,a),flip(a)].">
      <j1 rule="hyper" parents="58 3700 4995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5027">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,y) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,3442,a(flip),b,4995,a(flip))].">
      <j1 rule="hyper" parents="119 3442 4995"/>
    </justification>
  </clause>

  <clause id="5028">
    <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),4995(a,2,2)),flip(a)].">
      <j1 rule="para" parents="20 4995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5029">
    <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),4995(a,2,2)),flip(a)].">
      <j1 rule="para" parents="22 4995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5030">
    <literal><![CDATA[
      x * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4995(a,2),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4995 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5031">
    <literal><![CDATA[
      L(K(x \ y,z),x \ y,x) = y \ (x * T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(4995(a,2),502(a,1,1))].">
      <j1 rule="para" parents="4995 502"/>
    </justification>
  </clause>

  <clause id="5032">
    <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(4995(a,2),599(a,1,1))].">
      <j1 rule="para" parents="4995 599"/>
    </justification>
  </clause>

  <clause id="5033">
    <literal><![CDATA[
      K(x,x * (y \ 1)) = x \ T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(1751(a,1),4995(a,2,2))].">
      <j1 rule="para" parents="1751 4995"/>
    </justification>
  </clause>

  <clause id="5034">
    <literal><![CDATA[
      T(x,y) = K(x,y) * x
    ]]></literal>
    <justification jstring="[para(4995(a,2),2583(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4995 2583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5035">
    <literal><![CDATA[
      K(x,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4995(a,2),2590(a,1,1))].">
      <j1 rule="para" parents="4995 2590"/>
    </justification>
  </clause>

  <clause id="5036">
    <literal><![CDATA[
      (x * K(y,x)) * K(x,z) = K(y,x) * T(x,z)
    ]]></literal>
    <justification jstring="[para(4995(a,2),2881(a,1,2))].">
      <j1 rule="para" parents="4995 2881"/>
    </justification>
  </clause>

  <clause id="5037">
    <literal><![CDATA[
      (x \ (y * z)) \ (((x \ (y * z)) \ 1) \ 1) = K(x \ (y * z),z \ (y \ x))
    ]]></literal>
    <justification jstring="[para(3639(a,1),4995(a,2,2)),flip(a)].">
      <j1 rule="para" parents="3639 4995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5038">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3916(a,1),4995(a,2,2))].">
      <j1 rule="para" parents="3916 4995"/>
    </justification>
  </clause>

  <clause id="5039">
    <literal><![CDATA[
      (x * K(y,x)) * y = y * x
    ]]></literal>
    <justification jstring="[para(4995(a,2),4050(a,1,1,2))].">
      <j1 rule="para" parents="4995 4050"/>
    </justification>
  </clause>

  <clause id="5040">
    <literal><![CDATA[
      (x * y) / x = K(x,y) * y
    ]]></literal>
    <justification jstring="[para(4995(a,2),4054(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4995 4054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5041">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(4995(a,2),4052(a,1,2))].">
      <j1 rule="para" parents="4995 4052"/>
    </justification>
  </clause>

  <clause id="5042">
    <literal><![CDATA[
      (T(x,y) * z) / (K(x,y) * z) = x
    ]]></literal>
    <justification jstring="[para(4995(a,2),4378(a,1,2,1))].">
      <j1 rule="para" parents="4995 4378"/>
    </justification>
  </clause>

  <clause id="5043">
    <literal><![CDATA[
      x \ (T(x,y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(4995(a,2),4379(a,2,1))].">
      <j1 rule="para" parents="4995 4379"/>
    </justification>
  </clause>

  <clause id="5044">
    <literal><![CDATA[
      x * (K(x,y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(4995(a,2),4380(a,1,2,1))].">
      <j1 rule="para" parents="4995 4380"/>
    </justification>
  </clause>

  <clause id="5045">
    <literal><![CDATA[
      T(x,y) * (x \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(4995(a,2),4381(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4995 4381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5046">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(x,y) \ z
    ]]></literal>
    <justification jstring="[para(4995(a,2),4391(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4995 4391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5047">
    <literal><![CDATA[
      K(x,y) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(4995(a,2),4397(a,1,1))].">
      <j1 rule="para" parents="4995 4397"/>
    </justification>
  </clause>

  <clause id="5048">
    <literal><![CDATA[
      K(x,x \ y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4995(a,2),4400(a,1,1))].">
      <j1 rule="para" parents="4995 4400"/>
    </justification>
  </clause>

  <clause id="5049">
    <literal><![CDATA[
      K(x,y) \ (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[para(4995(a,2),4402(a,1,1))].">
      <j1 rule="para" parents="4995 4402"/>
    </justification>
  </clause>

  <clause id="5050">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(4995(a,2),4387(a,1,1))].">
      <j1 rule="para" parents="4995 4387"/>
    </justification>
  </clause>

  <clause id="5051">
    <literal><![CDATA[
      K(x,y) \ (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(4995(a,2),4404(a,1,1))].">
      <j1 rule="para" parents="4995 4404"/>
    </justification>
  </clause>

  <clause id="5052">
    <literal><![CDATA[
      K(x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(4995(a,2),4445(a,1,1))].">
      <j1 rule="para" parents="4995 4445"/>
    </justification>
  </clause>

  <clause id="5054">
    <literal><![CDATA[
      K(x,(y \ z) / z) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(4713(a,1),4995(a,2,2))].">
      <j1 rule="para" parents="4713 4995"/>
    </justification>
  </clause>

  <clause id="5056">
    <literal><![CDATA[
      T(x,y) * (x \ z) = K(y,x) \ z
    ]]></literal>
    <justification jstring="[para(4995(a,2),4900(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4995 4900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5057">
    <literal><![CDATA[
      T(x,x \ (x / y)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4469,a,4996,a),flip(a)].">
      <j1 rule="hyper" parents="4469 4996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5058">
    <literal><![CDATA[
      T(x,y) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(2730,a,4996,a),flip(a)].">
      <j1 rule="hyper" parents="2730 4996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5059">
    <literal><![CDATA[
      K(x \ (x / y),x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,4466,a,b,4996,a)].">
      <j1 rule="hyper" parents="334 4466 4996"/>
    </justification>
  </clause>

  <clause id="5060">
    <literal><![CDATA[
      K(x,y) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(334,a,4064,a,b,4996,a),flip(a)].">
      <j1 rule="hyper" parents="334 4064 4996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5061">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ 1 = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,2819,a,b,4996,a)].">
      <j1 rule="hyper" parents="334 2819 4996"/>
    </justification>
  </clause>

  <clause id="5062">
    <literal><![CDATA[
      K(x,y) = y / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,2511,a,b,4996,a),flip(a)].">
      <j1 rule="hyper" parents="334 2511 4996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5063">
    <literal><![CDATA[
      K(x,y) = (1 / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(334,a,2510,a,b,4996,a),flip(a)].">
      <j1 rule="hyper" parents="334 2510 4996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5064">
    <literal><![CDATA[
      K(x,y) = y * (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,1163,a,b,4996,a),flip(a)].">
      <j1 rule="hyper" parents="334 1163 4996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5065">
    <literal><![CDATA[
      T(T(x,y),z) \ T(x,z) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,155,a,b,4996,a)].">
      <j1 rule="hyper" parents="334 155 4996"/>
    </justification>
  </clause>

  <clause id="5066">
    <literal><![CDATA[
      K(T(x,y),y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,4065,a(flip),b,4996,a),flip(a)].">
      <j1 rule="hyper" parents="334 4065 4996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5067">
    <literal><![CDATA[
      ((x \ y) \ y) \ x = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,325,a(flip),b,4996,a)].">
      <j1 rule="hyper" parents="334 325 4996"/>
    </justification>
  </clause>

  <clause id="5068">
    <literal><![CDATA[
      ((x * y) / x) * K(y,x) = y
    ]]></literal>
    <justification jstring="[hyper(119,a,4996,a,b,4064,a)].">
      <j1 rule="hyper" parents="119 4996 4064"/>
    </justification>
  </clause>

  <clause id="5069">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,4996,a,b,2813,a)].">
      <j1 rule="hyper" parents="119 4996 2813"/>
    </justification>
  </clause>

  <clause id="5070">
    <literal><![CDATA[
      (1 / x) * K(y,x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4996,a,b,2509,a)].">
      <j1 rule="hyper" parents="119 4996 2509"/>
    </justification>
  </clause>

  <clause id="5071">
    <literal><![CDATA[
      ((x \ y) \ y) * K(x \ y,x) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,4996,a,b,325,a(flip))].">
      <j1 rule="hyper" parents="119 4996 325"/>
    </justification>
  </clause>

  <clause id="5072">
    <literal><![CDATA[
      K(x,y) / y = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,4996,a,b,2510,a)].">
      <j1 rule="hyper" parents="117 4996 2510"/>
    </justification>
  </clause>

  <clause id="5073">
    <literal><![CDATA[
      T(x,y) \ 1 = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4996,a,b,1163,a),flip(a)].">
      <j1 rule="hyper" parents="116 4996 1163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5074">
    <literal><![CDATA[
      T(x,y) = x / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(201,a,4996,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="201 4996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5075">
    <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),4996(a,2,1)),flip(a)].">
      <j1 rule="para" parents="20 4996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5076">
    <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),4996(a,2,1)),flip(a)].">
      <j1 rule="para" parents="22 4996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5077">
    <literal><![CDATA[
      K(x,y) != 1
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = y
    ]]></literal>
    <justification jstring="[para(4996(a,2),169(a,1)),flip(b)].">
      <j1 rule="para" parents="4996 169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5079">
    <literal><![CDATA[
      x / K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4996(a,2),345(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4996 345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5080">
    <literal><![CDATA[
      K((1 / x) \ y,y) = T(y,y * x) \ y
    ]]></literal>
    <justification jstring="[para(1752(a,1),4996(a,2,1))].">
      <j1 rule="para" parents="1752 4996"/>
    </justification>
  </clause>

  <clause id="5081">
    <literal><![CDATA[
      K(x,y) * T(y,x) = y
    ]]></literal>
    <justification jstring="[para(4996(a,2),2514(a,1,1))].">
      <j1 rule="para" parents="4996 2514"/>
    </justification>
  </clause>

  <clause id="5082">
    <literal><![CDATA[
      K(x,y) * ((y * x) / y) = x
    ]]></literal>
    <justification jstring="[para(4996(a,2),4061(a,1,1))].">
      <j1 rule="para" parents="4996 4061"/>
    </justification>
  </clause>

  <clause id="5083">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(4996(a,2),4411(a,2,1))].">
      <j1 rule="para" parents="4996 4411"/>
    </justification>
  </clause>

  <clause id="5084">
    <literal><![CDATA[
      ((x * y) / x) \ x = y \ (x * K(y,x))
    ]]></literal>
    <justification jstring="[para(4996(a,2),4413(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4996 4413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5086">
    <literal><![CDATA[
      T(x * K(y,x),y) = x
    ]]></literal>
    <justification jstring="[para(4996(a,2),4504(a,1,1,2))].">
      <j1 rule="para" parents="4996 4504"/>
    </justification>
  </clause>

  <clause id="5087">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4996(a,2),4506(a,1))].">
      <j1 rule="para" parents="4996 4506"/>
    </justification>
  </clause>

  <clause id="5088">
    <literal><![CDATA[
      K(x / y,z) * x = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(4996(a,2),4633(a,1,1))].">
      <j1 rule="para" parents="4996 4633"/>
    </justification>
  </clause>

  <clause id="5089">
    <literal><![CDATA[
      x * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) / y = z
    ]]></literal>
    <justification jstring="[para(4996(a,2),4710(a,1,2))].">
      <j1 rule="para" parents="4996 4710"/>
    </justification>
  </clause>

  <clause id="5090">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(4996(a,2),4898(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4996 4898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5091">
    <literal><![CDATA[
      K(x,y) * (T(y,x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(4996(a,2),4899(a,1,1))].">
      <j1 rule="para" parents="4996 4899"/>
    </justification>
  </clause>

  <clause id="5092">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * (T(y,x) \ z) = u
    ]]></literal>
    <justification jstring="[para(4996(a,2),4901(a,1,1))].">
      <j1 rule="para" parents="4996 4901"/>
    </justification>
  </clause>

  <clause id="5093">
    <literal><![CDATA[
      T(1 / x,y) * x = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,972,a(flip),b,5009,a)].">
      <j1 rule="hyper" parents="334 972 5009"/>
    </justification>
  </clause>

  <clause id="5094">
    <literal><![CDATA[
      K(x,y \ 1) / y = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,5009,a,b,4170,a)].">
      <j1 rule="hyper" parents="117 5009 4170"/>
    </justification>
  </clause>

  <clause id="5096">
    <literal><![CDATA[
      K(x \ (x / L(1 / y,z,u)),x) = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5009(a,2),2742(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5009 2742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5098">
    <literal><![CDATA[
      T(x,y) != x
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = 1
    ]]></literal>
    <justification jstring="[para(5014(a,1),121(a,1)),flip(a),flip(b)].">
      <j1 rule="para" parents="5014 121"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5099">
    <literal><![CDATA[
      (x \ y) * K(x,y / x) = y / x
    ]]></literal>
    <justification jstring="[para(107(a,1),5014(a,1,1))].">
      <j1 rule="para" parents="107 5014"/>
    </justification>
  </clause>

  <clause id="5100">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5014(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5014 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5101">
    <literal><![CDATA[
      T(x \ T(y,x),z) * K(z,T(x,y) \ y) = T(x,y) \ y
    ]]></literal>
    <justification jstring="[para(4639(a,1),5014(a,1,1))].">
      <j1 rule="para" parents="4639 5014"/>
    </justification>
  </clause>

  <clause id="5102">
    <literal><![CDATA[
      x * (y * K(x,y)) = T(x,y) * y
    ]]></literal>
    <justification jstring="[para(5014(a,1),4909(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5014 4909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5103">
    <literal><![CDATA[
      (x * y) * L(K(y,z),y,x) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5020,a,b,309,a),flip(a)].">
      <j1 rule="hyper" parents="119 5020 309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5104">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4944,a,b,5020,a)].">
      <j1 rule="hyper" parents="58 4944 5020"/>
    </justification>
  </clause>

  <clause id="5106">
    <literal><![CDATA[
      T(x,T(y,x / y)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4540,a,b,5020,a)].">
      <j1 rule="hyper" parents="58 4540 5020"/>
    </justification>
  </clause>

  <clause id="5109">
    <literal><![CDATA[
      T(x,y) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5020(a,2),38(a,1))].">
      <j1 rule="para" parents="5020 38"/>
    </justification>
  </clause>

  <clause id="5110">
    <literal><![CDATA[
      x \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5020(a,2),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5020 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5112">
    <literal><![CDATA[
      x * K(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(5020(a,1),439(a,1))].">
      <j1 rule="para" parents="5020 439"/>
    </justification>
  </clause>

  <clause id="5113">
    <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(5020(a,2),527(a,2,2))].">
      <j1 rule="para" parents="5020 527"/>
    </justification>
  </clause>

  <clause id="5114">
    <literal><![CDATA[
      T(x,y) != z * x
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5020(a,2),3466(a,1))].">
      <j1 rule="para" parents="5020 3466"/>
    </justification>
  </clause>

  <clause id="5115">
    <literal><![CDATA[
      K(T(x,y),z) * T(x,y) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(447,a,5034,a),flip(a)].">
      <j1 rule="hyper" parents="447 5034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5116">
    <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,5034,a),flip(a)].">
      <j1 rule="hyper" parents="58 20 5034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5119">
    <literal><![CDATA[
      x * (K(y,x) * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(119,a,5034,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 5034 17"/>
    </justification>
  </clause>

  <clause id="5121">
    <literal><![CDATA[
      L(x \ y,x,K(y,z)) = (K(y,z) * x) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(5034(a,2),92(a,2,2))].">
      <j1 rule="para" parents="5034 92"/>
    </justification>
  </clause>

  <clause id="5123">
    <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(5034(a,2),495(a,1,2,2))].">
      <j1 rule="para" parents="5034 495"/>
    </justification>
  </clause>

  <clause id="5124">
    <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(5034(a,2),527(a,2,2))].">
      <j1 rule="para" parents="5034 527"/>
    </justification>
  </clause>

  <clause id="5125">
    <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(5034(a,2),619(a,1,2))].">
      <j1 rule="para" parents="5034 619"/>
    </justification>
  </clause>

  <clause id="5126">
    <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(5034(a,2),708(a,1,1))].">
      <j1 rule="para" parents="5034 708"/>
    </justification>
  </clause>

  <clause id="5127">
    <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(5034(a,2),996(a,1,2,1))].">
      <j1 rule="para" parents="5034 996"/>
    </justification>
  </clause>

  <clause id="5128">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5034(a,2),3469(a,1))].">
      <j1 rule="para" parents="5034 3469"/>
    </justification>
  </clause>

  <clause id="5129">
    <literal><![CDATA[
      K(x,y / x) * (x \ y) = y / x
    ]]></literal>
    <justification jstring="[hyper(806,a,5058,a)].">
      <j1 rule="hyper" parents="806 5058"/>
    </justification>
  </clause>

  <clause id="5130">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,4630,a,b,5058,a)].">
      <j1 rule="hyper" parents="334 4630 5058"/>
    </justification>
  </clause>

  <clause id="5131">
    <literal><![CDATA[
      T(x,y) = 1 / (x \ K(y,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,3719,a,b,5058,a),flip(a)].">
      <j1 rule="hyper" parents="334 3719 5058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5133">
    <literal><![CDATA[
      x / T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5058(a,2),345(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5058 345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5134">
    <literal><![CDATA[
      L(T(x,y),K(y,x),z) = (z * K(y,x)) \ (z * x)
    ]]></literal>
    <justification jstring="[para(5058(a,2),92(a,1,1))].">
      <j1 rule="para" parents="5058 92"/>
    </justification>
  </clause>

  <clause id="5135">
    <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(5058(a,2),2808(a,1,2,1))].">
      <j1 rule="para" parents="5058 2808"/>
    </justification>
  </clause>

  <clause id="5136">
    <literal><![CDATA[
      K(x,y) \ y != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(5062(a,2),276(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5062 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5137">
    <literal><![CDATA[
      (1 / (1 / x)) \ K(y,x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(5062(a,2),2315(a,1,2))].">
      <j1 rule="para" parents="5062 2315"/>
    </justification>
  </clause>

  <clause id="5139">
    <literal><![CDATA[
      (1 / (1 / x)) / K(y,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(3701(a,1),5074(a,2,2)),flip(a)].">
      <j1 rule="para" parents="3701 5074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5140">
    <literal><![CDATA[
      (T(x,y) * y) / T(x,y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4596,a,5086,a)].">
      <j1 rule="hyper" parents="4596 5086"/>
    </justification>
  </clause>

  <clause id="5141">
    <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(1965,a,5086,a),flip(a)].">
      <j1 rule="hyper" parents="1965 5086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5142">
    <literal><![CDATA[
      K(x,y * K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,5086,a(flip),b,5074,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="118 5086 5074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5143">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) = T(x,z)
    ]]></literal>
    <justification jstring="[para(5086(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5086 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5144">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      z * K(y,z) = x
    ]]></literal>
    <justification jstring="[para(5086(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="5086 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5145">
    <literal><![CDATA[
      (x * y) / x != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5086(a,1),346(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="5086 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5146">
    <literal><![CDATA[
      T(x * K(y,x),z) = (y * T(x,z)) / y
    ]]></literal>
    <justification jstring="[para(5086(a,1),279(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5086 279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5147">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * y = y * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(5086(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5086 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5148">
    <literal><![CDATA[
      R(x * K(y,x),z,u) * y = y * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(5086(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5086 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5149">
    <literal><![CDATA[
      T((x * (y * K(z,y))) / x,z) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(5086(a,1),472(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5086 472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5150">
    <literal><![CDATA[
      T(1 / (1 / (x * K(y,x))),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(5086(a,1),2224(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5086 2224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5151">
    <literal><![CDATA[
      T(K(x,y) * y,x) = y
    ]]></literal>
    <justification jstring="[para(2524(a,2),5086(a,1,1))].">
      <j1 rule="para" parents="2524 5086"/>
    </justification>
  </clause>

  <clause id="5152">
    <literal><![CDATA[
      T(x \ K(y,x \ 1),y) = x \ 1
    ]]></literal>
    <justification jstring="[para(2563(a,1),5086(a,1,1))].">
      <j1 rule="para" parents="2563 5086"/>
    </justification>
  </clause>

  <clause id="5153">
    <literal><![CDATA[
      (x * K(y,x)) * ((y \ 1) \ 1) = ((y \ 1) \ 1) * x
    ]]></literal>
    <justification jstring="[para(5086(a,1),3111(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5086 3111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5154">
    <literal><![CDATA[
      T(K(x,y \ 1) / y,x) = 1 / y
    ]]></literal>
    <justification jstring="[para(3708(a,1),5086(a,1,1))].">
      <j1 rule="para" parents="3708 5086"/>
    </justification>
  </clause>

  <clause id="5155">
    <literal><![CDATA[
      T(x,y * K(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5086(a,1),4473(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5086 4473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5156">
    <literal><![CDATA[
      T(x,L(y * K(x,y),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5086(a,1),4494(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5086 4494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5157">
    <literal><![CDATA[
      L(x * K(y,x),y,x * K(y,x)) = L(x * K(y,x),y,x)
    ]]></literal>
    <justification jstring="[para(5086(a,1),4783(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5086 4783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5158">
    <literal><![CDATA[
      ((x \ (y * K(z,y))) * x) * z = z * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(5086(a,1),4847(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5086 4847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5160">
    <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(4990(a,1),493(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4990 493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5161">
    <literal><![CDATA[
      (x * y) \ (K(x,y) * (y * (x * z))) = L(L(z,x,y),y * x,K(x,y))
    ]]></literal>
    <justification jstring="[para(4990(a,1),491(a,1,1))].">
      <j1 rule="para" parents="4990 491"/>
    </justification>
  </clause>

  <clause id="5162">
    <literal><![CDATA[
      T(x * y,z) / (y * x) = (y * x) \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(4990(a,1),4856(a,1,1,1))].">
      <j1 rule="para" parents="4990 4856"/>
    </justification>
  </clause>

  <clause id="5163">
    <literal><![CDATA[
      K(x,y) = (1 / y) * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(334,a,1579,a,b,5005,a),flip(a)].">
      <j1 rule="hyper" parents="334 1579 5005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5164">
    <literal><![CDATA[
      R(K(x,y / z),y / z,z) = (((x * (y / z)) / x) * z) / y
    ]]></literal>
    <justification jstring="[para(5005(a,2),538(a,1,1))].">
      <j1 rule="para" parents="5005 538"/>
    </justification>
  </clause>

  <clause id="5165">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(y,(x * z) / x)
    ]]></literal>
    <justification jstring="[para(1019(a,1),5005(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1019 5005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5166">
    <literal><![CDATA[
      (x \ T(x * y,y)) / y = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(4133(a,1),5005(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4133 5005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5168">
    <literal><![CDATA[
      (x \ 1) \ K(y,x) = (y * ((x \ 1) \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(116,a,5007,a,b,1523,a)].">
      <j1 rule="hyper" parents="116 5007 1523"/>
    </justification>
  </clause>

  <clause id="5169">
    <literal><![CDATA[
      x \ K(y,1 / x) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(116,a,5007,a,b,1572,a(flip))].">
      <j1 rule="hyper" parents="116 5007 1572"/>
    </justification>
  </clause>

  <clause id="5170">
    <literal><![CDATA[
      (x \ y) \ (y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),5007(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 5007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5171">
    <literal><![CDATA[
      x * ((y * z) / y) = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[para(5007(a,2),151(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5007 151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5172">
    <literal><![CDATA[
      ((x * y) / x) \ z = (y * K(x,y)) \ z
    ]]></literal>
    <justification jstring="[para(5007(a,2),156(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5007 156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5173">
    <literal><![CDATA[
      x * (y * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * ((z * y) / z) = u
    ]]></literal>
    <justification jstring="[para(5007(a,2),356(a,1,2,2))].">
      <j1 rule="para" parents="5007 356"/>
    </justification>
  </clause>

  <clause id="5174">
    <literal><![CDATA[
      L(K(x,y \ z),y \ z,y) = z \ (y * ((x * (y \ z)) / x))
    ]]></literal>
    <justification jstring="[para(5007(a,2),502(a,1,1))].">
      <j1 rule="para" parents="5007 502"/>
    </justification>
  </clause>

  <clause id="5175">
    <literal><![CDATA[
      R(x,y,z) \ R((u * x) / u,y,z) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(881(a,2),5007(a,2,2)),flip(a)].">
      <j1 rule="para" parents="881 5007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5176">
    <literal><![CDATA[
      T(x,y) \ ((z * x) / z) = x * (T(x,y) \ K(z,x))
    ]]></literal>
    <justification jstring="[para(5007(a,2),1162(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5007 1162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5177">
    <literal><![CDATA[
      K(x,y) * K(x \ 1,x) = (x \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5008(a,2),3186(a,1,1))].">
      <j1 rule="para" parents="5008 3186"/>
    </justification>
  </clause>

  <clause id="5178">
    <literal><![CDATA[
      K(1 / x,y) / x = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,5010,a,b,197,a(flip))].">
      <j1 rule="hyper" parents="117 5010 197"/>
    </justification>
  </clause>

  <clause id="5179">
    <literal><![CDATA[
      ((x * y) / x) \ 1 = y \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5010,a,b,4634,a),flip(a)].">
      <j1 rule="hyper" parents="116 5010 4634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5180">
    <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(5010(a,2),495(a,1,2,2))].">
      <j1 rule="para" parents="5010 495"/>
    </justification>
  </clause>

  <clause id="5181">
    <literal><![CDATA[
      T(x,y * x) * (x \ 1) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(4553(a,2),5010(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4553 5010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5182">
    <literal><![CDATA[
      K(x,T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,5014,a,b,5016,a),flip(a)].">
      <j1 rule="hyper" parents="29 5014 5016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5183">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ y) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(1996,a,5182,a)].">
      <j1 rule="hyper" parents="1996 5182"/>
    </justification>
  </clause>

  <clause id="5184">
    <literal><![CDATA[
      K(x,x \ (y * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(17(a,1),5182(a,1,2))].">
      <j1 rule="para" parents="17 5182"/>
    </justification>
  </clause>

  <clause id="5185">
    <literal><![CDATA[
      K(x,L(T(y,x),z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(20(a,2),5182(a,1,2))].">
      <j1 rule="para" parents="20 5182"/>
    </justification>
  </clause>

  <clause id="5186">
    <literal><![CDATA[
      K(x,y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),5182(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 5182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5187">
    <literal><![CDATA[
      K(x,L(y / x,z,u)) = K(x,L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(255(a,1),5182(a,1,2)),flip(a)].">
      <j1 rule="para" parents="255 5182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5188">
    <literal><![CDATA[
      K(x,R(y / x,z,u)) = K(x,R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(256(a,1),5182(a,1,2)),flip(a)].">
      <j1 rule="para" parents="256 5182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5189">
    <literal><![CDATA[
      K(x,(x * y) * (x \ 1)) = K(x,R(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[para(810(a,1),5182(a,1,2)),flip(a)].">
      <j1 rule="para" parents="810 5182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5190">
    <literal><![CDATA[
      K(x,y) \ T(y,x) = T(T(y,x),x)
    ]]></literal>
    <justification jstring="[para(5182(a,1),5058(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5182 5058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5191">
    <literal><![CDATA[
      (x * y) * K(T(y,x),x * y) = T(y,x * y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4800,a,5017,a),flip(a)].">
      <j1 rule="hyper" parents="4800 5017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5192">
    <literal><![CDATA[
      (x * y) \ ((x * y) / x) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5017,a,b,1560,a)].">
      <j1 rule="hyper" parents="116 5017 1560"/>
    </justification>
  </clause>

  <clause id="5193">
    <literal><![CDATA[
      x / ((y * z) / y) = x / (z * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(55,a,5017,a)].">
      <j1 rule="hyper" parents="55 5017"/>
    </justification>
  </clause>

  <clause id="5194">
    <literal><![CDATA[
      (x / ((y * z) / y)) * (z * K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,5017,a(flip),b,75,a)].">
      <j1 rule="hyper" parents="119 5017 75"/>
    </justification>
  </clause>

  <clause id="5195">
    <literal><![CDATA[
      x \ ((y * x) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5017(a,2),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5017 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5196">
    <literal><![CDATA[
      T(x * K(y,x),y) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(5017(a,1),306(a,1,1))].">
      <j1 rule="para" parents="5017 306"/>
    </justification>
  </clause>

  <clause id="5197">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(5017(a,1),346(a,1))].">
      <j1 rule="para" parents="5017 346"/>
    </justification>
  </clause>

  <clause id="5198">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(5017(a,1),348(a,1))].">
      <j1 rule="para" parents="5017 348"/>
    </justification>
  </clause>

  <clause id="5199">
    <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),5017(a,1,1))].">
      <j1 rule="para" parents="101 5017"/>
    </justification>
  </clause>

  <clause id="5200">
    <literal><![CDATA[
      R(x * K(y,x),y,z) = ((y * x) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(5017(a,1),102(a,1,1))].">
      <j1 rule="para" parents="5017 102"/>
    </justification>
  </clause>

  <clause id="5201">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y / x = z
    ]]></literal>
    <justification jstring="[para(5017(a,1),353(a,1))].">
      <j1 rule="para" parents="5017 353"/>
    </justification>
  </clause>

  <clause id="5202">
    <literal><![CDATA[
      R(x / y,y,K(z,x)) \ ((z * x) / z) = y * K(z,x)
    ]]></literal>
    <justification jstring="[para(5017(a,2),518(a,1,2))].">
      <j1 rule="para" parents="5017 518"/>
    </justification>
  </clause>

  <clause id="5203">
    <literal><![CDATA[
      R(x * K(y,x),y,y \ 1) = (y * x) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(5017(a,1),536(a,1,1))].">
      <j1 rule="para" parents="5017 536"/>
    </justification>
  </clause>

  <clause id="5204">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(5017(a,1),699(a,1,1,1))].">
      <j1 rule="para" parents="5017 699"/>
    </justification>
  </clause>

  <clause id="5205">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(5017(a,1),807(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5017 807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5206">
    <literal><![CDATA[
      L(x * K(y,x),z,u) = (y * L(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(5017(a,1),875(a,1,1))].">
      <j1 rule="para" parents="5017 875"/>
    </justification>
  </clause>

  <clause id="5207">
    <literal><![CDATA[
      R(x * K(y,x),z,u) = (y * R(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(5017(a,1),881(a,1,1))].">
      <j1 rule="para" parents="5017 881"/>
    </justification>
  </clause>

  <clause id="5208">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = a(x / y,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(5017(a,2),83(a,1,2))].">
      <j1 rule="para" parents="5017 83"/>
    </justification>
  </clause>

  <clause id="5209">
    <literal><![CDATA[
      T(T(x * K(y,x),z),x * y) = L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(5017(a,1),1002(a,1,1,1))].">
      <j1 rule="para" parents="5017 1002"/>
    </justification>
  </clause>

  <clause id="5210">
    <literal><![CDATA[
      L(x * K(y * z,x),z,y) = (y * (z * x)) / (y * z)
    ]]></literal>
    <justification jstring="[para(5017(a,1),877(a,1,1))].">
      <j1 rule="para" parents="5017 877"/>
    </justification>
  </clause>

  <clause id="5211">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / (y * K(z,y))) * y
    ]]></literal>
    <justification jstring="[para(5017(a,1),1588(a,2,1,2))].">
      <j1 rule="para" parents="5017 1588"/>
    </justification>
  </clause>

  <clause id="5212">
    <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(1702(a,1),5017(a,1,1))].">
      <j1 rule="para" parents="1702 5017"/>
    </justification>
  </clause>

  <clause id="5213">
    <literal><![CDATA[
      (x * K(y,x)) \ ((y * (x * y)) / y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(5017(a,1),1717(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5017 1717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5214">
    <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(1951(a,1),5017(a,1,1))].">
      <j1 rule="para" parents="1951 5017"/>
    </justification>
  </clause>

  <clause id="5215">
    <literal><![CDATA[
      T(x * y,y * K(x,y)) = T(x * y,y)
    ]]></literal>
    <justification jstring="[para(5017(a,1),4117(a,1,2))].">
      <j1 rule="para" parents="5017 4117"/>
    </justification>
  </clause>

  <clause id="5216">
    <literal><![CDATA[
      T(x * K(y,x),y * x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(5017(a,1),4580(a,1,1))].">
      <j1 rule="para" parents="5017 4580"/>
    </justification>
  </clause>

  <clause id="5217">
    <literal><![CDATA[
      (x \ (y * K(x,y))) * x = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5017(a,1),4888(a,1,1,2))].">
      <j1 rule="para" parents="5017 4888"/>
    </justification>
  </clause>

  <clause id="5219">
    <literal><![CDATA[
      T(x,y) * (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5022(a,2),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5022 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5220">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ 1,x \ y) = y / x
    ]]></literal>
    <justification jstring="[hyper(30,a,3122,a(flip),b,5039,a),flip(a)].">
      <j1 rule="hyper" parents="30 3122 5039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5221">
    <literal><![CDATA[
      (x \ K(y,x \ 1)) * y = y * (x \ 1)
    ]]></literal>
    <justification jstring="[para(2563(a,1),5039(a,1,1))].">
      <j1 rule="para" parents="2563 5039"/>
    </justification>
  </clause>

  <clause id="5222">
    <literal><![CDATA[
      x / ((y * K(x,y)) * ((x \ 1) \ 1)) = (1 / (1 / x)) / (x * y)
    ]]></literal>
    <justification jstring="[para(5039(a,1),3614(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5039 3614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5223">
    <literal><![CDATA[
      K(x,y) = x / ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(334,a,2611,a,b,5060,a),flip(a)].">
      <j1 rule="hyper" parents="334 2611 5060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5224">
    <literal><![CDATA[
      K(x,y) / x = 1 / ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(5060(a,2),2612(a,1,1))].">
      <j1 rule="para" parents="5060 2612"/>
    </justification>
  </clause>

  <clause id="5225">
    <literal><![CDATA[
      K(x \ K(x,y),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(5060(a,2),3318(a,1,1,2))].">
      <j1 rule="para" parents="5060 3318"/>
    </justification>
  </clause>

  <clause id="5226">
    <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(5063(a,2),530(a,1,2))].">
      <j1 rule="para" parents="5063 530"/>
    </justification>
  </clause>

  <clause id="5227">
    <literal><![CDATA[
      (x * y) \ (x * K(z,y)) = L(T(y,z) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(5064(a,2),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5064 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5228">
    <literal><![CDATA[
      x * (T(y,z) \ 1) = x * (y \ K(z,y))
    ]]></literal>
    <justification jstring="[para(5064(a,2),152(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5064 152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5229">
    <literal><![CDATA[
      L(T(x \ y,z) \ 1,x \ y,x) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[para(5064(a,2),91(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5064 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5230">
    <literal><![CDATA[
      K(T(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,4995,a,b,5066,a),flip(a)].">
      <j1 rule="hyper" parents="334 4995 5066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5232">
    <literal><![CDATA[
      K(x,y) \ 1 = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4666,a(flip),b,5230,a)].">
      <j1 rule="hyper" parents="58 4666 5230"/>
    </justification>
  </clause>

  <clause id="5233">
    <literal><![CDATA[
      K(x,y) * K(y,x) = 1
    ]]></literal>
    <justification jstring="[hyper(119,a,5230,a(flip),b,4666,a(flip))].">
      <j1 rule="hyper" parents="119 5230 4666"/>
    </justification>
  </clause>

  <clause id="5234">
    <literal><![CDATA[
      K(x \ (y * x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(17(a,1),5230(a,1,1))].">
      <j1 rule="para" parents="17 5230"/>
    </justification>
  </clause>

  <clause id="5235">
    <literal><![CDATA[
      K(x / y,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(107(a,1),5230(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5236">
    <literal><![CDATA[
      K((x \ y) \ y,x \ y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(106(a,1),5230(a,1,1))].">
      <j1 rule="para" parents="106 5230"/>
    </justification>
  </clause>

  <clause id="5237">
    <literal><![CDATA[
      K(R(x,y,x),y * x) = K(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(824(a,1),5230(a,1,1)),flip(a)].">
      <j1 rule="para" parents="824 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5238">
    <literal><![CDATA[
      K(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5230(a,1),4460(a,1))].">
      <j1 rule="para" parents="5230 4460"/>
    </justification>
  </clause>

  <clause id="5239">
    <literal><![CDATA[
      K(x / (x / y),y \ x) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(4544(a,1),5230(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4544 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5240">
    <literal><![CDATA[
      K(x,y) \ x = x * K(y,x)
    ]]></literal>
    <justification jstring="[para(5230(a,1),4669(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5230 4669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5241">
    <literal><![CDATA[
      K(x,y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5230(a,1),4670(a,1,1))].">
      <j1 rule="para" parents="5230 4670"/>
    </justification>
  </clause>

  <clause id="5242">
    <literal><![CDATA[
      K(x * K(y,x),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5086(a,1),5230(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5086 5230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5243">
    <literal><![CDATA[
      1 / K(x,y) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(2498,a,5232,a)].">
      <j1 rule="hyper" parents="2498 5232"/>
    </justification>
  </clause>

  <clause id="5245">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) = K(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5232,a(flip),b,5024,a)].">
      <j1 rule="hyper" parents="119 5232 5024"/>
    </justification>
  </clause>

  <clause id="5246">
    <literal><![CDATA[
      K(x,y) != z \ 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5232(a,1),43(a,1))].">
      <j1 rule="para" parents="5232 43"/>
    </justification>
  </clause>

  <clause id="5247">
    <literal><![CDATA[
      x * K(y,z) != 1
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = x
    ]]></literal>
    <justification jstring="[para(5232(a,1),129(a,1,2))].">
      <j1 rule="para" parents="5232 129"/>
    </justification>
  </clause>

  <clause id="5248">
    <literal><![CDATA[
      1 / K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5232(a,1),345(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5232 345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5249">
    <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(5232(a,1),2178(a,2,1,2,1))].">
      <j1 rule="para" parents="5232 2178"/>
    </justification>
  </clause>

  <clause id="5251">
    <literal><![CDATA[
      T(x * K(y,z),x \ K(z,y)) = ((x * K(y,z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(5232(a,1),3981(a,1,2,2))].">
      <j1 rule="para" parents="5232 3981"/>
    </justification>
  </clause>

  <clause id="5252">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) = L(z,K(y,x),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(851,a,5233,a)].">
      <j1 rule="hyper" parents="851 5233"/>
    </justification>
  </clause>

  <clause id="5253">
    <literal><![CDATA[
      K(x,y) * z != 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5233(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="5233 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5254">
    <literal><![CDATA[
      K(x,y) \ 1 != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(5233(a,1),551(a,1,2))].">
      <j1 rule="para" parents="5233 551"/>
    </justification>
  </clause>

  <clause id="5255">
    <literal><![CDATA[
      1 / K(x \ 1,y) = K(y,1 / x)
    ]]></literal>
    <justification jstring="[hyper(334,a,3700,a,b,5243,a),flip(a)].">
      <j1 rule="hyper" parents="334 3700 5243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5257">
    <literal><![CDATA[
      ((x * y) / x) \ y != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5068(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5068 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5259">
    <literal><![CDATA[
      K(1 / x,L(x,y,z)) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(32,a,3694,a,b,5072,a),flip(a)].">
      <j1 rule="hyper" parents="32 3694 5072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5260">
    <literal><![CDATA[
      1 / (x \ K(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(5073(a,1),345(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5073 345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5261">
    <literal><![CDATA[
      T(x,y) * L(x \ K(y,x),z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[para(5073(a,1),2198(a,1,2,1))].">
      <j1 rule="para" parents="5073 2198"/>
    </justification>
  </clause>

  <clause id="5262">
    <literal><![CDATA[
      T(T(x,x \ 1),y) = (x \ K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(5073(a,1),2220(a,2,1))].">
      <j1 rule="para" parents="5073 2220"/>
    </justification>
  </clause>

  <clause id="5263">
    <literal><![CDATA[
      K(x,y) * K(y \ 1,y) = (T(y,x) \ 1) * y
    ]]></literal>
    <justification jstring="[para(5073(a,2),3497(a,2,1))].">
      <j1 rule="para" parents="5073 3497"/>
    </justification>
  </clause>

  <clause id="5264">
    <literal><![CDATA[
      K(x \ y,x) * (y / x) = x \ y
    ]]></literal>
    <justification jstring="[para(5(a,1),5082(a,1,2,1))].">
      <j1 rule="para" parents="5 5082"/>
    </justification>
  </clause>

  <clause id="5266">
    <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),5082(a,1,2,1))].">
      <j1 rule="para" parents="80 5082"/>
    </justification>
  </clause>

  <clause id="5268">
    <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(5155(a,1),4769(a,2,2))].">
      <j1 rule="para" parents="5155 4769"/>
    </justification>
  </clause>

  <clause id="5270">
    <literal><![CDATA[
      x \ (y * (x / y)) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,87,a,b,5186,a)].">
      <j1 rule="hyper" parents="58 87 5186"/>
    </justification>
  </clause>

  <clause id="5271">
    <literal><![CDATA[
      K(x,x \ (y \ x)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,4744,a(flip),b,5186,a),flip(a)].">
      <j1 rule="hyper" parents="58 4744 5186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5272">
    <literal><![CDATA[
      x * K(y,y \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5186,a(flip),b,87,a)].">
      <j1 rule="hyper" parents="119 5186 87"/>
    </justification>
  </clause>

  <clause id="5273">
    <literal><![CDATA[
      T(x,K(y,y \ x)) = x
    ]]></literal>
    <justification jstring="[para(5186(a,1),4987(a,1,2))].">
      <j1 rule="para" parents="5186 4987"/>
    </justification>
  </clause>

  <clause id="5275">
    <literal><![CDATA[
      (x \ y) / (y / x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),5223(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 5223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5276">
    <literal><![CDATA[
      x / (y / (y / x)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4548(a,1),5223(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4548 5223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5277">
    <literal><![CDATA[
      x * K(x / y,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,5235,a,b,85,a)].">
      <j1 rule="hyper" parents="119 5235 85"/>
    </justification>
  </clause>

  <clause id="5282">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(3442(a,1),5030(a,1,2))].">
      <j1 rule="para" parents="3442 5030"/>
    </justification>
  </clause>

  <clause id="5283">
    <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),5100(a,1,1))].">
      <j1 rule="para" parents="18 5100"/>
    </justification>
  </clause>

  <clause id="5284">
    <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),5100(a,1,1))].">
      <j1 rule="para" parents="20 5100"/>
    </justification>
  </clause>

  <clause id="5286">
    <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(331(a,1),5100(a,1,1))].">
      <j1 rule="para" parents="331 5100"/>
    </justification>
  </clause>

  <clause id="5287">
    <literal><![CDATA[
      K(x \ (x / y),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(4466(a,2),5100(a,1))].">
      <j1 rule="para" parents="4466 5100"/>
    </justification>
  </clause>

  <clause id="5288">
    <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),5110(a,1,2))].">
      <j1 rule="para" parents="20 5110"/>
    </justification>
  </clause>

  <clause id="5289">
    <literal><![CDATA[
      x \ ((x \ y) \ y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(106(a,1),5110(a,1,2))].">
      <j1 rule="para" parents="106 5110"/>
    </justification>
  </clause>

  <clause id="5290">
    <literal><![CDATA[
      x \ L(T(x,y),y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(731(a,2),5110(a,1,2))].">
      <j1 rule="para" parents="731 5110"/>
    </justification>
  </clause>

  <clause id="5292">
    <literal><![CDATA[
      T(K(x,y),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4997(a,2),5110(a,1))].">
      <j1 rule="para" parents="4997 5110"/>
    </justification>
  </clause>

  <clause id="5293">
    <literal><![CDATA[
      K(x,x \ (y * x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(17(a,1),5238(a,1,2))].">
      <j1 rule="para" parents="17 5238"/>
    </justification>
  </clause>

  <clause id="5294">
    <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),5238(a,1,2))].">
      <j1 rule="para" parents="20 5238"/>
    </justification>
  </clause>

  <clause id="5295">
    <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(1137(a,1),5238(a,1,2))].">
      <j1 rule="para" parents="1137 5238"/>
    </justification>
  </clause>

  <clause id="5297">
    <literal><![CDATA[
      K(T(x,x \ 1),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3462(a,2),5292(a,1))].">
      <j1 rule="para" parents="3462 5292"/>
    </justification>
  </clause>

  <clause id="5298">
    <literal><![CDATA[
      K(x,y \ 1) * (y \ x) = x * ((y \ x) / x)
    ]]></literal>
    <justification jstring="[para(4744(a,1),4991(a,1,1))].">
      <j1 rule="para" parents="4744 4991"/>
    </justification>
  </clause>

  <clause id="5299">
    <literal><![CDATA[
      K(x,y) * (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(5000(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5000 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5300">
    <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),5000(a,1,2))].">
      <j1 rule="para" parents="101 5000"/>
    </justification>
  </clause>

  <clause id="5301">
    <literal><![CDATA[
      (T(x,y) * R(x \ 1,x,z)) / ((z / (x * z)) * x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(670(a,2),5000(a,1,2))].">
      <j1 rule="para" parents="670 5000"/>
    </justification>
  </clause>

  <clause id="5302">
    <literal><![CDATA[
      (x * T(x \ y,y)) * (y \ 1) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[para(843(a,1),5004(a,2,1)),flip(a)].">
      <j1 rule="para" parents="843 5004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5303">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2750,a,5011,a)].">
      <j1 rule="hyper" parents="2750 5011"/>
    </justification>
  </clause>

  <clause id="5304">
    <literal><![CDATA[
      x * (y * T(y \ (x \ 1),z)) = K((x * y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(977,a,5011,a)].">
      <j1 rule="hyper" parents="977 5011"/>
    </justification>
  </clause>

  <clause id="5307">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K((x / y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1646,a(flip),b,5011,a)].">
      <j1 rule="hyper" parents="58 1646 5011"/>
    </justification>
  </clause>

  <clause id="5308">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1526,a(flip),b,5011,a)].">
      <j1 rule="hyper" parents="58 1526 5011"/>
    </justification>
  </clause>

  <clause id="5309">
    <literal><![CDATA[
      (x \ (x / y)) * x = (x / y) * K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5011,a(flip),b,1006,a),flip(a)].">
      <j1 rule="hyper" parents="119 5011 1006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5310">
    <literal><![CDATA[
      ((x * y) \ x) * (x * y) = x * K(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5011,a(flip),b,990,a),flip(a)].">
      <j1 rule="hyper" parents="119 5011 990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5311">
    <literal><![CDATA[
      L(x \ 1,x,y) * (y * x) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5011,a(flip),b,650,a),flip(a)].">
      <j1 rule="hyper" parents="119 5011 650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5312">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K((y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5011,a(flip),b,1526,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 5011 1526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5313">
    <literal><![CDATA[
      x \ K((x * y) \ 1,z) = y * T(y \ (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(116,a,5011,a(flip),b,956,a(flip))].">
      <j1 rule="hyper" parents="116 5011 956"/>
    </justification>
  </clause>

  <clause id="5315">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = K(x \ 1,z) * y
    ]]></literal>
    <justification jstring="[para(5011(a,1),1286(a,2,1))].">
      <j1 rule="para" parents="5011 1286"/>
    </justification>
  </clause>

  <clause id="5316">
    <literal><![CDATA[
      K(x \ 1,y) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(5011(a,1),1296(a,1,1))].">
      <j1 rule="para" parents="5011 1296"/>
    </justification>
  </clause>

  <clause id="5317">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = K(x \ 1,z) * y
    ]]></literal>
    <justification jstring="[para(5011(a,1),1456(a,2,1))].">
      <j1 rule="para" parents="5011 1456"/>
    </justification>
  </clause>

  <clause id="5318">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),x) = T(K(y \ 1,x),z)
    ]]></literal>
    <justification jstring="[para(5011(a,1),1600(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5011 1600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5319">
    <literal><![CDATA[
      K((x / y) \ 1,z) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(5011(a,1),1645(a,1,1))].">
      <j1 rule="para" parents="5011 1645"/>
    </justification>
  </clause>

  <clause id="5321">
    <literal><![CDATA[
      K((x * y) \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = z
    ]]></literal>
    <justification jstring="[para(5011(a,1),1637(a,1))].">
      <j1 rule="para" parents="5011 1637"/>
    </justification>
  </clause>

  <clause id="5322">
    <literal><![CDATA[
      (x * (y * T(y \ 1,z))) * y = (x * y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(5011(a,1),1780(a,2,2))].">
      <j1 rule="para" parents="5011 1780"/>
    </justification>
  </clause>

  <clause id="5323">
    <literal><![CDATA[
      (x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * K(y \ 1,u)) * z
    ]]></literal>
    <justification jstring="[para(5011(a,1),2380(a,2,1,2))].">
      <j1 rule="para" parents="5011 2380"/>
    </justification>
  </clause>

  <clause id="5324">
    <literal><![CDATA[
      (x * y) * ((z \ L(y \ z,y,x)) * z) = (x * K(y \ 1,z)) * z
    ]]></literal>
    <justification jstring="[para(5011(a,1),2381(a,2,1,2))].">
      <j1 rule="para" parents="5011 2381"/>
    </justification>
  </clause>

  <clause id="5326">
    <literal><![CDATA[
      x * ((y \ (x \ y)) * y) = y * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(5011(a,1),2576(a,2,2))].">
      <j1 rule="para" parents="5011 2576"/>
    </justification>
  </clause>

  <clause id="5327">
    <literal><![CDATA[
      K(x \ (x / L(y,z,u)),x) = L(K(y \ 1,x),z,u)
    ]]></literal>
    <justification jstring="[para(5011(a,1),2738(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5011 2738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5328">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K(1 / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1646,a(flip),b,5012,a)].">
      <j1 rule="hyper" parents="58 1646 5012"/>
    </justification>
  </clause>

  <clause id="5329">
    <literal><![CDATA[
      L(K(1 / x,x),y,z) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(5012(a,1),3354(a,1,1,1))].">
      <j1 rule="para" parents="5012 3354"/>
    </justification>
  </clause>

  <clause id="5330">
    <literal><![CDATA[
      (x * (y / x)) \ x = y \ (y / (y / x))
    ]]></literal>
    <justification jstring="[para(5018(a,2),1561(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5018 1561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5331">
    <literal><![CDATA[
      K(x,(x / y) / x) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(4142,a,5026,a)].">
      <j1 rule="hyper" parents="4142 5026"/>
    </justification>
  </clause>

  <clause id="5333">
    <literal><![CDATA[
      x \ (y * ((z * (y \ x)) / z)) = K(z,1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,4166,a,b,5026,a)].">
      <j1 rule="hyper" parents="58 4166 5026"/>
    </justification>
  </clause>

  <clause id="5334">
    <literal><![CDATA[
      K(x,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(5026(a,1),5110(a,1))].">
      <j1 rule="para" parents="5026 5110"/>
    </justification>
  </clause>

  <clause id="5335">
    <literal><![CDATA[
      x * (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(5042(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5042 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5336">
    <literal><![CDATA[
      x \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(5042(a,1),276(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5042 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5337">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[para(5042(a,1),313(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5042 313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5338">
    <literal><![CDATA[
      x * (K(y,x) * K(x,z)) = T(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(2070,a,5043,a)].">
      <j1 rule="hyper" parents="2070 5043"/>
    </justification>
  </clause>

  <clause id="5339">
    <literal><![CDATA[
      T(x,y) * T(z,K(x,y)) = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(593,a,5043,a),flip(a)].">
      <j1 rule="hyper" parents="593 5043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5340">
    <literal><![CDATA[
      T(x,y) * K(K(x,y),z) = x * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5020,a,b,5043,a),flip(a)].">
      <j1 rule="hyper" parents="119 5020 5043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5341">
    <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,4505,a,b,5043,a)].">
      <j1 rule="hyper" parents="119 4505 5043"/>
    </justification>
  </clause>

  <clause id="5343">
    <literal><![CDATA[
      K(x,y) * T(z,T(x,y)) = x \ (z * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,228,a(flip),b,5043,a),flip(a)].">
      <j1 rule="hyper" parents="58 228 5043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5344">
    <literal><![CDATA[
      T(x,y) \ (K(x,y) * z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,5043,a(flip),b,1154,a(flip))].">
      <j1 rule="hyper" parents="116 5043 1154"/>
    </justification>
  </clause>

  <clause id="5345">
    <literal><![CDATA[
      x \ y != K(x,z) * u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) * u = y
    ]]></literal>
    <justification jstring="[para(5043(a,1),42(a,1)),flip(a)].">
      <j1 rule="para" parents="5043 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5347">
    <literal><![CDATA[
      x \ ((x * y) / x) = K(x,y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(4106(a,1),5043(a,1,2))].">
      <j1 rule="para" parents="4106 5043"/>
    </justification>
  </clause>

  <clause id="5348">
    <literal><![CDATA[
      K(x,y) \ (x \ z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(610,a,5044,a),flip(a)].">
      <j1 rule="hyper" parents="610 5044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5350">
    <literal><![CDATA[
      ((x * y) / x) \ z = K(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(29,a,4634,a,b,5044,a)].">
      <j1 rule="hyper" parents="29 4634 5044"/>
    </justification>
  </clause>

  <clause id="5351">
    <literal><![CDATA[
      K(x,y) * (z * x) = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,1165,a,b,5044,a),flip(a)].">
      <j1 rule="hyper" parents="29 1165 5044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5352">
    <literal><![CDATA[
      K(x,y) * T(y,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,4730,a(flip),b,5044,a),flip(a)].">
      <j1 rule="hyper" parents="29 4730 5044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5353">
    <literal><![CDATA[
      K(x,y) * T(y,x * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,4729,a(flip),b,5044,a),flip(a)].">
      <j1 rule="hyper" parents="29 4729 5044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5354">
    <literal><![CDATA[
      K(x,y) * (T(y,z) * x) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,4693,a(flip),b,5044,a),flip(a)].">
      <j1 rule="hyper" parents="29 4693 5044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5355">
    <literal><![CDATA[
      K(x * y,x) * T(x,y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,4588,a(flip),b,5044,a),flip(a)].">
      <j1 rule="hyper" parents="29 4588 5044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5356">
    <literal><![CDATA[
      (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5044(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5044 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5358">
    <literal><![CDATA[
      T(x,y) * (K(x,y) * z) = T(T(x,y),y) * z
    ]]></literal>
    <justification jstring="[para(5230(a,1),5044(a,1,2,1))].">
      <j1 rule="para" parents="5230 5044"/>
    </justification>
  </clause>

  <clause id="5359">
    <literal><![CDATA[
      (x * y) / (T(x,z) * y) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(4912,a,5045,a)].">
      <j1 rule="hyper" parents="4912 5045"/>
    </justification>
  </clause>

  <clause id="5360">
    <literal><![CDATA[
      K(x,y) \ (y * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(4911,a,5045,a)].">
      <j1 rule="hyper" parents="4911 5045"/>
    </justification>
  </clause>

  <clause id="5361">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = K(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(992,a,5045,a)].">
      <j1 rule="hyper" parents="992 5045"/>
    </justification>
  </clause>

  <clause id="5362">
    <literal><![CDATA[
      T(x,y) * (x \ R(x,z,u)) = R(x,z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,3473,a,b,5045,a),flip(a)].">
      <j1 rule="hyper" parents="334 3473 5045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5363">
    <literal><![CDATA[
      x * (K(x,y) * (x \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,5044,a,b,5045,a)].">
      <j1 rule="hyper" parents="58 5044 5045"/>
    </justification>
  </clause>

  <clause id="5364">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,4697,a,b,5045,a)].">
      <j1 rule="hyper" parents="58 4697 5045"/>
    </justification>
  </clause>

  <clause id="5365">
    <literal><![CDATA[
      (x \ L(x,y,z)) * T(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3667,a(flip),b,5045,a)].">
      <j1 rule="hyper" parents="58 3667 5045"/>
    </justification>
  </clause>

  <clause id="5366">
    <literal><![CDATA[
      x \ (K(x,y) * z) = K(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,5045,a(flip),b,5044,a)].">
      <j1 rule="hyper" parents="116 5045 5044"/>
    </justification>
  </clause>

  <clause id="5367">
    <literal><![CDATA[
      x \ (K(y,x) * z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,5045,a(flip),b,4903,a(flip))].">
      <j1 rule="hyper" parents="116 5045 4903"/>
    </justification>
  </clause>

  <clause id="5368">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * (K(y,z) * u)) = L(y \ u,T(y,z),x)
    ]]></literal>
    <justification jstring="[para(5045(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5045 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5369">
    <literal><![CDATA[
      K(x * y,z) * (x * (y * u)) = T(x * y,z) * L(u,y,x)
    ]]></literal>
    <justification jstring="[para(13(a,2),5045(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13 5045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5370">
    <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),5045(a,1,2)),flip(a)].">
      <j1 rule="para" parents="110 5045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5371">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ z = u
    ]]></literal>
    <justification jstring="[para(5045(a,1),1190(a,1))].">
      <j1 rule="para" parents="5045 1190"/>
    </justification>
  </clause>

  <clause id="5372">
    <literal><![CDATA[
      K(x,y) * T(x,z) = T(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[para(4995(a,2),5045(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4995 5045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5373">
    <literal><![CDATA[
      K(x,y / z) \ y = z * T(z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4904,a,b,5046,a),flip(a)].">
      <j1 rule="hyper" parents="58 4904 5046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5374">
    <literal><![CDATA[
      K(x,y / (z \ 1)) * (z \ T(z * y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(119,a,4917,a,b,5046,a(flip))].">
      <j1 rule="hyper" parents="119 4917 5046"/>
    </justification>
  </clause>

  <clause id="5375">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) = x * T(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(17(a,2),5046(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17 5046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5378">
    <literal><![CDATA[
      K(x,y) * (x * (T(y,x) * z)) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(334,a,4909,a(flip),b,5047,a),flip(a)].">
      <j1 rule="hyper" parents="334 4909 5047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5379">
    <literal><![CDATA[
      K(x,x \ y) * (x * z) = ((x \ y) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(334,a,328,a(flip),b,5047,a),flip(a)].">
      <j1 rule="hyper" parents="334 328 5047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5380">
    <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),5047(a,2,1))].">
      <j1 rule="para" parents="22 5047"/>
    </justification>
  </clause>

  <clause id="5381">
    <literal><![CDATA[
      T(x,y) * (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(5047(a,1),356(a,1))].">
      <j1 rule="para" parents="5047 356"/>
    </justification>
  </clause>

  <clause id="5382">
    <literal><![CDATA[
      K(x,y) * (L(z,u,w) * x) = T(x,y) * L(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(244(a,1),5047(a,1,2))].">
      <j1 rule="para" parents="244 5047"/>
    </justification>
  </clause>

  <clause id="5383">
    <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(5047(a,1),530(a,1,1,1))].">
      <j1 rule="para" parents="5047 530"/>
    </justification>
  </clause>

  <clause id="5384">
    <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(5047(a,1),491(a,1,1))].">
      <j1 rule="para" parents="5047 491"/>
    </justification>
  </clause>

  <clause id="5385">
    <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(5047(a,1),506(a,1,2))].">
      <j1 rule="para" parents="5047 506"/>
    </justification>
  </clause>

  <clause id="5387">
    <literal><![CDATA[
      K(x,y) * (T(x,y) * z) = T(T(x,y),y) * z
    ]]></literal>
    <justification jstring="[para(5230(a,1),5047(a,1,1))].">
      <j1 rule="para" parents="5230 5047"/>
    </justification>
  </clause>

  <clause id="5388">
    <literal><![CDATA[
      T(x * (y / x),z) / T(y,z) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(117,a,4821,a,b,5048,a)].">
      <j1 rule="hyper" parents="117 4821 5048"/>
    </justification>
  </clause>

  <clause id="5389">
    <literal><![CDATA[
      K(x,(x \ 1) * y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4756(a,2),5048(a,1,1))].">
      <j1 rule="para" parents="4756 5048"/>
    </justification>
  </clause>

  <clause id="5390">
    <literal><![CDATA[
      K(x,y) \ (T(y,x) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(1190,a,5056,a),flip(a)].">
      <j1 rule="hyper" parents="1190 5056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5391">
    <literal><![CDATA[
      K(x,y) \ z = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,5045,a(flip),b,5056,a),flip(a)].">
      <j1 rule="hyper" parents="58 5045 5056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5392">
    <literal><![CDATA[
      K(x,y) * (y \ z) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(1188,a,5056,a(flip))].">
      <j1 rule="hyper" parents="1188 5056"/>
    </justification>
  </clause>

  <clause id="5393">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(451,a,5056,a(flip),b,5045,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="451 5056 5045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5394">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) = z
    ]]></literal>
    <justification jstring="[hyper(119,a,5045,a(flip),b,5056,a(flip))].">
      <j1 rule="hyper" parents="119 5045 5056"/>
    </justification>
  </clause>

  <clause id="5395">
    <literal><![CDATA[
      (K(x,y) \ z) / z = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,5056,a(flip),b,5045,a(flip))].">
      <j1 rule="hyper" parents="117 5056 5045"/>
    </justification>
  </clause>

  <clause id="5396">
    <literal><![CDATA[
      K(x,y) \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5056(a,1),597(a,1))].">
      <j1 rule="para" parents="5056 597"/>
    </justification>
  </clause>

  <clause id="5398">
    <literal><![CDATA[
      K(x,y) * (y \ K(y,x)) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(2788,a,5391,a)].">
      <j1 rule="hyper" parents="2788 5391"/>
    </justification>
  </clause>

  <clause id="5399">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(2786,a,5391,a)].">
      <j1 rule="hyper" parents="2786 5391"/>
    </justification>
  </clause>

  <clause id="5400">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * K(y,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(2076,a,5391,a)].">
      <j1 rule="hyper" parents="2076 5391"/>
    </justification>
  </clause>

  <clause id="5401">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z,z \ 1) = a(K(y,x),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(728,a,5391,a),flip(a)].">
      <j1 rule="hyper" parents="728 5391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5402">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(593,a,5391,a)].">
      <j1 rule="hyper" parents="593 5391"/>
    </justification>
  </clause>

  <clause id="5403">
    <literal><![CDATA[
      x / (K(y,z) * x) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(588,a,5391,a)].">
      <j1 rule="hyper" parents="588 5391"/>
    </justification>
  </clause>

  <clause id="5404">
    <literal><![CDATA[
      K(x,y) \ T(T(x,z),u) = T(T(x,z),u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,2535,a,b,5391,a),flip(a)].">
      <j1 rule="hyper" parents="334 2535 5391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5405">
    <literal><![CDATA[
      K(x,y \ 1) \ y = y * K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,1356,a(flip),b,5391,a),flip(a)].">
      <j1 rule="hyper" parents="334 1356 5391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5406">
    <literal><![CDATA[
      K(x,y) * (R(x,z,u) * K(y,x)) = R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,2532,a,b,5391,a)].">
      <j1 rule="hyper" parents="119 2532 5391"/>
    </justification>
  </clause>

  <clause id="5407">
    <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,3816,a(flip),b,5391,a),flip(a)].">
      <j1 rule="hyper" parents="58 3816 5391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5408">
    <literal><![CDATA[
      x * (K(y,z) * u) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = x
    ]]></literal>
    <justification jstring="[para(5391(a,1),129(a,1,2))].">
      <j1 rule="para" parents="5391 129"/>
    </justification>
  </clause>

  <clause id="5409">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * u = z
    ]]></literal>
    <justification jstring="[para(5391(a,1),134(a,1))].">
      <j1 rule="para" parents="5391 134"/>
    </justification>
  </clause>

  <clause id="5410">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      u = z
    ]]></literal>
    <justification jstring="[para(5391(a,1),263(a,1,2))].">
      <j1 rule="para" parents="5391 263"/>
    </justification>
  </clause>

  <clause id="5411">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(5391(a,1),264(a,1,2))].">
      <j1 rule="para" parents="5391 264"/>
    </justification>
  </clause>

  <clause id="5412">
    <literal><![CDATA[
      x / (K(y,z) * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(5391(a,1),345(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5391 345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5413">
    <literal><![CDATA[
      (K(x,y) \ z) * L(u,z,K(y,x)) = K(y,x) * (z * u)
    ]]></literal>
    <justification jstring="[para(5391(a,2),90(a,1,1))].">
      <j1 rule="para" parents="5391 90"/>
    </justification>
  </clause>

  <clause id="5414">
    <literal><![CDATA[
      L(K(x,y) * z,K(y,x),u) = (u * K(y,x)) \ (u * z)
    ]]></literal>
    <justification jstring="[para(5391(a,1),92(a,1,1))].">
      <j1 rule="para" parents="5391 92"/>
    </justification>
  </clause>

  <clause id="5415">
    <literal><![CDATA[
      L(x \ (K(y,z) * u),x,K(z,y)) = (K(z,y) * x) \ u
    ]]></literal>
    <justification jstring="[para(5391(a,1),311(a,1,1,2))].">
      <j1 rule="para" parents="5391 311"/>
    </justification>
  </clause>

  <clause id="5416">
    <literal><![CDATA[
      L(K(x,y) * (z \ u),K(y,x),z) = (z * K(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(5391(a,1),311(a,1,1))].">
      <j1 rule="para" parents="5391 311"/>
    </justification>
  </clause>

  <clause id="5417">
    <literal><![CDATA[
      x \ y != K(z,u) * (K(u,z) * w)
    ]]></literal>
    <literal><![CDATA[
      x * w = y
    ]]></literal>
    <justification jstring="[para(5391(a,1),355(a,2,2))].">
      <j1 rule="para" parents="5391 355"/>
    </justification>
  </clause>

  <clause id="5418">
    <literal><![CDATA[
      T((x \ K(y,z)) \ 1,K(z,y) * x) = (x \ K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(5391(a,1),601(a,1,2))].">
      <j1 rule="para" parents="5391 601"/>
    </justification>
  </clause>

  <clause id="5419">
    <literal><![CDATA[
      R(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5391(a,1),380(a,1,1,3))].">
      <j1 rule="para" parents="5391 380"/>
    </justification>
  </clause>

  <clause id="5420">
    <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(5391(a,1),4040(a,1,1))].">
      <j1 rule="para" parents="5391 4040"/>
    </justification>
  </clause>

  <clause id="5421">
    <literal><![CDATA[
      (K(x,y) * T(K(y,x) * z,u)) * K(y,x) = T(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(5391(a,1),4820(a,1,1))].">
      <j1 rule="para" parents="5391 4820"/>
    </justification>
  </clause>

  <clause id="5422">
    <literal><![CDATA[
      (K(x,y) \ 1) * z = K(x,y) \ z
    ]]></literal>
    <justification jstring="[para(5232(a,2),5391(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5232 5391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5423">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(119,a,5394,a(flip),b,5043,a),flip(a)].">
      <j1 rule="hyper" parents="119 5394 5043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5424">
    <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,5394,a(flip),b,187,a)].">
      <j1 rule="hyper" parents="119 5394 187"/>
    </justification>
  </clause>

  <clause id="5425">
    <literal><![CDATA[
      K(x,y) != z / u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5394(a,1),132(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5394 132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5426">
    <literal><![CDATA[
      K(x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5394(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5394 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5427">
    <literal><![CDATA[
      L((K(x,y) * z) \ u,K(x,y) * z,K(y,x)) = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(5394(a,1),92(a,2,1))].">
      <j1 rule="para" parents="5394 92"/>
    </justification>
  </clause>

  <clause id="5428">
    <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(5394(a,1),709(a,1,1,2))].">
      <j1 rule="para" parents="5394 709"/>
    </justification>
  </clause>

  <clause id="5429">
    <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(5394(a,1),491(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5394 491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5430">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ 1 = z
    ]]></literal>
    <justification jstring="[para(5395(a,1),174(a,1)),flip(b)].">
      <j1 rule="para" parents="5395 174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5431">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(5395(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5395 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5432">
    <literal><![CDATA[
      (x / y) / T(x,y \ 1) = x \ (x / y)
    ]]></literal>
    <justification jstring="[para(5057(a,1),273(a,1,2))].">
      <j1 rule="para" parents="5057 273"/>
    </justification>
  </clause>

  <clause id="5434">
    <literal><![CDATA[
      (x \ y) * K(((x \ y) \ (x \ 1)) \ 1,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(5059(a,1),1529(a,1,2))].">
      <j1 rule="para" parents="5059 1529"/>
    </justification>
  </clause>

  <clause id="5435">
    <literal><![CDATA[
      (x / y) * K(((x / y) \ (1 / y)) \ 1,z) = T(x,z) / y
    ]]></literal>
    <justification jstring="[para(5059(a,1),1542(a,1,2))].">
      <j1 rule="para" parents="5059 1542"/>
    </justification>
  </clause>

  <clause id="5437">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) / K(y,1 / x) = x
    ]]></literal>
    <justification jstring="[hyper(117,a,5069,a(flip),b,198,a(flip))].">
      <j1 rule="hyper" parents="117 5069 198"/>
    </justification>
  </clause>

  <clause id="5438">
    <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(5069(a,1),495(a,1,2,2))].">
      <j1 rule="para" parents="5069 495"/>
    </justification>
  </clause>

  <clause id="5439">
    <literal><![CDATA[
      K(x,y) * (1 / y) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2332,a,b,5070,a)].">
      <j1 rule="hyper" parents="58 2332 5070"/>
    </justification>
  </clause>

  <clause id="5440">
    <literal><![CDATA[
      K(x,y) \ (1 / T(y,x)) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(116,a,5070,a(flip),b,2332,a)].">
      <j1 rule="hyper" parents="116 5070 2332"/>
    </justification>
  </clause>

  <clause id="5441">
    <literal><![CDATA[
      T(x,y) \ (x * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(1227,a,5090,a)].">
      <j1 rule="hyper" parents="1227 5090"/>
    </justification>
  </clause>

  <clause id="5442">
    <literal><![CDATA[
      ((x * y) / x) * (y \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,4709,a,b,5090,a)].">
      <j1 rule="hyper" parents="58 4709 5090"/>
    </justification>
  </clause>

  <clause id="5443">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,4708,a,b,5090,a)].">
      <j1 rule="hyper" parents="58 4708 5090"/>
    </justification>
  </clause>

  <clause id="5444">
    <literal><![CDATA[
      ((x * y) / x) * z = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5090,a(flip),b,4708,a),flip(a)].">
      <j1 rule="hyper" parents="119 5090 4708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5445">
    <literal><![CDATA[
      K((x / y) / (y \ 1),z) = (T(x,z) / y) / (x / y)
    ]]></literal>
    <justification jstring="[hyper(117,a,4927,a(flip),b,5090,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="117 4927 5090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5446">
    <literal><![CDATA[
      x \ (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(5090(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5090 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5448">
    <literal><![CDATA[
      L(T(x \ y,z) \ u,x \ y,x) = y \ (x * (K(z,x \ y) * u))
    ]]></literal>
    <justification jstring="[para(5090(a,1),91(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5090 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5449">
    <literal><![CDATA[
      K(x,y) * (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(5090(a,1),1191(a,1))].">
      <j1 rule="para" parents="5090 1191"/>
    </justification>
  </clause>

  <clause id="5450">
    <literal><![CDATA[
      K(x,y) * (y \ z) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (T(y,x) \ z) = w
    ]]></literal>
    <justification jstring="[para(5090(a,1),1178(a,1))].">
      <j1 rule="para" parents="5090 1178"/>
    </justification>
  </clause>

  <clause id="5451">
    <literal><![CDATA[
      K(x,y) * T(T(y,x),z) = y * K(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4995(a,2),5090(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4995 5090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5452">
    <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,5091,a)].">
      <j1 rule="hyper" parents="117 101 5091"/>
    </justification>
  </clause>

  <clause id="5453">
    <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(5091(a,1),491(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5091 491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5454">
    <literal><![CDATA[
      K(x,y) * (K(z,T(y,x)) * u) = y * (T(T(y,x),z) \ u)
    ]]></literal>
    <justification jstring="[para(5090(a,1),5091(a,1,2))].">
      <j1 rule="para" parents="5090 5091"/>
    </justification>
  </clause>

  <clause id="5455">
    <literal><![CDATA[
      ((x * y) * (z * K(y,z))) / (T(y,z) * z) = R(x,y,z * K(y,z))
    ]]></literal>
    <justification jstring="[para(5102(a,1),15(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5102 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5456">
    <literal><![CDATA[
      T(x,y * K(x,y)) / (T(x,y) * y) = x / ((y * K(x,y)) * x)
    ]]></literal>
    <justification jstring="[para(5102(a,1),4606(a,1,2))].">
      <j1 rule="para" parents="5102 4606"/>
    </justification>
  </clause>

  <clause id="5457">
    <literal><![CDATA[
      K(x,T(y,T(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5109,a,5104,a)].">
      <j1 rule="hyper" parents="5109 5104"/>
    </justification>
  </clause>

  <clause id="5458">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(5104(a,2),5030(a,1))].">
      <j1 rule="para" parents="5104 5030"/>
    </justification>
  </clause>

  <clause id="5459">
    <literal><![CDATA[
      K(x / y,T(z,y \ x)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),5457(a,1,2,2))].">
      <j1 rule="para" parents="107 5457"/>
    </justification>
  </clause>

  <clause id="5460">
    <literal><![CDATA[
      K(x,T(y,x / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5109,a,5106,a)].">
      <j1 rule="hyper" parents="5109 5106"/>
    </justification>
  </clause>

  <clause id="5461">
    <literal><![CDATA[
      K(x * y,T(y,x)) = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),5460(a,1,2,2))].">
      <j1 rule="para" parents="6 5460"/>
    </justification>
  </clause>

  <clause id="5462">
    <literal><![CDATA[
      K(x,(y \ x) \ x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4533(a,1),5460(a,1,2))].">
      <j1 rule="para" parents="4533 5460"/>
    </justification>
  </clause>

  <clause id="5463">
    <literal><![CDATA[
      K(x,x / y) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(75(a,1),5462(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 5462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5465">
    <literal><![CDATA[
      T(x,x \ y) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(5130(a,1),4144(a,1,1))].">
      <j1 rule="para" parents="5130 4144"/>
    </justification>
  </clause>

  <clause id="5466">
    <literal><![CDATA[
      T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(5144,a,5143,a)].">
      <j1 rule="hyper" parents="5144 5143"/>
    </justification>
  </clause>

  <clause id="5467">
    <literal><![CDATA[
      T(x * K(x * y,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(4556,a,5143,a),flip(a)].">
      <j1 rule="hyper" parents="4556 5143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5468">
    <literal><![CDATA[
      T(x * K(y * R(x,z,u),x),y) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(1965,a,5143,a),flip(a)].">
      <j1 rule="hyper" parents="1965 5143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5469">
    <literal><![CDATA[
      T(x,y) != T(z,u)
    ]]></literal>
    <literal><![CDATA[
      T(z * K(y,z),u) = x
    ]]></literal>
    <justification jstring="[para(5143(a,1),44(a,2)),flip(b)].">
      <j1 rule="para" parents="5143 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5472">
    <literal><![CDATA[
      T(x,x \ K(x,y)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(5179(a,1),2293(a,1,2))].">
      <j1 rule="para" parents="5179 2293"/>
    </justification>
  </clause>

  <clause id="5473">
    <literal><![CDATA[
      (x * y) \ K(x * y,y) = (L(y,x,y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(4618(a,1),5179(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4618 5179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5474">
    <literal><![CDATA[
      (x * K(y,x)) \ 1 = x \ K(x,y)
    ]]></literal>
    <justification jstring="[para(5017(a,1),5179(a,1,1))].">
      <j1 rule="para" parents="5017 5179"/>
    </justification>
  </clause>

  <clause id="5475">
    <literal><![CDATA[
      1 / (x * K(y,x)) = K(x,y) / x
    ]]></literal>
    <justification jstring="[para(5017(a,1),5224(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5017 5224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5476">
    <literal><![CDATA[
      K(x,y) / (K(x,y) / x) = x * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5225,a(flip),b,4966,a),flip(a)].">
      <j1 rule="hyper" parents="119 5225 4966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5477">
    <literal><![CDATA[
      K(x,y) * K(x \ 1,x) = (x \ K(x,y)) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,5225,a(flip),b,85,a)].">
      <j1 rule="hyper" parents="119 5225 85"/>
    </justification>
  </clause>

  <clause id="5479">
    <literal><![CDATA[
      K(((x / y) \ 1) \ y,(x / y) \ 1) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(4195,a,5270,a)].">
      <j1 rule="hyper" parents="4195 5270"/>
    </justification>
  </clause>

  <clause id="5480">
    <literal><![CDATA[
      x * (K(x \ 1,x) * K(y,y \ (1 / (1 / x)))) = y * ((1 / (1 / x)) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3088,a,b,5272,a)].">
      <j1 rule="hyper" parents="58 3088 5272"/>
    </justification>
  </clause>

  <clause id="5481">
    <literal><![CDATA[
      R(x,x \ y,K(z,z \ y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(5272(a,1),517(a,1,2))].">
      <j1 rule="para" parents="5272 517"/>
    </justification>
  </clause>

  <clause id="5482">
    <literal><![CDATA[
      T(x,y) * K(x * y,(x * y) \ T(x,y)) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(4606(a,1),5272(a,2,2))].">
      <j1 rule="para" parents="4606 5272"/>
    </justification>
  </clause>

  <clause id="5484">
    <literal><![CDATA[
      K(x * y,x / (x * y)) = K(x * y,1 / y)
    ]]></literal>
    <justification jstring="[para(6(a,1),5331(a,1,2,1))].">
      <j1 rule="para" parents="6 5331"/>
    </justification>
  </clause>

  <clause id="5485">
    <literal><![CDATA[
      K(x,1 / (y \ x)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(72(a,1),5331(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 5331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5486">
    <literal><![CDATA[
      K(x,y) \ K(x,z) = T(x,y) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,4995,a,b,5337,a)].">
      <j1 rule="hyper" parents="116 4995 5337"/>
    </justification>
  </clause>

  <clause id="5487">
    <literal><![CDATA[
      x \ y != K(x,z) * u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) \ y = u
    ]]></literal>
    <justification jstring="[para(5337(a,1),38(a,1))].">
      <j1 rule="para" parents="5337 38"/>
    </justification>
  </clause>

  <clause id="5488">
    <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(5337(a,1),92(a,2,1))].">
      <j1 rule="para" parents="5337 92"/>
    </justification>
  </clause>

  <clause id="5489">
    <literal><![CDATA[
      L(x \ (T(y,z) \ u),x,K(y,z)) = (K(y,z) * x) \ (y \ u)
    ]]></literal>
    <justification jstring="[para(5337(a,1),92(a,2,2))].">
      <j1 rule="para" parents="5337 92"/>
    </justification>
  </clause>

  <clause id="5490">
    <literal><![CDATA[
      K(x,y) * (((y * x) / y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(33,a,4696,a(flip),b,5344,a),flip(a)].">
      <j1 rule="hyper" parents="33 4696 5344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5491">
    <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),5359(a,1,2,1))].">
      <j1 rule="para" parents="22 5359"/>
    </justification>
  </clause>

  <clause id="5493">
    <literal><![CDATA[
      K(x,y) * (y * z) = ((x * y) / x) * z
    ]]></literal>
    <justification jstring="[hyper(33,a,4696,a,b,5367,a),flip(a)].">
      <j1 rule="hyper" parents="33 4696 5367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5494">
    <literal><![CDATA[
      T(x,y) \ (z * x) = K(y,x) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(33,a,1177,a,b,5367,a)].">
      <j1 rule="hyper" parents="33 1177 5367"/>
    </justification>
  </clause>

  <clause id="5495">
    <literal><![CDATA[
      K(x,T(y,z)) * K(z,y) = T(T(y,z),x) \ y
    ]]></literal>
    <justification jstring="[hyper(119,a,4996,a,b,5390,a)].">
      <j1 rule="hyper" parents="119 4996 5390"/>
    </justification>
  </clause>

  <clause id="5496">
    <literal><![CDATA[
      T(x,y) \ T(x,z) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4995,a,b,5390,a),flip(a)].">
      <j1 rule="hyper" parents="119 4995 5390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5497">
    <literal><![CDATA[
      K(x,y \ z) * T(y,y \ z) = T(y \ z,x) \ z
    ]]></literal>
    <justification jstring="[hyper(119,a,106,a,b,5390,a)].">
      <j1 rule="hyper" parents="119 106 5390"/>
    </justification>
  </clause>

  <clause id="5498">
    <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,5390,a),flip(a)].">
      <j1 rule="hyper" parents="119 13 5390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5499">
    <literal><![CDATA[
      T(x,y) \ (T(x,z) * u) = K(y,x) * (K(x,z) * u)
    ]]></literal>
    <justification jstring="[hyper(119,a,5043,a(flip),b,5390,a),flip(a)].">
      <j1 rule="hyper" parents="119 5043 5390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5500">
    <literal><![CDATA[
      x \ (K(y,x) * z) = K(y,x) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(334,a,5367,a,b,5392,a)].">
      <j1 rule="hyper" parents="334 5367 5392"/>
    </justification>
  </clause>

  <clause id="5501">
    <literal><![CDATA[
      ((x \ y) \ y) \ z = K(x \ y,x) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(334,a,325,a(flip),b,5392,a)].">
      <j1 rule="hyper" parents="334 325 5392"/>
    </justification>
  </clause>

  <clause id="5502">
    <literal><![CDATA[
      x * (K(y,x) * (x \ z)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,5392,a,b,5367,a)].">
      <j1 rule="hyper" parents="119 5392 5367"/>
    </justification>
  </clause>

  <clause id="5504">
    <literal><![CDATA[
      K(x,y) * (T(y,x) \ z) = T(T(y,x),x) \ z
    ]]></literal>
    <justification jstring="[para(5182(a,1),5392(a,1,1))].">
      <j1 rule="para" parents="5182 5392"/>
    </justification>
  </clause>

  <clause id="5505">
    <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(5393(a,1),1696(a,1,2,2,1))].">
      <j1 rule="para" parents="5393 1696"/>
    </justification>
  </clause>

  <clause id="5506">
    <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(5393(a,1),1920(a,1,2,2,1))].">
      <j1 rule="para" parents="5393 1920"/>
    </justification>
  </clause>

  <clause id="5507">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5398(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5398 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5510">
    <literal><![CDATA[
      L(x,K(y,z) \ 1,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(29,a,450,a(flip),b,5422,a),flip(a)].">
      <j1 rule="hyper" parents="29 450 5422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5511">
    <literal><![CDATA[
      L(x,K(y,z),K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(5232(a,1),5510(a,1,2))].">
      <j1 rule="para" parents="5232 5510"/>
    </justification>
  </clause>

  <clause id="5513">
    <literal><![CDATA[
      L(x,K(y,z),K(z,y)) / (K(u,w) * x) = K(w,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,5511,a,b,5394,a)].">
      <j1 rule="hyper" parents="117 5511 5394"/>
    </justification>
  </clause>

  <clause id="5514">
    <literal><![CDATA[
      K(x,y) * (x / y) = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(4738,a,5423,a),flip(a)].">
      <j1 rule="hyper" parents="4738 5423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5515">
    <literal><![CDATA[
      K(x,y) * (x / y) = T(x,y) / y
    ]]></literal>
    <justification jstring="[hyper(4736,a,5423,a),flip(a)].">
      <j1 rule="hyper" parents="4736 5423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5516">
    <literal><![CDATA[
      K(x,y) * (((x * y) / x) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(4698,a,5423,a),flip(a)].">
      <j1 rule="hyper" parents="4698 5423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5517">
    <literal><![CDATA[
      x \ T(x * y,x) = K(x * y,x) * y
    ]]></literal>
    <justification jstring="[hyper(4545,a,5423,a)].">
      <j1 rule="hyper" parents="4545 5423"/>
    </justification>
  </clause>

  <clause id="5518">
    <literal><![CDATA[
      (x * y) / (K(z,x) * y) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,5423,a)].">
      <j1 rule="hyper" parents="130 5423"/>
    </justification>
  </clause>

  <clause id="5519">
    <literal><![CDATA[
      T(x,y) / (K(z,x) * K(x,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,5020,a,b,5423,a)].">
      <j1 rule="hyper" parents="117 5020 5423"/>
    </justification>
  </clause>

  <clause id="5520">
    <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,5423,a)].">
      <j1 rule="hyper" parents="117 101 5423"/>
    </justification>
  </clause>

  <clause id="5522">
    <literal><![CDATA[
      K(x,y) * (y * z) = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5423,a(flip),b,5360,a)].">
      <j1 rule="hyper" parents="119 5423 5360"/>
    </justification>
  </clause>

  <clause id="5523">
    <literal><![CDATA[
      (x * y) / (K(z,x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(5423(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5423 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5524">
    <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(5423(a,1),488(a,1,1))].">
      <j1 rule="para" parents="5423 488"/>
    </justification>
  </clause>

  <clause id="5525">
    <literal><![CDATA[
      x * (y * (K(x,y) * z)) = T(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(5423(a,1),4909(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5423 4909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5526">
    <literal><![CDATA[
      T(x,y) * (1 / y) = x * (1 / T(y,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,5439,a(flip),b,5043,a),flip(a)].">
      <j1 rule="hyper" parents="119 5439 5043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5527">
    <literal><![CDATA[
      K(x,y * K(x,y)) \ (1 / y) = 1 / (y * K(x,y))
    ]]></literal>
    <justification jstring="[para(5086(a,1),5440(a,1,2,2))].">
      <j1 rule="para" parents="5086 5440"/>
    </justification>
  </clause>

  <clause id="5528">
    <literal><![CDATA[
      K(x,y) * T(x,T(y,z)) = T(T(x,y),T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,4951,a(flip),b,5441,a),flip(a)].">
      <j1 rule="hyper" parents="58 4951 5441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5529">
    <literal><![CDATA[
      x * (K(x * y,x) * y) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5441,a(flip),b,4490,a(flip))].">
      <j1 rule="hyper" parents="119 5441 4490"/>
    </justification>
  </clause>

  <clause id="5530">
    <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),5441(a,1,1))].">
      <j1 rule="para" parents="20 5441"/>
    </justification>
  </clause>

  <clause id="5531">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(5441(a,1),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5441 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5532">
    <literal><![CDATA[
      K(x * y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(4758,a,5461,a),flip(a)].">
      <j1 rule="hyper" parents="4758 5461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5533">
    <literal><![CDATA[
      K(x,y) / ((x \ 1) \ 1) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[para(5472(a,1),273(a,1,2))].">
      <j1 rule="para" parents="5472 273"/>
    </justification>
  </clause>

  <clause id="5534">
    <literal><![CDATA[
      (x \ K(x,y)) * T((x \ 1) \ 1,z) = T(x,z) * (x \ K(x,y))
    ]]></literal>
    <justification jstring="[para(5472(a,1),243(a,1,2,1))].">
      <j1 rule="para" parents="5472 243"/>
    </justification>
  </clause>

  <clause id="5535">
    <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(5474(a,1),2649(a,2,2,2))].">
      <j1 rule="para" parents="5474 2649"/>
    </justification>
  </clause>

  <clause id="5536">
    <literal><![CDATA[
      (K(x,y) / x) \ 1 = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(192,a,5475,a)].">
      <j1 rule="hyper" parents="192 5475"/>
    </justification>
  </clause>

  <clause id="5537">
    <literal><![CDATA[
      1 / ((x \ 1) * K(y,x \ 1)) = K(1 / x,y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(3442(a,2),5475(a,2,1))].">
      <j1 rule="para" parents="3442 5475"/>
    </justification>
  </clause>

  <clause id="5538">
    <literal><![CDATA[
      K(1 / x,y) / (1 / x) = 1 / (K(y,x \ 1) / x)
    ]]></literal>
    <justification jstring="[para(3708(a,1),5475(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3708 5475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5539">
    <literal><![CDATA[
      K(((x * K(y,x)) \ 1) * z,u) = K((K(x,y) / x) * z,u)
    ]]></literal>
    <justification jstring="[para(5475(a,1),4281(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5475 4281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5540">
    <literal><![CDATA[
      (x / T(y,x)) * L(z,x / y,K(x,y)) = K(x,y) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(5514(a,1),90(a,1,1))].">
      <j1 rule="para" parents="5514 90"/>
    </justification>
  </clause>

  <clause id="5541">
    <literal><![CDATA[
      R(K(x,y),x / y,z) \ ((x / T(y,x)) * z) = (x / y) * z
    ]]></literal>
    <justification jstring="[para(5514(a,1),187(a,1,2,1))].">
      <j1 rule="para" parents="5514 187"/>
    </justification>
  </clause>

  <clause id="5542">
    <literal><![CDATA[
      1 / (x * K(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / x = z
    ]]></literal>
    <justification jstring="[para(5536(a,1),345(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5536 345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5544">
    <literal><![CDATA[
      (x \ 1) * ((y * ((x \ 1) \ 1)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(1523(a,2),5195(a,1))].">
      <j1 rule="para" parents="1523 5195"/>
    </justification>
  </clause>

  <clause id="5545">
    <literal><![CDATA[
      T(K(x * (1 / y),y \ 1) / y,x) = R(1 / y,x,1 / y)
    ]]></literal>
    <justification jstring="[para(3708(a,1),5205(a,1,1))].">
      <j1 rule="para" parents="3708 5205"/>
    </justification>
  </clause>

  <clause id="5546">
    <literal><![CDATA[
      K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(661(a,1),5297(a,1,1))].">
      <j1 rule="para" parents="661 5297"/>
    </justification>
  </clause>

  <clause id="5547">
    <literal><![CDATA[
      T(x,x * y) * K(y,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2533,a,5352,a)].">
      <j1 rule="hyper" parents="2533 5352"/>
    </justification>
  </clause>

  <clause id="5548">
    <literal><![CDATA[
      K(x,y) = T(y,y * x) \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5352,a(flip),b,2530,a),flip(a)].">
      <j1 rule="hyper" parents="116 5352 2530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5549">
    <literal><![CDATA[
      T(x,y) * K(x * y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2533,a,5355,a)].">
      <j1 rule="hyper" parents="2533 5355"/>
    </justification>
  </clause>

  <clause id="5550">
    <literal><![CDATA[
      T(x,x * y) \ T(x,y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5355,a(flip),b,5090,a),flip(a)].">
      <j1 rule="hyper" parents="116 5355 5090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5551">
    <literal><![CDATA[
      T(x,y) \ R(x,y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5355,a(flip),b,2530,a)].">
      <j1 rule="hyper" parents="116 5355 2530"/>
    </justification>
  </clause>

  <clause id="5552">
    <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),5426(a,1))].">
      <j1 rule="para" parents="17 5426"/>
    </justification>
  </clause>

  <clause id="5553">
    <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(256(a,1),5458(a,1,2))].">
      <j1 rule="para" parents="256 5458"/>
    </justification>
  </clause>

  <clause id="5554">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = T(R(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(5467(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5467 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5555">
    <literal><![CDATA[
      K(x,x * y) * K(y,x) = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5547,a(flip),b,5044,a),flip(a)].">
      <j1 rule="hyper" parents="116 5547 5044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5556">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5549,a(flip),b,5044,a),flip(a)].">
      <j1 rule="hyper" parents="116 5549 5044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5557">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = L(K(y * z,y),T(y,z),x)
    ]]></literal>
    <justification jstring="[para(5549(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5549 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5558">
    <literal><![CDATA[
      x \ R(y,z,y) != K(y * z,y)
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = x
    ]]></literal>
    <justification jstring="[para(5551(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="5551 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5559">
    <literal><![CDATA[
      K(x \ (x * y),x) = (y * x) * ((x * y) \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),4982(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 4982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5560">
    <literal><![CDATA[
      (x * (y * T(y \ z,u))) / (x * z) = K((x * z) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(955(a,1),4999(a,1,1))].">
      <j1 rule="para" parents="955 4999"/>
    </justification>
  </clause>

  <clause id="5562">
    <literal><![CDATA[
      R(x * ((y * (x \ 1)) / y),z,u) = K(y,R(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3400,a(flip),b,5006,a)].">
      <j1 rule="hyper" parents="58 3400 5006"/>
    </justification>
  </clause>

  <clause id="5563">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / z = K(y,(x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2673,a(flip),b,5006,a)].">
      <j1 rule="hyper" parents="58 2673 5006"/>
    </justification>
  </clause>

  <clause id="5565">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(5006(a,1),1138(a,2,2))].">
      <j1 rule="para" parents="5006 1138"/>
    </justification>
  </clause>

  <clause id="5566">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = K(z,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(5006(a,1),1787(a,2,1))].">
      <j1 rule="para" parents="5006 1787"/>
    </justification>
  </clause>

  <clause id="5567">
    <literal><![CDATA[
      K(x,(y * x) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      y * (x * ((y \ 1) / x)) = z
    ]]></literal>
    <justification jstring="[para(5006(a,1),1011(a,1))].">
      <j1 rule="para" parents="5006 1011"/>
    </justification>
  </clause>

  <clause id="5568">
    <literal><![CDATA[
      K(x,x * (y \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,4995,a,b,5033,a),flip(a)].">
      <j1 rule="hyper" parents="334 4995 5033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5569">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,4995,a,b,5038,a),flip(a)].">
      <j1 rule="hyper" parents="334 4995 5038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5570">
    <literal><![CDATA[
      K(x,y * K(z,1 / z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1855(a,2),5569(a,1,2,2))].">
      <j1 rule="para" parents="1855 5569"/>
    </justification>
  </clause>

  <clause id="5571">
    <literal><![CDATA[
      K(x,y * K(z \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1862(a,1),5569(a,1,2,2))].">
      <j1 rule="para" parents="1862 5569"/>
    </justification>
  </clause>

  <clause id="5572">
    <literal><![CDATA[
      K(x,K(y,y \ 1) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2237(a,2),5569(a,1,2))].">
      <j1 rule="para" parents="2237 5569"/>
    </justification>
  </clause>

  <clause id="5573">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3008(a,1),5569(a,1,2))].">
      <j1 rule="para" parents="3008 5569"/>
    </justification>
  </clause>

  <clause id="5574">
    <literal><![CDATA[
      K(x,y * T(z,z \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3009(a,1),5569(a,1,2))].">
      <j1 rule="para" parents="3009 5569"/>
    </justification>
  </clause>

  <clause id="5575">
    <literal><![CDATA[
      K(x,K(y \ 1,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(3031(a,1),5569(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3031 5569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5576">
    <literal><![CDATA[
      K(x,y / (1 / z)) = K(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(3029(a,1),5569(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3029 5569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5577">
    <literal><![CDATA[
      K(x,y * (1 / z)) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(3030(a,1),5569(a,1,2))].">
      <j1 rule="para" parents="3030 5569"/>
    </justification>
  </clause>

  <clause id="5578">
    <literal><![CDATA[
      K(x,(y / (z \ 1)) * (1 / z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3037(a,2),5569(a,1,2))].">
      <j1 rule="para" parents="3037 5569"/>
    </justification>
  </clause>

  <clause id="5579">
    <literal><![CDATA[
      K(x,(y \ 1) * (y * z)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(3042(a,1),5569(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3042 5569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5581">
    <literal><![CDATA[
      K(x,T(y,y \ 1) * z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3170(a,1),5569(a,1,2))].">
      <j1 rule="para" parents="3170 5569"/>
    </justification>
  </clause>

  <clause id="5582">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(3176(a,1),5569(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3176 5569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5583">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3185(a,1),5569(a,1,2))].">
      <j1 rule="para" parents="3185 5569"/>
    </justification>
  </clause>

  <clause id="5584">
    <literal><![CDATA[
      K(x,(1 / y) \ z) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(3202(a,1),5569(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3202 5569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5585">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ 1) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(3559(a,2),5569(a,1,2))].">
      <j1 rule="para" parents="3559 5569"/>
    </justification>
  </clause>

  <clause id="5586">
    <literal><![CDATA[
      K(x,(K(y \ 1,y) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(3899(a,2),5569(a,1,2))].">
      <j1 rule="para" parents="3899 5569"/>
    </justification>
  </clause>

  <clause id="5587">
    <literal><![CDATA[
      K(x,((1 / y) * z) \ u) = K(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[para(3912(a,1),5569(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3912 5569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5588">
    <literal><![CDATA[
      K(x,y * (z * K(u,1 / u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3554(a,1),5570(a,1,2))].">
      <j1 rule="para" parents="3554 5570"/>
    </justification>
  </clause>

  <clause id="5589">
    <literal><![CDATA[
      K(x,y * (z * K(u \ 1,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3517(a,1),5571(a,1,2))].">
      <j1 rule="para" parents="3517 5571"/>
    </justification>
  </clause>

  <clause id="5590">
    <literal><![CDATA[
      K(x,y \ (z / (1 / u))) = K(x,y \ (z / (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3569(a,1),5571(a,1,2))].">
      <j1 rule="para" parents="3569 5571"/>
    </justification>
  </clause>

  <clause id="5591">
    <literal><![CDATA[
      K(x,(K(y \ 1,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[para(3872(a,2),5571(a,1,2))].">
      <j1 rule="para" parents="3872 5571"/>
    </justification>
  </clause>

  <clause id="5592">
    <literal><![CDATA[
      K(x,y / (K(z,z \ 1) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(3990(a,2),5571(a,1,2))].">
      <j1 rule="para" parents="3990 5571"/>
    </justification>
  </clause>

  <clause id="5593">
    <literal><![CDATA[
      K(x,y / T(1 / z,u)) = K(x,y / T(z \ 1,u))
    ]]></literal>
    <justification jstring="[para(3991(a,1),5571(a,1,2))].">
      <j1 rule="para" parents="3991 5571"/>
    </justification>
  </clause>

  <clause id="5594">
    <literal><![CDATA[
      K(x,K(y,1 / y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1855(a,2),5572(a,1,2,1))].">
      <j1 rule="para" parents="1855 5572"/>
    </justification>
  </clause>

  <clause id="5595">
    <literal><![CDATA[
      K(x,y * ((1 / y) * z)) = K(x,L(z,y \ 1,y))
    ]]></literal>
    <justification jstring="[para(3215(a,1),5572(a,1,2))].">
      <j1 rule="para" parents="3215 5572"/>
    </justification>
  </clause>

  <clause id="5596">
    <literal><![CDATA[
      K(x,y * (z * (1 / u))) = K(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3582(a,1),5572(a,1,2))].">
      <j1 rule="para" parents="3582 5572"/>
    </justification>
  </clause>

  <clause id="5597">
    <literal><![CDATA[
      K(x,y * (z / (1 / u))) = K(x,y * (z / (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3583(a,1),5572(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3583 5572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5598">
    <literal><![CDATA[
      K(x,y * (z / ((u \ 1) \ 1))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(3584(a,1),5572(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3584 5572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5599">
    <literal><![CDATA[
      K(x,y * (z * ((u \ 1) \ 1))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(3585(a,1),5572(a,1,2))].">
      <j1 rule="para" parents="3585 5572"/>
    </justification>
  </clause>

  <clause id="5600">
    <literal><![CDATA[
      K(x,y * ((1 / z) * u)) = K(x,y * ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(3587(a,1),5572(a,1,2))].">
      <j1 rule="para" parents="3587 5572"/>
    </justification>
  </clause>

  <clause id="5601">
    <literal><![CDATA[
      K(x,y * ((1 / z) \ u)) = K(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(3588(a,1),5572(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3588 5572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5602">
    <literal><![CDATA[
      K(x,y \ ((1 / z) * u)) = K(x,y \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(3600(a,1),5572(a,1,2))].">
      <j1 rule="para" parents="3600 5572"/>
    </justification>
  </clause>

  <clause id="5603">
    <literal><![CDATA[
      K(x,y \ (z * ((1 / u) \ w))) = K(x,y \ (z * ((u \ 1) \ w)))
    ]]></literal>
    <justification jstring="[para(3613(a,1),5572(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3613 5572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5604">
    <literal><![CDATA[
      K(x,(y * (z / (1 / u))) \ w) = K(x,(y * (z / (u \ 1))) \ w)
    ]]></literal>
    <justification jstring="[para(3986(a,1),5572(a,1,2))].">
      <j1 rule="para" parents="3986 5572"/>
    </justification>
  </clause>

  <clause id="5605">
    <literal><![CDATA[
      K(x,T(y * K(z,z \ 1),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(4814(a,2),5572(a,1,2))].">
      <j1 rule="para" parents="4814 5572"/>
    </justification>
  </clause>

  <clause id="5606">
    <literal><![CDATA[
      K(x,y \ (z * (1 / u))) = K(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3598(a,1),5575(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3598 5575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5607">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ w) = K(x,R(y \ 1,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(4012(a,1),5575(a,1,2))].">
      <j1 rule="para" parents="4012 5575"/>
    </justification>
  </clause>

  <clause id="5608">
    <literal><![CDATA[
      K(x,K(y,1 / y) / z) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(3793(a,1),5594(a,1,2))].">
      <j1 rule="para" parents="3793 5594"/>
    </justification>
  </clause>

  <clause id="5609">
    <literal><![CDATA[
      K(x,(y \ z) / z) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,4995,a,b,5054,a),flip(a)].">
      <j1 rule="hyper" parents="334 4995 5054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5610">
    <literal><![CDATA[
      K(x,(y \ z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(5054(a,2),5110(a,1))].">
      <j1 rule="para" parents="5054 5110"/>
    </justification>
  </clause>

  <clause id="5613">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),5609(a,1,2,1))].">
      <j1 rule="para" parents="4 5609"/>
    </justification>
  </clause>

  <clause id="5614">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),5609(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 5609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5615">
    <literal><![CDATA[
      K(x,R(y / z,z,u) \ 1) = K(x,(z * u) / (y * u))
    ]]></literal>
    <justification jstring="[para(518(a,1),5609(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="518 5609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5616">
    <literal><![CDATA[
      K(x,y \ 1) * (((y \ z) / z) \ u) = T((y \ z) / z,x) \ u
    ]]></literal>
    <justification jstring="[para(5609(a,1),5392(a,1,1))].">
      <j1 rule="para" parents="5609 5392"/>
    </justification>
  </clause>

  <clause id="5617">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[hyper(334,a,3700,a,b,5613,a),flip(a)].">
      <j1 rule="hyper" parents="334 3700 5613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5618">
    <literal><![CDATA[
      K(x * y,x \ 1) * ((x * y) \ y) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(5613(a,1),5129(a,1,1))].">
      <j1 rule="para" parents="5613 5129"/>
    </justification>
  </clause>

  <clause id="5619">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(z / y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(334,a,5232,a,b,5614,a),flip(a)].">
      <j1 rule="hyper" parents="334 5232 5614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5620">
    <literal><![CDATA[
      K(x,1 / (y / z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3700,a,b,5614,a)].">
      <j1 rule="hyper" parents="58 3700 5614"/>
    </justification>
  </clause>

  <clause id="5621">
    <literal><![CDATA[
      K(x,y / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(5617(a,2),5334(a,1))].">
      <j1 rule="para" parents="5617 5334"/>
    </justification>
  </clause>

  <clause id="5622">
    <literal><![CDATA[
      K((x * y) / x,1 / ((x * y) / x)) = K(y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(334,a,3311,a(flip),b,5620,a),flip(a)].">
      <j1 rule="hyper" parents="334 3311 5620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5623">
    <literal><![CDATA[
      K(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ 1) = u
    ]]></literal>
    <justification jstring="[para(5620(a,1),5334(a,1))].">
      <j1 rule="para" parents="5620 5334"/>
    </justification>
  </clause>

  <clause id="5624">
    <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(5061(a,1),3749(a,2,1,2,1))].">
      <j1 rule="para" parents="5061 3749"/>
    </justification>
  </clause>

  <clause id="5625">
    <literal><![CDATA[
      K((1 / x) \ y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,4996,a,b,5080,a),flip(a)].">
      <j1 rule="hyper" parents="334 4996 5080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5626">
    <literal><![CDATA[
      K((x \ 1) \ y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4282,a(flip),b,5625,a)].">
      <j1 rule="hyper" parents="58 4282 5625"/>
    </justification>
  </clause>

  <clause id="5627">
    <literal><![CDATA[
      K(x * (y \ 1),x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),5625(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 5625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5628">
    <literal><![CDATA[
      K((x \ 1) \ y,y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5532,a,b,5626,a),flip(a)].">
      <j1 rule="hyper" parents="334 5532 5626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5629">
    <literal><![CDATA[
      K((x \ 1) * y,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5532,a,b,5627,a)].">
      <j1 rule="hyper" parents="58 5532 5627"/>
    </justification>
  </clause>

  <clause id="5630">
    <literal><![CDATA[
      K(((x * y) / x) \ z,z) = K(z * (y \ K(y,x)),z)
    ]]></literal>
    <justification jstring="[para(5179(a,1),5627(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5179 5627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5631">
    <literal><![CDATA[
      T(x * K(y \ x,x),y \ 1) = R(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(5627(a,1),5467(a,1,1,2))].">
      <j1 rule="para" parents="5627 5467"/>
    </justification>
  </clause>

  <clause id="5632">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x * y,y) = T((x \ 1) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5628,a(flip),b,4995,a(flip))].">
      <j1 rule="hyper" parents="119 5628 4995"/>
    </justification>
  </clause>

  <clause id="5633">
    <literal><![CDATA[
      K((1 / x) * y,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),5628(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 5628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5634">
    <literal><![CDATA[
      (x \ y) * ((y / x) \ z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),5083(a,1,2,1,1))].">
      <j1 rule="para" parents="5 5083"/>
    </justification>
  </clause>

  <clause id="5635">
    <literal><![CDATA[
      x * ((y / (y / x)) \ z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[para(4548(a,1),5083(a,1,2,1))].">
      <j1 rule="para" parents="4548 5083"/>
    </justification>
  </clause>

  <clause id="5636">
    <literal><![CDATA[
      (x * K(y,x)) \ y = x \ (y * K(x,y))
    ]]></literal>
    <justification jstring="[para(5017(a,1),5084(a,1,1))].">
      <j1 rule="para" parents="5017 5084"/>
    </justification>
  </clause>

  <clause id="5637">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) = K(z,x / y)
    ]]></literal>
    <justification jstring="[para(5088(a,1),5403(a,1,2))].">
      <j1 rule="para" parents="5088 5403"/>
    </justification>
  </clause>

  <clause id="5638">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x / y) = u
    ]]></literal>
    <justification jstring="[para(5088(a,1),5412(a,1,2))].">
      <j1 rule="para" parents="5088 5412"/>
    </justification>
  </clause>

  <clause id="5639">
    <literal><![CDATA[
      K(x,y) / (1 / T(y,x)) = 1 / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(201,a,5137,a)].">
      <j1 rule="hyper" parents="201 5137"/>
    </justification>
  </clause>

  <clause id="5640">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * T(y,x) = T(y,x) * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(5140(a,1),654(a,1,1,1))].">
      <j1 rule="para" parents="5140 654"/>
    </justification>
  </clause>

  <clause id="5641">
    <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(5140(a,1),1574(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5140 1574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5642">
    <literal><![CDATA[
      T(x * K(y \ x,x),y \ 1) = R(x,x \ (y \ x),x)
    ]]></literal>
    <justification jstring="[hyper(334,a,4784,a,b,5146,a),flip(a)].">
      <j1 rule="hyper" parents="334 4784 5146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5643">
    <literal><![CDATA[
      T(x,y) \ T(x * K(z,x),y) = K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,5146,a,b,5017,a(flip))].">
      <j1 rule="hyper" parents="116 5146 5017"/>
    </justification>
  </clause>

  <clause id="5644">
    <literal><![CDATA[
      T(x * K(y,x),z) \ T(x,z) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(5146(a,2),5060(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5146 5060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5645">
    <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(5146(a,2),5145(a,1))].">
      <j1 rule="para" parents="5146 5145"/>
    </justification>
  </clause>

  <clause id="5646">
    <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(5146(a,2),5195(a,1,2))].">
      <j1 rule="para" parents="5146 5195"/>
    </justification>
  </clause>

  <clause id="5647">
    <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(5166(a,1),789(a,1,1))].">
      <j1 rule="para" parents="5166 789"/>
    </justification>
  </clause>

  <clause id="5648">
    <literal><![CDATA[
      x * (y * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      u / ((z * y) / z) = x
    ]]></literal>
    <justification jstring="[para(5171(a,1),130(a,1))].">
      <j1 rule="para" parents="5171 130"/>
    </justification>
  </clause>

  <clause id="5649">
    <literal><![CDATA[
      K(x,y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(5219,a,5181,a)].">
      <j1 rule="hyper" parents="5219 5181"/>
    </justification>
  </clause>

  <clause id="5650">
    <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),5649(a,2,2))].">
      <j1 rule="para" parents="80 5649"/>
    </justification>
  </clause>

  <clause id="5651">
    <literal><![CDATA[
      K(x,(1 / x) * (y * x)) = K(x,L(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[para(3154(a,1),5185(a,1,2))].">
      <j1 rule="para" parents="3154 5185"/>
    </justification>
  </clause>

  <clause id="5652">
    <literal><![CDATA[
      x * ((y * (x / y)) \ y) = x / (x / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5330,a,b,xx)].">
      <j1 rule="hyper" parents="119 5330"/>
    </justification>
  </clause>

  <clause id="5653">
    <literal><![CDATA[
      x \ (y \ ((y * z) / y)) = x \ (K(y,z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(116,a,5347,a,b,5,a)].">
      <j1 rule="hyper" parents="116 5347 5"/>
    </justification>
  </clause>

  <clause id="5654">
    <literal><![CDATA[
      L(x \ (y \ z),x,K(y,z)) = (K(y,z) * x) \ (y \ ((y * z) / y))
    ]]></literal>
    <justification jstring="[para(5347(a,2),92(a,2,2))].">
      <j1 rule="para" parents="5347 92"/>
    </justification>
  </clause>

  <clause id="5655">
    <literal><![CDATA[
      (x * K(y,x)) \ z = K(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5172,a(flip),b,5350,a)].">
      <j1 rule="hyper" parents="58 5172 5350"/>
    </justification>
  </clause>

  <clause id="5656">
    <literal><![CDATA[
      K(x \ y,x) * ((x \ y) \ z) = (y / x) \ z
    ]]></literal>
    <justification jstring="[para(5(a,1),5350(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 5350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5658">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5350(a,2),597(a,1))].">
      <j1 rule="para" parents="5350 597"/>
    </justification>
  </clause>

  <clause id="5659">
    <literal><![CDATA[
      (x / (x / y)) \ z = K(y,y \ x) * (y \ z)
    ]]></literal>
    <justification jstring="[para(4548(a,1),5350(a,1,1))].">
      <j1 rule="para" parents="4548 5350"/>
    </justification>
  </clause>

  <clause id="5662">
    <literal><![CDATA[
      x \ y != K(x,z) * (x \ u)
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * u = y
    ]]></literal>
    <justification jstring="[para(5366(a,1),42(a,1)),flip(a)].">
      <j1 rule="para" parents="5366 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5663">
    <literal><![CDATA[
      K(x,y) * T(x,z) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,3470,a(flip),b,5372,a)].">
      <j1 rule="hyper" parents="334 3470 5372"/>
    </justification>
  </clause>

  <clause id="5664">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) / T(x,y) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,3470,a(flip),b,5372,a)].">
      <j1 rule="hyper" parents="117 3470 5372"/>
    </justification>
  </clause>

  <clause id="5665">
    <literal><![CDATA[
      K(x,y) * T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(5372(a,2),3480(a,1))].">
      <j1 rule="para" parents="5372 3480"/>
    </justification>
  </clause>

  <clause id="5666">
    <literal><![CDATA[
      K(x,(y \ z) / (y \ 1)) * (y \ T(z,x)) = y \ z
    ]]></literal>
    <justification jstring="[hyper(1090,a,5373,a)].">
      <j1 rule="hyper" parents="1090 5373"/>
    </justification>
  </clause>

  <clause id="5667">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) / K(y,x \ 1) = x
    ]]></literal>
    <justification jstring="[para(3700(a,1),5437(a,1,2))].">
      <j1 rule="para" parents="3700 5437"/>
    </justification>
  </clause>

  <clause id="5668">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ y)) / z) = K(z,x) * y
    ]]></literal>
    <justification jstring="[hyper(1411,a,5442,a)].">
      <j1 rule="hyper" parents="1411 5442"/>
    </justification>
  </clause>

  <clause id="5670">
    <literal><![CDATA[
      (x \ y) \ ((y / x) * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),5443(a,1,2,1,1))].">
      <j1 rule="para" parents="5 5443"/>
    </justification>
  </clause>

  <clause id="5671">
    <literal><![CDATA[
      x \ ((y / (y / x)) * z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(4548(a,1),5443(a,1,2,1))].">
      <j1 rule="para" parents="4548 5443"/>
    </justification>
  </clause>

  <clause id="5672">
    <literal><![CDATA[
      x \ ((x * K(y,x)) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(5017(a,1),5443(a,1,2,1))].">
      <j1 rule="para" parents="5017 5443"/>
    </justification>
  </clause>

  <clause id="5673">
    <literal><![CDATA[
      K(x,y) * (K((x * y) / x,z) * u) = y \ (T((x * y) / x,z) * u)
    ]]></literal>
    <justification jstring="[para(5044(a,1),5443(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5044 5443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5674">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),5444(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 5444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5675">
    <literal><![CDATA[
      (x * (K(y * z,x) * y)) * z = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5444(a,1),880(a,1,1))].">
      <j1 rule="para" parents="5444 880"/>
    </justification>
  </clause>

  <clause id="5676">
    <literal><![CDATA[
      (x / (x / y)) * z = y * (K(y \ x,y) * z)
    ]]></literal>
    <justification jstring="[para(4548(a,1),5444(a,1,1))].">
      <j1 rule="para" parents="4548 5444"/>
    </justification>
  </clause>

  <clause id="5677">
    <literal><![CDATA[
      (x * K(y,x)) * z = x * (K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(5017(a,1),5444(a,1,1))].">
      <j1 rule="para" parents="5017 5444"/>
    </justification>
  </clause>

  <clause id="5678">
    <literal><![CDATA[
      (x / y) * (K(y,y \ x) * z) = ((y * (x / y)) / y) * z
    ]]></literal>
    <justification jstring="[para(5186(a,1),5444(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5186 5444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5679">
    <literal><![CDATA[
      T(x,x \ (y * x)) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),5465(a,2,2))].">
      <j1 rule="para" parents="6 5465"/>
    </justification>
  </clause>

  <clause id="5680">
    <literal><![CDATA[
      K(x \ y,x) * ((y / x) * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),5490(a,1,2,1,1))].">
      <j1 rule="para" parents="5 5490"/>
    </justification>
  </clause>

  <clause id="5682">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),5493(a,2,1,1))].">
      <j1 rule="para" parents="5 5493"/>
    </justification>
  </clause>

  <clause id="5683">
    <literal><![CDATA[
      (K(x,y) * y) * z = K(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(5040(a,1),5493(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5040 5493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5684">
    <literal><![CDATA[
      x * (K(y,x) * T(z,x)) = K(y,x) * (z * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5494,a(flip),b,5367,a)].">
      <j1 rule="hyper" parents="119 5494 5367"/>
    </justification>
  </clause>

  <clause id="5685">
    <literal><![CDATA[
      T(x,y) \ T(x,z) = K(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,2065,a,b,5496,a),flip(a)].">
      <j1 rule="hyper" parents="334 2065 5496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5686">
    <literal><![CDATA[
      x * (K(y,x) * (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5500(a,1),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5500 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5687">
    <literal><![CDATA[
      K(x,x \ y) * ((y / x) \ z) = (x \ y) \ z
    ]]></literal>
    <justification jstring="[para(5(a,1),5516(a,1,2,1,1))].">
      <j1 rule="para" parents="5 5516"/>
    </justification>
  </clause>

  <clause id="5688">
    <literal><![CDATA[
      K(x \ y,x) * ((y / (y / x)) \ z) = x \ z
    ]]></literal>
    <justification jstring="[para(4548(a,1),5516(a,1,2,1))].">
      <j1 rule="para" parents="4548 5516"/>
    </justification>
  </clause>

  <clause id="5689">
    <literal><![CDATA[
      x \ T(x * y,x) != y * z
    ]]></literal>
    <literal><![CDATA[
      T(K(x * y,x),y) = z
    ]]></literal>
    <justification jstring="[para(5517(a,2),247(a,2)),flip(a)].">
      <j1 rule="para" parents="5517 247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5690">
    <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(5086(a,1),5519(a,1,1))].">
      <j1 rule="para" parents="5086 5519"/>
    </justification>
  </clause>

  <clause id="5691">
    <literal><![CDATA[
      R(K(x,y),y * z,u) * ((y * z) * u) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[para(5522(a,1),101(a,2,1))].">
      <j1 rule="para" parents="5522 101"/>
    </justification>
  </clause>

  <clause id="5693">
    <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(5522(a,1),506(a,1,1))].">
      <j1 rule="para" parents="5522 506"/>
    </justification>
  </clause>

  <clause id="5694">
    <literal><![CDATA[
      x * (K(y \ x,x) * (y \ 1)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[para(5627(a,1),5529(a,1,2,1))].">
      <j1 rule="para" parents="5627 5529"/>
    </justification>
  </clause>

  <clause id="5695">
    <literal><![CDATA[
      (x \ K(x,y)) * T(x,x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(678,a,5533,a)].">
      <j1 rule="hyper" parents="678 5533"/>
    </justification>
  </clause>

  <clause id="5696">
    <literal><![CDATA[
      K(x,(y \ 1) \ x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5568,a(flip),b,5573,a)].">
      <j1 rule="hyper" parents="58 5568 5573"/>
    </justification>
  </clause>

  <clause id="5697">
    <literal><![CDATA[
      K(x,(R(y,z,u) \ y) \ x) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(4267(a,1),5696(a,1,2,1))].">
      <j1 rule="para" parents="4267 5696"/>
    </justification>
  </clause>

  <clause id="5698">
    <literal><![CDATA[
      K(x \ (y \ 1),z * T(u,u \ 1)) = K(x \ (1 / y),z * u)
    ]]></literal>
    <justification jstring="[hyper(334,a,4284,a,b,5574,a),flip(a)].">
      <j1 rule="hyper" parents="334 4284 5574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5701">
    <literal><![CDATA[
      K(x,(1 / x) * y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(5583(a,2),5389(a,1,1))].">
      <j1 rule="para" parents="5583 5389"/>
    </justification>
  </clause>

  <clause id="5702">
    <literal><![CDATA[
      K((x / y) \ 1,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(5246,a,5619,a)].">
      <j1 rule="hyper" parents="5246 5619"/>
    </justification>
  </clause>

  <clause id="5703">
    <literal><![CDATA[
      K(x,(y / z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(5619(a,2),5241(a,1))].">
      <j1 rule="para" parents="5619 5241"/>
    </justification>
  </clause>

  <clause id="5704">
    <literal><![CDATA[
      K(1 / (x / y),z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(5546,a,5702,a)].">
      <j1 rule="hyper" parents="5546 5702"/>
    </justification>
  </clause>

  <clause id="5705">
    <literal><![CDATA[
      R(K(x / y,z),x / y,u) = K((y / x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,4446,a,b,5702,a)].">
      <j1 rule="hyper" parents="334 4446 5702"/>
    </justification>
  </clause>

  <clause id="5706">
    <literal><![CDATA[
      K((x / y) \ 1,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,5235,a(flip),b,5702,a),flip(a)].">
      <j1 rule="hyper" parents="334 5235 5702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5707">
    <literal><![CDATA[
      K(x / (y * x),z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),5702(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6 5702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5709">
    <literal><![CDATA[
      K((x \ y) / y,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),5702(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 5702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5710">
    <literal><![CDATA[
      K(x / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(5704(a,1),3445(a,1))].">
      <j1 rule="para" parents="5704 3445"/>
    </justification>
  </clause>

  <clause id="5711">
    <literal><![CDATA[
      K((x / ((1 / x) \ y)) \ 1,x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,4747,a(flip),b,5706,a),flip(a)].">
      <j1 rule="hyper" parents="334 4747 5706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5712">
    <literal><![CDATA[
      (x / y) \ K(x \ y,x) = T((x / y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5706,a(flip),b,5011,a)].">
      <j1 rule="hyper" parents="116 5706 5011"/>
    </justification>
  </clause>

  <clause id="5713">
    <literal><![CDATA[
      K((x * y) \ y,x * y) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(6(a,1),5706(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6 5706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5714">
    <literal><![CDATA[
      K(x \ (y \ x),x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),5706(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 5706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5715">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(5707(a,1),5277(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5707 5277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5716">
    <literal><![CDATA[
      K(x / (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / y,z) = u
    ]]></literal>
    <justification jstring="[para(5707(a,2),5546(a,1))].">
      <j1 rule="para" parents="5707 5546"/>
    </justification>
  </clause>

  <clause id="5718">
    <literal><![CDATA[
      x / (((y \ (x * z)) * y) / z) = K(y,x / (y / z))
    ]]></literal>
    <justification jstring="[para(1644(a,1),5637(a,1,2))].">
      <j1 rule="para" parents="1644 5637"/>
    </justification>
  </clause>

  <clause id="5719">
    <literal><![CDATA[
      K(x,y) / (K(x,y) / y) = 1 / (1 / y)
    ]]></literal>
    <justification jstring="[para(5072(a,2),5639(a,1,2))].">
      <j1 rule="para" parents="5072 5639"/>
    </justification>
  </clause>

  <clause id="5720">
    <literal><![CDATA[
      (x * K(y,x)) \ z = K(y,x) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(334,a,5391,a,b,5655,a),flip(a)].">
      <j1 rule="hyper" parents="334 5391 5655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5721">
    <literal><![CDATA[
      (x / (K(y,z) * T(y,u))) \ x = K(y,u) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(376,a,5663,a)].">
      <j1 rule="hyper" parents="376 5663"/>
    </justification>
  </clause>

  <clause id="5722">
    <literal><![CDATA[
      T(1 / x,y) \ 1 = x * K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,5667,a),flip(a)].">
      <j1 rule="hyper" parents="133 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5723">
    <literal><![CDATA[
      R(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(34,a,187,a,b,5672,a)].">
      <j1 rule="hyper" parents="34 187 5672"/>
    </justification>
  </clause>

  <clause id="5724">
    <literal><![CDATA[
      L(x,K(y,z),z) = x
    ]]></literal>
    <justification jstring="[hyper(29,a,309,a(flip),b,5672,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="29 309 5672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5725">
    <literal><![CDATA[
      (T(x,y) * K(z,x)) * u = T(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(5723(a,1),524(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5723 524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5726">
    <literal><![CDATA[
      (R(x,y,z) * K(u,x)) * w = R(x,y,z) * (K(u,x) * w)
    ]]></literal>
    <justification jstring="[para(5723(a,1),526(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5723 526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5727">
    <literal><![CDATA[
      L(x,K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(5724(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="5724 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5728">
    <literal><![CDATA[
      L(x,K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5724(a,1),45(a,2))].">
      <j1 rule="para" parents="5724 45"/>
    </justification>
  </clause>

  <clause id="5729">
    <literal><![CDATA[
      (x * K(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,x) * z) = u
    ]]></literal>
    <justification jstring="[para(5724(a,1),296(a,1,2))].">
      <j1 rule="para" parents="5724 296"/>
    </justification>
  </clause>

  <clause id="5731">
    <literal><![CDATA[
      R(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3617,a,5683,a)].">
      <j1 rule="hyper" parents="3617 5683"/>
    </justification>
  </clause>

  <clause id="5732">
    <literal><![CDATA[
      L(x,y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(493,a,5683,a)].">
      <j1 rule="hyper" parents="493 5683"/>
    </justification>
  </clause>

  <clause id="5733">
    <literal><![CDATA[
      a(K(x,y),y,z) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,5683,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="115 5683 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5734">
    <literal><![CDATA[
      L(x,y,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5732(a,1),45(a,2))].">
      <j1 rule="para" parents="5732 45"/>
    </justification>
  </clause>

  <clause id="5735">
    <literal><![CDATA[
      R(K(x,y / (z * y)),y / (z * y),u) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,5613,a(flip),b,5731,a),flip(a)].">
      <j1 rule="hyper" parents="334 5613 5731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5736">
    <literal><![CDATA[
      K(x / (x / y),y \ x) * K(z,x / (x / y)) = T(x / (x / y),z) \ y
    ]]></literal>
    <justification jstring="[para(4544(a,1),5685(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4544 5685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5737">
    <literal><![CDATA[
      (x * K(y,x)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(5720(a,2),5426(a,1))].">
      <j1 rule="para" parents="5720 5426"/>
    </justification>
  </clause>

  <clause id="5738">
    <literal><![CDATA[
      K(x / y,z) \ y != u
    ]]></literal>
    <literal><![CDATA[
      T(x / y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(75(a,1),5051(a,1,2))].">
      <j1 rule="para" parents="75 5051"/>
    </justification>
  </clause>

  <clause id="5739">
    <literal><![CDATA[
      L(x \ 1,T(x,y),y) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4062,a(flip),b,5192,a)].">
      <j1 rule="hyper" parents="58 4062 5192"/>
    </justification>
  </clause>

  <clause id="5740">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),y) = T(x,y) * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(5739(a,1),1921(a,1,1,2))].">
      <j1 rule="para" parents="5739 1921"/>
    </justification>
  </clause>

  <clause id="5741">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(5549(a,1),5336(a,1,2))].">
      <j1 rule="para" parents="5549 5336"/>
    </justification>
  </clause>

  <clause id="5742">
    <literal><![CDATA[
      K(x,x * y) * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      x \ L(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(5548(a,2),5371(a,1,2))].">
      <j1 rule="para" parents="5548 5371"/>
    </justification>
  </clause>

  <clause id="5743">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(5551(a,1),5371(a,1,2))].">
      <j1 rule="para" parents="5551 5371"/>
    </justification>
  </clause>

  <clause id="5744">
    <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),5381(a,1,2))].">
      <j1 rule="para" parents="17 5381"/>
    </justification>
  </clause>

  <clause id="5745">
    <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(5367(a,1),5381(a,1,2))].">
      <j1 rule="para" parents="5367 5381"/>
    </justification>
  </clause>

  <clause id="5746">
    <literal><![CDATA[
      K(x,y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(4995(a,2),5449(a,1,2))].">
      <j1 rule="para" parents="4995 5449"/>
    </justification>
  </clause>

  <clause id="5747">
    <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(2346(a,1),5531(a,1,2))].">
      <j1 rule="para" parents="2346 5531"/>
    </justification>
  </clause>

  <clause id="5748">
    <literal><![CDATA[
      T(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(5394(a,1),5531(a,1,2))].">
      <j1 rule="para" parents="5394 5531"/>
    </justification>
  </clause>

  <clause id="5749">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5496,a(flip),b,5550,a)].">
      <j1 rule="hyper" parents="58 5496 5550"/>
    </justification>
  </clause>

  <clause id="5750">
    <literal><![CDATA[
      K(x,x * y) * (x \ R(x,y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5550,a(flip),b,5486,a)].">
      <j1 rule="hyper" parents="119 5550 5486"/>
    </justification>
  </clause>

  <clause id="5751">
    <literal><![CDATA[
      K(x,y) * K(y,y * x) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(2067,a,5555,a)].">
      <j1 rule="hyper" parents="2067 5555"/>
    </justification>
  </clause>

  <clause id="5752">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5556(a,1),2067(a,1))].">
      <j1 rule="para" parents="5556 2067"/>
    </justification>
  </clause>

  <clause id="5753">
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(5532(a,2),5556(a,1,2))].">
      <j1 rule="para" parents="5532 5556"/>
    </justification>
  </clause>

  <clause id="5755">
    <literal><![CDATA[
      R(K(x,y / z),y / z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ 1) = w
    ]]></literal>
    <justification jstring="[para(5731(a,2),5623(a,1))].">
      <j1 rule="para" parents="5731 5623"/>
    </justification>
  </clause>

  <clause id="5756">
    <literal><![CDATA[
      K(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / y) = z
    ]]></literal>
    <justification jstring="[para(70(a,1),5703(a,1,2,1))].">
      <j1 rule="para" parents="70 5703"/>
    </justification>
  </clause>

  <clause id="5757">
    <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),5703(a,1,2,1))].">
      <j1 rule="para" parents="102 5703"/>
    </justification>
  </clause>

  <clause id="5759">
    <literal><![CDATA[
      K(x,y / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / z) = u
    ]]></literal>
    <justification jstring="[para(5613(a,2),5756(a,1))].">
      <j1 rule="para" parents="5613 5756"/>
    </justification>
  </clause>

  <clause id="5760">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = K(y,x) * K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),5749(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 5749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5761">
    <literal><![CDATA[
      K(x * y,y) * K(y,x) = y \ R(y,x,y)
    ]]></literal>
    <justification jstring="[para(5532(a,2),5749(a,1,1))].">
      <j1 rule="para" parents="5532 5749"/>
    </justification>
  </clause>

  <clause id="5762">
    <literal><![CDATA[
      K(x,y) * K(y,x * y) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[para(5649(a,2),5751(a,1,2))].">
      <j1 rule="para" parents="5649 5751"/>
    </justification>
  </clause>

  <clause id="5763">
    <literal><![CDATA[
      x \ y != K(x,z) * K(z * x,x)
    ]]></literal>
    <literal><![CDATA[
      R(x,z,x) = y
    ]]></literal>
    <justification jstring="[para(5753(a,2),42(a,1)),flip(a)].">
      <j1 rule="para" parents="5753 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5764">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y * x,x) * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5753(a,1),2067(a,1))].">
      <j1 rule="para" parents="5753 2067"/>
    </justification>
  </clause>

  <clause id="5765">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = z
    ]]></literal>
    <justification jstring="[para(5761(a,1),2073(a,1))].">
      <j1 rule="para" parents="5761 2073"/>
    </justification>
  </clause>

  <clause id="5766">
    <literal><![CDATA[
      T(T(x * K(x \ y,x),y),z) = L(T(x,z),x \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4970(a,1),4952(a,1,1,1))].">
      <j1 rule="para" parents="4970 4952"/>
    </justification>
  </clause>

  <clause id="5767">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = T(K(x,y \ 1),z)
    ]]></literal>
    <justification jstring="[para(4995(a,2),5002(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4995 5002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5769">
    <literal><![CDATA[
      x * K(y,T(z,x) \ 1) = K(y,z \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,5767,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="119 5767 17"/>
    </justification>
  </clause>

  <clause id="5771">
    <literal><![CDATA[
      K(x,T(1 / y,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(75(a,1),5767(a,2,1,2))].">
      <j1 rule="para" parents="75 5767"/>
    </justification>
  </clause>

  <clause id="5772">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(3696(a,1),5767(a,2,1))].">
      <j1 rule="para" parents="3696 5767"/>
    </justification>
  </clause>

  <clause id="5773">
    <literal><![CDATA[
      x * T(K(x,y \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(5767(a,1),5030(a,1,2))].">
      <j1 rule="para" parents="5767 5030"/>
    </justification>
  </clause>

  <clause id="5774">
    <literal><![CDATA[
      K(x,1 / T(1 / y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(5756,a,5771,a)].">
      <j1 rule="hyper" parents="5756 5771"/>
    </justification>
  </clause>

  <clause id="5775">
    <literal><![CDATA[
      K(x,1 / T(y,z)) = T(K(x,1 / y),z)
    ]]></literal>
    <justification jstring="[para(2221(a,1),5771(a,1,2))].">
      <j1 rule="para" parents="2221 5771"/>
    </justification>
  </clause>

  <clause id="5776">
    <literal><![CDATA[
      K(x,R(T(K(x,y),z),u,w)) = 1
    ]]></literal>
    <justification jstring="[para(5771(a,1),3488(a,1,2,1))].">
      <j1 rule="para" parents="5771 3488"/>
    </justification>
  </clause>

  <clause id="5777">
    <literal><![CDATA[
      K(x,y * K(z,y \ 1)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5722(a,1),5771(a,1,2))].">
      <j1 rule="para" parents="5722 5771"/>
    </justification>
  </clause>

  <clause id="5778">
    <literal><![CDATA[
      (x * K(y,x)) \ L(x,y,x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5352,a(flip),b,5036,a)].">
      <j1 rule="hyper" parents="116 5352 5036"/>
    </justification>
  </clause>

  <clause id="5779">
    <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(334,a,150,a,b,5147,a),flip(a)].">
      <j1 rule="hyper" parents="334 150 5147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5780">
    <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,5039,a,b,5147,a)].">
      <j1 rule="hyper" parents="30 5039 5147"/>
    </justification>
  </clause>

  <clause id="5781">
    <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,5039,a,b,5148,a)].">
      <j1 rule="hyper" parents="30 5039 5148"/>
    </justification>
  </clause>

  <clause id="5782">
    <literal><![CDATA[
      T(1 / (K(x,y) / x),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(5475(a,1),5150(a,1,1,2))].">
      <j1 rule="para" parents="5475 5150"/>
    </justification>
  </clause>

  <clause id="5783">
    <literal><![CDATA[
      (1 / (K(x,y) / x)) * y = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(119,a,5782,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 5782 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5784">
    <literal><![CDATA[
      (((x * y) / x) \ 1) \ 1 = (y \ 1) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,2304,a(flip),b,5168,a)].">
      <j1 rule="hyper" parents="334 2304 5168"/>
    </justification>
  </clause>

  <clause id="5785">
    <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,5206,a,b,5040,a(flip))].">
      <j1 rule="hyper" parents="117 5206 5040"/>
    </justification>
  </clause>

  <clause id="5786">
    <literal><![CDATA[
      L(x,y,z) / L(x * K(u,x),y,z) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5206(a,2),5223(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5206 5223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5787">
    <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,5207,a,b,5017,a(flip))].">
      <j1 rule="hyper" parents="116 5207 5017"/>
    </justification>
  </clause>

  <clause id="5788">
    <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(5207(a,2),4589(a,1,1))].">
      <j1 rule="para" parents="5207 4589"/>
    </justification>
  </clause>

  <clause id="5789">
    <literal><![CDATA[
      R(x * K(y,x),z,u) \ R(x,z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(5207(a,2),5060(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5207 5060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5790">
    <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(5207(a,2),5257(a,1,1))].">
      <j1 rule="para" parents="5207 5257"/>
    </justification>
  </clause>

  <clause id="5791">
    <literal><![CDATA[
      K(x \ 1,x) * K(y,x) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(2260,a,5263,a)].">
      <j1 rule="hyper" parents="2260 5263"/>
    </justification>
  </clause>

  <clause id="5792">
    <literal><![CDATA[
      (x \ T(y,x \ 1)) / (x \ y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,4089,a,b,5298,a)].">
      <j1 rule="hyper" parents="117 4089 5298"/>
    </justification>
  </clause>

  <clause id="5793">
    <literal><![CDATA[
      K((x / y) \ 1,z) \ (x * T(x \ y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(192,a,5307,a)].">
      <j1 rule="hyper" parents="192 5307"/>
    </justification>
  </clause>

  <clause id="5794">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) / z = K(((x * y) / z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(956(a,1),5307(a,1,1))].">
      <j1 rule="para" parents="956 5307"/>
    </justification>
  </clause>

  <clause id="5795">
    <literal><![CDATA[
      x \ (((y \ (x / z)) * y) * z) = K((x \ (y * z)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(1150(a,1),5308(a,1,2))].">
      <j1 rule="para" parents="1150 5308"/>
    </justification>
  </clause>

  <clause id="5796">
    <literal><![CDATA[
      x \ (y * (z * T(z \ (y \ x),u))) = K((x \ (y * z)) \ 1,u)
    ]]></literal>
    <justification jstring="[para(956(a,1),5308(a,1,2))].">
      <j1 rule="para" parents="956 5308"/>
    </justification>
  </clause>

  <clause id="5797">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((x \ (y / z)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(1644(a,1),5308(a,1,2))].">
      <j1 rule="para" parents="1644 5308"/>
    </justification>
  </clause>

  <clause id="5798">
    <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(2025(a,1),5308(a,1,2))].">
      <j1 rule="para" parents="2025 5308"/>
    </justification>
  </clause>

  <clause id="5799">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * x = (x / (y \ 1)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(3448(a,1),5309(a,2,2))].">
      <j1 rule="para" parents="3448 5309"/>
    </justification>
  </clause>

  <clause id="5800">
    <literal><![CDATA[
      x * K((x \ (y * z)) \ 1,y) = z * ((y \ (z \ x)) * y)
    ]]></literal>
    <justification jstring="[hyper(4891,a,5312,a),flip(a)].">
      <j1 rule="hyper" parents="4891 5312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5801">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K((y \ (x \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(1075,a,5312,a)].">
      <j1 rule="hyper" parents="1075 5312"/>
    </justification>
  </clause>

  <clause id="5802">
    <literal><![CDATA[
      x * K((x \ (y * z)) \ 1,u) = y * (z * T(z \ (y \ x),u))
    ]]></literal>
    <justification jstring="[hyper(977,a,5312,a),flip(a)].">
      <j1 rule="hyper" parents="977 5312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5803">
    <literal><![CDATA[
      (x * y) * K(((x * y) \ y) \ 1,z) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(764,a,5312,a),flip(a)].">
      <j1 rule="hyper" parents="764 5312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5804">
    <literal><![CDATA[
      T(K(x / y,z),x) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(246,a,5088,a,b,5312,a(flip))].">
      <j1 rule="hyper" parents="246 5088 5312"/>
    </justification>
  </clause>

  <clause id="5805">
    <literal><![CDATA[
      x * (y * K((y \ (x \ 1)) \ 1,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5312,a(flip),b,971,a(flip))].">
      <j1 rule="hyper" parents="119 5312 971"/>
    </justification>
  </clause>

  <clause id="5806">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) / y = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,5312,a(flip),b,465,a)].">
      <j1 rule="hyper" parents="117 5312 465"/>
    </justification>
  </clause>

  <clause id="5807">
    <literal><![CDATA[
      T(x * K((x \ y) \ 1,z),x) = T(y,x) * T(T(y,x) \ x,z)
    ]]></literal>
    <justification jstring="[para(5312(a,1),2022(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5312 2022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5808">
    <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(3997(a,1),5312(a,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3997 5312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5809">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = T(K(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(5287,a,5318,a)].">
      <j1 rule="hyper" parents="5287 5318"/>
    </justification>
  </clause>

  <clause id="5811">
    <literal><![CDATA[
      T(K(x \ 1,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z) \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(5318(a,1),5287(a,1))].">
      <j1 rule="para" parents="5318 5287"/>
    </justification>
  </clause>

  <clause id="5812">
    <literal><![CDATA[
      K(T(1 / x,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(75(a,1),5809(a,2,1,1))].">
      <j1 rule="para" parents="75 5809"/>
    </justification>
  </clause>

  <clause id="5813">
    <literal><![CDATA[
      K(T(x \ 1,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(3448(a,1),5809(a,2,1))].">
      <j1 rule="para" parents="3448 5809"/>
    </justification>
  </clause>

  <clause id="5814">
    <literal><![CDATA[
      K(1 / T(x,y),z) = T(K(1 / x,z),y)
    ]]></literal>
    <justification jstring="[para(2221(a,1),5812(a,1,1))].">
      <j1 rule="para" parents="2221 5812"/>
    </justification>
  </clause>

  <clause id="5815">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = 1 / T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(5813(a,1),5243(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5813 5243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5816">
    <literal><![CDATA[
      T(x,y) != K(1 / T(z,y),u)
    ]]></literal>
    <literal><![CDATA[
      K(1 / z,u) = x
    ]]></literal>
    <justification jstring="[para(5814(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="5814 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5817">
    <literal><![CDATA[
      x \ (K((x / y) \ 1,z) * y) = T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(549,a,5319,a)].">
      <j1 rule="hyper" parents="549 5319"/>
    </justification>
  </clause>

  <clause id="5818">
    <literal><![CDATA[
      K(((x \ 1) / (x \ y)) \ 1,z) * (x \ y) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,1030,a(flip),b,5319,a),flip(a)].">
      <j1 rule="hyper" parents="334 1030 5319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5820">
    <literal><![CDATA[
      K((x / (x * y)) \ 1,z) * (x * y) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),5319(a,2,2,1))].">
      <j1 rule="para" parents="4 5319"/>
    </justification>
  </clause>

  <clause id="5821">
    <literal><![CDATA[
      ((x \ y) \ ((x \ 1) \ (x \ y))) * (x \ y) = (x \ 1) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5220,a(flip),b,5326,a),flip(a)].">
      <j1 rule="hyper" parents="116 5220 5326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5822">
    <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(5326(a,2),3964(a,2,1))].">
      <j1 rule="para" parents="5326 3964"/>
    </justification>
  </clause>

  <clause id="5823">
    <literal><![CDATA[
      K(1 / ((1 / x) / y),z) = (T(y * x,z) / x) / y
    ]]></literal>
    <justification jstring="[para(1042(a,1),5328(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1042 5328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5824">
    <literal><![CDATA[
      K(x,y) * (T(y,z) * x) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5351,a,b,5354,a),flip(a)].">
      <j1 rule="hyper" parents="334 5351 5354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5825">
    <literal><![CDATA[
      T(T(x,y),z) * K(y,x) = x * K(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(2553,a,5451,a)].">
      <j1 rule="hyper" parents="2553 5451"/>
    </justification>
  </clause>

  <clause id="5826">
    <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(5451(a,1),2553(a,1))].">
      <j1 rule="para" parents="5451 2553"/>
    </justification>
  </clause>

  <clause id="5827">
    <literal><![CDATA[
      K(x,y) / (K(x,y) / x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(334,a,4969,a,b,5476,a),flip(a)].">
      <j1 rule="hyper" parents="334 4969 5476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5828">
    <literal><![CDATA[
      (1 / (1 / x)) \ K(x,y) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(192,a,5827,a)].">
      <j1 rule="hyper" parents="192 5827"/>
    </justification>
  </clause>

  <clause id="5829">
    <literal><![CDATA[
      K(x \ 1,y) / (x \ 1) = (1 / x) \ K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),5828(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 5828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5830">
    <literal><![CDATA[
      (x \ K(x,y)) * x = (x \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5177,a(flip),b,5477,a),flip(a)].">
      <j1 rule="hyper" parents="58 5177 5477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5831">
    <literal><![CDATA[
      (x * y) * (x / (x * y)) = x * K(x * y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5484,a(flip),b,87,a),flip(a)].">
      <j1 rule="hyper" parents="119 5484 87"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5832">
    <literal><![CDATA[
      T(T(x,y),y) \ x = K(y,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(5182(a,1),5495(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5182 5495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5833">
    <literal><![CDATA[
      K(T(x,T(y,z)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,5115,a,b,5528,a)].">
      <j1 rule="hyper" parents="30 5115 5528"/>
    </justification>
  </clause>

  <clause id="5834">
    <literal><![CDATA[
      K(x / T(y,z),y) = K(T(y,z) \ x,y)
    ]]></literal>
    <justification jstring="[para(107(a,1),5833(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 5833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5835">
    <literal><![CDATA[
      K(x,y) = (x * y) * ((y * x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(1413,a,5559,a)].">
      <j1 rule="hyper" parents="1413 5559"/>
    </justification>
  </clause>

  <clause id="5836">
    <literal><![CDATA[
      (x * y) \ K(x,y) = (y * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,691,a(flip),b,5559,a(flip))].">
      <j1 rule="hyper" parents="116 691 5559"/>
    </justification>
  </clause>

  <clause id="5837">
    <literal><![CDATA[
      ((x \ y) * x) \ 1 = y \ K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5835,a,b,149,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 5835 149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5839">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ 1) * u)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(3128(a,1),5585(a,1,2,2))].">
      <j1 rule="para" parents="3128 5585"/>
    </justification>
  </clause>

  <clause id="5840">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) \ u) = K(x,L(z,y,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(496(a,1),5586(a,1,2,1))].">
      <j1 rule="para" parents="496 5586"/>
    </justification>
  </clause>

  <clause id="5841">
    <literal><![CDATA[
      K(x,((((y \ 1) \ 1) * z) \ u) \ w) = K(x,((y * z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(3896(a,1),5586(a,1,2,1))].">
      <j1 rule="para" parents="3896 5586"/>
    </justification>
  </clause>

  <clause id="5842">
    <literal><![CDATA[
      K(x,y * (((z \ 1) \ 1) \ u)) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(3175(a,1),5589(a,1,2,2))].">
      <j1 rule="para" parents="3175 5589"/>
    </justification>
  </clause>

  <clause id="5843">
    <literal><![CDATA[
      K(x,((1 / y) * z) / u) = K(x,((y \ 1) * z) / u)
    ]]></literal>
    <justification jstring="[para(3152(a,1),5591(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3152 5591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5845">
    <literal><![CDATA[
      K(x,y / (z * (1 / u))) = K(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3050(a,1),5592(a,1,2,2))].">
      <j1 rule="para" parents="3050 5592"/>
    </justification>
  </clause>

  <clause id="5846">
    <literal><![CDATA[
      K(x,y / (((z \ 1) \ 1) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(3128(a,1),5592(a,1,2,2))].">
      <j1 rule="para" parents="3128 5592"/>
    </justification>
  </clause>

  <clause id="5847">
    <literal><![CDATA[
      K(x,T((1 / y) * z,u)) = K(x,T((y \ 1) * z,u))
    ]]></literal>
    <justification jstring="[para(3185(a,1),5605(a,1,2,1))].">
      <j1 rule="para" parents="3185 5605"/>
    </justification>
  </clause>

  <clause id="5849">
    <literal><![CDATA[
      K(x \ y,x) * (z * (y / x)) = (x \ y) * T(z,y / x)
    ]]></literal>
    <justification jstring="[para(17(a,2),5634(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17 5634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5853">
    <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(5643(a,1),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5643 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5854">
    <literal><![CDATA[
      T(x,y) \ T(x * K(x * z,x),y) = K(z * x,T(x,y))
    ]]></literal>
    <justification jstring="[para(5532(a,1),5643(a,1,2,1,2))].">
      <j1 rule="para" parents="5532 5643"/>
    </justification>
  </clause>

  <clause id="5855">
    <literal><![CDATA[
      T(x,y) \ T(z * T(z \ x,x),y) = K((x \ z) \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(5312(a,2),5643(a,1,2,1))].">
      <j1 rule="para" parents="5312 5643"/>
    </justification>
  </clause>

  <clause id="5856">
    <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(5466(a,1),5644(a,1,1,1))].">
      <j1 rule="para" parents="5466 5644"/>
    </justification>
  </clause>

  <clause id="5857">
    <literal><![CDATA[
      K(x \ y,x) \ ((y / x) \ z) = (x \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(123,a,5656,a)].">
      <j1 rule="hyper" parents="123 5656"/>
    </justification>
  </clause>

  <clause id="5859">
    <literal><![CDATA[
      T(x,x \ y) \ ((x \ y) \ z) = x \ ((y / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,5656,a(flip),b,5090,a),flip(a)].">
      <j1 rule="hyper" parents="116 5656 5090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5860">
    <literal><![CDATA[
      K(x \ y,x) * T(z,x \ y) = (y / x) \ (z * (x \ y))
    ]]></literal>
    <justification jstring="[para(17(a,2),5656(a,1,2))].">
      <j1 rule="para" parents="17 5656"/>
    </justification>
  </clause>

  <clause id="5861">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * z = u
    ]]></literal>
    <justification jstring="[para(5670(a,1),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5670 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5864">
    <literal><![CDATA[
      T(x,T(y,x)) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(17(a,2),5679(a,1,1,2))].">
      <j1 rule="para" parents="17 5679"/>
    </justification>
  </clause>

  <clause id="5865">
    <literal><![CDATA[
      T(x,y) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(4473(a,1),5864(a,1,1))].">
      <j1 rule="para" parents="4473 5864"/>
    </justification>
  </clause>

  <clause id="5866">
    <literal><![CDATA[
      ((x \ y) * x) \ x = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(360,a,5865,a),flip(a)].">
      <j1 rule="hyper" parents="360 5865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5867">
    <literal><![CDATA[
      (x * y) \ T(x,y) = (y * x) \ x
    ]]></literal>
    <justification jstring="[hyper(192,a,5865,a)].">
      <j1 rule="hyper" parents="192 5865"/>
    </justification>
  </clause>

  <clause id="5868">
    <literal><![CDATA[
      T(x,y) = (x * y) * ((y * x) \ x)
    ]]></literal>
    <justification jstring="[hyper(133,a,5865,a),flip(a)].">
      <j1 rule="hyper" parents="133 5865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5869">
    <literal><![CDATA[
      T(x * y,z) * ((y * x) \ x) = K(x * y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5867,a(flip),b,5344,a)].">
      <j1 rule="hyper" parents="119 5867 5344"/>
    </justification>
  </clause>

  <clause id="5870">
    <literal><![CDATA[
      ((x * y) \ y) * T(y * x,x \ 1) = T(y,x)
    ]]></literal>
    <justification jstring="[para(5867(a,1),4462(a,1,1))].">
      <j1 rule="para" parents="5867 4462"/>
    </justification>
  </clause>

  <clause id="5875">
    <literal><![CDATA[
      (x / (x / y)) \ ((x / y) \ z) = y \ ((y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,5687,a(flip),b,5635,a),flip(a)].">
      <j1 rule="hyper" parents="116 5687 5635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5876">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * z = z * K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,1),5769(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="107 5769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5877">
    <literal><![CDATA[
      ((x * K(y,x)) \ 1) \ 1 = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(5017(a,1),5784(a,1,1,1))].">
      <j1 rule="para" parents="5017 5784"/>
    </justification>
  </clause>

  <clause id="5878">
    <literal><![CDATA[
      (x \ K(x,y)) \ 1 = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(5179(a,1),5784(a,1,1))].">
      <j1 rule="para" parents="5179 5784"/>
    </justification>
  </clause>

  <clause id="5879">
    <literal><![CDATA[
      (x \ 1) * (x * K(y,x)) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(3253,a,5791,a)].">
      <j1 rule="hyper" parents="3253 5791"/>
    </justification>
  </clause>

  <clause id="5880">
    <literal><![CDATA[
      1 / T(K(x,y),z) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5772,a(flip),b,5815,a),flip(a)].">
      <j1 rule="hyper" parents="58 5772 5815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5881">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(192,a,5880,a)].">
      <j1 rule="hyper" parents="192 5880"/>
    </justification>
  </clause>

  <clause id="5882">
    <literal><![CDATA[
      T(K(x,y),z) * T(K(y,x),z) = 1
    ]]></literal>
    <justification jstring="[hyper(133,a,5880,a)].">
      <j1 rule="hyper" parents="133 5880"/>
    </justification>
  </clause>

  <clause id="5883">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(5880(a,1),5063(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5880 5063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5884">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,5881,a(flip),b,5073,a(flip))].">
      <j1 rule="hyper" parents="119 5881 5073"/>
    </justification>
  </clause>

  <clause id="5885">
    <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(553,a,5882,a)].">
      <j1 rule="hyper" parents="553 5882"/>
    </justification>
  </clause>

  <clause id="5886">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5245,a(flip),b,5883,a)].">
      <j1 rule="hyper" parents="58 5245 5883"/>
    </justification>
  </clause>

  <clause id="5887">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(5430,a,5886,a)].">
      <j1 rule="hyper" parents="5430 5886"/>
    </justification>
  </clause>

  <clause id="5888">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,5886,a,b,4995,a(flip))].">
      <j1 rule="hyper" parents="119 5886 4995"/>
    </justification>
  </clause>

  <clause id="5889">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5886,a(flip),b,4995,a(flip))].">
      <j1 rule="hyper" parents="119 5886 4995"/>
    </justification>
  </clause>

  <clause id="5890">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[para(5886(a,1),5034(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5886 5034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5891">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5886(a,1),5241(a,1,1))].">
      <j1 rule="para" parents="5886 5241"/>
    </justification>
  </clause>

  <clause id="5892">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) = T(K(z,y),x) * u
    ]]></literal>
    <justification jstring="[para(5886(a,1),5047(a,1,1))].">
      <j1 rule="para" parents="5886 5047"/>
    </justification>
  </clause>

  <clause id="5893">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y),x) = u
    ]]></literal>
    <justification jstring="[para(5887(a,1),5241(a,1))].">
      <j1 rule="para" parents="5887 5241"/>
    </justification>
  </clause>

  <clause id="5894">
    <literal><![CDATA[
      T(K(x,y) \ z,K(y,x)) = z / K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5201,a,5888,a),flip(a)].">
      <j1 rule="hyper" parents="5201 5888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5895">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(5198,a,5888,a),flip(a)].">
      <j1 rule="hyper" parents="5198 5888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5896">
    <literal><![CDATA[
      T(x,K(y,z)) * K(z,y) = K(z,y) * x
    ]]></literal>
    <justification jstring="[para(5888(a,1),5039(a,1,1))].">
      <j1 rule="para" parents="5888 5039"/>
    </justification>
  </clause>

  <clause id="5897">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5888(a,1),5196(a,1,1))].">
      <j1 rule="para" parents="5888 5196"/>
    </justification>
  </clause>

  <clause id="5898">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(5888(a,1),5197(a,1))].">
      <j1 rule="para" parents="5888 5197"/>
    </justification>
  </clause>

  <clause id="5899">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y) * x) = L(x,K(z,y),x)
    ]]></literal>
    <justification jstring="[para(5888(a,1),5216(a,1,1))].">
      <j1 rule="para" parents="5888 5216"/>
    </justification>
  </clause>

  <clause id="5900">
    <literal><![CDATA[
      T(K(x,y) * z,T(z,K(y,x))) = T(K(x,y) * z,z)
    ]]></literal>
    <justification jstring="[para(5888(a,1),5215(a,1,2))].">
      <j1 rule="para" parents="5888 5215"/>
    </justification>
  </clause>

  <clause id="5901">
    <literal><![CDATA[
      T(K(x,y),K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2072,a,5895,a),flip(a)].">
      <j1 rule="hyper" parents="2072 5895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5902">
    <literal><![CDATA[
      T(K(x,y),K(z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2066,a,5895,a),flip(a)].">
      <j1 rule="hyper" parents="2066 5895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5903">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(u,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(5895(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="5895 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5904">
    <literal><![CDATA[
      K(x,y) * K(x,z) = K(x,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5901,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 5901 17"/>
    </justification>
  </clause>

  <clause id="5905">
    <literal><![CDATA[
      K(x,y) * K(x,z) != K(x,z) * u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5901(a,1),248(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5901 248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5906">
    <literal><![CDATA[
      K(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5901(a,1),294(a,1,2))].">
      <j1 rule="para" parents="5901 294"/>
    </justification>
  </clause>

  <clause id="5907">
    <literal><![CDATA[
      K(x,y) \ K(z,x) = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5902,a(flip),b,5393,a),flip(a)].">
      <j1 rule="hyper" parents="119 5902 5393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5908">
    <literal><![CDATA[
      K(x,y) * K(z,y) = K(z,y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5902,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 5902 17"/>
    </justification>
  </clause>

  <clause id="5909">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(5889(a,1),5410(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5889 5410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5910">
    <literal><![CDATA[
      T(x,K(y,z)) * (x \ K(z,y)) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(5050,a,5890,a)].">
      <j1 rule="hyper" parents="5050 5890"/>
    </justification>
  </clause>

  <clause id="5911">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z / K(y,x)
    ]]></literal>
    <justification jstring="[para(5391(a,1),5894(a,1,1))].">
      <j1 rule="para" parents="5391 5894"/>
    </justification>
  </clause>

  <clause id="5912">
    <literal><![CDATA[
      (x * T(x \ y,z)) / K((x / y) \ 1,z) = T(y,K(z,(x / y) \ 1))
    ]]></literal>
    <justification jstring="[para(5793(a,1),5894(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5793 5894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5913">
    <literal><![CDATA[
      K(x,1 / x) * y = y * K(x,1 / x)
    ]]></literal>
    <justification jstring="[para(2245(a,1),5896(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2245 5896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5914">
    <literal><![CDATA[
      T(x,y) * (x \ K(x,z)) = K(x,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5050,a,5904,a)].">
      <j1 rule="hyper" parents="5050 5904"/>
    </justification>
  </clause>

  <clause id="5915">
    <literal><![CDATA[
      x * (T(x,y) \ K(z,x)) = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(5052,a,5907,a)].">
      <j1 rule="hyper" parents="5052 5907"/>
    </justification>
  </clause>

  <clause id="5916">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = (y * z) * K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(3796,a,5913,a)].">
      <j1 rule="hyper" parents="3796 5913"/>
    </justification>
  </clause>

  <clause id="5917">
    <literal><![CDATA[
      K(x,1 / x) * (y * z) = y * (z * K(x,1 / x))
    ]]></literal>
    <justification jstring="[hyper(334,a,3554,a(flip),b,5913,a),flip(a)].">
      <j1 rule="hyper" parents="334 3554 5913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5918">
    <literal><![CDATA[
      K(x,y * (K(z,1 / z) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(5913(a,2),5588(a,1,2,2))].">
      <j1 rule="para" parents="5913 5588"/>
    </justification>
  </clause>

  <clause id="5919">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(5232(a,1),5891(a,1))].">
      <j1 rule="para" parents="5232 5891"/>
    </justification>
  </clause>

  <clause id="5920">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(5245(a,2),5919(a,1))].">
      <j1 rule="para" parents="5245 5919"/>
    </justification>
  </clause>

  <clause id="5921">
    <literal><![CDATA[
      K(((1 / x) / (y / x)) \ 1,z) * (y / x) = T(y,z) / x
    ]]></literal>
    <justification jstring="[hyper(33,a,1079,a(flip),b,5817,a),flip(a)].">
      <j1 rule="hyper" parents="33 1079 5817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5922">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * (y * x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) * y = u
    ]]></literal>
    <justification jstring="[para(5824(a,1),5410(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5824 5410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5923">
    <literal><![CDATA[
      (x \ 1) * ((y * x) / y) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,5171,a,b,5879,a)].">
      <j1 rule="hyper" parents="58 5171 5879"/>
    </justification>
  </clause>

  <clause id="5924">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5910(a,1),5381(a,1))].">
      <j1 rule="para" parents="5910 5381"/>
    </justification>
  </clause>

  <clause id="5925">
    <literal><![CDATA[
      T(x,y) \ K(z,x) = T(x,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,5090,a,b,5915,a)].">
      <j1 rule="hyper" parents="29 5090 5915"/>
    </justification>
  </clause>

  <clause id="5926">
    <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(5915(a,1),4316(a,2,3))].">
      <j1 rule="para" parents="5915 4316"/>
    </justification>
  </clause>

  <clause id="5927">
    <literal><![CDATA[
      T(x,y) \ K(z,x) != T(x,z) \ u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = u
    ]]></literal>
    <justification jstring="[para(5925(a,1),42(a,1))].">
      <j1 rule="para" parents="5925 42"/>
    </justification>
  </clause>

  <clause id="5928">
    <literal><![CDATA[
      K(x,y * (((1 / (1 / z)) \ u) * w)) = K(x,y * ((z \ u) * w))
    ]]></literal>
    <justification jstring="[para(3807(a,1),5918(a,1,2,2))].">
      <j1 rule="para" parents="3807 5918"/>
    </justification>
  </clause>

  <clause id="5931">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = R(x,y,z) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(4038(a,1),5029(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4038 5029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5934">
    <literal><![CDATA[
      ((x * K(y,x)) \ ((y * (x * y)) / y)) \ ((y * (x * y)) / y) = x
    ]]></literal>
    <justification jstring="[para(5213(a,2),4617(a,1,1))].">
      <j1 rule="para" parents="5213 4617"/>
    </justification>
  </clause>

  <clause id="5935">
    <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(5513(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5513 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5936">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,22,a,b,5554,a),flip(a)].">
      <j1 rule="hyper" parents="334 22 5554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5937">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x / (z * y)) = u
    ]]></literal>
    <justification jstring="[para(4881(a,1),5638(a,1,2))].">
      <j1 rule="para" parents="4881 5638"/>
    </justification>
  </clause>

  <clause id="5938">
    <literal><![CDATA[
      K(x,L(y,x,x \ 1)) * (y * x) = x * ((y * x) / x)
    ]]></literal>
    <justification jstring="[para(5651(a,1),5701(a,1,1))].">
      <j1 rule="para" parents="5651 5701"/>
    </justification>
  </clause>

  <clause id="5939">
    <literal><![CDATA[
      ((x * y) / x) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * (y \ z) = u
    ]]></literal>
    <justification jstring="[para(5(a,1),5658(a,1,2))].">
      <j1 rule="para" parents="5 5658"/>
    </justification>
  </clause>

  <clause id="5940">
    <literal><![CDATA[
      K((x / y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(5705(a,1),396(a,1)),flip(b)].">
      <j1 rule="para" parents="5705 396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5941">
    <literal><![CDATA[
      K(1 / (x / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(3442(a,2),5940(a,1))].">
      <j1 rule="para" parents="3442 5940"/>
    </justification>
  </clause>

  <clause id="5942">
    <literal><![CDATA[
      ((x * y) / x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * (K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(5017(a,2),5729(a,1,1))].">
      <j1 rule="para" parents="5017 5729"/>
    </justification>
  </clause>

  <clause id="5943">
    <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),5744(a,1,2))].">
      <j1 rule="para" parents="20 5744"/>
    </justification>
  </clause>

  <clause id="5944">
    <literal><![CDATA[
      K(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) \ T(x,y) = u
    ]]></literal>
    <justification jstring="[para(2065(a,2),5746(a,1))].">
      <j1 rule="para" parents="2065 5746"/>
    </justification>
  </clause>

  <clause id="5945">
    <literal><![CDATA[
      x \ K(x * y,x \ 1) = y / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(4750(a,1),4978(a,1,2))].">
      <j1 rule="para" parents="4750 4978"/>
    </justification>
  </clause>

  <clause id="5946">
    <literal><![CDATA[
      (x \ K(x * y,x \ 1)) \ y = y / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(118,a,5945,a,b,154,a)].">
      <j1 rule="hyper" parents="118 5945 154"/>
    </justification>
  </clause>

  <clause id="5947">
    <literal><![CDATA[
      L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(4995(a,2),5001(a,1,1))].">
      <j1 rule="para" parents="4995 5001"/>
    </justification>
  </clause>

  <clause id="5949">
    <literal><![CDATA[
      K(x,L(1 / y,z,u) \ 1) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(75(a,1),5947(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 5947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5950">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3696(a,1),5947(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3696 5947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5951">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ 1) = L(K(x,K(z,y)),u,w)
    ]]></literal>
    <justification jstring="[para(5232(a,1),5947(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5232 5947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5952">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z),u,w) \ 1) = L(T(K(x,y),z),u,w)
    ]]></literal>
    <justification jstring="[para(5772(a,1),5947(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5772 5947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5953">
    <literal><![CDATA[
      L(K(x,y \ z),y \ z,y) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(401(a,1),5950(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="401 5950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5954">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ 1,u) * w = L(K(u,x),y,z) \ w
    ]]></literal>
    <justification jstring="[para(5950(a,1),5391(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5950 5391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5955">
    <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(5950(a,1),5947(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5950 5947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5956">
    <literal><![CDATA[
      x * ((x \ y) * K(z,x \ y)) = y * K(z,(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,5953,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="119 5953 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5957">
    <literal><![CDATA[
      K(L(1 / x,y,z) \ 1,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(5287,a,5096,a)].">
      <j1 rule="hyper" parents="5287 5096"/>
    </justification>
  </clause>

  <clause id="5958">
    <literal><![CDATA[
      K(1 / L(1 / x,y,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(5546,a,5957,a)].">
      <j1 rule="hyper" parents="5546 5957"/>
    </justification>
  </clause>

  <clause id="5959">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4297,a(flip),b,5957,a)].">
      <j1 rule="hyper" parents="58 4297 5957"/>
    </justification>
  </clause>

  <clause id="5960">
    <literal><![CDATA[
      L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),5957(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 5957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5961">
    <literal><![CDATA[
      L(K(1 / x,y),z,u) = K(1 / L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(3419(a,1),5957(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3419 5957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5962">
    <literal><![CDATA[
      K(L(K(x,y),z,u) \ 1,w) = L(K(K(y,x),w),z,u)
    ]]></literal>
    <justification jstring="[para(5243(a,1),5957(a,1,1,1,1))].">
      <j1 rule="para" parents="5243 5957"/>
    </justification>
  </clause>

  <clause id="5963">
    <literal><![CDATA[
      K(x,1 / L(1 / y,z,u)) = 1 / L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5957(a,1),5255(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5957 5255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5964">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = L(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(5959(a,1),5232(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5959 5232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5966">
    <literal><![CDATA[
      K(L(T(1 / x,y),z,u) \ 1,w) = L(T(K(x,w),y),z,u)
    ]]></literal>
    <justification jstring="[para(5812(a,1),5960(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5812 5960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5967">
    <literal><![CDATA[
      K(L(T(x \ 1,y),z,u) \ 1,w) = L(T(K(x,w),y),z,u)
    ]]></literal>
    <justification jstring="[para(5813(a,1),5960(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5813 5960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5968">
    <literal><![CDATA[
      K(1 / L(x,y,z),L(x,u,w)) = L(K(1 / x,x),y,z)
    ]]></literal>
    <justification jstring="[para(5259(a,1),5961(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5259 5961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5969">
    <literal><![CDATA[
      ((x \ y) * x) * K(z,(x \ y) * x) = (x \ (y * K(z,y))) * x
    ]]></literal>
    <justification jstring="[hyper(30,a,5039,a,b,5158,a)].">
      <j1 rule="hyper" parents="30 5039 5158"/>
    </justification>
  </clause>

  <clause id="5970">
    <literal><![CDATA[
      ((x * y) \ T(y * x,z)) * (x * y) = T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,5162,a)].">
      <j1 rule="hyper" parents="133 5162"/>
    </justification>
  </clause>

  <clause id="5971">
    <literal><![CDATA[
      T(x,y) \ ((z * x) / z) = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,5915,a(flip),b,5176,a),flip(a)].">
      <j1 rule="hyper" parents="334 5915 5176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5972">
    <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(5971(a,1),91(a,1,2,2,1))].">
      <j1 rule="para" parents="5971 91"/>
    </justification>
  </clause>

  <clause id="5973">
    <literal><![CDATA[
      (x * y) / (y * K(z,y)) = (x / (y * K(z,y))) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,5193,a(flip),b,5211,a)].">
      <j1 rule="hyper" parents="58 5193 5211"/>
    </justification>
  </clause>

  <clause id="5974">
    <literal><![CDATA[
      a(1 / R(x,y,z),x,x \ 1) = K(R(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3753,a,b,5303,a)].">
      <j1 rule="hyper" parents="58 3753 5303"/>
    </justification>
  </clause>

  <clause id="5975">
    <literal><![CDATA[
      R(K(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(5011(a,1),5303(a,1,1))].">
      <j1 rule="para" parents="5011 5303"/>
    </justification>
  </clause>

  <clause id="5976">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5731,a(flip),b,5975,a),flip(a)].">
      <j1 rule="hyper" parents="58 5731 5975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5977">
    <literal><![CDATA[
      K(R(1 / x,y,z) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),5975(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 5975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5978">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) * (y * z) = (K(x \ 1,u) * y) * z
    ]]></literal>
    <justification jstring="[para(5975(a,1),101(a,1,1))].">
      <j1 rule="para" parents="5975 101"/>
    </justification>
  </clause>

  <clause id="5979">
    <literal><![CDATA[
      R(K((x / y) \ 1,z),y,u) = K(((x * u) / (y * u)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(102(a,1),5975(a,2,1,1))].">
      <j1 rule="para" parents="102 5975"/>
    </justification>
  </clause>

  <clause id="5980">
    <literal><![CDATA[
      K(R(x \ 1,y,z) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3448(a,1),5975(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3448 5975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5981">
    <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(788(a,1),5976(a,1,1,1))].">
      <j1 rule="para" parents="788 5976"/>
    </justification>
  </clause>

  <clause id="5982">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) * w = R(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(5980(a,1),5391(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5980 5391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5983">
    <literal><![CDATA[
      (x * T(x \ y,z)) * (y \ 1) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(2011,a,5304,a)].">
      <j1 rule="hyper" parents="2011 5304"/>
    </justification>
  </clause>

  <clause id="5984">
    <literal><![CDATA[
      (1 / x) * (y * T(y \ x,z)) = K(((1 / x) * y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),5304(a,1,2,2,1,2))].">
      <j1 rule="para" parents="75 5304"/>
    </justification>
  </clause>

  <clause id="5985">
    <literal><![CDATA[
      x * ((y \ (x \ 1)) * y) = K((x * y) \ 1,y)
    ]]></literal>
    <justification jstring="[para(105(a,1),5304(a,1,2))].">
      <j1 rule="para" parents="105 5304"/>
    </justification>
  </clause>

  <clause id="5986">
    <literal><![CDATA[
      x * (y \ T(y * (x \ 1),z)) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(971(a,1),5304(a,1,2))].">
      <j1 rule="para" parents="971 5304"/>
    </justification>
  </clause>

  <clause id="5987">
    <literal><![CDATA[
      ((1 / x) * y) * T(((1 / x) * y) \ y,z) = K(x,z) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),5315(a,2,1,1))].">
      <j1 rule="para" parents="75 5315"/>
    </justification>
  </clause>

  <clause id="5988">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),T(x,z))
    ]]></literal>
    <justification jstring="[para(2619(a,1),5316(a,1,1))].">
      <j1 rule="para" parents="2619 5316"/>
    </justification>
  </clause>

  <clause id="5989">
    <literal><![CDATA[
      K(x \ 1,y) * (x \ K(x,z)) = K(x,z) * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(2784(a,1),5316(a,2,2,1))].">
      <j1 rule="para" parents="2784 5316"/>
    </justification>
  </clause>

  <clause id="5990">
    <literal><![CDATA[
      x * (y \ T(y * (x \ (y \ 1)),z)) = K(x \ 1,z) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(971(a,1),5317(a,1,2))].">
      <j1 rule="para" parents="971 5317"/>
    </justification>
  </clause>

  <clause id="5991">
    <literal><![CDATA[
      x * (K(x \ 1,y) * (x \ z)) = K(x \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(5316(a,2),5317(a,1,2))].">
      <j1 rule="para" parents="5316 5317"/>
    </justification>
  </clause>

  <clause id="5992">
    <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(5327(a,1),5287(a,1))].">
      <j1 rule="para" parents="5327 5287"/>
    </justification>
  </clause>

  <clause id="5993">
    <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(416(a,1),5333(a,1,2,2,1,2))].">
      <j1 rule="para" parents="416 5333"/>
    </justification>
  </clause>

  <clause id="5994">
    <literal><![CDATA[
      K(((x \ 1) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(5710,a,5445,a)].">
      <j1 rule="hyper" parents="5710 5445"/>
    </justification>
  </clause>

  <clause id="5995">
    <literal><![CDATA[
      1 / (x * K(y,x)) = K(y,x) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(5142(a,1),5527(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5142 5527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5996">
    <literal><![CDATA[
      K(x,y) \ (1 / y) = K(y,x) / y
    ]]></literal>
    <justification jstring="[hyper(5542,a,5995,a),flip(a)].">
      <j1 rule="hyper" parents="5542 5995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5997">
    <literal><![CDATA[
      K(x,y) * (1 / x) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(5426,a,5996,a)].">
      <j1 rule="hyper" parents="5426 5996"/>
    </justification>
  </clause>

  <clause id="5998">
    <literal><![CDATA[
      K(x \ 1,y) / (x \ 1) = K(y,x \ 1) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),5996(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 5996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5999">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / z = K(y,z / x)
    ]]></literal>
    <justification jstring="[hyper(334,a,5614,a(flip),b,5563,a),flip(a)].">
      <j1 rule="hyper" parents="334 5614 5563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6000">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * z = y * ((x * (y \ z)) / x)
    ]]></literal>
    <justification jstring="[hyper(133,a,5563,a)].">
      <j1 rule="hyper" parents="133 5563"/>
    </justification>
  </clause>

  <clause id="6001">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,((x * y) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(1008(a,1),5563(a,1,1))].">
      <j1 rule="para" parents="1008 5563"/>
    </justification>
  </clause>

  <clause id="6002">
    <literal><![CDATA[
      T(x * ((y * (x \ z)) / y),z) / z = K(y,(T(x,z) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(2371(a,1),5563(a,1,1))].">
      <j1 rule="para" parents="2371 5563"/>
    </justification>
  </clause>

  <clause id="6003">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,z / (x * y))
    ]]></literal>
    <justification jstring="[para(1008(a,1),5999(a,1,1))].">
      <j1 rule="para" parents="1008 5999"/>
    </justification>
  </clause>

  <clause id="6004">
    <literal><![CDATA[
      K(x,y * (((1 / z) * (u * z)) \ (u * (u * z)))) = K(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(3275(a,2),5601(a,1,2,2))].">
      <j1 rule="para" parents="3275 5601"/>
    </justification>
  </clause>

  <clause id="6005">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * ((1 / u) \ K(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(5179(a,2),5601(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5179 5601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6006">
    <literal><![CDATA[
      K(x,y \ ((z \ 1) * (z * u))) = K(x,y \ L(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(3146(a,1),5602(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3146 5602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6007">
    <literal><![CDATA[
      (((x * y) / x) \ z) * K(y,1 / y) = (1 / (1 / ((x * y) / x))) \ z
    ]]></literal>
    <justification jstring="[para(5622(a,1),3100(a,1,2))].">
      <j1 rule="para" parents="5622 3100"/>
    </justification>
  </clause>

  <clause id="6008">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(4882(a,1),5718(a,1,2))].">
      <j1 rule="para" parents="4882 5718"/>
    </justification>
  </clause>

  <clause id="6009">
    <literal><![CDATA[
      L(x,K(y,z),T(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(493,a,5725,a)].">
      <j1 rule="hyper" parents="493 5725"/>
    </justification>
  </clause>

  <clause id="6010">
    <literal><![CDATA[
      L(x,K(y,z),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(6009(a,1),45(a,2))].">
      <j1 rule="para" parents="6009 45"/>
    </justification>
  </clause>

  <clause id="6011">
    <literal><![CDATA[
      x \ (((x * y) \ z) \ z) = y * K((y \ (x \ 1)) \ 1,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,324,a(flip),b,5801,a)].">
      <j1 rule="hyper" parents="58 324 5801"/>
    </justification>
  </clause>

  <clause id="6012">
    <literal><![CDATA[
      K(x,y) * (z * K((z \ K(y,x)) \ 1,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5232(a,1),5805(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="5232 5805"/>
    </justification>
  </clause>

  <clause id="6013">
    <literal><![CDATA[
      (1 / x) \ K(x \ 1,y) = K(y,x \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,5998,a(flip),b,5829,a),flip(a)].">
      <j1 rule="hyper" parents="58 5998 5829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6014">
    <literal><![CDATA[
      (1 / x) \ K(x \ 1,y) = x * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5405,a(flip),b,6013,a),flip(a)].">
      <j1 rule="hyper" parents="334 5405 6013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6015">
    <literal><![CDATA[
      (x * y) * (x / (x * y)) = x * K(x * y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3700(a,1),5831(a,2,2))].">
      <j1 rule="para" parents="3700 5831"/>
    </justification>
  </clause>

  <clause id="6016">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = x * K(x * (1 / y),y)
    ]]></literal>
    <justification jstring="[para(3701(a,1),5831(a,2,2))].">
      <j1 rule="para" parents="3701 5831"/>
    </justification>
  </clause>

  <clause id="6017">
    <literal><![CDATA[
      K(x,y \ (T(1 / z,u) * w)) = K(x,y \ (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[para(2223(a,1),5839(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2223 5839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6018">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,T(K(z \ y,z),u))
    ]]></literal>
    <justification jstring="[para(4967(a,1),5847(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4967 5847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6019">
    <literal><![CDATA[
      K(x,y \ K(y,z)) * z = z * K(x,(z \ (z * y)) \ 1)
    ]]></literal>
    <justification jstring="[para(5179(a,1),5876(a,1,1,2))].">
      <j1 rule="para" parents="5179 5876"/>
    </justification>
  </clause>

  <clause id="6020">
    <literal><![CDATA[
      x * K(y,(x \ z) \ 1) = K(y,x / z) * x
    ]]></literal>
    <justification jstring="[para(5614(a,1),5876(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5614 5876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6021">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(247,a,6020,a)].">
      <j1 rule="hyper" parents="247 6020"/>
    </justification>
  </clause>

  <clause id="6022">
    <literal><![CDATA[
      T(x,y) != K(z,(y \ u) \ 1)
    ]]></literal>
    <literal><![CDATA[
      K(z,y / u) = x
    ]]></literal>
    <justification jstring="[para(6021(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="6021 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6023">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = y * (z * K(x,1 / x))
    ]]></literal>
    <justification jstring="[hyper(334,a,3554,a(flip),b,5916,a),flip(a)].">
      <j1 rule="hyper" parents="334 3554 5916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6024">
    <literal><![CDATA[
      (x * K(y,1 / y)) / z = K(y,1 / y) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(117,a,148,a(flip),b,5916,a)].">
      <j1 rule="hyper" parents="117 148 5916"/>
    </justification>
  </clause>

  <clause id="6025">
    <literal><![CDATA[
      K(x,1 / x) * (y * L(x,z,u)) = y * L((x \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(3657(a,1),5917(a,2,2))].">
      <j1 rule="para" parents="3657 5917"/>
    </justification>
  </clause>

  <clause id="6026">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5950,a(flip),b,5964,a),flip(a)].">
      <j1 rule="hyper" parents="58 5950 5964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6027">
    <literal><![CDATA[
      1 / L(K(x,y),z,u) = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(201,a,6026,a)].">
      <j1 rule="hyper" parents="201 6026"/>
    </justification>
  </clause>

  <clause id="6028">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(6026(a,1),5951(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6026 5951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6029">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(6027(a,1),276(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6027 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6030">
    <literal><![CDATA[
      ((x * K(y,z)) / (z * K(y,z))) * z = R(x,K(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(2551,a,5973,a),flip(a)].">
      <j1 rule="hyper" parents="2551 5973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6033">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K((1 / x) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(75(a,1),5991(a,1,2,1,1))].">
      <j1 rule="para" parents="75 5991"/>
    </justification>
  </clause>

  <clause id="6034">
    <literal><![CDATA[
      K(x,y \ 1) * (y \ z) = z * ((x * (z \ (y \ z))) / x)
    ]]></literal>
    <justification jstring="[para(72(a,1),6000(a,1,1,2,1))].">
      <j1 rule="para" parents="72 6000"/>
    </justification>
  </clause>

  <clause id="6035">
    <literal><![CDATA[
      R(K(x,(y / z) / (u * x)),y / z,z) = ((u * (x * ((u \ (y / z)) / x))) * z) / y
    ]]></literal>
    <justification jstring="[para(6003(a,1),538(a,1,1))].">
      <j1 rule="para" parents="6003 538"/>
    </justification>
  </clause>

  <clause id="6036">
    <literal><![CDATA[
      (x / y) * (z * K(y,1 / y)) = (x / (1 / (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(2965(a,1),6023(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2965 6023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6037">
    <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,538,a,b,6024,a)].">
      <j1 rule="hyper" parents="58 538 6024"/>
    </justification>
  </clause>

  <clause id="6038">
    <literal><![CDATA[
      L(x \ (y * z),x,K(z,y)) = (K(y,z) \ x) \ (z * y)
    ]]></literal>
    <justification jstring="[para(5391(a,2),4994(a,2,1))].">
      <j1 rule="para" parents="5391 4994"/>
    </justification>
  </clause>

  <clause id="6039">
    <literal><![CDATA[
      (K(x,y) \ z) \ (K(x,y) \ (z * u)) = L(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(116,a,5391,a,b,5413,a)].">
      <j1 rule="hyper" parents="116 5391 5413"/>
    </justification>
  </clause>

  <clause id="6040">
    <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(5394(a,1),5414(a,2,2))].">
      <j1 rule="para" parents="5394 5414"/>
    </justification>
  </clause>

  <clause id="6041">
    <literal><![CDATA[
      L(K(x \ y,x) * z,K(x,x \ y),y) = (x * (y / x)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(5272(a,1),5414(a,2,1))].">
      <j1 rule="para" parents="5272 5414"/>
    </justification>
  </clause>

  <clause id="6042">
    <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(5415(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="5415 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6043">
    <literal><![CDATA[
      (T(x,y) * K(z,x)) \ u = K(x,z) * (T(x,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(6010,a,5416,a),flip(a)].">
      <j1 rule="hyper" parents="6010 5416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6044">
    <literal><![CDATA[
      (L(x,y,z) * K(x,u)) \ w = K(u,x) * (L(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(4776,a,5416,a),flip(a)].">
      <j1 rule="hyper" parents="4776 5416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6045">
    <literal><![CDATA[
      (K(x,y) * T(y,z)) \ u = K(y,x) * (T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(2530(a,1),6043(a,1,1))].">
      <j1 rule="para" parents="2530 6043"/>
    </justification>
  </clause>

  <clause id="6046">
    <literal><![CDATA[
      K(x,y) * (T(x,x * y) \ z) = L(x,y,x) \ z
    ]]></literal>
    <justification jstring="[para(5547(a,1),6043(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5547 6043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6047">
    <literal><![CDATA[
      K(x,x * y) * (T(x,y) \ z) = R(x,y,x) \ z
    ]]></literal>
    <justification jstring="[para(5549(a,1),6043(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5549 6043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6048">
    <literal><![CDATA[
      K(x,x * y) * K(y,x) = R(x,y,x) \ x
    ]]></literal>
    <justification jstring="[para(4996(a,2),6047(a,1,2))].">
      <j1 rule="para" parents="4996 6047"/>
    </justification>
  </clause>

  <clause id="6049">
    <literal><![CDATA[
      R(x,y,x) \ x = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5742,a,6048,a),flip(a)].">
      <j1 rule="hyper" parents="5742 6048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6050">
    <literal><![CDATA[
      x \ (x \ L(x,y,x)) = R(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,6049,a(flip),b,1371,a)].">
      <j1 rule="hyper" parents="116 6049 1371"/>
    </justification>
  </clause>

  <clause id="6051">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = T(x,z) * (R(x,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(6050(a,1),3682(a,2,2))].">
      <j1 rule="para" parents="6050 3682"/>
    </justification>
  </clause>

  <clause id="6052">
    <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),5450(a,1,2))].">
      <j1 rule="para" parents="75 5450"/>
    </justification>
  </clause>

  <clause id="6053">
    <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(223(a,1),5468(a,2,3))].">
      <j1 rule="para" parents="223 5468"/>
    </justification>
  </clause>

  <clause id="6054">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5006(a,1),5544(a,1))].">
      <j1 rule="para" parents="5006 5544"/>
    </justification>
  </clause>

  <clause id="6055">
    <literal><![CDATA[
      K(x,T(y,y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(106(a,2),6054(a,1,2))].">
      <j1 rule="para" parents="106 6054"/>
    </justification>
  </clause>

  <clause id="6056">
    <literal><![CDATA[
      K(x,T(y / z,z / y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(2142(a,2),6054(a,1,2))].">
      <j1 rule="para" parents="2142 6054"/>
    </justification>
  </clause>

  <clause id="6057">
    <literal><![CDATA[
      K(x,T(y \ z,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(2459(a,2),6054(a,1,2))].">
      <j1 rule="para" parents="2459 6054"/>
    </justification>
  </clause>

  <clause id="6058">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(3512(a,2),6054(a,1,2))].">
      <j1 rule="para" parents="3512 6054"/>
    </justification>
  </clause>

  <clause id="6059">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,(z \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(4280(a,2),6054(a,1))].">
      <j1 rule="para" parents="4280 6054"/>
    </justification>
  </clause>

  <clause id="6061">
    <literal><![CDATA[
      R(x,x \ (y \ x),x) = R(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5631,a(flip),b,5642,a),flip(a)].">
      <j1 rule="hyper" parents="58 5631 5642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6062">
    <literal><![CDATA[
      R(K(x,y / (z * y)),R(1 / z,z,y),u) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(223(a,2),5735(a,1,2))].">
      <j1 rule="para" parents="223 5735"/>
    </justification>
  </clause>

  <clause id="6063">
    <literal><![CDATA[
      K(x \ y,L(y \ x,z,u)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(29,a,3720,a(flip),b,5780,a),flip(a)].">
      <j1 rule="hyper" parents="29 3720 5780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6064">
    <literal><![CDATA[
      K(x \ 1,L(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,3641,a(flip),b,5780,a),flip(a)].">
      <j1 rule="hyper" parents="29 3641 5780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6065">
    <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(5780(a,1),2526(a,1,1))].">
      <j1 rule="para" parents="5780 2526"/>
    </justification>
  </clause>

  <clause id="6066">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) = K(x \ 1,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,3515,a,b,6064,a)].">
      <j1 rule="hyper" parents="334 3515 6064"/>
    </justification>
  </clause>

  <clause id="6067">
    <literal><![CDATA[
      L(K(x \ 1,L(x,y,z)),u,w) = K(L(x,u,w) \ 1,x)
    ]]></literal>
    <justification jstring="[para(6064(a,2),2804(a,1,1))].">
      <j1 rule="para" parents="6064 2804"/>
    </justification>
  </clause>

  <clause id="6068">
    <literal><![CDATA[
      K(x \ (y \ 1),(y \ 1) \ x) = K(x \ (y \ 1),y * x)
    ]]></literal>
    <justification jstring="[para(501(a,1),6063(a,1,2)),flip(a)].">
      <j1 rule="para" parents="501 6063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6069">
    <literal><![CDATA[
      (x \ y) * (((x \ y) \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * (x * z) = u
    ]]></literal>
    <justification jstring="[para(5379(a,1),5861(a,1,2))].">
      <j1 rule="para" parents="5379 5861"/>
    </justification>
  </clause>

  <clause id="6070">
    <literal><![CDATA[
      K(x,L(y,x,x \ 1)) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),5938(a,2,2))].">
      <j1 rule="para" parents="6 5938"/>
    </justification>
  </clause>

  <clause id="6071">
    <literal><![CDATA[
      K(x,L(y,x,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4993,a,6070,a),flip(a)].">
      <j1 rule="hyper" parents="4993 6070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6072">
    <literal><![CDATA[
      K(1 / L(x,y,z),L(x,u,w)) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,3530,a(flip),b,5968,a),flip(a)].">
      <j1 rule="hyper" parents="334 3530 5968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6074">
    <literal><![CDATA[
      L(x,y,z) * K(1 / x,x) = 1 / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[para(6072(a,1),5018(a,2,2)),flip(a)].">
      <j1 rule="para" parents="6072 5018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6075">
    <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,5974,a(flip),b,220,a)].">
      <j1 rule="hyper" parents="119 5974 220"/>
    </justification>
  </clause>

  <clause id="6076">
    <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(3448(a,1),5992(a,1,1))].">
      <j1 rule="para" parents="3448 5992"/>
    </justification>
  </clause>

  <clause id="6077">
    <literal><![CDATA[
      R(x * y,K(z,y),y) = R(x,y,K(z,y)) * y
    ]]></literal>
    <justification jstring="[para(15(a,2),6030(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15 6030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6078">
    <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(6077(a,2),39(a,1))].">
      <j1 rule="para" parents="6077 39"/>
    </justification>
  </clause>

  <clause id="6079">
    <literal><![CDATA[
      L(x \ y,x,K(z,u)) = (K(u,z) \ x) \ (K(u,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(1788,a,6039,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="1788 6039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6080">
    <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),6039(a,1,2,2))].">
      <j1 rule="para" parents="90 6039"/>
    </justification>
  </clause>

  <clause id="6081">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,u,w)) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(5992,a,6067,a)].">
      <j1 rule="hyper" parents="5992 6067"/>
    </justification>
  </clause>

  <clause id="6083">
    <literal><![CDATA[
      L(x \ T(y,z),x,K(y,z)) = (K(z,y) \ x) \ T(T(y,z),z)
    ]]></literal>
    <justification jstring="[para(5190(a,1),6079(a,2,2))].">
      <j1 rule="para" parents="5190 6079"/>
    </justification>
  </clause>

  <clause id="6084">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,u,w)) = K(x \ 1,L(x,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(334,a,6066,a(flip),b,6081,a),flip(a)].">
      <j1 rule="hyper" parents="334 6066 6081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6086">
    <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(311(a,1),6084(a,1,1,1))].">
      <j1 rule="para" parents="311 6084"/>
    </justification>
  </clause>

  <clause id="6087">
    <literal><![CDATA[
      T(x * K(y,x),x \ K(x,y)) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,5877,a(flip),b,5251,a),flip(a)].">
      <j1 rule="hyper" parents="334 5877 5251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6088">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * y = (x * y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(5011(a,1),5322(a,1,1,2))].">
      <j1 rule="para" parents="5011 5322"/>
    </justification>
  </clause>

  <clause id="6091">
    <literal><![CDATA[
      (x * K(y \ 1,z)) \ ((x * y) * K(y \ 1,z)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,6088,a)].">
      <j1 rule="hyper" parents="123 6088"/>
    </justification>
  </clause>

  <clause id="6092">
    <literal><![CDATA[
      (x * K(y \ 1,z)) / y = (x / y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,148,a(flip),b,6088,a)].">
      <j1 rule="hyper" parents="117 148 6088"/>
    </justification>
  </clause>

  <clause id="6093">
    <literal><![CDATA[
      R(T(x,y * K(x \ 1,z)),y,K(x \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6091(a,1),1137(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6091 1137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6094">
    <literal><![CDATA[
      (T(x,y \ 1) / y) * K(y \ 1,x) = x / y
    ]]></literal>
    <justification jstring="[para(5014(a,1),6092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5014 6092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6095">
    <literal><![CDATA[
      (T(x,y \ 1) / y) \ (x / y) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,6094,a)].">
      <j1 rule="hyper" parents="123 6094"/>
    </justification>
  </clause>

  <clause id="6096">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3502,a,b,6095,a)].">
      <j1 rule="hyper" parents="58 3502 6095"/>
    </justification>
  </clause>

  <clause id="6097">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(6(a,1),6096(a,1,2,2))].">
      <j1 rule="para" parents="6 6096"/>
    </justification>
  </clause>

  <clause id="6098">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(5546,a,6097,a)].">
      <j1 rule="hyper" parents="5546 6097"/>
    </justification>
  </clause>

  <clause id="6099">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5584,a(flip),b,6097,a)].">
      <j1 rule="hyper" parents="58 5584 6097"/>
    </justification>
  </clause>

  <clause id="6100">
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,6098,a(flip),b,5270,a),flip(a)].">
      <j1 rule="hyper" parents="119 6098 5270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6101">
    <literal><![CDATA[
      K(x \ 1,y * x) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4757,a(flip),b,6099,a),flip(a)].">
      <j1 rule="hyper" parents="58 4757 6099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6102">
    <literal><![CDATA[
      (x \ 1) * (y / (x \ 1)) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,6099,a(flip),b,5270,a),flip(a)].">
      <j1 rule="hyper" parents="119 6099 5270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6103">
    <literal><![CDATA[
      T(x \ 1,y * x) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,6101,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 6101 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6104">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(6101(a,2),5715(a,2,2))].">
      <j1 rule="para" parents="6101 5715"/>
    </justification>
  </clause>

  <clause id="6105">
    <literal><![CDATA[
      T(x \ 1,y * x) = ((x \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(334,a,4658,a(flip),b,6103,a),flip(a)].">
      <j1 rule="hyper" parents="334 4658 6103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6106">
    <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(6103(a,1),2198(a,1,2,1,1))].">
      <j1 rule="para" parents="6103 2198"/>
    </justification>
  </clause>

  <clause id="6107">
    <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(6103(a,2),2198(a,1,1))].">
      <j1 rule="para" parents="6103 2198"/>
    </justification>
  </clause>

  <clause id="6108">
    <literal><![CDATA[
      T((x \ y) \ 1,y) = (((x \ y) \ 1) \ x) \ x
    ]]></literal>
    <justification jstring="[para(5(a,1),6105(a,1,2))].">
      <j1 rule="para" parents="5 6105"/>
    </justification>
  </clause>

  <clause id="6109">
    <literal><![CDATA[
      K(T(1 / x,y * x),z) = K(((x \ 1) \ y) \ y,z)
    ]]></literal>
    <justification jstring="[para(6105(a,1),3451(a,2,1))].">
      <j1 rule="para" parents="6105 3451"/>
    </justification>
  </clause>

  <clause id="6110">
    <literal><![CDATA[
      x * K((1 / y) \ 1,x * (1 / y)) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3089,a(flip),b,6100,a),flip(a)].">
      <j1 rule="hyper" parents="58 3089 6100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6111">
    <literal><![CDATA[
      (x \ 1) * ((y / x) / (x \ 1)) = (y / x) * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),6102(a,2,2,2))].">
      <j1 rule="para" parents="7 6102"/>
    </justification>
  </clause>

  <clause id="6112">
    <literal><![CDATA[
      x * K(y,x * (1 / y)) = y * (x / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),6110(a,1,2,1))].">
      <j1 rule="para" parents="75 6110"/>
    </justification>
  </clause>

  <clause id="6113">
    <literal><![CDATA[
      K(x,y * (1 / x)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(29,a,5272,a,b,6112,a),flip(a)].">
      <j1 rule="hyper" parents="29 5272 6112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6114">
    <literal><![CDATA[
      (x / y) * z != x * K(y,x * (1 / y))
    ]]></literal>
    <literal><![CDATA[
      T(y,x / y) = z
    ]]></literal>
    <justification jstring="[para(6112(a,2),247(a,2))].">
      <j1 rule="para" parents="6112 247"/>
    </justification>
  </clause>

  <clause id="6116">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y,x) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(5578(a,1),6112(a,1,2))].">
      <j1 rule="para" parents="5578 6112"/>
    </justification>
  </clause>

  <clause id="6117">
    <literal><![CDATA[
      K(x,y * (x \ 1)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5577,a(flip),b,6113,a)].">
      <j1 rule="hyper" parents="58 5577 6113"/>
    </justification>
  </clause>

  <clause id="6118">
    <literal><![CDATA[
      K(x * (1 / y),y) = 1 / K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(6113(a,1),5243(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6113 5243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6119">
    <literal><![CDATA[
      K(x,R(y,x,x \ 1)) = K(x,x \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,5189,a(flip),b,6117,a)].">
      <j1 rule="hyper" parents="58 5189 6117"/>
    </justification>
  </clause>

  <clause id="6120">
    <literal><![CDATA[
      K(x * (1 / y),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5243,a(flip),b,6118,a),flip(a)].">
      <j1 rule="hyper" parents="334 5243 6118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6121">
    <literal><![CDATA[
      K(x * (1 / y),y) = K(x / y,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5235,a,b,6120,a),flip(a)].">
      <j1 rule="hyper" parents="334 5235 6120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6122">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(334,a,4749,a,b,6120,a)].">
      <j1 rule="hyper" parents="334 4749 6120"/>
    </justification>
  </clause>

  <clause id="6123">
    <literal><![CDATA[
      K(x * (y \ 1),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4274,a(flip),b,6120,a)].">
      <j1 rule="hyper" parents="58 4274 6120"/>
    </justification>
  </clause>

  <clause id="6124">
    <literal><![CDATA[
      K((x \ 1) \ y,x \ 1) = K(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),6120(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6125">
    <literal><![CDATA[
      K(x \ y,x) * (y * (1 / x)) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(6120(a,1),5034(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6120 5034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6126">
    <literal><![CDATA[
      K(x / (1 / y),1 / y) = K(x * y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4278,a(flip),b,6121,a),flip(a)].">
      <j1 rule="hyper" parents="58 4278 6121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6127">
    <literal><![CDATA[
      x * K(x * (y \ 1),y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,6123,a,b,85,a)].">
      <j1 rule="hyper" parents="119 6123 85"/>
    </justification>
  </clause>

  <clause id="6128">
    <literal><![CDATA[
      K((1 / (1 / x)) * y,1 / x) = K(y * x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(334,a,4278,a(flip),b,6122,a),flip(a)].">
      <j1 rule="hyper" parents="334 4278 6122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6129">
    <literal><![CDATA[
      ((1 / x) \ y) * (1 / x) = y * K(y * x,1 / x)
    ]]></literal>
    <justification jstring="[para(75(a,1),6127(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="75 6127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6130">
    <literal><![CDATA[
      K(x,R(y,x,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),6119(a,2,2))].">
      <j1 rule="para" parents="4 6119"/>
    </justification>
  </clause>

  <clause id="6131">
    <literal><![CDATA[
      K(x,y) = x \ T(x,R(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(5087,a,6130,a),flip(a)].">
      <j1 rule="hyper" parents="5087 6130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6132">
    <literal><![CDATA[
      R(x,y,y \ 1) * K(y,x) = (y * x) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,6131,a,b,4056,a)].">
      <j1 rule="hyper" parents="119 6131 4056"/>
    </justification>
  </clause>

  <clause id="6133">
    <literal><![CDATA[
      K(x * y,y \ 1) = K(y * x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,4750,a(flip),b,6124,a),flip(a)].">
      <j1 rule="hyper" parents="58 4750 6124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6134">
    <literal><![CDATA[
      K(x,y * K(y * z,y \ 1)) = T(K(x,y),z * y)
    ]]></literal>
    <justification jstring="[para(6133(a,1),5777(a,1,2,2))].">
      <j1 rule="para" parents="6133 5777"/>
    </justification>
  </clause>

  <clause id="6135">
    <literal><![CDATA[
      K(x,y) * ((y * x) * (y \ 1)) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(6132(a,1),5406(a,1,2))].">
      <j1 rule="para" parents="6132 5406"/>
    </justification>
  </clause>

  <clause id="6136">
    <literal><![CDATA[
      K(x * y,1 / y) = K(y * x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3714,a(flip),b,6128,a),flip(a)].">
      <j1 rule="hyper" parents="58 3714 6128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6137">
    <literal><![CDATA[
      K((x \ y) * x,1 / x) = K(y,1 / x)
    ]]></literal>
    <justification jstring="[para(5(a,1),6136(a,2,1))].">
      <j1 rule="para" parents="5 6136"/>
    </justification>
  </clause>

  <clause id="6138">
    <literal><![CDATA[
      T(K(x,y),z * y) = T(K(x,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5777,a(flip),b,6134,a),flip(a)].">
      <j1 rule="hyper" parents="58 5777 6134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6139">
    <literal><![CDATA[
      T(K(x,y),z * y) * K(y,x) = K(K(x,y),y * z)
    ]]></literal>
    <justification jstring="[para(6138(a,2),5245(a,1,1))].">
      <j1 rule="para" parents="6138 5245"/>
    </justification>
  </clause>

  <clause id="6140">
    <literal><![CDATA[
      K(K(x,y),y * z) = K(z * y,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(5920,a,6139,a),flip(a)].">
      <j1 rule="hyper" parents="5920 6139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6141">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(y * x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5919,a,6140,a),flip(a)].">
      <j1 rule="hyper" parents="5919 6140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6142">
    <literal><![CDATA[
      K(x,x * y) * (R(y,z,u) * x) = R(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,4572,a(flip),b,5370,a),flip(a)].">
      <j1 rule="hyper" parents="334 4572 5370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6143">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * x) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,4500,a(flip),b,5370,a),flip(a)].">
      <j1 rule="hyper" parents="334 4500 5370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6144">
    <literal><![CDATA[
      K(x,x * y) * (L(y,z,u) * x) = L(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,4571,a(flip),b,5382,a),flip(a)].">
      <j1 rule="hyper" parents="334 4571 5382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6145">
    <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),5434(a,2,2))].">
      <j1 rule="para" parents="22 5434"/>
    </justification>
  </clause>

  <clause id="6146">
    <literal><![CDATA[
      K(x,y) * (K(x,y) * z) = y * (T(T(y,x),x) \ z)
    ]]></literal>
    <justification jstring="[para(5182(a,1),5454(a,1,2,1))].">
      <j1 rule="para" parents="5182 5454"/>
    </justification>
  </clause>

  <clause id="6147">
    <literal><![CDATA[
      K(1 / x,y) / (x \ 1) = 1 / (x \ K(y,1 / x))
    ]]></literal>
    <justification jstring="[para(3709(a,1),5537(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3709 5537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6148">
    <literal><![CDATA[
      K((K(x,y) / x) * z,u) = K((x \ K(x,y)) * z,u)
    ]]></literal>
    <justification jstring="[para(5474(a,1),5539(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5474 5539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6150">
    <literal><![CDATA[
      R(K(x,y \ 1),z,u) = K(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(5006(a,1),5562(a,1,1))].">
      <j1 rule="para" parents="5006 5562"/>
    </justification>
  </clause>

  <clause id="6151">
    <literal><![CDATA[
      K(x,R(y,x,z) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4461,a,6150,a),flip(a)].">
      <j1 rule="hyper" parents="4461 6150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6152">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3696(a,1),6150(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3696 6150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6153">
    <literal><![CDATA[
      K(x,R(y / z,u,w) \ 1) = R(K(x,z / y),u,w)
    ]]></literal>
    <justification jstring="[para(5614(a,1),6150(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5614 6150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6154">
    <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),6151(a,1,2,1))].">
      <j1 rule="para" parents="26 6151"/>
    </justification>
  </clause>

  <clause id="6155">
    <literal><![CDATA[
      T(x,R(y \ 1,z,u) \ 1) = x * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,6152,a(flip),b,4995,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 6152 4995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6156">
    <literal><![CDATA[
      R(K(x,y / z),y,u) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,5615,a(flip),b,6153,a),flip(a)].">
      <j1 rule="hyper" parents="58 5615 6153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6157">
    <literal><![CDATA[
      R(K(x,y / z),y,y \ 1) = K(x,(z * (y \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[para(536(a,1),6153(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="536 6153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6158">
    <literal><![CDATA[
      R(K(x,y / z),y,z \ 1) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(515(a,1),6153(a,1,2)),flip(a)].">
      <j1 rule="para" parents="515 6153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6159">
    <literal><![CDATA[
      R(K(x,(y / z) / u),y / z,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(7(a,1),6156(a,2,2,1))].">
      <j1 rule="para" parents="7 6156"/>
    </justification>
  </clause>

  <clause id="6160">
    <literal><![CDATA[
      R(K(x,y / (z / u)),y,u) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(7(a,1),6156(a,2,2,2))].">
      <j1 rule="para" parents="7 6156"/>
    </justification>
  </clause>

  <clause id="6161">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),6156(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6162">
    <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(4259(a,1),6156(a,1,1,2))].">
      <j1 rule="para" parents="4259 6156"/>
    </justification>
  </clause>

  <clause id="6163">
    <literal><![CDATA[
      R(K(x,(y / z) \ x),x,z) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[para(5463(a,1),6160(a,1,1))].">
      <j1 rule="para" parents="5463 6160"/>
    </justification>
  </clause>

  <clause id="6164">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(98(a,2),6161(a,1,2))].">
      <j1 rule="para" parents="98 6161"/>
    </justification>
  </clause>

  <clause id="6165">
    <literal><![CDATA[
      R(K(x,y),T(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4378(a,1),6161(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4378 6161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6166">
    <literal><![CDATA[
      (K(x,y) * T(y,z)) * u = K(x,y) * (T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(6165(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6165 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6167">
    <literal><![CDATA[
      R(K(x,y),y * z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),6164(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 6164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6168">
    <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(187(a,1),6164(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="187 6164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6169">
    <literal><![CDATA[
      R(K(x,y),K(z,y) * u,w) = K(x,R(y,T(y,z) \ u,w))
    ]]></literal>
    <justification jstring="[para(5367(a,1),6164(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5367 6164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6170">
    <literal><![CDATA[
      K(x * y,R(x,y,z)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(4461,a,6167,a),flip(a)].">
      <j1 rule="hyper" parents="4461 6167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6171">
    <literal><![CDATA[
      K(R(x,y * z,u) \ 1,y) = K(x \ 1,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,5975,a(flip),b,6167,a)].">
      <j1 rule="hyper" parents="58 5975 6167"/>
    </justification>
  </clause>

  <clause id="6172">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = T(K(x,R(y,u,w)),z)
    ]]></literal>
    <justification jstring="[para(6167(a,1),22(a,2,1))].">
      <j1 rule="para" parents="6167 22"/>
    </justification>
  </clause>

  <clause id="6173">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(4461,a,6163,a),flip(a)].">
      <j1 rule="hyper" parents="4461 6163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6174">
    <literal><![CDATA[
      R(K(x,(y / z) \ x),x,z) = K(x,(y / (x * z)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,5614,a,b,6163,a),flip(a)].">
      <j1 rule="hyper" parents="334 5614 6163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6175">
    <literal><![CDATA[
      K(x,(x * y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(6163(a,1),4461(a,1))].">
      <j1 rule="para" parents="6163 4461"/>
    </justification>
  </clause>

  <clause id="6177">
    <literal><![CDATA[
      K(x,(L(y,z,u) / y) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(1703(a,1),6173(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1703 6173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6178">
    <literal><![CDATA[
      L(x,T(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(493,a,6166,a)].">
      <j1 rule="hyper" parents="493 6166"/>
    </justification>
  </clause>

  <clause id="6179">
    <literal><![CDATA[
      (K(x,y) * T(y,z)) \ u = T(y,z) \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5415,a(flip),b,6178,a)].">
      <j1 rule="hyper" parents="58 5415 6178"/>
    </justification>
  </clause>

  <clause id="6180">
    <literal><![CDATA[
      L(x,T(y,z),K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(6178(a,1),45(a,2))].">
      <j1 rule="para" parents="6178 45"/>
    </justification>
  </clause>

  <clause id="6181">
    <literal><![CDATA[
      T(x,y) \ (K(x,z) * u) = K(x,z) * (T(x,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6045,a(flip),b,6179,a),flip(a)].">
      <j1 rule="hyper" parents="58 6045 6179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6182">
    <literal><![CDATA[
      T(x,x * y) * (L(x,y,x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,6046,a(flip),b,6181,a)].">
      <j1 rule="hyper" parents="119 6046 6181"/>
    </justification>
  </clause>

  <clause id="6183">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) = K(x,(((y * z) * u) / ((x * z) * u)) \ 1)
    ]]></literal>
    <justification jstring="[para(547(a,1),6154(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="547 6154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6184">
    <literal><![CDATA[
      K(x,((y \ z) * (z \ 1)) \ 1) = R(K(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),6157(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6185">
    <literal><![CDATA[
      R(K(x,y \ x),x,z) = K(x,((y * z) / (x * z)) \ 1)
    ]]></literal>
    <justification jstring="[para(6(a,1),6174(a,1,1,2,1))].">
      <j1 rule="para" parents="6 6174"/>
    </justification>
  </clause>

  <clause id="6186">
    <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),6185(a,2,2,1,2))].">
      <j1 rule="para" parents="7 6185"/>
    </justification>
  </clause>

  <clause id="6187">
    <literal><![CDATA[
      ((x * y) * ((z * ((x * y) \ x)) / z)) * y = (x * y) * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2359,a(flip),b,5565,a)].">
      <j1 rule="hyper" parents="58 2359 5565"/>
    </justification>
  </clause>

  <clause id="6188">
    <literal><![CDATA[
      (x * (y \ 1)) * ((z * ((x * (y \ 1)) \ x)) / z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[para(3696(a,1),5565(a,2,2))].">
      <j1 rule="para" parents="3696 5565"/>
    </justification>
  </clause>

  <clause id="6189">
    <literal><![CDATA[
      x * (y * ((z * (y \ (x \ y))) / z)) = K(z,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(1396,a,5566,a)].">
      <j1 rule="hyper" parents="1396 5566"/>
    </justification>
  </clause>

  <clause id="6190">
    <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(5678(a,2),5596(a,1,2,2))].">
      <j1 rule="para" parents="5678 5596"/>
    </justification>
  </clause>

  <clause id="6191">
    <literal><![CDATA[
      K(x,(y / R(y,z,u)) \ x) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(4259(a,2),5697(a,1,2,1))].">
      <j1 rule="para" parents="4259 5697"/>
    </justification>
  </clause>

  <clause id="6192">
    <literal><![CDATA[
      (K(x,y) * R(y,z,u)) * w = R(y,z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(2532(a,1),5726(a,1,1))].">
      <j1 rule="para" parents="2532 5726"/>
    </justification>
  </clause>

  <clause id="6193">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) = x \ (((y \ (x / z)) * y) * z)
    ]]></literal>
    <justification jstring="[para(4046(a,1),5797(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4046 5797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6194">
    <literal><![CDATA[
      K(x * y,T(y,z)) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(5646,a,5854,a),flip(a)].">
      <j1 rule="hyper" parents="5646 5854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6195">
    <literal><![CDATA[
      K(((1 / x) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(130,a,5921,a),flip(a)].">
      <j1 rule="hyper" parents="130 5921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6196">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(334,a,61,a(flip),b,5931,a),flip(a)].">
      <j1 rule="hyper" parents="334 61 5931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6198">
    <literal><![CDATA[
      L(K(x,y),z,u) \ w = L(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(5959(a,1),5954(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5959 5954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6199">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(1993,a,6198,a)].">
      <j1 rule="hyper" parents="1993 6198"/>
    </justification>
  </clause>

  <clause id="6200">
    <literal><![CDATA[
      L(K(x,y),z,u) * (L(K(y,x),z,u) * w) = w
    ]]></literal>
    <justification jstring="[hyper(299,a,6198,a),flip(a)].">
      <j1 rule="hyper" parents="299 6198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6201">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z,u) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,2074,a(flip),b,6199,a)].">
      <j1 rule="hyper" parents="58 2074 6199"/>
    </justification>
  </clause>

  <clause id="6202">
    <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(6199(a,1),5247(a,1)),flip(b)].">
      <j1 rule="para" parents="6199 5247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6203">
    <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(6200(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6200 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6204">
    <literal><![CDATA[
      K(x,y) \ L(K(x,y),z,u) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(5431,a,6201,a)].">
      <j1 rule="hyper" parents="5431 6201"/>
    </justification>
  </clause>

  <clause id="6205">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = L(K(x,y),u,z)
    ]]></literal>
    <justification jstring="[hyper(5409,a,6201,a)].">
      <j1 rule="hyper" parents="5409 6201"/>
    </justification>
  </clause>

  <clause id="6206">
    <literal><![CDATA[
      (K(x,y) / z) * (z * K(y,x)) = a(K(x,y) / z,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(716,a,6201,a)].">
      <j1 rule="hyper" parents="716 6201"/>
    </justification>
  </clause>

  <clause id="6207">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,L(x,z,u) \ 1) = a(u,z,K(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(5947(a,1),6201(a,1,2))].">
      <j1 rule="para" parents="5947 6201"/>
    </justification>
  </clause>

  <clause id="6208">
    <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(6205(a,1),5410(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6205 5410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6209">
    <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(2068(a,2),6208(a,1))].">
      <j1 rule="para" parents="2068 6208"/>
    </justification>
  </clause>

  <clause id="6210">
    <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(5967(a,1),5391(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5967 5391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6211">
    <literal><![CDATA[
      R(K(x,y),z,u) \ w = R(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(6152(a,1),5982(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6152 5982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6212">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 = R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(2785,a,6211,a)].">
      <j1 rule="hyper" parents="2785 6211"/>
    </justification>
  </clause>

  <clause id="6213">
    <literal><![CDATA[
      (x * y) / ((K(z,u) * x) * y) = R(K(u,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(634,a,6211,a)].">
      <j1 rule="hyper" parents="634 6211"/>
    </justification>
  </clause>

  <clause id="6214">
    <literal><![CDATA[
      x / (R(K(y,z),u,w) * x) = R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(588,a,6211,a)].">
      <j1 rule="hyper" parents="588 6211"/>
    </justification>
  </clause>

  <clause id="6215">
    <literal><![CDATA[
      R(K(x,y),z,u) \ (z * u) = (K(y,x) * z) * u
    ]]></literal>
    <justification jstring="[hyper(334,a,101,a(flip),b,6211,a),flip(a)].">
      <j1 rule="hyper" parents="334 101 6211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6216">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      R(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(6211(a,2),127(a,1)),flip(b)].">
      <j1 rule="para" parents="6211 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6217">
    <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(6211(a,1),345(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6211 345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6218">
    <literal><![CDATA[
      R(K(x,y),z,(K(y,x) * z) \ 1) = z * ((K(y,x) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(930,a,6212,a),flip(a)].">
      <j1 rule="hyper" parents="930 6212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6219">
    <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(6212(a,1),5946(a,1,1,2,2))].">
      <j1 rule="para" parents="6212 5946"/>
    </justification>
  </clause>

  <clause id="6220">
    <literal><![CDATA[
      ((x \ 1) * y) / ((x \ K(x,z)) * y) = R(K(z,x),x \ 1,y)
    ]]></literal>
    <justification jstring="[para(2783(a,1),6213(a,1,2,1))].">
      <j1 rule="para" parents="2783 6213"/>
    </justification>
  </clause>

  <clause id="6221">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5302,a(flip),b,5983,a),flip(a)].">
      <j1 rule="hyper" parents="58 5302 5983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6222">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) * (x \ 1) = K((y * (x \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(5312(a,1),5983(a,1,1))].">
      <j1 rule="para" parents="5312 5983"/>
    </justification>
  </clause>

  <clause id="6223">
    <literal><![CDATA[
      (1 / x) * (y * T(y \ x,z)) = K(((x \ 1) * y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,4288,a(flip),b,5984,a),flip(a)].">
      <j1 rule="hyper" parents="334 4288 5984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6224">
    <literal><![CDATA[
      K(((1 / x) * (y \ 1)) \ 1,z) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[para(971(a,1),5984(a,1,2)),flip(a)].">
      <j1 rule="para" parents="971 5984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6225">
    <literal><![CDATA[
      K(x \ y,y) / (y \ T(y * (x \ 1),y)) = x
    ]]></literal>
    <justification jstring="[hyper(117,a,6221,a(flip),b,5986,a)].">
      <j1 rule="hyper" parents="117 6221 5986"/>
    </justification>
  </clause>

  <clause id="6226">
    <literal><![CDATA[
      x \ T(x * (y \ 1),x) = y \ K(y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,6221,a(flip),b,5986,a),flip(a)].">
      <j1 rule="hyper" parents="116 6221 5986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6227">
    <literal><![CDATA[
      x * (y \ K(y \ x,x)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[para(6225(a,1),199(a,1,2,1))].">
      <j1 rule="para" parents="6225 199"/>
    </justification>
  </clause>

  <clause id="6228">
    <literal><![CDATA[
      (x \ K(x \ y,y)) * y = T((x \ 1) * y,y)
    ]]></literal>
    <justification jstring="[para(6226(a,1),4820(a,1,1))].">
      <j1 rule="para" parents="6226 4820"/>
    </justification>
  </clause>

  <clause id="6229">
    <literal><![CDATA[
      ((x * (K(y \ x,x) * (y \ 1))) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(6227(a,1),1582(a,2,2,1))].">
      <j1 rule="para" parents="6227 1582"/>
    </justification>
  </clause>

  <clause id="6230">
    <literal><![CDATA[
      x * T(x \ (y \ x),T(y,z)) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(3201,a,5988,a),flip(a)].">
      <j1 rule="hyper" parents="3201 5988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6231">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z / (x * y)) = u
    ]]></literal>
    <justification jstring="[para(6001(a,2),5703(a,1))].">
      <j1 rule="para" parents="6001 5703"/>
    </justification>
  </clause>

  <clause id="6232">
    <literal><![CDATA[
      K(x,y \ K(y,z)) * z = z * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),6019(a,2,2,2,1))].">
      <j1 rule="para" parents="4 6019"/>
    </justification>
  </clause>

  <clause id="6233">
    <literal><![CDATA[
      K(x,(y / (1 / (1 / z))) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(6036(a,1),5588(a,1,2))].">
      <j1 rule="para" parents="6036 5588"/>
    </justification>
  </clause>

  <clause id="6234">
    <literal><![CDATA[
      (x \ 1) \ ((y \ (y / x)) * y) = (y / x) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,5309,a,b,6111,a)].">
      <j1 rule="hyper" parents="116 5309 6111"/>
    </justification>
  </clause>

  <clause id="6235">
    <literal><![CDATA[
      (x / (y \ x)) / ((y \ x) \ 1) = ((y \ x) \ 1) \ ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(72(a,1),6234(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6236">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(3663(a,1),6177(a,1,2,1))].">
      <j1 rule="para" parents="3663 6177"/>
    </justification>
  </clause>

  <clause id="6237">
    <literal><![CDATA[
      x * (K(y,x \ 1) * (x \ z)) = K(y,x \ 1) * z
    ]]></literal>
    <justification jstring="[para(6034(a,2),6189(a,1,2))].">
      <j1 rule="para" parents="6034 6189"/>
    </justification>
  </clause>

  <clause id="6239">
    <literal><![CDATA[
      K(x,y \ 1) * (y * z) = y * (K(x,y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6237(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 6237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6242">
    <literal><![CDATA[
      1 \ (x * (K(y,x \ 1) * z)) = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(334,a,60,a,b,6239,a)].">
      <j1 rule="hyper" parents="334 60 6239"/>
    </justification>
  </clause>

  <clause id="6243">
    <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(6192(a,1),527(a,1))].">
      <j1 rule="para" parents="6192 527"/>
    </justification>
  </clause>

  <clause id="6244">
    <literal><![CDATA[
      K(((x \ 1) * (y \ 1)) \ 1,z) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[para(971(a,1),6223(a,1,2)),flip(a)].">
      <j1 rule="para" parents="971 6223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6245">
    <literal><![CDATA[
      K((((x \ y) \ 1) * (x \ 1)) \ 1,z) = (1 / (x \ y)) * (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(1030(a,1),6223(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1030 6223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6246">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x * y) = y / R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(5713(a,1),4979(a,1,2))].">
      <j1 rule="para" parents="5713 4979"/>
    </justification>
  </clause>

  <clause id="6247">
    <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(843(a,1),5164(a,2,1,1))].">
      <j1 rule="para" parents="843 5164"/>
    </justification>
  </clause>

  <clause id="6248">
    <literal><![CDATA[
      T(x \ y,z) \ T((x \ y) * (y \ x),z) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,2203,a,b,5229,a)].">
      <j1 rule="hyper" parents="58 2203 5229"/>
    </justification>
  </clause>

  <clause id="6249">
    <literal><![CDATA[
      ((x \ y) * T(x,x \ y)) \ ((y / x) * z) = L(x \ z,T(x,x \ y),x \ y)
    ]]></literal>
    <justification jstring="[para(5674(a,1),5368(a,1,2))].">
      <j1 rule="para" parents="5674 5368"/>
    </justification>
  </clause>

  <clause id="6250">
    <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(5380(a,1),5412(a,1,2))].">
      <j1 rule="para" parents="5380 5412"/>
    </justification>
  </clause>

  <clause id="6251">
    <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,6201,a(flip),b,5498,a)].">
      <j1 rule="hyper" parents="119 6201 5498"/>
    </justification>
  </clause>

  <clause id="6252">
    <literal><![CDATA[
      R(K(x,y),y / x,z) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,6211,a(flip),b,5541,a)].">
      <j1 rule="hyper" parents="58 6211 5541"/>
    </justification>
  </clause>

  <clause id="6253">
    <literal><![CDATA[
      T(K(x * (y \ 1),y \ 1) / y,x) = R(1 / y,x,1 / y)
    ]]></literal>
    <justification jstring="[para(4274(a,1),5545(a,1,1,1))].">
      <j1 rule="para" parents="4274 5545"/>
    </justification>
  </clause>

  <clause id="6254">
    <literal><![CDATA[
      L(T(x,y),x \ T(z,x),x) = T(L(x,x \ z,x),y)
    ]]></literal>
    <justification jstring="[para(4980(a,1),5766(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4980 5766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6255">
    <literal><![CDATA[
      L(T(x,y),x \ T(z,x),x) = L(T(x,y),x \ z,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,20,a,b,6254,a),flip(a)].">
      <j1 rule="hyper" parents="334 20 6254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6256">
    <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(6255(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6255 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6257">
    <literal><![CDATA[
      K(x,y / (x / (z \ 1))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x * z)) = u
    ]]></literal>
    <justification jstring="[para(6008(a,1),5937(a,1))].">
      <j1 rule="para" parents="6008 5937"/>
    </justification>
  </clause>

  <clause id="6258">
    <literal><![CDATA[
      R(K(x \ y,x),y,z) = K(((x * z) / (y * z)) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5706(a,1),5979(a,1,1))].">
      <j1 rule="para" parents="5706 5979"/>
    </justification>
  </clause>

  <clause id="6259">
    <literal><![CDATA[
      R(K(x \ (y / z),x),y / z,z) = K(((x * z) / y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),6258(a,2,1,1,2))].">
      <j1 rule="para" parents="7 6258"/>
    </justification>
  </clause>

  <clause id="6260">
    <literal><![CDATA[
      K(x / y,z) \ y != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (T(x / y,z) \ x) = w
    ]]></literal>
    <justification jstring="[para(5391(a,2),6052(a,1))].">
      <j1 rule="para" parents="5391 6052"/>
    </justification>
  </clause>

  <clause id="6261">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(3696(a,1),6059(a,1))].">
      <j1 rule="para" parents="3696 6059"/>
    </justification>
  </clause>

  <clause id="6262">
    <literal><![CDATA[
      K((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((1 / x) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(75(a,1),6261(a,1,1,1,1))].">
      <j1 rule="para" parents="75 6261"/>
    </justification>
  </clause>

  <clause id="6263">
    <literal><![CDATA[
      K(x * (y \ 1),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,x) = z
    ]]></literal>
    <justification jstring="[para(5626(a,1),6261(a,1))].">
      <j1 rule="para" parents="5626 6261"/>
    </justification>
  </clause>

  <clause id="6264">
    <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(4149(a,1),6083(a,1,1,2))].">
      <j1 rule="para" parents="4149 6083"/>
    </justification>
  </clause>

  <clause id="6265">
    <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,6214,a,b,6218,a)].">
      <j1 rule="hyper" parents="58 6214 6218"/>
    </justification>
  </clause>

  <clause id="6266">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ 1 = T(x,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,6165,a(flip),b,6218,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 6165 6218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6267">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ 1 = T(x,y) \ K(z,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,5925,a,b,6266,a),flip(a)].">
      <j1 rule="hyper" parents="334 5925 6266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6268">
    <literal><![CDATA[
      T(K(x * (y \ 1),y \ 1) / y,x) = R(1 / y,x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,3555,a(flip),b,6253,a),flip(a)].">
      <j1 rule="hyper" parents="334 3555 6253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6269">
    <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(6259(a,2),5940(a,1))].">
      <j1 rule="para" parents="6259 5940"/>
    </justification>
  </clause>

  <clause id="6270">
    <literal><![CDATA[
      (x * y) * K(R(y,x,y),x * y) = ((y * x) / R(y,x,y)) * y
    ]]></literal>
    <justification jstring="[hyper(1960,a,5199,a),flip(a)].">
      <j1 rule="hyper" parents="1960 5199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6271">
    <literal><![CDATA[
      (1 / (1 / x)) / (x * y) = x / (((x \ 1) \ 1) * y)
    ]]></literal>
    <justification jstring="[para(5153(a,1),5222(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5153 5222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6272">
    <literal><![CDATA[
      (1 / (1 / x)) / (x * (T(x,y) \ 1)) = x / (T(x,y) \ ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(1778(a,1),6271(a,2,2))].">
      <j1 rule="para" parents="1778 6271"/>
    </justification>
  </clause>

  <clause id="6273">
    <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(5261(a,1),5748(a,1))].">
      <j1 rule="para" parents="5261 5748"/>
    </justification>
  </clause>

  <clause id="6274">
    <literal><![CDATA[
      ((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(524(a,1),5300(a,1,1))].">
      <j1 rule="para" parents="524 5300"/>
    </justification>
  </clause>

  <clause id="6275">
    <literal><![CDATA[
      (K(x,y) * T(K(x,y) \ z,u)) * K(y,x) = T(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(5391(a,2),5421(a,1,1,2,1))].">
      <j1 rule="para" parents="5391 5421"/>
    </justification>
  </clause>

  <clause id="6276">
    <literal><![CDATA[
      T((K(x,y) * z) * K(y,x),u) = (K(x,y) * T(z,u)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(5394(a,1),5421(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5394 5421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6277">
    <literal><![CDATA[
      ((x * y) * z) / ((T(x,u) * y) * z) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(524(a,1),5452(a,1,2))].">
      <j1 rule="para" parents="524 5452"/>
    </justification>
  </clause>

  <clause id="6278">
    <literal><![CDATA[
      T(x,y) / (T(x,y) * y) = x / ((y * K(x,y)) * x)
    ]]></literal>
    <justification jstring="[para(5155(a,1),5456(a,1,1))].">
      <j1 rule="para" parents="5155 5456"/>
    </justification>
  </clause>

  <clause id="6279">
    <literal><![CDATA[
      T(x,y) / (T(x,y) * y) = x / (x * y)
    ]]></literal>
    <justification jstring="[para(5039(a,1),6278(a,2,2))].">
      <j1 rule="para" parents="5039 6278"/>
    </justification>
  </clause>

  <clause id="6280">
    <literal><![CDATA[
      (x / (x * y)) \ T(x,y) = T(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(192,a,6279,a)].">
      <j1 rule="hyper" parents="192 6279"/>
    </justification>
  </clause>

  <clause id="6281">
    <literal><![CDATA[
      (x \ K(x,y)) * T((x \ 1) \ 1,z) = K(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,5914,a(flip),b,5534,a),flip(a)].">
      <j1 rule="hyper" parents="334 5914 5534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6282">
    <literal><![CDATA[
      K(x \ 1,x) * (K(x,y) * K(x,z)) = (x \ K(x,y)) * T(x,z)
    ]]></literal>
    <justification jstring="[para(6281(a,1),3859(a,1,2))].">
      <j1 rule="para" parents="6281 3859"/>
    </justification>
  </clause>

  <clause id="6283">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = (x * (K(z,u) * y)) / (x * y)
    ]]></literal>
    <justification jstring="[para(5361(a,1),5560(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5361 5560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6284">
    <literal><![CDATA[
      R(K(x,y / z),y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * u) / (z * u)) = w
    ]]></literal>
    <justification jstring="[para(6153(a,1),5757(a,1))].">
      <j1 rule="para" parents="6153 5757"/>
    </justification>
  </clause>

  <clause id="6285">
    <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),6284(a,1,1,2))].">
      <j1 rule="para" parents="72 6284"/>
    </justification>
  </clause>

  <clause id="6286">
    <literal><![CDATA[
      ((x \ T(x * (y / z),u)) * z) / y = K((((x \ 1) * z) / y) \ 1,u)
    ]]></literal>
    <justification jstring="[para(1660(a,1),5794(a,1,1))].">
      <j1 rule="para" parents="1660 5794"/>
    </justification>
  </clause>

  <clause id="6287">
    <literal><![CDATA[
      x * K((x \ (y * z)) \ 1,z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(105(a,1),5802(a,2,2))].">
      <j1 rule="para" parents="105 5802"/>
    </justification>
  </clause>

  <clause id="6288">
    <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),5802(a,2,2,2,1))].">
      <j1 rule="para" parents="62 5802"/>
    </justification>
  </clause>

  <clause id="6289">
    <literal><![CDATA[
      T(x \ y,x) / ((x \ 1) \ (x \ y)) = (x \ y) / ((x \ 1) \ (y / x))
    ]]></literal>
    <justification jstring="[para(5821(a,1),4762(a,2,2))].">
      <j1 rule="para" parents="5821 4762"/>
    </justification>
  </clause>

  <clause id="6290">
    <literal><![CDATA[
      K(x,y * ((z \ L(u,1 / z,z)) * w)) = K(x,y * (((1 / z) * u) * w))
    ]]></literal>
    <justification jstring="[para(3094(a,1),5928(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3094 5928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6291">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = T(K(x,y) * z,z) / z
    ]]></literal>
    <justification jstring="[para(5668(a,1),6002(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5668 6002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6292">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = z \ T(z * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,4823,a(flip),b,6291,a),flip(a)].">
      <j1 rule="hyper" parents="334 4823 6291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6293">
    <literal><![CDATA[
      K(x,y / T(z \ y,y)) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(5703,a,6292,a)].">
      <j1 rule="hyper" parents="5703 6292"/>
    </justification>
  </clause>

  <clause id="6294">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(4767(a,1),6293(a,1,2))].">
      <j1 rule="para" parents="4767 6293"/>
    </justification>
  </clause>

  <clause id="6295">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * T(K(y,x) \ z,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5312(a,2),6012(a,1,2))].">
      <j1 rule="para" parents="5312 6012"/>
    </justification>
  </clause>

  <clause id="6296">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,x)),u) = K(x,y) * (T(z,u) * K(y,x))
    ]]></literal>
    <justification jstring="[para(5803(a,1),6012(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5803 6012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6297">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = x * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(6120(a,1),6016(a,2,2))].">
      <j1 rule="para" parents="6120 6016"/>
    </justification>
  </clause>

  <clause id="6298">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(334,a,315,a(flip),b,6297,a),flip(a)].">
      <j1 rule="hyper" parents="334 315 6297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6299">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(75(a,1),6033(a,2,1,1))].">
      <j1 rule="para" parents="75 6033"/>
    </justification>
  </clause>

  <clause id="6300">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * ((x \ 1) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,3612,a(flip),b,6299,a)].">
      <j1 rule="hyper" parents="58 3612 6299"/>
    </justification>
  </clause>

  <clause id="6301">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) = (1 / x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6299(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 6299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6303">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * z) = (x \ 1) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6300(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 6300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6304">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * T(z,x \ 1)) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[para(17(a,2),6300(a,1,2,2))].">
      <j1 rule="para" parents="17 6300"/>
    </justification>
  </clause>

  <clause id="6305">
    <literal><![CDATA[
      (K(x,y) * z) \ (K(x,y) * ((1 / x) * z)) = T(1 / x,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(451,a,6301,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="451 6301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6306">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(6301(a,1),356(a,1))].">
      <j1 rule="para" parents="6301 356"/>
    </justification>
  </clause>

  <clause id="6307">
    <literal><![CDATA[
      x * (K(x,y) * ((x \ 1) * z)) = L(K(x,y) * z,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,6303,a,b,450,a)].">
      <j1 rule="hyper" parents="119 6303 450"/>
    </justification>
  </clause>

  <clause id="6308">
    <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),6303(a,2,2))].">
      <j1 rule="para" parents="105 6303"/>
    </justification>
  </clause>

  <clause id="6309">
    <literal><![CDATA[
      ((x \ 1) * y) / ((x \ 1) * (K(x,z) * y)) = K(z,x)
    ]]></literal>
    <justification jstring="[para(6303(a,1),5403(a,1,2))].">
      <j1 rule="para" parents="6303 5403"/>
    </justification>
  </clause>

  <clause id="6310">
    <literal><![CDATA[
      ((x \ 1) * (K(y,x) * z)) / ((x \ 1) * z) = K(y,x)
    ]]></literal>
    <justification jstring="[para(5394(a,1),6309(a,1,2,2))].">
      <j1 rule="para" parents="5394 6309"/>
    </justification>
  </clause>

  <clause id="6311">
    <literal><![CDATA[
      L(K(x,y) * z,x \ 1,x) = T(x,y) * ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(5335,a,6307,a),flip(a)].">
      <j1 rule="hyper" parents="5335 6307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6312">
    <literal><![CDATA[
      T(x,y) * ((x \ 1) * (K(y,x) * z)) = L(z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(5394(a,1),6311(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5394 6311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6313">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = R(x,y,x) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,2193,a(flip),b,6051,a),flip(a)].">
      <j1 rule="hyper" parents="334 2193 6051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6314">
    <literal><![CDATA[
      x \ (K(x,y) * L(x,z,x)) = R(x,z,x) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(5365(a,1),6313(a,1,2))].">
      <j1 rule="para" parents="5365 6313"/>
    </justification>
  </clause>

  <clause id="6315">
    <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(4576(a,1),6142(a,1,2))].">
      <j1 rule="para" parents="4576 6142"/>
    </justification>
  </clause>

  <clause id="6316">
    <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(4576(a,1),6144(a,1,2))].">
      <j1 rule="para" parents="4576 6144"/>
    </justification>
  </clause>

  <clause id="6317">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) = K((x \ (y * z)) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5795,a(flip),b,6193,a),flip(a)].">
      <j1 rule="hyper" parents="334 5795 6193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6318">
    <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(5959(a,1),6207(a,1,1))].">
      <j1 rule="para" parents="5959 6207"/>
    </justification>
  </clause>

  <clause id="6319">
    <literal><![CDATA[
      K((x * ((1 / y) \ 1)) \ 1,z) / y = (1 / y) * K(((1 / y) \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(365,a,6222,a)].">
      <j1 rule="hyper" parents="365 6222"/>
    </justification>
  </clause>

  <clause id="6320">
    <literal><![CDATA[
      ((1 / x) * T((1 / x) \ y,z)) * (y \ 1) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5983,a,b,6224,a)].">
      <j1 rule="hyper" parents="58 5983 6224"/>
    </justification>
  </clause>

  <clause id="6321">
    <literal><![CDATA[
      ((x \ y) \ 1) \ ((y \ x) * y) = x / ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),6235(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 6235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6323">
    <literal><![CDATA[
      x / ((x \ L(x,y,z)) \ 1) = ((x \ L(x,y,z)) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(3959(a,1),6321(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3959 6321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6324">
    <literal><![CDATA[
      1 / ((1 / x) * (y \ T(y * x,z))) = K(z,((x \ 1) * (y \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[para(6244(a,1),5243(a,1,2))].">
      <j1 rule="para" parents="6244 5243"/>
    </justification>
  </clause>

  <clause id="6325">
    <literal><![CDATA[
      ((x * y) / R(x,y,x)) * x = (y * x) * K(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(5237(a,1),6270(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5237 6270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6326">
    <literal><![CDATA[
      ((x * y) / R(x,y,x)) * x = T(x,y * x) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,5191,a(flip),b,6325,a),flip(a)].">
      <j1 rule="hyper" parents="334 5191 6325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6327">
    <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),6326(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 6326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6328">
    <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,4820,a,b,6275,a)].">
      <j1 rule="hyper" parents="30 4820 6275"/>
    </justification>
  </clause>

  <clause id="6329">
    <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(6275(a,1),39(a,1))].">
      <j1 rule="para" parents="6275 39"/>
    </justification>
  </clause>

  <clause id="6330">
    <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(6276(a,2),39(a,1))].">
      <j1 rule="para" parents="6276 39"/>
    </justification>
  </clause>

  <clause id="6331">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ K(x,x \ 1) = ((x \ K(x,y)) * T(x,z)) \ 1
    ]]></literal>
    <justification jstring="[para(6282(a,1),3888(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6282 3888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6332">
    <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(6282(a,1),4323(a,1,2))].">
      <j1 rule="para" parents="6282 4323"/>
    </justification>
  </clause>

  <clause id="6333">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * (K(u,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(5425,a,6283,a)].">
      <j1 rule="hyper" parents="5425 6283"/>
    </justification>
  </clause>

  <clause id="6334">
    <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(5935,a,6295,a)].">
      <j1 rule="hyper" parents="5935 6295"/>
    </justification>
  </clause>

  <clause id="6335">
    <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,5252,a,b,6334,a)].">
      <j1 rule="hyper" parents="58 5252 6334"/>
    </justification>
  </clause>

  <clause id="6337">
    <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(6296(a,2),38(a,1))].">
      <j1 rule="para" parents="6296 38"/>
    </justification>
  </clause>

  <clause id="6338">
    <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(6328(a,1),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6328 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6339">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) = (y * z) / (y * (K(u,x) * z))
    ]]></literal>
    <justification jstring="[hyper(130,a,6333,a),flip(a)].">
      <j1 rule="hyper" parents="130 6333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6340">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * (K(y,x) * w)) = R(y,z,u) * w
    ]]></literal>
    <justification jstring="[para(1368(a,1),6333(a,1,1,2))].">
      <j1 rule="para" parents="1368 6333"/>
    </justification>
  </clause>

  <clause id="6341">
    <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(6333(a,1),506(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6333 506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6342">
    <literal><![CDATA[
      R(x,y,z) * (K(u,x) * w) = K(u,x) * (R(x,y,z) * w)
    ]]></literal>
    <justification jstring="[para(5394(a,1),6340(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5394 6340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6343">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * (y \ w)) = R(y,z,u) * (T(y,x) \ w)
    ]]></literal>
    <justification jstring="[para(5337(a,1),6340(a,1,2,2))].">
      <j1 rule="para" parents="5337 6340"/>
    </justification>
  </clause>

  <clause id="6344">
    <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(6335(a,1),38(a,1))].">
      <j1 rule="para" parents="6335 38"/>
    </justification>
  </clause>

  <clause id="6345">
    <literal><![CDATA[
      x * (y * ((z \ (y \ z)) * z)) = (x * K(y \ 1,z)) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,3678,a(flip),b,5324,a)].">
      <j1 rule="hyper" parents="58 3678 5324"/>
    </justification>
  </clause>

  <clause id="6346">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * z = x * (z * K(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(5326(a,1),6345(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5326 6345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6347">
    <literal><![CDATA[
      R(x,K(y \ 1,z),z) = x
    ]]></literal>
    <justification jstring="[hyper(2550,a,6346,a)].">
      <j1 rule="hyper" parents="2550 6346"/>
    </justification>
  </clause>

  <clause id="6348">
    <literal><![CDATA[
      R(x,K(y,z),z) = x
    ]]></literal>
    <justification jstring="[para(75(a,1),6347(a,1,2,1))].">
      <j1 rule="para" parents="75 6347"/>
    </justification>
  </clause>

  <clause id="6349">
    <literal><![CDATA[
      R(x,y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(6078,a,6348,a)].">
      <j1 rule="hyper" parents="6078 6348"/>
    </justification>
  </clause>

  <clause id="6350">
    <literal><![CDATA[
      (x * K(y,z)) * z = x * (K(y,z) * z)
    ]]></literal>
    <justification jstring="[para(6348(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6348 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6351">
    <literal><![CDATA[
      (x * K(y,z)) * z = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[para(6348(a,1),2549(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6348 2549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6352">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(6349(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6349 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6353">
    <literal><![CDATA[
      L(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(493,a,6350,a)].">
      <j1 rule="hyper" parents="493 6350"/>
    </justification>
  </clause>

  <clause id="6354">
    <literal><![CDATA[
      L(T(x,y),K(z,x),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6353(a,1),20(a,2,1))].">
      <j1 rule="para" parents="6353 20"/>
    </justification>
  </clause>

  <clause id="6355">
    <literal><![CDATA[
      L((x \ y) \ y,K(z,x),u) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(6353(a,1),331(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6353 331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6356">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,u) = x * (K(y,z) * T(z,u))
    ]]></literal>
    <justification jstring="[para(6353(a,1),461(a,1,2,1))].">
      <j1 rule="para" parents="6353 461"/>
    </justification>
  </clause>

  <clause id="6358">
    <literal><![CDATA[
      (x * K(y,z)) * L(z,u,w) = x * (K(y,z) * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(6353(a,1),458(a,1,2,1))].">
      <j1 rule="para" parents="6353 458"/>
    </justification>
  </clause>

  <clause id="6359">
    <literal><![CDATA[
      (x * K(y,z)) * R(z,u,w) = x * (K(y,z) * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(6353(a,1),459(a,1,2,1))].">
      <j1 rule="para" parents="6353 459"/>
    </justification>
  </clause>

  <clause id="6361">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * z) = T(z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5134,a(flip),b,6354,a)].">
      <j1 rule="hyper" parents="58 5134 6354"/>
    </justification>
  </clause>

  <clause id="6362">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,y) = x * z
    ]]></literal>
    <justification jstring="[hyper(119,a,6354,a(flip),b,5134,a(flip))].">
      <j1 rule="hyper" parents="119 6354 5134"/>
    </justification>
  </clause>

  <clause id="6363">
    <literal><![CDATA[
      x / T(y \ x,z) = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(378,a,6361,a)].">
      <j1 rule="hyper" parents="378 6361"/>
    </justification>
  </clause>

  <clause id="6365">
    <literal><![CDATA[
      (x * y) / T(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(201,a,6361,a)].">
      <j1 rule="hyper" parents="201 6361"/>
    </justification>
  </clause>

  <clause id="6367">
    <literal><![CDATA[
      (x * K(y,x \ z)) \ z = T(x \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6361(a,1,2))].">
      <j1 rule="para" parents="5 6361"/>
    </justification>
  </clause>

  <clause id="6368">
    <literal><![CDATA[
      (x / y) * K(z,y) = x / T(y,z)
    ]]></literal>
    <justification jstring="[para(6361(a,1),338(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6361 338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6370">
    <literal><![CDATA[
      (x / T(y,z)) * y = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(1477,a,6362,a)].">
      <j1 rule="hyper" parents="1477 6362"/>
    </justification>
  </clause>

  <clause id="6371">
    <literal><![CDATA[
      (x \ y) * K(y,x) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,4740,a,b,6362,a),flip(a)].">
      <j1 rule="hyper" parents="30 4740 6362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6373">
    <literal><![CDATA[
      (x \ K(x,y)) * K(y,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(30,a,5830,a(flip),b,6362,a),flip(a)].">
      <j1 rule="hyper" parents="30 5830 6362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6374">
    <literal><![CDATA[
      (x * T(y,z)) * K(z,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(30,a,1462,a(flip),b,6362,a),flip(a)].">
      <j1 rule="hyper" parents="30 1462 6362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6375">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(z,y) = u
    ]]></literal>
    <justification jstring="[para(6362(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6362 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6376">
    <literal><![CDATA[
      (x / y) \ (x / T(y,z)) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(987,a,6365,a)].">
      <j1 rule="hyper" parents="987 6365"/>
    </justification>
  </clause>

  <clause id="6377">
    <literal><![CDATA[
      x \ (y / T(x \ y,z)) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(639,a,6365,a)].">
      <j1 rule="hyper" parents="639 6365"/>
    </justification>
  </clause>

  <clause id="6378">
    <literal><![CDATA[
      T(x / T(y,z),y) = y \ (x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(451,a,6365,a(flip),b,1463,a(flip))].">
      <j1 rule="hyper" parents="451 6365 1463"/>
    </justification>
  </clause>

  <clause id="6379">
    <literal><![CDATA[
      (x * K(y,z)) / z = x / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,6365,a(flip),b,1463,a(flip))].">
      <j1 rule="hyper" parents="117 6365 1463"/>
    </justification>
  </clause>

  <clause id="6380">
    <literal><![CDATA[
      (x / y) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6365(a,1),589(a,1))].">
      <j1 rule="para" parents="6365 589"/>
    </justification>
  </clause>

  <clause id="6382">
    <literal><![CDATA[
      x * (K(y,x) * K(z,y)) = (y * x) / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(5942,a,6368,a)].">
      <j1 rule="hyper" parents="5942 6368"/>
    </justification>
  </clause>

  <clause id="6383">
    <literal><![CDATA[
      (x / y) * K(x,y) = T(x,y) / y
    ]]></literal>
    <justification jstring="[hyper(334,a,4488,a,b,6368,a),flip(a)].">
      <j1 rule="hyper" parents="334 4488 6368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6385">
    <literal><![CDATA[
      T(x / y,K(x,y)) = x / y
    ]]></literal>
    <justification jstring="[hyper(246,a,6368,a,b,5514,a)].">
      <j1 rule="hyper" parents="246 6368 5514"/>
    </justification>
  </clause>

  <clause id="6386">
    <literal><![CDATA[
      K(x \ y,x) * K(z,y / x) = x \ (y / T(y / x,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,6368,a(flip),b,5676,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 6368 5676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6387">
    <literal><![CDATA[
      T(x / y,K(y,x)) = x / y
    ]]></literal>
    <justification jstring="[hyper(5903,a,6385,a)].">
      <j1 rule="hyper" parents="5903 6385"/>
    </justification>
  </clause>

  <clause id="6388">
    <literal><![CDATA[
      K(x,y) * (y / x) = (y / x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6385(a,1),5896(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6385 5896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6389">
    <literal><![CDATA[
      x / T(x * y,y \ 1) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,5311,a,b,6370,a),flip(a)].">
      <j1 rule="hyper" parents="30 5311 6370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6390">
    <literal><![CDATA[
      x / T(x * y,y \ 1) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(30,a,5310,a,b,6370,a),flip(a)].">
      <j1 rule="hyper" parents="30 5310 6370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6391">
    <literal><![CDATA[
      (x / ((y \ z) \ z)) * y = x * K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(106(a,1),6370(a,1,1,2))].">
      <j1 rule="para" parents="106 6370"/>
    </justification>
  </clause>

  <clause id="6392">
    <literal><![CDATA[
      x \ (y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / T(x,z),x) = u
    ]]></literal>
    <justification jstring="[para(6370(a,1),298(a,1,2))].">
      <j1 rule="para" parents="6370 298"/>
    </justification>
  </clause>

  <clause id="6393">
    <literal><![CDATA[
      x \ y != (z * K(u,w)) / w
    ]]></literal>
    <literal><![CDATA[
      x * (z / T(w,u)) = y
    ]]></literal>
    <justification jstring="[para(6370(a,1),642(a,2,1))].">
      <j1 rule="para" parents="6370 642"/>
    </justification>
  </clause>

  <clause id="6394">
    <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(6370(a,1),533(a,1,1))].">
      <j1 rule="para" parents="6370 533"/>
    </justification>
  </clause>

  <clause id="6396">
    <literal><![CDATA[
      (x * K(y,z)) * z = (x * z) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6365(a,1),6370(a,1,1))].">
      <j1 rule="para" parents="6365 6370"/>
    </justification>
  </clause>

  <clause id="6398">
    <literal><![CDATA[
      x \ T(x * y,x) = y * K(x * y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),6371(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 6371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6399">
    <literal><![CDATA[
      (x \ T(y,x)) \ ((x \ y) * (K(y,x) * z)) = L(z,K(y,x),x \ y)
    ]]></literal>
    <justification jstring="[para(6371(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6371 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6400">
    <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(6373(a,1),102(a,2,2))].">
      <j1 rule="para" parents="6373 102"/>
    </justification>
  </clause>

  <clause id="6401">
    <literal><![CDATA[
      (x * y) / K(z,y) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,6374,a)].">
      <j1 rule="hyper" parents="130 6374"/>
    </justification>
  </clause>

  <clause id="6402">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,6374,a)].">
      <j1 rule="hyper" parents="116 5 6374"/>
    </justification>
  </clause>

  <clause id="6403">
    <literal><![CDATA[
      x * K(y,z) != u * z
    ]]></literal>
    <literal><![CDATA[
      u * T(z,y) = x
    ]]></literal>
    <justification jstring="[para(6374(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="6374 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6405">
    <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(6374(a,1),522(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6374 522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6407">
    <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(6379(a,1),4645(a,1,1,2))].">
      <j1 rule="para" parents="6379 4645"/>
    </justification>
  </clause>

  <clause id="6408">
    <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(6379(a,1),4647(a,1,1,1,2))].">
      <j1 rule="para" parents="6379 4647"/>
    </justification>
  </clause>

  <clause id="6409">
    <literal><![CDATA[
      x * (K(y,x) * K(y * x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[hyper(5942,a,6383,a)].">
      <j1 rule="hyper" parents="5942 6383"/>
    </justification>
  </clause>

  <clause id="6410">
    <literal><![CDATA[
      (x / ((y * z) / y)) * K(y,z) = x / z
    ]]></literal>
    <justification jstring="[hyper(117,a,5194,a(flip),b,6351,a),flip(a)].">
      <j1 rule="hyper" parents="117 5194 6351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6411">
    <literal><![CDATA[
      L(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(493,a,6352,a)].">
      <j1 rule="hyper" parents="493 6352"/>
    </justification>
  </clause>

  <clause id="6412">
    <literal><![CDATA[
      (x / y) * (y * K(z,y)) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(341,a,6352,a),flip(a)].">
      <j1 rule="hyper" parents="341 6352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6413">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * ((z * y) / z)
    ]]></literal>
    <justification jstring="[hyper(334,a,5171,a,b,6352,a),flip(a)].">
      <j1 rule="hyper" parents="334 5171 6352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6414">
    <literal><![CDATA[
      (x / (y * K(z,y))) * y = x / K(z,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,6352,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 6352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6415">
    <literal><![CDATA[
      a(x,y,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,6352,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="115 6352 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6417">
    <literal><![CDATA[
      (x * (y \ z)) * K(y,y \ z) = x * (z / y)
    ]]></literal>
    <justification jstring="[para(5041(a,1),6352(a,2,2))].">
      <j1 rule="para" parents="5041 6352"/>
    </justification>
  </clause>

  <clause id="6418">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6202,a,6415,a)].">
      <j1 rule="hyper" parents="6202 6415"/>
    </justification>
  </clause>

  <clause id="6419">
    <literal><![CDATA[
      a(x,1,y) = a(z,u,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,387,a,b,6415,a)].">
      <j1 rule="hyper" parents="334 387 6415"/>
    </justification>
  </clause>

  <clause id="6420">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,6415,a(flip),b,6201,a),flip(a)].">
      <j1 rule="hyper" parents="116 6415 6201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6421">
    <literal><![CDATA[
      L(K(x,y),y,z) = L(K(x,y),y,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,6411,a,b,6411,a)].">
      <j1 rule="hyper" parents="334 6411 6411"/>
    </justification>
  </clause>

  <clause id="6423">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5953,a(flip),b,6411,a)].">
      <j1 rule="hyper" parents="58 5953 6411"/>
    </justification>
  </clause>

  <clause id="6424">
    <literal><![CDATA[
      x * K(y,z \ x) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,6411,a(flip),b,5174,a(flip))].">
      <j1 rule="hyper" parents="119 6411 5174"/>
    </justification>
  </clause>

  <clause id="6426">
    <literal><![CDATA[
      K(L(x \ 1,x,y) \ 1,z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(6076,a,6418,a)].">
      <j1 rule="hyper" parents="6076 6418"/>
    </justification>
  </clause>

  <clause id="6427">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(5032,a,6418,a)].">
      <j1 rule="hyper" parents="5032 6418"/>
    </justification>
  </clause>

  <clause id="6428">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(u \ (u * x),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,691,a,b,6418,a),flip(a)].">
      <j1 rule="hyper" parents="334 691 6418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6430">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,6418,a(flip),b,5031,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 6418 5031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6431">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),x,u) = z
    ]]></literal>
    <justification jstring="[para(6418(a,1),4313(a,1))].">
      <j1 rule="para" parents="6418 4313"/>
    </justification>
  </clause>

  <clause id="6432">
    <literal><![CDATA[
      (x * y) * K(y,z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(6418(a,1),5103(a,1,2))].">
      <j1 rule="para" parents="6418 5103"/>
    </justification>
  </clause>

  <clause id="6433">
    <literal><![CDATA[
      L(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6420(a,2),5241(a,1))].">
      <j1 rule="para" parents="6420 5241"/>
    </justification>
  </clause>

  <clause id="6435">
    <literal><![CDATA[
      L(K(x,y \ z),y \ z,u) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,5953,a(flip),b,6421,a),flip(a)].">
      <j1 rule="hyper" parents="334 5953 6421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6437">
    <literal><![CDATA[
      L(K(x,y),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6421(a,1),3811(a,1))].">
      <j1 rule="para" parents="6421 3811"/>
    </justification>
  </clause>

  <clause id="6438">
    <literal><![CDATA[
      K(x,1 / (y \ z)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(5756,a,6423,a)].">
      <j1 rule="hyper" parents="5756 6423"/>
    </justification>
  </clause>

  <clause id="6439">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(118,a,6423,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 6423 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6440">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6021,a,b,6423,a)].">
      <j1 rule="hyper" parents="58 6021 6423"/>
    </justification>
  </clause>

  <clause id="6441">
    <literal><![CDATA[
      K(x,(y * z) \ y) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),6423(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 6423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6443">
    <literal><![CDATA[
      K(x,((y * z) * u) \ (y * (z * u))) = K(x,a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,2),6423(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 6423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6445">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),6423(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 6423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6446">
    <literal><![CDATA[
      K(x,(y \ (y / z)) \ 1) = K(x,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),6423(a,2,2))].">
      <j1 rule="para" parents="75 6423"/>
    </justification>
  </clause>

  <clause id="6447">
    <literal><![CDATA[
      K(x,L(y \ z,y,u) \ 1) = K(x,(u * z) \ (u * y))
    ]]></literal>
    <justification jstring="[para(92(a,2),6423(a,1,2,1))].">
      <j1 rule="para" parents="92 6423"/>
    </justification>
  </clause>

  <clause id="6448">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ y) = K(x,a(y,z,z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(725(a,1),6423(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="725 6423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6449">
    <literal><![CDATA[
      K(x,(T(y,z) * (y \ u)) \ 1) = K(x,(T(y,z) * u) \ y)
    ]]></literal>
    <justification jstring="[para(1154(a,1),6423(a,1,2,1))].">
      <j1 rule="para" parents="1154 6423"/>
    </justification>
  </clause>

  <clause id="6452">
    <literal><![CDATA[
      (((x \ y) \ 1) \ z) * ((x \ y) \ 1) = z * K((x \ y) * z,y \ x)
    ]]></literal>
    <justification jstring="[para(6423(a,1),4753(a,2,2))].">
      <j1 rule="para" parents="6423 4753"/>
    </justification>
  </clause>

  <clause id="6453">
    <literal><![CDATA[
      K((x \ y) \ 1,z) = K(z,y \ x) \ 1
    ]]></literal>
    <justification jstring="[para(6423(a,1),5232(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6423 5232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6454">
    <literal><![CDATA[
      K(x,(T(y,z) * (y \ u)) \ 1) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[para(5056(a,2),6423(a,1,2,1))].">
      <j1 rule="para" parents="5056 6423"/>
    </justification>
  </clause>

  <clause id="6455">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[para(5391(a,1),6423(a,1,2,1))].">
      <j1 rule="para" parents="5391 6423"/>
    </justification>
  </clause>

  <clause id="6456">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) \ 1) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(5391(a,1),6423(a,2,2))].">
      <j1 rule="para" parents="5391 6423"/>
    </justification>
  </clause>

  <clause id="6457">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,(z * u) \ T(z,y))
    ]]></literal>
    <justification jstring="[para(5441(a,1),6423(a,1,2,1))].">
      <j1 rule="para" parents="5441 6423"/>
    </justification>
  </clause>

  <clause id="6458">
    <literal><![CDATA[
      K(x,y \ z) * K(x * ((z \ y) \ 1),x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(6423(a,1),5556(a,1,1))].">
      <j1 rule="para" parents="6423 5556"/>
    </justification>
  </clause>

  <clause id="6459">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) \ 1) = L(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(6423(a,1),5947(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6423 5947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6460">
    <literal><![CDATA[
      T(x,y) != K(z,u \ y)
    ]]></literal>
    <literal><![CDATA[
      K(z,y / u) = x
    ]]></literal>
    <justification jstring="[para(6423(a,1),6022(a,2))].">
      <j1 rule="para" parents="6423 6022"/>
    </justification>
  </clause>

  <clause id="6461">
    <literal><![CDATA[
      K(x,R(y \ z,u,w) \ 1) = R(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(6423(a,1),6150(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6423 6150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6462">
    <literal><![CDATA[
      R(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(5113,a,6432,a)].">
      <j1 rule="hyper" parents="5113 6432"/>
    </justification>
  </clause>

  <clause id="6463">
    <literal><![CDATA[
      x \ (y * K(x \ y,z)) = T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(630,a,6432,a)].">
      <j1 rule="hyper" parents="630 6432"/>
    </justification>
  </clause>

  <clause id="6464">
    <literal><![CDATA[
      (x * K(y,z)) / T(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(608,a,6432,a)].">
      <j1 rule="hyper" parents="608 6432"/>
    </justification>
  </clause>

  <clause id="6465">
    <literal><![CDATA[
      (x / y) \ (x * K(y,z)) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(584,a,6432,a)].">
      <j1 rule="hyper" parents="584 6432"/>
    </justification>
  </clause>

  <clause id="6466">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) = T(z * x,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(451,a,xx,b,6432,a),flip(a)].">
      <j1 rule="hyper" parents="451 6432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6467">
    <literal><![CDATA[
      (x / y) * T(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(341,a,6432,a),flip(a)].">
      <j1 rule="hyper" parents="341 6432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6469">
    <literal><![CDATA[
      K(x,y) * (z * T(y,x)) = T(z * y,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(246,a,6432,a,b,5394,a),flip(a)].">
      <j1 rule="hyper" parents="246 6432 5394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6470">
    <literal><![CDATA[
      (x * y) \ (x * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,6432,a)].">
      <j1 rule="hyper" parents="123 6432"/>
    </justification>
  </clause>

  <clause id="6472">
    <literal><![CDATA[
      T((x * y) / T(z,y),z) = z \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(451,a,6432,a(flip),b,6370,a)].">
      <j1 rule="hyper" parents="451 6432 6370"/>
    </justification>
  </clause>

  <clause id="6473">
    <literal><![CDATA[
      x * T(x \ y,z) != y * u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(6432(a,1),336(a,1)),flip(b)].">
      <j1 rule="para" parents="6432 336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6474">
    <literal><![CDATA[
      (x / y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6432(a,1),341(a,1))].">
      <j1 rule="para" parents="6432 341"/>
    </justification>
  </clause>

  <clause id="6475">
    <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),6432(a,1,1))].">
      <j1 rule="para" parents="80 6432"/>
    </justification>
  </clause>

  <clause id="6476">
    <literal><![CDATA[
      R(x,T(y,x),K(x,z)) \ (y * T(x,z)) = T(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(6432(a,1),516(a,1,2))].">
      <j1 rule="para" parents="6432 516"/>
    </justification>
  </clause>

  <clause id="6477">
    <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(6432(a,1),554(a,1,2))].">
      <j1 rule="para" parents="6432 554"/>
    </justification>
  </clause>

  <clause id="6478">
    <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(6432(a,1),522(a,1,1))].">
      <j1 rule="para" parents="6432 522"/>
    </justification>
  </clause>

  <clause id="6480">
    <literal><![CDATA[
      K(x,y) * T(y * x,z) = (x * y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(4990(a,1),6432(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4990 6432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6481">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * y) * z) = T(z,y)
    ]]></literal>
    <justification jstring="[para(6432(a,1),6361(a,1,1))].">
      <j1 rule="para" parents="6432 6361"/>
    </justification>
  </clause>

  <clause id="6482">
    <literal><![CDATA[
      (x * T(y,z)) * T(z,y) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(6432(a,1),6362(a,1,1))].">
      <j1 rule="para" parents="6432 6362"/>
    </justification>
  </clause>

  <clause id="6483">
    <literal><![CDATA[
      (x / T(y,z)) * T(y,u) = (x * K(z,y)) * K(y,u)
    ]]></literal>
    <justification jstring="[para(6370(a,1),6432(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6370 6432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6484">
    <literal><![CDATA[
      (x * y) * (z * K(y,z)) = (x * T(y,z)) * z
    ]]></literal>
    <justification jstring="[para(6432(a,1),6351(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6432 6351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6492">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5031(a,1),6433(a,1))].">
      <j1 rule="para" parents="5031 6433"/>
    </justification>
  </clause>

  <clause id="6493">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(5953(a,1),6437(a,1))].">
      <j1 rule="para" parents="5953 6437"/>
    </justification>
  </clause>

  <clause id="6494">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ (y * z)) = K(x,1 / L(u,z,y))
    ]]></literal>
    <justification jstring="[para(13(a,2),6438(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13 6438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6495">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(75(a,1),6438(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 6438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6496">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = z * K(z * (x \ y),y \ x)
    ]]></literal>
    <justification jstring="[para(6438(a,1),6129(a,2,2))].">
      <j1 rule="para" parents="6438 6129"/>
    </justification>
  </clause>

  <clause id="6498">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = K(z \ y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(334,a,5058,a(flip),b,6439,a),flip(a)].">
      <j1 rule="hyper" parents="334 5058 6439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6499">
    <literal><![CDATA[
      (1 / (x \ y)) * T(z,y \ x) = z * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(119,a,6439,a(flip),b,3107,a)].">
      <j1 rule="hyper" parents="119 6439 3107"/>
    </justification>
  </clause>

  <clause id="6500">
    <literal><![CDATA[
      ((x \ y) \ 1) * T(z,y \ x) = z * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,6439,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 6439 17"/>
    </justification>
  </clause>

  <clause id="6501">
    <literal><![CDATA[
      T(x,(y * z) \ y) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),6439(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 6439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6502">
    <literal><![CDATA[
      T(x,((y * z) \ y) \ 1) = T(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6439(a,2,2))].">
      <j1 rule="para" parents="4 6439"/>
    </justification>
  </clause>

  <clause id="6504">
    <literal><![CDATA[
      T(x,y \ (y / z)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),6439(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 6439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6505">
    <literal><![CDATA[
      T(x \ y,y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ 1) \ 1 = z
    ]]></literal>
    <justification jstring="[para(6439(a,1),439(a,1))].">
      <j1 rule="para" parents="6439 439"/>
    </justification>
  </clause>

  <clause id="6506">
    <literal><![CDATA[
      T(x,y \ z) / ((z \ y) \ x) = x / ((x \ ((z \ y) \ x)) * x)
    ]]></literal>
    <justification jstring="[para(6439(a,1),4656(a,1,1))].">
      <j1 rule="para" parents="6439 4656"/>
    </justification>
  </clause>

  <clause id="6507">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(72(a,1),6440(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6508">
    <literal><![CDATA[
      T(x,K(y,x / z)) = T(x,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(6440(a,1),4473(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6440 4473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6509">
    <literal><![CDATA[
      T(K(x / (y / z),y / z),y) = K(x * (1 / (y / z)),z \ y)
    ]]></literal>
    <justification jstring="[para(6121(a,1),6440(a,1,1))].">
      <j1 rule="para" parents="6121 6440"/>
    </justification>
  </clause>

  <clause id="6511">
    <literal><![CDATA[
      (((x * y) \ x) * z) * K(z,y \ 1) = z * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,6441,a(flip),b,11,a(flip))].">
      <j1 rule="hyper" parents="119 6441 11"/>
    </justification>
  </clause>

  <clause id="6516">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) = x
    ]]></literal>
    <justification jstring="[hyper(32,a,6379,a(flip),b,6464,a),flip(a)].">
      <j1 rule="hyper" parents="32 6379 6464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6517">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(32,a,1475,a(flip),b,6464,a),flip(a)].">
      <j1 rule="hyper" parents="32 1475 6464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6518">
    <literal><![CDATA[
      (x / y) * ((y \ z) \ z) = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[para(6464(a,1),381(a,1,1))].">
      <j1 rule="para" parents="6464 381"/>
    </justification>
  </clause>

  <clause id="6519">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(451,a,xx,b,6516,a)].">
      <j1 rule="hyper" parents="451 6516"/>
    </justification>
  </clause>

  <clause id="6520">
    <literal><![CDATA[
      x / K(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(341,a,6516,a),flip(a)].">
      <j1 rule="hyper" parents="341 6516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6522">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(246,a,6516,a,b,5394,a)].">
      <j1 rule="hyper" parents="246 6516 5394"/>
    </justification>
  </clause>

  <clause id="6523">
    <literal><![CDATA[
      (x * K(y,z)) \ x = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,6516,a)].">
      <j1 rule="hyper" parents="123 6516"/>
    </justification>
  </clause>

  <clause id="6524">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(30,a,5896,a,b,6516,a),flip(a)].">
      <j1 rule="hyper" parents="30 5896 6516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6525">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * K(y,x) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,2065,a,b,6516,a),flip(a)].">
      <j1 rule="hyper" parents="30 2065 6516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6526">
    <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(6516(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6516 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6527">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      u * K(z,y) = x
    ]]></literal>
    <justification jstring="[para(6516(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="6516 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6528">
    <literal><![CDATA[
      (x * K(y,z)) \ x != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(6516(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6516 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6529">
    <literal><![CDATA[
      x / K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(z,y) = u
    ]]></literal>
    <justification jstring="[para(6516(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6516 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6530">
    <literal><![CDATA[
      x * L(y,K(z,u),x * K(u,z)) = (x * K(u,z)) * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(6516(a,1),90(a,1,1))].">
      <j1 rule="para" parents="6516 90"/>
    </justification>
  </clause>

  <clause id="6531">
    <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(6516(a,1),495(a,1,1))].">
      <j1 rule="para" parents="6516 495"/>
    </justification>
  </clause>

  <clause id="6532">
    <literal><![CDATA[
      (x * K(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(6516(a,1),6362(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6516 6362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6533">
    <literal><![CDATA[
      (x * K(y,z)) * (y * K(z,y)) = x * y
    ]]></literal>
    <justification jstring="[para(6516(a,1),6351(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6516 6351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6534">
    <literal><![CDATA[
      T(x,K(y,z)) / K(y,z) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(334,a,5896,a(flip),b,6520,a),flip(a)].">
      <j1 rule="hyper" parents="334 5896 6520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6535">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5911,a,b,6520,a)].">
      <j1 rule="hyper" parents="58 5911 6520"/>
    </justification>
  </clause>

  <clause id="6536">
    <literal><![CDATA[
      T(K(x,y) \ z,K(y,x)) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5894,a,b,6520,a)].">
      <j1 rule="hyper" parents="58 5894 6520"/>
    </justification>
  </clause>

  <clause id="6537">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(6520(a,1),259(a,1,1))].">
      <j1 rule="para" parents="6520 259"/>
    </justification>
  </clause>

  <clause id="6539">
    <literal><![CDATA[
      x / K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y)) = K(z,y) \ u
    ]]></literal>
    <justification jstring="[para(6520(a,2),286(a,1))].">
      <j1 rule="para" parents="6520 286"/>
    </justification>
  </clause>

  <clause id="6540">
    <literal><![CDATA[
      R((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(6520(a,1),314(a,1,1))].">
      <j1 rule="para" parents="6520 314"/>
    </justification>
  </clause>

  <clause id="6541">
    <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(6520(a,1),641(a,1,1,1))].">
      <j1 rule="para" parents="6520 641"/>
    </justification>
  </clause>

  <clause id="6542">
    <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(6520(a,1),641(a,1,1))].">
      <j1 rule="para" parents="6520 641"/>
    </justification>
  </clause>

  <clause id="6543">
    <literal><![CDATA[
      ((K(x,y) / z) * (z * K(y,x))) \ (K(x,y) / z) = 1 / (z / K(x,y))
    ]]></literal>
    <justification jstring="[para(6520(a,1),2122(a,1,1,2))].">
      <j1 rule="para" parents="6520 2122"/>
    </justification>
  </clause>

  <clause id="6545">
    <literal><![CDATA[
      K(x,1 / (K(y,z) / u)) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(6520(a,1),5620(a,2,2))].">
      <j1 rule="para" parents="6520 5620"/>
    </justification>
  </clause>

  <clause id="6546">
    <literal><![CDATA[
      (x * K(L(y \ 1,z,u) \ 1,w)) \ x = L(K(w,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,5950,a(flip),b,6523,a),flip(a)].">
      <j1 rule="hyper" parents="334 5950 6523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6547">
    <literal><![CDATA[
      K(x,y) != 1
    ]]></literal>
    <literal><![CDATA[
      z * K(y,x) = z
    ]]></literal>
    <justification jstring="[para(6523(a,1),169(a,1)),flip(b)].">
      <j1 rule="para" parents="6523 169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6548">
    <literal><![CDATA[
      ((x * K(y,z)) \ x) \ u = K(y,z) * u
    ]]></literal>
    <justification jstring="[para(6523(a,2),5391(a,1,1))].">
      <j1 rule="para" parents="6523 5391"/>
    </justification>
  </clause>

  <clause id="6549">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ K(x,y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(5556(a,1),6523(a,1,1))].">
      <j1 rule="para" parents="5556 6523"/>
    </justification>
  </clause>

  <clause id="6550">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ K(x * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(5749(a,1),6523(a,1,1))].">
      <j1 rule="para" parents="5749 6523"/>
    </justification>
  </clause>

  <clause id="6551">
    <literal><![CDATA[
      (x * (y * K(z,y))) \ (x * y) = K(y,z)
    ]]></literal>
    <justification jstring="[para(6352(a,1),6523(a,1,1))].">
      <j1 rule="para" parents="6352 6523"/>
    </justification>
  </clause>

  <clause id="6552">
    <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(6465(a,1),1058(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6465 1058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6553">
    <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(6465(a,1),5792(a,1,2))].">
      <j1 rule="para" parents="6465 5792"/>
    </justification>
  </clause>

  <clause id="6554">
    <literal><![CDATA[
      T(x,y * (1 / x)) = T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(6114,a,6467,a),flip(a)].">
      <j1 rule="hyper" parents="6114 6467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6555">
    <literal><![CDATA[
      (x * T(y,z)) / y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(1486,a,6467,a)].">
      <j1 rule="hyper" parents="1486 6467"/>
    </justification>
  </clause>

  <clause id="6556">
    <literal><![CDATA[
      (x * K(y,z)) / (x / y) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(117,a,6467,a(flip),b,468,a)].">
      <j1 rule="hyper" parents="117 6467 468"/>
    </justification>
  </clause>

  <clause id="6557">
    <literal><![CDATA[
      x * K(y \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(6467(a,1),359(a,1))].">
      <j1 rule="para" parents="6467 359"/>
    </justification>
  </clause>

  <clause id="6558">
    <literal><![CDATA[
      T(x * K(y,z),y) = y \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[para(6467(a,1),1464(a,1,1))].">
      <j1 rule="para" parents="6467 1464"/>
    </justification>
  </clause>

  <clause id="6559">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x / y = u
    ]]></literal>
    <justification jstring="[para(6467(a,1),1481(a,1))].">
      <j1 rule="para" parents="6467 1481"/>
    </justification>
  </clause>

  <clause id="6560">
    <literal><![CDATA[
      (x * y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6470(a,1),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6470 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6563">
    <literal><![CDATA[
      (x * (y / x)) \ (K(x,x \ y) * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(5048(a,1),6470(a,1,1))].">
      <j1 rule="para" parents="5048 6470"/>
    </justification>
  </clause>

  <clause id="6564">
    <literal><![CDATA[
      T(x,y \ (y / z)) = T(x,1 / z)
    ]]></literal>
    <justification jstring="[hyper(118,a,6495,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 6495 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6565">
    <literal><![CDATA[
      K(x,y \ (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(6495(a,2),5334(a,1))].">
      <j1 rule="para" parents="6495 5334"/>
    </justification>
  </clause>

  <clause id="6566">
    <literal><![CDATA[
      T(x * y,y \ 1) = ((x * y) \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(439,a,6501,a),flip(a)].">
      <j1 rule="hyper" parents="439 6501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6567">
    <literal><![CDATA[
      ((x * y) \ x) * T(z,y \ 1) = z * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,6501,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 6501 17"/>
    </justification>
  </clause>

  <clause id="6569">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * T(z,y) = z * (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(119,a,6502,a(flip),b,3107,a)].">
      <j1 rule="hyper" parents="119 6502 3107"/>
    </justification>
  </clause>

  <clause id="6571">
    <literal><![CDATA[
      T(x,L(y \ 1,y,z) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(221(a,2),6502(a,1,2,1))].">
      <j1 rule="para" parents="221 6502"/>
    </justification>
  </clause>

  <clause id="6572">
    <literal><![CDATA[
      T(x,y \ (y / z)) = T(x,(z \ u) / u)
    ]]></literal>
    <justification jstring="[hyper(334,a,4713,a,b,6504,a),flip(a)].">
      <j1 rule="hyper" parents="334 4713 6504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6575">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(1995,a,6507,a)].">
      <j1 rule="hyper" parents="1995 6507"/>
    </justification>
  </clause>

  <clause id="6576">
    <literal><![CDATA[
      K(x,T(y,z / y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(4533(a,2),6507(a,1,2))].">
      <j1 rule="para" parents="4533 6507"/>
    </justification>
  </clause>

  <clause id="6577">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4513(a,2),6507(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4513 6507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6578">
    <literal><![CDATA[
      T(x / T(y,z),K(y,z)) = K(z,y) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(246,a,6517,a,b,5394,a)].">
      <j1 rule="hyper" parents="246 6517 5394"/>
    </justification>
  </clause>

  <clause id="6579">
    <literal><![CDATA[
      (x / (y \ z)) * K(z / y,y) = x / (z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),6517(a,1,1,2))].">
      <j1 rule="para" parents="107 6517"/>
    </justification>
  </clause>

  <clause id="6580">
    <literal><![CDATA[
      (1 / x) * K(x,y) = K(x,y) / x
    ]]></literal>
    <justification jstring="[para(5021(a,1),6517(a,1,1))].">
      <j1 rule="para" parents="5021 6517"/>
    </justification>
  </clause>

  <clause id="6581">
    <literal><![CDATA[
      (x * K(y,x)) * K(y,x) = (T(y,x) * x) / y
    ]]></literal>
    <justification jstring="[para(5140(a,1),6517(a,1,1))].">
      <j1 rule="para" parents="5140 6517"/>
    </justification>
  </clause>

  <clause id="6582">
    <literal><![CDATA[
      (x * K(y,z)) / y = (x / y) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6464(a,1),6517(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6464 6517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6583">
    <literal><![CDATA[
      R(x,K(y,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(5124,a,6532,a)].">
      <j1 rule="hyper" parents="5124 6532"/>
    </justification>
  </clause>

  <clause id="6585">
    <literal><![CDATA[
      (x * K(y,z)) * y = (x * y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,6432,a,b,6532,a),flip(a)].">
      <j1 rule="hyper" parents="334 6432 6532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6586">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * y = T(y,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,2530,a,b,6532,a),flip(a)].">
      <j1 rule="hyper" parents="334 2530 6532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6588">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * T(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,6532,a)].">
      <j1 rule="hyper" parents="123 6532"/>
    </justification>
  </clause>

  <clause id="6589">
    <literal><![CDATA[
      (x * K(y,z)) \ ((x * y) * K(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,6432,a,b,6532,a)].">
      <j1 rule="hyper" parents="116 6432 6532"/>
    </justification>
  </clause>

  <clause id="6590">
    <literal><![CDATA[
      ((x / y) * K(y,z)) \ (x * K(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,6467,a(flip),b,6532,a)].">
      <j1 rule="hyper" parents="116 6467 6532"/>
    </justification>
  </clause>

  <clause id="6591">
    <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,461,a(flip),b,6532,a)].">
      <j1 rule="hyper" parents="116 461 6532"/>
    </justification>
  </clause>

  <clause id="6592">
    <literal><![CDATA[
      (x * y) * K(T(x,y),z) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(30,a,1402,a,b,6532,a),flip(a)].">
      <j1 rule="hyper" parents="30 1402 6532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6593">
    <literal><![CDATA[
      (x * (y * T(z,u))) \ ((x * (y * K(z,u))) * z) = a(x,y * K(z,u),z)
    ]]></literal>
    <justification jstring="[para(6532(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6532 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6594">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) = (y * T(x,z)) \ (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(6532(a,1),221(a,2,1))].">
      <j1 rule="para" parents="6532 221"/>
    </justification>
  </clause>

  <clause id="6595">
    <literal><![CDATA[
      x \ (y * T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y * K(x,z),x) = u
    ]]></literal>
    <justification jstring="[para(6532(a,1),298(a,1,2))].">
      <j1 rule="para" parents="6532 298"/>
    </justification>
  </clause>

  <clause id="6596">
    <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(6532(a,1),495(a,1,2,2))].">
      <j1 rule="para" parents="6532 495"/>
    </justification>
  </clause>

  <clause id="6597">
    <literal><![CDATA[
      (T(x,y) \ 1) * y = (x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(5069(a,1),6532(a,1,1))].">
      <j1 rule="para" parents="5069 6532"/>
    </justification>
  </clause>

  <clause id="6598">
    <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(6532(a,1),5753(a,1,2,1))].">
      <j1 rule="para" parents="6532 5753"/>
    </justification>
  </clause>

  <clause id="6599">
    <literal><![CDATA[
      (x * (y * K(z,y))) * z = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(6352(a,1),6532(a,1,1))].">
      <j1 rule="para" parents="6352 6532"/>
    </justification>
  </clause>

  <clause id="6600">
    <literal><![CDATA[
      R(x * K(y,z),K(u,w),u) = (x * z) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,6365,a,b,6583,a),flip(a)].">
      <j1 rule="hyper" parents="334 6365 6583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6601">
    <literal><![CDATA[
      T(x,(y / (1 / x)) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),6554(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 6554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6602">
    <literal><![CDATA[
      (x * K(y,z)) * y != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6555(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6555 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6603">
    <literal><![CDATA[
      T(K(x,y),y * z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),6575(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 6575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6604">
    <literal><![CDATA[
      (K(x,y) / x) * L(z,K(x,y),x \ 1) = (1 / x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(6580(a,1),3836(a,1,1))].">
      <j1 rule="para" parents="6580 3836"/>
    </justification>
  </clause>

  <clause id="6605">
    <literal><![CDATA[
      L(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(5123,a,6588,a)].">
      <j1 rule="hyper" parents="5123 6588"/>
    </justification>
  </clause>

  <clause id="6606">
    <literal><![CDATA[
      (x * K(y,z)) * L(y,u,w) = x * (K(y,z) * L(y,u,w))
    ]]></literal>
    <justification jstring="[para(6605(a,1),458(a,1,2,1))].">
      <j1 rule="para" parents="6605 458"/>
    </justification>
  </clause>

  <clause id="6608">
    <literal><![CDATA[
      L(x * y,K(y * x,z),u) = (y \ (y * x)) * y
    ]]></literal>
    <justification jstring="[para(6605(a,1),3672(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6605 3672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6609">
    <literal><![CDATA[
      L(x,x \ T(x,y),z) = x
    ]]></literal>
    <justification jstring="[para(4995(a,1),6605(a,1,2))].">
      <j1 rule="para" parents="4995 6605"/>
    </justification>
  </clause>

  <clause id="6612">
    <literal><![CDATA[
      (x * y) * K(z,T(x,y)) = K(z,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,6603,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 6603 17"/>
    </justification>
  </clause>

  <clause id="6613">
    <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(6603(a,1),5909(a,1,2))].">
      <j1 rule="para" parents="6603 5909"/>
    </justification>
  </clause>

  <clause id="6614">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(221(a,1),6426(a,1,1,1))].">
      <j1 rule="para" parents="221 6426"/>
    </justification>
  </clause>

  <clause id="6615">
    <literal><![CDATA[
      K((x \ y) \ 1,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(401(a,1),6426(a,1,1,1))].">
      <j1 rule="para" parents="401 6426"/>
    </justification>
  </clause>

  <clause id="6620">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,z) = ((x * y) \ x) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,6614,a(flip),b,5011,a),flip(a)].">
      <j1 rule="hyper" parents="116 6614 5011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6621">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * K(y,z) = T(1 / ((x * y) \ x),z)
    ]]></literal>
    <justification jstring="[para(6614(a,1),5027(a,1,2))].">
      <j1 rule="para" parents="6614 5027"/>
    </justification>
  </clause>

  <clause id="6622">
    <literal><![CDATA[
      K(1 / (x \ y),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(5546,a,6615,a)].">
      <j1 rule="hyper" parents="5546 6615"/>
    </justification>
  </clause>

  <clause id="6623">
    <literal><![CDATA[
      K((x \ y) \ 1,(z \ u) \ 1) = K(y \ x,u \ z)
    ]]></literal>
    <justification jstring="[hyper(334,a,6423,a(flip),b,6615,a),flip(a)].">
      <j1 rule="hyper" parents="334 6423 6615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6624">
    <literal><![CDATA[
      T(K(x / y,z),x) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5804,a,b,6615,a)].">
      <j1 rule="hyper" parents="58 5804 6615"/>
    </justification>
  </clause>

  <clause id="6625">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((y / z) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5797,a,b,6615,a)].">
      <j1 rule="hyper" parents="58 5797 6615"/>
    </justification>
  </clause>

  <clause id="6627">
    <literal><![CDATA[
      K((x \ (y * z)) \ 1,y) = K((y / (z \ 1)) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6317,a(flip),b,6615,a)].">
      <j1 rule="hyper" parents="58 6317 6615"/>
    </justification>
  </clause>

  <clause id="6628">
    <literal><![CDATA[
      (x \ y) \ K(y \ x,z) = T((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,6615,a(flip),b,5011,a)].">
      <j1 rule="hyper" parents="116 6615 5011"/>
    </justification>
  </clause>

  <clause id="6629">
    <literal><![CDATA[
      K((x * y) \ x,z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6615(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 6615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6630">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K((x * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(17(a,2),6615(a,1,1,1))].">
      <j1 rule="para" parents="17 6615"/>
    </justification>
  </clause>

  <clause id="6634">
    <literal><![CDATA[
      K((K(x,y) * z) \ 1,u) = K(z \ K(y,x),u)
    ]]></literal>
    <justification jstring="[para(5391(a,1),6615(a,1,1,1))].">
      <j1 rule="para" parents="5391 6615"/>
    </justification>
  </clause>

  <clause id="6636">
    <literal><![CDATA[
      (x * K(y \ x,z)) / y = T(x / y,z)
    ]]></literal>
    <justification jstring="[para(6615(a,1),5806(a,1,1,2))].">
      <j1 rule="para" parents="6615 5806"/>
    </justification>
  </clause>

  <clause id="6637">
    <literal><![CDATA[
      (((x \ y) * z) \ z) * ((x \ y) * z) = z * K(y \ x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[para(6615(a,1),5715(a,2,2))].">
      <j1 rule="para" parents="6615 5715"/>
    </justification>
  </clause>

  <clause id="6638">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(6615(a,1),5801(a,2,2))].">
      <j1 rule="para" parents="6615 5801"/>
    </justification>
  </clause>

  <clause id="6639">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = z * K(y \ x,z * (x \ y))
    ]]></literal>
    <justification jstring="[para(6615(a,1),6100(a,2,2))].">
      <j1 rule="para" parents="6615 6100"/>
    </justification>
  </clause>

  <clause id="6640">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(6615(a,1),5434(a,1,2))].">
      <j1 rule="para" parents="6615 5434"/>
    </justification>
  </clause>

  <clause id="6641">
    <literal><![CDATA[
      x * K((y * z) \ x,y) = z * ((y \ (z \ x)) * y)
    ]]></literal>
    <justification jstring="[para(6615(a,1),5800(a,1,2))].">
      <j1 rule="para" parents="6615 5800"/>
    </justification>
  </clause>

  <clause id="6642">
    <literal><![CDATA[
      x * K((y * z) \ x,z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(6615(a,1),6287(a,1,2))].">
      <j1 rule="para" parents="6615 6287"/>
    </justification>
  </clause>

  <clause id="6643">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(y * K(x \ y,z),y)
    ]]></literal>
    <justification jstring="[para(6615(a,1),5807(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6615 5807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6644">
    <literal><![CDATA[
      K(x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(6622(a,1),3445(a,1))].">
      <j1 rule="para" parents="6622 3445"/>
    </justification>
  </clause>

  <clause id="6645">
    <literal><![CDATA[
      K(1 / L(x \ y,z,u),w) = L(K(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[para(6622(a,1),5961(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6622 5961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6646">
    <literal><![CDATA[
      K(x,K(y,x / z)) * K(x / z,y) = K(z \ x,y)
    ]]></literal>
    <justification jstring="[hyper(5924,a,6624,a)].">
      <j1 rule="hyper" parents="5924 6624"/>
    </justification>
  </clause>

  <clause id="6647">
    <literal><![CDATA[
      K(x / y,x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(2547,a,6624,a)].">
      <j1 rule="hyper" parents="2547 6624"/>
    </justification>
  </clause>

  <clause id="6648">
    <literal><![CDATA[
      K(L(x,y,z) / u,x) = K(u \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2575,a(flip),b,6624,a)].">
      <j1 rule="hyper" parents="58 2575 6624"/>
    </justification>
  </clause>

  <clause id="6649">
    <literal><![CDATA[
      K(x / y,z) * x = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,6624,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 6624 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6650">
    <literal><![CDATA[
      T(x,y) != K(z \ y,u)
    ]]></literal>
    <literal><![CDATA[
      K(y / z,u) = x
    ]]></literal>
    <justification jstring="[para(6624(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="6624 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6651">
    <literal><![CDATA[
      K((x \ y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(72(a,1),6624(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 6624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6652">
    <literal><![CDATA[
      K((x \ y) \ y,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),6647(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 6647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6654">
    <literal><![CDATA[
      K((x * (y \ 1)) \ x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,3448,a(flip),b,6629,a),flip(a)].">
      <j1 rule="hyper" parents="334 3448 6629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6657">
    <literal><![CDATA[
      K(T(x,x \ y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(106(a,2),6651(a,1,1))].">
      <j1 rule="para" parents="106 6651"/>
    </justification>
  </clause>

  <clause id="6658">
    <literal><![CDATA[
      K((x \ y) \ y,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(6651(a,2),2547(a,1))].">
      <j1 rule="para" parents="6651 2547"/>
    </justification>
  </clause>

  <clause id="6659">
    <literal><![CDATA[
      K(L(x,x \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3449,a,b,6654,a)].">
      <j1 rule="hyper" parents="58 3449 6654"/>
    </justification>
  </clause>

  <clause id="6660">
    <literal><![CDATA[
      L(K(L(x,x \ 1,y),z),L(x,x \ 1,y),u) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(6431,a,6659,a)].">
      <j1 rule="hyper" parents="6431 6659"/>
    </justification>
  </clause>

  <clause id="6662">
    <literal><![CDATA[
      K(x,L(y,y \ 1,z)) = 1 / K(y,x)
    ]]></literal>
    <justification jstring="[para(6659(a,1),5243(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6659 5243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6663">
    <literal><![CDATA[
      K(x \ (x * y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6428(a,1),3811(a,1))].">
      <j1 rule="para" parents="6428 3811"/>
    </justification>
  </clause>

  <clause id="6664">
    <literal><![CDATA[
      (x \ K(y,x)) \ (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3294(a,1),6528(a,1,1))].">
      <j1 rule="para" parents="3294 6528"/>
    </justification>
  </clause>

  <clause id="6665">
    <literal><![CDATA[
      (x * (y * K(z,y))) \ (x * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6352(a,1),6528(a,1,1))].">
      <j1 rule="para" parents="6352 6528"/>
    </justification>
  </clause>

  <clause id="6666">
    <literal><![CDATA[
      T(K(x,y) \ z,K(y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(5894(a,2),6529(a,1))].">
      <j1 rule="para" parents="5894 6529"/>
    </justification>
  </clause>

  <clause id="6667">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5911(a,2),6529(a,1))].">
      <j1 rule="para" parents="5911 6529"/>
    </justification>
  </clause>

  <clause id="6668">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x / K(z,y) = u
    ]]></literal>
    <justification jstring="[para(7(a,1),6537(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7 6537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6669">
    <literal><![CDATA[
      K(x,L(y,y \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5243,a(flip),b,6662,a),flip(a)].">
      <j1 rule="hyper" parents="334 5243 6662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6670">
    <literal><![CDATA[
      K(x,L(y,y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6662(a,2),5248(a,1))].">
      <j1 rule="para" parents="6662 5248"/>
    </justification>
  </clause>

  <clause id="6671">
    <literal><![CDATA[
      K(x,L(1 / y,y,z)) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),6669(a,1,2,2))].">
      <j1 rule="para" parents="75 6669"/>
    </justification>
  </clause>

  <clause id="6672">
    <literal><![CDATA[
      K((x / y) \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(7(a,1),6663(a,1,1,2))].">
      <j1 rule="para" parents="7 6663"/>
    </justification>
  </clause>

  <clause id="6673">
    <literal><![CDATA[
      K(1 / ((x * y) \ x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6622(a,2),6663(a,1))].">
      <j1 rule="para" parents="6622 6663"/>
    </justification>
  </clause>

  <clause id="6675">
    <literal><![CDATA[
      x / T(x * (1 / y),y) = (x * (1 / y)) \ x
    ]]></literal>
    <justification jstring="[para(75(a,1),6390(a,1,2,2))].">
      <j1 rule="para" parents="75 6390"/>
    </justification>
  </clause>

  <clause id="6677">
    <literal><![CDATA[
      T(K(x \ 1,y) * y,K(x \ 1,y)) = x * ((y \ (x \ y)) * y)
    ]]></literal>
    <justification jstring="[hyper(246,a,6396,a(flip),b,6345,a)].">
      <j1 rule="hyper" parents="246 6396 6345"/>
    </justification>
  </clause>

  <clause id="6678">
    <literal><![CDATA[
      T(K(x * y,x),y) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(5689,a,6398,a)].">
      <j1 rule="hyper" parents="5689 6398"/>
    </justification>
  </clause>

  <clause id="6679">
    <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(6398(a,2),5227(a,1,1))].">
      <j1 rule="para" parents="6398 5227"/>
    </justification>
  </clause>

  <clause id="6680">
    <literal><![CDATA[
      K(x,K(y,y * x)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,6678,a(flip),b,5889,a),flip(a)].">
      <j1 rule="hyper" parents="115 6678 5889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6681">
    <literal><![CDATA[
      T(x,K(y,y * x)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,6680,a)].">
      <j1 rule="hyper" parents="51 6680"/>
    </justification>
  </clause>

  <clause id="6682">
    <literal><![CDATA[
      T(x,K(y,y * T(x,z))) = x
    ]]></literal>
    <justification jstring="[hyper(138,a,6681,a)].">
      <j1 rule="hyper" parents="138 6681"/>
    </justification>
  </clause>

  <clause id="6683">
    <literal><![CDATA[
      T(x \ y,K(x,y)) = x \ y
    ]]></literal>
    <justification jstring="[para(5(a,1),6681(a,1,2,2))].">
      <j1 rule="para" parents="5 6681"/>
    </justification>
  </clause>

  <clause id="6684">
    <literal><![CDATA[
      T(K(x,x * T(y,z)),y) = K(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(49,a,6682,a)].">
      <j1 rule="hyper" parents="49 6682"/>
    </justification>
  </clause>

  <clause id="6685">
    <literal><![CDATA[
      K(x,y) * (x \ y) = (x \ y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,6683,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 6683 17"/>
    </justification>
  </clause>

  <clause id="6687">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y = K(z,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(971(a,1),6402(a,1,1))].">
      <j1 rule="para" parents="971 6402"/>
    </justification>
  </clause>

  <clause id="6688">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ z)) = (y \ T(z,x)) \ (y \ z)
    ]]></literal>
    <justification jstring="[para(1030(a,1),6402(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1030 6402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6689">
    <literal><![CDATA[
      (((x \ (y / z)) * x) * z) \ y = K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[para(1150(a,1),6402(a,1,1))].">
      <j1 rule="para" parents="1150 6402"/>
    </justification>
  </clause>

  <clause id="6690">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(956(a,1),6402(a,1,1))].">
      <j1 rule="para" parents="956 6402"/>
    </justification>
  </clause>

  <clause id="6691">
    <literal><![CDATA[
      ((x * T(x \ y,z)) * u) \ (y * u) = K(z,(x * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(1584(a,1),6402(a,1,1))].">
      <j1 rule="para" parents="1584 6402"/>
    </justification>
  </clause>

  <clause id="6692">
    <literal><![CDATA[
      T(x * T(x \ y,z),u) \ T(y,u) = K(z,T(x,u) \ T(y,u))
    ]]></literal>
    <justification jstring="[para(2025(a,1),6402(a,1,1))].">
      <j1 rule="para" parents="2025 6402"/>
    </justification>
  </clause>

  <clause id="6693">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z = K(y,(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(4881(a,1),6402(a,1,1))].">
      <j1 rule="para" parents="4881 6402"/>
    </justification>
  </clause>

  <clause id="6694">
    <literal><![CDATA[
      x / ((y * z) / y) = (x / z) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6527,a,6410,a),flip(a)].">
      <j1 rule="hyper" parents="6527 6410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6695">
    <literal><![CDATA[
      (x / (y / z)) * K(z,z \ y) = x / (z \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6410(a,1,1,2,1))].">
      <j1 rule="para" parents="5 6410"/>
    </justification>
  </clause>

  <clause id="6696">
    <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(6410(a,1),1007(a,2,1,2))].">
      <j1 rule="para" parents="6410 1007"/>
    </justification>
  </clause>

  <clause id="6698">
    <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(6410(a,1),4851(a,1,2,1))].">
      <j1 rule="para" parents="6410 4851"/>
    </justification>
  </clause>

  <clause id="6699">
    <literal><![CDATA[
      (x / (y \ z)) * (z / y) = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[para(5041(a,1),6412(a,1,2))].">
      <j1 rule="para" parents="5041 6412"/>
    </justification>
  </clause>

  <clause id="6700">
    <literal><![CDATA[
      (x * ((y * z) / y)) * K(z,y) = x * z
    ]]></literal>
    <justification jstring="[hyper(6527,a,6413,a)].">
      <j1 rule="hyper" parents="6527 6413"/>
    </justification>
  </clause>

  <clause id="6701">
    <literal><![CDATA[
      (x * ((y * z) / y)) * y = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[para(6413(a,1),6532(a,1,1))].">
      <j1 rule="para" parents="6413 6532"/>
    </justification>
  </clause>

  <clause id="6702">
    <literal><![CDATA[
      (x / (y * K(z,y))) * y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,6520,a(flip),b,6414,a),flip(a)].">
      <j1 rule="hyper" parents="334 6520 6414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6704">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) = z \ (y * (x * T(x \ (y \ z),u)))
    ]]></literal>
    <justification jstring="[para(6427(a,1),502(a,1,1))].">
      <j1 rule="para" parents="6427 502"/>
    </justification>
  </clause>

  <clause id="6705">
    <literal><![CDATA[
      x \ (y \ T(y * x,z)) = K((y \ 1) \ x,z)
    ]]></literal>
    <justification jstring="[para(971(a,1),6427(a,1,2))].">
      <j1 rule="para" parents="971 6427"/>
    </justification>
  </clause>

  <clause id="6706">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) = K((y \ z) \ x,z)
    ]]></literal>
    <justification jstring="[para(1005(a,1),6427(a,1,2))].">
      <j1 rule="para" parents="1005 6427"/>
    </justification>
  </clause>

  <clause id="6709">
    <literal><![CDATA[
      x * (y * K((x \ z) \ y,z)) = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,6430,a(flip),b,1005,a(flip))].">
      <j1 rule="hyper" parents="119 6430 1005"/>
    </justification>
  </clause>

  <clause id="6711">
    <literal><![CDATA[
      (x * K(y \ x,z)) * (y \ 1) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(6430(a,1),1077(a,1,1))].">
      <j1 rule="para" parents="6430 1077"/>
    </justification>
  </clause>

  <clause id="6712">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6430(a,1),1089(a,1))].">
      <j1 rule="para" parents="6430 1089"/>
    </justification>
  </clause>

  <clause id="6714">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x \ y) = u
    ]]></literal>
    <justification jstring="[para(6430(a,2),6528(a,1,1))].">
      <j1 rule="para" parents="6430 6528"/>
    </justification>
  </clause>

  <clause id="6715">
    <literal><![CDATA[
      K((x \ y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(6453(a,2),5241(a,1))].">
      <j1 rule="para" parents="6453 5241"/>
    </justification>
  </clause>

  <clause id="6716">
    <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),6481(a,1,2))].">
      <j1 rule="para" parents="90 6481"/>
    </justification>
  </clause>

  <clause id="6718">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) = R(x,T(y,z),T(z,y))
    ]]></literal>
    <justification jstring="[hyper(117,a,6482,a(flip),b,4517,a)].">
      <j1 rule="hyper" parents="117 6482 4517"/>
    </justification>
  </clause>

  <clause id="6719">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(x,T(y,z),T(z,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,6482,a(flip),b,4520,a)].">
      <j1 rule="hyper" parents="116 6482 4520"/>
    </justification>
  </clause>

  <clause id="6721">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(6498(a,2),5136(a,1))].">
      <j1 rule="para" parents="6498 5136"/>
    </justification>
  </clause>

  <clause id="6722">
    <literal><![CDATA[
      T(x,K(y,(z / x) \ 1)) = T(x,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(5614(a,2),6508(a,1,2))].">
      <j1 rule="para" parents="5614 6508"/>
    </justification>
  </clause>

  <clause id="6723">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(6519(a,2),5426(a,1))].">
      <j1 rule="para" parents="6519 5426"/>
    </justification>
  </clause>

  <clause id="6724">
    <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(6522(a,1),109(a,2,1,1))].">
      <j1 rule="para" parents="6522 109"/>
    </justification>
  </clause>

  <clause id="6725">
    <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(6522(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6522 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6726">
    <literal><![CDATA[
      (K(x,y) \ z) * K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5391(a,2),6524(a,1,1))].">
      <j1 rule="para" parents="5391 6524"/>
    </justification>
  </clause>

  <clause id="6727">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) = (x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(5091(a,1),6524(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5091 6524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6728">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(5648,a,6533,a)].">
      <j1 rule="hyper" parents="5648 6533"/>
    </justification>
  </clause>

  <clause id="6729">
    <literal><![CDATA[
      x / (y * K(z,y)) = (x / y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,6533,a)].">
      <j1 rule="hyper" parents="117 7 6533"/>
    </justification>
  </clause>

  <clause id="6731">
    <literal><![CDATA[
      (K(x,y) * z) \ z = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(6534(a,1),4522(a,1,1))].">
      <j1 rule="para" parents="6534 4522"/>
    </justification>
  </clause>

  <clause id="6732">
    <literal><![CDATA[
      (x \ 1) * (((y * x) \ y) \ y) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,6566,a(flip),b,569,a)].">
      <j1 rule="hyper" parents="119 6566 569"/>
    </justification>
  </clause>

  <clause id="6733">
    <literal><![CDATA[
      T(x * (1 / y),y) = ((x * (1 / y)) \ x) \ x
    ]]></literal>
    <justification jstring="[para(75(a,1),6566(a,1,2))].">
      <j1 rule="para" parents="75 6566"/>
    </justification>
  </clause>

  <clause id="6734">
    <literal><![CDATA[
      T(x,y \ (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(6572(a,2),4714(a,1))].">
      <j1 rule="para" parents="6572 4714"/>
    </justification>
  </clause>

  <clause id="6736">
    <literal><![CDATA[
      R(T(x,y * K(x,z)),y,K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6589(a,1),1137(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6589 1137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6737">
    <literal><![CDATA[
      (x * K(y,z)) / y != u
    ]]></literal>
    <literal><![CDATA[
      (x / y) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6590(a,1),345(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6590 345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6738">
    <literal><![CDATA[
      (x * y) \ (T(x,z) * y) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(123,a,6592,a)].">
      <j1 rule="hyper" parents="123 6592"/>
    </justification>
  </clause>

  <clause id="6739">
    <literal><![CDATA[
      K(((x \ 1) * y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5813,a(flip),b,6630,a),flip(a)].">
      <j1 rule="hyper" parents="58 5813 6630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6741">
    <literal><![CDATA[
      K(x \ y,z) \ K(K(x \ y,z),y) = ((K(y / x,z) * y) / y) \ 1
    ]]></literal>
    <justification jstring="[para(6649(a,2),5179(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6649 5179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6742">
    <literal><![CDATA[
      x / ((x * y) / x) = K(y,x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(334,a,6388,a,b,6694,a),flip(a)].">
      <j1 rule="hyper" parents="334 6388 6694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6743">
    <literal><![CDATA[
      (x / (y \ z)) * K(y \ z,y) = x / (z / y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6694(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 6694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6744">
    <literal><![CDATA[
      x / (y / (y / z)) = (x / z) * K(z,y / z)
    ]]></literal>
    <justification jstring="[para(7(a,1),6694(a,1,2,1))].">
      <j1 rule="para" parents="7 6694"/>
    </justification>
  </clause>

  <clause id="6745">
    <literal><![CDATA[
      x / (y / (y / z)) = (x / z) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(4548(a,1),6694(a,1,2))].">
      <j1 rule="para" parents="4548 6694"/>
    </justification>
  </clause>

  <clause id="6746">
    <literal><![CDATA[
      K(x,((y / z) * K(z,u)) \ 1) = K(x,((u * z) / u) / y)
    ]]></literal>
    <justification jstring="[para(6694(a,1),5614(a,1,2,1))].">
      <j1 rule="para" parents="6694 5614"/>
    </justification>
  </clause>

  <clause id="6747">
    <literal><![CDATA[
      (x * (y / z)) * K(z \ y,z) = x * (z \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6700(a,1,1,2,1))].">
      <j1 rule="para" parents="5 6700"/>
    </justification>
  </clause>

  <clause id="6748">
    <literal><![CDATA[
      (x * (y / (y / z))) * K(z,z \ y) = x * z
    ]]></literal>
    <justification jstring="[para(4548(a,1),6700(a,1,1,2))].">
      <j1 rule="para" parents="4548 6700"/>
    </justification>
  </clause>

  <clause id="6749">
    <literal><![CDATA[
      (x / (y / z)) * (z \ y) = x * K(z \ y,z)
    ]]></literal>
    <justification jstring="[para(5041(a,1),6702(a,1,1,2))].">
      <j1 rule="para" parents="5041 6702"/>
    </justification>
  </clause>

  <clause id="6750">
    <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(6726(a,1),4855(a,1))].">
      <j1 rule="para" parents="6726 4855"/>
    </justification>
  </clause>

  <clause id="6754">
    <literal><![CDATA[
      x * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      (z * x) / T(T(z,x),y) = u
    ]]></literal>
    <justification jstring="[para(191(a,1),6380(a,1,1))].">
      <j1 rule="para" parents="191 6380"/>
    </justification>
  </clause>

  <clause id="6755">
    <literal><![CDATA[
      T(x,x \ T(x * y,y \ 1)) = T(x,L(y \ 1,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(6389(a,1),4431(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6389 4431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6756">
    <literal><![CDATA[
      x / T(x * (y / x),y \ x) = L((y / x) \ 1,y / x,x)
    ]]></literal>
    <justification jstring="[para(4887(a,1),6389(a,1,2))].">
      <j1 rule="para" parents="4887 6389"/>
    </justification>
  </clause>

  <clause id="6757">
    <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),6474(a,1,1))].">
      <j1 rule="para" parents="15 6474"/>
    </justification>
  </clause>

  <clause id="6758">
    <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),6493(a,1,2,1))].">
      <j1 rule="para" parents="92 6493"/>
    </justification>
  </clause>

  <clause id="6759">
    <literal><![CDATA[
      K(x,1 / (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(3700(a,2),6493(a,1))].">
      <j1 rule="para" parents="3700 6493"/>
    </justification>
  </clause>

  <clause id="6760">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(5391(a,1),6493(a,1,2,1))].">
      <j1 rule="para" parents="5391 6493"/>
    </justification>
  </clause>

  <clause id="6761">
    <literal><![CDATA[
      T(K(x,y / z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(6021(a,2),6493(a,1))].">
      <j1 rule="para" parents="6021 6493"/>
    </justification>
  </clause>

  <clause id="6762">
    <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(653(a,1),6560(a,1,1))].">
      <j1 rule="para" parents="653 6560"/>
    </justification>
  </clause>

  <clause id="6763">
    <literal><![CDATA[
      (x * y) * K(y * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * T(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(4990(a,1),6560(a,1,1))].">
      <j1 rule="para" parents="4990 6560"/>
    </justification>
  </clause>

  <clause id="6764">
    <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(6370(a,1),6560(a,1,1))].">
      <j1 rule="para" parents="6370 6560"/>
    </justification>
  </clause>

  <clause id="6765">
    <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(453(a,1),6565(a,1,2,2))].">
      <j1 rule="para" parents="453 6565"/>
    </justification>
  </clause>

  <clause id="6766">
    <literal><![CDATA[
      (x * ((y * z) / y)) * y != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6413(a,1),6602(a,1,1))].">
      <j1 rule="para" parents="6413 6602"/>
    </justification>
  </clause>

  <clause id="6767">
    <literal><![CDATA[
      K(1 / (x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5(a,1),6673(a,1,1,2,1))].">
      <j1 rule="para" parents="5 6673"/>
    </justification>
  </clause>

  <clause id="6769">
    <literal><![CDATA[
      T(K(x / y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5804(a,2),6715(a,1))].">
      <j1 rule="para" parents="5804 6715"/>
    </justification>
  </clause>

  <clause id="6770">
    <literal><![CDATA[
      x \ (y * (z * T(z \ (y \ x),u))) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * z) \ x,u) = w
    ]]></literal>
    <justification jstring="[para(5796(a,2),6715(a,1))].">
      <j1 rule="para" parents="5796 6715"/>
    </justification>
  </clause>

  <clause id="6771">
    <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),6721(a,1,2,1))].">
      <j1 rule="para" parents="17 6721"/>
    </justification>
  </clause>

  <clause id="6772">
    <literal><![CDATA[
      T(x,(y * z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(6(a,1),6734(a,1,2,2))].">
      <j1 rule="para" parents="6 6734"/>
    </justification>
  </clause>

  <clause id="6773">
    <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(3491(a,1),6761(a,1))].">
      <j1 rule="para" parents="3491 6761"/>
    </justification>
  </clause>

  <clause id="6774">
    <literal><![CDATA[
      K(x,K(x,y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(5901(a,1),6761(a,1))].">
      <j1 rule="para" parents="5901 6761"/>
    </justification>
  </clause>

  <clause id="6775">
    <literal><![CDATA[
      K(x / y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,x) = z
    ]]></literal>
    <justification jstring="[para(2521(a,1),6769(a,1))].">
      <j1 rule="para" parents="2521 6769"/>
    </justification>
  </clause>

  <clause id="6776">
    <literal><![CDATA[
      T(x,y) / ((y \ x) \ x) = T(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(30,a,4733,a(flip),b,6391,a),flip(a)].">
      <j1 rule="hyper" parents="30 4733 6391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6777">
    <literal><![CDATA[
      (T(x,y) \ y) * ((x \ y) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,6776,a)].">
      <j1 rule="hyper" parents="133 6776"/>
    </justification>
  </clause>

  <clause id="6778">
    <literal><![CDATA[
      (x * (y \ z)) / K(y \ z,y) = x * (z / y)
    ]]></literal>
    <justification jstring="[hyper(6668,a,6417,a)].">
      <j1 rule="hyper" parents="6668 6417"/>
    </justification>
  </clause>

  <clause id="6780">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,2360,a(flip),b,6424,a)].">
      <j1 rule="hyper" parents="334 2360 6424"/>
    </justification>
  </clause>

  <clause id="6781">
    <literal><![CDATA[
      T(x * y,K(y,z)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5375,a(flip),b,6466,a),flip(a)].">
      <j1 rule="hyper" parents="58 5375 6466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6782">
    <literal><![CDATA[
      (x * y) * K(y,T(x,z)) = T(y * x,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,6432,a,b,6781,a)].">
      <j1 rule="hyper" parents="334 6432 6781"/>
    </justification>
  </clause>

  <clause id="6783">
    <literal><![CDATA[
      x * T(y / x,T(x,z)) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),6781(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 6781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6784">
    <literal><![CDATA[
      T(x / y,T(y,z)) = y \ T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(123,a,6783,a),flip(a)].">
      <j1 rule="hyper" parents="123 6783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6785">
    <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(6784(a,2),4861(a,1))].">
      <j1 rule="para" parents="6784 4861"/>
    </justification>
  </clause>

  <clause id="6787">
    <literal><![CDATA[
      x * (K(y,x) * K(y,x)) = (T(y,x) * x) / y
    ]]></literal>
    <justification jstring="[hyper(5729,a,6581,a)].">
      <j1 rule="hyper" parents="5729 6581"/>
    </justification>
  </clause>

  <clause id="6788">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * T(y,x) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(6403,a,6586,a(flip))].">
      <j1 rule="hyper" parents="6403 6586"/>
    </justification>
  </clause>

  <clause id="6789">
    <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,6599,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="117 6599 101"/>
    </justification>
  </clause>

  <clause id="6790">
    <literal><![CDATA[
      ((x \ y) * z) * K(x,T(x \ y,z)) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(334,a,5682,a(flip),b,6612,a),flip(a)].">
      <j1 rule="hyper" parents="334 5682 6612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6793">
    <literal><![CDATA[
      K(T(K(x,y) * z,u) \ 1,w) = T(K(z \ K(y,x),w),u)
    ]]></literal>
    <justification jstring="[para(6634(a,1),5809(a,2,1))].">
      <j1 rule="para" parents="6634 5809"/>
    </justification>
  </clause>

  <clause id="6794">
    <literal><![CDATA[
      T(x,y) / (z \ x) = z * K(((z \ x) \ 1) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(4876,a,6638,a)].">
      <j1 rule="hyper" parents="4876 6638"/>
    </justification>
  </clause>

  <clause id="6795">
    <literal><![CDATA[
      K((x \ 1) \ y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,6398,a(flip),b,6638,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="29 6398 6638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6796">
    <literal><![CDATA[
      (x * K((y \ 1) \ x,z)) * y = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(6638(a,1),4820(a,1,1))].">
      <j1 rule="para" parents="6638 4820"/>
    </justification>
  </clause>

  <clause id="6797">
    <literal><![CDATA[
      T(x * K((y \ 1) \ x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(6638(a,1),4830(a,1,1))].">
      <j1 rule="para" parents="6638 4830"/>
    </justification>
  </clause>

  <clause id="6798">
    <literal><![CDATA[
      K((x \ 1) * y,x \ 1) = K(x \ y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(6261,a,6795,a),flip(a)].">
      <j1 rule="hyper" parents="6261 6795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6800">
    <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(334,a,3486,a,b,6701,a),flip(a)].">
      <j1 rule="hyper" parents="334 3486 6701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6804">
    <literal><![CDATA[
      (x * K(y,z / (z / u))) * K(u,u \ z) = (x / T(z / (z / u),y)) * u
    ]]></literal>
    <justification jstring="[para(6370(a,1),6748(a,1,1))].">
      <j1 rule="para" parents="6370 6748"/>
    </justification>
  </clause>

  <clause id="6805">
    <literal><![CDATA[
      T(x * y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6782(a,1),6560(a,1))].">
      <j1 rule="para" parents="6782 6560"/>
    </justification>
  </clause>

  <clause id="6806">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K((x \ y) \ z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(6493,a,6798,a)].">
      <j1 rule="hyper" parents="6493 6798"/>
    </justification>
  </clause>

  <clause id="6807">
    <literal><![CDATA[
      K(x * (y \ 1),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5532,a,b,6798,a)].">
      <j1 rule="hyper" parents="58 5532 6798"/>
    </justification>
  </clause>

  <clause id="6808">
    <literal><![CDATA[
      T(K(x \ y,x \ 1) / x,y) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[para(6807(a,1),6268(a,1,1,1))].">
      <j1 rule="para" parents="6807 6268"/>
    </justification>
  </clause>

  <clause id="6809">
    <literal><![CDATA[
      L(T(K(x,y \ z),u),y \ z,w) = T(K(x,(z \ y) \ 1),u)
    ]]></literal>
    <justification jstring="[para(6435(a,1),20(a,2,1))].">
      <j1 rule="para" parents="6435 20"/>
    </justification>
  </clause>

  <clause id="6810">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ z) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(1005(a,1),6492(a,1,2))].">
      <j1 rule="para" parents="1005 6492"/>
    </justification>
  </clause>

  <clause id="6811">
    <literal><![CDATA[
      L(x * y,K(y * x,z),u) = x * y
    ]]></literal>
    <justification jstring="[para(4(a,1),6608(a,2,1))].">
      <j1 rule="para" parents="4 6608"/>
    </justification>
  </clause>

  <clause id="6812">
    <literal><![CDATA[
      (x * K(y * z,u)) * (z * y) = x * (K(y * z,u) * (z * y))
    ]]></literal>
    <justification jstring="[hyper(119,a,6811,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 6811 13"/>
    </justification>
  </clause>

  <clause id="6813">
    <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),6666(a,1,1))].">
      <j1 rule="para" parents="4 6666"/>
    </justification>
  </clause>

  <clause id="6814">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5360(a,1),6666(a,1,1))].">
      <j1 rule="para" parents="5360 6666"/>
    </justification>
  </clause>

  <clause id="6815">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z != w
    ]]></literal>
    <literal><![CDATA[
      K(u,(x * y) \ z) = w
    ]]></literal>
    <justification jstring="[para(956(a,1),6714(a,1,1))].">
      <j1 rule="para" parents="956 6714"/>
    </justification>
  </clause>

  <clause id="6817">
    <literal><![CDATA[
      R(x,T(y,z),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(6718(a,1),530(a,1))].">
      <j1 rule="para" parents="6718 530"/>
    </justification>
  </clause>

  <clause id="6818">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),y,u) = z
    ]]></literal>
    <justification jstring="[para(6165(a,1),6817(a,1))].">
      <j1 rule="para" parents="6165 6817"/>
    </justification>
  </clause>

  <clause id="6819">
    <literal><![CDATA[
      R(x,K(y,z),T(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(527,a,6356,a)].">
      <j1 rule="hyper" parents="527 6356"/>
    </justification>
  </clause>

  <clause id="6820">
    <literal><![CDATA[
      R(x,K(y,z),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(6819(a,1),46(a,2))].">
      <j1 rule="para" parents="6819 46"/>
    </justification>
  </clause>

  <clause id="6821">
    <literal><![CDATA[
      x * (y \ R(y,x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[para(5556(a,1),6409(a,1,2))].">
      <j1 rule="para" parents="5556 6409"/>
    </justification>
  </clause>

  <clause id="6822">
    <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(6821(a,1),219(a,2,2))].">
      <j1 rule="para" parents="6821 219"/>
    </justification>
  </clause>

  <clause id="6823">
    <literal><![CDATA[
      K(x,(y * z) \ T(y,u)) = K(x,z \ K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6455,a(flip),b,6457,a),flip(a)].">
      <j1 rule="hyper" parents="58 6455 6457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6824">
    <literal><![CDATA[
      T(x,(y * z) \ T(y,u)) = T(x,z \ K(y,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,6823,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 6823 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6825">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) = (u \ 1) / (u \ K(u,y \ K(x,z)))
    ]]></literal>
    <justification jstring="[para(6823(a,1),5399(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6823 5399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6826">
    <literal><![CDATA[
      K(x,(y * z) \ z) = K(x,y \ K(z,y))
    ]]></literal>
    <justification jstring="[para(5867(a,1),6823(a,1,2))].">
      <j1 rule="para" parents="5867 6823"/>
    </justification>
  </clause>

  <clause id="6827">
    <literal><![CDATA[
      T(x,(y \ z) \ K(y,u)) = T(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),6824(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 6824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6828">
    <literal><![CDATA[
      L(K(x,y \ z),z,z \ 1) = K(x,((1 / z) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(3153(a,1),6459(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3153 6459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6829">
    <literal><![CDATA[
      K(x * y,z) * (y * x) = K(y,x) * T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,4865,a,b,6480,a)].">
      <j1 rule="hyper" parents="334 4865 6480"/>
    </justification>
  </clause>

  <clause id="6830">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,z) = ((y * x) \ y) \ K(x,z)
    ]]></literal>
    <justification jstring="[para(221(a,2),6620(a,1,1,1))].">
      <j1 rule="para" parents="221 6620"/>
    </justification>
  </clause>

  <clause id="6834">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) = K((z / y) \ x,z)
    ]]></literal>
    <justification jstring="[para(4894(a,1),6625(a,1,2))].">
      <j1 rule="para" parents="4894 6625"/>
    </justification>
  </clause>

  <clause id="6835">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) = K((x * y) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(6715,a,6627,a),flip(a)].">
      <j1 rule="hyper" parents="6715 6627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6836">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,(x \ 1) \ (x \ y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(6527,a,6640,a)].">
      <j1 rule="hyper" parents="6527 6640"/>
    </justification>
  </clause>

  <clause id="6837">
    <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(6640(a,1),4152(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6640 4152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6838">
    <literal><![CDATA[
      K((x * y) \ z,y) = K((y * x) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,6641,a,b,6642,a),flip(a)].">
      <j1 rule="hyper" parents="29 6641 6642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6839">
    <literal><![CDATA[
      1 / K((x * y) \ z,x) = K(x,(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(6838(a,1),5243(a,1,2))].">
      <j1 rule="para" parents="6838 5243"/>
    </justification>
  </clause>

  <clause id="6840">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(5248,a,6839,a),flip(a)].">
      <j1 rule="hyper" parents="5248 6839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6841">
    <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),6688(a,2,1))].">
      <j1 rule="para" parents="75 6688"/>
    </justification>
  </clause>

  <clause id="6842">
    <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(6711(a,2),791(a,1))].">
      <j1 rule="para" parents="6711 791"/>
    </justification>
  </clause>

  <clause id="6843">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = (1 / z) * K((((1 / z) \ x) \ 1) \ (z \ 1),y)
    ]]></literal>
    <justification jstring="[para(4284(a,1),6794(a,2,2))].">
      <j1 rule="para" parents="4284 6794"/>
    </justification>
  </clause>

  <clause id="6844">
    <literal><![CDATA[
      T(x * K(x * y,y \ 1),y) = y \ T(x * y,y \ 1)
    ]]></literal>
    <justification jstring="[para(6124(a,1),6797(a,1,1,2))].">
      <j1 rule="para" parents="6124 6797"/>
    </justification>
  </clause>

  <clause id="6845">
    <literal><![CDATA[
      K((x / y) \ z,x) = K((y \ x) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6706,a(flip),b,6834,a),flip(a)].">
      <j1 rule="hyper" parents="58 6706 6834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6846">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6459,a(flip),b,6447,a)].">
      <j1 rule="hyper" parents="58 6459 6447"/>
    </justification>
  </clause>

  <clause id="6847">
    <literal><![CDATA[
      K(x,(y * z) \ (y * x)) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(6433,a,6846,a),flip(a)].">
      <j1 rule="hyper" parents="6433 6846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6848">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),u,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(5(a,1),6846(a,2,2,1))].">
      <j1 rule="para" parents="5 6846"/>
    </justification>
  </clause>

  <clause id="6849">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),6846(a,2,2,2))].">
      <j1 rule="para" parents="5 6846"/>
    </justification>
  </clause>

  <clause id="6850">
    <literal><![CDATA[
      K(x,(y * (z / u)) \ (y * z)) = L(K(x,u),z,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),6846(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 6846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6851">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,L(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(92(a,2),6846(a,2,2))].">
      <j1 rule="para" parents="92 6846"/>
    </justification>
  </clause>

  <clause id="6852">
    <literal><![CDATA[
      L(K(x,y \ z),z,y \ 1) = K(x,(1 / y) * z)
    ]]></literal>
    <justification jstring="[para(3168(a,1),6846(a,2,2))].">
      <j1 rule="para" parents="3168 6846"/>
    </justification>
  </clause>

  <clause id="6853">
    <literal><![CDATA[
      K(x,(y * z) \ (y * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ x) = u
    ]]></literal>
    <justification jstring="[para(6846(a,1),6433(a,1))].">
      <j1 rule="para" parents="6846 6433"/>
    </justification>
  </clause>

  <clause id="6854">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[para(5(a,1),6847(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 6847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6855">
    <literal><![CDATA[
      K(x \ y,(x * z) \ y) = K(x \ y,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(5(a,1),6847(a,1,2,2))].">
      <j1 rule="para" parents="5 6847"/>
    </justification>
  </clause>

  <clause id="6856">
    <literal><![CDATA[
      K(x,L(y \ x,y,z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(92(a,2),6847(a,1,2))].">
      <j1 rule="para" parents="92 6847"/>
    </justification>
  </clause>

  <clause id="6857">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ x) = K(x,u \ (K(z,y) * x))
    ]]></literal>
    <justification jstring="[para(5394(a,1),6847(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5394 6847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6858">
    <literal><![CDATA[
      T(x,L(y \ x,y,z)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(118,a,6856,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 6856 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6859">
    <literal><![CDATA[
      T(x,(y \ z) \ x) = T(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[para(502(a,1),6858(a,1,2)),flip(a)].">
      <j1 rule="para" parents="502 6858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6860">
    <literal><![CDATA[
      K(x,L(y,z,u) \ (y * x)) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6236,a(flip),b,6854,a),flip(a)].">
      <j1 rule="hyper" parents="58 6236 6854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6861">
    <literal><![CDATA[
      K(x,((y * K(z,y)) \ u) \ x) = K(x,u \ (y * (K(z,y) * x)))
    ]]></literal>
    <justification jstring="[para(5677(a,1),6854(a,2,2,2))].">
      <j1 rule="para" parents="5677 6854"/>
    </justification>
  </clause>

  <clause id="6862">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,z) \ x) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[para(6108(a,2),6854(a,1,2,1))].">
      <j1 rule="para" parents="6108 6854"/>
    </justification>
  </clause>

  <clause id="6863">
    <literal><![CDATA[
      K(x,L(y \ z,y,K(z,u))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(4455,a,6851,a),flip(a)].">
      <j1 rule="hyper" parents="4455 6851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6864">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6846,a(flip),b,6851,a),flip(a)].">
      <j1 rule="hyper" parents="58 6846 6851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6865">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ T(y,z)) = K(x,u \ y)
    ]]></literal>
    <justification jstring="[para(5121(a,1),6863(a,1,2))].">
      <j1 rule="para" parents="5121 6863"/>
    </justification>
  </clause>

  <clause id="6866">
    <literal><![CDATA[
      K(x,T(y,z) \ z) = K(x,y \ T(z,y))
    ]]></literal>
    <justification jstring="[para(5081(a,1),6865(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5081 6865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6867">
    <literal><![CDATA[
      T(x,T(y,z) \ z) = T(x,y \ T(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,6866,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 6866 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6868">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ (y * K(u,y)))
    ]]></literal>
    <justification jstring="[hyper(5728,a,6848,a)].">
      <j1 rule="hyper" parents="5728 6848"/>
    </justification>
  </clause>

  <clause id="6869">
    <literal><![CDATA[
      (x * y) * K(z,u \ (x * y)) = x * (y * K(z,(x \ u) \ y))
    ]]></literal>
    <justification jstring="[hyper(119,a,6848,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 6848 13"/>
    </justification>
  </clause>

  <clause id="6870">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = T(K(x,z \ (y * u)),w)
    ]]></literal>
    <justification jstring="[para(6848(a,1),20(a,2,1))].">
      <j1 rule="para" parents="6848 20"/>
    </justification>
  </clause>

  <clause id="6871">
    <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(6848(a,1),5727(a,1)),flip(b)].">
      <j1 rule="para" parents="6848 5727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6872">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ y) \ x) = u
    ]]></literal>
    <justification jstring="[para(6848(a,1),6433(a,1))].">
      <j1 rule="para" parents="6848 6433"/>
    </justification>
  </clause>

  <clause id="6873">
    <literal><![CDATA[
      K(x,(y * ((y \ z) / u)) \ z) = L(K(x,u),y \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6850(a,1,2,2))].">
      <j1 rule="para" parents="5 6850"/>
    </justification>
  </clause>

  <clause id="6874">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(94(a,2),6850(a,1,2))].">
      <j1 rule="para" parents="94 6850"/>
    </justification>
  </clause>

  <clause id="6875">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(334,a,6026,a,b,6874,a),flip(a)].">
      <j1 rule="hyper" parents="334 6026 6874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6876">
    <literal><![CDATA[
      L(K(x,y),z * y,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(6(a,1),6874(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 6874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6877">
    <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(334,a,6411,a,b,6876,a)].">
      <j1 rule="hyper" parents="334 6411 6876"/>
    </justification>
  </clause>

  <clause id="6878">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z * y,K(y,x))
    ]]></literal>
    <justification jstring="[para(6876(a,1),6199(a,1,1))].">
      <j1 rule="para" parents="6876 6199"/>
    </justification>
  </clause>

  <clause id="6879">
    <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(6876(a,1),6209(a,1,1))].">
      <j1 rule="para" parents="6876 6209"/>
    </justification>
  </clause>

  <clause id="6880">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(5246,a,6875,a)].">
      <j1 rule="hyper" parents="5246 6875"/>
    </justification>
  </clause>

  <clause id="6881">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(6875(a,2),6029(a,1))].">
      <j1 rule="para" parents="6875 6029"/>
    </justification>
  </clause>

  <clause id="6882">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = (z * y) \ (z * (y * K(x,u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,13,a(flip),b,6880,a),flip(a)].">
      <j1 rule="hyper" parents="334 13 6880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6883">
    <literal><![CDATA[
      L(K(x,y),z * x,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(6(a,1),6880(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6 6880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6884">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K(L(x \ y,x,u),z)
    ]]></literal>
    <justification jstring="[para(72(a,1),6880(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6885">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(6437,a,6883,a),flip(a)].">
      <j1 rule="hyper" parents="6437 6883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6886">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * y)) = K(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,317,a,b,6883,a)].">
      <j1 rule="hyper" parents="58 317 6883"/>
    </justification>
  </clause>

  <clause id="6887">
    <literal><![CDATA[
      (x * (y * z)) / K(L(y,z,x),z) = x * (z * y)
    ]]></literal>
    <justification jstring="[para(6883(a,1),558(a,1,2))].">
      <j1 rule="para" parents="6883 558"/>
    </justification>
  </clause>

  <clause id="6888">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = a(u,z * y,K(x,y))
    ]]></literal>
    <justification jstring="[para(6883(a,1),6201(a,1,2))].">
      <j1 rule="para" parents="6883 6201"/>
    </justification>
  </clause>

  <clause id="6889">
    <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(6883(a,1),6208(a,1,2))].">
      <j1 rule="para" parents="6883 6208"/>
    </justification>
  </clause>

  <clause id="6890">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5649,a(flip),b,6885,a),flip(a)].">
      <j1 rule="hyper" parents="334 5649 6885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6891">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K((u * x) \ (u * y),z)
    ]]></literal>
    <justification jstring="[para(92(a,1),6884(a,2,1))].">
      <j1 rule="para" parents="92 6884"/>
    </justification>
  </clause>

  <clause id="6892">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(311(a,1),6884(a,2,1))].">
      <j1 rule="para" parents="311 6884"/>
    </justification>
  </clause>

  <clause id="6893">
    <literal><![CDATA[
      L(K(x \ T(y,z),u),T(y,z),z) = K((z * x) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(462(a,1),6884(a,2,1))].">
      <j1 rule="para" parents="462 6884"/>
    </justification>
  </clause>

  <clause id="6894">
    <literal><![CDATA[
      L(K((x \ y) \ z,u),z,x) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(502(a,1),6884(a,2,1))].">
      <j1 rule="para" parents="502 6884"/>
    </justification>
  </clause>

  <clause id="6895">
    <literal><![CDATA[
      L(K(L(x,y,z) \ x,u),x,z * y) = K(a(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(1988(a,2),6884(a,2,1))].">
      <j1 rule="para" parents="1988 6884"/>
    </justification>
  </clause>

  <clause id="6896">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = K((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(3153(a,1),6884(a,2,1))].">
      <j1 rule="para" parents="3153 6884"/>
    </justification>
  </clause>

  <clause id="6897">
    <literal><![CDATA[
      L(K(x,y \ z),z,y \ 1) = K(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(334,a,5583,a(flip),b,6852,a),flip(a)].">
      <j1 rule="hyper" parents="334 5583 6852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6898">
    <literal><![CDATA[
      T(x,L(y \ z,y,u)) = T(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(118,a,6864,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 6864 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6899">
    <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(6732(a,1),6864(a,2,2,1))].">
      <j1 rule="para" parents="6732 6864"/>
    </justification>
  </clause>

  <clause id="6900">
    <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),6881(a,1,2))].">
      <j1 rule="para" parents="94 6881"/>
    </justification>
  </clause>

  <clause id="6901">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(34,a,6523,a,b,6886,a)].">
      <j1 rule="hyper" parents="34 6523 6886"/>
    </justification>
  </clause>

  <clause id="6902">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * y)) = K(z,L(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(116,a,6887,a(flip),b,6520,a(flip))].">
      <j1 rule="hyper" parents="116 6887 6520"/>
    </justification>
  </clause>

  <clause id="6903">
    <literal><![CDATA[
      L(K(x \ y,z),y,y \ 1) = K(((y \ 1) * x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,4301,a(flip),b,6891,a),flip(a)].">
      <j1 rule="hyper" parents="334 4301 6891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6904">
    <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(5394(a,1),6891(a,2,1,1))].">
      <j1 rule="para" parents="5394 6891"/>
    </justification>
  </clause>

  <clause id="6905">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K((z * (x \ 1)) \ (z * y),x)
    ]]></literal>
    <justification jstring="[para(6795(a,1),6891(a,1,1))].">
      <j1 rule="para" parents="6795 6891"/>
    </justification>
  </clause>

  <clause id="6906">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(y \ (x * z),z)
    ]]></literal>
    <justification jstring="[hyper(6437,a,6894,a)].">
      <j1 rule="hyper" parents="6437 6894"/>
    </justification>
  </clause>

  <clause id="6907">
    <literal><![CDATA[
      K((x \ y) \ z,u \ (x * z)) = K(y \ (x * z),(x \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6848,a(flip),b,6894,a)].">
      <j1 rule="hyper" parents="58 6848 6894"/>
    </justification>
  </clause>

  <clause id="6908">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,z) = u
    ]]></literal>
    <justification jstring="[para(6894(a,1),6437(a,1))].">
      <j1 rule="para" parents="6894 6437"/>
    </justification>
  </clause>

  <clause id="6909">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,4281,a(flip),b,6896,a),flip(a)].">
      <j1 rule="hyper" parents="334 4281 6896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6910">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6886,a(flip),b,6902,a)].">
      <j1 rule="hyper" parents="58 6886 6902"/>
    </justification>
  </clause>

  <clause id="6911">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = u
    ]]></literal>
    <justification jstring="[para(6902(a,1),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6902 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6913">
    <literal><![CDATA[
      L(x,y,z \ 1) != K((z \ 1) * y,u)
    ]]></literal>
    <literal><![CDATA[
      K(z \ y,u) = x
    ]]></literal>
    <justification jstring="[para(6909(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="6909 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6914">
    <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,6888,a(flip),b,5671,a),flip(a)].">
      <j1 rule="hyper" parents="119 6888 5671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6915">
    <literal><![CDATA[
      K(x,L(L(y \ 1,y,z),z * y,u)) = K(x,1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[para(435(a,2),6494(a,1,2))].">
      <j1 rule="para" parents="435 6494"/>
    </justification>
  </clause>

  <clause id="6916">
    <literal><![CDATA[
      x / (K(y,z) * T(z,u)) = (x / T(z,u)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6820,a,6540,a),flip(a)].">
      <j1 rule="hyper" parents="6820 6540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6917">
    <literal><![CDATA[
      (x / T(y,y * z)) * K(y,z) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(5352(a,1),6916(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5352 6916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6918">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,y * z) = x / R(y,z,y)
    ]]></literal>
    <justification jstring="[para(5355(a,1),6916(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5355 6916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6919">
    <literal><![CDATA[
      (x / T(y,z)) * T(y,y * z) = (x / R(y,z,y)) * y
    ]]></literal>
    <justification jstring="[para(6918(a,1),6532(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6918 6532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6920">
    <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(334,a,4,a,b,6660,a),flip(a)].">
      <j1 rule="hyper" parents="334 4 6660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6921">
    <literal><![CDATA[
      a(x,T(y,z),T(z,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(709,a,6719,a),flip(a)].">
      <j1 rule="hyper" parents="709 6719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6922">
    <literal><![CDATA[
      a(x,T(y,z),T(z,y)) != 1
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = x * (y * z)
    ]]></literal>
    <justification jstring="[para(6719(a,1),169(a,1))].">
      <j1 rule="para" parents="6719 169"/>
    </justification>
  </clause>

  <clause id="6923">
    <literal><![CDATA[
      L(K(x,y \ z),z,z \ 1) = K(x,((z \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,5587,a(flip),b,6828,a),flip(a)].">
      <j1 rule="hyper" parents="334 5587 6828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6924">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,x * L(x \ 1,z,u)) = ((y * x) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(1817(a,1),6830(a,2,2))].">
      <j1 rule="para" parents="1817 6830"/>
    </justification>
  </clause>

  <clause id="6925">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(u * K(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(5391(a,1),6849(a,1,1,2))].">
      <j1 rule="para" parents="5391 6849"/>
    </justification>
  </clause>

  <clause id="6926">
    <literal><![CDATA[
      K(L(x,y / x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(6882(a,2),495(a,1))].">
      <j1 rule="para" parents="6882 495"/>
    </justification>
  </clause>

  <clause id="6927">
    <literal><![CDATA[
      K((x * y) \ 1,x) = K(y \ (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3293,a(flip),b,6892,a),flip(a)].">
      <j1 rule="hyper" parents="58 3293 6892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6928">
    <literal><![CDATA[
      x * ((x \ y) * K(z \ (x \ y),u)) = y * K((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,6892,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="119 6892 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6929">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K((y * (x \ 1)) \ z,x)
    ]]></literal>
    <justification jstring="[para(6795(a,1),6892(a,1,1))].">
      <j1 rule="para" parents="6795 6892"/>
    </justification>
  </clause>

  <clause id="6930">
    <literal><![CDATA[
      L(K((x \ y) \ (z \ u),y),z \ u,z) = K((z * (y / x)) \ u,y)
    ]]></literal>
    <justification jstring="[para(6845(a,1),6892(a,1,1))].">
      <j1 rule="para" parents="6845 6892"/>
    </justification>
  </clause>

  <clause id="6931">
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = K(y \ (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(5321,a,6927,a)].">
      <j1 rule="hyper" parents="5321 6927"/>
    </justification>
  </clause>

  <clause id="6932">
    <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(6895(a,1),1992(a,1,1))].">
      <j1 rule="para" parents="6895 1992"/>
    </justification>
  </clause>

  <clause id="6933">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,z * y) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,6483,a(flip),b,6919,a)].">
      <j1 rule="hyper" parents="58 6483 6919"/>
    </justification>
  </clause>

  <clause id="6934">
    <literal><![CDATA[
      (1 / x) \ K(y,((x \ 1) * z) \ 1) = x * K(y,z \ x)
    ]]></literal>
    <justification jstring="[hyper(116,a,6923,a(flip),b,3146,a)].">
      <j1 rule="hyper" parents="116 6923 3146"/>
    </justification>
  </clause>

  <clause id="6935">
    <literal><![CDATA[
      K(x,((y \ 1) * (y / z)) \ 1) = L(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),6923(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 6923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6936">
    <literal><![CDATA[
      R(x,K(y,z),L(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(527,a,6358,a)].">
      <j1 rule="hyper" parents="527 6358"/>
    </justification>
  </clause>

  <clause id="6937">
    <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(2648(a,2),6448(a,1,2))].">
      <j1 rule="para" parents="2648 6448"/>
    </justification>
  </clause>

  <clause id="6938">
    <literal><![CDATA[
      K(x,(T(y,z) * u) \ y) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6454,a(flip),b,6449,a),flip(a)].">
      <j1 rule="hyper" parents="58 6454 6449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6939">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) \ K(z,y)) = K(x,u \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6938(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 6938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6940">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) \ x = L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(5959(a,1),6546(a,1,1,2))].">
      <j1 rule="para" parents="5959 6546"/>
    </justification>
  </clause>

  <clause id="6941">
    <literal><![CDATA[
      x / L(K(y,z),u,w) = x * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(201,a,6940,a)].">
      <j1 rule="hyper" parents="201 6940"/>
    </justification>
  </clause>

  <clause id="6942">
    <literal><![CDATA[
      (x * (y * K(z,u))) * L(K(u,z),y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(137,a,6940,a),flip(a)].">
      <j1 rule="hyper" parents="137 6940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6943">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) = L(K(u,z),y,x)
    ]]></literal>
    <justification jstring="[para(90(a,1),6940(a,1,1))].">
      <j1 rule="para" parents="90 6940"/>
    </justification>
  </clause>

  <clause id="6944">
    <literal><![CDATA[
      (x * ((x \ y) * K(z,u))) \ y = L(K(u,z),x \ y,x)
    ]]></literal>
    <justification jstring="[para(460(a,1),6940(a,1,1))].">
      <j1 rule="para" parents="460 6940"/>
    </justification>
  </clause>

  <clause id="6945">
    <literal><![CDATA[
      (x * (y * K(z,u))) * w != x * y
    ]]></literal>
    <literal><![CDATA[
      L(K(u,z),y,x) = w
    ]]></literal>
    <justification jstring="[para(6942(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="6942 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6946">
    <literal><![CDATA[
      x \ T(x * K(y \ x,z),x) = K(T(y,x) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,6643,a(flip),b,6430,a(flip))].">
      <j1 rule="hyper" parents="116 6643 6430"/>
    </justification>
  </clause>

  <clause id="6947">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = x \ T(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(75(a,1),6946(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 6946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6948">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = K(y,T(x / z,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,6294,a,b,6947,a),flip(a)].">
      <j1 rule="hyper" parents="334 6294 6947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6949">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (y \ z)) \ u)
    ]]></literal>
    <justification jstring="[para(1005(a,1),6690(a,1,1,2))].">
      <j1 rule="para" parents="1005 6690"/>
    </justification>
  </clause>

  <clause id="6950">
    <literal><![CDATA[
      (x * (y * (z * T(z \ (y \ (x \ u)),w)))) \ u = K(w,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(956(a,1),6690(a,1,1,2))].">
      <j1 rule="para" parents="956 6690"/>
    </justification>
  </clause>

  <clause id="6951">
    <literal><![CDATA[
      (x * (((y \ ((x \ z) * u)) * y) / u)) \ z = K(y,(x * (y / u)) \ z)
    ]]></literal>
    <justification jstring="[para(1644(a,1),6690(a,1,1,2))].">
      <j1 rule="para" parents="1644 6690"/>
    </justification>
  </clause>

  <clause id="6952">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * z)) = L(T(z,y),y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,20,a,b,6716,a),flip(a)].">
      <j1 rule="hyper" parents="334 20 6716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6953">
    <literal><![CDATA[
      T(K(x \ K(x,y),z),y) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(5151(a,1),6793(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5151 6793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6954">
    <literal><![CDATA[
      K(x \ K(x,y),z) * y = y * K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,6953,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 6953 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6955">
    <literal><![CDATA[
      K(x,(x / L(y,z,u)) * y) = K(x,y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(1509(a,1),6860(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1509 6860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6956">
    <literal><![CDATA[
      L(K(x,y),z * y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(6877(a,1),3811(a,1))].">
      <j1 rule="para" parents="6877 3811"/>
    </justification>
  </clause>

  <clause id="6957">
    <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),6956(a,1,2))].">
      <j1 rule="para" parents="5 6956"/>
    </justification>
  </clause>

  <clause id="6958">
    <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),6956(a,1,2))].">
      <j1 rule="para" parents="7 6956"/>
    </justification>
  </clause>

  <clause id="6959">
    <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(6532(a,1),6956(a,1,2))].">
      <j1 rule="para" parents="6532 6956"/>
    </justification>
  </clause>

  <clause id="6960">
    <literal><![CDATA[
      K(x,(y * z) \ (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z \ u,z,y)) = w
    ]]></literal>
    <justification jstring="[para(6846(a,1),6957(a,1))].">
      <j1 rule="para" parents="6846 6957"/>
    </justification>
  </clause>

  <clause id="6961">
    <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),6900(a,1,2,1,2))].">
      <j1 rule="para" parents="72 6900"/>
    </justification>
  </clause>

  <clause id="6962">
    <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(5086(a,1),6952(a,2,1))].">
      <j1 rule="para" parents="5086 6952"/>
    </justification>
  </clause>

  <clause id="6963">
    <literal><![CDATA[
      K(x,L(y \ L(y,z,u),y,u * z)) = K(x,a(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(514(a,2),6443(a,1,2))].">
      <j1 rule="para" parents="514 6443"/>
    </justification>
  </clause>

  <clause id="6964">
    <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(6594(a,2),5180(a,1))].">
      <j1 rule="para" parents="6594 5180"/>
    </justification>
  </clause>

  <clause id="6965">
    <literal><![CDATA[
      T(x,x \ T(x * y,y \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,6571,a(flip),b,6755,a),flip(a)].">
      <j1 rule="hyper" parents="334 6571 6755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6967">
    <literal><![CDATA[
      T(x / y,(x / y) \ T(x,y \ 1)) = T(x / y,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),6965(a,1,2,2,1))].">
      <j1 rule="para" parents="7 6965"/>
    </justification>
  </clause>

  <clause id="6968">
    <literal><![CDATA[
      T(x / y,(x / y) \ T(x,y \ 1)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(334,a,107,a(flip),b,6967,a),flip(a)].">
      <j1 rule="hyper" parents="334 107 6967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6969">
    <literal><![CDATA[
      T(x,y \ 1) / (y \ x) = (x / y) \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(6968(a,1),273(a,1,2))].">
      <j1 rule="para" parents="6968 273"/>
    </justification>
  </clause>

  <clause id="6970">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) / ((y \ 1) \ x) = (x / (y \ 1)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3106(a,1),6969(a,2,2))].">
      <j1 rule="para" parents="3106 6969"/>
    </justification>
  </clause>

  <clause id="6971">
    <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),6756(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 6756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6972">
    <literal><![CDATA[
      K(x * y,z) * (y * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * T(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(4865(a,2),6763(a,1))].">
      <j1 rule="para" parents="4865 6763"/>
    </justification>
  </clause>

  <clause id="6973">
    <literal><![CDATA[
      K((x / y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,x) = u
    ]]></literal>
    <justification jstring="[para(6834(a,1),6810(a,1))].">
      <j1 rule="para" parents="6834 6810"/>
    </justification>
  </clause>

  <clause id="6974">
    <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,3711,a,b,6915,a)].">
      <j1 rule="hyper" parents="58 3711 6915"/>
    </justification>
  </clause>

  <clause id="6975">
    <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,6963,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 6963 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6976">
    <literal><![CDATA[
      K(x * (1 / (y / z)),z \ y) = K(x / (y / z),z \ y)
    ]]></literal>
    <justification jstring="[hyper(6761,a,6509,a),flip(a)].">
      <j1 rule="hyper" parents="6761 6509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6977">
    <literal><![CDATA[
      x / (K(y / (z / u),u \ z) * x) = K(u \ z,y * (1 / (z / u)))
    ]]></literal>
    <justification jstring="[para(6976(a,1),5403(a,1,2,1))].">
      <j1 rule="para" parents="6976 5403"/>
    </justification>
  </clause>

  <clause id="6978">
    <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(5014(a,1),6541(a,1,1,1))].">
      <j1 rule="para" parents="5014 6541"/>
    </justification>
  </clause>

  <clause id="6979">
    <literal><![CDATA[
      (((x / y) * T(y,z)) * u) \ (x * u) = K(z,((x / y) * u) \ (x * u))
    ]]></literal>
    <justification jstring="[para(75(a,1),6691(a,1,1,1,2,1))].">
      <j1 rule="para" parents="75 6691"/>
    </justification>
  </clause>

  <clause id="6980">
    <literal><![CDATA[
      K(x,T(y \ z,u) \ T(z,u)) = T(K(y,x) * z,u) \ T(z,u)
    ]]></literal>
    <justification jstring="[para(5361(a,1),6692(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5361 6692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6981">
    <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(6724(a,1),44(a,1))].">
      <j1 rule="para" parents="6724 44"/>
    </justification>
  </clause>

  <clause id="6982">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * y) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(6459(a,1),6758(a,1))].">
      <j1 rule="para" parents="6459 6758"/>
    </justification>
  </clause>

  <clause id="6983">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * y) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(6851(a,1),6982(a,1))].">
      <j1 rule="para" parents="6851 6982"/>
    </justification>
  </clause>

  <clause id="6984">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K((x \ y) \ z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,6423,a(flip),b,6806,a),flip(a)].">
      <j1 rule="hyper" parents="334 6423 6806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6985">
    <literal><![CDATA[
      (x * K(y * z,u)) * (z * y) = x * (K(z,y) * T(y * z,u))
    ]]></literal>
    <justification jstring="[para(6829(a,1),6812(a,2,2))].">
      <j1 rule="para" parents="6829 6812"/>
    </justification>
  </clause>

  <clause id="6986">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) = K(y \ K(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,5399,a(flip),b,6825,a),flip(a)].">
      <j1 rule="hyper" parents="334 5399 6825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6987">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ K(x,z),u) = w
    ]]></literal>
    <justification jstring="[para(6825(a,2),5507(a,1))].">
      <j1 rule="para" parents="6825 5507"/>
    </justification>
  </clause>

  <clause id="6988">
    <literal><![CDATA[
      K((x \ y) \ K(x,z),u) = K(y \ T(x,z),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),6986(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 6986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6989">
    <literal><![CDATA[
      K(T(x / y,T(y,x)) \ K(y,z),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4104(a,2),6988(a,1,1,1))].">
      <j1 rule="para" parents="4104 6988"/>
    </justification>
  </clause>

  <clause id="6990">
    <literal><![CDATA[
      K(x,(K(y,z) * (y \ u)) \ x) = K(x,u \ (y * (K(z,y) * x)))
    ]]></literal>
    <justification jstring="[para(5655(a,1),6861(a,1,2,1))].">
      <j1 rule="para" parents="5655 6861"/>
    </justification>
  </clause>

  <clause id="6991">
    <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(6869(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="6869 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6992">
    <literal><![CDATA[
      K((x \ 1) \ y,z \ (x * y)) = K(x * y,(x \ z) \ y)
    ]]></literal>
    <justification jstring="[para(60(a,1),6907(a,2,1))].">
      <j1 rule="para" parents="60 6907"/>
    </justification>
  </clause>

  <clause id="6993">
    <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(1365(a,1),6907(a,2,1))].">
      <j1 rule="para" parents="1365 6907"/>
    </justification>
  </clause>

  <clause id="6994">
    <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(6928(a,2),6528(a,1,1))].">
      <j1 rule="para" parents="6928 6528"/>
    </justification>
  </clause>

  <clause id="6995">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = (x / (y \ 1)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3106(a,1),6970(a,1,1))].">
      <j1 rule="para" parents="3106 6970"/>
    </justification>
  </clause>

  <clause id="6996">
    <literal><![CDATA[
      ((x / (y \ 1)) \ T(x,y)) \ T(x,y) = (y \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(192,a,6995,a)].">
      <j1 rule="hyper" parents="192 6995"/>
    </justification>
  </clause>

  <clause id="6997">
    <literal><![CDATA[
      ((x / y) / (y \ 1)) \ T(x / y,y) = (y \ x) / ((y \ 1) \ (x / y))
    ]]></literal>
    <justification jstring="[para(107(a,1),6995(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 6995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6998">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) != z
    ]]></literal>
    <literal><![CDATA[
      (x / (y \ 1)) \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(6996(a,1),345(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6996 345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6999">
    <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,6980,a,b,xx)].">
      <j1 rule="hyper" parents="119 6980"/>
    </justification>
  </clause>

  <clause id="7000">
    <literal><![CDATA[
      (K(x,y) * K(x * y,z)) * (y * x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,5394,a(flip),b,6985,a),flip(a)].">
      <j1 rule="hyper" parents="334 5394 6985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7001">
    <literal><![CDATA[
      (x * y) \ T(y * x,z) = K(y,x) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,5970,a,b,7000,a)].">
      <j1 rule="hyper" parents="30 5970 7000"/>
    </justification>
  </clause>

  <clause id="7002">
    <literal><![CDATA[
      K(1 / x,x) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(3530(a,1),5329(a,1,1))].">
      <j1 rule="para" parents="3530 5329"/>
    </justification>
  </clause>

  <clause id="7003">
    <literal><![CDATA[
      (x / L(x,y,z)) * (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,3693,a(flip),b,7002,a),flip(a)].">
      <j1 rule="hyper" parents="58 3693 7002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7005">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(3958(a,1),7003(a,1,1))].">
      <j1 rule="para" parents="3958 7003"/>
    </justification>
  </clause>

  <clause id="7006">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) / x = L(1 / x,y,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(365,a,7005,a)].">
      <j1 rule="hyper" parents="365 7005"/>
    </justification>
  </clause>

  <clause id="7007">
    <literal><![CDATA[
      T(L(x,y,z) \ x,x \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(246,a,7005,a,b,3996,a)].">
      <j1 rule="hyper" parents="246 7005 3996"/>
    </justification>
  </clause>

  <clause id="7008">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (L(x,y,z) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,7005,a)].">
      <j1 rule="hyper" parents="123 7005"/>
    </justification>
  </clause>

  <clause id="7009">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) / x = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,3950,a(flip),b,7006,a),flip(a)].">
      <j1 rule="hyper" parents="334 3950 7006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7010">
    <literal><![CDATA[
      T(x,x \ (L(x \ 1,y,z) \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(31,a,3994,a,b,7009,a)].">
      <j1 rule="hyper" parents="31 3994 7009"/>
    </justification>
  </clause>

  <clause id="7011">
    <literal><![CDATA[
      T(x,x \ (((y * x) \ y) \ 1)) = x
    ]]></literal>
    <justification jstring="[para(221(a,1),7010(a,1,2,2,1))].">
      <j1 rule="para" parents="221 7010"/>
    </justification>
  </clause>

  <clause id="7012">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) / y = y \ (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(7011(a,1),3943(a,1,2))].">
      <j1 rule="para" parents="7011 3943"/>
    </justification>
  </clause>

  <clause id="7013">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) / ((y \ 1) \ 1) = y \ (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4025,a,b,7012,a)].">
      <j1 rule="hyper" parents="58 4025 7012"/>
    </justification>
  </clause>

  <clause id="7014">
    <literal><![CDATA[
      L(T(x \ 1,y) \ z,x \ 1,x) = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(334,a,6242,a(flip),b,5448,a),flip(a)].">
      <j1 rule="hyper" parents="334 6242 5448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7015">
    <literal><![CDATA[
      ((x * T(y,z)) * z) / (T(y,z) * z) = R(x,y,z * K(y,z))
    ]]></literal>
    <justification jstring="[para(6484(a,1),5455(a,1,1))].">
      <j1 rule="para" parents="6484 5455"/>
    </justification>
  </clause>

  <clause id="7016">
    <literal><![CDATA[
      R(x,y,z * K(y,z)) = R(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(530,a,7015,a),flip(a)].">
      <j1 rule="hyper" parents="530 7015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7017">
    <literal><![CDATA[
      (x / R(y,y \ x,y)) * y = T(y,x) * T(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4557(a,1),6327(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4557 6327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7018">
    <literal><![CDATA[
      (x / R(y,y \ x,y)) * y = (y \ x) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,4128,a(flip),b,7017,a),flip(a)].">
      <j1 rule="hyper" parents="334 4128 7017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7019">
    <literal><![CDATA[
      x / R(y,y \ x,y) = (y \ x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,6532,a,b,7018,a),flip(a)].">
      <j1 rule="hyper" parents="30 6532 7018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7020">
    <literal><![CDATA[
      x / R(y,y \ x,y) = y \ (x * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(30,a,5217,a,b,7018,a),flip(a)].">
      <j1 rule="hyper" parents="30 5217 7018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7021">
    <literal><![CDATA[
      x / R(y,y \ x,y) = K(y,x) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,6685,a,b,7019,a),flip(a)].">
      <j1 rule="hyper" parents="334 6685 7019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7022">
    <literal><![CDATA[
      x / R(y,y \ x,y) = (y * K(x,y)) \ x
    ]]></literal>
    <justification jstring="[hyper(334,a,5636,a,b,7020,a),flip(a)].">
      <j1 rule="hyper" parents="334 5636 7020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7023">
    <literal><![CDATA[
      x / ((y \ x) \ T(x,y)) = (y * K(x,y)) \ x
    ]]></literal>
    <justification jstring="[para(4581(a,1),7022(a,1,2))].">
      <j1 rule="para" parents="4581 7022"/>
    </justification>
  </clause>

  <clause id="7024">
    <literal><![CDATA[
      ((x * K(y,x)) \ y) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(192,a,7023,a)].">
      <j1 rule="hyper" parents="192 7023"/>
    </justification>
  </clause>

  <clause id="7025">
    <literal><![CDATA[
      (x \ (y * K(x,y))) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5636(a,1),7024(a,1,1))].">
      <j1 rule="para" parents="5636 7024"/>
    </justification>
  </clause>

  <clause id="7026">
    <literal><![CDATA[
      (x \ ((x * y) / x)) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5017(a,2),7025(a,1,1,2))].">
      <j1 rule="para" parents="5017 7025"/>
    </justification>
  </clause>

  <clause id="7027">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / (y * T(z,y)) = R(x,y * K(z,y),z)
    ]]></literal>
    <justification jstring="[para(6532(a,1),6789(a,1,2))].">
      <j1 rule="para" parents="6532 6789"/>
    </justification>
  </clause>

  <clause id="7028">
    <literal><![CDATA[
      R(x,y * K(z,y),z) = R(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(530,a,7027,a),flip(a)].">
      <j1 rule="hyper" parents="530 7027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7029">
    <literal><![CDATA[
      R(x,y \ z,T(y,y \ z)) = R(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(5041(a,1),7028(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5041 7028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7030">
    <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(1005(a,1),6815(a,1,1,2))].">
      <j1 rule="para" parents="1005 6815"/>
    </justification>
  </clause>

  <clause id="7031">
    <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(6920(a,2),297(a,1)),flip(b)].">
      <j1 rule="para" parents="6920 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7032">
    <literal><![CDATA[
      K(L(x,x \ 1,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(2696(a,1),7031(a,1))].">
      <j1 rule="para" parents="2696 7031"/>
    </justification>
  </clause>

  <clause id="7033">
    <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(6232(a,2),6925(a,2,2,1))].">
      <j1 rule="para" parents="6232 6925"/>
    </justification>
  </clause>

  <clause id="7034">
    <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(6954(a,2),6925(a,2,2,1))].">
      <j1 rule="para" parents="6954 6925"/>
    </justification>
  </clause>

  <clause id="7035">
    <literal><![CDATA[
      K((x * (y / z)) \ u,y) = K((x * (z \ y)) \ u,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6892,a(flip),b,6930,a),flip(a)].">
      <j1 rule="hyper" parents="58 6892 6930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7036">
    <literal><![CDATA[
      K((x * (y / x)) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),7035(a,2,1,1))].">
      <j1 rule="para" parents="5 7035"/>
    </justification>
  </clause>

  <clause id="7037">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),7036(a,1,1,1,2))].">
      <j1 rule="para" parents="72 7036"/>
    </justification>
  </clause>

  <clause id="7038">
    <literal><![CDATA[
      T(x,((y \ x) * y) \ z) = (u * K(x \ z,x)) \ (u * x)
    ]]></literal>
    <justification jstring="[para(7037(a,1),6361(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7037 6361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7039">
    <literal><![CDATA[
      T(x,((y \ x) * y) \ z) = T(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(334,a,6361,a(flip),b,7038,a),flip(a)].">
      <j1 rule="hyper" parents="334 6361 7038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7040">
    <literal><![CDATA[
      T(x,x \ T(y,y \ x)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5866(a,1),7039(a,1,2))].">
      <j1 rule="para" parents="5866 7039"/>
    </justification>
  </clause>

  <clause id="7041">
    <literal><![CDATA[
      T(x,x \ y) / T(y,y \ x) = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(7040(a,1),273(a,1,2))].">
      <j1 rule="para" parents="7040 273"/>
    </justification>
  </clause>

  <clause id="7042">
    <literal><![CDATA[
      T(x,x \ y) / ((y \ x) \ x) = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(693,a,7041,a)].">
      <j1 rule="hyper" parents="693 7041"/>
    </justification>
  </clause>

  <clause id="7043">
    <literal><![CDATA[
      x \ T(y,y \ x) = y / ((y \ ((x \ y) \ y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6506,a(flip),b,7042,a),flip(a)].">
      <j1 rule="hyper" parents="58 6506 7042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7044">
    <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,3197,a,b,4799,a),flip(a)].">
      <j1 rule="hyper" parents="58 3197 4799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7045">
    <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(4920(a,2),38(a,1))].">
      <j1 rule="para" parents="4920 38"/>
    </justification>
  </clause>

  <clause id="7046">
    <literal><![CDATA[
      (x * y) \ (y * (K(x,y) * (x * z))) = L(L(z,x,y),y * x,K(x,y))
    ]]></literal>
    <justification jstring="[para(5522(a,1),5161(a,1,2))].">
      <j1 rule="para" parents="5522 5161"/>
    </justification>
  </clause>

  <clause id="7047">
    <literal><![CDATA[
      (x * (1 / T(y,z))) * T(y,z) = R(x,1 / T(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(5226,a,6401,a),flip(a)].">
      <j1 rule="hyper" parents="5226 6401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7048">
    <literal><![CDATA[
      R(x,1 / T(y,z),y) / y = (x * (1 / T(y,z))) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,7047,a(flip),b,6532,a)].">
      <j1 rule="hyper" parents="117 7047 6532"/>
    </justification>
  </clause>

  <clause id="7049">
    <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(7047(a,1),2945(a,1))].">
      <j1 rule="para" parents="7047 2945"/>
    </justification>
  </clause>

  <clause id="7050">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = (x * (1 / T(y,z))) * K(y,z)
    ]]></literal>
    <justification jstring="[para(4334(a,1),7048(a,1,1))].">
      <j1 rule="para" parents="4334 7048"/>
    </justification>
  </clause>

  <clause id="7051">
    <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(4334(a,1),7049(a,1))].">
      <j1 rule="para" parents="4334 7049"/>
    </justification>
  </clause>

  <clause id="7052">
    <literal><![CDATA[
      R(K(x,y),x * z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(5383,a,6274,a)].">
      <j1 rule="hyper" parents="5383 6274"/>
    </justification>
  </clause>

  <clause id="7053">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),7052(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 7052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7054">
    <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(7052(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7052 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7055">
    <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(5363(a,1),7052(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5363 7052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7056">
    <literal><![CDATA[
      K(R(x,x \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,391,a(flip),b,7053,a),flip(a)].">
      <j1 rule="hyper" parents="334 391 7053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7057">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) * (y * z) = (K(x,u) * y) * z
    ]]></literal>
    <justification jstring="[para(7053(a,2),101(a,1,1))].">
      <j1 rule="para" parents="7053 101"/>
    </justification>
  </clause>

  <clause id="7058">
    <literal><![CDATA[
      K((x * y) / ((z \ x) * y),u) = R(K(z,u),x,y)
    ]]></literal>
    <justification jstring="[para(98(a,1),7053(a,1,1))].">
      <j1 rule="para" parents="98 7053"/>
    </justification>
  </clause>

  <clause id="7059">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = (w * R(K(y,x),z,u)) \ w
    ]]></literal>
    <justification jstring="[para(7053(a,1),6523(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7053 6523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7060">
    <literal><![CDATA[
      K(R(x,x \ 1,y),L(z,x,x \ 1)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,6071,a(flip),b,7056,a),flip(a)].">
      <j1 rule="hyper" parents="334 6071 7056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7061">
    <literal><![CDATA[
      R(K(x / y,z),x,u) = K((x * u) / (y * u),z)
    ]]></literal>
    <justification jstring="[para(75(a,1),7058(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 7058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7062">
    <literal><![CDATA[
      R(K(x / (y / z),u),x,z) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(7(a,1),7061(a,2,1,2))].">
      <j1 rule="para" parents="7 7061"/>
    </justification>
  </clause>

  <clause id="7063">
    <literal><![CDATA[
      K((x * y) / z,x) = K(x / (z / y),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5731,a(flip),b,7062,a),flip(a)].">
      <j1 rule="hyper" parents="58 5731 7062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7064">
    <literal><![CDATA[
      K((x * y) / z,x) = K((z / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,6647,a(flip),b,7063,a),flip(a)].">
      <j1 rule="hyper" parents="334 6647 7063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7065">
    <literal><![CDATA[
      K((x * y) / z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K((z / y) \ x,x) = u
    ]]></literal>
    <justification jstring="[para(7063(a,2),6775(a,1))].">
      <j1 rule="para" parents="7063 6775"/>
    </justification>
  </clause>

  <clause id="7066">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) \ x = R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,6164,a(flip),b,7059,a),flip(a)].">
      <j1 rule="hyper" parents="58 6164 7059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7067">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) * R(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,6164,a(flip),b,7059,a(flip))].">
      <j1 rule="hyper" parents="119 6164 7059"/>
    </justification>
  </clause>

  <clause id="7068">
    <literal><![CDATA[
      T(x,y) * K(x * y,(y * x) \ x) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(5867(a,1),5482(a,1,2,2))].">
      <j1 rule="para" parents="5867 5482"/>
    </justification>
  </clause>

  <clause id="7069">
    <literal><![CDATA[
      K((T(x,y) \ T(z,y)) \ 1,x) = K((x \ z) \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,5855,a(flip),b,5798,a),flip(a)].">
      <j1 rule="hyper" parents="58 5855 5798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7070">
    <literal><![CDATA[
      K((T(x,y) \ T(z,y)) \ 1,x) = K(z \ x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,6615,a(flip),b,7069,a),flip(a)].">
      <j1 rule="hyper" parents="334 6615 7069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7071">
    <literal><![CDATA[
      K(T(x,y) \ T(z,y),z) = K(x \ z,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(6715,a,7070,a)].">
      <j1 rule="hyper" parents="6715 7070"/>
    </justification>
  </clause>

  <clause id="7072">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) = 1 / K(y \ x,T(x,z))
    ]]></literal>
    <justification jstring="[para(7071(a,1),5243(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7071 5243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7073">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) = K(T(x,z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,5243,a(flip),b,7072,a),flip(a)].">
      <j1 rule="hyper" parents="334 5243 7072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7074">
    <literal><![CDATA[
      (x * T(x \ y,z)) / K((x / y) \ 1,z) = T(y,K(z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(334,a,6722,a(flip),b,5912,a),flip(a)].">
      <j1 rule="hyper" parents="334 6722 5912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7075">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) / K((y / x) \ 1,z) = T(x,K(z,y \ x))
    ]]></literal>
    <justification jstring="[para(5312(a,1),7074(a,1,1))].">
      <j1 rule="para" parents="5312 7074"/>
    </justification>
  </clause>

  <clause id="7076">
    <literal><![CDATA[
      (1 / (1 / ((x * y) / x))) \ K(x,y) = (y \ 1) * K(y,1 / y)
    ]]></literal>
    <justification jstring="[para(5023(a,1),6007(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5023 6007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7077">
    <literal><![CDATA[
      (1 / (1 / ((x * y) / x))) \ K(x,y) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(334,a,5099,a(flip),b,7076,a),flip(a)].">
      <j1 rule="hyper" parents="334 5099 7076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7078">
    <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(6170(a,1),6168(a,1,1))].">
      <j1 rule="para" parents="6170 6168"/>
    </justification>
  </clause>

  <clause id="7080">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,(y \ 1) \ 1) = (x * K(z,y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(6188(a,1),6187(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6188 6187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7081">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = (x * (z \ 1)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(3696(a,1),7080(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3696 7080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7082">
    <literal><![CDATA[
      R(x / T(y,z),y,y \ 1) = (x * (y \ 1)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6394,a,7081,a)].">
      <j1 rule="hyper" parents="6394 7081"/>
    </justification>
  </clause>

  <clause id="7083">
    <literal><![CDATA[
      ((x * T(y,z)) * (y \ 1)) * K(z,y) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(6(a,1),7082(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 7082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7084">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) \ v5 = L(T(K(y,x),z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(5952(a,1),6210(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5952 6210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7085">
    <literal><![CDATA[
      L(T(K(x,y),z),z,z \ 1) * u = ((1 / z) * (K(y,x) * z)) \ u
    ]]></literal>
    <justification jstring="[para(3154(a,1),7084(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3154 7084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7086">
    <literal><![CDATA[
      ((1 / x) * (K(y,z) * x)) \ u = ((1 / x) * (K(z,y) * x)) * u
    ]]></literal>
    <justification jstring="[para(3154(a,1),7085(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3154 7085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7087">
    <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(334,a,24,a(flip),b,6256,a),flip(a)].">
      <j1 rule="hyper" parents="334 24 6256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7088">
    <literal><![CDATA[
      x / (T(x,y) \ ((x \ 1) \ 1)) = (1 / (1 / x)) / K(y,x)
    ]]></literal>
    <justification jstring="[para(5064(a,2),6272(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5064 6272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7089">
    <literal><![CDATA[
      x / (T(x,y) \ ((x \ 1) \ 1)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5139,a(flip),b,7088,a),flip(a)].">
      <j1 rule="hyper" parents="334 5139 7088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7090">
    <literal><![CDATA[
      x / (x * (1 / T(x,y))) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(2564(a,1),7089(a,1,2))].">
      <j1 rule="para" parents="2564 7089"/>
    </justification>
  </clause>

  <clause id="7091">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ x = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(192,a,7090,a)].">
      <j1 rule="hyper" parents="192 7090"/>
    </justification>
  </clause>

  <clause id="7092">
    <literal><![CDATA[
      ((x \ y) / (x \ 1)) \ T(x \ y,x) = (x \ y) / ((x \ 1) \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(6998,a,6289,a)].">
      <j1 rule="hyper" parents="6998 6289"/>
    </justification>
  </clause>

  <clause id="7093">
    <literal><![CDATA[
      L(T(1 / x,y),y,K(x,z)) = T(1 / x,K(x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(793,a,6305,a)].">
      <j1 rule="hyper" parents="793 6305"/>
    </justification>
  </clause>

  <clause id="7094">
    <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(7093(a,1),5966(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7093 5966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7095">
    <literal><![CDATA[
      L(T(K(x,y),z),z,K(x,u)) = T(K(x,y),K(x,u) * z)
    ]]></literal>
    <justification jstring="[hyper(334,a,5812,a(flip),b,7094,a),flip(a)].">
      <j1 rule="hyper" parents="334 5812 7094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7096">
    <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(7095(a,1),713(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7095 713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7097">
    <literal><![CDATA[
      ((K(x,y) / z) * (z * K(y,x))) \ (K(x,y) / z) = 1 / (z * K(y,x))
    ]]></literal>
    <justification jstring="[para(6520(a,1),6543(a,2,2))].">
      <j1 rule="para" parents="6520 6543"/>
    </justification>
  </clause>

  <clause id="7098">
    <literal><![CDATA[
      K(x \ y,z) \ K(K(x \ y,z),y) = K(y / x,z) \ 1
    ]]></literal>
    <justification jstring="[para(6(a,1),6741(a,2,1))].">
      <j1 rule="para" parents="6 6741"/>
    </justification>
  </clause>

  <clause id="7099">
    <literal><![CDATA[
      K(x \ y,z) \ K(K(x \ y,z),y) = K(z,y / x)
    ]]></literal>
    <justification jstring="[hyper(334,a,5232,a(flip),b,7098,a),flip(a)].">
      <j1 rule="hyper" parents="334 5232 7098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7101">
    <literal><![CDATA[
      K(x \ y,z) \ K(y,K(z,x \ y)) = K(z,y / x)
    ]]></literal>
    <justification jstring="[para(5886(a,1),7099(a,1,2))].">
      <j1 rule="para" parents="5886 7099"/>
    </justification>
  </clause>

  <clause id="7102">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(4894(a,1),6951(a,1,1,2))].">
      <j1 rule="para" parents="4894 6951"/>
    </justification>
  </clause>

  <clause id="7103">
    <literal><![CDATA[
      K(x \ y,z * (1 / (y / x))) = K(x \ y,z / (y / x))
    ]]></literal>
    <justification jstring="[hyper(5412,a,6977,a),flip(a)].">
      <j1 rule="hyper" parents="5412 6977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7104">
    <literal><![CDATA[
      K(x,((y / z) * u) \ (y * u)) = ((y * K(z,x)) * u) \ (y * u)
    ]]></literal>
    <justification jstring="[para(6467(a,1),6979(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6467 6979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7105">
    <literal><![CDATA[
      ((x * K(y,z)) * u) * K(z,((x / y) * u) \ (x * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(119,a,7104,a,b,xx)].">
      <j1 rule="hyper" parents="119 7104"/>
    </justification>
  </clause>

  <clause id="7106">
    <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(6606(a,1),7104(a,2,1))].">
      <j1 rule="para" parents="6606 7104"/>
    </justification>
  </clause>

  <clause id="7107">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) = (x * z) \ ((x * K(y,u)) * z)
    ]]></literal>
    <justification jstring="[para(7105(a,1),6523(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7105 6523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7108">
    <literal><![CDATA[
      ((x * K(y,z)) * K(y,u)) * K(z,y) = x * K(y,u)
    ]]></literal>
    <justification jstring="[para(6590(a,1),7105(a,1,2,2))].">
      <j1 rule="para" parents="6590 7105"/>
    </justification>
  </clause>

  <clause id="7109">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = (x * K(u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6516(a,1),7108(a,1,1,1))].">
      <j1 rule="para" parents="6516 7108"/>
    </justification>
  </clause>

  <clause id="7110">
    <literal><![CDATA[
      ((x * K(y,z)) * K(z,u)) / z = (x * K(z,u)) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,7109,a(flip),b,6370,a)].">
      <j1 rule="hyper" parents="117 7109 6370"/>
    </justification>
  </clause>

  <clause id="7111">
    <literal><![CDATA[
      ((x * K(y,z)) / z) * K(z,u) = (x * K(z,u)) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6737,a,7110,a)].">
      <j1 rule="hyper" parents="6737 7110"/>
    </justification>
  </clause>

  <clause id="7112">
    <literal><![CDATA[
      (x * K(y,z)) / T(y,u) = (x / T(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6379(a,1),7111(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6379 7111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7113">
    <literal><![CDATA[
      ((x / T(y,z)) * K(y,u)) \ (x * K(y,u)) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(192,a,7112,a)].">
      <j1 rule="hyper" parents="192 7112"/>
    </justification>
  </clause>

  <clause id="7114">
    <literal><![CDATA[
      (1 / T(x,y)) * K(x,z) = K(x,z) / T(x,y)
    ]]></literal>
    <justification jstring="[para(2(a,1),7112(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2 7112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7115">
    <literal><![CDATA[
      ((x \ y) * K(x,z)) \ (y * K(x,z)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(273(a,1),7113(a,1,1,1))].">
      <j1 rule="para" parents="273 7113"/>
    </justification>
  </clause>

  <clause id="7116">
    <literal><![CDATA[
      (x * y) \ ((x * K(z \ x,u)) * y) = K((z * y) \ (x * y),u)
    ]]></literal>
    <justification jstring="[para(72(a,1),7107(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 7107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7117">
    <literal><![CDATA[
      (x * y) * K((z * y) \ (x * y),u) = (x * K(z \ x,u)) * y
    ]]></literal>
    <justification jstring="[hyper(134,a,7116,a)].">
      <j1 rule="hyper" parents="134 7116"/>
    </justification>
  </clause>

  <clause id="7118">
    <literal><![CDATA[
      K((x * y) \ (z * y),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,6396,a(flip),b,7117,a),flip(a)].">
      <j1 rule="hyper" parents="29 6396 7117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7119">
    <literal><![CDATA[
      (x * (y * K(z \ u,y))) \ (x * y) = K(y,(z * y) \ (u * y))
    ]]></literal>
    <justification jstring="[para(7118(a,1),6551(a,1,1,2,2))].">
      <j1 rule="para" parents="7118 6551"/>
    </justification>
  </clause>

  <clause id="7120">
    <literal><![CDATA[
      K(x,(y * x) \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(7119(a,1),6665(a,1))].">
      <j1 rule="para" parents="7119 6665"/>
    </justification>
  </clause>

  <clause id="7121">
    <literal><![CDATA[
      K(x,(x * y) \ (z * x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(7120,a,6840,a),flip(a)].">
      <j1 rule="hyper" parents="7120 6840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7122">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / x) \ z) = u
    ]]></literal>
    <justification jstring="[para(7(a,1),7120(a,1,2,1))].">
      <j1 rule="para" parents="7 7120"/>
    </justification>
  </clause>

  <clause id="7123">
    <literal><![CDATA[
      K(x,(x * y) \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(6840(a,1),7120(a,1))].">
      <j1 rule="para" parents="6840 7120"/>
    </justification>
  </clause>

  <clause id="7124">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[para(5(a,1),7121(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 7121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7125">
    <literal><![CDATA[
      T(x,(x \ y) \ z) = T(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(118,a,7124,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 7124 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7126">
    <literal><![CDATA[
      K(x,y \ (((x \ y) * z) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),7124(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 7124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7127">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (x \ y)) \ u)
    ]]></literal>
    <justification jstring="[para(7124(a,1),6849(a,1,1))].">
      <j1 rule="para" parents="7124 6849"/>
    </justification>
  </clause>

  <clause id="7128">
    <literal><![CDATA[
      K(x,(y / x) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(7122,a,xx)].">
      <j1 rule="hyper" parents="7122"/>
    </justification>
  </clause>

  <clause id="7129">
    <literal><![CDATA[
      T(x,(y / x) \ z) = T(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(118,a,7128,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 7128 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7130">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (y / x)) \ u)
    ]]></literal>
    <justification jstring="[para(7128(a,1),6849(a,1,1))].">
      <j1 rule="para" parents="7128 6849"/>
    </justification>
  </clause>

  <clause id="7131">
    <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(7129(a,1),5075(a,1,1,1))].">
      <j1 rule="para" parents="7129 5075"/>
    </justification>
  </clause>

  <clause id="7132">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7127,a(flip),b,7130,a),flip(a)].">
      <j1 rule="hyper" parents="58 7127 7130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7133">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * (x \ z)) \ u)) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(7132(a,1),5399(a,1,2,2))].">
      <j1 rule="para" parents="7132 5399"/>
    </justification>
  </clause>

  <clause id="7134">
    <literal><![CDATA[
      (x \ y) / ((x \ 1) \ (y / x)) = ((y / x) / (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),6997(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 6997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7135">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(y,z)) = (y * z) \ (z * (T(y,z) * x))
    ]]></literal>
    <justification jstring="[para(5047(a,1),7046(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5047 7046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7136">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(y,z)) = L(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,238,a(flip),b,7135,a),flip(a)].">
      <j1 rule="hyper" parents="334 238 7135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7137">
    <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(7135(a,2),860(a,1))].">
      <j1 rule="para" parents="7135 860"/>
    </justification>
  </clause>

  <clause id="7138">
    <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(5435(a,1),7075(a,1,1))].">
      <j1 rule="para" parents="5435 7075"/>
    </justification>
  </clause>

  <clause id="7139">
    <literal><![CDATA[
      ((x \ y) / (x \ 1)) \ T(x \ y,x) = ((y / x) / (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,7134,a(flip),b,7092,a),flip(a)].">
      <j1 rule="hyper" parents="334 7134 7092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7140">
    <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,7097,a)].">
      <j1 rule="hyper" parents="134 7097"/>
    </justification>
  </clause>

  <clause id="7141">
    <literal><![CDATA[
      K(x,(y * (x / z)) \ u) = K(x,(y * (z \ x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6949,a(flip),b,7102,a),flip(a)].">
      <j1 rule="hyper" parents="58 6949 7102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7142">
    <literal><![CDATA[
      K(x,(y * (x / y)) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),7141(a,2,2,1))].">
      <j1 rule="para" parents="5 7141"/>
    </justification>
  </clause>

  <clause id="7143">
    <literal><![CDATA[
      K(x,(y * ((z \ x) \ x)) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(72(a,1),7141(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 7141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7144">
    <literal><![CDATA[
      K(x,((y / T(z,z \ x)) * z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(381(a,1),7143(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="381 7143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7145">
    <literal><![CDATA[
      K(x,(y * K(z \ x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(6370(a,1),7144(a,1,2,1))].">
      <j1 rule="para" parents="6370 7144"/>
    </justification>
  </clause>

  <clause id="7146">
    <literal><![CDATA[
      K(x,((y \ x) \ x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5071(a,1),7145(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5071 7145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7147">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) = K((x * (z \ y)) \ u,z)
    ]]></literal>
    <justification jstring="[hyper(5507,a,7133,a),flip(a)].">
      <j1 rule="hyper" parents="5507 7133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7148">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * (z \ y)) \ u,z) = w
    ]]></literal>
    <justification jstring="[para(7133(a,1),5507(a,1))].">
      <j1 rule="para" parents="7133 5507"/>
    </justification>
  </clause>

  <clause id="7149">
    <literal><![CDATA[
      a(K(x,y) / z,z,K(x,y)) * (1 / (z * K(y,x))) = K(x,y) / z
    ]]></literal>
    <justification jstring="[para(6206(a,1),7140(a,1,1))].">
      <j1 rule="para" parents="6206 7140"/>
    </justification>
  </clause>

  <clause id="7150">
    <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(4914(a,1),4530(a,1,1))].">
      <j1 rule="para" parents="4914 4530"/>
    </justification>
  </clause>

  <clause id="7151">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(4771(a,1),4938(a,1))].">
      <j1 rule="para" parents="4771 4938"/>
    </justification>
  </clause>

  <clause id="7152">
    <literal><![CDATA[
      T(x * K(y * L(x,z,u),x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(5212(a,1),807(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5212 807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7153">
    <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(5645,a,7152,a)].">
      <j1 rule="hyper" parents="5645 7152"/>
    </justification>
  </clause>

  <clause id="7154">
    <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(5214(a,1),1024(a,1,1,1))].">
      <j1 rule="para" parents="5214 1024"/>
    </justification>
  </clause>

  <clause id="7155">
    <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(971(a,1),5323(a,1,2))].">
      <j1 rule="para" parents="971 5323"/>
    </justification>
  </clause>

  <clause id="7156">
    <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(5780(a,1),5779(a,1,1,1))].">
      <j1 rule="para" parents="5780 5779"/>
    </justification>
  </clause>

  <clause id="7157">
    <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(5885(a,1),39(a,1))].">
      <j1 rule="para" parents="5885 39"/>
    </justification>
  </clause>

  <clause id="7158">
    <literal><![CDATA[
      K((x / y) \ 1,z \ (y / x)) = K(y / x,((z * x) / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5705,a(flip),b,6186,a)].">
      <j1 rule="hyper" parents="58 5705 6186"/>
    </justification>
  </clause>

  <clause id="7159">
    <literal><![CDATA[
      K((x / y) \ 1,z \ (y / x)) = K(y / x,y / (z * x))
    ]]></literal>
    <justification jstring="[hyper(334,a,5614,a(flip),b,7158,a),flip(a)].">
      <j1 rule="hyper" parents="334 5614 7158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7161">
    <literal><![CDATA[
      K(x / y,x / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / y,z \ (x / y)) = u
    ]]></literal>
    <justification jstring="[para(7159(a,1),5940(a,1))].">
      <j1 rule="para" parents="7159 5940"/>
    </justification>
  </clause>

  <clause id="7162">
    <literal><![CDATA[
      K(x,y * (((1 / z) * u) * w)) = K(x,y * (((z \ 1) * u) * w))
    ]]></literal>
    <justification jstring="[para(3193(a,1),6290(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3193 6290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7163">
    <literal><![CDATA[
      K(x,y * ((((K(z,u) / z) \ 1) * u) * w)) = K(x,y * ((u * (1 / (1 / z))) * w))
    ]]></literal>
    <justification jstring="[para(5783(a,1),7162(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5783 7162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7164">
    <literal><![CDATA[
      K(x,y \ z) * K((z \ y) \ x,x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5627(a,1),6458(a,1,2))].">
      <j1 rule="para" parents="5627 6458"/>
    </justification>
  </clause>

  <clause id="7165">
    <literal><![CDATA[
      K(x,y \ z) * K(y \ (z * x),x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(6906(a,1),7164(a,1,2))].">
      <j1 rule="para" parents="6906 7164"/>
    </justification>
  </clause>

  <clause id="7166">
    <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(6704(a,2),6770(a,1))].">
      <j1 rule="para" parents="6704 6770"/>
    </justification>
  </clause>

  <clause id="7167">
    <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(6795(a,1),7166(a,1,1))].">
      <j1 rule="para" parents="6795 7166"/>
    </justification>
  </clause>

  <clause id="7168">
    <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(1302(a,1),6762(a,1,1))].">
      <j1 rule="para" parents="1302 6762"/>
    </justification>
  </clause>

  <clause id="7169">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = x / (y \ T(x,y \ 1))
    ]]></literal>
    <justification jstring="[para(4091(a,1),6971(a,2,2))].">
      <j1 rule="para" parents="4091 6971"/>
    </justification>
  </clause>

  <clause id="7170">
    <literal><![CDATA[
      x / (y \ T(x,y \ 1)) = (T(x,y \ 1) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,4146,a(flip),b,7169,a),flip(a)].">
      <j1 rule="hyper" parents="58 4146 7169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7171">
    <literal><![CDATA[
      (T(x,(y \ 1) \ 1) / (y \ 1)) \ x = x / ((y \ 1) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(3106(a,1),7170(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3106 7170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7172">
    <literal><![CDATA[
      x / ((y \ 1) \ T(x,y)) = (T(x,y) / (y \ 1)) \ x
    ]]></literal>
    <justification jstring="[para(3106(a,1),7171(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3106 7171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7173">
    <literal><![CDATA[
      ((T(x,y) / (y \ 1)) \ x) \ x = (y \ 1) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(192,a,7172,a)].">
      <j1 rule="hyper" parents="192 7172"/>
    </justification>
  </clause>

  <clause id="7174">
    <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(6944(a,1),6994(a,1))].">
      <j1 rule="para" parents="6944 6994"/>
    </justification>
  </clause>

  <clause id="7175">
    <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),7174(a,1,1,2))].">
      <j1 rule="para" parents="75 7174"/>
    </justification>
  </clause>

  <clause id="7176">
    <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(5391(a,1),7174(a,1,1,2))].">
      <j1 rule="para" parents="5391 7174"/>
    </justification>
  </clause>

  <clause id="7177">
    <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(7124(a,1),7174(a,1,1))].">
      <j1 rule="para" parents="7124 7174"/>
    </justification>
  </clause>

  <clause id="7178">
    <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,7052,a(flip),b,7078,a),flip(a)].">
      <j1 rule="hyper" parents="58 7052 7078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7179">
    <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(7178(a,1),5403(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7178 5403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7180">
    <literal><![CDATA[
      K((x / y) \ z,L(y,u,w)) = K(x \ (z * y),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(5284,a,7131,a),flip(a)].">
      <j1 rule="hyper" parents="5284 7131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7181">
    <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(7179(a,2),5412(a,1))].">
      <j1 rule="para" parents="7179 5412"/>
    </justification>
  </clause>

  <clause id="7182">
    <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(266(a,2),4878(a,2,1,2,1,2))].">
      <j1 rule="para" parents="266 4878"/>
    </justification>
  </clause>

  <clause id="7183">
    <literal><![CDATA[
      K(x \ (y * z),(x \ (y * z)) \ 1) = K(x \ (y * z),z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(5289,a,5037,a)].">
      <j1 rule="hyper" parents="5289 5037"/>
    </justification>
  </clause>

  <clause id="7184">
    <literal><![CDATA[
      K(x \ (y * z),(y * z) \ x) = K(x \ (y * z),z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(6493,a,7183,a)].">
      <j1 rule="hyper" parents="6493 7183"/>
    </justification>
  </clause>

  <clause id="7185">
    <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,5135,a(flip),b,5090,a),flip(a)].">
      <j1 rule="hyper" parents="116 5135 5090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7186">
    <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(5047(a,1),5384(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5047 5384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7187">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(z,u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,13,a,b,7186,a),flip(a)].">
      <j1 rule="hyper" parents="334 13 7186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7188">
    <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(7186(a,2),495(a,1))].">
      <j1 rule="para" parents="7186 495"/>
    </justification>
  </clause>

  <clause id="7189">
    <literal><![CDATA[
      L(L(x,y * z,K(y,u)),z,y) = L(x,z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(1017,a,7187,a)].">
      <j1 rule="hyper" parents="1017 7187"/>
    </justification>
  </clause>

  <clause id="7190">
    <literal><![CDATA[
      x * (K(x \ 1,x) * K(y,y \ (1 / (x \ 1)))) = y * ((1 / (1 / x)) / y)
    ]]></literal>
    <justification jstring="[para(5590(a,1),5480(a,1,2,2))].">
      <j1 rule="para" parents="5590 5480"/>
    </justification>
  </clause>

  <clause id="7191">
    <literal><![CDATA[
      K(x,x \ y) * K(z,y / (y / x)) = T(y / (y / x),z) \ x
    ]]></literal>
    <justification jstring="[para(5239(a,1),5736(a,1,1))].">
      <j1 rule="para" parents="5239 5736"/>
    </justification>
  </clause>

  <clause id="7192">
    <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(3259(a,1),5926(a,1,3))].">
      <j1 rule="para" parents="3259 5926"/>
    </justification>
  </clause>

  <clause id="7193">
    <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(6146(a,1),6004(a,1,2,2,2))].">
      <j1 rule="para" parents="6146 6004"/>
    </justification>
  </clause>

  <clause id="7194">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * (u * K(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(6014(a,1),6005(a,2,2,2))].">
      <j1 rule="para" parents="6014 6005"/>
    </justification>
  </clause>

  <clause id="7195">
    <literal><![CDATA[
      (1 / x) * K(((1 / x) \ y) \ 1,z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(75(a,1),6319(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 6319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7197">
    <literal><![CDATA[
      (1 / x) * K(y \ (1 / x),z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(6615(a,1),7195(a,1,2))].">
      <j1 rule="para" parents="6615 7195"/>
    </justification>
  </clause>

  <clause id="7198">
    <literal><![CDATA[
      K((x * y) \ 1,x * y) = K(x \ (1 / y),x * y)
    ]]></literal>
    <justification jstring="[hyper(29,a,3803,a,b,7197,a)].">
      <j1 rule="hyper" parents="29 3803 7197"/>
    </justification>
  </clause>

  <clause id="7199">
    <literal><![CDATA[
      (1 / x) * K(y \ (x \ 1),z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(4284(a,1),7197(a,1,2))].">
      <j1 rule="para" parents="4284 7197"/>
    </justification>
  </clause>

  <clause id="7200">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,x * (y \ 1)) = K(x \ y,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(72(a,1),7198(a,2,1,2))].">
      <j1 rule="para" parents="72 7198"/>
    </justification>
  </clause>

  <clause id="7201">
    <literal><![CDATA[
      (x * K((y / x) \ 1,y / x)) * (x \ 1) = K(y \ x,y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,4370,a,b,7200,a)].">
      <j1 rule="hyper" parents="58 4370 7200"/>
    </justification>
  </clause>

  <clause id="7202">
    <literal><![CDATA[
      (x * K(y \ x,x \ y)) * (x \ 1) = K(y \ x,y * (x \ 1))
    ]]></literal>
    <justification jstring="[para(3305(a,1),7201(a,1,1,2))].">
      <j1 rule="para" parents="3305 7201"/>
    </justification>
  </clause>

  <clause id="7203">
    <literal><![CDATA[
      K(x \ y,x * (y \ 1)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(3988,a,7202,a),flip(a)].">
      <j1 rule="hyper" parents="3988 7202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7204">
    <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),7203(a,1,2,2))].">
      <j1 rule="para" parents="106 7203"/>
    </justification>
  </clause>

  <clause id="7205">
    <literal><![CDATA[
      K(x \ (y \ 1),(y \ 1) \ x) = K(x \ (1 / y),x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5698,a(flip),b,7204,a),flip(a)].">
      <j1 rule="hyper" parents="58 5698 7204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7206">
    <literal><![CDATA[
      K(x \ (1 / y),x * y) = K(x \ (y \ 1),y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6068,a(flip),b,7205,a),flip(a)].">
      <j1 rule="hyper" parents="58 6068 7205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7207">
    <literal><![CDATA[
      K((x * y) \ 1,x * y) = K(x \ (y \ 1),y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7198,a,b,7206,a)].">
      <j1 rule="hyper" parents="58 7198 7206"/>
    </justification>
  </clause>

  <clause id="7208">
    <literal><![CDATA[
      (T(x * y,z) / y) * (x \ 1) = (1 / y) * (x \ T(x * y,z))
    ]]></literal>
    <justification jstring="[para(1042(a,1),6320(a,1,1))].">
      <j1 rule="para" parents="1042 6320"/>
    </justification>
  </clause>

  <clause id="7209">
    <literal><![CDATA[
      (1 / x) * ((x \ y) \ T((x \ y) * x,x)) = (x \ T(y,x)) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1435(a,1),7208(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1435 7208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7211">
    <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(6432(a,1),6478(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6432 6478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7212">
    <literal><![CDATA[
      R(R(x,y,z),y * z,K(z,u)) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,15,a,b,7211,a),flip(a)].">
      <j1 rule="hyper" parents="334 15 7211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7213">
    <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(7211(a,2),530(a,1))].">
      <j1 rule="para" parents="7211 530"/>
    </justification>
  </clause>

  <clause id="7214">
    <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,7212,a)].">
      <j1 rule="hyper" parents="58 26 7212"/>
    </justification>
  </clause>

  <clause id="7215">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = (1 / z) * K((((z \ 1) \ x) \ 1) \ (z \ 1),y)
    ]]></literal>
    <justification jstring="[para(4305(a,1),6843(a,2,2))].">
      <j1 rule="para" parents="4305 6843"/>
    </justification>
  </clause>

  <clause id="7216">
    <literal><![CDATA[
      (x * (y * ((z \ (y \ (x \ u))) * z))) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(105(a,1),6950(a,1,1,2,2))].">
      <j1 rule="para" parents="105 6950"/>
    </justification>
  </clause>

  <clause id="7217">
    <literal><![CDATA[
      ((x * y) * ((z \ ((x * y) \ u)) * z)) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(3687(a,2),7216(a,1,1))].">
      <j1 rule="para" parents="3687 7216"/>
    </justification>
  </clause>

  <clause id="7218">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * (z * K(y,z)))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(5156(a,1),6962(a,1,1,2))].">
      <j1 rule="para" parents="5156 6962"/>
    </justification>
  </clause>

  <clause id="7219">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (T(y,z) * z)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(5102(a,1),7218(a,1,2,2))].">
      <j1 rule="para" parents="5102 7218"/>
    </justification>
  </clause>

  <clause id="7220">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) = w
    ]]></literal>
    <justification jstring="[para(7130(a,1),7177(a,1))].">
      <j1 rule="para" parents="7130 7177"/>
    </justification>
  </clause>

  <clause id="7221">
    <literal><![CDATA[
      x * (K(x \ 1,x) * K(y,y \ x)) = y * ((1 / (1 / x)) / y)
    ]]></literal>
    <justification jstring="[para(72(a,1),7190(a,1,2,2,2,2))].">
      <j1 rule="para" parents="72 7190"/>
    </justification>
  </clause>

  <clause id="7223">
    <literal><![CDATA[
      T(x * ((1 / (1 / y)) / x),K(z,y)) = y * (K(y \ 1,y) * K(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(334,a,4862,a,b,7221,a)].">
      <j1 rule="hyper" parents="334 4862 7221"/>
    </justification>
  </clause>

  <clause id="7224">
    <literal><![CDATA[
      (x \ T(y,x)) * ((x \ y) \ 1) = (1 / x) * ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(4875(a,1),7209(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4875 7209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7225">
    <literal><![CDATA[
      K(x,y) = (y \ T(x,y)) * ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,5163,a,b,7224,a)].">
      <j1 rule="hyper" parents="334 5163 7224"/>
    </justification>
  </clause>

  <clause id="7226">
    <literal><![CDATA[
      (x \ T(x * y,x)) * (y \ 1) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),7225(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 7225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7227">
    <literal><![CDATA[
      (x \ T(x * K(y,z),x)) * (K(z,y) * 1) = K(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(5391(a,1),7226(a,1,2))].">
      <j1 rule="para" parents="5391 7226"/>
    </justification>
  </clause>

  <clause id="7228">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * (K(z,x) * 1) = K(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(6294(a,2),7227(a,1,1))].">
      <j1 rule="para" parents="6294 7227"/>
    </justification>
  </clause>

  <clause id="7229">
    <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),7228(a,1,2))].">
      <j1 rule="para" parents="3 7228"/>
    </justification>
  </clause>

  <clause id="7230">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = K(((((z \ 1) \ x) \ 1) * z) \ 1,y) / z
    ]]></literal>
    <justification jstring="[hyper(334,a,7199,a(flip),b,7215,a),flip(a)].">
      <j1 rule="hyper" parents="334 7199 7215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7231">
    <literal><![CDATA[
      R((x \ (1 / y)) * x,y,z) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(4028(a,2),4883(a,1,1))].">
      <j1 rule="para" parents="4028 4883"/>
    </justification>
  </clause>

  <clause id="7232">
    <literal><![CDATA[
      K(x \ 1,x) * K(y,y \ x) = (x \ 1) * (y * (x / y))
    ]]></literal>
    <justification jstring="[hyper(4940,a,7223,a),flip(a)].">
      <j1 rule="hyper" parents="4940 7223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7233">
    <literal><![CDATA[
      (1 / x) * (y * (x / y)) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(3187,a,7232,a)].">
      <j1 rule="hyper" parents="3187 7232"/>
    </justification>
  </clause>

  <clause id="7234">
    <literal><![CDATA[
      x \ K(y,y \ (x \ 1)) = y * ((x \ 1) / y)
    ]]></literal>
    <justification jstring="[hyper(116,a,7233,a(flip),b,186,a(flip))].">
      <j1 rule="hyper" parents="116 7233 186"/>
    </justification>
  </clause>

  <clause id="7235">
    <literal><![CDATA[
      ((1 / R(x,y,z)) * x) * (x \ 1) = T(1 / R(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(5282,a,6075,a),flip(a)].">
      <j1 rule="hyper" parents="5282 6075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7236">
    <literal><![CDATA[
      (x / R(x,y,z)) * (x \ 1) = T(1 / R(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(1953(a,1),7235(a,1,1))].">
      <j1 rule="para" parents="1953 7235"/>
    </justification>
  </clause>

  <clause id="7237">
    <literal><![CDATA[
      (x / R(x,y,z)) * (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(334,a,4260,a(flip),b,7236,a),flip(a)].">
      <j1 rule="hyper" parents="334 4260 7236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7238">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(4263,a,7237,a)].">
      <j1 rule="hyper" parents="4263 7237"/>
    </justification>
  </clause>

  <clause id="7239">
    <literal><![CDATA[
      T(R(x,y,z) \ x,x \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(246,a,7238,a,b,4266,a)].">
      <j1 rule="hyper" parents="246 7238 4266"/>
    </justification>
  </clause>

  <clause id="7240">
    <literal><![CDATA[
      K(R(x,y,z) \ x,x \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,7239,a)].">
      <j1 rule="hyper" parents="50 7239"/>
    </justification>
  </clause>

  <clause id="7241">
    <literal><![CDATA[
      T(1 / x,R(x,y,z) \ x) = 1 / x
    ]]></literal>
    <justification jstring="[para(7240(a,1),5154(a,1,1,1))].">
      <j1 rule="para" parents="7240 5154"/>
    </justification>
  </clause>

  <clause id="7242">
    <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(7241(a,1),2178(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7241 2178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7243">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(334,a,5614,a(flip),b,6183,a),flip(a)].">
      <j1 rule="hyper" parents="334 5614 6183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7244">
    <literal><![CDATA[
      R(K(x,x / y),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6153,a(flip),b,7243,a)].">
      <j1 rule="hyper" parents="58 6153 7243"/>
    </justification>
  </clause>

  <clause id="7245">
    <literal><![CDATA[
      R(K(x,y \ x),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(5463(a,1),7244(a,1,1))].">
      <j1 rule="para" parents="5463 7244"/>
    </justification>
  </clause>

  <clause id="7246">
    <literal><![CDATA[
      K(x,((x * y) * z) / ((u * y) * z)) = K(R(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7052,a(flip),b,7245,a),flip(a)].">
      <j1 rule="hyper" parents="58 7052 7245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7247">
    <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),7246(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 7246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7248">
    <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(5675(a,1),7246(a,1,2,1))].">
      <j1 rule="para" parents="5675 7246"/>
    </justification>
  </clause>

  <clause id="7249">
    <literal><![CDATA[
      K(x,(y * z) / ((u * (x \ y)) * z)) = R(K(x,u \ x),y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7053,a(flip),b,7247,a),flip(a)].">
      <j1 rule="hyper" parents="58 7053 7247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7250">
    <literal><![CDATA[
      L(x \ y,T(x,x \ z),x \ z) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[para(227(a,1),6249(a,1,1)),flip(a)].">
      <j1 rule="para" parents="227 6249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7251">
    <literal><![CDATA[
      L(x \ y,(x \ z) \ z,x \ z) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1675,a(flip),b,7250,a)].">
      <j1 rule="hyper" parents="58 1675 7250"/>
    </justification>
  </clause>

  <clause id="7252">
    <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(6378(a,2),6407(a,2,2))].">
      <j1 rule="para" parents="6378 6407"/>
    </justification>
  </clause>

  <clause id="7253">
    <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),7154(a,2,1,1))].">
      <j1 rule="para" parents="4 7154"/>
    </justification>
  </clause>

  <clause id="7254">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = (((z \ (1 / x)) * z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(293,a,7231,a),flip(a)].">
      <j1 rule="hyper" parents="293 7231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7255">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = K(x \ (z \ 1),z) * y
    ]]></literal>
    <justification jstring="[para(6931(a,1),7254(a,2,1))].">
      <j1 rule="para" parents="6931 7254"/>
    </justification>
  </clause>

  <clause id="7256">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) = y / (K(z \ (x \ 1),x) * y)
    ]]></literal>
    <justification jstring="[para(7255(a,1),6008(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7255 6008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7257">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(334,a,5403,a(flip),b,7256,a),flip(a)].">
      <j1 rule="hyper" parents="334 5403 7256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7258">
    <literal><![CDATA[
      K(x,y / (x * (z * y))) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(6257,a,7257,a)].">
      <j1 rule="hyper" parents="6257 7257"/>
    </justification>
  </clause>

  <clause id="7260">
    <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(334,a,4726,a(flip),b,7252,a),flip(a)].">
      <j1 rule="hyper" parents="334 4726 7252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7261">
    <literal><![CDATA[
      (x \ (y * (T(z,x) \ z))) * x = ((x \ y) * x) * (T(z,x) \ z)
    ]]></literal>
    <justification jstring="[para(231(a,1),4850(a,1,1)),flip(a)].">
      <j1 rule="para" parents="231 4850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7263">
    <literal><![CDATA[
      ((x \ y) * x) * (T(z,x) \ z) = (x \ (y * K(x,z))) * x
    ]]></literal>
    <justification jstring="[para(4996(a,2),7261(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4996 7261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7264">
    <literal><![CDATA[
      (x \ (y * K(x,z))) * x = ((x \ y) * x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(4996(a,2),7263(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4996 7263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7266">
    <literal><![CDATA[
      x \ (y * K(x,z)) = (x \ y) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,6585,a,b,7264,a),flip(a)].">
      <j1 rule="hyper" parents="30 6585 7264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7267">
    <literal><![CDATA[
      x * ((x \ y) * K(x,z)) = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,7266,a)].">
      <j1 rule="hyper" parents="134 7266"/>
    </justification>
  </clause>

  <clause id="7268">
    <literal><![CDATA[
      T(x,y) \ (z * K(x,y)) = T(x \ z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(246,a,7266,a(flip),b,5337,a),flip(a)].">
      <j1 rule="hyper" parents="246 7266 5337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7270">
    <literal><![CDATA[
      (x * y) * K(x,z) = x * (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),7267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 7267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7271">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(6991,a,7270,a),flip(a)].">
      <j1 rule="hyper" parents="6991 7270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7272">
    <literal><![CDATA[
      R(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4339,a,7270,a)].">
      <j1 rule="hyper" parents="4339 7270"/>
    </justification>
  </clause>

  <clause id="7273">
    <literal><![CDATA[
      L(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4329,a,7270,a)].">
      <j1 rule="hyper" parents="4329 7270"/>
    </justification>
  </clause>

  <clause id="7274">
    <literal><![CDATA[
      T(x,y) * T(z,K(x,y)) = (x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5339,a,b,7270,a)].">
      <j1 rule="hyper" parents="334 5339 7270"/>
    </justification>
  </clause>

  <clause id="7275">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6727,a,b,7270,a)].">
      <j1 rule="hyper" parents="58 6727 7270"/>
    </justification>
  </clause>

  <clause id="7276">
    <literal><![CDATA[
      a(x,y,K(x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,7270,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="115 7270 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7277">
    <literal><![CDATA[
      (x * (y * K(x,z))) * x = (x * y) * T(x,z)
    ]]></literal>
    <justification jstring="[para(7270(a,1),6532(a,1,1))].">
      <j1 rule="para" parents="7270 6532"/>
    </justification>
  </clause>

  <clause id="7278">
    <literal><![CDATA[
      (x * (y * K(x,z))) / x = ((x * y) / x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(7270(a,1),6582(a,1,1))].">
      <j1 rule="para" parents="7270 6582"/>
    </justification>
  </clause>

  <clause id="7279">
    <literal><![CDATA[
      R(T(x,y),z,K(x,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7272(a,1),22(a,2,1))].">
      <j1 rule="para" parents="7272 22"/>
    </justification>
  </clause>

  <clause id="7280">
    <literal><![CDATA[
      (T(x,y) * z) * K(x,u) = T(x,y) * (z * K(x,u))
    ]]></literal>
    <justification jstring="[para(7272(a,1),524(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7272 524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7281">
    <literal><![CDATA[
      (L(x,y,z) * u) * K(x,w) = L(x,y,z) * (u * K(x,w))
    ]]></literal>
    <justification jstring="[para(7272(a,1),525(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7272 525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7282">
    <literal><![CDATA[
      (R(x,y,z) * u) * K(x,w) = R(x,y,z) * (u * K(x,w))
    ]]></literal>
    <justification jstring="[para(7272(a,1),526(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7272 526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7283">
    <literal><![CDATA[
      R(K(x,y),z,K(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7272(a,1),6164(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7272 6164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7284">
    <literal><![CDATA[
      x \ (y * T(x,z)) = T(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(7272(a,1),6476(a,1,1))].">
      <j1 rule="para" parents="7272 6476"/>
    </justification>
  </clause>

  <clause id="7285">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,u) = K(x,y) * (z * K(x,u))
    ]]></literal>
    <justification jstring="[para(7272(a,1),7057(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7272 7057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7286">
    <literal><![CDATA[
      R(x,y,T(x,z)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(7272(a,1),7214(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7272 7214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7287">
    <literal><![CDATA[
      L(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6202,a,7276,a)].">
      <j1 rule="hyper" parents="6202 7276"/>
    </justification>
  </clause>

  <clause id="7288">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(7174,a,7273,a)].">
      <j1 rule="hyper" parents="7174 7273"/>
    </justification>
  </clause>

  <clause id="7289">
    <literal><![CDATA[
      K(x,L(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6956,a,7273,a)].">
      <j1 rule="hyper" parents="6956 7273"/>
    </justification>
  </clause>

  <clause id="7290">
    <literal><![CDATA[
      L(K(x,y),z,x) = u \ (u * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,4,a,b,7273,a),flip(a)].">
      <j1 rule="hyper" parents="334 4 7273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7291">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6883,a(flip),b,7273,a)].">
      <j1 rule="hyper" parents="58 6883 7273"/>
    </justification>
  </clause>

  <clause id="7292">
    <literal><![CDATA[
      a(x,y,K(z,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,7273,a(flip),b,6205,a),flip(a)].">
      <j1 rule="hyper" parents="115 7273 6205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7293">
    <literal><![CDATA[
      (x * y) * K(z,x) = x * (y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(214,a,7292,a)].">
      <j1 rule="hyper" parents="214 7292"/>
    </justification>
  </clause>

  <clause id="7294">
    <literal><![CDATA[
      K((x * y) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(7166,a,7287,a)].">
      <j1 rule="hyper" parents="7166 7287"/>
    </justification>
  </clause>

  <clause id="7295">
    <literal><![CDATA[
      K(x,L(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6956,a,7287,a)].">
      <j1 rule="hyper" parents="6956 7287"/>
    </justification>
  </clause>

  <clause id="7296">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(y \ (x * z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6894,a(flip),b,7287,a),flip(a)].">
      <j1 rule="hyper" parents="58 6894 7287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7297">
    <literal><![CDATA[
      K(L(x,y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6883,a(flip),b,7287,a)].">
      <j1 rule="hyper" parents="58 6883 7287"/>
    </justification>
  </clause>

  <clause id="7299">
    <literal><![CDATA[
      x \ (y * K(z,x)) = (x \ y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(7287(a,1),487(a,1,2,2))].">
      <j1 rule="para" parents="7287 487"/>
    </justification>
  </clause>

  <clause id="7301">
    <literal><![CDATA[
      T(x,L(y,z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7289,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 7289 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7302">
    <literal><![CDATA[
      K(x,L(L(y,z,x),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(25(a,1),7289(a,1,2))].">
      <j1 rule="para" parents="25 7289"/>
    </justification>
  </clause>

  <clause id="7303">
    <literal><![CDATA[
      K(x,T((x \ y) \ z,u)) = K(x,T(y \ (x * z),u))
    ]]></literal>
    <justification jstring="[para(779(a,1),7289(a,1,2)),flip(a)].">
      <j1 rule="para" parents="779 7289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7304">
    <literal><![CDATA[
      L(x * K(y,x),z,y) = L(x,z,y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7289(a,1),5780(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7289 5780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7305">
    <literal><![CDATA[
      K(L(x,y,z),L(u,w,x)) = L(K(x,u),y * x,z)
    ]]></literal>
    <justification jstring="[para(7289(a,1),6883(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7289 6883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7306">
    <literal><![CDATA[
      K(x,(y * (x / y)) \ (x * z)) = K(x,K(y \ x,y) * z)
    ]]></literal>
    <justification jstring="[para(6041(a,1),7289(a,1,2))].">
      <j1 rule="para" parents="6041 7289"/>
    </justification>
  </clause>

  <clause id="7307">
    <literal><![CDATA[
      L(x,y,x) * K(x,z) = L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7291,a(flip),b,5028,a)].">
      <j1 rule="hyper" parents="119 7291 5028"/>
    </justification>
  </clause>

  <clause id="7308">
    <literal><![CDATA[
      K(T(x / (x / y),x),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(4645(a,2),7291(a,1,1))].">
      <j1 rule="para" parents="4645 7291"/>
    </justification>
  </clause>

  <clause id="7309">
    <literal><![CDATA[
      K(T(x / y,x),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(4648(a,1),7291(a,1,1))].">
      <j1 rule="para" parents="4648 7291"/>
    </justification>
  </clause>

  <clause id="7310">
    <literal><![CDATA[
      K(R(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4939(a,1),7291(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4939 7291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7311">
    <literal><![CDATA[
      T(x,L(y,z,y)) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(7291(a,1),5074(a,2,2))].">
      <j1 rule="para" parents="7291 5074"/>
    </justification>
  </clause>

  <clause id="7312">
    <literal><![CDATA[
      K(x,y) * L(x,z,x) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(7291(a,1),5116(a,1,1))].">
      <j1 rule="para" parents="7291 5116"/>
    </justification>
  </clause>

  <clause id="7313">
    <literal><![CDATA[
      T(x,L(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7295,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 7295 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7314">
    <literal><![CDATA[
      K(x,T(y / z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4648(a,1),7295(a,1,2))].">
      <j1 rule="para" parents="4648 7295"/>
    </justification>
  </clause>

  <clause id="7315">
    <literal><![CDATA[
      K(x,R(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4939(a,1),7295(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4939 7295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7316">
    <literal><![CDATA[
      K(L(L(x,y,z),u,w),z) = K(L(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(25(a,1),7297(a,1,1))].">
      <j1 rule="para" parents="25 7297"/>
    </justification>
  </clause>

  <clause id="7317">
    <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(7297(a,1),5787(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7297 5787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7318">
    <literal><![CDATA[
      K((x * (y / x)) \ (y * z),y) = K(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[para(6041(a,1),7297(a,1,1))].">
      <j1 rule="para" parents="6041 7297"/>
    </justification>
  </clause>

  <clause id="7319">
    <literal><![CDATA[
      T(x,(x * y) \ z) = T(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(311(a,1),7301(a,1,2))].">
      <j1 rule="para" parents="311 7301"/>
    </justification>
  </clause>

  <clause id="7320">
    <literal><![CDATA[
      R(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7053,a(flip),b,7310,a)].">
      <j1 rule="hyper" parents="58 7053 7310"/>
    </justification>
  </clause>

  <clause id="7321">
    <literal><![CDATA[
      R(x,y,x) * K(x,z) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7310,a(flip),b,5029,a)].">
      <j1 rule="hyper" parents="119 7310 5029"/>
    </justification>
  </clause>

  <clause id="7322">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4581(a,1),7310(a,1,1))].">
      <j1 rule="para" parents="4581 7310"/>
    </justification>
  </clause>

  <clause id="7323">
    <literal><![CDATA[
      K(T(x,x * y),z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(4629(a,1),7310(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4629 7310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7324">
    <literal><![CDATA[
      K(T(x,x \ y),z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(4695(a,1),7310(a,1,1))].">
      <j1 rule="para" parents="4695 7310"/>
    </justification>
  </clause>

  <clause id="7325">
    <literal><![CDATA[
      K(x,R(y,z,y)) = 1 / K(y,x)
    ]]></literal>
    <justification jstring="[para(7310(a,1),5243(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7310 5243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7326">
    <literal><![CDATA[
      K(x,y) * (R(x,z,x) * u) = R(T(x,y),z,x) * u
    ]]></literal>
    <justification jstring="[para(7310(a,1),5380(a,1,1))].">
      <j1 rule="para" parents="7310 5380"/>
    </justification>
  </clause>

  <clause id="7327">
    <literal><![CDATA[
      (K(x,y) * z) * x = K(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(7310(a,1),7057(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7310 7057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7328">
    <literal><![CDATA[
      T(x / L(y,z,y),y) = L(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(431,a,7313,a),flip(a)].">
      <j1 rule="hyper" parents="431 7313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7331">
    <literal><![CDATA[
      L(x,y,x) * T(z,x) = z * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7313,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7313 17"/>
    </justification>
  </clause>

  <clause id="7332">
    <literal><![CDATA[
      T(x,T(y / z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4648(a,1),7313(a,1,2))].">
      <j1 rule="para" parents="4648 7313"/>
    </justification>
  </clause>

  <clause id="7333">
    <literal><![CDATA[
      T(x,R(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4939(a,1),7313(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4939 7313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7334">
    <literal><![CDATA[
      R(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6164,a(flip),b,7315,a)].">
      <j1 rule="hyper" parents="58 6164 7315"/>
    </justification>
  </clause>

  <clause id="7335">
    <literal><![CDATA[
      R(x * K(y,x),z,x) = R(x,z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7315,a(flip),b,5787,a),flip(a)].">
      <j1 rule="hyper" parents="119 7315 5787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7336">
    <literal><![CDATA[
      K(x,T(y,y * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4629(a,1),7315(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4629 7315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7337">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4695(a,1),7315(a,1,2))].">
      <j1 rule="para" parents="4695 7315"/>
    </justification>
  </clause>

  <clause id="7338">
    <literal><![CDATA[
      K(x,R(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6167,a(flip),b,7320,a)].">
      <j1 rule="hyper" parents="58 6167 7320"/>
    </justification>
  </clause>

  <clause id="7339">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y / (z / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6160,a(flip),b,7320,a)].">
      <j1 rule="hyper" parents="58 6160 7320"/>
    </justification>
  </clause>

  <clause id="7340">
    <literal><![CDATA[
      K(x,(y / x) / z) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6159,a(flip),b,7320,a),flip(a)].">
      <j1 rule="hyper" parents="58 6159 7320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7341">
    <literal><![CDATA[
      R(x,y,z) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = x
    ]]></literal>
    <justification jstring="[para(7320(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="7320 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7343">
    <literal><![CDATA[
      (x * (K(y,x) * z)) * y = K(y,x) * ((x * z) * y)
    ]]></literal>
    <justification jstring="[para(7320(a,1),5691(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7320 5691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7344">
    <literal><![CDATA[
      T(x / y,R(y,z,y)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(470,a,7333,a)].">
      <j1 rule="hyper" parents="470 7333"/>
    </justification>
  </clause>

  <clause id="7345">
    <literal><![CDATA[
      T(x / R(y,z,y),y) = R(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(431,a,7333,a),flip(a)].">
      <j1 rule="hyper" parents="431 7333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7346">
    <literal><![CDATA[
      R(x,y,x) * T(z,x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7333,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7333 17"/>
    </justification>
  </clause>

  <clause id="7349">
    <literal><![CDATA[
      T(x,(y \ z) \ T(z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4581(a,1),7333(a,1,2))].">
      <j1 rule="para" parents="4581 7333"/>
    </justification>
  </clause>

  <clause id="7350">
    <literal><![CDATA[
      T(x,T(y,y \ z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4695(a,1),7333(a,1,2))].">
      <j1 rule="para" parents="4695 7333"/>
    </justification>
  </clause>

  <clause id="7351">
    <literal><![CDATA[
      (K(x,y) * z) * y = K(x,y) * (z * y)
    ]]></literal>
    <justification jstring="[para(7334(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7334 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7352">
    <literal><![CDATA[
      T(x,R(y,z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7338,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 7338 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7355">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,y / (z / x))
    ]]></literal>
    <justification jstring="[para(538(a,1),7352(a,1,2))].">
      <j1 rule="para" parents="538 7352"/>
    </justification>
  </clause>

  <clause id="7361">
    <literal><![CDATA[
      R(x / y,z,x / y) = R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),7286(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 7286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7365">
    <literal><![CDATA[
      T(x,y * K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6736,a(flip),b,7279,a),flip(a)].">
      <j1 rule="hyper" parents="58 6736 7279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7366">
    <literal><![CDATA[
      R(T(x,y),z,T(x,u)) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(7279(a,1),7214(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7279 7214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7369">
    <literal><![CDATA[
      K(x,y * K(x,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,7365,a(flip),b,5020,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 7365 5020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7372">
    <literal><![CDATA[
      T(x,y * L(K(x,z),u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5949(a,1),7365(a,1,2,2))].">
      <j1 rule="para" parents="5949 7365"/>
    </justification>
  </clause>

  <clause id="7375">
    <literal><![CDATA[
      T(x,y * K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6516(a,1),7365(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6516 7365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7376">
    <literal><![CDATA[
      T(x,y / (z / x)) = T(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[para(6695(a,1),7365(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6695 7365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7378">
    <literal><![CDATA[
      T(x,y * (z * x)) = T(x,y * (x * z))
    ]]></literal>
    <justification jstring="[para(6901(a,1),7365(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6901 7365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7379">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,u) = K(x,y) * (z * K(y,u))
    ]]></literal>
    <justification jstring="[para(7283(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7283 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7380">
    <literal><![CDATA[
      T(x,L(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(7311(a,2),5079(a,1))].">
      <j1 rule="para" parents="7311 5079"/>
    </justification>
  </clause>

  <clause id="7381">
    <literal><![CDATA[
      K(x,R(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7325(a,2),5248(a,1))].">
      <j1 rule="para" parents="7325 5248"/>
    </justification>
  </clause>

  <clause id="7382">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = (z / x) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7344,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7344 17"/>
    </justification>
  </clause>

  <clause id="7383">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(194(a,1),7308(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="194 7308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7384">
    <literal><![CDATA[
      K(T(x / (x / y),x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(7309(a,2),6672(a,1))].">
      <j1 rule="para" parents="7309 6672"/>
    </justification>
  </clause>

  <clause id="7385">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),7314(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 7314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7386">
    <literal><![CDATA[
      K(x,L(y \ z,y,u) \ (u * z)) = K(x,T(u * y,u * z))
    ]]></literal>
    <justification jstring="[para(483(a,1),7314(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="483 7314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7387">
    <literal><![CDATA[
      K(x,R(T(y / z,y * u),z,u)) = K(x,(z * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(539(a,1),7314(a,1,2))].">
      <j1 rule="para" parents="539 7314"/>
    </justification>
  </clause>

  <clause id="7388">
    <literal><![CDATA[
      K(T(x,y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6657,a(flip),b,7324,a),flip(a)].">
      <j1 rule="hyper" parents="58 6657 7324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7389">
    <literal><![CDATA[
      K(T(x,y),y / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,6440,a(flip),b,7388,a),flip(a)].">
      <j1 rule="hyper" parents="334 6440 7388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7390">
    <literal><![CDATA[
      K(T(x,K(y,z)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,2062,a(flip),b,7388,a),flip(a)].">
      <j1 rule="hyper" parents="334 2062 7388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7391">
    <literal><![CDATA[
      (K(x,y) * z) * K(T(y,z),x) = z
    ]]></literal>
    <justification jstring="[hyper(119,a,7388,a,b,6731,a)].">
      <j1 rule="hyper" parents="119 7388 6731"/>
    </justification>
  </clause>

  <clause id="7392">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,7388,a,b,5393,a)].">
      <j1 rule="hyper" parents="119 7388 5393"/>
    </justification>
  </clause>

  <clause id="7393">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,7388,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7388 17"/>
    </justification>
  </clause>

  <clause id="7394">
    <literal><![CDATA[
      T(K(x,y),z) * T(x,z) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(7388(a,1),5034(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7388 5034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7395">
    <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,7390,a(flip),b,5548,a(flip))].">
      <j1 rule="hyper" parents="119 7390 5548"/>
    </justification>
  </clause>

  <clause id="7396">
    <literal><![CDATA[
      T(x,(y \ z) \ z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),7332(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 7332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7397">
    <literal><![CDATA[
      T(x,y \ T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(x,z) / y) = u
    ]]></literal>
    <justification jstring="[para(7332(a,1),5458(a,1))].">
      <j1 rule="para" parents="7332 5458"/>
    </justification>
  </clause>

  <clause id="7398">
    <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(1505(a,1),7336(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1505 7336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7399">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ y))
    ]]></literal>
    <justification jstring="[para(1751(a,1),7336(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1751 7336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7400">
    <literal><![CDATA[
      K(x,T(y,z * y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4553(a,2),7336(a,1,2))].">
      <j1 rule="para" parents="4553 7336"/>
    </justification>
  </clause>

  <clause id="7401">
    <literal><![CDATA[
      K(x,T(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6575,a(flip),b,7337,a),flip(a)].">
      <j1 rule="hyper" parents="58 6575 7337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7402">
    <literal><![CDATA[
      K(x,T(y * z,y \ 1)) = K(x,T(y * z,z))
    ]]></literal>
    <justification jstring="[para(4430(a,1),7337(a,1,2))].">
      <j1 rule="para" parents="4430 7337"/>
    </justification>
  </clause>

  <clause id="7403">
    <literal><![CDATA[
      K(T(x,y),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,7388,a,b,7401,a)].">
      <j1 rule="hyper" parents="334 7388 7401"/>
    </justification>
  </clause>

  <clause id="7404">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[hyper(334,a,6870,a,b,7401,a)].">
      <j1 rule="hyper" parents="334 6870 7401"/>
    </justification>
  </clause>

  <clause id="7405">
    <literal><![CDATA[
      L(T(K(x,y \ z),u),y \ z,w) = K(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,6809,a,b,7401,a)].">
      <j1 rule="hyper" parents="334 6809 7401"/>
    </justification>
  </clause>

  <clause id="7406">
    <literal><![CDATA[
      (K(x,y) * z) \ z = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,6731,a,b,7401,a)].">
      <j1 rule="hyper" parents="334 6731 7401"/>
    </justification>
  </clause>

  <clause id="7407">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,6651,a,b,7401,a)].">
      <j1 rule="hyper" parents="334 6651 7401"/>
    </justification>
  </clause>

  <clause id="7408">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = K(x,T(R(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(334,a,6172,a,b,7401,a)].">
      <j1 rule="hyper" parents="334 6172 7401"/>
    </justification>
  </clause>

  <clause id="7409">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,5890,a,b,7401,a)].">
      <j1 rule="hyper" parents="334 5890 7401"/>
    </justification>
  </clause>

  <clause id="7410">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,5889,a,b,7401,a)].">
      <j1 rule="hyper" parents="334 5889 7401"/>
    </justification>
  </clause>

  <clause id="7411">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K(x \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,5809,a,b,7401,a)].">
      <j1 rule="hyper" parents="334 5809 7401"/>
    </justification>
  </clause>

  <clause id="7412">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,5767,a,b,7401,a),flip(a)].">
      <j1 rule="hyper" parents="334 5767 7401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7413">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,5393,a,b,7401,a)].">
      <j1 rule="hyper" parents="334 5393 7401"/>
    </justification>
  </clause>

  <clause id="7414">
    <literal><![CDATA[
      K(x / y,T(z,x)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,6624,a(flip),b,7401,a),flip(a)].">
      <j1 rule="hyper" parents="334 6624 7401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7415">
    <literal><![CDATA[
      K(x,T(y,K(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5901,a(flip),b,7401,a),flip(a)].">
      <j1 rule="hyper" parents="334 5901 7401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7416">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,3491,a(flip),b,7401,a),flip(a)].">
      <j1 rule="hyper" parents="334 3491 7401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7417">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,3490,a(flip),b,7401,a),flip(a)].">
      <j1 rule="hyper" parents="334 3490 7401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7418">
    <literal><![CDATA[
      K(x,T(y,T(T(x,z),u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,3482,a(flip),b,7401,a),flip(a)].">
      <j1 rule="hyper" parents="334 3482 7401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7419">
    <literal><![CDATA[
      K(x,T(y,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,1344,a(flip),b,7401,a),flip(a)].">
      <j1 rule="hyper" parents="334 1344 7401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7420">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,T(x,z)) = z
    ]]></literal>
    <justification jstring="[hyper(119,a,7401,a,b,6731,a)].">
      <j1 rule="hyper" parents="119 7401 6731"/>
    </justification>
  </clause>

  <clause id="7421">
    <literal><![CDATA[
      x * K(y,T(z,x)) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,7401,a,b,5393,a)].">
      <j1 rule="hyper" parents="119 7401 5393"/>
    </justification>
  </clause>

  <clause id="7422">
    <literal><![CDATA[
      x * K(y,T(z,u)) = x * T(K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(119,a,7401,a,b,4,a)].">
      <j1 rule="hyper" parents="119 7401 4"/>
    </justification>
  </clause>

  <clause id="7423">
    <literal><![CDATA[
      x * K(y,T(z,x)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,7401,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7401 17"/>
    </justification>
  </clause>

  <clause id="7424">
    <literal><![CDATA[
      x * T(K(x,y),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7401,a(flip),b,4995,a(flip))].">
      <j1 rule="hyper" parents="119 7401 4995"/>
    </justification>
  </clause>

  <clause id="7425">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = T(K(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(18(a,1),7401(a,1,2))].">
      <j1 rule="para" parents="18 7401"/>
    </justification>
  </clause>

  <clause id="7426">
    <literal><![CDATA[
      T(x,y) != K(z,T(u,y))
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = x
    ]]></literal>
    <justification jstring="[para(7401(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="7401 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7427">
    <literal><![CDATA[
      x * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(7401(a,2),294(a,1,2))].">
      <j1 rule="para" parents="7401 294"/>
    </justification>
  </clause>

  <clause id="7428">
    <literal><![CDATA[
      x * (y * K(z,T(u,x * y))) = L(K(z,u),y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(7401(a,2),649(a,1,2,2))].">
      <j1 rule="para" parents="7401 649"/>
    </justification>
  </clause>

  <clause id="7429">
    <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(7401(a,2),734(a,1,1))].">
      <j1 rule="para" parents="7401 734"/>
    </justification>
  </clause>

  <clause id="7430">
    <literal><![CDATA[
      x * T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7401(a,1),5030(a,1,2))].">
      <j1 rule="para" parents="7401 5030"/>
    </justification>
  </clause>

  <clause id="7431">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * x) = T(x,y) * K(z,T(u,x))
    ]]></literal>
    <justification jstring="[para(7401(a,2),5351(a,2,2))].">
      <j1 rule="para" parents="7401 5351"/>
    </justification>
  </clause>

  <clause id="7432">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(7401(a,2),5884(a,1,2))].">
      <j1 rule="para" parents="7401 5884"/>
    </justification>
  </clause>

  <clause id="7433">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) * K(u,z) = K(u,z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7401(a,2),5896(a,1,1))].">
      <j1 rule="para" parents="7401 5896"/>
    </justification>
  </clause>

  <clause id="7434">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) = K(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[para(7401(a,2),5892(a,2,1))].">
      <j1 rule="para" parents="7401 5892"/>
    </justification>
  </clause>

  <clause id="7435">
    <literal><![CDATA[
      T(K(x,y),y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(7401(a,1),6055(a,1))].">
      <j1 rule="para" parents="7401 6055"/>
    </justification>
  </clause>

  <clause id="7436">
    <literal><![CDATA[
      x * (K(x,T(y,z)) * (z * K(x,y))) = T(x,y) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7401(a,2),5341(a,1,2,1))].">
      <j1 rule="para" parents="7401 5341"/>
    </justification>
  </clause>

  <clause id="7437">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,K(z \ y,T(z,u)))
    ]]></literal>
    <justification jstring="[para(7401(a,2),6018(a,2,2))].">
      <j1 rule="para" parents="7401 6018"/>
    </justification>
  </clause>

  <clause id="7438">
    <literal><![CDATA[
      K(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(7401(a,2),6761(a,1))].">
      <j1 rule="para" parents="7401 6761"/>
    </justification>
  </clause>

  <clause id="7439">
    <literal><![CDATA[
      K(x / y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(7401(a,2),6769(a,1))].">
      <j1 rule="para" parents="7401 6769"/>
    </justification>
  </clause>

  <clause id="7440">
    <literal><![CDATA[
      K(x,T(L(y,z / y,u),w)) = T(L(K(x,y),z,u),w)
    ]]></literal>
    <justification jstring="[para(6874(a,1),7401(a,2,1))].">
      <j1 rule="para" parents="6874 7401"/>
    </justification>
  </clause>

  <clause id="7441">
    <literal><![CDATA[
      K(x,T(y,z)) \ 1 = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(5430,a,7403,a)].">
      <j1 rule="hyper" parents="5430 7403"/>
    </justification>
  </clause>

  <clause id="7442">
    <literal><![CDATA[
      K(T(T(x,y),z),u) = K(x,T(T(u,z),y))
    ]]></literal>
    <justification jstring="[hyper(334,a,7403,a(flip),b,7403,a),flip(a)].">
      <j1 rule="hyper" parents="334 7403 7403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7443">
    <literal><![CDATA[
      x * K(T(y,z),u) = x * K(y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7403,a,b,4,a)].">
      <j1 rule="hyper" parents="119 7403 4"/>
    </justification>
  </clause>

  <clause id="7444">
    <literal><![CDATA[
      x * K(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,7403,a,b,4995,a(flip))].">
      <j1 rule="hyper" parents="119 7403 4995"/>
    </justification>
  </clause>

  <clause id="7445">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7073,a,b,7403,a)].">
      <j1 rule="hyper" parents="58 7073 7403"/>
    </justification>
  </clause>

  <clause id="7446">
    <literal><![CDATA[
      (x * y) \ (T(x,z) * y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6738,a,b,7403,a)].">
      <j1 rule="hyper" parents="58 6738 7403"/>
    </justification>
  </clause>

  <clause id="7447">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ x = K(z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6523,a,b,7403,a)].">
      <j1 rule="hyper" parents="58 6523 7403"/>
    </justification>
  </clause>

  <clause id="7448">
    <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,5856,a,b,7403,a)].">
      <j1 rule="hyper" parents="58 5856 7403"/>
    </justification>
  </clause>

  <clause id="7449">
    <literal><![CDATA[
      K(x,T(y,x * z)) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7323,a(flip),b,7403,a),flip(a)].">
      <j1 rule="hyper" parents="58 7323 7403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7450">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6657,a(flip),b,7403,a),flip(a)].">
      <j1 rule="hyper" parents="58 6657 7403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7451">
    <literal><![CDATA[
      K(((x \ 1) \ y) \ y,z) = K(1 / x,T(z,y * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6109,a(flip),b,7403,a)].">
      <j1 rule="hyper" parents="58 6109 7403"/>
    </justification>
  </clause>

  <clause id="7452">
    <literal><![CDATA[
      (x / y) * K(z,T(y,u)) = x / T(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,7403,a(flip),b,6376,a)].">
      <j1 rule="hyper" parents="119 7403 6376"/>
    </justification>
  </clause>

  <clause id="7453">
    <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,7403,a(flip),b,5548,a(flip))].">
      <j1 rule="hyper" parents="119 7403 5548"/>
    </justification>
  </clause>

  <clause id="7454">
    <literal><![CDATA[
      T(x,T(y,z)) \ 1 = x \ K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,7403,a(flip),b,5064,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 7403 5064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7455">
    <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),7403(a,1,1))].">
      <j1 rule="para" parents="20 7403"/>
    </justification>
  </clause>

  <clause id="7456">
    <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),7403(a,1,1))].">
      <j1 rule="para" parents="22 7403"/>
    </justification>
  </clause>

  <clause id="7457">
    <literal><![CDATA[
      K(x / y,T(z,y)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),7403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 7403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7458">
    <literal><![CDATA[
      K(T(x,y),z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(107(a,1),7403(a,2,2))].">
      <j1 rule="para" parents="107 7403"/>
    </justification>
  </clause>

  <clause id="7459">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(230(a,1),7403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="230 7403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7460">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z),u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(216(a,1),7403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="216 7403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7461">
    <literal><![CDATA[
      K(T(x,y),L(y,z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(180(a,1),7403(a,2,2))].">
      <j1 rule="para" parents="180 7403"/>
    </justification>
  </clause>

  <clause id="7462">
    <literal><![CDATA[
      K(T(x,(1 / y) \ z),z * y) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(1097(a,1),7403(a,2,2))].">
      <j1 rule="para" parents="1097 7403"/>
    </justification>
  </clause>

  <clause id="7463">
    <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(1962(a,1),7403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1962 7403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7464">
    <literal><![CDATA[
      K(x \ T(x * y,z),T(u,x)) = K(x \ T(y * x,z),u)
    ]]></literal>
    <justification jstring="[para(4830(a,1),7403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4830 7403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7465">
    <literal><![CDATA[
      K(x,T(y,z)) * T(x,z) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(7403(a,1),5034(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7403 5034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7466">
    <literal><![CDATA[
      x / K(y,T(x,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7403(a,1),5074(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7403 5074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7467">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5273(a,1),7403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5273 7403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7468">
    <literal><![CDATA[
      1 / K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7403(a,1),5248(a,1,2))].">
      <j1 rule="para" parents="7403 5248"/>
    </justification>
  </clause>

  <clause id="7469">
    <literal><![CDATA[
      K(x,T(y,z)) \ u = K(y,T(x,z)) * u
    ]]></literal>
    <justification jstring="[para(7403(a,1),5391(a,1,1))].">
      <j1 rule="para" parents="7403 5391"/>
    </justification>
  </clause>

  <clause id="7470">
    <literal><![CDATA[
      (x * y) / (K(z,T(x,u)) * y) = T(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(7403(a,1),5518(a,1,2,1))].">
      <j1 rule="para" parents="7403 5518"/>
    </justification>
  </clause>

  <clause id="7471">
    <literal><![CDATA[
      K(x,T(y,z)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7403(a,1),5426(a,1,1))].">
      <j1 rule="para" parents="7403 5426"/>
    </justification>
  </clause>

  <clause id="7472">
    <literal><![CDATA[
      K(x,T(y,z)) * T(x,z) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(7403(a,1),5115(a,1,1))].">
      <j1 rule="para" parents="7403 5115"/>
    </justification>
  </clause>

  <clause id="7473">
    <literal><![CDATA[
      K(x,T(y,z)) \ (y * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,T(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7403(a,1),5396(a,1,1))].">
      <j1 rule="para" parents="7403 5396"/>
    </justification>
  </clause>

  <clause id="7474">
    <literal><![CDATA[
      a(x,y,K(z,T(y,u))) = 1
    ]]></literal>
    <justification jstring="[para(7403(a,1),6415(a,1,3))].">
      <j1 rule="para" parents="7403 6415"/>
    </justification>
  </clause>

  <clause id="7475">
    <literal><![CDATA[
      x / K(y,T(z,u)) = x * K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(7403(a,1),6520(a,1,2))].">
      <j1 rule="para" parents="7403 6520"/>
    </justification>
  </clause>

  <clause id="7476">
    <literal><![CDATA[
      x * K(y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w * K(z,T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(7403(a,1),6527(a,1,2))].">
      <j1 rule="para" parents="7403 6527"/>
    </justification>
  </clause>

  <clause id="7477">
    <literal><![CDATA[
      x / K(y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(z,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(7403(a,1),6529(a,1,2))].">
      <j1 rule="para" parents="7403 6529"/>
    </justification>
  </clause>

  <clause id="7478">
    <literal><![CDATA[
      (x * K(T(y,z),u)) * K(u,w) = (x * K(u,w)) * K(y,T(u,z))
    ]]></literal>
    <justification jstring="[para(7403(a,1),7109(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7403 7109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7479">
    <literal><![CDATA[
      K(x,T(y,z * K(x,u))) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(7365(a,1),7403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7365 7403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7480">
    <literal><![CDATA[
      L(K(x,T(y,z)),y,u) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(47,a,7474,a)].">
      <j1 rule="hyper" parents="47 7474"/>
    </justification>
  </clause>

  <clause id="7481">
    <literal><![CDATA[
      K(x,K(T(y,K(x,z)),u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7388(a,2),7415(a,1,2))].">
      <j1 rule="para" parents="7388 7415"/>
    </justification>
  </clause>

  <clause id="7482">
    <literal><![CDATA[
      K(x \ y,T(z,y \ x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(6439(a,1),7419(a,1,2))].">
      <j1 rule="para" parents="6439 7419"/>
    </justification>
  </clause>

  <clause id="7483">
    <literal><![CDATA[
      K(x,y / R(x,z,u)) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7416(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 7416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7484">
    <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(7417(a,1),5853(a,1,2))].">
      <j1 rule="para" parents="7417 5853"/>
    </justification>
  </clause>

  <clause id="7485">
    <literal><![CDATA[
      T(x,T(y * z,z \ 1)) = T(x,T(y * z,y))
    ]]></literal>
    <justification jstring="[para(6501(a,1),7350(a,1,2))].">
      <j1 rule="para" parents="6501 7350"/>
    </justification>
  </clause>

  <clause id="7486">
    <literal><![CDATA[
      K(x,y * K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,4995,a,b,7369,a),flip(a)].">
      <j1 rule="hyper" parents="334 4995 7369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7487">
    <literal><![CDATA[
      T(x,K(y,x * K(y,z))) = x
    ]]></literal>
    <justification jstring="[para(7369(a,2),2537(a,1,2))].">
      <j1 rule="para" parents="7369 2537"/>
    </justification>
  </clause>

  <clause id="7488">
    <literal><![CDATA[
      K(x,y * K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7369(a,2),5110(a,1))].">
      <j1 rule="para" parents="7369 5110"/>
    </justification>
  </clause>

  <clause id="7489">
    <literal><![CDATA[
      K(x,y * L(K(x,z),u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5949(a,1),7486(a,1,2,2))].">
      <j1 rule="para" parents="5949 7486"/>
    </justification>
  </clause>

  <clause id="7491">
    <literal><![CDATA[
      K(x,y / T(z,x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(6368(a,1),7486(a,1,2))].">
      <j1 rule="para" parents="6368 7486"/>
    </justification>
  </clause>

  <clause id="7492">
    <literal><![CDATA[
      K(x,y * T(x,z)) = K(x,y * x)
    ]]></literal>
    <justification jstring="[para(6432(a,1),7486(a,1,2))].">
      <j1 rule="para" parents="6432 7486"/>
    </justification>
  </clause>

  <clause id="7493">
    <literal><![CDATA[
      K(x,y * K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6516(a,1),7486(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6516 7486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7494">
    <literal><![CDATA[
      K(x,y / K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6520(a,2),7486(a,1,2))].">
      <j1 rule="para" parents="6520 7486"/>
    </justification>
  </clause>

  <clause id="7495">
    <literal><![CDATA[
      K(x,y / (z / x)) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[para(6695(a,1),7486(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6695 7486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7496">
    <literal><![CDATA[
      K(x \ y,z / (y / x)) = K(x \ y,z / (x \ y))
    ]]></literal>
    <justification jstring="[para(6743(a,1),7486(a,1,2))].">
      <j1 rule="para" parents="6743 7486"/>
    </justification>
  </clause>

  <clause id="7497">
    <literal><![CDATA[
      K(x,y \ T(z,x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(6836(a,1),7486(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6836 7486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7498">
    <literal><![CDATA[
      K(x,T(K(y,x) * z,u)) = K(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(6999(a,1),7486(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6999 7486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7499">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * T(x,z),x)
    ]]></literal>
    <justification jstring="[para(7486(a,1),6598(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7486 6598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7500">
    <literal><![CDATA[
      K(x,K(y,x * K(y,z))) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,7487,a)].">
      <j1 rule="hyper" parents="50 7487"/>
    </justification>
  </clause>

  <clause id="7501">
    <literal><![CDATA[
      K(x,(y * z) * (z \ K(u,x))) = K(x,R(y,z,z \ K(u,x)))
    ]]></literal>
    <justification jstring="[para(380(a,1),7493(a,1,2))].">
      <j1 rule="para" parents="380 7493"/>
    </justification>
  </clause>

  <clause id="7502">
    <literal><![CDATA[
      K(x * K(y,z),z) = 1 / K(z,x)
    ]]></literal>
    <justification jstring="[para(7493(a,1),5243(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7493 5243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7503">
    <literal><![CDATA[
      R(K(x,y),y * K(z,x),u) = K(x,y * K(z,x))
    ]]></literal>
    <justification jstring="[para(7493(a,1),5731(a,1,1))].">
      <j1 rule="para" parents="7493 5731"/>
    </justification>
  </clause>

  <clause id="7505">
    <literal><![CDATA[
      K(x,y \ K(z,x)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5610,a,7494,a),flip(a)].">
      <j1 rule="hyper" parents="5610 7494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7506">
    <literal><![CDATA[
      T(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(4648(a,1),7380(a,1,2))].">
      <j1 rule="para" parents="4648 7380"/>
    </justification>
  </clause>

  <clause id="7507">
    <literal><![CDATA[
      K(x,T(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(4695(a,1),7381(a,1,2))].">
      <j1 rule="para" parents="4695 7381"/>
    </justification>
  </clause>

  <clause id="7508">
    <literal><![CDATA[
      K(T(R(x,x \ y,y \ z),z),u) = K(((x \ y) * (y \ z)) \ z,u)
    ]]></literal>
    <justification jstring="[para(719(a,1),7383(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="719 7383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7509">
    <literal><![CDATA[
      K(T(x * K(y,z),x),u) = K(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(6548(a,1),7383(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6548 7383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7510">
    <literal><![CDATA[
      K((x * (y \ z)) \ (x * z),u) = L(K(T(y,z),u),z,x)
    ]]></literal>
    <justification jstring="[para(7383(a,1),6891(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7383 6891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7511">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = L(K(x,T(z,u)),u,y)
    ]]></literal>
    <justification jstring="[para(7385(a,1),6846(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7385 6846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7512">
    <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(7385(a,1),6982(a,1,1))].">
      <j1 rule="para" parents="7385 6982"/>
    </justification>
  </clause>

  <clause id="7513">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(216(a,1),7389(a,1,1))].">
      <j1 rule="para" parents="216 7389"/>
    </justification>
  </clause>

  <clause id="7514">
    <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(217(a,1),7389(a,1,1))].">
      <j1 rule="para" parents="217 7389"/>
    </justification>
  </clause>

  <clause id="7515">
    <literal><![CDATA[
      T(x,K(x,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(7391(a,1),7375(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7391 7375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7516">
    <literal><![CDATA[
      K(x,K(x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7391(a,1),7493(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7391 7493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7517">
    <literal><![CDATA[
      T(x,K(x,y) * L(K(z,x),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(334,a,2567,a(flip),b,7515,a),flip(a)].">
      <j1 rule="hyper" parents="334 2567 7515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7518">
    <literal><![CDATA[
      K(x,K(x,y) * z) = x \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,7515,a(flip),b,5020,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 7515 5020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7519">
    <literal><![CDATA[
      T(T(x,y),K(x,z) * u) = T(T(x,u),y)
    ]]></literal>
    <justification jstring="[para(7515(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7515 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7520">
    <literal><![CDATA[
      T(x,K(y,x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(5394(a,1),7515(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5394 7515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7522">
    <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(7515(a,1),5466(a,1,1))].">
      <j1 rule="para" parents="7515 5466"/>
    </justification>
  </clause>

  <clause id="7523">
    <literal><![CDATA[
      T(x,y * (K(z,x) * u)) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(6333(a,1),7515(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6333 7515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7524">
    <literal><![CDATA[
      K(x,T(x,y) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[para(5047(a,1),7516(a,1,2))].">
      <j1 rule="para" parents="5047 7516"/>
    </justification>
  </clause>

  <clause id="7525">
    <literal><![CDATA[
      K(x,K(y,x) \ z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5391(a,2),7516(a,1,2))].">
      <j1 rule="para" parents="5391 7516"/>
    </justification>
  </clause>

  <clause id="7526">
    <literal><![CDATA[
      K(x,K(y,x) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5394(a,1),7516(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5394 7516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7527">
    <literal><![CDATA[
      K(x,T(x,y) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(5337(a,1),7516(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5337 7516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7528">
    <literal><![CDATA[
      K(x,T(y,x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5392(a,1),7516(a,1,2))].">
      <j1 rule="para" parents="5392 7516"/>
    </justification>
  </clause>

  <clause id="7529">
    <literal><![CDATA[
      K(x,R(K(x,y),z,u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(6152(a,1),7516(a,1,2,1))].">
      <j1 rule="para" parents="6152 7516"/>
    </justification>
  </clause>

  <clause id="7530">
    <literal><![CDATA[
      K(x,y * (K(z,x) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(6333(a,1),7516(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6333 7516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7531">
    <literal><![CDATA[
      T(x,K(y,x) * z) = L(T(x,z),u,K(w \ 1,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,3808,a,b,7520,a),flip(a)].">
      <j1 rule="hyper" parents="334 3808 7520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7533">
    <literal><![CDATA[
      K(x,R(K(y,x),z,u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(5977(a,1),7526(a,1,2,1))].">
      <j1 rule="para" parents="5977 7526"/>
    </justification>
  </clause>

  <clause id="7534">
    <literal><![CDATA[
      K(x,(K(y,x) * z) * u) = K(x,z * u)
    ]]></literal>
    <justification jstring="[para(7057(a,1),7526(a,1,2))].">
      <j1 rule="para" parents="7057 7526"/>
    </justification>
  </clause>

  <clause id="7535">
    <literal><![CDATA[
      x / K(y,T(z,x)) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(6668,a,7393,a)].">
      <j1 rule="hyper" parents="6668 7393"/>
    </justification>
  </clause>

  <clause id="7536">
    <literal><![CDATA[
      K(T(x,L(y,z,u)),y \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2347,a,7393,a)].">
      <j1 rule="hyper" parents="2347 7393"/>
    </justification>
  </clause>

  <clause id="7537">
    <literal><![CDATA[
      K(x / y,z) * y = y * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),7393(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 7393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7538">
    <literal><![CDATA[
      K((x * y) / x,z) * x = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(230(a,1),7393(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="230 7393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7539">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (x * u) = L(K(z,T(y,u)),u,x)
    ]]></literal>
    <justification jstring="[para(7393(a,1),6943(a,1,1,2))].">
      <j1 rule="para" parents="7393 6943"/>
    </justification>
  </clause>

  <clause id="7540">
    <literal><![CDATA[
      T(x / ((y \ z) \ z),T(y,z)) = ((y \ z) \ z) \ x
    ]]></literal>
    <justification jstring="[hyper(431,a,7396,a),flip(a)].">
      <j1 rule="hyper" parents="431 7396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7541">
    <literal><![CDATA[
      K(x,y) * (z * K(y,T(x,z))) = z
    ]]></literal>
    <justification jstring="[para(7413(a,1),68(a,1,2,2))].">
      <j1 rule="para" parents="7413 68"/>
    </justification>
  </clause>

  <clause id="7542">
    <literal><![CDATA[
      (x \ y) \ (T(x,z) \ y) = K(z,T(x,x \ y))
    ]]></literal>
    <justification jstring="[para(5348(a,1),7413(a,1,2))].">
      <j1 rule="para" parents="5348 7413"/>
    </justification>
  </clause>

  <clause id="7544">
    <literal><![CDATA[
      L(x,y / z,K(z \ y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(7414(a,1),4454(a,1,3))].">
      <j1 rule="para" parents="7414 4454"/>
    </justification>
  </clause>

  <clause id="7548">
    <literal><![CDATA[
      T(x,T(y,T(T(x,z),u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7418,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 7418 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7549">
    <literal><![CDATA[
      K(x / y,z) \ y = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),7421(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 7421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7550">
    <literal><![CDATA[
      (x * y) / T(T(x,y),z) = K(z,x) * y
    ]]></literal>
    <justification jstring="[hyper(6754,a,7423,a)].">
      <j1 rule="hyper" parents="6754 7423"/>
    </justification>
  </clause>

  <clause id="7551">
    <literal><![CDATA[
      x * (y * K(z,T(u,y))) = x * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7423,a,b,4,a)].">
      <j1 rule="hyper" parents="119 7423 4"/>
    </justification>
  </clause>

  <clause id="7552">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,z)) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(29,a,5876,a(flip),b,7423,a),flip(a)].">
      <j1 rule="hyper" parents="29 5876 7423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7553">
    <literal><![CDATA[
      x * K(y,T(T(z,x),u)) = K(y,T(z,u)) * x
    ]]></literal>
    <justification jstring="[para(18(a,1),7423(a,1,2,2))].">
      <j1 rule="para" parents="18 7423"/>
    </justification>
  </clause>

  <clause id="7554">
    <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),7423(a,1,2,2))].">
      <j1 rule="para" parents="20 7423"/>
    </justification>
  </clause>

  <clause id="7555">
    <literal><![CDATA[
      K(x,y) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7423(a,1),38(a,1))].">
      <j1 rule="para" parents="7423 38"/>
    </justification>
  </clause>

  <clause id="7556">
    <literal><![CDATA[
      K(x,y / z) * z = z * K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7423(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 7423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7557">
    <literal><![CDATA[
      x * K(y,K(z,T(u,x))) = K(y,K(z,u)) * x
    ]]></literal>
    <justification jstring="[para(7401(a,2),7423(a,1,2,2))].">
      <j1 rule="para" parents="7401 7423"/>
    </justification>
  </clause>

  <clause id="7558">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(5773,a,7424,a),flip(a)].">
      <j1 rule="hyper" parents="5773 7424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7559">
    <literal><![CDATA[
      T(x,y) * K(K(x,y),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5340,a,b,7424,a)].">
      <j1 rule="hyper" parents="58 5340 7424"/>
    </justification>
  </clause>

  <clause id="7560">
    <literal><![CDATA[
      T(x,T(y,z)) != x * u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(7424(a,1),38(a,1))].">
      <j1 rule="para" parents="7424 38"/>
    </justification>
  </clause>

  <clause id="7561">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(7441(a,1),5241(a,1))].">
      <j1 rule="para" parents="7441 5241"/>
    </justification>
  </clause>

  <clause id="7562">
    <literal><![CDATA[
      T(T(x,y),z) * K(y,x) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(5826,a,7444,a)].">
      <j1 rule="hyper" parents="5826 7444"/>
    </justification>
  </clause>

  <clause id="7563">
    <literal><![CDATA[
      T(x,T(y,z)) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(7444(a,1),38(a,1))].">
      <j1 rule="para" parents="7444 38"/>
    </justification>
  </clause>

  <clause id="7564">
    <literal><![CDATA[
      K(x,T(y,x * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,7403,a(flip),b,7449,a),flip(a)].">
      <j1 rule="hyper" parents="334 7403 7449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7565">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,7401,a,b,7450,a),flip(a)].">
      <j1 rule="hyper" parents="334 7401 7450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7566">
    <literal><![CDATA[
      K(x / (y \ z),z \ y) = K((y \ z) \ x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(6057,a,7457,a)].">
      <j1 rule="hyper" parents="6057 7457"/>
    </justification>
  </clause>

  <clause id="7567">
    <literal><![CDATA[
      K(x \ (y \ x),z) = K(y \ 1,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5709,a(flip),b,7457,a),flip(a)].">
      <j1 rule="hyper" parents="58 5709 7457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7568">
    <literal><![CDATA[
      K(x \ y,z) * (y / x) = T(y / x,T(z,x))
    ]]></literal>
    <justification jstring="[para(7457(a,1),5034(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7457 5034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7569">
    <literal><![CDATA[
      K(x \ y,z) * (y / x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7457(a,1),5035(a,1,1))].">
      <j1 rule="para" parents="7457 5035"/>
    </justification>
  </clause>

  <clause id="7570">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(7457(a,2),6663(a,1))].">
      <j1 rule="para" parents="7457 6663"/>
    </justification>
  </clause>

  <clause id="7571">
    <literal><![CDATA[
      K(T(x,y),z \ 1) = K(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(5610,a,7458,a)].">
      <j1 rule="hyper" parents="5610 7458"/>
    </justification>
  </clause>

  <clause id="7572">
    <literal><![CDATA[
      (x / (y / z)) * K(u,z \ y) = x / T(y / z,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7458,a(flip),b,6376,a)].">
      <j1 rule="hyper" parents="119 7458 6376"/>
    </justification>
  </clause>

  <clause id="7573">
    <literal><![CDATA[
      K(x,y / R(T(x,z),u,w)) = K(x,R(T(x,z),u,w) \ y)
    ]]></literal>
    <justification jstring="[para(216(a,1),7458(a,1,1))].">
      <j1 rule="para" parents="216 7458"/>
    </justification>
  </clause>

  <clause id="7574">
    <literal><![CDATA[
      R(x,T(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(7459(a,1),6349(a,1,3))].">
      <j1 rule="para" parents="7459 6349"/>
    </justification>
  </clause>

  <clause id="7575">
    <literal><![CDATA[
      a(x,T(y,z),K(u,y)) = 1
    ]]></literal>
    <justification jstring="[para(7459(a,1),6415(a,1,3))].">
      <j1 rule="para" parents="7459 6415"/>
    </justification>
  </clause>

  <clause id="7576">
    <literal><![CDATA[
      R(x,K(y,z),L(T(z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(7459(a,1),6936(a,1,2))].">
      <j1 rule="para" parents="7459 6936"/>
    </justification>
  </clause>

  <clause id="7577">
    <literal><![CDATA[
      (x * T(y,z)) * K(u,y) = x * (T(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(7574(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7574 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7578">
    <literal><![CDATA[
      L(K(x,y),T(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(47,a,7575,a)].">
      <j1 rule="hyper" parents="47 7575"/>
    </justification>
  </clause>

  <clause id="7579">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5557,a,b,7578,a)].">
      <j1 rule="hyper" parents="58 5557 7578"/>
    </justification>
  </clause>

  <clause id="7580">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) = K(x,z * K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(6522(a,1),7467(a,1,2))].">
      <j1 rule="para" parents="6522 7467"/>
    </justification>
  </clause>

  <clause id="7581">
    <literal><![CDATA[
      K(x,y / T(z / T(u,z),x)) = K(x,y / (T(z,u) / u))
    ]]></literal>
    <justification jstring="[para(4638(a,1),7491(a,1,2,2))].">
      <j1 rule="para" parents="4638 7491"/>
    </justification>
  </clause>

  <clause id="7582">
    <literal><![CDATA[
      K(x,y * T(x,z)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5649,a(flip),b,7492,a),flip(a)].">
      <j1 rule="hyper" parents="334 5649 7492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7583">
    <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),7497(a,1,2,2))].">
      <j1 rule="para" parents="22 7497"/>
    </justification>
  </clause>

  <clause id="7584">
    <literal><![CDATA[
      K(x * K(y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,5243,a(flip),b,7502,a),flip(a)].">
      <j1 rule="hyper" parents="334 5243 7502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7585">
    <literal><![CDATA[
      K(x * K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7502(a,2),5248(a,1))].">
      <j1 rule="para" parents="7502 5248"/>
    </justification>
  </clause>

  <clause id="7586">
    <literal><![CDATA[
      K(x * T(y,z),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(1532(a,1),7584(a,1,1))].">
      <j1 rule="para" parents="1532 7584"/>
    </justification>
  </clause>

  <clause id="7587">
    <literal><![CDATA[
      K(x \ T(y,z),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(1529(a,1),7584(a,1,1))].">
      <j1 rule="para" parents="1529 7584"/>
    </justification>
  </clause>

  <clause id="7588">
    <literal><![CDATA[
      R(K(x,y),x * K(z,y),u) = K(x * K(z,y),y)
    ]]></literal>
    <justification jstring="[para(7584(a,1),4446(a,1,1))].">
      <j1 rule="para" parents="7584 4446"/>
    </justification>
  </clause>

  <clause id="7589">
    <literal><![CDATA[
      K(x * L(K(y,z),u,w),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5096(a,1),7584(a,1,1,2))].">
      <j1 rule="para" parents="5096 7584"/>
    </justification>
  </clause>

  <clause id="7591">
    <literal><![CDATA[
      K(x * T(y,z),y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(6374(a,1),7584(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6374 7584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7592">
    <literal><![CDATA[
      K(x * K(y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6516(a,1),7584(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6516 7584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7593">
    <literal><![CDATA[
      K(x * K(y,T(z,u)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7403(a,1),7584(a,1,1,2))].">
      <j1 rule="para" parents="7403 7584"/>
    </justification>
  </clause>

  <clause id="7594">
    <literal><![CDATA[
      K(x * K(y,z \ u),u / z) = K(x,u / z)
    ]]></literal>
    <justification jstring="[para(7389(a,1),7584(a,1,1,2))].">
      <j1 rule="para" parents="7389 7584"/>
    </justification>
  </clause>

  <clause id="7595">
    <literal><![CDATA[
      K(K(x,y) * z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(7391(a,1),7584(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7391 7584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7596">
    <literal><![CDATA[
      K(K(x,y) \ z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(7392(a,1),7584(a,1,1))].">
      <j1 rule="para" parents="7392 7584"/>
    </justification>
  </clause>

  <clause id="7597">
    <literal><![CDATA[
      K(K(x,y) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(7393(a,1),7584(a,1,1))].">
      <j1 rule="para" parents="7393 7584"/>
    </justification>
  </clause>

  <clause id="7598">
    <literal><![CDATA[
      K(x * K(y,z),T(z,u)) = K(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(7459(a,1),7584(a,1,1,2))].">
      <j1 rule="para" parents="7459 7584"/>
    </justification>
  </clause>

  <clause id="7599">
    <literal><![CDATA[
      K(x * L(K(y,z),u,w),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5949(a,1),7592(a,1,1,2))].">
      <j1 rule="para" parents="5949 7592"/>
    </justification>
  </clause>

  <clause id="7600">
    <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(7592(a,1),5789(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7592 5789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7603">
    <literal><![CDATA[
      K(T(x,y) * z,x) = K(x * z,x)
    ]]></literal>
    <justification jstring="[para(5047(a,1),7595(a,1,1))].">
      <j1 rule="para" parents="5047 7595"/>
    </justification>
  </clause>

  <clause id="7604">
    <literal><![CDATA[
      K(T(x,y) \ z,x) = K(x \ z,x)
    ]]></literal>
    <justification jstring="[para(5337(a,1),7595(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5337 7595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7606">
    <literal><![CDATA[
      K(R(K(x,y),z,u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(6152(a,1),7595(a,1,1,1))].">
      <j1 rule="para" parents="6152 7595"/>
    </justification>
  </clause>

  <clause id="7607">
    <literal><![CDATA[
      K(x * (K(y,z) * u),z) = K(x * u,z)
    ]]></literal>
    <justification jstring="[para(6333(a,1),7595(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6333 7595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7608">
    <literal><![CDATA[
      L(K(x,y),K(y,z) * x,u) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[para(7595(a,1),6418(a,1,1))].">
      <j1 rule="para" parents="7595 6418"/>
    </justification>
  </clause>

  <clause id="7609">
    <literal><![CDATA[
      K(K(x,y) * z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) = u
    ]]></literal>
    <justification jstring="[para(7596(a,1),6663(a,1))].">
      <j1 rule="para" parents="7596 6663"/>
    </justification>
  </clause>

  <clause id="7611">
    <literal><![CDATA[
      K(K(x,y) * z,T(y,u)) = K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(7459(a,1),7597(a,1,1,1))].">
      <j1 rule="para" parents="7459 7597"/>
    </justification>
  </clause>

  <clause id="7613">
    <literal><![CDATA[
      K(x,K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7518(a,2),5110(a,1))].">
      <j1 rule="para" parents="7518 5110"/>
    </justification>
  </clause>

  <clause id="7615">
    <literal><![CDATA[
      T(x * K(y,x),T(z,T(x,u))) = T(x * K(y,x),z)
    ]]></literal>
    <justification jstring="[para(5086(a,1),7548(a,1,2,2,1))].">
      <j1 rule="para" parents="5086 7548"/>
    </justification>
  </clause>

  <clause id="7616">
    <literal><![CDATA[
      T(x,T(y,x * z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7564,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 7564 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7617">
    <literal><![CDATA[
      K(x,T(y / (x * z),z)) = K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7564(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 7564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7618">
    <literal><![CDATA[
      T(x,T(y,x \ z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7565,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 7565 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7619">
    <literal><![CDATA[
      T(x,T(y,x \ z)) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7565,a(flip),b,4995,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 7565 4995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7620">
    <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),7565(a,1,2))].">
      <j1 rule="para" parents="22 7565"/>
    </justification>
  </clause>

  <clause id="7621">
    <literal><![CDATA[
      K(x * y,T(z,y \ 1)) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(6501(a,1),7565(a,1,2))].">
      <j1 rule="para" parents="6501 7565"/>
    </justification>
  </clause>

  <clause id="7622">
    <literal><![CDATA[
      R(K(x,T(y,z)),x * u,w) = K(R(x,u,w),T(y,x \ z))
    ]]></literal>
    <justification jstring="[para(7565(a,1),7052(a,1,1))].">
      <j1 rule="para" parents="7565 7052"/>
    </justification>
  </clause>

  <clause id="7623">
    <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(7576(a,1),555(a,1,1))].">
      <j1 rule="para" parents="7576 555"/>
    </justification>
  </clause>

  <clause id="7624">
    <literal><![CDATA[
      T(x,y * T(x,z)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7582,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 7582 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7625">
    <literal><![CDATA[
      K((1 / ((x * y) \ x)) * z,y) = K(z * (1 / ((x * y) \ x)),y)
    ]]></literal>
    <justification jstring="[para(6569(a,1),7586(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6569 7586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7626">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[para(17(a,1),7587(a,1,1,2))].">
      <j1 rule="para" parents="17 7587"/>
    </justification>
  </clause>

  <clause id="7628">
    <literal><![CDATA[
      K(x * T(y,z),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5532,a(flip),b,7591,a),flip(a)].">
      <j1 rule="hyper" parents="334 5532 7591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7629">
    <literal><![CDATA[
      K(T(x,y) * z,x) = K(z * T(x,y),x)
    ]]></literal>
    <justification jstring="[para(84(a,1),7593(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 7593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7630">
    <literal><![CDATA[
      K(T(x,T(y,z)) * u,y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(5803(a,1),7593(a,1,1))].">
      <j1 rule="para" parents="5803 7593"/>
    </justification>
  </clause>

  <clause id="7631">
    <literal><![CDATA[
      x * K(T(y,z) \ x,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,7604,a,b,85,a)].">
      <j1 rule="hyper" parents="119 7604 85"/>
    </justification>
  </clause>

  <clause id="7632">
    <literal><![CDATA[
      K(x / T(y,z),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5834,a,b,7604,a)].">
      <j1 rule="hyper" parents="58 5834 7604"/>
    </justification>
  </clause>

  <clause id="7633">
    <literal><![CDATA[
      T(x / y,T(z,y)) = T(x / y,T(z,x))
    ]]></literal>
    <justification jstring="[para(7(a,1),7616(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 7616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7634">
    <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(7618(a,1),5028(a,1,2,1))].">
      <j1 rule="para" parents="7618 5028"/>
    </justification>
  </clause>

  <clause id="7635">
    <literal><![CDATA[
      T(x * y,T(z,y \ 1)) = T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(6501(a,1),7618(a,1,2))].">
      <j1 rule="para" parents="6501 7618"/>
    </justification>
  </clause>

  <clause id="7637">
    <literal><![CDATA[
      T(x,x * (y / T(x,z))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),7624(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 7624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7640">
    <literal><![CDATA[
      K(x * (y / T(x,z)),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),7628(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 7628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7642">
    <literal><![CDATA[
      (x / T(y,z)) * K(y \ x,y) = T(x / T(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7632,a(flip),b,4995,a(flip))].">
      <j1 rule="hyper" parents="119 7632 4995"/>
    </justification>
  </clause>

  <clause id="7643">
    <literal><![CDATA[
      K(x \ (y * L(x,z,u)),x) = K((x \ y) * L(x,z,u),x)
    ]]></literal>
    <justification jstring="[para(1721(a,1),7632(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1721 7632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7644">
    <literal><![CDATA[
      L(K(x,y),z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7290(a,2),297(a,1)),flip(b)].">
      <j1 rule="para" parents="7290 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7646">
    <literal><![CDATA[
      K(x,(x * y) \ (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(6846(a,1),7644(a,1))].">
      <j1 rule="para" parents="6846 7644"/>
    </justification>
  </clause>

  <clause id="7647">
    <literal><![CDATA[
      K(L(x,y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(6883(a,1),7644(a,1))].">
      <j1 rule="para" parents="6883 7644"/>
    </justification>
  </clause>

  <clause id="7648">
    <literal><![CDATA[
      K(x,(x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(6849(a,1),7644(a,1))].">
      <j1 rule="para" parents="6849 7644"/>
    </justification>
  </clause>

  <clause id="7649">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(R(x,u,x),y) = z
    ]]></literal>
    <justification jstring="[para(4939(a,1),7647(a,1,1))].">
      <j1 rule="para" parents="4939 7647"/>
    </justification>
  </clause>

  <clause id="7650">
    <literal><![CDATA[
      T(x,y * (z * K(x,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(90(a,1),7372(a,1,2))].">
      <j1 rule="para" parents="90 7372"/>
    </justification>
  </clause>

  <clause id="7651">
    <literal><![CDATA[
      T(x,y * K(L(x,z,u),w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6883(a,1),7372(a,1,2,2))].">
      <j1 rule="para" parents="6883 7372"/>
    </justification>
  </clause>

  <clause id="7652">
    <literal><![CDATA[
      T(K(x,y),(z * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6501(a,2),7435(a,1))].">
      <j1 rule="para" parents="6501 7435"/>
    </justification>
  </clause>

  <clause id="7653">
    <literal><![CDATA[
      K((x * y) \ (x * z),T(z,u)) = K(y \ z,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6891,a(flip),b,7480,a)].">
      <j1 rule="hyper" parents="58 6891 7480"/>
    </justification>
  </clause>

  <clause id="7654">
    <literal><![CDATA[
      K(x,y / T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(6368(a,1),7488(a,1,2))].">
      <j1 rule="para" parents="6368 7488"/>
    </justification>
  </clause>

  <clause id="7655">
    <literal><![CDATA[
      K(x,y / (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (z / x)) = u
    ]]></literal>
    <justification jstring="[para(6695(a,1),7488(a,1,2))].">
      <j1 rule="para" parents="6695 7488"/>
    </justification>
  </clause>

  <clause id="7656">
    <literal><![CDATA[
      K(x,y * (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * x)) = u
    ]]></literal>
    <justification jstring="[para(6901(a,1),7488(a,1,2))].">
      <j1 rule="para" parents="6901 7488"/>
    </justification>
  </clause>

  <clause id="7657">
    <literal><![CDATA[
      K(x,y * (z * K(x,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(90(a,1),7489(a,1,2))].">
      <j1 rule="para" parents="90 7489"/>
    </justification>
  </clause>

  <clause id="7658">
    <literal><![CDATA[
      K(x,y * (z * K(u,x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(6942(a,1),7489(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6942 7489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7659">
    <literal><![CDATA[
      T(x,a(y,z,K(x,u))) = x
    ]]></literal>
    <justification jstring="[para(6201(a,1),7517(a,1,2))].">
      <j1 rule="para" parents="6201 7517"/>
    </justification>
  </clause>

  <clause id="7660">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,w)) = a(z,u,K(y,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7659(a,1),7423(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7659 7423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7661">
    <literal><![CDATA[
      K(x,(K(x,y) * z) * u) = K(x,z * u)
    ]]></literal>
    <justification jstring="[para(101(a,1),7529(a,1,2))].">
      <j1 rule="para" parents="101 7529"/>
    </justification>
  </clause>

  <clause id="7662">
    <literal><![CDATA[
      K(x,K(R(x,y,z),u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(7052(a,1),7529(a,1,2,1))].">
      <j1 rule="para" parents="7052 7529"/>
    </justification>
  </clause>

  <clause id="7663">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u)) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(6167(a,1),7533(a,1,2,1))].">
      <j1 rule="para" parents="6167 7533"/>
    </justification>
  </clause>

  <clause id="7664">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(7401(a,1),7561(a,1))].">
      <j1 rule="para" parents="7401 7561"/>
    </justification>
  </clause>

  <clause id="7665">
    <literal><![CDATA[
      K(x \ T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(1529(a,1),7585(a,1,1))].">
      <j1 rule="para" parents="1529 7585"/>
    </justification>
  </clause>

  <clause id="7666">
    <literal><![CDATA[
      K(K(x,y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) = u
    ]]></literal>
    <justification jstring="[para(7392(a,1),7585(a,1,1))].">
      <j1 rule="para" parents="7392 7585"/>
    </justification>
  </clause>

  <clause id="7667">
    <literal><![CDATA[
      K(x * (y * K(z,u)),u) = K(x * y,u)
    ]]></literal>
    <justification jstring="[para(90(a,1),7589(a,1,1))].">
      <j1 rule="para" parents="90 7589"/>
    </justification>
  </clause>

  <clause id="7668">
    <literal><![CDATA[
      K(x * K(y,L(z,u,w)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(6876(a,1),7589(a,1,1,2))].">
      <j1 rule="para" parents="6876 7589"/>
    </justification>
  </clause>

  <clause id="7669">
    <literal><![CDATA[
      K(x * (y * K(z,u)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(6942(a,1),7589(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6942 7589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7670">
    <literal><![CDATA[
      K(x * K(L(y,z,u),w),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6883(a,1),7599(a,1,1,2))].">
      <j1 rule="para" parents="6883 7599"/>
    </justification>
  </clause>

  <clause id="7671">
    <literal><![CDATA[
      K((K(x,y) * z) * u,x) = K(z * u,x)
    ]]></literal>
    <justification jstring="[para(101(a,1),7606(a,1,1))].">
      <j1 rule="para" parents="101 7606"/>
    </justification>
  </clause>

  <clause id="7672">
    <literal><![CDATA[
      K(K(R(x,y,z),u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(7052(a,1),7606(a,1,1,1))].">
      <j1 rule="para" parents="7052 7606"/>
    </justification>
  </clause>

  <clause id="7673">
    <literal><![CDATA[
      K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y * x,x) = z
    ]]></literal>
    <justification jstring="[para(4990(a,1),7609(a,1,1))].">
      <j1 rule="para" parents="4990 7609"/>
    </justification>
  </clause>

  <clause id="7674">
    <literal><![CDATA[
      K(T(x,y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(5392(a,1),7609(a,1,1))].">
      <j1 rule="para" parents="5392 7609"/>
    </justification>
  </clause>

  <clause id="7675">
    <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(7651(a,1),5075(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7651 5075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7676">
    <literal><![CDATA[
      K(x,R(x,y,z) * u) = K(x,u * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(4990(a,1),7662(a,1,2))].">
      <j1 rule="para" parents="4990 7662"/>
    </justification>
  </clause>

  <clause id="7677">
    <literal><![CDATA[
      K(x,T(R(x,y,z),u) \ w) = K(x,R(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(5337(a,1),7662(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5337 7662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7678">
    <literal><![CDATA[
      K(x,(y / R(x,z,u)) \ w) = K(x,(R(x,z,u) \ y) \ w)
    ]]></literal>
    <justification jstring="[para(5687(a,1),7662(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5687 7662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7679">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) * w) = K(x,R(x,z,u) * w)
    ]]></literal>
    <justification jstring="[para(5380(a,1),7662(a,1,2))].">
      <j1 rule="para" parents="5380 7662"/>
    </justification>
  </clause>

  <clause id="7680">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) \ z,x \ y) = u
    ]]></literal>
    <justification jstring="[para(5857(a,1),7666(a,1,1))].">
      <j1 rule="para" parents="5857 7666"/>
    </justification>
  </clause>

  <clause id="7681">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) = K(u * L(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(84(a,1),7668(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 7668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7682">
    <literal><![CDATA[
      K(K(L(x,y,z),u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(7391(a,1),7668(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7391 7668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7683">
    <literal><![CDATA[
      K(R(x,y,z) * u,x) = K(u * R(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(4990(a,1),7672(a,1,1))].">
      <j1 rule="para" parents="4990 7672"/>
    </justification>
  </clause>

  <clause id="7684">
    <literal><![CDATA[
      K(T(x,R(y,z,u)) * w,y) = K(x * w,y)
    ]]></literal>
    <justification jstring="[para(5091(a,1),7672(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5091 7672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7685">
    <literal><![CDATA[
      K((x \ 1) \ y,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,y) = z
    ]]></literal>
    <justification jstring="[para(5626(a,2),7673(a,1))].">
      <j1 rule="para" parents="5626 7673"/>
    </justification>
  </clause>

  <clause id="7686">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7124,a(flip),b,7271,a)].">
      <j1 rule="hyper" parents="58 7124 7271"/>
    </justification>
  </clause>

  <clause id="7687">
    <literal><![CDATA[
      T(x * K(y,z),y) = T(x,y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6595,a,7284,a)].">
      <j1 rule="hyper" parents="6595 7284"/>
    </justification>
  </clause>

  <clause id="7688">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(246,a,7284,a(flip),b,5343,a)].">
      <j1 rule="hyper" parents="246 7284 5343"/>
    </justification>
  </clause>

  <clause id="7689">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,y)) = T(z * K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(6750,a,7688,a),flip(a)].">
      <j1 rule="hyper" parents="6750 7688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7690">
    <literal><![CDATA[
      T(T(x,K(y,z)),y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(447,a,7688,a)].">
      <j1 rule="hyper" parents="447 7688"/>
    </justification>
  </clause>

  <clause id="7691">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = x * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,7424,a,b,7688,a),flip(a)].">
      <j1 rule="hyper" parents="334 7424 7688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7692">
    <literal><![CDATA[
      T(T(T(x,y),z),K(y,u)) = T(T(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(7688(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7688 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7693">
    <literal><![CDATA[
      T(x / y,T(y,z)) = T(y \ x,K(y,z))
    ]]></literal>
    <justification jstring="[para(107(a,1),7688(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 7688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7694">
    <literal><![CDATA[
      T((x * y) / x,T(x,z)) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(230(a,1),7688(a,1,1)),flip(a)].">
      <j1 rule="para" parents="230 7688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7695">
    <literal><![CDATA[
      T(x / y,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7690(a,1),696(a,1))].">
      <j1 rule="para" parents="7690 696"/>
    </justification>
  </clause>

  <clause id="7696">
    <literal><![CDATA[
      L(x,T(y,K(x,z)),x) = L(x,T(y,T(x,z)),x)
    ]]></literal>
    <justification jstring="[para(7690(a,1),4726(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7690 4726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7697">
    <literal><![CDATA[
      T(x * K(y,x),T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7690(a,1),5204(a,1))].">
      <j1 rule="para" parents="7690 5204"/>
    </justification>
  </clause>

  <clause id="7698">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(5895(a,1),7690(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5895 7690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7699">
    <literal><![CDATA[
      T(K(x,y),T(z,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5902(a,1),7690(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5902 7690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7700">
    <literal><![CDATA[
      T(x * K(y,z),T(z,y)) = T(K(y,z) * x,z)
    ]]></literal>
    <justification jstring="[para(6522(a,1),7690(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6522 7690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7701">
    <literal><![CDATA[
      T(K(x,y \ z),T(y,z)) = T(K(x,y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7350,a(flip),b,7699,a)].">
      <j1 rule="hyper" parents="58 7350 7699"/>
    </justification>
  </clause>

  <clause id="7702">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6840,a,b,7288,a)].">
      <j1 rule="hyper" parents="58 6840 7288"/>
    </justification>
  </clause>

  <clause id="7703">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z = K(y,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6693,a,b,7288,a)].">
      <j1 rule="hyper" parents="58 6693 7288"/>
    </justification>
  </clause>

  <clause id="7704">
    <literal><![CDATA[
      (((x \ (y / z)) * x) * z) \ y = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6689,a,b,7288,a)].">
      <j1 rule="hyper" parents="58 6689 7288"/>
    </justification>
  </clause>

  <clause id="7705">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(7288(a,1),6780(a,2,2))].">
      <j1 rule="para" parents="7288 6780"/>
    </justification>
  </clause>

  <clause id="7706">
    <literal><![CDATA[
      K(x,y \ (x \ (z * x))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(7288(a,1),7123(a,1))].">
      <j1 rule="para" parents="7288 7123"/>
    </justification>
  </clause>

  <clause id="7707">
    <literal><![CDATA[
      R(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(4339,a,7293,a)].">
      <j1 rule="hyper" parents="4339 7293"/>
    </justification>
  </clause>

  <clause id="7708">
    <literal><![CDATA[
      (x * (y * K(z,x))) / x = (x * y) / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,7293,a(flip),b,6370,a)].">
      <j1 rule="hyper" parents="117 7293 6370"/>
    </justification>
  </clause>

  <clause id="7710">
    <literal><![CDATA[
      R(x,y,K(z,T(x,u))) = x
    ]]></literal>
    <justification jstring="[hyper(140,a,7707,a(flip))].">
      <j1 rule="hyper" parents="140 7707"/>
    </justification>
  </clause>

  <clause id="7712">
    <literal><![CDATA[
      R(R(x,y,z),u,K(w,x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(7707(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7707 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7713">
    <literal><![CDATA[
      (L(x,y,z) * u) * K(w,x) = L(x,y,z) * (u * K(w,x))
    ]]></literal>
    <justification jstring="[para(7707(a,1),525(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7707 525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7714">
    <literal><![CDATA[
      R(x,y,T(K(z,x),u)) = x
    ]]></literal>
    <justification jstring="[para(1606(a,1),7707(a,1,3))].">
      <j1 rule="para" parents="1606 7707"/>
    </justification>
  </clause>

  <clause id="7718">
    <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(7710(a,1),525(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7710 525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7719">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,T(x,w)) = K(x,y) * (z * K(u,T(x,w)))
    ]]></literal>
    <justification jstring="[para(7710(a,1),7057(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7710 7057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7720">
    <literal><![CDATA[
      x \ (y * T(K(z,x),u)) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(7714(a,1),517(a,1,1))].">
      <j1 rule="para" parents="7714 517"/>
    </justification>
  </clause>

  <clause id="7721">
    <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(7712(a,1),885(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7712 885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7725">
    <literal><![CDATA[
      K((x * y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6838,a,b,7294,a)].">
      <j1 rule="hyper" parents="58 6838 7294"/>
    </justification>
  </clause>

  <clause id="7726">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6835,a,b,7294,a)].">
      <j1 rule="hyper" parents="58 6835 7294"/>
    </justification>
  </clause>

  <clause id="7727">
    <literal><![CDATA[
      K((x \ y) \ (x \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),7294(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 7294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7728">
    <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(1504(a,1),7294(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1504 7294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7729">
    <literal><![CDATA[
      x * K(y \ (z \ x),z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(7294(a,1),6641(a,1,2))].">
      <j1 rule="para" parents="7294 6641"/>
    </justification>
  </clause>

  <clause id="7730">
    <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(7296(a,1),5785(a,1,1,1,2))].">
      <j1 rule="para" parents="7296 5785"/>
    </justification>
  </clause>

  <clause id="7731">
    <literal><![CDATA[
      T(x / T(y,z),y) = (y \ x) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6392,a,7299,a)].">
      <j1 rule="hyper" parents="6392 7299"/>
    </justification>
  </clause>

  <clause id="7732">
    <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(6155(a,1),7307(a,2,1))].">
      <j1 rule="para" parents="6155 7307"/>
    </justification>
  </clause>

  <clause id="7733">
    <literal><![CDATA[
      K(x,y) * (L(y,z,y) \ u) = L(T(y,x),z,y) \ u
    ]]></literal>
    <justification jstring="[para(7307(a,1),6044(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7307 6044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7734">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,x) = x \ L(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,7312,a(flip),b,5045,a)].">
      <j1 rule="hyper" parents="116 7312 5045"/>
    </justification>
  </clause>

  <clause id="7735">
    <literal><![CDATA[
      R(x,y,x) \ T(x,z) = x \ L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(7312(a,1),6314(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7312 6314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7736">
    <literal><![CDATA[
      T(x,(x \ y) \ (x \ z)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),7319(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 7319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7737">
    <literal><![CDATA[
      K(x,y) * R(x,z,x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(3492,a,7321,a)].">
      <j1 rule="hyper" parents="3492 7321"/>
    </justification>
  </clause>

  <clause id="7738">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,7321,a(flip),b,5362,a)].">
      <j1 rule="hyper" parents="116 7321 5362"/>
    </justification>
  </clause>

  <clause id="7739">
    <literal><![CDATA[
      L(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4329,a,7327,a)].">
      <j1 rule="hyper" parents="4329 7327"/>
    </justification>
  </clause>

  <clause id="7740">
    <literal><![CDATA[
      (K(x,y) * z) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,5351,a(flip),b,7327,a),flip(a)].">
      <j1 rule="hyper" parents="334 5351 7327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7742">
    <literal><![CDATA[
      T(K(x \ y,x) * z,x \ y) = (y / x) \ (z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(246,a,7327,a,b,5634,a)].">
      <j1 rule="hyper" parents="246 7327 5634"/>
    </justification>
  </clause>

  <clause id="7743">
    <literal><![CDATA[
      (K(x,y) * (z * x)) \ (K(x,y) * z) = L(x \ 1,x,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7327(a,1),221(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7327 221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7744">
    <literal><![CDATA[
      L(T(x,y),z,K(x,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7739(a,1),20(a,2,1))].">
      <j1 rule="para" parents="7739 20"/>
    </justification>
  </clause>

  <clause id="7745">
    <literal><![CDATA[
      (K(x,y) * z) * R(x,u,w) = K(x,y) * (z * R(x,u,w))
    ]]></literal>
    <justification jstring="[para(7739(a,1),459(a,1,2,1))].">
      <j1 rule="para" parents="7739 459"/>
    </justification>
  </clause>

  <clause id="7748">
    <literal><![CDATA[
      L(K(x,y),z,K(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7739(a,1),6874(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7739 6874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7749">
    <literal><![CDATA[
      L(K(x,y),z,K(x,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7739(a,1),6880(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7739 6880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7750">
    <literal><![CDATA[
      L(x,y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(7739(a,1),7189(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7739 7189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7754">
    <literal><![CDATA[
      T(L(x / y,z,y \ x),y) = L(y \ x,z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,255,a,b,7750,a)].">
      <j1 rule="hyper" parents="334 255 7750"/>
    </justification>
  </clause>

  <clause id="7755">
    <literal><![CDATA[
      L(x / y,z,x / y) = L(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),7750(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 7750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7758">
    <literal><![CDATA[
      K(x,L(y,z,T(y,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7750(a,2),7295(a,1,2))].">
      <j1 rule="para" parents="7750 7295"/>
    </justification>
  </clause>

  <clause id="7759">
    <literal><![CDATA[
      L(L(T(x,y),z,u),w,K(x,v5)) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(7744(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7744 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7762">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(7744(a,1),7189(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7744 7189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7764">
    <literal><![CDATA[
      K(x,L(y,z,K(y,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6956,a,7748,a)].">
      <j1 rule="hyper" parents="6956 7748"/>
    </justification>
  </clause>

  <clause id="7765">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,y) = K(z \ (K(y,x) * u),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6904,a(flip),b,7748,a),flip(a)].">
      <j1 rule="hyper" parents="58 6904 7748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7766">
    <literal><![CDATA[
      K(x,L(y,z,K(x,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6956,a,7749,a)].">
      <j1 rule="hyper" parents="6956 7749"/>
    </justification>
  </clause>

  <clause id="7767">
    <literal><![CDATA[
      L(K(x,y),z,T(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6881,a,7758,a)].">
      <j1 rule="hyper" parents="6881 7758"/>
    </justification>
  </clause>

  <clause id="7768">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ (K(x,y) * u))
    ]]></literal>
    <justification jstring="[para(5427(a,1),7766(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5427 7766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7769">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,x) = K(z \ (T(x,y) \ u),x)
    ]]></literal>
    <justification jstring="[hyper(7166,a,7767,a)].">
      <j1 rule="hyper" parents="7166 7767"/>
    </justification>
  </clause>

  <clause id="7770">
    <literal><![CDATA[
      (x / L(y,z,y)) * y = y * (L(y,z,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7328,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 7328 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7771">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = (z / x) * L(x,y,x)
    ]]></literal>
    <justification jstring="[para(107(a,1),7331(a,1,2))].">
      <j1 rule="para" parents="107 7331"/>
    </justification>
  </clause>

  <clause id="7773">
    <literal><![CDATA[
      K(x * (y / R(z,u,z)),z) = K(x * (R(z,u,z) \ y),z)
    ]]></literal>
    <justification jstring="[para(7345(a,1),7586(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7345 7586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7775">
    <literal><![CDATA[
      L(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(4329,a,7351,a)].">
      <j1 rule="hyper" parents="4329 7351"/>
    </justification>
  </clause>

  <clause id="7777">
    <literal><![CDATA[
      T(K(x,y) * z,y) = K(x,y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(246,a,7351,a,b,5684,a)].">
      <j1 rule="hyper" parents="246 7351 5684"/>
    </justification>
  </clause>

  <clause id="7778">
    <literal><![CDATA[
      T(K(x,y) * z,y) = T(y,x) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(246,a,7351,a,b,5090,a)].">
      <j1 rule="hyper" parents="246 7351 5090"/>
    </justification>
  </clause>

  <clause id="7779">
    <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(7351(a,1),5353(a,1,2,2))].">
      <j1 rule="para" parents="7351 5353"/>
    </justification>
  </clause>

  <clause id="7780">
    <literal><![CDATA[
      L(T(x,y),z,K(u,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7775(a,1),20(a,2,1))].">
      <j1 rule="para" parents="7775 20"/>
    </justification>
  </clause>

  <clause id="7781">
    <literal><![CDATA[
      L(R(x,y,z),u,K(w,x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(7775(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7775 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7782">
    <literal><![CDATA[
      (K(x,y) * z) * T(y,u) = K(x,y) * (z * T(y,u))
    ]]></literal>
    <justification jstring="[para(7775(a,1),461(a,1,2,1))].">
      <j1 rule="para" parents="7775 461"/>
    </justification>
  </clause>

  <clause id="7783">
    <literal><![CDATA[
      L(K(x,y),z,K(u,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7775(a,1),6874(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7775 6874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7784">
    <literal><![CDATA[
      L(K(x,y),z,K(u,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7775(a,1),6880(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7775 6880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7785">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,y) = K(x,y) * (z * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,7783,a(flip),b,4317,a(flip))].">
      <j1 rule="hyper" parents="119 7783 4317"/>
    </justification>
  </clause>

  <clause id="7786">
    <literal><![CDATA[
      K(x,L(y,z,K(u,x))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6956,a,7784,a)].">
      <j1 rule="hyper" parents="6956 7784"/>
    </justification>
  </clause>

  <clause id="7787">
    <literal><![CDATA[
      T(x,L(y,z,K(u,x))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7786,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 7786 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7788">
    <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),7786(a,1,2))].">
      <j1 rule="para" parents="25 7786"/>
    </justification>
  </clause>

  <clause id="7789">
    <literal><![CDATA[
      T(x,(K(y,x) * z) \ (K(y,x) * u)) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6898,a(flip),b,7787,a)].">
      <j1 rule="hyper" parents="58 6898 7787"/>
    </justification>
  </clause>

  <clause id="7790">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,z)) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(334,a,4619,a(flip),b,7366,a),flip(a)].">
      <j1 rule="hyper" parents="334 4619 7366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7792">
    <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(7366(a,1),1381(a,1,1))].">
      <j1 rule="para" parents="7366 1381"/>
    </justification>
  </clause>

  <clause id="7793">
    <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(5086(a,1),7366(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5086 7366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7794">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7355,a,b,7376,a)].">
      <j1 rule="hyper" parents="58 7355 7376"/>
    </justification>
  </clause>

  <clause id="7795">
    <literal><![CDATA[
      K(x,T(y,(z \ u) \ y)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6439(a,1),7399(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6439 7399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7796">
    <literal><![CDATA[
      K(x \ 1,T(y,L(x,z,u))) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(177(a,1),7411(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="177 7411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7797">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = T(T(K(x,y),u),z)
    ]]></literal>
    <justification jstring="[para(7401(a,1),7425(a,2,1))].">
      <j1 rule="para" parents="7401 7425"/>
    </justification>
  </clause>

  <clause id="7798">
    <literal><![CDATA[
      K(x * y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(6613,a,7432,a)].">
      <j1 rule="hyper" parents="6613 7432"/>
    </justification>
  </clause>

  <clause id="7799">
    <literal><![CDATA[
      K(x,K(y,z)) * T(z,y) = T(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(7432(a,1),6788(a,1,1))].">
      <j1 rule="para" parents="7432 6788"/>
    </justification>
  </clause>

  <clause id="7800">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6141,a,b,7798,a)].">
      <j1 rule="hyper" parents="58 6141 7798"/>
    </justification>
  </clause>

  <clause id="7801">
    <literal><![CDATA[
      K(x \ y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),7798(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 7798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7802">
    <literal><![CDATA[
      K(x * y,K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7801(a,1),6663(a,1))].">
      <j1 rule="para" parents="7801 6663"/>
    </justification>
  </clause>

  <clause id="7803">
    <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,5856,a,b,7442,a)].">
      <j1 rule="hyper" parents="58 5856 7442"/>
    </justification>
  </clause>

  <clause id="7804">
    <literal><![CDATA[
      K(T(T(x,y),z),u) = K(x,T(T(u,y),z))
    ]]></literal>
    <justification jstring="[para(18(a,1),7442(a,1,1))].">
      <j1 rule="para" parents="18 7442"/>
    </justification>
  </clause>

  <clause id="7805">
    <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(7454(a,1),2095(a,1,2))].">
      <j1 rule="para" parents="7454 2095"/>
    </justification>
  </clause>

  <clause id="7806">
    <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),7461(a,1,1))].">
      <j1 rule="para" parents="22 7461"/>
    </justification>
  </clause>

  <clause id="7807">
    <literal><![CDATA[
      K(x,y) * T(x,T(z,y)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(5665,a,7465,a)].">
      <j1 rule="hyper" parents="5665 7465"/>
    </justification>
  </clause>

  <clause id="7808">
    <literal><![CDATA[
      K(x,y) \ T(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,7465,a(flip),b,5663,a)].">
      <j1 rule="hyper" parents="116 7465 5663"/>
    </justification>
  </clause>

  <clause id="7809">
    <literal><![CDATA[
      K(x,K(y,z)) * T(x,y) = T(T(x,y),K(y,z))
    ]]></literal>
    <justification jstring="[para(3461(a,1),7465(a,1,1,2))].">
      <j1 rule="para" parents="3461 7465"/>
    </justification>
  </clause>

  <clause id="7810">
    <literal><![CDATA[
      K(x,T(y,z * K(x,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,7403,a(flip),b,7479,a),flip(a)].">
      <j1 rule="hyper" parents="334 7403 7479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7811">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7339,a,b,7495,a)].">
      <j1 rule="hyper" parents="58 7339 7495"/>
    </justification>
  </clause>

  <clause id="7812">
    <literal><![CDATA[
      K(x,T(K(x,y) * z,u)) = K(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(5394(a,1),7498(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5394 7498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7813">
    <literal><![CDATA[
      T(T(x,y),K(x,z) * u) = T(T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,18,a,b,7519,a),flip(a)].">
      <j1 rule="hyper" parents="334 18 7519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7814">
    <literal><![CDATA[
      T(x,y * (K(x,z) * u)) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(5394(a,1),7523(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5394 7523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7815">
    <literal><![CDATA[
      K(x,y * (K(x,z) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(5394(a,1),7530(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5394 7530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7816">
    <literal><![CDATA[
      K(x,(y * x) * z) = K(x,(x * y) * z)
    ]]></literal>
    <justification jstring="[para(4990(a,1),7534(a,1,2,1))].">
      <j1 rule="para" parents="4990 7534"/>
    </justification>
  </clause>

  <clause id="7817">
    <literal><![CDATA[
      K(x,(T(y,x) * z) * u) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[para(5047(a,1),7534(a,1,2,1))].">
      <j1 rule="para" parents="5047 7534"/>
    </justification>
  </clause>

  <clause id="7818">
    <literal><![CDATA[
      K(x,(y \ T(z,x)) * u) = K(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[para(5818(a,1),7534(a,1,2,1))].">
      <j1 rule="para" parents="5818 7534"/>
    </justification>
  </clause>

  <clause id="7819">
    <literal><![CDATA[
      K(x,(T(y,x) / z) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(5921(a,1),7534(a,1,2,1))].">
      <j1 rule="para" parents="5921 7534"/>
    </justification>
  </clause>

  <clause id="7820">
    <literal><![CDATA[
      K(x,y * K(z,R(x,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7538(a,1),7663(a,1,2))].">
      <j1 rule="para" parents="7538 7663"/>
    </justification>
  </clause>

  <clause id="7821">
    <literal><![CDATA[
      K(x,y / (z / R(x,u,w))) = K(x,y / (R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(6579(a,1),7820(a,1,2))].">
      <j1 rule="para" parents="6579 7820"/>
    </justification>
  </clause>

  <clause id="7822">
    <literal><![CDATA[
      x \ (T(y / x,z) \ y) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(6260,a,7549,a)].">
      <j1 rule="hyper" parents="6260 7549"/>
    </justification>
  </clause>

  <clause id="7823">
    <literal><![CDATA[
      T(x / y,z) \ x = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(5738,a,7549,a)].">
      <j1 rule="hyper" parents="5738 7549"/>
    </justification>
  </clause>

  <clause id="7824">
    <literal><![CDATA[
      (x * L(y,z,y)) / T(T(x,y),u) = K(u,x) * L(y,z,y)
    ]]></literal>
    <justification jstring="[para(7313(a,1),7550(a,1,2,1))].">
      <j1 rule="para" parents="7313 7550"/>
    </justification>
  </clause>

  <clause id="7825">
    <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(6675(a,1),7556(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6675 7556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7826">
    <literal><![CDATA[
      K(x,T(y,T(z,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7559(a,1),7493(a,1,2))].">
      <j1 rule="para" parents="7559 7493"/>
    </justification>
  </clause>

  <clause id="7827">
    <literal><![CDATA[
      K(T(x,T(y,z)),z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(7559(a,1),7584(a,1,1))].">
      <j1 rule="para" parents="7559 7584"/>
    </justification>
  </clause>

  <clause id="7828">
    <literal><![CDATA[
      K(x,T(y,T(z,R(x,u,w)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7559(a,1),7820(a,1,2))].">
      <j1 rule="para" parents="7559 7820"/>
    </justification>
  </clause>

  <clause id="7829">
    <literal><![CDATA[
      K(x,T(y,x / z)) = K(x,T(y,z \ x))
    ]]></literal>
    <justification jstring="[para(7332(a,1),7826(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7332 7826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7830">
    <literal><![CDATA[
      T(T(x,y),z) * K(z,x) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(18(a,1),7562(a,1,1))].">
      <j1 rule="para" parents="18 7562"/>
    </justification>
  </clause>

  <clause id="7831">
    <literal><![CDATA[
      K(R(x,y,(x * y) \ z) \ 1,T(u,z)) = K(z \ (y * ((x * y) \ z)),u)
    ]]></literal>
    <justification jstring="[para(379(a,1),7567(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="379 7567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7832">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7403,a(flip),b,7571,a)].">
      <j1 rule="hyper" parents="58 7403 7571"/>
    </justification>
  </clause>

  <clause id="7833">
    <literal><![CDATA[
      K(x * T(y,z),T(z,u)) = K(x * y,T(z,u))
    ]]></literal>
    <justification jstring="[para(1532(a,1),7598(a,1,1))].">
      <j1 rule="para" parents="1532 7598"/>
    </justification>
  </clause>

  <clause id="7834">
    <literal><![CDATA[
      K(x * T(y,z),T(y,u)) = K(x * y,T(y,u))
    ]]></literal>
    <justification jstring="[para(6374(a,1),7598(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6374 7598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7835">
    <literal><![CDATA[
      K(x * (K(y,z) * u),y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(5394(a,1),7607(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5394 7607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7836">
    <literal><![CDATA[
      K(x * (T(y,z) * u),y) = K(x * (y * u),y)
    ]]></literal>
    <justification jstring="[para(5091(a,1),7607(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5091 7607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7837">
    <literal><![CDATA[
      K(x * (y / (z * y)),z \ 1) = K(x * ((z * y) \ y),z \ 1)
    ]]></literal>
    <justification jstring="[para(5618(a,1),7607(a,1,1,2))].">
      <j1 rule="para" parents="5618 7607"/>
    </justification>
  </clause>

  <clause id="7838">
    <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,7611,a(flip),b,4995,a(flip))].">
      <j1 rule="hyper" parents="119 7611 4995"/>
    </justification>
  </clause>

  <clause id="7839">
    <literal><![CDATA[
      T(x,T(y,x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7619(a,2),5030(a,1))].">
      <j1 rule="para" parents="7619 5030"/>
    </justification>
  </clause>

  <clause id="7840">
    <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(7630(a,1),5468(a,1,1,2))].">
      <j1 rule="para" parents="7630 5468"/>
    </justification>
  </clause>

  <clause id="7841">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ z,x) = (x \ z) * x
    ]]></literal>
    <justification jstring="[hyper(6557,a,7631,a)].">
      <j1 rule="hyper" parents="6557 7631"/>
    </justification>
  </clause>

  <clause id="7842">
    <literal><![CDATA[
      K(x,y * (z * L(K(x,u),w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(5949(a,1),7657(a,1,2,2,2))].">
      <j1 rule="para" parents="5949 7657"/>
    </justification>
  </clause>

  <clause id="7843">
    <literal><![CDATA[
      K(x,y * (z * L(K(u,x),w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(5096(a,1),7658(a,1,2,2,2))].">
      <j1 rule="para" parents="5096 7658"/>
    </justification>
  </clause>

  <clause id="7844">
    <literal><![CDATA[
      K(x,T(y * (z * K(u,x)),w)) = T(K(x,y * z),w)
    ]]></literal>
    <justification jstring="[para(7658(a,1),7401(a,2,1))].">
      <j1 rule="para" parents="7658 7401"/>
    </justification>
  </clause>

  <clause id="7845">
    <literal><![CDATA[
      K(x * (y / T(z,u)),u) = K(x * (y / z),u)
    ]]></literal>
    <justification jstring="[para(6517(a,1),7667(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6517 7667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7846">
    <literal><![CDATA[
      K(x * (y / R(z,u,z)),z) = K(x * (y / T(z,u)),z)
    ]]></literal>
    <justification jstring="[para(6918(a,1),7669(a,1,1,2))].">
      <j1 rule="para" parents="6918 7669"/>
    </justification>
  </clause>

  <clause id="7847">
    <literal><![CDATA[
      K(x,y \ ((x \ z) * x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),7686(a,2,2,2))].">
      <j1 rule="para" parents="5 7686"/>
    </justification>
  </clause>

  <clause id="7848">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,y) = T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6329,a,7687,a)].">
      <j1 rule="hyper" parents="6329 7687"/>
    </justification>
  </clause>

  <clause id="7849">
    <literal><![CDATA[
      (T(x,y) / y) * T(y,z) = T(x * K(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,6467,a,b,7687,a)].">
      <j1 rule="hyper" parents="334 6467 7687"/>
    </justification>
  </clause>

  <clause id="7850">
    <literal><![CDATA[
      x \ T(x * K(y,z),y) = K(x,y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,7687,a,b,5044,a)].">
      <j1 rule="hyper" parents="116 7687 5044"/>
    </justification>
  </clause>

  <clause id="7852">
    <literal><![CDATA[
      x \ T(x * K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(7687(a,2),5336(a,1,2))].">
      <j1 rule="para" parents="7687 5336"/>
    </justification>
  </clause>

  <clause id="7853">
    <literal><![CDATA[
      K(x,T(x * K(y,z),y)) = K(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(7687(a,2),7524(a,1,2))].">
      <j1 rule="para" parents="7687 7524"/>
    </justification>
  </clause>

  <clause id="7854">
    <literal><![CDATA[
      T(T(x,1 / y),K(1 / y,z)) = x * K(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[para(5775(a,2),7691(a,2,2))].">
      <j1 rule="para" parents="5775 7691"/>
    </justification>
  </clause>

  <clause id="7855">
    <literal><![CDATA[
      T(x \ y,K(x,z)) = x \ T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6784,a(flip),b,7693,a),flip(a)].">
      <j1 rule="hyper" parents="58 6784 7693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7856">
    <literal><![CDATA[
      T(x * y,K(y,z)) / y = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6785,a,7694,a)].">
      <j1 rule="hyper" parents="6785 7694"/>
    </justification>
  </clause>

  <clause id="7857">
    <literal><![CDATA[
      T(x * y,K(x,z)) = x * T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7694,a(flip),b,6784,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 7694 6784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7858">
    <literal><![CDATA[
      K(x,L(x \ y,x,z)) = K(x,z \ (x \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(6960,a,7702,a)].">
      <j1 rule="hyper" parents="6960 7702"/>
    </justification>
  </clause>

  <clause id="7859">
    <literal><![CDATA[
      x * (y * ((x \ 1) / y)) = K(y,x \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(5567,a,7702,a)].">
      <j1 rule="hyper" parents="5567 7702"/>
    </justification>
  </clause>

  <clause id="7860">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(T(z,x),x,y))
    ]]></literal>
    <justification jstring="[para(239(a,1),7702(a,1,2)),flip(a)].">
      <j1 rule="para" parents="239 7702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7861">
    <literal><![CDATA[
      L(K(x,y \ (x \ z)),u * x,w) = K(L(x,u,w),(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(7702(a,1),6883(a,1,1))].">
      <j1 rule="para" parents="7702 6883"/>
    </justification>
  </clause>

  <clause id="7862">
    <literal><![CDATA[
      K(x,y \ (x \ (y * z))) != u
    ]]></literal>
    <literal><![CDATA[
      L(K(x,x \ z),z,y) = u
    ]]></literal>
    <justification jstring="[para(7702(a,1),6961(a,1))].">
      <j1 rule="para" parents="7702 6961"/>
    </justification>
  </clause>

  <clause id="7863">
    <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(7725(a,1),5785(a,1,1,1,2))].">
      <j1 rule="para" parents="7725 5785"/>
    </justification>
  </clause>

  <clause id="7864">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7626,a(flip),b,7727,a)].">
      <j1 rule="hyper" parents="58 7626 7727"/>
    </justification>
  </clause>

  <clause id="7865">
    <literal><![CDATA[
      T(x / T(y,z),y) * y = (y \ x) * (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(7731(a,2),6351(a,1,1))].">
      <j1 rule="para" parents="7731 6351"/>
    </justification>
  </clause>

  <clause id="7866">
    <literal><![CDATA[
      T(x,y \ ((x \ z) * x)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7125,a(flip),b,7736,a)].">
      <j1 rule="hyper" parents="58 7125 7736"/>
    </justification>
  </clause>

  <clause id="7867">
    <literal><![CDATA[
      K(x,y) * R(T(y,x),z,y) = R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(5409,a,7737,a)].">
      <j1 rule="hyper" parents="5409 7737"/>
    </justification>
  </clause>

  <clause id="7868">
    <literal><![CDATA[
      K(x,y) * (x \ R(x,z,x)) = x \ R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,7737,a(flip),b,5363,a),flip(a)].">
      <j1 rule="hyper" parents="116 7737 5363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7869">
    <literal><![CDATA[
      T(K(x,y) * z,x) = K(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(246,a,7740,a,b,5044,a)].">
      <j1 rule="hyper" parents="246 7740 5044"/>
    </justification>
  </clause>

  <clause id="7870">
    <literal><![CDATA[
      (T(x,y) * (x \ z)) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[para(5045(a,2),7740(a,1,1))].">
      <j1 rule="para" parents="5045 7740"/>
    </justification>
  </clause>

  <clause id="7872">
    <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(7762(a,1),4923(a,1))].">
      <j1 rule="para" parents="7762 4923"/>
    </justification>
  </clause>

  <clause id="7873">
    <literal><![CDATA[
      K(x,L(T(y,z),u,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7762(a,1),7295(a,1,2))].">
      <j1 rule="para" parents="7762 7295"/>
    </justification>
  </clause>

  <clause id="7874">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6881,a,7873,a)].">
      <j1 rule="hyper" parents="6881 7873"/>
    </justification>
  </clause>

  <clause id="7875">
    <literal><![CDATA[
      K((x * y) \ z,T(x,u)) = K(y \ (x \ z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(7166,a,7874,a)].">
      <j1 rule="hyper" parents="7166 7874"/>
    </justification>
  </clause>

  <clause id="7876">
    <literal><![CDATA[
      K((x \ 1) * y,T(x \ 1,z)) = K(x \ y,T(x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(6913,a,7874,a),flip(a)].">
      <j1 rule="hyper" parents="6913 7874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7877">
    <literal><![CDATA[
      K((x \ y) \ z,T(x,u)) = K(y \ (x * z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6894,a(flip),b,7874,a),flip(a)].">
      <j1 rule="hyper" parents="58 6894 7874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7878">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,x) = T(z,x)
    ]]></literal>
    <justification jstring="[hyper(6344,a,7777,a)].">
      <j1 rule="hyper" parents="6344 7777"/>
    </justification>
  </clause>

  <clause id="7879">
    <literal><![CDATA[
      T(K(x,y \ z) * y,y \ z) = T(y \ z,x) \ z
    ]]></literal>
    <justification jstring="[hyper(334,a,5497,a(flip),b,7777,a),flip(a)].">
      <j1 rule="hyper" parents="334 5497 7777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7881">
    <literal><![CDATA[
      K(x,y) * T(K(x * y,x),y) = T(x \ R(x,y,x),y)
    ]]></literal>
    <justification jstring="[para(5556(a,1),7777(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5556 7777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7882">
    <literal><![CDATA[
      T(K(x,y) * (z / y),y) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[para(7(a,1),7778(a,2,2))].">
      <j1 rule="para" parents="7 7778"/>
    </justification>
  </clause>

  <clause id="7883">
    <literal><![CDATA[
      T(K(x,y) * (z * (1 / y)),y) = T(y,x) \ R(z,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2938(a,1),7778(a,2,2))].">
      <j1 rule="para" parents="2938 7778"/>
    </justification>
  </clause>

  <clause id="7884">
    <literal><![CDATA[
      T(K(x,y) * (z / T(y,u)),y) = T(y,x) \ (z * K(u,y))
    ]]></literal>
    <justification jstring="[para(6370(a,1),7778(a,2,2))].">
      <j1 rule="para" parents="6370 7778"/>
    </justification>
  </clause>

  <clause id="7885">
    <literal><![CDATA[
      K(x,T(T(x * T(y,z),u),y)) = T(K(x,x * T(y,z)),u)
    ]]></literal>
    <justification jstring="[para(6684(a,1),7797(a,2,1))].">
      <j1 rule="para" parents="6684 7797"/>
    </justification>
  </clause>

  <clause id="7886">
    <literal><![CDATA[
      K(x,y) * T(x,K(z,T(u,y))) = T(T(x,y),K(z,u))
    ]]></literal>
    <justification jstring="[para(7401(a,2),7807(a,1,2,2))].">
      <j1 rule="para" parents="7401 7807"/>
    </justification>
  </clause>

  <clause id="7887">
    <literal><![CDATA[
      K(x,T(y,z * K(u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6516(a,1),7810(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6516 7810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7888">
    <literal><![CDATA[
      K(x,T(y,z * (u * x))) = K(x,T(y,z * (x * u)))
    ]]></literal>
    <justification jstring="[para(6901(a,1),7810(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6901 7810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7889">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,x)) * w)) = K(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(7105(a,1),7810(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7105 7810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7890">
    <literal><![CDATA[
      K(x,T(y,K(z,x) * u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(7420(a,1),7810(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7420 7810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7891">
    <literal><![CDATA[
      T(T(x,y),T(x,z) \ u) = T(T(x,y),x \ u)
    ]]></literal>
    <justification jstring="[para(5337(a,1),7813(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5337 7813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7892">
    <literal><![CDATA[
      K(x,y * (z * (K(u,x) * w))) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(6333(a,1),7815(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6333 7815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7894">
    <literal><![CDATA[
      x / T(y \ x,z) = T(x / y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(33,a,6377,a,b,7822,a)].">
      <j1 rule="hyper" parents="33 6377 7822"/>
    </justification>
  </clause>

  <clause id="7895">
    <literal><![CDATA[
      L(K(x,(y \ 1) \ z),y \ 1,y) = y * (T(z / (y \ 1),x) \ z)
    ]]></literal>
    <justification jstring="[para(7822(a,1),501(a,1,1))].">
      <j1 rule="para" parents="7822 501"/>
    </justification>
  </clause>

  <clause id="7896">
    <literal><![CDATA[
      x / (y * K(z,y \ x)) = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(201,a,7823,a)].">
      <j1 rule="hyper" parents="201 7823"/>
    </justification>
  </clause>

  <clause id="7897">
    <literal><![CDATA[
      (T(x / y,z) \ x) \ x = T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(7823(a,2),6367(a,1,1))].">
      <j1 rule="para" parents="7823 6367"/>
    </justification>
  </clause>

  <clause id="7898">
    <literal><![CDATA[
      (x / y) * K(x,T(z,y \ x)) = K(x,z) * (x / y)
    ]]></literal>
    <justification jstring="[para(7829(a,1),7423(a,1,2))].">
      <j1 rule="para" parents="7829 7423"/>
    </justification>
  </clause>

  <clause id="7899">
    <literal><![CDATA[
      T(T(x,y) * K(z,x),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7687,a,b,7830,a)].">
      <j1 rule="hyper" parents="58 7687 7830"/>
    </justification>
  </clause>

  <clause id="7900">
    <literal><![CDATA[
      x \ (T(y,z) * T(x,y)) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7284,a,b,7830,a)].">
      <j1 rule="hyper" parents="58 7284 7830"/>
    </justification>
  </clause>

  <clause id="7901">
    <literal><![CDATA[
      T(x,y) * T(z,x) = z * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7830,a(flip),b,7284,a),flip(a)].">
      <j1 rule="hyper" parents="119 7830 7284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7902">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7832,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 7832 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7903">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7412,a(flip),b,7832,a)].">
      <j1 rule="hyper" parents="58 7412 7832"/>
    </justification>
  </clause>

  <clause id="7904">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,y)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(75(a,1),7832(a,2,2,2))].">
      <j1 rule="para" parents="75 7832"/>
    </justification>
  </clause>

  <clause id="7905">
    <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(7835(a,1),5786(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7835 5786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7906">
    <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(7835(a,1),5787(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7835 5787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7907">
    <literal><![CDATA[
      T(x * K(y,z),z) = T(x,z) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(764,a,7848,a),flip(a)].">
      <j1 rule="hyper" parents="764 7848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7908">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = (y * T(y \ u,x)) \ u
    ]]></literal>
    <justification jstring="[para(7848(a,1),6690(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7848 6690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7909">
    <literal><![CDATA[
      x \ T(L(y,x \ 1,x),K(x,z)) = T((x \ 1) * y,K(x,z))
    ]]></literal>
    <justification jstring="[para(450(a,1),7855(a,1,1)),flip(a)].">
      <j1 rule="para" parents="450 7855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7910">
    <literal><![CDATA[
      T(x * y,K(y,z)) = T(x,K(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(133,a,7856,a),flip(a)].">
      <j1 rule="hyper" parents="133 7856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7911">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7727,a(flip),b,7864,a),flip(a)].">
      <j1 rule="hyper" parents="58 7727 7864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7912">
    <literal><![CDATA[
      K(x \ (y * z),z) = K(x \ (z * y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7296,a(flip),b,7864,a),flip(a)].">
      <j1 rule="hyper" parents="58 7296 7864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7913">
    <literal><![CDATA[
      T(x,y \ ((x \ z) * x)) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(7866(a,2),5128(a,1))].">
      <j1 rule="para" parents="7866 5128"/>
    </justification>
  </clause>

  <clause id="7914">
    <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(7866(a,1),5075(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7866 5075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7915">
    <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(7867(a,1),5446(a,1,2))].">
      <j1 rule="para" parents="7867 5446"/>
    </justification>
  </clause>

  <clause id="7916">
    <literal><![CDATA[
      T(K(x,y) * z,x) / z = K(x,y) * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,7869,a,b,6532,a)].">
      <j1 rule="hyper" parents="117 7869 6532"/>
    </justification>
  </clause>

  <clause id="7917">
    <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),7869(a,2,2))].">
      <j1 rule="para" parents="20 7869"/>
    </justification>
  </clause>

  <clause id="7919">
    <literal><![CDATA[
      (x \ K(y,z)) * T((x \ K(y,z)) \ u,y) = x \ T(x * u,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,7878,a(flip),b,1135,a),flip(a)].">
      <j1 rule="hyper" parents="116 7878 1135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7920">
    <literal><![CDATA[
      K(x,y) * (z * T(z \ (K(x,y) \ u),x)) = T(u / z,x) * z
    ]]></literal>
    <justification jstring="[para(7878(a,1),1636(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7878 1636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7921">
    <literal><![CDATA[
      K(x,y) * T(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y) * z,y) = u
    ]]></literal>
    <justification jstring="[para(7878(a,1),6338(a,1,2))].">
      <j1 rule="para" parents="7878 6338"/>
    </justification>
  </clause>

  <clause id="7922">
    <literal><![CDATA[
      K(x,T(y,z * L(K(u,x),w,v5))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5096(a,1),7887(a,1,2,2,2))].">
      <j1 rule="para" parents="5096 7887"/>
    </justification>
  </clause>

  <clause id="7923">
    <literal><![CDATA[
      K(x,T(y,K(z,x) * u)) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,7401,a(flip),b,7890,a),flip(a)].">
      <j1 rule="hyper" parents="334 7401 7890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7924">
    <literal><![CDATA[
      x / T((y \ x) \ x,z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),7894(a,2,1,1))].">
      <j1 rule="para" parents="72 7894"/>
    </justification>
  </clause>

  <clause id="7925">
    <literal><![CDATA[
      T(x / (x / y),z) \ x = x / T(y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),7894(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 7894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7926">
    <literal><![CDATA[
      (x * y) / (x * K(z,y)) = T((x * y) / x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),7896(a,1,2,2,2))].">
      <j1 rule="para" parents="4 7896"/>
    </justification>
  </clause>

  <clause id="7927">
    <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(7896(a,1),4611(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7896 4611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7928">
    <literal><![CDATA[
      x / ((x * y) * K(z,y \ 1)) = T(x / (x * y),z)
    ]]></literal>
    <justification jstring="[para(6441(a,1),7896(a,1,2,2))].">
      <j1 rule="para" parents="6441 7896"/>
    </justification>
  </clause>

  <clause id="7929">
    <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(6675(a,1),7896(a,2,1))].">
      <j1 rule="para" parents="6675 7896"/>
    </justification>
  </clause>

  <clause id="7930">
    <literal><![CDATA[
      T((x \ y) \ y,z) = (T(x,z) \ y) \ y
    ]]></literal>
    <justification jstring="[para(72(a,1),7897(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 7897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7931">
    <literal><![CDATA[
      ((x \ T(y,x)) \ y) \ y = T(T(x,y) \ y,x)
    ]]></literal>
    <justification jstring="[para(4478(a,1),7897(a,1,1,1))].">
      <j1 rule="para" parents="4478 7897"/>
    </justification>
  </clause>

  <clause id="7932">
    <literal><![CDATA[
      T(x * K(y,x),T(z,y)) = T(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(5469,a,7899,a)].">
      <j1 rule="hyper" parents="5469 7899"/>
    </justification>
  </clause>

  <clause id="7933">
    <literal><![CDATA[
      x \ (K(y,z) * (x * y)) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(5351(a,2),7900(a,1,2))].">
      <j1 rule="para" parents="5351 7900"/>
    </justification>
  </clause>

  <clause id="7934">
    <literal><![CDATA[
      K(x,y) * (z * x) = z * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(5744,a,7901,a)].">
      <j1 rule="hyper" parents="5744 7901"/>
    </justification>
  </clause>

  <clause id="7936">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7558,a(flip),b,7902,a)].">
      <j1 rule="hyper" parents="58 7558 7902"/>
    </justification>
  </clause>

  <clause id="7937">
    <literal><![CDATA[
      T(x,T((y / z) \ 1,y)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(75(a,1),7902(a,2,2,2))].">
      <j1 rule="para" parents="75 7902"/>
    </justification>
  </clause>

  <clause id="7939">
    <literal><![CDATA[
      K(x,y \ K(z,y)) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[para(5073(a,1),7903(a,1,2))].">
      <j1 rule="para" parents="5073 7903"/>
    </justification>
  </clause>

  <clause id="7940">
    <literal><![CDATA[
      T(K(x,y),K(z,x) * u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7401,a(flip),b,7923,a)].">
      <j1 rule="hyper" parents="58 7401 7923"/>
    </justification>
  </clause>

  <clause id="7941">
    <literal><![CDATA[
      x / T(T(y,y \ x),z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(106(a,2),7924(a,1,2,1))].">
      <j1 rule="para" parents="106 7924"/>
    </justification>
  </clause>

  <clause id="7942">
    <literal><![CDATA[
      T(x,y) / T(R(x,z,u),w) = T(R(x,z,u),w) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(4873(a,1),7924(a,1,2,1))].">
      <j1 rule="para" parents="4873 7924"/>
    </justification>
  </clause>

  <clause id="7944">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ K(z,x) = K(z,x) / T(x,y)
    ]]></literal>
    <justification jstring="[para(5719(a,1),7925(a,1,1,1))].">
      <j1 rule="para" parents="5719 7925"/>
    </justification>
  </clause>

  <clause id="7945">
    <literal><![CDATA[
      T(T(x,y),x \ z) = (T(x,y) \ z) \ z
    ]]></literal>
    <justification jstring="[hyper(616,a,7930,a)].">
      <j1 rule="hyper" parents="616 7930"/>
    </justification>
  </clause>

  <clause id="7949">
    <literal><![CDATA[
      T(K(x,y),z * x) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(246,a,7934,a,b,6432,a)].">
      <j1 rule="hyper" parents="246 7934 6432"/>
    </justification>
  </clause>

  <clause id="7950">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (y * x) = y * T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(180(a,1),7934(a,2,2,2))].">
      <j1 rule="para" parents="180 7934"/>
    </justification>
  </clause>

  <clause id="7951">
    <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(7934(a,1),92(a,2,1))].">
      <j1 rule="para" parents="7934 92"/>
    </justification>
  </clause>

  <clause id="7952">
    <literal><![CDATA[
      T(K(x,y),z * x) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,7401,a(flip),b,7949,a),flip(a)].">
      <j1 rule="hyper" parents="334 7401 7949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7953">
    <literal><![CDATA[
      K(x,T(y,z * x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7401,a,b,7949,a)].">
      <j1 rule="hyper" parents="58 7401 7949"/>
    </justification>
  </clause>

  <clause id="7954">
    <literal><![CDATA[
      K(L(x,y,x),T(z,u)) = K(x,T(z,u * x))
    ]]></literal>
    <justification jstring="[hyper(334,a,7291,a,b,7953,a)].">
      <j1 rule="hyper" parents="334 7291 7953"/>
    </justification>
  </clause>

  <clause id="7955">
    <literal><![CDATA[
      K(x,T(y,z / x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),7953(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 7953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7956">
    <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),7953(a,1,2,2))].">
      <j1 rule="para" parents="80 7953"/>
    </justification>
  </clause>

  <clause id="7957">
    <literal><![CDATA[
      T(x,T(y,z / x)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7955,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 7955 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7958">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ x))
    ]]></literal>
    <justification jstring="[para(4713(a,1),7955(a,1,2))].">
      <j1 rule="para" parents="4713 7955"/>
    </justification>
  </clause>

  <clause id="7959">
    <literal><![CDATA[
      T(x \ y,T(z,y)) = T(x \ y,T(z,x))
    ]]></literal>
    <justification jstring="[para(72(a,1),7957(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 7957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7960">
    <literal><![CDATA[
      T(x,(y * z) \ z) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(6771,a,7936,a)].">
      <j1 rule="hyper" parents="6771 7936"/>
    </justification>
  </clause>

  <clause id="7961">
    <literal><![CDATA[
      K(T(x,(y / z) \ 1),y) = K(T(x,y \ z),y)
    ]]></literal>
    <justification jstring="[para(7937(a,1),7827(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7937 7827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7962">
    <literal><![CDATA[
      K(x,(y * z) \ z) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6826,a,b,7939,a)].">
      <j1 rule="hyper" parents="58 6826 7939"/>
    </justification>
  </clause>

  <clause id="7963">
    <literal><![CDATA[
      T(K(x,y),R(K(z,x),u,w) * v5) = T(K(x,y),v5)
    ]]></literal>
    <justification jstring="[para(5977(a,1),7940(a,1,2,1))].">
      <j1 rule="para" parents="5977 7940"/>
    </justification>
  </clause>

  <clause id="7964">
    <literal><![CDATA[
      T(K(x,y),z * K(u,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7538(a,1),7940(a,1,2))].">
      <j1 rule="para" parents="7538 7940"/>
    </justification>
  </clause>

  <clause id="7965">
    <literal><![CDATA[
      T(x,T(T(y,z),y \ u)) = T(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(7945(a,2),7396(a,1,2))].">
      <j1 rule="para" parents="7945 7396"/>
    </justification>
  </clause>

  <clause id="7966">
    <literal><![CDATA[
      K(x,T(y \ x,T(z,y))) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(7959(a,1),7826(a,1,2))].">
      <j1 rule="para" parents="7959 7826"/>
    </justification>
  </clause>

  <clause id="7967">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[hyper(334,a,7832,a,b,7962,a)].">
      <j1 rule="hyper" parents="334 7832 7962"/>
    </justification>
  </clause>

  <clause id="7968">
    <literal><![CDATA[
      T(K(x,y),z * L(K(u,x),w,v5)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5096(a,1),7964(a,1,2,2))].">
      <j1 rule="para" parents="5096 7964"/>
    </justification>
  </clause>

  <clause id="7969">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7691(a,2),7430(a,1))].">
      <j1 rule="para" parents="7691 7430"/>
    </justification>
  </clause>

  <clause id="7970">
    <literal><![CDATA[
      K(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5243(a,1),7468(a,1))].">
      <j1 rule="para" parents="5243 7468"/>
    </justification>
  </clause>

  <clause id="7971">
    <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(7072(a,2),7468(a,1))].">
      <j1 rule="para" parents="7072 7468"/>
    </justification>
  </clause>

  <clause id="7972">
    <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),7970(a,1,1))].">
      <j1 rule="para" parents="20 7970"/>
    </justification>
  </clause>

  <clause id="7973">
    <literal><![CDATA[
      (x * y) \ (T(x,z) * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6738(a,2),7970(a,1))].">
      <j1 rule="para" parents="6738 7970"/>
    </justification>
  </clause>

  <clause id="7974">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7388(a,1),7970(a,1))].">
      <j1 rule="para" parents="7388 7970"/>
    </justification>
  </clause>

  <clause id="7975">
    <literal><![CDATA[
      K((x \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7383(a,2),7970(a,1))].">
      <j1 rule="para" parents="7383 7970"/>
    </justification>
  </clause>

  <clause id="7976">
    <literal><![CDATA[
      K(x,T(y,x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7449(a,2),7970(a,1))].">
      <j1 rule="para" parents="7449 7970"/>
    </justification>
  </clause>

  <clause id="7977">
    <literal><![CDATA[
      K(x,y \ (z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ 1,y)) = u
    ]]></literal>
    <justification jstring="[para(7571(a,1),7970(a,1))].">
      <j1 rule="para" parents="7571 7970"/>
    </justification>
  </clause>

  <clause id="7978">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5809(a,2),7974(a,1))].">
      <j1 rule="para" parents="5809 7974"/>
    </justification>
  </clause>

  <clause id="7979">
    <literal><![CDATA[
      K(1 / T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5814(a,2),7974(a,1))].">
      <j1 rule="para" parents="5814 7974"/>
    </justification>
  </clause>

  <clause id="7980">
    <literal><![CDATA[
      K(x,T(y,x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7450(a,2),7974(a,1))].">
      <j1 rule="para" parents="7450 7974"/>
    </justification>
  </clause>

  <clause id="7981">
    <literal><![CDATA[
      T(K(x,y),z * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7952(a,2),7974(a,1))].">
      <j1 rule="para" parents="7952 7974"/>
    </justification>
  </clause>

  <clause id="7982">
    <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(6363(a,1),7506(a,1,2,1))].">
      <j1 rule="para" parents="6363 7506"/>
    </justification>
  </clause>

  <clause id="7984">
    <literal><![CDATA[
      K(x / y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5(a,1),7570(a,1,1,1))].">
      <j1 rule="para" parents="5 7570"/>
    </justification>
  </clause>

  <clause id="7985">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(17(a,1),7665(a,1,1,2))].">
      <j1 rule="para" parents="17 7665"/>
    </justification>
  </clause>

  <clause id="7986">
    <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),7828(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 7828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7987">
    <literal><![CDATA[
      T(x * y,T(z,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(6501(a,1),7839(a,1,2))].">
      <j1 rule="para" parents="6501 7839"/>
    </justification>
  </clause>

  <clause id="7988">
    <literal><![CDATA[
      K(x,T(y,z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7954(a,1),7032(a,1))].">
      <j1 rule="para" parents="7954 7032"/>
    </justification>
  </clause>

  <clause id="7989">
    <literal><![CDATA[
      T(K(x,y),x * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7401(a,1),7976(a,1))].">
      <j1 rule="para" parents="7401 7976"/>
    </justification>
  </clause>

  <clause id="7990">
    <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(4823(a,1),7984(a,1,1))].">
      <j1 rule="para" parents="4823 7984"/>
    </justification>
  </clause>

  <clause id="7991">
    <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(5200(a,2),7984(a,1,1))].">
      <j1 rule="para" parents="5200 7984"/>
    </justification>
  </clause>

  <clause id="7992">
    <literal><![CDATA[
      T(x \ (y / z),K(x,z)) = T(x,z) \ (y / T(z,x))
    ]]></literal>
    <justification jstring="[para(6368(a,1),7268(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6368 7268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7993">
    <literal><![CDATA[
      T(x / y,z) * T(y,K(x / y,z)) = x * K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,148,a(flip),b,7274,a),flip(a)].">
      <j1 rule="hyper" parents="334 148 7274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7994">
    <literal><![CDATA[
      (x * (y * T(x,z))) \ ((x * y) * T(x,z)) = a(x,y * K(x,z),x)
    ]]></literal>
    <justification jstring="[para(7277(a,1),6593(a,1,2))].">
      <j1 rule="para" parents="7277 6593"/>
    </justification>
  </clause>

  <clause id="7995">
    <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(334,a,6699,a,b,7335,a)].">
      <j1 rule="hyper" parents="334 6699 7335"/>
    </justification>
  </clause>

  <clause id="7996">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(6387(a,2),7361(a,1,1))].">
      <j1 rule="para" parents="6387 7361"/>
    </justification>
  </clause>

  <clause id="7997">
    <literal><![CDATA[
      K(x,y) * ((z / y) * R(y,u,y)) = R(y,u,y) * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[para(7382(a,1),6343(a,1,2))].">
      <j1 rule="para" parents="7382 6343"/>
    </justification>
  </clause>

  <clause id="7998">
    <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(741(a,1),7456(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="741 7456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7999">
    <literal><![CDATA[
      K(R(T(x,K(y,z)),u,w),z) = K(R(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(2523(a,1),7456(a,2,2))].">
      <j1 rule="para" parents="2523 7456"/>
    </justification>
  </clause>

  <clause id="8000">
    <literal><![CDATA[
      (x \ y) \ (T(x,z) \ y) = K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,7337,a(flip),b,7542,a),flip(a)].">
      <j1 rule="hyper" parents="334 7337 7542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8001">
    <literal><![CDATA[
      (x \ y) * K(z,T(x,y)) = T(x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(119,a,7337,a(flip),b,7542,a)].">
      <j1 rule="hyper" parents="119 7337 7542"/>
    </justification>
  </clause>

  <clause id="8002">
    <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(218(a,1),8001(a,1,2,2))].">
      <j1 rule="para" parents="218 8001"/>
    </justification>
  </clause>

  <clause id="8003">
    <literal><![CDATA[
      (T(x,y) \ z) \ (x \ z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8001(a,1),7447(a,1,1))].">
      <j1 rule="para" parents="8001 7447"/>
    </justification>
  </clause>

  <clause id="8004">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(7552(a,2),6493(a,1))].">
      <j1 rule="para" parents="7552 6493"/>
    </justification>
  </clause>

  <clause id="8005">
    <literal><![CDATA[
      K(x \ y,z \ (x \ y)) * (y / x) = T(y / x,T((x * z) \ y,x))
    ]]></literal>
    <justification jstring="[para(6855(a,1),7568(a,1,1))].">
      <j1 rule="para" parents="6855 7568"/>
    </justification>
  </clause>

  <clause id="8006">
    <literal><![CDATA[
      K(x * T(y,z \ u),u / z) = K(x * y,u / z)
    ]]></literal>
    <justification jstring="[para(1532(a,1),7594(a,1,1))].">
      <j1 rule="para" parents="1532 7594"/>
    </justification>
  </clause>

  <clause id="8007">
    <literal><![CDATA[
      K(x,T(y / (x * z),z)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(334,a,7288,a(flip),b,7617,a),flip(a)].">
      <j1 rule="hyper" parents="334 7288 7617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8008">
    <literal><![CDATA[
      K(x * L(y,z,u),T(y,x)) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(6058,a,7621,a),flip(a)].">
      <j1 rule="hyper" parents="6058 7621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8009">
    <literal><![CDATA[
      T(x * y,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x * y,y) = z
    ]]></literal>
    <justification jstring="[para(7635(a,1),3120(a,1))].">
      <j1 rule="para" parents="7635 3120"/>
    </justification>
  </clause>

  <clause id="8010">
    <literal><![CDATA[
      T(T(x * K(y,z),u),T(z,y)) = T(T(K(y,z) * x,z),u)
    ]]></literal>
    <justification jstring="[para(7700(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7700 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8011">
    <literal><![CDATA[
      K(((x \ 1) \ y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(6973,a,7726,a)].">
      <j1 rule="hyper" parents="6973 7726"/>
    </justification>
  </clause>

  <clause id="8012">
    <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(7734(a,1),5371(a,1,2))].">
      <j1 rule="para" parents="7734 5371"/>
    </justification>
  </clause>

  <clause id="8013">
    <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(7735(a,1),7731(a,2,1))].">
      <j1 rule="para" parents="7735 7731"/>
    </justification>
  </clause>

  <clause id="8014">
    <literal><![CDATA[
      K(x,T(y,z \ (u * y))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(6859(a,1),7795(a,1,2))].">
      <j1 rule="para" parents="6859 7795"/>
    </justification>
  </clause>

  <clause id="8015">
    <literal><![CDATA[
      K(x,K(y,z)) * T(x,y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,7688,a(flip),b,7809,a),flip(a)].">
      <j1 rule="hyper" parents="334 7688 7809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8016">
    <literal><![CDATA[
      T(x,y) * K(x,K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,3470,a,b,8015,a)].">
      <j1 rule="hyper" parents="58 3470 8015"/>
    </justification>
  </clause>

  <clause id="8017">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(30,a,7799,a,b,8015,a)].">
      <j1 rule="hyper" parents="30 7799 8015"/>
    </justification>
  </clause>

  <clause id="8018">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(30,a,6788,a,b,8015,a)].">
      <j1 rule="hyper" parents="30 6788 8015"/>
    </justification>
  </clause>

  <clause id="8019">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5893,a,8017,a)].">
      <j1 rule="hyper" parents="5893 8017"/>
    </justification>
  </clause>

  <clause id="8020">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,7800,a,b,8017,a)].">
      <j1 rule="hyper" parents="334 7800 8017"/>
    </justification>
  </clause>

  <clause id="8021">
    <literal><![CDATA[
      K(x * y,K(x,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,7798,a,b,8017,a)].">
      <j1 rule="hyper" parents="334 7798 8017"/>
    </justification>
  </clause>

  <clause id="8022">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,8017,a,b,4995,a(flip))].">
      <j1 rule="hyper" parents="119 8017 4995"/>
    </justification>
  </clause>

  <clause id="8023">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,K(x,z)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8017,a,b,11,a(flip))].">
      <j1 rule="hyper" parents="119 8017 11"/>
    </justification>
  </clause>

  <clause id="8024">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(8017(a,1),5034(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8017 5034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8025">
    <literal><![CDATA[
      K(x,K(y,z)) \ K(y,x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(8017(a,1),5058(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8017 5058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8026">
    <literal><![CDATA[
      K(x,K(y,z)) \ K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(y,x),z) = u
    ]]></literal>
    <justification jstring="[para(8017(a,1),5136(a,1,1))].">
      <j1 rule="para" parents="8017 5136"/>
    </justification>
  </clause>

  <clause id="8027">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8017(a,1),5887(a,1,1))].">
      <j1 rule="para" parents="8017 5887"/>
    </justification>
  </clause>

  <clause id="8028">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(8017(a,1),5893(a,1))].">
      <j1 rule="para" parents="8017 5893"/>
    </justification>
  </clause>

  <clause id="8029">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(8017(a,1),5889(a,1,2))].">
      <j1 rule="para" parents="8017 5889"/>
    </justification>
  </clause>

  <clause id="8030">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(8017(a,1),5890(a,1,1))].">
      <j1 rule="para" parents="8017 5890"/>
    </justification>
  </clause>

  <clause id="8031">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) * u) = T(K(x,y),z) * u
    ]]></literal>
    <justification jstring="[para(8017(a,1),5892(a,1,1))].">
      <j1 rule="para" parents="8017 5892"/>
    </justification>
  </clause>

  <clause id="8032">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8017(a,1),7409(a,1,1))].">
      <j1 rule="para" parents="8017 7409"/>
    </justification>
  </clause>

  <clause id="8033">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8017(a,1),7410(a,1,2))].">
      <j1 rule="para" parents="8017 7410"/>
    </justification>
  </clause>

  <clause id="8034">
    <literal><![CDATA[
      K(K(R(x \ 1,y,z) \ 1,u),w) = R(K(x,K(u,w)),y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,5980,a(flip),b,8019,a),flip(a)].">
      <j1 rule="hyper" parents="334 5980 8019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8035">
    <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,6150,a,b,8019,a)].">
      <j1 rule="hyper" parents="58 6150 8019"/>
    </justification>
  </clause>

  <clause id="8036">
    <literal><![CDATA[
      (x * K(y,z)) * K(y,K(z,u)) = x * T(K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(119,a,8019,a(flip),b,6470,a)].">
      <j1 rule="hyper" parents="119 8019 6470"/>
    </justification>
  </clause>

  <clause id="8037">
    <literal><![CDATA[
      (x / y) * K(z,K(u,y)) = x / T(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,8019,a(flip),b,6376,a)].">
      <j1 rule="hyper" parents="119 8019 6376"/>
    </justification>
  </clause>

  <clause id="8038">
    <literal><![CDATA[
      (x * K(y,z)) * K(y,K(z,x)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,8019,a(flip),b,11,a(flip))].">
      <j1 rule="hyper" parents="119 8019 11"/>
    </justification>
  </clause>

  <clause id="8039">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(8019(a,1),5030(a,1,2))].">
      <j1 rule="para" parents="8019 5030"/>
    </justification>
  </clause>

  <clause id="8040">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ u) = T(z,K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(8019(a,1),5392(a,1,1))].">
      <j1 rule="para" parents="8019 5392"/>
    </justification>
  </clause>

  <clause id="8041">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) \ u = w
    ]]></literal>
    <justification jstring="[para(8019(a,1),5449(a,1,1))].">
      <j1 rule="para" parents="8019 5449"/>
    </justification>
  </clause>

  <clause id="8042">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(8019(a,1),5919(a,1))].">
      <j1 rule="para" parents="8019 5919"/>
    </justification>
  </clause>

  <clause id="8043">
    <literal><![CDATA[
      K(L(K(x,y),z,u) \ 1,w) = L(K(y,K(x,w)),z,u)
    ]]></literal>
    <justification jstring="[para(8019(a,1),5962(a,2,1))].">
      <j1 rule="para" parents="8019 5962"/>
    </justification>
  </clause>

  <clause id="8044">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(7595(a,1),8019(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7595 8019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8045">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8017,a,b,8020,a)].">
      <j1 rule="hyper" parents="58 8017 8020"/>
    </justification>
  </clause>

  <clause id="8046">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8017,a,b,8021,a)].">
      <j1 rule="hyper" parents="58 8017 8021"/>
    </justification>
  </clause>

  <clause id="8047">
    <literal><![CDATA[
      K(x,T(y,T(z,K(u,x)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8022(a,1),7810(a,1,2,2))].">
      <j1 rule="para" parents="8022 7810"/>
    </justification>
  </clause>

  <clause id="8048">
    <literal><![CDATA[
      K(x,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(5891,a,8027,a)].">
      <j1 rule="hyper" parents="5891 8027"/>
    </justification>
  </clause>

  <clause id="8049">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(5241,a,8027,a)].">
      <j1 rule="hyper" parents="5241 8027"/>
    </justification>
  </clause>

  <clause id="8050">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8027(a,1),5891(a,1))].">
      <j1 rule="para" parents="8027 5891"/>
    </justification>
  </clause>

  <clause id="8051">
    <literal><![CDATA[
      K(x,K(x * y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(7802,a,8048,a),flip(a)].">
      <j1 rule="hyper" parents="7802 8048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8052">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8019,a,b,8048,a)].">
      <j1 rule="hyper" parents="334 8019 8048"/>
    </justification>
  </clause>

  <clause id="8053">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,8017,a,b,8048,a),flip(a)].">
      <j1 rule="hyper" parents="334 8017 8048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8054">
    <literal><![CDATA[
      x * K(y,K(x,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,8048,a,b,4995,a(flip))].">
      <j1 rule="hyper" parents="119 8048 4995"/>
    </justification>
  </clause>

  <clause id="8055">
    <literal><![CDATA[
      K(x,K(y,z)) * y = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(8048(a,1),5034(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8048 5034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8056">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * u) = T(y,K(x,z)) * u
    ]]></literal>
    <justification jstring="[para(8048(a,1),5047(a,1,1))].">
      <j1 rule="para" parents="8048 5047"/>
    </justification>
  </clause>

  <clause id="8057">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(y,K(x,y * z))
    ]]></literal>
    <justification jstring="[para(5649(a,2),8048(a,1,2))].">
      <j1 rule="para" parents="5649 8048"/>
    </justification>
  </clause>

  <clause id="8058">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,K(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(8048(a,1),5299(a,1,1))].">
      <j1 rule="para" parents="8048 5299"/>
    </justification>
  </clause>

  <clause id="8059">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(8048(a,1),5889(a,1,2))].">
      <j1 rule="para" parents="8048 5889"/>
    </justification>
  </clause>

  <clause id="8060">
    <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(8048(a,1),5473(a,1,2))].">
      <j1 rule="para" parents="8048 5473"/>
    </justification>
  </clause>

  <clause id="8061">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[para(7516(a,1),8048(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7516 8048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8062">
    <literal><![CDATA[
      K(x,K(y,L(z,u,K(x,w)))) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(7766(a,1),8048(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7766 8048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8063">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(8048(a,1),8022(a,1,2))].">
      <j1 rule="para" parents="8048 8022"/>
    </justification>
  </clause>

  <clause id="8064">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8048(a,1),8024(a,1,1))].">
      <j1 rule="para" parents="8048 8024"/>
    </justification>
  </clause>

  <clause id="8065">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,8017,a,b,8049,a),flip(a)].">
      <j1 rule="hyper" parents="334 8017 8049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8066">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,8017,a,b,8052,a),flip(a)].">
      <j1 rule="hyper" parents="334 8017 8052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8067">
    <literal><![CDATA[
      K(x,K(y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8049,a(flip),b,8052,a)].">
      <j1 rule="hyper" parents="58 8049 8052"/>
    </justification>
  </clause>

  <clause id="8068">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * K(y,x)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(8052(a,1),4990(a,1,1))].">
      <j1 rule="para" parents="8052 4990"/>
    </justification>
  </clause>

  <clause id="8069">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(8052(a,1),5919(a,1))].">
      <j1 rule="para" parents="8052 5919"/>
    </justification>
  </clause>

  <clause id="8070">
    <literal><![CDATA[
      K(x,K(R(y \ 1,z,u) \ 1,w)) = K(R(K(y,x),z,u),w)
    ]]></literal>
    <justification jstring="[para(5980(a,1),8052(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5980 8052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8071">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(8052(a,2),8022(a,1,2))].">
      <j1 rule="para" parents="8052 8022"/>
    </justification>
  </clause>

  <clause id="8072">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,7432,a,b,8053,a)].">
      <j1 rule="hyper" parents="334 7432 8053"/>
    </justification>
  </clause>

  <clause id="8073">
    <literal><![CDATA[
      K(x,K(y,x \ z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,7801,a(flip),b,8053,a),flip(a)].">
      <j1 rule="hyper" parents="334 7801 8053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8074">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,7800,a(flip),b,8053,a),flip(a)].">
      <j1 rule="hyper" parents="334 7800 8053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8075">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(119,a,8053,a,b,8027,a)].">
      <j1 rule="hyper" parents="119 8053 8027"/>
    </justification>
  </clause>

  <clause id="8076">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,(x \ 1) \ y))
    ]]></literal>
    <justification jstring="[hyper(119,a,8053,a,b,6705,a),flip(a)].">
      <j1 rule="hyper" parents="119 8053 6705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8077">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) * u = w
    ]]></literal>
    <justification jstring="[para(8053(a,2),5299(a,1,1))].">
      <j1 rule="para" parents="8053 5299"/>
    </justification>
  </clause>

  <clause id="8078">
    <literal><![CDATA[
      K(x,y) * K(x,K(z,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(8053(a,1),5889(a,1,2))].">
      <j1 rule="para" parents="8053 5889"/>
    </justification>
  </clause>

  <clause id="8079">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / (u / z)) \ 1)) * (u / z) = T(u,K(x,y)) / z
    ]]></literal>
    <justification jstring="[para(8053(a,2),5921(a,1,1))].">
      <j1 rule="para" parents="8053 5921"/>
    </justification>
  </clause>

  <clause id="8080">
    <literal><![CDATA[
      (x * K(y,K(z,u))) / K(y,z) = x / T(K(y,z),u)
    ]]></literal>
    <justification jstring="[para(8053(a,2),6379(a,1,1,2))].">
      <j1 rule="para" parents="8053 6379"/>
    </justification>
  </clause>

  <clause id="8081">
    <literal><![CDATA[
      (x * K(y,K(z,u \ x))) / u = T(x / u,K(y,z))
    ]]></literal>
    <justification jstring="[para(8053(a,2),6636(a,1,1,2))].">
      <j1 rule="para" parents="8053 6636"/>
    </justification>
  </clause>

  <clause id="8082">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,T(y,u)))
    ]]></literal>
    <justification jstring="[para(7403(a,1),8053(a,1,2))].">
      <j1 rule="para" parents="7403 8053"/>
    </justification>
  </clause>

  <clause id="8083">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(8053(a,1),7409(a,1,1))].">
      <j1 rule="para" parents="8053 7409"/>
    </justification>
  </clause>

  <clause id="8084">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(8053(a,2),7409(a,1,1))].">
      <j1 rule="para" parents="8053 7409"/>
    </justification>
  </clause>

  <clause id="8085">
    <literal><![CDATA[
      K(x,y) * K(x,K(z,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8053(a,1),7410(a,1,2))].">
      <j1 rule="para" parents="8053 7410"/>
    </justification>
  </clause>

  <clause id="8086">
    <literal><![CDATA[
      K(x,y) * K(y,K(x,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8053(a,2),7410(a,1,2))].">
      <j1 rule="para" parents="8053 7410"/>
    </justification>
  </clause>

  <clause id="8087">
    <literal><![CDATA[
      K(x,K(y,z)) / y = 1 / T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(117,a,8065,a(flip),b,5063,a(flip))].">
      <j1 rule="hyper" parents="117 8065 5063"/>
    </justification>
  </clause>

  <clause id="8088">
    <literal><![CDATA[
      K(x,K(y,z)) * (y \ u) = T(y,K(x,z)) \ u
    ]]></literal>
    <justification jstring="[para(8065(a,1),5392(a,1,1))].">
      <j1 rule="para" parents="8065 5392"/>
    </justification>
  </clause>

  <clause id="8089">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8065(a,1),5919(a,1))].">
      <j1 rule="para" parents="8065 5919"/>
    </justification>
  </clause>

  <clause id="8090">
    <literal><![CDATA[
      K(x,y) \ K(K(x,y),z) = T(K(x,y),z) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,8066,a,b,5064,a(flip))].">
      <j1 rule="hyper" parents="116 8066 5064"/>
    </justification>
  </clause>

  <clause id="8091">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,K(y,z)) * u) = u
    ]]></literal>
    <justification jstring="[hyper(118,a,8066,a(flip),b,5403,a),flip(a)].">
      <j1 rule="hyper" parents="118 8066 5403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8092">
    <literal><![CDATA[
      K(x,K(y,z)) \ u = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(8066(a,1),5391(a,1,1))].">
      <j1 rule="para" parents="8066 5391"/>
    </justification>
  </clause>

  <clause id="8093">
    <literal><![CDATA[
      x * (T(x,K(y,z)) \ u) = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(8066(a,1),5090(a,2,1))].">
      <j1 rule="para" parents="8066 5090"/>
    </justification>
  </clause>

  <clause id="8094">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ u) = T(x,K(y,z)) \ u
    ]]></literal>
    <justification jstring="[para(8066(a,1),5392(a,1,1))].">
      <j1 rule="para" parents="8066 5392"/>
    </justification>
  </clause>

  <clause id="8095">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) * w = u
    ]]></literal>
    <justification jstring="[para(8066(a,1),5409(a,1,1))].">
      <j1 rule="para" parents="8066 5409"/>
    </justification>
  </clause>

  <clause id="8096">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,K(y,z)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(8066(a,1),5411(a,1,1))].">
      <j1 rule="para" parents="8066 5411"/>
    </justification>
  </clause>

  <clause id="8097">
    <literal><![CDATA[
      K(x,K(y,z)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(8066(a,1),5426(a,1,1))].">
      <j1 rule="para" parents="8066 5426"/>
    </justification>
  </clause>

  <clause id="8098">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(8066(a,1),5431(a,1,1))].">
      <j1 rule="para" parents="8066 5431"/>
    </justification>
  </clause>

  <clause id="8099">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8066(a,1),5919(a,1))].">
      <j1 rule="para" parents="8066 5919"/>
    </justification>
  </clause>

  <clause id="8100">
    <literal><![CDATA[
      T(x,K(y,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,8067,a,b,5664,a)].">
      <j1 rule="hyper" parents="118 8067 5664"/>
    </justification>
  </clause>

  <clause id="8101">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,L(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(8067(a,1),6028(a,1,1))].">
      <j1 rule="para" parents="8067 6028"/>
    </justification>
  </clause>

  <clause id="8102">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / (u / z)) \ 1)) = K(x,(T(u,y) / z) / (u / z))
    ]]></literal>
    <justification jstring="[para(6195(a,1),8067(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6195 8067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8103">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,T(K(z,y),u))
    ]]></literal>
    <justification jstring="[para(7388(a,1),8067(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7388 8067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8104">
    <literal><![CDATA[
      K(x,y) * K(z,K(x,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8067(a,1),7410(a,1,2))].">
      <j1 rule="para" parents="8067 7410"/>
    </justification>
  </clause>

  <clause id="8105">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7969,a,8100,a),flip(a)].">
      <j1 rule="hyper" parents="7969 8100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8106">
    <literal><![CDATA[
      T(T(x * K(y,z),u),K(y,z)) = T(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(6981,a,8100,a)].">
      <j1 rule="hyper" parents="6981 8100"/>
    </justification>
  </clause>

  <clause id="8107">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6813,a,8100,a)].">
      <j1 rule="hyper" parents="6813 8100"/>
    </justification>
  </clause>

  <clause id="8108">
    <literal><![CDATA[
      T(x * y,K(z,y)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6805,a,8100,a),flip(a)].">
      <j1 rule="hyper" parents="6805 8100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8109">
    <literal><![CDATA[
      T(x * K(y,z),K(y,z)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(6723,a,8100,a),flip(a)].">
      <j1 rule="hyper" parents="6723 8100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8110">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6667,a,8100,a),flip(a)].">
      <j1 rule="hyper" parents="6667 8100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8111">
    <literal><![CDATA[
      T(K(x,y) \ z,K(x,y)) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(6666,a,8100,a),flip(a)].">
      <j1 rule="hyper" parents="6666 8100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8112">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(5903,a,8100,a)].">
      <j1 rule="hyper" parents="5903 8100"/>
    </justification>
  </clause>

  <clause id="8113">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(5552,a,8100,a)].">
      <j1 rule="hyper" parents="5552 8100"/>
    </justification>
  </clause>

  <clause id="8114">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) = T(T(x,u),K(z,y))
    ]]></literal>
    <justification jstring="[hyper(447,a,8100,a)].">
      <j1 rule="hyper" parents="447 8100"/>
    </justification>
  </clause>

  <clause id="8115">
    <literal><![CDATA[
      T(x \ y,K(z,x)) = x \ T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,7855,a(flip),b,8100,a),flip(a)].">
      <j1 rule="hyper" parents="334 7855 8100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8116">
    <literal><![CDATA[
      K(x,y) * T(z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8100,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="119 8100 17"/>
    </justification>
  </clause>

  <clause id="8117">
    <literal><![CDATA[
      K(x,y) \ T(z,K(x,y)) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,8100,a,b,5402,a)].">
      <j1 rule="hyper" parents="116 8100 5402"/>
    </justification>
  </clause>

  <clause id="8118">
    <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(8100(a,1),447(a,1,1))].">
      <j1 rule="para" parents="8100 447"/>
    </justification>
  </clause>

  <clause id="8119">
    <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(8100(a,1),447(a,1))].">
      <j1 rule="para" parents="8100 447"/>
    </justification>
  </clause>

  <clause id="8120">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(8100(a,1),5897(a,1,1))].">
      <j1 rule="para" parents="8100 5897"/>
    </justification>
  </clause>

  <clause id="8121">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(u,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(8100(a,1),5903(a,1))].">
      <j1 rule="para" parents="8100 5903"/>
    </justification>
  </clause>

  <clause id="8122">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[para(8100(a,1),5896(a,1,1))].">
      <j1 rule="para" parents="8100 5896"/>
    </justification>
  </clause>

  <clause id="8123">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8100(a,1),6667(a,1))].">
      <j1 rule="para" parents="8100 6667"/>
    </justification>
  </clause>

  <clause id="8124">
    <literal><![CDATA[
      T(T(x,K(y,z)),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(8100(a,1),7690(a,1,1))].">
      <j1 rule="para" parents="8100 7690"/>
    </justification>
  </clause>

  <clause id="8125">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(8100(a,1),7698(a,1,1))].">
      <j1 rule="para" parents="8100 7698"/>
    </justification>
  </clause>

  <clause id="8126">
    <literal><![CDATA[
      T(x * y,K(x,z)) = x * T(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(8100(a,1),7857(a,2,2))].">
      <j1 rule="para" parents="8100 7857"/>
    </justification>
  </clause>

  <clause id="8127">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8100(a,1),7969(a,1))].">
      <j1 rule="para" parents="8100 7969"/>
    </justification>
  </clause>

  <clause id="8128">
    <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(821,a,8112,a)].">
      <j1 rule="hyper" parents="821 8112"/>
    </justification>
  </clause>

  <clause id="8129">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(699,a,8112,a),flip(a)].">
      <j1 rule="hyper" parents="699 8112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8130">
    <literal><![CDATA[
      T(x * (y * K(x,z)),K(x,z)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(35,a,7275,a,b,8112,a),flip(a)].">
      <j1 rule="hyper" parents="35 7275 8112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8131">
    <literal><![CDATA[
      T(K(x,y),z) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8112,a(flip),b,4635,a)].">
      <j1 rule="hyper" parents="119 8112 4635"/>
    </justification>
  </clause>

  <clause id="8132">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) != u
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(8112(a,1),346(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="8112 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8133">
    <literal><![CDATA[
      (x * K(y,z)) / x = T(K(y,z),x)
    ]]></literal>
    <justification jstring="[para(8112(a,1),4636(a,1,2))].">
      <j1 rule="para" parents="8112 4636"/>
    </justification>
  </clause>

  <clause id="8134">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8112(a,1),5897(a,1,1))].">
      <j1 rule="para" parents="8112 5897"/>
    </justification>
  </clause>

  <clause id="8135">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,8067,a,b,8045,a),flip(a)].">
      <j1 rule="hyper" parents="334 8067 8045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8136">
    <literal><![CDATA[
      K(x,K(y,z / y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),8045(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 8045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8137">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,8053,a,b,8046,a),flip(a)].">
      <j1 rule="hyper" parents="334 8053 8046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8138">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8048,a,b,8046,a),flip(a)].">
      <j1 rule="hyper" parents="334 8048 8046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8139">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8046,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 8046 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8140">
    <literal><![CDATA[
      K(x,K(y,y \ z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),8046(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 8046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8141">
    <literal><![CDATA[
      K(x,K(y / z,z)) = K(x,K(y / z,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),8046(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 8046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8142">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z \ y))
    ]]></literal>
    <justification jstring="[para(5568(a,1),8046(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5568 8046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8143">
    <literal><![CDATA[
      K(x * y,x) * K(z,K(x,y)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[para(8046(a,1),7410(a,1,2))].">
      <j1 rule="para" parents="8046 7410"/>
    </justification>
  </clause>

  <clause id="8144">
    <literal><![CDATA[
      K(x,K(x * y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8048,a,b,8051,a),flip(a)].">
      <j1 rule="hyper" parents="334 8048 8051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8145">
    <literal><![CDATA[
      T(x,y * T(z,K(x,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(8054(a,1),7650(a,1,2,2))].">
      <j1 rule="para" parents="8054 7650"/>
    </justification>
  </clause>

  <clause id="8146">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * K(z,u)) = T(y * K(z,u),K(x,z))
    ]]></literal>
    <justification jstring="[para(7592(a,1),8055(a,1,1,2))].">
      <j1 rule="para" parents="7592 8055"/>
    </justification>
  </clause>

  <clause id="8147">
    <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,5435,a(flip),b,8063,a),flip(a)].">
      <j1 rule="hyper" parents="58 5435 8063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8148">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u) = R(x,K(y,z),T(u,K(y,z)))
    ]]></literal>
    <justification jstring="[para(8071(a,1),7016(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8071 7016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8149">
    <literal><![CDATA[
      K(x,K(y,x \ z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8053,a,b,8073,a),flip(a)].">
      <j1 rule="hyper" parents="334 8053 8073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8150">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8053,a,b,8074,a),flip(a)].">
      <j1 rule="hyper" parents="334 8053 8074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8151">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,8048,a,b,8074,a),flip(a)].">
      <j1 rule="hyper" parents="334 8048 8074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8152">
    <literal><![CDATA[
      T(T(K(x,y),z),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(168,a,5832,a,b,8075,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="168 5832 8075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8153">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7426,a,8152,a),flip(a)].">
      <j1 rule="hyper" parents="7426 8152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8154">
    <literal><![CDATA[
      T(K(x \ y,z),y) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(6650,a,8152,a),flip(a)].">
      <j1 rule="hyper" parents="6650 8152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8155">
    <literal><![CDATA[
      T(K(x,y \ z),z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(6460,a,8152,a),flip(a)].">
      <j1 rule="hyper" parents="6460 8152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8156">
    <literal><![CDATA[
      T(K(1 / T(x,y),z),y) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(5816,a,8152,a),flip(a)].">
      <j1 rule="hyper" parents="5816 8152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8157">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7797,a,b,8152,a)].">
      <j1 rule="hyper" parents="58 7797 8152"/>
    </justification>
  </clause>

  <clause id="8158">
    <literal><![CDATA[
      T(x,y) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      T(K(z,u),y) = x
    ]]></literal>
    <justification jstring="[para(8152(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="8152 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8159">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) * z = z * L(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(8152(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8152 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8160">
    <literal><![CDATA[
      R(T(K(x,y),z),u,w) * z = z * R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(8152(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8152 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8161">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) \ (z * L(K(x,y),u,w)) = z
    ]]></literal>
    <justification jstring="[para(8152(a,1),283(a,1,2,2,1))].">
      <j1 rule="para" parents="8152 283"/>
    </justification>
  </clause>

  <clause id="8162">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(7664,a,8153,a)].">
      <j1 rule="hyper" parents="7664 8153"/>
    </justification>
  </clause>

  <clause id="8163">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(6769,a,8153,a)].">
      <j1 rule="hyper" parents="6769 8153"/>
    </justification>
  </clause>

  <clause id="8164">
    <literal><![CDATA[
      K(x,T(y \ z,z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(6460,a,8153,a),flip(a)].">
      <j1 rule="hyper" parents="6460 8153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8165">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,y)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(6022,a,8153,a),flip(a)].">
      <j1 rule="hyper" parents="6022 8153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8166">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(z,y)) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(5811,a,8153,a)].">
      <j1 rule="hyper" parents="5811 8153"/>
    </justification>
  </clause>

  <clause id="8167">
    <literal><![CDATA[
      (x * K(y,z)) / x = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(281,a,8153,a)].">
      <j1 rule="hyper" parents="281 8153"/>
    </justification>
  </clause>

  <clause id="8168">
    <literal><![CDATA[
      K(x \ K(x,y),z) = K(x \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6953,a(flip),b,8153,a),flip(a)].">
      <j1 rule="hyper" parents="58 6953 8153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8169">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),z)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,7425,a(flip),b,8153,a),flip(a)].">
      <j1 rule="hyper" parents="35 7425 8153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8170">
    <literal><![CDATA[
      K(x,T(y,z)) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8153,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 8153 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8171">
    <literal><![CDATA[
      T(x,y) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      K(z,T(u,y)) = x
    ]]></literal>
    <justification jstring="[para(8153(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="8153 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8172">
    <literal><![CDATA[
      T(K(x,y \ z),y) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),8153(a,1,1,2))].">
      <j1 rule="para" parents="107 8153"/>
    </justification>
  </clause>

  <clause id="8173">
    <literal><![CDATA[
      K(x,T(y,z)) \ (z * K(x,y)) = z
    ]]></literal>
    <justification jstring="[para(8153(a,1),232(a,1,2,2))].">
      <j1 rule="para" parents="8153 232"/>
    </justification>
  </clause>

  <clause id="8174">
    <literal><![CDATA[
      x * K(y,z) != u * x
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8153(a,1),249(a,1,2))].">
      <j1 rule="para" parents="8153 249"/>
    </justification>
  </clause>

  <clause id="8175">
    <literal><![CDATA[
      R(K(x,T(y,z)),u,w) * z = z * R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(8153(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8153 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8176">
    <literal><![CDATA[
      (K(x,T(y,z * u)) * z) * u = (z * u) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(8153(a,1),656(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8153 656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8177">
    <literal><![CDATA[
      (K(x,T(y,z)) * u) * (u \ z) = z * R(K(x,y),u,u \ z)
    ]]></literal>
    <justification jstring="[para(8153(a,1),751(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8153 751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8178">
    <literal><![CDATA[
      T(K(x \ y,z),x) = K(y / x,z)
    ]]></literal>
    <justification jstring="[para(7457(a,1),8153(a,1,1))].">
      <j1 rule="para" parents="7457 8153"/>
    </justification>
  </clause>

  <clause id="8179">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(8153(a,1),7394(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8153 7394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8180">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(7984,a,8157,a)].">
      <j1 rule="hyper" parents="7984 8157"/>
    </justification>
  </clause>

  <clause id="8181">
    <literal><![CDATA[
      K((x * y) / x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(7570,a,8157,a),flip(a)].">
      <j1 rule="hyper" parents="7570 8157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8182">
    <literal><![CDATA[
      T(x,T(T(y,z),z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,8157,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 8157 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8183">
    <literal><![CDATA[
      K(R(T(x,y),z,u),T(w,y)) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,7456,a,b,8157,a)].">
      <j1 rule="hyper" parents="58 7456 8157"/>
    </justification>
  </clause>

  <clause id="8184">
    <literal><![CDATA[
      K(L(T(x,y),z,u),T(w,y)) = K(L(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,7455,a,b,8157,a)].">
      <j1 rule="hyper" parents="58 7455 8157"/>
    </justification>
  </clause>

  <clause id="8185">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(x,T(T(z,u),u * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7954,a(flip),b,8157,a),flip(a)].">
      <j1 rule="hyper" parents="58 7954 8157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8186">
    <literal><![CDATA[
      K(x,T(y \ z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),8157(a,1,2,1))].">
      <j1 rule="para" parents="107 8157"/>
    </justification>
  </clause>

  <clause id="8187">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(230(a,1),8157(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="230 8157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8188">
    <literal><![CDATA[
      K(x,T(T(T(y,z),z),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(109(a,2),8157(a,1,2))].">
      <j1 rule="para" parents="109 8157"/>
    </justification>
  </clause>

  <clause id="8189">
    <literal><![CDATA[
      K(x,y * K(z,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5086(a,1),8157(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5086 8157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8190">
    <literal><![CDATA[
      K((x * y) / x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8157(a,1),7570(a,1))].">
      <j1 rule="para" parents="8157 7570"/>
    </justification>
  </clause>

  <clause id="8191">
    <literal><![CDATA[
      K(x / (x / y),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(7384,a,8162,a),flip(a)].">
      <j1 rule="hyper" parents="7384 8162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8192">
    <literal><![CDATA[
      x * K(T(x,y),T(z,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,8162,a,b,4995,a(flip))].">
      <j1 rule="hyper" parents="119 8162 4995"/>
    </justification>
  </clause>

  <clause id="8194">
    <literal><![CDATA[
      K(K(x,y) * z,T(u,z)) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7509,a(flip),b,8162,a)].">
      <j1 rule="hyper" parents="58 7509 8162"/>
    </justification>
  </clause>

  <clause id="8196">
    <literal><![CDATA[
      K(x,T(y,z)) \ z = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,8162,a(flip),b,7413,a),flip(a)].">
      <j1 rule="hyper" parents="119 8162 7413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8197">
    <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),8162(a,1,2))].">
      <j1 rule="para" parents="20 8162"/>
    </justification>
  </clause>

  <clause id="8198">
    <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),8162(a,1,2))].">
      <j1 rule="para" parents="22 8162"/>
    </justification>
  </clause>

  <clause id="8199">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),8162(a,1,2))].">
      <j1 rule="para" parents="107 8162"/>
    </justification>
  </clause>

  <clause id="8200">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(230(a,1),8162(a,1,2)),flip(a)].">
      <j1 rule="para" parents="230 8162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8201">
    <literal><![CDATA[
      K(T(x,y),R(T(z,y * u),y,u)) = K(x,(y * u) \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(1137(a,1),8162(a,1,2))].">
      <j1 rule="para" parents="1137 8162"/>
    </justification>
  </clause>

  <clause id="8202">
    <literal><![CDATA[
      K(x \ T(x * y,y),z) = K(y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(4171(a,1),8162(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4171 8162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8203">
    <literal><![CDATA[
      K(T(x,y \ z),y) = K(x,z / (z / y))
    ]]></literal>
    <justification jstring="[para(4544(a,1),8162(a,1,2))].">
      <j1 rule="para" parents="4544 8162"/>
    </justification>
  </clause>

  <clause id="8204">
    <literal><![CDATA[
      L(x,K(y,z),T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(8162(a,1),4777(a,1,2))].">
      <j1 rule="para" parents="8162 4777"/>
    </justification>
  </clause>

  <clause id="8205">
    <literal><![CDATA[
      K(x * K(y,x),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(5086(a,1),8162(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5086 8162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8206">
    <literal><![CDATA[
      K(x,y * K(z,y)) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(5086(a,1),8162(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5086 8162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8207">
    <literal><![CDATA[
      K(K(x,y) * y,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(5151(a,1),8162(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5151 8162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8208">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) \ x = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(8162(a,1),5495(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8162 5495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8209">
    <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(8162(a,1),6167(a,1,1))].">
      <j1 rule="para" parents="8162 6167"/>
    </justification>
  </clause>

  <clause id="8210">
    <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(8162(a,1),6340(a,1,1))].">
      <j1 rule="para" parents="8162 6340"/>
    </justification>
  </clause>

  <clause id="8211">
    <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(8162(a,1),6883(a,1,1))].">
      <j1 rule="para" parents="8162 6883"/>
    </justification>
  </clause>

  <clause id="8212">
    <literal><![CDATA[
      K(T(x,y),z) * y = y * K(x,z)
    ]]></literal>
    <justification jstring="[para(8162(a,1),7423(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8162 7423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8213">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(y,x)) = z
    ]]></literal>
    <justification jstring="[para(8162(a,1),7541(a,1,2,2))].">
      <j1 rule="para" parents="8162 7541"/>
    </justification>
  </clause>

  <clause id="8214">
    <literal><![CDATA[
      K(x / (x / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8162(a,1),7384(a,1))].">
      <j1 rule="para" parents="8162 7384"/>
    </justification>
  </clause>

  <clause id="8215">
    <literal><![CDATA[
      L(x,K(y / z,u),z \ y) = x
    ]]></literal>
    <justification jstring="[para(107(a,1),8204(a,1,3))].">
      <j1 rule="para" parents="107 8204"/>
    </justification>
  </clause>

  <clause id="8216">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * x) = z * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8182,a(flip),b,7933,a),flip(a)].">
      <j1 rule="hyper" parents="119 8182 7933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8217">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = K(x,y) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,8182,a(flip),b,7808,a),flip(a)].">
      <j1 rule="hyper" parents="119 8182 7808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8218">
    <literal><![CDATA[
      T(x,T(y \ z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),8182(a,1,2,1))].">
      <j1 rule="para" parents="107 8182"/>
    </justification>
  </clause>

  <clause id="8219">
    <literal><![CDATA[
      T(x,(y * z) / y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(230(a,1),8182(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="230 8182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8220">
    <literal><![CDATA[
      T(x,T(T(y \ z,u),y)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(254(a,1),8182(a,1,2,1))].">
      <j1 rule="para" parents="254 8182"/>
    </justification>
  </clause>

  <clause id="8221">
    <literal><![CDATA[
      T(x,y * K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5086(a,1),8182(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5086 8182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8222">
    <literal><![CDATA[
      L(x,K(y \ 1,z),u \ (y \ u)) = x
    ]]></literal>
    <justification jstring="[para(5709(a,1),8215(a,1,2))].">
      <j1 rule="para" parents="5709 8215"/>
    </justification>
  </clause>

  <clause id="8223">
    <literal><![CDATA[
      T(T(x,y / z),K(y,y / z)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,7332,a(flip),b,8105,a),flip(a)].">
      <j1 rule="hyper" parents="334 7332 8105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8224">
    <literal><![CDATA[
      T(x,K(y,z)) * z = z * T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,8105,a(flip),b,108,a),flip(a)].">
      <j1 rule="hyper" parents="119 8105 108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8225">
    <literal><![CDATA[
      T(x,T(y,z)) * K(y,z) = K(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(8105(a,1),5896(a,1,1))].">
      <j1 rule="para" parents="8105 5896"/>
    </justification>
  </clause>

  <clause id="8226">
    <literal><![CDATA[
      T(T(x,y) * z,K(z,y)) = T(x,T(y,z)) * z
    ]]></literal>
    <justification jstring="[para(8105(a,1),7910(a,2,1))].">
      <j1 rule="para" parents="8105 7910"/>
    </justification>
  </clause>

  <clause id="8227">
    <literal><![CDATA[
      T(T(x,y) \ z,K(x,y)) = T(z / T(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(696,a,8125,a)].">
      <j1 rule="hyper" parents="696 8125"/>
    </justification>
  </clause>

  <clause id="8228">
    <literal><![CDATA[
      T(x,T(y,z)) != T(u,y)
    ]]></literal>
    <literal><![CDATA[
      T(u,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(8125(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="8125 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8229">
    <literal><![CDATA[
      K(x \ y,z) * y = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(6624(a,1),8131(a,1,1))].">
      <j1 rule="para" parents="6624 8131"/>
    </justification>
  </clause>

  <clause id="8230">
    <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(8133(a,1),5175(a,1,2,1))].">
      <j1 rule="para" parents="8133 5175"/>
    </justification>
  </clause>

  <clause id="8231">
    <literal><![CDATA[
      T(x,K(y,z / y)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8136,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 8136 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8232">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(y,K(x,x * z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8135,a,b,8137,a)].">
      <j1 rule="hyper" parents="334 8135 8137"/>
    </justification>
  </clause>

  <clause id="8233">
    <literal><![CDATA[
      K(x,K(y,x * z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8048,a,b,8137,a)].">
      <j1 rule="hyper" parents="58 8048 8137"/>
    </justification>
  </clause>

  <clause id="8234">
    <literal><![CDATA[
      K(x,K(y,x * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8048,a,b,8138,a)].">
      <j1 rule="hyper" parents="58 8048 8138"/>
    </justification>
  </clause>

  <clause id="8235">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,8100,a,b,8139,a),flip(a)].">
      <j1 rule="hyper" parents="334 8100 8139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8236">
    <literal><![CDATA[
      T(x,K(y,y \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),8139(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 8139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8237">
    <literal><![CDATA[
      K(x,K(y,y \ z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,8053,a,b,8140,a),flip(a)].">
      <j1 rule="hyper" parents="334 8053 8140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8238">
    <literal><![CDATA[
      T(x,K(y,y \ z)) = x * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,8140,a(flip),b,4995,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 8140 4995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8239">
    <literal><![CDATA[
      K(x,K(x \ y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),8144(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 8144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8240">
    <literal><![CDATA[
      T(x,K(y,x \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8149,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 8149 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8241">
    <literal><![CDATA[
      T(x,K(y,z * x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8150,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 8150 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8242">
    <literal><![CDATA[
      K(x,K(y * x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8067,a,b,8151,a)].">
      <j1 rule="hyper" parents="58 8067 8151"/>
    </justification>
  </clause>

  <clause id="8243">
    <literal><![CDATA[
      K(x / y,x / z) = K(y \ x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(6761,a,8154,a),flip(a)].">
      <j1 rule="hyper" parents="6761 8154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8244">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) = K((y * z) / x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6603,a(flip),b,8154,a)].">
      <j1 rule="hyper" parents="58 6603 8154"/>
    </justification>
  </clause>

  <clause id="8245">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[hyper(7989,a,8155,a)].">
      <j1 rule="hyper" parents="7989 8155"/>
    </justification>
  </clause>

  <clause id="8246">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) = K(x,(z * x) / y)
    ]]></literal>
    <justification jstring="[hyper(7981,a,8155,a)].">
      <j1 rule="hyper" parents="7981 8155"/>
    </justification>
  </clause>

  <clause id="8249">
    <literal><![CDATA[
      x * T(x \ y,T(z,y)) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,8163,a(flip),b,6427,a),flip(a)].">
      <j1 rule="hyper" parents="119 8163 6427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8251">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),T(y,u)) = K((K(y,z) * u) / x,y)
    ]]></literal>
    <justification jstring="[para(7515(a,1),8163(a,1,2))].">
      <j1 rule="para" parents="7515 8163"/>
    </justification>
  </clause>

  <clause id="8252">
    <literal><![CDATA[
      K(x,y \ z) * (z * K(z / y,x)) = z
    ]]></literal>
    <justification jstring="[para(8163(a,1),7541(a,1,2,2))].">
      <j1 rule="para" parents="8163 7541"/>
    </justification>
  </clause>

  <clause id="8254">
    <literal><![CDATA[
      T(x,T(y \ z,z)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(118,a,8164,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 8164 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8255">
    <literal><![CDATA[
      K(x,y / (y / z)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),8164(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 8164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8256">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8167(a,1),303(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8167 303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8257">
    <literal><![CDATA[
      K(x,T(y,z)) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8167(a,1),126(a,1,1))].">
      <j1 rule="para" parents="8167 126"/>
    </justification>
  </clause>

  <clause id="8258">
    <literal><![CDATA[
      R(T(K(x,T(y,z)),z * u),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(8167(a,1),969(a,1,1,1))].">
      <j1 rule="para" parents="8167 969"/>
    </justification>
  </clause>

  <clause id="8259">
    <literal><![CDATA[
      (x * (y * K(z,u))) / (x * y) = L(K(z,T(u,x * y)),y,x)
    ]]></literal>
    <justification jstring="[para(8167(a,1),877(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8167 877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8260">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,y \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(30,a,6232,a,b,8170,a),flip(a)].">
      <j1 rule="hyper" parents="30 6232 8170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8261">
    <literal><![CDATA[
      T(x,T(y,z)) * z = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,8170,a(flip),b,5043,a),flip(a)].">
      <j1 rule="hyper" parents="119 8170 5043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8262">
    <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),8170(a,1,1,2))].">
      <j1 rule="para" parents="20 8170"/>
    </justification>
  </clause>

  <clause id="8263">
    <literal><![CDATA[
      K(x,y \ z) * y = y * K(x,z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),8170(a,1,1,2))].">
      <j1 rule="para" parents="107 8170"/>
    </justification>
  </clause>

  <clause id="8264">
    <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(8170(a,1),102(a,2,2))].">
      <j1 rule="para" parents="8170 102"/>
    </justification>
  </clause>

  <clause id="8265">
    <literal><![CDATA[
      T(K(x,y),z) * (z / y) = (z / y) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6576(a,1),8170(a,1,1))].">
      <j1 rule="para" parents="6576 8170"/>
    </justification>
  </clause>

  <clause id="8266">
    <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(8170(a,1),5424(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="8170 5424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8267">
    <literal><![CDATA[
      K(x * K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8170(a,1),7609(a,1,1))].">
      <j1 rule="para" parents="8170 7609"/>
    </justification>
  </clause>

  <clause id="8268">
    <literal><![CDATA[
      K(x,(y * K(x,z)) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(8170(a,1),7661(a,1,2,1))].">
      <j1 rule="para" parents="8170 7661"/>
    </justification>
  </clause>

  <clause id="8269">
    <literal><![CDATA[
      K(x,T(y * K(x,z),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(8170(a,1),7812(a,1,2,1))].">
      <j1 rule="para" parents="8170 7812"/>
    </justification>
  </clause>

  <clause id="8271">
    <literal><![CDATA[
      x / (x * K(y,z)) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(117,a,8173,a(flip),b,7469,a(flip))].">
      <j1 rule="hyper" parents="117 8173 7469"/>
    </justification>
  </clause>

  <clause id="8272">
    <literal><![CDATA[
      (x \ y) * K(y / x,z) = T(x \ y,T(z,x))
    ]]></literal>
    <justification jstring="[para(8178(a,1),7424(a,1,2))].">
      <j1 rule="para" parents="8178 7424"/>
    </justification>
  </clause>

  <clause id="8273">
    <literal><![CDATA[
      K(x / ((y * z) \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(((y * z) \ y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(8178(a,1),7652(a,1))].">
      <j1 rule="para" parents="8178 7652"/>
    </justification>
  </clause>

  <clause id="8274">
    <literal><![CDATA[
      K((x \ y) \ 1,T(z,y)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(6644,a,8180,a)].">
      <j1 rule="hyper" parents="6644 8180"/>
    </justification>
  </clause>

  <clause id="8275">
    <literal><![CDATA[
      x * T(x \ y,T(z,x)) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,8180,a(flip),b,6427,a),flip(a)].">
      <j1 rule="hyper" parents="119 8180 6427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8276">
    <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),8180(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 8180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8277">
    <literal><![CDATA[
      K(x \ y,T(z,x)) / (x \ y) = (1 / (x \ y)) * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(8180(a,1),6580(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8180 6580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8278">
    <literal><![CDATA[
      (x * K(x / y,z)) / y = T(x / y,T(z,y))
    ]]></literal>
    <justification jstring="[para(8180(a,1),6636(a,1,1,2))].">
      <j1 rule="para" parents="8180 6636"/>
    </justification>
  </clause>

  <clause id="8279">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,T(y,x)) = K(u / (x * K(y,z)),y)
    ]]></literal>
    <justification jstring="[para(7365(a,1),8180(a,1,2))].">
      <j1 rule="para" parents="7365 8180"/>
    </justification>
  </clause>

  <clause id="8280">
    <literal><![CDATA[
      x \ (T((y * x) / y,z) * u) = K(y,x) * (K(x,T(z,y)) * u)
    ]]></literal>
    <justification jstring="[para(8181(a,1),5673(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8181 5673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8281">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8181(a,1),7570(a,1))].">
      <j1 rule="para" parents="8181 7570"/>
    </justification>
  </clause>

  <clause id="8282">
    <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),8186(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 8186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8283">
    <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),8186(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13 8186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8284">
    <literal><![CDATA[
      K(x,T((y * z) \ (y * u),z)) = K(x,L(u / z,z,y))
    ]]></literal>
    <justification jstring="[para(889(a,1),8187(a,1,2)),flip(a)].">
      <j1 rule="para" parents="889 8187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8285">
    <literal><![CDATA[
      K(x,L((y \ z) / u,u,y)) = K(x,T((y * u) \ z,u))
    ]]></literal>
    <justification jstring="[para(890(a,2),8187(a,1,2))].">
      <j1 rule="para" parents="890 8187"/>
    </justification>
  </clause>

  <clause id="8286">
    <literal><![CDATA[
      K(x,T(L(y,z,u),w / y)) = K(x,L(w / (w / y),z,u))
    ]]></literal>
    <justification jstring="[para(886(a,1),8187(a,1,2)),flip(a)].">
      <j1 rule="para" parents="886 8187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8287">
    <literal><![CDATA[
      K((x * y) / ((x / z) * y),u) = R(K(z,T(u,x)),x,y)
    ]]></literal>
    <justification jstring="[para(8191(a,1),7061(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8191 7061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8288">
    <literal><![CDATA[
      T(x,(y * z) / y) = x * K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(230(a,1),8192(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="230 8192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8289">
    <literal><![CDATA[
      T(x,y \ K(z,y \ 1)) = x * K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(5152(a,1),8192(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5152 8192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8290">
    <literal><![CDATA[
      K(T(x,y),(y * K(z,x)) \ u) = K(x,u / (y * K(z,x)))
    ]]></literal>
    <justification jstring="[para(7375(a,1),8199(a,1,1))].">
      <j1 rule="para" parents="7375 8199"/>
    </justification>
  </clause>

  <clause id="8291">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5165,a,b,8200,a)].">
      <j1 rule="hyper" parents="58 5165 8200"/>
    </justification>
  </clause>

  <clause id="8292">
    <literal><![CDATA[
      K(x,T(y,L(z,u,x))) = K(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(7297(a,1),8205(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7297 8205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8293">
    <literal><![CDATA[
      K(x,T(y,K(L(x,z,u),w) * v5)) = K(x * K(v5,x),y)
    ]]></literal>
    <justification jstring="[para(7682(a,1),8205(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7682 8205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8294">
    <literal><![CDATA[
      x / (K(T(y,z),x) * K(x * K(z,x),z)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(8206(a,1),5690(a,1,2,1))].">
      <j1 rule="para" parents="8206 5690"/>
    </justification>
  </clause>

  <clause id="8295">
    <literal><![CDATA[
      K(x,y * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8206(a,2),7970(a,1))].">
      <j1 rule="para" parents="8206 7970"/>
    </justification>
  </clause>

  <clause id="8296">
    <literal><![CDATA[
      K(K(x,y) * z,u) * z = z * K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(7509(a,1),8212(a,1,1))].">
      <j1 rule="para" parents="7509 8212"/>
    </justification>
  </clause>

  <clause id="8297">
    <literal><![CDATA[
      T(x,T(y * z,u) / y) = T(x,y \ T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4830(a,1),8218(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4830 8218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8298">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = T(x,T(R(z,u,w),y))
    ]]></literal>
    <justification jstring="[para(881(a,2),8219(a,1,2))].">
      <j1 rule="para" parents="881 8219"/>
    </justification>
  </clause>

  <clause id="8299">
    <literal><![CDATA[
      T(x,T(T(y \ (z \ y),T(z,u)),y)) = T(x,(((z \ 1) \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[para(6230(a,1),8219(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6230 8219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8300">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,T(x,y)) \ z) = ((y * x) / y) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(8219(a,1),4916(a,1,2,1))].">
      <j1 rule="para" parents="8219 4916"/>
    </justification>
  </clause>

  <clause id="8301">
    <literal><![CDATA[
      T(x,(y \ 1) \ K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,3932,a,b,8221,a)].">
      <j1 rule="hyper" parents="58 3932 8221"/>
    </justification>
  </clause>

  <clause id="8302">
    <literal><![CDATA[
      T(x,K(y,1 / z) / z) = T(x,T(1 / z,y))
    ]]></literal>
    <justification jstring="[para(2439(a,1),8221(a,1,2))].">
      <j1 rule="para" parents="2439 8221"/>
    </justification>
  </clause>

  <clause id="8303">
    <literal><![CDATA[
      T(x,K(y,x * z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,8233,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 8233 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8304">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,T(z * y,z))
    ]]></literal>
    <justification jstring="[para(8235(a,1),8124(a,1,1))].">
      <j1 rule="para" parents="8235 8124"/>
    </justification>
  </clause>

  <clause id="8305">
    <literal><![CDATA[
      T(x * K(y \ z,y),K(y,z)) = K(y \ z,y) * x
    ]]></literal>
    <justification jstring="[hyper(6723,a,8236,a),flip(a)].">
      <j1 rule="hyper" parents="6723 8236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8306">
    <literal><![CDATA[
      T(x,K(y,z / x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),8241(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 8241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8307">
    <literal><![CDATA[
      T(x / y,T(z \ x,y)) = T(x / y,x / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7633,a,b,8254,a)].">
      <j1 rule="hyper" parents="58 7633 8254"/>
    </justification>
  </clause>

  <clause id="8309">
    <literal><![CDATA[
      K(x,x \ y) * K(z,T(x,y)) = T(y / (y / x),z) \ x
    ]]></literal>
    <justification jstring="[para(8255(a,1),7191(a,1,2))].">
      <j1 rule="para" parents="8255 7191"/>
    </justification>
  </clause>

  <clause id="8310">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * K(z,z \ u) = (x / T(u / (u / z),y)) * z
    ]]></literal>
    <justification jstring="[para(8255(a,1),6804(a,1,1,2))].">
      <j1 rule="para" parents="8255 6804"/>
    </justification>
  </clause>

  <clause id="8311">
    <literal><![CDATA[
      K(x,y / (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(8255(a,2),7561(a,1))].">
      <j1 rule="para" parents="8255 7561"/>
    </justification>
  </clause>

  <clause id="8312">
    <literal><![CDATA[
      T(T(x,K(y,z)),x * y) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[para(8303(a,1),8124(a,1,1))].">
      <j1 rule="para" parents="8303 8124"/>
    </justification>
  </clause>

  <clause id="8313">
    <literal><![CDATA[
      T(x,K(y,z / x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,8100,a,b,8306,a),flip(a)].">
      <j1 rule="hyper" parents="334 8100 8306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8314">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(8052(a,2),8042(a,1))].">
      <j1 rule="para" parents="8052 8042"/>
    </justification>
  </clause>

  <clause id="8315">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8065(a,2),8042(a,1))].">
      <j1 rule="para" parents="8065 8042"/>
    </justification>
  </clause>

  <clause id="8316">
    <literal><![CDATA[
      K(x,K(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8237(a,2),8069(a,1))].">
      <j1 rule="para" parents="8237 8069"/>
    </justification>
  </clause>

  <clause id="8317">
    <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(7388(a,1),8099(a,1,2))].">
      <j1 rule="para" parents="7388 8099"/>
    </justification>
  </clause>

  <clause id="8318">
    <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(7403(a,1),8099(a,1,2))].">
      <j1 rule="para" parents="7403 8099"/>
    </justification>
  </clause>

  <clause id="8319">
    <literal><![CDATA[
      K(x,K(y,z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8045(a,2),8099(a,1))].">
      <j1 rule="para" parents="8045 8099"/>
    </justification>
  </clause>

  <clause id="8320">
    <literal><![CDATA[
      L(x,K(y \ 1,z),u \ (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(8222(a,1),45(a,2))].">
      <j1 rule="para" parents="8222 45"/>
    </justification>
  </clause>

  <clause id="8321">
    <literal><![CDATA[
      T(K(x,y \ z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),8256(a,1,1,2))].">
      <j1 rule="para" parents="107 8256"/>
    </justification>
  </clause>

  <clause id="8322">
    <literal><![CDATA[
      K(x \ y,T(z,y / x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(3484(a,1),8256(a,1))].">
      <j1 rule="para" parents="3484 8256"/>
    </justification>
  </clause>

  <clause id="8323">
    <literal><![CDATA[
      K(x \ y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(6624(a,1),8256(a,1))].">
      <j1 rule="para" parents="6624 8256"/>
    </justification>
  </clause>

  <clause id="8324">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7388(a,2),8256(a,1))].">
      <j1 rule="para" parents="7388 8256"/>
    </justification>
  </clause>

  <clause id="8325">
    <literal><![CDATA[
      T(K(x \ y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7414(a,1),8256(a,1,1))].">
      <j1 rule="para" parents="7414 8256"/>
    </justification>
  </clause>

  <clause id="8326">
    <literal><![CDATA[
      T(K(x \ y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7457(a,1),8256(a,1,1))].">
      <j1 rule="para" parents="7457 8256"/>
    </justification>
  </clause>

  <clause id="8327">
    <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(8153(a,1),8256(a,1,1,2))].">
      <j1 rule="para" parents="8153 8256"/>
    </justification>
  </clause>

  <clause id="8328">
    <literal><![CDATA[
      K(x,T(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),8281(a,1,2,1))].">
      <j1 rule="para" parents="107 8281"/>
    </justification>
  </clause>

  <clause id="8329">
    <literal><![CDATA[
      K(x \ y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7457(a,1),8281(a,1))].">
      <j1 rule="para" parents="7457 8281"/>
    </justification>
  </clause>

  <clause id="8330">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7467(a,1),8281(a,1))].">
      <j1 rule="para" parents="7467 8281"/>
    </justification>
  </clause>

  <clause id="8331">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z),u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(7460(a,1),8281(a,1))].">
      <j1 rule="para" parents="7460 8281"/>
    </justification>
  </clause>

  <clause id="8332">
    <literal><![CDATA[
      K(x \ y,T(z,y \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(7482(a,1),8281(a,1))].">
      <j1 rule="para" parents="7482 8281"/>
    </justification>
  </clause>

  <clause id="8333">
    <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(7455(a,2),8281(a,1))].">
      <j1 rule="para" parents="7455 8281"/>
    </justification>
  </clause>

  <clause id="8334">
    <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),8324(a,1,2))].">
      <j1 rule="para" parents="18 8324"/>
    </justification>
  </clause>

  <clause id="8335">
    <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),8324(a,1,2))].">
      <j1 rule="para" parents="22 8324"/>
    </justification>
  </clause>

  <clause id="8336">
    <literal><![CDATA[
      K(T(x,y),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),8324(a,1,2))].">
      <j1 rule="para" parents="107 8324"/>
    </justification>
  </clause>

  <clause id="8337">
    <literal><![CDATA[
      K(T(x,y),z \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(7314(a,1),8324(a,1))].">
      <j1 rule="para" parents="7314 8324"/>
    </justification>
  </clause>

  <clause id="8338">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(2073,a,8018,a)].">
      <j1 rule="hyper" parents="2073 8018"/>
    </justification>
  </clause>

  <clause id="8339">
    <literal><![CDATA[
      K(x,K(y,z)) != 1
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8018(a,1),5253(a,1)),flip(b)].">
      <j1 rule="para" parents="8018 5253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8340">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8018(a,1),5410(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8018 5410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8341">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) \ K(y,x) = T(K(y,x),T(z,y \ u))
    ]]></literal>
    <justification jstring="[para(7565(a,1),8025(a,1,1,2))].">
      <j1 rule="para" parents="7565 8025"/>
    </justification>
  </clause>

  <clause id="8342">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) = K(x,y) * K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7525(a,1),8029(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7525 8029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8343">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = K(x,K(y,z)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7415(a,1),8030(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7415 8030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8344">
    <literal><![CDATA[
      K(x,T(y,z)) != K(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8032(a,1),5905(a,1))].">
      <j1 rule="para" parents="8032 5905"/>
    </justification>
  </clause>

  <clause id="8345">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8032(a,1),5906(a,1))].">
      <j1 rule="para" parents="8032 5906"/>
    </justification>
  </clause>

  <clause id="8346">
    <literal><![CDATA[
      K(x,T(y,z)) \ K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = u
    ]]></literal>
    <justification jstring="[para(8032(a,1),6528(a,1,1))].">
      <j1 rule="para" parents="8032 6528"/>
    </justification>
  </clause>

  <clause id="8347">
    <literal><![CDATA[
      K(x,K(y,R(T(x,z),u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,7460,a(flip),b,8033,a),flip(a)].">
      <j1 rule="hyper" parents="115 7460 8033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8348">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(x,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8049,a(flip),b,8044,a),flip(a)].">
      <j1 rule="hyper" parents="334 8049 8044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8349">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,8019,a(flip),b,8044,a),flip(a)].">
      <j1 rule="hyper" parents="334 8019 8044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8350">
    <literal><![CDATA[
      T(K(x,y),T(z,K(u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7401,a(flip),b,8047,a)].">
      <j1 rule="hyper" parents="58 7401 8047"/>
    </justification>
  </clause>

  <clause id="8351">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,T(x,u))) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(7403(a,1),8059(a,1,2,2))].">
      <j1 rule="para" parents="7403 8059"/>
    </justification>
  </clause>

  <clause id="8352">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,8048,a,b,8061,a),flip(a)].">
      <j1 rule="hyper" parents="334 8048 8061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8353">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(2073,a,8072,a)].">
      <j1 rule="hyper" parents="2073 8072"/>
    </justification>
  </clause>

  <clause id="8354">
    <literal><![CDATA[
      K(x,K(y,z)) != K(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8072(a,1),38(a,1))].">
      <j1 rule="para" parents="8072 38"/>
    </justification>
  </clause>

  <clause id="8355">
    <literal><![CDATA[
      K(x,y) * K(x,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8078(a,2),7974(a,1))].">
      <j1 rule="para" parents="8078 7974"/>
    </justification>
  </clause>

  <clause id="8356">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(y,T(x,u)))
    ]]></literal>
    <justification jstring="[hyper(8050,a,8082,a)].">
      <j1 rule="hyper" parents="8050 8082"/>
    </justification>
  </clause>

  <clause id="8357">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,8084,a(flip),b,5685,a)].">
      <j1 rule="hyper" parents="119 8084 5685"/>
    </justification>
  </clause>

  <clause id="8358">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8085(a,1),5906(a,1))].">
      <j1 rule="para" parents="8085 5906"/>
    </justification>
  </clause>

  <clause id="8359">
    <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(5958(a,1),8103(a,2,2,1))].">
      <j1 rule="para" parents="5958 8103"/>
    </justification>
  </clause>

  <clause id="8360">
    <literal><![CDATA[
      T(x * K(y,y \ z),K(y,z)) = K(y,y \ z) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,8236,a(flip),b,8109,a)].">
      <j1 rule="hyper" parents="58 8236 8109"/>
    </justification>
  </clause>

  <clause id="8361">
    <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(8109(a,1),5899(a,1,1))].">
      <j1 rule="para" parents="8109 5899"/>
    </justification>
  </clause>

  <clause id="8362">
    <literal><![CDATA[
      T(x * T(y,z),K(y,z)) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(6432(a,1),8109(a,1,1))].">
      <j1 rule="para" parents="6432 8109"/>
    </justification>
  </clause>

  <clause id="8363">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,x) = K(y,x) * T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(8110(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8110 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8364">
    <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,8113,a(flip),b,5049,a)].">
      <j1 rule="hyper" parents="119 8113 5049"/>
    </justification>
  </clause>

  <clause id="8365">
    <literal><![CDATA[
      T(x \ K(x,y),K(z,x)) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[para(5901(a,1),8115(a,2,2))].">
      <j1 rule="para" parents="5901 8115"/>
    </justification>
  </clause>

  <clause id="8366">
    <literal><![CDATA[
      T(x \ y,K(z,x)) = x \ T(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(8100(a,1),8115(a,2,2))].">
      <j1 rule="para" parents="8100 8115"/>
    </justification>
  </clause>

  <clause id="8367">
    <literal><![CDATA[
      T(x * K(y,z),u) / x = x \ T(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(8122(a,1),4829(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8122 4829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8368">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z * x) = K(y,z * x) * x
    ]]></literal>
    <justification jstring="[para(8241(a,1),8122(a,1,1))].">
      <j1 rule="para" parents="8241 8122"/>
    </justification>
  </clause>

  <clause id="8369">
    <literal><![CDATA[
      T(x * y,K(z,x)) = x * T(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(8134,a,8126,a)].">
      <j1 rule="hyper" parents="8134 8126"/>
    </justification>
  </clause>

  <clause id="8370">
    <literal><![CDATA[
      K(x,K(y \ z,y)) = K(x,K(z / y,z))
    ]]></literal>
    <justification jstring="[para(5235(a,1),8141(a,1,2))].">
      <j1 rule="para" parents="5235 8141"/>
    </justification>
  </clause>

  <clause id="8371">
    <literal><![CDATA[
      K(1 / T(T(x,y),y),z) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(5816,a,8156,a),flip(a)].">
      <j1 rule="hyper" parents="5816 8156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8372">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ y) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7967,a(flip),b,8165,a)].">
      <j1 rule="hyper" parents="58 7967 8165"/>
    </justification>
  </clause>

  <clause id="8373">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,z / (z * y))
    ]]></literal>
    <justification jstring="[para(4(a,1),8165(a,1,2,1,1))].">
      <j1 rule="para" parents="4 8165"/>
    </justification>
  </clause>

  <clause id="8374">
    <literal><![CDATA[
      K((x / (x / y)) \ 1,z) = K(y \ 1,T(z,y \ x))
    ]]></literal>
    <justification jstring="[para(4544(a,1),8166(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4544 8166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8375">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K(x \ K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,7411,a,b,8168,a)].">
      <j1 rule="hyper" parents="334 7411 8168"/>
    </justification>
  </clause>

  <clause id="8376">
    <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(8169(a,1),8256(a,1,1))].">
      <j1 rule="para" parents="8169 8256"/>
    </justification>
  </clause>

  <clause id="8377">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) != T(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(8179(a,2),3479(a,2)),flip(a)].">
      <j1 rule="para" parents="8179 3479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8378">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) / T(z,y) = 1 / (K(z,x) * T(z,y))
    ]]></literal>
    <justification jstring="[para(8179(a,1),5072(a,2,2))].">
      <j1 rule="para" parents="8179 5072"/>
    </justification>
  </clause>

  <clause id="8379">
    <literal><![CDATA[
      (x * T(y,z)) / T(x,y) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(117,a,8216,a(flip),b,5351,a(flip))].">
      <j1 rule="hyper" parents="117 8216 5351"/>
    </justification>
  </clause>

  <clause id="8380">
    <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(8216(a,1),506(a,1,2))].">
      <j1 rule="para" parents="8216 506"/>
    </justification>
  </clause>

  <clause id="8381">
    <literal><![CDATA[
      T(K(x,y),z) * ((x \ z) * x) = (x \ z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7450(a,1),8216(a,1,1))].">
      <j1 rule="para" parents="7450 8216"/>
    </justification>
  </clause>

  <clause id="8382">
    <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(8217(a,2),240(a,1,1,1))].">
      <j1 rule="para" parents="8217 240"/>
    </justification>
  </clause>

  <clause id="8383">
    <literal><![CDATA[
      T(x * y,K(z,y)) = T(x,K(z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(334,a,8108,a,b,8224,a)].">
      <j1 rule="hyper" parents="334 8108 8224"/>
    </justification>
  </clause>

  <clause id="8384">
    <literal><![CDATA[
      K(x \ y,z) \ (y * K(y / x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = y
    ]]></literal>
    <justification jstring="[para(8229(a,1),297(a,1,2))].">
      <j1 rule="para" parents="8229 297"/>
    </justification>
  </clause>

  <clause id="8385">
    <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(8229(a,2),6398(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8229 6398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8386">
    <literal><![CDATA[
      T(x,K(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8238(a,2),5030(a,1))].">
      <j1 rule="para" parents="8238 5030"/>
    </justification>
  </clause>

  <clause id="8387">
    <literal><![CDATA[
      K(x / y,z \ (x / y)) = K(y \ x,(z * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(7161,a,8243,a)].">
      <j1 rule="hyper" parents="7161 8243"/>
    </justification>
  </clause>

  <clause id="8388">
    <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(451,a,2418,a,b,8252,a)].">
      <j1 rule="hyper" parents="451 2418 8252"/>
    </justification>
  </clause>

  <clause id="8389">
    <literal><![CDATA[
      K(x,((y * z) / y) \ 1) = K(x,T(z \ 1,y))
    ]]></literal>
    <justification jstring="[para(5179(a,2),8260(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5179 8260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8390">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,x \ K(x,z)) = K(x \ 1,K(y,z))
    ]]></literal>
    <justification jstring="[para(8260(a,1),8072(a,1,2))].">
      <j1 rule="para" parents="8260 8072"/>
    </justification>
  </clause>

  <clause id="8391">
    <literal><![CDATA[
      (x * (K(y,z) * K(x,u))) * K(z,y) = T(x,T(u,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(6527,a,8261,a)].">
      <j1 rule="hyper" parents="6527 8261"/>
    </justification>
  </clause>

  <clause id="8392">
    <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(8261(a,1),6537(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8261 6537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8393">
    <literal><![CDATA[
      K(x,(y / T(z,x)) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(6368(a,1),8268(a,1,2,1))].">
      <j1 rule="para" parents="6368 8268"/>
    </justification>
  </clause>

  <clause id="8394">
    <literal><![CDATA[
      K(x,T(T(K(y,x) * z,u),w)) = K(x,T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(6999(a,1),8269(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6999 8269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8395">
    <literal><![CDATA[
      K((x \ y) \ 1,T(z,y)) = K((y / x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,5702,a,b,8274,a),flip(a)].">
      <j1 rule="hyper" parents="334 5702 8274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8396">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = x * K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(881(a,2),8288(a,1,2))].">
      <j1 rule="para" parents="881 8288"/>
    </justification>
  </clause>

  <clause id="8397">
    <literal><![CDATA[
      K(K(x,y) * z,K(y,u)) = K(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(5394(a,1),8349(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5394 8349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8398">
    <literal><![CDATA[
      R(x,K(y,z) * u,K(u,K(y,w))) = x
    ]]></literal>
    <justification jstring="[para(8349(a,1),6462(a,1,3))].">
      <j1 rule="para" parents="8349 6462"/>
    </justification>
  </clause>

  <clause id="8399">
    <literal><![CDATA[
      K(x * K(y,z),K(y,u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(8170(a,1),8349(a,1,1))].">
      <j1 rule="para" parents="8170 8349"/>
    </justification>
  </clause>

  <clause id="8400">
    <literal><![CDATA[
      R(x,K(y,z),T(u,K(y,w))) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(7213,a,8398,a)].">
      <j1 rule="hyper" parents="7213 8398"/>
    </justification>
  </clause>

  <clause id="8401">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * K(u,K(y,z)) = x * (u * K(y,z))
    ]]></literal>
    <justification jstring="[para(8398(a,1),529(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8398 529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8402">
    <literal><![CDATA[
      K(x,K(y,(z / x) \ u)) = K(x,K(y,(x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(5687(a,1),8352(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5687 8352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8403">
    <literal><![CDATA[
      K(x,K(y \ z,T(y,u))) = K(y,K(z,T(x,u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,8239,a(flip),b,8356,a),flip(a)].">
      <j1 rule="hyper" parents="334 8239 8356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8404">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7687,a,b,8357,a)].">
      <j1 rule="hyper" parents="58 7687 8357"/>
    </justification>
  </clause>

  <clause id="8405">
    <literal><![CDATA[
      T(x \ K(x,y),T(x,z)) = T(x \ K(x,y),x)
    ]]></literal>
    <justification jstring="[para(8365(a,1),7698(a,1,1))].">
      <j1 rule="para" parents="8365 7698"/>
    </justification>
  </clause>

  <clause id="8406">
    <literal><![CDATA[
      x * T(x \ y,K(z,x)) = T(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,8366,a,b,xx)].">
      <j1 rule="hyper" parents="119 8366"/>
    </justification>
  </clause>

  <clause id="8407">
    <literal><![CDATA[
      T(x,K(y,z)) / z = T(x / z,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(4835,a,8369,a)].">
      <j1 rule="hyper" parents="4835 8369"/>
    </justification>
  </clause>

  <clause id="8408">
    <literal><![CDATA[
      K(x,K(y / z,y)) = K(x,K(z,z \ y))
    ]]></literal>
    <justification jstring="[hyper(8099,a,8370,a),flip(a)].">
      <j1 rule="hyper" parents="8099 8370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8409">
    <literal><![CDATA[
      K(1 / T(x,y / x),z) = K(1 / (y / (y / x)),z)
    ]]></literal>
    <justification jstring="[para(252(a,1),8371(a,1,1,2,1))].">
      <j1 rule="para" parents="252 8371"/>
    </justification>
  </clause>

  <clause id="8410">
    <literal><![CDATA[
      K(1 / T(T(x,x * y),y),z) = K(1 / L(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(735(a,1),8371(a,1,1,2,1))].">
      <j1 rule="para" parents="735 8371"/>
    </justification>
  </clause>

  <clause id="8411">
    <literal><![CDATA[
      T(x,1 / T(T(y,z),z)) = x / K(1 / y,x)
    ]]></literal>
    <justification jstring="[para(8371(a,1),5074(a,2,2))].">
      <j1 rule="para" parents="8371 5074"/>
    </justification>
  </clause>

  <clause id="8412">
    <literal><![CDATA[
      K(x,y \ T(z,z \ y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(5866(a,1),8372(a,1,2))].">
      <j1 rule="para" parents="5866 8372"/>
    </justification>
  </clause>

  <clause id="8413">
    <literal><![CDATA[
      K(x,y / (y * z)) = K(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7832,a(flip),b,8373,a),flip(a)].">
      <j1 rule="hyper" parents="58 7832 8373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8414">
    <literal><![CDATA[
      K(((x * y) / x) \ 1,z) = K(T(y,x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(5179(a,2),8375(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5179 8375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8415">
    <literal><![CDATA[
      T(x * K(y,x),K(y,z)) = x * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(5469,a,8404,a)].">
      <j1 rule="hyper" parents="5469 8404"/>
    </justification>
  </clause>

  <clause id="8416">
    <literal><![CDATA[
      T(x * K(y,T(x,z * (u * x))),y) = T(x,K(y,z * (x * u)))
    ]]></literal>
    <justification jstring="[para(7378(a,2),8404(a,1,1,2,2))].">
      <j1 rule="para" parents="7378 8404"/>
    </justification>
  </clause>

  <clause id="8417">
    <literal><![CDATA[
      T(T(x,y) / z,K(y,z)) = T(x,T(y,z)) / z
    ]]></literal>
    <justification jstring="[para(7688(a,1),8407(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7688 8407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8418">
    <literal><![CDATA[
      K(x,K(y / z,y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,8140,a(flip),b,8408,a),flip(a)].">
      <j1 rule="hyper" parents="334 8140 8408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8419">
    <literal><![CDATA[
      K(x,K(y / z,y)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8053,a(flip),b,8418,a),flip(a)].">
      <j1 rule="hyper" parents="334 8053 8418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8420">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),8418(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 8418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8421">
    <literal><![CDATA[
      K(x,K(y,y / z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(8099,a,8419,a)].">
      <j1 rule="hyper" parents="8099 8419"/>
    </justification>
  </clause>

  <clause id="8422">
    <literal><![CDATA[
      K(x,K(y,x / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8069,a,8419,a)].">
      <j1 rule="hyper" parents="8069 8419"/>
    </justification>
  </clause>

  <clause id="8423">
    <literal><![CDATA[
      K(x,K(x / y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(8042,a,8419,a)].">
      <j1 rule="hyper" parents="8042 8419"/>
    </justification>
  </clause>

  <clause id="8424">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6647(a,1),8419(a,1,2))].">
      <j1 rule="para" parents="6647 8419"/>
    </justification>
  </clause>

  <clause id="8425">
    <literal><![CDATA[
      K(x,K(y,z \ y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(8099,a,8420,a)].">
      <j1 rule="hyper" parents="8099 8420"/>
    </justification>
  </clause>

  <clause id="8426">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,8017,a,b,8420,a),flip(a)].">
      <j1 rule="hyper" parents="334 8017 8420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8427">
    <literal><![CDATA[
      (x / y) * K(x,K(z,y)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(8421(a,1),8022(a,1,2))].">
      <j1 rule="para" parents="8421 8022"/>
    </justification>
  </clause>

  <clause id="8428">
    <literal><![CDATA[
      T(x,K(y,x / z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8422,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 8422 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8429">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),8422(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 8422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8430">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x / z,y) = K(z \ x,y)
    ]]></literal>
    <justification jstring="[para(8422(a,1),6646(a,1,1))].">
      <j1 rule="para" parents="8422 6646"/>
    </justification>
  </clause>

  <clause id="8431">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(72(a,1),8423(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 8423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8432">
    <literal><![CDATA[
      K(x,K(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8424(a,2),8089(a,1))].">
      <j1 rule="para" parents="8424 8089"/>
    </justification>
  </clause>

  <clause id="8433">
    <literal><![CDATA[
      K(x,K(y,z \ y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8067,a,b,8425,a),flip(a)].">
      <j1 rule="hyper" parents="334 8067 8425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8434">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8142,a,b,8425,a)].">
      <j1 rule="hyper" parents="58 8142 8425"/>
    </justification>
  </clause>

  <clause id="8435">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(x,K(u \ z,y))
    ]]></literal>
    <justification jstring="[para(6854(a,1),8425(a,1,2))].">
      <j1 rule="para" parents="6854 8425"/>
    </justification>
  </clause>

  <clause id="8436">
    <literal><![CDATA[
      K(x,K(y \ x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8042,a,8426,a)].">
      <j1 rule="hyper" parents="8042 8426"/>
    </justification>
  </clause>

  <clause id="8437">
    <literal><![CDATA[
      K(1 / ((1 / x) / y),K(z,(y * x) / u)) = (T(y * x,K(z,u)) / x) / y
    ]]></literal>
    <justification jstring="[para(8428(a,1),5823(a,2,1,1))].">
      <j1 rule="para" parents="8428 5823"/>
    </justification>
  </clause>

  <clause id="8438">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,8053,a(flip),b,8429,a),flip(a)].">
      <j1 rule="hyper" parents="334 8053 8429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8439">
    <literal><![CDATA[
      K(x \ y,z) \ K(y,K(x,z)) = K(z,y / x)
    ]]></literal>
    <justification jstring="[para(8431(a,1),7101(a,1,2))].">
      <j1 rule="para" parents="8431 7101"/>
    </justification>
  </clause>

  <clause id="8440">
    <literal><![CDATA[
      T(x,K(y,z \ y)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8433,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 8433 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8441">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8142,a,b,8433,a)].">
      <j1 rule="hyper" parents="58 8142 8433"/>
    </justification>
  </clause>

  <clause id="8442">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8099,a,8434,a)].">
      <j1 rule="hyper" parents="8099 8434"/>
    </justification>
  </clause>

  <clause id="8443">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(8069,a,8434,a)].">
      <j1 rule="hyper" parents="8069 8434"/>
    </justification>
  </clause>

  <clause id="8444">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,8048,a,b,8434,a),flip(a)].">
      <j1 rule="hyper" parents="334 8048 8434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8445">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,8434,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 8434 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8446">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(3696(a,1),8434(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3696 8434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8447">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(3700(a,2),8434(a,1,2))].">
      <j1 rule="para" parents="3700 8434"/>
    </justification>
  </clause>

  <clause id="8448">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) = K(x,K(u,y))
    ]]></literal>
    <justification jstring="[para(5613(a,2),8434(a,1,2))].">
      <j1 rule="para" parents="5613 8434"/>
    </justification>
  </clause>

  <clause id="8449">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(6423(a,1),8434(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6423 8434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8450">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8434(a,2),8099(a,1))].">
      <j1 rule="para" parents="8434 8099"/>
    </justification>
  </clause>

  <clause id="8451">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ y) = T(x \ y,K(y,z))
    ]]></literal>
    <justification jstring="[para(8438(a,1),8064(a,1,1))].">
      <j1 rule="para" parents="8438 8064"/>
    </justification>
  </clause>

  <clause id="8452">
    <literal><![CDATA[
      T(x,K(y \ z,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(8134,a,8440,a)].">
      <j1 rule="hyper" parents="8134 8440"/>
    </justification>
  </clause>

  <clause id="8453">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(8089,a,8441,a)].">
      <j1 rule="hyper" parents="8089 8441"/>
    </justification>
  </clause>

  <clause id="8454">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(8069,a,8441,a)].">
      <j1 rule="hyper" parents="8069 8441"/>
    </justification>
  </clause>

  <clause id="8455">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8441,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 8441 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8456">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(75(a,1),8441(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 8441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8457">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(5613(a,2),8441(a,1,2))].">
      <j1 rule="para" parents="5613 8441"/>
    </justification>
  </clause>

  <clause id="8458">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[para(5614(a,1),8441(a,1,2))].">
      <j1 rule="para" parents="5614 8441"/>
    </justification>
  </clause>

  <clause id="8459">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6423(a,1),8441(a,1,2))].">
      <j1 rule="para" parents="6423 8441"/>
    </justification>
  </clause>

  <clause id="8460">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[para(8441(a,1),8029(a,1,2))].">
      <j1 rule="para" parents="8441 8029"/>
    </justification>
  </clause>

  <clause id="8461">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8048,a,b,8442,a),flip(a)].">
      <j1 rule="hyper" parents="334 8048 8442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8462">
    <literal><![CDATA[
      (x * K(y \ 1,z)) \ K(x,K(y,z)) = (K(y \ 1,z) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,8442,a(flip),b,5835,a(flip))].">
      <j1 rule="hyper" parents="116 8442 5835"/>
    </justification>
  </clause>

  <clause id="8463">
    <literal><![CDATA[
      K(x,y * ((z \ (y \ 1)) * z)) = K(x,K(y * z,z))
    ]]></literal>
    <justification jstring="[para(5985(a,2),8442(a,1,2))].">
      <j1 rule="para" parents="5985 8442"/>
    </justification>
  </clause>

  <clause id="8464">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8442(a,2),8099(a,1))].">
      <j1 rule="para" parents="8442 8099"/>
    </justification>
  </clause>

  <clause id="8465">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8048,a,b,8443,a),flip(a)].">
      <j1 rule="hyper" parents="334 8048 8443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8466">
    <literal><![CDATA[
      T(1 / x,K(y,z)) = K(y,K(x,z)) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,8443,a(flip),b,5093,a),flip(a)].">
      <j1 rule="hyper" parents="117 8443 5093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8467">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8443(a,2),8099(a,1))].">
      <j1 rule="para" parents="8443 8099"/>
    </justification>
  </clause>

  <clause id="8468">
    <literal><![CDATA[
      K(1 / x,K(y,z)) = K(y,K(z,x))
    ]]></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="8469">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(3700(a,2),8444(a,1,2))].">
      <j1 rule="para" parents="3700 8444"/>
    </justification>
  </clause>

  <clause id="8470">
    <literal><![CDATA[
      T(x,K(y \ z,u)) = T(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(6423(a,1),8445(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6423 8445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8471">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8445(a,2),8134(a,1))].">
      <j1 rule="para" parents="8445 8134"/>
    </justification>
  </clause>

  <clause id="8472">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8446(a,2),8099(a,1))].">
      <j1 rule="para" parents="8446 8099"/>
    </justification>
  </clause>

  <clause id="8473">
    <literal><![CDATA[
      K(x,K(y,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8447(a,2),8099(a,1))].">
      <j1 rule="para" parents="8447 8099"/>
    </justification>
  </clause>

  <clause id="8474">
    <literal><![CDATA[
      T(x,K(y,y / z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),8452(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 8452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8475">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,(T(u,x) / z) / (u / z))
    ]]></literal>
    <justification jstring="[para(5994(a,1),8453(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5994 8453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8476">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = T(x,T(y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(7969,a,8455,a),flip(a)].">
      <j1 rule="hyper" parents="7969 8455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8477">
    <literal><![CDATA[
      K(x,y \ 1) * T(z,K(x,y)) = z * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,8455,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 8455 17"/>
    </justification>
  </clause>

  <clause id="8478">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6423(a,1),8455(a,1,2))].">
      <j1 rule="para" parents="6423 8455"/>
    </justification>
  </clause>

  <clause id="8479">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(8455(a,1),7969(a,1))].">
      <j1 rule="para" parents="8455 7969"/>
    </justification>
  </clause>

  <clause id="8480">
    <literal><![CDATA[
      (T(x * y,K(z,u)) / y) / x = K(z,K(u,(1 / y) / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5823,a(flip),b,8468,a)].">
      <j1 rule="hyper" parents="58 5823 8468"/>
    </justification>
  </clause>

  <clause id="8481">
    <literal><![CDATA[
      K(1 / x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8468(a,2),8099(a,1))].">
      <j1 rule="para" parents="8468 8099"/>
    </justification>
  </clause>

  <clause id="8482">
    <literal><![CDATA[
      K(x,y \ T(z,z \ y)) = K(x,T(y \ z,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8164,a,b,8412,a),flip(a)].">
      <j1 rule="hyper" parents="334 8164 8412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8483">
    <literal><![CDATA[
      K(x,(y / z) / y) = K(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[para(661(a,1),8412(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="661 8412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8484">
    <literal><![CDATA[
      T(x,y / (y * z)) = T(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(118,a,8413,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 8413 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8485">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(8448(a,2),8099(a,1))].">
      <j1 rule="para" parents="8448 8099"/>
    </justification>
  </clause>

  <clause id="8486">
    <literal><![CDATA[
      K(x,K(y \ (z * u),u \ (z \ 1))) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(6992(a,1),8449(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6992 8449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8487">
    <literal><![CDATA[
      K(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(8449(a,1),8099(a,1))].">
      <j1 rule="para" parents="8449 8099"/>
    </justification>
  </clause>

  <clause id="8488">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(8457(a,2),8099(a,1))].">
      <j1 rule="para" parents="8457 8099"/>
    </justification>
  </clause>

  <clause id="8489">
    <literal><![CDATA[
      1 / T(x,K(y,z)) = T(1 / x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8087,a(flip),b,8466,a)].">
      <j1 rule="hyper" parents="334 8087 8466"/>
    </justification>
  </clause>

  <clause id="8490">
    <literal><![CDATA[
      T(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(8470(a,1),8134(a,1))].">
      <j1 rule="para" parents="8470 8134"/>
    </justification>
  </clause>

  <clause id="8491">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7969,a,8476,a),flip(a)].">
      <j1 rule="hyper" parents="7969 8476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8492">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8476(a,1),7969(a,1))].">
      <j1 rule="para" parents="8476 7969"/>
    </justification>
  </clause>

  <clause id="8493">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,5020,a(flip),b,8491,a),flip(a)].">
      <j1 rule="hyper" parents="334 5020 8491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8494">
    <literal><![CDATA[
      T(x * y,T(z,y)) = T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7635,a(flip),b,8491,a),flip(a)].">
      <j1 rule="hyper" parents="58 7635 8491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8495">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8491(a,2),5109(a,1))].">
      <j1 rule="para" parents="8491 5109"/>
    </justification>
  </clause>

  <clause id="8496">
    <literal><![CDATA[
      K(x,(y / z) / y) = K(x,y / (y * z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8413,a,b,8483,a),flip(a)].">
      <j1 rule="hyper" parents="334 8413 8483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8497">
    <literal><![CDATA[
      T(1 / (x * K(y,z)),K(z,y)) = 1 / (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(6522(a,1),8489(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6522 8489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8498">
    <literal><![CDATA[
      T(K(x,y),z \ 1) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7560,a,8493,a)].">
      <j1 rule="hyper" parents="7560 8493"/>
    </justification>
  </clause>

  <clause id="8499">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(5109,a,8493,a)].">
      <j1 rule="hyper" parents="5109 8493"/>
    </justification>
  </clause>

  <clause id="8500">
    <literal><![CDATA[
      T(K(x,y),z \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,7401,a(flip),b,8498,a),flip(a)].">
      <j1 rule="hyper" parents="334 7401 8498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8501">
    <literal><![CDATA[
      (x \ 1) * K(y,T(z,x)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,8498,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 8498 17"/>
    </justification>
  </clause>

  <clause id="8502">
    <literal><![CDATA[
      (x \ 1) * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(8498(a,1),294(a,1,2))].">
      <j1 rule="para" parents="8498 294"/>
    </justification>
  </clause>

  <clause id="8503">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ 1) = (z \ 1) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8498(a,1),8131(a,1,1))].">
      <j1 rule="para" parents="8498 8131"/>
    </justification>
  </clause>

  <clause id="8504">
    <literal><![CDATA[
      K(x,T(y,z \ x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7958,a(flip),b,8499,a)].">
      <j1 rule="hyper" parents="58 7958 8499"/>
    </justification>
  </clause>

  <clause id="8505">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7621,a(flip),b,8499,a),flip(a)].">
      <j1 rule="hyper" parents="58 7621 8499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8506">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,T(y * z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7402,a(flip),b,8499,a)].">
      <j1 rule="hyper" parents="58 7402 8499"/>
    </justification>
  </clause>

  <clause id="8507">
    <literal><![CDATA[
      K(x,T(y,z \ y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7399,a(flip),b,8499,a)].">
      <j1 rule="hyper" parents="58 7399 8499"/>
    </justification>
  </clause>

  <clause id="8508">
    <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),8499(a,1,2))].">
      <j1 rule="para" parents="20 8499"/>
    </justification>
  </clause>

  <clause id="8509">
    <literal><![CDATA[
      K(x,T(y,1 / z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(75(a,1),8499(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 8499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8510">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),z)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),8499(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 8499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8511">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u / z))
    ]]></literal>
    <justification jstring="[para(4716(a,1),8499(a,1,2))].">
      <j1 rule="para" parents="4716 8499"/>
    </justification>
  </clause>

  <clause id="8512">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6439(a,1),8499(a,1,2))].">
      <j1 rule="para" parents="6439 8499"/>
    </justification>
  </clause>

  <clause id="8514">
    <literal><![CDATA[
      K(T(x,y \ 1) \ 1,z) = T(K(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(5811,a,8500,a)].">
      <j1 rule="hyper" parents="5811 8500"/>
    </justification>
  </clause>

  <clause id="8515">
    <literal><![CDATA[
      T(K(x,y),z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(8500(a,1),3119(a,1))].">
      <j1 rule="para" parents="8500 3119"/>
    </justification>
  </clause>

  <clause id="8516">
    <literal><![CDATA[
      (x \ y) * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x \ y) = u
    ]]></literal>
    <justification jstring="[para(8504(a,1),7427(a,1,2))].">
      <j1 rule="para" parents="8504 7427"/>
    </justification>
  </clause>

  <clause id="8517">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ x) = (z \ x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8504(a,1),8170(a,1,1))].">
      <j1 rule="para" parents="8504 8170"/>
    </justification>
  </clause>

  <clause id="8518">
    <literal><![CDATA[
      T(x,T(y,z \ y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8507,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 8507 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8519">
    <literal><![CDATA[
      K((x \ y) \ z,T(y,x)) = K(z / (x \ y),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8180,a(flip),b,8507,a),flip(a)].">
      <j1 rule="hyper" parents="58 8180 8507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8520">
    <literal><![CDATA[
      (x \ y) * K(z,T(y,x)) = K(z,y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(8507(a,1),7423(a,1,2))].">
      <j1 rule="para" parents="8507 7423"/>
    </justification>
  </clause>

  <clause id="8521">
    <literal><![CDATA[
      K(x,T(y,z)) * (1 / z) = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8509(a,1),8170(a,1,1))].">
      <j1 rule="para" parents="8509 8170"/>
    </justification>
  </clause>

  <clause id="8522">
    <literal><![CDATA[
      K(x,y) * ((z \ y) * x) = (z \ y) * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,8518,a(flip),b,7933,a),flip(a)].">
      <j1 rule="hyper" parents="119 8518 7933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8523">
    <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(217(a,1),8494(a,1,2)),flip(a)].">
      <j1 rule="para" parents="217 8494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8525">
    <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),8505(a,1,2)),flip(a)].">
      <j1 rule="para" parents="176 8505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8526">
    <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),8505(a,2,2))].">
      <j1 rule="para" parents="177 8505"/>
    </justification>
  </clause>

  <clause id="8527">
    <literal><![CDATA[
      K(x / y,T(z,x \ y)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,5459,a(flip),b,8512,a),flip(a)].">
      <j1 rule="hyper" parents="334 5459 8512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8528">
    <literal><![CDATA[
      K(x,T(y,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8512(a,1),7507(a,1))].">
      <j1 rule="para" parents="8512 7507"/>
    </justification>
  </clause>

  <clause id="8529">
    <literal><![CDATA[
      K(x,T(y,z \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8512(a,1),7980(a,1))].">
      <j1 rule="para" parents="8512 7980"/>
    </justification>
  </clause>

  <clause id="8530">
    <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(881(a,2),8190(a,1,1))].">
      <j1 rule="para" parents="881 8190"/>
    </justification>
  </clause>

  <clause id="8531">
    <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(890(a,2),8190(a,1,1))].">
      <j1 rule="para" parents="890 8190"/>
    </justification>
  </clause>

  <clause id="8532">
    <literal><![CDATA[
      K(x,T(y,L(z,u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8205,a(flip),b,8292,a),flip(a)].">
      <j1 rule="hyper" parents="334 8205 8292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8533">
    <literal><![CDATA[
      K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ (x * u)))
    ]]></literal>
    <justification jstring="[para(502(a,1),8532(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="502 8532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8534">
    <literal><![CDATA[
      K(T(x,y \ z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(8203(a,2),8311(a,1))].">
      <j1 rule="para" parents="8203 8311"/>
    </justification>
  </clause>

  <clause id="8535">
    <literal><![CDATA[
      K(x,K(y,z / y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(5186(a,2),8316(a,1,2))].">
      <j1 rule="para" parents="5186 8316"/>
    </justification>
  </clause>

  <clause id="8536">
    <literal><![CDATA[
      K(x \ (y \ z),T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ z) / x,y) = u
    ]]></literal>
    <justification jstring="[para(7337(a,1),8323(a,1))].">
      <j1 rule="para" parents="7337 8323"/>
    </justification>
  </clause>

  <clause id="8537">
    <literal><![CDATA[
      K(((x \ y) \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7407(a,2),8323(a,1))].">
      <j1 rule="para" parents="7407 8323"/>
    </justification>
  </clause>

  <clause id="8538">
    <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(2575(a,1),8326(a,1))].">
      <j1 rule="para" parents="2575 8326"/>
    </justification>
  </clause>

  <clause id="8539">
    <literal><![CDATA[
      K(T(x \ y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7388(a,2),8326(a,1))].">
      <j1 rule="para" parents="7388 8326"/>
    </justification>
  </clause>

  <clause id="8540">
    <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(1509(a,1),8328(a,1,2,1))].">
      <j1 rule="para" parents="1509 8328"/>
    </justification>
  </clause>

  <clause id="8541">
    <literal><![CDATA[
      K((x / y) \ z,y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z / (x / y),y \ x) = u
    ]]></literal>
    <justification jstring="[para(284(a,1),8329(a,1,2))].">
      <j1 rule="para" parents="284 8329"/>
    </justification>
  </clause>

  <clause id="8542">
    <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(216(a,1),8337(a,1,1))].">
      <j1 rule="para" parents="216 8337"/>
    </justification>
  </clause>

  <clause id="8543">
    <literal><![CDATA[
      K(x,T(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(7403(a,1),8337(a,1))].">
      <j1 rule="para" parents="7403 8337"/>
    </justification>
  </clause>

  <clause id="8544">
    <literal><![CDATA[
      T(x,K(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8100(a,1),8386(a,1))].">
      <j1 rule="para" parents="8100 8386"/>
    </justification>
  </clause>

  <clause id="8545">
    <literal><![CDATA[
      K(x,K(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(5614(a,1),8450(a,1,2))].">
      <j1 rule="para" parents="5614 8450"/>
    </justification>
  </clause>

  <clause id="8546">
    <literal><![CDATA[
      T(x,K(y,z / (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(5613(a,2),8471(a,1,2))].">
      <j1 rule="para" parents="5613 8471"/>
    </justification>
  </clause>

  <clause id="8547">
    <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(6545(a,1),8473(a,1,2))].">
      <j1 rule="para" parents="6545 8473"/>
    </justification>
  </clause>

  <clause id="8548">
    <literal><![CDATA[
      T(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(6439(a,1),8492(a,1,2))].">
      <j1 rule="para" parents="6439 8492"/>
    </justification>
  </clause>

  <clause id="8549">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(8498(a,1),8515(a,1))].">
      <j1 rule="para" parents="8498 8515"/>
    </justification>
  </clause>

  <clause id="8550">
    <literal><![CDATA[
      K((x \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(7407(a,2),8549(a,1))].">
      <j1 rule="para" parents="7407 8549"/>
    </justification>
  </clause>

  <clause id="8551">
    <literal><![CDATA[
      K(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,z \ y),z) = u
    ]]></literal>
    <justification jstring="[para(8186(a,1),8549(a,1))].">
      <j1 rule="para" parents="8186 8549"/>
    </justification>
  </clause>

  <clause id="8552">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7399(a,2),8528(a,1))].">
      <j1 rule="para" parents="7399 8528"/>
    </justification>
  </clause>

  <clause id="8553">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(7795(a,1),8528(a,1))].">
      <j1 rule="para" parents="7795 8528"/>
    </justification>
  </clause>

  <clause id="8554">
    <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(8506(a,1),8529(a,1))].">
      <j1 rule="para" parents="8506 8529"/>
    </justification>
  </clause>

  <clause id="8555">
    <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(188(a,1),8535(a,1,2,2))].">
      <j1 rule="para" parents="188 8535"/>
    </justification>
  </clause>

  <clause id="8556">
    <literal><![CDATA[
      K(x,T(y,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3105(a,2),8552(a,1,2))].">
      <j1 rule="para" parents="3105 8552"/>
    </justification>
  </clause>

  <clause id="8557">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(4716(a,1),8552(a,1,2))].">
      <j1 rule="para" parents="4716 8552"/>
    </justification>
  </clause>

  <clause id="8558">
    <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(7936(a,1),8552(a,1,2))].">
      <j1 rule="para" parents="7936 8552"/>
    </justification>
  </clause>

  <clause id="8559">
    <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(4141(a,2),7817(a,1,2,1))].">
      <j1 rule="para" parents="4141 7817"/>
    </justification>
  </clause>

  <clause id="8560">
    <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),7819(a,1,2,1,1))].">
      <j1 rule="para" parents="18 7819"/>
    </justification>
  </clause>

  <clause id="8561">
    <literal><![CDATA[
      K(x / y,((x / (x / y)) / z) * u) = K(x / y,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(252(a,1),7819(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="252 7819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8562">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T(y \ x,u)) = K(z * ((x \ y) \ 1),T(y \ x,u))
    ]]></literal>
    <justification jstring="[para(6500(a,1),7833(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6500 7833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8563">
    <literal><![CDATA[
      T(T(x,y) \ T(x * z,u),x) = T(x,y) \ T(z * x,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,4820,a(flip),b,7841,a),flip(a)].">
      <j1 rule="hyper" parents="116 4820 7841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8564">
    <literal><![CDATA[
      K(x * (((y \ 1) \ z) / z),y) = K(x * (z \ ((y \ 1) \ z)),y)
    ]]></literal>
    <justification jstring="[para(4435(a,1),7845(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4435 7845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8565">
    <literal><![CDATA[
      T((1 / ((x * y) \ x)) * K(y,z),y) = ((1 / ((x * y) \ x)) / y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(700(a,1),7849(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="700 7849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8566">
    <literal><![CDATA[
      x \ T(y * (x / y),y) = K(x,y) * K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(5272(a,1),7850(a,1,2,1))].">
      <j1 rule="para" parents="5272 7850"/>
    </justification>
  </clause>

  <clause id="8567">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ x) / z)) = x * K(z,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(7859(a,1),3721(a,2,2))].">
      <j1 rule="para" parents="7859 3721"/>
    </justification>
  </clause>

  <clause id="8568">
    <literal><![CDATA[
      T(T(x,y) * (x \ z),x) = T(x,y) * (x \ T(z,x))
    ]]></literal>
    <justification jstring="[hyper(246,a,7870,a,b,1158,a)].">
      <j1 rule="hyper" parents="246 7870 1158"/>
    </justification>
  </clause>

  <clause id="8570">
    <literal><![CDATA[
      K(x,y) * K(z \ 1,x) = z * T(z \ K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(1040,a,7916,a),flip(a)].">
      <j1 rule="hyper" parents="1040 7916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8571">
    <literal><![CDATA[
      (x * (y * K(z,y))) / (x * K(z,y * K(z,y))) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(334,a,5149,a(flip),b,7926,a),flip(a)].">
      <j1 rule="hyper" parents="334 5149 7926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8572">
    <literal><![CDATA[
      T(x,T(y,z)) * K(z,x) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8182,a(flip),b,7932,a),flip(a)].">
      <j1 rule="hyper" parents="58 8182 7932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8573">
    <literal><![CDATA[
      T(x,T(T(y,z),y * u)) = T(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(4(a,1),7965(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 7965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8574">
    <literal><![CDATA[
      K(x,T(y \ x,z / y)) = K(x,T(y \ x,y \ z))
    ]]></literal>
    <justification jstring="[para(107(a,1),7966(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 7966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8575">
    <literal><![CDATA[
      K(R(K(x,y) * z,u,w),y) = K(R(z * K(x,y),u,w),y)
    ]]></literal>
    <justification jstring="[para(6535(a,1),7999(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6535 7999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8576">
    <literal><![CDATA[
      K((x \ 1) \ (y \ z),y) = K((x \ y) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4303,a(flip),b,8011,a),flip(a)].">
      <j1 rule="hyper" parents="58 4303 8011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8577">
    <literal><![CDATA[
      K(x,T(y \ z,u \ z)) = K(x,T(y \ z,u \ y))
    ]]></literal>
    <justification jstring="[para(5(a,1),8014(a,1,2,2,2))].">
      <j1 rule="para" parents="5 8014"/>
    </justification>
  </clause>

  <clause id="8578">
    <literal><![CDATA[
      K(x,T(y,(y \ z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(7125(a,2),8014(a,1,2))].">
      <j1 rule="para" parents="7125 8014"/>
    </justification>
  </clause>

  <clause id="8579">
    <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(8352(a,1),8040(a,1,1))].">
      <j1 rule="para" parents="8352 8040"/>
    </justification>
  </clause>

  <clause id="8580">
    <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,5090,a(flip),b,8056,a)].">
      <j1 rule="hyper" parents="116 5090 8056"/>
    </justification>
  </clause>

  <clause id="8581">
    <literal><![CDATA[
      K(x,K(y,z)) * (z / K(x,y)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(6520(a,2),8068(a,1,2))].">
      <j1 rule="para" parents="6520 8068"/>
    </justification>
  </clause>

  <clause id="8582">
    <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,5443,a(flip),b,8088,a)].">
      <j1 rule="hyper" parents="116 5443 8088"/>
    </justification>
  </clause>

  <clause id="8583">
    <literal><![CDATA[
      K(1 / x,y) \ K(K(1 / x,y),z) = K(1 / T(x,z),y) \ 1
    ]]></literal>
    <justification jstring="[para(5814(a,2),8090(a,2,1))].">
      <j1 rule="para" parents="5814 8090"/>
    </justification>
  </clause>

  <clause id="8584">
    <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(8156(a,1),8090(a,2,1))].">
      <j1 rule="para" parents="8156 8090"/>
    </justification>
  </clause>

  <clause id="8585">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(8130(a,1),8120(a,1,1))].">
      <j1 rule="para" parents="8130 8120"/>
    </justification>
  </clause>

  <clause id="8586">
    <literal><![CDATA[
      K(R(x / (x / y),z,u),w) = K(R(y,z,u),T(w,y \ x))
    ]]></literal>
    <justification jstring="[para(4544(a,1),8183(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4544 8183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8587">
    <literal><![CDATA[
      K(K(R(x,y,z),u) * w,T(x,v5)) = K(w,T(x,v5))
    ]]></literal>
    <justification jstring="[para(8183(a,1),7672(a,1,1,1))].">
      <j1 rule="para" parents="8183 7672"/>
    </justification>
  </clause>

  <clause id="8588">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(L(x,T(x,y) \ 1,u),z)
    ]]></literal>
    <justification jstring="[hyper(7032,a,8184,a)].">
      <j1 rule="hyper" parents="7032 8184"/>
    </justification>
  </clause>

  <clause id="8589">
    <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(1691(a,1),8184(a,1,1))].">
      <j1 rule="para" parents="1691 8184"/>
    </justification>
  </clause>

  <clause id="8590">
    <literal><![CDATA[
      K(x * K(y,z),(x / u) \ 1) = K(K(y,z) * x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7904,a(flip),b,8194,a),flip(a)].">
      <j1 rule="hyper" parents="58 7904 8194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8591">
    <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(6881,a,8197,a)].">
      <j1 rule="hyper" parents="6881 8197"/>
    </justification>
  </clause>

  <clause id="8592">
    <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(1691(a,1),8197(a,1,2))].">
      <j1 rule="para" parents="1691 8197"/>
    </justification>
  </clause>

  <clause id="8593">
    <literal><![CDATA[
      K(T(x * y,y) / x,z) = K(y,T(T(z,x),x * y))
    ]]></literal>
    <justification jstring="[hyper(8329,a,8202,a)].">
      <j1 rule="hyper" parents="8329 8202"/>
    </justification>
  </clause>

  <clause id="8594">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ x = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(8217(a,1),8208(a,1,1))].">
      <j1 rule="para" parents="8217 8208"/>
    </justification>
  </clause>

  <clause id="8595">
    <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(7823(a,1),8220(a,1,2,1,1))].">
      <j1 rule="para" parents="7823 8220"/>
    </justification>
  </clause>

  <clause id="8596">
    <literal><![CDATA[
      T(T(x,y / z),K(z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8474,a(flip),b,8223,a)].">
      <j1 rule="hyper" parents="58 8474 8223"/>
    </justification>
  </clause>

  <clause id="8597">
    <literal><![CDATA[
      T(T(x,y \ z),K(y,z)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(8121,a,8596,a)].">
      <j1 rule="hyper" parents="8121 8596"/>
    </justification>
  </clause>

  <clause id="8598">
    <literal><![CDATA[
      T(T(x,K(y,z)),z / y) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(447,a,8596,a)].">
      <j1 rule="hyper" parents="447 8596"/>
    </justification>
  </clause>

  <clause id="8599">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8114,a,b,8596,a)].">
      <j1 rule="hyper" parents="58 8114 8596"/>
    </justification>
  </clause>

  <clause id="8600">
    <literal><![CDATA[
      T(T(x,y \ z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(8596(a,1),8120(a,1,1))].">
      <j1 rule="para" parents="8596 8120"/>
    </justification>
  </clause>

  <clause id="8601">
    <literal><![CDATA[
      T(T(x,K(y,z)),z \ y) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8114,a,b,8597,a)].">
      <j1 rule="hyper" parents="58 8114 8597"/>
    </justification>
  </clause>

  <clause id="8603">
    <literal><![CDATA[
      T(x * K(y / z,x),z \ y) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5469,a,8599,a)].">
      <j1 rule="hyper" parents="5469 8599"/>
    </justification>
  </clause>

  <clause id="8604">
    <literal><![CDATA[
      T(x / (y / z),z \ y) = T((y / z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(696,a,8599,a),flip(a)].">
      <j1 rule="hyper" parents="696 8599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8605">
    <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(5582(a,1),8601(a,1,1,2))].">
      <j1 rule="para" parents="5582 8601"/>
    </justification>
  </clause>

  <clause id="8606">
    <literal><![CDATA[
      T(T(x,K(y,T(z,u))),z \ T(y,u)) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[para(7403(a,1),8601(a,1,1,2))].">
      <j1 rule="para" parents="7403 8601"/>
    </justification>
  </clause>

  <clause id="8607">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = K(z \ y,z) * T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(8218(a,1),8225(a,1,1))].">
      <j1 rule="para" parents="8218 8225"/>
    </justification>
  </clause>

  <clause id="8608">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) = K((x / z) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,7064,a(flip),b,8244,a),flip(a)].">
      <j1 rule="hyper" parents="334 7064 8244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8609">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((x / z) \ y,y) = u
    ]]></literal>
    <justification jstring="[para(8244(a,2),7065(a,1))].">
      <j1 rule="para" parents="8244 7065"/>
    </justification>
  </clause>

  <clause id="8610">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,6173,a(flip),b,8245,a),flip(a)].">
      <j1 rule="hyper" parents="334 6173 8245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8611">
    <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(4488(a,1),8249(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4488 8249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8612">
    <literal><![CDATA[
      T(K(x,y),z) * (z / y) = z / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,6368,a(flip),b,8265,a),flip(a)].">
      <j1 rule="hyper" parents="334 6368 8265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8613">
    <literal><![CDATA[
      K(x,y) * (K(z,y) / y) = K(z,y) / T(y,x)
    ]]></literal>
    <justification jstring="[para(5902(a,1),8612(a,1,1))].">
      <j1 rule="para" parents="5902 8612"/>
    </justification>
  </clause>

  <clause id="8614">
    <literal><![CDATA[
      K(x,y \ z) * (z / (z / y)) = z / T(z / y,x)
    ]]></literal>
    <justification jstring="[para(6440(a,1),8612(a,1,1))].">
      <j1 rule="para" parents="6440 8612"/>
    </justification>
  </clause>

  <clause id="8615">
    <literal><![CDATA[
      K(T(x,y),z) * (y / z) = y / T(z,x)
    ]]></literal>
    <justification jstring="[para(7388(a,2),8612(a,1,1))].">
      <j1 rule="para" parents="7388 8612"/>
    </justification>
  </clause>

  <clause id="8616">
    <literal><![CDATA[
      K(x,y) * (z / T(y,z)) = z / T(T(y,z),x)
    ]]></literal>
    <justification jstring="[para(8153(a,1),8612(a,1,1))].">
      <j1 rule="para" parents="8153 8612"/>
    </justification>
  </clause>

  <clause id="8617">
    <literal><![CDATA[
      T(x / T(y,z),y) = T(y,T(z,x)) \ x
    ]]></literal>
    <justification jstring="[para(8615(a,1),7882(a,1,1))].">
      <j1 rule="para" parents="8615 7882"/>
    </justification>
  </clause>

  <clause id="8618">
    <literal><![CDATA[
      T(x \ y,T(z,x)) != (x \ y) * u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(8272(a,1),38(a,1))].">
      <j1 rule="para" parents="8272 38"/>
    </justification>
  </clause>

  <clause id="8619">
    <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(6539,a,8278,a)].">
      <j1 rule="hyper" parents="6539 8278"/>
    </justification>
  </clause>

  <clause id="8620">
    <literal><![CDATA[
      T(x,K(y,z / y) / (z \ y)) = T(x,T(1 / (z \ y),y))
    ]]></literal>
    <justification jstring="[para(5485(a,1),8302(a,1,2,1))].">
      <j1 rule="para" parents="5485 8302"/>
    </justification>
  </clause>

  <clause id="8621">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * x) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(4650,a,8312,a)].">
      <j1 rule="hyper" parents="4650 8312"/>
    </justification>
  </clause>

  <clause id="8622">
    <literal><![CDATA[
      T(x * T(y,z),K(y,z)) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5351,a(flip),b,8362,a),flip(a)].">
      <j1 rule="hyper" parents="334 5351 8362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8623">
    <literal><![CDATA[
      K(x * T(y,z),T(u,K(y,z))) = K(K(y,z) * (x * y),u)
    ]]></literal>
    <justification jstring="[para(8362(a,1),7403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8362 7403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8624">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / (z * y)) = u
    ]]></literal>
    <justification jstring="[para(8389(a,1),5703(a,1))].">
      <j1 rule="para" parents="8389 5703"/>
    </justification>
  </clause>

  <clause id="8625">
    <literal><![CDATA[
      K((x / (x / y)) \ 1,z) = K(y \ 1,T(z,x))
    ]]></literal>
    <justification jstring="[para(75(a,1),8395(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 8395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8626">
    <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(8400(a,2),5419(a,1,1))].">
      <j1 rule="para" parents="8400 5419"/>
    </justification>
  </clause>

  <clause id="8627">
    <literal><![CDATA[
      T(x,y) * T(x \ K(x,z),x) = (x \ K(x,z)) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8405,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 8405 17"/>
    </justification>
  </clause>

  <clause id="8628">
    <literal><![CDATA[
      T(x,1 / T(T(y,z),z)) = T(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5074,a,b,8411,a),flip(a)].">
      <j1 rule="hyper" parents="334 5074 8411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8629">
    <literal><![CDATA[
      T(x,1 / T(y \ z,y)) = T(x,1 / (z / y))
    ]]></literal>
    <justification jstring="[para(107(a,1),8628(a,1,2,2,1))].">
      <j1 rule="para" parents="107 8628"/>
    </justification>
  </clause>

  <clause id="8630">
    <literal><![CDATA[
      K(L(x / (y \ 1),y \ 1,y) \ 1,z) = K(T(y * x,y \ 1) \ 1,z)
    ]]></literal>
    <justification jstring="[para(892(a,1),8414(a,1,1,1))].">
      <j1 rule="para" parents="892 8414"/>
    </justification>
  </clause>

  <clause id="8631">
    <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(8415(a,2),38(a,1))].">
      <j1 rule="para" parents="8415 38"/>
    </justification>
  </clause>

  <clause id="8632">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8415(a,1),5204(a,1,1))].">
      <j1 rule="para" parents="8415 5204"/>
    </justification>
  </clause>

  <clause id="8633">
    <literal><![CDATA[
      x / T(y,K(x,z)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8037,a(flip),b,8427,a)].">
      <j1 rule="hyper" parents="58 8037 8427"/>
    </justification>
  </clause>

  <clause id="8634">
    <literal><![CDATA[
      x / T(y,K(z,x)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(8100(a,1),8633(a,1,2))].">
      <j1 rule="para" parents="8100 8633"/>
    </justification>
  </clause>

  <clause id="8635">
    <literal><![CDATA[
      x / T(y,K(z,x)) = T(x / y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,8100,a,b,8634,a),flip(a)].">
      <j1 rule="hyper" parents="334 8100 8634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8636">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[para(8017(a,1),8430(a,1,1))].">
      <j1 rule="para" parents="8017 8430"/>
    </justification>
  </clause>

  <clause id="8637">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y / x,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(8053(a,1),8430(a,1,1))].">
      <j1 rule="para" parents="8053 8430"/>
    </justification>
  </clause>

  <clause id="8638">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(334,a,8449,a(flip),b,8435,a),flip(a)].">
      <j1 rule="hyper" parents="334 8449 8435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8639">
    <literal><![CDATA[
      K(x,y \ z) * K(z,K(y,x)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(5426,a,8439,a)].">
      <j1 rule="hyper" parents="5426 8439"/>
    </justification>
  </clause>

  <clause id="8640">
    <literal><![CDATA[
      T(x \ y,K(y,z)) = T(x,K(y,z)) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,8094,a(flip),b,8451,a),flip(a)].">
      <j1 rule="hyper" parents="58 8094 8451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8641">
    <literal><![CDATA[
      K(x,y \ T(z,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(8482(a,2),8543(a,1))].">
      <j1 rule="para" parents="8482 8543"/>
    </justification>
  </clause>

  <clause id="8642">
    <literal><![CDATA[
      K(T(x,y \ 1) \ 1,z) = K(T(x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,5809,a,b,8514,a),flip(a)].">
      <j1 rule="hyper" parents="334 5809 8514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8644">
    <literal><![CDATA[
      K(x,y) * T(y,T(z,x)) = T(y * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(2557,a,8572,a)].">
      <j1 rule="hyper" parents="2557 8572"/>
    </justification>
  </clause>

  <clause id="8645">
    <literal><![CDATA[
      K((x \ y) \ (z * y),y) = K((x \ 1) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7626,a(flip),b,8576,a),flip(a)].">
      <j1 rule="hyper" parents="58 7626 8576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8646">
    <literal><![CDATA[
      K(x \ y,T(x,y \ z)) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(7980,a,8578,a),flip(a)].">
      <j1 rule="hyper" parents="7980 8578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8647">
    <literal><![CDATA[
      K(x,T(y,(y * z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(4(a,1),8578(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 8578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8648">
    <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(6196(a,1),8581(a,1,1,2))].">
      <j1 rule="para" parents="6196 8581"/>
    </justification>
  </clause>

  <clause id="8649">
    <literal><![CDATA[
      (K(x,y) * T(x,K(z,u))) \ x = K(z,K(u,x)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(8019(a,1),8594(a,2,1))].">
      <j1 rule="para" parents="8019 8594"/>
    </justification>
  </clause>

  <clause id="8650">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(8603(a,1),5204(a,1,1))].">
      <j1 rule="para" parents="8603 5204"/>
    </justification>
  </clause>

  <clause id="8651">
    <literal><![CDATA[
      x * (T(x,y) \ (K(z,x) / x)) = K(z,x) / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(5092,a,8613,a)].">
      <j1 rule="hyper" parents="5092 8613"/>
    </justification>
  </clause>

  <clause id="8652">
    <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(8616(a,2),2944(a,2,1,2))].">
      <j1 rule="para" parents="8616 2944"/>
    </justification>
  </clause>

  <clause id="8653">
    <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(8616(a,2),6675(a,1,2,1,2))].">
      <j1 rule="para" parents="8616 6675"/>
    </justification>
  </clause>

  <clause id="8654">
    <literal><![CDATA[
      K(x,y) * T(z,T(z * x,y)) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8621,a(flip),b,108,a)].">
      <j1 rule="hyper" parents="119 8621 108"/>
    </justification>
  </clause>

  <clause id="8655">
    <literal><![CDATA[
      T(x * T(y,z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x * y) = u
    ]]></literal>
    <justification jstring="[para(8622(a,2),5744(a,1))].">
      <j1 rule="para" parents="8622 5744"/>
    </justification>
  </clause>

  <clause id="8656">
    <literal><![CDATA[
      T(x,1 / (((y \ z) \ z) \ z)) = T(x,1 / (z / y))
    ]]></literal>
    <justification jstring="[para(4480(a,1),8629(a,1,2,2))].">
      <j1 rule="para" parents="4480 8629"/>
    </justification>
  </clause>

  <clause id="8657">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ z,y) = K(z / x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,8091,a,b,8636,a)].">
      <j1 rule="hyper" parents="29 8091 8636"/>
    </justification>
  </clause>

  <clause id="8658">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ y,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,8091,a,b,8637,a)].">
      <j1 rule="hyper" parents="29 8091 8637"/>
    </justification>
  </clause>

  <clause id="8659">
    <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(5186(a,1),8637(a,1,2))].">
      <j1 rule="para" parents="5186 8637"/>
    </justification>
  </clause>

  <clause id="8660">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[hyper(334,a,8048,a,b,8638,a),flip(a)].">
      <j1 rule="hyper" parents="334 8048 8638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8661">
    <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(1366(a,1),8638(a,1,2,2))].">
      <j1 rule="para" parents="1366 8638"/>
    </justification>
  </clause>

  <clause id="8662">
    <literal><![CDATA[
      K(x,K(y,z \ (y * u))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(7686(a,1),8638(a,1,2))].">
      <j1 rule="para" parents="7686 8638"/>
    </justification>
  </clause>

  <clause id="8663">
    <literal><![CDATA[
      K(x,K(y,z \ (y \ u))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(7847(a,1),8638(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7847 8638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8664">
    <literal><![CDATA[
      K(x,y \ z) * K(x,K(z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(8053(a,1),8639(a,1,2))].">
      <j1 rule="para" parents="8053 8639"/>
    </justification>
  </clause>

  <clause id="8665">
    <literal><![CDATA[
      K(x,y) \ T(x,T(z,y)) = T(x * K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(5431,a,8644,a)].">
      <j1 rule="hyper" parents="5431 8644"/>
    </justification>
  </clause>

  <clause id="8666">
    <literal><![CDATA[
      K(x,y) * T(x * K(y,x),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(5409,a,8644,a)].">
      <j1 rule="hyper" parents="5409 8644"/>
    </justification>
  </clause>

  <clause id="8667">
    <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(8644(a,1),5410(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8644 5410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8668">
    <literal><![CDATA[
      T(x,(y \ x) \ (z * x)) = 1 / (x \ K((y \ 1) \ z,x))
    ]]></literal>
    <justification jstring="[para(8645(a,1),5131(a,2,2,2))].">
      <j1 rule="para" parents="8645 5131"/>
    </justification>
  </clause>

  <clause id="8669">
    <literal><![CDATA[
      K(x \ y,T(x,y * z)) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),8646(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8670">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(x \ (y / z),T(x,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),8646(a,1,2,2))].">
      <j1 rule="para" parents="75 8646"/>
    </justification>
  </clause>

  <clause id="8671">
    <literal><![CDATA[
      K(x * y,T(x,y \ z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(7980,a,8647,a),flip(a)].">
      <j1 rule="hyper" parents="7980 8647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8672">
    <literal><![CDATA[
      K(x,K(y,z \ (u * x))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(8050,a,8660,a)].">
      <j1 rule="hyper" parents="8050 8660"/>
    </justification>
  </clause>

  <clause id="8673">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z \ u)) = w
    ]]></literal>
    <justification jstring="[para(8660(a,2),8050(a,1))].">
      <j1 rule="para" parents="8660 8050"/>
    </justification>
  </clause>

  <clause id="8674">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z \ y) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(5906,a,8664,a)].">
      <j1 rule="hyper" parents="5906 8664"/>
    </justification>
  </clause>

  <clause id="8675">
    <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(7271(a,1),8664(a,1,2,2))].">
      <j1 rule="para" parents="7271 8664"/>
    </justification>
  </clause>

  <clause id="8676">
    <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,6867,a,b,8665,a),flip(a)].">
      <j1 rule="hyper" parents="119 6867 8665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8677">
    <literal><![CDATA[
      K(x * y,T(x,y \ z)) = K(y * x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,6194,a,b,8671,a),flip(a)].">
      <j1 rule="hyper" parents="334 6194 8671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8678">
    <literal><![CDATA[
      K(x,K(y,z \ (u * x))) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8459,a,b,8672,a),flip(a)].">
      <j1 rule="hyper" parents="334 8459 8672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8679">
    <literal><![CDATA[
      T(K(x,y),(z \ (u * x)) \ 1) = K(x,y) * K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(8672(a,1),8460(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8672 8460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8680">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z \ x) = K(y,x / z)
    ]]></literal>
    <justification jstring="[para(8048(a,1),8674(a,1,1))].">
      <j1 rule="para" parents="8048 8674"/>
    </justification>
  </clause>

  <clause id="8681">
    <literal><![CDATA[
      K(K(x,y),z) * K(y,z \ x) = K(y,x / z)
    ]]></literal>
    <justification jstring="[para(8052(a,2),8674(a,1,1))].">
      <j1 rule="para" parents="8052 8674"/>
    </justification>
  </clause>

  <clause id="8682">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(8067(a,1),8674(a,1,1))].">
      <j1 rule="para" parents="8067 8674"/>
    </justification>
  </clause>

  <clause id="8683">
    <literal><![CDATA[
      K(x * y,T(y,x \ z)) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6194,a,b,8677,a)].">
      <j1 rule="hyper" parents="58 6194 8677"/>
    </justification>
  </clause>

  <clause id="8684">
    <literal><![CDATA[
      K(x,K(y,(z * x) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8459,a,b,8678,a)].">
      <j1 rule="hyper" parents="58 8459 8678"/>
    </justification>
  </clause>

  <clause id="8685">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y / x) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(5409,a,8681,a)].">
      <j1 rule="hyper" parents="5409 8681"/>
    </justification>
  </clause>

  <clause id="8686">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(29,a,8091,a,b,8682,a)].">
      <j1 rule="hyper" parents="29 8091 8682"/>
    </justification>
  </clause>

  <clause id="8687">
    <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(7271(a,1),8682(a,1,1,2))].">
      <j1 rule="para" parents="7271 8682"/>
    </justification>
  </clause>

  <clause id="8688">
    <literal><![CDATA[
      K(x * y,T(y,x * z)) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),8683(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8689">
    <literal><![CDATA[
      K(x,K(y,(z / x) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(7(a,1),8684(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 8684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8690">
    <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(1506(a,1),8686(a,1,2,2))].">
      <j1 rule="para" parents="1506 8686"/>
    </justification>
  </clause>

  <clause id="8691">
    <literal><![CDATA[
      L(K(x,y),z * x,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(7305(a,1),6670(a,1))].">
      <j1 rule="para" parents="7305 6670"/>
    </justification>
  </clause>

  <clause id="8692">
    <literal><![CDATA[
      K(T(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) * u = w
    ]]></literal>
    <justification jstring="[para(5391(a,1),7471(a,1))].">
      <j1 rule="para" parents="5391 7471"/>
    </justification>
  </clause>

  <clause id="8693">
    <literal><![CDATA[
      K(x,R(y,K(z,x),u)) = K(x,y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6167,a(flip),b,7503,a)].">
      <j1 rule="hyper" parents="58 6167 7503"/>
    </justification>
  </clause>

  <clause id="8694">
    <literal><![CDATA[
      K(x,y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7503(a,1),396(a,1)),flip(b)].">
      <j1 rule="para" parents="7503 396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8695">
    <literal><![CDATA[
      K(x,y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(84(a,1),8694(a,1,2))].">
      <j1 rule="para" parents="84 8694"/>
    </justification>
  </clause>

  <clause id="8696">
    <literal><![CDATA[
      K(x,y * T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(1532(a,1),8694(a,1,2))].">
      <j1 rule="para" parents="1532 8694"/>
    </justification>
  </clause>

  <clause id="8697">
    <literal><![CDATA[
      K(x,T(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(5803(a,1),8694(a,1,2))].">
      <j1 rule="para" parents="5803 8694"/>
    </justification>
  </clause>

  <clause id="8698">
    <literal><![CDATA[
      K(x,y / (z / x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(6579(a,1),8694(a,1,2))].">
      <j1 rule="para" parents="6579 8694"/>
    </justification>
  </clause>

  <clause id="8699">
    <literal><![CDATA[
      K(x,K(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7392(a,1),8694(a,1,2))].">
      <j1 rule="para" parents="7392 8694"/>
    </justification>
  </clause>

  <clause id="8700">
    <literal><![CDATA[
      K(L(x,y,z),y * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = u
    ]]></literal>
    <justification jstring="[para(6885(a,2),8695(a,1))].">
      <j1 rule="para" parents="6885 8695"/>
    </justification>
  </clause>

  <clause id="8701">
    <literal><![CDATA[
      K(x,K(x,y) / z) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(8699,a,6445,a)].">
      <j1 rule="hyper" parents="8699 6445"/>
    </justification>
  </clause>

  <clause id="8702">
    <literal><![CDATA[
      K(x,y \ K(x,z)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(6774,a,8701,a)].">
      <j1 rule="hyper" parents="6774 8701"/>
    </justification>
  </clause>

  <clause id="8703">
    <literal><![CDATA[
      T(x,y \ K(x,z)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(118,a,8702,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 8702 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8704">
    <literal><![CDATA[
      (x \ K(x,y)) * (T(x,x \ 1) * z) = (K(x,y) / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(8703(a,1),4919(a,1,2,1))].">
      <j1 rule="para" parents="8703 4919"/>
    </justification>
  </clause>

  <clause id="8705">
    <literal><![CDATA[
      K(x,R(y,K(z,x),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,7493,a(flip),b,8693,a),flip(a)].">
      <j1 rule="hyper" parents="334 7493 8693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8707">
    <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),8705(a,1,2))].">
      <j1 rule="para" parents="26 8705"/>
    </justification>
  </clause>

  <clause id="8709">
    <literal><![CDATA[
      T(x,K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(7531(a,2),385(a,1)),flip(b)].">
      <j1 rule="para" parents="7531 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8710">
    <literal><![CDATA[
      T(x,(x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(y / x) * z) = u
    ]]></literal>
    <justification jstring="[para(5680(a,1),8709(a,1,2))].">
      <j1 rule="para" parents="5680 8709"/>
    </justification>
  </clause>

  <clause id="8712">
    <literal><![CDATA[
      K(R(x,K(y,z),u),z) = K(x * K(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7052,a(flip),b,7588,a)].">
      <j1 rule="hyper" parents="58 7052 7588"/>
    </justification>
  </clause>

  <clause id="8713">
    <literal><![CDATA[
      K(R(x,K(y,z),u),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,7584,a(flip),b,8712,a),flip(a)].">
      <j1 rule="hyper" parents="334 7584 8712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8715">
    <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),8713(a,1,1))].">
      <j1 rule="para" parents="26 8713"/>
    </justification>
  </clause>

  <clause id="8716">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6883,a(flip),b,7608,a)].">
      <j1 rule="hyper" parents="58 6883 7608"/>
    </justification>
  </clause>

  <clause id="8717">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,7595,a(flip),b,8716,a),flip(a)].">
      <j1 rule="hyper" parents="334 7595 8716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8719">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(K(y,z) \ (x \ u),y)
    ]]></literal>
    <justification jstring="[para(311(a,1),8717(a,1,1))].">
      <j1 rule="para" parents="311 8717"/>
    </justification>
  </clause>

  <clause id="8720">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(6693(a,2),7648(a,1))].">
      <j1 rule="para" parents="6693 7648"/>
    </justification>
  </clause>

  <clause id="8721">
    <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(7759(a,1),7188(a,1))].">
      <j1 rule="para" parents="7759 7188"/>
    </justification>
  </clause>

  <clause id="8722">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,x)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(6942(a,1),7842(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6942 7842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8723">
    <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(4437(a,1),7858(a,2,2,2,2))].">
      <j1 rule="para" parents="4437 7858"/>
    </justification>
  </clause>

  <clause id="8724">
    <literal><![CDATA[
      K(x,T(y,z * (u * K(w,x)))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(90(a,1),7922(a,1,2,2))].">
      <j1 rule="para" parents="90 7922"/>
    </justification>
  </clause>

  <clause id="8725">
    <literal><![CDATA[
      T(K(x,y),z * (u * K(w,x))) = T(K(x,y),z * u)
    ]]></literal>
    <justification jstring="[para(90(a,1),7968(a,1,2))].">
      <j1 rule="para" parents="90 7968"/>
    </justification>
  </clause>

  <clause id="8726">
    <literal><![CDATA[
      K((x * y) \ (z * y),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(7725(a,2),7985(a,1))].">
      <j1 rule="para" parents="7725 7985"/>
    </justification>
  </clause>

  <clause id="8727">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((z \ x) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(7727(a,1),7985(a,1))].">
      <j1 rule="para" parents="7727 7985"/>
    </justification>
  </clause>

  <clause id="8729">
    <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),8004(a,1,2,1,1))].">
      <j1 rule="para" parents="6 8004"/>
    </justification>
  </clause>

  <clause id="8730">
    <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(8082(a,2),8039(a,1,2))].">
      <j1 rule="para" parents="8082 8039"/>
    </justification>
  </clause>

  <clause id="8731">
    <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(8403(a,2),8318(a,1))].">
      <j1 rule="para" parents="8403 8318"/>
    </justification>
  </clause>

  <clause id="8732">
    <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(7800(a,1),8340(a,1,2))].">
      <j1 rule="para" parents="7800 8340"/>
    </justification>
  </clause>

  <clause id="8733">
    <literal><![CDATA[
      K(L(x,T(x,y) \ 1,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(8324,a,8588,a),flip(a)].">
      <j1 rule="hyper" parents="8324 8588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8734">
    <literal><![CDATA[
      K(L(x,T(x,y) \ 1,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(8588(a,1),8324(a,1))].">
      <j1 rule="para" parents="8588 8324"/>
    </justification>
  </clause>

  <clause id="8736">
    <literal><![CDATA[
      K(L(x,x \ K(y,x),z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(5073(a,1),8733(a,1,1,2))].">
      <j1 rule="para" parents="5073 8733"/>
    </justification>
  </clause>

  <clause id="8737">
    <literal><![CDATA[
      T(T(x,K(y,z)),z \ y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(8114(a,2),8600(a,1))].">
      <j1 rule="para" parents="8114 8600"/>
    </justification>
  </clause>

  <clause id="8738">
    <literal><![CDATA[
      K(x,T(1 / y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / (z * y)) = u
    ]]></literal>
    <justification jstring="[para(3704(a,2),8624(a,1))].">
      <j1 rule="para" parents="3704 8624"/>
    </justification>
  </clause>

  <clause id="8739">
    <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(7305(a,2),8691(a,1))].">
      <j1 rule="para" parents="7305 8691"/>
    </justification>
  </clause>

  <clause id="8740">
    <literal><![CDATA[
      T(K(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7388(a,1),8692(a,1,1))].">
      <j1 rule="para" parents="7388 8692"/>
    </justification>
  </clause>

  <clause id="8741">
    <literal><![CDATA[
      K(x,(y * x) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(7339(a,2),8698(a,1))].">
      <j1 rule="para" parents="7339 8698"/>
    </justification>
  </clause>

  <clause id="8742">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((x / z) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(7(a,1),8726(a,1,1,1))].">
      <j1 rule="para" parents="7 8726"/>
    </justification>
  </clause>

  <clause id="8743">
    <literal><![CDATA[
      K((x * y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ (y \ z),y) = u
    ]]></literal>
    <justification jstring="[para(7911(a,1),8726(a,1))].">
      <j1 rule="para" parents="7911 8726"/>
    </justification>
  </clause>

  <clause id="8744">
    <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(7403(a,1),8737(a,1,1,2))].">
      <j1 rule="para" parents="7403 8737"/>
    </justification>
  </clause>

  <clause id="8746">
    <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(5892(a,2),8740(a,1))].">
      <j1 rule="para" parents="5892 8740"/>
    </justification>
  </clause>

  <clause id="8747">
    <literal><![CDATA[
      L(K(x \ y,x),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z \ (x \ (z * y)),x) = u
    ]]></literal>
    <justification jstring="[para(6891(a,2),8743(a,1))].">
      <j1 rule="para" parents="6891 8743"/>
    </justification>
  </clause>

  <clause id="8748">
    <literal><![CDATA[
      L(K(x,y),z,T(x,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4329,a,7280,a)].">
      <j1 rule="hyper" parents="4329 7280"/>
    </justification>
  </clause>

  <clause id="8749">
    <literal><![CDATA[
      K(x,(T(x,y) * z) \ u) = K(x,z \ (T(x,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(7174,a,8748,a)].">
      <j1 rule="hyper" parents="7174 8748"/>
    </justification>
  </clause>

  <clause id="8750">
    <literal><![CDATA[
      K(x,L(y,z,T(x,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6956,a,8748,a)].">
      <j1 rule="hyper" parents="6956 8748"/>
    </justification>
  </clause>

  <clause id="8751">
    <literal><![CDATA[
      K(x,T(L(y,z,T(x,u)),w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(20(a,1),8750(a,1,2))].">
      <j1 rule="para" parents="20 8750"/>
    </justification>
  </clause>

  <clause id="8752">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,z / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(8543,a,7303,a),flip(a)].">
      <j1 rule="hyper" parents="8543 7303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8753">
    <literal><![CDATA[
      K(x,y / (x \ z)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8610,a(flip),b,8752,a),flip(a)].">
      <j1 rule="hyper" parents="58 8610 8752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8754">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8245,a(flip),b,8752,a)].">
      <j1 rule="hyper" parents="58 8245 8752"/>
    </justification>
  </clause>

  <clause id="8755">
    <literal><![CDATA[
      K(x,y / (z / x)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(7655,a,8753,a)].">
      <j1 rule="hyper" parents="7655 8753"/>
    </justification>
  </clause>

  <clause id="8756">
    <literal><![CDATA[
      T(x,y / (x \ z)) = T(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(118,a,8753,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 8753 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8757">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7811,a,b,8753,a)].">
      <j1 rule="hyper" parents="58 7811 8753"/>
    </justification>
  </clause>

  <clause id="8758">
    <literal><![CDATA[
      K(x,((x * y) / z) \ x) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(4(a,1),8753(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8759">
    <literal><![CDATA[
      R(K(x,(y / (z / u)) \ x),z / u,u) = K(x,z / ((x \ y) * u))
    ]]></literal>
    <justification jstring="[para(8753(a,1),6159(a,1,1))].">
      <j1 rule="para" parents="8753 6159"/>
    </justification>
  </clause>

  <clause id="8760">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,(x * y) / z)
    ]]></literal>
    <justification jstring="[hyper(334,a,7811,a,b,8754,a)].">
      <j1 rule="hyper" parents="334 7811 8754"/>
    </justification>
  </clause>

  <clause id="8761">
    <literal><![CDATA[
      T(x,(x * y) / z) = T(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8754,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 8754 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8762">
    <literal><![CDATA[
      K(x,(x \ y) / (x \ z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(5(a,1),8754(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 8754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8763">
    <literal><![CDATA[
      K(x,((y * x) / z) \ x) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(6(a,1),8755(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 8755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8764">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7794,a,b,8756,a)].">
      <j1 rule="hyper" parents="58 7794 8756"/>
    </justification>
  </clause>

  <clause id="8765">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),y) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(8551,a,8757,a)].">
      <j1 rule="hyper" parents="8551 8757"/>
    </justification>
  </clause>

  <clause id="8766">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8246,a,b,8757,a)].">
      <j1 rule="hyper" parents="58 8246 8757"/>
    </justification>
  </clause>

  <clause id="8767">
    <literal><![CDATA[
      K(x,(y \ (x * z)) / z) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(72(a,1),8758(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 8758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8768">
    <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(7021(a,1),8758(a,1,2,1))].">
      <j1 rule="para" parents="7021 8758"/>
    </justification>
  </clause>

  <clause id="8769">
    <literal><![CDATA[
      K(x,(y * x) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(8760(a,2),6175(a,1))].">
      <j1 rule="para" parents="8760 6175"/>
    </justification>
  </clause>

  <clause id="8770">
    <literal><![CDATA[
      K(x,(x \ y) / (z / x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(7655,a,8762,a)].">
      <j1 rule="hyper" parents="7655 8762"/>
    </justification>
  </clause>

  <clause id="8771">
    <literal><![CDATA[
      K(x,(x \ y) / z) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[para(4(a,1),8762(a,1,2,2))].">
      <j1 rule="para" parents="4 8762"/>
    </justification>
  </clause>

  <clause id="8772">
    <literal><![CDATA[
      K(x,(x * y) / (z * x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6173,a,b,8763,a)].">
      <j1 rule="hyper" parents="58 6173 8763"/>
    </justification>
  </clause>

  <clause id="8773">
    <literal><![CDATA[
      K(x,(y \ R(x,z,z \ 1)) / a(x,z,z \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(726(a,1),8767(a,1,2,1,2))].">
      <j1 rule="para" parents="726 8767"/>
    </justification>
  </clause>

  <clause id="8774">
    <literal><![CDATA[
      K(x,(x \ y) / z) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(6(a,1),8770(a,1,2,2))].">
      <j1 rule="para" parents="6 8770"/>
    </justification>
  </clause>

  <clause id="8775">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8771,a(flip),b,8774,a),flip(a)].">
      <j1 rule="hyper" parents="58 8771 8774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8776">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(334,a,7258,a(flip),b,8775,a),flip(a)].">
      <j1 rule="hyper" parents="334 7258 8775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8778">
    <literal><![CDATA[
      K(x,R(y / x,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[para(102(a,2),8775(a,2,2)),flip(a)].">
      <j1 rule="para" parents="102 8775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8779">
    <literal><![CDATA[
      K(x,T((y / z) \ x,y)) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(8171,a,8765,a)].">
      <j1 rule="hyper" parents="8171 8765"/>
    </justification>
  </clause>

  <clause id="8780">
    <literal><![CDATA[
      K(x,(y / z) \ (x \ 1)) = K(x,z / (y * x))
    ]]></literal>
    <justification jstring="[para(7(a,1),8776(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 8776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8781">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,((y \ z) / z) \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(4704(a,1),8776(a,1,2,2,1))].">
      <j1 rule="para" parents="4704 8776"/>
    </justification>
  </clause>

  <clause id="8782">
    <literal><![CDATA[
      K(x,y \ ((z \ y) * x)) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(72(a,1),8779(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="72 8779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8783">
    <literal><![CDATA[
      K(x,T(y \ x,x * z)) = K(x,z \ (y \ (x * z)))
    ]]></literal>
    <justification jstring="[hyper(7123,a,8782,a),flip(a)].">
      <j1 rule="hyper" parents="7123 8782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8784">
    <literal><![CDATA[
      K(x,(y / x) \ (z \ y)) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(7122,a,8782,a)].">
      <j1 rule="hyper" parents="7122 8782"/>
    </justification>
  </clause>

  <clause id="8785">
    <literal><![CDATA[
      K(x \ y,T(z \ (x \ y),y)) = K(x \ y,x \ (z \ y))
    ]]></literal>
    <justification jstring="[para(72(a,1),8784(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 8784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8786">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / z) \ x) = u
    ]]></literal>
    <justification jstring="[para(8246(a,2),8769(a,1))].">
      <j1 rule="para" parents="8246 8769"/>
    </justification>
  </clause>

  <clause id="8787">
    <literal><![CDATA[
      K(x,R(x \ y,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5188,a(flip),b,8778,a)].">
      <j1 rule="hyper" parents="58 5188 8778"/>
    </justification>
  </clause>

  <clause id="8788">
    <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(7379(a,1),1137(a,1,1,2))].">
      <j1 rule="para" parents="7379 1137"/>
    </justification>
  </clause>

  <clause id="8789">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,u)),K(y,u)) = K(y,u) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7379(a,1),8109(a,1,1))].">
      <j1 rule="para" parents="7379 8109"/>
    </justification>
  </clause>

  <clause id="8790">
    <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),7408(a,2,2))].">
      <j1 rule="para" parents="22 7408"/>
    </justification>
  </clause>

  <clause id="8791">
    <literal><![CDATA[
      K(x \ y,z) * K(u,y / x) = K(u,y / x) * K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2540(a,1),7433(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2540 7433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8792">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(8017(a,1),7434(a,1,1))].">
      <j1 rule="para" parents="8017 7434"/>
    </justification>
  </clause>

  <clause id="8793">
    <literal><![CDATA[
      K(1 / x,T(y,z * x)) = T(K(x \ 1,y),z)
    ]]></literal>
    <justification jstring="[hyper(8550,a,7451,a),flip(a)].">
      <j1 rule="hyper" parents="8550 7451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8794">
    <literal><![CDATA[
      K(1 / x,T(y,z * x)) = T(K(1 / x,y),z)
    ]]></literal>
    <justification jstring="[para(3442(a,2),8793(a,2,1))].">
      <j1 rule="para" parents="3442 8793"/>
    </justification>
  </clause>

  <clause id="8795">
    <literal><![CDATA[
      K(1 / x,T(y,z * x)) = K(1 / T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5814,a,b,8794,a),flip(a)].">
      <j1 rule="hyper" parents="334 5814 8794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8796">
    <literal><![CDATA[
      K(1 / x,T(y,z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8794(a,2),7974(a,1))].">
      <j1 rule="para" parents="8794 7974"/>
    </justification>
  </clause>

  <clause id="8797">
    <literal><![CDATA[
      K(1 / T(x,y / x),z) = K(1 / x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),8795(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 8795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8798">
    <literal><![CDATA[
      x * K(y \ z,x / (z / y)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7496,a,b,87,a)].">
      <j1 rule="hyper" parents="119 7496 87"/>
    </justification>
  </clause>

  <clause id="8800">
    <literal><![CDATA[
      ((x \ y) \ y) \ (z * T(x,x \ y)) = T(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(677(a,1),7540(a,1,1)),flip(a)].">
      <j1 rule="para" parents="677 7540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8801">
    <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(7554(a,2),549(a,1))].">
      <j1 rule="para" parents="7554 549"/>
    </justification>
  </clause>

  <clause id="8802">
    <literal><![CDATA[
      x * K(y,(1 / x) * (z * x)) = K(y,L(z,x,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(3154(a,1),7554(a,1,2,2))].">
      <j1 rule="para" parents="3154 7554"/>
    </justification>
  </clause>

  <clause id="8803">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K(z / (x \ y),y \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,6984,a,b,7566,a)].">
      <j1 rule="hyper" parents="334 6984 7566"/>
    </justification>
  </clause>

  <clause id="8804">
    <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(7583(a,1),5086(a,1,1,2))].">
      <j1 rule="para" parents="7583 5086"/>
    </justification>
  </clause>

  <clause id="8805">
    <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),7620(a,2,2))].">
      <j1 rule="para" parents="22 7620"/>
    </justification>
  </clause>

  <clause id="8806">
    <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(7735(a,1),7642(a,1,2,1))].">
      <j1 rule="para" parents="7735 7642"/>
    </justification>
  </clause>

  <clause id="8807">
    <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),7677(a,1,2,1))].">
      <j1 rule="para" parents="22 7677"/>
    </justification>
  </clause>

  <clause id="8808">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,7217,a(flip),b,7703,a)].">
      <j1 rule="hyper" parents="58 7217 7703"/>
    </justification>
  </clause>

  <clause id="8809">
    <literal><![CDATA[
      (x * (y * ((z \ (y \ (x \ u))) * z))) \ u = K(z,(x * y) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(3687(a,1),7703(a,1,1))].">
      <j1 rule="para" parents="3687 7703"/>
    </justification>
  </clause>

  <clause id="8810">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = y * K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(34,a,6523,a,b,7704,a),flip(a)].">
      <j1 rule="hyper" parents="34 6523 7704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8811">
    <literal><![CDATA[
      (((x \ y) * x) * z) \ (y * z) = K(x,z \ (x \ (y * z)))
    ]]></literal>
    <justification jstring="[para(6(a,1),7704(a,1,1,1,1,2))].">
      <j1 rule="para" parents="6 7704"/>
    </justification>
  </clause>

  <clause id="8812">
    <literal><![CDATA[
      (x * y) * K(z,x \ (z \ (x * y))) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,4867,a(flip),b,7705,a),flip(a)].">
      <j1 rule="hyper" parents="58 4867 7705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8813">
    <literal><![CDATA[
      x * K(y,z \ (y \ x)) = z * (y * ((z \ x) / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,4866,a(flip),b,7705,a),flip(a)].">
      <j1 rule="hyper" parents="58 4866 7705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8814">
    <literal><![CDATA[
      x \ (y * K(z,T(x,u))) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(7401(a,2),7720(a,1,2,2))].">
      <j1 rule="para" parents="7401 7720"/>
    </justification>
  </clause>

  <clause id="8815">
    <literal><![CDATA[
      (x * K(y \ (z \ x),z)) * u = (y * ((z \ (y \ x)) * z)) * u
    ]]></literal>
    <justification jstring="[hyper(52,a,7729,a)].">
      <j1 rule="hyper" parents="52 7729"/>
    </justification>
  </clause>

  <clause id="8816">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = x * (L(x,z,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(119,a,7733,a(flip),b,5441,a)].">
      <j1 rule="hyper" parents="119 7733 5441"/>
    </justification>
  </clause>

  <clause id="8817">
    <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,7785,a(flip),b,8117,a)].">
      <j1 rule="hyper" parents="119 7785 8117"/>
    </justification>
  </clause>

  <clause id="8818">
    <literal><![CDATA[
      K(x,T(y * (z * K(u,x)),w)) = K(x,T(y * z,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,7401,a,b,7844,a),flip(a)].">
      <j1 rule="hyper" parents="334 7401 7844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8819">
    <literal><![CDATA[
      K(x \ (y \ z),T(y,z)) = K(z / (y * x),y)
    ]]></literal>
    <justification jstring="[hyper(8323,a,7875,a),flip(a)].">
      <j1 rule="hyper" parents="8323 7875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8820">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) = K(z / (y \ x),y)
    ]]></literal>
    <justification jstring="[hyper(8323,a,7877,a),flip(a)].">
      <j1 rule="hyper" parents="8323 7877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8821">
    <literal><![CDATA[
      K((x * y) / z,x) = K(y / (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8244,a(flip),b,8820,a)].">
      <j1 rule="hyper" parents="58 8244 8820"/>
    </justification>
  </clause>

  <clause id="8822">
    <literal><![CDATA[
      K(x / (y \ z),y) * ((y * x) / z) = T((y * x) / z,y)
    ]]></literal>
    <justification jstring="[para(8821(a,1),5034(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8821 5034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8823">
    <literal><![CDATA[
      T(x * K(y,z / x),x \ z) = T(x \ z,y) \ z
    ]]></literal>
    <justification jstring="[para(8263(a,1),7879(a,1,1))].">
      <j1 rule="para" parents="8263 7879"/>
    </justification>
  </clause>

  <clause id="8824">
    <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(3944(a,1),7886(a,1,1))].">
      <j1 rule="para" parents="3944 7886"/>
    </justification>
  </clause>

  <clause id="8825">
    <literal><![CDATA[
      K(x,T(y,(z * x) * u)) = K(x,T(y,(x * z) * u))
    ]]></literal>
    <justification jstring="[para(84(a,1),7889(a,1,2,2,1))].">
      <j1 rule="para" parents="84 7889"/>
    </justification>
  </clause>

  <clause id="8826">
    <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(6205(a,1),7892(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6205 7892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8827">
    <literal><![CDATA[
      (x / y) * K(x,T(z,y)) = K(x,z) * (x / y)
    ]]></literal>
    <justification jstring="[para(8504(a,1),7898(a,1,2))].">
      <j1 rule="para" parents="8504 7898"/>
    </justification>
  </clause>

  <clause id="8828">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(334,a,6402,a(flip),b,7908,a),flip(a)].">
      <j1 rule="hyper" parents="334 6402 7908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8829">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ u) = w
    ]]></literal>
    <justification jstring="[para(7908(a,2),6714(a,1))].">
      <j1 rule="para" parents="7908 6714"/>
    </justification>
  </clause>

  <clause id="8830">
    <literal><![CDATA[
      T(x,(y * K(z,x)) \ u) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,8828,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 8828 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8831">
    <literal><![CDATA[
      K(x,(y \ T(z,x)) \ u) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(1529(a,1),8828(a,1,2,1))].">
      <j1 rule="para" parents="1529 8828"/>
    </justification>
  </clause>

  <clause id="8832">
    <literal><![CDATA[
      K(x,(y * K(x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(6516(a,1),8828(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6516 8828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8833">
    <literal><![CDATA[
      K(x,(K(x,y) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7391(a,1),8828(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7391 8828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8834">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7393(a,1),8828(a,1,2,1))].">
      <j1 rule="para" parents="7393 8828"/>
    </justification>
  </clause>

  <clause id="8835">
    <literal><![CDATA[
      K(T(x,y),(z * K(u,x)) \ w) = K(T(x,y),z \ w)
    ]]></literal>
    <justification jstring="[para(7459(a,1),8828(a,1,2,1,2))].">
      <j1 rule="para" parents="7459 8828"/>
    </justification>
  </clause>

  <clause id="8836">
    <literal><![CDATA[
      T(x,(K(y,x) * z) \ u) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7393(a,1),8830(a,1,2,1))].">
      <j1 rule="para" parents="7393 8830"/>
    </justification>
  </clause>

  <clause id="8837">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) = K(x,(y * (x * z)) \ u)
    ]]></literal>
    <justification jstring="[para(6901(a,1),8832(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6901 8832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8838">
    <literal><![CDATA[
      K(x,y \ T(x,z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6865,a(flip),b,8833,a),flip(a)].">
      <j1 rule="hyper" parents="58 6865 8833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8839">
    <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),8833(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 8833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8840">
    <literal><![CDATA[
      K(x,(y * (K(z,x) * u)) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(6333(a,1),8833(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6333 8833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8841">
    <literal><![CDATA[
      T(x,y \ T(x,z)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(118,a,8838,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 8838 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8842">
    <literal><![CDATA[
      K(x,T(y \ x,z)) = K(x,T(y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7445,a(flip),b,8838,a)].">
      <j1 rule="hyper" parents="58 7445 8838"/>
    </justification>
  </clause>

  <clause id="8843">
    <literal><![CDATA[
      K(x / y,z \ (x / y)) = K(x / y,z \ (y \ x))
    ]]></literal>
    <justification jstring="[para(107(a,1),8838(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 8838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8844">
    <literal><![CDATA[
      T(x,T(x,y) / z) = T(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(7397,a,8841,a)].">
      <j1 rule="hyper" parents="7397 8841"/>
    </justification>
  </clause>

  <clause id="8845">
    <literal><![CDATA[
      K(x,y \ (K(x,z) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7768,a(flip),b,8834,a)].">
      <j1 rule="hyper" parents="58 7768 8834"/>
    </justification>
  </clause>

  <clause id="8846">
    <literal><![CDATA[
      T(x,y \ (K(z,x) * u)) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7789,a(flip),b,8836,a),flip(a)].">
      <j1 rule="hyper" parents="58 7789 8836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8847">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x)) \ x) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(8330,a,8842,a),flip(a)].">
      <j1 rule="hyper" parents="8330 8842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8849">
    <literal><![CDATA[
      K(x,T(((y \ z) \ 1) \ x,z)) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[hyper(334,a,6862,a(flip),b,8842,a),flip(a)].">
      <j1 rule="hyper" parents="334 6862 8842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8851">
    <literal><![CDATA[
      K(x,T(y / z,y)) = K(x,z \ (K(x,u) * y))
    ]]></literal>
    <justification jstring="[hyper(334,a,7314,a,b,8845,a)].">
      <j1 rule="hyper" parents="334 7314 8845"/>
    </justification>
  </clause>

  <clause id="8852">
    <literal><![CDATA[
      K(x,y \ (T(z,x) * u)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(5091(a,1),8845(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5091 8845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8853">
    <literal><![CDATA[
      K(x,y \ (T(x,z) \ u)) = K(x,y \ (x \ u))
    ]]></literal>
    <justification jstring="[para(5337(a,1),8845(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5337 8845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8854">
    <literal><![CDATA[
      K(x,y \ (z \ T(u,x))) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(5666(a,1),8845(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5666 8845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8855">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,x) * w))) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(6333(a,1),8845(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6333 8845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8856">
    <literal><![CDATA[
      K(x,T(y \ (K(x,z) * u),w)) = T(K(x,y \ u),w)
    ]]></literal>
    <justification jstring="[para(8845(a,1),7401(a,2,1))].">
      <j1 rule="para" parents="8845 7401"/>
    </justification>
  </clause>

  <clause id="8857">
    <literal><![CDATA[
      K(x,y \ (z * K(x,u))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(8170(a,1),8845(a,1,2,2))].">
      <j1 rule="para" parents="8170 8845"/>
    </justification>
  </clause>

  <clause id="8859">
    <literal><![CDATA[
      T(x,y \ ((z / x) \ u)) = T(x,y \ ((x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(5656(a,1),8846(a,1,2,2))].">
      <j1 rule="para" parents="5656 8846"/>
    </justification>
  </clause>

  <clause id="8860">
    <literal><![CDATA[
      K(x,y \ (z * (u / x))) = K(x,y \ (z * (x \ u)))
    ]]></literal>
    <justification jstring="[para(6417(a,1),8857(a,1,2,2))].">
      <j1 rule="para" parents="6417 8857"/>
    </justification>
  </clause>

  <clause id="8861">
    <literal><![CDATA[
      K(x,y \ (z * (u * x))) = K(x,y \ (z * (x * u)))
    ]]></literal>
    <justification jstring="[para(6901(a,1),8857(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6901 8857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8862">
    <literal><![CDATA[
      K(x,(K(y \ x,y) * z) \ x) = K(x,(z * K(y \ x,y)) \ x)
    ]]></literal>
    <justification jstring="[para(6522(a,1),8847(a,1,2,1))].">
      <j1 rule="para" parents="6522 8847"/>
    </justification>
  </clause>

  <clause id="8863">
    <literal><![CDATA[
      K(x,y \ (K(x,z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ u) = w
    ]]></literal>
    <justification jstring="[para(8851(a,1),7438(a,1))].">
      <j1 rule="para" parents="8851 7438"/>
    </justification>
  </clause>

  <clause id="8864">
    <literal><![CDATA[
      K(x,y \ ((T(z,x) / u) \ z)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(75(a,1),8854(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 8854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8865">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ z) = z \ ((T(y,x) / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6841,a(flip),b,8864,a),flip(a)].">
      <j1 rule="hyper" parents="58 6841 8864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8866">
    <literal><![CDATA[
      K(x,(T(y,x) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(5803(a,1),8829(a,1,2,1))].">
      <j1 rule="para" parents="5803 8829"/>
    </justification>
  </clause>

  <clause id="8867">
    <literal><![CDATA[
      K(x,y \ (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * x)) = u
    ]]></literal>
    <justification jstring="[para(4990(a,1),8863(a,1,2,2))].">
      <j1 rule="para" parents="4990 8863"/>
    </justification>
  </clause>

  <clause id="8868">
    <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(6135(a,1),8863(a,1,2,2))].">
      <j1 rule="para" parents="6135 8863"/>
    </justification>
  </clause>

  <clause id="8869">
    <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(7944(a,1),7192(a,1,3,2))].">
      <j1 rule="para" parents="7944 7192"/>
    </justification>
  </clause>

  <clause id="8870">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) = K(z * ((x \ y) \ 1),x / y)
    ]]></literal>
    <justification jstring="[para(6500(a,1),8006(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6500 8006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8871">
    <literal><![CDATA[
      T(x,y) * K(y * L(x,z,u),x) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(8008(a,1),7153(a,1,2))].">
      <j1 rule="para" parents="8008 7153"/>
    </justification>
  </clause>

  <clause id="8872">
    <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(8031(a,2),8740(a,1))].">
      <j1 rule="para" parents="8031 8740"/>
    </justification>
  </clause>

  <clause id="8873">
    <literal><![CDATA[
      (x * K(y,z)) * T(K(z,y),u) = x * K(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(6516(a,1),8036(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6516 8036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8874">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(L(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(6026(a,1),8043(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6026 8043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8875">
    <literal><![CDATA[
      T(x,K(y,z \ x)) / z = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5020(a,2),8081(a,1,1))].">
      <j1 rule="para" parents="5020 8081"/>
    </justification>
  </clause>

  <clause id="8876">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,8400,a(flip),b,8148,a),flip(a)].">
      <j1 rule="hyper" parents="334 8400 8148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8878">
    <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,6942,a(flip),b,8159,a),flip(a)].">
      <j1 rule="hyper" parents="117 6942 8159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8879">
    <literal><![CDATA[
      ((1 / x) * (K(y,z) * x)) * x = x * L(K(y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3154(a,1),8159(a,1,1))].">
      <j1 rule="para" parents="3154 8159"/>
    </justification>
  </clause>

  <clause id="8880">
    <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),8160(a,1,1))].">
      <j1 rule="para" parents="22 8160"/>
    </justification>
  </clause>

  <clause id="8881">
    <literal><![CDATA[
      T(T(x,L(K(y,z),u,w)),L(K(y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(4942,a,8161,a)].">
      <j1 rule="hyper" parents="4942 8161"/>
    </justification>
  </clause>

  <clause id="8882">
    <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(696,a,8881,a)].">
      <j1 rule="hyper" parents="696 8881"/>
    </justification>
  </clause>

  <clause id="8883">
    <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(7365(a,1),8175(a,1,1,1,2))].">
      <j1 rule="para" parents="7365 8175"/>
    </justification>
  </clause>

  <clause id="8884">
    <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(8262(a,2),550(a,1))].">
      <j1 rule="para" parents="8262 550"/>
    </justification>
  </clause>

  <clause id="8885">
    <literal><![CDATA[
      T(x,K(y,z \ 1) / z) = x * K(T(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3974,a,b,8289,a)].">
      <j1 rule="hyper" parents="58 3974 8289"/>
    </justification>
  </clause>

  <clause id="8886">
    <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),8298(a,2,2))].">
      <j1 rule="para" parents="22 8298"/>
    </justification>
  </clause>

  <clause id="8887">
    <literal><![CDATA[
      K(x \ y,x) * (z * (y / x)) = T(z * (x \ y),K(x,y))
    ]]></literal>
    <justification jstring="[para(6747(a,1),8305(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6747 8305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8888">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,8029,a(flip),b,8342,a),flip(a)].">
      <j1 rule="hyper" parents="334 8029 8342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8889">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,8030,a(flip),b,8343,a),flip(a)].">
      <j1 rule="hyper" parents="334 8030 8343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8890">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),K(u,y) \ z)
    ]]></literal>
    <justification jstring="[para(5894(a,1),8889(a,1,2))].">
      <j1 rule="para" parents="5894 8889"/>
    </justification>
  </clause>

  <clause id="8891">
    <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(4553(a,1),8351(a,1,2,2,2))].">
      <j1 rule="para" parents="4553 8351"/>
    </justification>
  </clause>

  <clause id="8892">
    <literal><![CDATA[
      K(x \ 1,T(y,x \ z)) = K(x \ 1,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8625,a(flip),b,8374,a),flip(a)].">
      <j1 rule="hyper" parents="58 8625 8374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8893">
    <literal><![CDATA[
      K(x,T(T(T(x,y) * z,u),w)) = K(x,T(T(x * z,u),w))
    ]]></literal>
    <justification jstring="[para(5091(a,1),8394(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5091 8394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8894">
    <literal><![CDATA[
      K(x,K(y,(x \ z) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8689,a(flip),b,8402,a),flip(a)].">
      <j1 rule="hyper" parents="58 8689 8402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8895">
    <literal><![CDATA[
      K(x,K(y,z \ (x \ u))) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(8487,a,8894,a)].">
      <j1 rule="hyper" parents="8487 8894"/>
    </justification>
  </clause>

  <clause id="8896">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z \ u)) = K(x,T(y,(x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(8894(a,1),8033(a,1,2))].">
      <j1 rule="para" parents="8894 8033"/>
    </justification>
  </clause>

  <clause id="8897">
    <literal><![CDATA[
      K(1 / (x / (x / y)),z) = K(1 / y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,8797,a(flip),b,8409,a),flip(a)].">
      <j1 rule="hyper" parents="58 8797 8409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8898">
    <literal><![CDATA[
      K(1 / (x \ y),T(z,y)) = K(1 / (y / x),z)
    ]]></literal>
    <justification jstring="[para(72(a,1),8897(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 8897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8899">
    <literal><![CDATA[
      K(1 / (x / y),T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / (y \ x),z) = u
    ]]></literal>
    <justification jstring="[para(8898(a,1),8281(a,1))].">
      <j1 rule="para" parents="8898 8281"/>
    </justification>
  </clause>

  <clause id="8900">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y \ z,z))
    ]]></literal>
    <justification jstring="[para(5633(a,1),8463(a,2,2))].">
      <j1 rule="para" parents="5633 8463"/>
    </justification>
  </clause>

  <clause id="8901">
    <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),8508(a,2,2))].">
      <j1 rule="para" parents="20 8508"/>
    </justification>
  </clause>

  <clause id="8902">
    <literal><![CDATA[
      T(x,y) * K(y * R(x,z,u),x) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(8525(a,1),5141(a,1,2))].">
      <j1 rule="para" parents="8525 5141"/>
    </justification>
  </clause>

  <clause id="8903">
    <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(8525(a,2),8059(a,2,1))].">
      <j1 rule="para" parents="8525 8059"/>
    </justification>
  </clause>

  <clause id="8904">
    <literal><![CDATA[
      K(T(L(x,y,z) * u,u),x) = K(L(x,y,z) * u,x)
    ]]></literal>
    <justification jstring="[hyper(7561,a,8526,a)].">
      <j1 rule="hyper" parents="7561 8526"/>
    </justification>
  </clause>

  <clause id="8905">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * z,x)) = T(T(x,y) * z,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),8568(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 8568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8907">
    <literal><![CDATA[
      K(x,T(x \ y,z \ y)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8504,a(flip),b,8577,a),flip(a)].">
      <j1 rule="hyper" parents="334 8504 8577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8908">
    <literal><![CDATA[
      K(x,T(x \ y,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(8577(a,2),8529(a,1))].">
      <j1 rule="para" parents="8577 8529"/>
    </justification>
  </clause>

  <clause id="8909">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(T(u * x,x) / u,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,8185,a,b,8593,a)].">
      <j1 rule="hyper" parents="334 8185 8593"/>
    </justification>
  </clause>

  <clause id="8910">
    <literal><![CDATA[
      K(T(x * y,y) / x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(8734,a,8909,a),flip(a)].">
      <j1 rule="hyper" parents="8734 8909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8912">
    <literal><![CDATA[
      K(T(x,y) / (x / y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),8910(a,1,1,1,1))].">
      <j1 rule="para" parents="7 8910"/>
    </justification>
  </clause>

  <clause id="8913">
    <literal><![CDATA[
      T(x,y) \ ((x \ 1) \ K(z,x)) = x * (K(z,x) / T(x,y))
    ]]></literal>
    <justification jstring="[para(8651(a,1),3637(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8651 3637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8914">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,7596,a(flip),b,8719,a),flip(a)].">
      <j1 rule="hyper" parents="334 7596 8719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8916">
    <literal><![CDATA[
      K(T(x \ T(y,x),z) \ u,z) = K((T(x,y) \ y) \ u,z)
    ]]></literal>
    <justification jstring="[para(5101(a,1),8914(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5101 8914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8917">
    <literal><![CDATA[
      K((x * T(y,z)) \ u,z) = K((x * y) \ u,z)
    ]]></literal>
    <justification jstring="[para(6374(a,1),8914(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6374 8914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8918">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(6516(a,1),8914(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6516 8914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8919">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) = K((x * (z * y)) \ u,z)
    ]]></literal>
    <justification jstring="[para(6901(a,1),8914(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6901 8914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8920">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,y) = K(z \ u,y)
    ]]></literal>
    <justification jstring="[para(7420(a,1),8914(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7420 8914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8921">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,T(y,w)) = K(x \ u,T(y,w))
    ]]></literal>
    <justification jstring="[para(8162(a,1),8914(a,1,1,1,2))].">
      <j1 rule="para" parents="8162 8914"/>
    </justification>
  </clause>

  <clause id="8922">
    <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(6558(a,2),8918(a,1,1))].">
      <j1 rule="para" parents="6558 8918"/>
    </justification>
  </clause>

  <clause id="8923">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7765,a(flip),b,8920,a)].">
      <j1 rule="hyper" parents="58 7765 8920"/>
    </justification>
  </clause>

  <clause id="8925">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(5394(a,1),8923(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5394 8923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8926">
    <literal><![CDATA[
      K(x \ (y / z),z \ y) = K(x \ (z \ y),z \ y)
    ]]></literal>
    <justification jstring="[para(5264(a,1),8923(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5264 8923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8927">
    <literal><![CDATA[
      K(x \ (T(y,z) \ u),y) = K(x \ (y \ u),y)
    ]]></literal>
    <justification jstring="[para(5337(a,1),8923(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5337 8923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8929">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),T(y,w)) = K(x \ u,T(y,w))
    ]]></literal>
    <justification jstring="[para(8162(a,1),8923(a,1,1,2,1))].">
      <j1 rule="para" parents="8162 8923"/>
    </justification>
  </clause>

  <clause id="8930">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(8170(a,1),8923(a,1,1,2))].">
      <j1 rule="para" parents="8170 8923"/>
    </justification>
  </clause>

  <clause id="8931">
    <literal><![CDATA[
      K(x \ (y / (z * y)),z \ 1) = K(x \ ((z * y) \ y),z \ 1)
    ]]></literal>
    <justification jstring="[para(5618(a,1),8925(a,1,1,2))].">
      <j1 rule="para" parents="5618 8925"/>
    </justification>
  </clause>

  <clause id="8932">
    <literal><![CDATA[
      K(x \ (y * T(z,u)),u) = K(x \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(5820(a,1),8925(a,1,1,2))].">
      <j1 rule="para" parents="5820 8925"/>
    </justification>
  </clause>

  <clause id="8933">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(x \ (y * (u * z)),u)
    ]]></literal>
    <justification jstring="[para(6901(a,1),8930(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6901 8930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8934">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),T(z,w)) = K(x \ y,T(z,w))
    ]]></literal>
    <justification jstring="[para(8162(a,1),8930(a,1,1,2,2))].">
      <j1 rule="para" parents="8162 8930"/>
    </justification>
  </clause>

  <clause id="8935">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,x) = K(z \ (x \ u),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7769,a,b,8927,a)].">
      <j1 rule="hyper" parents="58 7769 8927"/>
    </justification>
  </clause>

  <clause id="8936">
    <literal><![CDATA[
      K((x * (y * z)) \ ((x * z) * y),z) = K(a(x,z,T(y,z)),z)
    ]]></literal>
    <justification jstring="[para(234(a,1),8932(a,1,1)),flip(a)].">
      <j1 rule="para" parents="234 8932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8938">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(w,K(z \ (x \ u),x))
    ]]></literal>
    <justification jstring="[para(8935(a,1),8053(a,2,2))].">
      <j1 rule="para" parents="8935 8053"/>
    </justification>
  </clause>

  <clause id="8939">
    <literal><![CDATA[
      K(T(x,y * (z * K(u,w))),w) = (v5 * K(w,T(x,y * z))) \ v5
    ]]></literal>
    <justification jstring="[para(8724(a,1),6523(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8724 6523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8940">
    <literal><![CDATA[
      K(x,(T(x,y) * z) \ u) = K(x,z \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(334,a,8853,a(flip),b,8749,a),flip(a)].">
      <j1 rule="hyper" parents="334 8853 8749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8942">
    <literal><![CDATA[
      K(x,y \ (z \ (x * y))) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(7976,a,8783,a),flip(a)].">
      <j1 rule="hyper" parents="7976 8783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8943">
    <literal><![CDATA[
      R(K(x,T(y,z)),y * u,w) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(7401(a,2),8790(a,1,1))].">
      <j1 rule="para" parents="7401 8790"/>
    </justification>
  </clause>

  <clause id="8944">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,x \ y) * u) = K(x,T(x \ y,z)) * u
    ]]></literal>
    <justification jstring="[para(8239(a,1),8792(a,1,1))].">
      <j1 rule="para" parents="8239 8792"/>
    </justification>
  </clause>

  <clause id="8945">
    <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),8805(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4 8805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8946">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(7(a,1),8808(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 8808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8947">
    <literal><![CDATA[
      K(x,((1 / y) * y) \ (x \ z)) = K(x,L(x,y,y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(3146(a,1),8808(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3146 8808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8948">
    <literal><![CDATA[
      (x * K(y,(z * u) \ (y \ w))) \ x = K((z * (u * y)) \ w,y)
    ]]></literal>
    <justification jstring="[para(8808(a,1),6523(a,1,1,2))].">
      <j1 rule="para" parents="8808 6523"/>
    </justification>
  </clause>

  <clause id="8949">
    <literal><![CDATA[
      (x * y) * K(y \ (z \ (x * y)),z) = ((z \ x) * z) * y
    ]]></literal>
    <justification jstring="[para(6(a,1),8810(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6 8810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8950">
    <literal><![CDATA[
      x * (y * ((x \ z) / y)) != z * u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(8813(a,1),38(a,1))].">
      <j1 rule="para" parents="8813 38"/>
    </justification>
  </clause>

  <clause id="8951">
    <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(1378,a,8814,a),flip(a)].">
      <j1 rule="hyper" parents="1378 8814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8952">
    <literal><![CDATA[
      K(x,T(y * (z / T(u,x)),w)) = K(x,T(y * (z / u),w))
    ]]></literal>
    <justification jstring="[para(6517(a,1),8818(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6517 8818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8953">
    <literal><![CDATA[
      K(x,(y * (x * z)) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8808,a(flip),b,8837,a),flip(a)].">
      <j1 rule="hyper" parents="58 8808 8837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8954">
    <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(8837(a,1),6883(a,1,1))].">
      <j1 rule="para" parents="8837 6883"/>
    </justification>
  </clause>

  <clause id="8955">
    <literal><![CDATA[
      K(x / y,z \ (y \ x)) = K(y \ x,(z * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8387,a(flip),b,8843,a),flip(a)].">
      <j1 rule="hyper" parents="58 8387 8843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8956">
    <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(491(a,1),8855(a,1,2))].">
      <j1 rule="para" parents="491 8855"/>
    </justification>
  </clause>

  <clause id="8957">
    <literal><![CDATA[
      K(x,T(y \ (K(x,z) * u),w)) = K(x,T(y \ u,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,7401,a,b,8856,a),flip(a)].">
      <j1 rule="hyper" parents="334 7401 8856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8958">
    <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(8859(a,1),5075(a,1,1,1))].">
      <j1 rule="para" parents="8859 5075"/>
    </justification>
  </clause>

  <clause id="8959">
    <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,7962,a(flip),b,8860,a),flip(a)].">
      <j1 rule="hyper" parents="58 7962 8860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8960">
    <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(5761(a,1),8873(a,1,1))].">
      <j1 rule="para" parents="5761 8873"/>
    </justification>
  </clause>

  <clause id="8961">
    <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(246,a,8880,a(flip),b,4134,a(flip))].">
      <j1 rule="hyper" parents="246 8880 4134"/>
    </justification>
  </clause>

  <clause id="8962">
    <literal><![CDATA[
      K(x,K(y,z \ 1) / z) = K(T(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(5109,a,8885,a)].">
      <j1 rule="hyper" parents="5109 8885"/>
    </justification>
  </clause>

  <clause id="8963">
    <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(5711(a,1),8962(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5711 8962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8964">
    <literal><![CDATA[
      T(x,R(T(y,y \ z),u,w)) = T(x,R(z / (z / y),u,w))
    ]]></literal>
    <justification jstring="[para(4548(a,1),8886(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4548 8886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8965">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,8888,a(flip),b,8890,a),flip(a)].">
      <j1 rule="hyper" parents="334 8888 8890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8967">
    <literal><![CDATA[
      T(K(x,y),z * K(y,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(6520(a,1),8965(a,1,2))].">
      <j1 rule="para" parents="6520 8965"/>
    </justification>
  </clause>

  <clause id="8968">
    <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(8967(a,1),8876(a,1,2))].">
      <j1 rule="para" parents="8967 8876"/>
    </justification>
  </clause>

  <clause id="8969">
    <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(1814(a,1),8905(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1814 8905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8970">
    <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(1969(a,1),8905(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1969 8905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8971">
    <literal><![CDATA[
      K(((x \ 1) * (y * x)) \ z,x) = K(L(y,x,x \ 1) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,4308,a(flip),b,8919,a),flip(a)].">
      <j1 rule="hyper" parents="334 4308 8919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8972">
    <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(8926(a,1),5789(a,1,1,1,2))].">
      <j1 rule="para" parents="8926 5789"/>
    </justification>
  </clause>

  <clause id="8973">
    <literal><![CDATA[
      K(x \ (y * z),T(z,u)) = K(x \ (z * y),T(z,u))
    ]]></literal>
    <justification jstring="[para(4990(a,1),8929(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4990 8929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8974">
    <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(491(a,1),8933(a,2,1))].">
      <j1 rule="para" parents="491 8933"/>
    </justification>
  </clause>

  <clause id="8975">
    <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),8943(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 8943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8976">
    <literal><![CDATA[
      K(x,(x * y) \ ((x * z) * y)) = K(x,R(T(z,y),x,y))
    ]]></literal>
    <justification jstring="[hyper(5295,a,8945,a)].">
      <j1 rule="hyper" parents="5295 8945"/>
    </justification>
  </clause>

  <clause id="8977">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(7706,a,8946,a)].">
      <j1 rule="hyper" parents="7706 8946"/>
    </justification>
  </clause>

  <clause id="8978">
    <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(8953(a,1),6883(a,1,1))].">
      <j1 rule="para" parents="8953 6883"/>
    </justification>
  </clause>

  <clause id="8979">
    <literal><![CDATA[
      K(x,T(y \ T(x,z),u)) = K(x,T(y \ x,u))
    ]]></literal>
    <justification jstring="[para(5034(a,2),8957(a,1,2,1,2))].">
      <j1 rule="para" parents="5034 8957"/>
    </justification>
  </clause>

  <clause id="8980">
    <literal><![CDATA[
      K(x,T(y \ T(T(x,z),u),w)) = K(x,T(y \ T(x,u),w))
    ]]></literal>
    <justification jstring="[para(7472(a,1),8957(a,1,2,1,2))].">
      <j1 rule="para" parents="7472 8957"/>
    </justification>
  </clause>

  <clause id="8981">
    <literal><![CDATA[
      K(x \ (y * z),T(z,y)) = K((x / y) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,8608,a(flip),b,8973,a),flip(a)].">
      <j1 rule="hyper" parents="334 8608 8973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8982">
    <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(6532(a,1),8973(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6532 8973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8983">
    <literal><![CDATA[
      K(((x * y) / x) \ z,z) = K(y \ z,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7653,a(flip),b,8981,a),flip(a)].">
      <j1 rule="hyper" parents="58 7653 8981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8984">
    <literal><![CDATA[
      K(x * (y \ K(y,z)),x) = K(y \ x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5630,a(flip),b,8983,a)].">
      <j1 rule="hyper" parents="58 5630 8983"/>
    </justification>
  </clause>

  <clause id="8985">
    <literal><![CDATA[
      K((x \ K(x,y)) * z,z) = K(x \ z,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(7673,a,8984,a)].">
      <j1 rule="hyper" parents="7673 8984"/>
    </justification>
  </clause>

  <clause id="8986">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,391,a(flip),b,8975,a),flip(a)].">
      <j1 rule="hyper" parents="334 391 8975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8987">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,7401,a(flip),b,8986,a),flip(a)].">
      <j1 rule="hyper" parents="334 7401 8986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8988">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(7220,a,8977,a)].">
      <j1 rule="hyper" parents="7220 8977"/>
    </justification>
  </clause>

  <clause id="8989">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * y) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7130,a,b,8977,a)].">
      <j1 rule="hyper" parents="58 7130 8977"/>
    </justification>
  </clause>

  <clause id="8990">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * z) \ (u * x))) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(8977(a,1),5399(a,1,2,2))].">
      <j1 rule="para" parents="8977 5399"/>
    </justification>
  </clause>

  <clause id="8991">
    <literal><![CDATA[
      L(K(x,(y * z) \ ((u \ w) * x)),u \ w,u) = K(x,(u * (y * (z / x))) \ w)
    ]]></literal>
    <justification jstring="[para(8977(a,1),6849(a,1,1))].">
      <j1 rule="para" parents="8977 6849"/>
    </justification>
  </clause>

  <clause id="8992">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ (y * y))) = K(x,K(z * (u / y),y))
    ]]></literal>
    <justification jstring="[para(8977(a,1),8425(a,1,2))].">
      <j1 rule="para" parents="8977 8425"/>
    </justification>
  </clause>

  <clause id="8993">
    <literal><![CDATA[
      K(x,((y * K(x \ z,y)) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(5039(a,1),8988(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5039 8988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8994">
    <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(7453(a,1),39(a,1))].">
      <j1 rule="para" parents="7453 39"/>
    </justification>
  </clause>

  <clause id="8995">
    <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(1502(a,1),7511(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1502 7511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8996">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,5185,a(flip),b,7860,a),flip(a)].">
      <j1 rule="hyper" parents="334 5185 7860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8997">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z,x,y)) = u
    ]]></literal>
    <justification jstring="[para(7860(a,2),5294(a,1))].">
      <j1 rule="para" parents="7860 5294"/>
    </justification>
  </clause>

  <clause id="8998">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = T(x \ R(x,y,x),y)
    ]]></literal>
    <justification jstring="[para(6678(a,1),7881(a,1,2))].">
      <j1 rule="para" parents="6678 7881"/>
    </justification>
  </clause>

  <clause id="8999">
    <literal><![CDATA[
      T(x \ R(x,y,x),y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5743,a,8998,a),flip(a)].">
      <j1 rule="hyper" parents="5743 8998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9000">
    <literal><![CDATA[
      (x * (y \ R(y,x,y))) / x = y \ R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(281,a,8999,a)].">
      <j1 rule="hyper" parents="281 8999"/>
    </justification>
  </clause>

  <clause id="9001">
    <literal><![CDATA[
      (T(x * y,x) / x) / y = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(6821(a,1),9000(a,1,1))].">
      <j1 rule="para" parents="6821 9000"/>
    </justification>
  </clause>

  <clause id="9003">
    <literal><![CDATA[
      K(x,T(y,z) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ x,z)) = u
    ]]></literal>
    <justification jstring="[para(8838(a,1),7971(a,1))].">
      <j1 rule="para" parents="8838 7971"/>
    </justification>
  </clause>

  <clause id="9005">
    <literal><![CDATA[
      T(x * y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8491(a,1),7987(a,1))].">
      <j1 rule="para" parents="8491 7987"/>
    </justification>
  </clause>

  <clause id="9006">
    <literal><![CDATA[
      K(x,T(y,K(L(x,z,u),w) * v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(334,a,8205,a(flip),b,8293,a),flip(a)].">
      <j1 rule="hyper" parents="334 8205 8293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9007">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u) * (u * z))) = K(x,T(y,u * (z * x)))
    ]]></literal>
    <justification jstring="[para(4992(a,1),9006(a,1,2,2))].">
      <j1 rule="para" parents="4992 9006"/>
    </justification>
  </clause>

  <clause id="9008">
    <literal><![CDATA[
      K(1 / T(T(x,y),y * x),z) = K(1 / L(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(4562(a,1),8410(a,1,1,2))].">
      <j1 rule="para" parents="4562 8410"/>
    </justification>
  </clause>

  <clause id="9009">
    <literal><![CDATA[
      (x \ 1) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) * (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(8157(a,1),8502(a,1,2))].">
      <j1 rule="para" parents="8157 8502"/>
    </justification>
  </clause>

  <clause id="9010">
    <literal><![CDATA[
      (x \ y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) * (x \ y) = u
    ]]></literal>
    <justification jstring="[para(8157(a,1),8516(a,1,2))].">
      <j1 rule="para" parents="8157 8516"/>
    </justification>
  </clause>

  <clause id="9011">
    <literal><![CDATA[
      K(x / (y * z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) / z,y) = u
    ]]></literal>
    <justification jstring="[para(8819(a,1),8536(a,1))].">
      <j1 rule="para" parents="8819 8536"/>
    </justification>
  </clause>

  <clause id="9012">
    <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,8871,a(flip),b,5338,a),flip(a)].">
      <j1 rule="hyper" parents="116 8871 5338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9013">
    <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,8871,a(flip),b,5044,a),flip(a)].">
      <j1 rule="hyper" parents="116 8871 5044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9014">
    <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(8871(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8871 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9015">
    <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(8871(a,1),5336(a,1,2))].">
      <j1 rule="para" parents="8871 5336"/>
    </justification>
  </clause>

  <clause id="9016">
    <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,8902,a(flip),b,5338,a),flip(a)].">
      <j1 rule="hyper" parents="116 8902 5338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9017">
    <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,8902,a(flip),b,5044,a),flip(a)].">
      <j1 rule="hyper" parents="116 8902 5044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9018">
    <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(8902(a,1),5725(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8902 5725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9019">
    <literal><![CDATA[
      K(x,T(x \ y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(8512(a,1),8908(a,1))].">
      <j1 rule="para" parents="8512 8908"/>
    </justification>
  </clause>

  <clause id="9020">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * y))) = K(x,R(T(z,y),x,y))
    ]]></literal>
    <justification jstring="[hyper(7648,a,8976,a)].">
      <j1 rule="hyper" parents="7648 8976"/>
    </justification>
  </clause>

  <clause id="9021">
    <literal><![CDATA[
      K(1 / T(x,y),T(z,y * x)) = K(1 / L(x,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(7979,a,9008,a)].">
      <j1 rule="hyper" parents="7979 9008"/>
    </justification>
  </clause>

  <clause id="9022">
    <literal><![CDATA[
      K(1 / x,T(T(y,z * x),z)) = K(1 / L(x,z,x),y)
    ]]></literal>
    <justification jstring="[hyper(7979,a,9021,a)].">
      <j1 rule="hyper" parents="7979 9021"/>
    </justification>
  </clause>

  <clause id="9023">
    <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),9022(a,1,2))].">
      <j1 rule="para" parents="18 9022"/>
    </justification>
  </clause>

  <clause id="9024">
    <literal><![CDATA[
      K(1 / L(x,y,x),z) = K(1 / x,T(T(z,y),y))
    ]]></literal>
    <justification jstring="[hyper(8796,a,9023,a),flip(a)].">
      <j1 rule="hyper" parents="8796 9023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9025">
    <literal><![CDATA[
      K(1 / L(x,y,x),z) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,8157,a(flip),b,9024,a),flip(a)].">
      <j1 rule="hyper" parents="334 8157 9024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9027">
    <literal><![CDATA[
      L(K(x,y),z,L(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4329,a,7281,a)].">
      <j1 rule="hyper" parents="4329 7281"/>
    </justification>
  </clause>

  <clause id="9028">
    <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(7281(a,1),6528(a,1,1))].">
      <j1 rule="para" parents="7281 6528"/>
    </justification>
  </clause>

  <clause id="9029">
    <literal><![CDATA[
      K(L(x,y,L(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(8691,a,9027,a)].">
      <j1 rule="hyper" parents="8691 9027"/>
    </justification>
  </clause>

  <clause id="9030">
    <literal><![CDATA[
      x * K(L(x,y,L(x,z,u)),w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(119,a,9029,a,b,4995,a(flip))].">
      <j1 rule="hyper" parents="119 9029 4995"/>
    </justification>
  </clause>

  <clause id="9031">
    <literal><![CDATA[
      K(x,(R(x,y,z) \ u) \ w) = K(x,u \ (R(x,y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(6991,a,7282,a),flip(a)].">
      <j1 rule="hyper" parents="6991 7282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9032">
    <literal><![CDATA[
      K(x,x \ (x * y)) = K(x,K(z \ x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7142,a(flip),b,7306,a)].">
      <j1 rule="hyper" parents="58 7142 7306"/>
    </justification>
  </clause>

  <clause id="9033">
    <literal><![CDATA[
      K(x,x \ (y * x)) = K(x,K(z \ x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(8867,a,9032,a)].">
      <j1 rule="hyper" parents="8867 9032"/>
    </justification>
  </clause>

  <clause id="9035">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),9032(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 9032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9036">
    <literal><![CDATA[
      K(x,y * K(z \ x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7580,a(flip),b,9035,a)].">
      <j1 rule="hyper" parents="58 7580 9035"/>
    </justification>
  </clause>

  <clause id="9038">
    <literal><![CDATA[
      K(x,(x / y) * z) = K(x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(5680(a,1),9035(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5680 9035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9040">
    <literal><![CDATA[
      K(x,y \ T(z,((y \ 1) \ (y \ z)) \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(6836(a,1),9036(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6836 9036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9041">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(9033(a,1),5293(a,1))].">
      <j1 rule="para" parents="9033 5293"/>
    </justification>
  </clause>

  <clause id="9042">
    <literal><![CDATA[
      K(x,((y \ x) \ x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(5501(a,2),9041(a,1,2))].">
      <j1 rule="para" parents="5501 9041"/>
    </justification>
  </clause>

  <clause id="9043">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(K(z \ x,z) * y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7036,a(flip),b,7318,a)].">
      <j1 rule="hyper" parents="58 7036 7318"/>
    </justification>
  </clause>

  <clause id="9044">
    <literal><![CDATA[
      K(K(x \ y,x) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6663,a,9043,a),flip(a)].">
      <j1 rule="hyper" parents="6663 9043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9046">
    <literal><![CDATA[
      K(K(x \ y,x) * z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(9043(a,1),1413(a,1))].">
      <j1 rule="para" parents="9043 1413"/>
    </justification>
  </clause>

  <clause id="9048">
    <literal><![CDATA[
      (K(x \ y,x) * z) * K(z,y) = T(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,9044,a(flip),b,4995,a(flip))].">
      <j1 rule="hyper" parents="119 9044 4995"/>
    </justification>
  </clause>

  <clause id="9049">
    <literal><![CDATA[
      K(K(x,y) * z,y * x) = K(z,y * x)
    ]]></literal>
    <justification jstring="[para(4(a,1),9044(a,1,1,1,1))].">
      <j1 rule="para" parents="4 9044"/>
    </justification>
  </clause>

  <clause id="9050">
    <literal><![CDATA[
      K(T(x,y) * z,y * x) = K(x * z,y * x)
    ]]></literal>
    <justification jstring="[para(5047(a,1),9049(a,1,1))].">
      <j1 rule="para" parents="5047 9049"/>
    </justification>
  </clause>

  <clause id="9051">
    <literal><![CDATA[
      K(((x \ y) \ y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(5501(a,2),9046(a,1,1))].">
      <j1 rule="para" parents="5501 9046"/>
    </justification>
  </clause>

  <clause id="9052">
    <literal><![CDATA[
      K((x \ y) * z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) * z,y) = u
    ]]></literal>
    <justification jstring="[para(5680(a,1),9046(a,1,1))].">
      <j1 rule="para" parents="5680 9046"/>
    </justification>
  </clause>

  <clause id="9053">
    <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,6914,a(flip),b,7572,a),flip(a)].">
      <j1 rule="hyper" parents="58 6914 7572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9054">
    <literal><![CDATA[
      K(x,y / R(T(x,z),u,w)) = K(x,R(x,u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,8807,a(flip),b,7573,a),flip(a)].">
      <j1 rule="hyper" parents="334 8807 7573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9056">
    <literal><![CDATA[
      K(x,y / (T(z,u) / u)) = K(x,y / (z / T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(7654,a,7581,a),flip(a)].">
      <j1 rule="hyper" parents="7654 7581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9057">
    <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,7052,a(flip),b,7622,a),flip(a)].">
      <j1 rule="hyper" parents="58 7052 7622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9058">
    <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,9057,a,b,5400,a),flip(a)].">
      <j1 rule="hyper" parents="115 9057 5400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9059">
    <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),9057(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 9057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9060">
    <literal><![CDATA[
      L(K(x,y),z,L(y,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4329,a,7713,a)].">
      <j1 rule="hyper" parents="4329 7713"/>
    </justification>
  </clause>

  <clause id="9061">
    <literal><![CDATA[
      K(L(x,y,L(z,u,w)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(8691,a,9060,a)].">
      <j1 rule="hyper" parents="8691 9060"/>
    </justification>
  </clause>

  <clause id="9062">
    <literal><![CDATA[
      K(x,L(y,z,L(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6956,a,9060,a)].">
      <j1 rule="hyper" parents="6956 9060"/>
    </justification>
  </clause>

  <clause id="9063">
    <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(4594(a,1),9061(a,1,1))].">
      <j1 rule="para" parents="4594 9061"/>
    </justification>
  </clause>

  <clause id="9064">
    <literal><![CDATA[
      R(K(x,y),z,R(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4339,a,7745,a)].">
      <j1 rule="hyper" parents="4339 7745"/>
    </justification>
  </clause>

  <clause id="9065">
    <literal><![CDATA[
      K(x,y) * ((y * x) * R(x,z,u)) = (x * y) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(4990(a,1),7745(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4990 7745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9066">
    <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(7745(a,1),5356(a,1,1,2))].">
      <j1 rule="para" parents="7745 5356"/>
    </justification>
  </clause>

  <clause id="9067">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,7052,a(flip),b,9064,a)].">
      <j1 rule="hyper" parents="58 7052 9064"/>
    </justification>
  </clause>

  <clause id="9068">
    <literal><![CDATA[
      K(x,R(y,z,R(x,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6167,a(flip),b,9064,a)].">
      <j1 rule="hyper" parents="58 6167 9064"/>
    </justification>
  </clause>

  <clause id="9069">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (w / R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,6160,a(flip),b,9064,a)].">
      <j1 rule="hyper" parents="58 6160 9064"/>
    </justification>
  </clause>

  <clause id="9070">
    <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(9067(a,1),5034(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9067 5034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9071">
    <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(790(a,1),9068(a,1,2))].">
      <j1 rule="para" parents="790 9068"/>
    </justification>
  </clause>

  <clause id="9072">
    <literal><![CDATA[
      T(L(x / y,z,x / y),y) = L(y \ x,z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[para(7755(a,2),7754(a,1,1))].">
      <j1 rule="para" parents="7755 7754"/>
    </justification>
  </clause>

  <clause id="9073">
    <literal><![CDATA[
      K(x * (R(y,z,y) \ u),y) = K(x * (u / T(y,z)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7846,a(flip),b,7773,a),flip(a)].">
      <j1 rule="hyper" parents="58 7846 7773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9074">
    <literal><![CDATA[
      K(x * (R(x,y,x) \ z),x) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,7640,a(flip),b,9073,a),flip(a)].">
      <j1 rule="hyper" parents="334 7640 9073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9075">
    <literal><![CDATA[
      K(R(x,y,x) * z,x) = K(x * z,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),9074(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 9074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9076">
    <literal><![CDATA[
      K(x * R(y,z,y),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7683,a(flip),b,9075,a)].">
      <j1 rule="hyper" parents="58 7683 9075"/>
    </justification>
  </clause>

  <clause id="9077">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = 1 / (x \ K(x * y,x))
    ]]></literal>
    <justification jstring="[para(9076(a,1),5131(a,2,2,2))].">
      <j1 rule="para" parents="9076 5131"/>
    </justification>
  </clause>

  <clause id="9078">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5131,a,b,9077,a),flip(a)].">
      <j1 rule="hyper" parents="334 5131 9077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9079">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = x * K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5020,a(flip),b,9078,a),flip(a)].">
      <j1 rule="hyper" parents="334 5020 9078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9080">
    <literal><![CDATA[
      K(x,y * R(x,z,x)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(5109,a,9079,a)].">
      <j1 rule="hyper" parents="5109 9079"/>
    </justification>
  </clause>

  <clause id="9081">
    <literal><![CDATA[
      K(x,R(x,y,x) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7676,a,b,9080,a)].">
      <j1 rule="hyper" parents="58 7676 9080"/>
    </justification>
  </clause>

  <clause id="9082">
    <literal><![CDATA[
      K(R(x,y,x),R(x,z,x) * u) = K(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(7649,a,9081,a)].">
      <j1 rule="hyper" parents="7649 9081"/>
    </justification>
  </clause>

  <clause id="9083">
    <literal><![CDATA[
      T(K(x,y) * z,T(y,u)) = K(x,y) * T(z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(6560,a,7838,a),flip(a)].">
      <j1 rule="hyper" parents="6560 7838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9084">
    <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(9083(a,2),6634(a,1,1,1))].">
      <j1 rule="para" parents="9083 6634"/>
    </justification>
  </clause>

  <clause id="9085">
    <literal><![CDATA[
      T(T(x,1 / y),K(1 / y,z)) = T(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,5020,a,b,7854,a),flip(a)].">
      <j1 rule="hyper" parents="334 5020 7854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9086">
    <literal><![CDATA[
      T(T(x,1 / y),K(z,1 / y)) = T(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8134,a,9085,a)].">
      <j1 rule="hyper" parents="8134 9085"/>
    </justification>
  </clause>

  <clause id="9087">
    <literal><![CDATA[
      T(x,1 / T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(1 / y,z)) = u
    ]]></literal>
    <justification jstring="[para(9085(a,1),7969(a,1))].">
      <j1 rule="para" parents="9085 7969"/>
    </justification>
  </clause>

  <clause id="9088">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(u,z / y)) = T(x,1 / T(y / z,u))
    ]]></literal>
    <justification jstring="[para(5620(a,1),9086(a,1,2))].">
      <j1 rule="para" parents="5620 9086"/>
    </justification>
  </clause>

  <clause id="9089">
    <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(7885(a,2),7974(a,1))].">
      <j1 rule="para" parents="7885 7974"/>
    </justification>
  </clause>

  <clause id="9090">
    <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),7942(a,2,1))].">
      <j1 rule="para" parents="22 7942"/>
    </justification>
  </clause>

  <clause id="9091">
    <literal><![CDATA[
      T(x / y,z) * T(y,K(z,x / y)) = x * K(x / y,z)
    ]]></literal>
    <justification jstring="[para(8100(a,1),7993(a,1,2))].">
      <j1 rule="para" parents="8100 7993"/>
    </justification>
  </clause>

  <clause id="9092">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(R(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(5980(a,1),8034(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5980 8034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9093">
    <literal><![CDATA[
      R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w) \ 1))
    ]]></literal>
    <justification jstring="[para(8019(a,1),8035(a,1,1))].">
      <j1 rule="para" parents="8019 8035"/>
    </justification>
  </clause>

  <clause id="9094">
    <literal><![CDATA[
      K(R(K(x,y),z,u),w) = K(y,R(K(x,w),z,u))
    ]]></literal>
    <justification jstring="[para(5980(a,1),8070(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5980 8070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9095">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(y,R(K(x,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9092,a,b,9094,a)].">
      <j1 rule="hyper" parents="58 9092 9094"/>
    </justification>
  </clause>

  <clause id="9096">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,R(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(8048(a,1),9095(a,1,1))].">
      <j1 rule="para" parents="8048 9095"/>
    </justification>
  </clause>

  <clause id="9097">
    <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),8076(a,1,2,1))].">
      <j1 rule="para" parents="7 8076"/>
    </justification>
  </clause>

  <clause id="9098">
    <literal><![CDATA[
      T(x * K(y,z),K(u,y)) = T(x,K(u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(8058,a,8146,a),flip(a)].">
      <j1 rule="hyper" parents="8058 8146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9099">
    <literal><![CDATA[
      T(K(x,y) * z,K(u,y)) = K(x,y) * T(z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(6330,a,9098,a),flip(a)].">
      <j1 rule="hyper" parents="6330 9098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9100">
    <literal><![CDATA[
      T(K(x,y) * z,K(u,y)) = K(x,y) * T(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(8100(a,1),9099(a,2,2))].">
      <j1 rule="para" parents="8100 9099"/>
    </justification>
  </clause>

  <clause id="9101">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,u)) = K(x,y) * T(z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(8134,a,9100,a)].">
      <j1 rule="hyper" parents="8134 9100"/>
    </justification>
  </clause>

  <clause id="9102">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,K(x,u)) = T(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(6344,a,9101,a)].">
      <j1 rule="hyper" parents="6344 9101"/>
    </justification>
  </clause>

  <clause id="9103">
    <literal><![CDATA[
      T(x * K(y,z),K(y,u)) = T(x,K(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6337,a,9101,a),flip(a)].">
      <j1 rule="hyper" parents="6337 9101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9104">
    <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),9102(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 9102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9105">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) = T(x,K(z,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(9102(a,1),6275(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9102 6275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9106">
    <literal><![CDATA[
      T(x * K(y,z * x),K(y,z)) = K(y,z * x) * x
    ]]></literal>
    <justification jstring="[hyper(334,a,8368,a(flip),b,9103,a),flip(a)].">
      <j1 rule="hyper" parents="334 8368 9103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9107">
    <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(8055(a,1),9104(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8055 9104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9108">
    <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(5959(a,1),9105(a,2,2))].">
      <j1 rule="para" parents="5959 9105"/>
    </justification>
  </clause>

  <clause id="9109">
    <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(9106(a,1),4514(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9106 4514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9110">
    <literal><![CDATA[
      R(K(x,y),T(y,z) * u,w) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,8198,a(flip),b,8209,a),flip(a)].">
      <j1 rule="hyper" parents="334 8198 8209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9112">
    <literal><![CDATA[
      K(x,R(y,T(y,z) \ u,w)) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),9110(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 9110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9113">
    <literal><![CDATA[
      R(K(x,y),K(z,y) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,6169,a,b,9112,a)].">
      <j1 rule="hyper" parents="58 6169 9112"/>
    </justification>
  </clause>

  <clause id="9115">
    <literal><![CDATA[
      R(K(x,y),K(y,z) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(5394(a,1),9113(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5394 9113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9116">
    <literal><![CDATA[
      R(K(x,y),y \ K(y,z),u) = R(K(x,y),y \ 1,u)
    ]]></literal>
    <justification jstring="[para(5398(a,1),9113(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5398 9113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9117">
    <literal><![CDATA[
      R(K(x,y),z * K(u,y),w) = R(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[para(7538(a,1),9113(a,1,2))].">
      <j1 rule="para" parents="7538 9113"/>
    </justification>
  </clause>

  <clause id="9118">
    <literal><![CDATA[
      R(K(x,y),z * (K(u,y) * w),v5) = R(K(x,y),z * w,v5)
    ]]></literal>
    <justification jstring="[para(6333(a,1),9115(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6333 9115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9119">
    <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(9116(a,2),1699(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9116 1699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9120">
    <literal><![CDATA[
      L(K(x,y),z * T(x,u),w) = K(L(x,z,w),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,8184,a(flip),b,8211,a),flip(a)].">
      <j1 rule="hyper" parents="334 8184 8211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9122">
    <literal><![CDATA[
      L(K(x,y),x * z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(105(a,1),9120(a,1,2))].">
      <j1 rule="para" parents="105 9120"/>
    </justification>
  </clause>

  <clause id="9123">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(227(a,1),9120(a,1,2)),flip(a)].">
      <j1 rule="para" parents="227 9120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9124">
    <literal><![CDATA[
      K(L(x,y,z),x * y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(6437,a,9122,a),flip(a)].">
      <j1 rule="hyper" parents="6437 9122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9125">
    <literal><![CDATA[
      K(L(x,y,z),(z \ u) \ (x * y)) = K(x,u \ (z * (x * y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,6848,a(flip),b,9122,a),flip(a)].">
      <j1 rule="hyper" parents="58 6848 9122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9126">
    <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(8162(a,1),9122(a,1,1))].">
      <j1 rule="para" parents="8162 9122"/>
    </justification>
  </clause>

  <clause id="9127">
    <literal><![CDATA[
      L(K(x,y),K(z,x),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8736,a(flip),b,9123,a),flip(a)].">
      <j1 rule="hyper" parents="58 8736 9123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9128">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,9127,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 9127 13"/>
    </justification>
  </clause>

  <clause id="9129">
    <literal><![CDATA[
      L(L(K(x,y),z,u),K(w,x),v5) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(9127(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9127 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9130">
    <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(9127(a,1),459(a,1,2,1))].">
      <j1 rule="para" parents="9127 459"/>
    </justification>
  </clause>

  <clause id="9131">
    <literal><![CDATA[
      L(K(x,y),L(K(z,x),u,w),v5) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5096(a,1),9127(a,1,2))].">
      <j1 rule="para" parents="5096 9127"/>
    </justification>
  </clause>

  <clause id="9132">
    <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,9131,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 9131 13"/>
    </justification>
  </clause>

  <clause id="9133">
    <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(9129(a,2),6941(a,1,2))].">
      <j1 rule="para" parents="9129 6941"/>
    </justification>
  </clause>

  <clause id="9134">
    <literal><![CDATA[
      (x * (K(y,z) * K(z,u))) * K(u,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6527,a,9128,a)].">
      <j1 rule="hyper" parents="6527 9128"/>
    </justification>
  </clause>

  <clause id="9135">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(527,a,9128,a)].">
      <j1 rule="hyper" parents="527 9128"/>
    </justification>
  </clause>

  <clause id="9136">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = x * (K(u,y) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7109,a,b,9128,a)].">
      <j1 rule="hyper" parents="58 7109 9128"/>
    </justification>
  </clause>

  <clause id="9137">
    <literal><![CDATA[
      x * (K(y,z) * K(z,z * y)) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,6933,a(flip),b,9128,a),flip(a)].">
      <j1 rule="hyper" parents="58 6933 9128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9138">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[para(2065(a,2),9128(a,2,2))].">
      <j1 rule="para" parents="2065 9128"/>
    </justification>
  </clause>

  <clause id="9139">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(9135(a,1),46(a,2))].">
      <j1 rule="para" parents="9135 46"/>
    </justification>
  </clause>

  <clause id="9140">
    <literal><![CDATA[
      R(x,T(K(y,z),u),K(z,w)) = x
    ]]></literal>
    <justification jstring="[para(1606(a,1),9135(a,1,2))].">
      <j1 rule="para" parents="1606 9135"/>
    </justification>
  </clause>

  <clause id="9141">
    <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(9135(a,1),2861(a,1,1,1))].">
      <j1 rule="para" parents="9135 2861"/>
    </justification>
  </clause>

  <clause id="9142">
    <literal><![CDATA[
      R(x,L(K(y,z),u,w),K(z,v5)) = x
    ]]></literal>
    <justification jstring="[para(5096(a,1),9135(a,1,2))].">
      <j1 rule="para" parents="5096 9135"/>
    </justification>
  </clause>

  <clause id="9143">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(9135(a,1),6477(a,1,1))].">
      <j1 rule="para" parents="9135 6477"/>
    </justification>
  </clause>

  <clause id="9144">
    <literal><![CDATA[
      R(x,T(K(y,z),u),T(K(z,w),v5)) = x
    ]]></literal>
    <justification jstring="[para(5771(a,1),9140(a,1,3))].">
      <j1 rule="para" parents="5771 9140"/>
    </justification>
  </clause>

  <clause id="9145">
    <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(9142(a,1),518(a,1,1))].">
      <j1 rule="para" parents="9142 518"/>
    </justification>
  </clause>

  <clause id="9146">
    <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(9144(a,1),965(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9144 965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9147">
    <literal><![CDATA[
      K(x,y) * K(y,y \ x) = a(y,x / y,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4539,a(flip),b,9143,a),flip(a)].">
      <j1 rule="hyper" parents="58 4539 9143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9148">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(9143(a,2),2073(a,1))].">
      <j1 rule="para" parents="9143 2073"/>
    </justification>
  </clause>

  <clause id="9150">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5760,a,b,9147,a)].">
      <j1 rule="hyper" parents="58 5760 9147"/>
    </justification>
  </clause>

  <clause id="9151">
    <literal><![CDATA[
      a(x,y / x,x) \ K(y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(9147(a,1),6523(a,1,1))].">
      <j1 rule="para" parents="9147 6523"/>
    </justification>
  </clause>

  <clause id="9152">
    <literal><![CDATA[
      a(x,y / x,x) * K(x,y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(9147(a,1),6525(a,1,1))].">
      <j1 rule="para" parents="9147 6525"/>
    </justification>
  </clause>

  <clause id="9153">
    <literal><![CDATA[
      a(x,(x * y) / x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),9150(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 9150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9154">
    <literal><![CDATA[
      x \ R(x,T(y,x),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(231(a,1),9153(a,1,2)),flip(a)].">
      <j1 rule="para" parents="231 9153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9155">
    <literal><![CDATA[
      x \ R(x,y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(4687(a,1),9154(a,1,2))].">
      <j1 rule="para" parents="4687 9154"/>
    </justification>
  </clause>

  <clause id="9156">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,x) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(7915,a,9155,a)].">
      <j1 rule="hyper" parents="7915 9155"/>
    </justification>
  </clause>

  <clause id="9157">
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5765,a,9155,a)].">
      <j1 rule="hyper" parents="5765 9155"/>
    </justification>
  </clause>

  <clause id="9158">
    <literal><![CDATA[
      K(x * y,y) * K(y,x) = a(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(5764,a,9155,a)].">
      <j1 rule="hyper" parents="5764 9155"/>
    </justification>
  </clause>

  <clause id="9159">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5752,a,9155,a)].">
      <j1 rule="hyper" parents="5752 9155"/>
    </justification>
  </clause>

  <clause id="9160">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5741,a,9155,a)].">
      <j1 rule="hyper" parents="5741 9155"/>
    </justification>
  </clause>

  <clause id="9161">
    <literal><![CDATA[
      R(x,y,x) / x = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(4041,a,9155,a)].">
      <j1 rule="hyper" parents="4041 9155"/>
    </justification>
  </clause>

  <clause id="9162">
    <literal><![CDATA[
      x * a(x,y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,9155,a)].">
      <j1 rule="hyper" parents="134 9155"/>
    </justification>
  </clause>

  <clause id="9163">
    <literal><![CDATA[
      K(x,y \ z) * K(y \ (z * x),x) = a(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7165,a,b,9155,a)].">
      <j1 rule="hyper" parents="58 7165 9155"/>
    </justification>
  </clause>

  <clause id="9164">
    <literal><![CDATA[
      K(x,y) * K(y,y \ x) = a(y,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5760,a(flip),b,9155,a)].">
      <j1 rule="hyper" parents="58 5760 9155"/>
    </justification>
  </clause>

  <clause id="9165">
    <literal><![CDATA[
      T(x,y) * a(x,z,x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,9155,a(flip),b,7738,a)].">
      <j1 rule="hyper" parents="119 9155 7738"/>
    </justification>
  </clause>

  <clause id="9166">
    <literal><![CDATA[
      T(x,y) \ R(x,z,x) = K(y,x) * a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,9155,a(flip),b,5390,a),flip(a)].">
      <j1 rule="hyper" parents="119 9155 5390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9167">
    <literal><![CDATA[
      a(x,y,x) * x = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(9155(a,1),4036(a,1,1))].">
      <j1 rule="para" parents="9155 4036"/>
    </justification>
  </clause>

  <clause id="9168">
    <literal><![CDATA[
      R(x,y,x) \ x = a(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(9155(a,1),4267(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9155 4267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9169">
    <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(9155(a,1),5449(a,1,2))].">
      <j1 rule="para" parents="9155 5449"/>
    </justification>
  </clause>

  <clause id="9170">
    <literal><![CDATA[
      K(x,x * y) * a(x,y,x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(9155(a,1),5750(a,1,2))].">
      <j1 rule="para" parents="9155 5750"/>
    </justification>
  </clause>

  <clause id="9171">
    <literal><![CDATA[
      a(x,x \ (y \ x),x) = x \ R(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(6061(a,1),9155(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6061 9155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9172">
    <literal><![CDATA[
      a(x,y,x) \ K(x,y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(9155(a,1),6549(a,1,1))].">
      <j1 rule="para" parents="9155 6549"/>
    </justification>
  </clause>

  <clause id="9173">
    <literal><![CDATA[
      a(x,y,x) \ K(x * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(9155(a,1),6550(a,1,1))].">
      <j1 rule="para" parents="9155 6550"/>
    </justification>
  </clause>

  <clause id="9174">
    <literal><![CDATA[
      T(x * y,x) / x = y * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(9155(a,1),6821(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9155 6821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9175">
    <literal><![CDATA[
      x \ R(T(x,y),z,x) = K(x,y) * a(x,z,x)
    ]]></literal>
    <justification jstring="[para(9155(a,1),7868(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9155 7868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9176">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(9162(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9162 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9177">
    <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(9162(a,1),239(a,1,1))].">
      <j1 rule="para" parents="9162 239"/>
    </justification>
  </clause>

  <clause id="9178">
    <literal><![CDATA[
      K(x,y) * a(y,x,y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(5409,a,9157,a)].">
      <j1 rule="hyper" parents="5409 9157"/>
    </justification>
  </clause>

  <clause id="9179">
    <literal><![CDATA[
      a(x,y,x) * K(y,x) = K(y * x,x)
    ]]></literal>
    <justification jstring="[hyper(6527,a,9158,a)].">
      <j1 rule="hyper" parents="6527 9158"/>
    </justification>
  </clause>

  <clause id="9180">
    <literal><![CDATA[
      a(x,y,x) * K(y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(6527,a,9159,a)].">
      <j1 rule="hyper" parents="6527 9159"/>
    </justification>
  </clause>

  <clause id="9181">
    <literal><![CDATA[
      a(x,y,x) * K(x,x * y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(9159(a,1),6525(a,1,1))].">
      <j1 rule="para" parents="9159 6525"/>
    </justification>
  </clause>

  <clause id="9182">
    <literal><![CDATA[
      K(x,y) * a(y,x,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(5409,a,9160,a)].">
      <j1 rule="hyper" parents="5409 9160"/>
    </justification>
  </clause>

  <clause id="9183">
    <literal><![CDATA[
      (x * y) \ T(y * x,y) = a(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7001,a,b,9160,a)].">
      <j1 rule="hyper" parents="58 7001 9160"/>
    </justification>
  </clause>

  <clause id="9184">
    <literal><![CDATA[
      (x * y) * a(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,9160,a(flip),b,7001,a)].">
      <j1 rule="hyper" parents="119 9160 7001"/>
    </justification>
  </clause>

  <clause id="9185">
    <literal><![CDATA[
      a(x,y,x) * (y * x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(9160(a,1),7000(a,1,1))].">
      <j1 rule="para" parents="9160 7000"/>
    </justification>
  </clause>

  <clause id="9186">
    <literal><![CDATA[
      K(x,y) * a(x,x \ y,x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),9170(a,1,1,2))].">
      <j1 rule="para" parents="5 9170"/>
    </justification>
  </clause>

  <clause id="9187">
    <literal><![CDATA[
      a(x,y \ 1,x) \ K(y \ x,x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(5627(a,1),9173(a,1,2))].">
      <j1 rule="para" parents="5627 9173"/>
    </justification>
  </clause>

  <clause id="9188">
    <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,1971,a,b,9174,a)].">
      <j1 rule="hyper" parents="58 1971 9174"/>
    </justification>
  </clause>

  <clause id="9189">
    <literal><![CDATA[
      (x \ y) * a(x,x \ y,x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(5(a,1),9174(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 9174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9190">
    <literal><![CDATA[
      T(x * a(y,x,y),y) = y \ T(y * x,y)
    ]]></literal>
    <justification jstring="[para(9174(a,1),107(a,1,1))].">
      <j1 rule="para" parents="9174 107"/>
    </justification>
  </clause>

  <clause id="9191">
    <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(9174(a,2),238(a,1,2,2))].">
      <j1 rule="para" parents="9174 238"/>
    </justification>
  </clause>

  <clause id="9192">
    <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(9174(a,2),490(a,1,2,2))].">
      <j1 rule="para" parents="9174 490"/>
    </justification>
  </clause>

  <clause id="9193">
    <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(9174(a,2),861(a,1,2,2,2))].">
      <j1 rule="para" parents="9174 861"/>
    </justification>
  </clause>

  <clause id="9194">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(5556(a,2),9176(a,1))].">
      <j1 rule="para" parents="5556 9176"/>
    </justification>
  </clause>

  <clause id="9195">
    <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(6569(a,1),9180(a,2,1))].">
      <j1 rule="para" parents="6569 9180"/>
    </justification>
  </clause>

  <clause id="9196">
    <literal><![CDATA[
      a(x,y,x) != 1
    ]]></literal>
    <literal><![CDATA[
      T(x * y,x) = y * x
    ]]></literal>
    <justification jstring="[para(9183(a,1),169(a,1))].">
      <j1 rule="para" parents="9183 169"/>
    </justification>
  </clause>

  <clause id="9197">
    <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(9184(a,1),989(a,1,1,2))].">
      <j1 rule="para" parents="9184 989"/>
    </justification>
  </clause>

  <clause id="9198">
    <literal><![CDATA[
      a(x,y,x) * T(x,z) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(9156(a,1),4036(a,1,1))].">
      <j1 rule="para" parents="9156 4036"/>
    </justification>
  </clause>

  <clause id="9199">
    <literal><![CDATA[
      a(x,x \ y,x) = T(x,y) \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(4619(a,1),9156(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4619 9156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9200">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = a(x / y,z,x / y) * (x / y)
    ]]></literal>
    <justification jstring="[para(6387(a,1),9198(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6387 9198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9201">
    <literal><![CDATA[
      x * a(y,y \ x,y) = T(y * (x / y),y)
    ]]></literal>
    <justification jstring="[hyper(119,a,9164,a(flip),b,8566,a)].">
      <j1 rule="hyper" parents="119 9164 8566"/>
    </justification>
  </clause>

  <clause id="9202">
    <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(9166(a,2),8692(a,1))].">
      <j1 rule="para" parents="9166 8692"/>
    </justification>
  </clause>

  <clause id="9203">
    <literal><![CDATA[
      a(x,x \ (y \ x),x) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,9155,a(flip),b,9171,a),flip(a)].">
      <j1 rule="hyper" parents="334 9155 9171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9204">
    <literal><![CDATA[
      T(x,y \ x) \ ((x \ (y \ x)) \ (y \ x)) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9199,a(flip),b,9203,a)].">
      <j1 rule="hyper" parents="58 9199 9203"/>
    </justification>
  </clause>

  <clause id="9205">
    <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(9175(a,1),91(a,1,2,2,1))].">
      <j1 rule="para" parents="9175 91"/>
    </justification>
  </clause>

  <clause id="9206">
    <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(9175(a,1),4124(a,1,1,1))].">
      <j1 rule="para" parents="9175 4124"/>
    </justification>
  </clause>

  <clause id="9207">
    <literal><![CDATA[
      L(K(x,y),K(z,y),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6945,a,9134,a)].">
      <j1 rule="hyper" parents="6945 9134"/>
    </justification>
  </clause>

  <clause id="9208">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * K(z,y) = x * K(u,y)
    ]]></literal>
    <justification jstring="[para(2065(a,2),9134(a,1,1,2))].">
      <j1 rule="para" parents="2065 9134"/>
    </justification>
  </clause>

  <clause id="9209">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,z) = x * (K(y,z) * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,9207,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 9207 13"/>
    </justification>
  </clause>

  <clause id="9210">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * K(u,y)) = x * K(u,y)
    ]]></literal>
    <justification jstring="[para(9207(a,1),6530(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9207 6530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9211">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = x * (K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(2065(a,2),9136(a,2,2))].">
      <j1 rule="para" parents="2065 9136"/>
    </justification>
  </clause>

  <clause id="9212">
    <literal><![CDATA[
      (x / T(y,z)) * T(y,u) = x * (K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6764,a,9138,a)].">
      <j1 rule="hyper" parents="6764 9138"/>
    </justification>
  </clause>

  <clause id="9213">
    <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(246,a,9138,a,b,649,a)].">
      <j1 rule="hyper" parents="246 9138 649"/>
    </justification>
  </clause>

  <clause id="9214">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(u,y)) = (x / T(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6368(a,1),9138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6368 9138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9215">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * (K(z,y) * K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(30,a,9134,a,b,9208,a(flip))].">
      <j1 rule="hyper" parents="30 9134 9208"/>
    </justification>
  </clause>

  <clause id="9216">
    <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(451,a,5233,a(flip),b,9210,a)].">
      <j1 rule="hyper" parents="451 5233 9210"/>
    </justification>
  </clause>

  <clause id="9217">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ 1 = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5233,a(flip),b,9210,a)].">
      <j1 rule="hyper" parents="116 5233 9210"/>
    </justification>
  </clause>

  <clause id="9218">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ 1 = K(y,x) * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,5908,a,b,9217,a),flip(a)].">
      <j1 rule="hyper" parents="334 5908 9217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9219">
    <literal><![CDATA[
      R(x,K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(527,a,9211,a)].">
      <j1 rule="hyper" parents="527 9211"/>
    </justification>
  </clause>

  <clause id="9220">
    <literal><![CDATA[
      L(K(x,y),K(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(493,a,9211,a)].">
      <j1 rule="hyper" parents="493 9211"/>
    </justification>
  </clause>

  <clause id="9221">
    <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(3097(a,1),9211(a,1,1))].">
      <j1 rule="para" parents="3097 9211"/>
    </justification>
  </clause>

  <clause id="9222">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * K(u,z)) = x * K(u,z)
    ]]></literal>
    <justification jstring="[para(6516(a,1),9211(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6516 9211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9223">
    <literal><![CDATA[
      R(x / K(y,z),K(u,w),K(v5,u)) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,6520,a(flip),b,9219,a),flip(a)].">
      <j1 rule="hyper" parents="334 6520 9219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9224">
    <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(9220(a,1),296(a,1,2))].">
      <j1 rule="para" parents="9220 296"/>
    </justification>
  </clause>

  <clause id="9225">
    <literal><![CDATA[
      L(K(x,T(y,z)),K(y,u),w) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8162(a,1),9220(a,1,2))].">
      <j1 rule="para" parents="8162 9220"/>
    </justification>
  </clause>

  <clause id="9226">
    <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,9225,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 9225 13"/>
    </justification>
  </clause>

  <clause id="9227">
    <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(9223(a,1),1423(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9223 1423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9228">
    <literal><![CDATA[
      (x * y) * (K(y,z) * K(u,y)) = (x * K(u,y)) * T(y,z)
    ]]></literal>
    <justification jstring="[para(6365(a,1),9212(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6365 9212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9229">
    <literal><![CDATA[
      x / (K(y,z) * K(u,y)) = x * (K(z,y) * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(341,a,9215,a),flip(a)].">
      <j1 rule="hyper" parents="341 9215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9230">
    <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(9215(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9215 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9231">
    <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(9222(a,1),5179(a,1,1,1))].">
      <j1 rule="para" parents="9222 5179"/>
    </justification>
  </clause>

  <clause id="9232">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ 1 = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(4229,a,9229,a)].">
      <j1 rule="hyper" parents="4229 9229"/>
    </justification>
  </clause>

  <clause id="9233">
    <literal><![CDATA[
      x / (K(y,z) * K(z,u)) = x * (K(u,z) * K(z,y))
    ]]></literal>
    <justification jstring="[para(2065(a,1),9229(a,1,2))].">
      <j1 rule="para" parents="2065 9229"/>
    </justification>
  </clause>

  <clause id="9234">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = x * (y \ L(y,z,y))
    ]]></literal>
    <justification jstring="[para(5751(a,1),9137(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5751 9137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9235">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K((K(z,u) * y) / x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8929,a(flip),b,8251,a)].">
      <j1 rule="hyper" parents="58 8929 8251"/>
    </justification>
  </clause>

  <clause id="9236">
    <literal><![CDATA[
      K((K(x,y) * z) / u,x) = K(z / u,x)
    ]]></literal>
    <justification jstring="[hyper(8323,a,9235,a),flip(a)].">
      <j1 rule="hyper" parents="8323 9235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9238">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = (w * K(z / u,x)) \ w
    ]]></literal>
    <justification jstring="[para(9236(a,1),6523(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9236 6523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9239">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[hyper(334,a,6523,a(flip),b,9238,a),flip(a)].">
      <j1 rule="hyper" parents="334 6523 9238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9240">
    <literal><![CDATA[
      K(x,(T(y,x) * z) / u) = K(x,(y * z) / u)
    ]]></literal>
    <justification jstring="[para(5091(a,1),9239(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5091 9239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9241">
    <literal><![CDATA[
      K(x,(T(y / (z \ u),x) * K(z \ u,z)) / w) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[para(6743(a,1),9240(a,2,2,1))].">
      <j1 rule="para" parents="6743 9240"/>
    </justification>
  </clause>

  <clause id="9242">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / (x * K(z,u)),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8921,a(flip),b,8279,a)].">
      <j1 rule="hyper" parents="58 8921 8279"/>
    </justification>
  </clause>

  <clause id="9243">
    <literal><![CDATA[
      K(x / (y * K(z,u)),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(8329,a,9242,a),flip(a)].">
      <j1 rule="hyper" parents="8329 9242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9245">
    <literal><![CDATA[
      K(x / ((y * K(z,u)) * w),u) = K(x / (y * w),u)
    ]]></literal>
    <justification jstring="[para(7105(a,1),9243(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7105 9243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9246">
    <literal><![CDATA[
      K(x / (K(y,z) * u),z) = K(x / u,z)
    ]]></literal>
    <justification jstring="[para(7420(a,1),9243(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7420 9243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9247">
    <literal><![CDATA[
      K(x / ((K(y,z) * u) * w),z) = K(x / (u * w),z)
    ]]></literal>
    <justification jstring="[para(7057(a,1),9246(a,1,1,2))].">
      <j1 rule="para" parents="7057 9246"/>
    </justification>
  </clause>

  <clause id="9248">
    <literal><![CDATA[
      K(x / ((K(y,z) * u) * w),y) = K(x / (u * w),y)
    ]]></literal>
    <justification jstring="[para(7391(a,1),9245(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7391 9245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9249">
    <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(522(a,1),9247(a,1,1))].">
      <j1 rule="para" parents="522 9247"/>
    </justification>
  </clause>

  <clause id="9250">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / (y * K(u,x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8835,a(flip),b,8290,a)].">
      <j1 rule="hyper" parents="58 8835 8290"/>
    </justification>
  </clause>

  <clause id="9251">
    <literal><![CDATA[
      K(x,y / (z * K(u,x))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(8336,a,9250,a),flip(a)].">
      <j1 rule="hyper" parents="8336 9250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9253">
    <literal><![CDATA[
      K(x,y / (T(z,x) / u)) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[para(1542(a,1),9251(a,1,2,2))].">
      <j1 rule="para" parents="1542 9251"/>
    </justification>
  </clause>

  <clause id="9254">
    <literal><![CDATA[
      K(x,y / K(z,z \ K(u,x))) = K(x,y / (z * (K(u,x) / z)))
    ]]></literal>
    <justification jstring="[para(5048(a,1),9251(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5048 9251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9255">
    <literal><![CDATA[
      K(x,y / (T(z,x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(5803(a,1),9251(a,1,2,2))].">
      <j1 rule="para" parents="5803 9251"/>
    </justification>
  </clause>

  <clause id="9256">
    <literal><![CDATA[
      K(x,y / (z * K(x,u))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(6516(a,1),9251(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6516 9251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9257">
    <literal><![CDATA[
      K(x,y / (K(x,z) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(7391(a,1),9251(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7391 9251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9258">
    <literal><![CDATA[
      K(x,y / ((z * K(u,x)) * w)) = K(x,y / (z * w))
    ]]></literal>
    <justification jstring="[para(7105(a,1),9256(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7105 9256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9259">
    <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),9257(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15 9257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9260">
    <literal><![CDATA[
      K(x,y / (T(z \ T(u,z),x) / w)) = K(x,y / ((T(z,u) \ u) / w))
    ]]></literal>
    <justification jstring="[para(4639(a,1),9253(a,1,2,2,1))].">
      <j1 rule="para" parents="4639 9253"/>
    </justification>
  </clause>

  <clause id="9261">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(84(a,1),9258(a,1,2,2,1))].">
      <j1 rule="para" parents="84 9258"/>
    </justification>
  </clause>

  <clause id="9262">
    <literal><![CDATA[
      K(x,y / (((x \ z) * x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(315(a,1),9258(a,1,2,2,1))].">
      <j1 rule="para" parents="315 9258"/>
    </justification>
  </clause>

  <clause id="9263">
    <literal><![CDATA[
      K(x,y / ((K(x,z) * u) * w)) = K(x,y / (u * w))
    ]]></literal>
    <justification jstring="[para(7391(a,1),9258(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7391 9258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9264">
    <literal><![CDATA[
      K(x,y / ((K(z,x) * u) * w)) = K(x,y / (u * w))
    ]]></literal>
    <justification jstring="[para(7393(a,1),9258(a,1,2,2,1))].">
      <j1 rule="para" parents="7393 9258"/>
    </justification>
  </clause>

  <clause id="9265">
    <literal><![CDATA[
      K(x,y / ((z * (K(u,x) * w)) * v5)) = K(x,y / ((z * w) * v5))
    ]]></literal>
    <justification jstring="[para(6333(a,1),9263(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6333 9263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9266">
    <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(522(a,1),9264(a,1,2))].">
      <j1 rule="para" parents="522 9264"/>
    </justification>
  </clause>

  <clause id="9267">
    <literal><![CDATA[
      K(x,R(y,K(x,z),u)) = K(x,y * K(x,z))
    ]]></literal>
    <justification jstring="[para(6(a,1),9259(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 9259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9268">
    <literal><![CDATA[
      K(x,R(y,K(x,z),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,7486,a(flip),b,9267,a),flip(a)].">
      <j1 rule="hyper" parents="334 7486 9267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9271">
    <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),9268(a,1,2))].">
      <j1 rule="para" parents="26 9268"/>
    </justification>
  </clause>

  <clause id="9272">
    <literal><![CDATA[
      ((x * (y * K(z,y))) / x) / ((x * y) / x) = K(T(z,x),y)
    ]]></literal>
    <justification jstring="[para(5017(a,1),8291(a,1,1,1,2))].">
      <j1 rule="para" parents="5017 8291"/>
    </justification>
  </clause>

  <clause id="9273">
    <literal><![CDATA[
      T(K(x,y),T(z,x \ u)) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(8026,a,8341,a),flip(a)].">
      <j1 rule="hyper" parents="8026 8341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9274">
    <literal><![CDATA[
      T(K(x,y),T(z,x * u)) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),9273(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 9273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9275">
    <literal><![CDATA[
      1 / (K(x,y) * T(x,z)) = K(y,x) / T(x,z)
    ]]></literal>
    <justification jstring="[para(8162(a,1),8378(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8162 8378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9276">
    <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(9275(a,1),4324(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9275 4324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9277">
    <literal><![CDATA[
      (K(x,y) / T(y,z)) \ 1 = K(y,z) * T(y,x)
    ]]></literal>
    <justification jstring="[para(9275(a,1),5721(a,1,1))].">
      <j1 rule="para" parents="9275 5721"/>
    </justification>
  </clause>

  <clause id="9279">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,x \ K(x,z)) = K(y,K(z,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(334,a,8053,a,b,8390,a),flip(a)].">
      <j1 rule="hyper" parents="334 8053 8390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9280">
    <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(334,a,8379,a,b,8391,a)].">
      <j1 rule="hyper" parents="334 8379 8391"/>
    </justification>
  </clause>

  <clause id="9281">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = x * K(T(x,z \ y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(4548(a,1),8396(a,1,2,1))].">
      <j1 rule="para" parents="4548 8396"/>
    </justification>
  </clause>

  <clause id="9282">
    <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(7285(a,1),8401(a,2,2))].">
      <j1 rule="para" parents="7285 8401"/>
    </justification>
  </clause>

  <clause id="9283">
    <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(6566(a,1),8560(a,2,2,1,1))].">
      <j1 rule="para" parents="6566 8560"/>
    </justification>
  </clause>

  <clause id="9284">
    <literal><![CDATA[
      K(R(x / (x / y),z,u),w) = K(R(y,z,u),T(w,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,9057,a(flip),b,8586,a),flip(a)].">
      <j1 rule="hyper" parents="334 9057 8586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9285">
    <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),9284(a,1,1)),flip(a)].">
      <j1 rule="para" parents="102 9284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9286">
    <literal><![CDATA[
      K(x,L(y,z / T(y,u),w)) = L(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[para(8162(a,1),8591(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8162 8591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9287">
    <literal><![CDATA[
      L(K(x,y),z * T(y,u),w) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[para(6(a,1),9286(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 9286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9288">
    <literal><![CDATA[
      L(K(x,y),y * z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(191(a,1),9286(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="191 9286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9289">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(273(a,1),9286(a,1,2,2))].">
      <j1 rule="para" parents="273 9286"/>
    </justification>
  </clause>

  <clause id="9290">
    <literal><![CDATA[
      L(K(x,y),z * K(y,u),w) = K(x,L(y,z / y,w))
    ]]></literal>
    <justification jstring="[para(6464(a,1),9286(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6464 9286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9292">
    <literal><![CDATA[
      K((x \ y) \ (z * u),L(z,u,x)) = K(y \ (x * (z * u)),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6894,a(flip),b,9288,a),flip(a)].">
      <j1 rule="hyper" parents="58 6894 9288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9293">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(y,z,x)) = x * ((y * z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,9288,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 9288 13"/>
    </justification>
  </clause>

  <clause id="9294">
    <literal><![CDATA[
      L(K(x,y / z),y,u) = K(x,L(y / z,z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),9288(a,1,2))].">
      <j1 rule="para" parents="7 9288"/>
    </justification>
  </clause>

  <clause id="9295">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(x,L(y,K(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(5044(a,1),9288(a,1,2))].">
      <j1 rule="para" parents="5044 9288"/>
    </justification>
  </clause>

  <clause id="9296">
    <literal><![CDATA[
      K(x,L(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y,z),y) = u
    ]]></literal>
    <justification jstring="[para(9288(a,1),8691(a,1))].">
      <j1 rule="para" parents="9288 8691"/>
    </justification>
  </clause>

  <clause id="9297">
    <literal><![CDATA[
      K(x,L(y,z * K(y,u),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(6959,a,9287,a)].">
      <j1 rule="hyper" parents="6959 9287"/>
    </justification>
  </clause>

  <clause id="9298">
    <literal><![CDATA[
      K(x,L(y,K(y,z) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(7423(a,1),9297(a,1,2,2))].">
      <j1 rule="para" parents="7423 9297"/>
    </justification>
  </clause>

  <clause id="9299">
    <literal><![CDATA[
      L(K(x,y),z * K(y,u),w) = L(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[hyper(334,a,6874,a(flip),b,9290,a),flip(a)].">
      <j1 rule="hyper" parents="334 6874 9290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9300">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z * K(x,u),w) = a(w,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(9299(a,2),6201(a,1,2))].">
      <j1 rule="para" parents="9299 6201"/>
    </justification>
  </clause>

  <clause id="9301">
    <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(9299(a,2),8874(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9299 8874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9302">
    <literal><![CDATA[
      T(T(x,K(y,T(z,z))),z \ T(y,z)) = T(x,y / T(z,y))
    ]]></literal>
    <justification jstring="[para(4488(a,1),8606(a,2,2))].">
      <j1 rule="para" parents="4488 8606"/>
    </justification>
  </clause>

  <clause id="9303">
    <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(334,a,8587,a(flip),b,8623,a),flip(a)].">
      <j1 rule="hyper" parents="334 8587 8623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9304">
    <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(8049(a,1),8649(a,2,2))].">
      <j1 rule="para" parents="8049 8649"/>
    </justification>
  </clause>

  <clause id="9305">
    <literal><![CDATA[
      K(x,y) * T(z,T(x * z,y)) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4834(a,2),8654(a,1,2))].">
      <j1 rule="para" parents="4834 8654"/>
    </justification>
  </clause>

  <clause id="9306">
    <literal><![CDATA[
      T(x,(y \ x) \ (z * x)) = T(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(334,a,5131,a,b,8668,a),flip(a)].">
      <j1 rule="hyper" parents="334 5131 8668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9307">
    <literal><![CDATA[
      T(x,(y \ 1) \ (x \ z)) = x * K(x,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(7913,a,9306,a),flip(a)].">
      <j1 rule="hyper" parents="7913 9306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9308">
    <literal><![CDATA[
      K(x,(y \ 1) \ (x \ z)) = K(x,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(5109,a,9307,a)].">
      <j1 rule="hyper" parents="5109 9307"/>
    </justification>
  </clause>

  <clause id="9309">
    <literal><![CDATA[
      K(x / y,z \ (y \ x)) = K(y \ x,y \ (z \ x))
    ]]></literal>
    <justification jstring="[hyper(8323,a,8785,a)].">
      <j1 rule="hyper" parents="8323 8785"/>
    </justification>
  </clause>

  <clause id="9310">
    <literal><![CDATA[
      K(x \ y,(z * x) \ y) = K(x \ y,x \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8955,a(flip),b,9309,a)].">
      <j1 rule="hyper" parents="58 8955 9309"/>
    </justification>
  </clause>

  <clause id="9311">
    <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),9310(a,2,2))].">
      <j1 rule="para" parents="75 9310"/>
    </justification>
  </clause>

  <clause id="9312">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,x \ (x * y)) = K(z / ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[para(4(a,1),8803(a,2,2))].">
      <j1 rule="para" parents="4 8803"/>
    </justification>
  </clause>

  <clause id="9313">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * y))) = ((z * x) * y) \ ((x * z) * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),8811(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 8811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9315">
    <literal><![CDATA[
      T(x * (y \ z),K(y,z)) = (y \ z) * T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5849,a(flip),b,8887,a),flip(a)].">
      <j1 rule="hyper" parents="58 5849 8887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9316">
    <literal><![CDATA[
      K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(8340,a,8896,a),flip(a)].">
      <j1 rule="hyper" parents="8340 8896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9317">
    <literal><![CDATA[
      K(x,T(y,z \ (x * u))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8533,a(flip),b,9316,a)].">
      <j1 rule="hyper" parents="58 8533 9316"/>
    </justification>
  </clause>

  <clause id="9318">
    <literal><![CDATA[
      K(x,T(y,(x * z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(4(a,1),9316(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 9316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9319">
    <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),9318(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 9318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9320">
    <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(8913(a,1),502(a,1,1,1))].">
      <j1 rule="para" parents="8913 502"/>
    </justification>
  </clause>

  <clause id="9321">
    <literal><![CDATA[
      K((T(x,y) \ y) \ z,u) = K((x \ T(y,x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(7674,a,8916,a),flip(a)].">
      <j1 rule="hyper" parents="7674 8916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9322">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(x,K(w,z \ (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,8053,a(flip),b,8938,a),flip(a)].">
      <j1 rule="hyper" parents="334 8053 8938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9323">
    <literal><![CDATA[
      K(x,(((x \ y) * x) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(8949(a,1),8829(a,1,2,1))].">
      <j1 rule="para" parents="8949 8829"/>
    </justification>
  </clause>

  <clause id="9324">
    <literal><![CDATA[
      K(x,T(y \ T(T(x,z),u),w)) = K(T(x,w),y \ T(x,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,7403,a,b,8980,a),flip(a)].">
      <j1 rule="hyper" parents="334 7403 8980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9325">
    <literal><![CDATA[
      K(x,T(y \ T(T(x,z),u),w)) = K(x,T(y \ x,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,8979,a(flip),b,8980,a),flip(a)].">
      <j1 rule="hyper" parents="334 8979 8980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9327">
    <literal><![CDATA[
      K(x,K(y * (z / u),u)) = K(x,K(u,(y * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(8673,a,8992,a),flip(a)].">
      <j1 rule="hyper" parents="8673 8992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9328">
    <literal><![CDATA[
      K(x,K(y * (z / u),u)) = K(x,K(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,8425,a(flip),b,9327,a),flip(a)].">
      <j1 rule="hyper" parents="334 8425 9327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9329">
    <literal><![CDATA[
      K(x,y) * K(x,K(z * u,y)) = K(x,T(y,z * (u / y)))
    ]]></literal>
    <justification jstring="[para(9328(a,1),8085(a,1,2))].">
      <j1 rule="para" parents="9328 8085"/>
    </justification>
  </clause>

  <clause id="9330">
    <literal><![CDATA[
      T(K(x \ y,x) * z,y) = K(x \ y,x) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6560,a,9048,a),flip(a)].">
      <j1 rule="hyper" parents="6560 9048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9331">
    <literal><![CDATA[
      T(K(x \ (y * x),x) * z,y * x) = K(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(5234(a,1),9330(a,2,1))].">
      <j1 rule="para" parents="5234 9330"/>
    </justification>
  </clause>

  <clause id="9332">
    <literal><![CDATA[
      K(T(x,y \ z),R(y,u,w)) = K(T(x,z),R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(5253,a,9058,a),flip(a)].">
      <j1 rule="hyper" parents="5253 9058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9333">
    <literal><![CDATA[
      K(x,y) * ((y * R(x,z,u)) * x) = (x * y) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(1951(a,2),9065(a,1,2))].">
      <j1 rule="para" parents="1951 9065"/>
    </justification>
  </clause>

  <clause id="9334">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (R(x,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(334,a,7821,a(flip),b,9069,a),flip(a)].">
      <j1 rule="hyper" parents="334 7821 9069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9335">
    <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(334,a,22,a,b,9070,a),flip(a)].">
      <j1 rule="hyper" parents="334 22 9070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9336">
    <literal><![CDATA[
      L(x \ y,z,T(x \ y,u)) = L(x \ y,z,y / x)
    ]]></literal>
    <justification jstring="[hyper(888,a,9072,a),flip(a)].">
      <j1 rule="hyper" parents="888 9072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9337">
    <literal><![CDATA[
      L(x \ y,z,y / x) = L(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7750,a(flip),b,9336,a),flip(a)].">
      <j1 rule="hyper" parents="58 7750 9336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9338">
    <literal><![CDATA[
      L(x \ y,x,x \ y) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(783,a,9337,a),flip(a)].">
      <j1 rule="hyper" parents="783 9337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9339">
    <literal><![CDATA[
      L(T(x \ y,z),x,x \ y) = T(T(y / x,y),z)
    ]]></literal>
    <justification jstring="[para(9338(a,1),20(a,2,1))].">
      <j1 rule="para" parents="9338 20"/>
    </justification>
  </clause>

  <clause id="9340">
    <literal><![CDATA[
      T(x / y,z) * T(y,K(x,z)) = x * K(x / y,z)
    ]]></literal>
    <justification jstring="[para(8313(a,1),9091(a,1,2))].">
      <j1 rule="para" parents="8313 9091"/>
    </justification>
  </clause>

  <clause id="9341">
    <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(4488(a,2),9340(a,2,2,1))].">
      <j1 rule="para" parents="4488 9340"/>
    </justification>
  </clause>

  <clause id="9342">
    <literal><![CDATA[
      R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(334,a,8441,a(flip),b,9093,a),flip(a)].">
      <j1 rule="hyper" parents="334 8441 9093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9343">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[para(8441(a,1),9342(a,1,1))].">
      <j1 rule="para" parents="8441 9342"/>
    </justification>
  </clause>

  <clause id="9344">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(y,K(z,R(x,u,w)))
    ]]></literal>
    <justification jstring="[para(8444(a,1),9342(a,1,1))].">
      <j1 rule="para" parents="8444 9342"/>
    </justification>
  </clause>

  <clause id="9345">
    <literal><![CDATA[
      K(x,R(K(y,z),u,w)) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,9096,a(flip),b,9343,a)].">
      <j1 rule="hyper" parents="58 9096 9343"/>
    </justification>
  </clause>

  <clause id="9346">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) = K(z,K(x,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,9343,a(flip),b,9344,a),flip(a)].">
      <j1 rule="hyper" parents="58 9343 9344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9347">
    <literal><![CDATA[
      K(x,R(K(y,z),u,w)) = K(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,9095,a(flip),b,9344,a)].">
      <j1 rule="hyper" parents="58 9095 9344"/>
    </justification>
  </clause>

  <clause id="9348">
    <literal><![CDATA[
      T(x,R(K(y,z),u,w)) = T(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(118,a,9345,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 9345 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9349">
    <literal><![CDATA[
      T(x,R(K(y,z),u,w)) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(118,a,9347,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 9347 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9350">
    <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(6162(a,1),9347(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6162 9347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9351">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w))) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,9348,a(flip),b,9349,a)].">
      <j1 rule="hyper" parents="58 9348 9349"/>
    </justification>
  </clause>

  <clause id="9352">
    <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(9351(a,1),9104(a,2,2))].">
      <j1 rule="para" parents="9351 9104"/>
    </justification>
  </clause>

  <clause id="9353">
    <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(9126(a,2),8333(a,1))].">
      <j1 rule="para" parents="9126 8333"/>
    </justification>
  </clause>

  <clause id="9354">
    <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),9353(a,1,2,1))].">
      <j1 rule="para" parents="104 9353"/>
    </justification>
  </clause>

  <clause id="9355">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(y * z,y)) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,6917,a(flip),b,9214,a),flip(a)].">
      <j1 rule="hyper" parents="334 6917 9214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9356">
    <literal><![CDATA[
      (x / y) * a(y,z,y) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(9160(a,1),9355(a,1,2))].">
      <j1 rule="para" parents="9160 9355"/>
    </justification>
  </clause>

  <clause id="9357">
    <literal><![CDATA[
      L(x,y,x) \ x = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,3969,a,b,9356,a)].">
      <j1 rule="hyper" parents="29 3969 9356"/>
    </justification>
  </clause>

  <clause id="9358">
    <literal><![CDATA[
      (x * y) / L(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),9356(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 9356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9359">
    <literal><![CDATA[
      L(x,y,x) \ 1 = x \ a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,9357,a(flip),b,1510,a),flip(a)].">
      <j1 rule="hyper" parents="116 9357 1510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9360">
    <literal><![CDATA[
      a(x,y,x) \ x = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(9357(a,1),3960(a,1,1))].">
      <j1 rule="para" parents="9357 3960"/>
    </justification>
  </clause>

  <clause id="9361">
    <literal><![CDATA[
      L(x \ L(y,z,y),x,a(y,z,y)) = (a(y,z,y) * x) \ y
    ]]></literal>
    <justification jstring="[para(9360(a,1),311(a,1,1,2))].">
      <j1 rule="para" parents="9360 311"/>
    </justification>
  </clause>

  <clause id="9362">
    <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(9360(a,1),1387(a,2,1))].">
      <j1 rule="para" parents="9360 1387"/>
    </justification>
  </clause>

  <clause id="9363">
    <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(9359(a,1),7056(a,1,1,2))].">
      <j1 rule="para" parents="9359 7056"/>
    </justification>
  </clause>

  <clause id="9364">
    <literal><![CDATA[
      (x / L(y,z,y)) * y = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(1712,a,9358,a)].">
      <j1 rule="hyper" parents="1712 9358"/>
    </justification>
  </clause>

  <clause id="9365">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (x * y) = L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(192,a,9358,a)].">
      <j1 rule="hyper" parents="192 9358"/>
    </justification>
  </clause>

  <clause id="9366">
    <literal><![CDATA[
      x * (L(x,y,x) \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7770,a(flip),b,9364,a)].">
      <j1 rule="hyper" parents="58 7770 9364"/>
    </justification>
  </clause>

  <clause id="9367">
    <literal><![CDATA[
      (x * L(y,z,y)) * a(y,z,y) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),9364(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 9364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9368">
    <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(939(a,1),9365(a,1,2))].">
      <j1 rule="para" parents="939 9365"/>
    </justification>
  </clause>

  <clause id="9369">
    <literal><![CDATA[
      (T(x * y,x) / x) \ (y * x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(9174(a,2),9365(a,1,1))].">
      <j1 rule="para" parents="9174 9365"/>
    </justification>
  </clause>

  <clause id="9370">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = z / a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(586,a,9366,a),flip(a)].">
      <j1 rule="hyper" parents="586 9366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9371">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = u * a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8816,a,b,9366,a)].">
      <j1 rule="hyper" parents="58 8816 9366"/>
    </justification>
  </clause>

  <clause id="9372">
    <literal><![CDATA[
      L(x,y,x) \ (x * z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1509,a,b,9366,a)].">
      <j1 rule="hyper" parents="58 1509 9366"/>
    </justification>
  </clause>

  <clause id="9373">
    <literal><![CDATA[
      K(x,y) * (z * a(x,u,x)) = T(x,y) * (L(x,u,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,9366,a(flip),b,5049,a)].">
      <j1 rule="hyper" parents="119 9366 5049"/>
    </justification>
  </clause>

  <clause id="9374">
    <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(7762(a,1),9366(a,1,2,1))].">
      <j1 rule="para" parents="7762 9366"/>
    </justification>
  </clause>

  <clause id="9375">
    <literal><![CDATA[
      (x / y) \ (x / a(y,z,y)) = L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,9370,a(flip),b,7771,a(flip))].">
      <j1 rule="hyper" parents="116 9370 7771"/>
    </justification>
  </clause>

  <clause id="9376">
    <literal><![CDATA[
      (x \ y) * a(x,z,x) = L(x,z,x) \ y
    ]]></literal>
    <justification jstring="[para(5(a,1),9372(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 9372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9377">
    <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(8229(a,1),9369(a,1,2))].">
      <j1 rule="para" parents="8229 9369"/>
    </justification>
  </clause>

  <clause id="9378">
    <literal><![CDATA[
      K(x,y) * (z * a(y,u,y)) = y * (L(T(y,x),u,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,9371,a(flip),b,5360,a)].">
      <j1 rule="hyper" parents="119 9371 5360"/>
    </justification>
  </clause>

  <clause id="9379">
    <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(9371(a,2),38(a,1))].">
      <j1 rule="para" parents="9371 38"/>
    </justification>
  </clause>

  <clause id="9380">
    <literal><![CDATA[
      (x * y) * (K(y,z) * K(u,y)) = x * (K(u,y) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,6356,a(flip),b,9228,a),flip(a)].">
      <j1 rule="hyper" parents="334 6356 9228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9381">
    <literal><![CDATA[
      K(T(x,y),z) * ((y * z) / y) = (y * (z * K(x,z))) / y
    ]]></literal>
    <justification jstring="[hyper(133,a,9272,a)].">
      <j1 rule="hyper" parents="133 9272"/>
    </justification>
  </clause>

  <clause id="9382">
    <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(9279(a,1),6361(a,1,1))].">
      <j1 rule="para" parents="9279 6361"/>
    </justification>
  </clause>

  <clause id="9383">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,9298,a(flip),b,9295,a),flip(a)].">
      <j1 rule="hyper" parents="334 9298 9295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9385">
    <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(6910(a,1),9383(a,1,1))].">
      <j1 rule="para" parents="6910 9383"/>
    </justification>
  </clause>

  <clause id="9386">
    <literal><![CDATA[
      a(x,y * K(z,u),K(z,w)) = a(x,y,K(z,w))
    ]]></literal>
    <justification jstring="[hyper(6208,a,9300,a)].">
      <j1 rule="hyper" parents="6208 9300"/>
    </justification>
  </clause>

  <clause id="9387">
    <literal><![CDATA[
      a(x,y * K(z,u),K(u,w)) = a(x,y,K(u,w))
    ]]></literal>
    <justification jstring="[para(6516(a,1),9386(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6516 9386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9388">
    <literal><![CDATA[
      (x * y) \ ((x * (y * K(z,u))) * K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6526,a,b,9387,a)].">
      <j1 rule="hyper" parents="58 6526 9387"/>
    </justification>
  </clause>

  <clause id="9389">
    <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(334,a,8043,a,b,9301,a),flip(a)].">
      <j1 rule="hyper" parents="334 8043 9301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9390">
    <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),9302(a,1,1,2,2))].">
      <j1 rule="para" parents="104 9302"/>
    </justification>
  </clause>

  <clause id="9391">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(x,K(w,u \ z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8895,a(flip),b,9322,a),flip(a)].">
      <j1 rule="hyper" parents="334 8895 9322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9392">
    <literal><![CDATA[
      K(x,K(y,(T(x,z) * u) \ w)) = K(x,K(y,w \ u))
    ]]></literal>
    <justification jstring="[hyper(8089,a,9391,a)].">
      <j1 rule="hyper" parents="8089 9391"/>
    </justification>
  </clause>

  <clause id="9393">
    <literal><![CDATA[
      K(T(x,y),z \ T(T(x,u),w)) = K(T(x,y),z \ T(x,w))
    ]]></literal>
    <justification jstring="[hyper(7561,a,9324,a)].">
      <j1 rule="hyper" parents="7561 9324"/>
    </justification>
  </clause>

  <clause id="9394">
    <literal><![CDATA[
      K(x,T(y,z * (u / y))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(8355,a,9329,a),flip(a)].">
      <j1 rule="hyper" parents="8355 9329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9395">
    <literal><![CDATA[
      K(x,T(y,z * (u * y))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(6(a,1),9394(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6 9394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9396">
    <literal><![CDATA[
      K(x,T(y \ z,u * z)) = K(x,T(y \ z,u * y))
    ]]></literal>
    <justification jstring="[para(72(a,1),9394(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="72 9394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9397">
    <literal><![CDATA[
      K(x,T(y,z * (y * u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(7378(a,1),9395(a,1,2))].">
      <j1 rule="para" parents="7378 9395"/>
    </justification>
  </clause>

  <clause id="9398">
    <literal><![CDATA[
      K(x * y,T(x,z * y)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(7988,a,9397,a),flip(a)].">
      <j1 rule="hyper" parents="7988 9397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9400">
    <literal><![CDATA[
      K(x * y,T(y,z * x)) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6194,a,b,9398,a)].">
      <j1 rule="hyper" parents="58 6194 9398"/>
    </justification>
  </clause>

  <clause id="9401">
    <literal><![CDATA[
      K(x,T(y \ x,z * y)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(7988,a,9396,a),flip(a)].">
      <j1 rule="hyper" parents="7988 9396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9402">
    <literal><![CDATA[
      K(x,T(y \ x,z / y)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),9401(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 9401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9403">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8574,a(flip),b,9402,a)].">
      <j1 rule="hyper" parents="58 8574 9402"/>
    </justification>
  </clause>

  <clause id="9404">
    <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,9335,a(flip),b,5363,a),flip(a)].">
      <j1 rule="hyper" parents="116 9335 5363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9405">
    <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(9335(a,1),7343(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9335 7343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9406">
    <literal><![CDATA[
      K(x,x * y) * (z * a(x,y,x)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(334,a,6182,a(flip),b,9373,a),flip(a)].">
      <j1 rule="hyper" parents="334 6182 9373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9407">
    <literal><![CDATA[
      K(x,x * y) * z != K(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      u * a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(9406(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="9406 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9408">
    <literal><![CDATA[
      K(x,y) * (z * L(x,y,x)) = K(x,x * y) * (z * x)
    ]]></literal>
    <justification jstring="[para(9367(a,1),9406(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9367 9406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9409">
    <literal><![CDATA[
      (x * y) * (K(y,z) * K(y * z,y)) = x * R(y,z,y)
    ]]></literal>
    <justification jstring="[para(5355(a,1),9380(a,2,2))].">
      <j1 rule="para" parents="5355 9380"/>
    </justification>
  </clause>

  <clause id="9410">
    <literal><![CDATA[
      (x * y) * a(y,z,y) = x * R(y,z,y)
    ]]></literal>
    <justification jstring="[para(9160(a,1),9409(a,1,2))].">
      <j1 rule="para" parents="9160 9409"/>
    </justification>
  </clause>

  <clause id="9411">
    <literal><![CDATA[
      (x / y) * R(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(341,a,9410,a),flip(a)].">
      <j1 rule="hyper" parents="341 9410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9412">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z,y)) = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,9410,a)].">
      <j1 rule="hyper" parents="123 9410"/>
    </justification>
  </clause>

  <clause id="9413">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,9410,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 9410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9414">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7382,a,b,9411,a)].">
      <j1 rule="hyper" parents="58 7382 9411"/>
    </justification>
  </clause>

  <clause id="9415">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (x * R(y,z,y)) = y
    ]]></literal>
    <justification jstring="[para(9411(a,1),1957(a,1,1))].">
      <j1 rule="para" parents="9411 1957"/>
    </justification>
  </clause>

  <clause id="9416">
    <literal><![CDATA[
      (x / y) * ((y \ z) \ T(z,y)) = x * a(y,y \ z,y)
    ]]></literal>
    <justification jstring="[para(4581(a,1),9411(a,1,2))].">
      <j1 rule="para" parents="4581 9411"/>
    </justification>
  </clause>

  <clause id="9417">
    <literal><![CDATA[
      K(x,y) * ((z / y) * R(y,u,y)) = y * (L(T(y,x),u,y) \ z)
    ]]></literal>
    <justification jstring="[para(9411(a,2),9378(a,1,2))].">
      <j1 rule="para" parents="9411 9378"/>
    </justification>
  </clause>

  <clause id="9418">
    <literal><![CDATA[
      (x * y) * a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x * R(y,z,y) = u
    ]]></literal>
    <justification jstring="[para(9412(a,1),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9412 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9419">
    <literal><![CDATA[
      x * (y \ L(y,z,y)) = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9234,a(flip),b,9413,a)].">
      <j1 rule="hyper" parents="58 9234 9413"/>
    </justification>
  </clause>

  <clause id="9420">
    <literal><![CDATA[
      (x * y) * a(x,z,x) = R(x,z,x) * y
    ]]></literal>
    <justification jstring="[hyper(597,a,9414,a),flip(a)].">
      <j1 rule="hyper" parents="597 9414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9421">
    <literal><![CDATA[
      (R(x,y,x) \ z) * a(x,y,x) = x \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,1367,a(flip),b,9414,a),flip(a)].">
      <j1 rule="hyper" parents="58 1367 9414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9422">
    <literal><![CDATA[
      x * (y * a(x,z,x)) = R(x,z,x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,9414,a(flip),b,1366,a)].">
      <j1 rule="hyper" parents="119 9414 1366"/>
    </justification>
  </clause>

  <clause id="9423">
    <literal><![CDATA[
      (x / R(y,z,y)) * a(y,z,y) = x / y
    ]]></literal>
    <justification jstring="[para(9415(a,1),338(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9415 338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9424">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z,y))) / x) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(9381(a,1),5403(a,1,2))].">
      <j1 rule="para" parents="9381 5403"/>
    </justification>
  </clause>

  <clause id="9425">
    <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(9393(a,1),7970(a,1))].">
      <j1 rule="para" parents="9393 7970"/>
    </justification>
  </clause>

  <clause id="9426">
    <literal><![CDATA[
      K(x,T((y \ z) / z,u)) = ((u * x) / u) / ((u * (x * K(y \ 1,x))) / u)
    ]]></literal>
    <justification jstring="[para(5709(a,1),9424(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5709 9424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9427">
    <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(9248(a,1),9424(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9248 9424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9428">
    <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),7387(a,1,2,1,1))].">
      <j1 rule="para" parents="72 7387"/>
    </justification>
  </clause>

  <clause id="9429">
    <literal><![CDATA[
      L(x,T(y,K(x,z)),x) = T(x,x * y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(8145(a,1),7395(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8145 7395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9430">
    <literal><![CDATA[
      L(x,T(y,K(x,z)),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,5547,a(flip),b,9429,a),flip(a)].">
      <j1 rule="hyper" parents="334 5547 9429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9432">
    <literal><![CDATA[
      L(x,T(y,T(x,z)),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7696,a(flip),b,9430,a)].">
      <j1 rule="hyper" parents="58 7696 9430"/>
    </justification>
  </clause>

  <clause id="9434">
    <literal><![CDATA[
      L(x,y / T(x,z),x) = L(x,T(x,z) \ y,x)
    ]]></literal>
    <justification jstring="[para(107(a,1),9432(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 9432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9435">
    <literal><![CDATA[
      L(K(x,T((y \ z) \ u,w)),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[para(7401(a,2),7404(a,1,1))].">
      <j1 rule="para" parents="7401 7404"/>
    </justification>
  </clause>

  <clause id="9436">
    <literal><![CDATA[
      L(K(x,T(y \ z,u)),y \ z,w) = K(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(7401(a,2),7405(a,1,1))].">
      <j1 rule="para" parents="7401 7405"/>
    </justification>
  </clause>

  <clause id="9437">
    <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(334,a,7403,a(flip),b,7463,a),flip(a)].">
      <j1 rule="hyper" parents="334 7403 7463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9439">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * x,x)
    ]]></literal>
    <justification jstring="[para(7591(a,1),7499(a,2,2))].">
      <j1 rule="para" parents="7591 7499"/>
    </justification>
  </clause>

  <clause id="9440">
    <literal><![CDATA[
      R(x,y * K(x,z),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5763,a,9439,a),flip(a)].">
      <j1 rule="hyper" parents="5763 9439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9442">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,9440,a(flip),b,9162,a),flip(a)].">
      <j1 rule="hyper" parents="116 9440 9162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9443">
    <literal><![CDATA[
      a(x,y * K(x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9442(a,2),9176(a,1))].">
      <j1 rule="para" parents="9442 9176"/>
    </justification>
  </clause>

  <clause id="9444">
    <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(5896(a,1),7792(a,1,2,1))].">
      <j1 rule="para" parents="5896 7792"/>
    </justification>
  </clause>

  <clause id="9445">
    <literal><![CDATA[
      T((x \ 1) * y,K(x,z)) = (x \ 1) * T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(869,a,7909,a),flip(a)].">
      <j1 rule="hyper" parents="869 7909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9446">
    <literal><![CDATA[
      K(x,y) * T((x \ 1) * z,K(x,y)) = (x \ 1) * (z * K(x,y))
    ]]></literal>
    <justification jstring="[para(9445(a,2),6308(a,1,2))].">
      <j1 rule="para" parents="9445 6308"/>
    </justification>
  </clause>

  <clause id="9447">
    <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(5902(a,1),8177(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5902 8177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9448">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = (u * (K(x,y) * z)) / (u * z)
    ]]></literal>
    <justification jstring="[para(7423(a,1),8259(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7423 8259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9449">
    <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(8334,a,8589,a),flip(a)].">
      <j1 rule="hyper" parents="8334 8589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9450">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(7217(a,1),8720(a,1))].">
      <j1 rule="para" parents="7217 8720"/>
    </justification>
  </clause>

  <clause id="9451">
    <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(8048(a,1),8746(a,1,1))].">
      <j1 rule="para" parents="8048 8746"/>
    </justification>
  </clause>

  <clause id="9452">
    <literal><![CDATA[
      x * K(y,(x \ 1) * (z * x)) = K(y,L(z,x,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(5583(a,1),8802(a,1,2))].">
      <j1 rule="para" parents="5583 8802"/>
    </justification>
  </clause>

  <clause id="9453">
    <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(648(a,1),8839(a,1,2))].">
      <j1 rule="para" parents="648 8839"/>
    </justification>
  </clause>

  <clause id="9454">
    <literal><![CDATA[
      K(x,a(K(x,y),z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,5776,a(flip),b,9453,a),flip(a)].">
      <j1 rule="hyper" parents="58 5776 9453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9455">
    <literal><![CDATA[
      T(a(K(x,y),z,u),x) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(5077,a,9454,a)].">
      <j1 rule="hyper" parents="5077 9454"/>
    </justification>
  </clause>

  <clause id="9456">
    <literal><![CDATA[
      a(K(x,y),z,u) * x = x * a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(552,a,9454,a)].">
      <j1 rule="hyper" parents="552 9454"/>
    </justification>
  </clause>

  <clause id="9458">
    <literal><![CDATA[
      T(x,a(K(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,9454,a)].">
      <j1 rule="hyper" parents="51 9454"/>
    </justification>
  </clause>

  <clause id="9459">
    <literal><![CDATA[
      T(T(x,y),a(K(x,z),u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(9458(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9458 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9460">
    <literal><![CDATA[
      K(x,y) * a(K(x,z),u,w) = a(K(x,z),u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[para(9458(a,1),7393(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9458 7393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9461">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) * x = x * K(a(K(x,y),z,u),w)
    ]]></literal>
    <justification jstring="[para(9455(a,1),7393(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9455 7393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9462">
    <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(8936(a,1),8019(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8936 8019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9463">
    <literal><![CDATA[
      K(x,L(x,y,y \ 1) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(165(a,1),8947(a,1,2)),flip(a)].">
      <j1 rule="para" parents="165 8947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9465">
    <literal><![CDATA[
      K((x \ 1) \ y,((x \ 1) \ y) \ z) = K((x \ 1) \ y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(3166(a,1),9463(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3166 9463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9466">
    <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,9143,a,b,9012,a)].">
      <j1 rule="hyper" parents="58 9143 9012"/>
    </justification>
  </clause>

  <clause id="9467">
    <literal><![CDATA[
      K(x,y) * (y \ R(y,x,L(y,z,u))) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(5409,a,9013,a)].">
      <j1 rule="hyper" parents="5409 9013"/>
    </justification>
  </clause>

  <clause id="9468">
    <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(9013(a,1),2067(a,1))].">
      <j1 rule="para" parents="9013 2067"/>
    </justification>
  </clause>

  <clause id="9469">
    <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,9143,a,b,9016,a)].">
      <j1 rule="hyper" parents="58 9143 9016"/>
    </justification>
  </clause>

  <clause id="9470">
    <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(9017(a,1),2067(a,1))].">
      <j1 rule="para" parents="9017 2067"/>
    </justification>
  </clause>

  <clause id="9471">
    <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(491(a,1),9125(a,2,2))].">
      <j1 rule="para" parents="491 9125"/>
    </justification>
  </clause>

  <clause id="9472">
    <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(856,a,9133,a)].">
      <j1 rule="hyper" parents="856 9133"/>
    </justification>
  </clause>

  <clause id="9473">
    <literal><![CDATA[
      K(R(x,y / x,z),u) = K((y * z) / ((y / x) * z),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(8281,a,9285,a)].">
      <j1 rule="hyper" parents="8281 9285"/>
    </justification>
  </clause>

  <clause id="9474">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(y,z,x)) = x * (y * (z * K(u,y)))
    ]]></literal>
    <justification jstring="[para(7293(a,1),9293(a,2,2))].">
      <j1 rule="para" parents="7293 9293"/>
    </justification>
  </clause>

  <clause id="9475">
    <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(648(a,1),9319(a,1,2,2))].">
      <j1 rule="para" parents="648 9319"/>
    </justification>
  </clause>

  <clause id="9476">
    <literal><![CDATA[
      K(x,T(y,a(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8331,a,9475,a),flip(a)].">
      <j1 rule="hyper" parents="8331 9475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9477">
    <literal><![CDATA[
      K(x,y / a(x,z,u)) = K(x,a(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(8328,a,9476,a)].">
      <j1 rule="hyper" parents="8328 9476"/>
    </justification>
  </clause>

  <clause id="9480">
    <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(334,a,5208,a,b,9388,a)].">
      <j1 rule="hyper" parents="334 5208 9388"/>
    </justification>
  </clause>

  <clause id="9481">
    <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,9388,a(flip),b,156,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 9388 156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9482">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,u)) = K(x,T(z \ (y * x),u))
    ]]></literal>
    <justification jstring="[hyper(6433,a,9435,a)].">
      <j1 rule="hyper" parents="6433 9435"/>
    </justification>
  </clause>

  <clause id="9483">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,y)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,8766,a(flip),b,9482,a),flip(a)].">
      <j1 rule="hyper" parents="334 8766 9482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9484">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(9482(a,2),8786(a,1))].">
      <j1 rule="para" parents="9482 8786"/>
    </justification>
  </clause>

  <clause id="9485">
    <literal><![CDATA[
      K(x,((y * z) / y) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(4(a,1),9483(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4 9483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9486">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,(z / (z / y)) \ x)
    ]]></literal>
    <justification jstring="[para(4548(a,1),9485(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4548 9485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9487">
    <literal><![CDATA[
      K(x,T((y / (z * y)) \ x,z)) = K(x,R(1 / (1 / (1 / z)),z,y) \ x)
    ]]></literal>
    <justification jstring="[para(4657(a,2),9485(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4657 9485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9488">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9403,a(flip),b,9486,a),flip(a)].">
      <j1 rule="hyper" parents="58 9403 9486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9489">
    <literal><![CDATA[
      K(x,T(y \ x,x * z)) = K(x,((x * z) / y) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8758,a(flip),b,9488,a),flip(a)].">
      <j1 rule="hyper" parents="58 8758 9488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9490">
    <literal><![CDATA[
      K(x,((x * y) / z) / y) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(7976,a,9489,a),flip(a)].">
      <j1 rule="hyper" parents="7976 9489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9491">
    <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,9054,a(flip),b,9490,a)].">
      <j1 rule="hyper" parents="58 9054 9490"/>
    </justification>
  </clause>

  <clause id="9492">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,u)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(7644,a,9436,a),flip(a)].">
      <j1 rule="hyper" parents="7644 9436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9493">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ y,u)) = w
    ]]></literal>
    <justification jstring="[para(9436(a,1),3811(a,1))].">
      <j1 rule="para" parents="9436 3811"/>
    </justification>
  </clause>

  <clause id="9494">
    <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,7876,a,b,9492,a)].">
      <j1 rule="hyper" parents="58 7876 9492"/>
    </justification>
  </clause>

  <clause id="9495">
    <literal><![CDATA[
      K(x,T(y,z * R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9067,a(flip),b,9437,a)].">
      <j1 rule="hyper" parents="58 9067 9437"/>
    </justification>
  </clause>

  <clause id="9497">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),9495(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 9495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9498">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,7986,a(flip),b,9497,a)].">
      <j1 rule="hyper" parents="58 7986 9497"/>
    </justification>
  </clause>

  <clause id="9500">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(4(a,1),9498(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 9498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9501">
    <literal><![CDATA[
      K(x,T(y,(x * z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(187(a,1),9498(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="187 9498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9502">
    <literal><![CDATA[
      K(x,T(y \ (R(x,z,u) * w),w)) = K(x,(R(x,z,u) * w) / y)
    ]]></literal>
    <justification jstring="[hyper(8543,a,9500,a),flip(a)].">
      <j1 rule="hyper" parents="8543 9500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9503">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,y) * K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,8033,a,b,9500,a),flip(a)].">
      <j1 rule="hyper" parents="334 8033 9500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9504">
    <literal><![CDATA[
      K(x,T(y,(z * x) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8825,a,b,9501,a)].">
      <j1 rule="hyper" parents="58 8825 9501"/>
    </justification>
  </clause>

  <clause id="9505">
    <literal><![CDATA[
      K(x,T(y / ((z * x) * u),z * u)) = K(x,((z * x) * u) \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),9504(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 9504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9506">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(8344,a,9503,a)].">
      <j1 rule="hyper" parents="8344 9503"/>
    </justification>
  </clause>

  <clause id="9507">
    <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(9503(a,2),8340(a,1))].">
      <j1 rule="para" parents="9503 8340"/>
    </justification>
  </clause>

  <clause id="9508">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),9506(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 9506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9509">
    <literal><![CDATA[
      K(x,K(y,(x * z) * u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(101(a,1),9506(a,1,2,2))].">
      <j1 rule="para" parents="101 9506"/>
    </justification>
  </clause>

  <clause id="9510">
    <literal><![CDATA[
      K(x,K(y,z \ R(x,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8487,a,9508,a)].">
      <j1 rule="hyper" parents="8487 9508"/>
    </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(75(a,1),9510(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 9510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9512">
    <literal><![CDATA[
      K(x,K(y,z * R(x,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8485,a,9511,a),flip(a)].">
      <j1 rule="hyper" parents="8485 9511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9513">
    <literal><![CDATA[
      K(x,K(y,(y * z) * u)) = K(y,K(x,z * u))
    ]]></literal>
    <justification jstring="[hyper(8050,a,9509,a)].">
      <j1 rule="hyper" parents="8050 9509"/>
    </justification>
  </clause>

  <clause id="9514">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9029,a(flip),b,9449,a)].">
      <j1 rule="hyper" parents="58 9029 9449"/>
    </justification>
  </clause>

  <clause id="9516">
    <literal><![CDATA[
      K(x,T(y,z * (u * x))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9007,a(flip),b,9514,a)].">
      <j1 rule="hyper" parents="58 9007 9514"/>
    </justification>
  </clause>

  <clause id="9518">
    <literal><![CDATA[
      K(x,T(y,z * (x * u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,7888,a(flip),b,9516,a)].">
      <j1 rule="hyper" parents="58 7888 9516"/>
    </justification>
  </clause>

  <clause id="9519">
    <literal><![CDATA[
      K(x,T(y,z * (u / x))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(7(a,1),9516(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7 9516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9520">
    <literal><![CDATA[
      K(x,T(y,z * u)) * (z * (u * x)) = (z * (u * x)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(9516(a,1),8170(a,1,1))].">
      <j1 rule="para" parents="9516 8170"/>
    </justification>
  </clause>

  <clause id="9521">
    <literal><![CDATA[
      K(x,T(y,z * (x \ u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(5(a,1),9518(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 9518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9522">
    <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(9521(a,1),8328(a,1))].">
      <j1 rule="para" parents="9521 8328"/>
    </justification>
  </clause>

  <clause id="9523">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(8174,a,9452,a)].">
      <j1 rule="hyper" parents="8174 9452"/>
    </justification>
  </clause>

  <clause id="9524">
    <literal><![CDATA[
      R(K(x,T(T(y,z),z)),z,u) = K(R(x,z / x,u),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,8287,a(flip),b,9473,a)].">
      <j1 rule="hyper" parents="334 8287 9473"/>
    </justification>
  </clause>

  <clause id="9525">
    <literal><![CDATA[
      K(R(x,y / x,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(8157(a,1),9524(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8157 9524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9527">
    <literal><![CDATA[
      R(K(x,y),z * x,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(6(a,1),9525(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6 9525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9528">
    <literal><![CDATA[
      K(x,R(y,z / y,u)) = w / (R(K(y,x),z,u) * w)
    ]]></literal>
    <justification jstring="[para(9525(a,1),5403(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9525 5403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9529">
    <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(7597(a,1),9527(a,1,1))].">
      <j1 rule="para" parents="7597 9527"/>
    </justification>
  </clause>

  <clause id="9530">
    <literal><![CDATA[
      K(x,R(y,z / y,u)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,6214,a(flip),b,9528,a),flip(a)].">
      <j1 rule="hyper" parents="334 6214 9528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9531">
    <literal><![CDATA[
      K(x,R(y,z / y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(9528(a,2),6217(a,1))].">
      <j1 rule="para" parents="9528 6217"/>
    </justification>
  </clause>

  <clause id="9532">
    <literal><![CDATA[
      K(x,R(y,z / y,u)) = K(x,R(y,y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,6164,a,b,9530,a),flip(a)].">
      <j1 rule="hyper" parents="334 6164 9530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9533">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(6(a,1),9530(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 9530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9534">
    <literal><![CDATA[
      R(K(x,y \ z),z,u) = K(x,R(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),9530(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 9530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9535">
    <literal><![CDATA[
      R(K(x,y),z * K(u,y),w) = K(x,R(y,z / T(y,u),w))
    ]]></literal>
    <justification jstring="[para(6379(a,1),9530(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6379 9530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9536">
    <literal><![CDATA[
      R(K(x,y),z * T(y,u),w) = K(x,R(y,z * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(6555(a,1),9530(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6555 9530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9537">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(T(x,w),R(T(y,w),z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,8198,a,b,9533,a),flip(a)].">
      <j1 rule="hyper" parents="334 8198 9533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9538">
    <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(7493(a,1),9533(a,1,1))].">
      <j1 rule="para" parents="7493 9533"/>
    </justification>
  </clause>

  <clause id="9539">
    <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(4040(a,1),9534(a,2,2))].">
      <j1 rule="para" parents="4040 9534"/>
    </justification>
  </clause>

  <clause id="9540">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(9532(a,1),9531(a,1))].">
      <j1 rule="para" parents="9532 9531"/>
    </justification>
  </clause>

  <clause id="9541">
    <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(187(a,1),9540(a,1,2,2))].">
      <j1 rule="para" parents="187 9540"/>
    </justification>
  </clause>

  <clause id="9542">
    <literal><![CDATA[
      R(K(x,y),z * y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(9537(a,2),8335(a,1))].">
      <j1 rule="para" parents="9537 8335"/>
    </justification>
  </clause>

  <clause id="9543">
    <literal><![CDATA[
      K(x,R(y,z / T(y,u),w)) = R(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,9117,a(flip),b,9535,a),flip(a)].">
      <j1 rule="hyper" parents="58 9117 9535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9545">
    <literal><![CDATA[
      R(K(x,y),z * T(y,u),w) = K(x,R(y,z,w))
    ]]></literal>
    <justification jstring="[para(6(a,1),9543(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 9543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9546">
    <literal><![CDATA[
      K(x,R(y,z * K(y,u),w)) = K(x,R(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9545,a(flip),b,9536,a),flip(a)].">
      <j1 rule="hyper" parents="58 9545 9536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9548">
    <literal><![CDATA[
      K(x,R(y,K(y,z) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(7423(a,1),9546(a,1,2,2))].">
      <j1 rule="para" parents="7423 9546"/>
    </justification>
  </clause>

  <clause id="9549">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = (v5 * K(w,R(x,z,u))) \ v5
    ]]></literal>
    <justification jstring="[para(9548(a,1),6523(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9548 6523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9550">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(334,a,6523,a(flip),b,9549,a),flip(a)].">
      <j1 rule="hyper" parents="334 6523 9549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9551">
    <literal><![CDATA[
      R(K(x,y),K(x,z) * u,w) = K(R(x,x \ u,w),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7055,a(flip),b,9550,a)].">
      <j1 rule="hyper" parents="58 7055 9550"/>
    </justification>
  </clause>

  <clause id="9552">
    <literal><![CDATA[
      K(R(x,K(y,x) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(5394(a,1),9550(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5394 9550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9554">
    <literal><![CDATA[
      R(K(x,y),K(x,z) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(334,a,7053,a(flip),b,9551,a),flip(a)].">
      <j1 rule="hyper" parents="334 7053 9551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9555">
    <literal><![CDATA[
      R(K(x,y),z / x,u) = R(K(x,y),x \ z,u)
    ]]></literal>
    <justification jstring="[para(5129(a,1),9554(a,1,2))].">
      <j1 rule="para" parents="5129 9554"/>
    </justification>
  </clause>

  <clause id="9556">
    <literal><![CDATA[
      R(K(x,y),z * (K(u,x) * w),v5) = R(K(x,y),z * w,v5)
    ]]></literal>
    <justification jstring="[para(6333(a,1),9554(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6333 9554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9557">
    <literal><![CDATA[
      R(K(x,y),x \ y,z) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(9555(a,1),6252(a,1,1))].">
      <j1 rule="para" parents="9555 6252"/>
    </justification>
  </clause>

  <clause id="9558">
    <literal><![CDATA[
      R(K(x,y),z * (u * K(w,x)),v5) = R(K(x,y),z * u,v5)
    ]]></literal>
    <justification jstring="[para(7538(a,1),9556(a,1,2,2))].">
      <j1 rule="para" parents="7538 9556"/>
    </justification>
  </clause>

  <clause id="9559">
    <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(4870(a,2),9474(a,2,2))].">
      <j1 rule="para" parents="4870 9474"/>
    </justification>
  </clause>

  <clause id="9560">
    <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(9557(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="9557 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9561">
    <literal><![CDATA[
      K(L(x,y,z),R(z,u,w)) = K(x,R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,5787,a(flip),b,7317,a),flip(a)].">
      <j1 rule="hyper" parents="334 5787 7317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9562">
    <literal><![CDATA[
      K((x \ 1) \ y,R(x,z,u)) = K(x * y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(501(a,1),9561(a,1,1)),flip(a)].">
      <j1 rule="para" parents="501 9561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9563">
    <literal><![CDATA[
      K((x \ 1) * y,R(x \ 1,z,u)) = K(x \ y,R(x \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(6261,a,9562,a),flip(a)].">
      <j1 rule="hyper" parents="6261 9562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9564">
    <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(7437(a,2),8731(a,1))].">
      <j1 rule="para" parents="7437 8731"/>
    </justification>
  </clause>

  <clause id="9565">
    <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(7448(a,2),7970(a,1))].">
      <j1 rule="para" parents="7448 7970"/>
    </justification>
  </clause>

  <clause id="9566">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * K(z,w) = (x * K(z,w)) * K(y,T(z,u))
    ]]></literal>
    <justification jstring="[para(7403(a,1),7478(a,1,1,2))].">
      <j1 rule="para" parents="7403 7478"/>
    </justification>
  </clause>

  <clause id="9567">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z * (1 / ((x * y) \ x)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4281,a(flip),b,7625,a)].">
      <j1 rule="hyper" parents="58 4281 7625"/>
    </justification>
  </clause>

  <clause id="9568">
    <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(7629(a,1),7803(a,1,1,1,1,2))].">
      <j1 rule="para" parents="7629 7803"/>
    </justification>
  </clause>

  <clause id="9569">
    <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(7861(a,1),8691(a,1))].">
      <j1 rule="para" parents="7861 8691"/>
    </justification>
  </clause>

  <clause id="9570">
    <literal><![CDATA[
      K(x,(y \ K(x,z)) \ u) = (y \ T(y * u,x)) \ u
    ]]></literal>
    <justification jstring="[para(7919(a,1),6402(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7919 6402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9571">
    <literal><![CDATA[
      K(x,(y \ K(x,z)) \ u) = K(x,(y \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(334,a,6687,a(flip),b,9570,a),flip(a)].">
      <j1 rule="hyper" parents="334 6687 9570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9572">
    <literal><![CDATA[
      K(x,((y \ 1) \ K(x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(334,a,5582,a(flip),b,9571,a),flip(a)].">
      <j1 rule="hyper" parents="334 5582 9571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9573">
    <literal><![CDATA[
      K(x,y) * (z * T(z \ (K(x,y) \ u),x)) = z * T(z \ u,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,465,a(flip),b,7920,a),flip(a)].">
      <j1 rule="hyper" parents="334 465 7920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9574">
    <literal><![CDATA[
      (1 / (x \ y)) * K(y / x,z) = K(y / x,z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(8180(a,1),8277(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8180 8277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9575">
    <literal><![CDATA[
      K(1 / x,y) / (x \ 1) = x * K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(359,a,9574,a),flip(a)].">
      <j1 rule="hyper" parents="359 9574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9576">
    <literal><![CDATA[
      1 / (x \ K(y,1 / x)) = x * K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6147,a(flip),b,9575,a)].">
      <j1 rule="hyper" parents="58 6147 9575"/>
    </justification>
  </clause>

  <clause id="9577">
    <literal><![CDATA[
      1 / ((x * (y \ 1)) / x) = y * K(1 / y,x)
    ]]></literal>
    <justification jstring="[para(5169(a,1),9576(a,1,2))].">
      <j1 rule="para" parents="5169 9576"/>
    </justification>
  </clause>

  <clause id="9578">
    <literal><![CDATA[
      1 / ((x * ((y / z) \ 1)) / x) = (y / z) * K(z / y,x)
    ]]></literal>
    <justification jstring="[para(5704(a,1),9577(a,2,2))].">
      <j1 rule="para" parents="5704 9577"/>
    </justification>
  </clause>

  <clause id="9579">
    <literal><![CDATA[
      x / (K(T(y,z),x) * K(x,z)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(5242(a,1),8294(a,1,2,2))].">
      <j1 rule="para" parents="5242 8294"/>
    </justification>
  </clause>

  <clause id="9580">
    <literal><![CDATA[
      T(x * K(y,x),z) \ x = K(T(z,y),x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(192,a,9579,a)].">
      <j1 rule="hyper" parents="192 9579"/>
    </justification>
  </clause>

  <clause id="9582">
    <literal><![CDATA[
      T((x * y) / x,z) \ y = K(T(z,x),y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(5017(a,2),9580(a,1,1,1))].">
      <j1 rule="para" parents="5017 9580"/>
    </justification>
  </clause>

  <clause id="9583">
    <literal><![CDATA[
      T((x * y) / x,z) \ y = K(y,x) * K(T(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,2065,a,b,9582,a),flip(a)].">
      <j1 rule="hyper" parents="334 2065 9582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9584">
    <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(1689(a,1),9583(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1689 9583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9585">
    <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(8363(a,1),7934(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8363 7934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9586">
    <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(8066(a,1),8364(a,1,1))].">
      <j1 rule="para" parents="8066 8364"/>
    </justification>
  </clause>

  <clause id="9587">
    <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(454(a,1),8564(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="454 8564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9588">
    <literal><![CDATA[
      K(x,(y * z) \ (x \ y)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(8950,a,8567,a)].">
      <j1 rule="hyper" parents="8950 8567"/>
    </justification>
  </clause>

  <clause id="9589">
    <literal><![CDATA[
      K((x * y) \ (z \ x),z) = (u * K(z,y \ (z \ 1))) \ u
    ]]></literal>
    <justification jstring="[para(9588(a,1),6523(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9588 6523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9590">
    <literal><![CDATA[
      K((x * y) \ (z \ x),z) = K(y \ (z \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,6523,a(flip),b,9589,a),flip(a)].">
      <j1 rule="hyper" parents="334 6523 9589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9591">
    <literal><![CDATA[
      K((x \ y) \ (z \ 1),z) = K(y \ (z \ x),z)
    ]]></literal>
    <justification jstring="[para(5(a,1),9590(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 9590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9592">
    <literal><![CDATA[
      (x * (y * K(z,y))) / (x * K(z,y)) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(5142(a,1),8571(a,1,2,2))].">
      <j1 rule="para" parents="5142 8571"/>
    </justification>
  </clause>

  <clause id="9594">
    <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(8583(a,2),5241(a,1))].">
      <j1 rule="para" parents="8583 5241"/>
    </justification>
  </clause>

  <clause id="9595">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = (y / z) \ (x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(334,a,5860,a(flip),b,8607,a),flip(a)].">
      <j1 rule="hyper" parents="334 5860 8607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9596">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = K(x,y / z) * K(z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,9595,a(flip),b,5044,a)].">
      <j1 rule="hyper" parents="116 9595 5044"/>
    </justification>
  </clause>

  <clause id="9597">
    <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(8661(a,2),8487(a,1))].">
      <j1 rule="para" parents="8661 8487"/>
    </justification>
  </clause>

  <clause id="9598">
    <literal><![CDATA[
      T(K(x,y),(z \ (u * x)) \ 1) = T(K(x,y),z \ u)
    ]]></literal>
    <justification jstring="[hyper(334,a,8029,a(flip),b,8679,a),flip(a)].">
      <j1 rule="hyper" parents="334 8029 8679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9599">
    <literal><![CDATA[
      T(K(x,y),z \ (u * x)) = T(K(x,y),z \ u)
    ]]></literal>
    <justification jstring="[hyper(8515,a,9598,a)].">
      <j1 rule="hyper" parents="8515 9598"/>
    </justification>
  </clause>

  <clause id="9600">
    <literal><![CDATA[
      T(K(x,y),z \ (u / x)) = T(K(x,y),z \ u)
    ]]></literal>
    <justification jstring="[para(7(a,1),9599(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 9599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9601">
    <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(9600(a,1),5028(a,1,2,1))].">
      <j1 rule="para" parents="9600 5028"/>
    </justification>
  </clause>

  <clause id="9602">
    <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(8704(a,1),5632(a,1,2,1))].">
      <j1 rule="para" parents="8704 5632"/>
    </justification>
  </clause>

  <clause id="9603">
    <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,9477,a(flip),b,8773,a)].">
      <j1 rule="hyper" parents="58 9477 8773"/>
    </justification>
  </clause>

  <clause id="9604">
    <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(6726(a,1),8789(a,1,1,2))].">
      <j1 rule="para" parents="6726 8789"/>
    </justification>
  </clause>

  <clause id="9605">
    <literal><![CDATA[
      K(x,y / z) * K(z \ y,z) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6386,a(flip),b,8791,a),flip(a)].">
      <j1 rule="hyper" parents="58 6386 8791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9606">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * u = (z * K((x \ 1) \ (y \ z),y)) * u
    ]]></literal>
    <justification jstring="[para(3688(a,1),8815(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3688 8815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9607">
    <literal><![CDATA[
      K(x,(K(y \ x,y) * z) \ x) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,7145,a(flip),b,8862,a),flip(a)].">
      <j1 rule="hyper" parents="334 7145 8862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9609">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ x) * x)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6857,a(flip),b,9607,a)].">
      <j1 rule="hyper" parents="58 6857 9607"/>
    </justification>
  </clause>

  <clause id="9610">
    <literal><![CDATA[
      K(x,y \ (z * (x / z))) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(5048(a,1),9609(a,1,2,2))].">
      <j1 rule="para" parents="5048 9609"/>
    </justification>
  </clause>

  <clause id="9611">
    <literal><![CDATA[
      K(x,y \ ((z \ x) * z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(72(a,1),9610(a,1,2,2,2))].">
      <j1 rule="para" parents="72 9610"/>
    </justification>
  </clause>

  <clause id="9612">
    <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(9611(a,1),6900(a,1))].">
      <j1 rule="para" parents="9611 6900"/>
    </justification>
  </clause>

  <clause id="9613">
    <literal><![CDATA[
      T(K(x,y),T(z,u * x)) = T(K(x,y),T(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(8730,a,8891,a),flip(a)].">
      <j1 rule="hyper" parents="8730 8891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9614">
    <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,7701,a(flip),b,9613,a),flip(a)].">
      <j1 rule="hyper" parents="58 7701 9613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9615">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8420,a(flip),b,8900,a),flip(a)].">
      <j1 rule="hyper" parents="334 8420 8900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9616">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(75(a,1),9615(a,1,2,2,1,2))].">
      <j1 rule="para" parents="75 9615"/>
    </justification>
  </clause>

  <clause id="9617">
    <literal><![CDATA[
      K(x,(y \ 1) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5583,a(flip),b,9616,a)].">
      <j1 rule="hyper" parents="58 5583 9616"/>
    </justification>
  </clause>

  <clause id="9618">
    <literal><![CDATA[
      K(T(x,y * (z * K(u,w))),w) = K(x,T(w,y * z))
    ]]></literal>
    <justification jstring="[hyper(334,a,7447,a(flip),b,8939,a),flip(a)].">
      <j1 rule="hyper" parents="334 7447 8939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9619">
    <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(8944(a,1),5922(a,1))].">
      <j1 rule="para" parents="8944 5922"/>
    </justification>
  </clause>

  <clause id="9620">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * y) \ (z \ u),z) = w
    ]]></literal>
    <justification jstring="[para(8948(a,1),6528(a,1))].">
      <j1 rule="para" parents="8948 6528"/>
    </justification>
  </clause>

  <clause id="9621">
    <literal><![CDATA[
      K((x * (y * z)) \ u,y) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * z) \ (y \ u),y) = w
    ]]></literal>
    <justification jstring="[para(8919(a,1),9620(a,1))].">
      <j1 rule="para" parents="8919 9620"/>
    </justification>
  </clause>

  <clause id="9622">
    <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(7401(a,2),8968(a,1,2))].">
      <j1 rule="para" parents="7401 8968"/>
    </justification>
  </clause>

  <clause id="9623">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(y,z)) = T(x,1 / T(y / z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8231,a(flip),b,9088,a)].">
      <j1 rule="hyper" parents="58 8231 9088"/>
    </justification>
  </clause>

  <clause id="9624">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(z,z / y)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[para(107(a,1),9088(a,2,2,2))].">
      <j1 rule="para" parents="107 9088"/>
    </justification>
  </clause>

  <clause id="9625">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(y,z)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8474,a(flip),b,9624,a)].">
      <j1 rule="hyper" parents="58 8474 9624"/>
    </justification>
  </clause>

  <clause id="9626">
    <literal><![CDATA[
      T(x,1 / T(y / z,y)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9623,a(flip),b,9625,a)].">
      <j1 rule="hyper" parents="58 9623 9625"/>
    </justification>
  </clause>

  <clause id="9627">
    <literal><![CDATA[
      T(x,T(1 / (y / z),y)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(9087,a,9626,a)].">
      <j1 rule="hyper" parents="9087 9626"/>
    </justification>
  </clause>

  <clause id="9628">
    <literal><![CDATA[
      T(x,1 / ((y \ z) \ z)) = T(x,T(1 / y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),9627(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 9627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9629">
    <literal><![CDATA[
      T(x,T(1 / (y \ z),z)) = T(x,1 / (z / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8656,a(flip),b,9628,a),flip(a)].">
      <j1 rule="hyper" parents="58 8656 9628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9630">
    <literal><![CDATA[
      T(x,K(y,z / y) / (z \ y)) = T(x,1 / (y / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8620,a,b,9629,a)].">
      <j1 rule="hyper" parents="58 8620 9629"/>
    </justification>
  </clause>

  <clause id="9631">
    <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(9174(a,1),9188(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9174 9188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9632">
    <literal><![CDATA[
      K(x,y / (z * (K(u,x) / z))) = K(x,y * K(z \ K(u,x),z))
    ]]></literal>
    <justification jstring="[para(6520(a,1),9254(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6520 9254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9633">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = x * K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(9332(a,1),9281(a,2,2))].">
      <j1 rule="para" parents="9332 9281"/>
    </justification>
  </clause>

  <clause id="9634">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = T(x,R(y / (y / z),u,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,8396,a,b,9633,a)].">
      <j1 rule="hyper" parents="334 8396 9633"/>
    </justification>
  </clause>

  <clause id="9635">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = T(x,R(T(z,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,8886,a(flip),b,9634,a),flip(a)].">
      <j1 rule="hyper" parents="58 8886 9634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9636">
    <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,8964,a,b,9635,a)].">
      <j1 rule="hyper" parents="58 8964 9635"/>
    </justification>
  </clause>

  <clause id="9637">
    <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),9636(a,1,2,1))].">
      <j1 rule="para" parents="106 9636"/>
    </justification>
  </clause>

  <clause id="9638">
    <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(3992(a,1),9637(a,1,2,1,1))].">
      <j1 rule="para" parents="3992 9637"/>
    </justification>
  </clause>

  <clause id="9639">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * x) * z) = K(y,R(T(x,z),y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9020,a(flip),b,9313,a),flip(a)].">
      <j1 rule="hyper" parents="58 9020 9313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9640">
    <literal><![CDATA[
      T(K(x,y) * z,x * y) = K(x,y) * T(z,x * y)
    ]]></literal>
    <justification jstring="[para(5234(a,1),9331(a,1,1,1))].">
      <j1 rule="para" parents="5234 9331"/>
    </justification>
  </clause>

  <clause id="9641">
    <literal><![CDATA[
      T(x * K(y,z),z * y) = T(x,z * y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6337,a,9640,a),flip(a)].">
      <j1 rule="hyper" parents="6337 9640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9642">
    <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(9641(a,2),238(a,1,2,2))].">
      <j1 rule="para" parents="9641 238"/>
    </justification>
  </clause>

  <clause id="9643">
    <literal><![CDATA[
      a(T(x,y),z,T(x,y)) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(9379,a,9374,a),flip(a)].">
      <j1 rule="hyper" parents="9379 9374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9645">
    <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(5960(a,1),9389(a,2,1,1))].">
      <j1 rule="para" parents="5960 9389"/>
    </justification>
  </clause>

  <clause id="9646">
    <literal><![CDATA[
      R(x,y,x) * (T(x,z) \ u) = x * (L(T(x,z),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7997,a(flip),b,9417,a)].">
      <j1 rule="hyper" parents="58 7997 9417"/>
    </justification>
  </clause>

  <clause id="9647">
    <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(9646(a,1),7326(a,1,2))].">
      <j1 rule="para" parents="9646 7326"/>
    </justification>
  </clause>

  <clause id="9648">
    <literal><![CDATA[
      ((x \ 1) * y) * K(x,z) = (x \ 1) * (y * K(x,z))
    ]]></literal>
    <justification jstring="[hyper(294,a,9446,a)].">
      <j1 rule="hyper" parents="294 9446"/>
    </justification>
  </clause>

  <clause id="9650">
    <literal><![CDATA[
      a(x \ 1,y,K(x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,9648,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="115 9648 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9651">
    <literal><![CDATA[
      L(K(x,y),z,y \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6202,a,9650,a)].">
      <j1 rule="hyper" parents="6202 9650"/>
    </justification>
  </clause>

  <clause id="9652">
    <literal><![CDATA[
      a(x,y,K(x \ 1,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,4355,a(flip),b,9650,a)].">
      <j1 rule="hyper" parents="58 4355 9650"/>
    </justification>
  </clause>

  <clause id="9653">
    <literal><![CDATA[
      (x * y) * K(x \ 1,z) = x * (y * K(x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(214,a,9652,a)].">
      <j1 rule="hyper" parents="214 9652"/>
    </justification>
  </clause>

  <clause id="9654">
    <literal><![CDATA[
      L(K(x \ 1,y),z,x) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(47,a,9652,a)].">
      <j1 rule="hyper" parents="47 9652"/>
    </justification>
  </clause>

  <clause id="9655">
    <literal><![CDATA[
      K(L(x,y,z \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(9354,a,9651,a)].">
      <j1 rule="hyper" parents="9354 9651"/>
    </justification>
  </clause>

  <clause id="9658">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (z * (x \ 1)),x) = K(y \ T(z,x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6893,a(flip),b,9651,a)].">
      <j1 rule="hyper" parents="58 6893 9651"/>
    </justification>
  </clause>

  <clause id="9659">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,y)) = K(((x \ 1) \ z) / y,x)
    ]]></literal>
    <justification jstring="[hyper(8531,a,9655,a)].">
      <j1 rule="hyper" parents="8531 9655"/>
    </justification>
  </clause>

  <clause id="9661">
    <literal><![CDATA[
      K(L(x,y,x) \ 1,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(5992,a,9654,a)].">
      <j1 rule="hyper" parents="5992 9654"/>
    </justification>
  </clause>

  <clause id="9663">
    <literal><![CDATA[
      K(R(x,y,x) \ 1,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(4939(a,1),9661(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4939 9661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9664">
    <literal><![CDATA[
      R(K(x,y),z,x \ 1) = K((x \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5980,a(flip),b,9663,a)].">
      <j1 rule="hyper" parents="58 5980 9663"/>
    </justification>
  </clause>

  <clause id="9665">
    <literal><![CDATA[
      (K(x \ 1,y) * z) * x = K(x \ 1,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(9663(a,1),5978(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9663 5978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9666">
    <literal><![CDATA[
      R(K(x,y),z,x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,3448,a(flip),b,9664,a),flip(a)].">
      <j1 rule="hyper" parents="334 3448 9664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9667">
    <literal><![CDATA[
      K(x,R(y,z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9542,a,9666,a)].">
      <j1 rule="hyper" parents="9542 9666"/>
    </justification>
  </clause>

  <clause id="9668">
    <literal><![CDATA[
      (K(x,y) * z) * (x \ 1) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[para(9666(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9666 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9669">
    <literal><![CDATA[
      R(x * K(y,x),z,y \ 1) = R(x,z,y \ 1) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,9667,a(flip),b,5787,a),flip(a)].">
      <j1 rule="hyper" parents="119 9667 5787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9670">
    <literal><![CDATA[
      R(x,y,K(x \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4339,a,9653,a)].">
      <j1 rule="hyper" parents="4339 9653"/>
    </justification>
  </clause>

  <clause id="9671">
    <literal><![CDATA[
      x * (y * K(x \ 1,x * y)) = y / R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6246,a(flip),b,9653,a),flip(a)].">
      <j1 rule="hyper" parents="58 6246 9653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9673">
    <literal><![CDATA[
      R(T(x,y),z,K(x \ 1,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(9670(a,1),22(a,2,1))].">
      <j1 rule="para" parents="9670 22"/>
    </justification>
  </clause>

  <clause id="9675">
    <literal><![CDATA[
      T(x,y * K(x \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6093,a(flip),b,9673,a),flip(a)].">
      <j1 rule="hyper" parents="58 6093 9673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9677">
    <literal><![CDATA[
      K(x,y * K(x \ 1,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,9675,a(flip),b,5020,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 9675 5020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9679">
    <literal><![CDATA[
      T(x,K(y,x \ 1) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(7420(a,1),9675(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7420 9675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9680">
    <literal><![CDATA[
      T(x,K(x \ 1,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(7423(a,1),9675(a,1,2))].">
      <j1 rule="para" parents="7423 9675"/>
    </justification>
  </clause>

  <clause id="9681">
    <literal><![CDATA[
      T(x,K(y,1 / x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(3700(a,2),9679(a,1,2,1))].">
      <j1 rule="para" parents="3700 9679"/>
    </justification>
  </clause>

  <clause id="9682">
    <literal><![CDATA[
      T(x \ 1,K(x,y) * z) = T(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(3448(a,1),9680(a,1,2,1))].">
      <j1 rule="para" parents="3448 9680"/>
    </justification>
  </clause>

  <clause id="9683">
    <literal><![CDATA[
      K(K(x,1 / y) * z,y) = y / T(y,z)
    ]]></literal>
    <justification jstring="[para(9681(a,1),5062(a,2,2))].">
      <j1 rule="para" parents="9681 5062"/>
    </justification>
  </clause>

  <clause id="9684">
    <literal><![CDATA[
      K(x,y * K(x \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,4995,a,b,9677,a),flip(a)].">
      <j1 rule="hyper" parents="334 4995 9677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9686">
    <literal><![CDATA[
      K(x,y * K(z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6516(a,1),9684(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6516 9684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9687">
    <literal><![CDATA[
      K(x \ y,z * K(u,y \ x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(6423(a,1),9686(a,1,2,2))].">
      <j1 rule="para" parents="6423 9686"/>
    </justification>
  </clause>

  <clause id="9688">
    <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(9682(a,1),957(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9682 957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9690">
    <literal><![CDATA[
      K(K(x,1 / y) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5062,a,b,9683,a),flip(a)].">
      <j1 rule="hyper" parents="334 5062 9683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9691">
    <literal><![CDATA[
      K(K(x,y) * z,y \ 1) = K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),9690(a,1,1,1,2))].">
      <j1 rule="para" parents="72 9690"/>
    </justification>
  </clause>

  <clause id="9692">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(3700(a,1),9690(a,1,1,1))].">
      <j1 rule="para" parents="3700 9690"/>
    </justification>
  </clause>

  <clause id="9693">
    <literal><![CDATA[
      K(T(x,1 / y) / z,y) = K(x / z,y)
    ]]></literal>
    <justification jstring="[para(5921(a,1),9690(a,1,1))].">
      <j1 rule="para" parents="5921 9690"/>
    </justification>
  </clause>

  <clause id="9695">
    <literal><![CDATA[
      (K(x,y \ 1) * z) * K(z,y) = T(K(x,y \ 1) * z,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,9692,a(flip),b,4995,a(flip))].">
      <j1 rule="hyper" parents="119 9692 4995"/>
    </justification>
  </clause>

  <clause id="9696">
    <literal><![CDATA[
      K(K(x,x \ y) * z,x / y) = K(z,x / y)
    ]]></literal>
    <justification jstring="[para(5479(a,1),9692(a,1,1,1))].">
      <j1 rule="para" parents="5479 9692"/>
    </justification>
  </clause>

  <clause id="9697">
    <literal><![CDATA[
      K(x \ T(y,z \ 1),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(5818(a,1),9692(a,1,1))].">
      <j1 rule="para" parents="5818 9692"/>
    </justification>
  </clause>

  <clause id="9698">
    <literal><![CDATA[
      K(x * K(y,z \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7538(a,1),9692(a,1,1))].">
      <j1 rule="para" parents="7538 9692"/>
    </justification>
  </clause>

  <clause id="9699">
    <literal><![CDATA[
      K(x * K(y,z \ u),u \ z) = K(x,u \ z)
    ]]></literal>
    <justification jstring="[para(6423(a,1),9698(a,1,1,2))].">
      <j1 rule="para" parents="6423 9698"/>
    </justification>
  </clause>

  <clause id="9700">
    <literal><![CDATA[
      K(((x * y) \ x) * z,y) = K(z * ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[para(6511(a,1),9698(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6511 9698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9701">
    <literal><![CDATA[
      K(T(x / (1 / (1 / y)),1 / z) / (1 / y),z) = K((x / y) / (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(3068(a,1),9693(a,2,1))].">
      <j1 rule="para" parents="3068 9693"/>
    </justification>
  </clause>

  <clause id="9702">
    <literal><![CDATA[
      K(x \ y,(y \ x) * z) = K(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[para(84(a,1),9687(a,1,2)),flip(a)].">
      <j1 rule="para" parents="84 9687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9703">
    <literal><![CDATA[
      K(x \ y,z * (x / y)) = K(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[para(6417(a,1),9687(a,1,2))].">
      <j1 rule="para" parents="6417 9687"/>
    </justification>
  </clause>

  <clause id="9704">
    <literal><![CDATA[
      K((x / y) \ z,y / x) = K((y \ x) \ z,y / x)
    ]]></literal>
    <justification jstring="[para(5687(a,1),9696(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5687 9696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9705">
    <literal><![CDATA[
      K(x * (y / z),y \ z) = K(x * (z \ y),y \ z)
    ]]></literal>
    <justification jstring="[para(6417(a,1),9699(a,1,1))].">
      <j1 rule="para" parents="6417 9699"/>
    </justification>
  </clause>

  <clause id="9706">
    <literal><![CDATA[
      L(x,y,K(x \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4329,a,9665,a)].">
      <j1 rule="hyper" parents="4329 9665"/>
    </justification>
  </clause>

  <clause id="9709">
    <literal><![CDATA[
      L(x \ 1,y,K(x,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(3448(a,1),9706(a,1,3))].">
      <j1 rule="para" parents="3448 9706"/>
    </justification>
  </clause>

  <clause id="9710">
    <literal><![CDATA[
      (K(x,y) * (z * x)) \ (K(x,y) * z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[para(9709(a,1),950(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9709 950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9714">
    <literal><![CDATA[
      (x \ 1) * T(K(x,y) * z,x \ 1) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(295,a,9668,a)].">
      <j1 rule="hyper" parents="295 9668"/>
    </justification>
  </clause>

  <clause id="9715">
    <literal><![CDATA[
      T(K(x,y) * z,x \ 1) = K(x,y) * T(z,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(246,a,9668,a,b,6304,a)].">
      <j1 rule="hyper" parents="246 9668 6304"/>
    </justification>
  </clause>

  <clause id="9716">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = z * K(y \ x,z * (y / x))
    ]]></literal>
    <justification jstring="[para(9703(a,2),6639(a,2,2))].">
      <j1 rule="para" parents="9703 6639"/>
    </justification>
  </clause>

  <clause id="9717">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = z * K(z * (y / x),y \ x)
    ]]></literal>
    <justification jstring="[para(9705(a,2),6496(a,2,2))].">
      <j1 rule="para" parents="9705 6496"/>
    </justification>
  </clause>

  <clause id="9718">
    <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),9715(a,2,2))].">
      <j1 rule="para" parents="20 9715"/>
    </justification>
  </clause>

  <clause id="9719">
    <literal><![CDATA[
      x * (((x * y) \ y) * (x * y)) = y / R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(5715(a,2),9671(a,1,2))].">
      <j1 rule="para" parents="5715 9671"/>
    </justification>
  </clause>

  <clause id="9720">
    <literal><![CDATA[
      x * (((x * y) \ y) * (x * y)) = y / (y / (x * y))
    ]]></literal>
    <justification jstring="[para(223(a,1),9719(a,2,2))].">
      <j1 rule="para" parents="223 9719"/>
    </justification>
  </clause>

  <clause id="9721">
    <literal><![CDATA[
      R(x * K(y,x),z,y \ 1) = K(y,x) * R(x,z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,2532,a(flip),b,9669,a),flip(a)].">
      <j1 rule="hyper" parents="334 2532 9669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9722">
    <literal><![CDATA[
      T(K(x,y \ 1) * z,y) = K(x,y \ 1) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6560,a,9695,a),flip(a)].">
      <j1 rule="hyper" parents="6560 9695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9724">
    <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,9721,a,b,5502,a)].">
      <j1 rule="hyper" parents="116 9721 5502"/>
    </justification>
  </clause>

  <clause id="9725">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y * K(w,x),z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9558,a(flip),b,9538,a)].">
      <j1 rule="hyper" parents="58 9558 9538"/>
    </justification>
  </clause>

  <clause id="9726">
    <literal><![CDATA[
      K(x,R(y * K(z,x),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(9542,a,9725,a),flip(a)].">
      <j1 rule="hyper" parents="9542 9725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9728">
    <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(9725(a,1),9542(a,1))].">
      <j1 rule="para" parents="9725 9542"/>
    </justification>
  </clause>

  <clause id="9729">
    <literal><![CDATA[
      K(x,R(y * K(x,z),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(6516(a,1),9726(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6516 9726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9730">
    <literal><![CDATA[
      K(x,R(K(y,x) * z,u,w)) = K(x,R(z * K(y,x),u,w))
    ]]></literal>
    <justification jstring="[para(8023(a,1),9729(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8023 9729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9731">
    <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(668(a,1),9563(a,1,2)),flip(a)].">
      <j1 rule="para" parents="668 9563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9732">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * K(z,w) = x * (K(z,w) * K(y,T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,9226,a(flip),b,9566,a),flip(a)].">
      <j1 rule="hyper" parents="334 9226 9566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9733">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z * (((x * y) \ x) \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,4274,a(flip),b,9567,a),flip(a)].">
      <j1 rule="hyper" parents="334 4274 9567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9734">
    <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),9573(a,1,2,2,1,2))].">
      <j1 rule="para" parents="4 9573"/>
    </justification>
  </clause>

  <clause id="9735">
    <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(7921,a,9586,a)].">
      <j1 rule="hyper" parents="7921 9586"/>
    </justification>
  </clause>

  <clause id="9736">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,9605,a(flip),b,9596,a),flip(a)].">
      <j1 rule="hyper" parents="334 9605 9596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9737">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),T(y,z)) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9274,a(flip),b,9614,a)].">
      <j1 rule="hyper" parents="58 9274 9614"/>
    </justification>
  </clause>

  <clause id="9738">
    <literal><![CDATA[
      K(x,T(y \ (z * x),T(y,z))) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(7974,a,9737,a)].">
      <j1 rule="hyper" parents="7974 9737"/>
    </justification>
  </clause>

  <clause id="9739">
    <literal><![CDATA[
      K(x,T(y \ (z * x),T(y,z))) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,8765,a(flip),b,9738,a),flip(a)].">
      <j1 rule="hyper" parents="334 8765 9738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9740">
    <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(334,a,6191,a(flip),b,9739,a),flip(a)].">
      <j1 rule="hyper" parents="334 6191 9739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9741">
    <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,5846,a(flip),b,9632,a),flip(a)].">
      <j1 rule="hyper" parents="58 5846 9632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9742">
    <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(5987(a,1),9734(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5987 9734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9743">
    <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(8740,a,9735,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8740 9735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9744">
    <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),7508(a,1,1))].">
      <j1 rule="para" parents="22 7508"/>
    </justification>
  </clause>

  <clause id="9745">
    <literal><![CDATA[
      K(R(x,y,z),u * K(x,w)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,5789,a(flip),b,7600,a),flip(a)].">
      <j1 rule="hyper" parents="334 5789 7600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9746">
    <literal><![CDATA[
      K(R(x,y,z),u * K(w,x)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(6516(a,1),9745(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6516 9745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9747">
    <literal><![CDATA[
      K(L(x,y,z),T(u,x \ w)) = K(L(x,y,z),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(5288,a,7634,a),flip(a)].">
      <j1 rule="hyper" parents="5288 7634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9748">
    <literal><![CDATA[
      K(T(x,y \ z),L(y,u,w)) = 1 / K(L(y,u,w),T(x,z))
    ]]></literal>
    <justification jstring="[para(9747(a,1),5243(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9747 5243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9749">
    <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,7475,a(flip),b,9748,a),flip(a)].">
      <j1 rule="hyper" parents="114 7475 9748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9750">
    <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),9749(a,2,2))].">
      <j1 rule="para" parents="20 9749"/>
    </justification>
  </clause>

  <clause id="9751">
    <literal><![CDATA[
      K(x,T(L(y,z,u),y \ w)) = K(x,L(T(y,w),z,u))
    ]]></literal>
    <justification jstring="[hyper(7970,a,9750,a)].">
      <j1 rule="hyper" parents="7970 9750"/>
    </justification>
  </clause>

  <clause id="9752">
    <literal><![CDATA[
      K(x,L((y \ z) \ z,u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(331(a,1),9751(a,1,2))].">
      <j1 rule="para" parents="331 9751"/>
    </justification>
  </clause>

  <clause id="9753">
    <literal><![CDATA[
      T(x,L((y \ z) \ z,u,w)) = T(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(118,a,9752,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 9752 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9754">
    <literal><![CDATA[
      K(x,L(T(y,z * y),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(4513(a,2),9752(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4513 9752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9755">
    <literal><![CDATA[
      T(x,L(T(y,z * y),u,w)) = T(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(4513(a,2),9753(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4513 9753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9756">
    <literal><![CDATA[
      L(x \ 1,x,K(x,y) * z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9710,a(flip),b,7743,a),flip(a)].">
      <j1 rule="hyper" parents="58 9710 7743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9758">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(8170(a,1),9756(a,1,3))].">
      <j1 rule="para" parents="8170 9756"/>
    </justification>
  </clause>

  <clause id="9759">
    <literal><![CDATA[
      L(x \ 1,T(x,y),z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(6964,a,9758,a)].">
      <j1 rule="hyper" parents="6964 9758"/>
    </justification>
  </clause>

  <clause id="9761">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),z) = T(x,z) * ((y * T(x,z)) \ y)
    ]]></literal>
    <justification jstring="[para(9759(a,1),2201(a,1,1,2))].">
      <j1 rule="para" parents="9759 2201"/>
    </justification>
  </clause>

  <clause id="9764">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = a(x,y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(709,a,7994,a),flip(a)].">
      <j1 rule="hyper" parents="709 7994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9765">
    <literal><![CDATA[
      a(x,y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9764(a,1),9443(a,1))].">
      <j1 rule="para" parents="9764 9443"/>
    </justification>
  </clause>

  <clause id="9766">
    <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),7998(a,2,1))].">
      <j1 rule="para" parents="24 7998"/>
    </justification>
  </clause>

  <clause id="9767">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ ((z * x) * u))) = 1
    ]]></literal>
    <justification jstring="[para(8201(a,1),8347(a,1,2))].">
      <j1 rule="para" parents="8201 8347"/>
    </justification>
  </clause>

  <clause id="9768">
    <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,8230,a(flip),b,6211,a(flip))].">
      <j1 rule="hyper" parents="116 8230 6211"/>
    </justification>
  </clause>

  <clause id="9769">
    <literal><![CDATA[
      R(K(x,T(T(y,z),z * u)),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(7401(a,2),8258(a,1,1))].">
      <j1 rule="para" parents="7401 8258"/>
    </justification>
  </clause>

  <clause id="9770">
    <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(7475(a,1),8264(a,1,1))].">
      <j1 rule="para" parents="7475 8264"/>
    </justification>
  </clause>

  <clause id="9771">
    <literal><![CDATA[
      T(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) / z) = u
    ]]></literal>
    <justification jstring="[para(9302(a,1),8744(a,1))].">
      <j1 rule="para" parents="9302 8744"/>
    </justification>
  </clause>

  <clause id="9772">
    <literal><![CDATA[
      x / (x / R(K(y,z),u,w)) = (R(K(y,z),u,w) \ x) \ x
    ]]></literal>
    <justification jstring="[para(8961(a,1),4547(a,1,2))].">
      <j1 rule="para" parents="8961 4547"/>
    </justification>
  </clause>

  <clause id="9773">
    <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(334,a,7398,a(flip),b,8995,a),flip(a)].">
      <j1 rule="hyper" parents="334 7398 8995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9774">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (z * u)) = R(K(x,T(y,z * u)),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,8975,a(flip),b,9428,a),flip(a)].">
      <j1 rule="hyper" parents="58 8975 9428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9775">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = K((u * z) / (u * (x \ z)),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,6283,a,b,9448,a),flip(a)].">
      <j1 rule="hyper" parents="334 6283 9448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9776">
    <literal><![CDATA[
      L(T(K(x,T(y,z * u)),u),u,z) = (z * (K(x,y) * u)) / (z * u)
    ]]></literal>
    <justification jstring="[para(7425(a,1),9448(a,1,1))].">
      <j1 rule="para" parents="7425 9448"/>
    </justification>
  </clause>

  <clause id="9777">
    <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(9481(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="9481 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9778">
    <literal><![CDATA[
      K(x,y) * K(L(x,z,u) * y,x) = L(x,y,L(x,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(8904(a,1),9584(a,1,2))].">
      <j1 rule="para" parents="8904 9584"/>
    </justification>
  </clause>

  <clause id="9779">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) * K(x,u) = L(x,u,L(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(2067,a,9778,a)].">
      <j1 rule="hyper" parents="2067 9778"/>
    </justification>
  </clause>

  <clause id="9780">
    <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(2986(a,1),9744(a,2,1,1))].">
      <j1 rule="para" parents="2986 9744"/>
    </justification>
  </clause>

  <clause id="9781">
    <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(8530,a,9766,a)].">
      <j1 rule="hyper" parents="8530 9766"/>
    </justification>
  </clause>

  <clause id="9782">
    <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),9781(a,1,2))].">
      <j1 rule="para" parents="18 9781"/>
    </justification>
  </clause>

  <clause id="9783">
    <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,9059,a(flip),b,9782,a)].">
      <j1 rule="hyper" parents="58 9059 9782"/>
    </justification>
  </clause>

  <clause id="9784">
    <literal><![CDATA[
      K(L(R(x,y,z),u,x),w) = K(R(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(8281,a,9783,a),flip(a)].">
      <j1 rule="hyper" parents="8281 9783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9786">
    <literal><![CDATA[
      K(R(L(x,y,x),z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(24(a,2),9784(a,1,1))].">
      <j1 rule="para" parents="24 9784"/>
    </justification>
  </clause>

  <clause id="9787">
    <literal><![CDATA[
      K(R(x,x \ a(x,y,x),z),u) = K(L(x,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9363,a(flip),b,9786,a),flip(a)].">
      <j1 rule="hyper" parents="58 9363 9786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9788">
    <literal><![CDATA[
      K(R(x,x \ a(x,y,x),z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,7291,a(flip),b,9787,a),flip(a)].">
      <j1 rule="hyper" parents="334 7291 9787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9791">
    <literal><![CDATA[
      (K(x,y) * a(x,z,x)) * u = K(x,y) * (a(x,z,x) * u)
    ]]></literal>
    <justification jstring="[para(9788(a,1),7057(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9788 7057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9792">
    <literal><![CDATA[
      K(x,x * y) * (a(x,y,x) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(9170(a,1),9791(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9170 9791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9793">
    <literal><![CDATA[
      a(x,y,x) * z = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(9407,a,9792,a),flip(a)].">
      <j1 rule="hyper" parents="9407 9792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9794">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(5409,a,9792,a)].">
      <j1 rule="hyper" parents="5409 9792"/>
    </justification>
  </clause>

  <clause id="9795">
    <literal><![CDATA[
      K(x,y) * (a(x,y,x) \ z) = K(x,x * y) * z
    ]]></literal>
    <justification jstring="[hyper(356,a,9792,a),flip(a)].">
      <j1 rule="hyper" parents="356 9792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9796">
    <literal><![CDATA[
      x / a(y,z,y) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(352,a,9793,a)].">
      <j1 rule="hyper" parents="352 9793"/>
    </justification>
  </clause>

  <clause id="9797">
    <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(334,a,9631,a(flip),b,9793,a),flip(a)].">
      <j1 rule="hyper" parents="334 9631 9793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9798">
    <literal><![CDATA[
      a(x,y,x) * (R(x,y,x) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(334,a,9421,a(flip),b,9793,a),flip(a)].">
      <j1 rule="hyper" parents="334 9421 9793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9799">
    <literal><![CDATA[
      a(x,y,x) * (x * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(334,a,9420,a(flip),b,9793,a),flip(a)].">
      <j1 rule="hyper" parents="334 9420 9793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9800">
    <literal><![CDATA[
      a(x,y,x) * (z * x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,9410,a(flip),b,9793,a),flip(a)].">
      <j1 rule="hyper" parents="334 9410 9793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9801">
    <literal><![CDATA[
      a(x,y,x) * (x \ z) = L(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(334,a,9376,a(flip),b,9793,a),flip(a)].">
      <j1 rule="hyper" parents="334 9376 9793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9802">
    <literal><![CDATA[
      a(x,y,x) * (z / x) = z / L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,9356,a(flip),b,9793,a),flip(a)].">
      <j1 rule="hyper" parents="334 9356 9793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9803">
    <literal><![CDATA[
      a(x,x \ y,x) * y = T(x * (y / x),x)
    ]]></literal>
    <justification jstring="[hyper(334,a,9201,a(flip),b,9793,a),flip(a)].">
      <j1 rule="hyper" parents="334 9201 9793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9804">
    <literal><![CDATA[
      (a(x,y,x) \ z) * a(x,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(264,a,9793,a),flip(a)].">
      <j1 rule="hyper" parents="264 9793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9805">
    <literal><![CDATA[
      T(x,a(y,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(250,a,9793,a)].">
      <j1 rule="hyper" parents="250 9793"/>
    </justification>
  </clause>

  <clause id="9806">
    <literal><![CDATA[
      T(a(x,y,x),z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(246,a,9793,a,b,xx)].">
      <j1 rule="hyper" parents="246 9793"/>
    </justification>
  </clause>

  <clause id="9807">
    <literal><![CDATA[
      (x * a(y,z,y)) / x = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,9793,a)].">
      <j1 rule="hyper" parents="130 9793"/>
    </justification>
  </clause>

  <clause id="9808">
    <literal><![CDATA[
      a(x,y,x) \ (z * a(x,y,x)) = z
    ]]></literal>
    <justification jstring="[hyper(123,a,9793,a)].">
      <j1 rule="hyper" parents="123 9793"/>
    </justification>
  </clause>

  <clause id="9809">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,9410,a(flip),b,9793,a)].">
      <j1 rule="hyper" parents="117 9410 9793"/>
    </justification>
  </clause>

  <clause id="9810">
    <literal><![CDATA[
      a(x,y,x) \ (z / x) = z / R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,9423,a(flip),b,9793,a)].">
      <j1 rule="hyper" parents="116 9423 9793"/>
    </justification>
  </clause>

  <clause id="9811">
    <literal><![CDATA[
      a(x,y,x) \ (x \ z) = R(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,9421,a(flip),b,9793,a)].">
      <j1 rule="hyper" parents="116 9421 9793"/>
    </justification>
  </clause>

  <clause id="9812">
    <literal><![CDATA[
      a(x,y,x) \ (L(x,y,x) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,9376,a(flip),b,9793,a)].">
      <j1 rule="hyper" parents="116 9376 9793"/>
    </justification>
  </clause>

  <clause id="9813">
    <literal><![CDATA[
      a(x,y,x) \ (z * x) = z * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,9367,a(flip),b,9793,a)].">
      <j1 rule="hyper" parents="116 9367 9793"/>
    </justification>
  </clause>

  <clause id="9814">
    <literal><![CDATA[
      x \ (a(x,y,x) * z) = L(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,9793,a,b,9366,a)].">
      <j1 rule="hyper" parents="116 9793 9366"/>
    </justification>
  </clause>

  <clause id="9815">
    <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,9793,a,b,656,a)].">
      <j1 rule="hyper" parents="116 9793 656"/>
    </justification>
  </clause>

  <clause id="9816">
    <literal><![CDATA[
      K(x,a(y,z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,9793,a,b,84,a),flip(a)].">
      <j1 rule="hyper" parents="115 9793 84"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9817">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = (z * a(x,y,x)) \ u
    ]]></literal>
    <justification jstring="[hyper(56,a,9793,a)].">
      <j1 rule="hyper" parents="56 9793"/>
    </justification>
  </clause>

  <clause id="9818">
    <literal><![CDATA[
      a(x,y,x) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9793(a,2),38(a,1))].">
      <j1 rule="para" parents="9793 38"/>
    </justification>
  </clause>

  <clause id="9819">
    <literal><![CDATA[
      (a(x,y,x) \ z) * a(x,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(9793(a,1),264(a,1))].">
      <j1 rule="para" parents="9793 264"/>
    </justification>
  </clause>

  <clause id="9820">
    <literal><![CDATA[
      (x * y) \ ((x * a(z,u,z)) * y) = R(T(a(z,u,z),x * y),x,y)
    ]]></literal>
    <justification jstring="[para(9793(a,1),648(a,1,2,1))].">
      <j1 rule="para" parents="9793 648"/>
    </justification>
  </clause>

  <clause id="9821">
    <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(9793(a,1),793(a,1,1))].">
      <j1 rule="para" parents="9793 793"/>
    </justification>
  </clause>

  <clause id="9822">
    <literal><![CDATA[
      a(x,y,x) * (z * x) != u
    ]]></literal>
    <literal><![CDATA[
      z * R(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9793(a,2),9418(a,1))].">
      <j1 rule="para" parents="9793 9418"/>
    </justification>
  </clause>

  <clause id="9823">
    <literal><![CDATA[
      a(x,y,x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9805(a,1),294(a,1,2))].">
      <j1 rule="para" parents="9805 294"/>
    </justification>
  </clause>

  <clause id="9824">
    <literal><![CDATA[
      x * K(y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(9816(a,2),128(a,1,2))].">
      <j1 rule="para" parents="9816 128"/>
    </justification>
  </clause>

  <clause id="9825">
    <literal><![CDATA[
      T(a(x,y,x),z) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,9155,a,b,9806,a),flip(a)].">
      <j1 rule="hyper" parents="334 9155 9806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9826">
    <literal><![CDATA[
      x * a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) * x = u
    ]]></literal>
    <justification jstring="[para(9806(a,1),294(a,1,2))].">
      <j1 rule="para" parents="9806 294"/>
    </justification>
  </clause>

  <clause id="9827">
    <literal><![CDATA[
      R(a(x,y,x),z,u) * w = w * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(9806(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9806 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9828">
    <literal><![CDATA[
      x * (y \ L(y,z,y)) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,9419,a,b,9796,a)].">
      <j1 rule="hyper" parents="58 9419 9796"/>
    </justification>
  </clause>

  <clause id="9829">
    <literal><![CDATA[
      (x / y) \ (a(y,z,y) \ x) = L(y,z,y)
    ]]></literal>
    <justification jstring="[para(9796(a,1),9375(a,1,2))].">
      <j1 rule="para" parents="9796 9375"/>
    </justification>
  </clause>

  <clause id="9830">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) / (x * y) = L(a(z,u,z),y,x)
    ]]></literal>
    <justification jstring="[para(9807(a,1),877(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9807 877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9831">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u != w
    ]]></literal>
    <literal><![CDATA[
      (z * a(x,y,x)) \ u = w
    ]]></literal>
    <justification jstring="[para(9808(a,1),361(a,1,1,2))].">
      <j1 rule="para" parents="9808 361"/>
    </justification>
  </clause>

  <clause id="9832">
    <literal><![CDATA[
      K(x,a(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(2(a,1),9824(a,1))].">
      <j1 rule="para" parents="2 9824"/>
    </justification>
  </clause>

  <clause id="9833">
    <literal><![CDATA[
      T(a(1 / x,y,1 / x),z) = (1 / x) \ R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[para(3324(a,1),9825(a,2,2))].">
      <j1 rule="para" parents="3324 9825"/>
    </justification>
  </clause>

  <clause id="9836">
    <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(9799(a,1),530(a,1,1,1))].">
      <j1 rule="para" parents="9799 530"/>
    </justification>
  </clause>

  <clause id="9837">
    <literal><![CDATA[
      (x * R(x \ y,z,x \ y)) / y = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(117,a,9800,a(flip),b,151,a(flip))].">
      <j1 rule="hyper" parents="117 9800 151"/>
    </justification>
  </clause>

  <clause id="9838">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) = u
    ]]></literal>
    <justification jstring="[para(9800(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9800 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9839">
    <literal><![CDATA[
      a(x,y,x) \ y = x \ ((x * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4617,a(flip),b,9801,a)].">
      <j1 rule="hyper" parents="116 4617 9801"/>
    </justification>
  </clause>

  <clause id="9840">
    <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),9809(a,1,2))].">
      <j1 rule="para" parents="90 9809"/>
    </justification>
  </clause>

  <clause id="9841">
    <literal><![CDATA[
      (x / y) * L(y,z,y) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[para(7(a,1),9813(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 9813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9842">
    <literal><![CDATA[
      a(x,y,x) \ (x * z) = L(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(635,a,9814,a),flip(a)].">
      <j1 rule="hyper" parents="635 9814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9843">
    <literal><![CDATA[
      a(x,y,x) * (L(x,y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(119,a,4,a(flip),b,9814,a),flip(a)].">
      <j1 rule="hyper" parents="119 4 9814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9844">
    <literal><![CDATA[
      L(x,y,x) \ z != x \ u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) * z = u
    ]]></literal>
    <justification jstring="[para(9814(a,1),42(a,1))].">
      <j1 rule="para" parents="9814 42"/>
    </justification>
  </clause>

  <clause id="9845">
    <literal><![CDATA[
      a(x,y,x) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(9828(a,1),263(a,1)),flip(b)].">
      <j1 rule="para" parents="9828 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9846">
    <literal><![CDATA[
      (x / y) \ (a(y,z,y) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      L(y,z,y) = u
    ]]></literal>
    <justification jstring="[para(9841(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9841 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9847">
    <literal><![CDATA[
      K(x * y,y) * (K(y,x) * z) = a(y,x,y) * z
    ]]></literal>
    <justification jstring="[para(5532(a,2),9794(a,1,1))].">
      <j1 rule="para" parents="5532 9794"/>
    </justification>
  </clause>

  <clause id="9848">
    <literal><![CDATA[
      K(x,y) * (K(y,y * x) * z) = a(y,x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(5409,a,9795,a)].">
      <j1 rule="hyper" parents="5409 9795"/>
    </justification>
  </clause>

  <clause id="9849">
    <literal><![CDATA[
      K(x * y,y) * (x * (K(y,x) * z)) = a(y,x,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(5522(a,1),9847(a,1,2))].">
      <j1 rule="para" parents="5522 9847"/>
    </justification>
  </clause>

  <clause id="9850">
    <literal><![CDATA[
      K(x,y) * (K(y,x * y) * z) = a(y,x,y) \ z
    ]]></literal>
    <justification jstring="[para(5649(a,2),9848(a,1,2,1))].">
      <j1 rule="para" parents="5649 9848"/>
    </justification>
  </clause>

  <clause id="9851">
    <literal><![CDATA[
      K(x,y) * (K(y,y * x) * z) = (y \ R(y,x,y)) \ z
    ]]></literal>
    <justification jstring="[para(9155(a,2),9848(a,2,1))].">
      <j1 rule="para" parents="9155 9848"/>
    </justification>
  </clause>

  <clause id="9852">
    <literal><![CDATA[
      T(x,R(a(y,z,y),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(250,a,9827,a)].">
      <j1 rule="hyper" parents="250 9827"/>
    </justification>
  </clause>

  <clause id="9853">
    <literal><![CDATA[
      (x * (y * R(z,u,z))) / (x * (y * z)) = L(a(z,u,z),y * z,x)
    ]]></literal>
    <justification jstring="[para(9410(a,1),9830(a,1,1,2))].">
      <j1 rule="para" parents="9410 9830"/>
    </justification>
  </clause>

  <clause id="9854">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ (K(x * y,x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(5394(a,1),9851(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5394 9851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9855">
    <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(9769(a,1),6212(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9769 6212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9856">
    <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(8669(a,1),9776(a,1,1,1))].">
      <j1 rule="para" parents="8669 9776"/>
    </justification>
  </clause>

  <clause id="9857">
    <literal><![CDATA[
      (x * y) \ ((x * a(z,u,z)) * y) = R(a(z,u,z),x,y)
    ]]></literal>
    <justification jstring="[para(9806(a,1),9820(a,2,1))].">
      <j1 rule="para" parents="9806 9820"/>
    </justification>
  </clause>

  <clause id="9858">
    <literal><![CDATA[
      (x * y) \ ((T(z * x,z) / z) * y) = R(a(z,x,z),x,y)
    ]]></literal>
    <justification jstring="[para(9174(a,2),9857(a,1,2,1))].">
      <j1 rule="para" parents="9174 9857"/>
    </justification>
  </clause>

  <clause id="9860">
    <literal><![CDATA[
      T(x * K(y,x),K(x,z) * u) = T(x,u) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[para(7515(a,1),7522(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7515 7522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9861">
    <literal><![CDATA[
      T(x * K(y,x),K(x,z) * u) = T(x * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,5466,a(flip),b,9860,a),flip(a)].">
      <j1 rule="hyper" parents="334 5466 9860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9863">
    <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,5468,a(flip),b,9861,a),flip(a)].">
      <j1 rule="hyper" parents="58 5468 9861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9864">
    <literal><![CDATA[
      K(x * K(L(y,z,u),w),L(y,v5,v6)) = K(x,L(y,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(334,a,5075,a(flip),b,7675,a),flip(a)].">
      <j1 rule="hyper" parents="334 5075 7675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9865">
    <literal><![CDATA[
      K(x * K(y,z),L(y,u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(384(a,1),9864(a,1,1,2,1))].">
      <j1 rule="para" parents="384 9864"/>
    </justification>
  </clause>

  <clause id="9866">
    <literal><![CDATA[
      K(x * y,L(y,z,u)) = K(y * x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(84(a,1),9865(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 9865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9867">
    <literal><![CDATA[
      K(x \ T(y,z),L(z,u,w)) = K(x \ y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(6836(a,1),9865(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6836 9865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9868">
    <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),9867(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 9867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9869">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,L(y,w,v5)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(4329,a,7718,a)].">
      <j1 rule="hyper" parents="4329 7718"/>
    </justification>
  </clause>

  <clause id="9870">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9773,a(flip),b,9869,a)].">
      <j1 rule="hyper" parents="58 9773 9869"/>
    </justification>
  </clause>

  <clause id="9872">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),9870(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 9870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9873">
    <literal><![CDATA[
      R(x,y,T(x * K(z,x),u)) = R(x,y,x * K(z,x))
    ]]></literal>
    <justification jstring="[para(5086(a,1),7793(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5086 7793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9874">
    <literal><![CDATA[
      R(x,y,x * K(z,x)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(5086(a,1),9873(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5086 9873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9875">
    <literal><![CDATA[
      R(x \ y,z,y / x) = R(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[para(5041(a,1),9874(a,1,3))].">
      <j1 rule="para" parents="5041 9874"/>
    </justification>
  </clause>

  <clause id="9876">
    <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(4985(a,1),7956(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4985 7956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9877">
    <literal><![CDATA[
      T(x / y,T((y * z) \ x,y)) = T(x / y,T(z \ (y \ x),y))
    ]]></literal>
    <justification jstring="[hyper(7569,a,8005,a),flip(a)].">
      <j1 rule="hyper" parents="7569 8005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9878">
    <literal><![CDATA[
      T(x / y,T(z \ (y \ x),y)) = T(x / y,x / (y * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8307,a(flip),b,9877,a),flip(a)].">
      <j1 rule="hyper" parents="58 8307 9877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9879">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) * (y / u) = T(y,K(x,z)) / u
    ]]></literal>
    <justification jstring="[para(8102(a,1),8079(a,1,1))].">
      <j1 rule="para" parents="8102 8079"/>
    </justification>
  </clause>

  <clause id="9880">
    <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(9879(a,1),103(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9879 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9881">
    <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(9879(a,1),5408(a,1,2))].">
      <j1 rule="para" parents="9879 5408"/>
    </justification>
  </clause>

  <clause id="9882">
    <literal><![CDATA[
      T(x / y,K(((x / y) \ (1 / y)) \ 1,z)) = T(x,K(z,y \ x)) / y
    ]]></literal>
    <justification jstring="[para(6508(a,1),8147(a,2,1))].">
      <j1 rule="para" parents="6508 8147"/>
    </justification>
  </clause>

  <clause id="9883">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,(((y \ 1) \ 1) \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8220,a(flip),b,8299,a)].">
      <j1 rule="hyper" parents="58 8220 8299"/>
    </justification>
  </clause>

  <clause id="9884">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,((y \ 1) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,4713,a(flip),b,9883,a),flip(a)].">
      <j1 rule="hyper" parents="334 4713 9883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9886">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,3926,a(flip),b,9884,a),flip(a)].">
      <j1 rule="hyper" parents="334 3926 9884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9887">
    <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,9732,a(flip),b,8310,a)].">
      <j1 rule="hyper" parents="58 9732 8310"/>
    </justification>
  </clause>

  <clause id="9888">
    <literal><![CDATA[
      K(x,K(y,z)) * ((K(x,y) * z) \ u) = (z * K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(6535(a,1),8579(a,2,1))].">
      <j1 rule="para" parents="6535 8579"/>
    </justification>
  </clause>

  <clause id="9889">
    <literal><![CDATA[
      K(x,y * ((K(x,z) * u) \ w)) = K(x,y * ((u * K(x,z)) \ w))
    ]]></literal>
    <justification jstring="[para(9888(a,1),7815(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9888 7815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9890">
    <literal><![CDATA[
      K(x,K(y,z)) * ((K(y,z) * x) \ u) = (x * K(y,z)) \ u
    ]]></literal>
    <justification jstring="[para(8053(a,1),9888(a,1,1))].">
      <j1 rule="para" parents="8053 9888"/>
    </justification>
  </clause>

  <clause id="9891">
    <literal><![CDATA[
      K(1 / T(x,y),z) \ K(K(1 / T(x,y),z),y) = K(z,1 / x)
    ]]></literal>
    <justification jstring="[hyper(334,a,5232,a(flip),b,8584,a),flip(a)].">
      <j1 rule="hyper" parents="334 5232 8584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9892">
    <literal><![CDATA[
      K(x,1 / T(T(y,z),z)) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(9594,a,9891,a)].">
      <j1 rule="hyper" parents="9594 9891"/>
    </justification>
  </clause>

  <clause id="9893">
    <literal><![CDATA[
      K(x,1 / ((y * z) / y)) = K(x,1 / T(z,y))
    ]]></literal>
    <justification jstring="[para(230(a,1),9892(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="230 9892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9894">
    <literal><![CDATA[
      K(x,1 / T(y,z / y)) = K(x,1 / (z / (z / y)))
    ]]></literal>
    <justification jstring="[para(252(a,1),9892(a,1,2,2,1))].">
      <j1 rule="para" parents="252 9892"/>
    </justification>
  </clause>

  <clause id="9895">
    <literal><![CDATA[
      K(x,K(y,z) / y) = K(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[para(5224(a,2),9893(a,1,2))].">
      <j1 rule="para" parents="5224 9893"/>
    </justification>
  </clause>

  <clause id="9896">
    <literal><![CDATA[
      K(x,K(1 / y,z) / (1 / y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,5774,a(flip),b,9895,a),flip(a)].">
      <j1 rule="hyper" parents="334 5774 9895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9897">
    <literal><![CDATA[
      K(x,1 / (K(y,z \ 1) / z)) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(5538(a,1),9896(a,1,2))].">
      <j1 rule="para" parents="5538 9896"/>
    </justification>
  </clause>

  <clause id="9898">
    <literal><![CDATA[
      K(x,y * K(y \ 1,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6545,a(flip),b,9897,a)].">
      <j1 rule="hyper" parents="58 6545 9897"/>
    </justification>
  </clause>

  <clause id="9899">
    <literal><![CDATA[
      K(x,y * K(1 / y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(3442(a,2),9898(a,1,2,2))].">
      <j1 rule="para" parents="3442 9898"/>
    </justification>
  </clause>

  <clause id="9900">
    <literal><![CDATA[
      T(K(x,y),z / (1 / y)) = K(x,1 / (z / (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(58,a,5774,a(flip),b,9894,a)].">
      <j1 rule="hyper" parents="58 5774 9894"/>
    </justification>
  </clause>

  <clause id="9901">
    <literal><![CDATA[
      K(T(x,y) / y,z) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(29,a,8249,a(flip),b,8611,a)].">
      <j1 rule="hyper" parents="29 8249 8611"/>
    </justification>
  </clause>

  <clause id="9902">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(334,a,8780,a(flip),b,8781,a),flip(a)].">
      <j1 rule="hyper" parents="334 8780 8781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9903">
    <literal><![CDATA[
      K(x,R(x \ y,x,z / y)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,8787,a,b,9902,a)].">
      <j1 rule="hyper" parents="58 8787 9902"/>
    </justification>
  </clause>

  <clause id="9904">
    <literal><![CDATA[
      K(x,R(x \ (y / z),x,y / (y / z))) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(75(a,1),9903(a,2,2,2,1))].">
      <j1 rule="para" parents="75 9903"/>
    </justification>
  </clause>

  <clause id="9905">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (y \ 1)) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(3688(a,1),8809(a,1,1,2))].">
      <j1 rule="para" parents="3688 8809"/>
    </justification>
  </clause>

  <clause id="9906">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,K(x,v5)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(334,a,7843,a(flip),b,8826,a),flip(a)].">
      <j1 rule="hyper" parents="334 7843 8826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9908">
    <literal><![CDATA[
      K(x,T(1 \ ((y \ z) * x),z)) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,9482,a(flip),b,8849,a)].">
      <j1 rule="hyper" parents="58 9482 8849"/>
    </justification>
  </clause>

  <clause id="9909">
    <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(334,a,7805,a(flip),b,8951,a),flip(a)].">
      <j1 rule="hyper" parents="334 7805 8951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9910">
    <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,8960,a(flip),b,9909,a)].">
      <j1 rule="hyper" parents="58 8960 9909"/>
    </justification>
  </clause>

  <clause id="9911">
    <literal><![CDATA[
      T(x,T(y,z)) \ R(x,y,x) = K(y * x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(8732,a,9910,a),flip(a)].">
      <j1 rule="hyper" parents="8732 9910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9912">
    <literal><![CDATA[
      K(x,T(y,z)) * a(y,x,y) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(9202,a,9911,a)].">
      <j1 rule="hyper" parents="9202 9911"/>
    </justification>
  </clause>

  <clause id="9913">
    <literal><![CDATA[
      K(x,T(y,z)) * a(y,x,y) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,6194,a(flip),b,9912,a),flip(a)].">
      <j1 rule="hyper" parents="334 6194 9912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9914">
    <literal><![CDATA[
      K(x / y,z) * a(z,y \ x,z) = K((y \ x) * z,T(z,y))
    ]]></literal>
    <justification jstring="[para(8180(a,1),9912(a,1,1))].">
      <j1 rule="para" parents="8180 9912"/>
    </justification>
  </clause>

  <clause id="9915">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (K(x,T(y,z)) * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(9912(a,1),9365(a,1,1))].">
      <j1 rule="para" parents="9912 9365"/>
    </justification>
  </clause>

  <clause id="9916">
    <literal><![CDATA[
      a(x,y,x) * K(y,T(x,z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(9826,a,9913,a)].">
      <j1 rule="hyper" parents="9826 9913"/>
    </justification>
  </clause>

  <clause id="9917">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(x,T(y,z)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7476,a,9916,a)].">
      <j1 rule="hyper" parents="7476 9916"/>
    </justification>
  </clause>

  <clause id="9918">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (y * K(x,T(y,z))) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(2539(a,1),9915(a,1,2))].">
      <j1 rule="para" parents="2539 9915"/>
    </justification>
  </clause>

  <clause id="9919">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K(y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7473,a,9918,a)].">
      <j1 rule="hyper" parents="7473 9918"/>
    </justification>
  </clause>

  <clause id="9920">
    <literal><![CDATA[
      T(x,T(x * y,z)) * K(y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4834(a,1),9919(a,1,1))].">
      <j1 rule="para" parents="4834 9919"/>
    </justification>
  </clause>

  <clause id="9921">
    <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(334,a,4532,a(flip),b,8969,a),flip(a)].">
      <j1 rule="hyper" parents="334 4532 8969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9922">
    <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(334,a,4531,a(flip),b,8970,a),flip(a)].">
      <j1 rule="hyper" parents="334 4531 8970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9923">
    <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(7270(a,2),8982(a,1,1,2))].">
      <j1 rule="para" parents="7270 8982"/>
    </justification>
  </clause>

  <clause id="9924">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) = K((x * y) \ (u * z),z)
    ]]></literal>
    <justification jstring="[hyper(5507,a,8990,a),flip(a)].">
      <j1 rule="hyper" parents="5507 8990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9925">
    <literal><![CDATA[
      K((x * (y \ z)) \ u,y) = K((x * z) \ (u * y),y)
    ]]></literal>
    <justification jstring="[hyper(7148,a,9924,a)].">
      <j1 rule="hyper" parents="7148 9924"/>
    </justification>
  </clause>

  <clause id="9926">
    <literal><![CDATA[
      K((x * (y \ 1)) \ z,y) = K(x \ (z * y),y)
    ]]></literal>
    <justification jstring="[para(3(a,1),9925(a,2,1,1))].">
      <j1 rule="para" parents="3 9925"/>
    </justification>
  </clause>

  <clause id="9927">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6929,a,b,9926,a)].">
      <j1 rule="hyper" parents="58 6929 9926"/>
    </justification>
  </clause>

  <clause id="9928">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(z \ ((z * y) * x),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6905,a,b,9926,a)].">
      <j1 rule="hyper" parents="58 6905 9926"/>
    </justification>
  </clause>

  <clause id="9929">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(z \ (x * (z * y)),x)
    ]]></literal>
    <justification jstring="[hyper(334,a,7912,a(flip),b,9928,a),flip(a)].">
      <j1 rule="hyper" parents="334 7912 9928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9930">
    <literal><![CDATA[
      K(x \ ((x * y) * z),z) \ K(z * y,z) = a(x,y,K(z * y,z))
    ]]></literal>
    <justification jstring="[para(9928(a,1),1990(a,1,1))].">
      <j1 rule="para" parents="9928 1990"/>
    </justification>
  </clause>

  <clause id="9931">
    <literal><![CDATA[
      L(K(x * y,y),x,z) = K(z \ ((z * x) * y),y)
    ]]></literal>
    <justification jstring="[para(5532(a,2),9928(a,1,1))].">
      <j1 rule="para" parents="5532 9928"/>
    </justification>
  </clause>

  <clause id="9932">
    <literal><![CDATA[
      L(K(x * y,y),x,z) = K(z \ (y * (z * x)),y)
    ]]></literal>
    <justification jstring="[para(5532(a,2),9929(a,1,1))].">
      <j1 rule="para" parents="5532 9929"/>
    </justification>
  </clause>

  <clause id="9933">
    <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(9929(a,1),7304(a,2,1))].">
      <j1 rule="para" parents="9929 7304"/>
    </justification>
  </clause>

  <clause id="9934">
    <literal><![CDATA[
      K(x,y \ ((y * z) * x)) * K(x * z,x) = a(y,z,K(x * z,x))
    ]]></literal>
    <justification jstring="[hyper(5426,a,9930,a)].">
      <j1 rule="hyper" parents="5426 9930"/>
    </justification>
  </clause>

  <clause id="9935">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[hyper(30,a,6199,a,b,9934,a)].">
      <j1 rule="hyper" parents="30 6199 9934"/>
    </justification>
  </clause>

  <clause id="9936">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,y) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[para(5(a,1),9935(a,2,2,2,1))].">
      <j1 rule="para" parents="5 9935"/>
    </justification>
  </clause>

  <clause id="9937">
    <literal><![CDATA[
      L(K(x,y * x),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[para(5649(a,2),9935(a,1,1))].">
      <j1 rule="para" parents="5649 9935"/>
    </justification>
  </clause>

  <clause id="9938">
    <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(309(a,1),9937(a,2,2))].">
      <j1 rule="para" parents="309 9937"/>
    </justification>
  </clause>

  <clause id="9939">
    <literal><![CDATA[
      L(K(L(x,y,z),y * L(x,y,z)),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,6890,a(flip),b,9938,a),flip(a)].">
      <j1 rule="hyper" parents="334 6890 9938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9941">
    <literal><![CDATA[
      K(x,(((K(y,x \ z) / y) \ 1) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(5536(a,2),8993(a,1,2,1,1))].">
      <j1 rule="para" parents="5536 8993"/>
    </justification>
  </clause>

  <clause id="9942">
    <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),9053(a,1,2,2))].">
      <j1 rule="para" parents="180 9053"/>
    </justification>
  </clause>

  <clause id="9943">
    <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,6793,a(flip),b,9084,a),flip(a)].">
      <j1 rule="hyper" parents="58 6793 9084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9944">
    <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,6989,a(flip),b,9943,a),flip(a)].">
      <j1 rule="hyper" parents="58 6989 9943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9945">
    <literal><![CDATA[
      T(K(x \ T(y,z),u),T(y,x)) = K((x / y) \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(8158,a,9944,a)].">
      <j1 rule="hyper" parents="8158 9944"/>
    </justification>
  </clause>

  <clause id="9946">
    <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(2075(a,2),9130(a,2,2))].">
      <j1 rule="para" parents="2075 9130"/>
    </justification>
  </clause>

  <clause id="9947">
    <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(6516(a,1),9130(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6516 9130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9948">
    <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(2068(a,1),9132(a,2,2))].">
      <j1 rule="para" parents="2068 9132"/>
    </justification>
  </clause>

  <clause id="9949">
    <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(6941(a,1),9145(a,1,1))].">
      <j1 rule="para" parents="6941 9145"/>
    </justification>
  </clause>

  <clause id="9950">
    <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(9200(a,2),39(a,1))].">
      <j1 rule="para" parents="9200 39"/>
    </justification>
  </clause>

  <clause id="9951">
    <literal><![CDATA[
      K(x,y / ((T(z,u) \ u) / w)) = K(x,y / ((z \ T(u,z)) / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9253,a(flip),b,9260,a),flip(a)].">
      <j1 rule="hyper" parents="58 9253 9260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9952">
    <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(8053(a,1),9304(a,1,1,1))].">
      <j1 rule="para" parents="8053 9304"/>
    </justification>
  </clause>

  <clause id="9953">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z / ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[para(4(a,1),9312(a,1,2))].">
      <j1 rule="para" parents="4 9312"/>
    </justification>
  </clause>

  <clause id="9954">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) = K(x / ((y * z) \ y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9733,a(flip),b,9953,a)].">
      <j1 rule="hyper" parents="58 9733 9953"/>
    </justification>
  </clause>

  <clause id="9955">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(((y * z) \ y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(9954(a,2),8273(a,1))].">
      <j1 rule="para" parents="9954 8273"/>
    </justification>
  </clause>

  <clause id="9956">
    <literal><![CDATA[
      T(x / T(y,x),z) * T(y,T(x,z)) = x * K(T(x,y) / y,z)
    ]]></literal>
    <justification jstring="[para(7688(a,1),9341(a,1,2))].">
      <j1 rule="para" parents="7688 9341"/>
    </justification>
  </clause>

  <clause id="9957">
    <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(9465(a,1),6640(a,1,2))].">
      <j1 rule="para" parents="9465 6640"/>
    </justification>
  </clause>

  <clause id="9958">
    <literal><![CDATA[
      (x / a(y,z,K(u,w))) * K(u,w) = x * L(K(u,w),z,y)
    ]]></literal>
    <justification jstring="[para(6201(a,1),9472(a,1,1,2))].">
      <j1 rule="para" parents="6201 9472"/>
    </justification>
  </clause>

  <clause id="9959">
    <literal><![CDATA[
      (x * K((y \ 1) \ (z \ x),z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(4896,a,9606,a),flip(a)].">
      <j1 rule="hyper" parents="4896 9606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9960">
    <literal><![CDATA[
      (x * K((y \ z) \ x,z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(8576(a,1),9959(a,1,1,2))].">
      <j1 rule="para" parents="8576 9959"/>
    </justification>
  </clause>

  <clause id="9961">
    <literal><![CDATA[
      x \ R(x * K(y,x),y,y \ 1) = K(y,x) * a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(725(a,1),9724(a,2,2))].">
      <j1 rule="para" parents="725 9724"/>
    </justification>
  </clause>

  <clause id="9962">
    <literal><![CDATA[
      K(x,y) * a(y,x,x \ 1) = y \ ((x * y) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(5203(a,1),9961(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5203 9961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9963">
    <literal><![CDATA[
      K(x,(x \ ((y * x) * (y \ 1))) \ z) = K(x,a(x,y,y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(9962(a,1),8834(a,1,2,1))].">
      <j1 rule="para" parents="9962 8834"/>
    </justification>
  </clause>

  <clause id="9964">
    <literal><![CDATA[
      K(x,((y * x) * (y \ 1)) \ (x * z)) = K(x,a(x,y,y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7271,a(flip),b,9963,a)].">
      <j1 rule="hyper" parents="58 7271 9963"/>
    </justification>
  </clause>

  <clause id="9965">
    <literal><![CDATA[
      T(x / y,K(((x / y) \ (1 / y)) \ 1,z)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8875,a(flip),b,9882,a),flip(a)].">
      <j1 rule="hyper" parents="334 8875 9882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9966">
    <literal><![CDATA[
      T(x / y,K(z,((x / y) \ (1 / y)) \ 1)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(8134,a,9965,a)].">
      <j1 rule="hyper" parents="8134 9965"/>
    </justification>
  </clause>

  <clause id="9967">
    <literal><![CDATA[
      T(x / y,K(z,(1 / y) \ (x / y))) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(6423(a,1),9966(a,1,2))].">
      <j1 rule="para" parents="6423 9966"/>
    </justification>
  </clause>

  <clause id="9968">
    <literal><![CDATA[
      (x / T(y / (y / z),u)) * z = x * (T(y / (y / z),u) \ z)
    ]]></literal>
    <justification jstring="[para(8309(a,1),9887(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8309 9887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9969">
    <literal><![CDATA[
      (x / T(1 / (1 / y),z)) * y = x * (y * (1 / T(y,z)))
    ]]></literal>
    <justification jstring="[para(7091(a,1),9968(a,2,2))].">
      <j1 rule="para" parents="7091 9968"/>
    </justification>
  </clause>

  <clause id="9970">
    <literal><![CDATA[
      K(x,T((y \ z) * x,z)) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[para(60(a,1),9908(a,1,2,1))].">
      <j1 rule="para" parents="60 9908"/>
    </justification>
  </clause>

  <clause id="9971">
    <literal><![CDATA[
      K(x,T(((y \ z) \ 1) \ x,y)) = K(x,T((y \ z) * x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8782,a(flip),b,9970,a)].">
      <j1 rule="hyper" parents="334 8782 9970"/>
    </justification>
  </clause>

  <clause id="9972">
    <literal><![CDATA[
      K(x,T(1 \ ((y \ z) * x),y)) = K(x,T((y \ z) * x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9482,a(flip),b,9971,a)].">
      <j1 rule="hyper" parents="58 9482 9971"/>
    </justification>
  </clause>

  <clause id="9973">
    <literal><![CDATA[
      K(x,T((y \ z) * x,z)) = K(x,T((y \ z) * x,y))
    ]]></literal>
    <justification jstring="[para(60(a,1),9972(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="60 9972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9974">
    <literal><![CDATA[
      K(x \ (y * T(z,u)),T(z,w)) = K(x \ (z * y),T(z,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,8934,a(flip),b,9923,a),flip(a)].">
      <j1 rule="hyper" parents="58 8934 9923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9976">
    <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,9931,a,b,9974,a)].">
      <j1 rule="hyper" parents="58 9931 9974"/>
    </justification>
  </clause>

  <clause id="9977">
    <literal><![CDATA[
      L(K(x * y,T(y,z)),x,u) = K(u \ (y * (u * x)),T(y,z))
    ]]></literal>
    <justification jstring="[para(7834(a,1),9976(a,1,1))].">
      <j1 rule="para" parents="7834 9976"/>
    </justification>
  </clause>

  <clause id="9979">
    <literal><![CDATA[
      K(x \ (y * (x * z)),T(y,u * z)) = L(K(y * z,T(y,u)),z,x)
    ]]></literal>
    <justification jstring="[para(9400(a,1),9977(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9400 9977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9980">
    <literal><![CDATA[
      L(K(x * y,T(x,z)),y,z) = K((z / (z * y)) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(8609,a,9979,a),flip(a)].">
      <j1 rule="hyper" parents="8609 9979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9981">
    <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,7067,a(flip),b,9947,a)].">
      <j1 rule="hyper" parents="117 7067 9947"/>
    </justification>
  </clause>

  <clause id="9982">
    <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(6527,a,9948,a)].">
      <j1 rule="hyper" parents="6527 9948"/>
    </justification>
  </clause>

  <clause id="9983">
    <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(334,a,2068,a(flip),b,9949,a),flip(a)].">
      <j1 rule="hyper" parents="334 2068 9949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9984">
    <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(9107(a,1),9952(a,1,1))].">
      <j1 rule="para" parents="9107 9952"/>
    </justification>
  </clause>

  <clause id="9985">
    <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(8053(a,1),9984(a,2,1))].">
      <j1 rule="para" parents="8053 9984"/>
    </justification>
  </clause>

  <clause id="9986">
    <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(8048(a,1),9985(a,2,2))].">
      <j1 rule="para" parents="8048 9985"/>
    </justification>
  </clause>

  <clause id="9987">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * K(w,u) = x * L(K(w,u),z,y)
    ]]></literal>
    <justification jstring="[para(6201(a,1),9982(a,1,1,2))].">
      <j1 rule="para" parents="6201 9982"/>
    </justification>
  </clause>

  <clause id="9988">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) = x * a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(30,a,9958,a,b,9987,a)].">
      <j1 rule="hyper" parents="30 9958 9987"/>
    </justification>
  </clause>

  <clause id="9989">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) \ x = a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(585,a,9988,a)].">
      <j1 rule="hyper" parents="585 9988"/>
    </justification>
  </clause>

  <clause id="9990">
    <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(9988(a,1),276(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9988 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9991">
    <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(324(a,1),9990(a,1))].">
      <j1 rule="para" parents="324 9990"/>
    </justification>
  </clause>

  <clause id="9992">
    <literal><![CDATA[
      K(x,y) * T(y,K(z,y) * (x * y)) = L(y,K(z,y) * x,y)
    ]]></literal>
    <justification jstring="[para(7597(a,1),7779(a,1,1))].">
      <j1 rule="para" parents="7597 7779"/>
    </justification>
  </clause>

  <clause id="9993">
    <literal><![CDATA[
      L(x,K(y,x) * z,x) = K(z,x) * T(x,z * x)
    ]]></literal>
    <justification jstring="[para(7520(a,1),9992(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7520 9992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9995">
    <literal><![CDATA[
      L(x,K(y,x) * z,x) = L(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,5353,a(flip),b,9993,a),flip(a)].">
      <j1 rule="hyper" parents="334 5353 9993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9997">
    <literal><![CDATA[
      L(x,T(x,y) \ z,x) = L(x,x \ z,x)
    ]]></literal>
    <justification jstring="[para(5392(a,1),9995(a,1,2))].">
      <j1 rule="para" parents="5392 9995"/>
    </justification>
  </clause>

  <clause id="9998">
    <literal><![CDATA[
      L(x,y / T(x,z),x) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9434,a,b,9997,a)].">
      <j1 rule="hyper" parents="58 9434 9997"/>
    </justification>
  </clause>

  <clause id="10000">
    <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,7260,a,b,9998,a)].">
      <j1 rule="hyper" parents="58 7260 9998"/>
    </justification>
  </clause>

  <clause id="10002">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),L(y,u,w)) = K(x \ z,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,5075,a(flip),b,7914,a),flip(a)].">
      <j1 rule="hyper" parents="334 5075 7914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10003">
    <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),10002(a,1,1,2,1))].">
      <j1 rule="para" parents="4 10002"/>
    </justification>
  </clause>

  <clause id="10004">
    <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(4040(a,2),8276(a,1,1))].">
      <j1 rule="para" parents="4040 8276"/>
    </justification>
  </clause>

  <clause id="10005">
    <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(334,a,8033,a,b,8282,a)].">
      <j1 rule="hyper" parents="334 8033 8282"/>
    </justification>
  </clause>

  <clause id="10006">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,x) \ z) = ((y * x) / y) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(4123(a,1),8300(a,1,2,1))].">
      <j1 rule="para" parents="4123 8300"/>
    </justification>
  </clause>

  <clause id="10007">
    <literal><![CDATA[
      K(L(x / (y \ 1),y \ 1,y) \ 1,z) = K(T(y * x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,8642,a(flip),b,8630,a),flip(a)].">
      <j1 rule="hyper" parents="334 8642 8630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10008">
    <literal><![CDATA[
      (x * y) / (x * (y * K(z,u))) = L(T(K(u,z),x * y),y,x)
    ]]></literal>
    <justification jstring="[para(8725(a,1),8878(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8725 8878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10009">
    <literal><![CDATA[
      (x * y) / (x * (y * K(z,u))) = L(K(u,T(z,x * y)),y,x)
    ]]></literal>
    <justification jstring="[para(7401(a,2),10008(a,2,1))].">
      <j1 rule="para" parents="7401 10008"/>
    </justification>
  </clause>

  <clause id="10011">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = (u * z) / (u * (K(y,x) * z))
    ]]></literal>
    <justification jstring="[para(7393(a,1),10009(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7393 10009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10012">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = (x * y) / (x * (K(u,z) * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9775,a(flip),b,10011,a)].">
      <j1 rule="hyper" parents="58 9775 10011"/>
    </justification>
  </clause>

  <clause id="10013">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = K(z,(x * y) / (x * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(334,a,6339,a,b,10012,a),flip(a)].">
      <j1 rule="hyper" parents="334 6339 10012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10014">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) = (y * (K(x,u) * z)) / (y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6283,a(flip),b,10013,a),flip(a)].">
      <j1 rule="hyper" parents="58 6283 10013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10015">
    <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(9422(a,1),9177(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9422 9177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10016">
    <literal><![CDATA[
      L(T(x,a(y,z,y)),a(y,z,y),y) = x
    ]]></literal>
    <justification jstring="[hyper(334,a,4,a(flip),b,10015,a),flip(a)].">
      <j1 rule="hyper" parents="334 4 10015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10018">
    <literal><![CDATA[
      L(x,a(y,z,y),y) = x
    ]]></literal>
    <justification jstring="[para(9805(a,1),10016(a,1,1))].">
      <j1 rule="para" parents="9805 10016"/>
    </justification>
  </clause>

  <clause id="10020">
    <literal><![CDATA[
      L(x,a(y,z,y),T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(9643(a,1),10018(a,1,2))].">
      <j1 rule="para" parents="9643 10018"/>
    </justification>
  </clause>

  <clause id="10021">
    <literal><![CDATA[
      (T(x,y) * a(x,z,x)) * u = T(x,y) * (a(x,z,x) * u)
    ]]></literal>
    <justification jstring="[hyper(1392,a,10020,a),flip(a)].">
      <j1 rule="hyper" parents="1392 10020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10022">
    <literal><![CDATA[
      T(x,y) * (a(x,z,x) * u) = R(T(x,y),z,x) * u
    ]]></literal>
    <justification jstring="[para(9165(a,1),10021(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9165 10021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10023">
    <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(334,a,8049,a(flip),b,9462,a),flip(a)].">
      <j1 rule="hyper" parents="334 8049 9462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10024">
    <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(7804(a,1),9855(a,1,1))].">
      <j1 rule="para" parents="7804 9855"/>
    </justification>
  </clause>

  <clause id="10025">
    <literal><![CDATA[
      (x * (K(y \ x,y) * z)) / (x * z) = L(K(y \ x,y),z,x)
    ]]></literal>
    <justification jstring="[para(8153(a,1),9856(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8153 9856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10026">
    <literal><![CDATA[
      L(K(x \ y,x),z,y) * (y * z) = y * (K(x \ y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,10025,a)].">
      <j1 rule="hyper" parents="133 10025"/>
    </justification>
  </clause>

  <clause id="10028">
    <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),10026(a,1,1,1,1))].">
      <j1 rule="para" parents="4 10026"/>
    </justification>
  </clause>

  <clause id="10029">
    <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(5418(a,1),10004(a,2,2))].">
      <j1 rule="para" parents="5418 10004"/>
    </justification>
  </clause>

  <clause id="10030">
    <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(10004(a,1),8434(a,2,2))].">
      <j1 rule="para" parents="10004 8434"/>
    </justification>
  </clause>

  <clause id="10031">
    <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(8089,a,10023,a)].">
      <j1 rule="hyper" parents="8089 10023"/>
    </justification>
  </clause>

  <clause id="10032">
    <literal><![CDATA[
      ((x * y) \ ((x * K(z,u)) * y)) \ 1 = (x * y) \ ((x * K(u,z)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9769,a(flip),b,10024,a),flip(a)].">
      <j1 rule="hyper" parents="58 9769 10024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10033">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) \ 1 = (x * z) \ ((x * K(u,y)) * z)
    ]]></literal>
    <justification jstring="[para(7107(a,2),10032(a,1,1))].">
      <j1 rule="para" parents="7107 10032"/>
    </justification>
  </clause>

  <clause id="10034">
    <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(10033(a,1),5241(a,1))].">
      <j1 rule="para" parents="10033 5241"/>
    </justification>
  </clause>

  <clause id="10035">
    <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(1390(a,1),7623(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1390 7623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10036">
    <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(6152(a,1),7732(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6152 7732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10037">
    <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(334,a,3489,a,b,10036,a),flip(a)].">
      <j1 rule="hyper" parents="334 3489 10036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10038">
    <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(334,a,6947,a,b,8385,a),flip(a)].">
      <j1 rule="hyper" parents="334 6947 8385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10039">
    <literal><![CDATA[
      K(x,K((1 / y) / z,(z * y) / u)) = (T(z * y,K(x,u)) / y) / z
    ]]></literal>
    <justification jstring="[hyper(8481,a,8437,a)].">
      <j1 rule="hyper" parents="8481 8437"/>
    </justification>
  </clause>

  <clause id="10040">
    <literal><![CDATA[
      K(x,K((1 / y) / z,(z * y) / u)) = K(x,K(u,(1 / y) / z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8480,a(flip),b,10039,a),flip(a)].">
      <j1 rule="hyper" parents="334 8480 10039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10041">
    <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(537(a,2),10040(a,1,2,2))].">
      <j1 rule="para" parents="537 10040"/>
    </justification>
  </clause>

  <clause id="10042">
    <literal><![CDATA[
      T((1 / ((x * y) \ x)) * K(y,z),y) = (y \ (1 / ((x * y) \ x))) * T(y,z)
    ]]></literal>
    <justification jstring="[para(7012(a,1),8565(a,2,1))].">
      <j1 rule="para" parents="7012 8565"/>
    </justification>
  </clause>

  <clause id="10043">
    <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(334,a,9946,a(flip),b,8883,a),flip(a)].">
      <j1 rule="hyper" parents="334 9946 8883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10044">
    <literal><![CDATA[
      K(L(x,y,z),(u * (w * x)) \ v5) = K(L(x,y,z),(u * (x * w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(8691,a,8954,a),flip(a)].">
      <j1 rule="hyper" parents="8691 8954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10045">
    <literal><![CDATA[
      K((x * (y * z)) \ (x * ((z * u) * y)),y) = K(L(u,y * z,x),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,7316,a(flip),b,8974,a),flip(a)].">
      <j1 rule="hyper" parents="334 7316 8974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10046">
    <literal><![CDATA[
      K((x * y) \ (z \ (x * ((y * u) * z))),z) = K(L(u,z * y,x),z)
    ]]></literal>
    <justification jstring="[hyper(9621,a,10045,a)].">
      <j1 rule="hyper" parents="9621 10045"/>
    </justification>
  </clause>

  <clause id="10048">
    <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(8978(a,1),8691(a,1))].">
      <j1 rule="para" parents="8978 8691"/>
    </justification>
  </clause>

  <clause id="10049">
    <literal><![CDATA[
      x \ (K(y,z) * (K(u,y) * x)) = T(K(u,y),x) * T(K(y,z),x)
    ]]></literal>
    <justification jstring="[para(7940(a,1),9146(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7940 9146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10051">
    <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(1622(a,1),9191(a,1,2,2))].">
      <j1 rule="para" parents="1622 9191"/>
    </justification>
  </clause>

  <clause id="10052">
    <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(6267(a,1),9276(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6267 9276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10053">
    <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(7401(a,2),9280(a,1,2))].">
      <j1 rule="para" parents="7401 9280"/>
    </justification>
  </clause>

  <clause id="10054">
    <literal><![CDATA[
      ((x * y) * a(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(9643(a,1),9368(a,1,1,2))].">
      <j1 rule="para" parents="9643 9368"/>
    </justification>
  </clause>

  <clause id="10055">
    <literal><![CDATA[
      (x * R(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(9410(a,1),10054(a,1,1))].">
      <j1 rule="para" parents="9410 10054"/>
    </justification>
  </clause>

  <clause id="10057">
    <literal><![CDATA[
      (x * R(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,7762,a(flip),b,10055,a),flip(a)].">
      <j1 rule="hyper" parents="334 7762 10055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10059">
    <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(10057(a,2),8721(a,1))].">
      <j1 rule="para" parents="10057 8721"/>
    </justification>
  </clause>

  <clause id="10060">
    <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(8048(a,1),9382(a,1,1))].">
      <j1 rule="para" parents="8048 9382"/>
    </justification>
  </clause>

  <clause id="10061">
    <literal><![CDATA[
      K(x,T((y \ z) / z,u)) = K(x,T(y \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,9424,a(flip),b,9426,a),flip(a)].">
      <j1 rule="hyper" parents="334 9424 9426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10062">
    <literal><![CDATA[
      T(x,T((y \ z) / z,u)) = T(x,T(y \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,10061,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 10061 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10063">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,u)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(75(a,1),10061(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="75 10061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10064">
    <literal><![CDATA[
      T(x,T((y / z) \ 1,u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(75(a,1),10062(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="75 10062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10065">
    <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(10063(a,1),9917(a,1,1))].">
      <j1 rule="para" parents="10063 9917"/>
    </justification>
  </clause>

  <clause id="10066">
    <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(6582(a,1),10064(a,2,2,1))].">
      <j1 rule="para" parents="6582 10064"/>
    </justification>
  </clause>

  <clause id="10067">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T(y \ x,u)) = K((x \ y) \ z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(9493,a,9494,a)].">
      <j1 rule="hyper" parents="9493 9494"/>
    </justification>
  </clause>

  <clause id="10068">
    <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,8562,a(flip),b,10067,a)].">
      <j1 rule="hyper" parents="58 8562 10067"/>
    </justification>
  </clause>

  <clause id="10069">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),T(z \ y,z)) = K((y \ z) \ x,y / z)
    ]]></literal>
    <justification jstring="[hyper(334,a,8186,a(flip),b,10068,a),flip(a)].">
      <j1 rule="hyper" parents="334 8186 10068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10070">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),y / z) = K((y \ z) \ x,y / z)
    ]]></literal>
    <justification jstring="[hyper(8328,a,10069,a)].">
      <j1 rule="hyper" parents="8328 10069"/>
    </justification>
  </clause>

  <clause id="10071">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) = K((x \ y) \ z,x / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8870,a,b,10070,a)].">
      <j1 rule="hyper" parents="58 8870 10070"/>
    </justification>
  </clause>

  <clause id="10072">
    <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(9101(a,2),9604(a,1,1))].">
      <j1 rule="para" parents="9101 9604"/>
    </justification>
  </clause>

  <clause id="10073">
    <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(5299,a,9647,a),flip(a)].">
      <j1 rule="hyper" parents="5299 9647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10074">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (y \ 1),1 / y)
    ]]></literal>
    <justification jstring="[para(3124(a,1),9701(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3124 9701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10075">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(334,a,4275,a,b,10074,a),flip(a)].">
      <j1 rule="hyper" parents="334 4275 10074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10076">
    <literal><![CDATA[
      K((x / y) / (1 / y),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4275,a,b,10075,a)].">
      <j1 rule="hyper" parents="58 4275 10075"/>
    </justification>
  </clause>

  <clause id="10077">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[para(10076(a,1),5018(a,2,2))].">
      <j1 rule="para" parents="10076 5018"/>
    </justification>
  </clause>

  <clause id="10078">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ (x \ u)) = K(x,(y * (z \ x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(7030,a,9905,a),flip(a)].">
      <j1 rule="hyper" parents="7030 9905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10079">
    <literal><![CDATA[
      K(x,(y * (z \ x)) \ (u * x)) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(7706,a,10078,a),flip(a)].">
      <j1 rule="hyper" parents="7706 10078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10080">
    <literal><![CDATA[
      K(x,(y * ((z \ x) \ 1)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7143,a(flip),b,10079,a),flip(a)].">
      <j1 rule="hyper" parents="58 7143 10079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10081">
    <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(5783(a,1),10080(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5783 10080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10082">
    <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),9921(a,1,1,2,1))].">
      <j1 rule="para" parents="4 9921"/>
    </justification>
  </clause>

  <clause id="10083">
    <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),9922(a,1,1,2,1))].">
      <j1 rule="para" parents="4 9922"/>
    </justification>
  </clause>

  <clause id="10084">
    <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,5587,a,b,9941,a)].">
      <j1 rule="hyper" parents="58 5587 9941"/>
    </justification>
  </clause>

  <clause id="10085">
    <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,7917,a,b,10035,a)].">
      <j1 rule="hyper" parents="58 7917 10035"/>
    </justification>
  </clause>

  <clause id="10086">
    <literal><![CDATA[
      K(x / y,z) * K(K(y \ x,z) * x,x) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4766(a,1),10038(a,2,1))].">
      <j1 rule="para" parents="4766 10038"/>
    </justification>
  </clause>

  <clause id="10087">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10086,a(flip),b,8385,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 10086 8385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10088">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(T(x,y) / y,z)
    ]]></literal>
    <justification jstring="[para(4488(a,2),10087(a,2,2,1))].">
      <j1 rule="para" parents="4488 10087"/>
    </justification>
  </clause>

  <clause id="10089">
    <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,228,a(flip),b,10051,a),flip(a)].">
      <j1 rule="hyper" parents="58 228 10051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10090">
    <literal><![CDATA[
      L(a(x,T(y,z),x),T(y,z),z) = R(a(x,y,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,9858,a(flip),b,10089,a),flip(a)].">
      <j1 rule="hyper" parents="334 9858 10089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10091">
    <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(5086(a,1),10090(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5086 10090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10092">
    <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(7477,a,10053,a),flip(a)].">
      <j1 rule="hyper" parents="7477 10053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10093">
    <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(5989(a,1),10060(a,1,2))].">
      <j1 rule="para" parents="5989 10060"/>
    </justification>
  </clause>

  <clause id="10094">
    <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(8097,a,10093,a)].">
      <j1 rule="hyper" parents="8097 10093"/>
    </justification>
  </clause>

  <clause id="10095">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,x) * T(z \ 1,y)) = T(z \ K(z,x),y)
    ]]></literal>
    <justification jstring="[para(8441(a,1),10094(a,1,1))].">
      <j1 rule="para" parents="8441 10094"/>
    </justification>
  </clause>

  <clause id="10096">
    <literal><![CDATA[
      K(x,T(y,z)) * T(x \ 1,z) = T(x \ K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(9451,a,10095,a)].">
      <j1 rule="hyper" parents="9451 10095"/>
    </justification>
  </clause>

  <clause id="10097">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (K(x,y) \ u)) = K(z,x) * u
    ]]></literal>
    <justification jstring="[hyper(8120,a,10072,a),flip(a)].">
      <j1 rule="hyper" parents="8120 10072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10099">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * u) = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(4(a,1),10097(a,1,2,2))].">
      <j1 rule="para" parents="4 10097"/>
    </justification>
  </clause>

  <clause id="10100">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (K(y,x) * u)) = K(z,x) * u
    ]]></literal>
    <justification jstring="[para(5391(a,1),10097(a,1,2,2))].">
      <j1 rule="para" parents="5391 10097"/>
    </justification>
  </clause>

  <clause id="10101">
    <literal><![CDATA[
      T(x,y) \ (T(x,z) * u) = K(x,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(334,a,5499,a,b,10099,a)].">
      <j1 rule="hyper" parents="334 5499 10099"/>
    </justification>
  </clause>

  <clause id="10102">
    <literal><![CDATA[
      K(x,y) * (K(x * y,x) * z) = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(334,a,9794,a(flip),b,10099,a),flip(a)].">
      <j1 rule="hyper" parents="334 9794 10099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10103">
    <literal><![CDATA[
      K(x,y) * (K(y,z) * (K(y,x) * u)) = K(y,z) * u
    ]]></literal>
    <justification jstring="[para(5394(a,1),10099(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5394 10099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10104">
    <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(6880(a,1),10099(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6880 10099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10105">
    <literal><![CDATA[
      a(x,y,x) * (K(x,x * y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(5394(a,1),10102(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5394 10102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10106">
    <literal><![CDATA[
      a(x,x \ y,x) * (K(x,y) * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),10105(a,1,2,1,2))].">
      <j1 rule="para" parents="5 10105"/>
    </justification>
  </clause>

  <clause id="10107">
    <literal><![CDATA[
      K(x,y) * (K(z,y) * u) = K(z,y) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(5409,a,10100,a)].">
      <j1 rule="hyper" parents="5409 10100"/>
    </justification>
  </clause>

  <clause id="10108">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * u) = K(x,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(5409,a,10103,a)].">
      <j1 rule="hyper" parents="5409 10103"/>
    </justification>
  </clause>

  <clause id="10109">
    <literal><![CDATA[
      K(x,y) * (K(y,T(x,z)) * u) = K(y,K(x,z)) * u
    ]]></literal>
    <justification jstring="[para(8792(a,1),10103(a,1,2))].">
      <j1 rule="para" parents="8792 10103"/>
    </justification>
  </clause>

  <clause id="10110">
    <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(10107(a,1),1699(a,1,1,1,1))].">
      <j1 rule="para" parents="10107 1699"/>
    </justification>
  </clause>

  <clause id="10111">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(8053(a,2),10108(a,1,1))].">
      <j1 rule="para" parents="8053 10108"/>
    </justification>
  </clause>

  <clause id="10112">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(8053(a,2),10111(a,2,2,1))].">
      <j1 rule="para" parents="8053 10111"/>
    </justification>
  </clause>

  <clause id="10113">
    <literal><![CDATA[
      K(x,y) * (K(z,K(u,x)) * (K(x,y) \ w)) = K(z,K(u,x)) * w
    ]]></literal>
    <justification jstring="[hyper(356,a,10112,a),flip(a)].">
      <j1 rule="hyper" parents="356 10112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10114">
    <literal><![CDATA[
      K(x,y) * (K(z,K(x,u)) * (K(x,y) \ w)) = K(u,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(8053(a,2),10113(a,1,2,1))].">
      <j1 rule="para" parents="8053 10113"/>
    </justification>
  </clause>

  <clause id="10115">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) * y,1 / y)
    ]]></literal>
    <justification jstring="[para(6126(a,1),10077(a,2,2))].">
      <j1 rule="para" parents="6126 10077"/>
    </justification>
  </clause>

  <clause id="10116">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(6137(a,1),10115(a,2,2))].">
      <j1 rule="para" parents="6137 10115"/>
    </justification>
  </clause>

  <clause id="10117">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = K(x,1 / y) / y
    ]]></literal>
    <justification jstring="[hyper(334,a,2439,a(flip),b,10116,a),flip(a)].">
      <j1 rule="hyper" parents="334 2439 10116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10118">
    <literal><![CDATA[
      x / ((y / (x \ y)) / (1 / (x \ y))) = K(y,1 / (x \ y)) / (x \ y)
    ]]></literal>
    <justification jstring="[para(72(a,1),10117(a,1,1))].">
      <j1 rule="para" parents="72 10117"/>
    </justification>
  </clause>

  <clause id="10119">
    <literal><![CDATA[
      K(x,1 / (y \ x)) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(72(a,1),10118(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 10118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10121">
    <literal><![CDATA[
      K(x,y / x) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(5485(a,1),10119(a,1,1))].">
      <j1 rule="para" parents="5485 10119"/>
    </justification>
  </clause>

  <clause id="10122">
    <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(10121(a,2),2142(a,1,2))].">
      <j1 rule="para" parents="10121 2142"/>
    </justification>
  </clause>

  <clause id="10123">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ ((L(y,z,u) * (y \ x)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7742,a(flip),b,10085,a)].">
      <j1 rule="hyper" parents="58 7742 10085"/>
    </justification>
  </clause>

  <clause id="10124">
    <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(334,a,7719,a(flip),b,10092,a),flip(a)].">
      <j1 rule="hyper" parents="334 7719 10092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10125">
    <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(6880(a,1),10104(a,1,1))].">
      <j1 rule="para" parents="6880 10104"/>
    </justification>
  </clause>

  <clause id="10126">
    <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(7431(a,2),10124(a,2,2))].">
      <j1 rule="para" parents="7431 10124"/>
    </justification>
  </clause>

  <clause id="10127">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * (K(y,x) * z)) = T(z,T(u,K(x,y)))
    ]]></literal>
    <justification jstring="[hyper(8392,a,10126,a),flip(a)].">
      <j1 rule="hyper" parents="8392 10126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10128">
    <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(5394(a,1),10127(a,1,2,2))].">
      <j1 rule="para" parents="5394 10127"/>
    </justification>
  </clause>

  <clause id="10129">
    <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(8296(a,1),10128(a,1,2))].">
      <j1 rule="para" parents="8296 10128"/>
    </justification>
  </clause>

  <clause id="10130">
    <literal><![CDATA[
      K((x \ y) \ z,L(x,u,w)) = K(y \ (x * z),L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(6065,a,7730,a),flip(a)].">
      <j1 rule="hyper" parents="6065 7730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10131">
    <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(7730(a,1),6065(a,1))].">
      <j1 rule="para" parents="7730 6065"/>
    </justification>
  </clause>

  <clause id="10132">
    <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,7615,a(flip),b,7840,a)].">
      <j1 rule="hyper" parents="58 7615 7840"/>
    </justification>
  </clause>

  <clause id="10134">
    <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,5468,a(flip),b,10132,a),flip(a)].">
      <j1 rule="hyper" parents="58 5468 10132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10135">
    <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(8182(a,1),10134(a,1,2))].">
      <j1 rule="para" parents="8182 10134"/>
    </justification>
  </clause>

  <clause id="10136">
    <literal><![CDATA[
      K((x * y) \ z,L(y,u,w)) = K(x \ (y \ z),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(6065,a,7863,a),flip(a)].">
      <j1 rule="hyper" parents="6065 7863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10137">
    <literal><![CDATA[
      K(L(x,y,z),u * (K(x,w) * v5)) = K(L(x,y,z),u * v5)
    ]]></literal>
    <justification jstring="[hyper(334,a,5786,a(flip),b,7905,a),flip(a)].">
      <j1 rule="hyper" parents="334 5786 7905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10138">
    <literal><![CDATA[
      K(x * (K(y,z) * u),R(y,w,v5)) = K(x * u,R(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(334,a,5787,a(flip),b,7906,a),flip(a)].">
      <j1 rule="hyper" parents="334 5787 7906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10139">
    <literal><![CDATA[
      K(x * y,R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(5119(a,1),10138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5119 10138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10140">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(8110(a,1),8626(a,1,1,3))].">
      <j1 rule="para" parents="8110 8626"/>
    </justification>
  </clause>

  <clause id="10141">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5391(a,1),10140(a,2,2))].">
      <j1 rule="para" parents="5391 10140"/>
    </justification>
  </clause>

  <clause id="10142">
    <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,6857,a(flip),b,8768,a)].">
      <j1 rule="hyper" parents="58 6857 8768"/>
    </justification>
  </clause>

  <clause id="10143">
    <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(7528(a,1),8804(a,1,1,2))].">
      <j1 rule="para" parents="7528 8804"/>
    </justification>
  </clause>

  <clause id="10144">
    <literal><![CDATA[
      K(x,(y * (z * (u / x))) \ w) = K(x,(y * (z * u)) \ (w * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,8989,a(flip),b,8991,a),flip(a)].">
      <j1 rule="hyper" parents="58 8989 8991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10145">
    <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,9497,a(flip),b,9071,a)].">
      <j1 rule="hyper" parents="58 9497 9071"/>
    </justification>
  </clause>

  <clause id="10147">
    <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),10145(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 10145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10148">
    <literal><![CDATA[
      K(x,(R(x,y,z) \ u) \ w) = K(x,u \ (w * R(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,7678,a(flip),b,10147,a)].">
      <j1 rule="hyper" parents="58 7678 10147"/>
    </justification>
  </clause>

  <clause id="10149">
    <literal><![CDATA[
      K(x,y \ (R(x,z,u) * w)) = K(x,y \ (w * R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,9031,a(flip),b,10148,a)].">
      <j1 rule="hyper" parents="58 9031 10148"/>
    </justification>
  </clause>

  <clause id="10150">
    <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(8099,a,9350,a)].">
      <j1 rule="hyper" parents="8099 9350"/>
    </justification>
  </clause>

  <clause id="10151">
    <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(8367(a,1),9377(a,1,1))].">
      <j1 rule="para" parents="8367 9377"/>
    </justification>
  </clause>

  <clause id="10152">
    <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(1366(a,1),9740(a,1,2,1))].">
      <j1 rule="para" parents="1366 9740"/>
    </justification>
  </clause>

  <clause id="10153">
    <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(7671(a,1),9863(a,1,1,2))].">
      <j1 rule="para" parents="7671 9863"/>
    </justification>
  </clause>

  <clause id="10154">
    <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,5468,a(flip),b,10153,a),flip(a)].">
      <j1 rule="hyper" parents="58 5468 10153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10156">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = T(y,K(x,z)) / y
    ]]></literal>
    <justification jstring="[hyper(334,a,153,a(flip),b,9880,a),flip(a)].">
      <j1 rule="hyper" parents="334 153 9880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10157">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,5009,a,b,10156,a),flip(a)].">
      <j1 rule="hyper" parents="334 5009 10156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10159">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8048,a,b,10157,a),flip(a)].">
      <j1 rule="hyper" parents="334 8048 10157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10160">
    <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),10028(a,2,2,1,1))].">
      <j1 rule="para" parents="4 10028"/>
    </justification>
  </clause>

  <clause id="10161">
    <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(10160(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="10160 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10163">
    <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(10014(a,2),10161(a,1))].">
      <j1 rule="para" parents="10014 10161"/>
    </justification>
  </clause>

  <clause id="10164">
    <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(10044(a,2),10048(a,1))].">
      <j1 rule="para" parents="10044 10048"/>
    </justification>
  </clause>

  <clause id="10165">
    <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(10150(a,1),8099(a,1))].">
      <j1 rule="para" parents="10150 8099"/>
    </justification>
  </clause>

  <clause id="10166">
    <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(8229(a,1),10151(a,1,1,2,1))].">
      <j1 rule="para" parents="8229 10151"/>
    </justification>
  </clause>

  <clause id="10167">
    <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),10152(a,1,2,2))].">
      <j1 rule="para" parents="176 10152"/>
    </justification>
  </clause>

  <clause id="10168">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(334,a,2018,a(flip),b,4957,a),flip(a)].">
      <j1 rule="hyper" parents="334 2018 4957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10169">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,y) \ y) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[para(7941(a,1),10168(a,1,2))].">
      <j1 rule="para" parents="7941 10168"/>
    </justification>
  </clause>

  <clause id="10170">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,y) \ y) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,4700,a(flip),b,10169,a),flip(a)].">
      <j1 rule="hyper" parents="334 4700 10169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10171">
    <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(10170(a,1),741(a,1,2))].">
      <j1 rule="para" parents="10170 741"/>
    </justification>
  </clause>

  <clause id="10172">
    <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(5881(a,1),5249(a,1,2,1))].">
      <j1 rule="para" parents="5881 5249"/>
    </justification>
  </clause>

  <clause id="10173">
    <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(8740,a,10172,a)].">
      <j1 rule="hyper" parents="8740 10172"/>
    </justification>
  </clause>

  <clause id="10174">
    <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(7401(a,2),10173(a,1,2,1))].">
      <j1 rule="para" parents="7401 10173"/>
    </justification>
  </clause>

  <clause id="10175">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,K(u,z)) = y \ (y * x)
    ]]></literal>
    <justification jstring="[para(5394(a,1),5429(a,2,2))].">
      <j1 rule="para" parents="5394 5429"/>
    </justification>
  </clause>

  <clause id="10176">
    <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(10175(a,2),297(a,1))].">
      <j1 rule="para" parents="10175 297"/>
    </justification>
  </clause>

  <clause id="10178">
    <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(245(a,1),5505(a,1,2)),flip(a)].">
      <j1 rule="para" parents="245 5505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10179">
    <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(5232(a,1),10178(a,1,1,2,1))].">
      <j1 rule="para" parents="5232 10178"/>
    </justification>
  </clause>

  <clause id="10180">
    <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(244(a,1),5506(a,1,2)),flip(a)].">
      <j1 rule="para" parents="244 5506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10181">
    <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(5232(a,1),10180(a,1,1,2,1))].">
      <j1 rule="para" parents="5232 10180"/>
    </justification>
  </clause>

  <clause id="10182">
    <literal><![CDATA[
      K(x,y) * (L(K(y,x),z,u) * w) = a(u,z,K(x,y)) * w
    ]]></literal>
    <justification jstring="[para(6201(a,1),10181(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6201 10181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10183">
    <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,10125,a,b,10182,a)].">
      <j1 rule="hyper" parents="58 10125 10182"/>
    </justification>
  </clause>

  <clause id="10184">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (L(K(z,u),y,x) * w) = K(z,u) * w
    ]]></literal>
    <justification jstring="[para(6200(a,1),10182(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6200 10182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10185">
    <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,5394,a(flip),b,10184,a),flip(a)].">
      <j1 rule="hyper" parents="116 5394 10184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10186">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = a(x,y,K(u,z)) * w
    ]]></literal>
    <justification jstring="[hyper(58,a,10183,a(flip),b,10185,a),flip(a)].">
      <j1 rule="hyper" parents="58 10183 10185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10187">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * x) = a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(588,a,10186,a)].">
      <j1 rule="hyper" parents="588 10186"/>
    </justification>
  </clause>

  <clause id="10188">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ K(w,u) = K(w,u) * a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,7660,a,b,10186,a),flip(a)].">
      <j1 rule="hyper" parents="334 7660 10186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10189">
    <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,7149,a(flip),b,10186,a)].">
      <j1 rule="hyper" parents="119 7149 10186"/>
    </justification>
  </clause>

  <clause id="10190">
    <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(10186(a,1),134(a,1))].">
      <j1 rule="para" parents="10186 134"/>
    </justification>
  </clause>

  <clause id="10191">
    <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(10188(a,2),38(a,1))].">
      <j1 rule="para" parents="10188 38"/>
    </justification>
  </clause>

  <clause id="10192">
    <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(6074(a,1),5993(a,1,2,2,1,2))].">
      <j1 rule="para" parents="6074 5993"/>
    </justification>
  </clause>

  <clause id="10193">
    <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(3708(a,1),6053(a,1,1))].">
      <j1 rule="para" parents="3708 6053"/>
    </justification>
  </clause>

  <clause id="10194">
    <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(4299(a,1),10193(a,1,1,1))].">
      <j1 rule="para" parents="4299 10193"/>
    </justification>
  </clause>

  <clause id="10195">
    <literal><![CDATA[
      (T(x * (y \ 1),x) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(5694(a,1),6229(a,1,1,1))].">
      <j1 rule="para" parents="5694 6229"/>
    </justification>
  </clause>

  <clause id="10196">
    <literal><![CDATA[
      (x \ R(x,y \ 1,x)) / (T(x * (y \ 1),x) / x) = y
    ]]></literal>
    <justification jstring="[hyper(117,a,9001,a(flip),b,10195,a(flip))].">
      <j1 rule="hyper" parents="117 9001 10195"/>
    </justification>
  </clause>

  <clause id="10197">
    <literal><![CDATA[
      x * T(K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      w * T(K(z,y),u) = x
    ]]></literal>
    <justification jstring="[para(9144(a,1),7157(a,1)),flip(a)].">
      <j1 rule="para" parents="9144 7157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10198">
    <literal><![CDATA[
      K(x,y * (((z * K(u,z)) * u) * w)) = K(x,y * ((u * (1 / (1 / z))) * w))
    ]]></literal>
    <justification jstring="[para(5536(a,1),7163(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5536 7163"/>
    </justification>
  </clause>

  <clause id="10199">
    <literal><![CDATA[
      K(x,y * ((z * (1 / (1 / u))) * w)) = K(x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[para(5039(a,1),10198(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5039 10198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10200">
    <literal><![CDATA[
      ((x \ y) \ y) \ R((x \ y) \ y,z,u) = x \ (y \ ((R(x,z,u) * (x \ y)) * x))
    ]]></literal>
    <justification jstring="[hyper(1233,a,7185,a)].">
      <j1 rule="hyper" parents="1233 7185"/>
    </justification>
  </clause>

  <clause id="10201">
    <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(8162(a,1),8210(a,1,2,2,1))].">
      <j1 rule="para" parents="8162 8210"/>
    </justification>
  </clause>

  <clause id="10203">
    <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,8580,a(flip),b,8582,a),flip(a)].">
      <j1 rule="hyper" parents="58 8580 8582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10204">
    <literal><![CDATA[
      x \ (T((y * x) / y,K(z,u)) * w) = x * (T(T(x,K(z,u)),y) \ w)
    ]]></literal>
    <justification jstring="[para(472(a,1),10203(a,1,2,1))].">
      <j1 rule="para" parents="472 10203"/>
    </justification>
  </clause>

  <clause id="10205">
    <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,8280,a(flip),b,10204,a)].">
      <j1 rule="hyper" parents="58 8280 10204"/>
    </justification>
  </clause>

  <clause id="10206">
    <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(7401(a,2),10205(a,1,2,1,2))].">
      <j1 rule="para" parents="7401 10205"/>
    </justification>
  </clause>

  <clause id="10207">
    <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,3945,a(flip),b,8605,a)].">
      <j1 rule="hyper" parents="58 3945 8605"/>
    </justification>
  </clause>

  <clause id="10208">
    <literal><![CDATA[
      T(x,y / (((z \ 1) \ 1) \ u)) = T(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(8737,a,10207,a),flip(a)].">
      <j1 rule="hyper" parents="8737 10207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10209">
    <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(6520(a,1),8619(a,1,1,2,1))].">
      <j1 rule="para" parents="6520 8619"/>
    </justification>
  </clause>

  <clause id="10210">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ y) * K(x,K(y,z \ u)) = K(x,y / ((y \ z) \ u))
    ]]></literal>
    <justification jstring="[para(8662(a,1),8675(a,1,2))].">
      <j1 rule="para" parents="8662 8675"/>
    </justification>
  </clause>

  <clause id="10211">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((y \ z) \ u)) = K(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(8662(a,1),8687(a,1,1))].">
      <j1 rule="para" parents="8662 8687"/>
    </justification>
  </clause>

  <clause id="10212">
    <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,8824,a),flip(a)].">
      <j1 rule="hyper" parents="120 8824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10213">
    <literal><![CDATA[
      T((x \ 1) * y,K(z,T(u,x \ y))) = T((x \ 1) * y,K(z,u))
    ]]></literal>
    <justification jstring="[para(3939(a,1),10212(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3939 10212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10214">
    <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(6273,a,10213,a)].">
      <j1 rule="hyper" parents="6273 10213"/>
    </justification>
  </clause>

  <clause id="10215">
    <literal><![CDATA[
      K(T(x,((y \ 1) / ((1 / (y \ 1)) \ z)) \ 1),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,8962,a(flip),b,8963,a),flip(a)].">
      <j1 rule="hyper" parents="334 8962 8963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10217">
    <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),10215(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="72 10215"/>
    </justification>
  </clause>

  <clause id="10219">
    <literal><![CDATA[
      K(T(x,(y \ 1) \ (y \ z)),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,7961,a(flip),b,10217,a)].">
      <j1 rule="hyper" parents="58 7961 10217"/>
    </justification>
  </clause>

  <clause id="10220">
    <literal><![CDATA[
      K(T(x,y \ z),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(8534,a,10219,a)].">
      <j1 rule="hyper" parents="8534 10219"/>
    </justification>
  </clause>

  <clause id="10221">
    <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(334,a,7578,a(flip),b,9014,a),flip(a)].">
      <j1 rule="hyper" parents="334 7578 9014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10223">
    <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(5959(a,1),9108(a,1,1,2))].">
      <j1 rule="para" parents="5959 9108"/>
    </justification>
  </clause>

  <clause id="10224">
    <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(4848,a,10223,a),flip(a)].">
      <j1 rule="hyper" parents="4848 10223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10225">
    <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(6198(a,1),10224(a,1,1))].">
      <j1 rule="para" parents="6198 10224"/>
    </justification>
  </clause>

  <clause id="10226">
    <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(334,a,6198,a(flip),b,10225,a),flip(a)].">
      <j1 rule="hyper" parents="334 6198 10225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10227">
    <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(334,a,243,a(flip),b,10226,a),flip(a)].">
      <j1 rule="hyper" parents="334 243 10226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10228">
    <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,8560,a(flip),b,9283,a)].">
      <j1 rule="hyper" parents="58 8560 9283"/>
    </justification>
  </clause>

  <clause id="10229">
    <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(245(a,1),9405(a,2,1))].">
      <j1 rule="para" parents="245 9405"/>
    </justification>
  </clause>

  <clause id="10230">
    <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,9333,a(flip),b,10229,a),flip(a)].">
      <j1 rule="hyper" parents="58 9333 10229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10231">
    <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(1718(a,1),9466(a,1,2))].">
      <j1 rule="para" parents="1718 9466"/>
    </justification>
  </clause>

  <clause id="10232">
    <literal><![CDATA[
      x \ R(x,y,L(x,z,u)) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(709,a,10231,a),flip(a)].">
      <j1 rule="hyper" parents="709 10231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10233">
    <literal><![CDATA[
      K(x * L(y,z,u),y) * K(y,x) = a(y,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9468,a,10232,a)].">
      <j1 rule="hyper" parents="9468 10232"/>
    </justification>
  </clause>

  <clause id="10234">
    <literal><![CDATA[
      K(x,y) * K(y * L(x,z,u),x) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(9015,a,10232,a)].">
      <j1 rule="hyper" parents="9015 10232"/>
    </justification>
  </clause>

  <clause id="10235">
    <literal><![CDATA[
      K(x,y) * a(y,x,L(y,z,u)) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(10232(a,1),9467(a,1,2))].">
      <j1 rule="para" parents="10232 9467"/>
    </justification>
  </clause>

  <clause id="10236">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) * K(x,u) = a(x,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(7681(a,2),10233(a,1,1))].">
      <j1 rule="para" parents="7681 10233"/>
    </justification>
  </clause>

  <clause id="10237">
    <literal><![CDATA[
      K(x,y) * K(y,x * L(y,z,u)) = a(y,x,L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(10234(a,1),9232(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10234 9232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10238">
    <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(10235(a,1),38(a,1))].">
      <j1 rule="para" parents="10235 38"/>
    </justification>
  </clause>

  <clause id="10239">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) \ x = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9779,a(flip),b,10236,a)].">
      <j1 rule="hyper" parents="58 9779 10236"/>
    </justification>
  </clause>

  <clause id="10240">
    <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(10239(a,1),7115(a,1,1,1))].">
      <j1 rule="para" parents="10239 7115"/>
    </justification>
  </clause>

  <clause id="10241">
    <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(1964(a,1),9469(a,1,2))].">
      <j1 rule="para" parents="1964 9469"/>
    </justification>
  </clause>

  <clause id="10242">
    <literal><![CDATA[
      x * a(x,y,R(x,z,u)) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(712,a,10241,a)].">
      <j1 rule="hyper" parents="712 10241"/>
    </justification>
  </clause>

  <clause id="10243">
    <literal><![CDATA[
      x \ R(x,y,R(x,z,u)) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(709,a,10241,a),flip(a)].">
      <j1 rule="hyper" parents="709 10241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10244">
    <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(10241(a,1),709(a,1))].">
      <j1 rule="para" parents="10241 709"/>
    </justification>
  </clause>

  <clause id="10245">
    <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,10135,a,b,10242,a)].">
      <j1 rule="hyper" parents="116 10135 10242"/>
    </justification>
  </clause>

  <clause id="10246">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,x) = a(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9470,a,10243,a)].">
      <j1 rule="hyper" parents="9470 10243"/>
    </justification>
  </clause>

  <clause id="10247">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) \ x = a(x,y,R(x,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(10243(a,1),4267(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10243 4267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10248">
    <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(10243(a,1),9404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10243 9404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10249">
    <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(4931(a,1),10247(a,2,1))].">
      <j1 rule="para" parents="4931 10247"/>
    </justification>
  </clause>

  <clause id="10250">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) * K(x,y * R(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(10246(a,1),6525(a,1,1))].">
      <j1 rule="para" parents="10246 6525"/>
    </justification>
  </clause>

  <clause id="10251">
    <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(7684(a,1),10246(a,1,1))].">
      <j1 rule="para" parents="7684 10246"/>
    </justification>
  </clause>

  <clause id="10252">
    <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(10246(a,1),8873(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10246 8873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10253">
    <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),10250(a,1,2,2))].">
      <j1 rule="para" parents="7 10250"/>
    </justification>
  </clause>

  <clause id="10254">
    <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(5487,a,10248,a)].">
      <j1 rule="hyper" parents="5487 10248"/>
    </justification>
  </clause>

  <clause id="10255">
    <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(5345,a,10248,a)].">
      <j1 rule="hyper" parents="5345 10248"/>
    </justification>
  </clause>

  <clause id="10256">
    <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(10255(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="10255 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10257">
    <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(910(a,1),10256(a,1))].">
      <j1 rule="para" parents="910 10256"/>
    </justification>
  </clause>

  <clause id="10258">
    <literal><![CDATA[
      ((1 / x) * T((1 / x) \ K(y,z),y)) * u = K(y,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(1658,a,9742,a)].">
      <j1 rule="hyper" parents="1658 9742"/>
    </justification>
  </clause>

  <clause id="10259">
    <literal><![CDATA[
      (K(x,y) * K((1 / z) \ 1,x)) * u = K(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(8570(a,2),10258(a,1,1))].">
      <j1 rule="para" parents="8570 10258"/>
    </justification>
  </clause>

  <clause id="10260">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(75(a,1),10259(a,1,1,2,1))].">
      <j1 rule="para" parents="75 10259"/>
    </justification>
  </clause>

  <clause id="10261">
    <literal><![CDATA[
      L(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(493,a,10260,a)].">
      <j1 rule="hyper" parents="493 10260"/>
    </justification>
  </clause>

  <clause id="10262">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(334,a,10099,a(flip),b,10260,a),flip(a)].">
      <j1 rule="hyper" parents="334 10099 10260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10263">
    <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(10260(a,1),298(a,1,2))].">
      <j1 rule="para" parents="10260 298"/>
    </justification>
  </clause>

  <clause id="10265">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(y,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(2065(a,1),10260(a,1,1))].">
      <j1 rule="para" parents="2065 10260"/>
    </justification>
  </clause>

  <clause id="10266">
    <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(10260(a,1),6213(a,1,2))].">
      <j1 rule="para" parents="10260 6213"/>
    </justification>
  </clause>

  <clause id="10269">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ u = K(x,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6040,a(flip),b,10261,a)].">
      <j1 rule="hyper" parents="58 6040 10261"/>
    </justification>
  </clause>

  <clause id="10271">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),K(z,w)) = x
    ]]></literal>
    <justification jstring="[para(7403(a,1),10261(a,1,2))].">
      <j1 rule="para" parents="7403 10261"/>
    </justification>
  </clause>

  <clause id="10272">
    <literal><![CDATA[
      (K(x,y) * K(z,T(x,u))) * w = K(x,y) * (K(z,T(x,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(1392,a,10271,a),flip(a)].">
      <j1 rule="hyper" parents="1392 10271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10273">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(x,y) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(2065(a,1),10262(a,1,1))].">
      <j1 rule="para" parents="2065 10262"/>
    </justification>
  </clause>

  <clause id="10274">
    <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(5030,a,10265,a),flip(a)].">
      <j1 rule="hyper" parents="5030 10265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10275">
    <literal><![CDATA[
      (K(x,y) * z) / (K(u,y) * z) = K(x,y) * K(y,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,10100,a(flip),b,10265,a)].">
      <j1 rule="hyper" parents="117 10100 10265"/>
    </justification>
  </clause>

  <clause id="10276">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) \ u = K(y,x) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(2065(a,1),10269(a,1,1))].">
      <j1 rule="para" parents="2065 10269"/>
    </justification>
  </clause>

  <clause id="10277">
    <literal><![CDATA[
      R(K(x,y),K(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3617,a,10273,a)].">
      <j1 rule="hyper" parents="3617 10273"/>
    </justification>
  </clause>

  <clause id="10278">
    <literal><![CDATA[
      L(x,K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(493,a,10273,a)].">
      <j1 rule="hyper" parents="493 10273"/>
    </justification>
  </clause>

  <clause id="10279">
    <literal><![CDATA[
      (K(x,y) * z) / (K(x,u) * z) = K(u,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,10103,a(flip),b,10273,a)].">
      <j1 rule="hyper" parents="117 10103 10273"/>
    </justification>
  </clause>

  <clause id="10280">
    <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,10273,a(flip),b,5039,a)].">
      <j1 rule="hyper" parents="117 10273 5039"/>
    </justification>
  </clause>

  <clause id="10281">
    <literal><![CDATA[
      K(x,y) * (K(y,x * y) * z) = (y \ L(y,x,y)) * z
    ]]></literal>
    <justification jstring="[para(5762(a,1),10273(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5762 10273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10285">
    <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(10277(a,1),3749(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10277 3749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10286">
    <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(8170(a,1),10275(a,1,1))].">
      <j1 rule="para" parents="8170 10275"/>
    </justification>
  </clause>

  <clause id="10287">
    <literal><![CDATA[
      (K(x,T(y,z)) * K(y,u)) \ w = K(y,T(x,z)) * (K(u,y) * w)
    ]]></literal>
    <justification jstring="[para(7403(a,1),10276(a,1,1,1))].">
      <j1 rule="para" parents="7403 10276"/>
    </justification>
  </clause>

  <clause id="10288">
    <literal><![CDATA[
      x / (K(y \ x,z) * (y * (x / y))) = K(z,y \ x) * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4976(a,1),10279(a,1,1))].">
      <j1 rule="para" parents="4976 10279"/>
    </justification>
  </clause>

  <clause id="10289">
    <literal><![CDATA[
      (x \ L(x,y,x)) * z = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,9850,a(flip),b,10281,a),flip(a)].">
      <j1 rule="hyper" parents="58 9850 10281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10290">
    <literal><![CDATA[
      (x \ L(x,y,x)) \ z = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,9808,a(flip),b,10289,a)].">
      <j1 rule="hyper" parents="116 9808 10289"/>
    </justification>
  </clause>

  <clause id="10291">
    <literal><![CDATA[
      (R(x,y,x) \ x) * z = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[para(6049(a,2),10289(a,1,1))].">
      <j1 rule="para" parents="6049 10289"/>
    </justification>
  </clause>

  <clause id="10292">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ z = (R(x,y,x) \ x) * z
    ]]></literal>
    <justification jstring="[para(9155(a,2),10291(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9155 10291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10293">
    <literal><![CDATA[
      (R(x,y,x) \ x) * (K(x * y,x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,9854,a(flip),b,10292,a),flip(a)].">
      <j1 rule="hyper" parents="58 9854 10292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10294">
    <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(10049(a,1),10263(a,1))].">
      <j1 rule="para" parents="10049 10263"/>
    </justification>
  </clause>

  <clause id="10295">
    <literal><![CDATA[
      R(K(x,y),K(z,y),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5412,a,10266,a),flip(a)].">
      <j1 rule="hyper" parents="5412 10266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10297">
    <literal><![CDATA[
      (x * K(y,z)) / (x * K(u,z)) = K(y,T(z,x)) * K(T(z,x),u)
    ]]></literal>
    <justification jstring="[para(8170(a,1),10286(a,1,2))].">
      <j1 rule="para" parents="8170 10286"/>
    </justification>
  </clause>

  <clause id="10298">
    <literal><![CDATA[
      (x * K(y,z)) / (x * K(u,z)) = K(y,T(z,x)) * K(z,T(u,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,7443,a(flip),b,10297,a),flip(a)].">
      <j1 rule="hyper" parents="334 7443 10297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10299">
    <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(219(a,2),10288(a,1,2,2,2))].">
      <j1 rule="para" parents="219 10288"/>
    </justification>
  </clause>

  <clause id="10300">
    <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,10129,a(flip),b,10274,a)].">
      <j1 rule="hyper" parents="58 10129 10274"/>
    </justification>
  </clause>

  <clause id="10301">
    <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(5086(a,1),10091(a,2,2))].">
      <j1 rule="para" parents="5086 10091"/>
    </justification>
  </clause>

  <clause id="10302">
    <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(10154(a,1),10200(a,2,2,2,1,1))].">
      <j1 rule="para" parents="10154 10200"/>
    </justification>
  </clause>

  <clause id="10303">
    <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(8134,a,10209,a)].">
      <j1 rule="hyper" parents="8134 10209"/>
    </justification>
  </clause>

  <clause id="10304">
    <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(10244,a,10245,a)].">
      <j1 rule="hyper" parents="10244 10245"/>
    </justification>
  </clause>

  <clause id="10305">
    <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(10135(a,1),10249(a,1,1))].">
      <j1 rule="para" parents="10135 10249"/>
    </justification>
  </clause>

  <clause id="10306">
    <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(9230,a,10280,a)].">
      <j1 rule="hyper" parents="9230 10280"/>
    </justification>
  </clause>

  <clause id="10307">
    <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(6520(a,1),10303(a,2,2,1))].">
      <j1 rule="para" parents="6520 10303"/>
    </justification>
  </clause>

  <clause id="10308">
    <literal><![CDATA[
      T(x,R(x * K(y,x),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(343,a,4768,a),flip(a)].">
      <j1 rule="hyper" parents="343 4768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10310">
    <literal><![CDATA[
      T(x \ y,R(y / x,z,u)) = x \ y
    ]]></literal>
    <justification jstring="[para(5041(a,1),10308(a,1,2,1))].">
      <j1 rule="para" parents="5041 10308"/>
    </justification>
  </clause>

  <clause id="10311">
    <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(10310(a,1),7439(a,1,2))].">
      <j1 rule="para" parents="10310 7439"/>
    </justification>
  </clause>

  <clause id="10312">
    <literal><![CDATA[
      ((x * (y * ((x \ (z / u)) / y))) * u) / z = K(y,z / ((x * y) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6159,a(flip),b,6035,a),flip(a)].">
      <j1 rule="hyper" parents="58 6159 6035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10313">
    <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(3756(a,1),6145(a,1,2,1,1))].">
      <j1 rule="para" parents="3756 6145"/>
    </justification>
  </clause>

  <clause id="10314">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(R(x,y,z),u) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3448(a,1),10313(a,1,2))].">
      <j1 rule="para" parents="3448 10313"/>
    </justification>
  </clause>

  <clause id="10315">
    <literal><![CDATA[
      R(K(x,y),R(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6243,a,6342,a)].">
      <j1 rule="hyper" parents="6243 6342"/>
    </justification>
  </clause>

  <clause id="10316">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) = (v5 * K(y,x)) \ v5
    ]]></literal>
    <justification jstring="[para(10315(a,1),7066(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10315 7066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10317">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(10316(a,2),6528(a,1))].">
      <j1 rule="para" parents="10316 6528"/>
    </justification>
  </clause>

  <clause id="10318">
    <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(6160(a,1),10317(a,1))].">
      <j1 rule="para" parents="6160 10317"/>
    </justification>
  </clause>

  <clause id="10319">
    <literal><![CDATA[
      ((x * T(x \ (y / z),y / z)) * z) / y = K(x \ (y / z),(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(5755,a,6247,a),flip(a)].">
      <j1 rule="hyper" parents="5755 6247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10320">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),z / y))) / z = K(x \ (z / y),(y / z) \ 1)
    ]]></literal>
    <justification jstring="[para(1636(a,1),10319(a,1,1))].">
      <j1 rule="para" parents="1636 10319"/>
    </justification>
  </clause>

  <clause id="10321">
    <literal><![CDATA[
      K(((x * y) / z) \ 1,z / y) = K(x \ (z / y),(y / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5794,a(flip),b,10320,a)].">
      <j1 rule="hyper" parents="58 5794 10320"/>
    </justification>
  </clause>

  <clause id="10322">
    <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(1826(a,2),7155(a,1,2))].">
      <j1 rule="para" parents="1826 7155"/>
    </justification>
  </clause>

  <clause id="10323">
    <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(7403(a,1),8266(a,2,1,2))].">
      <j1 rule="para" parents="7403 8266"/>
    </justification>
  </clause>

  <clause id="10324">
    <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(5402(a,1),8361(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5402 8361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10325">
    <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(10324(a,2),8009(a,1))].">
      <j1 rule="para" parents="10324 8009"/>
    </justification>
  </clause>

  <clause id="10326">
    <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(8958(a,1),5284(a,1))].">
      <j1 rule="para" parents="8958 5284"/>
    </justification>
  </clause>

  <clause id="10327">
    <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(4473(a,1),9197(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4473 9197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10328">
    <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(10261(a,1),9213(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10261 9213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10329">
    <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(2065(a,1),10328(a,1,2,2))].">
      <j1 rule="para" parents="2065 10328"/>
    </justification>
  </clause>

  <clause id="10330">
    <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(10329(a,1),6402(a,1,1))].">
      <j1 rule="para" parents="10329 6402"/>
    </justification>
  </clause>

  <clause id="10331">
    <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(6726(a,1),10330(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6726 10330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10332">
    <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),9303(a,1,1,2))].">
      <j1 rule="para" parents="22 9303"/>
    </justification>
  </clause>

  <clause id="10333">
    <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(8053(a,2),9447(a,1,2,1))].">
      <j1 rule="para" parents="8053 9447"/>
    </justification>
  </clause>

  <clause id="10334">
    <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(9491(a,2),8331(a,1))].">
      <j1 rule="para" parents="9491 8331"/>
    </justification>
  </clause>

  <clause id="10335">
    <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(5288,a,9601,a),flip(a)].">
      <j1 rule="hyper" parents="5288 9601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10336">
    <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(7401(a,2),9688(a,2,2,1))].">
      <j1 rule="para" parents="7401 9688"/>
    </justification>
  </clause>

  <clause id="10337">
    <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(9815(a,1),9821(a,1))].">
      <j1 rule="para" parents="9815 9821"/>
    </justification>
  </clause>

  <clause id="10338">
    <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(7416(a,1),10251(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7416 10251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10339">
    <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(334,a,10246,a(flip),b,10338,a),flip(a)].">
      <j1 rule="hyper" parents="334 10246 10338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10341">
    <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),10339(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 10339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10342">
    <literal><![CDATA[
      a(x,T(y,x),R(x,z,u)) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(391(a,1),10339(a,1,2,2))].">
      <j1 rule="para" parents="391 10339"/>
    </justification>
  </clause>

  <clause id="10343">
    <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(10341(a,1),10253(a,1,1))].">
      <j1 rule="para" parents="10341 10253"/>
    </justification>
  </clause>

  <clause id="10344">
    <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(334,a,7483,a(flip),b,10343,a),flip(a)].">
      <j1 rule="hyper" parents="334 7483 10343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10345">
    <literal><![CDATA[
      x * (y * (z \ T(z * (y \ (z \ 1)),z))) = (x * K(y \ 1,z)) * (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(296,a,10322,a)].">
      <j1 rule="hyper" parents="296 10322"/>
    </justification>
  </clause>

  <clause id="10346">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * (z \ 1) = x * (K(y \ 1,z) * (z \ 1))
    ]]></literal>
    <justification jstring="[para(5990(a,1),10345(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5990 10345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10347">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * (z \ 1) = x * (T(z,y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(5392(a,1),10346(a,2,2))].">
      <j1 rule="para" parents="5392 10346"/>
    </justification>
  </clause>

  <clause id="10348">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (T(z,(1 / y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),10347(a,1,1,2,1))].">
      <j1 rule="para" parents="75 10347"/>
    </justification>
  </clause>

  <clause id="10349">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (T(z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),10348(a,2,2,1,2))].">
      <j1 rule="para" parents="75 10348"/>
    </justification>
  </clause>

  <clause id="10350">
    <literal><![CDATA[
      x \ T(x * (y \ 1),y) = T(y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(6842,a,10349,a)].">
      <j1 rule="hyper" parents="6842 10349"/>
    </justification>
  </clause>

  <clause id="10351">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (z \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,5228,a(flip),b,10349,a),flip(a)].">
      <j1 rule="hyper" parents="334 5228 10349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10352">
    <literal><![CDATA[
      (x * (y \ 1)) \ (x * (T(y,z) \ 1)) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,10349,a(flip),b,7081,a(flip))].">
      <j1 rule="hyper" parents="116 10349 7081"/>
    </justification>
  </clause>

  <clause id="10355">
    <literal><![CDATA[
      (x * K(y,z)) * (T(y,z) \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(6516(a,1),10349(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6516 10349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10356">
    <literal><![CDATA[
      x \ T(x * (y \ 1),y) = ((y \ x) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(334,a,325,a(flip),b,10350,a),flip(a)].">
      <j1 rule="hyper" parents="334 325 10350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10357">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,y) = x * (y \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7081,a(flip),b,10351,a)].">
      <j1 rule="hyper" parents="58 7081 10351"/>
    </justification>
  </clause>

  <clause id="10358">
    <literal><![CDATA[
      L(K(x,y),y \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5438,a,10352,a)].">
      <j1 rule="hyper" parents="5438 10352"/>
    </justification>
  </clause>

  <clause id="10359">
    <literal><![CDATA[
      L(K((x \ y) \ (z \ 1),z),z \ 1,u) = K(y \ (z \ x),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,9591,a(flip),b,10358,a),flip(a)].">
      <j1 rule="hyper" parents="334 9591 10358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10360">
    <literal><![CDATA[
      a(x,y \ 1,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10358,a,b,1992,a),flip(a)].">
      <j1 rule="hyper" parents="115 10358 1992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10363">
    <literal><![CDATA[
      a(x,y \ 1,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10358,a(flip),b,6205,a),flip(a)].">
      <j1 rule="hyper" parents="115 10358 6205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10364">
    <literal><![CDATA[
      L(K(x,y),x \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6202,a,10360,a)].">
      <j1 rule="hyper" parents="6202 10360"/>
    </justification>
  </clause>

  <clause id="10365">
    <literal><![CDATA[
      a(x,y,K(z,y \ 1)) = 1
    ]]></literal>
    <justification jstring="[hyper(4350,a,10360,a)].">
      <j1 rule="hyper" parents="4350 10360"/>
    </justification>
  </clause>

  <clause id="10366">
    <literal><![CDATA[
      (x * (y \ 1)) * K(y,z) = x * ((y \ 1) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(214,a,10363,a)].">
      <j1 rule="hyper" parents="214 10363"/>
    </justification>
  </clause>

  <clause id="10367">
    <literal><![CDATA[
      (x * y) * K(z,y \ 1) = x * (y * K(z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(214,a,10365,a)].">
      <j1 rule="hyper" parents="214 10365"/>
    </justification>
  </clause>

  <clause id="10369">
    <literal><![CDATA[
      L(K(x,y),1 / x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4320,a,b,10364,a)].">
      <j1 rule="hyper" parents="58 4320 10364"/>
    </justification>
  </clause>

  <clause id="10370">
    <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(2964(a,1),10369(a,1,2))].">
      <j1 rule="para" parents="2964 10369"/>
    </justification>
  </clause>

  <clause id="10371">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y,z) = x / (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,10355,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 10355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10372">
    <literal><![CDATA[
      (x * K(y * K(z,y),z)) * (y \ 1) = x * ((y * K(z,y)) \ 1)
    ]]></literal>
    <justification jstring="[para(5086(a,1),10355(a,1,2,1))].">
      <j1 rule="para" parents="5086 10355"/>
    </justification>
  </clause>

  <clause id="10373">
    <literal><![CDATA[
      T((x \ 1) * y,x) = (((x \ y) \ y) \ 1) * y
    ]]></literal>
    <justification jstring="[para(10356(a,1),4820(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10356 4820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10374">
    <literal><![CDATA[
      (x * T(y,z)) * (y \ K(z,y)) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,7083,a(flip),b,10357,a),flip(a)].">
      <j1 rule="hyper" parents="58 7083 10357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10375">
    <literal><![CDATA[
      L((x / (y \ 1)) / y,z,u) * T(y,w) = L(x,z,u) / (T(y,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(7168,a,10371,a)].">
      <j1 rule="hyper" parents="7168 10371"/>
    </justification>
  </clause>

  <clause id="10376">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * x = x / (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5799,a,b,10371,a)].">
      <j1 rule="hyper" parents="58 5799 10371"/>
    </justification>
  </clause>

  <clause id="10377">
    <literal><![CDATA[
      x / (T(y,x) \ 1) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6116,a(flip),b,10371,a),flip(a)].">
      <j1 rule="hyper" parents="58 6116 10371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10378">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) \ y = (((x \ y) \ y) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,4440,a(flip),b,10373,a)].">
      <j1 rule="hyper" parents="58 4440 10373"/>
    </justification>
  </clause>

  <clause id="10379">
    <literal><![CDATA[
      T(((x / y) \ 1) * x,x / y) = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(75(a,1),10373(a,2,1,1,1))].">
      <j1 rule="para" parents="75 10373"/>
    </justification>
  </clause>

  <clause id="10380">
    <literal><![CDATA[
      x / (y \ K(x,y)) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(5073(a,1),10377(a,1,2))].">
      <j1 rule="para" parents="5073 10377"/>
    </justification>
  </clause>

  <clause id="10381">
    <literal><![CDATA[
      x \ (y / (x \ K(y,x))) = (y / (x \ 1)) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,10380,a,b,xx)].">
      <j1 rule="hyper" parents="116 10380"/>
    </justification>
  </clause>

  <clause id="10382">
    <literal><![CDATA[
      (x * y) * (x \ K(y,x)) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(582,a,10374,a)].">
      <j1 rule="hyper" parents="582 10374"/>
    </justification>
  </clause>

  <clause id="10383">
    <literal><![CDATA[
      R(x,y,K(y \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4339,a,10366,a)].">
      <j1 rule="hyper" parents="4339 10366"/>
    </justification>
  </clause>

  <clause id="10384">
    <literal><![CDATA[
      R(x,y \ z,K(y / z,u)) = x
    ]]></literal>
    <justification jstring="[para(8274(a,1),10383(a,1,3))].">
      <j1 rule="para" parents="8274 10383"/>
    </justification>
  </clause>

  <clause id="10385">
    <literal><![CDATA[
      x \ (y * K(x / y,z)) = (x \ y) * K(x / y,z)
    ]]></literal>
    <justification jstring="[para(10384(a,1),517(a,1,1))].">
      <j1 rule="para" parents="10384 517"/>
    </justification>
  </clause>

  <clause id="10386">
    <literal><![CDATA[
      R(x,y,K(z,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(527,a,10367,a)].">
      <j1 rule="hyper" parents="527 10367"/>
    </justification>
  </clause>

  <clause id="10387">
    <literal><![CDATA[
      x / (x * (y * K(z,y \ 1))) = T(x / (x * y),z)
    ]]></literal>
    <justification jstring="[para(10367(a,1),7928(a,1,2))].">
      <j1 rule="para" parents="10367 7928"/>
    </justification>
  </clause>

  <clause id="10389">
    <literal><![CDATA[
      R(x,y \ 1,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(3283(a,1),10386(a,1,3))].">
      <j1 rule="para" parents="3283 10386"/>
    </justification>
  </clause>

  <clause id="10390">
    <literal><![CDATA[
      R(x,y \ z,K(u,z \ y)) = x
    ]]></literal>
    <justification jstring="[para(6423(a,1),10386(a,1,3))].">
      <j1 rule="para" parents="6423 10386"/>
    </justification>
  </clause>

  <clause id="10391">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) * K(x,y)) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(6978,a,10389,a)].">
      <j1 rule="hyper" parents="6978 10389"/>
    </justification>
  </clause>

  <clause id="10392">
    <literal><![CDATA[
      R(x,y \ 1,K(z,T(y,u))) = x
    ]]></literal>
    <justification jstring="[para(7403(a,1),10389(a,1,3))].">
      <j1 rule="para" parents="7403 10389"/>
    </justification>
  </clause>

  <clause id="10393">
    <literal><![CDATA[
      x \ (y * K(z,y \ x)) = (x \ y) * K(z,y \ x)
    ]]></literal>
    <justification jstring="[para(10390(a,1),517(a,1,1))].">
      <j1 rule="para" parents="10390 517"/>
    </justification>
  </clause>

  <clause id="10394">
    <literal><![CDATA[
      R(x,(y * K(z,y)) \ 1,K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(5086(a,1),10392(a,1,3,2))].">
      <j1 rule="para" parents="5086 10392"/>
    </justification>
  </clause>

  <clause id="10395">
    <literal><![CDATA[
      R(x,y \ K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(5474(a,1),10394(a,1,2))].">
      <j1 rule="para" parents="5474 10394"/>
    </justification>
  </clause>

  <clause id="10396">
    <literal><![CDATA[
      (x * K(y,z)) / (z \ 1) = x / (z \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6400,a(flip),b,10395,a)].">
      <j1 rule="hyper" parents="58 6400 10395"/>
    </justification>
  </clause>

  <clause id="10397">
    <literal><![CDATA[
      T(x,y) / (T(y,x) \ 1) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(5069(a,1),10391(a,1,2))].">
      <j1 rule="para" parents="5069 10391"/>
    </justification>
  </clause>

  <clause id="10398">
    <literal><![CDATA[
      (x / (y \ 1)) \ T(x,y) = T(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(192,a,10397,a)].">
      <j1 rule="hyper" parents="192 10397"/>
    </justification>
  </clause>

  <clause id="10399">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = T(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,6995,a,b,10398,a)].">
      <j1 rule="hyper" parents="58 6995 10398"/>
    </justification>
  </clause>

  <clause id="10400">
    <literal><![CDATA[
      ((x / y) / (y \ 1)) \ (y \ x) = T(y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,7139,a(flip),b,10398,a)].">
      <j1 rule="hyper" parents="58 7139 10398"/>
    </justification>
  </clause>

  <clause id="10401">
    <literal><![CDATA[
      (x \ ((y \ 1) \ x)) * x = (T(y,x) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(10399(a,1),4763(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10399 4763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10403">
    <literal><![CDATA[
      T(x,y) / (y \ 1) = x / (y \ K(y,x))
    ]]></literal>
    <justification jstring="[para(5020(a,2),10396(a,1,1))].">
      <j1 rule="para" parents="5020 10396"/>
    </justification>
  </clause>

  <clause id="10404">
    <literal><![CDATA[
      (T(x,y) / (y \ 1)) \ x = y \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(118,a,10403,a,b,154,a)].">
      <j1 rule="hyper" parents="118 10403 154"/>
    </justification>
  </clause>

  <clause id="10405">
    <literal><![CDATA[
      x \ (x / (y \ K(y,x))) = (x / (y \ 1)) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,10403,a(flip),b,4141,a(flip))].">
      <j1 rule="hyper" parents="116 10403 4141"/>
    </justification>
  </clause>

  <clause id="10406">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = (x \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(10404(a,1),7173(a,1,1))].">
      <j1 rule="para" parents="10404 7173"/>
    </justification>
  </clause>

  <clause id="10407">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = (x \ ((x \ 1) \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(334,a,2042,a,b,10406,a),flip(a)].">
      <j1 rule="hyper" parents="334 2042 10406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10408">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = y * (((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(334,a,4137,a(flip),b,10406,a),flip(a)].">
      <j1 rule="hyper" parents="334 4137 10406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10409">
    <literal><![CDATA[
      x \ ((y \ K(y,x)) \ x) = ((y \ 1) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,10406,a,b,4137,a(flip))].">
      <j1 rule="hyper" parents="116 10406 4137"/>
    </justification>
  </clause>

  <clause id="10410">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) \ y = (y \ (x \ y)) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),10401(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 10401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10411">
    <literal><![CDATA[
      x / ((x \ (y \ x)) * x) = T(1 / y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(201,a,10410,a)].">
      <j1 rule="hyper" parents="201 10410"/>
    </justification>
  </clause>

  <clause id="10412">
    <literal><![CDATA[
      T(1 / (x \ y),y) \ 1 = x \ T(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7043,a,b,10411,a),flip(a)].">
      <j1 rule="hyper" parents="58 7043 10411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10413">
    <literal><![CDATA[
      T(1 / (x / y),x) \ 1 = x / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(75(a,1),10411(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="75 10411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10414">
    <literal><![CDATA[
      (x \ T(y,y \ x)) \ 1 = T((x \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[para(10412(a,1),2223(a,1,1))].">
      <j1 rule="para" parents="10412 2223"/>
    </justification>
  </clause>

  <clause id="10415">
    <literal><![CDATA[
      ((((x / y) \ 1) * x) \ x) \ x = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(75(a,1),10378(a,2,1,1,1))].">
      <j1 rule="para" parents="75 10378"/>
    </justification>
  </clause>

  <clause id="10416">
    <literal><![CDATA[
      ((x / y) \ 1) * (y * (x / y)) = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,2046,a(flip),b,10379,a)].">
      <j1 rule="hyper" parents="58 2046 10379"/>
    </justification>
  </clause>

  <clause id="10417">
    <literal><![CDATA[
      (x \ y) * K(x / y,y) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,1561,a(flip),b,10385,a),flip(a)].">
      <j1 rule="hyper" parents="58 1561 10385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10418">
    <literal><![CDATA[
      T(x \ y,z) * ((y \ x) * K(z,x \ y)) = T((x \ y) * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10393,a(flip),b,6248,a)].">
      <j1 rule="hyper" parents="119 10393 6248"/>
    </justification>
  </clause>

  <clause id="10419">
    <literal><![CDATA[
      (x \ y) / (T(x,x \ y) \ 1) = (y / x) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(201,a,10400,a)].">
      <j1 rule="hyper" parents="201 10400"/>
    </justification>
  </clause>

  <clause id="10420">
    <literal><![CDATA[
      ((x \ (y * x)) \ 1) * (y * x) = (y \ 1) * (x * ((y * x) / x))
    ]]></literal>
    <justification jstring="[para(6(a,1),10416(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6 10416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10421">
    <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(10416(a,1),6864(a,2,2,1))].">
      <j1 rule="para" parents="10416 6864"/>
    </justification>
  </clause>

  <clause id="10422">
    <literal><![CDATA[
      K(x \ (y * (z \ 1)),z) = K(x \ (z \ y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6894,a(flip),b,10359,a)].">
      <j1 rule="hyper" parents="58 6894 10359"/>
    </justification>
  </clause>

  <clause id="10423">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (x \ z),x) = K(y \ T(z,x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9658,a(flip),b,10422,a),flip(a)].">
      <j1 rule="hyper" parents="58 9658 10422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10424">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (x \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,9697,a(flip),b,10423,a),flip(a)].">
      <j1 rule="hyper" parents="334 9697 10423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10425">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,x) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(7985,a,10424,a)].">
      <j1 rule="hyper" parents="7985 10424"/>
    </justification>
  </clause>

  <clause id="10426">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,y) = K((x * y) \ (z * y),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8971,a(flip),b,10425,a)].">
      <j1 rule="hyper" parents="58 8971 10425"/>
    </justification>
  </clause>

  <clause id="10427">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,7118,a(flip),b,10426,a),flip(a)].">
      <j1 rule="hyper" parents="334 7118 10426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10428">
    <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(10427(a,1),5643(a,1,2,1,2))].">
      <j1 rule="para" parents="10427 5643"/>
    </justification>
  </clause>

  <clause id="10429">
    <literal><![CDATA[
      (x * K(y,z)) * (y \ 1) = x * ((y * K(z,y)) \ 1)
    ]]></literal>
    <justification jstring="[para(5242(a,1),10372(a,1,1,2))].">
      <j1 rule="para" parents="5242 10372"/>
    </justification>
  </clause>

  <clause id="10430">
    <literal><![CDATA[
      (x * K(y,z)) * (y \ 1) = x * (K(y,z) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(5655(a,1),10429(a,2,2))].">
      <j1 rule="para" parents="5655 10429"/>
    </justification>
  </clause>

  <clause id="10432">
    <literal><![CDATA[
      L(x \ 1,K(x,y),z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(493,a,10430,a)].">
      <j1 rule="hyper" parents="493 10430"/>
    </justification>
  </clause>

  <clause id="10433">
    <literal><![CDATA[
      ((x \ (y * x)) \ 1) * (y * x) = (y \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(6(a,1),10420(a,2,2,2))].">
      <j1 rule="para" parents="6 10420"/>
    </justification>
  </clause>

  <clause id="10434">
    <literal><![CDATA[
      (T(x,y) \ 1) * (x * y) = (x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(17(a,2),10433(a,1,1,1))].">
      <j1 rule="para" parents="17 10433"/>
    </justification>
  </clause>

  <clause id="10435">
    <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(10434(a,1),6864(a,2,2,2))].">
      <j1 rule="para" parents="10434 6864"/>
    </justification>
  </clause>

  <clause id="10436">
    <literal><![CDATA[
      T((x \ y) * (y \ x),z) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(5747,a,10418,a),flip(a)].">
      <j1 rule="hyper" parents="5747 10418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10437">
    <literal><![CDATA[
      K(x,(y \ z) * (z \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(5098,a,10436,a)].">
      <j1 rule="hyper" parents="5098 10436"/>
    </justification>
  </clause>

  <clause id="10438">
    <literal><![CDATA[
      T(x,(y \ z) * (z \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,10436,a)].">
      <j1 rule="hyper" parents="49 10436"/>
    </justification>
  </clause>

  <clause id="10439">
    <literal><![CDATA[
      K(x,y * ((z * y) \ z)) = 1
    ]]></literal>
    <justification jstring="[para(4(a,1),10437(a,1,2,1))].">
      <j1 rule="para" parents="4 10437"/>
    </justification>
  </clause>

  <clause id="10440">
    <literal><![CDATA[
      T(x,y * ((z * y) \ z)) = x
    ]]></literal>
    <justification jstring="[para(4(a,1),10438(a,1,2,1))].">
      <j1 rule="para" parents="4 10438"/>
    </justification>
  </clause>

  <clause id="10443">
    <literal><![CDATA[
      T(x * ((y * x) \ y),z) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(5077,a,10439,a)].">
      <j1 rule="hyper" parents="5077 10439"/>
    </justification>
  </clause>

  <clause id="10444">
    <literal><![CDATA[
      x / (y * ((z * y) \ z)) = (y * ((z * y) \ z)) \ x
    ]]></literal>
    <justification jstring="[hyper(171,a,5275,a,b,10439,a(flip))].">
      <j1 rule="hyper" parents="171 5275 10439"/>
    </justification>
  </clause>

  <clause id="10445">
    <literal><![CDATA[
      x / (y * ((z * y) \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      (y * ((z * y) \ z)) \ x = u
    ]]></literal>
    <justification jstring="[para(10440(a,1),431(a,1))].">
      <j1 rule="para" parents="10440 431"/>
    </justification>
  </clause>

  <clause id="10446">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),z) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[para(221(a,2),10443(a,1,1,2))].">
      <j1 rule="para" parents="221 10443"/>
    </justification>
  </clause>

  <clause id="10447">
    <literal><![CDATA[
      T(x,y) * ((z * T(x,y)) \ z) = x * ((z * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9761,a(flip),b,10446,a)].">
      <j1 rule="hyper" parents="58 9761 10446"/>
    </justification>
  </clause>

  <clause id="10448">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5740,a(flip),b,10446,a)].">
      <j1 rule="hyper" parents="58 5740 10446"/>
    </justification>
  </clause>

  <clause id="10451">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ T(x,z) = 1 / ((y * T(x,z)) \ y)
    ]]></literal>
    <justification jstring="[para(10447(a,1),1918(a,1,1))].">
      <j1 rule="para" parents="10447 1918"/>
    </justification>
  </clause>

  <clause id="10452">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,T(y,u)) = K(x \ z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(5646,a,10428,a),flip(a)].">
      <j1 rule="hyper" parents="5646 10428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10453">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,T(x,u)) = K((x \ y) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[para(3153(a,1),10452(a,1,1,1))].">
      <j1 rule="para" parents="3153 10452"/>
    </justification>
  </clause>

  <clause id="10454">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,u)) = K((x \ y) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,4288,a(flip),b,10453,a)].">
      <j1 rule="hyper" parents="58 4288 10453"/>
    </justification>
  </clause>

  <clause id="10455">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,u)) = K(y \ (x * z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,7877,a(flip),b,10454,a),flip(a)].">
      <j1 rule="hyper" parents="334 7877 10454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10456">
    <literal><![CDATA[
      K(x \ (y * z),T(y,x)) = K(((y \ 1) \ z) / x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9659,a(flip),b,10455,a),flip(a)].">
      <j1 rule="hyper" parents="58 9659 10455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10457">
    <literal><![CDATA[
      K(((x \ 1) \ y) / z,x) = K((x * y) / z,x)
    ]]></literal>
    <justification jstring="[hyper(8329,a,10456,a),flip(a)].">
      <j1 rule="hyper" parents="8329 10456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10458">
    <literal><![CDATA[
      K(((x \ 1) \ y) / z,x) = K((z / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,7064,a(flip),b,10457,a),flip(a)].">
      <j1 rule="hyper" parents="334 7064 10457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10459">
    <literal><![CDATA[
      K((x / ((y \ 1) * z)) \ y,y) = K(z / x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),10458(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 10458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10460">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),z) = K(y \ z,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),10459(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6 10459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10461">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),(z \ 1) \ 1) = K(y \ z,z)
    ]]></literal>
    <justification jstring="[hyper(3698,a,10460,a)].">
      <j1 rule="hyper" parents="3698 10460"/>
    </justification>
  </clause>

  <clause id="10462">
    <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(9622(a,1),10323(a,2,1))].">
      <j1 rule="para" parents="9622 10323"/>
    </justification>
  </clause>

  <clause id="10463">
    <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(334,a,10141,a(flip),b,10462,a),flip(a)].">
      <j1 rule="hyper" parents="334 10141 10462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10464">
    <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(7403(a,1),10463(a,1,1,2))].">
      <j1 rule="para" parents="7403 10463"/>
    </justification>
  </clause>

  <clause id="10465">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * (u * K(z,y)) = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(8170(a,1),10464(a,1,2))].">
      <j1 rule="para" parents="8170 10464"/>
    </justification>
  </clause>

  <clause id="10466">
    <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(9460(a,2),10465(a,1,1))].">
      <j1 rule="para" parents="9460 10465"/>
    </justification>
  </clause>

  <clause id="10467">
    <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(8100(a,1),10332(a,1,2))].">
      <j1 rule="para" parents="8100 10332"/>
    </justification>
  </clause>

  <clause id="10468">
    <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(9344(a,1),10333(a,1,2))].">
      <j1 rule="para" parents="9344 10333"/>
    </justification>
  </clause>

  <clause id="10469">
    <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(10096(a,1),10336(a,2,2))].">
      <j1 rule="para" parents="10096 10336"/>
    </justification>
  </clause>

  <clause id="10470">
    <literal><![CDATA[
      L(x \ 1,T(K(x,y),z),z) * (K(x,y) * z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(334,a,105,a(flip),b,10469,a),flip(a)].">
      <j1 rule="hyper" parents="334 105 10469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10471">
    <literal><![CDATA[
      L(x \ 1,K(x,T(y,z)),z) * (K(x,y) * z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(7401(a,2),10470(a,1,1,2))].">
      <j1 rule="para" parents="7401 10470"/>
    </justification>
  </clause>

  <clause id="10472">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(10432(a,1),10471(a,1,1))].">
      <j1 rule="para" parents="10432 10471"/>
    </justification>
  </clause>

  <clause id="10473">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,6303,a,b,10472,a)].">
      <j1 rule="hyper" parents="58 6303 10472"/>
    </justification>
  </clause>

  <clause id="10474">
    <literal><![CDATA[
      ((x \ 1) * y) / ((x \ K(x,z)) * y) = K(z,x)
    ]]></literal>
    <justification jstring="[para(10472(a,1),6309(a,1,2))].">
      <j1 rule="para" parents="10472 6309"/>
    </justification>
  </clause>

  <clause id="10476">
    <literal><![CDATA[
      L(x,y \ 1,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(2787,a,10473,a)].">
      <j1 rule="hyper" parents="2787 10473"/>
    </justification>
  </clause>

  <clause id="10477">
    <literal><![CDATA[
      L(x,y,K(y \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,4321,a(flip),b,10476,a)].">
      <j1 rule="hyper" parents="58 4321 10476"/>
    </justification>
  </clause>

  <clause id="10478">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,K(y,u)) = x
    ]]></literal>
    <justification jstring="[para(8162(a,1),10476(a,1,3))].">
      <j1 rule="para" parents="8162 10476"/>
    </justification>
  </clause>

  <clause id="10479">
    <literal><![CDATA[
      L(x,y,K(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(10477(a,1),45(a,2))].">
      <j1 rule="para" parents="10477 45"/>
    </justification>
  </clause>

  <clause id="10480">
    <literal><![CDATA[
      L(x,y \ z,K(y / z,u)) = x
    ]]></literal>
    <justification jstring="[para(8274(a,1),10477(a,1,3))].">
      <j1 rule="para" parents="8274 10477"/>
    </justification>
  </clause>

  <clause id="10481">
    <literal><![CDATA[
      L(x,(y * z) \ z,K(y,u)) = x
    ]]></literal>
    <justification jstring="[para(6(a,1),10480(a,1,3,1))].">
      <j1 rule="para" parents="6 10480"/>
    </justification>
  </clause>

  <clause id="10482">
    <literal><![CDATA[
      R(K(x,y),y \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6220,a(flip),b,10474,a)].">
      <j1 rule="hyper" parents="58 6220 10474"/>
    </justification>
  </clause>

  <clause id="10484">
    <literal><![CDATA[
      L(K((x / y) \ x,z),x \ (x / (1 / (1 / y))),u) = K(1 / (x \ (x / y)),z)
    ]]></literal>
    <justification jstring="[para(6622(a,1),10370(a,1,1))].">
      <j1 rule="para" parents="6622 10370"/>
    </justification>
  </clause>

  <clause id="10485">
    <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),10484(a,1,1,1))].">
      <j1 rule="para" parents="75 10484"/>
    </justification>
  </clause>

  <clause id="10487">
    <literal><![CDATA[
      L(K(x,y),1 / (1 / (z \ (z / x))),u) = K(1 / (z \ (z / x)),y)
    ]]></literal>
    <justification jstring="[para(2964(a,2),10485(a,1,2))].">
      <j1 rule="para" parents="2964 10485"/>
    </justification>
  </clause>

  <clause id="10488">
    <literal><![CDATA[
      L(K(x,y),z \ (z / x),u) = K(1 / (z \ (z / x)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4322,a(flip),b,10487,a)].">
      <j1 rule="hyper" parents="58 4322 10487"/>
    </justification>
  </clause>

  <clause id="10489">
    <literal><![CDATA[
      L(K(x,y),z \ (z / x),u) = K((z / x) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,6622,a(flip),b,10488,a),flip(a)].">
      <j1 rule="hyper" parents="334 6622 10488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10490">
    <literal><![CDATA[
      L(K(x,y),z \ (z / x),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,692,a(flip),b,10489,a),flip(a)].">
      <j1 rule="hyper" parents="334 692 10489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10492">
    <literal><![CDATA[
      (x / y) \ (x * (K(y,z) * (x \ (x / y)))) = T(K(y,z),x \ (x / y))
    ]]></literal>
    <justification jstring="[para(10490(a,1),814(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10490 814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10493">
    <literal><![CDATA[
      (x / y) \ (x * (K(y,z) * (x \ (x / y)))) = T(K(y,z),1 / y)
    ]]></literal>
    <justification jstring="[hyper(334,a,6564,a(flip),b,10492,a),flip(a)].">
      <j1 rule="hyper" parents="334 6564 10492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10495">
    <literal><![CDATA[
      (x / y) \ (x * (K(y,z) * (x \ (x / y)))) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,1352,a(flip),b,10493,a),flip(a)].">
      <j1 rule="hyper" parents="334 1352 10493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10496">
    <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(2544(a,1),10467(a,1,2))].">
      <j1 rule="para" parents="2544 10467"/>
    </justification>
  </clause>

  <clause id="10498">
    <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(10496(a,1),5468(a,1,1,2))].">
      <j1 rule="para" parents="10496 5468"/>
    </justification>
  </clause>

  <clause id="10499">
    <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(5466(a,1),10498(a,1,1))].">
      <j1 rule="para" parents="5466 10498"/>
    </justification>
  </clause>

  <clause id="10500">
    <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,7253,a(flip),b,10499,a),flip(a)].">
      <j1 rule="hyper" parents="58 7253 10499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10501">
    <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(10500(a,1),9018(a,2,1))].">
      <j1 rule="para" parents="10500 9018"/>
    </justification>
  </clause>

  <clause id="10502">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = (x * (u * ((x \ y) / u))) * (y \ z)
    ]]></literal>
    <justification jstring="[para(4866(a,1),4880(a,2,1))].">
      <j1 rule="para" parents="4866 4880"/>
    </justification>
  </clause>

  <clause id="10503">
    <literal><![CDATA[
      ((K(x,y) * z) * (z \ x)) / T(x,y) = a(K(x,y),z,z \ x)
    ]]></literal>
    <justification jstring="[para(9459(a,1),5127(a,1,2))].">
      <j1 rule="para" parents="9459 5127"/>
    </justification>
  </clause>

  <clause id="10505">
    <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(5091(a,1),5453(a,2,2))].">
      <j1 rule="para" parents="5091 5453"/>
    </justification>
  </clause>

  <clause id="10506">
    <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(10505(a,2),495(a,1))].">
      <j1 rule="para" parents="10505 495"/>
    </justification>
  </clause>

  <clause id="10508">
    <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(6374(a,1),6405(a,2,1))].">
      <j1 rule="para" parents="6374 6405"/>
    </justification>
  </clause>

  <clause id="10509">
    <literal><![CDATA[
      R(R(x,y,T(z,u)),y * T(z,u),K(u,z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,15,a,b,10508,a),flip(a)].">
      <j1 rule="hyper" parents="334 15 10508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10512">
    <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(227(a,1),10509(a,1,2))].">
      <j1 rule="para" parents="227 10509"/>
    </justification>
  </clause>

  <clause id="10513">
    <literal><![CDATA[
      R(R(x,y / z,z),y,K(z \ y,z)) = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[para(7029(a,1),10512(a,1,1))].">
      <j1 rule="para" parents="7029 10512"/>
    </justification>
  </clause>

  <clause id="10514">
    <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(334,a,4822,a,b,6552,a)].">
      <j1 rule="hyper" parents="334 4822 6552"/>
    </justification>
  </clause>

  <clause id="10515">
    <literal><![CDATA[
      (T(x,y) / z) / K(((1 / z) / (x / z)) \ 1,y) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,9967,a(flip),b,7138,a),flip(a)].">
      <j1 rule="hyper" parents="334 9967 7138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10516">
    <literal><![CDATA[
      (T(x,y) / z) / K(((z \ 1) / (x / z)) \ 1,y) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(4304(a,1),10515(a,1,2))].">
      <j1 rule="para" parents="4304 10515"/>
    </justification>
  </clause>

  <clause id="10517">
    <literal><![CDATA[
      (T(x,y) / z) * K(y,((z \ 1) / (x / z)) \ 1) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6529,a,10516,a)].">
      <j1 rule="hyper" parents="6529 10516"/>
    </justification>
  </clause>

  <clause id="10518">
    <literal><![CDATA[
      (T(x,y) / z) * K(y,(x / z) / (z \ 1)) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5614(a,1),10517(a,1,2))].">
      <j1 rule="para" parents="5614 10517"/>
    </justification>
  </clause>

  <clause id="10519">
    <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(7401(a,2),10518(a,1,1,1))].">
      <j1 rule="para" parents="7401 10518"/>
    </justification>
  </clause>

  <clause id="10520">
    <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,5313,a,b,7182,a)].">
      <j1 rule="hyper" parents="58 5313 7182"/>
    </justification>
  </clause>

  <clause id="10521">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = (y \ T(y * K(x \ 1,x),z)) / x
    ]]></literal>
    <justification jstring="[para(4309(a,1),10520(a,1,2))].">
      <j1 rule="para" parents="4309 10520"/>
    </justification>
  </clause>

  <clause id="10522">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = ((y \ T(y,z)) * K(x \ 1,x)) / x
    ]]></literal>
    <justification jstring="[para(4874(a,1),10521(a,2,1))].">
      <j1 rule="para" parents="4874 10521"/>
    </justification>
  </clause>

  <clause id="10523">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = (K(y,z) * K(x \ 1,x)) / x
    ]]></literal>
    <justification jstring="[para(4995(a,2),10522(a,2,1,1))].">
      <j1 rule="para" parents="4995 10522"/>
    </justification>
  </clause>

  <clause id="10524">
    <literal><![CDATA[
      K((x * ((y \ 1) / x)) \ 1,z) = x * (K(y,z) / T(x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(6393,a,10523,a),flip(a)].">
      <j1 rule="hyper" parents="6393 10523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10525">
    <literal><![CDATA[
      K((x * ((y \ 1) / x)) \ 1,z) = x * (K(y,z) / ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(106(a,1),10524(a,2,2,2))].">
      <j1 rule="para" parents="106 10524"/>
    </justification>
  </clause>

  <clause id="10526">
    <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(4035(a,1),7995(a,1,1))].">
      <j1 rule="para" parents="4035 7995"/>
    </justification>
  </clause>

  <clause id="10527">
    <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(7315(a,1),8013(a,2,2))].">
      <j1 rule="para" parents="7315 8013"/>
    </justification>
  </clause>

  <clause id="10528">
    <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(334,a,8002,a(flip),b,10527,a),flip(a)].">
      <j1 rule="hyper" parents="334 8002 10527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10530">
    <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(203(a,1),8648(a,1,1))].">
      <j1 rule="para" parents="203 8648"/>
    </justification>
  </clause>

  <clause id="10532">
    <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(6520(a,1),10530(a,1,2))].">
      <j1 rule="para" parents="6520 10530"/>
    </justification>
  </clause>

  <clause id="10533">
    <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(10314(a,1),10532(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10314 10532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10534">
    <literal><![CDATA[
      K(R(x,y,z),u) * (x \ R(x,y,z)) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,2,a(flip),b,10533,a),flip(a)].">
      <j1 rule="hyper" parents="334 2 10533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10535">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (y \ R(T(y,x),z,u)) = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(5409,a,10534,a)].">
      <j1 rule="hyper" parents="5409 10534"/>
    </justification>
  </clause>

  <clause id="10536">
    <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(9347(a,1),10535(a,1,1))].">
      <j1 rule="para" parents="9347 10535"/>
    </justification>
  </clause>

  <clause id="10537">
    <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(7970,a,8922,a)].">
      <j1 rule="hyper" parents="7970 8922"/>
    </justification>
  </clause>

  <clause id="10538">
    <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,7788,a(flip),b,8956,a),flip(a)].">
      <j1 rule="hyper" parents="58 7788 8956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10540">
    <literal><![CDATA[
      K(x,L(y,K(z,x) * u,w)) = K(x,(w * u) \ (w * (u * y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8840,a(flip),b,10538,a),flip(a)].">
      <j1 rule="hyper" parents="58 8840 10538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10542">
    <literal><![CDATA[
      K(x,L(y,K(z,x) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(13(a,2),10540(a,2,2))].">
      <j1 rule="para" parents="13 10540"/>
    </justification>
  </clause>

  <clause id="10543">
    <literal><![CDATA[
      K(x,L(y,K(x,z) \ u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(5391(a,2),10542(a,1,2,2))].">
      <j1 rule="para" parents="5391 10542"/>
    </justification>
  </clause>

  <clause id="10544">
    <literal><![CDATA[
      K(x,L(y,K(x,z) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(5394(a,1),10542(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5394 10542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10545">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = (y \ 1) / (y \ K(y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(10544(a,1),5399(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10544 5399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10546">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = K(L(x,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5399,a(flip),b,10545,a),flip(a)].">
      <j1 rule="hyper" parents="334 5399 10545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10547">
    <literal><![CDATA[
      K(L(x,T(y,z),u),z) = K(L(x,y,u),z)
    ]]></literal>
    <justification jstring="[para(5081(a,1),10546(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5081 10546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10548">
    <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,10144,a(flip),b,8959,a),flip(a)].">
      <j1 rule="hyper" parents="58 10144 8959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10549">
    <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(9791(a,1),9205(a,1,2,2))].">
      <j1 rule="para" parents="9791 9205"/>
    </justification>
  </clause>

  <clause id="10550">
    <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,8715,a(flip),b,9249,a),flip(a)].">
      <j1 rule="hyper" parents="58 8715 9249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10552">
    <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),10550(a,1,1))].">
      <j1 rule="para" parents="15 10550"/>
    </justification>
  </clause>

  <clause id="10553">
    <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,8575,a,b,10552,a)].">
      <j1 rule="hyper" parents="58 8575 10552"/>
    </justification>
  </clause>

  <clause id="10554">
    <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,9529,a,b,10553,a)].">
      <j1 rule="hyper" parents="58 9529 10553"/>
    </justification>
  </clause>

  <clause id="10555">
    <literal><![CDATA[
      R(K(x,y),z * x,u) = K(R(x,K(w,y) * z,u),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9118,a(flip),b,10554,a)].">
      <j1 rule="hyper" parents="58 9118 10554"/>
    </justification>
  </clause>

  <clause id="10557">
    <literal><![CDATA[
      K(R(x,K(y,z) * u,w),z) = K(R(x,u,w),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9527,a(flip),b,10555,a),flip(a)].">
      <j1 rule="hyper" parents="58 9527 10555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10558">
    <literal><![CDATA[
      T(x,R(y,K(z,x) * u,w)) = 1 / (x \ K(R(y,u,w),x))
    ]]></literal>
    <justification jstring="[para(10557(a,1),5131(a,2,2,2))].">
      <j1 rule="para" parents="10557 5131"/>
    </justification>
  </clause>

  <clause id="10559">
    <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(10558(a,2),5260(a,1))].">
      <j1 rule="para" parents="10558 5260"/>
    </justification>
  </clause>

  <clause id="10560">
    <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,8707,a(flip),b,9266,a),flip(a)].">
      <j1 rule="hyper" parents="58 8707 9266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10562">
    <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),10560(a,1,2))].">
      <j1 rule="para" parents="15 10560"/>
    </justification>
  </clause>

  <clause id="10563">
    <literal><![CDATA[
      K(x,R(y,K(z,x) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(9728,a,10562,a),flip(a)].">
      <j1 rule="hyper" parents="9728 10562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10564">
    <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,9730,a,b,10562,a)].">
      <j1 rule="hyper" parents="58 9730 10562"/>
    </justification>
  </clause>

  <clause id="10566">
    <literal><![CDATA[
      K(x,R(y,K(x,z) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(5394(a,1),10563(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5394 10563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10567">
    <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(573(a,1),10566(a,1,2)),flip(a)].">
      <j1 rule="para" parents="573 10566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10568">
    <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,10564,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 10564 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10569">
    <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(5392(a,1),10568(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5392 10568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10570">
    <literal><![CDATA[
      T(x,R(T(x,y) \ z,u,w)) = T(x,R(x \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(10559,a,10569,a),flip(a)].">
      <j1 rule="hyper" parents="10559 10569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10572">
    <literal><![CDATA[
      T(x,R(y / T(x,z),u,w)) = T(x,R(x \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(5553,a,10570,a)].">
      <j1 rule="hyper" parents="5553 10570"/>
    </justification>
  </clause>

  <clause id="10573">
    <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(9565,a,9568,a),flip(a)].">
      <j1 rule="hyper" parents="9565 9568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10574">
    <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,8893,a(flip),b,10573,a),flip(a)].">
      <j1 rule="hyper" parents="58 8893 10573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10576">
    <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(459(a,1),9840(a,1,1))].">
      <j1 rule="para" parents="459 9840"/>
    </justification>
  </clause>

  <clause id="10577">
    <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),10502(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 10502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10578">
    <literal><![CDATA[
      (x / y) \ T(x * K(y,z),(x / y) \ 1) = T(x * (y / x),z)
    ]]></literal>
    <justification jstring="[para(4176(a,1),10514(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4176 10514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10579">
    <literal><![CDATA[
      K(x * K(y,z),(x / y) \ 1) = T(x * (y / x),z) / T(y,z)
    ]]></literal>
    <justification jstring="[para(10578(a,1),6553(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10578 6553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10580">
    <literal><![CDATA[
      K(x * K(y,z),(x / y) \ 1) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,5388,a(flip),b,10579,a),flip(a)].">
      <j1 rule="hyper" parents="334 5388 10579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10581">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) = K(z,z \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8590,a(flip),b,10580,a)].">
      <j1 rule="hyper" parents="58 8590 10580"/>
    </justification>
  </clause>

  <clause id="10582">
    <literal><![CDATA[
      ((x \ y) \ R(x \ y,z,x \ y)) * (y / x) = R(y / x,z,x \ y)
    ]]></literal>
    <justification jstring="[para(5041(a,1),10526(a,2,1))].">
      <j1 rule="para" parents="5041 10526"/>
    </justification>
  </clause>

  <clause id="10583">
    <literal><![CDATA[
      a(x \ y,z,x \ y) * (y / x) = R(y / x,z,x \ y)
    ]]></literal>
    <justification jstring="[para(9155(a,1),10582(a,1,1))].">
      <j1 rule="para" parents="9155 10582"/>
    </justification>
  </clause>

  <clause id="10584">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = a(y \ x,z,y \ x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(334,a,7996,a,b,10583,a)].">
      <j1 rule="hyper" parents="334 7996 10583"/>
    </justification>
  </clause>

  <clause id="10585">
    <literal><![CDATA[
      a(x / y,z,x / y) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(9950,a,10584,a)].">
      <j1 rule="hyper" parents="9950 10584"/>
    </justification>
  </clause>

  <clause id="10586">
    <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(7375(a,1),10537(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7375 10537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10588">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * (u / x)))
    ]]></literal>
    <justification jstring="[hyper(7977,a,10548,a),flip(a)].">
      <j1 rule="hyper" parents="7977 10548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10589">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * u))
    ]]></literal>
    <justification jstring="[hyper(334,a,9519,a(flip),b,10588,a),flip(a)].">
      <j1 rule="hyper" parents="334 9519 10588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10590">
    <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),10589(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 10589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10591">
    <literal><![CDATA[
      K(x,y \ ((z * (x \ u)) * x)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(8004,a,10590,a),flip(a)].">
      <j1 rule="hyper" parents="8004 10590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10592">
    <literal><![CDATA[
      K(x,x \ (y * z)) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(5293,a,10591,a),flip(a)].">
      <j1 rule="hyper" parents="5293 10591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10593">
    <literal><![CDATA[
      K(x,y \ ((x \ y) * z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7126,a(flip),b,10591,a),flip(a)].">
      <j1 rule="hyper" parents="58 7126 10591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10594">
    <literal><![CDATA[
      K(x,x \ (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(10591(a,1),5293(a,1))].">
      <j1 rule="para" parents="10591 5293"/>
    </justification>
  </clause>

  <clause id="10595">
    <literal><![CDATA[
      T(x,x \ (y * z)) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,10592,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 10592 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10596">
    <literal><![CDATA[
      K(x,x \ (y * (x * z))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),10592(a,2,2,2))].">
      <j1 rule="para" parents="4 10592"/>
    </justification>
  </clause>

  <clause id="10597">
    <literal><![CDATA[
      (x * K(y,z * (y \ u))) \ x = K(y \ (z * u),y)
    ]]></literal>
    <justification jstring="[para(10592(a,1),6523(a,1,1,2))].">
      <j1 rule="para" parents="10592 6523"/>
    </justification>
  </clause>

  <clause id="10598">
    <literal><![CDATA[
      K(x,K(y,z * (y \ u))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(10592(a,1),8140(a,1,2))].">
      <j1 rule="para" parents="10592 8140"/>
    </justification>
  </clause>

  <clause id="10599">
    <literal><![CDATA[
      K(x,x \ ((x \ y) \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),10593(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 10593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10600">
    <literal><![CDATA[
      T(x,y * (x \ z)) = (x \ (y * z)) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(439,a,10595,a),flip(a)].">
      <j1 rule="hyper" parents="439 10595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10601">
    <literal><![CDATA[
      K(x,x \ (y * (z * x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8861,a,b,10596,a)].">
      <j1 rule="hyper" parents="58 8861 10596"/>
    </justification>
  </clause>

  <clause id="10602">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[para(4(a,1),10599(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 10599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10603">
    <literal><![CDATA[
      K(x,y \ (x \ z)) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(7648,a,10602,a)].">
      <j1 rule="hyper" parents="7648 10602"/>
    </justification>
  </clause>

  <clause id="10604">
    <literal><![CDATA[
      K(x,x \ (y \ (z * x))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(7123,a,10602,a),flip(a)].">
      <j1 rule="hyper" parents="7123 10602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10605">
    <literal><![CDATA[
      K(x,x \ (y \ (x * z))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(10602(a,1),7646(a,1))].">
      <j1 rule="para" parents="10602 7646"/>
    </justification>
  </clause>

  <clause id="10606">
    <literal><![CDATA[
      K(x,x \ (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(10602(a,1),7648(a,1))].">
      <j1 rule="para" parents="10602 7648"/>
    </justification>
  </clause>

  <clause id="10607">
    <literal><![CDATA[
      K(x,y \ (x \ (y * z))) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(4(a,1),10603(a,2,2,2))].">
      <j1 rule="para" parents="4 10603"/>
    </justification>
  </clause>

  <clause id="10608">
    <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),10604(a,1,2,2,2))].">
      <j1 rule="para" parents="101 10604"/>
    </justification>
  </clause>

  <clause id="10609">
    <literal><![CDATA[
      L(K(x,x \ y),y,z) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(7862,a,10607,a)].">
      <j1 rule="hyper" parents="7862 10607"/>
    </justification>
  </clause>

  <clause id="10610">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,5184,a(flip),b,10607,a),flip(a)].">
      <j1 rule="hyper" parents="334 5184 10607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10611">
    <literal><![CDATA[
      (x * y) * K(z,z \ y) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[para(10607(a,1),8812(a,1,2))].">
      <j1 rule="para" parents="10607 8812"/>
    </justification>
  </clause>

  <clause id="10612">
    <literal><![CDATA[
      a(x,y,K(z,z \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10609,a,b,1992,a),flip(a)].">
      <j1 rule="hyper" parents="115 10609 1992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10613">
    <literal><![CDATA[
      L(K(x \ y,x),y,z) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(6202,a,10612,a)].">
      <j1 rule="hyper" parents="6202 10612"/>
    </justification>
  </clause>

  <clause id="10614">
    <literal><![CDATA[
      K(x \ (y \ (x * z)),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(8747,a,10613,a)].">
      <j1 rule="hyper" parents="8747 10613"/>
    </justification>
  </clause>

  <clause id="10615">
    <literal><![CDATA[
      K((x * y) \ z,y) = K(y \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(7166,a,10613,a)].">
      <j1 rule="hyper" parents="7166 10613"/>
    </justification>
  </clause>

  <clause id="10617">
    <literal><![CDATA[
      (x * y) * K(z \ y,z) = x * ((z \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10613,a(flip),b,475,a)].">
      <j1 rule="hyper" parents="119 10613 475"/>
    </justification>
  </clause>

  <clause id="10618">
    <literal><![CDATA[
      K(x,L(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8997,a,10610,a)].">
      <j1 rule="hyper" parents="8997 10610"/>
    </justification>
  </clause>

  <clause id="10619">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9296,a,10618,a)].">
      <j1 rule="hyper" parents="9296 10618"/>
    </justification>
  </clause>

  <clause id="10622">
    <literal><![CDATA[
      T(x,L(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,10618,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 10618 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10624">
    <literal><![CDATA[
      (x * (y * z)) * K(z,y) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,10618,a(flip),b,6902,a)].">
      <j1 rule="hyper" parents="119 10618 6902"/>
    </justification>
  </clause>

  <clause id="10625">
    <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(513(a,1),10618(a,1,2))].">
      <j1 rule="para" parents="513 10618"/>
    </justification>
  </clause>

  <clause id="10627">
    <literal><![CDATA[
      K(L(x,y,z),L(u,x,w)) = L(K(x,u),y * x,z)
    ]]></literal>
    <justification jstring="[para(10618(a,1),6883(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10618 6883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10628">
    <literal><![CDATA[
      (x * (y * z)) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = u
    ]]></literal>
    <justification jstring="[para(10618(a,1),6911(a,1,2))].">
      <j1 rule="para" parents="10618 6911"/>
    </justification>
  </clause>

  <clause id="10629">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(L(x,y,v5),L(y,u,w))
    ]]></literal>
    <justification jstring="[para(10618(a,1),9385(a,1,1))].">
      <j1 rule="para" parents="10618 9385"/>
    </justification>
  </clause>

  <clause id="10630">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,L(y,x,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,10618,a,b,10619,a),flip(a)].">
      <j1 rule="hyper" parents="334 10618 10619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10633">
    <literal><![CDATA[
      L(x,y,z) * T(y,x) = y * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10622,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 10622 17"/>
    </justification>
  </clause>

  <clause id="10634">
    <literal><![CDATA[
      L(x,y,z) = (z * T(y,x)) \ (z * (T(y,x) * x))
    ]]></literal>
    <justification jstring="[para(10622(a,1),7219(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10622 7219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10638">
    <literal><![CDATA[
      K(x,L(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(10630(a,1),7647(a,1))].">
      <j1 rule="para" parents="10630 7647"/>
    </justification>
  </clause>

  <clause id="10640">
    <literal><![CDATA[
      K(x,(y * x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(311(a,1),10638(a,1,2))].">
      <j1 rule="para" parents="311 10638"/>
    </justification>
  </clause>

  <clause id="10641">
    <literal><![CDATA[
      K(x \ (y \ z),y) = K(y \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(5(a,1),10614(a,1,1,2,2))].">
      <j1 rule="para" parents="5 10614"/>
    </justification>
  </clause>

  <clause id="10642">
    <literal><![CDATA[
      K(x \ (y \ (z * x)),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(8726,a,10615,a),flip(a)].">
      <j1 rule="hyper" parents="8726 10615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10643">
    <literal><![CDATA[
      K(x \ (y \ z),x) * z = z * K(z / (y * x),x)
    ]]></literal>
    <justification jstring="[para(10615(a,1),8229(a,1,1))].">
      <j1 rule="para" parents="10615 8229"/>
    </justification>
  </clause>

  <clause id="10644">
    <literal><![CDATA[
      K(x \ (y \ z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x \ z),x) = u
    ]]></literal>
    <justification jstring="[para(10615(a,1),8743(a,1))].">
      <j1 rule="para" parents="10615 8743"/>
    </justification>
  </clause>

  <clause id="10645">
    <literal><![CDATA[
      R(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(866,a,10624,a)].">
      <j1 rule="hyper" parents="866 10624"/>
    </justification>
  </clause>

  <clause id="10646">
    <literal><![CDATA[
      (x / (y * z)) * (z * y) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(341,a,10624,a),flip(a)].">
      <j1 rule="hyper" parents="341 10624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10647">
    <literal><![CDATA[
      K(x,T(y,z * (x * y))) * (z * (y * x)) = z * (x * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,10624,a(flip),b,8196,a)].">
      <j1 rule="hyper" parents="119 10624 8196"/>
    </justification>
  </clause>

  <clause id="10648">
    <literal><![CDATA[
      K(x * (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (z * y),z) = u
    ]]></literal>
    <justification jstring="[para(10624(a,1),7585(a,1,1))].">
      <j1 rule="para" parents="10624 7585"/>
    </justification>
  </clause>

  <clause id="10649">
    <literal><![CDATA[
      R(x,y,T(z,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(7213,a,10645,a)].">
      <j1 rule="hyper" parents="7213 10645"/>
    </justification>
  </clause>

  <clause id="10650">
    <literal><![CDATA[
      R(x,y,K(z \ y,z)) = x
    ]]></literal>
    <justification jstring="[para(5(a,1),10645(a,1,2))].">
      <j1 rule="para" parents="5 10645"/>
    </justification>
  </clause>

  <clause id="10651">
    <literal><![CDATA[
      R(x,y / z,z) = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10513,a(flip),b,10650,a),flip(a)].">
      <j1 rule="hyper" parents="58 10513 10650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10653">
    <literal><![CDATA[
      (x * T(y,z)) / (y * z) = R(x / z,z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,540,a(flip),b,10649,a)].">
      <j1 rule="hyper" parents="58 540 10649"/>
    </justification>
  </clause>

  <clause id="10654">
    <literal><![CDATA[
      R(x,y,z / y) = R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(107(a,1),10649(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 10649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10656">
    <literal><![CDATA[
      R(x,y,z) * (z * y) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(10649(a,1),528(a,1,1))].">
      <j1 rule="para" parents="10649 528"/>
    </justification>
  </clause>

  <clause id="10658">
    <literal><![CDATA[
      R(x,y,K(z,T(u,y))) = R(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(7401(a,2),10649(a,1,3))].">
      <j1 rule="para" parents="7401 10649"/>
    </justification>
  </clause>

  <clause id="10660">
    <literal><![CDATA[
      R(K(x,(y / (z / u)) \ x),u \ z,u) = K(x,z / ((x \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8759,a(flip),b,10651,a),flip(a)].">
      <j1 rule="hyper" parents="58 8759 10651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10661">
    <literal><![CDATA[
      R(K(x,(y / z) / u),z \ y,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6159,a(flip),b,10651,a),flip(a)].">
      <j1 rule="hyper" parents="58 6159 10651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10662">
    <literal><![CDATA[
      R(x / (y / z),z \ y,z) = (x * z) / y
    ]]></literal>
    <justification jstring="[hyper(58,a,538,a(flip),b,10651,a),flip(a)].">
      <j1 rule="hyper" parents="58 538 10651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10665">
    <literal><![CDATA[
      R(x,y \ z,y) * z = (x * (z / y)) * y
    ]]></literal>
    <justification jstring="[para(10651(a,1),520(a,1,1))].">
      <j1 rule="para" parents="10651 520"/>
    </justification>
  </clause>

  <clause id="10666">
    <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(10633(a,1),1511(a,1,2,2))].">
      <j1 rule="para" parents="10633 1511"/>
    </justification>
  </clause>

  <clause id="10667">
    <literal><![CDATA[
      x * K(y \ (z \ u),z) = x * K(z \ (y \ u),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10641,a,b,4,a)].">
      <j1 rule="hyper" parents="119 10641 4"/>
    </justification>
  </clause>

  <clause id="10669">
    <literal><![CDATA[
      (x * T(y,z)) / (y * z) = (x * y) / (z * y)
    ]]></literal>
    <justification jstring="[hyper(117,a,6432,a(flip),b,10646,a)].">
      <j1 rule="hyper" parents="117 6432 10646"/>
    </justification>
  </clause>

  <clause id="10670">
    <literal><![CDATA[
      R(R(x,y,x) / x,x,z) = (z * R(x,y,x)) / (z * x)
    ]]></literal>
    <justification jstring="[para(7346(a,1),10653(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7346 10653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10671">
    <literal><![CDATA[
      R(x / ((y * z) / y),z,y) = (x * y) / (y * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),10662(a,1,2))].">
      <j1 rule="para" parents="4 10662"/>
    </justification>
  </clause>

  <clause id="10672">
    <literal><![CDATA[
      K(x,K(y / z,u * z)) = K(x,K(y / z,u * y))
    ]]></literal>
    <justification jstring="[para(75(a,1),10598(a,1,2,2,2))].">
      <j1 rule="para" parents="75 10598"/>
    </justification>
  </clause>

  <clause id="10673">
    <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(10600(a,2),5415(a,1,1))].">
      <j1 rule="para" parents="10600 5415"/>
    </justification>
  </clause>

  <clause id="10674">
    <literal><![CDATA[
      K(T(x,y * (x \ z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u,y * z)) = w
    ]]></literal>
    <justification jstring="[para(10600(a,2),7975(a,1,1))].">
      <j1 rule="para" parents="10600 7975"/>
    </justification>
  </clause>

  <clause id="10677">
    <literal><![CDATA[
      K(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (x \ (u \ y))) = z
    ]]></literal>
    <justification jstring="[para(5(a,1),10594(a,1,2,2))].">
      <j1 rule="para" parents="5 10594"/>
    </justification>
  </clause>

  <clause id="10678">
    <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),10606(a,1,2,2))].">
      <j1 rule="para" parents="17 10606"/>
    </justification>
  </clause>

  <clause id="10679">
    <literal><![CDATA[
      K(L(x,y,z),L(u,x,w)) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,6883,a(flip),b,10627,a),flip(a)].">
      <j1 rule="hyper" parents="334 6883 10627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10680">
    <literal><![CDATA[
      K(L(x,y,z),(u * x) \ (u * w)) = K(L(x,y,z),x \ w)
    ]]></literal>
    <justification jstring="[hyper(6983,a,10679,a)].">
      <j1 rule="hyper" parents="6983 10679"/>
    </justification>
  </clause>

  <clause id="10681">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = w
    ]]></literal>
    <justification jstring="[para(10618(a,2),10628(a,1,2))].">
      <j1 rule="para" parents="10618 10628"/>
    </justification>
  </clause>

  <clause id="10682">
    <literal><![CDATA[
      L(x,T(y,x),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,13,a,b,10634,a)].">
      <j1 rule="hyper" parents="334 13 10634"/>
    </justification>
  </clause>

  <clause id="10684">
    <literal><![CDATA[
      L(x,y / x,z) = L(x,x \ y,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),10682(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 10682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10688">
    <literal><![CDATA[
      L(x,x \ (y \ z),y) = (y * ((y \ z) / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,580,a(flip),b,10684,a),flip(a)].">
      <j1 rule="hyper" parents="58 580 10684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10689">
    <literal><![CDATA[
      L(x,x \ y,z) = (z * (y / x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,94,a(flip),b,10684,a),flip(a)].">
      <j1 rule="hyper" parents="58 94 10684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10690">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(10684(a,1),6926(a,1,1))].">
      <j1 rule="para" parents="10684 6926"/>
    </justification>
  </clause>

  <clause id="10691">
    <literal><![CDATA[
      K(x,T(L(y,y \ z,u),u * z)) = K(x,(u * z) / (u * (z / y)))
    ]]></literal>
    <justification jstring="[para(10689(a,2),8164(a,1,2,1))].">
      <j1 rule="para" parents="10689 8164"/>
    </justification>
  </clause>

  <clause id="10692">
    <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(10689(a,2),8263(a,1,1,2))].">
      <j1 rule="para" parents="10689 8263"/>
    </justification>
  </clause>

  <clause id="10693">
    <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),10640(a,1,2))].">
      <j1 rule="para" parents="9 10640"/>
    </justification>
  </clause>

  <clause id="10694">
    <literal><![CDATA[
      ((x * y) * z) / (z * y) = R(x * K(y,z),y,z)
    ]]></literal>
    <justification jstring="[para(6728(a,1),10671(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6728 10671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10695">
    <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(7423(a,1),10694(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7423 10694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10696">
    <literal><![CDATA[
      K(x \ (y * z),x) = K(y * (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(6528,a,10597,a),flip(a)].">
      <j1 rule="hyper" parents="6528 10597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10697">
    <literal><![CDATA[
      K(x \ (y * z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * (x \ z),x) = u
    ]]></literal>
    <justification jstring="[para(10597(a,1),6528(a,1))].">
      <j1 rule="para" parents="10597 6528"/>
    </justification>
  </clause>

  <clause id="10698">
    <literal><![CDATA[
      K(x * (y \ (x \ z)),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),10696(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 10696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10699">
    <literal><![CDATA[
      K(L(x,y,z),L(y,u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9383,a(flip),b,10629,a),flip(a)].">
      <j1 rule="hyper" parents="58 9383 10629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10700">
    <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(10629(a,2),7647(a,1))].">
      <j1 rule="para" parents="10629 7647"/>
    </justification>
  </clause>

  <clause id="10701">
    <literal><![CDATA[
      K((x * y) \ z,L(y,u,w)) = K(y \ (x \ z),L(y,u,w))
    ]]></literal>
    <justification jstring="[para(311(a,1),10699(a,1,1))].">
      <j1 rule="para" parents="311 10699"/>
    </justification>
  </clause>

  <clause id="10702">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) = R(a(y,z,y),y,x)
    ]]></literal>
    <justification jstring="[para(9161(a,1),10670(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9161 10670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10703">
    <literal><![CDATA[
      R(a(x,y,x),x,z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(9838,a,10702,a),flip(a)].">
      <j1 rule="hyper" parents="9838 10702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10705">
    <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,523,a,b,10703,a)].">
      <j1 rule="hyper" parents="58 523 10703"/>
    </justification>
  </clause>

  <clause id="10706">
    <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),10700(a,1,2,1))].">
      <j1 rule="para" parents="104 10700"/>
    </justification>
  </clause>

  <clause id="10707">
    <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),10706(a,1,2))].">
      <j1 rule="para" parents="5 10706"/>
    </justification>
  </clause>

  <clause id="10708">
    <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),10706(a,1,2))].">
      <j1 rule="para" parents="7 10706"/>
    </justification>
  </clause>

  <clause id="10709">
    <literal><![CDATA[
      K(L(x,y,z),u \ (x \ (u * w))) = K(L(x,y,z),x \ w)
    ]]></literal>
    <justification jstring="[hyper(9569,a,10680,a)].">
      <j1 rule="hyper" parents="9569 10680"/>
    </justification>
  </clause>

  <clause id="10711">
    <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),10701(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7 10701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10712">
    <literal><![CDATA[
      K(x \ ((x \ y) \ z),L(x,u,w)) = K(y \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(10326,a,10711,a)].">
      <j1 rule="hyper" parents="10326 10711"/>
    </justification>
  </clause>

  <clause id="10713">
    <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),10691(a,1,2))].">
      <j1 rule="para" parents="20 10691"/>
    </justification>
  </clause>

  <clause id="10714">
    <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(10164,a,10625,a)].">
      <j1 rule="hyper" parents="10164 10625"/>
    </justification>
  </clause>

  <clause id="10715">
    <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,10709,a(flip),b,10714,a),flip(a)].">
      <j1 rule="hyper" parents="58 10709 10714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10717">
    <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,10715,a,b,5028,a)].">
      <j1 rule="hyper" parents="119 10715 5028"/>
    </justification>
  </clause>

  <clause id="10718">
    <literal><![CDATA[
      L(T(x,x \ y),z,u) = (L(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(5112,a,10717,a),flip(a)].">
      <j1 rule="hyper" parents="5112 10717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10719">
    <literal><![CDATA[
      T(L(x,y,z),L(x,y,z) \ u) = L(T(x,x \ u),y,z)
    ]]></literal>
    <justification jstring="[hyper(5030,a,10717,a)].">
      <j1 rule="hyper" parents="5030 10717"/>
    </justification>
  </clause>

  <clause id="10720">
    <literal><![CDATA[
      L((x \ y) \ y,z,u) = (L(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,854,a(flip),b,10718,a)].">
      <j1 rule="hyper" parents="58 854 10718"/>
    </justification>
  </clause>

  <clause id="10726">
    <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(10720(a,2),5067(a,1,1))].">
      <j1 rule="para" parents="10720 5067"/>
    </justification>
  </clause>

  <clause id="10727">
    <literal><![CDATA[
      T(x,L(x,y,z) \ u) = T(x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(142,a,10719,a)].">
      <j1 rule="hyper" parents="142 10719"/>
    </justification>
  </clause>

  <clause id="10728">
    <literal><![CDATA[
      T(x,L(x,y,z) \ u) = K(x,x \ u) * x
    ]]></literal>
    <justification jstring="[hyper(334,a,5034,a(flip),b,10727,a),flip(a)].">
      <j1 rule="hyper" parents="334 5034 10727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10731">
    <literal><![CDATA[
      K(x,L(x,y,z) \ u) = K(x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(5114,a,10728,a)].">
      <j1 rule="hyper" parents="5114 10728"/>
    </justification>
  </clause>

  <clause id="10733">
    <literal><![CDATA[
      K(L(x,y,z) \ u,x) = w / (K(x,x \ u) * w)
    ]]></literal>
    <justification jstring="[para(10731(a,1),5403(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10731 5403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10734">
    <literal><![CDATA[
      K(L(x,y,z) \ u,x) = K(x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,5403,a(flip),b,10733,a),flip(a)].">
      <j1 rule="hyper" parents="334 5403 10733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10735">
    <literal><![CDATA[
      K(x / L(y,z,u),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(8538,a,10734,a)].">
      <j1 rule="hyper" parents="8538 10734"/>
    </justification>
  </clause>

  <clause id="10736">
    <literal><![CDATA[
      K(x \ (y * L(x,z,u)),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(6(a,1),10735(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 10735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10737">
    <literal><![CDATA[
      K((x \ y) * L(x,z,u),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7643,a(flip),b,10736,a)].">
      <j1 rule="hyper" parents="58 7643 10736"/>
    </justification>
  </clause>

  <clause id="10738">
    <literal><![CDATA[
      T(x * L(y,z,u),K(x,y)) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(10736(a,1),4984(a,1,2))].">
      <j1 rule="para" parents="10736 4984"/>
    </justification>
  </clause>

  <clause id="10740">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),10737(a,1,1,1))].">
      <j1 rule="para" parents="4 10737"/>
    </justification>
  </clause>

  <clause id="10741">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = K(x,y) * a(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,9182,a,b,10740,a),flip(a)].">
      <j1 rule="hyper" parents="334 9182 10740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10742">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = (w * T(y,x)) \ (w * R(y,x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,7579,a,b,10740,a),flip(a)].">
      <j1 rule="hyper" parents="334 7579 10740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10743">
    <literal><![CDATA[
      K(x * (y * z),z) = K(z * (x * y),z)
    ]]></literal>
    <justification jstring="[para(90(a,1),10740(a,1,1))].">
      <j1 rule="para" parents="90 10740"/>
    </justification>
  </clause>

  <clause id="10744">
    <literal><![CDATA[
      K(x * (y * z),y) = K(y * (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(10648,a,10743,a)].">
      <j1 rule="hyper" parents="10648 10743"/>
    </justification>
  </clause>

  <clause id="10745">
    <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),10738(a,1,1,2))].">
      <j1 rule="para" parents="92 10738"/>
    </justification>
  </clause>

  <clause id="10746">
    <literal><![CDATA[
      a(x,y,L(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(10238,a,10741,a)].">
      <j1 rule="hyper" parents="10238 10741"/>
    </justification>
  </clause>

  <clause id="10747">
    <literal><![CDATA[
      (x / y) * R(y,z,y) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(10746(a,2),9411(a,2,2))].">
      <j1 rule="para" parents="10746 9411"/>
    </justification>
  </clause>

  <clause id="10749">
    <literal><![CDATA[
      x * R(y,z,L(y,u,w)) = x * R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(33,a,10221,a,b,10742,a(flip))].">
      <j1 rule="hyper" parents="33 10221 10742"/>
    </justification>
  </clause>

  <clause id="10750">
    <literal><![CDATA[
      (x / y) * R(y,z,L(y,u,w)) = x * a(y,z,L(y,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(334,a,10747,a(flip),b,10749,a),flip(a)].">
      <j1 rule="hyper" parents="334 10747 10749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10751">
    <literal><![CDATA[
      R(x,y,L(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(287,a,10749,a),flip(a)].">
      <j1 rule="hyper" parents="287 10749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10752">
    <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(10749(a,1),10576(a,1,1,2))].">
      <j1 rule="para" parents="10749 10576"/>
    </justification>
  </clause>

  <clause id="10754">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,5205,a,b,10751,a)].">
      <j1 rule="hyper" parents="334 5205 10751"/>
    </justification>
  </clause>

  <clause id="10755">
    <literal><![CDATA[
      R(L(x,y,z),u,L(x,w,v5)) = L(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(10751(a,1),24(a,2,1))].">
      <j1 rule="para" parents="10751 24"/>
    </justification>
  </clause>

  <clause id="10756">
    <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(10755(a,1),7381(a,1,2))].">
      <j1 rule="para" parents="10755 7381"/>
    </justification>
  </clause>

  <clause id="10758">
    <literal><![CDATA[
      K(L(x,y,z) \ u,L(x,y,z)) = K(x \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(5286,a,10726,a),flip(a)].">
      <j1 rule="hyper" parents="5286 10726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10759">
    <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(10644,a,10758,a)].">
      <j1 rule="hyper" parents="10644 10758"/>
    </justification>
  </clause>

  <clause id="10760">
    <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,7728,a(flip),b,10759,a),flip(a)].">
      <j1 rule="hyper" parents="58 7728 10759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10761">
    <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,9853,a(flip),b,10752,a)].">
      <j1 rule="hyper" parents="58 9853 10752"/>
    </justification>
  </clause>

  <clause id="10763">
    <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),10761(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 10761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10764">
    <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,10712,a(flip),b,10760,a)].">
      <j1 rule="hyper" parents="58 10712 10760"/>
    </justification>
  </clause>

  <clause id="10765">
    <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),10666(a,1,1,1))].">
      <j1 rule="para" parents="105 10666"/>
    </justification>
  </clause>

  <clause id="10766">
    <literal><![CDATA[
      K(L(x,y,z),x * T(y,x)) = K(x,y * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(1710,a,10765,a),flip(a)].">
      <j1 rule="hyper" parents="1710 10765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10767">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,y * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(105(a,1),10766(a,1,2))].">
      <j1 rule="para" parents="105 10766"/>
    </justification>
  </clause>

  <clause id="10768">
    <literal><![CDATA[
      K(x,y * L(x,y,z)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(8700,a,10767,a),flip(a)].">
      <j1 rule="hyper" parents="8700 10767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10770">
    <literal><![CDATA[
      L(K(x,x * y),z * x,u) = K(L(x,z,u),y * L(x,y,w))
    ]]></literal>
    <justification jstring="[para(10768(a,1),6883(a,1,1))].">
      <j1 rule="para" parents="10768 6883"/>
    </justification>
  </clause>

  <clause id="10771">
    <literal><![CDATA[
      K(L(x,y,z),u * L(x,u,w)) = K(L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(8691,a,10770,a),flip(a)].">
      <j1 rule="hyper" parents="8691 10770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10772">
    <literal><![CDATA[
      L(K(L(x,y,z),x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(10771(a,1),9939(a,1,1))].">
      <j1 rule="para" parents="10771 9939"/>
    </justification>
  </clause>

  <clause id="10773">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(9124(a,1),10772(a,1,1))].">
      <j1 rule="para" parents="9124 10772"/>
    </justification>
  </clause>

  <clause id="10775">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9936,a(flip),b,10773,a)].">
      <j1 rule="hyper" parents="58 9936 10773"/>
    </justification>
  </clause>

  <clause id="10776">
    <literal><![CDATA[
      K(x,y \ ((y * z) * x)) = K(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9935,a(flip),b,10773,a)].">
      <j1 rule="hyper" parents="58 9935 10773"/>
    </justification>
  </clause>

  <clause id="10778">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(6872,a,10775,a)].">
      <j1 rule="hyper" parents="6872 10775"/>
    </justification>
  </clause>

  <clause id="10779">
    <literal><![CDATA[
      K(x,x * ((y * z) \ y)) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(6853,a,10775,a),flip(a)].">
      <j1 rule="hyper" parents="6853 10775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10780">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,u) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(334,a,10773,a,b,10775,a)].">
      <j1 rule="hyper" parents="334 10773 10775"/>
    </justification>
  </clause>

  <clause id="10781">
    <literal><![CDATA[
      K(x,x * (y \ (x \ z))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7847,a(flip),b,10775,a),flip(a)].">
      <j1 rule="hyper" parents="58 7847 10775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10783">
    <literal><![CDATA[
      K(x,y \ ((y * z) * x)) = K(x,z * x)
    ]]></literal>
    <justification jstring="[hyper(334,a,5649,a,b,10776,a),flip(a)].">
      <j1 rule="hyper" parents="334 5649 10776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10784">
    <literal><![CDATA[
      L(K(x,y * x),y,z) = K(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9937,a,b,10783,a)].">
      <j1 rule="hyper" parents="58 9937 10783"/>
    </justification>
  </clause>

  <clause id="10786">
    <literal><![CDATA[
      a(x,y,K(z,y * z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10784,a,b,1992,a),flip(a)].">
      <j1 rule="hyper" parents="115 10784 1992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10787">
    <literal><![CDATA[
      a(x,y,K(y * z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10784,a(flip),b,6205,a),flip(a)].">
      <j1 rule="hyper" parents="115 10784 6205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10788">
    <literal><![CDATA[
      L(K(x * y,y),x,z) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(6202,a,10786,a)].">
      <j1 rule="hyper" parents="6202 10786"/>
    </justification>
  </clause>

  <clause id="10789">
    <literal><![CDATA[
      a(x,y,K(z,y \ z)) = 1
    ]]></literal>
    <justification jstring="[para(5(a,1),10787(a,1,3,1))].">
      <j1 rule="para" parents="5 10787"/>
    </justification>
  </clause>

  <clause id="10790">
    <literal><![CDATA[
      L(K(x * y,y),x,z) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5532,a(flip),b,10788,a),flip(a)].">
      <j1 rule="hyper" parents="334 5532 10788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10791">
    <literal><![CDATA[
      K(x \ (y * (x * z)),y) = K(z * y,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9932,a(flip),b,10788,a)].">
      <j1 rule="hyper" parents="58 9932 10788"/>
    </justification>
  </clause>

  <clause id="10792">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(5532(a,1),10790(a,1,1))].">
      <j1 rule="para" parents="5532 10790"/>
    </justification>
  </clause>

  <clause id="10793">
    <literal><![CDATA[
      K((x * (y \ 1)) \ z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(7167,a,10792,a)].">
      <j1 rule="hyper" parents="7167 10792"/>
    </justification>
  </clause>

  <clause id="10794">
    <literal><![CDATA[
      K(x \ (y * z),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9927,a(flip),b,10792,a)].">
      <j1 rule="hyper" parents="58 9927 10792"/>
    </justification>
  </clause>

  <clause id="10796">
    <literal><![CDATA[
      K((x / y) \ z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(8742,a,10794,a)].">
      <j1 rule="hyper" parents="8742 10794"/>
    </justification>
  </clause>

  <clause id="10797">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(x * (y \ z),x)
    ]]></literal>
    <justification jstring="[hyper(8727,a,10794,a)].">
      <j1 rule="hyper" parents="8727 10794"/>
    </justification>
  </clause>

  <clause id="10798">
    <literal><![CDATA[
      K(x * ((y * x) \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(8726,a,10794,a),flip(a)].">
      <j1 rule="hyper" parents="8726 10794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10799">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(z * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(6908,a,10794,a)].">
      <j1 rule="hyper" parents="6908 10794"/>
    </justification>
  </clause>

  <clause id="10801">
    <literal><![CDATA[
      K(x,y \ z) * K(x * (y \ z),x) = a(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(10794(a,1),9163(a,1,2))].">
      <j1 rule="para" parents="10794 9163"/>
    </justification>
  </clause>

  <clause id="10802">
    <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,10764,a(flip),b,10797,a),flip(a)].">
      <j1 rule="hyper" parents="58 10764 10797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10804">
    <literal><![CDATA[
      K((x * (1 / y)) \ z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7147,a,b,10793,a)].">
      <j1 rule="hyper" parents="58 7147 10793"/>
    </justification>
  </clause>

  <clause id="10805">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x * (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(10780(a,1),3811(a,1))].">
      <j1 rule="para" parents="10780 3811"/>
    </justification>
  </clause>

  <clause id="10806">
    <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(1509(a,1),10805(a,1,2))].">
      <j1 rule="para" parents="1509 10805"/>
    </justification>
  </clause>

  <clause id="10807">
    <literal><![CDATA[
      a(x,(y \ z) \ 1,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ y,x) = u
    ]]></literal>
    <justification jstring="[para(10801(a,1),9194(a,1))].">
      <j1 rule="para" parents="10801 9194"/>
    </justification>
  </clause>

  <clause id="10808">
    <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(334,a,10130,a(flip),b,10802,a),flip(a)].">
      <j1 rule="hyper" parents="334 10130 10802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10809">
    <literal><![CDATA[
      K(L(x,y,z) * (x \ u),L(x,y,z)) = K(u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,691,a(flip),b,10808,a),flip(a)].">
      <j1 rule="hyper" parents="334 691 10808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10810">
    <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),10809(a,1,1,2))].">
      <j1 rule="para" parents="4 10809"/>
    </justification>
  </clause>

  <clause id="10811">
    <literal><![CDATA[
      K((x \ y) \ z,L(x,u,w)) = K(x * (y \ z),L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,10802,a(flip),b,10810,a)].">
      <j1 rule="hyper" parents="58 10802 10810"/>
    </justification>
  </clause>

  <clause id="10812">
    <literal><![CDATA[
      K((x \ y) \ z,L(x,u,w)) = K((y \ z) * x,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,9866,a,b,10811,a),flip(a)].">
      <j1 rule="hyper" parents="334 9866 10811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10813">
    <literal><![CDATA[
      K(x \ (y * z),L(y,u,w)) = K((x \ z) * y,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(10131,a,10812,a)].">
      <j1 rule="hyper" parents="10131 10812"/>
    </justification>
  </clause>

  <clause id="10814">
    <literal><![CDATA[
      K(x \ (y * z),L(z,u,w)) = K((x \ y) * z,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,10003,a,b,10813,a)].">
      <j1 rule="hyper" parents="58 10003 10813"/>
    </justification>
  </clause>

  <clause id="10815">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,L(u,z,x)) = K(y \ (x * (u * z)),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9292,a(flip),b,10813,a),flip(a)].">
      <j1 rule="hyper" parents="58 9292 10813"/>
      <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(58,a,7180,a,b,10814,a)].">
      <j1 rule="hyper" parents="58 7180 10814"/>
    </justification>
  </clause>

  <clause id="10817">
    <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(5044(a,1),10549(a,1,2))].">
      <j1 rule="para" parents="5044 10549"/>
    </justification>
  </clause>

  <clause id="10818">
    <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(10022(a,1),10817(a,1,2))].">
      <j1 rule="para" parents="10022 10817"/>
    </justification>
  </clause>

  <clause id="10819">
    <literal><![CDATA[
      L(x,y \ R(T(y,z),u,y),y) = x
    ]]></literal>
    <justification jstring="[hyper(299,a,10818,a),flip(a)].">
      <j1 rule="hyper" parents="299 10818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10821">
    <literal><![CDATA[
      L(x,K(y,z) * a(y,u,y),y) = x
    ]]></literal>
    <justification jstring="[para(9175(a,1),10819(a,1,2))].">
      <j1 rule="para" parents="9175 10819"/>
    </justification>
  </clause>

  <clause id="10822">
    <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(4941(a,1),4625(a,2,1))].">
      <j1 rule="para" parents="4941 4625"/>
    </justification>
  </clause>

  <clause id="10823">
    <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(10822(a,2),342(a,1)),flip(b)].">
      <j1 rule="para" parents="10822 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10824">
    <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(5621,a,5981,a),flip(a)].">
      <j1 rule="hyper" parents="5621 5981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10826">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,z / (y * z)) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,5702,a(flip),b,10824,a),flip(a)].">
      <j1 rule="hyper" parents="334 5702 10824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10827">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5621,a,10826,a)].">
      <j1 rule="hyper" parents="5621 10826"/>
    </justification>
  </clause>

  <clause id="10828">
    <literal><![CDATA[
      K(R(1 / x,x,y) / z,x \ 1) = K(y / (z * (x * y)),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(5940,a,10827,a)].">
      <j1 rule="hyper" parents="5940 10827"/>
    </justification>
  </clause>

  <clause id="10830">
    <literal><![CDATA[
      K(x \ R(1 / y,y,z),y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(10311,a,10828,a)].">
      <j1 rule="hyper" parents="10311 10828"/>
    </justification>
  </clause>

  <clause id="10831">
    <literal><![CDATA[
      K(x \ R(y \ 1,y,z),y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,4302,a(flip),b,10830,a)].">
      <j1 rule="hyper" parents="58 4302 10830"/>
    </justification>
  </clause>

  <clause id="10832">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ (x / (z * x)),z \ 1)
    ]]></literal>
    <justification jstring="[para(223(a,1),10830(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="223 10830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10833">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ ((z * x) \ x),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,8931,a(flip),b,10832,a),flip(a)].">
      <j1 rule="hyper" parents="334 8931 10832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10834">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),(z \ 1) \ 1) = K(y \ (x / ((z \ 1) * x)),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,3696,a(flip),b,10832,a),flip(a)].">
      <j1 rule="hyper" parents="334 3696 10832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10835">
    <literal><![CDATA[
      K(x \ (y / ((z \ 1) * y)),z) = K(x \ z,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10461,a(flip),b,10834,a),flip(a)].">
      <j1 rule="hyper" parents="58 10461 10834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10837">
    <literal><![CDATA[
      K(x \ R(y \ 1,y,z),y \ 1) = K(x \ (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[para(3244(a,2),10835(a,1,1,2))].">
      <j1 rule="para" parents="3244 10835"/>
    </justification>
  </clause>

  <clause id="10838">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ (z \ 1),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,10831,a(flip),b,10837,a)].">
      <j1 rule="hyper" parents="58 10831 10837"/>
    </justification>
  </clause>

  <clause id="10840">
    <literal><![CDATA[
      K(x \ ((y * z) \ z),y \ 1) = K(x \ (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,10833,a(flip),b,10838,a)].">
      <j1 rule="hyper" parents="58 10833 10838"/>
    </justification>
  </clause>

  <clause id="10842">
    <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(6520(a,1),6037(a,1,1,2))].">
      <j1 rule="para" parents="6520 6037"/>
    </justification>
  </clause>

  <clause id="10843">
    <literal><![CDATA[
      L(T(x,y),x \ (z * K(u,x)),x) = T(L(x,x \ z,x),y)
    ]]></literal>
    <justification jstring="[para(10000(a,1),6408(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10000 6408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10844">
    <literal><![CDATA[
      L(T(x,y),x \ (K(z,x) * u),x) = T(L(x,x \ u,x),y)
    ]]></literal>
    <justification jstring="[para(7393(a,1),10843(a,1,2,2))].">
      <j1 rule="para" parents="7393 10843"/>
    </justification>
  </clause>

  <clause id="10846">
    <literal><![CDATA[
      L(T(x,y),x \ (K(z,x) * u),x) = L(T(x,y),x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,20,a,b,10844,a),flip(a)].">
      <j1 rule="hyper" parents="334 20 10844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10847">
    <literal><![CDATA[
      L(T(x,y),T(x,z) \ u,x) = L(T(x,y),x \ u,x)
    ]]></literal>
    <justification jstring="[para(5367(a,1),10846(a,1,2))].">
      <j1 rule="para" parents="5367 10846"/>
    </justification>
  </clause>

  <clause id="10848">
    <literal><![CDATA[
      L(T(x,y),T(z / T(x,u),x),x) = L(T(x,y),x \ z,x)
    ]]></literal>
    <justification jstring="[para(8617(a,2),10847(a,1,2))].">
      <j1 rule="para" parents="8617 10847"/>
    </justification>
  </clause>

  <clause id="10849">
    <literal><![CDATA[
      L(T(x,y),z / T(x,u),x) = L(T(x,y),x \ z,x)
    ]]></literal>
    <justification jstring="[hyper(7872,a,10848,a)].">
      <j1 rule="hyper" parents="7872 10848"/>
    </justification>
  </clause>

  <clause id="10850">
    <literal><![CDATA[
      R(x,x \ 1,y \ R(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(334,a,10196,a(flip),b,6822,a),flip(a)].">
      <j1 rule="hyper" parents="334 10196 6822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10852">
    <literal><![CDATA[
      R(x,x \ 1,a(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(9155(a,1),10850(a,1,3))].">
      <j1 rule="para" parents="9155 10850"/>
    </justification>
  </clause>

  <clause id="10853">
    <literal><![CDATA[
      (x \ 1) * a(y,x \ 1,y) = x \ a(y,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(10852(a,1),436(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10852 436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10854">
    <literal><![CDATA[
      T(x \ a(y,x \ 1,y),y) = y \ T(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(10853(a,1),9190(a,1,1))].">
      <j1 rule="para" parents="10853 9190"/>
    </justification>
  </clause>

  <clause id="10855">
    <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(10854(a,1),2178(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10854 2178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10856">
    <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(3478(a,1),8382(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3478 8382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10857">
    <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(3478(a,1),10856(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3478 10856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10859">
    <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(10857(a,1),657(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10857 657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10861">
    <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(9512(a,1),8903(a,1,2))].">
      <j1 rule="para" parents="9512 8903"/>
    </justification>
  </clause>

  <clause id="10862">
    <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(8053(a,1),10861(a,1,2))].">
      <j1 rule="para" parents="8053 10861"/>
    </justification>
  </clause>

  <clause id="10864">
    <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(8525(a,1),10862(a,2,1))].">
      <j1 rule="para" parents="8525 10862"/>
    </justification>
  </clause>

  <clause id="10865">
    <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,10252,a(flip),b,10864,a)].">
      <j1 rule="hyper" parents="58 10252 10864"/>
    </justification>
  </clause>

  <clause id="10866">
    <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(10197,a,10865,a)].">
      <j1 rule="hyper" parents="10197 10865"/>
    </justification>
  </clause>

  <clause id="10867">
    <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(10294,a,10866,a)].">
      <j1 rule="hyper" parents="10294 10866"/>
    </justification>
  </clause>

  <clause id="10868">
    <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(7970,a,9063,a),flip(a)].">
      <j1 rule="hyper" parents="7970 9063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10869">
    <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(5900(a,1),9444(a,1,2))].">
      <j1 rule="para" parents="5900 9444"/>
    </justification>
  </clause>

  <clause id="10870">
    <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(334,a,8350,a(flip),b,10869,a),flip(a)].">
      <j1 rule="hyper" parents="334 8350 10869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10872">
    <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),9471(a,1,2,1))].">
      <j1 rule="para" parents="4 9471"/>
    </justification>
  </clause>

  <clause id="10874">
    <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),10872(a,1,2))].">
      <j1 rule="para" parents="13 10872"/>
    </justification>
  </clause>

  <clause id="10875">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(L(z,y,x),x * y,u))
    ]]></literal>
    <justification jstring="[hyper(8739,a,10874,a)].">
      <j1 rule="hyper" parents="8739 10874"/>
    </justification>
  </clause>

  <clause id="10876">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(z,x * y,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,7302,a(flip),b,10875,a),flip(a)].">
      <j1 rule="hyper" parents="334 7302 10875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10878">
    <literal><![CDATA[
      K(L(x,(x \ y) * z,u),z) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),10876(a,2,2,2))].">
      <j1 rule="para" parents="5 10876"/>
    </justification>
  </clause>

  <clause id="10879">
    <literal><![CDATA[
      K(x,L(y * ((z * y) \ z),u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,10439,a(flip),b,10878,a),flip(a)].">
      <j1 rule="hyper" parents="58 10439 10878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10880">
    <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(4576(a,1),10878(a,1,1,2))].">
      <j1 rule="para" parents="4576 10878"/>
    </justification>
  </clause>

  <clause id="10881">
    <literal><![CDATA[
      K(x,y \ K(z,L(x,u,w))) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(10878(a,1),7505(a,1,2,2))].">
      <j1 rule="para" parents="10878 7505"/>
    </justification>
  </clause>

  <clause id="10882">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,6937,a(flip),b,10879,a)].">
      <j1 rule="hyper" parents="58 6937 10879"/>
    </justification>
  </clause>

  <clause id="10884">
    <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,6939,a(flip),b,10881,a),flip(a)].">
      <j1 rule="hyper" parents="58 6939 10881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10885">
    <literal><![CDATA[
      K(x,y \ K(z,L(L(x,u,w),v5,v6))) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(10878(a,1),10881(a,1,2,2))].">
      <j1 rule="para" parents="10878 10881"/>
    </justification>
  </clause>

  <clause id="10886">
    <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),10884(a,1,2,1,1))].">
      <j1 rule="para" parents="20 10884"/>
    </justification>
  </clause>

  <clause id="10887">
    <literal><![CDATA[
      K(x,y \ L(T(x,z),u,w)) = K(x,y \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(6493,a,10886,a)].">
      <j1 rule="hyper" parents="6493 10886"/>
    </justification>
  </clause>

  <clause id="10888">
    <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(1209(a,1),10887(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1209 10887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10889">
    <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(1219(a,1),10887(a,1,2,2,1))].">
      <j1 rule="para" parents="1219 10887"/>
    </justification>
  </clause>

  <clause id="10890">
    <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(7381,a,10880,a)].">
      <j1 rule="hyper" parents="7381 10880"/>
    </justification>
  </clause>

  <clause id="10892">
    <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,10547,a(flip),b,10890,a),flip(a)].">
      <j1 rule="hyper" parents="58 10547 10890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10893">
    <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(10892(a,1),10756(a,1))].">
      <j1 rule="para" parents="10892 10756"/>
    </justification>
  </clause>

  <clause id="10894">
    <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,228,a(flip),b,9642,a)].">
      <j1 rule="hyper" parents="58 228 9642"/>
    </justification>
  </clause>

  <clause id="10895">
    <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(10034,a,10894,a)].">
      <j1 rule="hyper" parents="10034 10894"/>
    </justification>
  </clause>

  <clause id="10896">
    <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(9450,a,10895,a)].">
      <j1 rule="hyper" parents="9450 10895"/>
    </justification>
  </clause>

  <clause id="10897">
    <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),10896(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 10896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10898">
    <literal><![CDATA[
      L(K(x,y),T(z,y * x),y * x) = K(x,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8996,a(flip),b,10897,a),flip(a)].">
      <j1 rule="hyper" parents="334 8996 10897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10899">
    <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,10898,a(flip),b,9642,a)].">
      <j1 rule="hyper" parents="119 10898 9642"/>
    </justification>
  </clause>

  <clause id="10900">
    <literal><![CDATA[
      K(x,L(y,x,((y * x) * z) / (y * x))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[para(230(a,1),10898(a,1,2)),flip(a)].">
      <j1 rule="para" parents="230 10898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10901">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10638,a,10900,a),flip(a)].">
      <j1 rule="hyper" parents="10638 10900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10902">
    <literal><![CDATA[
      L(K(x,y),z,y * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(10900(a,1),10638(a,1))].">
      <j1 rule="para" parents="10900 10638"/>
    </justification>
  </clause>

  <clause id="10905">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(10901(a,1),10160(a,1,1))].">
      <j1 rule="para" parents="10901 10160"/>
    </justification>
  </clause>

  <clause id="10907">
    <literal><![CDATA[
      (x * y) * T(z * K(y,x),x * y) = z * (y * x)
    ]]></literal>
    <justification jstring="[hyper(10681,a,10899,a),flip(a)].">
      <j1 rule="hyper" parents="10681 10899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10908">
    <literal><![CDATA[
      (x * K(y,z)) * (z * y) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(294,a,10907,a)].">
      <j1 rule="hyper" parents="294 10907"/>
    </justification>
  </clause>

  <clause id="10909">
    <literal><![CDATA[
      (x * K(y,z)) / (z * y) = (x / (z * y)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,10646,a(flip),b,10908,a)].">
      <j1 rule="hyper" parents="117 10646 10908"/>
    </justification>
  </clause>

  <clause id="10910">
    <literal><![CDATA[
      (x / (y * z)) * K(y,z) = x / (z * y)
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,10908,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 10908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10912">
    <literal><![CDATA[
      ((x * K(y,z)) * z) \ (x * (y * z)) = L(y,z,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,10908,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="116 10908 90"/>
    </justification>
  </clause>

  <clause id="10913">
    <literal><![CDATA[
      (x / y) * K(z,z \ y) = x / ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),10910(a,1,1,2))].">
      <j1 rule="para" parents="5 10910"/>
    </justification>
  </clause>

  <clause id="10914">
    <literal><![CDATA[
      (x / y) * K(y / z,z) = x / (z * (y / z))
    ]]></literal>
    <justification jstring="[para(7(a,1),10910(a,1,1,2))].">
      <j1 rule="para" parents="7 10910"/>
    </justification>
  </clause>

  <clause id="10915">
    <literal><![CDATA[
      (x / (y * z)) * (z * K(y,z)) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(10910(a,1),6351(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10910 6351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10916">
    <literal><![CDATA[
      K(x,y / (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x * z)) = u
    ]]></literal>
    <justification jstring="[para(10910(a,1),7488(a,1,2))].">
      <j1 rule="para" parents="10910 7488"/>
    </justification>
  </clause>

  <clause id="10917">
    <literal><![CDATA[
      K(x / (y * z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / (z * y),y) = u
    ]]></literal>
    <justification jstring="[para(10910(a,1),7585(a,1,1))].">
      <j1 rule="para" parents="10910 7585"/>
    </justification>
  </clause>

  <clause id="10918">
    <literal><![CDATA[
      T(x / ((y \ z) * y),K(y,z)) = K(y,y \ z) * (x / z)
    ]]></literal>
    <justification jstring="[para(10913(a,1),8360(a,1,1))].">
      <j1 rule="para" parents="10913 8360"/>
    </justification>
  </clause>

  <clause id="10919">
    <literal><![CDATA[
      1 / ((x * ((x / y) \ 1)) / x) = x / (x * (y / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,9578,a,b,10914,a)].">
      <j1 rule="hyper" parents="58 9578 10914"/>
    </justification>
  </clause>

  <clause id="10920">
    <literal><![CDATA[
      (x / y) * K(z \ y,z) = x / (z * (y / z))
    ]]></literal>
    <justification jstring="[para(5235(a,1),10914(a,1,2))].">
      <j1 rule="para" parents="5235 10914"/>
    </justification>
  </clause>

  <clause id="10921">
    <literal><![CDATA[
      (x / (y * z)) * ((y * z) / y) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[hyper(5173,a,10915,a)].">
      <j1 rule="hyper" parents="5173 10915"/>
    </justification>
  </clause>

  <clause id="10922">
    <literal><![CDATA[
      (x * ((x / y) \ 1)) / x = (x / (x * (y / x))) \ 1
    ]]></literal>
    <justification jstring="[hyper(192,a,10919,a),flip(a)].">
      <j1 rule="hyper" parents="192 10919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10923">
    <literal><![CDATA[
      x / (x * (((y / x) \ 1) \ 1)) = ((x * ((x / y) \ 1)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(10922(a,2),3238(a,2,1))].">
      <j1 rule="para" parents="10922 3238"/>
    </justification>
  </clause>

  <clause id="10924">
    <literal><![CDATA[
      (x * (y * K(z,y))) \ (x * (z * y)) = L(z,y,x * K(z,y))
    ]]></literal>
    <justification jstring="[para(6351(a,1),10912(a,1,1))].">
      <j1 rule="para" parents="6351 10912"/>
    </justification>
  </clause>

  <clause id="10925">
    <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(10121(a,2),10923(a,2,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10121 10923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10926">
    <literal><![CDATA[
      K((x / y) \ z,R((x / y) \ 1,x / y,y)) = K(((x / y) \ 1) * z,y / x)
    ]]></literal>
    <justification jstring="[hyper(334,a,3703,a(flip),b,9731,a),flip(a)].">
      <j1 rule="hyper" parents="334 3703 9731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10927">
    <literal><![CDATA[
      K((x / y) \ z,T(y / x,x / y)) = K(((x / y) \ 1) * z,y / x)
    ]]></literal>
    <justification jstring="[para(668(a,1),10926(a,1,2))].">
      <j1 rule="para" parents="668 10926"/>
    </justification>
  </clause>

  <clause id="10928">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) = K((x / y) \ z,y / x)
    ]]></literal>
    <justification jstring="[hyper(6056,a,10927,a),flip(a)].">
      <j1 rule="hyper" parents="6056 10927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10929">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) = K((y \ x) \ z,y / x)
    ]]></literal>
    <justification jstring="[hyper(334,a,9704,a(flip),b,10928,a),flip(a)].">
      <j1 rule="hyper" parents="334 9704 10928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10930">
    <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(6461(a,1),10030(a,1,2))].">
      <j1 rule="para" parents="6461 10030"/>
    </justification>
  </clause>

  <clause id="10931">
    <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,9347,a(flip),b,10930,a)].">
      <j1 rule="hyper" parents="58 9347 10930"/>
    </justification>
  </clause>

  <clause id="10932">
    <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),10227(a,1,1))].">
      <j1 rule="para" parents="105 10227"/>
    </justification>
  </clause>

  <clause id="10933">
    <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(10496(a,1),10501(a,1,2,1))].">
      <j1 rule="para" parents="10496 10501"/>
    </justification>
  </clause>

  <clause id="10934">
    <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(5392(a,1),10933(a,1,2))].">
      <j1 rule="para" parents="5392 10933"/>
    </justification>
  </clause>

  <clause id="10936">
    <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(7401(a,2),10536(a,1,2,2,1))].">
      <j1 rule="para" parents="7401 10536"/>
    </justification>
  </clause>

  <clause id="10937">
    <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(8019(a,1),10695(a,1,1,2))].">
      <j1 rule="para" parents="8019 10695"/>
    </justification>
  </clause>

  <clause id="10938">
    <literal><![CDATA[
      x / (y * K(1 / z,z)) = K(z,1 / z) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(3553,a,10842,a)].">
      <j1 rule="hyper" parents="3553 10842"/>
    </justification>
  </clause>

  <clause id="10940">
    <literal><![CDATA[
      K(x,1 / x) * (y / L(x,z,u)) = y / (1 / (1 / L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(6074(a,1),10938(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6074 10938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10941">
    <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(334,a,9872,a(flip),b,10868,a),flip(a)].">
      <j1 rule="hyper" parents="334 9872 10868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10943">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K((L(x,y,z) * w) / u,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,8180,a(flip),b,10941,a),flip(a)].">
      <j1 rule="hyper" parents="334 8180 10941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10944">
    <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(5391(a,1),10936(a,1,2))].">
      <j1 rule="para" parents="5391 10936"/>
    </justification>
  </clause>

  <clause id="10945">
    <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(10944(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="10944 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10946">
    <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(1372(a,1),4731(a,1,1))].">
      <j1 rule="para" parents="1372 4731"/>
    </justification>
  </clause>

  <clause id="10947">
    <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(1391(a,1),10946(a,1,2))].">
      <j1 rule="para" parents="1391 10946"/>
    </justification>
  </clause>

  <clause id="10948">
    <literal><![CDATA[
      a(x,T(y,x),R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(709,a,10947,a),flip(a)].">
      <j1 rule="hyper" parents="709 10947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10949">
    <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,4933,a,b,10948,a)].">
      <j1 rule="hyper" parents="58 4933 10948"/>
    </justification>
  </clause>

  <clause id="10950">
    <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,10304,a(flip),b,10949,a)].">
      <j1 rule="hyper" parents="58 10304 10949"/>
    </justification>
  </clause>

  <clause id="10951">
    <literal><![CDATA[
      a(x,y,R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(4932,a,10950,a)].">
      <j1 rule="hyper" parents="4932 10950"/>
    </justification>
  </clause>

  <clause id="10952">
    <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(10951(a,1),10305(a,2,1))].">
      <j1 rule="para" parents="10951 10305"/>
    </justification>
  </clause>

  <clause id="10953">
    <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,10247,a(flip),b,10952,a)].">
      <j1 rule="hyper" parents="58 10247 10952"/>
    </justification>
  </clause>

  <clause id="10954">
    <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(311(a,1),6086(a,1,2)),flip(a)].">
      <j1 rule="para" parents="311 6086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10955">
    <literal><![CDATA[
      K((x \ (y \ z)) \ 1,L(x \ (y \ z),u,w)) = K(z \ (y * x),(y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(334,a,6615,a(flip),b,10954,a),flip(a)].">
      <j1 rule="hyper" parents="334 6615 10954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10956">
    <literal><![CDATA[
      K((x \ (y \ z)) \ 1,(y * x) \ z) = K(z \ (y * x),(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(311(a,1),10955(a,1,2))].">
      <j1 rule="para" parents="311 10955"/>
    </justification>
  </clause>

  <clause id="10957">
    <literal><![CDATA[
      K((x \ (y \ z)) \ 1,(y * x) \ z) = K(z \ (y * x),x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(334,a,7184,a(flip),b,10956,a),flip(a)].">
      <j1 rule="hyper" parents="334 7184 10956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10958">
    <literal><![CDATA[
      x * K(1 \ (y * x),x \ (y \ 1)) = y \ (((y * x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(10957(a,1),6011(a,2,2)),flip(a)].">
      <j1 rule="para" parents="10957 6011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10959">
    <literal><![CDATA[
      x * K(y * x,x \ (y \ 1)) = y \ (((y * x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(60(a,1),10958(a,1,2,1))].">
      <j1 rule="para" parents="60 10958"/>
    </justification>
  </clause>

  <clause id="10960">
    <literal><![CDATA[
      K((1 / x) * y,y \ ((1 / x) \ 1)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(29,a,3503,a(flip),b,10959,a),flip(a)].">
      <j1 rule="hyper" parents="29 3503 10959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10961">
    <literal><![CDATA[
      K((1 / x) * y,y \ x) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(75(a,1),10960(a,1,2,2))].">
      <j1 rule="para" parents="75 10960"/>
    </justification>
  </clause>

  <clause id="10962">
    <literal><![CDATA[
      K((x \ 1) \ y,y \ (x \ 1)) = K(x * y,y \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(72(a,1),10961(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 10961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10963">
    <literal><![CDATA[
      ((x \ 1) \ y) \ K(x * y,y \ (x \ 1)) = 1 / ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,10962,a(flip),b,2481,a)].">
      <j1 rule="hyper" parents="116 10962 2481"/>
    </justification>
  </clause>

  <clause id="10964">
    <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(6359(a,1),7721(a,2,1))].">
      <j1 rule="para" parents="6359 7721"/>
    </justification>
  </clause>

  <clause id="10965">
    <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(6146(a,1),9282(a,1,1,2))].">
      <j1 rule="para" parents="6146 9282"/>
    </justification>
  </clause>

  <clause id="10966">
    <literal><![CDATA[
      K(x,T(y / ((K(x,z) * u) * w),v5)) = K(x,T(y / (u * w),v5))
    ]]></literal>
    <justification jstring="[hyper(334,a,9424,a(flip),b,9427,a),flip(a)].">
      <j1 rule="hyper" parents="334 9424 9427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10967">
    <literal><![CDATA[
      K(x,T(y / ((z * T(x,u)) * w),v5)) = K(x,T(y / ((z * x) * w),v5))
    ]]></literal>
    <justification jstring="[para(8216(a,1),10966(a,1,2,1,2,1))].">
      <j1 rule="para" parents="8216 10966"/>
    </justification>
  </clause>

  <clause id="10968">
    <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),9957(a,1,2,2,1))].">
      <j1 rule="para" parents="5 9957"/>
    </justification>
  </clause>

  <clause id="10969">
    <literal><![CDATA[
      x \ T(y,((x \ 1) \ (x \ y)) \ z) = x \ T(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(6712,a,10968,a),flip(a)].">
      <j1 rule="hyper" parents="6712 10968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10971">
    <literal><![CDATA[
      K(x,y \ T(z,z \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(10969(a,1),9040(a,1,2))].">
      <j1 rule="para" parents="10969 9040"/>
    </justification>
  </clause>

  <clause id="10972">
    <literal><![CDATA[
      T(x,y \ T(z,z \ x)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(118,a,10971,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 10971 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10973">
    <literal><![CDATA[
      K(x,y \ ((z \ x) \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(106(a,1),10971(a,1,2,2))].">
      <j1 rule="para" parents="106 10971"/>
    </justification>
  </clause>

  <clause id="10974">
    <literal><![CDATA[
      T(x,y \ (x / z)) = T(x,y \ (z \ x))
    ]]></literal>
    <justification jstring="[para(661(a,1),10972(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="661 10972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10975">
    <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(6765,a,10973,a),flip(a)].">
      <j1 rule="hyper" parents="6765 10973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10976">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) = (((x / (1 / (x \ y))) / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,9630,a(flip),b,10122,a)].">
      <j1 rule="hyper" parents="58 9630 10122"/>
    </justification>
  </clause>

  <clause id="10977">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) = (1 / ((x / ((x \ y) \ 1)) / x)) \ 1
    ]]></literal>
    <justification jstring="[para(2977(a,2),10976(a,2,1))].">
      <j1 rule="para" parents="2977 10976"/>
    </justification>
  </clause>

  <clause id="10978">
    <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(10977(a,2),595(a,1))].">
      <j1 rule="para" parents="10977 595"/>
    </justification>
  </clause>

  <clause id="10979">
    <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(334,a,6520,a(flip),b,10964,a),flip(a)].">
      <j1 rule="hyper" parents="334 6520 10964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10980">
    <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(8348(a,1),10965(a,1,2))].">
      <j1 rule="para" parents="8348 10965"/>
    </justification>
  </clause>

  <clause id="10981">
    <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(8048(a,1),10980(a,1,2))].">
      <j1 rule="para" parents="8048 10980"/>
    </justification>
  </clause>

  <clause id="10983">
    <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(10981(a,1),7657(a,1,2,2))].">
      <j1 rule="para" parents="10981 7657"/>
    </justification>
  </clause>

  <clause id="10984">
    <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,7892,a(flip),b,10983,a),flip(a)].">
      <j1 rule="hyper" parents="58 7892 10983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10986">
    <literal><![CDATA[
      K(x,y * (z * (x * (T(T(x,u),u) \ w)))) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[hyper(334,a,8722,a(flip),b,10984,a),flip(a)].">
      <j1 rule="hyper" parents="334 8722 10984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10988">
    <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(6359(a,1),10979(a,1,1,1))].">
      <j1 rule="para" parents="6359 10979"/>
    </justification>
  </clause>

  <clause id="10989">
    <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(2162(a,2),10988(a,1,1))].">
      <j1 rule="para" parents="2162 10988"/>
    </justification>
  </clause>

  <clause id="10990">
    <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(2524(a,1),10989(a,1,1,1,1,2))].">
      <j1 rule="para" parents="2524 10989"/>
    </justification>
  </clause>

  <clause id="10991">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x = (x * (K(w,y) * R(y,z,u))) * K(y,w)
    ]]></literal>
    <justification jstring="[para(9592(a,1),10990(a,1,1,1))].">
      <j1 rule="para" parents="9592 10990"/>
    </justification>
  </clause>

  <clause id="10992">
    <literal><![CDATA[
      (x * (K(y,z) * R(z,u,w))) * K(z,y) = x * R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(921,a,10991,a),flip(a)].">
      <j1 rule="hyper" parents="921 10991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10994">
    <literal><![CDATA[
      (x * (R(y,z,u) * K(w,y))) * K(y,w) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(2532(a,2),10992(a,1,1,2))].">
      <j1 rule="para" parents="2532 10992"/>
    </justification>
  </clause>

  <clause id="10995">
    <literal><![CDATA[
      L(K(x,y),R(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6945,a,10994,a)].">
      <j1 rule="hyper" parents="6945 10994"/>
    </justification>
  </clause>

  <clause id="10996">
    <literal><![CDATA[
      a(x,R(y,z,u),K(y,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10995,a,b,1992,a),flip(a)].">
      <j1 rule="hyper" parents="115 10995 1992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10997">
    <literal><![CDATA[
      K(x,(y \ 1) * R(x,z,u)) = K(x,y \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6897,a(flip),b,10995,a)].">
      <j1 rule="hyper" parents="58 6897 10995"/>
    </justification>
  </clause>

  <clause id="10998">
    <literal><![CDATA[
      K(x,(y \ z) \ R(x,u,w)) = K(x,z \ (y * R(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,6848,a(flip),b,10995,a),flip(a)].">
      <j1 rule="hyper" parents="58 6848 10995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10999">
    <literal><![CDATA[
      K(x,R(x,y,z) * (u \ 1)) = K(x,u \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7676,a,b,10997,a)].">
      <j1 rule="hyper" parents="58 7676 10997"/>
    </justification>
  </clause>

  <clause id="11000">
    <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(1758(a,2),5808(a,2,2,1))].">
      <j1 rule="para" parents="1758 5808"/>
    </justification>
  </clause>

  <clause id="11001">
    <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(5955(a,1),6318(a,1,2))].">
      <j1 rule="para" parents="5955 6318"/>
    </justification>
  </clause>

  <clause id="11002">
    <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(5959(a,1),11001(a,2,3))].">
      <j1 rule="para" parents="5959 11001"/>
    </justification>
  </clause>

  <clause id="11003">
    <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(8053(a,1),6679(a,1,2,2))].">
      <j1 rule="para" parents="8053 6679"/>
    </justification>
  </clause>

  <clause id="11004">
    <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(8067(a,1),9933(a,2,2))].">
      <j1 rule="para" parents="8067 9933"/>
    </justification>
  </clause>

  <clause id="11005">
    <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(5745,a,10934,a)].">
      <j1 rule="hyper" parents="5745 10934"/>
    </justification>
  </clause>

  <clause id="11006">
    <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),11000(a,2,2,1,1,2))].">
      <j1 rule="para" parents="61 11000"/>
    </justification>
  </clause>

  <clause id="11007">
    <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),11006(a,2,2))].">
      <j1 rule="para" parents="20 11006"/>
    </justification>
  </clause>

  <clause id="11009">
    <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(334,a,686,a(flip),b,11007,a),flip(a)].">
      <j1 rule="hyper" parents="334 686 11007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11010">
    <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(334,a,1556,a(flip),b,11009,a),flip(a)].">
      <j1 rule="hyper" parents="334 1556 11009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11011">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K(L(x,y,z),u) = x \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3448(a,1),11010(a,1,2))].">
      <j1 rule="para" parents="3448 11010"/>
    </justification>
  </clause>

  <clause id="11012">
    <literal><![CDATA[
      K(x \ L(T(x,y),z,u),x) = K(x \ L(x,z,u),x)
    ]]></literal>
    <justification jstring="[para(11011(a,1),7670(a,1,1))].">
      <j1 rule="para" parents="11011 7670"/>
    </justification>
  </clause>

  <clause id="11013">
    <literal><![CDATA[
      K(x \ L(T(x,y),z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(334,a,3664,a(flip),b,11012,a),flip(a)].">
      <j1 rule="hyper" parents="334 3664 11012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11015">
    <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(7401(a,2),11003(a,2,1,1))].">
      <j1 rule="para" parents="7401 11003"/>
    </justification>
  </clause>

  <clause id="11016">
    <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(8046(a,1),11004(a,2,2))].">
      <j1 rule="para" parents="8046 11004"/>
    </justification>
  </clause>

  <clause id="11017">
    <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(8104(a,1),11016(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8104 11016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11018">
    <literal><![CDATA[
      K(x \ (y * (x * z)),y) * K(x,K(y,z)) = K((x / (x * z)) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,9980,a(flip),b,11017,a),flip(a)].">
      <j1 rule="hyper" parents="334 9980 11017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11019">
    <literal><![CDATA[
      K((x / (x * y)) \ z,z) = K(y * z,z) * K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(10791(a,1),11018(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10791 11018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11020">
    <literal><![CDATA[
      K((x / (x * y)) \ z,z) = K(z * y,z) * K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(5532(a,1),11019(a,2,1))].">
      <j1 rule="para" parents="5532 11019"/>
    </justification>
  </clause>

  <clause id="11022">
    <literal><![CDATA[
      K((x / (x * y)) \ z,z) = K(z * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,8143,a(flip),b,11020,a),flip(a)].">
      <j1 rule="hyper" parents="334 8143 11020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11023">
    <literal><![CDATA[
      K(x * (y \ z),T(x,y)) = K((y / z) \ x,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),11022(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 11022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11024">
    <literal><![CDATA[
      K((x \ y) * z,T(z,x)) = K((x / y) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6194,a,b,11023,a)].">
      <j1 rule="hyper" parents="58 6194 11023"/>
    </justification>
  </clause>

  <clause id="11025">
    <literal><![CDATA[
      K(x / y,z) * a(z,y \ x,z) = K((y / x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9914,a,b,11024,a)].">
      <j1 rule="hyper" parents="58 9914 11024"/>
    </justification>
  </clause>

  <clause id="11026">
    <literal><![CDATA[
      K(x,y / z) * K((z / y) \ x,x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(5409,a,11025,a)].">
      <j1 rule="hyper" parents="5409 11025"/>
    </justification>
  </clause>

  <clause id="11027">
    <literal><![CDATA[
      T(x,(y / z) \ x) \ T(x,z / y) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(5944,a,11026,a)].">
      <j1 rule="hyper" parents="5944 11026"/>
    </justification>
  </clause>

  <clause id="11028">
    <literal><![CDATA[
      T(x,(y / z) \ x) \ T(x,(y / z) \ 1) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(4716(a,2),11027(a,1,2))].">
      <j1 rule="para" parents="4716 11027"/>
    </justification>
  </clause>

  <clause id="11029">
    <literal><![CDATA[
      T(x,(y / z) \ x) \ ((x \ ((y / z) \ x)) \ ((y / z) \ x)) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(4426(a,2),11028(a,1,2))].">
      <j1 rule="para" parents="4426 11028"/>
    </justification>
  </clause>

  <clause id="11030">
    <literal><![CDATA[
      a(x,(y / z) \ 1,x) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9204,a(flip),b,11029,a)].">
      <j1 rule="hyper" parents="58 9204 11029"/>
    </justification>
  </clause>

  <clause id="11031">
    <literal><![CDATA[
      a(x,(y * z) \ z,x) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(6(a,1),11030(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6 11030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11033">
    <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(8692,a,11005,a)].">
      <j1 rule="hyper" parents="8692 11005"/>
    </justification>
  </clause>

  <clause id="11034">
    <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(7441(a,1),11015(a,2,1))].">
      <j1 rule="para" parents="7441 11015"/>
    </justification>
  </clause>

  <clause id="11035">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = K(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,9225,a(flip),b,11034,a),flip(a)].">
      <j1 rule="hyper" parents="334 9225 11034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11038">
    <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(6294(a,2),11035(a,1,1))].">
      <j1 rule="para" parents="6294 11035"/>
    </justification>
  </clause>

  <clause id="11039">
    <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(7500(a,1),11038(a,1,2,2))].">
      <j1 rule="para" parents="7500 11038"/>
    </justification>
  </clause>

  <clause id="11040">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) \ K(x,z) = K(y,T(y * K(x,z),x))
    ]]></literal>
    <justification jstring="[hyper(304,a,11039,a)].">
      <j1 rule="hyper" parents="304 11039"/>
    </justification>
  </clause>

  <clause id="11041">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) * K(z,y) = K(x,T(x * K(z,y),z))
    ]]></literal>
    <justification jstring="[hyper(5426,a,11040,a)].">
      <j1 rule="hyper" parents="5426 11040"/>
    </justification>
  </clause>

  <clause id="11042">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,T(y * K(z,x),z))
    ]]></literal>
    <justification jstring="[para(6948(a,1),11041(a,1,1))].">
      <j1 rule="para" parents="6948 11041"/>
    </justification>
  </clause>

  <clause id="11043">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,7853,a(flip),b,11042,a),flip(a)].">
      <j1 rule="hyper" parents="334 7853 11042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11044">
    <literal><![CDATA[
      K(x * K(y,z),x) = K(x,x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7229,a(flip),b,11043,a)].">
      <j1 rule="hyper" parents="58 7229 11043"/>
    </justification>
  </clause>

  <clause id="11045">
    <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(11044(a,1),5936(a,1,1,1,2))].">
      <j1 rule="para" parents="11044 5936"/>
    </justification>
  </clause>

  <clause id="11046">
    <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(5020(a,2),11045(a,1,1,1))].">
      <j1 rule="para" parents="5020 11045"/>
    </justification>
  </clause>

  <clause id="11047">
    <literal><![CDATA[
      R(T(x,K(y,z)),K(z,y),x) = T(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5898,a,11046,a)].">
      <j1 rule="hyper" parents="5898 11046"/>
    </justification>
  </clause>

  <clause id="11048">
    <literal><![CDATA[
      T(x,x * K(y,z)) \ T(K(z,y) * x,x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(11047(a,1),10870(a,1,1))].">
      <j1 rule="para" parents="11047 10870"/>
    </justification>
  </clause>

  <clause id="11049">
    <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(9925(a,1),11048(a,1,1,2,2))].">
      <j1 rule="para" parents="9925 11048"/>
    </justification>
  </clause>

  <clause id="11050">
    <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(5369(a,1),5385(a,1,1))].">
      <j1 rule="para" parents="5369 5385"/>
    </justification>
  </clause>

  <clause id="11051">
    <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(11050(a,1),9392(a,1,2,2))].">
      <j1 rule="para" parents="11050 9392"/>
    </justification>
  </clause>

  <clause id="11052">
    <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(9768(a,1),6219(a,1,1))].">
      <j1 rule="para" parents="9768 6219"/>
    </justification>
  </clause>

  <clause id="11053">
    <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(6212(a,1),11052(a,2,2))].">
      <j1 rule="para" parents="6212 11052"/>
    </justification>
  </clause>

  <clause id="11054">
    <literal><![CDATA[
      R(T(K(x,y),z),u,w) \ z = z / R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7963(a,1),11053(a,1,1,1))].">
      <j1 rule="para" parents="7963 11053"/>
    </justification>
  </clause>

  <clause id="11055">
    <literal><![CDATA[
      x / (x / R(K(y,z),u,w)) = R(T(K(y,z),x),u,w)
    ]]></literal>
    <justification jstring="[hyper(201,a,11054,a)].">
      <j1 rule="hyper" parents="201 11054"/>
    </justification>
  </clause>

  <clause id="11057">
    <literal><![CDATA[
      (R(K(x,y),z,u) \ w) \ w = R(T(K(x,y),w),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9772,a(flip),b,11055,a)].">
      <j1 rule="hyper" parents="58 9772 11055"/>
    </justification>
  </clause>

  <clause id="11058">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = R(T(K(y,x),z * u),z,u)
    ]]></literal>
    <justification jstring="[para(6215(a,1),11057(a,1,1))].">
      <j1 rule="para" parents="6215 11057"/>
    </justification>
  </clause>

  <clause id="11059">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = R(K(y,T(x,z * u)),z,u)
    ]]></literal>
    <justification jstring="[para(7401(a,2),11058(a,2,1))].">
      <j1 rule="para" parents="7401 11058"/>
    </justification>
  </clause>

  <clause id="11060">
    <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(8592(a,1),11059(a,2,1))].">
      <j1 rule="para" parents="8592 11059"/>
    </justification>
  </clause>

  <clause id="11061">
    <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(334,a,7539,a(flip),b,7106,a),flip(a)].">
      <j1 rule="hyper" parents="334 7539 7106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11062">
    <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),11061(a,2,1,2))].">
      <j1 rule="para" parents="177 11061"/>
    </justification>
  </clause>

  <clause id="11063">
    <literal><![CDATA[
      L(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1709(a,1),11062(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1709 11062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11064">
    <literal><![CDATA[
      K((x \ 1) * L(y,z,u),y) = K(x \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(6913,a,11063,a),flip(a)].">
      <j1 rule="hyper" parents="6913 11063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11065">
    <literal><![CDATA[
      a(x,L(y,z,u),K(w,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,11063,a,b,1992,a),flip(a)].">
      <j1 rule="hyper" parents="115 11063 1992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11066">
    <literal><![CDATA[
      K((x \ y) \ L(z,u,w),z) = K(y \ (x * L(z,u,w)),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6894,a(flip),b,11063,a),flip(a)].">
      <j1 rule="hyper" parents="58 6894 11063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11067">
    <literal><![CDATA[
      L(K(x,y),L(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6202,a,11065,a)].">
      <j1 rule="hyper" parents="6202 11065"/>
    </justification>
  </clause>

  <clause id="11068">
    <literal><![CDATA[
      K(x,(y \ z) \ L(x,u,w)) = K(x,z \ (y * L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,6848,a(flip),b,11067,a),flip(a)].">
      <j1 rule="hyper" parents="58 6848 11067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11070">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,10740,a(flip),b,11064,a),flip(a)].">
      <j1 rule="hyper" parents="58 10740 11064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11072">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5627,a(flip),b,11070,a),flip(a)].">
      <j1 rule="hyper" parents="334 5627 11070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11073">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,y) = w
    ]]></literal>
    <justification jstring="[para(11070(a,2),6263(a,1))].">
      <j1 rule="para" parents="11070 6263"/>
    </justification>
  </clause>

  <clause id="11074">
    <literal><![CDATA[
      (L(x,y,z) * K((u \ x) \ x,x)) * u = (x \ (L(x,y,z) * u)) * x
    ]]></literal>
    <justification jstring="[para(11072(a,1),9960(a,1,1,2))].">
      <j1 rule="para" parents="11072 9960"/>
    </justification>
  </clause>

  <clause id="11075">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K((y \ x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(11073,a,11066,a),flip(a)].">
      <j1 rule="hyper" parents="11073 11066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11077">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,10799,a(flip),b,11075,a),flip(a)].">
      <j1 rule="hyper" parents="334 10799 11075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11078">
    <literal><![CDATA[
      K(x \ (y * L(x,z,u)),x) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = w
    ]]></literal>
    <justification jstring="[para(11075(a,2),6658(a,1))].">
      <j1 rule="para" parents="11075 6658"/>
    </justification>
  </clause>

  <clause id="11079">
    <literal><![CDATA[
      K(x \ (y * (z * x)),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * z,x) = u
    ]]></literal>
    <justification jstring="[para(90(a,1),11078(a,1,1,2))].">
      <j1 rule="para" parents="90 11078"/>
    </justification>
  </clause>

  <clause id="11081">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(u * (x \ (y * z)),u)
    ]]></literal>
    <justification jstring="[para(90(a,1),11077(a,1,1,2))].">
      <j1 rule="para" parents="90 11077"/>
    </justification>
  </clause>

  <clause id="11082">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(y * ((x * y) \ (z * u)),y)
    ]]></literal>
    <justification jstring="[hyper(8743,a,11081,a)].">
      <j1 rule="hyper" parents="8743 11081"/>
    </justification>
  </clause>

  <clause id="11083">
    <literal><![CDATA[
      K(x \ (y * (z * u)),z) = K(z * (x \ (y * u)),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8933,a(flip),b,11081,a)].">
      <j1 rule="hyper" parents="58 8933 11081"/>
    </justification>
  </clause>

  <clause id="11084">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,L(u,z,x)) = K(u * (y \ (x * z)),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,10815,a,b,11083,a)].">
      <j1 rule="hyper" parents="58 10815 11083"/>
    </justification>
  </clause>

  <clause id="11085">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(x \ (z * u),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,10798,a(flip),b,11082,a),flip(a)].">
      <j1 rule="hyper" parents="334 10798 11082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11086">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K((u * z) \ (u * (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,10046,a(flip),b,11085,a)].">
      <j1 rule="hyper" parents="58 10046 11085"/>
    </justification>
  </clause>

  <clause id="11087">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(13(a,2),11086(a,2,1))].">
      <j1 rule="para" parents="13 11086"/>
    </justification>
  </clause>

  <clause id="11088">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(10893,a,11087,a),flip(a)].">
      <j1 rule="hyper" parents="10893 11087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11089">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10690,a,11088,a)].">
      <j1 rule="hyper" parents="10690 11088"/>
    </justification>
  </clause>

  <clause id="11090">
    <literal><![CDATA[
      K(x,L(y,T(x,z),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6609(a,1),11088(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6609 11088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11091">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(11088(a,1),10690(a,1))].">
      <j1 rule="para" parents="11088 10690"/>
    </justification>
  </clause>

  <clause id="11092">
    <literal><![CDATA[
      K(x,(y * T(x,z)) \ u) = K(x,T(x,z) \ (y \ u))
    ]]></literal>
    <justification jstring="[para(311(a,1),11090(a,1,2))].">
      <j1 rule="para" parents="311 11090"/>
    </justification>
  </clause>

  <clause id="11093">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) = K(x,L(y / z,y,u))
    ]]></literal>
    <justification jstring="[hyper(10708,a,11089,a)].">
      <j1 rule="hyper" parents="10708 11089"/>
    </justification>
  </clause>

  <clause id="11094">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10707,a,11089,a)].">
      <j1 rule="hyper" parents="10707 11089"/>
    </justification>
  </clause>

  <clause id="11095">
    <literal><![CDATA[
      K(x,L(y,z * x,u)) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(8691,a,11089,a),flip(a)].">
      <j1 rule="hyper" parents="8691 11089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11096">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = K(x,L(T(z,u),u,y))
    ]]></literal>
    <justification jstring="[hyper(7512,a,11089,a)].">
      <j1 rule="hyper" parents="7512 11089"/>
    </justification>
  </clause>

  <clause id="11097">
    <literal><![CDATA[
      K(x,(y * ((y \ z) / u)) \ z) = K(x,L(u,y \ z,y))
    ]]></literal>
    <justification jstring="[hyper(7175,a,11089,a)].">
      <j1 rule="hyper" parents="7175 11089"/>
    </justification>
  </clause>

  <clause id="11098">
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(6982,a,11089,a),flip(a)].">
      <j1 rule="hyper" parents="6982 11089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11099">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(6958,a,11089,a)].">
      <j1 rule="hyper" parents="6958 11089"/>
    </justification>
  </clause>

  <clause id="11100">
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) = K(x,L(y \ z,y,u))
    ]]></literal>
    <justification jstring="[hyper(6957,a,11089,a),flip(a)].">
      <j1 rule="hyper" parents="6957 11089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11101">
    <literal><![CDATA[
      K(L(x,y,z),u) \ 1 = L(K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,5232,a,b,11089,a)].">
      <j1 rule="hyper" parents="334 5232 11089"/>
    </justification>
  </clause>

  <clause id="11102">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6205,a,b,11089,a)].">
      <j1 rule="hyper" parents="58 6205 11089"/>
    </justification>
  </clause>

  <clause id="11103">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,y \ 1,y)) = y * (T(z / (y \ 1),x) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7895,a(flip),b,11089,a),flip(a)].">
      <j1 rule="hyper" parents="58 7895 11089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11104">
    <literal><![CDATA[
      K(x,L(T(y,z),y,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7480,a(flip),b,11089,a),flip(a)].">
      <j1 rule="hyper" parents="58 7480 11089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11105">
    <literal><![CDATA[
      K(x \ y,L(z,y,y \ 1)) = K(((y \ 1) * x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6903,a(flip),b,11089,a),flip(a)].">
      <j1 rule="hyper" parents="58 6903 11089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11106">
    <literal><![CDATA[
      K((x \ y) \ z,L(u,z,x)) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6894,a(flip),b,11089,a),flip(a)].">
      <j1 rule="hyper" parents="58 6894 11089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11107">
    <literal><![CDATA[
      K(x,L((y \ z) \ u,u,y)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6848,a(flip),b,11089,a),flip(a)].">
      <j1 rule="hyper" parents="58 6848 11089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11108">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u)) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5947,a(flip),b,11089,a),flip(a)].">
      <j1 rule="hyper" parents="58 5947 11089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11109">
    <literal><![CDATA[
      x * K(y,L(z,u \ x,u)) = u * ((u \ x) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,11089,a(flip),b,91,a)].">
      <j1 rule="hyper" parents="119 11089 91"/>
    </justification>
  </clause>

  <clause id="11110">
    <literal><![CDATA[
      (x * y) * K(z,L(u,y,x)) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,11089,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 11089 13"/>
    </justification>
  </clause>

  <clause id="11111">
    <literal><![CDATA[
      x \ K(y,L(z,x \ 1,x)) = (x \ 1) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,11089,a(flip),b,265,a)].">
      <j1 rule="hyper" parents="116 11089 265"/>
    </justification>
  </clause>

  <clause id="11113">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),y,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(311(a,1),11089(a,2,2))].">
      <j1 rule="para" parents="311 11089"/>
    </justification>
  </clause>

  <clause id="11114">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),y \ z,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(502(a,1),11089(a,2,2))].">
      <j1 rule="para" parents="502 11089"/>
    </justification>
  </clause>

  <clause id="11115">
    <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(11089(a,1),481(a,1,2,2))].">
      <j1 rule="para" parents="11089 481"/>
    </justification>
  </clause>

  <clause id="11116">
    <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(11089(a,1),1519(a,1,2,1))].">
      <j1 rule="para" parents="11089 1519"/>
    </justification>
  </clause>

  <clause id="11117">
    <literal><![CDATA[
      K(x,L(y,z,u)) * a(u,z,K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11089(a,1),1992(a,1,1))].">
      <j1 rule="para" parents="11089 1992"/>
    </justification>
  </clause>

  <clause id="11118">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,L(u,y,x)) = K(z,u)
    ]]></literal>
    <justification jstring="[para(11089(a,1),3966(a,1,2))].">
      <j1 rule="para" parents="11089 3966"/>
    </justification>
  </clause>

  <clause id="11119">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(11089(a,1),6199(a,1,1))].">
      <j1 rule="para" parents="11089 6199"/>
    </justification>
  </clause>

  <clause id="11120">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(11089(a,1),6201(a,1,2))].">
      <j1 rule="para" parents="11089 6201"/>
    </justification>
  </clause>

  <clause id="11121">
    <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(11089(a,1),6209(a,1,1))].">
      <j1 rule="para" parents="11089 6209"/>
    </justification>
  </clause>

  <clause id="11122">
    <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(11089(a,1),6957(a,1))].">
      <j1 rule="para" parents="11089 6957"/>
    </justification>
  </clause>

  <clause id="11123">
    <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(11089(a,1),7166(a,1))].">
      <j1 rule="para" parents="11089 7166"/>
    </justification>
  </clause>

  <clause id="11124">
    <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(11089(a,1),7174(a,1))].">
      <j1 rule="para" parents="11089 7174"/>
    </justification>
  </clause>

  <clause id="11125">
    <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(11089(a,1),7175(a,1))].">
      <j1 rule="para" parents="11089 7175"/>
    </justification>
  </clause>

  <clause id="11126">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(11089(a,1),8101(a,2,2))].">
      <j1 rule="para" parents="11089 8101"/>
    </justification>
  </clause>

  <clause id="11127">
    <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(11089(a,1),8882(a,1,2))].">
      <j1 rule="para" parents="11089 8882"/>
    </justification>
  </clause>

  <clause id="11128">
    <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(4663(a,2),11094(a,1,2,2))].">
      <j1 rule="para" parents="4663 11094"/>
    </justification>
  </clause>

  <clause id="11129">
    <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(11094(a,1),10692(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11094 10692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11130">
    <literal><![CDATA[
      K(x,K(y,L(z,u * y,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(11095(a,2),8067(a,1,2))].">
      <j1 rule="para" parents="11095 8067"/>
    </justification>
  </clause>

  <clause id="11131">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(34,a,6026,a,b,11101,a)].">
      <j1 rule="hyper" parents="34 6026 11101"/>
    </justification>
  </clause>

  <clause id="11132">
    <literal><![CDATA[
      L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(11101(a,1),5241(a,1))].">
      <j1 rule="para" parents="11101 5241"/>
    </justification>
  </clause>

  <clause id="11133">
    <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(11101(a,1),5254(a,1))].">
      <j1 rule="para" parents="11101 5254"/>
    </justification>
  </clause>

  <clause id="11134">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = K(L(x,u,y),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(7512,a,11131,a)].">
      <j1 rule="hyper" parents="7512 11131"/>
    </justification>
  </clause>

  <clause id="11135">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(y,K(z,L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(334,a,8053,a,b,11131,a),flip(a)].">
      <j1 rule="hyper" parents="334 8053 11131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11136">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) = K(L(u,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6943,a,b,11131,a)].">
      <j1 rule="hyper" parents="58 6943 11131"/>
    </justification>
  </clause>

  <clause id="11137">
    <literal><![CDATA[
      K(L(x,y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,11089,a(flip),b,11131,a),flip(a)].">
      <j1 rule="hyper" parents="58 11089 11131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11138">
    <literal><![CDATA[
      L(K((x \ 1) \ y,z),x \ 1,x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(501(a,1),11131(a,2,1))].">
      <j1 rule="para" parents="501 11131"/>
    </justification>
  </clause>

  <clause id="11139">
    <literal><![CDATA[
      K(L(x,y,z),u) * a(z,y,K(x,u)) = K(x,u)
    ]]></literal>
    <justification jstring="[para(11131(a,1),1992(a,1,1))].">
      <j1 rule="para" parents="11131 1992"/>
    </justification>
  </clause>

  <clause id="11140">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(w,K(y,L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(11131(a,2),5886(a,1,1))].">
      <j1 rule="para" parents="11131 5886"/>
    </justification>
  </clause>

  <clause id="11141">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(11131(a,1),6201(a,1,2))].">
      <j1 rule="para" parents="11131 6201"/>
    </justification>
  </clause>

  <clause id="11142">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(y,K(w,L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(11131(a,2),8049(a,1,1))].">
      <j1 rule="para" parents="11131 8049"/>
    </justification>
  </clause>

  <clause id="11143">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w)) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(11131(a,2),8067(a,1,2))].">
      <j1 rule="para" parents="11131 8067"/>
    </justification>
  </clause>

  <clause id="11144">
    <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(11131(a,2),8089(a,1))].">
      <j1 rule="para" parents="11131 8089"/>
    </justification>
  </clause>

  <clause id="11145">
    <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(11131(a,2),8099(a,1,2))].">
      <j1 rule="para" parents="11131 8099"/>
    </justification>
  </clause>

  <clause id="11146">
    <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(11131(a,2),8315(a,1,1))].">
      <j1 rule="para" parents="11131 8315"/>
    </justification>
  </clause>

  <clause id="11147">
    <literal><![CDATA[
      K(x,L(y,z * x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11095,a,b,11137,a)].">
      <j1 rule="hyper" parents="58 11095 11137"/>
    </justification>
  </clause>

  <clause id="11148">
    <literal><![CDATA[
      L(x,y,z) \ L(T(x,u),y,z) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5028,a,b,11137,a)].">
      <j1 rule="hyper" parents="58 5028 11137"/>
    </justification>
  </clause>

  <clause id="11149">
    <literal><![CDATA[
      K(x,L(y,x \ z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11088,a(flip),b,11137,a),flip(a)].">
      <j1 rule="hyper" parents="58 11088 11137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11150">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (K(y,L(x,z,u)) * w) = w
    ]]></literal>
    <justification jstring="[hyper(118,a,11137,a(flip),b,5403,a),flip(a)].">
      <j1 rule="hyper" parents="118 11137 5403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11151">
    <literal><![CDATA[
      K(x \ (y \ z),L(u,x,y)) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(311(a,1),11137(a,1,1)),flip(a)].">
      <j1 rule="para" parents="311 11137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11152">
    <literal><![CDATA[
      K((x \ 1) \ y,L(z,x \ 1,x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(501(a,1),11137(a,1,1)),flip(a)].">
      <j1 rule="para" parents="501 11137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11153">
    <literal><![CDATA[
      K(x \ T(y,z),L(u,x,z)) = K((z * x) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(462(a,1),11137(a,1,1)),flip(a)].">
      <j1 rule="para" parents="462 11137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11154">
    <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(710(a,1),11137(a,1,1)),flip(a)].">
      <j1 rule="para" parents="710 11137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11155">
    <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(11137(a,1),5449(a,1,1))].">
      <j1 rule="para" parents="11137 5449"/>
    </justification>
  </clause>

  <clause id="11156">
    <literal><![CDATA[
      K(x,L(y,z,u)) * L(x,z,u) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(11137(a,1),5116(a,1,1))].">
      <j1 rule="para" parents="11137 5116"/>
    </justification>
  </clause>

  <clause id="11157">
    <literal><![CDATA[
      ((x * y) * K(z,L(u,y,x))) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(11137(a,1),6591(a,1,1,2))].">
      <j1 rule="para" parents="11137 6591"/>
    </justification>
  </clause>

  <clause id="11158">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(z,K(x,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(11137(a,1),8053(a,1,2))].">
      <j1 rule="para" parents="11137 8053"/>
    </justification>
  </clause>

  <clause id="11159">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(11137(a,1),8067(a,1,2))].">
      <j1 rule="para" parents="11137 8067"/>
    </justification>
  </clause>

  <clause id="11160">
    <literal><![CDATA[
      x * K(y,K(z,L(x,u,w))) = T(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(11137(a,1),8063(a,1,2,2))].">
      <j1 rule="para" parents="11137 8063"/>
    </justification>
  </clause>

  <clause id="11161">
    <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(11137(a,1),8099(a,1,2))].">
      <j1 rule="para" parents="11137 8099"/>
    </justification>
  </clause>

  <clause id="11162">
    <literal><![CDATA[
      K(x \ y,L(z,y,u)) = K(x \ y,L(z,x,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),11147(a,1,2,2))].">
      <j1 rule="para" parents="5 11147"/>
    </justification>
  </clause>

  <clause id="11163">
    <literal><![CDATA[
      K(x,L(y,z / x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),11147(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 11147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11164">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(11137(a,2),11091(a,1))].">
      <j1 rule="para" parents="11137 11091"/>
    </justification>
  </clause>

  <clause id="11165">
    <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(6205(a,2),11132(a,1))].">
      <j1 rule="para" parents="6205 11132"/>
    </justification>
  </clause>

  <clause id="11166">
    <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(6851(a,1),11132(a,1))].">
      <j1 rule="para" parents="6851 11132"/>
    </justification>
  </clause>

  <clause id="11167">
    <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(6873(a,2),11132(a,1))].">
      <j1 rule="para" parents="6873 11132"/>
    </justification>
  </clause>

  <clause id="11168">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,L(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(6943(a,2),11132(a,1))].">
      <j1 rule="para" parents="6943 11132"/>
    </justification>
  </clause>

  <clause id="11169">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(11131(a,1),11132(a,1))].">
      <j1 rule="para" parents="11131 11132"/>
    </justification>
  </clause>

  <clause id="11170">
    <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(8053(a,2),11164(a,1))].">
      <j1 rule="para" parents="8053 11164"/>
    </justification>
  </clause>

  <clause id="11171">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,u,z)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[para(508(a,1),11100(a,2,2))].">
      <j1 rule="para" parents="508 11100"/>
    </justification>
  </clause>

  <clause id="11172">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = K(x,L(y,x \ u,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,11149,a,b,11102,a),flip(a)].">
      <j1 rule="hyper" parents="334 11149 11102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11173">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(u,z) = K(u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7660,a(flip),b,11102,a)].">
      <j1 rule="hyper" parents="58 7660 11102"/>
    </justification>
  </clause>

  <clause id="11174">
    <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(11118(a,1),6361(a,1,1))].">
      <j1 rule="para" parents="11118 6361"/>
    </justification>
  </clause>

  <clause id="11175">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(6879,a,11119,a)].">
      <j1 rule="hyper" parents="6879 11119"/>
    </justification>
  </clause>

  <clause id="11176">
    <literal><![CDATA[
      T(x,L(y,z,u)) * K(y,x) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,11119,a(flip),b,5043,a),flip(a)].">
      <j1 rule="hyper" parents="119 11119 5043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11177">
    <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(11119(a,1),2067(a,1))].">
      <j1 rule="para" parents="11119 2067"/>
    </justification>
  </clause>

  <clause id="11178">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z * x,K(y,x))
    ]]></literal>
    <justification jstring="[para(11147(a,1),11119(a,1,1))].">
      <j1 rule="para" parents="11147 11119"/>
    </justification>
  </clause>

  <clause id="11179">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,z))) = a(x,y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(8053(a,2),11175(a,1,3))].">
      <j1 rule="para" parents="8053 11175"/>
    </justification>
  </clause>

  <clause id="11180">
    <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(11120(a,1),2073(a,1))].">
      <j1 rule="para" parents="11120 2073"/>
    </justification>
  </clause>

  <clause id="11181">
    <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,9301,a,b,11126,a)].">
      <j1 rule="hyper" parents="58 9301 11126"/>
    </justification>
  </clause>

  <clause id="11182">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w)) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8101,a(flip),b,11126,a)].">
      <j1 rule="hyper" parents="58 8101 11126"/>
    </justification>
  </clause>

  <clause id="11183">
    <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,11135,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 11135 13"/>
    </justification>
  </clause>

  <clause id="11184">
    <literal><![CDATA[
      L(K(x,K(y,y * z)),u,w) = K(x,K(z * x,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(8232(a,1),11135(a,1,1))].">
      <j1 rule="para" parents="8232 11135"/>
    </justification>
  </clause>

  <clause id="11185">
    <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(11139(a,1),5417(a,2,2))].">
      <j1 rule="para" parents="11139 5417"/>
    </justification>
  </clause>

  <clause id="11186">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(6889,a,11141,a)].">
      <j1 rule="hyper" parents="6889 11141"/>
    </justification>
  </clause>

  <clause id="11187">
    <literal><![CDATA[
      T(x,L(y,z,u)) \ T(x,y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(5944,a,11141,a)].">
      <j1 rule="hyper" parents="5944 11141"/>
    </justification>
  </clause>

  <clause id="11188">
    <literal><![CDATA[
      (x * y) / T(x,L(y,z,u)) = y * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(11141(a,1),6382(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11141 6382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11189">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y * u,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(11141(a,1),6889(a,1))].">
      <j1 rule="para" parents="11141 6889"/>
    </justification>
  </clause>

  <clause id="11190">
    <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(11140(a,1),11141(a,1,2))].">
      <j1 rule="para" parents="11140 11141"/>
    </justification>
  </clause>

  <clause id="11191">
    <literal><![CDATA[
      x / T(x / y,L(y,z,u)) = y * a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(11186(a,1),9942(a,2,2))].">
      <j1 rule="para" parents="11186 9942"/>
    </justification>
  </clause>

  <clause id="11192">
    <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,10335,a,b,11142,a)].">
      <j1 rule="hyper" parents="58 10335 11142"/>
    </justification>
  </clause>

  <clause id="11193">
    <literal><![CDATA[
      K(x,1 / L(K(y,z),u,w)) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(6027(a,2),11143(a,1,2))].">
      <j1 rule="para" parents="6027 11143"/>
    </justification>
  </clause>

  <clause id="11194">
    <literal><![CDATA[
      K(x,K(y,L(z,z,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(6418(a,1),11143(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6418 11143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11195">
    <literal><![CDATA[
      K(x,K(y / z,L(u,y,w))) = K(x,K(u,L(y / z,z,w)))
    ]]></literal>
    <justification jstring="[para(9294(a,1),11143(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9294 11143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11196">
    <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,11150,a(flip),b,5530,a),flip(a)].">
      <j1 rule="hyper" parents="119 11150 5530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11197">
    <literal><![CDATA[
      K(x,K(y,L(z \ 1,u,w))) = K(y,K(z,L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(8472,a,11158,a),flip(a)].">
      <j1 rule="hyper" parents="8472 11158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11198">
    <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(11158(a,2),5030(a,1,2))].">
      <j1 rule="para" parents="11158 5030"/>
    </justification>
  </clause>

  <clause id="11199">
    <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(10688(a,1),11162(a,2,2))].">
      <j1 rule="para" parents="10688 11162"/>
    </justification>
  </clause>

  <clause id="11200">
    <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(11187(a,1),169(a,1)),flip(b)].">
      <j1 rule="para" parents="11187 169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11201">
    <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(5870(a,1),11098(a,2,2,2))].">
      <j1 rule="para" parents="5870 11098"/>
    </justification>
  </clause>

  <clause id="11202">
    <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(416(a,1),11107(a,1,2,1,1))].">
      <j1 rule="para" parents="416 11107"/>
    </justification>
  </clause>

  <clause id="11203">
    <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),11110(a,1,2,2))].">
      <j1 rule="para" parents="25 11110"/>
    </justification>
  </clause>

  <clause id="11204">
    <literal><![CDATA[
      (x * y) * z != x * (y * K(u,w))
    ]]></literal>
    <literal><![CDATA[
      K(u,L(w,y,x)) = z
    ]]></literal>
    <justification jstring="[para(11110(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="11110 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11205">
    <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(11110(a,1),336(a,1)),flip(b)].">
      <j1 rule="para" parents="11110 336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11206">
    <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(7452(a,1),11110(a,2,2))].">
      <j1 rule="para" parents="7452 11110"/>
    </justification>
  </clause>

  <clause id="11207">
    <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(11110(a,1),7817(a,2,2,1))].">
      <j1 rule="para" parents="11110 7817"/>
    </justification>
  </clause>

  <clause id="11208">
    <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(11110(a,1),9240(a,2,2,1))].">
      <j1 rule="para" parents="11110 9240"/>
    </justification>
  </clause>

  <clause id="11209">
    <literal><![CDATA[
      (x * y) * K(z,K(u,L(w,y,x))) = x * (y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(11089(a,1),11110(a,1,2,2))].">
      <j1 rule="para" parents="11089 11110"/>
    </justification>
  </clause>

  <clause id="11210">
    <literal><![CDATA[
      (x * (y / z)) * K(z,L(u,y,x)) = x * ((y / z) * K(z,u))
    ]]></literal>
    <justification jstring="[para(11163(a,1),11110(a,1,2))].">
      <j1 rule="para" parents="11163 11110"/>
    </justification>
  </clause>

  <clause id="11211">
    <literal><![CDATA[
      K(x,L(T(y,z),z \ 1,z)) = z * (K(x,y) * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(119,a,8501,a(flip),b,11111,a),flip(a)].">
      <j1 rule="hyper" parents="119 8501 11111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11212">
    <literal><![CDATA[
      L(K((x \ 1) \ (y \ z),y),x \ 1,x) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,10696,a,b,11138,a),flip(a)].">
      <j1 rule="hyper" parents="334 10696 11138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11213">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(11148(a,1),5288(a,1))].">
      <j1 rule="para" parents="11148 5288"/>
    </justification>
  </clause>

  <clause id="11214">
    <literal><![CDATA[
      K((x * ((y \ 1) \ 1)) \ z,u) = K(y \ (x \ z),L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,4294,a,b,11151,a)].">
      <j1 rule="hyper" parents="334 4294 11151"/>
    </justification>
  </clause>

  <clause id="11215">
    <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(11151(a,2),8069(a,1,2))].">
      <j1 rule="para" parents="11151 8069"/>
    </justification>
  </clause>

  <clause id="11216">
    <literal><![CDATA[
      K((x \ 1) \ y,x * z) = K(x * y,(x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(501(a,1),11152(a,1,2))].">
      <j1 rule="para" parents="501 11152"/>
    </justification>
  </clause>

  <clause id="11217">
    <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(11156(a,1),8863(a,1,2,2))].">
      <j1 rule="para" parents="11156 8863"/>
    </justification>
  </clause>

  <clause id="11219">
    <literal><![CDATA[
      K(x,(y * T(x,z)) \ u) = K(x,x \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(334,a,7527,a(flip),b,11092,a),flip(a)].">
      <j1 rule="hyper" parents="334 7527 11092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11221">
    <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(311(a,1),11130(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="311 11130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11222">
    <literal><![CDATA[
      a(x,y \ z,K(u,y)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(29,a,11102,a,b,11172,a)].">
      <j1 rule="hyper" parents="29 11102 11172"/>
    </justification>
  </clause>

  <clause id="11223">
    <literal><![CDATA[
      a(x,y * z,K(u,y)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(4(a,1),11222(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 11222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11224">
    <literal><![CDATA[
      x * ((x \ y) * K(y,z)) = T(y,L(z,x \ y,x))
    ]]></literal>
    <justification jstring="[hyper(9777,a,11176,a)].">
      <j1 rule="hyper" parents="9777 11176"/>
    </justification>
  </clause>

  <clause id="11225">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,u)) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(7484,a,11176,a)].">
      <j1 rule="hyper" parents="7484 11176"/>
    </justification>
  </clause>

  <clause id="11226">
    <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(4729(a,1),11188(a,1,1))].">
      <j1 rule="para" parents="4729 11188"/>
    </justification>
  </clause>

  <clause id="11227">
    <literal><![CDATA[
      K(x,1 / L(K(y,z),u,w)) = K(x,L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,11182,a,b,11193,a),flip(a)].">
      <j1 rule="hyper" parents="334 11182 11193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11228">
    <literal><![CDATA[
      K(x * y,(x \ 1) \ (x \ z)) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),11216(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 11216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11229">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),u) = T(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(11225(a,1),5143(a,1,1))].">
      <j1 rule="para" parents="11225 5143"/>
    </justification>
  </clause>

  <clause id="11230">
    <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(11225(a,1),5209(a,1,1))].">
      <j1 rule="para" parents="11225 5209"/>
    </justification>
  </clause>

  <clause id="11231">
    <literal><![CDATA[
      K((x \ 1) \ (x \ y),z) = K(y,(x \ 1) \ (x \ z))
    ]]></literal>
    <justification jstring="[para(5(a,1),11228(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 11228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11232">
    <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(6597(a,1),11096(a,1,2,1))].">
      <j1 rule="para" parents="6597 11096"/>
    </justification>
  </clause>

  <clause id="11233">
    <literal><![CDATA[
      K(((x \ y) / z) \ y,L(z,x \ y,x)) = K(((x \ y) / z) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9311,a(flip),b,11097,a),flip(a)].">
      <j1 rule="hyper" parents="58 9311 11097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11234">
    <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,11231,a(flip),b,11105,a)].">
      <j1 rule="hyper" parents="58 11231 11105"/>
    </justification>
  </clause>

  <clause id="11235">
    <literal><![CDATA[
      x \ (y * K(z,y \ (x * u))) = (x \ y) * K(z,(x \ y) \ u)
    ]]></literal>
    <justification jstring="[para(11114(a,1),487(a,1,2,2))].">
      <j1 rule="para" parents="11114 487"/>
    </justification>
  </clause>

  <clause id="11236">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(11178(a,1),11121(a,1))].">
      <j1 rule="para" parents="11178 11121"/>
    </justification>
  </clause>

  <clause id="11237">
    <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(8048(a,1),11144(a,1,1))].">
      <j1 rule="para" parents="8048 11144"/>
    </justification>
  </clause>

  <clause id="11238">
    <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(11143(a,2),11161(a,1))].">
      <j1 rule="para" parents="11143 11161"/>
    </justification>
  </clause>

  <clause id="11239">
    <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(4442(a,1),11171(a,2,2,1))].">
      <j1 rule="para" parents="4442 11171"/>
    </justification>
  </clause>

  <clause id="11240">
    <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,9645,a(flip),b,11181,a)].">
      <j1 rule="hyper" parents="58 9645 11181"/>
    </justification>
  </clause>

  <clause id="11241">
    <literal><![CDATA[
      K(x,K(y * z,L(y,u,w))) = K(x,K(z * x,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(11237,a,11184,a)].">
      <j1 rule="hyper" parents="11237 11184"/>
    </justification>
  </clause>

  <clause id="11242">
    <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(11191(a,1),9736(a,2,2))].">
      <j1 rule="para" parents="11191 9736"/>
    </justification>
  </clause>

  <clause id="11243">
    <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(509(a,1),11195(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="509 11195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11244">
    <literal><![CDATA[
      K(x,K(y * z,L(y,u,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(334,a,8242,a(flip),b,11241,a),flip(a)].">
      <j1 rule="hyper" parents="334 8242 11241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11245">
    <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(11209(a,1),11198(a,1))].">
      <j1 rule="para" parents="11209 11198"/>
    </justification>
  </clause>

  <clause id="11246">
    <literal><![CDATA[
      L(K((x \ y) \ z,y),x \ 1,x) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[para(8576(a,1),11212(a,1,1))].">
      <j1 rule="para" parents="8576 11212"/>
    </justification>
  </clause>

  <clause id="11247">
    <literal><![CDATA[
      K(x \ (y \ z),L(u,x,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(11162(a,1),11123(a,1))].">
      <j1 rule="para" parents="11162 11123"/>
    </justification>
  </clause>

  <clause id="11248">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),x,y) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(11089(a,2),11247(a,1))].">
      <j1 rule="para" parents="11089 11247"/>
    </justification>
  </clause>

  <clause id="11249">
    <literal><![CDATA[
      K((x * ((y \ 1) \ 1)) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * y) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(11214(a,2),11247(a,1))].">
      <j1 rule="para" parents="11214 11247"/>
    </justification>
  </clause>

  <clause id="11250">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(11110(a,1),11157(a,1,1))].">
      <j1 rule="para" parents="11110 11157"/>
    </justification>
  </clause>

  <clause id="11251">
    <literal><![CDATA[
      L(x,y * K(x,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(6596,a,11250,a)].">
      <j1 rule="hyper" parents="6596 11250"/>
    </justification>
  </clause>

  <clause id="11252">
    <literal><![CDATA[
      L(x,y,z) = (z * (y * K(x,y))) \ (z * (x * y))
    ]]></literal>
    <justification jstring="[para(105(a,1),11250(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="105 11250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11253">
    <literal><![CDATA[
      L(x,y \ T(z,x),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(6836(a,1),11251(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6836 11251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11255">
    <literal><![CDATA[
      L(x,K(x,y) * z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(7423(a,1),11251(a,1,2))].">
      <j1 rule="para" parents="7423 11251"/>
    </justification>
  </clause>

  <clause id="11256">
    <literal><![CDATA[
      L(x,T(y,x) \ z,u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(8001(a,1),11251(a,1,2))].">
      <j1 rule="para" parents="8001 11251"/>
    </justification>
  </clause>

  <clause id="11259">
    <literal><![CDATA[
      L(T(x,y),K(x,z) * u,w) = L(T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(8162(a,1),11255(a,1,2,1))].">
      <j1 rule="para" parents="8162 11255"/>
    </justification>
  </clause>

  <clause id="11260">
    <literal><![CDATA[
      T(x,y) * L(y,z \ x,z) = z * ((z \ T(x,y)) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,11253,a(flip),b,91,a)].">
      <j1 rule="hyper" parents="119 11253 91"/>
    </justification>
  </clause>

  <clause id="11262">
    <literal><![CDATA[
      L(T(x,y),z / x,u) = L(T(x,y),x \ z,u)
    ]]></literal>
    <justification jstring="[para(5129(a,1),11259(a,1,2))].">
      <j1 rule="para" parents="5129 11259"/>
    </justification>
  </clause>

  <clause id="11263">
    <literal><![CDATA[
      L(T(x,y),T(x,z) \ u,w) = L(T(x,y),x \ u,w)
    ]]></literal>
    <justification jstring="[para(5337(a,1),11259(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5337 11259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11265">
    <literal><![CDATA[
      L(x,y,z * K(x,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,10924,a(flip),b,11252,a)].">
      <j1 rule="hyper" parents="334 10924 11252"/>
    </justification>
  </clause>

  <clause id="11268">
    <literal><![CDATA[
      K(x,L(T(y,z),y \ u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(11263(a,1),11094(a,1,2))].">
      <j1 rule="para" parents="11263 11094"/>
    </justification>
  </clause>

  <clause id="11269">
    <literal><![CDATA[
      K(x,(y * z) / (y * (z / u))) = K(x,L(T(u,y * z),z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,10713,a(flip),b,11268,a)].">
      <j1 rule="hyper" parents="58 10713 11268"/>
    </justification>
  </clause>

  <clause id="11270">
    <literal><![CDATA[
      K(x,L(T(y,z),u / y,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(11262(a,2),11268(a,1,2))].">
      <j1 rule="para" parents="11262 11268"/>
    </justification>
  </clause>

  <clause id="11271">
    <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),11270(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 11270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11272">
    <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(11190(a,1),5906(a,1))].">
      <j1 rule="para" parents="11190 5906"/>
    </justification>
  </clause>

  <clause id="11273">
    <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(11146,a,11192,a)].">
      <j1 rule="hyper" parents="11146 11192"/>
    </justification>
  </clause>

  <clause id="11274">
    <literal><![CDATA[
      K(K(L(x,y,z) \ 1,u) \ 1,w) = K(w,K(x,L(u,y,z)))
    ]]></literal>
    <justification jstring="[hyper(334,a,11197,a(flip),b,11240,a),flip(a)].">
      <j1 rule="hyper" parents="334 11197 11240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11275">
    <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(10007(a,1),11274(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10007 11274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11276">
    <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(9868(a,1),11273(a,1,2))].">
      <j1 rule="para" parents="9868 11273"/>
    </justification>
  </clause>

  <clause id="11277">
    <literal><![CDATA[
      x * (T(y / (x \ 1),z) \ y) = K(z,x * y)
    ]]></literal>
    <justification jstring="[para(501(a,1),11103(a,1,2)),flip(a)].">
      <j1 rule="para" parents="501 11103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11278">
    <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(11277(a,1),3456(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11277 3456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11279">
    <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(6198(a,1),11127(a,1,1))].">
      <j1 rule="para" parents="6198 11127"/>
    </justification>
  </clause>

  <clause id="11280">
    <literal><![CDATA[
      K(((x \ y) \ y) * z,L(z,x \ y,x)) = K(((x \ y) / z) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10816,a(flip),b,11233,a)].">
      <j1 rule="hyper" parents="58 10816 11233"/>
    </justification>
  </clause>

  <clause id="11281">
    <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(334,a,6941,a(flip),b,11279,a),flip(a)].">
      <j1 rule="hyper" parents="334 6941 11279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11282">
    <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(8121,a,11281,a)].">
      <j1 rule="hyper" parents="8121 11281"/>
    </justification>
  </clause>

  <clause id="11283">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = (L(x,y,z) * K(u,x)) * u
    ]]></literal>
    <justification jstring="[para(6652(a,1),11074(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6652 11074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11284">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,6532,a(flip),b,11283,a),flip(a)].">
      <j1 rule="hyper" parents="334 6532 11283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11285">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[para(1503(a,1),11284(a,1,1))].">
      <j1 rule="para" parents="1503 11284"/>
    </justification>
  </clause>

  <clause id="11286">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ (L(y,z,u) * T(x,y))
    ]]></literal>
    <justification jstring="[para(11285(a,1),10123(a,2,2))].">
      <j1 rule="para" parents="11285 10123"/>
    </justification>
  </clause>

  <clause id="11287">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = T(L(y,z,u) * K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(334,a,6558,a,b,11286,a),flip(a)].">
      <j1 rule="hyper" parents="334 6558 11286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11288">
    <literal><![CDATA[
      (x * (y / z)) * K(u,L(T(z,w),y,x)) = x * (y / T(z,T(u,w)))
    ]]></literal>
    <justification jstring="[para(11270(a,1),11206(a,1,2))].">
      <j1 rule="para" parents="11270 11206"/>
    </justification>
  </clause>

  <clause id="11289">
    <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(10136(a,1),11221(a,1,2))].">
      <j1 rule="para" parents="10136 11221"/>
    </justification>
  </clause>

  <clause id="11290">
    <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,11276,a(flip),b,11289,a)].">
      <j1 rule="hyper" parents="58 11276 11289"/>
    </justification>
  </clause>

  <clause id="11291">
    <literal><![CDATA[
      K(x,K(y,(z * (u * y)) \ w)) = K(y,K(x,(z * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(11215,a,11290,a),flip(a)].">
      <j1 rule="hyper" parents="11215 11290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11292">
    <literal><![CDATA[
      K(x,K(y,(z * (u * x)) \ w)) = K(x,K(y,(z * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(8050,a,11291,a)].">
      <j1 rule="hyper" parents="8050 11291"/>
    </justification>
  </clause>

  <clause id="11293">
    <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,10031,a(flip),b,11292,a)].">
      <j1 rule="hyper" parents="58 10031 11292"/>
    </justification>
  </clause>

  <clause id="11294">
    <literal><![CDATA[
      K(x,K(y,a(z,x,T(u,x)))) = 1
    ]]></literal>
    <justification jstring="[hyper(334,a,9767,a(flip),b,11293,a),flip(a)].">
      <j1 rule="hyper" parents="334 9767 11293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11296">
    <literal><![CDATA[
      K(x,K(y,a(z,x,u))) = 1
    ]]></literal>
    <justification jstring="[para(230(a,1),11294(a,1,2,2,3))].">
      <j1 rule="para" parents="230 11294"/>
    </justification>
  </clause>

  <clause id="11298">
    <literal><![CDATA[
      T(a(x,y,z),K(u,y)) = a(x,y,z) * 1
    ]]></literal>
    <justification jstring="[para(11296(a,1),8022(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11296 8022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11299">
    <literal><![CDATA[
      T(a(x,y,z),K(u,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,3,a(flip),b,11298,a),flip(a)].">
      <j1 rule="hyper" parents="334 3 11298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11300">
    <literal><![CDATA[
      T(a(x,y \ z,u),K(y,z)) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(8386,a,11299,a)].">
      <j1 rule="hyper" parents="8386 11299"/>
    </justification>
  </clause>

  <clause id="11301">
    <literal><![CDATA[
      a(x,y \ z,u) * K(y,z) = K(y,z) * a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,11300,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 11300 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11302">
    <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(3840(a,1),11202(a,1,2))].">
      <j1 rule="para" parents="3840 11202"/>
    </justification>
  </clause>

  <clause id="11303">
    <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(5232(a,1),11275(a,2,1))].">
      <j1 rule="para" parents="5232 11275"/>
    </justification>
  </clause>

  <clause id="11304">
    <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(334,a,8019,a(flip),b,11303,a),flip(a)].">
      <j1 rule="hyper" parents="334 8019 11303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11305">
    <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(11304(a,2),8464(a,1))].">
      <j1 rule="para" parents="11304 8464"/>
    </justification>
  </clause>

  <clause id="11306">
    <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(5391(a,1),11116(a,1,2))].">
      <j1 rule="para" parents="5391 11116"/>
    </justification>
  </clause>

  <clause id="11307">
    <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(11137(a,1),11306(a,1,2,1))].">
      <j1 rule="para" parents="11137 11306"/>
    </justification>
  </clause>

  <clause id="11308">
    <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(5047(a,1),11307(a,1,2))].">
      <j1 rule="para" parents="5047 11307"/>
    </justification>
  </clause>

  <clause id="11309">
    <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(11176(a,1),11308(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11176 11308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11310">
    <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(11269(a,1),11129(a,1,2))].">
      <j1 rule="para" parents="11269 11129"/>
    </justification>
  </clause>

  <clause id="11311">
    <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,11288,a(flip),b,11310,a),flip(a)].">
      <j1 rule="hyper" parents="58 11288 11310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11312">
    <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,10812,a(flip),b,11199,a),flip(a)].">
      <j1 rule="hyper" parents="58 10812 11199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11313">
    <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(11287(a,1),11242(a,1,2))].">
      <j1 rule="para" parents="11287 11242"/>
    </justification>
  </clause>

  <clause id="11314">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = K(L(x,z,y),u) * K(u,x)
    ]]></literal>
    <justification jstring="[hyper(7852,a,11313,a),flip(a)].">
      <j1 rule="hyper" parents="7852 11313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11315">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = K(x,L(u,z,y)) * K(u,x)
    ]]></literal>
    <justification jstring="[para(11137(a,1),11314(a,2,1))].">
      <j1 rule="para" parents="11137 11314"/>
    </justification>
  </clause>

  <clause id="11316">
    <literal><![CDATA[
      x * a(y,z,K(x \ u,x)) = x * a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(11185,a,11315,a),flip(a)].">
      <j1 rule="hyper" parents="11185 11315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11317">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,11119,a(flip),b,11315,a),flip(a)].">
      <j1 rule="hyper" parents="334 11119 11315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11318">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(287,a,11316,a),flip(a)].">
      <j1 rule="hyper" parents="287 11316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11321">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),11318(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="4 11318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11322">
    <literal><![CDATA[
      a(x,y,K(z * u,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(5234(a,1),11318(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5234 11318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11323">
    <literal><![CDATA[
      a(x,y,K(z,u \ z)) = a(x,y,K(u,u \ z))
    ]]></literal>
    <justification jstring="[para(5236(a,1),11318(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5236 11318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11324">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u)) = a(x,y,K(z \ u,u))
    ]]></literal>
    <justification jstring="[para(5714(a,1),11318(a,1,3))].">
      <j1 rule="para" parents="5714 11318"/>
    </justification>
  </clause>

  <clause id="11325">
    <literal><![CDATA[
      a(x,y,K(z \ (u * w),w)) = a(x,y,K(z \ u,w))
    ]]></literal>
    <justification jstring="[para(10642(a,1),11318(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10642 11318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11326">
    <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(11321(a,2),10188(a,1,1))].">
      <j1 rule="para" parents="11321 10188"/>
    </justification>
  </clause>

  <clause id="11327">
    <literal><![CDATA[
      a(x,y,K(x * z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(334,a,7276,a(flip),b,11322,a),flip(a)].">
      <j1 rule="hyper" parents="334 7276 11322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11328">
    <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(11322(a,1),11309(a,2,2,2))].">
      <j1 rule="para" parents="11322 11309"/>
    </justification>
  </clause>

  <clause id="11329">
    <literal><![CDATA[
      L(K(x * y,y),z,x) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(47,a,11327,a)].">
      <j1 rule="hyper" parents="47 11327"/>
    </justification>
  </clause>

  <clause id="11330">
    <literal><![CDATA[
      x * (y * K(x * z,T(z,x * y))) = K(x * z,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(11329(a,1),7428(a,2,1))].">
      <j1 rule="para" parents="11329 7428"/>
    </justification>
  </clause>

  <clause id="11331">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(11317(a,1),297(a,1)),flip(b)].">
      <j1 rule="para" parents="11317 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11332">
    <literal><![CDATA[
      a(x,y,K(z,z * u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(10191,a,11326,a)].">
      <j1 rule="hyper" parents="10191 11326"/>
    </justification>
  </clause>

  <clause id="11333">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),11332(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5 11332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11334">
    <literal><![CDATA[
      a(x,y,K(z,u * z)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(5649(a,2),11332(a,1,3))].">
      <j1 rule="para" parents="5649 11332"/>
    </justification>
  </clause>

  <clause id="11335">
    <literal><![CDATA[
      a(x,y,K(z,u \ z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,11323,a,b,11333,a)].">
      <j1 rule="hyper" parents="58 11323 11333"/>
    </justification>
  </clause>

  <clause id="11336">
    <literal><![CDATA[
      a(x,y,K(z \ u,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(5462(a,1),11335(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5462 11335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11337">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,11324,a,b,11336,a)].">
      <j1 rule="hyper" parents="58 11324 11336"/>
    </justification>
  </clause>

  <clause id="11338">
    <literal><![CDATA[
      a(x,y,K(z \ u,w)) = a(x,y,K(w,u \ z))
    ]]></literal>
    <justification jstring="[para(6615(a,1),11337(a,1,3))].">
      <j1 rule="para" parents="6615 11337"/>
    </justification>
  </clause>

  <clause id="11339">
    <literal><![CDATA[
      x * (y * K(x * z,T(z,y))) = K(x * z,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(8688(a,1),11330(a,1,2,2))].">
      <j1 rule="para" parents="8688 11330"/>
    </justification>
  </clause>

  <clause id="11340">
    <literal><![CDATA[
      K(x * y,y) * (x * z) = x * (K(x * y,y) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7551,a(flip),b,11339,a),flip(a)].">
      <j1 rule="hyper" parents="58 7551 11339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11341">
    <literal><![CDATA[
      x * (K(x * y,y) * (K(y,x) * z)) = a(y,x,y) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9849,a(flip),b,11340,a),flip(a)].">
      <j1 rule="hyper" parents="58 9849 11340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11342">
    <literal><![CDATA[
      a(x,y,x) * (y * z) = y * (a(x,y,x) * z)
    ]]></literal>
    <justification jstring="[para(9847(a,1),11341(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9847 11341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11343">
    <literal><![CDATA[
      x * (a(y,x,y) * (x \ z)) = a(y,x,y) * z
    ]]></literal>
    <justification jstring="[hyper(356,a,11342,a),flip(a)].">
      <j1 rule="hyper" parents="356 11342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11344">
    <literal><![CDATA[
      K((x \ (y \ z)) \ u,(y * ((y \ z) / x)) \ z) = K(x * (z \ (y * u)),x)
    ]]></literal>
    <justification jstring="[hyper(334,a,11084,a(flip),b,11312,a),flip(a)].">
      <j1 rule="hyper" parents="334 11084 11312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11345">
    <literal><![CDATA[
      K((x \ (y \ z)) \ u,L(x,y \ z,y)) = K(x * (z \ (y * u)),x)
    ]]></literal>
    <justification jstring="[hyper(11167,a,11344,a)].">
      <j1 rule="hyper" parents="11167 11344"/>
    </justification>
  </clause>

  <clause id="11346">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,L(u,x \ y,x)) = K(u * (y \ (x * z)),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,10812,a(flip),b,11345,a)].">
      <j1 rule="hyper" parents="58 10812 11345"/>
    </justification>
  </clause>

  <clause id="11347">
    <literal><![CDATA[
      K(((x \ y) / z) \ y,z) = K(z * (y \ (x * y)),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11280,a(flip),b,11346,a)].">
      <j1 rule="hyper" parents="58 11280 11346"/>
    </justification>
  </clause>

  <clause id="11348">
    <literal><![CDATA[
      K(((x \ y) / z) \ y,z) = K(z * T(x,y),z)
    ]]></literal>
    <justification jstring="[para(17(a,2),11347(a,2,1,2))].">
      <j1 rule="para" parents="17 11347"/>
    </justification>
  </clause>

  <clause id="11349">
    <literal><![CDATA[
      K(x * ((y \ z) \ z),x) = K(x * T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,10796,a(flip),b,11348,a)].">
      <j1 rule="hyper" parents="58 10796 11348"/>
    </justification>
  </clause>

  <clause id="11350">
    <literal><![CDATA[
      K(x,x * ((y \ z) \ z)) = u / (K(x * T(y,z),x) * u)
    ]]></literal>
    <justification jstring="[para(11349(a,1),5403(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11349 5403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11351">
    <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(11349(a,1),11048(a,1,1,2,2))].">
      <j1 rule="para" parents="11349 11048"/>
    </justification>
  </clause>

  <clause id="11352">
    <literal><![CDATA[
      K(x,x * ((y \ z) \ z)) = K(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,5403,a(flip),b,11350,a),flip(a)].">
      <j1 rule="hyper" parents="334 5403 11350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11353">
    <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(334,a,5360,a(flip),b,11328,a),flip(a)].">
      <j1 rule="hyper" parents="334 5360 11328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11354">
    <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(1758(a,2),11234(a,1,2))].">
      <j1 rule="para" parents="1758 11234"/>
    </justification>
  </clause>

  <clause id="11355">
    <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(7086(a,1),7193(a,1,2,2))].">
      <j1 rule="para" parents="7086 7193"/>
    </justification>
  </clause>

  <clause id="11356">
    <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(6367(a,1),7927(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6367 7927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11357">
    <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(334,a,8010,a(flip),b,11356,a),flip(a)].">
      <j1 rule="hyper" parents="334 8010 11356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11358">
    <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(7879(a,1),11357(a,2,1))].">
      <j1 rule="para" parents="7879 11357"/>
    </justification>
  </clause>

  <clause id="11359">
    <literal><![CDATA[
      T(x,T(y / T(y / z,u),w)) = T(x,T(T(z \ y,u) \ y,w))
    ]]></literal>
    <justification jstring="[para(11358(a,1),8595(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11358 8595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11360">
    <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(5044(a,1),9066(a,1,1))].">
      <j1 rule="para" parents="5044 9066"/>
    </justification>
  </clause>

  <clause id="11361">
    <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(709,a,11360,a),flip(a)].">
      <j1 rule="hyper" parents="709 11360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11362">
    <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(11360(a,1),709(a,1))].">
      <j1 rule="para" parents="11360 709"/>
    </justification>
  </clause>

  <clause id="11363">
    <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(5337(a,1),11361(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5337 11361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11364">
    <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(5391(a,1),9221(a,1,1,1))].">
      <j1 rule="para" parents="5391 9221"/>
    </justification>
  </clause>

  <clause id="11365">
    <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(10298(a,1),9231(a,1,1))].">
      <j1 rule="para" parents="10298 9231"/>
    </justification>
  </clause>

  <clause id="11366">
    <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(9814(a,1),9362(a,1,2,2,1))].">
      <j1 rule="para" parents="9814 9362"/>
    </justification>
  </clause>

  <clause id="11367">
    <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),9480(a,2,1))].">
      <j1 rule="para" parents="7 9480"/>
    </justification>
  </clause>

  <clause id="11368">
    <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(334,a,6378,a,b,11367,a)].">
      <j1 rule="hyper" parents="334 6378 11367"/>
    </justification>
  </clause>

  <clause id="11369">
    <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(10525(a,2),9741(a,2,2,2))].">
      <j1 rule="para" parents="10525 9741"/>
    </justification>
  </clause>

  <clause id="11370">
    <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(334,a,5604,a(flip),b,10081,a),flip(a)].">
      <j1 rule="hyper" parents="334 5604 10081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11371">
    <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(10277(a,1),10285(a,2,2,1,1))].">
      <j1 rule="para" parents="10277 10285"/>
    </justification>
  </clause>

  <clause id="11372">
    <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(5232(a,1),11371(a,2,2,1))].">
      <j1 rule="para" parents="5232 11371"/>
    </justification>
  </clause>

  <clause id="11374">
    <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(5232(a,1),11372(a,1,1,2,1))].">
      <j1 rule="para" parents="5232 11372"/>
    </justification>
  </clause>

  <clause id="11375">
    <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,5420,a(flip),b,11374,a)].">
      <j1 rule="hyper" parents="58 5420 11374"/>
    </justification>
  </clause>

  <clause id="11376">
    <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(11374(a,1),519(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11374 519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11377">
    <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(11374(a,2),10179(a,1,1))].">
      <j1 rule="para" parents="11374 10179"/>
    </justification>
  </clause>

  <clause id="11379">
    <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(8019(a,1),11377(a,1,1,1,2,1))].">
      <j1 rule="para" parents="8019 11377"/>
    </justification>
  </clause>

  <clause id="11380">
    <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),10577(a,2,2,2,1,1,2))].">
      <j1 rule="para" parents="75 10577"/>
    </justification>
  </clause>

  <clause id="11381">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * u = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[hyper(598,a,11380,a)].">
      <j1 rule="hyper" parents="598 11380"/>
    </justification>
  </clause>

  <clause id="11384">
    <literal><![CDATA[
      ((x * y) * (z * (((x * y) \ u) / z))) / u = K(z,u / ((x * z) * y))
    ]]></literal>
    <justification jstring="[para(11381(a,1),10312(a,1,1))].">
      <j1 rule="para" parents="11381 10312"/>
    </justification>
  </clause>

  <clause id="11385">
    <literal><![CDATA[
      K(x,y / ((z * u) * x)) = K(x,y / ((z * x) * u))
    ]]></literal>
    <justification jstring="[hyper(6231,a,11384,a)].">
      <j1 rule="hyper" parents="6231 11384"/>
    </justification>
  </clause>

  <clause id="11386">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(10916,a,11385,a),flip(a)].">
      <j1 rule="hyper" parents="10916 11385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11387">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) = K(x,1 / (z * x))
    ]]></literal>
    <justification jstring="[hyper(334,a,5617,a(flip),b,11385,a),flip(a)].">
      <j1 rule="hyper" parents="334 5617 11385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11388">
    <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),11385(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="105 11385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11389">
    <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),11385(a,1,2))].">
      <j1 rule="para" parents="102 11385"/>
    </justification>
  </clause>

  <clause id="11390">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / (z * x)) = u
    ]]></literal>
    <justification jstring="[para(11385(a,2),5759(a,1))].">
      <j1 rule="para" parents="11385 5759"/>
    </justification>
  </clause>

  <clause id="11391">
    <literal><![CDATA[
      K(x,1 / ((y / z) * x)) = K(x,z / (y * x))
    ]]></literal>
    <justification jstring="[para(7(a,1),11387(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 11387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11392">
    <literal><![CDATA[
      K(x,((y * x) * z) / (x * (y * (y \ z)))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[hyper(10163,a,11386,a),flip(a)].">
      <j1 rule="hyper" parents="10163 11386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11393">
    <literal><![CDATA[
      K(x,y / ((x * z) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,9261,a(flip),b,11386,a)].">
      <j1 rule="hyper" parents="58 9261 11386"/>
    </justification>
  </clause>

  <clause id="11394">
    <literal><![CDATA[
      K(x,(y * x) / ((z * x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,7338,a(flip),b,11389,a),flip(a)].">
      <j1 rule="hyper" parents="58 7338 11389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11396">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,((y * x) * z) / (x * z))
    ]]></literal>
    <justification jstring="[para(5(a,1),11392(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 11392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11397">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[para(15(a,2),11396(a,2,2))].">
      <j1 rule="para" parents="15 11396"/>
    </justification>
  </clause>

  <clause id="11399">
    <literal><![CDATA[
      K(x,R(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10902,a,11397,a),flip(a)].">
      <j1 rule="hyper" parents="10902 11397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11400">
    <literal><![CDATA[
      K(x,R(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(11397(a,1),10902(a,1))].">
      <j1 rule="para" parents="11397 10902"/>
    </justification>
  </clause>

  <clause id="11401">
    <literal><![CDATA[
      R(K(x \ y,x),y,z) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(9540,a,11399,a)].">
      <j1 rule="hyper" parents="9540 11399"/>
    </justification>
  </clause>

  <clause id="11403">
    <literal><![CDATA[
      T(x,R(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,11399,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 11399 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11404">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9904,a(flip),b,11399,a)].">
      <j1 rule="hyper" parents="58 9904 11399"/>
    </justification>
  </clause>

  <clause id="11406">
    <literal><![CDATA[
      K(x,R(R(y,x,z),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(26(a,1),11399(a,1,2))].">
      <j1 rule="para" parents="26 11399"/>
    </justification>
  </clause>

  <clause id="11407">
    <literal><![CDATA[
      K(1 / x,y / (1 / x)) = K(1 / x,y * x)
    ]]></literal>
    <justification jstring="[para(535(a,1),11399(a,1,2)),flip(a)].">
      <j1 rule="para" parents="535 11399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11409">
    <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(546(a,1),11403(a,1,2))].">
      <j1 rule="para" parents="546 11403"/>
    </justification>
  </clause>

  <clause id="11410">
    <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(628(a,1),11400(a,1,2))].">
      <j1 rule="para" parents="628 11400"/>
    </justification>
  </clause>

  <clause id="11411">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(9639(a,2),11400(a,1))].">
      <j1 rule="para" parents="9639 11400"/>
    </justification>
  </clause>

  <clause id="11412">
    <literal><![CDATA[
      K(x / (y * z),y) = K(y \ (x / z),y)
    ]]></literal>
    <justification jstring="[hyper(6269,a,11401,a)].">
      <j1 rule="hyper" parents="6269 11401"/>
    </justification>
  </clause>

  <clause id="11413">
    <literal><![CDATA[
      (((x \ y) * x) * z) / (y * z) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(4983,a,11401,a)].">
      <j1 rule="hyper" parents="4983 11401"/>
    </justification>
  </clause>

  <clause id="11414">
    <literal><![CDATA[
      K(x,y / (x * z)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(10916,a,11404,a)].">
      <j1 rule="hyper" parents="10916 11404"/>
    </justification>
  </clause>

  <clause id="11416">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,11385,a(flip),b,11404,a)].">
      <j1 rule="hyper" parents="58 11385 11404"/>
    </justification>
  </clause>

  <clause id="11417">
    <literal><![CDATA[
      K(x,x \ ((x * y) / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8772,a(flip),b,11404,a),flip(a)].">
      <j1 rule="hyper" parents="58 8772 11404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11418">
    <literal><![CDATA[
      K(x / (y * z),z) = K(z \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(10917,a,11412,a)].">
      <j1 rule="hyper" parents="10917 11412"/>
    </justification>
  </clause>

  <clause id="11419">
    <literal><![CDATA[
      K((x \ y) / z,x) = K(x \ (y / z),x)
    ]]></literal>
    <justification jstring="[hyper(9011,a,11412,a)].">
      <j1 rule="hyper" parents="9011 11412"/>
    </justification>
  </clause>

  <clause id="11420">
    <literal><![CDATA[
      K(x,y / ((x * z) * u)) = K(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,11393,a,b,11414,a)].">
      <j1 rule="hyper" parents="58 11393 11414"/>
    </justification>
  </clause>

  <clause id="11421">
    <literal><![CDATA[
      K(x,x \ ((y \ 1) \ (x * z))) = K(x,z / T(y \ 1,y * (x * z)))
    ]]></literal>
    <justification jstring="[para(4613(a,1),11417(a,1,2,2))].">
      <j1 rule="para" parents="4613 11417"/>
    </justification>
  </clause>

  <clause id="11422">
    <literal><![CDATA[
      K(x \ (y \ z),x) * z = z * K(x \ (z / y),x)
    ]]></literal>
    <justification jstring="[para(11418(a,1),10643(a,2,2))].">
      <j1 rule="para" parents="11418 10643"/>
    </justification>
  </clause>

  <clause id="11423">
    <literal><![CDATA[
      K(x \ (y / z),x) * z = z * K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(11419(a,1),7537(a,1,1))].">
      <j1 rule="para" parents="11419 7537"/>
    </justification>
  </clause>

  <clause id="11424">
    <literal><![CDATA[
      R(K(x,R(y,x,z)),(y * x) * z,u) = K(x,R(y,x * z,u))
    ]]></literal>
    <justification jstring="[hyper(9541,a,11406,a)].">
      <j1 rule="hyper" parents="9541 11406"/>
    </justification>
  </clause>

  <clause id="11425">
    <literal><![CDATA[
      K(x,y * K(1 / y,z * y)) = T(K(x,y),z / (1 / y))
    ]]></literal>
    <justification jstring="[para(11407(a,1),9899(a,1,2,2))].">
      <j1 rule="para" parents="11407 9899"/>
    </justification>
  </clause>

  <clause id="11426">
    <literal><![CDATA[
      K(x \ y,x) * (y * z) = ((x \ y) * x) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,11413,a)].">
      <j1 rule="hyper" parents="133 11413"/>
    </justification>
  </clause>

  <clause id="11427">
    <literal><![CDATA[
      (x \ y) \ (((x \ y) * x) * z) = (y / x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(116,a,11426,a(flip),b,5634,a)].">
      <j1 rule="hyper" parents="116 11426 5634"/>
    </justification>
  </clause>

  <clause id="11428">
    <literal><![CDATA[
      K((x * T(y,x * y)) \ z,x * y) * (z * u) = (((x * y) \ z) * (x * y)) * u
    ]]></literal>
    <justification jstring="[para(8917(a,2),11426(a,1,1))].">
      <j1 rule="para" parents="8917 11426"/>
    </justification>
  </clause>

  <clause id="11429">
    <literal><![CDATA[
      K(x,x \ (y / ((x \ z) * u))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9262,a(flip),b,11416,a),flip(a)].">
      <j1 rule="hyper" parents="58 9262 11416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11430">
    <literal><![CDATA[
      T(x,y / ((x * z) * u)) = T(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(118,a,11420,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 11420 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11431">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(7555,a,11423,a)].">
      <j1 rule="hyper" parents="7555 11423"/>
    </justification>
  </clause>

  <clause id="11432">
    <literal><![CDATA[
      K(x \ (y / z),T(x,y)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8670,a(flip),b,11431,a)].">
      <j1 rule="hyper" parents="58 8670 11431"/>
    </justification>
  </clause>

  <clause id="11433">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = (u * K(z \ (x \ y),x)) \ u
    ]]></literal>
    <justification jstring="[para(11432(a,1),6523(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11432 6523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11434">
    <literal><![CDATA[
      x * L(y,z,z \ x) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(637,a,11427,a),flip(a)].">
      <j1 rule="hyper" parents="637 11427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11435">
    <literal><![CDATA[
      ((x * y) / x) \ ((x * y) * z) = y \ (((x \ (x * y)) * x) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11427(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 11427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11436">
    <literal><![CDATA[
      (x / y) * (y * T(z,x)) = L(z,y,y \ x) * x
    ]]></literal>
    <justification jstring="[hyper(429,a,11434,a),flip(a)].">
      <j1 rule="hyper" parents="429 11434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11437">
    <literal><![CDATA[
      L(x \ y,x,x \ z) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,11434,a),flip(a)].">
      <j1 rule="hyper" parents="116 151 11434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11438">
    <literal><![CDATA[
      L(x,y,z / y) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(29,a,485,a,b,11434,a)].">
      <j1 rule="hyper" parents="29 485 11434"/>
    </justification>
  </clause>

  <clause id="11439">
    <literal><![CDATA[
      ((x / y) * (y * z)) \ K(x,L(z,y,y \ x)) = (L(z,y,y \ x) * x) \ 1
    ]]></literal>
    <justification jstring="[para(11434(a,1),5836(a,1,1))].">
      <j1 rule="para" parents="11434 5836"/>
    </justification>
  </clause>

  <clause id="11440">
    <literal><![CDATA[
      x * K(y,L(z,u,u \ x)) = (x / u) * (u * K(y,z))
    ]]></literal>
    <justification jstring="[para(11089(a,1),11434(a,1,2))].">
      <j1 rule="para" parents="11089 11434"/>
    </justification>
  </clause>

  <clause id="11441">
    <literal><![CDATA[
      L(T(x,y),y,y \ z) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,715,a(flip),b,11438,a),flip(a)].">
      <j1 rule="hyper" parents="58 715 11438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11442">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) \ z) = L(x,y \ z,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),11438(a,1,3)),flip(a)].">
      <j1 rule="para" parents="72 11438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11443">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),T(x,y) \ y) = y \ ((T(y,x) / x) * z)
    ]]></literal>
    <justification jstring="[para(4488(a,2),11437(a,2,2,1))].">
      <j1 rule="para" parents="4488 11437"/>
    </justification>
  </clause>

  <clause id="11444">
    <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(6523(a,1),11437(a,1,3))].">
      <j1 rule="para" parents="6523 11437"/>
    </justification>
  </clause>

  <clause id="11445">
    <literal><![CDATA[
      K(x,(x * y) / (z * u)) = K(x,y / ((x \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11417,a(flip),b,11429,a),flip(a)].">
      <j1 rule="hyper" parents="58 11417 11429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11446">
    <literal><![CDATA[
      K(x,y / ((x \ z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z * u) / y) \ x) = w
    ]]></literal>
    <justification jstring="[para(11445(a,1),6175(a,1))].">
      <j1 rule="para" parents="11445 6175"/>
    </justification>
  </clause>

  <clause id="11447">
    <literal><![CDATA[
      (x / y) * (y * K(z,T(u,y))) = x * K(z,x \ ((x / y) * (u * y)))
    ]]></literal>
    <justification jstring="[para(11441(a,1),11440(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11441 11440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11448">
    <literal><![CDATA[
      T(K(x,y),z / (1 / y)) = T(K(x,y),z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9899,a(flip),b,11425,a),flip(a)].">
      <j1 rule="hyper" parents="58 9899 11425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11449">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,1 / (z / (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(58,a,9900,a(flip),b,11448,a),flip(a)].">
      <j1 rule="hyper" parents="58 9900 11448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11450">
    <literal><![CDATA[
      K(x,1 / (y / (y / (1 / z)))) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6577,a(flip),b,11449,a),flip(a)].">
      <j1 rule="hyper" parents="58 6577 11449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11451">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(334,a,6523,a(flip),b,11433,a),flip(a)].">
      <j1 rule="hyper" parents="334 6523 11433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11452">
    <literal><![CDATA[
      K(x,T(x \ (y / z),y)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(7970,a,11451,a)].">
      <j1 rule="hyper" parents="7970 11451"/>
    </justification>
  </clause>

  <clause id="11453">
    <literal><![CDATA[
      K(x,(y \ z) \ (x \ z)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),11452(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 11452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11454">
    <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,8723,a,b,11453,a)].">
      <j1 rule="hyper" parents="58 8723 11453"/>
    </justification>
  </clause>

  <clause id="11455">
    <literal><![CDATA[
      R(K(x,y),(y * x) * z,u) = K(x,R(y,x * z,u))
    ]]></literal>
    <justification jstring="[para(11399(a,1),11424(a,1,1))].">
      <j1 rule="para" parents="11399 11424"/>
    </justification>
  </clause>

  <clause id="11457">
    <literal><![CDATA[
      ((x * y) / x) \ ((x * y) * z) = y \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11435(a,2,2,1,1))].">
      <j1 rule="para" parents="4 11435"/>
    </justification>
  </clause>

  <clause id="11458">
    <literal><![CDATA[
      K(x,y) * (x \ ((y * x) * z)) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(5939,a,11457,a)].">
      <j1 rule="hyper" parents="5939 11457"/>
    </justification>
  </clause>

  <clause id="11459">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(5662,a,11458,a(flip))].">
      <j1 rule="hyper" parents="5662 11458"/>
    </justification>
  </clause>

  <clause id="11460">
    <literal><![CDATA[
      L(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(5160,a,11459,a)].">
      <j1 rule="hyper" parents="5160 11459"/>
    </justification>
  </clause>

  <clause id="11461">
    <literal><![CDATA[
      (x * y) \ (K(x,y) * z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(611,a,11459,a)].">
      <j1 rule="hyper" parents="611 11459"/>
    </justification>
  </clause>

  <clause id="11462">
    <literal><![CDATA[
      (x * y) * ((y * x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(356,a,11459,a),flip(a)].">
      <j1 rule="hyper" parents="356 11459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11463">
    <literal><![CDATA[
      (x * y) * (K(y,x) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,10905,a(flip),b,11459,a)].">
      <j1 rule="hyper" parents="58 10905 11459"/>
    </justification>
  </clause>

  <clause id="11464">
    <literal><![CDATA[
      (x * y) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(116,a,11459,a(flip),b,10905,a(flip))].">
      <j1 rule="hyper" parents="116 11459 10905"/>
    </justification>
  </clause>

  <clause id="11465">
    <literal><![CDATA[
      K(x,(x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * x) * z) = u
    ]]></literal>
    <justification jstring="[para(11459(a,1),7613(a,1,2))].">
      <j1 rule="para" parents="11459 7613"/>
    </justification>
  </clause>

  <clause id="11466">
    <literal><![CDATA[
      K(x,y \ ((x * z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ ((z * x) * u)) = w
    ]]></literal>
    <justification jstring="[para(11459(a,1),8863(a,1,2,2))].">
      <j1 rule="para" parents="11459 8863"/>
    </justification>
  </clause>

  <clause id="11467">
    <literal><![CDATA[
      K(x \ ((y * z) * u),z) = K(x \ ((z * y) * u),z)
    ]]></literal>
    <justification jstring="[para(11459(a,1),8923(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11459 8923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11469">
    <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(11459(a,1),5693(a,1,2))].">
      <j1 rule="para" parents="11459 5693"/>
    </justification>
  </clause>

  <clause id="11470">
    <literal><![CDATA[
      L(x,T(y,z),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(7137,a,11460,a)].">
      <j1 rule="hyper" parents="7137 11460"/>
    </justification>
  </clause>

  <clause id="11471">
    <literal><![CDATA[
      L(x,y,z) = (y * z) \ (z * (T(y,z) * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7135,a(flip),b,11460,a),flip(a)].">
      <j1 rule="hyper" parents="58 7135 11460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11472">
    <literal><![CDATA[
      (x * y) * L(z,x,y) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,11460,a(flip),b,7135,a(flip))].">
      <j1 rule="hyper" parents="119 11460 7135"/>
    </justification>
  </clause>

  <clause id="11473">
    <literal><![CDATA[
      L(x,y * z,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(11460(a,1),45(a,2))].">
      <j1 rule="para" parents="11460 45"/>
    </justification>
  </clause>

  <clause id="11474">
    <literal><![CDATA[
      L(x,T(y,z) * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(5182(a,1),11460(a,1,3))].">
      <j1 rule="para" parents="5182 11460"/>
    </justification>
  </clause>

  <clause id="11475">
    <literal><![CDATA[
      L(L(x,y,z),u * w,K(w,u)) = L(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,11460,a,b,11470,a)].">
      <j1 rule="hyper" parents="334 11460 11470"/>
    </justification>
  </clause>

  <clause id="11476">
    <literal><![CDATA[
      L(x,(y \ z) \ z,y \ z) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1675,a(flip),b,11470,a)].">
      <j1 rule="hyper" parents="58 1675 11470"/>
    </justification>
  </clause>

  <clause id="11477">
    <literal><![CDATA[
      L(T(x,y) \ z,x,y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,508,a(flip),b,11470,a),flip(a)].">
      <j1 rule="hyper" parents="58 508 11470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11478">
    <literal><![CDATA[
      L(x,y / z,z) = L(x,z \ y,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),11470(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 11470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11482">
    <literal><![CDATA[
      L(x,y,T(z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(10506,a,11474,a),flip(a)].">
      <j1 rule="hyper" parents="10506 11474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11483">
    <literal><![CDATA[
      L(x,y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(11474(a,1),10506(a,1))].">
      <j1 rule="para" parents="11474 10506"/>
    </justification>
  </clause>

  <clause id="11485">
    <literal><![CDATA[
      L(x,y,z \ K(y,z \ 1)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(5152(a,1),11482(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5152 11482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11486">
    <literal><![CDATA[
      L(x,T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(7136(a,1),11473(a,1))].">
      <j1 rule="para" parents="7136 11473"/>
    </justification>
  </clause>

  <clause id="11489">
    <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(6439(a,1),11486(a,1,2))].">
      <j1 rule="para" parents="6439 11486"/>
    </justification>
  </clause>

  <clause id="11490">
    <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(334,a,1674,a(flip),b,11461,a),flip(a)].">
      <j1 rule="hyper" parents="334 1674 11461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11491">
    <literal><![CDATA[
      L(x \ ((y * z) \ u),x,z * y) = ((z * y) * x) \ (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(11461(a,1),311(a,1,1,2))].">
      <j1 rule="para" parents="11461 311"/>
    </justification>
  </clause>

  <clause id="11492">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * z) = (y * x) \ (x * z)
    ]]></literal>
    <justification jstring="[para(5047(a,1),11461(a,1,2))].">
      <j1 rule="para" parents="5047 11461"/>
    </justification>
  </clause>

  <clause id="11493">
    <literal><![CDATA[
      (x * y) \ (R(y,z,u) * T(x,y)) = (y * x) \ (R(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(6143(a,1),11461(a,1,2))].">
      <j1 rule="para" parents="6143 11461"/>
    </justification>
  </clause>

  <clause id="11494">
    <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(334,a,4567,a,b,11462,a)].">
      <j1 rule="hyper" parents="334 4567 11462"/>
    </justification>
  </clause>

  <clause id="11495">
    <literal><![CDATA[
      L(x,K(y,z),z * y) = x
    ]]></literal>
    <justification jstring="[hyper(857,a,11463,a)].">
      <j1 rule="hyper" parents="857 11463"/>
    </justification>
  </clause>

  <clause id="11496">
    <literal><![CDATA[
      ((x \ y) * x) \ (y * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(116,a,149,a(flip),b,11463,a)].">
      <j1 rule="hyper" parents="116 149 11463"/>
    </justification>
  </clause>

  <clause id="11497">
    <literal><![CDATA[
      K(x,y) * ((x * y) \ z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,11463,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 11463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11499">
    <literal><![CDATA[
      (x * y) * (1 / T(x,y)) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(5439(a,1),11463(a,1,2))].">
      <j1 rule="para" parents="5439 11463"/>
    </justification>
  </clause>

  <clause id="11500">
    <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(11463(a,1),8190(a,1,1,1))].">
      <j1 rule="para" parents="11463 8190"/>
    </justification>
  </clause>

  <clause id="11501">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,T(x,z)) * u) = (z * K(x,y)) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(7434(a,1),11463(a,1,2))].">
      <j1 rule="para" parents="7434 11463"/>
    </justification>
  </clause>

  <clause id="11502">
    <literal><![CDATA[
      L(x,K(y \ z,y),z) = x
    ]]></literal>
    <justification jstring="[para(5(a,1),11495(a,1,3))].">
      <j1 rule="para" parents="5 11495"/>
    </justification>
  </clause>

  <clause id="11503">
    <literal><![CDATA[
      L(x,K(y,y \ z),z) = x
    ]]></literal>
    <justification jstring="[para(5236(a,1),11502(a,1,2))].">
      <j1 rule="para" parents="5236 11502"/>
    </justification>
  </clause>

  <clause id="11504">
    <literal><![CDATA[
      (x * (y / x)) \ (y * z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,6041,a(flip),b,11503,a)].">
      <j1 rule="hyper" parents="58 6041 11503"/>
    </justification>
  </clause>

  <clause id="11505">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) = x * ((y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,11497,a(flip),b,5441,a)].">
      <j1 rule="hyper" parents="119 11497 5441"/>
    </justification>
  </clause>

  <clause id="11506">
    <literal><![CDATA[
      ((x * y) / x) \ ((y * x) \ z) = y \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,11497,a(flip),b,5442,a)].">
      <j1 rule="hyper" parents="116 11497 5442"/>
    </justification>
  </clause>

  <clause id="11507">
    <literal><![CDATA[
      ((x * y) \ z) * L(u,(y * x) \ z,K(y,x)) = K(y,x) * (((y * x) \ z) * u)
    ]]></literal>
    <justification jstring="[para(11497(a,1),90(a,1,1))].">
      <j1 rule="para" parents="11497 90"/>
    </justification>
  </clause>

  <clause id="11508">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x * ((y * x) \ z) = u
    ]]></literal>
    <justification jstring="[para(11497(a,1),5531(a,1,2))].">
      <j1 rule="para" parents="11497 5531"/>
    </justification>
  </clause>

  <clause id="11509">
    <literal><![CDATA[
      T((x * y) \ z,K(y,x)) = ((y * x) \ z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(11497(a,1),6524(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11497 6524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11510">
    <literal><![CDATA[
      K(x,y * ((z * x) \ u)) = K(x,y * ((x * z) \ u))
    ]]></literal>
    <justification jstring="[para(11497(a,1),7530(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11497 7530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11511">
    <literal><![CDATA[
      (x * y) * K(z,L(u,x,y)) = y * (T(x,y) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(11133,a,11471,a)].">
      <j1 rule="hyper" parents="11133 11471"/>
    </justification>
  </clause>

  <clause id="11513">
    <literal><![CDATA[
      (x * (T(y,x) * z)) / L(z,y,x) = y * x
    ]]></literal>
    <justification jstring="[hyper(201,a,11471,a(flip))].">
      <j1 rule="hyper" parents="201 11471"/>
    </justification>
  </clause>

  <clause id="11514">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * (K(x,T(y,z)) * u)) = L(u,K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7401(a,2),11471(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7401 11471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11515">
    <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(1776(a,1),11499(a,2,1))].">
      <j1 rule="para" parents="1776 11499"/>
    </justification>
  </clause>

  <clause id="11517">
    <literal><![CDATA[
      K(x \ y,x) * (y \ z) = (x * (y / x)) \ z
    ]]></literal>
    <justification jstring="[para(5(a,1),11504(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 11504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11518">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * ((y * x) \ z)) = w
    ]]></literal>
    <justification jstring="[para(11505(a,2),549(a,1))].">
      <j1 rule="para" parents="11505 549"/>
    </justification>
  </clause>

  <clause id="11519">
    <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(8130(a,1),11505(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8130 11505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11520">
    <literal><![CDATA[
      K(x,L(y,T(z,u),u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11475(a,1),7764(a,1,2))].">
      <j1 rule="para" parents="11475 7764"/>
    </justification>
  </clause>

  <clause id="11521">
    <literal><![CDATA[
      K(x,L(y,z / u,u)) = K(x,L(y,u \ z,u))
    ]]></literal>
    <justification jstring="[para(107(a,1),11520(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 11520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11522">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,x) \ z) = x \ ((y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10006,a,b,11506,a)].">
      <j1 rule="hyper" parents="58 10006 11506"/>
    </justification>
  </clause>

  <clause id="11523">
    <literal><![CDATA[
      L(x,y,T((y * x) \ z,K(x,y))) = L(x,y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(11509(a,2),11265(a,1,3))].">
      <j1 rule="para" parents="11509 11265"/>
    </justification>
  </clause>

  <clause id="11524">
    <literal><![CDATA[
      a(x,y,x) * (T(x * y,x) \ z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(9844,a,11522,a)].">
      <j1 rule="hyper" parents="9844 11522"/>
    </justification>
  </clause>

  <clause id="11525">
    <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),11493(a,2,2))].">
      <j1 rule="para" parents="101 11493"/>
    </justification>
  </clause>

  <clause id="11526">
    <literal><![CDATA[
      K(x,y / T(z \ 1,z * (x * y))) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(10605,a,11421,a),flip(a)].">
      <j1 rule="hyper" parents="10605 11421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11527">
    <literal><![CDATA[
      x * K(y,x \ ((x / z) * (u * z))) = (x / z) * (K(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7551,a(flip),b,11447,a),flip(a)].">
      <j1 rule="hyper" parents="58 7551 11447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11528">
    <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,11409,a)].">
      <j1 rule="hyper" parents="58 22 11409"/>
    </justification>
  </clause>

  <clause id="11529">
    <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(8271(a,1),11444(a,2,2,1))].">
      <j1 rule="para" parents="8271 11444"/>
    </justification>
  </clause>

  <clause id="11530">
    <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(3928(a,1),11454(a,2,2))].">
      <j1 rule="para" parents="3928 11454"/>
    </justification>
  </clause>

  <clause id="11531">
    <literal><![CDATA[
      K(x,y) * (((x * y) \ y) * z) = ((y * x) \ y) * z
    ]]></literal>
    <justification jstring="[para(10481(a,1),11507(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10481 11507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11532">
    <literal><![CDATA[
      a(x,y,z) = ((y * z) * x) \ (R(x,y,z) * T(y * z,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,9,a,b,11525,a)].">
      <j1 rule="hyper" parents="334 9 11525"/>
    </justification>
  </clause>

  <clause id="11533">
    <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,11525,a)].">
      <j1 rule="hyper" parents="119 9 11525"/>
    </justification>
  </clause>

  <clause id="11534">
    <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(334,a,4495,a(flip),b,11528,a),flip(a)].">
      <j1 rule="hyper" parents="334 4495 11528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11535">
    <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(334,a,8907,a(flip),b,11530,a),flip(a)].">
      <j1 rule="hyper" parents="334 8907 11530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11536">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,y \ ((1 / z) \ y))) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8499,a(flip),b,11535,a),flip(a)].">
      <j1 rule="hyper" parents="334 8499 11535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11537">
    <literal><![CDATA[
      K(x,T(x \ y,z)) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(10638,a,11536,a),flip(a)].">
      <j1 rule="hyper" parents="10638 11536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11538">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,u)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,10618,a,b,11537,a)].">
      <j1 rule="hyper" parents="334 10618 11537"/>
    </justification>
  </clause>

  <clause id="11539">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) = K(z,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,10581,a,b,11537,a)].">
      <j1 rule="hyper" parents="334 10581 11537"/>
    </justification>
  </clause>

  <clause id="11540">
    <literal><![CDATA[
      K(x,y \ (x \ (z * y))) = K(x,T(x \ z,y))
    ]]></literal>
    <justification jstring="[hyper(10678,a,11537,a(flip))].">
      <j1 rule="hyper" parents="10678 11537"/>
    </justification>
  </clause>

  <clause id="11541">
    <literal><![CDATA[
      K(x,x \ T(x * y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),11537(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 11537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11542">
    <literal><![CDATA[
      K(x,x \ T(y,z)) \ 1 = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[para(11537(a,1),7441(a,1,1))].">
      <j1 rule="para" parents="11537 7441"/>
    </justification>
  </clause>

  <clause id="11543">
    <literal><![CDATA[
      K(x,T(y,z) / x) = K(x,T(y / x,z))
    ]]></literal>
    <justification jstring="[para(4816(a,1),11541(a,1,2))].">
      <j1 rule="para" parents="4816 11541"/>
    </justification>
  </clause>

  <clause id="11544">
    <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(3064(a,1),11543(a,2,2,1))].">
      <j1 rule="para" parents="3064 11543"/>
    </justification>
  </clause>

  <clause id="11545">
    <literal><![CDATA[
      K(x,T(x \ y,z)) * (K(y,z) * x) = T(K(y,z) * x,x \ y)
    ]]></literal>
    <justification jstring="[para(11539(a,1),5034(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11539 5034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11546">
    <literal><![CDATA[
      K(x,T(x \ y,y \ (x * z))) = K(x,(y \ (x * z)) \ z)
    ]]></literal>
    <justification jstring="[para(66(a,1),11540(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="66 11540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11547">
    <literal><![CDATA[
      K(x \ T(y,z),x) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(5241,a,11542,a)].">
      <j1 rule="hyper" parents="5241 11542"/>
    </justification>
  </clause>

  <clause id="11548">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,u)) = K(x,T(x \ y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(334,a,8499,a,b,11538,a),flip(a)].">
      <j1 rule="hyper" parents="334 8499 11538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11550">
    <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(11548(a,2),8552(a,1))].">
      <j1 rule="para" parents="11548 8552"/>
    </justification>
  </clause>

  <clause id="11551">
    <literal><![CDATA[
      K(x,T(x \ y,y \ z)) = K(x,(y \ (x * z)) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9317,a(flip),b,11546,a)].">
      <j1 rule="hyper" parents="58 9317 11546"/>
    </justification>
  </clause>

  <clause id="11552">
    <literal><![CDATA[
      K(x,(y \ (x * z)) \ z) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(9019,a,11551,a),flip(a)].">
      <j1 rule="hyper" parents="9019 11551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11553">
    <literal><![CDATA[
      K(x,x \ T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(2696(a,1),11550(a,1,2))].">
      <j1 rule="para" parents="2696 11550"/>
    </justification>
  </clause>

  <clause id="11554">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,T(z \ x,y)) = u
    ]]></literal>
    <justification jstring="[para(10581(a,2),11553(a,1))].">
      <j1 rule="para" parents="10581 11553"/>
    </justification>
  </clause>

  <clause id="11555">
    <literal><![CDATA[
      T(K(x,y) * z,z \ x) = T(z,z \ x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9619,a,11545,a),flip(a)].">
      <j1 rule="hyper" parents="9619 11545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11556">
    <literal><![CDATA[
      (x \ y) * T(K(y,z) * x,x \ y) = (y / x) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(11555(a,2),4919(a,1,2))].">
      <j1 rule="para" parents="11555 4919"/>
    </justification>
  </clause>

  <clause id="11557">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ x) = (x / z) * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(294,a,11556,a)].">
      <j1 rule="hyper" parents="294 11556"/>
    </justification>
  </clause>

  <clause id="11558">
    <literal><![CDATA[
      ((x / y) * (y * K(x,z))) / T(x,z) = a(K(x,z),y,y \ x)
    ]]></literal>
    <justification jstring="[para(11557(a,1),10503(a,1,1))].">
      <j1 rule="para" parents="11557 10503"/>
    </justification>
  </clause>

  <clause id="11559">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = T(a(K(x,z),y,y \ x),x)
    ]]></literal>
    <justification jstring="[para(11558(a,1),11368(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11558 11368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11560">
    <literal><![CDATA[
      K(x \ 1,T(y * x,z)) = K(x \ 1,T(y,z) * x)
    ]]></literal>
    <justification jstring="[para(3065(a,1),11544(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3065 11544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11561">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = a(K(x,z),y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,9455,a(flip),b,11559,a),flip(a)].">
      <j1 rule="hyper" parents="334 9455 11559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11562">
    <literal><![CDATA[
      a(K(x,y),z,z \ x) = a(x / z,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5208,a(flip),b,11561,a),flip(a)].">
      <j1 rule="hyper" parents="58 5208 11561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11563">
    <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),11562(a,2,1))].">
      <j1 rule="para" parents="6 11562"/>
    </justification>
  </clause>

  <clause id="11564">
    <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),11563(a,1,3))].">
      <j1 rule="para" parents="17 11563"/>
    </justification>
  </clause>

  <clause id="11565">
    <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(11564(a,1),5126(a,1,2))].">
      <j1 rule="para" parents="11564 5126"/>
    </justification>
  </clause>

  <clause id="11566">
    <literal><![CDATA[
      (K(x * y,z) * y) * T(x,y) = x * (y * K(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6251,a(flip),b,11565,a),flip(a)].">
      <j1 rule="hyper" parents="58 6251 11565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11567">
    <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(11566(a,2),38(a,1))].">
      <j1 rule="para" parents="11566 38"/>
    </justification>
  </clause>

  <clause id="11568">
    <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(334,a,22,a,b,11534,a),flip(a)].">
      <j1 rule="hyper" parents="334 22 11534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11569">
    <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(11430(a,1),11568(a,1,1))].">
      <j1 rule="para" parents="11430 11568"/>
    </justification>
  </clause>

  <clause id="11570">
    <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),11569(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 11569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11571">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(614,a,11570,a),flip(a)].">
      <j1 rule="hyper" parents="614 11570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11573">
    <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(11570(a,1),5491(a,1,2,1))].">
      <j1 rule="para" parents="11570 5491"/>
    </justification>
  </clause>

  <clause id="11574">
    <literal><![CDATA[
      R((x \ y) \ y,z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,855,a(flip),b,11571,a)].">
      <j1 rule="hyper" parents="58 855 11571"/>
    </justification>
  </clause>

  <clause id="11575">
    <literal><![CDATA[
      (R(x,y,z) \ (x * u)) \ (x * u) = R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11571(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 11571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11576">
    <literal><![CDATA[
      (R(x / y,z,u) \ x) \ x = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(661(a,1),11571(a,1,1)),flip(a)].">
      <j1 rule="para" parents="661 11571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11581">
    <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(5788(a,1),11574(a,2,1))].">
      <j1 rule="para" parents="5788 11574"/>
    </justification>
  </clause>

  <clause id="11583">
    <literal><![CDATA[
      K(x,R(x / y,z,u) \ w) = K(x,R(y \ x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(11576(a,1),7146(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11576 7146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11584">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = (x * u) \ (x * (R(x,y,z) * u))
    ]]></literal>
    <justification jstring="[para(1370(a,1),11575(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1370 11575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11585">
    <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(334,a,239,a(flip),b,11584,a),flip(a)].">
      <j1 rule="hyper" parents="334 239 11584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11586">
    <literal><![CDATA[
      T(x,R(x,y,z) * u) = T(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(1012,a,11585,a),flip(a)].">
      <j1 rule="hyper" parents="1012 11585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11587">
    <literal><![CDATA[
      T(x,x * (R(x,y,z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),11586(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 11586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11589">
    <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(11586(a,1),5076(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11586 5076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11590">
    <literal><![CDATA[
      T(x,x * ((x \ y) * z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(517(a,1),11587(a,1,2,2))].">
      <j1 rule="para" parents="517 11587"/>
    </justification>
  </clause>

  <clause id="11591">
    <literal><![CDATA[
      T(x,y * K(x \ y,z)) = T(x,x * T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(5020(a,2),11590(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5020 11590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11592">
    <literal><![CDATA[
      K(R(x,y,z) * u,R(x,w,v5)) = K(x * u,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(334,a,5076,a(flip),b,11589,a),flip(a)].">
      <j1 rule="hyper" parents="334 5076 11589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11593">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(7673,a,11592,a)].">
      <j1 rule="hyper" parents="7673 11592"/>
    </justification>
  </clause>

  <clause id="11594">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,z,u)) = K(x * y,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,10139,a,b,11593,a),flip(a)].">
      <j1 rule="hyper" parents="334 10139 11593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11595">
    <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(11594(a,1),10754(a,1,1,2))].">
      <j1 rule="para" parents="11594 10754"/>
    </justification>
  </clause>

  <clause id="11596">
    <literal><![CDATA[
      K((L(x,y,x) * y) \ z,y * x) * (z * u) = (((y * x) \ z) * (y * x)) * u
    ]]></literal>
    <justification jstring="[para(4564(a,1),11428(a,1,1,1,1))].">
      <j1 rule="para" parents="4564 11428"/>
    </justification>
  </clause>

  <clause id="11597">
    <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(5047(a,1),11469(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5047 11469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11598">
    <literal><![CDATA[
      K(R(x,y,z) \ u,R(x,y,z)) = K(x \ u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(6250,a,11573,a),flip(a)].">
      <j1 rule="hyper" parents="6250 11573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11599">
    <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(11598(a,1),4980(a,1,1,2))].">
      <j1 rule="para" parents="11598 4980"/>
    </justification>
  </clause>

  <clause id="11600">
    <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(5781(a,1),11595(a,1,1))].">
      <j1 rule="para" parents="5781 11595"/>
    </justification>
  </clause>

  <clause id="11601">
    <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(5532(a,1),11600(a,1,1,1,2))].">
      <j1 rule="para" parents="5532 11600"/>
    </justification>
  </clause>

  <clause id="11602">
    <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,11601,a)].">
      <j1 rule="hyper" parents="58 22 11601"/>
    </justification>
  </clause>

  <clause id="11603">
    <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(5467(a,1),11602(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5467 11602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11604">
    <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,10751,a(flip),b,11603,a)].">
      <j1 rule="hyper" parents="58 10751 11603"/>
    </justification>
  </clause>

  <clause id="11605">
    <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(11603(a,1),10750(a,1,2))].">
      <j1 rule="para" parents="11603 10750"/>
    </justification>
  </clause>

  <clause id="11606">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,11604,a)].">
      <j1 rule="hyper" parents="145 11604"/>
    </justification>
  </clause>

  <clause id="11607">
    <literal><![CDATA[
      (R(x,y,R(x,z,u)) * z) * u = R(R(x,y,x),z,u) * (z * u)
    ]]></literal>
    <justification jstring="[para(11604(a,1),526(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11604 526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11609">
    <literal><![CDATA[
      K(x,R(y,z,R(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11606(a,2),7315(a,1,2))].">
      <j1 rule="para" parents="11606 7315"/>
    </justification>
  </clause>

  <clause id="11610">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,R(z,u,R(T(z,y),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(8335,a,11609,a),flip(a)].">
      <j1 rule="hyper" parents="8335 11609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11611">
    <literal><![CDATA[
      K(x,R(y,z,R(T(y,u),w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8324,a,11610,a),flip(a)].">
      <j1 rule="hyper" parents="8324 11610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11613">
    <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(11611(a,1),10535(a,1,1))].">
      <j1 rule="para" parents="11611 10535"/>
    </justification>
  </clause>

  <clause id="11614">
    <literal><![CDATA[
      (R(x,y,R(x,z,u)) * z) * u = (R(x,y,x) * z) * u
    ]]></literal>
    <justification jstring="[hyper(334,a,101,a(flip),b,11607,a),flip(a)].">
      <j1 rule="hyper" parents="334 101 11607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11615">
    <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(10500(a,1),11614(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10500 11614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11616">
    <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(5449,a,11613,a)].">
      <j1 rule="hyper" parents="5449 11613"/>
    </justification>
  </clause>

  <clause id="11617">
    <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(10500(a,1),11613(a,1,2,2))].">
      <j1 rule="para" parents="10500 11613"/>
    </justification>
  </clause>

  <clause id="11618">
    <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(10244,a,11616,a)].">
      <j1 rule="hyper" parents="10244 11616"/>
    </justification>
  </clause>

  <clause id="11619">
    <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(11616(a,1),10244(a,1))].">
      <j1 rule="para" parents="11616 10244"/>
    </justification>
  </clause>

  <clause id="11620">
    <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(10248(a,1),11617(a,1,2))].">
      <j1 rule="para" parents="10248 11617"/>
    </justification>
  </clause>

  <clause id="11621">
    <literal><![CDATA[
      x \ R(x,y,R(T(x,z),u,w)) = a(x,y,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(5411,a,11620,a),flip(a)].">
      <j1 rule="hyper" parents="5411 11620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11622">
    <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(11620(a,1),5410(a,1)),flip(b)].">
      <j1 rule="para" parents="11620 5410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11623">
    <literal><![CDATA[
      a(T(x,y),z,R(T(x,y),u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(11619,a,11621,a)].">
      <j1 rule="hyper" parents="11619 11621"/>
    </justification>
  </clause>

  <clause id="11626">
    <literal><![CDATA[
      a(R(x,y,z),u,x) \ 1 = a(x,u,R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(11623(a,1),10953(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11623 10953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11627">
    <literal><![CDATA[
      a(R(x,y,z),u,x) = a(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(43,a,11626,a)].">
      <j1 rule="hyper" parents="43 11626"/>
    </justification>
  </clause>

  <clause id="11629">
    <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(334,a,7150,a,b,11627,a)].">
      <j1 rule="hyper" parents="334 7150 11627"/>
    </justification>
  </clause>

  <clause id="11631">
    <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(11618(a,2),11622(a,1))].">
      <j1 rule="para" parents="11618 11622"/>
    </justification>
  </clause>

  <clause id="11632">
    <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(334,a,7403,a(flip),b,11388,a),flip(a)].">
      <j1 rule="hyper" parents="334 7403 11388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11633">
    <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(334,a,7026,a(flip),b,11581,a),flip(a)].">
      <j1 rule="hyper" parents="334 7026 11581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11634">
    <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(7024(a,1),11633(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7024 11633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11635">
    <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(11634(a,1),9416(a,1,2))].">
      <j1 rule="para" parents="11634 9416"/>
    </justification>
  </clause>

  <clause id="11636">
    <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(5781(a,1),11599(a,1,1))].">
      <j1 rule="para" parents="5781 11599"/>
    </justification>
  </clause>

  <clause id="11637">
    <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,11636,a)].">
      <j1 rule="hyper" parents="58 22 11636"/>
    </justification>
  </clause>

  <clause id="11638">
    <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(4980(a,1),11637(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4980 11637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11639">
    <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(334,a,24,a(flip),b,11638,a),flip(a)].">
      <j1 rule="hyper" parents="334 24 11638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11640">
    <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(11639(a,1),1408(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11639 1408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11641">
    <literal><![CDATA[
      K(T(x,y * z),u / ((y * T(x,y * z)) * z)) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(334,a,8007,a(flip),b,11632,a),flip(a)].">
      <j1 rule="hyper" parents="334 8007 11632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11642">
    <literal><![CDATA[
      K(x,T(y / ((z * T(x,z * u)) * u),z * u)) = K(x,(z * u) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(7970,a,11641,a)].">
      <j1 rule="hyper" parents="7970 11641"/>
    </justification>
  </clause>

  <clause id="11643">
    <literal><![CDATA[
      K(x,T(y / ((z * x) * u),z * u)) = K(x,(z * u) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,10967,a(flip),b,11642,a)].">
      <j1 rule="hyper" parents="58 10967 11642"/>
    </justification>
  </clause>

  <clause id="11645">
    <literal><![CDATA[
      K(x,((y * x) * z) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9505,a(flip),b,11643,a)].">
      <j1 rule="hyper" parents="58 9505 11643"/>
    </justification>
  </clause>

  <clause id="11646">
    <literal><![CDATA[
      K(x,((x \ y) * z) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(9323,a,11645,a),flip(a)].">
      <j1 rule="hyper" parents="9323 11645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11647">
    <literal><![CDATA[
      K(x,((y * x) * (y \ 1)) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(164(a,1),11645(a,2,2))].">
      <j1 rule="para" parents="164 11645"/>
    </justification>
  </clause>

  <clause id="11648">
    <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(11645(a,1),6900(a,1))].">
      <j1 rule="para" parents="11645 6900"/>
    </justification>
  </clause>

  <clause id="11649">
    <literal><![CDATA[
      K(x,a(x,y,y \ 1) \ z) = K(x,x \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9964,a(flip),b,11647,a)].">
      <j1 rule="hyper" parents="58 9964 11647"/>
    </justification>
  </clause>

  <clause id="11651">
    <literal><![CDATA[
      K(x,a(x,y,y \ 1) \ z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11649(a,2,2))].">
      <j1 rule="para" parents="4 11649"/>
    </justification>
  </clause>

  <clause id="11652">
    <literal><![CDATA[
      K(x,y \ R(x,z,z \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9603,a(flip),b,11651,a),flip(a)].">
      <j1 rule="hyper" parents="58 9603 11651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11653">
    <literal><![CDATA[
      K(x,y \ ((z * x) * (z \ 1))) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(8868,a,11652,a)].">
      <j1 rule="hyper" parents="8868 11652"/>
    </justification>
  </clause>

  <clause id="11655">
    <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,9774,a(flip),b,11653,a)].">
      <j1 rule="hyper" parents="58 9774 11653"/>
    </justification>
  </clause>

  <clause id="11656">
    <literal><![CDATA[
      K(x,((x \ y) * z) \ 1) = K(x,(y * z) \ x)
    ]]></literal>
    <justification jstring="[para(61(a,1),11646(a,1,2,2))].">
      <j1 rule="para" parents="61 11646"/>
    </justification>
  </clause>

  <clause id="11657">
    <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),11490(a,1,1))].">
      <j1 rule="para" parents="90 11490"/>
    </justification>
  </clause>

  <clause id="11658">
    <literal><![CDATA[
      (x * (y * z)) \ (z * T(x * y,L(z,y,x))) = a(x,y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(7950(a,1),11657(a,1,2))].">
      <j1 rule="para" parents="7950 11657"/>
    </justification>
  </clause>

  <clause id="11659">
    <literal><![CDATA[
      (x / (1 / y)) * (1 / T(y,y \ (x / (1 / y)))) = (T(x,y) / (1 / y)) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(581,a,11515,a)].">
      <j1 rule="hyper" parents="581 11515"/>
    </justification>
  </clause>

  <clause id="11661">
    <literal><![CDATA[
      (x / (1 / y)) * (1 / T(y,(x / (1 / y)) / y)) = (T(x,y) / (1 / y)) * (1 / y)
    ]]></literal>
    <justification jstring="[para(4495(a,2),11659(a,1,2,2))].">
      <j1 rule="para" parents="4495 11659"/>
    </justification>
  </clause>

  <clause id="11662">
    <literal><![CDATA[
      (T(x,y) / (1 / y)) * (1 / y) = (x / (1 / y)) * (1 / T(y,x))
    ]]></literal>
    <justification jstring="[para(6601(a,1),11661(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6601 11661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11663">
    <literal><![CDATA[
      T(x,y) / (1 / T(y,x)) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(424,a,11662,a)].">
      <j1 rule="hyper" parents="424 11662"/>
    </justification>
  </clause>

  <clause id="11664">
    <literal><![CDATA[
      T(x,y / x) / (1 / (x \ y)) = x / (1 / (y / x))
    ]]></literal>
    <justification jstring="[para(107(a,1),11663(a,1,2,2))].">
      <j1 rule="para" parents="107 11663"/>
    </justification>
  </clause>

  <clause id="11665">
    <literal><![CDATA[
      (x / (1 / (x \ y))) / x = x \ (x / (1 / (y / x)))
    ]]></literal>
    <justification jstring="[para(11664(a,1),4541(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11664 4541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11666">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) = x \ (x / ((y / x) \ 1))
    ]]></literal>
    <justification jstring="[para(11665(a,2),2981(a,1,1))].">
      <j1 rule="para" parents="11665 2981"/>
    </justification>
  </clause>

  <clause id="11667">
    <literal><![CDATA[
      x * ((x / ((x \ y) \ 1)) / x) = x / ((y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(10978,a,11666,a)].">
      <j1 rule="hyper" parents="10978 11666"/>
    </justification>
  </clause>

  <clause id="11668">
    <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(4775(a,1),11060(a,1,1))].">
      <j1 rule="para" parents="4775 11060"/>
    </justification>
  </clause>

  <clause id="11669">
    <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(5583(a,1),11278(a,2,2,2,2))].">
      <j1 rule="para" parents="5583 11278"/>
    </justification>
  </clause>

  <clause id="11670">
    <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,10986,a(flip),b,11355,a)].">
      <j1 rule="hyper" parents="58 10986 11355"/>
    </justification>
  </clause>

  <clause id="11671">
    <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(8879(a,1),11670(a,1,2,2))].">
      <j1 rule="para" parents="8879 11670"/>
    </justification>
  </clause>

  <clause id="11672">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ K(u,x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7842,a(flip),b,11671,a),flip(a)].">
      <j1 rule="hyper" parents="58 7842 11671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11674">
    <literal><![CDATA[
      K(x,y * (z \ K(u,x))) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,5842,a(flip),b,11672,a)].">
      <j1 rule="hyper" parents="58 5842 11672"/>
    </justification>
  </clause>

  <clause id="11675">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,K(z,u)) = K(z,K(u,x * (y \ K(w,u))))
    ]]></literal>
    <justification jstring="[para(11674(a,2),8454(a,2,2))].">
      <j1 rule="para" parents="11674 8454"/>
    </justification>
  </clause>

  <clause id="11676">
    <literal><![CDATA[
      K(x,K(y,z * (u \ K(w,y)))) = K(x,K(y,z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(8467,a,11675,a),flip(a)].">
      <j1 rule="hyper" parents="8467 11675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11677">
    <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(7501(a,1),11676(a,1,2))].">
      <j1 rule="para" parents="7501 11676"/>
    </justification>
  </clause>

  <clause id="11678">
    <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(269(a,1),11677(a,2,2,2))].">
      <j1 rule="para" parents="269 11677"/>
    </justification>
  </clause>

  <clause id="11679">
    <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,9346,a,b,11678,a)].">
      <j1 rule="hyper" parents="58 9346 11678"/>
    </justification>
  </clause>

  <clause id="11680">
    <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(334,a,8048,a,b,11679,a),flip(a)].">
      <j1 rule="hyper" parents="334 8048 11679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11681">
    <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(2493(a,1),11364(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2493 11364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11682">
    <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(6524(a,1),11681(a,2,1))].">
      <j1 rule="para" parents="6524 11681"/>
    </justification>
  </clause>

  <clause id="11683">
    <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(334,a,9105,a,b,11682,a),flip(a)].">
      <j1 rule="hyper" parents="334 9105 11682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11684">
    <literal><![CDATA[
      (K(x,y) \ z) * (K(x,y) * K(u,x)) = T(z * K(u,x),K(x,y))
    ]]></literal>
    <justification jstring="[para(2497(a,1),11683(a,1,1,1))].">
      <j1 rule="para" parents="2497 11683"/>
    </justification>
  </clause>

  <clause id="11685">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * K(u,y)) = T(z * K(u,y),K(y,x))
    ]]></literal>
    <justification jstring="[para(5391(a,1),11684(a,1,1))].">
      <j1 rule="para" parents="5391 11684"/>
    </justification>
  </clause>

  <clause id="11686">
    <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,10306,a(flip),b,11685,a),flip(a)].">
      <j1 rule="hyper" parents="58 10306 11685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11687">
    <literal><![CDATA[
      x * K(K(y,z) * K(z,u),x) = T(T(x,K(z,u)),K(z,y))
    ]]></literal>
    <justification jstring="[para(8107(a,1),11686(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8107 11686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11688">
    <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,10287,a(flip),b,11365,a),flip(a)].">
      <j1 rule="hyper" parents="58 10287 11365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11689">
    <literal><![CDATA[
      K(x,y * K(((z \ 1) \ 1) \ K(u,x),(z \ 1) \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,7494,a(flip),b,11369,a),flip(a)].">
      <j1 rule="hyper" parents="334 7494 11369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11691">
    <literal><![CDATA[
      K(x,y * K(z \ K(u,x),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3257(a,1),11689(a,1,2,2))].">
      <j1 rule="para" parents="3257 11689"/>
    </justification>
  </clause>

  <clause id="11693">
    <literal><![CDATA[
      K(x,y * (K(z,x) / u)) = K(x,y * (u \ K(z,x)))
    ]]></literal>
    <justification jstring="[para(6747(a,1),11691(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6747 11691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11694">
    <literal><![CDATA[
      K(x,y * (K(z,x) / u)) = K(x,y * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(334,a,11674,a(flip),b,11693,a),flip(a)].">
      <j1 rule="hyper" parents="334 11674 11693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11696">
    <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),11370(a,2,2,1,2))].">
      <j1 rule="para" parents="72 11370"/>
    </justification>
  </clause>

  <clause id="11698">
    <literal><![CDATA[
      K(x,((1 / (K(y,x \ z) / y)) * z) \ (u * x)) = K(x,(((z \ x) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(6423(a,1),11696(a,1,2,1,1,2,1))].">
      <j1 rule="para" parents="6423 11696"/>
    </justification>
  </clause>

  <clause id="11699">
    <literal><![CDATA[
      K(x,(((y \ x) \ 1) * z) \ u) = K(x,((x \ y) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,10084,a(flip),b,11698,a),flip(a)].">
      <j1 rule="hyper" parents="58 10084 11698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11700">
    <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(4690(a,1),11635(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4690 11635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11701">
    <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(8170(a,1),11668(a,1,1,2))].">
      <j1 rule="para" parents="8170 11668"/>
    </justification>
  </clause>

  <clause id="11702">
    <literal><![CDATA[
      R(K(x,L(y,z,L(y,u,w))),L(y,u,w),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9028,a,11701,a),flip(a)].">
      <j1 rule="hyper" parents="9028 11701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11703">
    <literal><![CDATA[
      R(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(9062(a,1),11702(a,1,1))].">
      <j1 rule="para" parents="9062 11702"/>
    </justification>
  </clause>

  <clause id="11704">
    <literal><![CDATA[
      K((L(x,y,z) * u) / w,x) = K(L(x,y,z) / (w / u),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7062,a(flip),b,11703,a)].">
      <j1 rule="hyper" parents="58 7062 11703"/>
    </justification>
  </clause>

  <clause id="11706">
    <literal><![CDATA[
      K((L(x,y,z) * u) / w,x) = K((w / u) \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(334,a,6648,a(flip),b,11704,a),flip(a)].">
      <j1 rule="hyper" parents="334 6648 11704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11707">
    <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,10943,a,b,11706,a)].">
      <j1 rule="hyper" parents="58 10943 11706"/>
    </justification>
  </clause>

  <clause id="11708">
    <literal><![CDATA[
      K(x / (L(y,z,u) \ w),y) = K((w / x) \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(8537,a,11707,a)].">
      <j1 rule="hyper" parents="8537 11707"/>
    </justification>
  </clause>

  <clause id="11709">
    <literal><![CDATA[
      K(x / (L(y,z,u) \ w),y) = K((w / x) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,11072,a(flip),b,11708,a),flip(a)].">
      <j1 rule="hyper" parents="334 11072 11708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11711">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (T(y / ((1 / x) \ 1),z) \ y)))) = (1 / x) \ K(z,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(2497(a,1),11669(a,2,2))].">
      <j1 rule="para" parents="2497 11669"/>
    </justification>
  </clause>

  <clause id="11712">
    <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),11711(a,1,2,2,2,2,1,1,2))].">
      <j1 rule="para" parents="75 11711"/>
    </justification>
  </clause>

  <clause id="11713">
    <literal><![CDATA[
      (1 / x) \ K(y,(x \ 1) * z) = x * (1 / (1 / K(y,x \ z)))
    ]]></literal>
    <justification jstring="[para(7822(a,1),11712(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7822 11712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11714">
    <literal><![CDATA[
      (1 / x) \ K(y,(x \ 1) * z) = x * K(y,x \ z)
    ]]></literal>
    <justification jstring="[para(2497(a,1),11713(a,2,2))].">
      <j1 rule="para" parents="2497 11713"/>
    </justification>
  </clause>

  <clause id="11715">
    <literal><![CDATA[
      (1 / x) \ K(y,(x \ 1) * z) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ z) = u
    ]]></literal>
    <justification jstring="[para(11714(a,2),38(a,1))].">
      <j1 rule="para" parents="11714 38"/>
    </justification>
  </clause>

  <clause id="11716">
    <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(7403(a,1),11688(a,2,2,1))].">
      <j1 rule="para" parents="7403 11688"/>
    </justification>
  </clause>

  <clause id="11717">
    <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),11716(a,2,2))].">
      <j1 rule="para" parents="3 11716"/>
    </justification>
  </clause>

  <clause id="11718">
    <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(4576(a,1),4587(a,2,2,1,1))].">
      <j1 rule="para" parents="4576 4587"/>
    </justification>
  </clause>

  <clause id="11719">
    <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,11718,a)].">
      <j1 rule="hyper" parents="123 11718"/>
    </justification>
  </clause>

  <clause id="11720">
    <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(5157(a,1),5268(a,1,1,1,1))].">
      <j1 rule="para" parents="5157 5268"/>
    </justification>
  </clause>

  <clause id="11721">
    <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(7156(a,1),11720(a,1,1))].">
      <j1 rule="para" parents="7156 11720"/>
    </justification>
  </clause>

  <clause id="11722">
    <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(334,a,5640,a(flip),b,11721,a),flip(a)].">
      <j1 rule="hyper" parents="334 5640 11721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11723">
    <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),11722(a,1,1,2))].">
      <j1 rule="para" parents="25 11722"/>
    </justification>
  </clause>

  <clause id="11724">
    <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,8221,a(flip),b,11723,a)].">
      <j1 rule="hyper" parents="58 8221 11723"/>
    </justification>
  </clause>

  <clause id="11725">
    <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,8523,a(flip),b,11724,a)].">
      <j1 rule="hyper" parents="58 8523 11724"/>
    </justification>
  </clause>

  <clause id="11726">
    <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(11725(a,1),5374(a,1,2,2))].">
      <j1 rule="para" parents="11725 5374"/>
    </justification>
  </clause>

  <clause id="11727">
    <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(7514(a,1),11726(a,1,1))].">
      <j1 rule="para" parents="7514 11726"/>
    </justification>
  </clause>

  <clause id="11728">
    <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(5045(a,1),6837(a,2,2))].">
      <j1 rule="para" parents="5045 6837"/>
    </justification>
  </clause>

  <clause id="11729">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),x \ y,T(x,x \ y)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,6563,a(flip),b,11728,a),flip(a)].">
      <j1 rule="hyper" parents="334 6563 11728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11731">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),y / x,x) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4926,a(flip),b,11729,a)].">
      <j1 rule="hyper" parents="58 4926 11729"/>
    </justification>
  </clause>

  <clause id="11732">
    <literal><![CDATA[
      K((x \ 1) \ (x \ y),L(z,y / x,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(11132,a,11731,a)].">
      <j1 rule="hyper" parents="11132 11731"/>
    </justification>
  </clause>

  <clause id="11733">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ L(z,x / y,y))) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11231,a(flip),b,11732,a)].">
      <j1 rule="hyper" parents="58 11231 11732"/>
    </justification>
  </clause>

  <clause id="11734">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),x / y,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1758(a,2),11733(a,1,2))].">
      <j1 rule="para" parents="1758 11733"/>
    </justification>
  </clause>

  <clause id="11735">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),y \ x,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11521,a(flip),b,11734,a)].">
      <j1 rule="hyper" parents="58 11521 11734"/>
    </justification>
  </clause>

  <clause id="11736">
    <literal><![CDATA[
      K(R(x \ y,z,u),w \ (y / x)) = K(R(x \ y,z,u),w \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(5790,a,8972,a),flip(a)].">
      <j1 rule="hyper" parents="5790 8972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11737">
    <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(5202(a,1),11736(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5202 11736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11738">
    <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(1828(a,2),9192(a,1,2,2))].">
      <j1 rule="para" parents="1828 9192"/>
    </justification>
  </clause>

  <clause id="11739">
    <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(3705(a,1),10065(a,1,1))].">
      <j1 rule="para" parents="3705 10065"/>
    </justification>
  </clause>

  <clause id="11740">
    <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),10110(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6 10110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11742">
    <literal><![CDATA[
      (K(x,y) * K(z,y)) * u = K(z,y) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(10295(a,1),11740(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10295 11740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11744">
    <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(11742(a,1),5972(a,1,2,2))].">
      <j1 rule="para" parents="11742 5972"/>
    </justification>
  </clause>

  <clause id="11745">
    <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(5423(a,1),11744(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5423 11744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11746">
    <literal><![CDATA[
      L(x,T(y,z) \ ((u * y) / u),T(y,z)) = K(y,u) * (K(u,y) * x)
    ]]></literal>
    <justification jstring="[hyper(334,a,5364,a(flip),b,11745,a),flip(a)].">
      <j1 rule="hyper" parents="334 5364 11745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11748">
    <literal><![CDATA[
      L(x,T(y,z) \ ((u * y) / u),T(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(334,a,5394,a(flip),b,11746,a),flip(a)].">
      <j1 rule="hyper" parents="334 5394 11746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11750">
    <literal><![CDATA[
      L(x,K(y,z) * K(u,z),T(z,u)) = x
    ]]></literal>
    <justification jstring="[para(5971(a,1),11748(a,1,2))].">
      <j1 rule="para" parents="5971 11748"/>
    </justification>
  </clause>

  <clause id="11751">
    <literal><![CDATA[
      L(x,K(y,z) * K(u,z),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(11750(a,1),45(a,2))].">
      <j1 rule="para" parents="11750 45"/>
    </justification>
  </clause>

  <clause id="11752">
    <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(9167(a,1),10705(a,1,1,1))].">
      <j1 rule="para" parents="9167 10705"/>
    </justification>
  </clause>

  <clause id="11753">
    <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(526(a,1),11752(a,1,1))].">
      <j1 rule="para" parents="526 11752"/>
    </justification>
  </clause>

  <clause id="11754">
    <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(11606(a,1),11753(a,1,1,1,1))].">
      <j1 rule="para" parents="11606 11753"/>
    </justification>
  </clause>

  <clause id="11755">
    <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(11754(a,1),9836(a,1))].">
      <j1 rule="para" parents="11754 9836"/>
    </justification>
  </clause>

  <clause id="11757">
    <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(334,a,1408,a(flip),b,11640,a),flip(a)].">
      <j1 rule="hyper" parents="334 1408 11640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11758">
    <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),11757(a,2,3))].">
      <j1 rule="para" parents="22 11757"/>
    </justification>
  </clause>

  <clause id="11759">
    <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),11738(a,1,2)),flip(a)].">
      <j1 rule="para" parents="90 11738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11760">
    <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(10929(a,1),11739(a,1,1))].">
      <j1 rule="para" parents="10929 11739"/>
    </justification>
  </clause>

  <clause id="11761">
    <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(5702(a,1),11760(a,1,2))].">
      <j1 rule="para" parents="5702 11760"/>
    </justification>
  </clause>

  <clause id="11762">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a((y / x) \ 1,z,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[para(8527(a,1),11761(a,1,2))].">
      <j1 rule="para" parents="8527 11761"/>
    </justification>
  </clause>

  <clause id="11763">
    <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(3781(a,2),4201(a,1,1))].">
      <j1 rule="para" parents="3781 4201"/>
    </justification>
  </clause>

  <clause id="11764">
    <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(1241(a,1),6106(a,2,1))].">
      <j1 rule="para" parents="1241 6106"/>
    </justification>
  </clause>

  <clause id="11765">
    <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,11764,a(flip),b,6107,a),flip(a)].">
      <j1 rule="hyper" parents="58 11764 6107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11766">
    <literal><![CDATA[
      T(x \ L(x,y,z),u * x) = T(x \ L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[para(1241(a,1),11765(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1241 11765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11767">
    <literal><![CDATA[
      x \ ((x / ((y * z) / y)) * ((z \ 1) * ((y * z) / y))) = T(x \ (x / z),(y * z) / y)
    ]]></literal>
    <justification jstring="[para(5023(a,1),6696(a,1,2,2,1))].">
      <j1 rule="para" parents="5023 6696"/>
    </justification>
  </clause>

  <clause id="11769">
    <literal><![CDATA[
      x \ ((x / ((y * z) / y)) * ((T(z,y) \ 1) * z)) = T(x \ (x / z),(y * z) / y)
    ]]></literal>
    <justification jstring="[para(5923(a,1),11767(a,1,2,2))].">
      <j1 rule="para" parents="5923 11767"/>
    </justification>
  </clause>

  <clause id="11770">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * ((T(y,x) \ 1) * y) = T(1 \ (1 / y),(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(166,a,11769,a)].">
      <j1 rule="hyper" parents="166 11769"/>
    </justification>
  </clause>

  <clause id="11771">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * ((T(y,x) \ 1) * y) = T(1 / y,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(60(a,1),11770(a,2,1))].">
      <j1 rule="para" parents="60 11770"/>
    </justification>
  </clause>

  <clause id="11772">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ (y \ 1) = (T(y,x) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(116,a,2577,a(flip),b,11771,a)].">
      <j1 rule="hyper" parents="116 2577 11771"/>
    </justification>
  </clause>

  <clause id="11773">
    <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,9265,a(flip),b,7248,a),flip(a)].">
      <j1 rule="hyper" parents="58 9265 7248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11775">
    <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(6441(a,1),7825(a,2,1))].">
      <j1 rule="para" parents="6441 7825"/>
    </justification>
  </clause>

  <clause id="11776">
    <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),11775(a,2,1,2))].">
      <j1 rule="para" parents="75 11775"/>
    </justification>
  </clause>

  <clause id="11778">
    <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(334,a,7777,a,b,11776,a),flip(a)].">
      <j1 rule="hyper" parents="334 7777 11776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11779">
    <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(334,a,7883,a(flip),b,11778,a),flip(a)].">
      <j1 rule="hyper" parents="334 7883 11778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11780">
    <literal><![CDATA[
      x / (T(y,z) \ R(x,y \ 1,y)) = T((x * (1 / y)) \ x,z)
    ]]></literal>
    <justification jstring="[para(11779(a,1),7929(a,1,2))].">
      <j1 rule="para" parents="11779 7929"/>
    </justification>
  </clause>

  <clause id="11781">
    <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(11352(a,1),11351(a,1,2,1,1))].">
      <j1 rule="para" parents="11352 11351"/>
    </justification>
  </clause>

  <clause id="11782">
    <literal><![CDATA[
      K(x,T(x * ((y \ z) \ z),u)) = K(x,T(x * T(y,z),u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11048,a(flip),b,11781,a),flip(a)].">
      <j1 rule="hyper" parents="58 11048 11781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11783">
    <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(4805(a,1),4621(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4805 4621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11784">
    <literal><![CDATA[
      T(x / T(y,x),z) * T(y,y * T(y \ x,z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(10823,a,11783,a),flip(a)].">
      <j1 rule="hyper" parents="10823 11783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11785">
    <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(5423(a,1),5524(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5423 5524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11787">
    <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(5731(a,1),5535(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5731 5535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11788">
    <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(5232(a,1),11787(a,2,1,2))].">
      <j1 rule="para" parents="5232 11787"/>
    </justification>
  </clause>

  <clause id="11790">
    <literal><![CDATA[
      (x * K(y,x)) * (T(x,z) * (x \ K(x,y))) = T(x,z)
    ]]></literal>
    <justification jstring="[para(6516(a,1),11788(a,2,1))].">
      <j1 rule="para" parents="6516 11788"/>
    </justification>
  </clause>

  <clause id="11791">
    <literal><![CDATA[
      T(x,y) / (T(x,y) * (x \ K(x,z))) = x * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(130,a,11790,a)].">
      <j1 rule="hyper" parents="130 11790"/>
    </justification>
  </clause>

  <clause id="11792">
    <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(11791(a,1),3242(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11791 3242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11793">
    <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(6087(a,1),11792(a,2,1))].">
      <j1 rule="para" parents="6087 11792"/>
    </justification>
  </clause>

  <clause id="11794">
    <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(5878(a,1),11793(a,1,2,2))].">
      <j1 rule="para" parents="5878 11793"/>
    </justification>
  </clause>

  <clause id="11795">
    <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(8301(a,1),11794(a,1,2))].">
      <j1 rule="para" parents="8301 11794"/>
    </justification>
  </clause>

  <clause id="11796">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ T(x,z) = T(x,z) * T(x \ K(x,y),x)
    ]]></literal>
    <justification jstring="[para(8405(a,1),11795(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8405 11795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11797">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ T(x,z) = (x \ K(x,y)) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,8627,a(flip),b,11796,a),flip(a)].">
      <j1 rule="hyper" parents="334 8627 11796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11799">
    <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(11797(a,1),6623(a,1,2,1))].">
      <j1 rule="para" parents="11797 6623"/>
    </justification>
  </clause>

  <clause id="11800">
    <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(11797(a,2),10963(a,1,2,1))].">
      <j1 rule="para" parents="11797 10963"/>
    </justification>
  </clause>

  <clause id="11801">
    <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(8913(a,1),11799(a,1,1,1))].">
      <j1 rule="para" parents="8913 11799"/>
    </justification>
  </clause>

  <clause id="11802">
    <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(202(a,1),8652(a,1,1,1))].">
      <j1 rule="para" parents="202 8652"/>
    </justification>
  </clause>

  <clause id="11803">
    <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(202(a,1),11802(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="202 11802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11804">
    <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(202(a,1),11803(a,2,2,3,1))].">
      <j1 rule="para" parents="202 11803"/>
    </justification>
  </clause>

  <clause id="11805">
    <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(239(a,1),8788(a,1,1)),flip(a)].">
      <j1 rule="para" parents="239 8788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11806">
    <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(10278(a,1),11805(a,2,1))].">
      <j1 rule="para" parents="10278 11805"/>
    </justification>
  </clause>

  <clause id="11807">
    <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(334,a,8100,a,b,11806,a),flip(a)].">
      <j1 rule="hyper" parents="334 8100 11806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11809">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(u,y) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(9139,a,11807,a),flip(a)].">
      <j1 rule="hyper" parents="9139 11807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11810">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,u)) = T(x,K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(8119,a,11809,a)].">
      <j1 rule="hyper" parents="8119 11809"/>
    </justification>
  </clause>

  <clause id="11812">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(2065(a,2),11809(a,2,2))].">
      <j1 rule="para" parents="2065 11809"/>
    </justification>
  </clause>

  <clause id="11813">
    <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(11809(a,1),9986(a,1,1))].">
      <j1 rule="para" parents="11809 9986"/>
    </justification>
  </clause>

  <clause id="11814">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,u)) = T(x,K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[para(2065(a,2),11810(a,2,2))].">
      <j1 rule="para" parents="2065 11810"/>
    </justification>
  </clause>

  <clause id="11815">
    <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(11810(a,1),8118(a,1))].">
      <j1 rule="para" parents="11810 8118"/>
    </justification>
  </clause>

  <clause id="11816">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(447,a,11812,a)].">
      <j1 rule="hyper" parents="447 11812"/>
    </justification>
  </clause>

  <clause id="11817">
    <literal><![CDATA[
      x * K(x,K(y,z) * K(u,y)) = T(T(x,K(y,z)),K(y,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,5020,a(flip),b,11812,a)].">
      <j1 rule="hyper" parents="334 5020 11812"/>
    </justification>
  </clause>

  <clause id="11818">
    <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,11687,a,b,11812,a)].">
      <j1 rule="hyper" parents="58 11687 11812"/>
    </justification>
  </clause>

  <clause id="11819">
    <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,9351,a,b,11812,a)].">
      <j1 rule="hyper" parents="58 9351 11812"/>
    </justification>
  </clause>

  <clause id="11820">
    <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(9525(a,1),11814(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9525 11814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11821">
    <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(11814(a,1),10331(a,2,1))].">
      <j1 rule="para" parents="11814 10331"/>
    </justification>
  </clause>

  <clause id="11822">
    <literal><![CDATA[
      T(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,11812,a(flip),b,11816,a)].">
      <j1 rule="hyper" parents="58 11812 11816"/>
    </justification>
  </clause>

  <clause id="11823">
    <literal><![CDATA[
      T(x * K(K(y,z) * K(u,y),x),K(y,u) * K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(5469,a,11822,a)].">
      <j1 rule="hyper" parents="5469 11822"/>
    </justification>
  </clause>

  <clause id="11824">
    <literal><![CDATA[
      x * K(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(5128,a,11822,a)].">
      <j1 rule="hyper" parents="5128 11822"/>
    </justification>
  </clause>

  <clause id="11825">
    <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(11817(a,1),5030(a,1))].">
      <j1 rule="para" parents="11817 5030"/>
    </justification>
  </clause>

  <clause id="11826">
    <literal><![CDATA[
      x * K(K(y,z) * K(u,y),x) = T(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(2065(a,2),11818(a,1,2,1))].">
      <j1 rule="para" parents="2065 11818"/>
    </justification>
  </clause>

  <clause id="11827">
    <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(11823(a,1),5204(a,1,1))].">
      <j1 rule="para" parents="11823 5204"/>
    </justification>
  </clause>

  <clause id="11828">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),u) = K(u,K(y,x) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(29,a,11818,a,b,11824,a)].">
      <j1 rule="hyper" parents="29 11818 11824"/>
    </justification>
  </clause>

  <clause id="11829">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(x,z) * K(y,x))
    ]]></literal>
    <justification jstring="[para(2065(a,2),11828(a,1,1))].">
      <j1 rule="para" parents="2065 11828"/>
    </justification>
  </clause>

  <clause id="11830">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(y,x) * K(x,z))
    ]]></literal>
    <justification jstring="[para(2065(a,1),11829(a,2,2))].">
      <j1 rule="para" parents="2065 11829"/>
    </justification>
  </clause>

  <clause id="11831">
    <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,11830,a,b,5063,a(flip))].">
      <j1 rule="hyper" parents="117 11830 5063"/>
    </justification>
  </clause>

  <clause id="11832">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(x,y) * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(29,a,5020,a(flip),b,11826,a),flip(a)].">
      <j1 rule="hyper" parents="29 5020 11826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11833">
    <literal><![CDATA[
      K(x,K(y,z) * K(u,y)) = K(x,K(z,y) * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11830,a(flip),b,11832,a),flip(a)].">
      <j1 rule="hyper" parents="58 11830 11832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11834">
    <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),11825(a,1))].">
      <j1 rule="para" parents="18 11825"/>
    </justification>
  </clause>

  <clause id="11835">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(K(z,y) * K(y,u),x)
    ]]></literal>
    <justification jstring="[hyper(5100,a,11813,a),flip(a)].">
      <j1 rule="hyper" parents="5100 11813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11836">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,11828,a(flip),b,11835,a),flip(a)].">
      <j1 rule="hyper" parents="334 11828 11835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11837">
    <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(6161(a,1),11835(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6161 11835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11838">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(K(y,z) * K(u,y),x)
    ]]></literal>
    <justification jstring="[hyper(334,a,11832,a,b,11836,a),flip(a)].">
      <j1 rule="hyper" parents="334 11832 11836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11839">
    <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,10114,a,b,11836,a)].">
      <j1 rule="hyper" parents="58 10114 11836"/>
    </justification>
  </clause>

  <clause id="11840">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,u)) = K(x,K(z,y) * K(u,z))
    ]]></literal>
    <justification jstring="[para(8067(a,1),11836(a,1,1))].">
      <j1 rule="para" parents="8067 11836"/>
    </justification>
  </clause>

  <clause id="11841">
    <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(8399(a,1),11836(a,1,1))].">
      <j1 rule="para" parents="8399 11836"/>
    </justification>
  </clause>

  <clause id="11842">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,u)) = K(x,K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,11833,a(flip),b,11840,a),flip(a)].">
      <j1 rule="hyper" parents="334 11833 11840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11843">
    <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,11810,a(flip),b,11819,a),flip(a)].">
      <j1 rule="hyper" parents="58 11810 11819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11844">
    <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(334,a,4996,a,b,11821,a),flip(a)].">
      <j1 rule="hyper" parents="334 4996 11821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11845">
    <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(5391(a,1),11844(a,1,2))].">
      <j1 rule="para" parents="5391 11844"/>
    </justification>
  </clause>

  <clause id="11846">
    <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(334,a,11832,a(flip),b,11845,a),flip(a)].">
      <j1 rule="hyper" parents="334 11832 11845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11847">
    <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(11827,a,11843,a)].">
      <j1 rule="hyper" parents="11827 11843"/>
    </justification>
  </clause>

  <clause id="11848">
    <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(334,a,5020,a(flip),b,11847,a)].">
      <j1 rule="hyper" parents="334 5020 11847"/>
    </justification>
  </clause>

  <clause id="11849">
    <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(9349(a,1),11820(a,2,1))].">
      <j1 rule="para" parents="9349 11820"/>
    </justification>
  </clause>

  <clause id="11850">
    <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,5020,a(flip),b,11848,a)].">
      <j1 rule="hyper" parents="29 5020 11848"/>
    </justification>
  </clause>

  <clause id="11851">
    <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(334,a,11816,a(flip),b,11849,a),flip(a)].">
      <j1 rule="hyper" parents="334 11816 11849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11852">
    <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(9525(a,1),11851(a,1,2,2))].">
      <j1 rule="para" parents="9525 11851"/>
    </justification>
  </clause>

  <clause id="11853">
    <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(334,a,11822,a,b,11852,a)].">
      <j1 rule="hyper" parents="334 11822 11852"/>
    </justification>
  </clause>

  <clause id="11854">
    <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,9233,a(flip),b,11831,a)].">
      <j1 rule="hyper" parents="58 9233 11831"/>
    </justification>
  </clause>

  <clause id="11855">
    <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(8048(a,1),11839(a,1,2,2,2))].">
      <j1 rule="para" parents="8048 11839"/>
    </justification>
  </clause>

  <clause id="11856">
    <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(8399(a,1),11841(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8399 11841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11857">
    <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(11856(a,1),7585(a,1))].">
      <j1 rule="para" parents="11856 7585"/>
    </justification>
  </clause>

  <clause id="11859">
    <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(11835(a,1),11857(a,1))].">
      <j1 rule="para" parents="11835 11857"/>
    </justification>
  </clause>

  <clause id="11860">
    <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(6972,a,11854,a)].">
      <j1 rule="hyper" parents="6972 11854"/>
    </justification>
  </clause>

  <clause id="11861">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,u)) = K(z,K(x,y) * K(u,x))
    ]]></literal>
    <justification jstring="[hyper(5686,a,11855,a)].">
      <j1 rule="hyper" parents="5686 11855"/>
    </justification>
  </clause>

  <clause id="11862">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,K(z,u)) = K(z,K(y,x) * K(u,y))
    ]]></literal>
    <justification jstring="[para(8048(a,1),11861(a,1,1))].">
      <j1 rule="para" parents="8048 11861"/>
    </justification>
  </clause>

  <clause id="11863">
    <literal><![CDATA[
      1 / T(K(x,y) * K(y,z),u) = 1 * T(K(y,x) * K(z,y),u)
    ]]></literal>
    <justification jstring="[para(2063(a,1),11860(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2063 11860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11864">
    <literal><![CDATA[
      1 / T(K(x,y) * K(y,z),u) = T(K(y,x) * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,2,a(flip),b,11863,a),flip(a)].">
      <j1 rule="hyper" parents="334 2 11863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11866">
    <literal><![CDATA[
      1 / T(K(x,y) * K(y,z),u) = T(K(z,y) * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(2065(a,1),11864(a,2,1))].">
      <j1 rule="para" parents="2065 11864"/>
    </justification>
  </clause>

  <clause id="11867">
    <literal><![CDATA[
      1 / T(K(x,y) * K(z,x),u) = T(K(y,x) * K(x,z),u)
    ]]></literal>
    <justification jstring="[para(2065(a,2),11866(a,1,2,1))].">
      <j1 rule="para" parents="2065 11866"/>
    </justification>
  </clause>

  <clause id="11868">
    <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(11867(a,1),276(a,1,1)),flip(b)].">
      <j1 rule="para" parents="11867 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11869">
    <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(9345(a,1),11837(a,2,2))].">
      <j1 rule="para" parents="9345 11837"/>
    </justification>
  </clause>

  <clause id="11870">
    <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(334,a,11835,a(flip),b,11869,a),flip(a)].">
      <j1 rule="hyper" parents="334 11835 11869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11871">
    <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(6161(a,1),11870(a,1,1,2))].">
      <j1 rule="para" parents="6161 11870"/>
    </justification>
  </clause>

  <clause id="11872">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,z),u) * u) = (K(y,x) * (x \ 1)) * u
    ]]></literal>
    <justification jstring="[para(6310(a,1),9119(a,2,1,1))].">
      <j1 rule="para" parents="6310 9119"/>
    </justification>
  </clause>

  <clause id="11873">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,z),u) * u) = (T(x,y) \ 1) * u
    ]]></literal>
    <justification jstring="[para(5392(a,1),11872(a,2,1))].">
      <j1 rule="para" parents="5392 11872"/>
    </justification>
  </clause>

  <clause id="11875">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ 1,z) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(167(a,1),11873(a,1,2,1,2,2))].">
      <j1 rule="para" parents="167 11873"/>
    </justification>
  </clause>

  <clause id="11876">
    <literal><![CDATA[
      (x \ 1) * (K(y,x) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(10482(a,1),11875(a,1,2,1))].">
      <j1 rule="para" parents="10482 11875"/>
    </justification>
  </clause>

  <clause id="11877">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * z) = L(z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(11876(a,1),6312(a,1,2))].">
      <j1 rule="para" parents="11876 6312"/>
    </justification>
  </clause>

  <clause id="11879">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,y) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4797,a(flip),b,11877,a)].">
      <j1 rule="hyper" parents="58 4797 11877"/>
    </justification>
  </clause>

  <clause id="11881">
    <literal><![CDATA[
      L(x,((y \ z) \ z) \ 1,(y \ z) \ z) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7044,a(flip),b,11879,a)].">
      <j1 rule="hyper" parents="58 7044 11879"/>
    </justification>
  </clause>

  <clause id="11884">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z) \ z) = K(x,((((z \ x) \ x) \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(11881(a,1),10975(a,1,2,1))].">
      <j1 rule="para" parents="11881 10975"/>
    </justification>
  </clause>

  <clause id="11885">
    <literal><![CDATA[
      K(x,((((y \ x) \ x) \ 1) * z) \ 1) = K(x,((y \ 1) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(6765,a,11884,a),flip(a)].">
      <j1 rule="hyper" parents="6765 11884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11887">
    <literal><![CDATA[
      K(x,((x \ (y \ x)) * z) \ 1) = K(x,((y \ 1) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,11699,a(flip),b,11885,a)].">
      <j1 rule="hyper" parents="58 11699 11885"/>
    </justification>
  </clause>

  <clause id="11888">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ 1) = K(x,((y \ x) * z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11656,a(flip),b,11887,a),flip(a)].">
      <j1 rule="hyper" parents="58 11656 11887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11889">
    <literal><![CDATA[
      K(x,((y \ x) * (y / z)) \ x) = L(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,6935,a(flip),b,11888,a),flip(a)].">
      <j1 rule="hyper" parents="58 6935 11888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11890">
    <literal><![CDATA[
      L(K(x,y),z,z \ 1) = L(K(x,y),z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(9612,a,11889,a),flip(a)].">
      <j1 rule="hyper" parents="9612 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11891">
    <literal><![CDATA[
      L(K(x,y),z,z \ x) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(11132,a,11890,a),flip(a)].">
      <j1 rule="hyper" parents="11132 11890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11892">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) = K(x,L(y,z,z \ x))
    ]]></literal>
    <justification jstring="[hyper(11132,a,11891,a),flip(a)].">
      <j1 rule="hyper" parents="11132 11891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11893">
    <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(11891(a,1),11132(a,1))].">
      <j1 rule="para" parents="11891 11132"/>
    </justification>
  </clause>

  <clause id="11894">
    <literal><![CDATA[
      K(x,L(y,z \ x,(z \ x) \ 1)) = K(x,L(y,z \ x,z))
    ]]></literal>
    <justification jstring="[para(11442(a,1),11892(a,2,2))].">
      <j1 rule="para" parents="11442 11892"/>
    </justification>
  </clause>

  <clause id="11895">
    <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,11354,a(flip),b,11894,a),flip(a)].">
      <j1 rule="hyper" parents="58 11354 11894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11896">
    <literal><![CDATA[
      K((((x \ y) \ 1) * (x \ 1)) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11735,a(flip),b,11895,a),flip(a)].">
      <j1 rule="hyper" parents="58 11735 11895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11897">
    <literal><![CDATA[
      K(((((x \ 1) \ y) \ 1) * x) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(11249,a,11896,a)].">
      <j1 rule="hyper" parents="11249 11896"/>
    </justification>
  </clause>

  <clause id="11899">
    <literal><![CDATA[
      (1 / (x \ y)) * (x \ T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6245,a(flip),b,11896,a)].">
      <j1 rule="hyper" parents="58 6245 11896"/>
    </justification>
  </clause>

  <clause id="11900">
    <literal><![CDATA[
      (1 / (x \ y)) \ K(y,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,11896,a(flip),b,6245,a(flip))].">
      <j1 rule="hyper" parents="116 11896 6245"/>
    </justification>
  </clause>

  <clause id="11902">
    <literal><![CDATA[
      (1 / x) * (y \ T(y * x,z)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11899(a,1,1,2))].">
      <j1 rule="para" parents="4 11899"/>
    </justification>
  </clause>

  <clause id="11903">
    <literal><![CDATA[
      (1 / x) \ K(y,z) = (y / x) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),11900(a,1,1,2))].">
      <j1 rule="para" parents="75 11900"/>
    </justification>
  </clause>

  <clause id="11904">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = K(x,y) / z
    ]]></literal>
    <justification jstring="[para(11897(a,1),7230(a,2,1))].">
      <j1 rule="para" parents="11897 7230"/>
    </justification>
  </clause>

  <clause id="11905">
    <literal><![CDATA[
      T(x,y) / ((1 / y) \ x) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,5072,a(flip),b,11904,a),flip(a)].">
      <j1 rule="hyper" parents="334 5072 11904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11906">
    <literal><![CDATA[
      (K(x,y) / z) \ T(x,y) = (1 / z) \ x
    ]]></literal>
    <justification jstring="[hyper(192,a,11904,a)].">
      <j1 rule="hyper" parents="192 11904"/>
    </justification>
  </clause>

  <clause id="11907">
    <literal><![CDATA[
      (1 / (x \ K(y,z))) \ y = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(31,a,183,a,b,11904,a),flip(a)].">
      <j1 rule="hyper" parents="31 183 11904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11909">
    <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(10446(a,1),11905(a,2,2))].">
      <j1 rule="para" parents="10446 11905"/>
    </justification>
  </clause>

  <clause id="11910">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / z = u
    ]]></literal>
    <justification jstring="[para(11906(a,1),345(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11906 345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11911">
    <literal><![CDATA[
      K(x,((y \ 1) * (z \ 1)) \ 1) = 1 / K(z * y,x)
    ]]></literal>
    <justification jstring="[para(11902(a,1),6324(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11902 6324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11912">
    <literal><![CDATA[
      K(x,((y \ 1) * (z \ 1)) \ 1) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5243,a(flip),b,11911,a),flip(a)].">
      <j1 rule="hyper" parents="334 5243 11911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11913">
    <literal><![CDATA[
      (1 / x) \ K(y,z * x) = x * K(y,(z \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(11912(a,1),6934(a,1,2))].">
      <j1 rule="para" parents="11912 6934"/>
    </justification>
  </clause>

  <clause id="11914">
    <literal><![CDATA[
      x * K(y,((z / x) \ 1) \ x) = (1 / x) \ K(y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),11913(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 11913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11915">
    <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(6924(a,1),11909(a,1,1))].">
      <j1 rule="para" parents="6924 11909"/>
    </justification>
  </clause>

  <clause id="11916">
    <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(9755(a,1),11226(a,1,2))].">
      <j1 rule="para" parents="9755 11226"/>
    </justification>
  </clause>

  <clause id="11917">
    <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(4601(a,1),11916(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4601 11916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11918">
    <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),11917(a,2,2))].">
      <j1 rule="para" parents="18 11917"/>
    </justification>
  </clause>

  <clause id="11919">
    <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(334,a,7824,a(flip),b,11918,a),flip(a)].">
      <j1 rule="hyper" parents="334 7824 11918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11920">
    <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(11137(a,1),11919(a,2,1))].">
      <j1 rule="para" parents="11137 11919"/>
    </justification>
  </clause>

  <clause id="11921">
    <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(334,a,7312,a(flip),b,11920,a),flip(a)].">
      <j1 rule="hyper" parents="334 7312 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))) = L(T(x,L(y,u,z)),y,x)
    ]]></literal>
    <justification jstring="[para(7400(a,1),11921(a,1,2,3))].">
      <j1 rule="para" parents="7400 11921"/>
    </justification>
  </clause>

  <clause id="11923">
    <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(4507(a,1),11922(a,1,2,3))].">
      <j1 rule="para" parents="4507 11922"/>
    </justification>
  </clause>

  <clause id="11924">
    <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,11353,a,b,11923,a)].">
      <j1 rule="hyper" parents="58 11353 11923"/>
    </justification>
  </clause>

  <clause id="11925">
    <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(11089(a,1),11924(a,1,1))].">
      <j1 rule="para" parents="11089 11924"/>
    </justification>
  </clause>

  <clause id="11926">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = K(y * x,L(x,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(2523(a,1),11925(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2523 11925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11927">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = K(L(x,z,u),y * x) * x
    ]]></literal>
    <justification jstring="[hyper(334,a,5391,a(flip),b,11926,a),flip(a)].">
      <j1 rule="hyper" parents="334 5391 11926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11928">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = K(x,L(y * x,z,u)) * x
    ]]></literal>
    <justification jstring="[para(11137(a,1),11927(a,2,1))].">
      <j1 rule="para" parents="11137 11927"/>
    </justification>
  </clause>

  <clause id="11929">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = T(x,L(y * x,z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,5034,a,b,11928,a),flip(a)].">
      <j1 rule="hyper" parents="334 5034 11928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11930">
    <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,11230,a,b,11929,a)].">
      <j1 rule="hyper" parents="58 11230 11929"/>
    </justification>
  </clause>

  <clause id="11931">
    <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),11737(a,2,1,1))].">
      <j1 rule="para" parents="4 11737"/>
    </justification>
  </clause>

  <clause id="11932">
    <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(334,a,9746,a(flip),b,11931,a),flip(a)].">
      <j1 rule="hyper" parents="334 9746 11931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11934">
    <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),11932(a,1,1,1))].">
      <j1 rule="para" parents="4 11932"/>
    </justification>
  </clause>

  <clause id="11935">
    <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),11934(a,1,2,2))].">
      <j1 rule="para" parents="4 11934"/>
    </justification>
  </clause>

  <clause id="11936">
    <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(5096(a,1),11935(a,1,2,1,3))].">
      <j1 rule="para" parents="5096 11935"/>
    </justification>
  </clause>

  <clause id="11937">
    <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(334,a,5956,a(flip),b,5641,a),flip(a)].">
      <j1 rule="hyper" parents="334 5956 5641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11938">
    <literal><![CDATA[
      ((x * y) * K(T(z,(1 / y) \ x),x * y)) / y = x * K(z,(x \ (1 / y)) \ 1)
    ]]></literal>
    <justification jstring="[para(5017(a,1),11937(a,1,1))].">
      <j1 rule="para" parents="5017 11937"/>
    </justification>
  </clause>

  <clause id="11939">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(x \ (1 / y)) \ 1)
    ]]></literal>
    <justification jstring="[para(7462(a,1),11938(a,1,1,2))].">
      <j1 rule="para" parents="7462 11938"/>
    </justification>
  </clause>

  <clause id="11940">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(1 / y) \ x)
    ]]></literal>
    <justification jstring="[para(6423(a,1),11939(a,2,2))].">
      <j1 rule="para" parents="6423 11939"/>
    </justification>
  </clause>

  <clause id="11941">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(5584(a,1),11940(a,2,2))].">
      <j1 rule="para" parents="5584 11940"/>
    </justification>
  </clause>

  <clause id="11942">
    <literal><![CDATA[
      (x * K(y,(z \ 1) \ x)) * z = (x * z) * K(y,x * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,11941,a)].">
      <j1 rule="hyper" parents="133 11941"/>
    </justification>
  </clause>

  <clause id="11943">
    <literal><![CDATA[
      (x \ y) * K(z,(x \ 1) \ (x \ y)) = x \ (y * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(30,a,5969,a(flip),b,11942,a),flip(a)].">
      <j1 rule="hyper" parents="30 5969 11942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11944">
    <literal><![CDATA[
      (x \ y) \ (x \ (y * K(z,y))) = K(z,(x \ 1) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(123,a,11943,a)].">
      <j1 rule="hyper" parents="123 11943"/>
    </justification>
  </clause>

  <clause id="11945">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ K(y,T(z,u))) = K(u,(x \ 1) \ (x \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(8104(a,1),11944(a,1,2,2))].">
      <j1 rule="para" parents="8104 11944"/>
    </justification>
  </clause>

  <clause id="11946">
    <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(7241(a,1),7242(a,2,2,1,1))].">
      <j1 rule="para" parents="7241 7242"/>
    </justification>
  </clause>

  <clause id="11947">
    <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),11946(a,2,2,1))].">
      <j1 rule="para" parents="75 11946"/>
    </justification>
  </clause>

  <clause id="11949">
    <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(334,a,4037,a(flip),b,11947,a),flip(a)].">
      <j1 rule="hyper" parents="334 4037 11947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11950">
    <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),11949(a,1,1,2,1))].">
      <j1 rule="para" parents="75 11949"/>
    </justification>
  </clause>

  <clause id="11951">
    <literal><![CDATA[
      T(x \ R(x,y,z),R(x,u,w) \ x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(4037(a,1),11950(a,1,1))].">
      <j1 rule="para" parents="4037 11950"/>
    </justification>
  </clause>

  <clause id="11952">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ 1) \ 1 = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(6505,a,11951,a)].">
      <j1 rule="hyper" parents="6505 11951"/>
    </justification>
  </clause>

  <clause id="11953">
    <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(11952(a,1),11763(a,1,1,1))].">
      <j1 rule="para" parents="11952 11763"/>
    </justification>
  </clause>

  <clause id="11954">
    <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(812,a,11953,a)].">
      <j1 rule="hyper" parents="812 11953"/>
    </justification>
  </clause>

  <clause id="11955">
    <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),11954(a,1,1,2))].">
      <j1 rule="para" parents="101 11954"/>
    </justification>
  </clause>

  <clause id="11956">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1 = T(a(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(9(a,2),11955(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 11955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11957">
    <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(8019(a,1),9585(a,2,1))].">
      <j1 rule="para" parents="8019 9585"/>
    </justification>
  </clause>

  <clause id="11958">
    <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,4017,a(flip),b,9638,a),flip(a)].">
      <j1 rule="hyper" parents="58 4017 9638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11960">
    <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(334,a,3787,a(flip),b,11958,a),flip(a)].">
      <j1 rule="hyper" parents="334 3787 11958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11961">
    <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(2236(a,1),11960(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2236 11960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11963">
    <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(10257,a,10302,a)].">
      <j1 rule="hyper" parents="10257 10302"/>
    </justification>
  </clause>

  <clause id="11964">
    <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(11362,a,11963,a)].">
      <j1 rule="hyper" parents="11362 11963"/>
    </justification>
  </clause>

  <clause id="11966">
    <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(10230(a,1),11964(a,2,2,2))].">
      <j1 rule="para" parents="10230 11964"/>
    </justification>
  </clause>

  <clause id="11967">
    <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),11966(a,2,2,2,1))].">
      <j1 rule="para" parents="5 11966"/>
    </justification>
  </clause>

  <clause id="11968">
    <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),11967(a,2,2))].">
      <j1 rule="para" parents="4 11967"/>
    </justification>
  </clause>

  <clause id="11970">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,10243,a(flip),b,11968,a),flip(a)].">
      <j1 rule="hyper" parents="334 10243 11968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11971">
    <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,11363,a(flip),b,11970,a),flip(a)].">
      <j1 rule="hyper" parents="58 11363 11970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11973">
    <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(334,a,7322,a(flip),b,10888,a),flip(a)].">
      <j1 rule="hyper" parents="334 7322 10888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11975">
    <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(11973(a,2),11217(a,1))].">
      <j1 rule="para" parents="11973 11217"/>
    </justification>
  </clause>

  <clause id="11976">
    <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(8988(a,1),11049(a,1,2,1,1))].">
      <j1 rule="para" parents="8988 11049"/>
    </justification>
  </clause>

  <clause id="11977">
    <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(334,a,8792,a(flip),b,11957,a),flip(a)].">
      <j1 rule="hyper" parents="334 8792 11957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11978">
    <literal><![CDATA[
      K(x,T((y * (x \ z)) \ u,w)) = K(x,T((y * z) \ (u * x),w))
    ]]></literal>
    <justification jstring="[hyper(58,a,11048,a(flip),b,11976,a),flip(a)].">
      <j1 rule="hyper" parents="58 11048 11976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11979">
    <literal><![CDATA[
      K(x,T((y * z) \ (u * x),y * z)) = K(x,u / (y * (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(9522,a,11978,a),flip(a)].">
      <j1 rule="hyper" parents="9522 11978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11980">
    <literal><![CDATA[
      K(x,(y * x) / (z * u)) = K(x,y / (z * (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(8328,a,11979,a)].">
      <j1 rule="hyper" parents="8328 11979"/>
    </justification>
  </clause>

  <clause id="11981">
    <literal><![CDATA[
      K(x,y / (z * (x \ u))) = K(x,((z * u) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(8769,a,11980,a),flip(a)].">
      <j1 rule="hyper" parents="8769 11980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11982">
    <literal><![CDATA[
      R(K(x,((y * z) / (u / w)) \ x),w \ u,w) = K(x,u / ((y * (x \ z)) * w))
    ]]></literal>
    <justification jstring="[para(11981(a,1),10661(a,1,1))].">
      <j1 rule="para" parents="11981 10661"/>
    </justification>
  </clause>

  <clause id="11983">
    <literal><![CDATA[
      K(x,y / ((x \ (z * u)) * w)) = K(x,y / ((z * (x \ u)) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,10660,a(flip),b,11982,a)].">
      <j1 rule="hyper" parents="58 10660 11982"/>
    </justification>
  </clause>

  <clause id="11984">
    <literal><![CDATA[
      K(x,y / ((z * (x \ u)) * w)) = K(x,(((z * u) * w) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(11446,a,11983,a),flip(a)].">
      <j1 rule="hyper" parents="11446 11983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11985">
    <literal><![CDATA[
      K(x,(((y * z) * u) / (z * u)) \ x) = R(K(x,y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7249,a(flip),b,11984,a),flip(a)].">
      <j1 rule="hyper" parents="58 7249 11984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11986">
    <literal><![CDATA[
      R(K(x,y \ x),z,u) = K(x,R(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(15(a,2),11985(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15 11985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11987">
    <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(544(a,1),11986(a,2,2,1))].">
      <j1 rule="para" parents="544 11986"/>
    </justification>
  </clause>

  <clause id="11988">
    <literal><![CDATA[
      K(x,R(y \ x,z,u) \ x) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(5462(a,1),11986(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5462 11986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11989">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ x) = R(K(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(5696(a,1),11986(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5696 11986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11990">
    <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(11583(a,1),11986(a,1,1))].">
      <j1 rule="para" parents="11583 11986"/>
    </justification>
  </clause>

  <clause id="11991">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ x) = R(K(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5607,a,b,11989,a)].">
      <j1 rule="hyper" parents="58 5607 11989"/>
    </justification>
  </clause>

  <clause id="11992">
    <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(11988(a,1),11990(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11988 11990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11993">
    <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(5607(a,1),11987(a,1,1))].">
      <j1 rule="para" parents="5607 11987"/>
    </justification>
  </clause>

  <clause id="11994">
    <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),4459(a,1,1,2))].">
      <j1 rule="para" parents="75 4459"/>
    </justification>
  </clause>

  <clause id="11995">
    <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),11994(a,1,1))].">
      <j1 rule="para" parents="20 11994"/>
    </justification>
  </clause>

  <clause id="11996">
    <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(3154(a,1),11995(a,1,1))].">
      <j1 rule="para" parents="3154 11995"/>
    </justification>
  </clause>

  <clause id="11997">
    <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),11996(a,1,2,2,2))].">
      <j1 rule="para" parents="75 11996"/>
    </justification>
  </clause>

  <clause id="11998">
    <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),11997(a,1,2,2))].">
      <j1 rule="para" parents="20 11997"/>
    </justification>
  </clause>

  <clause id="11999">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ ((1 / x) * (y * x))) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(3154(a,1),11998(a,1,2,2))].">
      <j1 rule="para" parents="3154 11998"/>
    </justification>
  </clause>

  <clause id="12000">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * x) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),11999(a,1,2))].">
      <j1 rule="para" parents="4 11999"/>
    </justification>
  </clause>

  <clause id="12002">
    <literal><![CDATA[
      1 / R(T(x,y),x \ 1,y * x) = (L(y,x,x \ 1) \ (x * y)) \ 1
    ]]></literal>
    <justification jstring="[para(12000(a,1),4421(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12000 4421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12003">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = R(T(y,x),y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(192,a,12002,a)].">
      <j1 rule="hyper" parents="192 12002"/>
    </justification>
  </clause>

  <clause id="12004">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) \ (x * y) = R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3218,a(flip),b,12003,a)].">
      <j1 rule="hyper" parents="58 3218 12003"/>
    </justification>
  </clause>

  <clause id="12005">
    <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(7603(a,1),6264(a,1,3))].">
      <j1 rule="para" parents="7603 6264"/>
    </justification>
  </clause>

  <clause id="12007">
    <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(9090(a,1),8806(a,1,1))].">
      <j1 rule="para" parents="9090 8806"/>
    </justification>
  </clause>

  <clause id="12008">
    <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(10260(a,1),9227(a,2,2))].">
      <j1 rule="para" parents="10260 9227"/>
    </justification>
  </clause>

  <clause id="12009">
    <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(5391(a,1),9559(a,1,1,2,2))].">
      <j1 rule="para" parents="5391 9559"/>
    </justification>
  </clause>

  <clause id="12010">
    <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,8062,a(flip),b,11051,a),flip(a)].">
      <j1 rule="hyper" parents="58 8062 11051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12011">
    <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(8050,a,12010,a)].">
      <j1 rule="hyper" parents="8050 12010"/>
    </justification>
  </clause>

  <clause id="12013">
    <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(8940(a,1),12011(a,1,2))].">
      <j1 rule="para" parents="8940 12011"/>
    </justification>
  </clause>

  <clause id="12014">
    <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,8663,a(flip),b,12013,a)].">
      <j1 rule="hyper" parents="58 8663 12013"/>
    </justification>
  </clause>

  <clause id="12015">
    <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(9343(a,1),11379(a,1,1,1,2))].">
      <j1 rule="para" parents="9343 11379"/>
    </justification>
  </clause>

  <clause id="12016">
    <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(7087(a,1),11629(a,1,1,2))].">
      <j1 rule="para" parents="7087 11629"/>
    </justification>
  </clause>

  <clause id="12017">
    <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(652(a,1),12016(a,1,1))].">
      <j1 rule="para" parents="652 12016"/>
    </justification>
  </clause>

  <clause id="12018">
    <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(245(a,1),12017(a,1,2)),flip(a)].">
      <j1 rule="para" parents="245 12017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12019">
    <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(334,a,1408,a(flip),b,12018,a),flip(a)].">
      <j1 rule="hyper" parents="334 1408 12018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12020">
    <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),12019(a,2,3))].">
      <j1 rule="para" parents="22 12019"/>
    </justification>
  </clause>

  <clause id="12021">
    <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,11627,a(flip),b,12020,a)].">
      <j1 rule="hyper" parents="58 11627 12020"/>
    </justification>
  </clause>

  <clause id="12022">
    <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(11631,a,12021,a)].">
      <j1 rule="hyper" parents="11631 12021"/>
    </justification>
  </clause>

  <clause id="12024">
    <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,11971,a(flip),b,12022,a),flip(a)].">
      <j1 rule="hyper" parents="58 11971 12022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12026">
    <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,11758,a,b,12024,a)].">
      <j1 rule="hyper" parents="58 11758 12024"/>
    </justification>
  </clause>

  <clause id="12027">
    <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(9765,a,12026,a)].">
      <j1 rule="hyper" parents="9765 12026"/>
    </justification>
  </clause>

  <clause id="12028">
    <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(12027(a,1),11700(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12027 11700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12029">
    <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),12028(a,2,2,2))].">
      <j1 rule="para" parents="17 12028"/>
    </justification>
  </clause>

  <clause id="12030">
    <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(10342(a,1),12029(a,2,2))].">
      <j1 rule="para" parents="10342 12029"/>
    </justification>
  </clause>

  <clause id="12031">
    <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,11605,a(flip),b,12030,a)].">
      <j1 rule="hyper" parents="58 11605 12030"/>
    </justification>
  </clause>

  <clause id="12032">
    <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(384(a,1),12031(a,1,2,3))].">
      <j1 rule="para" parents="384 12031"/>
    </justification>
  </clause>

  <clause id="12033">
    <literal><![CDATA[
      a(R(x,y,z),u,R(x,y,z)) = a(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(9818,a,12032,a)].">
      <j1 rule="hyper" parents="9818 12032"/>
    </justification>
  </clause>

  <clause id="12034">
    <literal><![CDATA[
      R(a(x,y,x),x * z,u) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(11755,a,12033,a)].">
      <j1 rule="hyper" parents="11755 12033"/>
    </justification>
  </clause>

  <clause id="12035">
    <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,12027,a(flip),b,12033,a),flip(a)].">
      <j1 rule="hyper" parents="58 12027 12033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12036">
    <literal><![CDATA[
      a(x,y,R(x,x \ z,u)) = R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),12034(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 12034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12037">
    <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,12036,a(flip),b,10254,a),flip(a)].">
      <j1 rule="hyper" parents="119 12036 10254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12038">
    <literal><![CDATA[
      R(x,y,R(x,x \ z,u)) = x * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,12036,a(flip),b,10243,a),flip(a)].">
      <j1 rule="hyper" parents="119 12036 10243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12039">
    <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,10500,a(flip),b,12038,a),flip(a)].">
      <j1 rule="hyper" parents="58 10500 12038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12040">
    <literal><![CDATA[
      a(x,x \ y,R(x,z,u)) * K(x,y) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(12035(a,1),10344(a,1,1))].">
      <j1 rule="para" parents="12035 10344"/>
    </justification>
  </clause>

  <clause id="12041">
    <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,11301,a(flip),b,12040,a)].">
      <j1 rule="hyper" parents="58 11301 12040"/>
    </justification>
  </clause>

  <clause id="12042">
    <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(9643(a,1),12039(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9643 12039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12043">
    <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(334,a,12037,a,b,12042,a),flip(a)].">
      <j1 rule="hyper" parents="334 12037 12042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12045">
    <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(12043(a,1),11615(a,2,1,1))].">
      <j1 rule="para" parents="12043 11615"/>
    </justification>
  </clause>

  <clause id="12046">
    <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(7315(a,1),12007(a,1,2))].">
      <j1 rule="para" parents="7315 12007"/>
    </justification>
  </clause>

  <clause id="12048">
    <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(11013(a,1),12046(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11013 12046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12049">
    <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(334,a,3,a(flip),b,12048,a),flip(a)].">
      <j1 rule="hyper" parents="334 3 12048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12051">
    <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,10528,a(flip),b,12049,a),flip(a)].">
      <j1 rule="hyper" parents="58 10528 12049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12052">
    <literal><![CDATA[
      R(T(x,y),z,x) \ T(x,y) = x \ L(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,7734,a(flip),b,12051,a),flip(a)].">
      <j1 rule="hyper" parents="334 7734 12051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12053">
    <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(8817(a,1),12008(a,2,2))].">
      <j1 rule="para" parents="8817 12008"/>
    </justification>
  </clause>

  <clause id="12054">
    <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(334,a,7001,a(flip),b,12053,a),flip(a)].">
      <j1 rule="hyper" parents="334 7001 12053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12055">
    <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(8066(a,1),12054(a,2,1))].">
      <j1 rule="para" parents="8066 12054"/>
    </justification>
  </clause>

  <clause id="12056">
    <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(8397(a,1),12055(a,2,2))].">
      <j1 rule="para" parents="8397 12055"/>
    </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))) = K(u,K(z,x) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,11842,a(flip),b,12056,a),flip(a)].">
      <j1 rule="hyper" parents="334 11842 12056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12059">
    <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(9223(a,1),12057(a,1,2))].">
      <j1 rule="para" parents="9223 12057"/>
    </justification>
  </clause>

  <clause id="12061">
    <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(12059(a,1),11717(a,1,2))].">
      <j1 rule="para" parents="12059 11717"/>
    </justification>
  </clause>

  <clause id="12062">
    <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(5363(a,1),12009(a,1,1,2))].">
      <j1 rule="para" parents="5363 12009"/>
    </justification>
  </clause>

  <clause id="12063">
    <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(10543(a,1),12062(a,1,2))].">
      <j1 rule="para" parents="10543 12062"/>
    </justification>
  </clause>

  <clause id="12064">
    <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(9289(a,1),12063(a,1,2))].">
      <j1 rule="para" parents="9289 12063"/>
    </justification>
  </clause>

  <clause id="12066">
    <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(5391(a,1),12064(a,2,2,1,1))].">
      <j1 rule="para" parents="5391 12064"/>
    </justification>
  </clause>

  <clause id="12067">
    <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(8107(a,1),12066(a,2,2,1))].">
      <j1 rule="para" parents="8107 12066"/>
    </justification>
  </clause>

  <clause id="12068">
    <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(7910(a,2),12067(a,2,2))].">
      <j1 rule="para" parents="7910 12067"/>
    </justification>
  </clause>

  <clause id="12069">
    <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),12068(a,2,2,1))].">
      <j1 rule="para" parents="7 12068"/>
    </justification>
  </clause>

  <clause id="12070">
    <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(12069(a,1),6280(a,1,1,2))].">
      <j1 rule="para" parents="12069 6280"/>
    </justification>
  </clause>

  <clause id="12071">
    <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(11862(a,1),12015(a,1,1,1))].">
      <j1 rule="para" parents="11862 12015"/>
    </justification>
  </clause>

  <clause id="12072">
    <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(3729(a,1),3999(a,1,1))].">
      <j1 rule="para" parents="3729 3999"/>
    </justification>
  </clause>

  <clause id="12073">
    <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(3729(a,1),12072(a,1,2,1,1))].">
      <j1 rule="para" parents="3729 12072"/>
    </justification>
  </clause>

  <clause id="12074">
    <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(7005(a,1),12073(a,1,2,1))].">
      <j1 rule="para" parents="7005 12073"/>
    </justification>
  </clause>

  <clause id="12075">
    <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(334,a,4341,a(flip),b,12074,a),flip(a)].">
      <j1 rule="hyper" parents="334 4341 12074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12076">
    <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(12075(a,1),439(a,1,2))].">
      <j1 rule="para" parents="12075 439"/>
    </justification>
  </clause>

  <clause id="12077">
    <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),7096(a,2,2,1,2))].">
      <j1 rule="para" parents="5 7096"/>
    </justification>
  </clause>

  <clause id="12078">
    <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(334,a,244,a(flip),b,12077,a),flip(a)].">
      <j1 rule="hyper" parents="334 244 12077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12079">
    <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(244(a,1),12078(a,1,2))].">
      <j1 rule="para" parents="244 12078"/>
    </justification>
  </clause>

  <clause id="12080">
    <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(5391(a,1),12079(a,1,2,2))].">
      <j1 rule="para" parents="5391 12079"/>
    </justification>
  </clause>

  <clause id="12081">
    <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(5409,a,12080,a),flip(a)].">
      <j1 rule="hyper" parents="5409 12080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12082">
    <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(334,a,3411,a(flip),b,12080,a),flip(a)].">
      <j1 rule="hyper" parents="334 3411 12080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12083">
    <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(12081(a,2),5410(a,1,2)),flip(b)].">
      <j1 rule="para" parents="12081 5410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12084">
    <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(7270(a,1),11519(a,2,2,1))].">
      <j1 rule="para" parents="7270 11519"/>
    </justification>
  </clause>

  <clause id="12085">
    <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(9209(a,1),12084(a,2,2,1,2))].">
      <j1 rule="para" parents="9209 12084"/>
    </justification>
  </clause>

  <clause id="12086">
    <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(6777(a,1),10171(a,1,1,1))].">
      <j1 rule="para" parents="6777 10171"/>
    </justification>
  </clause>

  <clause id="12087">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,x * (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(4489(a,1),12086(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4489 12086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12088">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,7637,a(flip),b,12087,a),flip(a)].">
      <j1 rule="hyper" parents="334 7637 12087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12090">
    <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(334,a,526,a(flip),b,10859,a),flip(a)].">
      <j1 rule="hyper" parents="334 526 10859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12091">
    <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(2173,a,12090,a)].">
      <j1 rule="hyper" parents="2173 12090"/>
    </justification>
  </clause>

  <clause id="12092">
    <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(5404(a,1),12091(a,1,1,2,1))].">
      <j1 rule="para" parents="5404 12091"/>
    </justification>
  </clause>

  <clause id="12093">
    <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(5825(a,1),12092(a,1,1,2,1))].">
      <j1 rule="para" parents="5825 12092"/>
    </justification>
  </clause>

  <clause id="12094">
    <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(8192(a,1),12093(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8192 12093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12095">
    <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,4674,a(flip),b,12094,a),flip(a)].">
      <j1 rule="hyper" parents="58 4674 12094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12097">
    <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(12095(a,1),1383(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12095 1383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12098">
    <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(5391(a,1),12097(a,1,1))].">
      <j1 rule="para" parents="5391 12097"/>
    </justification>
  </clause>

  <clause id="12099">
    <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(10201(a,1),12098(a,1,1))].">
      <j1 rule="para" parents="10201 12098"/>
    </justification>
  </clause>

  <clause id="12100">
    <literal><![CDATA[
      R(K(x,y),R(T(x,z),u,w),v5) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,12099,a),flip(a)].">
      <j1 rule="hyper" parents="347 12099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12103">
    <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,6158,a(flip),b,12100,a)].">
      <j1 rule="hyper" parents="58 6158 12100"/>
    </justification>
  </clause>

  <clause id="12104">
    <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(334,a,7513,a(flip),b,12103,a),flip(a)].">
      <j1 rule="hyper" parents="334 7513 12103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12105">
    <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,7679,a(flip),b,12104,a),flip(a)].">
      <j1 rule="hyper" parents="58 7679 12104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12107">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) = K(x,y \ R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,10999,a(flip),b,12105,a),flip(a)].">
      <j1 rule="hyper" parents="334 10999 12105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12108">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(8542,a,12107,a)].">
      <j1 rule="hyper" parents="8542 12107"/>
    </justification>
  </clause>

  <clause id="12110">
    <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,7322,a(flip),b,10889,a),flip(a)].">
      <j1 rule="hyper" parents="58 7322 10889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12112">
    <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(5232(a,1),12082(a,2,1,2,1))].">
      <j1 rule="para" parents="5232 12082"/>
    </justification>
  </clause>

  <clause id="12113">
    <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(6201(a,1),12112(a,2,1))].">
      <j1 rule="para" parents="6201 12112"/>
    </justification>
  </clause>

  <clause id="12114">
    <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(6026(a,1),12113(a,1,2,2,2,1))].">
      <j1 rule="para" parents="6026 12113"/>
    </justification>
  </clause>

  <clause id="12115">
    <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(12083,a,12114,a)].">
      <j1 rule="hyper" parents="12083 12114"/>
    </justification>
  </clause>

  <clause id="12116">
    <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,11002,a(flip),b,12115,a)].">
      <j1 rule="hyper" parents="58 11002 12115"/>
    </justification>
  </clause>

  <clause id="12117">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = L(a(x,y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(11089(a,1),12116(a,1,3))].">
      <j1 rule="para" parents="11089 12116"/>
    </justification>
  </clause>

  <clause id="12118">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,147,a(flip),b,12117,a),flip(a)].">
      <j1 rule="hyper" parents="334 147 12117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12120">
    <literal><![CDATA[
      a(x,y,K(z,(u * w) \ v5)) = a(x,y,K(z,w \ (u \ v5)))
    ]]></literal>
    <justification jstring="[para(311(a,1),12118(a,1,3,2))].">
      <j1 rule="para" parents="311 12118"/>
    </justification>
  </clause>

  <clause id="12121">
    <literal><![CDATA[
      a(x,y,K((z \ u) \ w,v5)) = a(x,y,K(u \ (z * w),v5))
    ]]></literal>
    <justification jstring="[para(11106(a,1),12118(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11106 12118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12122">
    <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(9135(a,1),9141(a,1,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9135 9141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12123">
    <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),12122(a,2,1,2,1))].">
      <j1 rule="para" parents="4 12122"/>
    </justification>
  </clause>

  <clause id="12125">
    <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(9135(a,1),12123(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9135 12123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12126">
    <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(2069(a,1),12125(a,2,2))].">
      <j1 rule="para" parents="2069 12125"/>
    </justification>
  </clause>

  <clause id="12127">
    <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,9981,a,b,12126,a)].">
      <j1 rule="hyper" parents="58 9981 12126"/>
    </justification>
  </clause>

  <clause id="12128">
    <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(343,a,12127,a),flip(a)].">
      <j1 rule="hyper" parents="343 12127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12129">
    <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(5401(a,1),12127(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5401 12127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12130">
    <literal><![CDATA[
      x / a(K(y,z),u,u \ 1) = x * a(K(z,y),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(5401(a,1),12129(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5401 12129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12131">
    <literal><![CDATA[
      a(K(x,y),z,z \ 1) \ 1 = a(K(y,x),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(4229,a,12130,a)].">
      <j1 rule="hyper" parents="4229 12130"/>
    </justification>
  </clause>

  <clause id="12132">
    <literal><![CDATA[
      K(x,a(K(y,z),u,u \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(12131(a,1),10882(a,1,2))].">
      <j1 rule="para" parents="12131 10882"/>
    </justification>
  </clause>

  <clause id="12133">
    <literal><![CDATA[
      T(x,a(K(y,z),u,u \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,12132,a)].">
      <j1 rule="hyper" parents="51 12132"/>
    </justification>
  </clause>

  <clause id="12134">
    <literal><![CDATA[
      T(x,a(K(y,z),u \ 1,u)) = x
    ]]></literal>
    <justification jstring="[para(3843(a,1),12133(a,1,2))].">
      <j1 rule="para" parents="3843 12133"/>
    </justification>
  </clause>

  <clause id="12135">
    <literal><![CDATA[
      T(a(K(x,y),z \ 1,z),u) = a(K(x,y),z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(49,a,12134,a)].">
      <j1 rule="hyper" parents="49 12134"/>
    </justification>
  </clause>

  <clause id="12136">
    <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(334,a,3816,a,b,12135,a),flip(a)].">
      <j1 rule="hyper" parents="334 3816 12135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12137">
    <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(5407(a,2),12136(a,1,1))].">
      <j1 rule="para" parents="5407 12136"/>
    </justification>
  </clause>

  <clause id="12138">
    <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,10174,a,b,12137,a)].">
      <j1 rule="hyper" parents="58 10174 12137"/>
    </justification>
  </clause>

  <clause id="12139">
    <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,7434,a,b,12138,a)].">
      <j1 rule="hyper" parents="58 7434 12138"/>
    </justification>
  </clause>

  <clause id="12140">
    <literal><![CDATA[
      K(x,K(y,R(z,u \ 1,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(10945,a,12139,a)].">
      <j1 rule="hyper" parents="10945 12139"/>
    </justification>
  </clause>

  <clause id="12141">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ 1))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(2946(a,1),12140(a,1,2,2))].">
      <j1 rule="para" parents="2946 12140"/>
    </justification>
  </clause>

  <clause id="12142">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ 1))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8067,a,b,12141,a),flip(a)].">
      <j1 rule="hyper" parents="334 8067 12141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12143">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ K(w,x)))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,11680,a,b,12141,a)].">
      <j1 rule="hyper" parents="58 11680 12141"/>
    </justification>
  </clause>

  <clause id="12144">
    <literal><![CDATA[
      K(x,K(y,z * (u \ 1))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(536(a,1),12142(a,1,2,2))].">
      <j1 rule="para" parents="536 12142"/>
    </justification>
  </clause>

  <clause id="12145">
    <literal><![CDATA[
      T(x,K(y,z * (u \ 1))) = T(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(118,a,12144,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 12144 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12146">
    <literal><![CDATA[
      K(x,K(y,z / (1 / u))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(75(a,1),12144(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="75 12144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12147">
    <literal><![CDATA[
      K(x,K(y,z / (u \ 1))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(5573(a,1),12144(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5573 12144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12148">
    <literal><![CDATA[
      K(x,K(y,z * (1 / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(5577(a,2),12144(a,1,2))].">
      <j1 rule="para" parents="5577 12144"/>
    </justification>
  </clause>

  <clause id="12149">
    <literal><![CDATA[
      T(T(x,y),K(y,z / u)) = T(x,T(y,(z * (u \ 1)) \ 1))
    ]]></literal>
    <justification jstring="[hyper(8479,a,12145,a),flip(a)].">
      <j1 rule="hyper" parents="8479 12145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12150">
    <literal><![CDATA[
      T(x,K(y,z * (x \ 1))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8306,a(flip),b,12145,a),flip(a)].">
      <j1 rule="hyper" parents="334 8306 12145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12151">
    <literal><![CDATA[
      T(x \ 1,K(y,z * x)) = T(x \ 1,K(y,z))
    ]]></literal>
    <justification jstring="[para(5573(a,1),12150(a,1,2))].">
      <j1 rule="para" parents="5573 12150"/>
    </justification>
  </clause>

  <clause id="12152">
    <literal><![CDATA[
      K(x,K(y,(1 / z) / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8545,a,12146,a)].">
      <j1 rule="hyper" parents="8545 12146"/>
    </justification>
  </clause>

  <clause id="12153">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8545,a,12147,a)].">
      <j1 rule="hyper" parents="8545 12147"/>
    </justification>
  </clause>

  <clause id="12154">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8099,a,12147,a)].">
      <j1 rule="hyper" parents="8099 12147"/>
    </justification>
  </clause>

  <clause id="12155">
    <literal><![CDATA[
      K(x,K(T(y,z),z * u)) = K(x,K(y,(u \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(7389(a,1),12147(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7389 12147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12156">
    <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(12151(a,1),5261(a,1,1))].">
      <j1 rule="para" parents="12151 5261"/>
    </justification>
  </clause>

  <clause id="12157">
    <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(12152(a,1),11179(a,1,3))].">
      <j1 rule="para" parents="12152 11179"/>
    </justification>
  </clause>

  <clause id="12158">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),12153(a,2,2,2))].">
      <j1 rule="para" parents="7 12153"/>
    </justification>
  </clause>

  <clause id="12159">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) = K(x,K(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,8067,a,b,12154,a),flip(a)].">
      <j1 rule="hyper" parents="334 8067 12154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12160">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(8050,a,12158,a)].">
      <j1 rule="hyper" parents="8050 12158"/>
    </justification>
  </clause>

  <clause id="12161">
    <literal><![CDATA[
      K(x,K(y * z,L(u,z \ 1,z))) = K(u,K(x,T(z * y,z)))
    ]]></literal>
    <justification jstring="[hyper(11305,a,12159,a),flip(a)].">
      <j1 rule="hyper" parents="11305 12159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12162">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y * z)) = w
    ]]></literal>
    <justification jstring="[para(12159(a,2),8099(a,1))].">
      <j1 rule="para" parents="12159 8099"/>
    </justification>
  </clause>

  <clause id="12163">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8475,a(flip),b,12160,a)].">
      <j1 rule="hyper" parents="58 8475 12160"/>
    </justification>
  </clause>

  <clause id="12165">
    <literal><![CDATA[
      K(x,K(y,z)) * (z / u) = T(z,K(x,y)) / u
    ]]></literal>
    <justification jstring="[para(12163(a,1),9879(a,1,1))].">
      <j1 rule="para" parents="12163 9879"/>
    </justification>
  </clause>

  <clause id="12166">
    <literal><![CDATA[
      R(K(x,K(y,z)),z / u,u) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(12163(a,1),10159(a,1,1))].">
      <j1 rule="para" parents="12163 10159"/>
    </justification>
  </clause>

  <clause id="12167">
    <literal><![CDATA[
      R(K(x,K(y,z)),y / u,u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(8067(a,1),12166(a,1,1))].">
      <j1 rule="para" parents="8067 12166"/>
    </justification>
  </clause>

  <clause id="12169">
    <literal><![CDATA[
      K(x,K(y,R(z,x / u,u))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9344,a(flip),b,12167,a)].">
      <j1 rule="hyper" parents="58 9344 12167"/>
    </justification>
  </clause>

  <clause id="12170">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(72(a,1),12169(a,1,2,2,2))].">
      <j1 rule="para" parents="72 12169"/>
    </justification>
  </clause>

  <clause id="12171">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,K(x,y)) / u) = z / u
    ]]></literal>
    <justification jstring="[hyper(8095,a,12165,a)].">
      <j1 rule="hyper" parents="8095 12165"/>
    </justification>
  </clause>

  <clause id="12172">
    <literal><![CDATA[
      T(x,K(y,z)) / (u \ x) = K(y,K(z,x)) * u
    ]]></literal>
    <justification jstring="[para(72(a,1),12165(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 12165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12174">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(x,K(z,y)) / u) = x / u
    ]]></literal>
    <justification jstring="[para(8017(a,1),12171(a,1,1))].">
      <j1 rule="para" parents="8017 12171"/>
    </justification>
  </clause>

  <clause id="12175">
    <literal><![CDATA[
      T(x,K(y,z)) / (u \ x) = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(8053(a,1),12172(a,2,1))].">
      <j1 rule="para" parents="8053 12172"/>
    </justification>
  </clause>

  <clause id="12176">
    <literal><![CDATA[
      K((T(x,y) / z) / (x / z),u) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(9881,a,12174,a)].">
      <j1 rule="hyper" parents="9881 12174"/>
    </justification>
  </clause>

  <clause id="12177">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ T(x,K(y,z)) = u \ x
    ]]></literal>
    <justification jstring="[hyper(192,a,12175,a)].">
      <j1 rule="hyper" parents="192 12175"/>
    </justification>
  </clause>

  <clause id="12178">
    <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(11766(a,1),12176(a,1,1,1,1))].">
      <j1 rule="para" parents="11766 12176"/>
    </justification>
  </clause>

  <clause id="12179">
    <literal><![CDATA[
      L(x \ y,x,K(y,K(z,u))) = x \ y
    ]]></literal>
    <justification jstring="[hyper(5125,a,12177,a)].">
      <j1 rule="hyper" parents="5125 12177"/>
    </justification>
  </clause>

  <clause id="12180">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,u \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(48,a,12179,a)].">
      <j1 rule="hyper" parents="48 12179"/>
    </justification>
  </clause>

  <clause id="12181">
    <literal><![CDATA[
      a(K(x * y,K(z,u)),x,y) = 1
    ]]></literal>
    <justification jstring="[para(4(a,1),12180(a,1,3))].">
      <j1 rule="para" parents="4 12180"/>
    </justification>
  </clause>

  <clause id="12182">
    <literal><![CDATA[
      a(K(K(x,y),z),u,u \ z) = 1
    ]]></literal>
    <justification jstring="[para(5886(a,2),12180(a,1,1))].">
      <j1 rule="para" parents="5886 12180"/>
    </justification>
  </clause>

  <clause id="12183">
    <literal><![CDATA[
      a(K(x,K(y,z * u)),z,u) = 1
    ]]></literal>
    <justification jstring="[para(8017(a,1),12181(a,1,1))].">
      <j1 rule="para" parents="8017 12181"/>
    </justification>
  </clause>

  <clause id="12184">
    <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(334,a,8075,a,b,12182,a),flip(a)].">
      <j1 rule="hyper" parents="334 8075 12182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12186">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (u \ K(w,z)) = K(w,z) * K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(12143(a,1),10468(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12143 10468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12187">
    <literal><![CDATA[
      K(x,K(y,T(z * u,z))) = K(x,K(y,(u \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(7403(a,1),12155(a,1,2))].">
      <j1 rule="para" parents="7403 12155"/>
    </justification>
  </clause>

  <clause id="12188">
    <literal><![CDATA[
      T(x,T(y,(z * (u \ 1)) \ 1)) = T(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(7969,a,12149,a),flip(a)].">
      <j1 rule="hyper" parents="7969 12149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12189">
    <literal><![CDATA[
      T(x,T(y,z * (u \ 1))) = T(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(8492,a,12188,a)].">
      <j1 rule="hyper" parents="8492 12188"/>
    </justification>
  </clause>

  <clause id="12190">
    <literal><![CDATA[
      T(x,T(y,z * (u \ 1))) = x * K(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(334,a,5020,a(flip),b,12189,a),flip(a)].">
      <j1 rule="hyper" parents="334 5020 12189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12191">
    <literal><![CDATA[
      K(x,T(y,z * (u \ 1))) = K(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(5109,a,12190,a)].">
      <j1 rule="hyper" parents="5109 12190"/>
    </justification>
  </clause>

  <clause id="12192">
    <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(12191(a,1),11655(a,1,1))].">
      <j1 rule="para" parents="12191 11655"/>
    </justification>
  </clause>

  <clause id="12193">
    <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),12161(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 12161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12194">
    <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(12170(a,1),12184(a,2,2))].">
      <j1 rule="para" parents="12170 12184"/>
    </justification>
  </clause>

  <clause id="12195">
    <literal><![CDATA[
      K(x,K(y,T(z * (u / z),z))) = K(x,K(u,L(y,z \ 1,z)))
    ]]></literal>
    <justification jstring="[hyper(8050,a,12193,a)].">
      <j1 rule="hyper" parents="8050 12193"/>
    </justification>
  </clause>

  <clause id="12196">
    <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,12187,a(flip),b,12195,a)].">
      <j1 rule="hyper" parents="58 12187 12195"/>
    </justification>
  </clause>

  <clause id="12197">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(z,K(x,L(u,y \ 1,y)))
    ]]></literal>
    <justification jstring="[para(12196(a,1),9097(a,2,2))].">
      <j1 rule="para" parents="12196 9097"/>
    </justification>
  </clause>

  <clause id="12198">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(x,K(z,L(u,y \ 1,y)))
    ]]></literal>
    <justification jstring="[para(8048(a,1),12197(a,2,2))].">
      <j1 rule="para" parents="8048 12197"/>
    </justification>
  </clause>

  <clause id="12199">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (u \ K(y,z)) = T(K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(334,a,8059,a(flip),b,12186,a),flip(a)].">
      <j1 rule="hyper" parents="334 8059 12186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12201">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (u \ K(x,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(8053(a,2),12199(a,1,1,1))].">
      <j1 rule="para" parents="8053 12199"/>
    </justification>
  </clause>

  <clause id="12202">
    <literal><![CDATA[
      K(x,T(y,z)) / (u \ K(x,y)) = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(117,a,7401,a,b,12201,a)].">
      <j1 rule="hyper" parents="117 7401 12201"/>
    </justification>
  </clause>

  <clause id="12203">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) / u) = K(x,T(y,z)) / u
    ]]></literal>
    <justification jstring="[para(75(a,1),12202(a,1,2)),flip(a)].">
      <j1 rule="para" parents="75 12202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12204">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,T(y,z)) / u) = K(x,y) / u
    ]]></literal>
    <justification jstring="[hyper(8095,a,12203,a)].">
      <j1 rule="hyper" parents="8095 12203"/>
    </justification>
  </clause>

  <clause id="12205">
    <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(12204(a,1),6535(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12204 6535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12206">
    <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(8019(a,2),12205(a,2,2))].">
      <j1 rule="para" parents="8019 12205"/>
    </justification>
  </clause>

  <clause id="12207">
    <literal><![CDATA[
      K(x,(K(y,z) / u) / (u \ 1)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(29,a,10519,a,b,12206,a)].">
      <j1 rule="hyper" parents="29 10519 12206"/>
    </justification>
  </clause>

  <clause id="12209">
    <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(8053(a,2),12194(a,2,2))].">
      <j1 rule="para" parents="8053 12194"/>
    </justification>
  </clause>

  <clause id="12210">
    <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(5886(a,1),12209(a,1,1))].">
      <j1 rule="para" parents="5886 12209"/>
    </justification>
  </clause>

  <clause id="12211">
    <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(334,a,11836,a(flip),b,12210,a)].">
      <j1 rule="hyper" parents="334 11836 12210"/>
    </justification>
  </clause>

  <clause id="12212">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x)) * K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(334,a,12183,a(flip),b,12211,a),flip(a)].">
      <j1 rule="hyper" parents="334 12183 12211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12213">
    <literal><![CDATA[
      K(x,K(y,z) * K(z,R(y,u,u \ x))) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,11850,a(flip),b,12212,a)].">
      <j1 rule="hyper" parents="58 11850 12212"/>
    </justification>
  </clause>

  <clause id="12214">
    <literal><![CDATA[
      K(x * y,K(z,u) * K(u,R(z,x,y))) = 1
    ]]></literal>
    <justification jstring="[para(4(a,1),12213(a,1,2,2,2,3))].">
      <j1 rule="para" parents="4 12213"/>
    </justification>
  </clause>

  <clause id="12215">
    <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(8219(a,1),12192(a,1,1,2))].">
      <j1 rule="para" parents="8219 12192"/>
    </justification>
  </clause>

  <clause id="12216">
    <literal><![CDATA[
      K(x,((y \ (z * x)) * (z \ 1)) \ x) = R(K(x,y),z * x,z \ 1)
    ]]></literal>
    <justification jstring="[para(5457(a,1),12215(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5457 12215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12217">
    <literal><![CDATA[
      K(x,((y \ (z * x)) * (z \ 1)) \ x) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,9527,a(flip),b,12216,a),flip(a)].">
      <j1 rule="hyper" parents="334 9527 12216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12219">
    <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(517(a,1),12217(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="517 12217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12220">
    <literal><![CDATA[
      R(K(R(x,y,y \ 1),z),y,x) = K(x,(((z \ y) * x) * (y \ 1)) \ x)
    ]]></literal>
    <justification jstring="[hyper(9540,a,12219,a)].">
      <j1 rule="hyper" parents="9540 12219"/>
    </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(7341,a,12220,a)].">
      <j1 rule="hyper" parents="7341 12220"/>
    </justification>
  </clause>

  <clause id="12222">
    <literal><![CDATA[
      K(x,((y \ z) * (z \ 1)) \ (x \ x)) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11645,a(flip),b,12221,a)].">
      <j1 rule="hyper" parents="58 11645 12221"/>
    </justification>
  </clause>

  <clause id="12224">
    <literal><![CDATA[
      K(x,((y \ z) * (z \ 1)) \ 1) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[para(61(a,1),12222(a,1,2,2))].">
      <j1 rule="para" parents="61 12222"/>
    </justification>
  </clause>

  <clause id="12225">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6184,a(flip),b,12224,a)].">
      <j1 rule="hyper" parents="58 6184 12224"/>
    </justification>
  </clause>

  <clause id="12227">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) \ 1 = K(y,R(x,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(12225(a,2),5232(a,1,1))].">
      <j1 rule="para" parents="12225 5232"/>
    </justification>
  </clause>

  <clause id="12228">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,R(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(6216,a,12227,a)].">
      <j1 rule="hyper" parents="6216 12227"/>
    </justification>
  </clause>

  <clause id="12229">
    <literal><![CDATA[
      K(x,(y * z) * (z \ 1)) = R(K(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[para(269(a,2),12228(a,2,2)),flip(a)].">
      <j1 rule="para" parents="269 12228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12230">
    <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(5445(a,2),12178(a,1,1))].">
      <j1 rule="para" parents="5445 12178"/>
    </justification>
  </clause>

  <clause id="12231">
    <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(8314,a,12230,a)].">
      <j1 rule="hyper" parents="8314 12230"/>
    </justification>
  </clause>

  <clause id="12232">
    <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(12162,a,12231,a)].">
      <j1 rule="hyper" parents="12162 12231"/>
    </justification>
  </clause>

  <clause id="12233">
    <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),12232(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 12232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12234">
    <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(12233(a,1),8042(a,1))].">
      <j1 rule="para" parents="12233 8042"/>
    </justification>
  </clause>

  <clause id="12235">
    <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(3247(a,1),9587(a,2,1,2))].">
      <j1 rule="para" parents="3247 9587"/>
    </justification>
  </clause>

  <clause id="12236">
    <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(454(a,1),12235(a,1,1,2,2))].">
      <j1 rule="para" parents="454 12235"/>
    </justification>
  </clause>

  <clause id="12237">
    <literal><![CDATA[
      K(x * T((y * z) \ z,y),y \ 1) = K(x * R(y \ 1,y,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(3235(a,1),12236(a,1,1,2))].">
      <j1 rule="para" parents="3235 12236"/>
    </justification>
  </clause>

  <clause id="12238">
    <literal><![CDATA[
      K(x * R(y \ 1,y,z),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,4298,a(flip),b,12237,a),flip(a)].">
      <j1 rule="hyper" parents="58 4298 12237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12239">
    <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(8019(a,1),12156(a,1,2,1,2))].">
      <j1 rule="para" parents="8019 12156"/>
    </justification>
  </clause>

  <clause id="12240">
    <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(8434(a,1),12239(a,1,2,1,2))].">
      <j1 rule="para" parents="8434 12239"/>
    </justification>
  </clause>

  <clause id="12241">
    <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(8057(a,1),12240(a,1,2,1,2))].">
      <j1 rule="para" parents="8057 12240"/>
    </justification>
  </clause>

  <clause id="12242">
    <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(8234(a,1),12241(a,1,2,1,2))].">
      <j1 rule="para" parents="8234 12241"/>
    </justification>
  </clause>

  <clause id="12243">
    <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(4998(a,2),12242(a,1,2,1))].">
      <j1 rule="para" parents="4998 12242"/>
    </justification>
  </clause>

  <clause id="12244">
    <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(5943,a,12243,a)].">
      <j1 rule="hyper" parents="5943 12243"/>
    </justification>
  </clause>

  <clause id="12245">
    <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(8465(a,1),12244(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8465 12244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12246">
    <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(1556(a,1),12245(a,2,2))].">
      <j1 rule="para" parents="1556 12245"/>
    </justification>
  </clause>

  <clause id="12247">
    <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(334,a,8094,a(flip),b,12246,a),flip(a)].">
      <j1 rule="hyper" parents="334 8094 12246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12248">
    <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),6993(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 6993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12249">
    <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(334,a,7407,a(flip),b,12248,a),flip(a)].">
      <j1 rule="hyper" parents="334 7407 12248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12251">
    <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(334,a,9502,a(flip),b,12249,a),flip(a)].">
      <j1 rule="hyper" parents="334 9502 12249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12252">
    <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(10674,a,12251,a)].">
      <j1 rule="hyper" parents="10674 12251"/>
    </justification>
  </clause>

  <clause id="12253">
    <literal><![CDATA[
      K(x,T((R(x,y,z) \ u) \ w,w)) = K(x,(R(x,y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(9507,a,12252,a)].">
      <j1 rule="hyper" parents="9507 12252"/>
    </justification>
  </clause>

  <clause id="12254">
    <literal><![CDATA[
      K(x,(R(x,y,z) * u) / w) = K(x,u / (R(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(8543,a,12253,a),flip(a)].">
      <j1 rule="hyper" parents="8543 12253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12256">
    <literal><![CDATA[
      K(x,R(x,y,z) / (u / w)) = K(x,w / (R(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(10318,a,12254,a)].">
      <j1 rule="hyper" parents="10318 12254"/>
    </justification>
  </clause>

  <clause id="12257">
    <literal><![CDATA[
      K(x,y / (R(x,z,u) \ w)) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(6773,a,12256,a),flip(a)].">
      <j1 rule="hyper" parents="6773 12256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12258">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9334,a,b,12257,a)].">
      <j1 rule="hyper" parents="58 9334 12257"/>
    </justification>
  </clause>

  <clause id="12259">
    <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,11773,a,b,12258,a)].">
      <j1 rule="hyper" parents="58 11773 12258"/>
    </justification>
  </clause>

  <clause id="12260">
    <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),12259(a,2,2,1))].">
      <j1 rule="para" parents="15 12259"/>
    </justification>
  </clause>

  <clause id="12261">
    <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,9552,a(flip),b,12260,a),flip(a)].">
      <j1 rule="hyper" parents="58 9552 12260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12263">
    <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(5391(a,1),10029(a,1,1,1))].">
      <j1 rule="para" parents="5391 10029"/>
    </justification>
  </clause>

  <clause id="12264">
    <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(7396(a,1),11239(a,1,2,1,1))].">
      <j1 rule="para" parents="7396 11239"/>
    </justification>
  </clause>

  <clause id="12265">
    <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(11374(a,1),12263(a,1,1))].">
      <j1 rule="para" parents="11374 12263"/>
    </justification>
  </clause>

  <clause id="12266">
    <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,6456,a(flip),b,12265,a)].">
      <j1 rule="hyper" parents="58 6456 12265"/>
    </justification>
  </clause>

  <clause id="12268">
    <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,11871,a(flip),b,12266,a)].">
      <j1 rule="hyper" parents="58 11871 12266"/>
    </justification>
  </clause>

  <clause id="12269">
    <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,11846,a(flip),b,12268,a),flip(a)].">
      <j1 rule="hyper" parents="58 11846 12268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12270">
    <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(334,a,11850,a(flip),b,12269,a),flip(a)].">
      <j1 rule="hyper" parents="334 11850 12269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12271">
    <literal><![CDATA[
      K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(334,a,12214,a(flip),b,12270,a),flip(a)].">
      <j1 rule="hyper" parents="334 12214 12270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12273">
    <literal><![CDATA[
      K(a(K(x,y),z,u),K(x,y) * (z * u)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,6456,a(flip),b,12271,a)].">
      <j1 rule="hyper" parents="58 6456 12271"/>
    </justification>
  </clause>

  <clause id="12274">
    <literal><![CDATA[
      1 * (((K(x,y) * z) * u) / (K(x,y) * (z * u))) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(12273(a,1),5266(a,1,1))].">
      <j1 rule="para" parents="12273 5266"/>
    </justification>
  </clause>

  <clause id="12275">
    <literal><![CDATA[
      1 * (K(x,y) * R(K(y,x),z,u)) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(11375(a,1),12274(a,1,2))].">
      <j1 rule="para" parents="11375 12274"/>
    </justification>
  </clause>

  <clause id="12276">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(120,a,12275,a)].">
      <j1 rule="hyper" parents="120 12275"/>
    </justification>
  </clause>

  <clause id="12277">
    <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(8066(a,1),12275(a,1,2,1))].">
      <j1 rule="para" parents="8066 12275"/>
    </justification>
  </clause>

  <clause id="12278">
    <literal><![CDATA[
      K(x,y) * a(K(x,y),z,u) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(5409,a,12276,a)].">
      <j1 rule="hyper" parents="5409 12276"/>
    </justification>
  </clause>

  <clause id="12279">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(y,x) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(2077,a,12276,a)].">
      <j1 rule="hyper" parents="2077 12276"/>
    </justification>
  </clause>

  <clause id="12280">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,R(x,z,u) \ 1) = a(K(y,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(6150(a,1),12276(a,1,2))].">
      <j1 rule="para" parents="6150 12276"/>
    </justification>
  </clause>

  <clause id="12281">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z * x,u)
    ]]></literal>
    <justification jstring="[para(9533(a,1),12276(a,1,2))].">
      <j1 rule="para" parents="9533 12276"/>
    </justification>
  </clause>

  <clause id="12282">
    <literal><![CDATA[
      K(x,y) * (R(K(y,x),z,u) * w) = a(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(12276(a,1),10179(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12276 10179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12283">
    <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(12276(a,1),11853(a,2,2))].">
      <j1 rule="para" parents="12276 11853"/>
    </justification>
  </clause>

  <clause id="12284">
    <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(12276(a,1),11871(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12276 11871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12286">
    <literal><![CDATA[
      (x * a(K(y,z),u,w)) * (K(y,z) * R(K(z,y),u,w)) = x
    ]]></literal>
    <justification jstring="[para(12276(a,1),12128(a,1,1,2))].">
      <j1 rule="para" parents="12276 12128"/>
    </justification>
  </clause>

  <clause id="12287">
    <literal><![CDATA[
      a(K(x,y),K(z,y),u) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10295,a(flip),b,12278,a),flip(a)].">
      <j1 rule="hyper" parents="115 10295 12278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12288">
    <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(12278(a,1),10466(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12278 10466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12289">
    <literal><![CDATA[
      L(x,K(y,z),K(u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,12287,a)].">
      <j1 rule="hyper" parents="47 12287"/>
    </justification>
  </clause>

  <clause id="12290">
    <literal><![CDATA[
      (K(x,y) * K(z,y)) \ u = K(y,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6040,a(flip),b,12289,a)].">
      <j1 rule="hyper" parents="58 6040 12289"/>
    </justification>
  </clause>

  <clause id="12291">
    <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(12279(a,1),10043(a,2,2))].">
      <j1 rule="para" parents="12279 10043"/>
    </justification>
  </clause>

  <clause id="12292">
    <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,9216,a,b,12290,a)].">
      <j1 rule="hyper" parents="58 9216 12290"/>
    </justification>
  </clause>

  <clause id="12293">
    <literal><![CDATA[
      K(x,y) * (a(K(x,y),z,u) * w) = R(K(x,y),z,u) * w
    ]]></literal>
    <justification jstring="[hyper(5409,a,12282,a)].">
      <j1 rule="hyper" parents="5409 12282"/>
    </justification>
  </clause>

  <clause id="12294">
    <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(11859,a,12284,a)].">
      <j1 rule="hyper" parents="11859 12284"/>
    </justification>
  </clause>

  <clause id="12297">
    <literal><![CDATA[
      (x * a(K(y,z),u,w)) * a(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[para(12276(a,1),12286(a,1,2))].">
      <j1 rule="para" parents="12276 12286"/>
    </justification>
  </clause>

  <clause id="12299">
    <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,12297,a)].">
      <j1 rule="hyper" parents="116 106 12297"/>
    </justification>
  </clause>

  <clause id="12300">
    <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,9408,a(flip),b,12293,a)].">
      <j1 rule="hyper" parents="58 9408 12293"/>
    </justification>
  </clause>

  <clause id="12301">
    <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(12294(a,1),12071(a,1,1,1))].">
      <j1 rule="para" parents="12294 12071"/>
    </justification>
  </clause>

  <clause id="12302">
    <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(9344(a,1),12277(a,1,2,2))].">
      <j1 rule="para" parents="9344 12277"/>
    </justification>
  </clause>

  <clause id="12303">
    <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),12292(a,2,2))].">
      <j1 rule="para" parents="3 12292"/>
    </justification>
  </clause>

  <clause id="12304">
    <literal><![CDATA[
      K(K(x,y) * K(x,z),K(z,x) * K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,12303,a)].">
      <j1 rule="hyper" parents="50 12303"/>
    </justification>
  </clause>

  <clause id="12305">
    <literal><![CDATA[
      K(K(x,y) * K(x,z),(K(x,y) * K(x,z)) \ 1) = 1
    ]]></literal>
    <justification jstring="[para(9217(a,2),12304(a,1,2))].">
      <j1 rule="para" parents="9217 12304"/>
    </justification>
  </clause>

  <clause id="12306">
    <literal><![CDATA[
      K((K(x,y) * K(x,z)) \ 1,K(x,y) * K(x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,12305,a,b,5233,a),flip(a)].">
      <j1 rule="hyper" parents="115 12305 5233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12307">
    <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(12306(a,1),3216(a,1,1,2))].">
      <j1 rule="para" parents="12306 3216"/>
    </justification>
  </clause>

  <clause id="12308">
    <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(11862(a,1),12302(a,1,2))].">
      <j1 rule="para" parents="11862 12302"/>
    </justification>
  </clause>

  <clause id="12309">
    <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(9456(a,1),12300(a,1,2))].">
      <j1 rule="para" parents="9456 12300"/>
    </justification>
  </clause>

  <clause id="12310">
    <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(5299,a,12309,a)].">
      <j1 rule="hyper" parents="5299 12309"/>
    </justification>
  </clause>

  <clause id="12311">
    <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(334,a,10037,a,b,12310,a),flip(a)].">
      <j1 rule="hyper" parents="334 10037 12310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12312">
    <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(334,a,12291,a(flip),b,12288,a),flip(a)].">
      <j1 rule="hyper" parents="334 12291 12288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12313">
    <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(395(a,1),12301(a,1,1)),flip(a)].">
      <j1 rule="para" parents="395 12301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12314">
    <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(334,a,9461,a(flip),b,12313,a),flip(a)].">
      <j1 rule="hyper" parents="334 9461 12313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12315">
    <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(8019(a,1),12314(a,1,2,1,1))].">
      <j1 rule="para" parents="8019 12314"/>
    </justification>
  </clause>

  <clause id="12316">
    <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(9343(a,1),12315(a,1,2,1))].">
      <j1 rule="para" parents="9343 12315"/>
    </justification>
  </clause>

  <clause id="12317">
    <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(5034(a,2),12316(a,1,2))].">
      <j1 rule="para" parents="5034 12316"/>
    </justification>
  </clause>

  <clause id="12318">
    <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,9352,a,b,12317,a)].">
      <j1 rule="hyper" parents="58 9352 12317"/>
    </justification>
  </clause>

  <clause id="12319">
    <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(8055(a,1),12318(a,1,1))].">
      <j1 rule="para" parents="8055 12318"/>
    </justification>
  </clause>

  <clause id="12320">
    <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(11834,a,12319,a)].">
      <j1 rule="hyper" parents="11834 12319"/>
    </justification>
  </clause>

  <clause id="12321">
    <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,12283,a(flip),b,12320,a),flip(a)].">
      <j1 rule="hyper" parents="58 12283 12320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12322">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) = K(x,a(K(w,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(29,a,5020,a(flip),b,12321,a),flip(a)].">
      <j1 rule="hyper" parents="29 5020 12321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12323">
    <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,12294,a,b,12322,a)].">
      <j1 rule="hyper" parents="58 12294 12322"/>
    </justification>
  </clause>

  <clause id="12324">
    <literal><![CDATA[
      1 * K(x,a(K(y,z),u,w)) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[para(12323(a,1),12308(a,1,2))].">
      <j1 rule="para" parents="12323 12308"/>
    </justification>
  </clause>

  <clause id="12325">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(y,a(K(z,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(120,a,12324,a),flip(a)].">
      <j1 rule="hyper" parents="120 12324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12326">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,12322,a,b,12325,a),flip(a)].">
      <j1 rule="hyper" parents="334 12322 12325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12327">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(x,a(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(8048(a,1),12325(a,1,1))].">
      <j1 rule="para" parents="8048 12325"/>
    </justification>
  </clause>

  <clause id="12328">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(8048(a,1),12326(a,1,1))].">
      <j1 rule="para" parents="8048 12326"/>
    </justification>
  </clause>

  <clause id="12329">
    <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),12307(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3 12307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12330">
    <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(9218(a,1),12329(a,2,3))].">
      <j1 rule="para" parents="9218 12329"/>
    </justification>
  </clause>

  <clause id="12331">
    <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(9218(a,1),12330(a,1,1))].">
      <j1 rule="para" parents="9218 12330"/>
    </justification>
  </clause>

  <clause id="12332">
    <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,6062,a(flip),b,5647,a),flip(a)].">
      <j1 rule="hyper" parents="58 6062 5647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12334">
    <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,6286,a(flip),b,12332,a)].">
      <j1 rule="hyper" parents="58 6286 12332"/>
    </justification>
  </clause>

  <clause id="12335">
    <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,10321,a(flip),b,12334,a)].">
      <j1 rule="hyper" parents="58 10321 12334"/>
    </justification>
  </clause>

  <clause id="12336">
    <literal><![CDATA[
      K((x \ 1) \ (y / (z * y)),z \ 1) = K(x * (y / (z * y)),z \ 1)
    ]]></literal>
    <justification jstring="[para(6(a,1),12335(a,1,2,1))].">
      <j1 rule="para" parents="6 12335"/>
    </justification>
  </clause>

  <clause id="12337">
    <literal><![CDATA[
      K((x \ 1) \ ((y * z) \ z),y \ 1) = K(x * (z / (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,8931,a(flip),b,12336,a)].">
      <j1 rule="hyper" parents="58 8931 12336"/>
    </justification>
  </clause>

  <clause id="12338">
    <literal><![CDATA[
      K((x \ 1) \ ((y * z) \ z),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,7837,a(flip),b,12337,a),flip(a)].">
      <j1 rule="hyper" parents="334 7837 12337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12339">
    <literal><![CDATA[
      K((x \ 1) \ (y \ 1),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,10840,a(flip),b,12338,a)].">
      <j1 rule="hyper" parents="58 10840 12338"/>
    </justification>
  </clause>

  <clause id="12340">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y \ 1) = K(x * (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(7685,a,12339,a),flip(a)].">
      <j1 rule="hyper" parents="7685 12339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12342">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,6807,a(flip),b,12340,a),flip(a)].">
      <j1 rule="hyper" parents="334 6807 12340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12343">
    <literal><![CDATA[
      K(x * R(y \ 1,y,z),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,12238,a,b,12342,a)].">
      <j1 rule="hyper" parents="58 12238 12342"/>
    </justification>
  </clause>

  <clause id="12345">
    <literal><![CDATA[
      T(K(x \ y,x \ 1) / x,y) = R(1 / x,y,z / (x * z))
    ]]></literal>
    <justification jstring="[para(12343(a,1),10194(a,1,1,1))].">
      <j1 rule="para" parents="12343 10194"/>
    </justification>
  </clause>

  <clause id="12346">
    <literal><![CDATA[
      R(1 / x,y,z / (x * z)) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,6808,a(flip),b,12345,a),flip(a)].">
      <j1 rule="hyper" parents="58 6808 12345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12348">
    <literal><![CDATA[
      R(1 / (x / y),z,(x / y) \ 1) = R(1 / (x / y),z,y / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),12346(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="7 12346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12349">
    <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(12348(a,1),9833(a,2,2))].">
      <j1 rule="para" parents="12348 9833"/>
    </justification>
  </clause>

  <clause id="12350">
    <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(334,a,1267,a(flip),b,12349,a),flip(a)].">
      <j1 rule="hyper" parents="334 1267 12349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12351">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x * R(x \ y,z,y / x)) / y
    ]]></literal>
    <justification jstring="[hyper(334,a,1768,a(flip),b,12350,a),flip(a)].">
      <j1 rule="hyper" parents="334 1768 12350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12352">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x * R(x \ y,z,x \ y)) / y
    ]]></literal>
    <justification jstring="[para(9875(a,1),12351(a,2,1,2))].">
      <j1 rule="para" parents="9875 12351"/>
    </justification>
  </clause>

  <clause id="12353">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,9837,a(flip),b,12352,a),flip(a)].">
      <j1 rule="hyper" parents="334 9837 12352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12354">
    <literal><![CDATA[
      T(a(1 / (x / y),z,(x / y) \ 1),u) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[para(3842(a,1),12353(a,1,1))].">
      <j1 rule="para" parents="3842 12353"/>
    </justification>
  </clause>

  <clause id="12355">
    <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(7077(a,1),6698(a,2,1))].">
      <j1 rule="para" parents="7077 6698"/>
    </justification>
  </clause>

  <clause id="12356">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ T(1 / y,(x * y) / x) = (1 / y) * (1 / (1 / ((x * y) / x)))
    ]]></literal>
    <justification jstring="[para(3104(a,1),12355(a,1,2))].">
      <j1 rule="para" parents="3104 12355"/>
    </justification>
  </clause>

  <clause id="12357">
    <literal><![CDATA[
      (1 / x) * (1 / (1 / ((y * x) / y))) = (1 / ((y * x) / y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(2577(a,1),12356(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2577 12356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12358">
    <literal><![CDATA[
      (1 / x) * (1 / (1 / ((y * x) / y))) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(334,a,11772,a(flip),b,12357,a),flip(a)].">
      <j1 rule="hyper" parents="334 11772 12357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12360">
    <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(5303(a,1),5624(a,1,1))].">
      <j1 rule="para" parents="5303 5624"/>
    </justification>
  </clause>

  <clause id="12361">
    <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(5303(a,1),12360(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5303 12360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12362">
    <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(5232(a,1),12361(a,2,2,1))].">
      <j1 rule="para" parents="5232 12361"/>
    </justification>
  </clause>

  <clause id="12363">
    <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(6150(a,1),12362(a,2,2))].">
      <j1 rule="para" parents="6150 12362"/>
    </justification>
  </clause>

  <clause id="12364">
    <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(5011(a,1),12363(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5011 12363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12365">
    <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(6150(a,1),12364(a,2,1,2))].">
      <j1 rule="para" parents="6150 12364"/>
    </justification>
  </clause>

  <clause id="12366">
    <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,12280,a(flip),b,12365,a),flip(a)].">
      <j1 rule="hyper" parents="58 12280 12365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12367">
    <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),2307(a,1,2,1))].">
      <j1 rule="para" parents="7 2307"/>
    </justification>
  </clause>

  <clause id="12368">
    <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),12367(a,1,2))].">
      <j1 rule="para" parents="69 12367"/>
    </justification>
  </clause>

  <clause id="12370">
    <literal><![CDATA[
      (x / (x * L(x \ 1,y,z))) / x = 1 / (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(277,a,12368,a),flip(a)].">
      <j1 rule="hyper" parents="277 12368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12373">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) / x = 1 / (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(3360(a,1),12370(a,1,1))].">
      <j1 rule="para" parents="3360 12370"/>
    </justification>
  </clause>

  <clause id="12374">
    <literal><![CDATA[
      1 / (x * L(x \ 1,y,z)) = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,7009,a(flip),b,12373,a),flip(a)].">
      <j1 rule="hyper" parents="58 7009 12373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12375">
    <literal><![CDATA[
      1 / (x * L(x \ 1,y,z)) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,3732,a,b,12374,a),flip(a)].">
      <j1 rule="hyper" parents="334 3732 12374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12376">
    <literal><![CDATA[
      1 / ((x \ 1) * L((x \ 1) \ 1,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(334,a,3734,a(flip),b,12375,a),flip(a)].">
      <j1 rule="hyper" parents="334 3734 12375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12377">
    <literal><![CDATA[
      (1 / (x * L(x \ 1,y,z))) \ (L(x \ 1,y,z) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(12375(a,2),7008(a,1,1))].">
      <j1 rule="para" parents="12375 7008"/>
    </justification>
  </clause>

  <clause id="12378">
    <literal><![CDATA[
      1 / (x \ L(x,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(1241(a,1),12376(a,1,2))].">
      <j1 rule="para" parents="1241 12376"/>
    </justification>
  </clause>

  <clause id="12379">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ 1 = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(192,a,12378,a)].">
      <j1 rule="hyper" parents="192 12378"/>
    </justification>
  </clause>

  <clause id="12380">
    <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(12378(a,1),5008(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12378 5008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12381">
    <literal><![CDATA[
      1 / (L(x,y,z) \ x) = (L(x,y,z) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(334,a,3728,a,b,12379,a)].">
      <j1 rule="hyper" parents="334 3728 12379"/>
    </justification>
  </clause>

  <clause id="12382">
    <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(1773(a,1),12379(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1773 12379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12383">
    <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(12382(a,1),3661(a,1,1))].">
      <j1 rule="para" parents="12382 3661"/>
    </justification>
  </clause>

  <clause id="12384">
    <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(334,a,8067,a,b,12380,a),flip(a)].">
      <j1 rule="hyper" parents="334 8067 12380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12385">
    <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(12380(a,2),8099(a,1))].">
      <j1 rule="para" parents="12380 8099"/>
    </justification>
  </clause>

  <clause id="12386">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) / ((y \ 1) \ 1) = 1 / (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(12377(a,1),11915(a,1,2))].">
      <j1 rule="para" parents="12377 11915"/>
    </justification>
  </clause>

  <clause id="12387">
    <literal><![CDATA[
      1 / (x * ((y * x) \ y)) = x \ (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7013,a(flip),b,12386,a),flip(a)].">
      <j1 rule="hyper" parents="58 7013 12386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12388">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) / y = 1 / (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4025,a(flip),b,12386,a)].">
      <j1 rule="hyper" parents="58 4025 12386"/>
    </justification>
  </clause>

  <clause id="12389">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ 1 = x \ (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(10445,a,12387,a)].">
      <j1 rule="hyper" parents="10445 12387"/>
    </justification>
  </clause>

  <clause id="12390">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) / y = (y * ((x * y) \ x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(334,a,10444,a(flip),b,12388,a),flip(a)].">
      <j1 rule="hyper" parents="334 10444 12388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12391">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) \ (1 / ((y * x) \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(192,a,12390,a)].">
      <j1 rule="hyper" parents="192 12390"/>
    </justification>
  </clause>

  <clause id="12392">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) * T(x,z) = T(x,z) / (x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[para(12391(a,1),4879(a,1,2,1))].">
      <j1 rule="para" parents="12391 4879"/>
    </justification>
  </clause>

  <clause id="12393">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) * T(x,z) = (x * ((y * x) \ y)) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,10444,a(flip),b,12392,a),flip(a)].">
      <j1 rule="hyper" parents="334 10444 12392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12394">
    <literal><![CDATA[
      (x \ (1 / ((y * x) \ y))) * T(x,z) = (x * ((y * x) \ y)) \ T(x,z)
    ]]></literal>
    <justification jstring="[para(12389(a,1),12393(a,1,1))].">
      <j1 rule="para" parents="12389 12393"/>
    </justification>
  </clause>

  <clause id="12395">
    <literal><![CDATA[
      T((1 / ((x * y) \ x)) * K(y,z),y) = (y * ((x * y) \ x)) \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10042,a,b,12394,a)].">
      <j1 rule="hyper" parents="58 10042 12394"/>
    </justification>
  </clause>

  <clause id="12396">
    <literal><![CDATA[
      T(T(1 / ((x * y) \ x),z),y) = (y * ((x * y) \ x)) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(6621(a,1),12395(a,1,1))].">
      <j1 rule="para" parents="6621 12395"/>
    </justification>
  </clause>

  <clause id="12397">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ T(x,z) = T(1 / ((y * x) \ y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,901,a(flip),b,12396,a),flip(a)].">
      <j1 rule="hyper" parents="58 901 12396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12398">
    <literal><![CDATA[
      1 / ((x * T(y,z)) \ x) = T(1 / ((x * y) \ x),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10451,a(flip),b,12397,a)].">
      <j1 rule="hyper" parents="58 10451 12397"/>
    </justification>
  </clause>

  <clause id="12399">
    <literal><![CDATA[
      T(1 / ((x * y) \ x),z) \ 1 = (x * T(y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(192,a,12398,a)].">
      <j1 rule="hyper" parents="192 12398"/>
    </justification>
  </clause>

  <clause id="12400">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,z) = ((x * T(y,z)) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(12399(a,1),2223(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12399 2223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12401">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) \ 1,u) \ x) = K(x,1 \ (((y * T(z,u)) \ y) * x))
    ]]></literal>
    <justification jstring="[para(12400(a,2),6854(a,1,2,1))].">
      <j1 rule="para" parents="12400 6854"/>
    </justification>
  </clause>

  <clause id="12402">
    <literal><![CDATA[
      K(x,T((((y * z) \ y) \ 1) \ x,u)) = K(x,1 \ (((y * T(z,u)) \ y) * x))
    ]]></literal>
    <justification jstring="[hyper(9003,a,12401,a)].">
      <j1 rule="hyper" parents="9003 12401"/>
    </justification>
  </clause>

  <clause id="12403">
    <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(7401(a,2),9109(a,2,2))].">
      <j1 rule="para" parents="7401 9109"/>
    </justification>
  </clause>

  <clause id="12404">
    <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(9029(a,1),10240(a,1,1,2))].">
      <j1 rule="para" parents="9029 10240"/>
    </justification>
  </clause>

  <clause id="12406">
    <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(9030(a,1),12404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9030 12404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12407">
    <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,3961,a(flip),b,12406,a),flip(a)].">
      <j1 rule="hyper" parents="58 3961 12406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12409">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = (a(x,y,x) * K(x,w)) \ T(x,w)
    ]]></literal>
    <justification jstring="[para(10746(a,1),12407(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10746 12407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12411">
    <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(7810(a,1),12403(a,2,2))].">
      <j1 rule="para" parents="7810 12403"/>
    </justification>
  </clause>

  <clause id="12412">
    <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(334,a,7475,a(flip),b,12411,a),flip(a)].">
      <j1 rule="hyper" parents="334 7475 12411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12414">
    <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(334,a,7719,a(flip),b,12412,a),flip(a)].">
      <j1 rule="hyper" parents="334 7719 12412"/>
      <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) * (K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(334,a,7551,a(flip),b,12414,a),flip(a)].">
      <j1 rule="hyper" parents="334 7551 12414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12416">
    <literal><![CDATA[
      (x * K(y,z * x)) / K(y,z) = K(y,z * x) * (K(z,y) * x)
    ]]></literal>
    <justification jstring="[para(8152(a,1),12415(a,1,2))].">
      <j1 rule="para" parents="8152 12415"/>
    </justification>
  </clause>

  <clause id="12417">
    <literal><![CDATA[
      (x * K(y,z * x)) * K(z,y) = K(y,z * x) * (K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(6529,a,12416,a)].">
      <j1 rule="hyper" parents="6529 12416"/>
    </justification>
  </clause>

  <clause id="12419">
    <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(12417(a,1),9224(a,1))].">
      <j1 rule="para" parents="12417 9224"/>
    </justification>
  </clause>

  <clause id="12420">
    <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),1774(a,1,1))].">
      <j1 rule="para" parents="146 1774"/>
    </justification>
  </clause>

  <clause id="12421">
    <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,12420,a),flip(a)].">
      <j1 rule="hyper" parents="58 146 12420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12424">
    <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(6739(a,1),10299(a,1,2,1))].">
      <j1 rule="para" parents="6739 10299"/>
    </justification>
  </clause>

  <clause id="12425">
    <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(4196(a,1),12424(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4196 12424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12426">
    <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(8381(a,1),12425(a,2,2))].">
      <j1 rule="para" parents="8381 12425"/>
    </justification>
  </clause>

  <clause id="12427">
    <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),12426(a,2,2,1))].">
      <j1 rule="para" parents="4 12426"/>
    </justification>
  </clause>

  <clause id="12428">
    <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(12004(a,1),12427(a,1,1,2))].">
      <j1 rule="para" parents="12004 12427"/>
    </justification>
  </clause>

  <clause id="12429">
    <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(8987(a,1),12428(a,1,1))].">
      <j1 rule="para" parents="8987 12428"/>
    </justification>
  </clause>

  <clause id="12431">
    <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(12004(a,1),12429(a,1,2,1))].">
      <j1 rule="para" parents="12004 12429"/>
    </justification>
  </clause>

  <clause id="12432">
    <literal><![CDATA[
      T(K(x,y),z) * K(R(T(y,z),y \ 1,z * y),L(z,y,y \ 1)) = (y * z) / (z * T(y,x))
    ]]></literal>
    <justification jstring="[para(5579(a,1),12431(a,1,2))].">
      <j1 rule="para" parents="5579 12431"/>
    </justification>
  </clause>

  <clause id="12433">
    <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(7806(a,1),12432(a,1,2))].">
      <j1 rule="para" parents="7806 12432"/>
    </justification>
  </clause>

  <clause id="12434">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x),y) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7060(a,1),12433(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7060 12433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12435">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x) * K(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,7907,a,b,12434,a),flip(a)].">
      <j1 rule="hyper" parents="334 7907 12434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12437">
    <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(9082(a,1),6315(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9082 6315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12438">
    <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(334,a,7869,a,b,12437,a),flip(a)].">
      <j1 rule="hyper" parents="334 7869 12437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12440">
    <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(5047(a,1),12438(a,2,1))].">
      <j1 rule="para" parents="5047 12438"/>
    </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) = T(u * R(x,y,z),u * x)
    ]]></literal>
    <justification jstring="[hyper(334,a,10083,a(flip),b,12440,a),flip(a)].">
      <j1 rule="hyper" parents="334 10083 12440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12442">
    <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(4561(a,2),12441(a,1,2))].">
      <j1 rule="para" parents="4561 12441"/>
    </justification>
  </clause>

  <clause id="12443">
    <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(9078(a,1),12442(a,1,2,1))].">
      <j1 rule="para" parents="9078 12442"/>
    </justification>
  </clause>

  <clause id="12444">
    <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(4553(a,2),12443(a,1,2,1))].">
      <j1 rule="para" parents="4553 12443"/>
    </justification>
  </clause>

  <clause id="12446">
    <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(9082(a,1),6316(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9082 6316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12447">
    <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(334,a,7869,a,b,12446,a),flip(a)].">
      <j1 rule="hyper" parents="334 7869 12446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12449">
    <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(5047(a,1),12447(a,2,1))].">
      <j1 rule="para" parents="5047 12447"/>
    </justification>
  </clause>

  <clause id="12450">
    <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(9175(a,1),9206(a,1,2))].">
      <j1 rule="para" parents="9175 9206"/>
    </justification>
  </clause>

  <clause id="12451">
    <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(5878(a,1),11800(a,1,1,1))].">
      <j1 rule="para" parents="5878 11800"/>
    </justification>
  </clause>

  <clause id="12452">
    <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(216(a,1),12450(a,1,3)),flip(a)].">
      <j1 rule="para" parents="216 12450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12453">
    <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(334,a,10821,a(flip),b,12452,a),flip(a)].">
      <j1 rule="hyper" parents="334 10821 12452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12455">
    <literal><![CDATA[
      (K(x,y) * a(x,z,x)) \ u = R(T(x,y),z,x) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,4908,a(flip),b,12453,a),flip(a)].">
      <j1 rule="hyper" parents="58 4908 12453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12456">
    <literal><![CDATA[
      (K(x,y) * a(x,z,x)) \ u = x * (R(T(x,y),z,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(334,a,1978,a(flip),b,12455,a),flip(a)].">
      <j1 rule="hyper" parents="334 1978 12455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12457">
    <literal><![CDATA[
      (a(x,y,x) * K(x,z)) \ u = x * (R(T(x,z),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9817,a,b,12456,a)].">
      <j1 rule="hyper" parents="58 9817 12456"/>
    </justification>
  </clause>

  <clause id="12458">
    <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,12409,a,b,12457,a)].">
      <j1 rule="hyper" parents="58 12409 12457"/>
    </justification>
  </clause>

  <clause id="12459">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = x * (x \ L(x,y,x))
    ]]></literal>
    <justification jstring="[para(12052(a,1),12458(a,2,2))].">
      <j1 rule="para" parents="12052 12458"/>
    </justification>
  </clause>

  <clause id="12460">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,5,a(flip),b,12459,a),flip(a)].">
      <j1 rule="hyper" parents="334 5 12459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12462">
    <literal><![CDATA[
      L(L(x,y,z),u,L(x,w,v5)) = L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(12460(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12460 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12463">
    <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(12462(a,1),10290(a,1,1,2))].">
      <j1 rule="para" parents="12462 10290"/>
    </justification>
  </clause>

  <clause id="12464">
    <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(11797(a,1),12451(a,1,1))].">
      <j1 rule="para" parents="11797 12451"/>
    </justification>
  </clause>

  <clause id="12465">
    <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(11797(a,1),12464(a,1,2,1))].">
      <j1 rule="para" parents="11797 12464"/>
    </justification>
  </clause>

  <clause id="12466">
    <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(5878(a,1),12465(a,1,2,2,2))].">
      <j1 rule="para" parents="5878 12465"/>
    </justification>
  </clause>

  <clause id="12467">
    <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(10854(a,1),10855(a,2,2,1,1))].">
      <j1 rule="para" parents="10854 10855"/>
    </justification>
  </clause>

  <clause id="12468">
    <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(334,a,1761,a(flip),b,12467,a),flip(a)].">
      <j1 rule="hyper" parents="334 1761 12467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12469">
    <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(2115(a,1),12468(a,2,2))].">
      <j1 rule="para" parents="2115 12468"/>
    </justification>
  </clause>

  <clause id="12470">
    <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(949(a,1),12469(a,2,2,1))].">
      <j1 rule="para" parents="949 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 \ R(x,z,u)),y)
    ]]></literal>
    <justification jstring="[para(1272(a,1),12470(a,2,2,1,2))].">
      <j1 rule="para" parents="1272 12470"/>
    </justification>
  </clause>

  <clause id="12472">
    <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(1761(a,1),12471(a,1,1))].">
      <j1 rule="para" parents="1761 12471"/>
    </justification>
  </clause>

  <clause id="12473">
    <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(334,a,9617,a(flip),b,9876,a),flip(a)].">
      <j1 rule="hyper" parents="334 9617 9876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12474">
    <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(334,a,8053,a(flip),b,12473,a),flip(a)].">
      <j1 rule="hyper" parents="334 8053 12473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12476">
    <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(3004(a,1),9780(a,1,1,1,2))].">
      <j1 rule="para" parents="3004 9780"/>
    </justification>
  </clause>

  <clause id="12477">
    <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(334,a,4,a(flip),b,11376,a),flip(a)].">
      <j1 rule="hyper" parents="334 4 11376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12479">
    <literal><![CDATA[
      L(x,K(y,z),K(u,y) * R(K(y,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(11374(a,1),12477(a,1,3))].">
      <j1 rule="para" parents="11374 12477"/>
    </justification>
  </clause>

  <clause id="12481">
    <literal><![CDATA[
      L(x,K(y,z),a(K(y,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(12276(a,1),12479(a,1,3))].">
      <j1 rule="para" parents="12276 12479"/>
    </justification>
  </clause>

  <clause id="12482">
    <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(1392,a,12481,a),flip(a)].">
      <j1 rule="hyper" parents="1392 12481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12483">
    <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,12312,a(flip),b,12482,a),flip(a)].">
      <j1 rule="hyper" parents="58 12312 12482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12484">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) * z = z * a(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(5394(a,1),12483(a,1,2))].">
      <j1 rule="para" parents="5394 12483"/>
    </justification>
  </clause>

  <clause id="12485">
    <literal><![CDATA[
      x * a(K(y,T(z,x)),u,w) = a(K(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(8157(a,1),12484(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8157 12484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12486">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) = T(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(247,a,12485,a),flip(a)].">
      <j1 rule="hyper" parents="247 12485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12487">
    <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(11089(a,1),12070(a,1,2,2))].">
      <j1 rule="para" parents="11089 12070"/>
    </justification>
  </clause>

  <clause id="12489">
    <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(3929(a,1),12476(a,1,1,1))].">
      <j1 rule="para" parents="3929 12476"/>
    </justification>
  </clause>

  <clause id="12490">
    <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),12489(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="104 12489"/>
      <j2 rule="flip"/>
    </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 * (((x \ y) \ 1) \ 1))),z)
    ]]></literal>
    <justification jstring="[para(3004(a,1),12490(a,2,1,3,2))].">
      <j1 rule="para" parents="3004 12490"/>
    </justification>
  </clause>

  <clause id="12495">
    <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),12494(a,2,1,3))].">
      <j1 rule="para" parents="4 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),z)
    ]]></literal>
    <justification jstring="[para(3547(a,1),12495(a,2,1))].">
      <j1 rule="para" parents="3547 12495"/>
    </justification>
  </clause>

  <clause id="12500">
    <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),12499(a,1,1,1,1,2))].">
      <j1 rule="para" parents="72 12499"/>
    </justification>
  </clause>

  <clause id="12502">
    <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(3004(a,1),12500(a,1,1,2))].">
      <j1 rule="para" parents="3004 12500"/>
    </justification>
  </clause>

  <clause id="12503">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ y,z) = K(R(y,y \ x,x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4306,a(flip),b,12502,a)].">
      <j1 rule="hyper" parents="58 4306 12502"/>
    </justification>
  </clause>

  <clause id="12505">
    <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),12503(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="17 12503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12506">
    <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(10448(a,1),12505(a,2,1,1))].">
      <j1 rule="para" parents="10448 12505"/>
    </justification>
  </clause>

  <clause id="12507">
    <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(334,a,7510,a(flip),b,12506,a),flip(a)].">
      <j1 rule="hyper" parents="334 7510 12506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12508">
    <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),12507(a,1,1,3))].">
      <j1 rule="para" parents="17 12507"/>
    </justification>
  </clause>

  <clause id="12509">
    <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(7403(a,1),12508(a,2,1))].">
      <j1 rule="para" parents="7403 12508"/>
    </justification>
  </clause>

  <clause id="12510">
    <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,7053,a(flip),b,12509,a)].">
      <j1 rule="hyper" parents="58 7053 12509"/>
    </justification>
  </clause>

  <clause id="12511">
    <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(12510(a,1),6800(a,2,2))].">
      <j1 rule="para" parents="12510 6800"/>
    </justification>
  </clause>

  <clause id="12512">
    <literal><![CDATA[
      (K(x * y,z) * ((x * y) / x)) * x = x * (y * K(y * x,T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(334,a,90,a(flip),b,12511,a),flip(a)].">
      <j1 rule="hyper" parents="334 90 12511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12513">
    <literal><![CDATA[
      (K(x * y,z) * ((x * y) / x)) * x = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,7551,a(flip),b,12512,a),flip(a)].">
      <j1 rule="hyper" parents="334 7551 12512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12514">
    <literal><![CDATA[
      (K(x * y,z) * y) * T(x,y) = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(6766,a,12513,a)].">
      <j1 rule="hyper" parents="6766 12513"/>
    </justification>
  </clause>

  <clause id="12515">
    <literal><![CDATA[
      K(x * y,z) * x = x * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(11567,a,12514,a),flip(a)].">
      <j1 rule="hyper" parents="11567 12514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12516">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(8257,a,12515,a),flip(a)].">
      <j1 rule="hyper" parents="8257 12515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12517">
    <literal><![CDATA[
      K(x * y,T(z,x)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(7555,a,12515,a)].">
      <j1 rule="hyper" parents="7555 12515"/>
    </justification>
  </clause>

  <clause id="12518">
    <literal><![CDATA[
      K(x * (y \ 1),T(z,y)) = K((y \ 1) * x,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,8503,a,b,12515,a)].">
      <j1 rule="hyper" parents="30 8503 12515"/>
    </justification>
  </clause>

  <clause id="12519">
    <literal><![CDATA[
      K((x \ 1) * y,T(z,x)) = K(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(30,a,8501,a(flip),b,12515,a),flip(a)].">
      <j1 rule="hyper" parents="30 8501 12515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12521">
    <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(12515(a,1),10142(a,1,2,2))].">
      <j1 rule="para" parents="12515 10142"/>
    </justification>
  </clause>

  <clause id="12523">
    <literal><![CDATA[
      K((x \ y) * x,z) = K(y,T(z,x \ y))
    ]]></literal>
    <justification jstring="[para(5(a,1),12516(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 12516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12524">
    <literal><![CDATA[
      K(x * (y / x),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(7(a,1),12516(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 12516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12526">
    <literal><![CDATA[
      K(x * y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(12516(a,1),8281(a,1))].">
      <j1 rule="para" parents="12516 8281"/>
    </justification>
  </clause>

  <clause id="12527">
    <literal><![CDATA[
      K((x * y) * (z / (y * x)),u) = K(z * K(x,y),T(u,x * y))
    ]]></literal>
    <justification jstring="[para(10646(a,1),12516(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10646 12516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12528">
    <literal><![CDATA[
      K(x * y,(z * x) \ x) = K(y * x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(8729,a,12517,a)].">
      <j1 rule="hyper" parents="8729 12517"/>
    </justification>
  </clause>

  <clause id="12530">
    <literal><![CDATA[
      K((x \ y) * x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(5(a,1),12517(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 12517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12531">
    <literal><![CDATA[
      K(x * y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(12517(a,1),8281(a,1))].">
      <j1 rule="para" parents="12517 8281"/>
    </justification>
  </clause>

  <clause id="12532">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(4121(a,2),12524(a,1,1))].">
      <j1 rule="para" parents="4121 12524"/>
    </justification>
  </clause>

  <clause id="12533">
    <literal><![CDATA[
      K(x * K((x \ y) \ 1,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[para(5806(a,1),12524(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5806 12524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12534">
    <literal><![CDATA[
      K(x * K(y \ x,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[para(6636(a,1),12524(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6636 12524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12535">
    <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(12524(a,1),8658(a,1,1,2))].">
      <j1 rule="para" parents="12524 8658"/>
    </justification>
  </clause>

  <clause id="12536">
    <literal><![CDATA[
      T(x,(y \ z) * y) = x / K(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(12530(a,1),5074(a,2,2))].">
      <j1 rule="para" parents="12530 5074"/>
    </justification>
  </clause>

  <clause id="12537">
    <literal><![CDATA[
      K((x \ y) * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(12523(a,2),8529(a,1))].">
      <j1 rule="para" parents="12523 8529"/>
    </justification>
  </clause>

  <clause id="12538">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,12517,a(flip),b,12532,a),flip(a)].">
      <j1 rule="hyper" parents="334 12517 12532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12539">
    <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,12538,a(flip),b,5170,a)].">
      <j1 rule="hyper" parents="119 12538 5170"/>
    </justification>
  </clause>

  <clause id="12540">
    <literal><![CDATA[
      T(x,(y \ z) * y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,7466,a(flip),b,12536,a),flip(a)].">
      <j1 rule="hyper" parents="334 7466 12536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12541">
    <literal><![CDATA[
      T(x,T(y * z,y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),12540(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 12540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12542">
    <literal><![CDATA[
      T(x,T(T(y * z,u),y)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4820(a,1),12540(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4820 12540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12543">
    <literal><![CDATA[
      T(x,T(y * z,y)) = x * K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,5020,a(flip),b,12541,a),flip(a)].">
      <j1 rule="hyper" parents="334 5020 12541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12544">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8304,a,b,12541,a)].">
      <j1 rule="hyper" parents="58 8304 12541"/>
    </justification>
  </clause>

  <clause id="12545">
    <literal><![CDATA[
      T(x,T(y * z,z \ 1)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7485,a,b,12541,a)].">
      <j1 rule="hyper" parents="58 7485 12541"/>
    </justification>
  </clause>

  <clause id="12546">
    <literal><![CDATA[
      K(x / y,y * z) = K(y \ x,z * y)
    ]]></literal>
    <justification jstring="[hyper(8618,a,12543,a)].">
      <j1 rule="hyper" parents="8618 12543"/>
    </justification>
  </clause>

  <clause id="12547">
    <literal><![CDATA[
      K(x,T((y \ 1) * z,y)) = K(x,z * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(8495,a,12543,a)].">
      <j1 rule="hyper" parents="8495 12543"/>
    </justification>
  </clause>

  <clause id="12548">
    <literal><![CDATA[
      K(T(x,y),z * y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(8377,a,12543,a),flip(a)].">
      <j1 rule="hyper" parents="8377 12543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12549">
    <literal><![CDATA[
      K(T(x,y),y * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(7563,a,12543,a)].">
      <j1 rule="hyper" parents="7563 12543"/>
    </justification>
  </clause>

  <clause id="12550">
    <literal><![CDATA[
      T(K(x,y * z),y) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(7560,a,12543,a)].">
      <j1 rule="hyper" parents="7560 12543"/>
    </justification>
  </clause>

  <clause id="12551">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(5109,a,12543,a)].">
      <j1 rule="hyper" parents="5109 12543"/>
    </justification>
  </clause>

  <clause id="12552">
    <literal><![CDATA[
      T(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12543(a,2),5030(a,1))].">
      <j1 rule="para" parents="12543 5030"/>
    </justification>
  </clause>

  <clause id="12553">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(7970,a,12548,a)].">
      <j1 rule="hyper" parents="7970 12548"/>
    </justification>
  </clause>

  <clause id="12554">
    <literal><![CDATA[
      T(x * y,T(z,x)) \ 1 = (x * y) \ K(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(116,a,12549,a(flip),b,5064,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 12549 5064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12555">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) \ u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(12549(a,1),12155(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12549 12155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12556">
    <literal><![CDATA[
      L(x,y,K(z,u * y)) = L(x,y,K(z,y * u))
    ]]></literal>
    <justification jstring="[para(12550(a,1),11482(a,1,3))].">
      <j1 rule="para" parents="12550 11482"/>
    </justification>
  </clause>

  <clause id="12557">
    <literal><![CDATA[
      K(x,T((1 / y) * z,y)) = K(x,z * (1 / y))
    ]]></literal>
    <justification jstring="[hyper(8556,a,12551,a)].">
      <j1 rule="hyper" parents="8556 12551"/>
    </justification>
  </clause>

  <clause id="12558">
    <literal><![CDATA[
      K(x,T(y * (z \ x),z)) = K(x,(z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(8554,a,12551,a)].">
      <j1 rule="hyper" parents="8554 12551"/>
    </justification>
  </clause>

  <clause id="12559">
    <literal><![CDATA[
      K(x,(y \ z) * y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(5(a,1),12551(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 12551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12560">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,T(y,z) * z)
    ]]></literal>
    <justification jstring="[para(105(a,1),12551(a,1,2,1))].">
      <j1 rule="para" parents="105 12551"/>
    </justification>
  </clause>

  <clause id="12561">
    <literal><![CDATA[
      K(x,K(y,z * y)) * K(x,z * y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(8358,a,12553,a)].">
      <j1 rule="hyper" parents="8358 12553"/>
    </justification>
  </clause>

  <clause id="12562">
    <literal><![CDATA[
      T(x,T(y * z,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,12553,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 12553 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12563">
    <literal><![CDATA[
      K(x,T(y,z \ y)) = K(x,(z \ y) * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),12553(a,1,2,1))].">
      <j1 rule="para" parents="5 12553"/>
    </justification>
  </clause>

  <clause id="12564">
    <literal><![CDATA[
      K(x,y * (z / y)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),12553(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 12553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12565">
    <literal><![CDATA[
      T(K(x,y * z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12553(a,1),8256(a,1,1))].">
      <j1 rule="para" parents="12553 8256"/>
    </justification>
  </clause>

  <clause id="12566">
    <literal><![CDATA[
      K(x,T(T(y * z,u),y)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4820(a,1),12559(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4820 12559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12567">
    <literal><![CDATA[
      T(x,y * (z / y)) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),12562(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 12562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12568">
    <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(12562(a,1),12264(a,1,2,1,1))].">
      <j1 rule="para" parents="12562 12264"/>
    </justification>
  </clause>

  <clause id="12569">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,T(y,z) * z)
    ]]></literal>
    <justification jstring="[para(4121(a,2),12564(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4121 12564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12570">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),z)) = K(x,y / (T(z,y) \ 1))
    ]]></literal>
    <justification jstring="[para(10377(a,2),12564(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10377 12564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12571">
    <literal><![CDATA[
      T(x,T(T(y * z,u),z)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4832(a,1),12567(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4832 12567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12572">
    <literal><![CDATA[
      T(T(x,y * z),K(y,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(8118,a,12544,a)].">
      <j1 rule="hyper" parents="8118 12544"/>
    </justification>
  </clause>

  <clause id="12573">
    <literal><![CDATA[
      T(K(x,y) * z,x * y) = T(z * K(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(6522(a,1),12544(a,1,1))].">
      <j1 rule="para" parents="6522 12544"/>
    </justification>
  </clause>

  <clause id="12574">
    <literal><![CDATA[
      K(1 / x,x * T(y,z)) = K(x \ 1,T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,11560,a,b,12546,a),flip(a)].">
      <j1 rule="hyper" parents="334 11560 12546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12575">
    <literal><![CDATA[
      K(1 / x,y * x) = K(1 / x,x * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,3442,a,b,12546,a)].">
      <j1 rule="hyper" parents="334 3442 12546"/>
    </justification>
  </clause>

  <clause id="12576">
    <literal><![CDATA[
      K(x,T(y,z) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,12553,a(flip),b,12560,a),flip(a)].">
      <j1 rule="hyper" parents="58 12553 12560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12577">
    <literal><![CDATA[
      T(x,T(y,z) * z) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,12576,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 12576 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12578">
    <literal><![CDATA[
      K(x,y * (z * K(y,z))) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(5086(a,1),12576(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5086 12576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12579">
    <literal><![CDATA[
      T(x,T(y \ z,u) * y) = T(x,y * T(z / y,u))
    ]]></literal>
    <justification jstring="[para(254(a,1),12577(a,1,2,1))].">
      <j1 rule="para" parents="254 12577"/>
    </justification>
  </clause>

  <clause id="12580">
    <literal><![CDATA[
      K(x,(y \ z) * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(12563(a,1),8528(a,1))].">
      <j1 rule="para" parents="12563 8528"/>
    </justification>
  </clause>

  <clause id="12581">
    <literal><![CDATA[
      T(T(x,y * z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12572(a,1),5897(a,1,1))].">
      <j1 rule="para" parents="12572 5897"/>
    </justification>
  </clause>

  <clause id="12582">
    <literal><![CDATA[
      x * K(1 / y,z * y) = x * K(1 / y,y * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,12575,a,b,4,a)].">
      <j1 rule="hyper" parents="119 12575 4"/>
    </justification>
  </clause>

  <clause id="12583">
    <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(5015(a,2),12526(a,1,1))].">
      <j1 rule="para" parents="5015 12526"/>
    </justification>
  </clause>

  <clause id="12584">
    <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(6432(a,1),12531(a,1,1))].">
      <j1 rule="para" parents="6432 12531"/>
    </justification>
  </clause>

  <clause id="12585">
    <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(11461(a,1),12537(a,1,1,1))].">
      <j1 rule="para" parents="11461 12537"/>
    </justification>
  </clause>

  <clause id="12586">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(8304(a,2),12552(a,1))].">
      <j1 rule="para" parents="8304 12552"/>
    </justification>
  </clause>

  <clause id="12587">
    <literal><![CDATA[
      K(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(7401(a,2),12565(a,1))].">
      <j1 rule="para" parents="7401 12565"/>
    </justification>
  </clause>

  <clause id="12588">
    <literal><![CDATA[
      K(x,T(y * z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(8506(a,2),12587(a,1))].">
      <j1 rule="para" parents="8506 12587"/>
    </justification>
  </clause>

  <clause id="12589">
    <literal><![CDATA[
      K(x,T(y,z) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12569(a,1),12587(a,1))].">
      <j1 rule="para" parents="12569 12587"/>
    </justification>
  </clause>

  <clause id="12590">
    <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(653(a,1),12588(a,1,2,1))].">
      <j1 rule="para" parents="653 12588"/>
    </justification>
  </clause>

  <clause id="12591">
    <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(11472(a,1),12588(a,1,2,1))].">
      <j1 rule="para" parents="11472 12588"/>
    </justification>
  </clause>

  <clause id="12592">
    <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(12540(a,1),12589(a,1,2,1))].">
      <j1 rule="para" parents="12540 12589"/>
    </justification>
  </clause>

  <clause id="12593">
    <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(465(a,1),12518(a,1,1))].">
      <j1 rule="para" parents="465 12518"/>
    </justification>
  </clause>

  <clause id="12594">
    <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(2092(a,1),12519(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2092 12519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12595">
    <literal><![CDATA[
      T(x,y) * K(y * x,y \ 1) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(12528(a,1),7068(a,1,2))].">
      <j1 rule="para" parents="12528 7068"/>
    </justification>
  </clause>

  <clause id="12596">
    <literal><![CDATA[
      T(x,T(T(y * z,y),u)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(18(a,1),12542(a,1,2))].">
      <j1 rule="para" parents="18 12542"/>
    </justification>
  </clause>

  <clause id="12597">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y)) = R(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,12229,a(flip),b,12547,a),flip(a)].">
      <j1 rule="hyper" parents="334 12229 12547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12598">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ 1))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8487,a,12555,a)].">
      <j1 rule="hyper" parents="8487 12555"/>
    </justification>
  </clause>

  <clause id="12599">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,x * y))
    ]]></literal>
    <justification jstring="[para(12555(a,1),8076(a,2,2))].">
      <j1 rule="para" parents="12555 8076"/>
    </justification>
  </clause>

  <clause id="12600">
    <literal><![CDATA[
      K(x \ y,(1 / (y / x)) * z) = K(x \ y,z * (1 / (y / x)))
    ]]></literal>
    <justification jstring="[hyper(8322,a,12557,a)].">
      <j1 rule="hyper" parents="8322 12557"/>
    </justification>
  </clause>

  <clause id="12601">
    <literal><![CDATA[
      K(x,(y \ x) * R(y,z,u)) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,10167,a(flip),b,12558,a),flip(a)].">
      <j1 rule="hyper" parents="58 10167 12558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12602">
    <literal><![CDATA[
      K(x / y,T(z * y,u)) = K(y \ x,T(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(7984,a,12566,a),flip(a)].">
      <j1 rule="hyper" parents="7984 12566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12603">
    <literal><![CDATA[
      K(x,T(y * x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x * y,z)) = u
    ]]></literal>
    <justification jstring="[para(12566(a,1),5238(a,1))].">
      <j1 rule="para" parents="12566 5238"/>
    </justification>
  </clause>

  <clause id="12604">
    <literal><![CDATA[
      T(x,T(T(y * z,z),u)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(18(a,1),12571(a,1,2))].">
      <j1 rule="para" parents="18 12571"/>
    </justification>
  </clause>

  <clause id="12605">
    <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(466(a,1),12571(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="466 12571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12606">
    <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(8275(a,1),12596(a,1,2,1,1))].">
      <j1 rule="para" parents="8275 12596"/>
    </justification>
  </clause>

  <clause id="12607">
    <literal><![CDATA[
      K(x,K(y \ (z * u),z * u)) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8486,a(flip),b,12598,a),flip(a)].">
      <j1 rule="hyper" parents="58 8486 12598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12608">
    <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(465(a,1),12604(a,1,2,1,1))].">
      <j1 rule="para" parents="465 12604"/>
    </justification>
  </clause>

  <clause id="12609">
    <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(6694(a,2),12604(a,2,2,1))].">
      <j1 rule="para" parents="6694 12604"/>
    </justification>
  </clause>

  <clause id="12610">
    <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(8067(a,1),12586(a,1,1,2))].">
      <j1 rule="para" parents="8067 12586"/>
    </justification>
  </clause>

  <clause id="12611">
    <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(8046(a,1),12586(a,1,1,2))].">
      <j1 rule="para" parents="8046 12586"/>
    </justification>
  </clause>

  <clause id="12612">
    <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(8157(a,1),12586(a,1,1,2))].">
      <j1 rule="para" parents="8157 12586"/>
    </justification>
  </clause>

  <clause id="12613">
    <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(334,a,12061,a(flip),b,12554,a),flip(a)].">
      <j1 rule="hyper" parents="334 12061 12554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12614">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z * y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(8045(a,1),12561(a,1,1))].">
      <j1 rule="para" parents="8045 12561"/>
    </justification>
  </clause>

  <clause id="12615">
    <literal><![CDATA[
      K(x,y * z) * K(x,K(z,y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(5906,a,12614,a)].">
      <j1 rule="hyper" parents="5906 12614"/>
    </justification>
  </clause>

  <clause id="12616">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z * x) = K(y,x * z)
    ]]></literal>
    <justification jstring="[para(8048(a,1),12614(a,1,1))].">
      <j1 rule="para" parents="8048 12614"/>
    </justification>
  </clause>

  <clause id="12617">
    <literal><![CDATA[
      K(x,y * z) * K(z,K(y,x)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(8053(a,2),12615(a,1,2))].">
      <j1 rule="para" parents="8053 12615"/>
    </justification>
  </clause>

  <clause id="12618">
    <literal><![CDATA[
      K(x,y / (T(z,y) \ 1)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8510,a(flip),b,12570,a),flip(a)].">
      <j1 rule="hyper" parents="58 8510 12570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12619">
    <literal><![CDATA[
      K(x,(y / z) / (z \ 1)) = K(x,(z \ 1) \ (z \ y))
    ]]></literal>
    <justification jstring="[para(10419(a,1),12618(a,1,2))].">
      <j1 rule="para" parents="10419 12618"/>
    </justification>
  </clause>

  <clause id="12620">
    <literal><![CDATA[
      K(T(K(x,y) * z,x * y),u) = K(z * K(x,y),T(u,y * x))
    ]]></literal>
    <justification jstring="[para(12573(a,2),7403(a,1,1))].">
      <j1 rule="para" parents="12573 7403"/>
    </justification>
  </clause>

  <clause id="12621">
    <literal><![CDATA[
      K(1 / x,T(y * x,z)) = K(1 / x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,3442,a,b,12574,a)].">
      <j1 rule="hyper" parents="334 3442 12574"/>
    </justification>
  </clause>

  <clause id="12622">
    <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(4816(a,1),12579(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4816 12579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12623">
    <literal><![CDATA[
      x * K(1 / (y / z),(y / z) * u) = x * K(z / y,u * (y / z))
    ]]></literal>
    <justification jstring="[para(5704(a,1),12582(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5704 12582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12624">
    <literal><![CDATA[
      x * (y * K(z,K(u,x * y))) = T(x * y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,12599,a)].">
      <j1 rule="hyper" parents="134 12599"/>
    </justification>
  </clause>

  <clause id="12625">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ K(z,u))) = K(z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,12207,a(flip),b,12619,a),flip(a)].">
      <j1 rule="hyper" parents="58 12207 12619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12626">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ K(y,T(z,u))) = K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11945,a,b,12625,a)].">
      <j1 rule="hyper" parents="58 11945 12625"/>
    </justification>
  </clause>

  <clause id="12627">
    <literal><![CDATA[
      (x \ K(y,z)) * K(y,K(z,u)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,12625,a(flip),b,11945,a)].">
      <j1 rule="hyper" parents="119 12625 11945"/>
    </justification>
  </clause>

  <clause id="12628">
    <literal><![CDATA[
      K(1 / x,T(y / (1 / x),z)) = K(1 / x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(11410,a,12621,a)].">
      <j1 rule="hyper" parents="11410 12621"/>
    </justification>
  </clause>

  <clause id="12629">
    <literal><![CDATA[
      K(1 / (x / y),(x / y) * T(z,x)) = K(1 / (y \ x),z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(8899,a,12621,a),flip(a)].">
      <j1 rule="hyper" parents="8899 12621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12630">
    <literal><![CDATA[
      T(1 / x,T(y * x,z)) = T(1 / x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,12621,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 12621 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12631">
    <literal><![CDATA[
      T(x * y,K(z,L(u,y,x))) = T(x * y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(11245,a,12624,a)].">
      <j1 rule="hyper" parents="11245 12624"/>
    </justification>
  </clause>

  <clause id="12632">
    <literal><![CDATA[
      (x * (y * K(z,u))) / T(x * y,K(z,u)) = L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[para(12631(a,1),11115(a,1,2))].">
      <j1 rule="para" parents="12631 11115"/>
    </justification>
  </clause>

  <clause id="12634">
    <literal><![CDATA[
      (x \ K(y,z)) * K(z,K(y,u)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,8048,a,b,12626,a)].">
      <j1 rule="hyper" parents="119 8048 12626"/>
    </justification>
  </clause>

  <clause id="12635">
    <literal><![CDATA[
      (x \ K(y,z)) * K(u,K(y,z)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,8053,a(flip),b,12626,a)].">
      <j1 rule="hyper" parents="119 8053 12626"/>
    </justification>
  </clause>

  <clause id="12636">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,9523,a(flip),b,12597,a),flip(a)].">
      <j1 rule="hyper" parents="58 9523 12597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12637">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,12228,a(flip),b,12636,a)].">
      <j1 rule="hyper" parents="58 12228 12636"/>
    </justification>
  </clause>

  <clause id="12638">
    <literal><![CDATA[
      K(x,L(y / z,z,z \ 1)) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(536(a,1),12637(a,1,2)),flip(a)].">
      <j1 rule="para" parents="536 12637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12639">
    <literal><![CDATA[
      K(x,K(y,L(z,u,u \ 1))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(12637(a,1),12142(a,1,2))].">
      <j1 rule="para" parents="12637 12142"/>
    </justification>
  </clause>

  <clause id="12640">
    <literal><![CDATA[
      K(x,K(y,L(z,u \ 1,u))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(3158(a,1),12639(a,1,2,2))].">
      <j1 rule="para" parents="3158 12639"/>
    </justification>
  </clause>

  <clause id="12641">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(12640(a,1),12198(a,2,2))].">
      <j1 rule="para" parents="12640 12198"/>
    </justification>
  </clause>

  <clause id="12642">
    <literal><![CDATA[
      (x \ y) * K(y,K(z,u)) = x \ T(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),12641(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 12641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12643">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(z,K(u,x))
    ]]></literal>
    <justification jstring="[para(8053(a,2),12641(a,2,2))].">
      <j1 rule="para" parents="8053 12641"/>
    </justification>
  </clause>

  <clause id="12645">
    <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(12632(a,1),107(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12632 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12646">
    <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(12632(a,1),5276(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12632 5276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12647">
    <literal><![CDATA[
      K(x \ y,(1 / (y / x)) * z) = K(x \ y,z / (y / x))
    ]]></literal>
    <justification jstring="[hyper(334,a,7103,a(flip),b,12600,a),flip(a)].">
      <j1 rule="hyper" parents="334 7103 12600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12648">
    <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(4663(a,2),12647(a,1,1))].">
      <j1 rule="para" parents="4663 12647"/>
    </justification>
  </clause>

  <clause id="12649">
    <literal><![CDATA[
      K(x,K(y * z,(y \ u) \ z)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8432,a,12607,a),flip(a)].">
      <j1 rule="hyper" parents="8432 12607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12650">
    <literal><![CDATA[
      K(x,K(y * z,z \ (y \ u))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8487,a,12649,a)].">
      <j1 rule="hyper" parents="8487 12649"/>
    </justification>
  </clause>

  <clause id="12651">
    <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(5650(a,2),12650(a,2,2))].">
      <j1 rule="para" parents="5650 12650"/>
    </justification>
  </clause>

  <clause id="12652">
    <literal><![CDATA[
      T(x,T(y * T((y * z) / y,u),w)) = T(x,T(T(z,u) * y,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,12542,a(flip),b,12605,a),flip(a)].">
      <j1 rule="hyper" parents="334 12542 12605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12653">
    <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),12652(a,1,2,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 12652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12654">
    <literal><![CDATA[
      x * K(y / z,(z / y) * u) = x * K(y / z,u * (z / y))
    ]]></literal>
    <justification jstring="[para(5704(a,1),12623(a,1,2))].">
      <j1 rule="para" parents="5704 12623"/>
    </justification>
  </clause>

  <clause id="12655">
    <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(334,a,8637,a(flip),b,12654,a),flip(a)].">
      <j1 rule="hyper" parents="334 8637 12654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12656">
    <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(12654(a,1),39(a,2))].">
      <j1 rule="para" parents="12654 39"/>
    </justification>
  </clause>

  <clause id="12657">
    <literal><![CDATA[
      K(1 / (x \ y),z * (y / x)) = K(x / y,(y / x) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(5941,a,12629,a),flip(a)].">
      <j1 rule="hyper" parents="5941 12629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12658">
    <literal><![CDATA[
      K(x / y,(y / x) * T(z,y)) = K(y \ x,z * (y / x))
    ]]></literal>
    <justification jstring="[hyper(6767,a,12657,a),flip(a)].">
      <j1 rule="hyper" parents="6767 12657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12659">
    <literal><![CDATA[
      ((x * y) * ((T(y,x) * x) \ z)) / (x * y) = z / (T(y,x) * x)
    ]]></literal>
    <justification jstring="[hyper(5089,a,12539,a)].">
      <j1 rule="hyper" parents="5089 12539"/>
    </justification>
  </clause>

  <clause id="12660">
    <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,12604,a(flip),b,12609,a),flip(a)].">
      <j1 rule="hyper" parents="58 12604 12609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12661">
    <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(10300(a,1),12613(a,1,1))].">
      <j1 rule="para" parents="10300 12613"/>
    </justification>
  </clause>

  <clause id="12662">
    <literal><![CDATA[
      K(x,T(y,z)) * K(u,T(x,z)) = T(K(x,y) * K(u,x),z)
    ]]></literal>
    <justification jstring="[hyper(11868,a,12661,a),flip(a)].">
      <j1 rule="hyper" parents="11868 12661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12663">
    <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(12662(a,1),10272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12662 10272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12664">
    <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,11033,a(flip),b,12663,a),flip(a)].">
      <j1 rule="hyper" parents="58 11033 12663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12665">
    <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(465(a,1),12622(a,2,2))].">
      <j1 rule="para" parents="465 12622"/>
    </justification>
  </clause>

  <clause id="12666">
    <literal><![CDATA[
      K(x \ T(x * y,z),T(u,x)) = K((x \ 1) * T(y / (x \ 1),z),u)
    ]]></literal>
    <justification jstring="[para(971(a,1),12593(a,1,1))].">
      <j1 rule="para" parents="971 12593"/>
    </justification>
  </clause>

  <clause id="12667">
    <literal><![CDATA[
      K((x \ 1) * T(y / (x \ 1),z),u) = K(x \ T(y * x,z),u)
    ]]></literal>
    <justification jstring="[hyper(7990,a,12666,a),flip(a)].">
      <j1 rule="hyper" parents="7990 12666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12668">
    <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(334,a,4493,a(flip),b,12645,a),flip(a)].">
      <j1 rule="hyper" parents="334 4493 12645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12669">
    <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(7401(a,2),12668(a,2,1))].">
      <j1 rule="para" parents="7401 12668"/>
    </justification>
  </clause>

  <clause id="12670">
    <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(10867(a,1),12664(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10867 12664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12672">
    <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(12670(a,1),12045(a,2,1))].">
      <j1 rule="para" parents="12670 12045"/>
    </justification>
  </clause>

  <clause id="12673">
    <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(12036(a,1),12672(a,2,1,1))].">
      <j1 rule="para" parents="12036 12672"/>
    </justification>
  </clause>

  <clause id="12675">
    <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(7366(a,1),12673(a,1,1,1))].">
      <j1 rule="para" parents="7366 12673"/>
    </justification>
  </clause>

  <clause id="12677">
    <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(10073(a,1),12675(a,1,1))].">
      <j1 rule="para" parents="10073 12675"/>
    </justification>
  </clause>

  <clause id="12678">
    <literal><![CDATA[
      (R(a(x,y,x),z,u) * z) * u = (z * a(x,y,x)) * u
    ]]></literal>
    <justification jstring="[para(9371(a,1),12677(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9371 12677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12679">
    <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,12678,a(flip),b,711,a)].">
      <j1 rule="hyper" parents="116 12678 711"/>
    </justification>
  </clause>

  <clause id="12680">
    <literal><![CDATA[
      a(R(a(x,y,x),z,u),z,u) = K(z,T(a(x,y,x),u))
    ]]></literal>
    <justification jstring="[hyper(11411,a,12679,a),flip(a)].">
      <j1 rule="hyper" parents="11411 12679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12681">
    <literal><![CDATA[
      a(R(a(x,y,x),z,u),z,u) = K(z,a(x,y,x))
    ]]></literal>
    <justification jstring="[para(9806(a,1),12680(a,2,2))].">
      <j1 rule="para" parents="9806 12680"/>
    </justification>
  </clause>

  <clause id="12682">
    <literal><![CDATA[
      a(R(a(x,y,x),z,u),z,u) = 1
    ]]></literal>
    <justification jstring="[hyper(334,a,9816,a(flip),b,12681,a),flip(a)].">
      <j1 rule="hyper" parents="334 9816 12681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12685">
    <literal><![CDATA[
      L(x,y,R(a(z,u,z),y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,12682,a)].">
      <j1 rule="hyper" parents="47 12682"/>
    </justification>
  </clause>

  <clause id="12686">
    <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(12685(a,1),11513(a,1,2))].">
      <j1 rule="para" parents="12685 11513"/>
    </justification>
  </clause>

  <clause id="12687">
    <literal><![CDATA[
      (R(a(x,y,x),z,u) * (z * u)) / u = z * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(9852(a,1),12686(a,1,1,2,1))].">
      <j1 rule="para" parents="9852 12686"/>
    </justification>
  </clause>

  <clause id="12688">
    <literal><![CDATA[
      x * R(a(y,z,y),x,u) = a(y,z,y) * x
    ]]></literal>
    <justification jstring="[hyper(531,a,12687,a),flip(a)].">
      <j1 rule="hyper" parents="531 12687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12689">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,9793,a(flip),b,12688,a),flip(a)].">
      <j1 rule="hyper" parents="29 9793 12688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12691">
    <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,523,a,b,12689,a)].">
      <j1 rule="hyper" parents="58 523 12689"/>
    </justification>
  </clause>

  <clause id="12692">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12034,a(flip),b,12689,a)].">
      <j1 rule="hyper" parents="58 12034 12689"/>
    </justification>
  </clause>

  <clause id="12693">
    <literal><![CDATA[
      a(x,y * K(z,y),x) = L(a(x,y,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10301,a(flip),b,12689,a),flip(a)].">
      <j1 rule="hyper" parents="58 10301 12689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12694">
    <literal><![CDATA[
      (a(x,y,x) * z) * u = a(x,y,x) * (z * u)
    ]]></literal>
    <justification jstring="[para(12689(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12689 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12696">
    <literal><![CDATA[
      a(a(x,y,x),z,u) = 1
    ]]></literal>
    <justification jstring="[para(12689(a,1),12682(a,1,1))].">
      <j1 rule="para" parents="12689 12682"/>
    </justification>
  </clause>

  <clause id="12697">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[para(12689(a,1),12685(a,1,3))].">
      <j1 rule="para" parents="12689 12685"/>
    </justification>
  </clause>

  <clause id="12698">
    <literal><![CDATA[
      a(x,y,x) * ((a(x,y,x) \ z) * u) = z * u
    ]]></literal>
    <justification jstring="[hyper(928,a,12696,a)].">
      <j1 rule="hyper" parents="928 12696"/>
    </justification>
  </clause>

  <clause id="12700">
    <literal><![CDATA[
      (a(x,y,x) * z) \ x = z \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9361,a(flip),b,12697,a)].">
      <j1 rule="hyper" parents="58 9361 12697"/>
    </justification>
  </clause>

  <clause id="12701">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,311,a(flip),b,12697,a)].">
      <j1 rule="hyper" parents="58 311 12697"/>
    </justification>
  </clause>

  <clause id="12702">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(12697(a,1),45(a,2))].">
      <j1 rule="para" parents="12697 45"/>
    </justification>
  </clause>

  <clause id="12703">
    <literal><![CDATA[
      (a(x,y,x) * z) / u = a(x,y,x) * (z / u)
    ]]></literal>
    <justification jstring="[para(12697(a,1),556(a,1,2))].">
      <j1 rule="para" parents="12697 556"/>
    </justification>
  </clause>

  <clause id="12704">
    <literal><![CDATA[
      x \ (a(y,z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,y) \ x) \ u = w
    ]]></literal>
    <justification jstring="[para(12697(a,1),782(a,1)),flip(a)].">
      <j1 rule="para" parents="12697 782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12705">
    <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(12697(a,1),492(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12697 492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12708">
    <literal><![CDATA[
      K(x,R(x,y,z) \ u) = K(x,u) * a(x,x \ u,x)
    ]]></literal>
    <justification jstring="[para(12692(a,1),12041(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12692 12041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12710">
    <literal><![CDATA[
      (x * y) \ L(y,x,y) = T(y * x,y) \ y
    ]]></literal>
    <justification jstring="[para(9185(a,1),12700(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9185 12700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12712">
    <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(5780(a,1),12693(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5780 12693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12713">
    <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(4886(a,1),12710(a,1,1))].">
      <j1 rule="para" parents="4886 12710"/>
    </justification>
  </clause>

  <clause id="12714">
    <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(12694(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12694 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12715">
    <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(12694(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12694 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12716">
    <literal><![CDATA[
      a(x,y,x) * ((a(x,y,x) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      z * u = w
    ]]></literal>
    <justification jstring="[para(12694(a,1),581(a,1))].">
      <j1 rule="para" parents="12694 581"/>
    </justification>
  </clause>

  <clause id="12717">
    <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(12694(a,1),495(a,1,2,2))].">
      <j1 rule="para" parents="12694 495"/>
    </justification>
  </clause>

  <clause id="12718">
    <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(12694(a,1),632(a,1))].">
      <j1 rule="para" parents="12694 632"/>
    </justification>
  </clause>

  <clause id="12719">
    <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(12694(a,1),709(a,1,1,2))].">
      <j1 rule="para" parents="12694 709"/>
    </justification>
  </clause>

  <clause id="12720">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = a(y,z,y) * (x * u)
    ]]></literal>
    <justification jstring="[para(9793(a,1),12694(a,1,1))].">
      <j1 rule="para" parents="9793 12694"/>
    </justification>
  </clause>

  <clause id="12721">
    <literal><![CDATA[
      (x * a(y,z,y)) \ u = x \ (a(y,z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(9831,a,12701,a)].">
      <j1 rule="hyper" parents="9831 12701"/>
    </justification>
  </clause>

  <clause id="12722">
    <literal><![CDATA[
      (x * y) \ (a(y,z,y) \ u) = (x * R(y,z,y)) \ u
    ]]></literal>
    <justification jstring="[para(9800(a,1),12701(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9800 12701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12723">
    <literal><![CDATA[
      (a(x,y,x) \ z) / u = a(x,y,x) \ (z / u)
    ]]></literal>
    <justification jstring="[hyper(639,a,12703,a),flip(a)].">
      <j1 rule="hyper" parents="639 12703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12724">
    <literal><![CDATA[
      (a(x,y,x) * z) / u = (z / u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,9793,a(flip),b,12703,a),flip(a)].">
      <j1 rule="hyper" parents="334 9793 12703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12725">
    <literal><![CDATA[
      a(x,y,x) * (x / z) = R(x,y,x) / z
    ]]></literal>
    <justification jstring="[para(9167(a,1),12703(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9167 12703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12726">
    <literal><![CDATA[
      (x / y) * a(x,z,x) = R(x,z,x) / y
    ]]></literal>
    <justification jstring="[hyper(9823,a,12725,a)].">
      <j1 rule="hyper" parents="9823 12725"/>
    </justification>
  </clause>

  <clause id="12727">
    <literal><![CDATA[
      (x * a(y,x,y)) * z = x * (a(y,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(334,a,11342,a(flip),b,12720,a),flip(a)].">
      <j1 rule="hyper" parents="334 11342 12720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12728">
    <literal><![CDATA[
      a(x,y,x) \ (x / z) = L(x,y,x) / z
    ]]></literal>
    <justification jstring="[para(9360(a,1),12723(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9360 12723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12729">
    <literal><![CDATA[
      (x * a(y,z,y)) / u = (x / u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(9793(a,1),12724(a,1,1))].">
      <j1 rule="para" parents="9793 12724"/>
    </justification>
  </clause>

  <clause id="12730">
    <literal><![CDATA[
      K(x,R(x,y,z) \ u) = K(x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(334,a,9186,a(flip),b,12708,a),flip(a)].">
      <j1 rule="hyper" parents="334 9186 12708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12732">
    <literal><![CDATA[
      K(x,x \ ((x * R(T(x,y),z,u)) / w)) = K(x,w \ x)
    ]]></literal>
    <justification jstring="[hyper(10334,a,12730,a),flip(a)].">
      <j1 rule="hyper" parents="10334 12730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12733">
    <literal><![CDATA[
      K(x,x \ ((x * y) * z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(187(a,1),12730(a,1,2)),flip(a)].">
      <j1 rule="para" parents="187 12730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12734">
    <literal><![CDATA[
      K(x,x \ (y * z)) = K(x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[para(517(a,1),12730(a,1,2)),flip(a)].">
      <j1 rule="para" parents="517 12730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12735">
    <literal><![CDATA[
      K(x,y * ((x * y) \ z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(379(a,1),12730(a,1,2))].">
      <j1 rule="para" parents="379 12730"/>
    </justification>
  </clause>

  <clause id="12736">
    <literal><![CDATA[
      K(x,x \ ((y * x) * z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(11466,a,12733,a)].">
      <j1 rule="hyper" parents="11466 12733"/>
    </justification>
  </clause>

  <clause id="12737">
    <literal><![CDATA[
      K(x,y * (x \ (y \ (z * u)))) = K(x,(x \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(10677,a,12734,a)].">
      <j1 rule="hyper" parents="10677 12734"/>
    </justification>
  </clause>

  <clause id="12738">
    <literal><![CDATA[
      K(x,(x \ y) * z) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(10594,a,12734,a),flip(a)].">
      <j1 rule="hyper" parents="10594 12734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12739">
    <literal><![CDATA[
      K(x,y * ((y * x) \ z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11510,a,b,12735,a)].">
      <j1 rule="hyper" parents="58 11510 12735"/>
    </justification>
  </clause>

  <clause id="12740">
    <literal><![CDATA[
      T(x,(x \ y) * z) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,12738,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 12738 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12741">
    <literal><![CDATA[
      K(x,(y * x) * (x \ z)) = K(x,T(y,x) * z)
    ]]></literal>
    <justification jstring="[para(17(a,2),12738(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="17 12738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12742">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ z) = K(x \ y,x * (y \ z))
    ]]></literal>
    <justification jstring="[para(5(a,1),12739(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 12739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12743">
    <literal><![CDATA[
      T(x,(y / x) * z) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(8710,a,12740,a)].">
      <j1 rule="hyper" parents="8710 12740"/>
    </justification>
  </clause>

  <clause id="12744">
    <literal><![CDATA[
      T(x,(x \ y) * z) \ u = T(x,y * (x \ z)) \ u
    ]]></literal>
    <justification jstring="[hyper(56,a,12740,a)].">
      <j1 rule="hyper" parents="56 12740"/>
    </justification>
  </clause>

  <clause id="12745">
    <literal><![CDATA[
      K(x,(y * x) * (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(12741(a,2),8697(a,1))].">
      <j1 rule="para" parents="12741 8697"/>
    </justification>
  </clause>

  <clause id="12746">
    <literal><![CDATA[
      K(x,y * (x \ T(z,y))) = K(x,(x \ z) * y)
    ]]></literal>
    <justification jstring="[para(17(a,2),12737(a,1,2,2,2))].">
      <j1 rule="para" parents="17 12737"/>
    </justification>
  </clause>

  <clause id="12747">
    <literal><![CDATA[
      K((x \ y) * z,x) = K(y * (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(5927,a,12744,a)].">
      <j1 rule="hyper" parents="5927 12744"/>
    </justification>
  </clause>

  <clause id="12748">
    <literal><![CDATA[
      K(x \ (y * z),x) = K((x \ y) * z,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,10696,a,b,12747,a)].">
      <j1 rule="hyper" parents="334 10696 12747"/>
    </justification>
  </clause>

  <clause id="12749">
    <literal><![CDATA[
      K(x \ ((x * y) * z),x) = K(y * z,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),12748(a,2,1,1))].">
      <j1 rule="para" parents="4 12748"/>
    </justification>
  </clause>

  <clause id="12750">
    <literal><![CDATA[
      K(x \ ((y * x) * z),x) = K(y * z,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11467,a,b,12749,a)].">
      <j1 rule="hyper" parents="58 11467 12749"/>
    </justification>
  </clause>

  <clause id="12751">
    <literal><![CDATA[
      K(x * ((x * y) \ z),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),12750(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 12750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12752">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(x * (y \ z),x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),12751(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 12751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12753">
    <literal><![CDATA[
      K((x / y) \ z,y \ x) = K(y * (x \ z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(7680,a,12752,a)].">
      <j1 rule="hyper" parents="7680 12752"/>
    </justification>
  </clause>

  <clause id="12754">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),z \ u)) = a(x,y,K(w,z \ u))
    ]]></literal>
    <justification jstring="[para(12752(a,1),11318(a,1,3))].">
      <j1 rule="para" parents="12752 11318"/>
    </justification>
  </clause>

  <clause id="12755">
    <literal><![CDATA[
      K(x / (y / z),z \ y) = K(z * (y \ x),z \ y)
    ]]></literal>
    <justification jstring="[hyper(8541,a,12753,a)].">
      <j1 rule="hyper" parents="8541 12753"/>
    </justification>
  </clause>

  <clause id="12756">
    <literal><![CDATA[
      a(x,y,x) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      (z * a(x,y,x)) * u = w
    ]]></literal>
    <justification jstring="[para(9808(a,1),12716(a,1,2,1))].">
      <j1 rule="para" parents="9808 12716"/>
    </justification>
  </clause>

  <clause id="12757">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11417,a(flip),b,12732,a)].">
      <j1 rule="hyper" parents="58 11417 12732"/>
    </justification>
  </clause>

  <clause id="12758">
    <literal><![CDATA[
      K(x,y \ R(x,z,u)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12108,a(flip),b,12757,a)].">
      <j1 rule="hyper" parents="58 12108 12757"/>
    </justification>
  </clause>

  <clause id="12761">
    <literal><![CDATA[
      K(R(x,y,z),u \ x) = K(x,R(u,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12261,a(flip),b,12758,a)].">
      <j1 rule="hyper" parents="58 12261 12758"/>
    </justification>
  </clause>

  <clause id="12762">
    <literal><![CDATA[
      K(x,y \ (z * R(x,u,w))) = K(x,(z \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,10998,a(flip),b,12758,a)].">
      <j1 rule="hyper" parents="58 10998 12758"/>
    </justification>
  </clause>

  <clause id="12764">
    <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,11936,a(flip),b,12761,a),flip(a)].">
      <j1 rule="hyper" parents="58 11936 12761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12766">
    <literal><![CDATA[
      K(x,y \ (z * R(x,u,w))) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(334,a,10778,a(flip),b,12762,a),flip(a)].">
      <j1 rule="hyper" parents="334 10778 12762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12767">
    <literal><![CDATA[
      K(x,y \ (R(x,z,u) * w)) = K(x,x * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,10149,a,b,12766,a)].">
      <j1 rule="hyper" parents="58 10149 12766"/>
    </justification>
  </clause>

  <clause id="12768">
    <literal><![CDATA[
      K(x,(y / R(x,z,u)) \ w) = K(x,x * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,10147,a,b,12766,a)].">
      <j1 rule="hyper" parents="58 10147 12766"/>
    </justification>
  </clause>

  <clause id="12770">
    <literal><![CDATA[
      K(x,x * (R(x,y,z) \ u)) = K(x,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),12767(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 12767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12771">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * u))) = K(x,x * (y \ (x \ (z * u))))
    ]]></literal>
    <justification jstring="[para(1376(a,1),12767(a,1,2,2))].">
      <j1 rule="para" parents="1376 12767"/>
    </justification>
  </clause>

  <clause id="12773">
    <literal><![CDATA[
      K(x,(x * y) * z) = K(x,x * (y * z))
    ]]></literal>
    <justification jstring="[para(187(a,1),12770(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="187 12770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12774">
    <literal><![CDATA[
      K(x,(y * x) * z) = K(x,x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(11465,a,12773,a)].">
      <j1 rule="hyper" parents="11465 12773"/>
    </justification>
  </clause>

  <clause id="12776">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * u))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(334,a,10781,a(flip),b,12771,a),flip(a)].">
      <j1 rule="hyper" parents="334 10781 12771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12777">
    <literal><![CDATA[
      K(x,y \ (x \ (z * u))) = K(x,y \ ((x \ z) * u))
    ]]></literal>
    <justification jstring="[para(5(a,1),12776(a,1,2,2,2,1))].">
      <j1 rule="para" parents="5 12776"/>
    </justification>
  </clause>

  <clause id="12778">
    <literal><![CDATA[
      K(x,(y * (z / u)) \ ((x \ (y * x)) * z)) = L(K(x,u),z,y * x)
    ]]></literal>
    <justification jstring="[hyper(11648,a,12777,a),flip(a)].">
      <j1 rule="hyper" parents="11648 12777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12779">
    <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(9797(a,1),12691(a,1,1,1))].">
      <j1 rule="para" parents="9797 12691"/>
    </justification>
  </clause>

  <clause id="12780">
    <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),12778(a,1,2,2,1))].">
      <j1 rule="para" parents="17 12778"/>
    </justification>
  </clause>

  <clause id="12781">
    <literal><![CDATA[
      L(K(x,y),z,u * x) = K(x,(u * (z / y)) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8852,a(flip),b,12780,a),flip(a)].">
      <j1 rule="hyper" parents="58 8852 12780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12782">
    <literal><![CDATA[
      L(K(x,y),z,u * x) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,6850,a(flip),b,12781,a),flip(a)].">
      <j1 rule="hyper" parents="334 6850 12781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12783">
    <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(12782(a,1),11050(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12782 11050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12784">
    <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,11759,a(flip),b,12712,a)].">
      <j1 rule="hyper" parents="58 11759 12712"/>
    </justification>
  </clause>

  <clause id="12785">
    <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,11992,a(flip),b,12764,a)].">
      <j1 rule="hyper" parents="58 11992 12764"/>
    </justification>
  </clause>

  <clause id="12786">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(5731(a,1),12785(a,1,1))].">
      <j1 rule="para" parents="5731 12785"/>
    </justification>
  </clause>

  <clause id="12787">
    <literal><![CDATA[
      R(K(x,y),K(x,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4671(a,1),12786(a,2,1))].">
      <j1 rule="para" parents="4671 12786"/>
    </justification>
  </clause>

  <clause id="12788">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 = K(y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(12786(a,2),5232(a,1,1))].">
      <j1 rule="para" parents="12786 5232"/>
    </justification>
  </clause>

  <clause id="12790">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) * u = K(x,y) * (K(x,z) * u)
    ]]></literal>
    <justification jstring="[para(12787(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12787 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12791">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(6216,a,12788,a)].">
      <j1 rule="hyper" parents="6216 12788"/>
    </justification>
  </clause>

  <clause id="12792">
    <literal><![CDATA[
      K(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(12788(a,1),6216(a,1))].">
      <j1 rule="para" parents="12788 6216"/>
    </justification>
  </clause>

  <clause id="12793">
    <literal><![CDATA[
      K(x,R(y,z,u)) * 1 = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,3,a,b,12791,a)].">
      <j1 rule="hyper" parents="334 3 12791"/>
    </justification>
  </clause>

  <clause id="12794">
    <literal><![CDATA[
      x * R(K(x,y),z,u) = T(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,12791,a,b,4995,a(flip))].">
      <j1 rule="hyper" parents="119 12791 4995"/>
    </justification>
  </clause>

  <clause id="12795">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,R(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,12786,a(flip),b,12791,a)].">
      <j1 rule="hyper" parents="58 12786 12791"/>
    </justification>
  </clause>

  <clause id="12796">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(12791(a,1),101(a,1,1))].">
      <j1 rule="para" parents="12791 101"/>
    </justification>
  </clause>

  <clause id="12799">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(12791(a,1),12276(a,1,2))].">
      <j1 rule="para" parents="12791 12276"/>
    </justification>
  </clause>

  <clause id="12800">
    <literal><![CDATA[
      K(R(x,y,z),R(x * y,y * z,u)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(7181,a,12795,a),flip(a)].">
      <j1 rule="hyper" parents="7181 12795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12802">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(12793(a,1),127(a,1)),flip(b)].">
      <j1 rule="para" parents="12793 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12803">
    <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(12794(a,1),12311(a,2,1))].">
      <j1 rule="para" parents="12794 12311"/>
    </justification>
  </clause>

  <clause id="12804">
    <literal><![CDATA[
      K(R(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(12795(a,2),12792(a,1))].">
      <j1 rule="para" parents="12795 12792"/>
    </justification>
  </clause>

  <clause id="12805">
    <literal><![CDATA[
      K(R(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(12786(a,1),12802(a,1))].">
      <j1 rule="para" parents="12786 12802"/>
    </justification>
  </clause>

  <clause id="12806">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12281,a(flip),b,12799,a)].">
      <j1 rule="hyper" parents="58 12281 12799"/>
    </justification>
  </clause>

  <clause id="12807">
    <literal><![CDATA[
      K(a(K(x,y),z * y,u),w) = a(K(y,K(x,w)),z,u)
    ]]></literal>
    <justification jstring="[para(12806(a,2),12326(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12806 12326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12808">
    <literal><![CDATA[
      ((x * y) * z) / ((K(u,x) * y) * z) = T(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(12796(a,1),5520(a,1,2))].">
      <j1 rule="para" parents="12796 5520"/>
    </justification>
  </clause>

  <clause id="12809">
    <literal><![CDATA[
      L(x,K(y,z),K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(493,a,12790,a)].">
      <j1 rule="hyper" parents="493 12790"/>
    </justification>
  </clause>

  <clause id="12810">
    <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(12790(a,1),12331(a,1,2))].">
      <j1 rule="para" parents="12790 12331"/>
    </justification>
  </clause>

  <clause id="12811">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ u = K(z,x) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6040,a(flip),b,12809,a)].">
      <j1 rule="hyper" parents="58 6040 12809"/>
    </justification>
  </clause>

  <clause id="12812">
    <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,12328,a,b,12807,a)].">
      <j1 rule="hyper" parents="58 12328 12807"/>
    </justification>
  </clause>

  <clause id="12813">
    <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,6331,a(flip),b,12811,a),flip(a)].">
      <j1 rule="hyper" parents="58 6331 12811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12814">
    <literal><![CDATA[
      ((x * y) * z) / (T(y,x) * z) = T(R(x,y,z),y)
    ]]></literal>
    <justification jstring="[para(5034(a,2),12808(a,1,2,1))].">
      <j1 rule="para" parents="5034 12808"/>
    </justification>
  </clause>

  <clause id="12815">
    <literal><![CDATA[
      R(T(x,y),T(y,x),z) = T(R(x,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(4521,a,12814,a)].">
      <j1 rule="hyper" parents="4521 12814"/>
    </justification>
  </clause>

  <clause id="12816">
    <literal><![CDATA[
      R(x,T(y,x),z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(140,a,12815,a(flip))].">
      <j1 rule="hyper" parents="140 12815"/>
    </justification>
  </clause>

  <clause id="12822">
    <literal><![CDATA[
      R(x,y,z) \ ((y * x) * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[para(12816(a,1),516(a,1,1))].">
      <j1 rule="para" parents="12816 516"/>
    </justification>
  </clause>

  <clause id="12823">
    <literal><![CDATA[
      R(x,y,T(z,y * x)) \ (z * (y * x)) = T(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(12816(a,1),965(a,1,1))].">
      <j1 rule="para" parents="12816 965"/>
    </justification>
  </clause>

  <clause id="12824">
    <literal><![CDATA[
      K(x,(((y * x) * z) / R(x,y,z)) \ u) = K(x,(T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(12822(a,1),7678(a,2,2,1))].">
      <j1 rule="para" parents="12822 7678"/>
    </justification>
  </clause>

  <clause id="12825">
    <literal><![CDATA[
      K(x,R(R(x * y,y * z,u),y,z)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12805,a,12800,a)].">
      <j1 rule="hyper" parents="12805 12800"/>
    </justification>
  </clause>

  <clause id="12826">
    <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(12824(a,2),8866(a,1))].">
      <j1 rule="para" parents="12824 8866"/>
    </justification>
  </clause>

  <clause id="12827">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ 1 = K(z,x) * (x * (K(y,x) / x))
    ]]></literal>
    <justification jstring="[para(3499(a,1),12813(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3499 12813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12828">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ 1 = x * (K(z,x) * (K(y,x) / x))
    ]]></literal>
    <justification jstring="[hyper(334,a,5522,a(flip),b,12827,a),flip(a)].">
      <j1 rule="hyper" parents="334 5522 12827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12829">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ 1 = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[para(8613(a,1),12828(a,2,2))].">
      <j1 rule="para" parents="8613 12828"/>
    </justification>
  </clause>

  <clause id="12830">
    <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(12829(a,1),11801(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12829 11801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12831">
    <literal><![CDATA[
      K(x,x * (((y * x) * z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(12768(a,1),12826(a,1))].">
      <j1 rule="para" parents="12768 12826"/>
    </justification>
  </clause>

  <clause id="12833">
    <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),12779(a,1,1))].">
      <j1 rule="para" parents="101 12779"/>
    </justification>
  </clause>

  <clause id="12834">
    <literal><![CDATA[
      ((x * (a(y,x,y) * z)) * u) / ((x * z) * u) = a(y,R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(12727(a,1),12833(a,1,1,1))].">
      <j1 rule="para" parents="12727 12833"/>
    </justification>
  </clause>

  <clause id="12835">
    <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),12834(a,1,2,1))].">
      <j1 rule="para" parents="5 12834"/>
    </justification>
  </clause>

  <clause id="12836">
    <literal><![CDATA[
      a(x,R(y,y \ z,u),x) = ((a(x,y,x) * z) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(11343(a,1),12835(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11343 12835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12837">
    <literal><![CDATA[
      a(x,R(y,y \ z,u),x) = R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,15,a,b,12836,a),flip(a)].">
      <j1 rule="hyper" parents="334 15 12836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12838">
    <literal><![CDATA[
      R(a(x,y,x),y * z,u) = a(x,R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),12837(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 12837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12839">
    <literal><![CDATA[
      a(x,R(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12689,a(flip),b,12838,a),flip(a)].">
      <j1 rule="hyper" parents="58 12689 12838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12840">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = a(x,R(y,w,v5),x)
    ]]></literal>
    <justification jstring="[hyper(334,a,12689,a,b,12839,a)].">
      <j1 rule="hyper" parents="334 12689 12839"/>
    </justification>
  </clause>

  <clause id="12841">
    <literal><![CDATA[
      a(x,y,x) * (R(y,z,u) * x) = T(x * R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(12839(a,1),9185(a,1,1))].">
      <j1 rule="para" parents="12839 9185"/>
    </justification>
  </clause>

  <clause id="12842">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = a(x,z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(12839(a,1),9198(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12839 9198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12844">
    <literal><![CDATA[
      a(x,R(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = w
    ]]></literal>
    <justification jstring="[para(12840(a,1),392(a,1)),flip(b)].">
      <j1 rule="para" parents="12840 392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12845">
    <literal><![CDATA[
      a(x,(y \ z) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,T(y,z),x) = u
    ]]></literal>
    <justification jstring="[para(4619(a,1),12844(a,1,2))].">
      <j1 rule="para" parents="4619 12844"/>
    </justification>
  </clause>

  <clause id="12846">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,9198,a(flip),b,12842,a),flip(a)].">
      <j1 rule="hyper" parents="334 9198 12842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12847">
    <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(12846(a,1),12444(a,1,2))].">
      <j1 rule="para" parents="12846 12444"/>
    </justification>
  </clause>

  <clause id="12848">
    <literal><![CDATA[
      R(x,y,z) * R(u,x,u) = T(u * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(9822,a,12841,a)].">
      <j1 rule="hyper" parents="9822 12841"/>
    </justification>
  </clause>

  <clause id="12849">
    <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(12848(a,2),4482(a,1,1))].">
      <j1 rule="para" parents="12848 4482"/>
    </justification>
  </clause>

  <clause id="12850">
    <literal><![CDATA[
      T(x * R(y,z,u),x * y) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(825(a,1),12847(a,1,2)),flip(a)].">
      <j1 rule="para" parents="825 12847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12852">
    <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(12850(a,1),5062(a,2,2)),flip(a)].">
      <j1 rule="para" parents="12850 5062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12853">
    <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,12435,a(flip),b,12852,a)].">
      <j1 rule="hyper" parents="58 12435 12852"/>
    </justification>
  </clause>

  <clause id="12854">
    <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(12281(a,1),12853(a,1,1))].">
      <j1 rule="para" parents="12281 12853"/>
    </justification>
  </clause>

  <clause id="12855">
    <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,12486,a,b,12854,a),flip(a)].">
      <j1 rule="hyper" parents="58 12486 12854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12856">
    <literal><![CDATA[
      K(x * y,x * R(y,z,u)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(176(a,1),12855(a,2,1,2))].">
      <j1 rule="para" parents="176 12855"/>
    </justification>
  </clause>

  <clause id="12857">
    <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(6818,a,12856,a)].">
      <j1 rule="hyper" parents="6818 12856"/>
    </justification>
  </clause>

  <clause id="12858">
    <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),12856(a,1,1))].">
      <j1 rule="para" parents="7 12856"/>
    </justification>
  </clause>

  <clause id="12859">
    <literal><![CDATA[
      K(x,(y \ x) * R(y,z,u)) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9038,a(flip),b,12858,a)].">
      <j1 rule="hyper" parents="58 9038 12858"/>
    </justification>
  </clause>

  <clause id="12860">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12601,a(flip),b,12859,a)].">
      <j1 rule="hyper" parents="58 12601 12859"/>
    </justification>
  </clause>

  <clause id="12861">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(y \ x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(5235(a,1),12860(a,2,1))].">
      <j1 rule="para" parents="5235 12860"/>
    </justification>
  </clause>

  <clause id="12862">
    <literal><![CDATA[
      L(T(x,R(y,z,u)),y,T(x,w)) = T(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10059,a,12849,a)].">
      <j1 rule="hyper" parents="10059 12849"/>
    </justification>
  </clause>

  <clause id="12863">
    <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(12856(a,1),12857(a,1,1))].">
      <j1 rule="para" parents="12856 12857"/>
    </justification>
  </clause>

  <clause id="12864">
    <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(12694(a,1),12715(a,1,2))].">
      <j1 rule="para" parents="12694 12715"/>
    </justification>
  </clause>

  <clause id="12865">
    <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(861,a,12864,a)].">
      <j1 rule="hyper" parents="861 12864"/>
    </justification>
  </clause>

  <clause id="12866">
    <literal><![CDATA[
      L(x,y,a(z,u,z) * w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(12702,a,12865,a),flip(a)].">
      <j1 rule="hyper" parents="12702 12865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12868">
    <literal><![CDATA[
      L(x,y,a(z,u,z) \ w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),12866(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5 12866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12869">
    <literal><![CDATA[
      L(x,y,R(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(9167(a,1),12866(a,1,3))].">
      <j1 rule="para" parents="9167 12866"/>
    </justification>
  </clause>

  <clause id="12870">
    <literal><![CDATA[
      L(x,y,K(z * u,z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(9180(a,1),12866(a,1,3))].">
      <j1 rule="para" parents="9180 12866"/>
    </justification>
  </clause>

  <clause id="12871">
    <literal><![CDATA[
      L(x,y,K(z,z * u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(9181(a,1),12866(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9181 12866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12872">
    <literal><![CDATA[
      L(x,y,T(z * u,z)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(9185(a,1),12866(a,1,3))].">
      <j1 rule="para" parents="9185 12866"/>
    </justification>
  </clause>

  <clause id="12873">
    <literal><![CDATA[
      L(x,y,K(z,z \ u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(9152(a,1),12866(a,1,3))].">
      <j1 rule="para" parents="9152 12866"/>
    </justification>
  </clause>

  <clause id="12874">
    <literal><![CDATA[
      L(x,y,z * a(u,w,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(9793(a,1),12866(a,1,3))].">
      <j1 rule="para" parents="9793 12866"/>
    </justification>
  </clause>

  <clause id="12875">
    <literal><![CDATA[
      L(x,y,R(z,u,z) \ w) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(9798(a,1),12866(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9798 12866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12876">
    <literal><![CDATA[
      L(x,y,z * R(u,w,u)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(9800(a,1),12866(a,1,3))].">
      <j1 rule="para" parents="9800 12866"/>
    </justification>
  </clause>

  <clause id="12877">
    <literal><![CDATA[
      L(x,y,L(z,u,z) \ w) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(9801(a,1),12866(a,1,3))].">
      <j1 rule="para" parents="9801 12866"/>
    </justification>
  </clause>

  <clause id="12879">
    <literal><![CDATA[
      L(x,y,T(z,z * u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(4629(a,1),12869(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4629 12869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12880">
    <literal><![CDATA[
      L(x,y,T(z,z \ u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(4695(a,1),12869(a,1,3))].">
      <j1 rule="para" parents="4695 12869"/>
    </justification>
  </clause>

  <clause id="12881">
    <literal><![CDATA[
      L(x,y,(z \ u) \ u) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(7790(a,1),12869(a,1,3))].">
      <j1 rule="para" parents="7790 12869"/>
    </justification>
  </clause>

  <clause id="12882">
    <literal><![CDATA[
      L(x,y,K(z \ u,z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(9151(a,1),12868(a,1,3))].">
      <j1 rule="para" parents="9151 12868"/>
    </justification>
  </clause>

  <clause id="12883">
    <literal><![CDATA[
      L(x,y,L(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(9360(a,1),12868(a,1,3))].">
      <j1 rule="para" parents="9360 12868"/>
    </justification>
  </clause>

  <clause id="12884">
    <literal><![CDATA[
      L(x,y,z / R(u,w,u)) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(9810(a,1),12868(a,1,3))].">
      <j1 rule="para" parents="9810 12868"/>
    </justification>
  </clause>

  <clause id="12885">
    <literal><![CDATA[
      L(x,y,T(z / u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(4648(a,1),12883(a,1,3))].">
      <j1 rule="para" parents="4648 12883"/>
    </justification>
  </clause>

  <clause id="12886">
    <literal><![CDATA[
      L(x,y,T(z,u) / u) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(9189(a,1),12874(a,1,3))].">
      <j1 rule="para" parents="9189 12874"/>
    </justification>
  </clause>

  <clause id="12887">
    <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,12005,a(flip),b,12870,a),flip(a)].">
      <j1 rule="hyper" parents="58 12005 12870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12888">
    <literal><![CDATA[
      L(x,y,K(z,u * z)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(5649(a,2),12871(a,1,3))].">
      <j1 rule="para" parents="5649 12871"/>
    </justification>
  </clause>

  <clause id="12889">
    <literal><![CDATA[
      L(x,y,K(z * u,(z * u) * (u \ 1))) = L(x,y,K(u * z,u \ 1))
    ]]></literal>
    <justification jstring="[para(6133(a,1),12871(a,2,3))].">
      <j1 rule="para" parents="6133 12871"/>
    </justification>
  </clause>

  <clause id="12890">
    <literal><![CDATA[
      L(x,y \ z,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(5734,a,12873,a),flip(a)].">
      <j1 rule="hyper" parents="5734 12873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12891">
    <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(334,a,12697,a,b,12873,a)].">
      <j1 rule="hyper" parents="334 12697 12873"/>
    </justification>
  </clause>

  <clause id="12892">
    <literal><![CDATA[
      L(x \ y,z,K(x,y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,7775,a(flip),b,12873,a),flip(a)].">
      <j1 rule="hyper" parents="58 7775 12873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12893">
    <literal><![CDATA[
      L(x,y,K(z \ u,u)) = L(x,y,K(z \ u,z))
    ]]></literal>
    <justification jstring="[para(5183(a,1),12873(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5183 12873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12894">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) * z = K(x,y) * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(1392,a,12890,a),flip(a)].">
      <j1 rule="hyper" parents="1392 12890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12895">
    <literal><![CDATA[
      (K(x,y) * z) / (x \ y) = K(x,y) * (z / (x \ y))
    ]]></literal>
    <justification jstring="[para(12892(a,1),556(a,1,2))].">
      <j1 rule="para" parents="12892 556"/>
    </justification>
  </clause>

  <clause id="12896">
    <literal><![CDATA[
      L(x,y * z,T(y,z)) = L(x,y * z,y)
    ]]></literal>
    <justification jstring="[hyper(11483,a,12879,a),flip(a)].">
      <j1 rule="hyper" parents="11483 12879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12897">
    <literal><![CDATA[
      L(x,y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z \ u) \ u) = w
    ]]></literal>
    <justification jstring="[para(12880(a,1),2176(a,1))].">
      <j1 rule="para" parents="12880 2176"/>
    </justification>
  </clause>

  <clause id="12898">
    <literal><![CDATA[
      L(x,y,T(z * u,u \ 1)) = L(x,y,T(z * u,z))
    ]]></literal>
    <justification jstring="[para(6501(a,1),12880(a,1,3))].">
      <j1 rule="para" parents="6501 12880"/>
    </justification>
  </clause>

  <clause id="12899">
    <literal><![CDATA[
      L(x,y / z,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(7544,a,12882,a)].">
      <j1 rule="hyper" parents="7544 12882"/>
    </justification>
  </clause>

  <clause id="12900">
    <literal><![CDATA[
      L(x,y \ z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(4455,a,12882,a),flip(a)].">
      <j1 rule="hyper" parents="4455 12882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12901">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(u,z \ 1))
    ]]></literal>
    <justification jstring="[para(4750(a,1),12882(a,1,3))].">
      <j1 rule="para" parents="4750 12882"/>
    </justification>
  </clause>

  <clause id="12902">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) = L(x,y,K(u,u \ z))
    ]]></literal>
    <justification jstring="[para(5236(a,1),12882(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5236 12882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12903">
    <literal><![CDATA[
      K(x,y) * ((x / y) * z) = (x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(12899(a,1),5540(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12899 5540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12904">
    <literal><![CDATA[
      (K(x,y) * (y \ x)) \ z = (y \ x) \ (K(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,311,a(flip),b,12900,a)].">
      <j1 rule="hyper" parents="58 311 12900"/>
    </justification>
  </clause>

  <clause id="12905">
    <literal><![CDATA[
      L(x,y,y / z) = L(x,y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(11483,a,12885,a)].">
      <j1 rule="hyper" parents="11483 12885"/>
    </justification>
  </clause>

  <clause id="12906">
    <literal><![CDATA[
      L(x,y * z,(y * z) / y) = L(x,y * z,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),12905(a,2,3))].">
      <j1 rule="para" parents="4 12905"/>
    </justification>
  </clause>

  <clause id="12907">
    <literal><![CDATA[
      L(x,y,z / T(u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(4488(a,1),12886(a,1,3))].">
      <j1 rule="para" parents="4488 12886"/>
    </justification>
  </clause>

  <clause id="12908">
    <literal><![CDATA[
      L(x,T(y,z),T(y,z) \ z) = L(x,T(y,z),y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11438,a(flip),b,12907,a)].">
      <j1 rule="hyper" parents="58 11438 12907"/>
    </justification>
  </clause>

  <clause id="12909">
    <literal><![CDATA[
      L(x,y,(z \ T(u,z \ u)) \ w) = L(x,y,(u / z) \ w)
    ]]></literal>
    <justification jstring="[para(4675(a,1),12875(a,1,3,1))].">
      <j1 rule="para" parents="4675 12875"/>
    </justification>
  </clause>

  <clause id="12910">
    <literal><![CDATA[
      L(x,y,z * T(u,u \ w)) = L(x,y,z * T(u,w))
    ]]></literal>
    <justification jstring="[para(4695(a,1),12876(a,1,3,2))].">
      <j1 rule="para" parents="4695 12876"/>
    </justification>
  </clause>

  <clause id="12911">
    <literal><![CDATA[
      L(x,y,T(z / u,z) \ w) = L(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(4648(a,1),12877(a,1,3,1))].">
      <j1 rule="para" parents="4648 12877"/>
    </justification>
  </clause>

  <clause id="12912">
    <literal><![CDATA[
      L(x,y,K(z,u) * (z \ u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(7021(a,1),12884(a,1,3))].">
      <j1 rule="para" parents="7021 12884"/>
    </justification>
  </clause>

  <clause id="12913">
    <literal><![CDATA[
      L(x,y,K(z \ u,u)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,12882,a(flip),b,12893,a),flip(a)].">
      <j1 rule="hyper" parents="334 12882 12893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12914">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(6652(a,1),12913(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6652 12913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12915">
    <literal><![CDATA[
      L(x,y,K(z,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(10479,a,12914,a),flip(a)].">
      <j1 rule="hyper" parents="10479 12914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12917">
    <literal><![CDATA[
      (K(x,y \ 1) * y) * z = K(x,y \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1392,a,12915,a),flip(a)].">
      <j1 rule="hyper" parents="1392 12915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12922">
    <literal><![CDATA[
      K(x,y) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(5409,a,12903,a)].">
      <j1 rule="hyper" parents="5409 12903"/>
    </justification>
  </clause>

  <clause id="12923">
    <literal><![CDATA[
      L(x,y * z,z * K(y,z)) = L(x,y * z,z)
    ]]></literal>
    <justification jstring="[para(5017(a,1),12906(a,1,3))].">
      <j1 rule="para" parents="5017 12906"/>
    </justification>
  </clause>

  <clause id="12924">
    <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,12912,a)].">
      <j1 rule="hyper" parents="58 13 12912"/>
    </justification>
  </clause>

  <clause id="12925">
    <literal><![CDATA[
      R(K(x,y),x \ y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9560,a,12922,a)].">
      <j1 rule="hyper" parents="9560 12922"/>
    </justification>
  </clause>

  <clause id="12926">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),12925(a,1,2))].">
      <j1 rule="para" parents="4 12925"/>
    </justification>
  </clause>

  <clause id="12928">
    <literal><![CDATA[
      K(x,R(y \ 1,y,z) \ x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11989,a,b,12926,a)].">
      <j1 rule="hyper" parents="58 11989 12926"/>
    </justification>
  </clause>

  <clause id="12929">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,12928,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 12928 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12930">
    <literal><![CDATA[
      R(K(x,x * y),y * z,u) = K(x,((z * u) / ((y * z) * u)) \ x)
    ]]></literal>
    <justification jstring="[para(12928(a,1),11993(a,1,1))].">
      <j1 rule="para" parents="12928 11993"/>
    </justification>
  </clause>

  <clause id="12931">
    <literal><![CDATA[
      T(x,(y / (z * y)) \ x) = T(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3940,a(flip),b,12929,a)].">
      <j1 rule="hyper" parents="58 3940 12929"/>
    </justification>
  </clause>

  <clause id="12932">
    <literal><![CDATA[
      T(x,(y / z) \ x) = T(x,x * (z / y))
    ]]></literal>
    <justification jstring="[para(7(a,1),12931(a,1,2,1,2))].">
      <j1 rule="para" parents="7 12931"/>
    </justification>
  </clause>

  <clause id="12933">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,x * (y / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8764,a,b,12932,a)].">
      <j1 rule="hyper" parents="58 8764 12932"/>
    </justification>
  </clause>

  <clause id="12934">
    <literal><![CDATA[
      x * K(x,x * (y / z)) = T(x,(y * x) / z)
    ]]></literal>
    <justification jstring="[hyper(334,a,5020,a(flip),b,12933,a)].">
      <j1 rule="hyper" parents="334 5020 12933"/>
    </justification>
  </clause>

  <clause id="12935">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,x * (y / z))
    ]]></literal>
    <justification jstring="[hyper(29,a,5020,a(flip),b,12934,a)].">
      <j1 rule="hyper" parents="29 5020 12934"/>
    </justification>
  </clause>

  <clause id="12936">
    <literal><![CDATA[
      K(x,(y / z) \ x) = K(x,x * (z / y))
    ]]></literal>
    <justification jstring="[hyper(8769,a,12935,a)].">
      <j1 rule="hyper" parents="8769 12935"/>
    </justification>
  </clause>

  <clause id="12937">
    <literal><![CDATA[
      K(x,x * (y / ((z * x) * u))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11394,a(flip),b,12935,a),flip(a)].">
      <j1 rule="hyper" parents="58 11394 12935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12938">
    <literal><![CDATA[
      (x * K(y,y * (z / u))) \ x = K((u / z) \ y,y)
    ]]></literal>
    <justification jstring="[para(12936(a,1),6523(a,1,1,2))].">
      <j1 rule="para" parents="12936 6523"/>
    </justification>
  </clause>

  <clause id="12939">
    <literal><![CDATA[
      R(K(x,x * (y / z)),x * u,w) = K(R(x,u,w),(z / y) \ x)
    ]]></literal>
    <justification jstring="[para(12936(a,1),7052(a,1,1))].">
      <j1 rule="para" parents="12936 7052"/>
    </justification>
  </clause>

  <clause id="12940">
    <literal><![CDATA[
      L(x,y,T(z * u,u \ 1)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(334,a,12872,a(flip),b,12898,a),flip(a)].">
      <j1 rule="hyper" parents="334 12872 12898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12941">
    <literal><![CDATA[
      (x \ y) \ (K(y,x) \ z) = (T(x,y) \ y) \ z
    ]]></literal>
    <justification jstring="[para(5392(a,1),12904(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5392 12904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12942">
    <literal><![CDATA[
      (x \ y) \ (K(x,y) * z) = (T(x,y) \ y) \ z
    ]]></literal>
    <justification jstring="[para(5391(a,1),12941(a,1,2))].">
      <j1 rule="para" parents="5391 12941"/>
    </justification>
  </clause>

  <clause id="12943">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),x \ y) = y \ ((T(y,x) / x) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11443,a(flip),b,12908,a),flip(a)].">
      <j1 rule="hyper" parents="58 11443 12908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12944">
    <literal><![CDATA[
      L(x,y,(z / u) * T(u,w)) = L(x,y,z * K(u,u \ w))
    ]]></literal>
    <justification jstring="[para(6467(a,1),12910(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6467 12910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12945">
    <literal><![CDATA[
      (x * K(y,x \ 1)) * z = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[para(2338(a,1),12917(a,1,1))].">
      <j1 rule="para" parents="2338 12917"/>
    </justification>
  </clause>

  <clause id="12946">
    <literal><![CDATA[
      K((x / y) \ z,z) = K(z * (y / x),z)
    ]]></literal>
    <justification jstring="[hyper(6528,a,12938,a),flip(a)].">
      <j1 rule="hyper" parents="6528 12938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12947">
    <literal><![CDATA[
      K(x / y,z) * a(z,y \ x,z) = K(z * (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11025,a,b,12946,a)].">
      <j1 rule="hyper" parents="58 11025 12946"/>
    </justification>
  </clause>

  <clause id="12948">
    <literal><![CDATA[
      (x * K(y,x \ 1)) * z = x * (K(y,x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(334,a,6239,a(flip),b,12945,a),flip(a)].">
      <j1 rule="hyper" parents="334 6239 12945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12949">
    <literal><![CDATA[
      L(x,K(y,z \ 1),z) = x
    ]]></literal>
    <justification jstring="[hyper(493,a,12948,a)].">
      <j1 rule="hyper" parents="493 12948"/>
    </justification>
  </clause>

  <clause id="12955">
    <literal><![CDATA[
      L(x,K(y,z \ u),u \ z) = x
    ]]></literal>
    <justification jstring="[para(6423(a,1),12949(a,1,2))].">
      <j1 rule="para" parents="6423 12949"/>
    </justification>
  </clause>

  <clause id="12956">
    <literal><![CDATA[
      L(x,K(y,z),u \ (u / z)) = x
    ]]></literal>
    <justification jstring="[para(6446(a,1),12949(a,1,2))].">
      <j1 rule="para" parents="6446 12949"/>
    </justification>
  </clause>

  <clause id="12957">
    <literal><![CDATA[
      L(x,K(y,z \ u),u \ z) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(12955(a,1),45(a,2))].">
      <j1 rule="para" parents="12955 45"/>
    </justification>
  </clause>

  <clause id="12958">
    <literal><![CDATA[
      L(x,K(y,z),u \ (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(12956(a,1),45(a,2))].">
      <j1 rule="para" parents="12956 45"/>
    </justification>
  </clause>

  <clause id="12959">
    <literal><![CDATA[
      a(x,y / z,x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,9182,a,b,12947,a)].">
      <j1 rule="hyper" parents="29 9182 12947"/>
    </justification>
  </clause>

  <clause id="12961">
    <literal><![CDATA[
      a(x,y / (z * y),x) = a(x,z \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,11031,a(flip),b,12959,a),flip(a)].">
      <j1 rule="hyper" parents="334 11031 12959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12962">
    <literal><![CDATA[
      a(x,(y \ z) \ z,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),12959(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 12959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12963">
    <literal><![CDATA[
      a(x,T(y,z),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(12845,a,12962,a)].">
      <j1 rule="hyper" parents="12845 12962"/>
    </justification>
  </clause>

  <clause id="12964">
    <literal><![CDATA[
      a(x,y * K(z,y),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(5934(a,1),12962(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5934 12962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12965">
    <literal><![CDATA[
      a(x,T(y / z,u),x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,12959,a(flip),b,12963,a),flip(a)].">
      <j1 rule="hyper" parents="334 12959 12963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12967">
    <literal><![CDATA[
      L(x,T(y,z),x) = a(x,y,x) \ x
    ]]></literal>
    <justification jstring="[para(12963(a,1),9360(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12963 9360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12968">
    <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(12963(a,1),9195(a,1,1))].">
      <j1 rule="para" parents="12963 9195"/>
    </justification>
  </clause>

  <clause id="12969">
    <literal><![CDATA[
      L(a(x,y,x),y,z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12693,a(flip),b,12964,a)].">
      <j1 rule="hyper" parents="58 12693 12964"/>
    </justification>
  </clause>

  <clause id="12972">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,9360,a(flip),b,12967,a),flip(a)].">
      <j1 rule="hyper" parents="334 9360 12967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12973">
    <literal><![CDATA[
      L(x,T(y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(12967(a,2),9845(a,1))].">
      <j1 rule="para" parents="12967 9845"/>
    </justification>
  </clause>

  <clause id="12974">
    <literal><![CDATA[
      L(x,T(y,z),x) = T(x,T(x * y,u)) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,9920,a,b,12972,a),flip(a)].">
      <j1 rule="hyper" parents="334 9920 12972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12977">
    <literal><![CDATA[
      L(x,y / z,x) = L(x,z \ y,x)
    ]]></literal>
    <justification jstring="[para(107(a,1),12972(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 12972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12981">
    <literal><![CDATA[
      L(x,y * K(z,y),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(5086(a,1),12972(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5086 12972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12983">
    <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(4040(a,2),12977(a,1,2))].">
      <j1 rule="para" parents="4040 12977"/>
    </justification>
  </clause>

  <clause id="12984">
    <literal><![CDATA[
      L(x,R(y * K(z,y),z,u),x) = L(x,(z * u) \ ((z * y) * u),x)
    ]]></literal>
    <justification jstring="[para(5200(a,2),12977(a,1,2))].">
      <j1 rule="para" parents="5200 12977"/>
    </justification>
  </clause>

  <clause id="12985">
    <literal><![CDATA[
      L(x,R(y * K(z,y),u,w),x) = L(x,R(y,u,w),x)
    ]]></literal>
    <justification jstring="[para(5781(a,1),12981(a,1,2))].">
      <j1 rule="para" parents="5781 12981"/>
    </justification>
  </clause>

  <clause id="12986">
    <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(4221(a,1),12961(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4221 12961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12987">
    <literal><![CDATA[
      a(x,R(y \ z,y,u),x) = a(x,(y * u) \ (z * u),x)
    ]]></literal>
    <justification jstring="[para(666(a,1),12965(a,1,2))].">
      <j1 rule="para" parents="666 12965"/>
    </justification>
  </clause>

  <clause id="12988">
    <literal><![CDATA[
      T(x,T(x * y,z)) = T(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8994,a,12974,a),flip(a)].">
      <j1 rule="hyper" parents="8994 12974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12989">
    <literal><![CDATA[
      T(x,T(x * (x \ y),z)) = T(x,y * K(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,11591,a,b,12988,a),flip(a)].">
      <j1 rule="hyper" parents="334 11591 12988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12990">
    <literal><![CDATA[
      T(x / T(y,x),z) * T(y,T(y * (y \ x),z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(12988(a,2),11784(a,1,2))].">
      <j1 rule="para" parents="12988 11784"/>
    </justification>
  </clause>

  <clause id="12992">
    <literal><![CDATA[
      T(x,y * K(x \ y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),12989(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 12989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12993">
    <literal><![CDATA[
      T(x \ y,y * K(x,T(z,y))) = T(x \ y,T(y,z))
    ]]></literal>
    <justification jstring="[para(7407(a,1),12992(a,1,2,2))].">
      <j1 rule="para" parents="7407 12992"/>
    </justification>
  </clause>

  <clause id="12994">
    <literal><![CDATA[
      T(x \ y,K(x,z) * y) = T(x \ y,T(y,z))
    ]]></literal>
    <justification jstring="[para(7423(a,1),12993(a,1,2))].">
      <j1 rule="para" parents="7423 12993"/>
    </justification>
  </clause>

  <clause id="12995">
    <literal><![CDATA[
      a(x,(y * z) \ (u * z),x) = a(x,y \ u,x)
    ]]></literal>
    <justification jstring="[hyper(12844,a,12987,a),flip(a)].">
      <j1 rule="hyper" parents="12844 12987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12997">
    <literal><![CDATA[
      L(x,(y * z) \ (u * z),x) = (w / x) \ (a(x,y \ u,x) \ w)
    ]]></literal>
    <justification jstring="[para(12995(a,1),9829(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12995 9829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12998">
    <literal><![CDATA[
      L(x,y,K(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(12891(a,1),385(a,1)),flip(b)].">
      <j1 rule="para" parents="12891 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12999">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(12902(a,2),12998(a,1))].">
      <j1 rule="para" parents="12902 12998"/>
    </justification>
  </clause>

  <clause id="13000">
    <literal><![CDATA[
      L(x,y,z * K(u,u \ w)) = L(x,y,z * K(u,w))
    ]]></literal>
    <justification jstring="[para(6467(a,1),12944(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6467 12944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13001">
    <literal><![CDATA[
      K(R(x,y,z),(u / w) \ x) = K(R(x,y,z),x * (w / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,7052,a(flip),b,12939,a),flip(a)].">
      <j1 rule="hyper" parents="58 7052 12939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13002">
    <literal><![CDATA[
      L(x,(y * z) \ (u * z),x) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ u,x) = w
    ]]></literal>
    <justification jstring="[para(12997(a,2),9846(a,1))].">
      <j1 rule="para" parents="12997 9846"/>
    </justification>
  </clause>

  <clause id="13003">
    <literal><![CDATA[
      R(K(x,x * y),y * z,u) = K(x,x * (((y * z) * u) / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,12936,a(flip),b,12930,a),flip(a)].">
      <j1 rule="hyper" parents="334 12936 12930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13005">
    <literal><![CDATA[
      L(x,(y * z) \ ((y * u) * z),x) = L(x,R(u,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12985,a(flip),b,12984,a),flip(a)].">
      <j1 rule="hyper" parents="58 12985 12984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13006">
    <literal><![CDATA[
      L(x,R(y,z,u),x) = L(x,z \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(13002,a,13005,a),flip(a)].">
      <j1 rule="hyper" parents="13002 13005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13008">
    <literal><![CDATA[
      L(x,R(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),13006(a,2,2))].">
      <j1 rule="para" parents="4 13006"/>
    </justification>
  </clause>

  <clause id="13009">
    <literal><![CDATA[
      R(K(x,x * y),y * z,u) = K(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(15(a,2),13003(a,2,2,2))].">
      <j1 rule="para" parents="15 13003"/>
    </justification>
  </clause>

  <clause id="13010">
    <literal><![CDATA[
      K(x,R(x * y,y * z,u)) = K(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12802,a,13009,a)].">
      <j1 rule="hyper" parents="12802 13009"/>
    </justification>
  </clause>

  <clause id="13011">
    <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(269(a,1),12889(a,1,3,2))].">
      <j1 rule="para" parents="269 12889"/>
    </justification>
  </clause>

  <clause id="13012">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(u * z,u))
    ]]></literal>
    <justification jstring="[para(6170(a,1),13011(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6170 13011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13013">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,12870,a(flip),b,13012,a),flip(a)].">
      <j1 rule="hyper" parents="334 12870 13012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13015">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,12901,a(flip),b,13013,a)].">
      <j1 rule="hyper" parents="58 12901 13013"/>
    </justification>
  </clause>

  <clause id="13016">
    <literal><![CDATA[
      L(x,y,K(z \ u,w)) = L(x,y,K(w,u \ z))
    ]]></literal>
    <justification jstring="[para(6423(a,1),13015(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6423 13015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13017">
    <literal><![CDATA[
      L(x,y,K(z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(13016(a,2),12999(a,1))].">
      <j1 rule="para" parents="13016 12999"/>
    </justification>
  </clause>

  <clause id="13018">
    <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),13017(a,1,3,1))].">
      <j1 rule="para" parents="4 13017"/>
    </justification>
  </clause>

  <clause id="13019">
    <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),12990(a,1,2,2,1))].">
      <j1 rule="para" parents="5 12990"/>
    </justification>
  </clause>

  <clause id="13020">
    <literal><![CDATA[
      x * K(T(x,y) / y,z) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9956,a(flip),b,13019,a)].">
      <j1 rule="hyper" parents="58 9956 13019"/>
    </justification>
  </clause>

  <clause id="13021">
    <literal><![CDATA[
      K(T(x,y) / y,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,6430,a(flip),b,13020,a),flip(a)].">
      <j1 rule="hyper" parents="29 6430 13020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13022">
    <literal><![CDATA[
      K(x / T(y,x),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9901,a(flip),b,13021,a)].">
      <j1 rule="hyper" parents="58 9901 13021"/>
    </justification>
  </clause>

  <clause id="13023">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(13021(a,1),10088(a,2,2))].">
      <j1 rule="para" parents="13021 10088"/>
    </justification>
  </clause>

  <clause id="13024">
    <literal><![CDATA[
      (x \ (x * K(y \ x,z))) \ (x * K(x / y,z)) = L(x,K(y \ x,z),x)
    ]]></literal>
    <justification jstring="[para(13023(a,1),10166(a,1,1,2))].">
      <j1 rule="para" parents="13023 10166"/>
    </justification>
  </clause>

  <clause id="13025">
    <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),13024(a,1,1))].">
      <j1 rule="para" parents="4 13024"/>
    </justification>
  </clause>

  <clause id="13026">
    <literal><![CDATA[
      L(x,K(y \ x,z),x) = x
    ]]></literal>
    <justification jstring="[hyper(8384,a,13025,a)].">
      <j1 rule="hyper" parents="8384 13025"/>
    </justification>
  </clause>

  <clause id="13028">
    <literal><![CDATA[
      L(x,K(y,z),x) = x
    ]]></literal>
    <justification jstring="[para(75(a,1),13026(a,1,2,1))].">
      <j1 rule="para" parents="75 13026"/>
    </justification>
  </clause>

  <clause id="13029">
    <literal><![CDATA[
      T(K(x,y) * z,z) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10325,a,13028,a)].">
      <j1 rule="hyper" parents="10325 13028"/>
    </justification>
  </clause>

  <clause id="13032">
    <literal><![CDATA[
      T(x * T(x \ y,z),y) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(5088(a,1),13029(a,1,1))].">
      <j1 rule="para" parents="5088 13029"/>
    </justification>
  </clause>

  <clause id="13033">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,2022,a,b,13032,a)].">
      <j1 rule="hyper" parents="58 2022 13032"/>
    </justification>
  </clause>

  <clause id="13034">
    <literal><![CDATA[
      K(T(x,y) \ y,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(6473,a,13033,a)].">
      <j1 rule="hyper" parents="6473 13033"/>
    </justification>
  </clause>

  <clause id="13035">
    <literal><![CDATA[
      K(x / y,z) * a(z,T(y,x) \ x,z) = K(z * (T(y,x) \ x),z)
    ]]></literal>
    <justification jstring="[para(13034(a,1),9182(a,1,1))].">
      <j1 rule="para" parents="13034 9182"/>
    </justification>
  </clause>

  <clause id="13036">
    <literal><![CDATA[
      T(x,y / z) \ R(x,T(z,y) \ y,x) = K(x * (T(z,y) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(9169,a,13035,a)].">
      <j1 rule="hyper" parents="9169 13035"/>
    </justification>
  </clause>

  <clause id="13037">
    <literal><![CDATA[
      T(x,T(y,z) \ z) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(5558,a,13036,a)].">
      <j1 rule="hyper" parents="5558 13036"/>
    </justification>
  </clause>

  <clause id="13038">
    <literal><![CDATA[
      T(x,y \ T(z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6867,a(flip),b,13037,a)].">
      <j1 rule="hyper" parents="58 6867 13037"/>
    </justification>
  </clause>

  <clause id="13039">
    <literal><![CDATA[
      T(x,T(y \ T(z,y),u)) = K(x,u) * T(x * K(u,x),z / y)
    ]]></literal>
    <justification jstring="[para(13037(a,1),8676(a,2,2))].">
      <j1 rule="para" parents="13037 8676"/>
    </justification>
  </clause>

  <clause id="13040">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / z) = T(x,y / T(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9390,a(flip),b,13038,a),flip(a)].">
      <j1 rule="hyper" parents="58 9390 13038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13041">
    <literal><![CDATA[
      T(x,y / T(z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(8650,a,13040,a),flip(a)].">
      <j1 rule="hyper" parents="8650 13040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13042">
    <literal><![CDATA[
      T(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(13040(a,1),8650(a,1))].">
      <j1 rule="para" parents="13040 8650"/>
    </justification>
  </clause>

  <clause id="13043">
    <literal><![CDATA[
      T(x,T(y,z) / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(9771,a,13041,a)].">
      <j1 rule="hyper" parents="9771 13041"/>
    </justification>
  </clause>

  <clause id="13044">
    <literal><![CDATA[
      T(x,y / T(T(z,y),u)) = T(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[para(18(a,1),13041(a,1,2,2))].">
      <j1 rule="para" parents="18 13041"/>
    </justification>
  </clause>

  <clause id="13045">
    <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(13041(a,1),13042(a,1,2,2))].">
      <j1 rule="para" parents="13041 13042"/>
    </justification>
  </clause>

  <clause id="13046">
    <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(12994(a,1),13044(a,1,2,2,1))].">
      <j1 rule="para" parents="12994 13044"/>
    </justification>
  </clause>

  <clause id="13047">
    <literal><![CDATA[
      T(x,T(y \ T(z,y),u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,8666,a(flip),b,13039,a),flip(a)].">
      <j1 rule="hyper" parents="334 8666 13039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13048">
    <literal><![CDATA[
      (K(x,y) * ((x \ y) * z)) \ ((K(x,y) * (x \ y)) * (z * u)) = L(u,z,y / x)
    ]]></literal>
    <justification jstring="[para(12894(a,1),12924(a,1,1))].">
      <j1 rule="para" parents="12894 12924"/>
    </justification>
  </clause>

  <clause id="13049">
    <literal><![CDATA[
      (K(x,y) * ((x \ y) * z)) \ (K(x,y) * ((x \ y) * (z * u))) = L(u,z,y / x)
    ]]></literal>
    <justification jstring="[para(12894(a,1),13048(a,1,2))].">
      <j1 rule="para" parents="12894 13048"/>
    </justification>
  </clause>

  <clause id="13050">
    <literal><![CDATA[
      L(L(x,y,z \ u),(z \ u) * y,K(z,u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[hyper(861,a,13049,a)].">
      <j1 rule="hyper" parents="861 13049"/>
    </justification>
  </clause>

  <clause id="13051">
    <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),12983(a,2,2))].">
      <j1 rule="para" parents="9 12983"/>
    </justification>
  </clause>

  <clause id="13052">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),x) = L(x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,13008,a(flip),b,13051,a)].">
      <j1 rule="hyper" parents="58 13008 13051"/>
    </justification>
  </clause>

  <clause id="13054">
    <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(12694(a,1),12705(a,2,1))].">
      <j1 rule="para" parents="12694 12705"/>
    </justification>
  </clause>

  <clause id="13055">
    <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(334,a,12703,a(flip),b,13054,a),flip(a)].">
      <j1 rule="hyper" parents="334 12703 13054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13056">
    <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),13055(a,2,2))].">
      <j1 rule="para" parents="15 13055"/>
    </justification>
  </clause>

  <clause id="13057">
    <literal><![CDATA[
      R(a(x,y,x) * z,u,w) = a(x,y,x) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(12697(a,1),13056(a,1,2))].">
      <j1 rule="para" parents="12697 13056"/>
    </justification>
  </clause>

  <clause id="13058">
    <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(13057(a,2),12472(a,1,1,2))].">
      <j1 rule="para" parents="13057 12472"/>
    </justification>
  </clause>

  <clause id="13059">
    <literal><![CDATA[
      R(a(x,y,x) * z,u,w) * v5 = a(x,y,x) * (R(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(13057(a,2),12694(a,1,1))].">
      <j1 rule="para" parents="13057 12694"/>
    </justification>
  </clause>

  <clause id="13060">
    <literal><![CDATA[
      R(x * a(y,z,y),u,w) * v5 = a(y,z,y) * (R(x,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(9793(a,1),13059(a,1,1,1))].">
      <j1 rule="para" parents="9793 13059"/>
    </justification>
  </clause>

  <clause id="13061">
    <literal><![CDATA[
      R(x * a(y,z,y),u,w) = R(x,u,w) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,12720,a,b,13060,a),flip(a)].">
      <j1 rule="hyper" parents="30 12720 13060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13062">
    <literal><![CDATA[
      R(a(x,y,x) \ z,u,w) = a(x,y,x) \ R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(4031,a,13061,a),flip(a)].">
      <j1 rule="hyper" parents="4031 13061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13064">
    <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(12694(a,1),12714(a,1,2,1))].">
      <j1 rule="para" parents="12694 12714"/>
    </justification>
  </clause>

  <clause id="13065">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) = a(u,(x * (y * z)) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(5210(a,1),12784(a,2,2))].">
      <j1 rule="para" parents="5210 12784"/>
    </justification>
  </clause>

  <clause id="13066">
    <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(9193,a,13065,a)].">
      <j1 rule="hyper" parents="9193 13065"/>
    </justification>
  </clause>

  <clause id="13067">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * (z * y)) / (u * z),x)
    ]]></literal>
    <justification jstring="[para(12969(a,1),13066(a,1,1))].">
      <j1 rule="para" parents="12969 13066"/>
    </justification>
  </clause>

  <clause id="13068">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * z) \ (u * (z * y)),x)
    ]]></literal>
    <justification jstring="[hyper(334,a,12959,a(flip),b,13067,a),flip(a)].">
      <j1 rule="hyper" parents="334 12959 13067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13070">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(13(a,2),13068(a,2,2))].">
      <j1 rule="para" parents="13 13068"/>
    </justification>
  </clause>

  <clause id="13071">
    <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(12694(a,1),13064(a,1,2))].">
      <j1 rule="para" parents="12694 13064"/>
    </justification>
  </clause>

  <clause id="13072">
    <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(863,a,13071,a)].">
      <j1 rule="hyper" parents="863 13071"/>
    </justification>
  </clause>

  <clause id="13073">
    <literal><![CDATA[
      a(a(x,y,x) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(12702,a,13072,a),flip(a)].">
      <j1 rule="hyper" parents="12702 13072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13075">
    <literal><![CDATA[
      a(a(x,y,x) \ z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),13073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13076">
    <literal><![CDATA[
      a(R(x,y,x),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(9167(a,1),13073(a,1,1))].">
      <j1 rule="para" parents="9167 13073"/>
    </justification>
  </clause>

  <clause id="13077">
    <literal><![CDATA[
      a(K(x * y,y),z,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(9179(a,1),13073(a,1,1))].">
      <j1 rule="para" parents="9179 13073"/>
    </justification>
  </clause>

  <clause id="13078">
    <literal><![CDATA[
      a(T(x * y,x),z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(9185(a,1),13073(a,1,1))].">
      <j1 rule="para" parents="9185 13073"/>
    </justification>
  </clause>

  <clause id="13079">
    <literal><![CDATA[
      a(K(x,x \ y),z,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(9152(a,1),13073(a,1,1))].">
      <j1 rule="para" parents="9152 13073"/>
    </justification>
  </clause>

  <clause id="13080">
    <literal><![CDATA[
      a(x * a(y,z,y),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(9793(a,1),13073(a,1,1))].">
      <j1 rule="para" parents="9793 13073"/>
    </justification>
  </clause>

  <clause id="13081">
    <literal><![CDATA[
      a(R(x,y,x) * z,u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[para(9799(a,1),13073(a,1,1))].">
      <j1 rule="para" parents="9799 13073"/>
    </justification>
  </clause>

  <clause id="13082">
    <literal><![CDATA[
      a(T(x * (y / x),x),z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(9803(a,1),13073(a,1,1))].">
      <j1 rule="para" parents="9803 13073"/>
    </justification>
  </clause>

  <clause id="13083">
    <literal><![CDATA[
      a(T(x,x \ y),z,u) = a(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4695(a,1),13076(a,1,1))].">
      <j1 rule="para" parents="4695 13076"/>
    </justification>
  </clause>

  <clause id="13084">
    <literal><![CDATA[
      a((x \ y) \ y,z,u) = a(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(7790(a,1),13076(a,1,1))].">
      <j1 rule="para" parents="7790 13076"/>
    </justification>
  </clause>

  <clause id="13085">
    <literal><![CDATA[
      a(K(x \ y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(9151(a,1),13075(a,1,1))].">
      <j1 rule="para" parents="9151 13075"/>
    </justification>
  </clause>

  <clause id="13086">
    <literal><![CDATA[
      a(K(x \ 1,y),z,u) = a(K(x \ y,y),z,u)
    ]]></literal>
    <justification jstring="[para(9187(a,1),13075(a,1,1))].">
      <j1 rule="para" parents="9187 13075"/>
    </justification>
  </clause>

  <clause id="13087">
    <literal><![CDATA[
      a(L(x,y,x),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(9360(a,1),13075(a,1,1))].">
      <j1 rule="para" parents="9360 13075"/>
    </justification>
  </clause>

  <clause id="13088">
    <literal><![CDATA[
      a(T(x / y,x),z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(4648(a,1),13087(a,1,1))].">
      <j1 rule="para" parents="4648 13087"/>
    </justification>
  </clause>

  <clause id="13089">
    <literal><![CDATA[
      a(T(x,x \ y),z,u) = a((x \ y) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(6355(a,1),13087(a,1,1))].">
      <j1 rule="para" parents="6355 13087"/>
    </justification>
  </clause>

  <clause id="13090">
    <literal><![CDATA[
      a(T(x,y) / y,z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(9189(a,1),13080(a,1,1))].">
      <j1 rule="para" parents="9189 13080"/>
    </justification>
  </clause>

  <clause id="13091">
    <literal><![CDATA[
      a(K(x,y \ x),z,u) = a(K(y,y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13077(a,1,1,1))].">
      <j1 rule="para" parents="5 13077"/>
    </justification>
  </clause>

  <clause id="13092">
    <literal><![CDATA[
      a(T(x * y,y \ 1),z,u) = a(T(x * y,x),z,u)
    ]]></literal>
    <justification jstring="[para(6501(a,1),13083(a,1,1))].">
      <j1 rule="para" parents="6501 13083"/>
    </justification>
  </clause>

  <clause id="13093">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12861,a,b,13085,a)].">
      <j1 rule="hyper" parents="58 12861 13085"/>
    </justification>
  </clause>

  <clause id="13094">
    <literal><![CDATA[
      a(T(x,x \ y) * z,u,w) = a(T(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(4695(a,1),13081(a,1,1,1))].">
      <j1 rule="para" parents="4695 13081"/>
    </justification>
  </clause>

  <clause id="13095">
    <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(4097(a,1),13089(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4097 13089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13096">
    <literal><![CDATA[
      a(K(x,y \ x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,13079,a(flip),b,13091,a),flip(a)].">
      <j1 rule="hyper" parents="334 13079 13091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13097">
    <literal><![CDATA[
      a(K(x \ y,y),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5462(a,1),13096(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5462 13096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13098">
    <literal><![CDATA[
      a(K(x \ 1,y),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13086,a,b,13097,a)].">
      <j1 rule="hyper" parents="58 13086 13097"/>
    </justification>
  </clause>

  <clause id="13099">
    <literal><![CDATA[
      a(K(x,y \ 1),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(3448(a,1),13098(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3448 13098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13100">
    <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(11455(a,2),13098(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11455 13098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13101">
    <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,12280,a,b,13099,a)].">
      <j1 rule="hyper" parents="58 12280 13099"/>
    </justification>
  </clause>

  <clause id="13102">
    <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(12795(a,1),13099(a,2,1))].">
      <j1 rule="para" parents="12795 13099"/>
    </justification>
  </clause>

  <clause id="13103">
    <literal><![CDATA[
      a(T(x * y,y \ 1),z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,13078,a(flip),b,13092,a),flip(a)].">
      <j1 rule="hyper" parents="334 13078 13092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13104">
    <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,5778,a,b,13093,a)].">
      <j1 rule="hyper" parents="58 5778 13093"/>
    </justification>
  </clause>

  <clause id="13105">
    <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,12366,a,b,13102,a)].">
      <j1 rule="hyper" parents="58 12366 13102"/>
    </justification>
  </clause>

  <clause id="13106">
    <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(6171(a,1),13100(a,2,1))].">
      <j1 rule="para" parents="6171 13100"/>
    </justification>
  </clause>

  <clause id="13107">
    <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(334,a,13098,a(flip),b,13106,a),flip(a)].">
      <j1 rule="hyper" parents="334 13098 13106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13108">
    <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(11455(a,1),13107(a,1,1))].">
      <j1 rule="para" parents="11455 13107"/>
    </justification>
  </clause>

  <clause id="13109">
    <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(12795(a,1),13108(a,2,1))].">
      <j1 rule="para" parents="12795 13108"/>
    </justification>
  </clause>

  <clause id="13110">
    <literal><![CDATA[
      a(K(x,R(y,z,u)),w,v5) = R(a(K(x,y),w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(13101(a,1),13105(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13101 13105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13111">
    <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(334,a,12863,a(flip),b,13110,a),flip(a)].">
      <j1 rule="hyper" parents="334 12863 13110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13112">
    <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,13109,a(flip),b,13111,a)].">
      <j1 rule="hyper" parents="58 13109 13111"/>
    </justification>
  </clause>

  <clause id="13113">
    <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(13052(a,1),13104(a,1,2))].">
      <j1 rule="para" parents="13052 13104"/>
    </justification>
  </clause>

  <clause id="13114">
    <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(5737,a,13113,a)].">
      <j1 rule="hyper" parents="5737 13113"/>
    </justification>
  </clause>

  <clause id="13115">
    <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),12594(a,2,1,2,2,1,2))].">
      <j1 rule="para" parents="60 12594"/>
    </justification>
  </clause>

  <clause id="13116">
    <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),13115(a,2,1,2))].">
      <j1 rule="para" parents="2 13115"/>
    </justification>
  </clause>

  <clause id="13117">
    <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(13116(a,2),8329(a,1))].">
      <j1 rule="para" parents="13116 8329"/>
    </justification>
  </clause>

  <clause id="13118">
    <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,11742,a(flip),b,12810,a)].">
      <j1 rule="hyper" parents="58 11742 12810"/>
    </justification>
  </clause>

  <clause id="13119">
    <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,6038,a(flip),b,12887,a),flip(a)].">
      <j1 rule="hyper" parents="58 6038 12887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13120">
    <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(7524(a,1),13119(a,1,1,1))].">
      <j1 rule="para" parents="7524 13119"/>
    </justification>
  </clause>

  <clause id="13121">
    <literal><![CDATA[
      (K(x,x * y) \ z) \ T(x * y,x) = (K(x,y) \ z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(4149(a,1),13120(a,1,2,1))].">
      <j1 rule="para" parents="4149 13120"/>
    </justification>
  </clause>

  <clause id="13123">
    <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(5394(a,1),13118(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5394 13118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13124">
    <literal><![CDATA[
      L(x,K(y,z) * K(y,u),K(z,y) * K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(334,a,5394,a(flip),b,13123,a),flip(a)].">
      <j1 rule="hyper" parents="334 5394 13123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13127">
    <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),13058(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13128">
    <literal><![CDATA[
      R(x,y \ R(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(1382,a,13127,a)].">
      <j1 rule="hyper" parents="1382 13127"/>
    </justification>
  </clause>

  <clause id="13129">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[para(13128(a,1),4577(a,1,1))].">
      <j1 rule="para" parents="13128 4577"/>
    </justification>
  </clause>

  <clause id="13130">
    <literal><![CDATA[
      L(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,13052,a(flip),b,13129,a)].">
      <j1 rule="hyper" parents="58 13052 13129"/>
    </justification>
  </clause>

  <clause id="13131">
    <literal><![CDATA[
      R(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(7151,a,13130,a),flip(a)].">
      <j1 rule="hyper" parents="7151 13130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13132">
    <literal><![CDATA[
      1 / a(x,y,z) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(3161,a,13130,a)].">
      <j1 rule="hyper" parents="3161 13130"/>
    </justification>
  </clause>

  <clause id="13134">
    <literal><![CDATA[
      L(T(x,y),a(z,u,w),x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7762,a(flip),b,13130,a)].">
      <j1 rule="hyper" parents="58 7762 13130"/>
    </justification>
  </clause>

  <clause id="13135">
    <literal><![CDATA[
      a(x,a(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(48,a,13130,a)].">
      <j1 rule="hyper" parents="48 13130"/>
    </justification>
  </clause>

  <clause id="13136">
    <literal><![CDATA[
      T(x,x * a(y,z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(13130(a,1),735(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13130 735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13137">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = a(y,z,u) * (x / a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,13131,a(flip),b,4675,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 13131 4675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13138">
    <literal><![CDATA[
      a(x,a(y,z,u),x) \ w = w
    ]]></literal>
    <justification jstring="[hyper(289,a,13135,a(flip))].">
      <j1 rule="hyper" parents="289 13135"/>
    </justification>
  </clause>

  <clause id="13139">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ 1 = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,13135,a(flip),b,2277,a(flip))].">
      <j1 rule="hyper" parents="116 13135 2277"/>
    </justification>
  </clause>

  <clause id="13140">
    <literal><![CDATA[
      a(x,a(y,z,u),x) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      w = v5
    ]]></literal>
    <justification jstring="[para(13135(a,2),166(a,1,1))].">
      <j1 rule="para" parents="13135 166"/>
    </justification>
  </clause>

  <clause id="13141">
    <literal><![CDATA[
      x * (y \ L(y,a(z,u,w),y)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,9828,a,b,13138,a)].">
      <j1 rule="hyper" parents="58 9828 13138"/>
    </justification>
  </clause>

  <clause id="13142">
    <literal><![CDATA[
      a(x,y,z) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),13139(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 13139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13143">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,13114,a(flip),b,13141,a)].">
      <j1 rule="hyper" parents="58 13114 13141"/>
    </justification>
  </clause>

  <clause id="13144">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(9172(a,1),13140(a,1))].">
      <j1 rule="para" parents="9172 13140"/>
    </justification>
  </clause>

  <clause id="13146">
    <literal><![CDATA[
      a(K(x,K(y,z)),u * y,w) = K(x,K(z,y \ R(y,u,w)))
    ]]></literal>
    <justification jstring="[para(13143(a,1),12327(a,2,2))].">
      <j1 rule="para" parents="13143 12327"/>
    </justification>
  </clause>

  <clause id="13147">
    <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,13137,a,b,5272,a),flip(a)].">
      <j1 rule="hyper" parents="116 13137 5272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13148">
    <literal><![CDATA[
      T(a(x,y,z),x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,11956,a(flip),b,13142,a)].">
      <j1 rule="hyper" parents="334 11956 13142"/>
    </justification>
  </clause>

  <clause id="13149">
    <literal><![CDATA[
      a(x,y,z) * x = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,13148,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 13148 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13150">
    <literal><![CDATA[
      T(a(1 / x,y,z),x \ 1) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(4354(a,2),13148(a,1,1))].">
      <j1 rule="para" parents="4354 13148"/>
    </justification>
  </clause>

  <clause id="13151">
    <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,10189,a(flip),b,13149,a),flip(a)].">
      <j1 rule="hyper" parents="58 10189 13149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13152">
    <literal><![CDATA[
      a((x / y) \ 1,z,(x / y) \ 1) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,12354,a(flip),b,13150,a),flip(a)].">
      <j1 rule="hyper" parents="58 12354 13150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13153">
    <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,12812,a(flip),b,13146,a),flip(a)].">
      <j1 rule="hyper" parents="58 12812 13146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13154">
    <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,8661,a,b,13153,a)].">
      <j1 rule="hyper" parents="58 8661 13153"/>
    </justification>
  </clause>

  <clause id="13155">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11762,a,b,13152,a)].">
      <j1 rule="hyper" parents="58 11762 13152"/>
    </justification>
  </clause>

  <clause id="13156">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(8053(a,2),13154(a,2,1))].">
      <j1 rule="para" parents="8053 13154"/>
    </justification>
  </clause>

  <clause id="13157">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) \ z)) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(9597,a,13156,a)].">
      <j1 rule="hyper" parents="9597 13156"/>
    </justification>
  </clause>

  <clause id="13158">
    <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,10150,a(flip),b,13157,a)].">
      <j1 rule="hyper" parents="58 10150 13157"/>
    </justification>
  </clause>

  <clause id="13159">
    <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(13147(a,2),5110(a,1))].">
      <j1 rule="para" parents="13147 5110"/>
    </justification>
  </clause>

  <clause id="13160">
    <literal><![CDATA[
      K(x,y * (1 / (z * K(x,u)))) = K(x,y * (K(u,x) / z))
    ]]></literal>
    <justification jstring="[para(13151(a,1),9906(a,1,2,2))].">
      <j1 rule="para" parents="13151 9906"/>
    </justification>
  </clause>

  <clause id="13161">
    <literal><![CDATA[
      K(x,y * ((z * K(x,u)) \ 1)) = K(x,y * (K(u,x) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5577,a(flip),b,13160,a)].">
      <j1 rule="hyper" parents="58 5577 13160"/>
    </justification>
  </clause>

  <clause id="13162">
    <literal><![CDATA[
      K(x,y * ((K(x,z) * u) \ 1)) = K(x,y * (K(z,x) / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9889,a,b,13161,a)].">
      <j1 rule="hyper" parents="58 9889 13161"/>
    </justification>
  </clause>

  <clause id="13163">
    <literal><![CDATA[
      K(x,y * ((K(x,z) * u) \ 1)) = K(x,y * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(334,a,11694,a(flip),b,13162,a),flip(a)].">
      <j1 rule="hyper" parents="334 11694 13162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13165">
    <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,10567,a,b,13163,a)].">
      <j1 rule="hyper" parents="58 10567 13163"/>
    </justification>
  </clause>

  <clause id="13166">
    <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(8067(a,1),13158(a,2,1))].">
      <j1 rule="para" parents="8067 13158"/>
    </justification>
  </clause>

  <clause id="13167">
    <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(11399(a,1),13166(a,2,1,2))].">
      <j1 rule="para" parents="11399 13166"/>
    </justification>
  </clause>

  <clause id="13168">
    <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(10165,a,13167,a)].">
      <j1 rule="hyper" parents="10165 13167"/>
    </justification>
  </clause>

  <clause id="13171">
    <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,10931,a(flip),b,13168,a)].">
      <j1 rule="hyper" parents="58 10931 13168"/>
    </justification>
  </clause>

  <clause id="13174">
    <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(269(a,1),13165(a,2,2))].">
      <j1 rule="para" parents="269 13165"/>
    </justification>
  </clause>

  <clause id="13175">
    <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(334,a,9729,a(flip),b,13174,a),flip(a)].">
      <j1 rule="hyper" parents="334 9729 13174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13177">
    <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,9271,a(flip),b,13175,a)].">
      <j1 rule="hyper" parents="58 9271 13175"/>
    </justification>
  </clause>

  <clause id="13178">
    <literal><![CDATA[
      K(x,R(y,z,(K(x,u) * z) \ 1)) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(334,a,12637,a(flip),b,13177,a),flip(a)].">
      <j1 rule="hyper" parents="334 12637 13177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13180">
    <literal><![CDATA[
      R(K(x,y),z,(K(x,u) * z) \ 1) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(12792,a,13178,a)].">
      <j1 rule="hyper" parents="12792 13178"/>
    </justification>
  </clause>

  <clause id="13181">
    <literal><![CDATA[
      x / (K(y,L(z,u,u \ 1)) * x) = u * ((K(y,z) * u) \ 1)
    ]]></literal>
    <justification jstring="[para(13180(a,1),6265(a,1,2,1))].">
      <j1 rule="para" parents="13180 6265"/>
    </justification>
  </clause>

  <clause id="13182">
    <literal><![CDATA[
      x * ((K(y,z) * x) \ 1) = K(L(z,x,x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(5412,a,13181,a),flip(a)].">
      <j1 rule="hyper" parents="5412 13181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13184">
    <literal><![CDATA[
      x * ((K(y,z) * x) \ 1) = K(z,L(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(334,a,11137,a(flip),b,13182,a),flip(a)].">
      <j1 rule="hyper" parents="334 11137 13182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13185">
    <literal><![CDATA[
      x \ K(y,L(z,x,x \ 1)) = (K(z,y) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,11137,a(flip),b,13182,a)].">
      <j1 rule="hyper" parents="116 11137 13182"/>
    </justification>
  </clause>

  <clause id="13186">
    <literal><![CDATA[
      K(x,((K(y,x) * (z \ 1)) \ 1) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(13185(a,1),9572(a,1,2,1))].">
      <j1 rule="para" parents="13185 9572"/>
    </justification>
  </clause>

  <clause id="13187">
    <literal><![CDATA[
      K(x,(((y \ 1) * K(z,x)) \ 1) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(7538(a,1),13186(a,1,2,1,1))].">
      <j1 rule="para" parents="7538 13186"/>
    </justification>
  </clause>

  <clause id="13188">
    <literal><![CDATA[
      K(x,((y * K(z,x)) \ 1) \ u) = K(x,(y \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5841,a(flip),b,13187,a)].">
      <j1 rule="hyper" parents="58 5841 13187"/>
    </justification>
  </clause>

  <clause id="13189">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ u) = K(x,((y / z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1542(a,1),13188(a,1,2,1,1))].">
      <j1 rule="para" parents="1542 13188"/>
    </justification>
  </clause>

  <clause id="13190">
    <literal><![CDATA[
      (T(x,y) / z) \ x = z * K(y,((x / z) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,13189,a(flip),b,8865,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 13189 8865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13191">
    <literal><![CDATA[
      (T(x,y) / z) \ x = (1 / z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,11914,a(flip),b,13190,a),flip(a)].">
      <j1 rule="hyper" parents="334 11914 13190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13192">
    <literal><![CDATA[
      (1 / (x \ T(y,z))) \ K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[para(72(a,1),13191(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 13191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13194">
    <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(13192(a,2),7514(a,2,2)),flip(a)].">
      <j1 rule="para" parents="13192 7514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13195">
    <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(4837(a,1),13095(a,2,1))].">
      <j1 rule="para" parents="4837 13095"/>
    </justification>
  </clause>

  <clause id="13196">
    <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,13084,a(flip),b,13195,a)].">
      <j1 rule="hyper" parents="58 13084 13195"/>
    </justification>
  </clause>

  <clause id="13197">
    <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(10807,a,12986,a)].">
      <j1 rule="hyper" parents="10807 12986"/>
    </justification>
  </clause>

  <clause id="13198">
    <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(334,a,7514,a(flip),b,13194,a),flip(a)].">
      <j1 rule="hyper" parents="334 7514 13194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13199">
    <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),13198(a,1,2,1,2,2))].">
      <j1 rule="para" parents="20 13198"/>
    </justification>
  </clause>

  <clause id="13200">
    <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),13199(a,1,2,1,2,2,1))].">
      <j1 rule="para" parents="20 13199"/>
    </justification>
  </clause>

  <clause id="13201">
    <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,10885,a(flip),b,13200,a)].">
      <j1 rule="hyper" parents="58 10885 13200"/>
    </justification>
  </clause>

  <clause id="13203">
    <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),13201(a,1,2))].">
      <j1 rule="para" parents="75 13201"/>
    </justification>
  </clause>

  <clause id="13204">
    <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,12110,a,b,13203,a)].">
      <j1 rule="hyper" parents="58 12110 13203"/>
    </justification>
  </clause>

  <clause id="13206">
    <literal><![CDATA[
      K(x,y \ L(L(x,z,x),u,w)) = K(x,y \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(11975,a,13204,a),flip(a)].">
      <j1 rule="hyper" parents="11975 13204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13208">
    <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(13206(a,1),11727(a,1,1))].">
      <j1 rule="para" parents="13206 11727"/>
    </justification>
  </clause>

  <clause id="13209">
    <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(11068(a,1),13208(a,1,1))].">
      <j1 rule="para" parents="11068 13208"/>
    </justification>
  </clause>

  <clause id="13211">
    <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),13209(a,1,1,2))].">
      <j1 rule="para" parents="60 13209"/>
    </justification>
  </clause>

  <clause id="13212">
    <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(5043(a,1),13211(a,1,2))].">
      <j1 rule="para" parents="5043 13211"/>
    </justification>
  </clause>

  <clause id="13213">
    <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(12419,a,13212,a)].">
      <j1 rule="hyper" parents="12419 13212"/>
    </justification>
  </clause>

  <clause id="13214">
    <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(2065(a,1),13213(a,1,2))].">
      <j1 rule="para" parents="2065 13213"/>
    </justification>
  </clause>

  <clause id="13215">
    <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(10237(a,1),13214(a,1,2))].">
      <j1 rule="para" parents="10237 13214"/>
    </justification>
  </clause>

  <clause id="13216">
    <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,13215,a)].">
      <j1 rule="hyper" parents="123 13215"/>
    </justification>
  </clause>

  <clause id="13217">
    <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(13216(a,1),12463(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13216 12463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13218">
    <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,13217,a,b,13139,a(flip))].">
      <j1 rule="hyper" parents="114 13217 13139"/>
    </justification>
  </clause>

  <clause id="13219">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z)) = a(x,u,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,10746,a(flip),b,13218,a),flip(a)].">
      <j1 rule="hyper" parents="334 10746 13218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13221">
    <literal><![CDATA[
      L(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,10763,a(flip),b,13219,a)].">
      <j1 rule="hyper" parents="58 10763 13219"/>
    </justification>
  </clause>

  <clause id="13224">
    <literal><![CDATA[
      a(x,L(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,13070,a(flip),b,13221,a)].">
      <j1 rule="hyper" parents="58 13070 13221"/>
    </justification>
  </clause>

  <clause id="13225">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,z)) = y * a(z,u,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,13221,a(flip),b,4918,a),flip(a)].">
      <j1 rule="hyper" parents="119 13221 4918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13226">
    <literal><![CDATA[
      (x * y) * a(z,u,z) = x * (y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,13221,a(flip),b,4915,a)].">
      <j1 rule="hyper" parents="119 13221 4915"/>
    </justification>
  </clause>

  <clause id="13228">
    <literal><![CDATA[
      x \ (y * a(z,u,z)) = (x \ y) * a(z,u,z)
    ]]></literal>
    <justification jstring="[para(13221(a,1),487(a,1,2,2))].">
      <j1 rule="para" parents="13221 487"/>
    </justification>
  </clause>

  <clause id="13231">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = x * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,13224,a(flip),b,9155,a),flip(a)].">
      <j1 rule="hyper" parents="119 13224 9155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13232">
    <literal><![CDATA[
      a(x,(y * z) \ u,x) = a(x,z \ (y \ u),x)
    ]]></literal>
    <justification jstring="[para(311(a,1),13224(a,1,2))].">
      <j1 rule="para" parents="311 13224"/>
    </justification>
  </clause>

  <clause id="13233">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = a(x,y,x) \ x
    ]]></literal>
    <justification jstring="[para(13224(a,1),9360(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13224 9360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13234">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,9162,a(flip),b,13231,a),flip(a)].">
      <j1 rule="hyper" parents="334 9162 13231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13235">
    <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(13234(a,1),12449(a,1,2,1))].">
      <j1 rule="para" parents="13234 12449"/>
    </justification>
  </clause>

  <clause id="13236">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,9360,a(flip),b,13233,a),flip(a)].">
      <j1 rule="hyper" parents="334 9360 13233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13237">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,x) = L(x,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(1988(a,2),13236(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1988 13236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13238">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,z)) = a(z,u,z) * y
    ]]></literal>
    <justification jstring="[hyper(334,a,9793,a,b,13225,a),flip(a)].">
      <j1 rule="hyper" parents="334 9793 13225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13239">
    <literal><![CDATA[
      x \ (a(y,z,y) * u) = (x \ u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,9793,a,b,13225,a)].">
      <j1 rule="hyper" parents="116 9793 13225"/>
    </justification>
  </clause>

  <clause id="13240">
    <literal><![CDATA[
      (x \ K(y,z)) * a(y,y \ z,y) = x \ K(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,9186,a(flip),b,13225,a),flip(a)].">
      <j1 rule="hyper" parents="116 9186 13225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13241">
    <literal><![CDATA[
      (x \ y) * a(y,z,y) = x \ R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,9162,a(flip),b,13225,a),flip(a)].">
      <j1 rule="hyper" parents="116 9162 13225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13242">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (u * a(x,y,x))
    ]]></literal>
    <justification jstring="[hyper(9826,a,13226,a)].">
      <j1 rule="hyper" parents="9826 13226"/>
    </justification>
  </clause>

  <clause id="13243">
    <literal><![CDATA[
      R(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4339,a,13226,a)].">
      <j1 rule="hyper" parents="4339 13226"/>
    </justification>
  </clause>

  <clause id="13244">
    <literal><![CDATA[
      x \ (y * (z * a(u,w,u))) = (x \ (y * z)) * a(u,w,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,13226,a(flip),b,13225,a)].">
      <j1 rule="hyper" parents="116 13226 13225"/>
    </justification>
  </clause>

  <clause id="13245">
    <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(13226(a,1),522(a,1,1))].">
      <j1 rule="para" parents="13226 522"/>
    </justification>
  </clause>

  <clause id="13246">
    <literal><![CDATA[
      (x * y) * a(z,u,z) = x * (a(z,u,z) * y)
    ]]></literal>
    <justification jstring="[para(9793(a,2),13226(a,2,2))].">
      <j1 rule="para" parents="9793 13226"/>
    </justification>
  </clause>

  <clause id="13247">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) \ w = (x * y) \ (a(z,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(13226(a,1),12721(a,1,1))].">
      <j1 rule="para" parents="13226 12721"/>
    </justification>
  </clause>

  <clause id="13248">
    <literal><![CDATA[
      a(x * (y * a(z,u,z)),w,v5) = a(x * y,w,v5)
    ]]></literal>
    <justification jstring="[para(13226(a,1),13080(a,1,1))].">
      <j1 rule="para" parents="13226 13080"/>
    </justification>
  </clause>

  <clause id="13249">
    <literal><![CDATA[
      L(T(x,y),y,a(z,u,z)) = T(x,y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(10337,a,13243,a)].">
      <j1 rule="hyper" parents="10337 13243"/>
    </justification>
  </clause>

  <clause id="13250">
    <literal><![CDATA[
      R(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(13243(a,1),46(a,2))].">
      <j1 rule="para" parents="13243 46"/>
    </justification>
  </clause>

  <clause id="13252">
    <literal><![CDATA[
      x \ (y * a(z,u,z)) = a(z,u,z) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,9793,a,b,13228,a),flip(a)].">
      <j1 rule="hyper" parents="334 9793 13228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13253">
    <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,13197,a(flip),b,13232,a),flip(a)].">
      <j1 rule="hyper" parents="58 13197 13232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13254">
    <literal><![CDATA[
      (x \ (y * x)) * a(z,u,z) = T(y * a(z,u,z),x)
    ]]></literal>
    <justification jstring="[hyper(246,a,12720,a,b,13238,a),flip(a)].">
      <j1 rule="hyper" parents="246 12720 13238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13256">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ u = (z \ u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(12704,a,13239,a)].">
      <j1 rule="hyper" parents="12704 13239"/>
    </justification>
  </clause>

  <clause id="13257">
    <literal><![CDATA[
      a(x,y,x) \ (z \ (a(x,y,x) * u)) = z \ u
    ]]></literal>
    <justification jstring="[hyper(116,a,13239,a,b,9793,a)].">
      <j1 rule="hyper" parents="116 13239 9793"/>
    </justification>
  </clause>

  <clause id="13258">
    <literal><![CDATA[
      (x * y) / (y * a(z,u,z)) = a(z,u,z) \ x
    ]]></literal>
    <justification jstring="[hyper(12718,a,13242,a)].">
      <j1 rule="hyper" parents="12718 13242"/>
    </justification>
  </clause>

  <clause id="13259">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (a(x,y,x) * u)
    ]]></literal>
    <justification jstring="[para(9793(a,2),13242(a,2,2))].">
      <j1 rule="para" parents="9793 13242"/>
    </justification>
  </clause>

  <clause id="13260">
    <literal><![CDATA[
      a(x,y,x) * (z * (a(x,y,x) \ u)) = z * u
    ]]></literal>
    <justification jstring="[para(9804(a,1),13242(a,2,2))].">
      <j1 rule="para" parents="9804 13242"/>
    </justification>
  </clause>

  <clause id="13261">
    <literal><![CDATA[
      a(x,y,x) * (z \ (a(x,y,x) \ u)) = z \ u
    ]]></literal>
    <justification jstring="[para(9804(a,1),13252(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9804 13252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13262">
    <literal><![CDATA[
      ((a(x,y,x) * z) \ u) * a(x,y,x) = z \ u
    ]]></literal>
    <justification jstring="[para(4(a,1),13256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 13256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13263">
    <literal><![CDATA[
      a(x,y,x) \ (z \ u) = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13257(a,1,2,2))].">
      <j1 rule="para" parents="5 13257"/>
    </justification>
  </clause>

  <clause id="13264">
    <literal><![CDATA[
      a(x,y,x) \ (z \ (x * u)) = z \ (L(x,y,x) * u)
    ]]></literal>
    <justification jstring="[para(9843(a,1),13257(a,1,2,2))].">
      <j1 rule="para" parents="9843 13257"/>
    </justification>
  </clause>

  <clause id="13265">
    <literal><![CDATA[
      x / (y * a(z,u,z)) = a(z,u,z) \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(589,a,13258,a)].">
      <j1 rule="hyper" parents="589 13258"/>
    </justification>
  </clause>

  <clause id="13266">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = x * (a(y,z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(12756,a,13259,a)].">
      <j1 rule="hyper" parents="12756 13259"/>
    </justification>
  </clause>

  <clause id="13267">
    <literal><![CDATA[
      a(x,y,x) \ (z * u) = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,13259,a)].">
      <j1 rule="hyper" parents="116 151 13259"/>
    </justification>
  </clause>

  <clause id="13269">
    <literal><![CDATA[
      (a(x,y,x) \ z) * u = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(12716,a,13260,a),flip(a)].">
      <j1 rule="hyper" parents="12716 13260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13270">
    <literal><![CDATA[
      a(x,y,x) * (z \ L(x,y,x)) = z \ x
    ]]></literal>
    <justification jstring="[para(9360(a,1),13261(a,1,2,2))].">
      <j1 rule="para" parents="9360 13261"/>
    </justification>
  </clause>

  <clause id="13271">
    <literal><![CDATA[
      a(x,y,x) \ (z \ x) = z \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,13270,a)].">
      <j1 rule="hyper" parents="123 13270"/>
    </justification>
  </clause>

  <clause id="13272">
    <literal><![CDATA[
      a(x \ L(y,z,y),u,w) = a(x \ y,u,w)
    ]]></literal>
    <justification jstring="[para(13270(a,1),13073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13270 13073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13273">
    <literal><![CDATA[
      (x \ (a(y,z,y) \ u)) * a(y,z,y) != w
    ]]></literal>
    <literal><![CDATA[
      x \ u = w
    ]]></literal>
    <justification jstring="[para(13263(a,1),9819(a,1,1))].">
      <j1 rule="para" parents="13263 9819"/>
    </justification>
  </clause>

  <clause id="13274">
    <literal><![CDATA[
      L(x,y,z / (u * a(w,v5,w))) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(13265(a,2),12868(a,1,3))].">
      <j1 rule="para" parents="13265 12868"/>
    </justification>
  </clause>

  <clause id="13277">
    <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(13266(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13266 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13278">
    <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(13266(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13266 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13279">
    <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,11366,a(flip),b,13267,a)].">
      <j1 rule="hyper" parents="58 11366 13267"/>
    </justification>
  </clause>

  <clause id="13280">
    <literal><![CDATA[
      a(x * K(y * z,y),u,w) = a(x * K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(9182(a,1),13248(a,1,1,2))].">
      <j1 rule="para" parents="9182 13248"/>
    </justification>
  </clause>

  <clause id="13281">
    <literal><![CDATA[
      a(x * K(y,y \ z),u,w) = a(x * K(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(9186(a,1),13248(a,1,1,2))].">
      <j1 rule="para" parents="9186 13248"/>
    </justification>
  </clause>

  <clause id="13282">
    <literal><![CDATA[
      T(x,y * a(z,u,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(12702,a,13249,a),flip(a)].">
      <j1 rule="hyper" parents="12702 13249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13284">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,13282,a(flip),b,5020,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 13282 5020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13285">
    <literal><![CDATA[
      K(x * a(y,z,y),u) = u / T(u,x)
    ]]></literal>
    <justification jstring="[para(13282(a,1),5062(a,2,2))].">
      <j1 rule="para" parents="13282 5062"/>
    </justification>
  </clause>

  <clause id="13286">
    <literal><![CDATA[
      T(x,y * L(z,u,z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(9367(a,1),13282(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9367 13282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13287">
    <literal><![CDATA[
      T(x,y * R(z,u,z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(9410(a,1),13282(a,1,2))].">
      <j1 rule="para" parents="9410 13282"/>
    </justification>
  </clause>

  <clause id="13288">
    <literal><![CDATA[
      T(x,R(y,z,y) * u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(9420(a,1),13282(a,1,2))].">
      <j1 rule="para" parents="9420 13282"/>
    </justification>
  </clause>

  <clause id="13289">
    <literal><![CDATA[
      T(x,y / R(z,u,z)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(9423(a,1),13282(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9423 13282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13290">
    <literal><![CDATA[
      T(x,a(y,z,y) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(9793(a,2),13282(a,1,2))].">
      <j1 rule="para" parents="9793 13282"/>
    </justification>
  </clause>

  <clause id="13291">
    <literal><![CDATA[
      T(x,a(y,z,y) \ u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(9804(a,1),13282(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9804 13282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13292">
    <literal><![CDATA[
      T(x,R(y,z,y) / u) = T(x,y / u)
    ]]></literal>
    <justification jstring="[para(12726(a,1),13282(a,1,2))].">
      <j1 rule="para" parents="12726 13282"/>
    </justification>
  </clause>

  <clause id="13293">
    <literal><![CDATA[
      T(x,y \ R(z,u,z)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(13241(a,1),13282(a,1,2))].">
      <j1 rule="para" parents="13241 13282"/>
    </justification>
  </clause>

  <clause id="13294">
    <literal><![CDATA[
      T(x,y * (a(z,u,z) * w)) = T(x,y * w)
    ]]></literal>
    <justification jstring="[para(13246(a,1),13282(a,1,2))].">
      <j1 rule="para" parents="13246 13282"/>
    </justification>
  </clause>

  <clause id="13296">
    <literal><![CDATA[
      T(x,T(y * z,y) \ u) = T(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(11524(a,1),13290(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11524 13290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13297">
    <literal><![CDATA[
      T(x,(a(y,z,y) \ u) * w) = T(x,u * w)
    ]]></literal>
    <justification jstring="[para(12698(a,1),13290(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12698 13290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13298">
    <literal><![CDATA[
      T(x,(R(y,z,y) \ y) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(10291(a,2),13291(a,1,2))].">
      <j1 rule="para" parents="10291 13291"/>
    </justification>
  </clause>

  <clause id="13299">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,4995,a,b,13284,a),flip(a)].">
      <j1 rule="hyper" parents="334 4995 13284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13300">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(13284(a,2),5110(a,1))].">
      <j1 rule="para" parents="13284 5110"/>
    </justification>
  </clause>

  <clause id="13301">
    <literal><![CDATA[
      K(x,T(y,z) / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(9189(a,1),13299(a,1,2))].">
      <j1 rule="para" parents="9189 13299"/>
    </justification>
  </clause>

  <clause id="13302">
    <literal><![CDATA[
      K(x,y / L(z,u,z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(9356(a,1),13299(a,1,2))].">
      <j1 rule="para" parents="9356 13299"/>
    </justification>
  </clause>

  <clause id="13303">
    <literal><![CDATA[
      K(x,y * L(z,u,z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(9367(a,1),13299(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9367 13299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13304">
    <literal><![CDATA[
      K(x,L(y,z,y) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(9376(a,1),13299(a,1,2))].">
      <j1 rule="para" parents="9376 13299"/>
    </justification>
  </clause>

  <clause id="13305">
    <literal><![CDATA[
      K(x,y * R(z,u,z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(9410(a,1),13299(a,1,2))].">
      <j1 rule="para" parents="9410 13299"/>
    </justification>
  </clause>

  <clause id="13306">
    <literal><![CDATA[
      K(x,R(y,z,y) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(9420(a,1),13299(a,1,2))].">
      <j1 rule="para" parents="9420 13299"/>
    </justification>
  </clause>

  <clause id="13307">
    <literal><![CDATA[
      K(x,a(y,z,y) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(9793(a,2),13299(a,1,2))].">
      <j1 rule="para" parents="9793 13299"/>
    </justification>
  </clause>

  <clause id="13308">
    <literal><![CDATA[
      K(x,a(y,z,y) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(9804(a,1),13299(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9804 13299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13309">
    <literal><![CDATA[
      K(x,R(y,z,y) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(12726(a,1),13299(a,1,2))].">
      <j1 rule="para" parents="12726 13299"/>
    </justification>
  </clause>

  <clause id="13310">
    <literal><![CDATA[
      K(x,(a(y,z,y) * u) / w) = K(x,u / w)
    ]]></literal>
    <justification jstring="[para(12724(a,2),13299(a,1,2))].">
      <j1 rule="para" parents="12724 13299"/>
    </justification>
  </clause>

  <clause id="13311">
    <literal><![CDATA[
      K(x,y \ R(z,u,z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(13241(a,1),13299(a,1,2))].">
      <j1 rule="para" parents="13241 13299"/>
    </justification>
  </clause>

  <clause id="13312">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(13226(a,1),13299(a,1,2))].">
      <j1 rule="para" parents="13226 13299"/>
    </justification>
  </clause>

  <clause id="13313">
    <literal><![CDATA[
      K(x,y \ (a(z,u,z) * w)) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(13239(a,2),13299(a,1,2))].">
      <j1 rule="para" parents="13239 13299"/>
    </justification>
  </clause>

  <clause id="13314">
    <literal><![CDATA[
      K(x,y * (a(z,u,z) * w)) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(13246(a,1),13299(a,1,2))].">
      <j1 rule="para" parents="13246 13299"/>
    </justification>
  </clause>

  <clause id="13315">
    <literal><![CDATA[
      K(x,(a(y,z,y) * u) \ w) = K(x,u \ w)
    ]]></literal>
    <justification jstring="[para(13262(a,1),13299(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13262 13299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13316">
    <literal><![CDATA[
      K(x,L(y,z,y) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(9843(a,1),13307(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9843 13307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13317">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(10106(a,1),13307(a,1,2))].">
      <j1 rule="para" parents="10106 13307"/>
    </justification>
  </clause>

  <clause id="13318">
    <literal><![CDATA[
      K(x,T(y * z,y) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(11524(a,1),13307(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11524 13307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13319">
    <literal><![CDATA[
      K(x,(a(y,z,y) \ u) * w) = K(x,u * w)
    ]]></literal>
    <justification jstring="[para(12698(a,1),13307(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12698 13307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13320">
    <literal><![CDATA[
      K(x,y * (a(z,u,z) \ w)) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(13260(a,1),13307(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13260 13307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13321">
    <literal><![CDATA[
      K(x,y \ (a(z,u,z) \ w)) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(13261(a,1),13307(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13261 13307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13322">
    <literal><![CDATA[
      K(x,(y \ R(y,z,y)) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(9153(a,1),13308(a,1,2,1))].">
      <j1 rule="para" parents="9153 13308"/>
    </justification>
  </clause>

  <clause id="13323">
    <literal><![CDATA[
      K(x,L(y,z,y) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(12728(a,1),13308(a,1,2))].">
      <j1 rule="para" parents="12728 13308"/>
    </justification>
  </clause>

  <clause id="13324">
    <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),13301(a,1,2,1))].">
      <j1 rule="para" parents="20 13301"/>
    </justification>
  </clause>

  <clause id="13325">
    <literal><![CDATA[
      K(x,y / T(z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4488(a,1),13301(a,1,2))].">
      <j1 rule="para" parents="4488 13301"/>
    </justification>
  </clause>

  <clause id="13326">
    <literal><![CDATA[
      K(x,y / T(z,y)) = K(x,T(y / z,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,7314,a,b,13325,a),flip(a)].">
      <j1 rule="hyper" parents="334 7314 13325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13327">
    <literal><![CDATA[
      K(x * a(y,z,y),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,5062,a,b,13285,a),flip(a)].">
      <j1 rule="hyper" parents="334 5062 13285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13328">
    <literal><![CDATA[
      K(x * a(y,z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(13285(a,2),5133(a,1))].">
      <j1 rule="para" parents="13285 5133"/>
    </justification>
  </clause>

  <clause id="13333">
    <literal><![CDATA[
      K(a(x,y,x) * z,u) = K(z,u)
    ]]></literal>
    <justification jstring="[para(9793(a,2),13327(a,1,1))].">
      <j1 rule="para" parents="9793 13327"/>
    </justification>
  </clause>

  <clause id="13334">
    <literal><![CDATA[
      K((x * a(y,z,y)) / u,w) = K(x / u,w)
    ]]></literal>
    <justification jstring="[para(12729(a,2),13327(a,1,1))].">
      <j1 rule="para" parents="12729 13327"/>
    </justification>
  </clause>

  <clause id="13335">
    <literal><![CDATA[
      K(x * (y * a(z,u,z)),w) = K(x * y,w)
    ]]></literal>
    <justification jstring="[para(13226(a,1),13327(a,1,1))].">
      <j1 rule="para" parents="13226 13327"/>
    </justification>
  </clause>

  <clause id="13336">
    <literal><![CDATA[
      K(x \ (a(y,z,y) * u),w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[para(13239(a,2),13327(a,1,1))].">
      <j1 rule="para" parents="13239 13327"/>
    </justification>
  </clause>

  <clause id="13337">
    <literal><![CDATA[
      K((a(x,y,x) \ z) \ u,w) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[para(13256(a,2),13327(a,1,1))].">
      <j1 rule="para" parents="13256 13327"/>
    </justification>
  </clause>

  <clause id="13338">
    <literal><![CDATA[
      K(L(x,y,x) * z,u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(9843(a,1),13333(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9843 13333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13339">
    <literal><![CDATA[
      K(T(x * y,x) \ z,u) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(11524(a,1),13333(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11524 13333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13340">
    <literal><![CDATA[
      K((a(x,y,x) \ z) * u,w) = K(z * u,w)
    ]]></literal>
    <justification jstring="[para(12698(a,1),13333(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12698 13333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13341">
    <literal><![CDATA[
      K(x \ (a(y,z,y) \ u),w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[para(13261(a,1),13333(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13261 13333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13342">
    <literal><![CDATA[
      K(x \ L(y,z,y),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(13270(a,1),13333(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13270 13333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13343">
    <literal><![CDATA[
      T(x,y * ((z \ u) \ u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(12088(a,1),13286(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12088 13286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13344">
    <literal><![CDATA[
      T(x,y * T(z,z * u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4629(a,1),13287(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4629 13287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13345">
    <literal><![CDATA[
      T(x,((y \ z) \ z) * u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(7790(a,1),13288(a,1,2,1))].">
      <j1 rule="para" parents="7790 13288"/>
    </justification>
  </clause>

  <clause id="13346">
    <literal><![CDATA[
      T(x,y / T(z,z \ u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(4695(a,1),13289(a,1,2,2))].">
      <j1 rule="para" parents="4695 13289"/>
    </justification>
  </clause>

  <clause id="13347">
    <literal><![CDATA[
      T(x,y / ((z \ u) \ u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(7790(a,1),13289(a,1,2,2))].">
      <j1 rule="para" parents="7790 13289"/>
    </justification>
  </clause>

  <clause id="13348">
    <literal><![CDATA[
      T(x,((y \ z) \ z) / u) = T(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(7790(a,1),13292(a,1,2,1))].">
      <j1 rule="para" parents="7790 13292"/>
    </justification>
  </clause>

  <clause id="13349">
    <literal><![CDATA[
      T(x,y \ T(z,z * u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(4629(a,1),13293(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4629 13293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13350">
    <literal><![CDATA[
      T(x,y \ T(z,z \ u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(4695(a,1),13293(a,1,2,2))].">
      <j1 rule="para" parents="4695 13293"/>
    </justification>
  </clause>

  <clause id="13351">
    <literal><![CDATA[
      T(x,y \ ((z \ u) \ u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(7790(a,1),13293(a,1,2,2))].">
      <j1 rule="para" parents="7790 13293"/>
    </justification>
  </clause>

  <clause id="13352">
    <literal><![CDATA[
      T(x,K(y * z,y) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(10293(a,1),13298(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10293 13298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13353">
    <literal><![CDATA[
      K(x,y / T(z / u,z)) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[para(4648(a,1),13302(a,1,2,2))].">
      <j1 rule="para" parents="4648 13302"/>
    </justification>
  </clause>

  <clause id="13354">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(12088(a,1),13303(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12088 13303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13355">
    <literal><![CDATA[
      K(x,T(y / z,y) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4648(a,1),13304(a,1,2,1))].">
      <j1 rule="para" parents="4648 13304"/>
    </justification>
  </clause>

  <clause id="13356">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,((y \ z) \ z) \ u)
    ]]></literal>
    <justification jstring="[para(6355(a,1),13304(a,1,2,1))].">
      <j1 rule="para" parents="6355 13304"/>
    </justification>
  </clause>

  <clause id="13357">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(12088(a,1),13304(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12088 13304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13358">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4629(a,1),13305(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4629 13305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13360">
    <literal><![CDATA[
      K(x,T(y,y * z) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(4629(a,1),13306(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4629 13306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13361">
    <literal><![CDATA[
      K(x,((y \ z) \ z) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(7790(a,1),13309(a,1,2,1))].">
      <j1 rule="para" parents="7790 13309"/>
    </justification>
  </clause>

  <clause id="13362">
    <literal><![CDATA[
      K(x,y \ T(z,z \ u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(4695(a,1),13311(a,1,2,2))].">
      <j1 rule="para" parents="4695 13311"/>
    </justification>
  </clause>

  <clause id="13363">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(7790(a,1),13311(a,1,2,2))].">
      <j1 rule="para" parents="7790 13311"/>
    </justification>
  </clause>

  <clause id="13364">
    <literal><![CDATA[
      K(x,T(y / z,y) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(4648(a,1),13316(a,1,2,1))].">
      <j1 rule="para" parents="4648 13316"/>
    </justification>
  </clause>

  <clause id="13365">
    <literal><![CDATA[
      K(x,K(y * z,y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(9854(a,1),13322(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9854 13322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13366">
    <literal><![CDATA[
      K(x,T(y / z,y) / u) = K(x,(z \ y) / u)
    ]]></literal>
    <justification jstring="[para(4648(a,1),13323(a,1,2,1))].">
      <j1 rule="para" parents="4648 13323"/>
    </justification>
  </clause>

  <clause id="13367">
    <literal><![CDATA[
      K(x \ T(y / z,y),u) = K(x \ (z \ y),u)
    ]]></literal>
    <justification jstring="[para(4648(a,1),13342(a,1,1,2))].">
      <j1 rule="para" parents="4648 13342"/>
    </justification>
  </clause>

  <clause id="13368">
    <literal><![CDATA[
      K(x,T(y,z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(9189(a,1),13300(a,1,2))].">
      <j1 rule="para" parents="9189 13300"/>
    </justification>
  </clause>

  <clause id="13369">
    <literal><![CDATA[
      K(x,R(y,z,y) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / u) = w
    ]]></literal>
    <justification jstring="[para(12726(a,1),13300(a,1,2))].">
      <j1 rule="para" parents="12726 13300"/>
    </justification>
  </clause>

  <clause id="13370">
    <literal><![CDATA[
      K(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(13326(a,2),7438(a,1))].">
      <j1 rule="para" parents="13326 7438"/>
    </justification>
  </clause>

  <clause id="13371">
    <literal><![CDATA[
      T(x,y * T(z * u,z)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(9185(a,1),13294(a,1,2,2))].">
      <j1 rule="para" parents="9185 13294"/>
    </justification>
  </clause>

  <clause id="13372">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(9151(a,1),13297(a,1,2,1))].">
      <j1 rule="para" parents="9151 13297"/>
    </justification>
  </clause>

  <clause id="13373">
    <literal><![CDATA[
      K(x,T(y * z,y) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[para(9185(a,1),13310(a,1,2,1))].">
      <j1 rule="para" parents="9185 13310"/>
    </justification>
  </clause>

  <clause id="13374">
    <literal><![CDATA[
      K(x,(y * R(z,u,z)) / w) = K(x,(y * z) / w)
    ]]></literal>
    <justification jstring="[para(9800(a,1),13310(a,1,2,1))].">
      <j1 rule="para" parents="9800 13310"/>
    </justification>
  </clause>

  <clause id="13375">
    <literal><![CDATA[
      K(x,y * K(z,z * u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(9170(a,1),13312(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9170 13312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13376">
    <literal><![CDATA[
      K(x,y * T(z * u,z)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(9184(a,1),13312(a,1,2,2))].">
      <j1 rule="para" parents="9184 13312"/>
    </justification>
  </clause>

  <clause id="13377">
    <literal><![CDATA[
      K(x,y * K(z,z \ u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(9186(a,1),13312(a,1,2,2))].">
      <j1 rule="para" parents="9186 13312"/>
    </justification>
  </clause>

  <clause id="13378">
    <literal><![CDATA[
      K(x,y * (T(z,u) / u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(9189(a,1),13312(a,1,2,2))].">
      <j1 rule="para" parents="9189 13312"/>
    </justification>
  </clause>

  <clause id="13379">
    <literal><![CDATA[
      K(x,y * (z * L(u,w,u))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(9367(a,1),13312(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9367 13312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13380">
    <literal><![CDATA[
      K(x,y * (L(z,u,z) \ w)) = K(x,y * (z \ w))
    ]]></literal>
    <justification jstring="[para(9376(a,1),13312(a,1,2,2))].">
      <j1 rule="para" parents="9376 13312"/>
    </justification>
  </clause>

  <clause id="13381">
    <literal><![CDATA[
      K(x,y * (z \ R(u,w,u))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(13241(a,1),13312(a,1,2,2))].">
      <j1 rule="para" parents="13241 13312"/>
    </justification>
  </clause>

  <clause id="13382">
    <literal><![CDATA[
      K(x,y * (z * (u * a(w,v5,w)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(13226(a,1),13312(a,1,2,2))].">
      <j1 rule="para" parents="13226 13312"/>
    </justification>
  </clause>

  <clause id="13383">
    <literal><![CDATA[
      K(x,y \ T(z * u,z)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(9185(a,1),13313(a,1,2,2))].">
      <j1 rule="para" parents="9185 13313"/>
    </justification>
  </clause>

  <clause id="13384">
    <literal><![CDATA[
      K(x,y \ (z * R(u,w,u))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(9800(a,1),13313(a,1,2,2))].">
      <j1 rule="para" parents="9800 13313"/>
    </justification>
  </clause>

  <clause id="13385">
    <literal><![CDATA[
      K(x,y \ (L(z,u,z) * w)) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(9843(a,1),13313(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9843 13313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13386">
    <literal><![CDATA[
      K(x,y * (K(z,z \ u) * w)) = K(x,y * (K(z,u) * w))
    ]]></literal>
    <justification jstring="[para(10106(a,1),13314(a,1,2,2))].">
      <j1 rule="para" parents="10106 13314"/>
    </justification>
  </clause>

  <clause id="13387">
    <literal><![CDATA[
      K(x,y * (z \ (a(u,w,u) \ v5))) = K(x,y * (z \ v5))
    ]]></literal>
    <justification jstring="[para(13261(a,1),13314(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13261 13314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13388">
    <literal><![CDATA[
      K(x,y * (z \ L(u,w,u))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(13270(a,1),13314(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13270 13314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13389">
    <literal><![CDATA[
      K(x,K(y * z,z) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(9179(a,1),13315(a,1,2,1))].">
      <j1 rule="para" parents="9179 13315"/>
    </justification>
  </clause>

  <clause id="13390">
    <literal><![CDATA[
      K(x,K(y * z,y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(9180(a,1),13315(a,1,2,1))].">
      <j1 rule="para" parents="9180 13315"/>
    </justification>
  </clause>

  <clause id="13391">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(9843(a,1),13315(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9843 13315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13392">
    <literal><![CDATA[
      K(x,(T(y * z,y) \ u) \ w) = K(x,((z * y) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(11524(a,1),13315(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11524 13315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13393">
    <literal><![CDATA[
      K(x,(y * (z * a(u,w,u))) \ v5) = K(x,(y * z) \ v5)
    ]]></literal>
    <justification jstring="[para(13242(a,1),13315(a,1,2,1))].">
      <j1 rule="para" parents="13242 13315"/>
    </justification>
  </clause>

  <clause id="13394">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(9151(a,1),13319(a,1,2,1))].">
      <j1 rule="para" parents="9151 13319"/>
    </justification>
  </clause>

  <clause id="13395">
    <literal><![CDATA[
      K(x,(R(y,z,y) \ u) * w) = K(x,(y \ u) * w)
    ]]></literal>
    <justification jstring="[para(9811(a,1),13319(a,1,2,1))].">
      <j1 rule="para" parents="9811 13319"/>
    </justification>
  </clause>

  <clause id="13396">
    <literal><![CDATA[
      K(x,y * K(z \ u,z)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(9151(a,1),13320(a,1,2,2))].">
      <j1 rule="para" parents="9151 13320"/>
    </justification>
  </clause>

  <clause id="13397">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(z \ u,u))
    ]]></literal>
    <justification jstring="[para(9187(a,1),13321(a,1,2,2))].">
      <j1 rule="para" parents="9187 13321"/>
    </justification>
  </clause>

  <clause id="13398">
    <literal><![CDATA[
      K(T(x * y,x) / z,u) = K((y * x) / z,u)
    ]]></literal>
    <justification jstring="[para(9184(a,1),13334(a,1,1,1))].">
      <j1 rule="para" parents="9184 13334"/>
    </justification>
  </clause>

  <clause id="13399">
    <literal><![CDATA[
      K(x * K(y,y \ z),u) = K(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[para(9186(a,1),13335(a,1,1,2))].">
      <j1 rule="para" parents="9186 13335"/>
    </justification>
  </clause>

  <clause id="13400">
    <literal><![CDATA[
      K(x * (y \ R(z,u,z)),w) = K(x * (y \ z),w)
    ]]></literal>
    <justification jstring="[para(13241(a,1),13335(a,1,1,2))].">
      <j1 rule="para" parents="13241 13335"/>
    </justification>
  </clause>

  <clause id="13401">
    <literal><![CDATA[
      K(x \ T(y * z,y),u) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(9185(a,1),13336(a,1,1,2))].">
      <j1 rule="para" parents="9185 13336"/>
    </justification>
  </clause>

  <clause id="13402">
    <literal><![CDATA[
      K(x \ K(y,y \ z),u) = K(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[para(9152(a,1),13336(a,1,1,2))].">
      <j1 rule="para" parents="9152 13336"/>
    </justification>
  </clause>

  <clause id="13403">
    <literal><![CDATA[
      K((L(x,y,x) * z) \ u,w) = K((x * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(9842(a,1),13337(a,1,1,1))].">
      <j1 rule="para" parents="9842 13337"/>
    </justification>
  </clause>

  <clause id="13404">
    <literal><![CDATA[
      K(K(x * y,x) * z,u) = K(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[para(9173(a,1),13340(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9173 13340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13405">
    <literal><![CDATA[
      K((x * R(y,z,y)) \ u,w) = K((x * y) \ u,w)
    ]]></literal>
    <justification jstring="[para(12722(a,1),13341(a,1,1))].">
      <j1 rule="para" parents="12722 13341"/>
    </justification>
  </clause>

  <clause id="13406">
    <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,13296,a(flip),b,8665,a),flip(a)].">
      <j1 rule="hyper" parents="119 13296 8665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13407">
    <literal><![CDATA[
      T(x,((y \ z) * y) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13296(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13408">
    <literal><![CDATA[
      K(x,K(y \ z,y * (z \ u)) * w) = K(x,K(y \ z,u) * w)
    ]]></literal>
    <justification jstring="[para(12742(a,1),13317(a,1,2,1))].">
      <j1 rule="para" parents="12742 13317"/>
    </justification>
  </clause>

  <clause id="13409">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13318(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13410">
    <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(13318(a,1),8680(a,1,1,2))].">
      <j1 rule="para" parents="13318 8680"/>
    </justification>
  </clause>

  <clause id="13411">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13339(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13413">
    <literal><![CDATA[
      T(x,y * T(T(z / u,w),z)) = T(x,y * T(u \ z,w))
    ]]></literal>
    <justification jstring="[para(7897(a,1),13343(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7897 13343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13414">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) = x \ T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,13344,a(flip),b,5020,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 13344 5020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13415">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) = x \ T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(116,a,13345,a(flip),b,5020,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 13345 5020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13417">
    <literal><![CDATA[
      T(x,y / T((z \ u) \ u,w)) = T(x,y / T(T(z,w),u))
    ]]></literal>
    <justification jstring="[para(7930(a,2),13347(a,1,2,2))].">
      <j1 rule="para" parents="7930 13347"/>
    </justification>
  </clause>

  <clause id="13418">
    <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(8823(a,1),13347(a,2,2,2))].">
      <j1 rule="para" parents="8823 13347"/>
    </justification>
  </clause>

  <clause id="13419">
    <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(13348(a,1),12589(a,1,2,1))].">
      <j1 rule="para" parents="13348 12589"/>
    </justification>
  </clause>

  <clause id="13420">
    <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,13349,a(flip),b,8665,a),flip(a)].">
      <j1 rule="hyper" parents="119 13349 8665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13421">
    <literal><![CDATA[
      T(x,y \ T(T(z,u),z \ w)) = T(x,y \ T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(7891(a,1),13350(a,1,2,2))].">
      <j1 rule="para" parents="7891 13350"/>
    </justification>
  </clause>

  <clause id="13422">
    <literal><![CDATA[
      T(x \ T(y,y \ z),x \ T(y,z)) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,675,a(flip),b,13351,a),flip(a)].">
      <j1 rule="hyper" parents="58 675 13351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13423">
    <literal><![CDATA[
      T(x,K(y,z) * ((z * y) * u)) = T(x,T(z * y,z) * u)
    ]]></literal>
    <justification jstring="[para(5047(a,1),13352(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5047 13352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13424">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) = w / (K(y * T(z,u),x) * w)
    ]]></literal>
    <justification jstring="[hyper(334,a,5403,a,b,13354,a),flip(a)].">
      <j1 rule="hyper" parents="334 5403 13354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13425">
    <literal><![CDATA[
      K(x,y * T(z,u * z)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4513(a,2),13354(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4513 13354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13426">
    <literal><![CDATA[
      K(x,y * T(T(z / u,w),z)) = K(x,y * T(u \ z,w))
    ]]></literal>
    <justification jstring="[para(7897(a,1),13354(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7897 13354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13427">
    <literal><![CDATA[
      K(T(x / y,x) \ z,u) = (w * K(u,(y \ x) \ z)) \ w
    ]]></literal>
    <justification jstring="[para(13355(a,1),6523(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13355 6523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13428">
    <literal><![CDATA[
      K(x,L(((y \ z) \ z) \ u,w,v5)) = K(L(x,w,v5),T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(11169,a,13357,a)].">
      <j1 rule="hyper" parents="11169 13357"/>
    </justification>
  </clause>

  <clause id="13429">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = (w * K(T(y,z) \ u,x)) \ w
    ]]></literal>
    <justification jstring="[hyper(334,a,6523,a,b,13357,a),flip(a)].">
      <j1 rule="hyper" parents="334 6523 13357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13430">
    <literal><![CDATA[
      K(x,T(((y / z) \ 1) * y,y) \ u) = K(x,(((z \ y) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(10415(a,1),13357(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10415 13357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13431">
    <literal><![CDATA[
      K(x * y,z * T(x,y)) = K(x * y,z * x)
    ]]></literal>
    <justification jstring="[hyper(8696,a,13358,a),flip(a)].">
      <j1 rule="hyper" parents="8696 13358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13432">
    <literal><![CDATA[
      K(x,L(T(y,y * z) * u,w,v5)) = K(L(x,w,v5),T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(11169,a,13360,a)].">
      <j1 rule="hyper" parents="11169 13360"/>
    </justification>
  </clause>

  <clause id="13433">
    <literal><![CDATA[
      K(x,T(y * (1 / z),z) / u) = K(x,T(y * (1 / z),y) / u)
    ]]></literal>
    <justification jstring="[para(6733(a,2),13361(a,1,2,1))].">
      <j1 rule="para" parents="6733 13361"/>
    </justification>
  </clause>

  <clause id="13434">
    <literal><![CDATA[
      K(x,y \ T(z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(8641,a,13362,a),flip(a)].">
      <j1 rule="hyper" parents="8641 13362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13435">
    <literal><![CDATA[
      K(x,y \ T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(13362(a,1),8641(a,1))].">
      <j1 rule="para" parents="13362 8641"/>
    </justification>
  </clause>

  <clause id="13436">
    <literal><![CDATA[
      K(x,T(y,z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(4490(a,2),13435(a,1,2))].">
      <j1 rule="para" parents="4490 13435"/>
    </justification>
  </clause>

  <clause id="13437">
    <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(6439(a,1),13435(a,1,2,2))].">
      <j1 rule="para" parents="6439 13435"/>
    </justification>
  </clause>

  <clause id="13438">
    <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(8254(a,1),13435(a,1,2,2))].">
      <j1 rule="para" parents="8254 13435"/>
    </justification>
  </clause>

  <clause id="13439">
    <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(13037(a,1),13435(a,1,2,2))].">
      <j1 rule="para" parents="13037 13435"/>
    </justification>
  </clause>

  <clause id="13440">
    <literal><![CDATA[
      T(x,y * ((z \ u) * z)) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),13371(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13441">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) = x \ T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(116,a,13372,a(flip),b,5020,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 13372 5020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13442">
    <literal><![CDATA[
      K(K(x \ y,x) * z,u) = u / T(u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(13372(a,1),5062(a,2,2))].">
      <j1 rule="para" parents="13372 5062"/>
    </justification>
  </clause>

  <clause id="13443">
    <literal><![CDATA[
      K(x,((y \ z) * y) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13373(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13444">
    <literal><![CDATA[
      K(x,y * ((z \ u) * z)) = K(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="13445">
    <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(10804(a,2),13377(a,2,2,2))].">
      <j1 rule="para" parents="10804 13377"/>
    </justification>
  </clause>

  <clause id="13446">
    <literal><![CDATA[
      K(x,y * (z / T(u,z))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(4488(a,1),13378(a,1,2,2))].">
      <j1 rule="para" parents="4488 13378"/>
    </justification>
  </clause>

  <clause id="13447">
    <literal><![CDATA[
      K(x,K(y,z \ y) \ u) = K(x,K(z,z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13389(a,1,2,1,1))].">
      <j1 rule="para" parents="5 13389"/>
    </justification>
  </clause>

  <clause id="13448">
    <literal><![CDATA[
      K(x,K(y \ z,y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13390(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13449">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ y) \ u)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(5656(a,1),13394(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5656 13394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13450">
    <literal><![CDATA[
      K(x,(y / (z \ u)) * K(u,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(6743(a,1),13396(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6743 13396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13451">
    <literal><![CDATA[
      K(((x \ y) * x) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13398(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13452">
    <literal><![CDATA[
      K(x \ (y * z),T(x,y)) = K(x \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11547,a(flip),b,13401,a)].">
      <j1 rule="hyper" parents="58 11547 13401"/>
    </justification>
  </clause>

  <clause id="13453">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13401(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13454">
    <literal><![CDATA[
      K(x \ K(y,z \ 1),u) = K(x \ K(y,z \ y),u)
    ]]></literal>
    <justification jstring="[para(5271(a,1),13402(a,1,1,2))].">
      <j1 rule="para" parents="5271 13402"/>
    </justification>
  </clause>

  <clause id="13455">
    <literal><![CDATA[
      K(x \ K(y,(z * y) * u),w) = K(x \ K(y,z * u),w)
    ]]></literal>
    <justification jstring="[para(12736(a,1),13402(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12736 13402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13456">
    <literal><![CDATA[
      K(K(x * y,y) * z,u) = K(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5532(a,2),13404(a,1,1,1))].">
      <j1 rule="para" parents="5532 13404"/>
    </justification>
  </clause>

  <clause id="13457">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ y)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(6772,a,13407,a),flip(a)].">
      <j1 rule="hyper" parents="6772 13407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13458">
    <literal><![CDATA[
      K(x,T(T(y * z,u),y) \ w) = K(x,T(z * y,u) \ w)
    ]]></literal>
    <justification jstring="[para(4820(a,1),13409(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4820 13409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13459">
    <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(1771(a,1),13411(a,1,1,1,1))].">
      <j1 rule="para" parents="1771 13411"/>
    </justification>
  </clause>

  <clause id="13460">
    <literal><![CDATA[
      K(x * (y \ z),(1 / (z \ y)) * x) = K(x * (y \ z),x * (1 / (z \ y)))
    ]]></literal>
    <justification jstring="[para(6499(a,1),13431(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6499 13431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13461">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * T(z,u)) = K(x,((u \ z) * u) * y)
    ]]></literal>
    <justification jstring="[hyper(12592,a,13444,a),flip(a)].">
      <j1 rule="hyper" parents="12592 13444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13462">
    <literal><![CDATA[
      K(x,y * T((z \ 1) \ u,z)) = K(x,y * ((z \ K(z,u)) \ u))
    ]]></literal>
    <justification jstring="[para(10407(a,2),13444(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10407 13444"/>
      <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(4820(a,1),13453(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4820 13453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13464">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(13453(a,2),7665(a,1))].">
      <j1 rule="para" parents="13453 7665"/>
    </justification>
  </clause>

  <clause id="13465">
    <literal><![CDATA[
      L(x,y,z / T(u * (w / u),u)) = L(x,y,z / w)
    ]]></literal>
    <justification jstring="[para(9201(a,1),13274(a,1,3,2))].">
      <j1 rule="para" parents="9201 13274"/>
    </justification>
  </clause>

  <clause id="13466">
    <literal><![CDATA[
      K(x,(y * ((z \ u) \ u)) / w) = K(x,(y * T(z,u)) / w)
    ]]></literal>
    <justification jstring="[para(7790(a,1),13374(a,1,2,1,2))].">
      <j1 rule="para" parents="7790 13374"/>
    </justification>
  </clause>

  <clause id="13467">
    <literal><![CDATA[
      K(x,y * (z * L(T(u,w),v5,u))) = K(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(7762(a,1),13379(a,1,2,2,2))].">
      <j1 rule="para" parents="7762 13379"/>
    </justification>
  </clause>

  <clause id="13468">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) \ w)) = K(x,y * (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[para(12088(a,1),13380(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12088 13380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13469">
    <literal><![CDATA[
      K(x,y * (z \ T(u,u * w))) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(4629(a,1),13381(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4629 13381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13470">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) \ w))) = K(x,y \ (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(7790(a,1),13384(a,1,2,2,2))].">
      <j1 rule="para" parents="7790 13384"/>
    </justification>
  </clause>

  <clause id="13471">
    <literal><![CDATA[
      K(x,y \ (T(z / u,z) * w)) = K(x,y \ ((u \ z) * w))
    ]]></literal>
    <justification jstring="[para(4648(a,1),13385(a,1,2,2,1))].">
      <j1 rule="para" parents="4648 13385"/>
    </justification>
  </clause>

  <clause id="13472">
    <literal><![CDATA[
      K(x,y \ (((z \ u) \ u) * w)) = K(x,y \ (T(z,u) * w))
    ]]></literal>
    <justification jstring="[para(12088(a,1),13385(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12088 13385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13473">
    <literal><![CDATA[
      K(x,y * (z \ T(u / w,u))) = K(x,y * (z \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(4648(a,1),13388(a,1,2,2,2))].">
      <j1 rule="para" parents="4648 13388"/>
    </justification>
  </clause>

  <clause id="13474">
    <literal><![CDATA[
      K(x,(T(y,y \ z) \ u) * w) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(4695(a,1),13395(a,1,2,1,1))].">
      <j1 rule="para" parents="4695 13395"/>
    </justification>
  </clause>

  <clause id="13475">
    <literal><![CDATA[
      K(x * (y \ T(z,z * u)),w) = K(x * (y \ T(z,u)),w)
    ]]></literal>
    <justification jstring="[para(4629(a,1),13400(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4629 13400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13476">
    <literal><![CDATA[
      K((x * y) \ z,y * x) * (z * u) = (((y * x) \ z) * (y * x)) * u
    ]]></literal>
    <justification jstring="[para(13403(a,1),11596(a,1,1))].">
      <j1 rule="para" parents="13403 11596"/>
    </justification>
  </clause>

  <clause id="13477">
    <literal><![CDATA[
      K((x * T(y,y \ z)) \ u,w) = K((x * T(y,z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(4695(a,1),13405(a,1,1,1,2))].">
      <j1 rule="para" parents="4695 13405"/>
    </justification>
  </clause>

  <clause id="13478">
    <literal><![CDATA[
      K((x \ 1) \ (y \ z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ y) \ z,y) = u
    ]]></literal>
    <justification jstring="[para(8645(a,1),13464(a,1))].">
      <j1 rule="para" parents="8645 13464"/>
    </justification>
  </clause>

  <clause id="13479">
    <literal><![CDATA[
      T(x * a(y,z,y),u) = T(x,u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(17(a,2),13254(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17 13254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13480">
    <literal><![CDATA[
      T(a(x,y,x) * z,u) = T(z,u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(9793(a,2),13479(a,1,1))].">
      <j1 rule="para" parents="9793 13479"/>
    </justification>
  </clause>

  <clause id="13481">
    <literal><![CDATA[
      K(x,T(a(y,z,y) * u,w)) = K(x,T(u,w))
    ]]></literal>
    <justification jstring="[para(13480(a,2),13299(a,1,2))].">
      <j1 rule="para" parents="13480 13299"/>
    </justification>
  </clause>

  <clause id="13482">
    <literal><![CDATA[
      K(x,y * T(a(z,u,z) * w,v5)) = K(x,y * T(w,v5))
    ]]></literal>
    <justification jstring="[para(13480(a,2),13312(a,1,2,2))].">
      <j1 rule="para" parents="13480 13312"/>
    </justification>
  </clause>

  <clause id="13483">
    <literal><![CDATA[
      K(x,T(K(y,y \ z) * u,w)) = K(x,T(K(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(10106(a,1),13481(a,1,2,1))].">
      <j1 rule="para" parents="10106 13481"/>
    </justification>
  </clause>

  <clause id="13484">
    <literal><![CDATA[
      K(x,y * (z \ (L(u,w,u) * v5))) = K(x,y * (z \ (u * v5)))
    ]]></literal>
    <justification jstring="[para(13264(a,1),13320(a,1,2,2))].">
      <j1 rule="para" parents="13264 13320"/>
    </justification>
  </clause>

  <clause id="13485">
    <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(4719(a,1),13324(a,1,2,1,1))].">
      <j1 rule="para" parents="4719 13324"/>
    </justification>
  </clause>

  <clause id="13486">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13414(a,2),5110(a,1))].">
      <j1 rule="para" parents="13414 5110"/>
    </justification>
  </clause>

  <clause id="13487">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(13415(a,2),5110(a,1))].">
      <j1 rule="para" parents="13415 5110"/>
    </justification>
  </clause>

  <clause id="13488">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(13441(a,2),5110(a,1))].">
      <j1 rule="para" parents="13441 5110"/>
    </justification>
  </clause>

  <clause id="13489">
    <literal><![CDATA[
      K(K(x \ y,x) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) * z,u) = w
    ]]></literal>
    <justification jstring="[para(13442(a,2),5133(a,1))].">
      <j1 rule="para" parents="13442 5133"/>
    </justification>
  </clause>

  <clause id="13490">
    <literal><![CDATA[
      L(x,y,(z * (u / z)) \ z) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12907,a(flip),b,13465,a)].">
      <j1 rule="hyper" parents="58 12907 13465"/>
    </justification>
  </clause>

  <clause id="13491">
    <literal><![CDATA[
      L(x,y,z / (u * z)) = L(x,y,(z * u) \ z)
    ]]></literal>
    <justification jstring="[para(6(a,1),13490(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="6 13490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13492">
    <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(5094(a,2),13490(a,2,3))].">
      <j1 rule="para" parents="5094 13490"/>
    </justification>
  </clause>

  <clause id="13493">
    <literal><![CDATA[
      L(x,y,z \ (z / (z / u))) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(5330(a,1),13490(a,1,3))].">
      <j1 rule="para" parents="5330 13490"/>
    </justification>
  </clause>

  <clause id="13494">
    <literal><![CDATA[
      L(x,y,(z \ u) / u) = L(x,y,u \ (u / z))
    ]]></literal>
    <justification jstring="[para(72(a,1),13493(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="72 13493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13495">
    <literal><![CDATA[
      L(x,y,z \ K(u,u \ w)) = L(x,y,z \ K(u,w))
    ]]></literal>
    <justification jstring="[para(13240(a,1),12874(a,1,3))].">
      <j1 rule="para" parents="13240 12874"/>
    </justification>
  </clause>

  <clause id="13496">
    <literal><![CDATA[
      K(x \ K(y,y \ z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(13240(a,1),13328(a,1,1))].">
      <j1 rule="para" parents="13240 13328"/>
    </justification>
  </clause>

  <clause id="13497">
    <literal><![CDATA[
      K(x,y * (z * (T(u,w) / w))) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(9189(a,1),13382(a,1,2,2,2))].">
      <j1 rule="para" parents="9189 13382"/>
    </justification>
  </clause>

  <clause id="13498">
    <literal><![CDATA[
      K(x,y * (z * (u \ K(w,w \ v5)))) = K(x,y * (z * (u \ K(w,v5))))
    ]]></literal>
    <justification jstring="[para(13240(a,1),13382(a,1,2,2,2))].">
      <j1 rule="para" parents="13240 13382"/>
    </justification>
  </clause>

  <clause id="13499">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,u))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(9151(a,1),13387(a,1,2,2,2))].">
      <j1 rule="para" parents="9151 13387"/>
    </justification>
  </clause>

  <clause id="13500">
    <literal><![CDATA[
      K(x,(y * K(z * u,u)) \ w) = K(x,(y * K(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(9178(a,1),13393(a,1,2,1,2))].">
      <j1 rule="para" parents="9178 13393"/>
    </justification>
  </clause>

  <clause id="13501">
    <literal><![CDATA[
      K(x,y * T(T(z * u,z),w)) = K(x,y * T(u * z,w))
    ]]></literal>
    <justification jstring="[para(9185(a,1),13482(a,1,2,2,1))].">
      <j1 rule="para" parents="9185 13482"/>
    </justification>
  </clause>

  <clause id="13502">
    <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(10600(a,2),13487(a,1,2,1))].">
      <j1 rule="para" parents="10600 13487"/>
    </justification>
  </clause>

  <clause id="13503">
    <literal><![CDATA[
      K((x * (y / x)) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) * (y \ z),u) = w
    ]]></literal>
    <justification jstring="[para(11517(a,1),13489(a,1,1))].">
      <j1 rule="para" parents="11517 13489"/>
    </justification>
  </clause>

  <clause id="13504">
    <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(709,a,13244,a),flip(a)].">
      <j1 rule="hyper" parents="709 13244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13505">
    <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),13244(a,2,1))].">
      <j1 rule="para" parents="13 13244"/>
    </justification>
  </clause>

  <clause id="13506">
    <literal><![CDATA[
      (x * (y * (z * a(u,w,u)))) \ v5 = (x * (y * z)) \ (a(u,w,u) \ v5)
    ]]></literal>
    <justification jstring="[para(13226(a,1),13247(a,1,1,2))].">
      <j1 rule="para" parents="13226 13247"/>
    </justification>
  </clause>

  <clause id="13507">
    <literal><![CDATA[
      K(x,y * ((z / (z / u)) \ w)) = K(x,y * (K(u,z) * (u \ w)))
    ]]></literal>
    <justification jstring="[para(5659(a,2),13386(a,1,2,2))].">
      <j1 rule="para" parents="5659 13386"/>
    </justification>
  </clause>

  <clause id="13508">
    <literal><![CDATA[
      T(x,T(y * z,y) * u) = T(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(11459(a,1),13423(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11459 13423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13509">
    <literal><![CDATA[
      T(x,((y \ z) * y) * u) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13508(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13510">
    <literal><![CDATA[
      T(x,T(T(y * z,u),y) * w) = T(x,T(z * y,u) * w)
    ]]></literal>
    <justification jstring="[para(4820(a,1),13509(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4820 13509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13511">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13424(a,2),5412(a,1))].">
      <j1 rule="para" parents="13424 5412"/>
    </justification>
  </clause>

  <clause id="13512">
    <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),13511(a,1,2,2))].">
      <j1 rule="para" parents="106 13511"/>
    </justification>
  </clause>

  <clause id="13513">
    <literal><![CDATA[
      K(T(x / y,x) \ z,u) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,6523,a(flip),b,13427,a),flip(a)].">
      <j1 rule="hyper" parents="334 6523 13427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13514">
    <literal><![CDATA[
      K(((x \ y) \ y) \ z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(72(a,1),13513(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 13513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13515">
    <literal><![CDATA[
      K(T(x,x \ y) \ z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(106(a,2),13514(a,1,1,1))].">
      <j1 rule="para" parents="106 13514"/>
    </justification>
  </clause>

  <clause id="13516">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(13429(a,2),6528(a,1))].">
      <j1 rule="para" parents="13429 6528"/>
    </justification>
  </clause>

  <clause id="13517">
    <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),13516(a,1,2,1))].">
      <j1 rule="para" parents="106 13516"/>
    </justification>
  </clause>

  <clause id="13518">
    <literal><![CDATA[
      K(x,((y \ z) * y) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(12589,a,13461,a),flip(a)].">
      <j1 rule="hyper" parents="12589 13461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13519">
    <literal><![CDATA[
      K(x,y * (z * (u / T(w,u)))) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(4488(a,1),13497(a,1,2,2,2))].">
      <j1 rule="para" parents="4488 13497"/>
    </justification>
  </clause>

  <clause id="13520">
    <literal><![CDATA[
      K(x,y * T((z / u) \ 1,z)) = K(x,y * ((z / u) \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(5712(a,1),13499(a,1,2,2))].">
      <j1 rule="para" parents="5712 13499"/>
    </justification>
  </clause>

  <clause id="13521">
    <literal><![CDATA[
      K(x,y * (z * T(T(u / w,u),v5))) = K(x,y * (z * T(w \ u,v5)))
    ]]></literal>
    <justification jstring="[para(9339(a,1),13467(a,1,2,2,2))].">
      <j1 rule="para" parents="9339 13467"/>
    </justification>
  </clause>

  <clause id="13522">
    <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(13428(a,2),11169(a,1))].">
      <j1 rule="para" parents="13428 11169"/>
    </justification>
  </clause>

  <clause id="13523">
    <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(13432(a,2),11169(a,1))].">
      <j1 rule="para" parents="13432 11169"/>
    </justification>
  </clause>

  <clause id="13524">
    <literal><![CDATA[
      K(x,T(y * (1 / z),z) / u) = K(x,((1 / z) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(334,a,13373,a(flip),b,13433,a),flip(a)].">
      <j1 rule="hyper" parents="334 13373 13433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13525">
    <literal><![CDATA[
      K(x,T(y * (1 / z),z) / u) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(334,a,5843,a(flip),b,13524,a),flip(a)].">
      <j1 rule="hyper" parents="334 5843 13524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13526">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * a(u,w,u)))) = L(z,y,x) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(13226(a,1),13505(a,1,2,2))].">
      <j1 rule="para" parents="13226 13505"/>
    </justification>
  </clause>

  <clause id="13527">
    <literal><![CDATA[
      L(x * a(y,z,y),u,w) = L(x,u,w) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(495,a,13526,a)].">
      <j1 rule="hyper" parents="495 13526"/>
    </justification>
  </clause>

  <clause id="13528">
    <literal><![CDATA[
      L(a(x,y,x) \ z,u,w) = a(x,y,x) \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(3679,a,13527,a),flip(a)].">
      <j1 rule="hyper" parents="3679 13527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13529">
    <literal><![CDATA[
      x * L(y * a(x,z,x),u,w) = R(x,z,x) * L(y,u,w)
    ]]></literal>
    <justification jstring="[para(13527(a,2),9422(a,1,2))].">
      <j1 rule="para" parents="13527 9422"/>
    </justification>
  </clause>

  <clause id="13530">
    <literal><![CDATA[
      K(x,L(y * a(z,u,z),w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(13527(a,2),13299(a,1,2))].">
      <j1 rule="para" parents="13527 13299"/>
    </justification>
  </clause>

  <clause id="13531">
    <literal><![CDATA[
      K(x,L(a(y,z,y) * u,w,v5)) = K(x,L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(9793(a,2),13530(a,1,2,1))].">
      <j1 rule="para" parents="9793 13530"/>
    </justification>
  </clause>

  <clause id="13532">
    <literal><![CDATA[
      K(x,L(T(y * z,y) \ u,w,v5)) = K(x,L((z * y) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(11524(a,1),13531(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11524 13531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13533">
    <literal><![CDATA[
      L(a(x,y,x) \ z,u,w) * v5 = L(z,u,w) * (a(x,y,x) \ v5)
    ]]></literal>
    <justification jstring="[para(13528(a,2),13269(a,1,1))].">
      <j1 rule="para" parents="13528 13269"/>
    </justification>
  </clause>

  <clause id="13534">
    <literal><![CDATA[
      R(x,y,x) * L(R(x,y,x) \ z,u,w) = x * L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(9421(a,1),13529(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9421 13529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13535">
    <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(334,a,11102,a,b,13532,a)].">
      <j1 rule="hyper" parents="334 11102 13532"/>
    </justification>
  </clause>

  <clause id="13536">
    <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(13271(a,1),13533(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13271 13533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13537">
    <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,13534,a(flip),b,11719,a),flip(a)].">
      <j1 rule="hyper" parents="119 13534 11719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13539">
    <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(13406(a,2),8667(a,1))].">
      <j1 rule="para" parents="13406 8667"/>
    </justification>
  </clause>

  <clause id="13540">
    <literal><![CDATA[
      T(x,T(y \ T(z,z * u),w)) = T(x,T(y \ T(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(334,a,8666,a(flip),b,13420,a),flip(a)].">
      <j1 rule="hyper" parents="334 8666 13420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13541">
    <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(13266(a,1),13278(a,1,2))].">
      <j1 rule="para" parents="13266 13278"/>
    </justification>
  </clause>

  <clause id="13542">
    <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,2195,a(flip),b,13537,a)].">
      <j1 rule="hyper" parents="58 2195 13537"/>
    </justification>
  </clause>

  <clause id="13543">
    <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),13537(a,1,1,1))].">
      <j1 rule="para" parents="5 13537"/>
    </justification>
  </clause>

  <clause id="13545">
    <literal><![CDATA[
      T((x * y) * L((x * y) \ x,z,u),x) = (y * L(y \ 1,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(334,a,1920,a(flip),b,13542,a),flip(a)].">
      <j1 rule="hyper" parents="334 1920 13542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13546">
    <literal><![CDATA[
      T(x * (y * L(y \ 1,z,u)),x) = (y * L(y \ 1,z,u)) * x
    ]]></literal>
    <justification jstring="[para(951(a,1),13545(a,1,1))].">
      <j1 rule="para" parents="951 13545"/>
    </justification>
  </clause>

  <clause id="13547">
    <literal><![CDATA[
      R(x,y * L(y \ 1,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(4585,a,13546,a)].">
      <j1 rule="hyper" parents="4585 13546"/>
    </justification>
  </clause>

  <clause id="13548">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[para(1241(a,1),13547(a,1,2))].">
      <j1 rule="para" parents="1241 13547"/>
    </justification>
  </clause>

  <clause id="13549">
    <literal><![CDATA[
      R(T(x,y),z \ L(z,u,w),x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7366,a(flip),b,13548,a)].">
      <j1 rule="hyper" parents="58 7366 13548"/>
    </justification>
  </clause>

  <clause id="13550">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,13548,a(flip),b,9162,a),flip(a)].">
      <j1 rule="hyper" parents="115 13548 9162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13551">
    <literal><![CDATA[
      L(x,a(y,z,y) * u,w) = L(x,u,w * a(y,z,y))
    ]]></literal>
    <justification jstring="[hyper(12717,a,13541,a)].">
      <j1 rule="hyper" parents="12717 13541"/>
    </justification>
  </clause>

  <clause id="13552">
    <literal><![CDATA[
      L(x,a(y,z,y) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(334,a,12874,a(flip),b,13551,a),flip(a)].">
      <j1 rule="hyper" parents="334 12874 13551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13554">
    <literal><![CDATA[
      L(x,a(y,z,y) \ u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),13552(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 13552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13555">
    <literal><![CDATA[
      L(x,R(y,z,y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(9167(a,1),13552(a,1,2))].">
      <j1 rule="para" parents="9167 13552"/>
    </justification>
  </clause>

  <clause id="13556">
    <literal><![CDATA[
      L(x,K(y * z,y),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(9180(a,1),13552(a,1,2))].">
      <j1 rule="para" parents="9180 13552"/>
    </justification>
  </clause>

  <clause id="13557">
    <literal><![CDATA[
      L(x,K(y,y * z),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[para(9181(a,1),13552(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9181 13552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13558">
    <literal><![CDATA[
      L(x,T(y * z,y),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(9185(a,1),13552(a,1,2))].">
      <j1 rule="para" parents="9185 13552"/>
    </justification>
  </clause>

  <clause id="13559">
    <literal><![CDATA[
      L(x,K(y,y \ z),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[para(9152(a,1),13552(a,1,2))].">
      <j1 rule="para" parents="9152 13552"/>
    </justification>
  </clause>

  <clause id="13560">
    <literal><![CDATA[
      L(x,L(y,z,y) \ u,w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(9801(a,1),13552(a,1,2))].">
      <j1 rule="para" parents="9801 13552"/>
    </justification>
  </clause>

  <clause id="13561">
    <literal><![CDATA[
      L(x,y / L(z,u,z),w) = L(x,y / z,w)
    ]]></literal>
    <justification jstring="[para(9802(a,1),13552(a,1,2))].">
      <j1 rule="para" parents="9802 13552"/>
    </justification>
  </clause>

  <clause id="13562">
    <literal><![CDATA[
      L(x,T(y * (z / y),y),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(9803(a,1),13552(a,1,2))].">
      <j1 rule="para" parents="9803 13552"/>
    </justification>
  </clause>

  <clause id="13563">
    <literal><![CDATA[
      L(x,K(y,y \ z) * u,w) = L(x,K(y,z) * u,w)
    ]]></literal>
    <justification jstring="[para(10106(a,1),13552(a,1,2))].">
      <j1 rule="para" parents="10106 13552"/>
    </justification>
  </clause>

  <clause id="13564">
    <literal><![CDATA[
      L(x,T(y,y \ z),u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4695(a,1),13555(a,1,2))].">
      <j1 rule="para" parents="4695 13555"/>
    </justification>
  </clause>

  <clause id="13565">
    <literal><![CDATA[
      L(x,(y \ z) \ z,u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(7790(a,1),13555(a,1,2))].">
      <j1 rule="para" parents="7790 13555"/>
    </justification>
  </clause>

  <clause id="13566">
    <literal><![CDATA[
      L(x,a(y,z,y) \ 1,u) = x
    ]]></literal>
    <justification jstring="[hyper(334,a,384,a(flip),b,13554,a),flip(a)].">
      <j1 rule="hyper" parents="334 384 13554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13567">
    <literal><![CDATA[
      L(x,K(y \ z,y),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(9151(a,1),13554(a,1,2))].">
      <j1 rule="para" parents="9151 13554"/>
    </justification>
  </clause>

  <clause id="13568">
    <literal><![CDATA[
      L(x,R(y,z,y) \ y,u) = x
    ]]></literal>
    <justification jstring="[para(9168(a,2),13566(a,1,2))].">
      <j1 rule="para" parents="9168 13566"/>
    </justification>
  </clause>

  <clause id="13569">
    <literal><![CDATA[
      L((x * y) \ (x * z),R(u,w,u) \ u,v5) = L(y \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,92,a,b,13568,a),flip(a)].">
      <j1 rule="hyper" parents="334 92 13568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13570">
    <literal><![CDATA[
      L(x,K(y * z,(y * z) * (z \ 1)),u) = L(x,K(z * y,z \ 1),u)
    ]]></literal>
    <justification jstring="[para(6133(a,1),13557(a,2,2))].">
      <j1 rule="para" parents="6133 13557"/>
    </justification>
  </clause>

  <clause id="13571">
    <literal><![CDATA[
      L(x,y * z,z) = L(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(11486,a,13558,a),flip(a)].">
      <j1 rule="hyper" parents="11486 13558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13572">
    <literal><![CDATA[
      L(x,(y \ z) * y,u) = L(x,T(z,y),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13558(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13573">
    <literal><![CDATA[
      L(x,K(y,z),z \ y) = x
    ]]></literal>
    <justification jstring="[hyper(12957,a,13559,a),flip(a)].">
      <j1 rule="hyper" parents="12957 13559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13574">
    <literal><![CDATA[
      (x \ y) * (K(y,x) * z) = (x \ T(y,x)) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,13573,a(flip),b,6399,a),flip(a)].">
      <j1 rule="hyper" parents="119 13573 6399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13575">
    <literal><![CDATA[
      L(x,y * (z / T(y,z)),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(4524(a,1),13562(a,1,2))].">
      <j1 rule="para" parents="4524 13562"/>
    </justification>
  </clause>

  <clause id="13576">
    <literal><![CDATA[
      L(x,T(y,z),y \ z) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(11486,a,13564,a),flip(a)].">
      <j1 rule="hyper" parents="11486 13564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13577">
    <literal><![CDATA[
      L(x,T(y * z,z \ 1),u) = L(x,T(y * z,y),u)
    ]]></literal>
    <justification jstring="[para(6501(a,1),13564(a,1,2))].">
      <j1 rule="para" parents="6501 13564"/>
    </justification>
  </clause>

  <clause id="13578">
    <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(13564(a,1),4925(a,1))].">
      <j1 rule="para" parents="13564 4925"/>
    </justification>
  </clause>

  <clause id="13579">
    <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(13564(a,1),11489(a,1))].">
      <j1 rule="para" parents="13564 11489"/>
    </justification>
  </clause>

  <clause id="13580">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ 1),u) = L(x,T(T(y,z),z \ y),u)
    ]]></literal>
    <justification jstring="[para(13457(a,1),13564(a,1,2))].">
      <j1 rule="para" parents="13457 13564"/>
    </justification>
  </clause>

  <clause id="13582">
    <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(13565(a,1),6899(a,1,2))].">
      <j1 rule="para" parents="13565 6899"/>
    </justification>
  </clause>

  <clause id="13583">
    <literal><![CDATA[
      L(x,K(y * z,y \ 1),u) = L(x,K(z,y \ 1),u)
    ]]></literal>
    <justification jstring="[para(4750(a,1),13567(a,1,2))].">
      <j1 rule="para" parents="4750 13567"/>
    </justification>
  </clause>

  <clause id="13584">
    <literal><![CDATA[
      L(x,T(y,z \ y),u) = L(x,z * (y / z),u)
    ]]></literal>
    <justification jstring="[para(4150(a,1),13572(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4150 13572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13585">
    <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,13558,a,b,13575,a)].">
      <j1 rule="hyper" parents="58 13558 13575"/>
    </justification>
  </clause>

  <clause id="13586">
    <literal><![CDATA[
      L(T(x,y) \ z,x,x \ y) = y \ ((T(y,x) / x) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,12943,a(flip),b,13576,a),flip(a)].">
      <j1 rule="hyper" parents="58 12943 13576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13587">
    <literal><![CDATA[
      L(x,T(y / z,y) \ u,w) = L(x,(z \ y) \ u,w)
    ]]></literal>
    <justification jstring="[para(4648(a,1),13560(a,1,2,1))].">
      <j1 rule="para" parents="4648 13560"/>
    </justification>
  </clause>

  <clause id="13588">
    <literal><![CDATA[
      L(x,(y * z) / y,u) = L(x,y * (z / y),u)
    ]]></literal>
    <justification jstring="[para(556(a,1),13561(a,1,2)),flip(a)].">
      <j1 rule="para" parents="556 13561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13589">
    <literal><![CDATA[
      K(x,y) * ((y \ T(x,y)) \ z) = (y \ x) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,13574,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 13574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13590">
    <literal><![CDATA[
      K(x,y) * ((T(y,x) \ x) \ z) = (y \ x) \ z
    ]]></literal>
    <justification jstring="[para(4490(a,2),13589(a,1,2,1))].">
      <j1 rule="para" parents="4490 13589"/>
    </justification>
  </clause>

  <clause id="13591">
    <literal><![CDATA[
      L(x,T(y * z,z \ 1),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,13558,a(flip),b,13577,a),flip(a)].">
      <j1 rule="hyper" parents="334 13558 13577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13592">
    <literal><![CDATA[
      L(x,y * z,z \ 1) = L(x,z * y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(11486,a,13591,a)].">
      <j1 rule="hyper" parents="11486 13591"/>
    </justification>
  </clause>

  <clause id="13593">
    <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(13591(a,1),11201(a,1,2))].">
      <j1 rule="para" parents="13591 11201"/>
    </justification>
  </clause>

  <clause id="13594">
    <literal><![CDATA[
      L(x,(x / y) \ z,u) = L(x,(y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,11256,a(flip),b,13587,a)].">
      <j1 rule="hyper" parents="58 11256 13587"/>
    </justification>
  </clause>

  <clause id="13595">
    <literal><![CDATA[
      L(x,T(T(y,z),y / T(z,y)),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(4484(a,1),13585(a,1,2,1))].">
      <j1 rule="para" parents="4484 13585"/>
    </justification>
  </clause>

  <clause id="13596">
    <literal><![CDATA[
      L(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      L(x,T(y,u),x) = z
    ]]></literal>
    <justification jstring="[para(13595(a,1),12973(a,1))].">
      <j1 rule="para" parents="13595 12973"/>
    </justification>
  </clause>

  <clause id="13597">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(13041(a,1),13595(a,1,2))].">
      <j1 rule="para" parents="13041 13595"/>
    </justification>
  </clause>

  <clause id="13598">
    <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(9920(a,2),13596(a,1))].">
      <j1 rule="para" parents="9920 13596"/>
    </justification>
  </clause>

  <clause id="13599">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ 1),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13580,a,b,13597,a)].">
      <j1 rule="hyper" parents="58 13580 13597"/>
    </justification>
  </clause>

  <clause id="13600">
    <literal><![CDATA[
      L(x,T(y,z),z \ 1) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(11486,a,13599,a)].">
      <j1 rule="hyper" parents="11486 13599"/>
    </justification>
  </clause>

  <clause id="13602">
    <literal><![CDATA[
      L(x,y * (z / y),(y \ z) \ 1) = L(x,z,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,13584,a(flip),b,13600,a)].">
      <j1 rule="hyper" parents="58 13584 13600"/>
    </justification>
  </clause>

  <clause id="13603">
    <literal><![CDATA[
      L(x \ y,x,z) != u
    ]]></literal>
    <literal><![CDATA[
      (z * x) \ (z * y) = u
    ]]></literal>
    <justification jstring="[para(13569(a,1),3811(a,1))].">
      <j1 rule="para" parents="13569 3811"/>
    </justification>
  </clause>

  <clause id="13604">
    <literal><![CDATA[
      a(x \ L(y \ z,y,u),w,v5) = a(x \ ((u * y) \ (u * z)),w,v5)
    ]]></literal>
    <justification jstring="[para(13569(a,1),13272(a,1,1,2))].">
      <j1 rule="para" parents="13569 13272"/>
    </justification>
  </clause>

  <clause id="13605">
    <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),13603(a,1,1))].">
      <j1 rule="para" parents="92 13603"/>
    </justification>
  </clause>

  <clause id="13606">
    <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(269(a,1),13570(a,1,2,2))].">
      <j1 rule="para" parents="269 13570"/>
    </justification>
  </clause>

  <clause id="13607">
    <literal><![CDATA[
      L(x,K(y * z,y \ 1),u) = L(x,K(z * y,z),u)
    ]]></literal>
    <justification jstring="[para(6170(a,1),13606(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6170 13606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13608">
    <literal><![CDATA[
      L(x,K(y * z,y \ 1),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,13556,a(flip),b,13607,a),flip(a)].">
      <j1 rule="hyper" parents="334 13556 13607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13610">
    <literal><![CDATA[
      L(x,K(y,z),y \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(5728,a,13608,a),flip(a)].">
      <j1 rule="hyper" parents="5728 13608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13611">
    <literal><![CDATA[
      L(x,K(y,z \ 1),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13583,a(flip),b,13608,a)].">
      <j1 rule="hyper" parents="58 13583 13608"/>
    </justification>
  </clause>

  <clause id="13612">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * z) = (K(x,y) / x) * z
    ]]></literal>
    <justification jstring="[para(13610(a,1),6604(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13610 6604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13614">
    <literal><![CDATA[
      L(x,K(y \ 1,z),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(3696(a,1),13611(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3696 13611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13615">
    <literal><![CDATA[
      L(x,K(y,z),u \ (z \ u)) = x
    ]]></literal>
    <justification jstring="[hyper(8320,a,13614,a),flip(a)].">
      <j1 rule="hyper" parents="8320 13614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13616">
    <literal><![CDATA[
      (K(x,y) / x) * ((1 / x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(6306,a,13612,a),flip(a)].">
      <j1 rule="hyper" parents="6306 13612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13617">
    <literal><![CDATA[
      (K(x,y) / x) * (x * (T(y,x) * z)) = (1 / x) * (x * (y * z))
    ]]></literal>
    <justification jstring="[para(5378(a,1),13612(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5378 13612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13618">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) / x) * z = u
    ]]></literal>
    <justification jstring="[para(13616(a,1),597(a,1))].">
      <j1 rule="para" parents="13616 597"/>
    </justification>
  </clause>

  <clause id="13619">
    <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(13617(a,2),3165(a,1))].">
      <j1 rule="para" parents="13617 3165"/>
    </justification>
  </clause>

  <clause id="13620">
    <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(13266(a,1),13277(a,1,2,1))].">
      <j1 rule="para" parents="13266 13277"/>
    </justification>
  </clause>

  <clause id="13621">
    <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(6441(a,1),13445(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6441 13445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13622">
    <literal><![CDATA[
      K(x,y * K((z * (1 / u)) \ w,u)) = K(x,y * K(u * (z \ w),w \ z))
    ]]></literal>
    <justification jstring="[para(6423(a,1),13621(a,2,2,2))].">
      <j1 rule="para" parents="6423 13621"/>
    </justification>
  </clause>

  <clause id="13624">
    <literal><![CDATA[
      K(x,y * K(z * (u \ w),w \ u)) = K(x,y * K(z * (u \ w),z))
    ]]></literal>
    <justification jstring="[para(10804(a,1),13622(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10804 13622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13625">
    <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(13506(a,1),13504(a,1,1))].">
      <j1 rule="para" parents="13506 13504"/>
    </justification>
  </clause>

  <clause id="13626">
    <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(13535(a,1),11165(a,1))].">
      <j1 rule="para" parents="13535 11165"/>
    </justification>
  </clause>

  <clause id="13627">
    <literal><![CDATA[
      a(x * a(y,z,y),u,w) = a(x,a(y,z,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(12719,a,13620,a),flip(a)].">
      <j1 rule="hyper" parents="12719 13620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13628">
    <literal><![CDATA[
      a(x,a(y,z,y) * u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,13080,a(flip),b,13627,a),flip(a)].">
      <j1 rule="hyper" parents="58 13080 13627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13630">
    <literal><![CDATA[
      a(x,R(y,z,y),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(9167(a,1),13628(a,1,2))].">
      <j1 rule="para" parents="9167 13628"/>
    </justification>
  </clause>

  <clause id="13631">
    <literal><![CDATA[
      a(x,T(y * z,y),u) = a(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(9185(a,1),13628(a,1,2))].">
      <j1 rule="para" parents="9185 13628"/>
    </justification>
  </clause>

  <clause id="13632">
    <literal><![CDATA[
      a(x,T(y,y \ z),u) = a(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4695(a,1),13630(a,1,2))].">
      <j1 rule="para" parents="4695 13630"/>
    </justification>
  </clause>

  <clause id="13633">
    <literal><![CDATA[
      a(x,(y \ z) * y,u) = a(x,T(z,y),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13631(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13634">
    <literal><![CDATA[
      a(x \ y,T(x,y),z) = a(y / x,x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4929,a(flip),b,13632,a),flip(a)].">
      <j1 rule="hyper" parents="58 4929 13632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13635">
    <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(13633(a,1),4655(a,1,2))].">
      <j1 rule="para" parents="13633 4655"/>
    </justification>
  </clause>

  <clause id="13636">
    <literal><![CDATA[
      a(x,y,z * a(u,w,u)) = (x * (y * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(13273,a,13625,a),flip(a)].">
      <j1 rule="hyper" parents="13273 13625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13637">
    <literal><![CDATA[
      a(x,y,z * a(u,w,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,9,a,b,13636,a),flip(a)].">
      <j1 rule="hyper" parents="334 9 13636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13638">
    <literal><![CDATA[
      a(x,y,a(z,u,z) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(9793(a,2),13637(a,1,3))].">
      <j1 rule="para" parents="9793 13637"/>
    </justification>
  </clause>

  <clause id="13639">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,u) \ v5)) = a(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(13260(a,1),13638(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13260 13638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13640">
    <literal><![CDATA[
      a(x,y,z * K(u,u * w)) = a(x,y,z * K(u,w))
    ]]></literal>
    <justification jstring="[para(9172(a,1),13639(a,1,3,2))].">
      <j1 rule="para" parents="9172 13639"/>
    </justification>
  </clause>

  <clause id="13641">
    <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(13234(a,1),13235(a,1,2,2,1))].">
      <j1 rule="para" parents="13234 13235"/>
    </justification>
  </clause>

  <clause id="13643">
    <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(4553(a,2),13641(a,1,2))].">
      <j1 rule="para" parents="4553 13641"/>
    </justification>
  </clause>

  <clause id="13645">
    <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(13287(a,1),13643(a,1,2))].">
      <j1 rule="para" parents="13287 13643"/>
    </justification>
  </clause>

  <clause id="13646">
    <literal><![CDATA[
      T(T(x,x * y) * L(y,z,u),x) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(824(a,1),13645(a,1,2)),flip(a)].">
      <j1 rule="para" parents="824 13645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13648">
    <literal><![CDATA[
      T(x * L(y,z,u),x * y) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,10082,a(flip),b,13646,a)].">
      <j1 rule="hyper" parents="58 10082 13646"/>
    </justification>
  </clause>

  <clause id="13649">
    <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,13648,a(flip),b,5020,a(flip))].">
      <j1 rule="hyper" parents="116 13648 5020"/>
    </justification>
  </clause>

  <clause id="13650">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = K(x,y) * K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(9148,a,13649,a),flip(a)].">
      <j1 rule="hyper" parents="9148 13649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13651">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,11141,a(flip),b,13650,a),flip(a)].">
      <j1 rule="hyper" parents="334 11141 13650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13652">
    <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),13651(a,1,1))].">
      <j1 rule="para" parents="7 13651"/>
    </justification>
  </clause>

  <clause id="13653">
    <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,6955,a(flip),b,13652,a)].">
      <j1 rule="hyper" parents="58 6955 13652"/>
    </justification>
  </clause>

  <clause id="13654">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(10735(a,1),13653(a,2,3))].">
      <j1 rule="para" parents="10735 13653"/>
    </justification>
  </clause>

  <clause id="13655">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,11318,a(flip),b,13654,a),flip(a)].">
      <j1 rule="hyper" parents="334 11318 13654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13657">
    <literal><![CDATA[
      K(x,x * (L(y,z,u) \ y)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(10806,a,13655,a)].">
      <j1 rule="hyper" parents="10806 13655"/>
    </justification>
  </clause>

  <clause id="13658">
    <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,5778,a,b,13657,a)].">
      <j1 rule="hyper" parents="58 5778 13657"/>
    </justification>
  </clause>

  <clause id="13659">
    <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),13657(a,1,2))].">
      <j1 rule="para" parents="7 13657"/>
    </justification>
  </clause>

  <clause id="13660">
    <literal><![CDATA[
      K(x * (L(y,z,u) \ y),x) = w / (a(u,z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(13657(a,1),5403(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13657 5403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13661">
    <literal><![CDATA[
      K(x * (L(y,z,u) \ y),x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,10187,a(flip),b,13660,a),flip(a)].">
      <j1 rule="hyper" parents="334 10187 13660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13662">
    <literal><![CDATA[
      L(x,y,a(z,u,K(w,y))) = x
    ]]></literal>
    <justification jstring="[para(13661(a,1),5732(a,1,3))].">
      <j1 rule="para" parents="13661 5732"/>
    </justification>
  </clause>

  <clause id="13663">
    <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(13661(a,1),11321(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13661 11321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13664">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * u) * w = a(x,y,K(z,u)) * (u * w)
    ]]></literal>
    <justification jstring="[hyper(1392,a,13662,a),flip(a)].">
      <j1 rule="hyper" parents="1392 13662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13665">
    <literal><![CDATA[
      a(x,y,K(L(z,u,w) \ z,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(334,a,27,a(flip),b,13663,a),flip(a)].">
      <j1 rule="hyper" parents="334 27 13663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13666">
    <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,11338,a(flip),b,13663,a)].">
      <j1 rule="hyper" parents="58 11338 13663"/>
    </justification>
  </clause>

  <clause id="13667">
    <literal><![CDATA[
      T(L(x,y,z) \ x,L(u,w,v5)) = T(L(x,y,z) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(11200,a,13665,a)].">
      <j1 rule="hyper" parents="11200 13665"/>
    </justification>
  </clause>

  <clause id="13669">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(u,w,v5))) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,11338,a(flip),b,13665,a)].">
      <j1 rule="hyper" parents="58 11338 13665"/>
    </justification>
  </clause>

  <clause id="13670">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = K(a(z,y,x),u) * 1
    ]]></literal>
    <justification jstring="[para(13665(a,1),6932(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13665 6932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13671">
    <literal><![CDATA[
      T(x,L(y \ L(y,z,u),w,v5)) = T(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(11200,a,13669,a)].">
      <j1 rule="hyper" parents="11200 13669"/>
    </justification>
  </clause>

  <clause id="13673">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = K(a(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,3,a(flip),b,13670,a),flip(a)].">
      <j1 rule="hyper" parents="334 3 13670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13675">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = w / (K(a(u,z,y),x) * w)
    ]]></literal>
    <justification jstring="[para(13673(a,1),5403(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13673 5403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13676">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = K(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,5403,a(flip),b,13675,a),flip(a)].">
      <j1 rule="hyper" parents="334 5403 13675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13677">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,13676,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 13676 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13679">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = T(x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6975,a(flip),b,13671,a)].">
      <j1 rule="hyper" parents="58 6975 13671"/>
    </justification>
  </clause>

  <clause id="13680">
    <literal><![CDATA[
      T(x,y \ L(y,z,u)) = x * K(x,a(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(5128,a,13679,a),flip(a)].">
      <j1 rule="hyper" parents="5128 13679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13682">
    <literal><![CDATA[
      T(x * K(y \ L(y,z,u),x),a(u,z,y) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(334,a,5086,a(flip),b,13679,a),flip(a)].">
      <j1 rule="hyper" parents="334 5086 13679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13683">
    <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(13679(a,2),731(a,1,1))].">
      <j1 rule="para" parents="13679 731"/>
    </justification>
  </clause>

  <clause id="13684">
    <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(13680(a,2),5030(a,1))].">
      <j1 rule="para" parents="13680 5030"/>
    </justification>
  </clause>

  <clause id="13685">
    <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(6775,a,13659,a)].">
      <j1 rule="hyper" parents="6775 13659"/>
    </justification>
  </clause>

  <clause id="13686">
    <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,10799,a(flip),b,13685,a)].">
      <j1 rule="hyper" parents="58 10799 13685"/>
    </justification>
  </clause>

  <clause id="13687">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K((y / x) \ y,y))
    ]]></literal>
    <justification jstring="[para(11709(a,1),13686(a,2,3))].">
      <j1 rule="para" parents="11709 13686"/>
    </justification>
  </clause>

  <clause id="13688">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),13687(a,2,3,1))].">
      <j1 rule="para" parents="75 13687"/>
    </justification>
  </clause>

  <clause id="13691">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = w / (a(u,z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(13688(a,1),5403(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13688 5403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13692">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,10187,a(flip),b,13691,a),flip(a)].">
      <j1 rule="hyper" parents="334 10187 13691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13693">
    <literal><![CDATA[
      T(x,x * (y \ L(y,z,u))) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,13692,a(flip),b,4995,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 13692 4995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13694">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)),L(w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      x = v7
    ]]></literal>
    <justification jstring="[para(13692(a,1),4776(a,1,2))].">
      <j1 rule="para" parents="13692 4776"/>
    </justification>
  </clause>

  <clause id="13695">
    <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(13692(a,1),5030(a,1,2))].">
      <j1 rule="para" parents="13692 5030"/>
    </justification>
  </clause>

  <clause id="13696">
    <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(13237(a,1),13658(a,1,2))].">
      <j1 rule="para" parents="13237 13658"/>
    </justification>
  </clause>

  <clause id="13697">
    <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(5737,a,13696,a)].">
      <j1 rule="hyper" parents="5737 13696"/>
    </justification>
  </clause>

  <clause id="13698">
    <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(8012,a,13697,a)].">
      <j1 rule="hyper" parents="8012 13697"/>
    </justification>
  </clause>

  <clause id="13699">
    <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(13677(a,1),13698(a,1,2,1))].">
      <j1 rule="para" parents="13677 13698"/>
    </justification>
  </clause>

  <clause id="13700">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(5290,a,13699,a)].">
      <j1 rule="hyper" parents="5290 13699"/>
    </justification>
  </clause>

  <clause id="13701">
    <literal><![CDATA[
      x \ T(x,a(y,z,u)) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(13134(a,1),13699(a,1,2))].">
      <j1 rule="para" parents="13134 13699"/>
    </justification>
  </clause>

  <clause id="13702">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(13144,a,13700,a),flip(a)].">
      <j1 rule="hyper" parents="13144 13700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13703">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,a(x,y,u)) = w
    ]]></literal>
    <justification jstring="[para(13700(a,1),13144(a,1))].">
      <j1 rule="para" parents="13700 13144"/>
    </justification>
  </clause>

  <clause id="13704">
    <literal><![CDATA[
      (x * y) * a(z,u,K(y,w)) = x * T(y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,13702,a,b,6470,a)].">
      <j1 rule="hyper" parents="119 13702 6470"/>
    </justification>
  </clause>

  <clause id="13705">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,13702,a,b,4995,a(flip))].">
      <j1 rule="hyper" parents="119 13702 4995"/>
    </justification>
  </clause>

  <clause id="13707">
    <literal><![CDATA[
      a(x,y,K(z,a(u,w,v5))) = 1
    ]]></literal>
    <justification jstring="[para(13702(a,1),27(a,1,3))].">
      <j1 rule="para" parents="13702 27"/>
    </justification>
  </clause>

  <clause id="13708">
    <literal><![CDATA[
      a(x,y,K(z,u)) != 1
    ]]></literal>
    <literal><![CDATA[
      T(z,a(x,y,u)) = z
    ]]></literal>
    <justification jstring="[para(13702(a,2),51(a,1))].">
      <j1 rule="para" parents="13702 51"/>
    </justification>
  </clause>

  <clause id="13709">
    <literal><![CDATA[
      a(x,y,K(z,u)) * z = T(z,a(x,y,u))
    ]]></literal>
    <justification jstring="[para(13702(a,2),5034(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13702 5034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13710">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(13702(a,2),5030(a,1,2))].">
      <j1 rule="para" parents="13702 5030"/>
    </justification>
  </clause>

  <clause id="13711">
    <literal><![CDATA[
      a(x,y,K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(13702(a,2),9832(a,1))].">
      <j1 rule="para" parents="13702 9832"/>
    </justification>
  </clause>

  <clause id="13712">
    <literal><![CDATA[
      T(x,L(a(y,z,u),w,v5)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(11200,a,13707,a)].">
      <j1 rule="hyper" parents="11200 13707"/>
    </justification>
  </clause>

  <clause id="13713">
    <literal><![CDATA[
      K(x,a(y,z,a(u,w,v5))) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,13702,a(flip),b,13707,a)].">
      <j1 rule="hyper" parents="58 13702 13707"/>
    </justification>
  </clause>

  <clause id="13714">
    <literal><![CDATA[
      a(x,y,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(6419(a,1),13711(a,1))].">
      <j1 rule="para" parents="6419 13711"/>
    </justification>
  </clause>

  <clause id="13715">
    <literal><![CDATA[
      T(a(x,y,a(z,u,w)),v5) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(5077,a,13713,a)].">
      <j1 rule="hyper" parents="5077 13713"/>
    </justification>
  </clause>

  <clause id="13716">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(552,a,13713,a)].">
      <j1 rule="hyper" parents="552 13713"/>
    </justification>
  </clause>

  <clause id="13717">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) \ v5) * a(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[hyper(443,a,13713,a)].">
      <j1 rule="hyper" parents="443 13713"/>
    </justification>
  </clause>

  <clause id="13718">
    <literal><![CDATA[
      K(x,a(y,z,a(u,w,v5))) = a(v6,v7,K(v8,a(v9,v10,v11)))
    ]]></literal>
    <justification jstring="[hyper(334,a,13707,a,b,13713,a),flip(a)].">
      <j1 rule="hyper" parents="334 13707 13713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13719">
    <literal><![CDATA[
      T(x,a(y,z,a(u,w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,13713,a)].">
      <j1 rule="hyper" parents="51 13713"/>
    </justification>
  </clause>

  <clause id="13720">
    <literal><![CDATA[
      x / a(y,z,a(u,w,v5)) = a(y,z,a(u,w,v5)) \ x
    ]]></literal>
    <justification jstring="[hyper(171,a,5275,a,b,13713,a(flip))].">
      <j1 rule="hyper" parents="171 5275 13713"/>
    </justification>
  </clause>

  <clause id="13721">
    <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,6886,a,b,13713,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="168 6886 13713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13722">
    <literal><![CDATA[
      a(x,y,K(z,L(y,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      1 = v5
    ]]></literal>
    <justification jstring="[para(10878(a,1),13714(a,1,3))].">
      <j1 rule="para" parents="10878 13714"/>
    </justification>
  </clause>

  <clause id="13723">
    <literal><![CDATA[
      T(x,a(y,z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(168,a,13701,a,b,10365,a(flip))].">
      <j1 rule="hyper" parents="168 13701 10365"/>
    </justification>
  </clause>

  <clause id="13725">
    <literal><![CDATA[
      T(x,a(y,z,L(u,w,v5))) = x * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,12118,a(flip),b,13701,a),flip(a)].">
      <j1 rule="hyper" parents="119 12118 13701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13727">
    <literal><![CDATA[
      (a(x,y,y \ 1) \ z) * a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[hyper(2419,a,13723,a)].">
      <j1 rule="hyper" parents="2419 13723"/>
    </justification>
  </clause>

  <clause id="13728">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ u = T(u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,10186,a,b,13709,a)].">
      <j1 rule="hyper" parents="58 10186 13709"/>
    </justification>
  </clause>

  <clause id="13729">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(34,a,5058,a(flip),b,13728,a),flip(a)].">
      <j1 rule="hyper" parents="34 5058 13728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13730">
    <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,13729,a,b,8000,a)].">
      <j1 rule="hyper" parents="119 13729 8000"/>
    </justification>
  </clause>

  <clause id="13731">
    <literal><![CDATA[
      (x / y) * a(z,u,K(w,y)) = x / T(y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,13729,a,b,6376,a)].">
      <j1 rule="hyper" parents="119 13729 6376"/>
    </justification>
  </clause>

  <clause id="13732">
    <literal><![CDATA[
      a(x,y,z) * a(x,y,K(z,u)) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(119,a,13729,a,b,4995,a(flip))].">
      <j1 rule="hyper" parents="119 13729 4995"/>
    </justification>
  </clause>

  <clause id="13733">
    <literal><![CDATA[
      K(a(x,y,z),u \ L(u,w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,13669,a(flip),b,13729,a),flip(a)].">
      <j1 rule="hyper" parents="58 13669 13729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13734">
    <literal><![CDATA[
      K(x,a(y,z,u) \ x) = a(y,z,K(u,a(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(13159,a,13729,a(flip))].">
      <j1 rule="hyper" parents="13159 13729"/>
    </justification>
  </clause>

  <clause id="13735">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u * a(x,y,z)) = a(x,y,z) * u
    ]]></literal>
    <justification jstring="[para(13729(a,2),4990(a,1,1))].">
      <j1 rule="para" parents="13729 4990"/>
    </justification>
  </clause>

  <clause id="13736">
    <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(13729(a,2),5035(a,1,1))].">
      <j1 rule="para" parents="13729 5035"/>
    </justification>
  </clause>

  <clause id="13737">
    <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(13729(a,2),5048(a,1,1))].">
      <j1 rule="para" parents="13729 5048"/>
    </justification>
  </clause>

  <clause id="13738">
    <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(13729(a,2),5449(a,1,1))].">
      <j1 rule="para" parents="13729 5449"/>
    </justification>
  </clause>

  <clause id="13739">
    <literal><![CDATA[
      ((x * y) * z) * a(x,y,K(z,u)) = (x * (y * z)) * T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(13729(a,2),6475(a,1,2))].">
      <j1 rule="para" parents="13729 6475"/>
    </justification>
  </clause>

  <clause id="13740">
    <literal><![CDATA[
      x * K(y \ L(y,z,u),a(w,v5,v6)) = x
    ]]></literal>
    <justification jstring="[hyper(6547,a,13733,a)].">
      <j1 rule="hyper" parents="6547 13733"/>
    </justification>
  </clause>

  <clause id="13741">
    <literal><![CDATA[
      T(a(x,y,z),a(u,w,v5) \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(13740(a,1),13682(a,1,1))].">
      <j1 rule="para" parents="13740 13682"/>
    </justification>
  </clause>

  <clause id="13742">
    <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(431,a,13712,a),flip(a)].">
      <j1 rule="hyper" parents="431 13712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13743">
    <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(11337(a,1),13710(a,1,2))].">
      <j1 rule="para" parents="11337 13710"/>
    </justification>
  </clause>

  <clause id="13744">
    <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(13725(a,2),13710(a,1))].">
      <j1 rule="para" parents="13725 13710"/>
    </justification>
  </clause>

  <clause id="13745">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * v6) = v5 * (v6 * a(x,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(334,a,357,a(flip),b,13716,a),flip(a)].">
      <j1 rule="hyper" parents="334 357 13716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13746">
    <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,13716,a,b,927,a)].">
      <j1 rule="hyper" parents="116 13716 927"/>
    </justification>
  </clause>

  <clause id="13747">
    <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(13716(a,1),123(a,1))].">
      <j1 rule="para" parents="13716 123"/>
    </justification>
  </clause>

  <clause id="13748">
    <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(13716(a,1),264(a,1))].">
      <j1 rule="para" parents="13716 264"/>
    </justification>
  </clause>

  <clause id="13749">
    <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(13716(a,1),709(a,1,2,1))].">
      <j1 rule="para" parents="13716 709"/>
    </justification>
  </clause>

  <clause id="13750">
    <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(13716(a,2),1426(a,1,2,2))].">
      <j1 rule="para" parents="13716 1426"/>
    </justification>
  </clause>

  <clause id="13751">
    <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,13717,a(flip),b,927,a),flip(a)].">
      <j1 rule="hyper" parents="116 13717 927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13752">
    <literal><![CDATA[
      a(x,y,K(z,a(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      1 = v6
    ]]></literal>
    <justification jstring="[para(13718(a,1),9832(a,1))].">
      <j1 rule="para" parents="13718 9832"/>
    </justification>
  </clause>

  <clause id="13753">
    <literal><![CDATA[
      a(x,y,a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      1 = v6
    ]]></literal>
    <justification jstring="[para(13702(a,2),13752(a,1,3))].">
      <j1 rule="para" parents="13702 13752"/>
    </justification>
  </clause>

  <clause id="13754">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      1 = v6
    ]]></literal>
    <justification jstring="[para(13666(a,2),13753(a,1))].">
      <j1 rule="para" parents="13666 13753"/>
    </justification>
  </clause>

  <clause id="13755">
    <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(13720(a,1),1421(a,1,1,2))].">
      <j1 rule="para" parents="13720 1421"/>
    </justification>
  </clause>

  <clause id="13756">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * v6) = v5 * (a(x,y,a(z,u,w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(334,a,13721,a,b,13745,a),flip(a)].">
      <j1 rule="hyper" parents="334 13721 13745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13757">
    <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(13745(a,2),11(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13745 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13758">
    <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(1772(a,1),13745(a,2,2))].">
      <j1 rule="para" parents="1772 13745"/>
    </justification>
  </clause>

  <clause id="13759">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ (v5 \ v6) = v5 \ (a(x,y,a(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(13747,a,13751,a)].">
      <j1 rule="hyper" parents="13747 13751"/>
    </justification>
  </clause>

  <clause id="13760">
    <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,13756,a)].">
      <j1 rule="hyper" parents="116 151 13756"/>
    </justification>
  </clause>

  <clause id="13761">
    <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,13756,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 13756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13762">
    <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(13756(a,2),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13756 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13763">
    <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,13761,a)].">
      <j1 rule="hyper" parents="116 4 13761"/>
    </justification>
  </clause>

  <clause id="13764">
    <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),13759(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13 13759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13765">
    <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(13742(a,1),1775(a,1,1))].">
      <j1 rule="para" parents="13742 1775"/>
    </justification>
  </clause>

  <clause id="13766">
    <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,12383,a(flip),b,13758,a)].">
      <j1 rule="hyper" parents="117 12383 13758"/>
    </justification>
  </clause>

  <clause id="13767">
    <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,358,a(flip),b,13739,a(flip))].">
      <j1 rule="hyper" parents="116 358 13739"/>
    </justification>
  </clause>

  <clause id="13768">
    <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(334,a,13693,a(flip),b,13683,a),flip(a)].">
      <j1 rule="hyper" parents="334 13693 13683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13769">
    <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(13760(a,1),13764(a,1,2))].">
      <j1 rule="para" parents="13760 13764"/>
    </justification>
  </clause>

  <clause id="13770">
    <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(13760(a,1),13769(a,1,2,2))].">
      <j1 rule="para" parents="13760 13769"/>
    </justification>
  </clause>

  <clause id="13771">
    <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(636,a,13770,a)].">
      <j1 rule="hyper" parents="636 13770"/>
    </justification>
  </clause>

  <clause id="13772">
    <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,13771,a(flip),b,3675,a),flip(a)].">
      <j1 rule="hyper" parents="119 13771 3675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13773">
    <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(13226(a,1),13245(a,1,2))].">
      <j1 rule="para" parents="13226 13245"/>
    </justification>
  </clause>

  <clause id="13774">
    <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(530,a,13773,a),flip(a)].">
      <j1 rule="hyper" parents="530 13773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13775">
    <literal><![CDATA[
      R(x,y,z * a(u,w,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(13250,a,13774,a),flip(a)].">
      <j1 rule="hyper" parents="13250 13774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13777">
    <literal><![CDATA[
      R(x,y,z \ R(u,w,u)) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(13241(a,1),13775(a,1,3))].">
      <j1 rule="para" parents="13241 13775"/>
    </justification>
  </clause>

  <clause id="13778">
    <literal><![CDATA[
      R(x,y,z \ ((u \ w) \ w)) = R(x,y,z \ T(u,w))
    ]]></literal>
    <justification jstring="[para(7790(a,1),13777(a,1,3,2))].">
      <j1 rule="para" parents="7790 13777"/>
    </justification>
  </clause>

  <clause id="13779">
    <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(13062(a,2),13279(a,2,2))].">
      <j1 rule="para" parents="13062 13279"/>
    </justification>
  </clause>

  <clause id="13780">
    <literal><![CDATA[
      L(x,y,((z \ u) * z) \ (u * (1 / z))) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[para(6298(a,1),13492(a,1,3,1))].">
      <j1 rule="para" parents="6298 13492"/>
    </justification>
  </clause>

  <clause id="13781">
    <literal><![CDATA[
      L(x,y,K(z,z \ u) * (1 / z)) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[para(11496(a,1),13780(a,1,3))].">
      <j1 rule="para" parents="11496 13780"/>
    </justification>
  </clause>

  <clause id="13782">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1) / u) = L(x,y,K(u,u \ z) / u)
    ]]></literal>
    <justification jstring="[para(5997(a,1),13781(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5997 13781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13783">
    <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),13543(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13784">
    <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(13772(a,2),13766(a,1,2))].">
      <j1 rule="para" parents="13772 13766"/>
    </justification>
  </clause>

  <clause id="13785">
    <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(9812(a,1),13779(a,2,2,1))].">
      <j1 rule="para" parents="9812 13779"/>
    </justification>
  </clause>

  <clause id="13786">
    <literal><![CDATA[
      L(x,y,x) * R(L(x,y,x) \ z,u,w) = x * R(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(9360(a,1),13785(a,1,2,1,1))].">
      <j1 rule="para" parents="9360 13785"/>
    </justification>
  </clause>

  <clause id="13788">
    <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(13786(a,1),3355(a,1))].">
      <j1 rule="para" parents="13786 3355"/>
    </justification>
  </clause>

  <clause id="13789">
    <literal><![CDATA[
      L((x \ 1) * R((x \ 1) \ 1,y,z),u,x \ 1) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(13788,a,1272,a)].">
      <j1 rule="hyper" parents="13788 1272"/>
    </justification>
  </clause>

  <clause id="13790">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,x \ 1) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1272(a,1),13789(a,1,1))].">
      <j1 rule="para" parents="1272 13789"/>
    </justification>
  </clause>

  <clause id="13791">
    <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(12383(a,1),13784(a,1,2,1))].">
      <j1 rule="para" parents="12383 13784"/>
    </justification>
  </clause>

  <clause id="13792">
    <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(13791(a,1),3962(a,1,1))].">
      <j1 rule="para" parents="13791 3962"/>
    </justification>
  </clause>

  <clause id="13793">
    <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),13253(a,1,2,2))].">
      <j1 rule="para" parents="13 13253"/>
    </justification>
  </clause>

  <clause id="13794">
    <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(3684(a,1),13793(a,1,2))].">
      <j1 rule="para" parents="3684 13793"/>
    </justification>
  </clause>

  <clause id="13795">
    <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(4347,a,13794,a)].">
      <j1 rule="hyper" parents="4347 13794"/>
    </justification>
  </clause>

  <clause id="13796">
    <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(334,a,12959,a(flip),b,13795,a)].">
      <j1 rule="hyper" parents="334 12959 13795"/>
    </justification>
  </clause>

  <clause id="13798">
    <literal><![CDATA[
      a(x,a(y,z,u) \ 1,x) = a(x,u \ L(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(205(a,1),13796(a,1,2,2))].">
      <j1 rule="para" parents="205 13796"/>
    </justification>
  </clause>

  <clause id="13799">
    <literal><![CDATA[
      a(x,a(y,z,u) \ 1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(334,a,13550,a(flip),b,13798,a),flip(a)].">
      <j1 rule="hyper" parents="334 13550 13798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13800">
    <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(13798(a,1),10327(a,1,1,2))].">
      <j1 rule="para" parents="13798 10327"/>
    </justification>
  </clause>

  <clause id="13801">
    <literal><![CDATA[
      T(x * (a(y,z,u) \ 1),x) = (a(y,z,u) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(9196,a,13799,a)].">
      <j1 rule="hyper" parents="9196 13799"/>
    </justification>
  </clause>

  <clause id="13803">
    <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(13558(a,1),13582(a,1,2))].">
      <j1 rule="para" parents="13558 13582"/>
    </justification>
  </clause>

  <clause id="13804">
    <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(13749,a,13762,a)].">
      <j1 rule="hyper" parents="13749 13762"/>
    </justification>
  </clause>

  <clause id="13805">
    <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),12651(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13 12651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13806">
    <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(12881(a,1),12568(a,1,2))].">
      <j1 rule="para" parents="12881 12568"/>
    </justification>
  </clause>

  <clause id="13809">
    <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(194(a,1),12648(a,1,2,1))].">
      <j1 rule="para" parents="194 12648"/>
    </justification>
  </clause>

  <clause id="13810">
    <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(7970,a,13809,a),flip(a)].">
      <j1 rule="hyper" parents="7970 13809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13813">
    <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(334,a,12602,a,b,13810,a),flip(a)].">
      <j1 rule="hyper" parents="334 12602 13810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13815">
    <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(334,a,12621,a(flip),b,13813,a),flip(a)].">
      <j1 rule="hyper" parents="334 12621 13813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13817">
    <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(334,a,5704,a(flip),b,13815,a),flip(a)].">
      <j1 rule="hyper" parents="334 5704 13815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13819">
    <literal><![CDATA[
      K((((x / y) \ 1) \ y) \ y,z / (y / (((x / y) \ 1) \ y))) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(334,a,12658,a(flip),b,13817,a),flip(a)].">
      <j1 rule="hyper" parents="334 12658 13817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13821">
    <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),13819(a,1,2,2))].">
      <j1 rule="para" parents="72 13819"/>
    </justification>
  </clause>

  <clause id="13823">
    <literal><![CDATA[
      K((((x / y) \ 1) \ y) \ y,z / (1 / (x / y))) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,5576,a,b,13821,a)].">
      <j1 rule="hyper" parents="58 5576 13821"/>
    </justification>
  </clause>

  <clause id="13824">
    <literal><![CDATA[
      K((x / y) \ 1,T(z / (1 / (x / y)),y)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(7975,a,13823,a)].">
      <j1 rule="hyper" parents="7975 13823"/>
    </justification>
  </clause>

  <clause id="13825">
    <literal><![CDATA[
      K(1 / (x / y),T(z / (1 / (x / y)),y)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(5546,a,13824,a)].">
      <j1 rule="hyper" parents="5546 13824"/>
    </justification>
  </clause>

  <clause id="13826">
    <literal><![CDATA[
      K(1 / (x / y),(x / y) * T(z,y)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,12628,a(flip),b,13825,a)].">
      <j1 rule="hyper" parents="58 12628 13825"/>
    </justification>
  </clause>

  <clause id="13827">
    <literal><![CDATA[
      K(x / y,(y / x) * T(z,x)) = K(y \ x,z * (y / x))
    ]]></literal>
    <justification jstring="[hyper(5941,a,13826,a)].">
      <j1 rule="hyper" parents="5941 13826"/>
    </justification>
  </clause>

  <clause id="13828">
    <literal><![CDATA[
      K((x / y) \ x,z * ((x / y) / x)) = K(y,T(((x / y) / x) * T(z,x),x))
    ]]></literal>
    <justification jstring="[hyper(8214,a,13827,a),flip(a)].">
      <j1 rule="hyper" parents="8214 13827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13829">
    <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(4116(a,1),13827(a,2,1))].">
      <j1 rule="para" parents="4116 13827"/>
    </justification>
  </clause>

  <clause id="13830">
    <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(13828(a,1),6672(a,1))].">
      <j1 rule="para" parents="13828 6672"/>
    </justification>
  </clause>

  <clause id="13831">
    <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(13755(a,1),1422(a,1))].">
      <j1 rule="para" parents="13755 1422"/>
    </justification>
  </clause>

  <clause id="13832">
    <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(1422,a,13765,a),flip(a)].">
      <j1 rule="hyper" parents="1422 13765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13834">
    <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(1773(a,1),13832(a,1,2,2))].">
      <j1 rule="para" parents="1773 13832"/>
    </justification>
  </clause>

  <clause id="13835">
    <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,932,a(flip),b,13834,a)].">
      <j1 rule="hyper" parents="58 932 13834"/>
    </justification>
  </clause>

  <clause id="13836">
    <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,13751,a(flip),b,13835,a(flip))].">
      <j1 rule="hyper" parents="119 13751 13835"/>
    </justification>
  </clause>

  <clause id="13837">
    <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(13836(a,1),2889(a,2,1,1))].">
      <j1 rule="para" parents="13836 2889"/>
    </justification>
  </clause>

  <clause id="13838">
    <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(334,a,7207,a(flip),b,12830,a),flip(a)].">
      <j1 rule="hyper" parents="334 7207 12830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13839">
    <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,13792,a),flip(a)].">
      <j1 rule="hyper" parents="58 146 13792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13840">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),v5,v6)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(709,a,13839,a)].">
      <j1 rule="hyper" parents="709 13839"/>
    </justification>
  </clause>

  <clause id="13842">
    <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,3847,a(flip),b,13840,a)].">
      <j1 rule="hyper" parents="58 3847 13840"/>
    </justification>
  </clause>

  <clause id="13843">
    <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(334,a,13840,a,b,13842,a)].">
      <j1 rule="hyper" parents="334 13840 13842"/>
    </justification>
  </clause>

  <clause id="13844">
    <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(9277(a,1),13838(a,2,1,2))].">
      <j1 rule="para" parents="9277 13838"/>
    </justification>
  </clause>

  <clause id="13845">
    <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(7284(a,1),13844(a,2,1))].">
      <j1 rule="para" parents="7284 13844"/>
    </justification>
  </clause>

  <clause id="13846">
    <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(3461(a,1),13845(a,2,1,1))].">
      <j1 rule="para" parents="3461 13845"/>
    </justification>
  </clause>

  <clause id="13847">
    <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(6370(a,1),13846(a,2,2))].">
      <j1 rule="para" parents="6370 13846"/>
    </justification>
  </clause>

  <clause id="13848">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = 1
    ]]></literal>
    <justification jstring="[hyper(334,a,12304,a(flip),b,13847,a),flip(a)].">
      <j1 rule="hyper" parents="334 12304 13847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13850">
    <literal><![CDATA[
      K((x \ K(x,y)) * T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = 1
    ]]></literal>
    <justification jstring="[para(11797(a,1),13848(a,1,1))].">
      <j1 rule="para" parents="11797 13848"/>
    </justification>
  </clause>

  <clause id="13851">
    <literal><![CDATA[
      1 / (((x \ K(x,y)) \ 1) \ T(x,z)) = ((x \ K(x,y)) * T(x,z)) \ 1
    ]]></literal>
    <justification jstring="[para(13850(a,1),12466(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13850 12466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13852">
    <literal><![CDATA[
      1 / (((x \ K(x,y)) \ 1) \ T(x,z)) = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,12829,a(flip),b,13851,a),flip(a)].">
      <j1 rule="hyper" parents="334 12829 13851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13854">
    <literal><![CDATA[
      1 / (((x \ 1) \ K(y,x)) \ T(x,z)) = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[para(5878(a,1),13852(a,1,2,1))].">
      <j1 rule="para" parents="5878 13852"/>
    </justification>
  </clause>

  <clause id="13855">
    <literal><![CDATA[
      1 / ((x \ K(x,y)) * T(x,z)) = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[para(11797(a,1),13854(a,1,2))].">
      <j1 rule="para" parents="11797 13854"/>
    </justification>
  </clause>

  <clause id="13856">
    <literal><![CDATA[
      (x * (K(y,x) / T(x,z))) \ 1 = (x \ K(x,y)) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(192,a,13855,a)].">
      <j1 rule="hyper" parents="192 13855"/>
    </justification>
  </clause>

  <clause id="13857">
    <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(13856(a,1),3214(a,1,1,1))].">
      <j1 rule="para" parents="13856 3214"/>
    </justification>
  </clause>

  <clause id="13858">
    <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(190(a,1),12646(a,2,2))].">
      <j1 rule="para" parents="190 12646"/>
    </justification>
  </clause>

  <clause id="13859">
    <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(334,a,5009,a,b,13858,a),flip(a)].">
      <j1 rule="hyper" parents="334 5009 13858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13861">
    <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(334,a,8053,a,b,13859,a),flip(a)].">
      <j1 rule="hyper" parents="334 8053 13859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13862">
    <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(12669(a,1),13861(a,1,2))].">
      <j1 rule="para" parents="12669 13861"/>
    </justification>
  </clause>

  <clause id="13863">
    <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(11238,a,13862,a)].">
      <j1 rule="hyper" parents="11238 13862"/>
    </justification>
  </clause>

  <clause id="13864">
    <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(8050,a,13863,a)].">
      <j1 rule="hyper" parents="8050 13863"/>
    </justification>
  </clause>

  <clause id="13865">
    <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,7481,a(flip),b,13864,a)].">
      <j1 rule="hyper" parents="58 7481 13864"/>
    </justification>
  </clause>

  <clause id="13867">
    <literal><![CDATA[
      K(x,K(y * z,L(u,z,y))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[para(5185(a,1),13865(a,1,2))].">
      <j1 rule="para" parents="5185 13865"/>
    </justification>
  </clause>

  <clause id="13868">
    <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(10585(a,1),12968(a,1,1))].">
      <j1 rule="para" parents="10585 12968"/>
    </justification>
  </clause>

  <clause id="13870">
    <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,12643,a(flip),b,12487,a)].">
      <j1 rule="hyper" parents="58 12643 12487"/>
    </justification>
  </clause>

  <clause id="13871">
    <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(10137(a,1),13870(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10137 13870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13872">
    <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(8067(a,1),13871(a,2,2))].">
      <j1 rule="para" parents="8067 13871"/>
    </justification>
  </clause>

  <clause id="13874">
    <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(13867(a,1),13872(a,2,2))].">
      <j1 rule="para" parents="13867 13872"/>
    </justification>
  </clause>

  <clause id="13875">
    <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(8048(a,1),13874(a,2,2))].">
      <j1 rule="para" parents="8048 13874"/>
    </justification>
  </clause>

  <clause id="13876">
    <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(11089(a,1),13875(a,1,1,2))].">
      <j1 rule="para" parents="11089 13875"/>
    </justification>
  </clause>

  <clause id="13877">
    <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,10932,a,b,13876,a)].">
      <j1 rule="hyper" parents="58 10932 13876"/>
    </justification>
  </clause>

  <clause id="13878">
    <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(12069(a,1),13877(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12069 13877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13879">
    <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(13878(a,1),549(a,1))].">
      <j1 rule="para" parents="13878 549"/>
    </justification>
  </clause>

  <clause id="13880">
    <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(334,a,9983,a(flip),b,12783,a),flip(a)].">
      <j1 rule="hyper" parents="334 9983 12783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13882">
    <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(334,a,6201,a(flip),b,13880,a),flip(a)].">
      <j1 rule="hyper" parents="334 6201 13880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13883">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x * z,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13882(a,1),3829(a,1)),flip(b)].">
      <j1 rule="para" parents="13882 3829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13884">
    <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(12829(a,1),13857(a,1,1))].">
      <j1 rule="para" parents="12829 13857"/>
    </justification>
  </clause>

  <clause id="13885">
    <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(13856(a,1),13884(a,1,2,2))].">
      <j1 rule="para" parents="13856 13884"/>
    </justification>
  </clause>

  <clause id="13886">
    <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(8869(a,1),13885(a,1,2))].">
      <j1 rule="para" parents="8869 13885"/>
    </justification>
  </clause>

  <clause id="13887">
    <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(6332(a,1),13886(a,1,2))].">
      <j1 rule="para" parents="6332 13886"/>
    </justification>
  </clause>

  <clause id="13888">
    <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(13124(a,1),13887(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13124 13887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13889">
    <literal><![CDATA[
      ((((x \ K(x,y)) * T(x,z)) \ 1) \ 1) * u = (x * (K(y,x) / T(x,z))) \ u
    ]]></literal>
    <justification jstring="[para(13856(a,1),13888(a,1,1,1,1))].">
      <j1 rule="para" parents="13856 13888"/>
    </justification>
  </clause>

  <clause id="13890">
    <literal><![CDATA[
      ((x * (K(y,x) / T(x,z))) \ 1) * u = (x * (K(y,x) / T(x,z))) \ u
    ]]></literal>
    <justification jstring="[para(12829(a,1),13889(a,1,1,1))].">
      <j1 rule="para" parents="12829 13889"/>
    </justification>
  </clause>

  <clause id="13891">
    <literal><![CDATA[
      (x * (K(y,x) / T(x,z))) \ u = ((x \ K(x,y)) * T(x,z)) * u
    ]]></literal>
    <justification jstring="[para(13856(a,1),13890(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13856 13890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13892">
    <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(13891(a,1),9320(a,1,1))].">
      <j1 rule="para" parents="13891 9320"/>
    </justification>
  </clause>

  <clause id="13893">
    <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(8913(a,1),13892(a,1,2))].">
      <j1 rule="para" parents="8913 13892"/>
    </justification>
  </clause>

  <clause id="13894">
    <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,10052,a(flip),b,13893,a)].">
      <j1 rule="hyper" parents="58 10052 13893"/>
    </justification>
  </clause>

  <clause id="13895">
    <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(5090(a,1),13894(a,1,2))].">
      <j1 rule="para" parents="5090 13894"/>
    </justification>
  </clause>

  <clause id="13896">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ (T(x,z) * u) = ((x \ K(x,y)) * T(x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(11751,a,13895,a),flip(a)].">
      <j1 rule="hyper" parents="11751 13895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13898">
    <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(5878(a,1),9602(a,1,1,1))].">
      <j1 rule="para" parents="5878 9602"/>
    </justification>
  </clause>

  <clause id="13899">
    <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(13896(a,1),13898(a,1,1))].">
      <j1 rule="para" parents="13896 13898"/>
    </justification>
  </clause>

  <clause id="13900">
    <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(5695(a,1),13899(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5695 13899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13901">
    <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(5581(a,1),13900(a,2,2))].">
      <j1 rule="para" parents="5581 13900"/>
    </justification>
  </clause>

  <clause id="13902">
    <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(6148(a,1),13901(a,2,2))].">
      <j1 rule="para" parents="6148 13901"/>
    </justification>
  </clause>

  <clause id="13903">
    <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(8985(a,1),13902(a,2,2))].">
      <j1 rule="para" parents="8985 13902"/>
    </justification>
  </clause>

  <clause id="13904">
    <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),13903(a,2,2,1))].">
      <j1 rule="para" parents="4 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) * T(z,T(x * z,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,6432,a(flip),b,13904,a),flip(a)].">
      <j1 rule="hyper" parents="334 6432 13904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13907">
    <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(334,a,9305,a(flip),b,13905,a),flip(a)].">
      <j1 rule="hyper" parents="334 9305 13905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13908">
    <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(5878(a,1),13907(a,1,1,1))].">
      <j1 rule="para" parents="5878 13907"/>
    </justification>
  </clause>

  <clause id="13909">
    <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(13896(a,1),13908(a,1,1))].">
      <j1 rule="para" parents="13896 13908"/>
    </justification>
  </clause>

  <clause id="13910">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,x \ 1) * z) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(5695(a,1),13909(a,1,1,1))].">
      <j1 rule="para" parents="5695 13909"/>
    </justification>
  </clause>

  <clause id="13911">
    <literal><![CDATA[
      T(K(x,y) * z,x * z) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3925,a(flip),b,13910,a)].">
      <j1 rule="hyper" parents="58 3925 13910"/>
    </justification>
  </clause>

  <clause id="13912">
    <literal><![CDATA[
      T(K(x,y) * z,x * z) = T(z,z * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4553(a,1),13911(a,2,1))].">
      <j1 rule="para" parents="4553 13911"/>
    </justification>
  </clause>

  <clause id="13913">
    <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(13692(a,1),13912(a,2,2))].">
      <j1 rule="para" parents="13692 13912"/>
    </justification>
  </clause>

  <clause id="13914">
    <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(13692(a,1),13913(a,1,1,1))].">
      <j1 rule="para" parents="13692 13913"/>
    </justification>
  </clause>

  <clause id="13915">
    <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(1751(a,1),13800(a,2,1))].">
      <j1 rule="para" parents="1751 13800"/>
    </justification>
  </clause>

  <clause id="13916">
    <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(334,a,13243,a(flip),b,13915,a),flip(a)].">
      <j1 rule="hyper" parents="334 13243 13915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13918">
    <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(9410(a,1),13916(a,1,1))].">
      <j1 rule="para" parents="9410 13916"/>
    </justification>
  </clause>

  <clause id="13919">
    <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,10057,a(flip),b,13918,a)].">
      <j1 rule="hyper" parents="58 10057 13918"/>
    </justification>
  </clause>

  <clause id="13920">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x * a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,13768,a(flip),b,13919,a),flip(a)].">
      <j1 rule="hyper" parents="58 13768 13919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13921">
    <literal><![CDATA[
      T(T(x,a(y,z,u) \ x),x * u) = T(x,L(u * x,z,y))
    ]]></literal>
    <justification jstring="[para(13920(a,2),11930(a,1,1))].">
      <j1 rule="para" parents="13920 11930"/>
    </justification>
  </clause>

  <clause id="13922">
    <literal><![CDATA[
      T(T(x,x * y),a(z,u,y) \ x) = T(x,L(y * x,u,z))
    ]]></literal>
    <justification jstring="[hyper(447,a,13921,a)].">
      <j1 rule="hyper" parents="447 13921"/>
    </justification>
  </clause>

  <clause id="13923">
    <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(5606(a,1),8388(a,1,1))].">
      <j1 rule="para" parents="5606 8388"/>
    </justification>
  </clause>

  <clause id="13924">
    <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(269(a,1),13923(a,1,1,2,2))].">
      <j1 rule="para" parents="269 13923"/>
    </justification>
  </clause>

  <clause id="13925">
    <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(3550(a,1),10192(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3550 10192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13926">
    <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(2306(a,1),13925(a,2,2,2))].">
      <j1 rule="para" parents="2306 13925"/>
    </justification>
  </clause>

  <clause id="13928">
    <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(12358(a,1),13926(a,2,2))].">
      <j1 rule="para" parents="12358 13926"/>
    </justification>
  </clause>

  <clause id="13929">
    <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(334,a,5391,a(flip),b,13928,a),flip(a)].">
      <j1 rule="hyper" parents="334 5391 13928"/>
      <j2 rule="flip"/>
    </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)))) = (T(L(y,z,u),x) \ 1) * L((y \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,6025,a(flip),b,13929,a),flip(a)].">
      <j1 rule="hyper" parents="334 6025 13929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13931">
    <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(3550(a,1),13930(a,1,2,2,2))].">
      <j1 rule="para" parents="3550 13930"/>
    </justification>
  </clause>

  <clause id="13933">
    <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(5391(a,1),13931(a,1,2,2))].">
      <j1 rule="para" parents="5391 13931"/>
    </justification>
  </clause>

  <clause id="13934">
    <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(10940(a,1),13933(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10940 13933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13935">
    <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(334,a,11450,a(flip),b,13934,a),flip(a)].">
      <j1 rule="hyper" parents="334 11450 13934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13936">
    <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(202(a,1),13935(a,2,2))].">
      <j1 rule="para" parents="202 13935"/>
    </justification>
  </clause>

  <clause id="13937">
    <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(3656(a,1),10214(a,1,2,1,2,2,2))].">
      <j1 rule="para" parents="3656 10214"/>
    </justification>
  </clause>

  <clause id="13938">
    <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(3922(a,1),13937(a,1,2,1,2,2))].">
      <j1 rule="para" parents="3922 13937"/>
    </justification>
  </clause>

  <clause id="13939">
    <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(8048(a,1),13938(a,1,2,1))].">
      <j1 rule="para" parents="8048 13938"/>
    </justification>
  </clause>

  <clause id="13940">
    <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(8892(a,1),13939(a,1,2,1,2))].">
      <j1 rule="para" parents="8892 13939"/>
    </justification>
  </clause>

  <clause id="13941">
    <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(7796(a,1),13940(a,1,2,1,2))].">
      <j1 rule="para" parents="7796 13940"/>
    </justification>
  </clause>

  <clause id="13943">
    <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(8461(a,1),13941(a,1,2,1))].">
      <j1 rule="para" parents="8461 13941"/>
    </justification>
  </clause>

  <clause id="13944">
    <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(3656(a,1),13943(a,1,2,2,1,2,1,2,2))].">
      <j1 rule="para" parents="3656 13943"/>
    </justification>
  </clause>

  <clause id="13945">
    <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(3922(a,1),13944(a,1,2,2,1,2,1,2))].">
      <j1 rule="para" parents="3922 13944"/>
    </justification>
  </clause>

  <clause id="13946">
    <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(8019(a,1),13945(a,1,2,2,1,2))].">
      <j1 rule="para" parents="8019 13945"/>
    </justification>
  </clause>

  <clause id="13947">
    <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(10220(a,1),13946(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="10220 13946"/>
    </justification>
  </clause>

  <clause id="13948">
    <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(7536(a,1),13947(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="7536 13947"/>
    </justification>
  </clause>

  <clause id="13950">
    <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(8444(a,1),13948(a,1,2,2,1,2))].">
      <j1 rule="para" parents="8444 13948"/>
    </justification>
  </clause>

  <clause id="13951">
    <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(4998(a,2),13950(a,1,2,2,1))].">
      <j1 rule="para" parents="4998 13950"/>
    </justification>
  </clause>

  <clause id="13952">
    <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(9718(a,2),13951(a,1,2))].">
      <j1 rule="para" parents="9718 13951"/>
    </justification>
  </clause>

  <clause id="13953">
    <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,9714,a(flip),b,13952,a)].">
      <j1 rule="hyper" parents="58 9714 13952"/>
    </justification>
  </clause>

  <clause id="13954">
    <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(1556(a,1),13953(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1556 13953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13955">
    <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(334,a,8094,a(flip),b,13954,a),flip(a)].">
      <j1 rule="hyper" parents="334 8094 13954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13956">
    <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(1241(a,1),13955(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1241 13955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13957">
    <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,12247,a,b,13956,a)].">
      <j1 rule="hyper" parents="58 12247 13956"/>
    </justification>
  </clause>

  <clause id="13958">
    <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(1241(a,1),13957(a,1,1))].">
      <j1 rule="para" parents="1241 13957"/>
    </justification>
  </clause>

  <clause id="13959">
    <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(13958(a,1),12384(a,1,2))].">
      <j1 rule="para" parents="13958 12384"/>
    </justification>
  </clause>

  <clause id="13960">
    <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(12385,a,13959,a),flip(a)].">
      <j1 rule="hyper" parents="12385 13959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13961">
    <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(334,a,8053,a,b,13960,a),flip(a)].">
      <j1 rule="hyper" parents="334 8053 13960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13962">
    <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,12233,a(flip),b,13961,a)].">
      <j1 rule="hyper" parents="58 12233 13961"/>
    </justification>
  </clause>

  <clause id="13963">
    <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(334,a,8048,a,b,13962,a),flip(a)].">
      <j1 rule="hyper" parents="334 8048 13962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13964">
    <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(12234,a,13963,a)].">
      <j1 rule="hyper" parents="12234 13963"/>
    </justification>
  </clause>

  <clause id="13965">
    <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,13805,a,b,13964,a)].">
      <j1 rule="hyper" parents="58 13805 13964"/>
    </justification>
  </clause>

  <clause id="13966">
    <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(334,a,12014,a(flip),b,13965,a),flip(a)].">
      <j1 rule="hyper" parents="334 12014 13965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13967">
    <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(8319,a,13966,a)].">
      <j1 rule="hyper" parents="8319 13966"/>
    </justification>
  </clause>

  <clause id="13968">
    <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(13966(a,1),8319(a,1))].">
      <j1 rule="para" parents="13966 8319"/>
    </justification>
  </clause>

  <clause id="13969">
    <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(8555,a,13967,a)].">
      <j1 rule="hyper" parents="8555 13967"/>
    </justification>
  </clause>

  <clause id="13970">
    <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,12474,a,b,13969,a)].">
      <j1 rule="hyper" parents="58 12474 13969"/>
    </justification>
  </clause>

  <clause id="13971">
    <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(9564,a,13970,a)].">
      <j1 rule="hyper" parents="9564 13970"/>
    </justification>
  </clause>

  <clause id="13972">
    <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,13171,a(flip),b,13971,a)].">
      <j1 rule="hyper" parents="58 13171 13971"/>
    </justification>
  </clause>

  <clause id="13973">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = a(K(y,K(x,z * u)),z,u)
    ]]></literal>
    <justification jstring="[para(9513(a,1),13972(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9513 13972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13974">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(334,a,12183,a(flip),b,13973,a),flip(a)].">
      <j1 rule="hyper" parents="334 12183 13973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13975">
    <literal><![CDATA[
      K(x,K(a(y,z,u),y * (z * u))) = 1
    ]]></literal>
    <justification jstring="[hyper(13968,a,13974,a)].">
      <j1 rule="hyper" parents="13968 13974"/>
    </justification>
  </clause>

  <clause id="13978">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,a(y,z,u)) * 1
    ]]></literal>
    <justification jstring="[para(13975(a,1),10005(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13975 10005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13979">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,3,a(flip),b,13978,a),flip(a)].">
      <j1 rule="hyper" parents="334 3 13978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13981">
    <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,9539,a,b,13979,a)].">
      <j1 rule="hyper" parents="58 9539 13979"/>
    </justification>
  </clause>

  <clause id="13982">
    <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(13143(a,2),13981(a,1,1))].">
      <j1 rule="para" parents="13143 13981"/>
    </justification>
  </clause>

  <clause id="13983">
    <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,13110,a,b,13982,a)].">
      <j1 rule="hyper" parents="58 13110 13982"/>
    </justification>
  </clause>

  <clause id="13984">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,13112,a(flip),b,13983,a)].">
      <j1 rule="hyper" parents="58 13112 13983"/>
    </justification>
  </clause>

  <clause id="13986">
    <literal><![CDATA[
      a(K(x,y),z,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12806,a(flip),b,13984,a)].">
      <j1 rule="hyper" parents="58 12806 13984"/>
    </justification>
  </clause>

  <clause id="13987">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,13702,a,b,13986,a),flip(a)].">
      <j1 rule="hyper" parents="334 13702 13986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13988">
    <literal><![CDATA[
      a(K(x,y),z,z \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(334,a,10789,a(flip),b,13987,a),flip(a)].">
      <j1 rule="hyper" parents="334 10789 13987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13989">
    <literal><![CDATA[
      a(K(x * y,z),x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(334,a,10787,a(flip),b,13987,a),flip(a)].">
      <j1 rule="hyper" parents="334 10787 13987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13990">
    <literal><![CDATA[
      x * a(K(y,z),u,w) = x * a(z,u,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,13987,a,b,4,a)].">
      <j1 rule="hyper" parents="119 13987 4"/>
    </justification>
  </clause>

  <clause id="13991">
    <literal><![CDATA[
      a(x,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,5733,a(flip),b,13987,a),flip(a)].">
      <j1 rule="hyper" parents="58 5733 13987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13992">
    <literal><![CDATA[
      a(x,y,K(z,u)) != 1
    ]]></literal>
    <literal><![CDATA[
      L(u,y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(13987(a,1),47(a,1))].">
      <j1 rule="para" parents="13987 47"/>
    </justification>
  </clause>

  <clause id="13993">
    <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(13987(a,1),12299(a,1,1,2))].">
      <j1 rule="para" parents="13987 12299"/>
    </justification>
  </clause>

  <clause id="13994">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(13987(a,2),13703(a,1))].">
      <j1 rule="para" parents="13987 13703"/>
    </justification>
  </clause>

  <clause id="13995">
    <literal><![CDATA[
      a(x * y,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(13883,a,13991,a)].">
      <j1 rule="hyper" parents="13883 13991"/>
    </justification>
  </clause>

  <clause id="13996">
    <literal><![CDATA[
      L(K(x,y),z,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6202,a,13991,a)].">
      <j1 rule="hyper" parents="6202 13991"/>
    </justification>
  </clause>

  <clause id="13999">
    <literal><![CDATA[
      a(x,y,K(z,x * y)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,11563,a(flip),b,13988,a)].">
      <j1 rule="hyper" parents="58 11563 13988"/>
    </justification>
  </clause>

  <clause id="14000">
    <literal><![CDATA[
      L(x \ y,x,K(y,z)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(47,a,13988,a)].">
      <j1 rule="hyper" parents="47 13988"/>
    </justification>
  </clause>

  <clause id="14001">
    <literal><![CDATA[
      (x / y) * (y * K(x,z)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(171,a,11558,a,b,13988,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="171 11558 13988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14002">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(171,a,10503,a,b,13988,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="171 10503 13988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14003">
    <literal><![CDATA[
      L(x,y,K(y * x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,13989,a)].">
      <j1 rule="hyper" parents="47 13989"/>
    </justification>
  </clause>

  <clause id="14004">
    <literal><![CDATA[
      K(x,(y \ z) \ y) = K(x,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6848,a(flip),b,13996,a),flip(a)].">
      <j1 rule="hyper" parents="58 6848 13996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14006">
    <literal><![CDATA[
      (x * y) * K(z,x * y) = x * (y * K(z,x * y))
    ]]></literal>
    <justification jstring="[hyper(214,a,13999,a)].">
      <j1 rule="hyper" parents="214 13999"/>
    </justification>
  </clause>

  <clause id="14007">
    <literal><![CDATA[
      a(x,y,K(x * y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,11337,a(flip),b,13999,a)].">
      <j1 rule="hyper" parents="58 11337 13999"/>
    </justification>
  </clause>

  <clause id="14008">
    <literal><![CDATA[
      a(x,x \ y,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[para(5(a,1),13999(a,1,3,2))].">
      <j1 rule="para" parents="5 13999"/>
    </justification>
  </clause>

  <clause id="14009">
    <literal><![CDATA[
      a(x,y,K(z,y * x)) = 1
    ]]></literal>
    <justification jstring="[para(12548(a,1),13999(a,1,3))].">
      <j1 rule="para" parents="12548 13999"/>
    </justification>
  </clause>

  <clause id="14010">
    <literal><![CDATA[
      L(x,y,K(z,y * x)) = x
    ]]></literal>
    <justification jstring="[hyper(12999,a,14003,a)].">
      <j1 rule="hyper" parents="12999 14003"/>
    </justification>
  </clause>

  <clause id="14011">
    <literal><![CDATA[
      T(x * y,L(z,y,x)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(11200,a,14007,a)].">
      <j1 rule="hyper" parents="11200 14007"/>
    </justification>
  </clause>

  <clause id="14012">
    <literal><![CDATA[
      a(x,x \ y,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[para(5(a,1),14007(a,1,3,1))].">
      <j1 rule="para" parents="5 14007"/>
    </justification>
  </clause>

  <clause id="14013">
    <literal><![CDATA[
      a(x,y,K(y * x,z)) = 1
    ]]></literal>
    <justification jstring="[para(12516(a,1),14007(a,1,3))].">
      <j1 rule="para" parents="12516 14007"/>
    </justification>
  </clause>

  <clause id="14014">
    <literal><![CDATA[
      x * ((x \ y) * K(z,y)) = y * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(928,a,14008,a)].">
      <j1 rule="hyper" parents="928 14008"/>
    </justification>
  </clause>

  <clause id="14015">
    <literal><![CDATA[
      (x * y) * K(z,y * x) = x * (y * K(z,y * x))
    ]]></literal>
    <justification jstring="[hyper(214,a,14009,a)].">
      <j1 rule="hyper" parents="214 14009"/>
    </justification>
  </clause>

  <clause id="14016">
    <literal><![CDATA[
      a(x,y,K(z,z * (y * x))) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,11332,a,b,14009,a)].">
      <j1 rule="hyper" parents="58 11332 14009"/>
    </justification>
  </clause>

  <clause id="14017">
    <literal><![CDATA[
      L(x,y,K(z,x * y)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,12556,a,b,14010,a)].">
      <j1 rule="hyper" parents="58 12556 14010"/>
    </justification>
  </clause>

  <clause id="14018">
    <literal><![CDATA[
      L(x \ y,x,K(z,y)) = x \ y
    ]]></literal>
    <justification jstring="[para(5(a,1),14010(a,1,3,2))].">
      <j1 rule="para" parents="5 14010"/>
    </justification>
  </clause>

  <clause id="14019">
    <literal><![CDATA[
      T(x,L(y,z \ x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(11200,a,14012,a)].">
      <j1 rule="hyper" parents="11200 14012"/>
    </justification>
  </clause>

  <clause id="14020">
    <literal><![CDATA[
      T(x * y,L(z,x,y)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(11200,a,14013,a)].">
      <j1 rule="hyper" parents="11200 14013"/>
    </justification>
  </clause>

  <clause id="14021">
    <literal><![CDATA[
      L(x,x \ y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(5(a,1),14017(a,1,3,2))].">
      <j1 rule="para" parents="5 14017"/>
    </justification>
  </clause>

  <clause id="14022">
    <literal><![CDATA[
      (K(x,y) * z) \ T(x,y) = z \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,5121,a(flip),b,14000,a)].">
      <j1 rule="hyper" parents="58 5121 14000"/>
    </justification>
  </clause>

  <clause id="14023">
    <literal><![CDATA[
      L(x \ (y \ z),x,K(y,z)) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(12999,a,14018,a)].">
      <j1 rule="hyper" parents="12999 14018"/>
    </justification>
  </clause>

  <clause id="14024">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,14018,a(flip),b,2534,a(flip))].">
      <j1 rule="hyper" parents="119 14018 2534"/>
    </justification>
  </clause>

  <clause id="14025">
    <literal><![CDATA[
      (x \ y) * K(y,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,14019,a(flip),b,11224,a),flip(a)].">
      <j1 rule="hyper" parents="116 14019 11224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14026">
    <literal><![CDATA[
      T(x,(y \ x) \ z) = T(x,x \ (y * z))
    ]]></literal>
    <justification jstring="[para(502(a,1),14019(a,1,2)),flip(a)].">
      <j1 rule="para" parents="502 14019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14027">
    <literal><![CDATA[
      K(x,T(y,z) * L(z,u \ y,u)) = K(x,L(z,u \ y,u) * y)
    ]]></literal>
    <justification jstring="[para(14019(a,1),12576(a,1,2,1))].">
      <j1 rule="para" parents="14019 12576"/>
    </justification>
  </clause>

  <clause id="14028">
    <literal><![CDATA[
      T(x,y) / (z * K(x,y)) = x / z
    ]]></literal>
    <justification jstring="[hyper(130,a,14001,a)].">
      <j1 rule="hyper" parents="130 14001"/>
    </justification>
  </clause>

  <clause id="14029">
    <literal><![CDATA[
      (x / y) \ T(x,z) = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,14001,a)].">
      <j1 rule="hyper" parents="123 14001"/>
    </justification>
  </clause>

  <clause id="14030">
    <literal><![CDATA[
      T(x,y) / (z \ x) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(117,a,14001,a(flip),b,11557,a)].">
      <j1 rule="hyper" parents="117 14001 11557"/>
    </justification>
  </clause>

  <clause id="14031">
    <literal><![CDATA[
      T(x,y) * K(x * y,z) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,14001,a(flip),b,4913,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 14001 4913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14032">
    <literal><![CDATA[
      x * (y * K(x * y,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),14001(a,1,1))].">
      <j1 rule="para" parents="6 14001"/>
    </justification>
  </clause>

  <clause id="14033">
    <literal><![CDATA[
      (x / (y / z)) * (y / T(z,x)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(6368(a,1),14001(a,1,2))].">
      <j1 rule="para" parents="6368 14001"/>
    </justification>
  </clause>

  <clause id="14034">
    <literal><![CDATA[
      K(x,y) * (x / z) = T(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(365,a,14002,a),flip(a)].">
      <j1 rule="hyper" parents="365 14002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14036">
    <literal><![CDATA[
      (T(x,y) \ z) * ((x \ z) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[para(5392(a,1),14002(a,1,1))].">
      <j1 rule="para" parents="5392 14002"/>
    </justification>
  </clause>

  <clause id="14038">
    <literal><![CDATA[
      K(x,y) * (1 / z) = K(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(34,a,11906,a,b,14022,a),flip(a)].">
      <j1 rule="hyper" parents="34 11906 14022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14039">
    <literal><![CDATA[
      (K(x,y) \ z) \ T(y,x) = z \ y
    ]]></literal>
    <justification jstring="[para(5391(a,2),14022(a,1,1))].">
      <j1 rule="para" parents="5391 14022"/>
    </justification>
  </clause>

  <clause id="14040">
    <literal><![CDATA[
      (K(x,y) * z) \ y = z \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5394(a,1),14022(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5394 14022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14041">
    <literal><![CDATA[
      (T(x,y) * z) \ y = (x * z) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5091(a,1),14022(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5091 14022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14042">
    <literal><![CDATA[
      ((x / T(y,x)) * z) \ T(x,y) = ((x / y) * z) \ x
    ]]></literal>
    <justification jstring="[para(12903(a,1),14022(a,1,1))].">
      <j1 rule="para" parents="12903 14022"/>
    </justification>
  </clause>

  <clause id="14043">
    <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(14022(a,1),13778(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="14022 13778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14044">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ x) = z \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(9010,a,14025,a)].">
      <j1 rule="hyper" parents="9010 14025"/>
    </justification>
  </clause>

  <clause id="14045">
    <literal><![CDATA[
      x \ T(y,T(z,x)) = K(y,z) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(8516,a,14025,a),flip(a)].">
      <j1 rule="hyper" parents="8516 14025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14046">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(6527,a,14025,a)].">
      <j1 rule="hyper" parents="6527 14025"/>
    </justification>
  </clause>

  <clause id="14048">
    <literal><![CDATA[
      (x \ y) \ (x \ T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,14025,a)].">
      <j1 rule="hyper" parents="123 14025"/>
    </justification>
  </clause>

  <clause id="14050">
    <literal><![CDATA[
      (x \ T(y,z)) / (x \ y) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(117,a,14025,a(flip),b,8517,a)].">
      <j1 rule="hyper" parents="117 14025 8517"/>
    </justification>
  </clause>

  <clause id="14051">
    <literal><![CDATA[
      (x \ T(y,z)) / T(y,z) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,14025,a(flip),b,6467,a)].">
      <j1 rule="hyper" parents="117 14025 6467"/>
    </justification>
  </clause>

  <clause id="14052">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K(x * y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),14025(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 14025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14054">
    <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),14025(a,2,2))].">
      <j1 rule="para" parents="20 14025"/>
    </justification>
  </clause>

  <clause id="14056">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(K(x,y),z \ x) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(14025(a,1),5836(a,2,1))].">
      <j1 rule="para" parents="14025 5836"/>
    </justification>
  </clause>

  <clause id="14059">
    <literal><![CDATA[
      T(x \ T(y,z),K(z,y)) = K(y,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(14025(a,1),6522(a,1,1))].">
      <j1 rule="para" parents="14025 6522"/>
    </justification>
  </clause>

  <clause id="14060">
    <literal><![CDATA[
      K(x * (y \ T(z,u)),z) = K(x * (y \ z),z)
    ]]></literal>
    <justification jstring="[para(14025(a,1),7669(a,1,1,2))].">
      <j1 rule="para" parents="14025 7669"/>
    </justification>
  </clause>

  <clause id="14061">
    <literal><![CDATA[
      (x \ y) / (x \ T(y,z)) = K(z,T(y,x \ y))
    ]]></literal>
    <justification jstring="[para(14025(a,1),8271(a,1,2))].">
      <j1 rule="para" parents="14025 8271"/>
    </justification>
  </clause>

  <clause id="14063">
    <literal><![CDATA[
      x / (y * K(z,x)) = T(x,z) / y
    ]]></literal>
    <justification jstring="[para(6516(a,1),14028(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6516 14028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14064">
    <literal><![CDATA[
      (1 / x) \ K(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11903,a,b,14029,a)].">
      <j1 rule="hyper" parents="58 11903 14029"/>
    </justification>
  </clause>

  <clause id="14067">
    <literal><![CDATA[
      K(x,y) * (1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / z = u
    ]]></literal>
    <justification jstring="[para(14030(a,1),11910(a,1))].">
      <j1 rule="para" parents="14030 11910"/>
    </justification>
  </clause>

  <clause id="14068">
    <literal><![CDATA[
      K(x,y) \ (y / z) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(5431,a,14034,a)].">
      <j1 rule="hyper" parents="5431 14034"/>
    </justification>
  </clause>

  <clause id="14069">
    <literal><![CDATA[
      K(x,y) * (T(y,x) / z) = y / z
    ]]></literal>
    <justification jstring="[hyper(5409,a,14034,a)].">
      <j1 rule="hyper" parents="5409 14034"/>
    </justification>
  </clause>

  <clause id="14071">
    <literal><![CDATA[
      (x / y) \ (T(x,z) / y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,14034,a(flip),b,8827,a)].">
      <j1 rule="hyper" parents="116 14034 8827"/>
    </justification>
  </clause>

  <clause id="14072">
    <literal><![CDATA[
      (T(x,y) / z) \ K(K(x,y),x / z) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(14034(a,1),5836(a,1,1))].">
      <j1 rule="para" parents="14034 5836"/>
    </justification>
  </clause>

  <clause id="14073">
    <literal><![CDATA[
      T(T(x,y) / z,K(x,y)) = (x / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(14034(a,1),6535(a,1,1))].">
      <j1 rule="para" parents="14034 6535"/>
    </justification>
  </clause>

  <clause id="14075">
    <literal><![CDATA[
      K(x,y) * (K(y,x) / z) = 1 / z
    ]]></literal>
    <justification jstring="[hyper(5409,a,14038,a)].">
      <j1 rule="hyper" parents="5409 14038"/>
    </justification>
  </clause>

  <clause id="14077">
    <literal><![CDATA[
      K(x,T(y,z)) / z = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8521,a(flip),b,14038,a),flip(a)].">
      <j1 rule="hyper" parents="58 8521 14038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14078">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3075,a,14038,a(flip))].">
      <j1 rule="hyper" parents="3075 14038"/>
    </justification>
  </clause>

  <clause id="14079">
    <literal><![CDATA[
      (x * y) * (K(y,x) / z) = (y * x) * (1 / z)
    ]]></literal>
    <justification jstring="[hyper(119,a,14038,a(flip),b,11464,a)].">
      <j1 rule="hyper" parents="119 14038 11464"/>
    </justification>
  </clause>

  <clause id="14080">
    <literal><![CDATA[
      K(x,y) / (z \ 1) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(72(a,1),14038(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 14038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14081">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(14038(a,1),6535(a,1,1))].">
      <j1 rule="para" parents="14038 6535"/>
    </justification>
  </clause>

  <clause id="14082">
    <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(14038(a,1),6190(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="14038 6190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14083">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(12802,a,14078,a)].">
      <j1 rule="hyper" parents="12802 14078"/>
    </justification>
  </clause>

  <clause id="14084">
    <literal><![CDATA[
      K(R(x,y,y \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,12786,a(flip),b,14078,a)].">
      <j1 rule="hyper" parents="58 12786 14078"/>
    </justification>
  </clause>

  <clause id="14085">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,12636,a(flip),b,14078,a)].">
      <j1 rule="hyper" parents="58 12636 14078"/>
    </justification>
  </clause>

  <clause id="14086">
    <literal><![CDATA[
      (K(x,y) * z) \ K(x,y) = z \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,14078,a(flip),b,269,a)].">
      <j1 rule="hyper" parents="116 14078 269"/>
    </justification>
  </clause>

  <clause id="14088">
    <literal><![CDATA[
      T(x,R(y,z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,14083,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 14083 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14089">
    <literal><![CDATA[
      K(x,y * (z \ 1)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(536(a,1),14083(a,1,2))].">
      <j1 rule="para" parents="536 14083"/>
    </justification>
  </clause>

  <clause id="14093">
    <literal><![CDATA[
      K(x * (y \ 1),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(536(a,1),14084(a,1,1))].">
      <j1 rule="para" parents="536 14084"/>
    </justification>
  </clause>

  <clause id="14094">
    <literal><![CDATA[
      K(x,L(y,z,z \ x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11893,a,14085,a)].">
      <j1 rule="hyper" parents="11893 14085"/>
    </justification>
  </clause>

  <clause id="14095">
    <literal><![CDATA[
      K(L(x,y,y \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(11213,a,14085,a)].">
      <j1 rule="hyper" parents="11213 14085"/>
    </justification>
  </clause>

  <clause id="14096">
    <literal><![CDATA[
      L(K(x,y),z,z \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11091,a,14085,a)].">
      <j1 rule="hyper" parents="11091 14085"/>
    </justification>
  </clause>

  <clause id="14098">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,L(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(334,a,14078,a,b,14085,a)].">
      <j1 rule="hyper" parents="334 14078 14085"/>
    </justification>
  </clause>

  <clause id="14100">
    <literal><![CDATA[
      T(x,L(y,z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,14085,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 14085 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14101">
    <literal><![CDATA[
      a(x \ 1,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,14085,a,b,11117,a),flip(a)].">
      <j1 rule="hyper" parents="115 14085 11117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14102">
    <literal><![CDATA[
      K(x,L(y,z \ x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11894,a(flip),b,14085,a)].">
      <j1 rule="hyper" parents="58 11894 14085"/>
    </justification>
  </clause>

  <clause id="14103">
    <literal><![CDATA[
      (K(x,y) * z) \ 1 = z \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,14085,a(flip),b,13184,a),flip(a)].">
      <j1 rule="hyper" parents="116 14085 13184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14104">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(3153(a,1),14085(a,1,2))].">
      <j1 rule="para" parents="3153 14085"/>
    </justification>
  </clause>

  <clause id="14105">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3158(a,1),14085(a,1,2))].">
      <j1 rule="para" parents="3158 14085"/>
    </justification>
  </clause>

  <clause id="14106">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3166(a,1),14085(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3166 14085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14107">
    <literal><![CDATA[
      K(x,L((1 / y) * z,u,w)) = K(x,L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(3156(a,1),14085(a,1,2))].">
      <j1 rule="para" parents="3156 14085"/>
    </justification>
  </clause>

  <clause id="14109">
    <literal><![CDATA[
      T(x,a(y \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(13708,a,14101,a)].">
      <j1 rule="hyper" parents="13708 14101"/>
    </justification>
  </clause>

  <clause id="14110">
    <literal><![CDATA[
      a(1 / x,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,4354,a,b,14101,a)].">
      <j1 rule="hyper" parents="58 4354 14101"/>
    </justification>
  </clause>

  <clause id="14111">
    <literal><![CDATA[
      a(x,x \ 1,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,4355,a(flip),b,14101,a)].">
      <j1 rule="hyper" parents="58 4355 14101"/>
    </justification>
  </clause>

  <clause id="14112">
    <literal><![CDATA[
      x / a(y \ 1,y,z) = a(y \ 1,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(2685,a,14109,a),flip(a)].">
      <j1 rule="hyper" parents="2685 14109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14114">
    <literal><![CDATA[
      L(K(x,y),z \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6202,a,14111,a)].">
      <j1 rule="hyper" parents="6202 14111"/>
    </justification>
  </clause>

  <clause id="14116">
    <literal><![CDATA[
      R(x,y,y \ 1) * T(z,x) = z * R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,14088,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 14088 17"/>
    </justification>
  </clause>

  <clause id="14117">
    <literal><![CDATA[
      T(x,y * (z \ 1)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(536(a,1),14088(a,1,2))].">
      <j1 rule="para" parents="536 14088"/>
    </justification>
  </clause>

  <clause id="14118">
    <literal><![CDATA[
      T(x,R(y,z \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3001(a,1),14088(a,1,2))].">
      <j1 rule="para" parents="3001 14088"/>
    </justification>
  </clause>

  <clause id="14120">
    <literal><![CDATA[
      ((x / y) * (y * z)) \ K(x,z) = (L(z,y,y \ x) * x) \ 1
    ]]></literal>
    <justification jstring="[para(14094(a,1),11439(a,1,2))].">
      <j1 rule="para" parents="14094 11439"/>
    </justification>
  </clause>

  <clause id="14121">
    <literal><![CDATA[
      K((1 / x) * y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(3153(a,1),14095(a,1,1))].">
      <j1 rule="para" parents="3153 14095"/>
    </justification>
  </clause>

  <clause id="14124">
    <literal><![CDATA[
      K((x \ 1) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(3166(a,1),14095(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3166 14095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14125">
    <literal><![CDATA[
      K(x,y) / (z * K(x,y)) = 1 / z
    ]]></literal>
    <justification jstring="[hyper(117,a,14096,a(flip),b,3146,a)].">
      <j1 rule="hyper" parents="117 14096 3146"/>
    </justification>
  </clause>

  <clause id="14127">
    <literal><![CDATA[
      L(x,y,y \ 1) * T(z,x) = z * L(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,14100,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 14100 17"/>
    </justification>
  </clause>

  <clause id="14128">
    <literal><![CDATA[
      T(x,(1 / y) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(3153(a,1),14100(a,1,2))].">
      <j1 rule="para" parents="3153 14100"/>
    </justification>
  </clause>

  <clause id="14129">
    <literal><![CDATA[
      T(x,T((1 / y) * z,u)) = T(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(3157(a,1),14100(a,1,2))].">
      <j1 rule="para" parents="3157 14100"/>
    </justification>
  </clause>

  <clause id="14130">
    <literal><![CDATA[
      T(x,(y \ 1) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(3166(a,1),14100(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3166 14100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14131">
    <literal><![CDATA[
      K(x,(y * z) \ x) = K(x,z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(11124,a,14102,a)].">
      <j1 rule="hyper" parents="11124 14102"/>
    </justification>
  </clause>

  <clause id="14133">
    <literal><![CDATA[
      K(x * y,L(z,y,x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),14102(a,1,2,2))].">
      <j1 rule="para" parents="4 14102"/>
    </justification>
  </clause>

  <clause id="14134">
    <literal><![CDATA[
      K(x,(y \ x) \ z) = K(x,x \ (y * z))
    ]]></literal>
    <justification jstring="[para(502(a,1),14102(a,1,2)),flip(a)].">
      <j1 rule="para" parents="502 14102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14135">
    <literal><![CDATA[
      K(x,(y * z) \ 1) = K(x,z \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(11124,a,14105,a)].">
      <j1 rule="hyper" parents="11124 14105"/>
    </justification>
  </clause>

  <clause id="14137">
    <literal><![CDATA[
      K(x,y * ((1 / y) * z)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5595,a,b,14105,a)].">
      <j1 rule="hyper" parents="58 5595 14105"/>
    </justification>
  </clause>

  <clause id="14138">
    <literal><![CDATA[
      x \ K(y,T(z,x)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,14105,a(flip),b,11211,a(flip))].">
      <j1 rule="hyper" parents="116 14105 11211"/>
    </justification>
  </clause>

  <clause id="14139">
    <literal><![CDATA[
      K(x,T((y \ 1) \ z,u)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(624(a,1),14105(a,1,2)),flip(a)].">
      <j1 rule="para" parents="624 14105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14140">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) = K(x,L(y * z,u,w))
    ]]></literal>
    <justification jstring="[para(626(a,1),14105(a,1,2)),flip(a)].">
      <j1 rule="para" parents="626 14105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14141">
    <literal><![CDATA[
      (x \ 1) * K(y,z) = x \ K(y,z)
    ]]></literal>
    <justification jstring="[para(14105(a,1),11111(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14105 11111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14142">
    <literal><![CDATA[
      L(K(x,y),z \ 1,z) = u \ (u * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,4,a,b,14114,a),flip(a)].">
      <j1 rule="hyper" parents="334 4 14114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14143">
    <literal><![CDATA[
      K((x \ y) \ z,y) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11246,a(flip),b,14114,a),flip(a)].">
      <j1 rule="hyper" parents="58 11246 14114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14144">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(2942(a,1),14118(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2942 14118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14145">
    <literal><![CDATA[
      (K(x,y) \ z) \ (y * x) = z \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,13121,a(flip),b,14039,a)].">
      <j1 rule="hyper" parents="58 13121 14039"/>
    </justification>
  </clause>

  <clause id="14146">
    <literal><![CDATA[
      T(x \ T(y,z),(K(z,y) * x) \ y) = (K(z,y) * x) \ y
    ]]></literal>
    <justification jstring="[hyper(455,a,xx,b,14040,a)].">
      <j1 rule="hyper" parents="455 14040"/>
    </justification>
  </clause>

  <clause id="14147">
    <literal><![CDATA[
      1 / (x \ K(y,z)) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(34,a,11907,a,b,14040,a)].">
      <j1 rule="hyper" parents="34 11907 14040"/>
    </justification>
  </clause>

  <clause id="14148">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = (T(K(x,y),z) * z) \ y
    ]]></literal>
    <justification jstring="[para(4121(a,2),14040(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4121 14040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14150">
    <literal><![CDATA[
      (((x * y) \ y) * z) \ T(y,x) = (((y * x) \ y) * z) \ y
    ]]></literal>
    <justification jstring="[para(11531(a,1),14040(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11531 14040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14151">
    <literal><![CDATA[
      (x * K(y * x,z)) \ z = x \ T(z,x * y)
    ]]></literal>
    <justification jstring="[para(12515(a,1),14040(a,1,1))].">
      <j1 rule="para" parents="12515 14040"/>
    </justification>
  </clause>

  <clause id="14152">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y = K(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(116,a,4,a(flip),b,14046,a)].">
      <j1 rule="hyper" parents="116 4 14046"/>
    </justification>
  </clause>

  <clause id="14156">
    <literal><![CDATA[
      T(x,y) \ (y \ T(x * y,z)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(17(a,2),14048(a,1,1))].">
      <j1 rule="para" parents="17 14048"/>
    </justification>
  </clause>

  <clause id="14157">
    <literal><![CDATA[
      T(x,y) / (1 / y) = x / (K(y,x) / y)
    ]]></literal>
    <justification jstring="[para(6580(a,1),14063(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6580 14063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14159">
    <literal><![CDATA[
      K(x,(y \ 1) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(11715,a,14064,a),flip(a)].">
      <j1 rule="hyper" parents="11715 14064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14163">
    <literal><![CDATA[
      x / (y * K(x,z)) = K(z,x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,14028,a(flip),b,14068,a),flip(a)].">
      <j1 rule="hyper" parents="119 14028 14068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14164">
    <literal><![CDATA[
      T(x,(T(y,z) / u) \ 1) = T(x,(y / u) \ K(z,y))
    ]]></literal>
    <justification jstring="[para(14068(a,1),6439(a,1,2,1))].">
      <j1 rule="para" parents="14068 6439"/>
    </justification>
  </clause>

  <clause id="14165">
    <literal><![CDATA[
      K(x \ y,x) * (((x \ y) \ y) / z) = x / z
    ]]></literal>
    <justification jstring="[para(106(a,1),14069(a,1,2,1))].">
      <j1 rule="para" parents="106 14069"/>
    </justification>
  </clause>

  <clause id="14166">
    <literal><![CDATA[
      K(x,y) * (x / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) / z = u
    ]]></literal>
    <justification jstring="[para(14069(a,1),5410(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14069 5410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14169">
    <literal><![CDATA[
      (T(x,y) \ z) \ 1 = (x \ z) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(5337(a,1),14086(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5337 14086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14171">
    <literal><![CDATA[
      ((x * K(y,z)) \ u) \ K(x,K(y,z)) = ((K(y,z) * x) \ u) \ 1
    ]]></literal>
    <justification jstring="[para(9890(a,1),14086(a,1,1))].">
      <j1 rule="para" parents="9890 14086"/>
    </justification>
  </clause>

  <clause id="14173">
    <literal><![CDATA[
      K(x,y * (z \ K(u,x))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11674,a,b,14089,a)].">
      <j1 rule="hyper" parents="58 11674 14089"/>
    </justification>
  </clause>

  <clause id="14174">
    <literal><![CDATA[
      K(x,y * (1 / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5577,a,b,14089,a)].">
      <j1 rule="hyper" parents="58 5577 14089"/>
    </justification>
  </clause>

  <clause id="14175">
    <literal><![CDATA[
      K(x,y / (z \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5573,a(flip),b,14089,a),flip(a)].">
      <j1 rule="hyper" parents="58 5573 14089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14176">
    <literal><![CDATA[
      K(x,y / (1 / z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(75(a,1),14089(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 14089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14177">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4274,a,b,14093,a)].">
      <j1 rule="hyper" parents="58 4274 14093"/>
    </justification>
  </clause>

  <clause id="14178">
    <literal><![CDATA[
      K(x / (y \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4276,a(flip),b,14093,a),flip(a)].">
      <j1 rule="hyper" parents="58 4276 14093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14179">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),14093(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 14093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14181">
    <literal><![CDATA[
      x \ K(y,z) != u \ 1
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * x = u
    ]]></literal>
    <justification jstring="[para(14103(a,1),43(a,1))].">
      <j1 rule="para" parents="14103 43"/>
    </justification>
  </clause>

  <clause id="14182">
    <literal><![CDATA[
      K(((x \ K(y,z)) \ 1) * u,w) = K((K(z,y) * x) * u,w)
    ]]></literal>
    <justification jstring="[para(14103(a,1),4290(a,1,1,1,1))].">
      <j1 rule="para" parents="14103 4290"/>
    </justification>
  </clause>

  <clause id="14185">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,y * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(14103(a,1),14089(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14103 14089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14186">
    <literal><![CDATA[
      K(x * (y \ z),x * (1 / (z \ y))) = K(x * (y \ z),(z \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,13460,a(flip),b,14104,a)].">
      <j1 rule="hyper" parents="58 13460 14104"/>
    </justification>
  </clause>

  <clause id="14187">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,z \ y)) = K(x,u / ((y \ z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(13437,a,14106,a),flip(a)].">
      <j1 rule="hyper" parents="13437 14106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14188">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,12551,a,b,14106,a)].">
      <j1 rule="hyper" parents="334 12551 14106"/>
    </justification>
  </clause>

  <clause id="14189">
    <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,13485,a,b,14106,a)].">
      <j1 rule="hyper" parents="58 13485 14106"/>
    </justification>
  </clause>

  <clause id="14190">
    <literal><![CDATA[
      K(x,(1 / y) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5584,a,b,14106,a)].">
      <j1 rule="hyper" parents="58 5584 14106"/>
    </justification>
  </clause>

  <clause id="14191">
    <literal><![CDATA[
      K(x,(y \ x) \ z) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9308,a(flip),b,14106,a)].">
      <j1 rule="hyper" parents="58 9308 14106"/>
    </justification>
  </clause>

  <clause id="14192">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(14106(a,1),11089(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14106 11089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14194">
    <literal><![CDATA[
      T(x,y * (1 / z)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3924,a,b,14117,a)].">
      <j1 rule="hyper" parents="58 3924 14117"/>
    </justification>
  </clause>

  <clause id="14195">
    <literal><![CDATA[
      L(x,y \ 1,z) * (z * (y \ 1)) = z * ((y \ 1) * T(x,z / y))
    ]]></literal>
    <justification jstring="[para(14117(a,1),649(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14117 649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14196">
    <literal><![CDATA[
      T(x,y / (K(z,u) * w)) = T(x,y * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(14103(a,1),14117(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14103 14117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14197">
    <literal><![CDATA[
      K((x \ 1) * y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4281,a(flip),b,14121,a)].">
      <j1 rule="hyper" parents="58 4281 14121"/>
    </justification>
  </clause>

  <clause id="14199">
    <literal><![CDATA[
      K((x \ y) \ z,y) = K(x * (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(13478,a,14124,a)].">
      <j1 rule="hyper" parents="13478 14124"/>
    </justification>
  </clause>

  <clause id="14200">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(6262,a,14124,a)].">
      <j1 rule="hyper" parents="6262 14124"/>
    </justification>
  </clause>

  <clause id="14205">
    <literal><![CDATA[
      K((x \ 1) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(14124(a,1),6261(a,1))].">
      <j1 rule="para" parents="14124 6261"/>
    </justification>
  </clause>

  <clause id="14206">
    <literal><![CDATA[
      (x * K(y * x,z)) * y = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(14124(a,1),6796(a,1,1,2))].">
      <j1 rule="para" parents="14124 6796"/>
    </justification>
  </clause>

  <clause id="14207">
    <literal><![CDATA[
      T(x * K(y * x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(14124(a,1),6797(a,1,1,2))].">
      <j1 rule="para" parents="14124 6797"/>
    </justification>
  </clause>

  <clause id="14211">
    <literal><![CDATA[
      (x * K(y * (z \ x),z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(14124(a,1),9959(a,1,1,2))].">
      <j1 rule="para" parents="14124 9959"/>
    </justification>
  </clause>

  <clause id="14212">
    <literal><![CDATA[
      K(x,y) / ((L(z,u,w) \ z) * K(x,y)) = (L(z,u,w) \ z) \ 1
    ]]></literal>
    <justification jstring="[hyper(334,a,12381,a(flip),b,14125,a),flip(a)].">
      <j1 rule="hyper" parents="334 12381 14125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14215">
    <literal><![CDATA[
      1 / (x * K(y,z)) = K(z,y) / x
    ]]></literal>
    <justification jstring="[para(6516(a,1),14125(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6516 14125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14216">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3931,a(flip),b,14128,a),flip(a)].">
      <j1 rule="hyper" parents="58 3931 14128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14217">
    <literal><![CDATA[
      T(x,(y \ 1) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3927,a(flip),b,14128,a)].">
      <j1 rule="hyper" parents="58 3927 14128"/>
    </justification>
  </clause>

  <clause id="14218">
    <literal><![CDATA[
      T(x,(y \ K(z,u)) \ w) = T(x,(K(u,z) * y) * w)
    ]]></literal>
    <justification jstring="[para(14103(a,1),14130(a,1,2,1))].">
      <j1 rule="para" parents="14103 14130"/>
    </justification>
  </clause>

  <clause id="14220">
    <literal><![CDATA[
      K(x,y * (T(1 / y,z) * u)) = K(x,K(1 / y,z) * u)
    ]]></literal>
    <justification jstring="[para(5044(a,1),14137(a,1,2,2))].">
      <j1 rule="para" parents="5044 14137"/>
    </justification>
  </clause>

  <clause id="14221">
    <literal><![CDATA[
      K(x,(y \ z) * K(z,u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(11899(a,1),14137(a,1,2,2))].">
      <j1 rule="para" parents="11899 14137"/>
    </justification>
  </clause>

  <clause id="14222">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ 1) = z \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9009,a,14141,a)].">
      <j1 rule="hyper" parents="9009 14141"/>
    </justification>
  </clause>

  <clause id="14227">
    <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(14141(a,1),705(a,2,2))].">
      <j1 rule="para" parents="14141 705"/>
    </justification>
  </clause>

  <clause id="14230">
    <literal><![CDATA[
      T(x,y * ((1 / z) * K(u,w))) = T(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(14141(a,1),3936(a,2,2,2))].">
      <j1 rule="para" parents="14141 3936"/>
    </justification>
  </clause>

  <clause id="14232">
    <literal><![CDATA[
      K(x,y * ((1 / z) * K(u,w))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(14141(a,1),5600(a,2,2,2))].">
      <j1 rule="para" parents="14141 5600"/>
    </justification>
  </clause>

  <clause id="14233">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ 1) = K(z,y)
    ]]></literal>
    <justification jstring="[para(14141(a,1),6523(a,1,1))].">
      <j1 rule="para" parents="14141 6523"/>
    </justification>
  </clause>

  <clause id="14234">
    <literal><![CDATA[
      (x \ K(y,z)) * y = (x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[para(14141(a,1),6532(a,1,1))].">
      <j1 rule="para" parents="14141 6532"/>
    </justification>
  </clause>

  <clause id="14236">
    <literal><![CDATA[
      T(x \ K(y,z),K(z,y)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(14141(a,1),6522(a,1,1))].">
      <j1 rule="para" parents="14141 6522"/>
    </justification>
  </clause>

  <clause id="14239">
    <literal><![CDATA[
      (K(x,y) * z) \ K(u,w) = (z \ K(y,x)) * K(u,w)
    ]]></literal>
    <justification jstring="[para(14103(a,1),14141(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14103 14141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14240">
    <literal><![CDATA[
      T(x,y / (z \ 1)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(4224,a,14144,a)].">
      <j1 rule="hyper" parents="4224 14144"/>
    </justification>
  </clause>

  <clause id="14246">
    <literal><![CDATA[
      K(x / (x / y),z / u) = K(y,T(z * (1 / u),x))
    ]]></literal>
    <justification jstring="[hyper(8214,a,14174,a),flip(a)].">
      <j1 rule="hyper" parents="8214 14174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14248">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * K(u,y / z)) = K(x,T(y * (1 / z),u))
    ]]></literal>
    <justification jstring="[para(14174(a,1),8189(a,1,2,2))].">
      <j1 rule="para" parents="14174 8189"/>
    </justification>
  </clause>

  <clause id="14249">
    <literal><![CDATA[
      K(x,y * z) * (z \ T(z * y,x)) = y
    ]]></literal>
    <justification jstring="[para(14175(a,1),5374(a,1,1))].">
      <j1 rule="para" parents="14175 5374"/>
    </justification>
  </clause>

  <clause id="14250">
    <literal><![CDATA[
      K(x,L(y / (z \ 1),u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(14175(a,1),11089(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14175 11089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14252">
    <literal><![CDATA[
      K((x * (y \ 1)) * y,z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),14178(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 14178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14253">
    <literal><![CDATA[
      K(x / (1 / y),z) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,14124,a,b,14179,a),flip(a)].">
      <j1 rule="hyper" parents="334 14124 14179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14255">
    <literal><![CDATA[
      K(x,L((1 / y) \ z,u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(14190(a,1),11089(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14190 11089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14259">
    <literal><![CDATA[
      T(x,y / (z \ K(u,w))) = T(x,y * (K(w,u) * z))
    ]]></literal>
    <justification jstring="[para(14147(a,1),14194(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14147 14194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14263">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z) = K(y,T(z,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,12524,a(flip),b,14197,a),flip(a)].">
      <j1 rule="hyper" parents="58 12524 14197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14264">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),14197(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 14197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14265">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K(y * x,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,12516,a,b,14200,a),flip(a)].">
      <j1 rule="hyper" parents="334 12516 14200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14266">
    <literal><![CDATA[
      K((x \ K(y,z)) * y,u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(11907(a,1),14200(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11907 14200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14267">
    <literal><![CDATA[
      (K(x,y) / z) \ 1 = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(192,a,14215,a)].">
      <j1 rule="hyper" parents="192 14215"/>
    </justification>
  </clause>

  <clause id="14268">
    <literal><![CDATA[
      T(K(x,y) / z,z * K(y,x)) = (z * K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(14215(a,1),107(a,1,1))].">
      <j1 rule="para" parents="14215 107"/>
    </justification>
  </clause>

  <clause id="14273">
    <literal><![CDATA[
      K(x,y * (z / ((u * K(w,v5)) \ 1))) = K(x,y * (z / (K(v5,w) / u)))
    ]]></literal>
    <justification jstring="[para(14215(a,1),5597(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="14215 5597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14274">
    <literal><![CDATA[
      K(x,(y / (1 / (K(z,u) / w))) * v5) = K(x,(y / (w * K(u,z))) * v5)
    ]]></literal>
    <justification jstring="[para(14215(a,1),6233(a,1,2,1,2,2))].">
      <j1 rule="para" parents="14215 6233"/>
    </justification>
  </clause>

  <clause id="14275">
    <literal><![CDATA[
      1 / T(x * K(y,z),y) = K(z,y) / T(x,y)
    ]]></literal>
    <justification jstring="[para(7687(a,2),14215(a,1,2))].">
      <j1 rule="para" parents="7687 14215"/>
    </justification>
  </clause>

  <clause id="14276">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) = K(x,y * (K(w,u) / z))
    ]]></literal>
    <justification jstring="[para(14215(a,1),14174(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14215 14174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14277">
    <literal><![CDATA[
      K(x,y / (K(z,u) / w)) = K(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(14215(a,1),14176(a,1,2,2))].">
      <j1 rule="para" parents="14215 14176"/>
    </justification>
  </clause>

  <clause id="14279">
    <literal><![CDATA[
      T(x,(y \ 1) / z) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,14117,a(flip),b,14217,a)].">
      <j1 rule="hyper" parents="58 14117 14217"/>
    </justification>
  </clause>

  <clause id="14280">
    <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(14217(a,1),8328(a,1,2))].">
      <j1 rule="para" parents="14217 8328"/>
    </justification>
  </clause>

  <clause id="14281">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) * z) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),14240(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 14240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14282">
    <literal><![CDATA[
      K(x,T(y,(z \ 1) / u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[para(14240(a,1),8511(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14240 8511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14283">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(12531,a,14252,a)].">
      <j1 rule="hyper" parents="12531 14252"/>
    </justification>
  </clause>

  <clause id="14286">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = K(K(u,u \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,4277,a,b,14264,a),flip(a)].">
      <j1 rule="hyper" parents="334 4277 14264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14288">
    <literal><![CDATA[
      ((x * ((x \ y) * K(x / y,y))) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(14267(a,1),10925(a,1,1,1,2))].">
      <j1 rule="para" parents="14267 10925"/>
    </justification>
  </clause>

  <clause id="14289">
    <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,13136,a(flip),b,14281,a)].">
      <j1 rule="hyper" parents="58 13136 14281"/>
    </justification>
  </clause>

  <clause id="14290">
    <literal><![CDATA[
      L(x,y / x,z) \ (z * y) = T(z * (y / x),x)
    ]]></literal>
    <justification jstring="[hyper(792,a,14011,a)].">
      <j1 rule="hyper" parents="792 14011"/>
    </justification>
  </clause>

  <clause id="14291">
    <literal><![CDATA[
      L(x \ y,x,z) \ (z * y) = T(z * x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(620,a,14011,a)].">
      <j1 rule="hyper" parents="620 14011"/>
    </justification>
  </clause>

  <clause id="14292">
    <literal><![CDATA[
      L(x,y,z) \ (z * (y * x)) = T(z * y,x)
    ]]></literal>
    <justification jstring="[hyper(559,a,14011,a)].">
      <j1 rule="hyper" parents="559 14011"/>
    </justification>
  </clause>

  <clause id="14293">
    <literal><![CDATA[
      L(x,y,z) * T(z * y,x) = z * (y * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,14011,a(flip),b,482,a)].">
      <j1 rule="hyper" parents="119 14011 482"/>
    </justification>
  </clause>

  <clause id="14294">
    <literal><![CDATA[
      L(x,y,z) = (z * (y * x)) / T(z * y,x)
    ]]></literal>
    <justification jstring="[para(14011(a,1),481(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14011 481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14295">
    <literal><![CDATA[
      (x * (y * z)) \ (z * T(x * y,z)) = a(x,y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(14011(a,1),11658(a,1,2,2))].">
      <j1 rule="para" parents="14011 11658"/>
    </justification>
  </clause>

  <clause id="14296">
    <literal><![CDATA[
      T(x,(y \ z) \ y) = T(x,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(118,a,14004,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 14004 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14297">
    <literal><![CDATA[
      K(x,L(y,z \ y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11205,a,14014,a)].">
      <j1 rule="hyper" parents="11205 14014"/>
    </justification>
  </clause>

  <clause id="14298">
    <literal><![CDATA[
      (x / y) * (y * K(z,x)) = x * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(6069,a,14014,a)].">
      <j1 rule="hyper" parents="6069 14014"/>
    </justification>
  </clause>

  <clause id="14299">
    <literal><![CDATA[
      x \ (y * K(z,y)) = (x \ y) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,14014,a)].">
      <j1 rule="hyper" parents="123 14014"/>
    </justification>
  </clause>

  <clause id="14300">
    <literal><![CDATA[
      x \ ((y * z) / y) = (x \ z) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,5017,a,b,14014,a)].">
      <j1 rule="hyper" parents="116 5017 14014"/>
    </justification>
  </clause>

  <clause id="14302">
    <literal><![CDATA[
      (x \ (y \ z)) * K(y,y \ z) = x \ (z / y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5041,a(flip),b,14014,a),flip(a)].">
      <j1 rule="hyper" parents="116 5041 14014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14303">
    <literal><![CDATA[
      K(x,L(y * z,z,y)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),14297(a,1,2,2))].">
      <j1 rule="para" parents="4 14297"/>
    </justification>
  </clause>

  <clause id="14304">
    <literal><![CDATA[
      K((x * y) \ z,x * y) = K(y \ (x \ z),x * y)
    ]]></literal>
    <justification jstring="[hyper(11247,a,14303,a)].">
      <j1 rule="hyper" parents="11247 14303"/>
    </justification>
  </clause>

  <clause id="14305">
    <literal><![CDATA[
      (K(x,y) * (y / z)) * z = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(598,a,14024,a)].">
      <j1 rule="hyper" parents="598 14024"/>
    </justification>
  </clause>

  <clause id="14306">
    <literal><![CDATA[
      (x * K(y,x)) / z = K(y,x) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(365,a,14024,a)].">
      <j1 rule="hyper" parents="365 14024"/>
    </justification>
  </clause>

  <clause id="14307">
    <literal><![CDATA[
      (1 / x) * ((K(y,z) / x) \ y) = y * K(z,y)
    ]]></literal>
    <justification jstring="[para(14075(a,1),14024(a,1,1))].">
      <j1 rule="para" parents="14075 14024"/>
    </justification>
  </clause>

  <clause id="14308">
    <literal><![CDATA[
      T(T(x,x \ (y * z)),u) \ T(x,u) = K((y \ x) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[para(14026(a,1),5065(a,1,1,1))].">
      <j1 rule="para" parents="14026 5065"/>
    </justification>
  </clause>

  <clause id="14310">
    <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(451,a,6522,a(flip),b,14033,a)].">
      <j1 rule="hyper" parents="451 6522 14033"/>
    </justification>
  </clause>

  <clause id="14312">
    <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(3960(a,1),14036(a,1,2,1))].">
      <j1 rule="para" parents="3960 14036"/>
    </justification>
  </clause>

  <clause id="14314">
    <literal><![CDATA[
      (x * ((x * y) / x)) \ y = (x * y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4121(a,1),14041(a,1,1))].">
      <j1 rule="para" parents="4121 14041"/>
    </justification>
  </clause>

  <clause id="14315">
    <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(8109(a,1),14041(a,2,2))].">
      <j1 rule="para" parents="8109 14041"/>
    </justification>
  </clause>

  <clause id="14316">
    <literal><![CDATA[
      K(x / y,z) * (y \ (y \ x)) = y \ T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(8180(a,1),14044(a,1,1))].">
      <j1 rule="para" parents="8180 14044"/>
    </justification>
  </clause>

  <clause id="14318">
    <literal><![CDATA[
      K(x,y) * (z \ T(y,T(x,z))) = z \ y
    ]]></literal>
    <justification jstring="[hyper(119,a,14045,a,b,5391,a)].">
      <j1 rule="hyper" parents="119 14045 5391"/>
    </justification>
  </clause>

  <clause id="14319">
    <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(14045(a,1),12579(a,1,2,1,1))].">
      <j1 rule="para" parents="14045 12579"/>
    </justification>
  </clause>

  <clause id="14320">
    <literal><![CDATA[
      (x \ T(y * x,z)) / (x \ (y * x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,12516,a(flip),b,14050,a),flip(a)].">
      <j1 rule="hyper" parents="334 12516 14050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14321">
    <literal><![CDATA[
      L(x * K(y * x,z),y,z) = (z * y) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(14052(a,1),462(a,1,1))].">
      <j1 rule="para" parents="14052 462"/>
    </justification>
  </clause>

  <clause id="14323">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x * y) = u
    ]]></literal>
    <justification jstring="[para(14052(a,2),6528(a,1,1))].">
      <j1 rule="para" parents="14052 6528"/>
    </justification>
  </clause>

  <clause id="14325">
    <literal><![CDATA[
      K(x * K(y * x,z),T(u,y)) = K(y \ T(x * y,z),u)
    ]]></literal>
    <justification jstring="[para(14052(a,1),7464(a,1,1))].">
      <j1 rule="para" parents="14052 7464"/>
    </justification>
  </clause>

  <clause id="14326">
    <literal><![CDATA[
      x \ T(x * y,T(z,y)) = y * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(12516(a,1),14052(a,2,2))].">
      <j1 rule="para" parents="12516 14052"/>
    </justification>
  </clause>

  <clause id="14327">
    <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(14071(a,1),5837(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14071 5837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14328">
    <literal><![CDATA[
      (1 / x) * K(y,z / x) = K(y,x \ z) / x
    ]]></literal>
    <justification jstring="[para(107(a,1),14077(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 14077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14329">
    <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(14077(a,2),705(a,2,2))].">
      <j1 rule="para" parents="14077 705"/>
    </justification>
  </clause>

  <clause id="14330">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = K(y,T(z,x)) / T(x,u)
    ]]></literal>
    <justification jstring="[para(14077(a,1),6368(a,1,1))].">
      <j1 rule="para" parents="14077 6368"/>
    </justification>
  </clause>

  <clause id="14331">
    <literal><![CDATA[
      T(x,(y * z) \ x) = T(x,z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(118,a,14131,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 14131 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14332">
    <literal><![CDATA[
      K(x,x \ ((y \ x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(14134(a,1),9042(a,1))].">
      <j1 rule="para" parents="14134 9042"/>
    </justification>
  </clause>

  <clause id="14333">
    <literal><![CDATA[
      T(x,(y * z) \ 1) = T(x,z \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(118,a,14135,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 14135 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14334">
    <literal><![CDATA[
      (x \ K(y,T(z,x))) \ 1 = (x \ 1) \ K(z,y)
    ]]></literal>
    <justification jstring="[para(14138(a,2),14103(a,1,1))].">
      <j1 rule="para" parents="14138 14103"/>
    </justification>
  </clause>

  <clause id="14335">
    <literal><![CDATA[
      K(x \ ((y \ x) * z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(9051,a,14143,a),flip(a)].">
      <j1 rule="hyper" parents="9051 14143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14338">
    <literal><![CDATA[
      (x * y) / (z \ (y * x)) = K(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(201,a,14145,a)].">
      <j1 rule="hyper" parents="201 14145"/>
    </justification>
  </clause>

  <clause id="14339">
    <literal><![CDATA[
      (K(x,y) * z) \ (x * y) = z \ (y * x)
    ]]></literal>
    <justification jstring="[para(4(a,1),14145(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 14145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14340">
    <literal><![CDATA[
      (T(x,y) * z) \ (x * y) = (x * z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(5049(a,1),14145(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5049 14145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14341">
    <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(14163(a,1),10066(a,1,2,1,1))].">
      <j1 rule="para" parents="14163 10066"/>
    </justification>
  </clause>

  <clause id="14342">
    <literal><![CDATA[
      K(x,y) * (y / (z \ 1)) = y / (z \ K(y,x))
    ]]></literal>
    <justification jstring="[para(14141(a,1),14163(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14141 14163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14343">
    <literal><![CDATA[
      K((x \ y) \ K(x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ T(x,z),u) = w
    ]]></literal>
    <justification jstring="[para(14169(a,1),6715(a,1,1))].">
      <j1 rule="para" parents="14169 6715"/>
    </justification>
  </clause>

  <clause id="14344">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ K(z,w))) = K(x,y / (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[para(14169(a,1),14089(a,1,2,2))].">
      <j1 rule="para" parents="14169 14089"/>
    </justification>
  </clause>

  <clause id="14345">
    <literal><![CDATA[
      T(x,y * ((z \ u) \ K(z,w))) = T(x,y / (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[para(14169(a,1),14117(a,1,2,2))].">
      <j1 rule="para" parents="14169 14117"/>
    </justification>
  </clause>

  <clause id="14346">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(14188(a,1),12587(a,1))].">
      <j1 rule="para" parents="14188 12587"/>
    </justification>
  </clause>

  <clause id="14347">
    <literal><![CDATA[
      K(x,(y \ x) * (x \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(9042,a,14191,a),flip(a)].">
      <j1 rule="hyper" parents="9042 14191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14348">
    <literal><![CDATA[
      x * (y * K(x * (z \ y),z)) = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(14199(a,1),6709(a,1,2,2))].">
      <j1 rule="para" parents="14199 6709"/>
    </justification>
  </clause>

  <clause id="14349">
    <literal><![CDATA[
      (x * K(y,z)) * (y / x) = T(x * (y / x),z)
    ]]></literal>
    <justification jstring="[para(7(a,1),14206(a,1,1,2,1))].">
      <j1 rule="para" parents="7 14206"/>
    </justification>
  </clause>

  <clause id="14352">
    <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(451,a,6749,a,b,14249,a)].">
      <j1 rule="hyper" parents="451 6749 14249"/>
    </justification>
  </clause>

  <clause id="14353">
    <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(451,a,6518,a,b,14249,a)].">
      <j1 rule="hyper" parents="451 6518 14249"/>
    </justification>
  </clause>

  <clause id="14354">
    <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(451,a,4293,a,b,14249,a)].">
      <j1 rule="hyper" parents="451 4293 14249"/>
    </justification>
  </clause>

  <clause id="14355">
    <literal><![CDATA[
      K((1 / x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(14265(a,2),12531(a,1))].">
      <j1 rule="para" parents="14265 12531"/>
    </justification>
  </clause>

  <clause id="14356">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z) = K(y,T(z,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(334,a,8499,a,b,14283,a),flip(a)].">
      <j1 rule="hyper" parents="334 8499 14283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14357">
    <literal><![CDATA[
      ((x \ y) / z) \ (y / x) = z * K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5041,a(flip),b,14298,a)].">
      <j1 rule="hyper" parents="116 5041 14298"/>
    </justification>
  </clause>

  <clause id="14359">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,y * z) = x \ (L(z,y,z) * y)
    ]]></literal>
    <justification jstring="[para(4618(a,1),14300(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4618 14300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14361">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) / z) = (y / x) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,5041,a(flip),b,14305,a),flip(a)].">
      <j1 rule="hyper" parents="117 5041 14305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14362">
    <literal><![CDATA[
      T(K(x,y) * (y / T(z,K(x,y))),z) = z \ (y * T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(14306(a,1),6472(a,1,1))].">
      <j1 rule="para" parents="14306 6472"/>
    </justification>
  </clause>

  <clause id="14363">
    <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(334,a,1274,a,b,14318,a),flip(a)].">
      <j1 rule="hyper" parents="334 1274 14318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14364">
    <literal><![CDATA[
      K(x \ (y * z),z) = K((x \ z) * y,z)
    ]]></literal>
    <justification jstring="[hyper(11079,a,14335,a),flip(a)].">
      <j1 rule="hyper" parents="11079 14335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14365">
    <literal><![CDATA[
      (x * y) / (z \ (y * x)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(334,a,5391,a(flip),b,14338,a),flip(a)].">
      <j1 rule="hyper" parents="334 5391 14338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14366">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * (y * x)) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,12000,a(flip),b,14339,a),flip(a)].">
      <j1 rule="hyper" parents="34 12000 14339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14367">
    <literal><![CDATA[
      (K(x,x \ y) * z) \ y = z \ ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(5(a,1),14339(a,1,2))].">
      <j1 rule="para" parents="5 14339"/>
    </justification>
  </clause>

  <clause id="14368">
    <literal><![CDATA[
      K(x,K(y,(z \ y) * u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(14347(a,1),10598(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14347 10598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14369">
    <literal><![CDATA[
      K((x \ y) * z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,10794,a(flip),b,14364,a),flip(a)].">
      <j1 rule="hyper" parents="58 10794 14364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14370">
    <literal><![CDATA[
      K(x,y) * ((y * x) / z) = (x * y) / z
    ]]></literal>
    <justification jstring="[para(75(a,1),14365(a,1,2)),flip(a)].">
      <j1 rule="para" parents="75 14365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14371">
    <literal><![CDATA[
      K((x / y) * z,x) = K(x * (y \ z),x)
    ]]></literal>
    <justification jstring="[hyper(9052,a,14369,a)].">
      <j1 rule="hyper" parents="9052 14369"/>
    </justification>
  </clause>

  <clause id="14372">
    <literal><![CDATA[
      ((x * y) / z) \ T(x,y) = ((y * x) / z) \ x
    ]]></literal>
    <justification jstring="[para(14370(a,1),14022(a,1,1))].">
      <j1 rule="para" parents="14370 14022"/>
    </justification>
  </clause>

  <clause id="14373">
    <literal><![CDATA[
      ((x * y) / z) \ K(x,y) = ((y * x) / z) \ 1
    ]]></literal>
    <justification jstring="[para(14370(a,1),14086(a,1,1))].">
      <j1 rule="para" parents="14370 14086"/>
    </justification>
  </clause>

  <clause id="14374">
    <literal><![CDATA[
      K((x * y) * (T(x,y) \ z),x * y) = K(y * z,x * y)
    ]]></literal>
    <justification jstring="[para(191(a,1),14371(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="191 14371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14375">
    <literal><![CDATA[
      L(a(x,y,z),u,K(w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(13992,a,13707,a)].">
      <j1 rule="hyper" parents="13992 13707"/>
    </justification>
  </clause>

  <clause id="14376">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,K(w,v5)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(13992,a,13669,a)].">
      <j1 rule="hyper" parents="13992 13669"/>
    </justification>
  </clause>

  <clause id="14379">
    <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,11050,a,b,14375,a)].">
      <j1 rule="hyper" parents="58 11050 14375"/>
    </justification>
  </clause>

  <clause id="14380">
    <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,8380,a,b,14375,a)].">
      <j1 rule="hyper" parents="58 8380 14375"/>
    </justification>
  </clause>

  <clause id="14381">
    <literal><![CDATA[
      (x * (K(y,x) * (z * u))) \ (K(y,x) * ((x * z) * u)) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5693,a,b,14375,a)].">
      <j1 rule="hyper" parents="58 5693 14375"/>
    </justification>
  </clause>

  <clause id="14382">
    <literal><![CDATA[
      a(x,y,z) = (x * (T(y,x) * z)) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11597,a(flip),b,14375,a),flip(a)].">
      <j1 rule="hyper" parents="58 11597 14375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14383">
    <literal><![CDATA[
      (K(x,y) * z) * a(u,w,v5) = K(x,y) * (z * a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(119,a,14375,a(flip),b,4317,a(flip))].">
      <j1 rule="hyper" parents="119 14375 4317"/>
    </justification>
  </clause>

  <clause id="14384">
    <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(14375(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14375 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14385">
    <literal><![CDATA[
      (K(x,y) * z) / a(u,w,v5) = K(x,y) * (z / a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(14375(a,1),556(a,1,2))].">
      <j1 rule="para" parents="14375 556"/>
    </justification>
  </clause>

  <clause id="14387">
    <literal><![CDATA[
      (K(x,y) * z) \ (x \ ((x * y) / x)) = z \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5654,a(flip),b,14023,a)].">
      <j1 rule="hyper" parents="58 5654 14023"/>
    </justification>
  </clause>

  <clause id="14388">
    <literal><![CDATA[
      L(x \ (T(y,z) \ z),x,K(T(y,z),z)) = x \ (y \ T(z,y))
    ]]></literal>
    <justification jstring="[para(4490(a,1),14023(a,2,2))].">
      <j1 rule="para" parents="4490 14023"/>
    </justification>
  </clause>

  <clause id="14389">
    <literal><![CDATA[
      K(x,y) * (K(z,u) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / T(u,z) = w
    ]]></literal>
    <justification jstring="[para(5072(a,2),14067(a,1,2))].">
      <j1 rule="para" parents="5072 14067"/>
    </justification>
  </clause>

  <clause id="14390">
    <literal><![CDATA[
      L(K(x,y),z \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(14142(a,2),297(a,1)),flip(b)].">
      <j1 rule="para" parents="14142 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14392">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(11089(a,1),14390(a,1))].">
      <j1 rule="para" parents="11089 14390"/>
    </justification>
  </clause>

  <clause id="14393">
    <literal><![CDATA[
      K(L(x,y \ 1,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(11131(a,1),14390(a,1))].">
      <j1 rule="para" parents="11131 14390"/>
    </justification>
  </clause>

  <clause id="14394">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3196(a,1),14392(a,1,2))].">
      <j1 rule="para" parents="3196 14392"/>
    </justification>
  </clause>

  <clause id="14395">
    <literal><![CDATA[
      K(x,y * ((1 / y) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(5595(a,2),14392(a,1))].">
      <j1 rule="para" parents="5595 14392"/>
    </justification>
  </clause>

  <clause id="14396">
    <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(7014(a,1),14392(a,1,2))].">
      <j1 rule="para" parents="7014 14392"/>
    </justification>
  </clause>

  <clause id="14397">
    <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(7014(a,1),14393(a,1,1))].">
      <j1 rule="para" parents="7014 14393"/>
    </justification>
  </clause>

  <clause id="14398">
    <literal><![CDATA[
      K(x,(1 / y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(3153(a,1),14394(a,1,2))].">
      <j1 rule="para" parents="3153 14394"/>
    </justification>
  </clause>

  <clause id="14399">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(12637(a,2),14394(a,1))].">
      <j1 rule="para" parents="12637 14394"/>
    </justification>
  </clause>

  <clause id="14400">
    <literal><![CDATA[
      K(x,y * (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(12638(a,1),14394(a,1))].">
      <j1 rule="para" parents="12638 14394"/>
    </justification>
  </clause>

  <clause id="14401">
    <literal><![CDATA[
      K(x,T(y * (z \ 1),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(629(a,1),14399(a,1,2))].">
      <j1 rule="para" parents="629 14399"/>
    </justification>
  </clause>

  <clause id="14402">
    <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(4498(a,1),14166(a,1,2))].">
      <j1 rule="para" parents="4498 14166"/>
    </justification>
  </clause>

  <clause id="14403">
    <literal><![CDATA[
      K((1 / x) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(4281(a,2),14205(a,1))].">
      <j1 rule="para" parents="4281 14205"/>
    </justification>
  </clause>

  <clause id="14404">
    <literal><![CDATA[
      K((x \ K(y,z)) * y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ T(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(14234(a,2),14205(a,1,1))].">
      <j1 rule="para" parents="14234 14205"/>
    </justification>
  </clause>

  <clause id="14405">
    <literal><![CDATA[
      (x * (y * z)) / T(x * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(14292(a,1),345(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14292 345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14407">
    <literal><![CDATA[
      L(x,y,z) * (x \ (z * y)) = (z * (y * x)) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,14293,a(flip),b,11285,a),flip(a)].">
      <j1 rule="hyper" parents="117 14293 11285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14409">
    <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(6368(a,1),14293(a,2,2))].">
      <j1 rule="para" parents="6368 14293"/>
    </justification>
  </clause>

  <clause id="14411">
    <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(4640(a,2),14346(a,1,2))].">
      <j1 rule="para" parents="4640 14346"/>
    </justification>
  </clause>

  <clause id="14412">
    <literal><![CDATA[
      K(x,(1 / y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(5584(a,2),14346(a,1))].">
      <j1 rule="para" parents="5584 14346"/>
    </justification>
  </clause>

  <clause id="14413">
    <literal><![CDATA[
      K(x,y / T(z \ 1,z * (x * y))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(11526(a,2),14346(a,1))].">
      <j1 rule="para" parents="11526 14346"/>
    </justification>
  </clause>

  <clause id="14414">
    <literal><![CDATA[
      K((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(4282(a,1),14355(a,1))].">
      <j1 rule="para" parents="4282 14355"/>
    </justification>
  </clause>

  <clause id="14415">
    <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(5525(a,1),14395(a,1,2,2))].">
      <j1 rule="para" parents="5525 14395"/>
    </justification>
  </clause>

  <clause id="14416">
    <literal><![CDATA[
      K(x,(y \ z) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(11899(a,1),14395(a,1,2,2))].">
      <j1 rule="para" parents="11899 14395"/>
    </justification>
  </clause>

  <clause id="14417">
    <literal><![CDATA[
      K(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(5583(a,1),14398(a,1))].">
      <j1 rule="para" parents="5583 14398"/>
    </justification>
  </clause>

  <clause id="14418">
    <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(14147(a,1),14398(a,1,2,1))].">
      <j1 rule="para" parents="14147 14398"/>
    </justification>
  </clause>

  <clause id="14419">
    <literal><![CDATA[
      K(x,y * (z \ K(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(5073(a,1),14400(a,1,2,2))].">
      <j1 rule="para" parents="5073 14400"/>
    </justification>
  </clause>

  <clause id="14420">
    <literal><![CDATA[
      K(x,y * (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(5577(a,2),14400(a,1))].">
      <j1 rule="para" parents="5577 14400"/>
    </justification>
  </clause>

  <clause id="14421">
    <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(14169(a,1),14400(a,1,2,2))].">
      <j1 rule="para" parents="14169 14400"/>
    </justification>
  </clause>

  <clause id="14422">
    <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(2015(a,1),14412(a,1,2))].">
      <j1 rule="para" parents="2015 14412"/>
    </justification>
  </clause>

  <clause id="14423">
    <literal><![CDATA[
      K(x / (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(14253(a,2),14414(a,1))].">
      <j1 rule="para" parents="14253 14414"/>
    </justification>
  </clause>

  <clause id="14424">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(14106(a,2),14417(a,1))].">
      <j1 rule="para" parents="14106 14417"/>
    </justification>
  </clause>

  <clause id="14425">
    <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(14267(a,1),14417(a,1,2,1))].">
      <j1 rule="para" parents="14267 14417"/>
    </justification>
  </clause>

  <clause id="14426">
    <literal><![CDATA[
      K(x / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ 1),z) = u
    ]]></literal>
    <justification jstring="[para(72(a,1),14423(a,1,1,2))].">
      <j1 rule="para" parents="72 14423"/>
    </justification>
  </clause>

  <clause id="14427">
    <literal><![CDATA[
      K(x * (1 / (1 / y)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(14177(a,2),14423(a,1))].">
      <j1 rule="para" parents="14177 14423"/>
    </justification>
  </clause>

  <clause id="14428">
    <literal><![CDATA[
      K(x * (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ 1),z) = u
    ]]></literal>
    <justification jstring="[para(14177(a,2),14426(a,1))].">
      <j1 rule="para" parents="14177 14426"/>
    </justification>
  </clause>

  <clause id="14429">
    <literal><![CDATA[
      T(x,y) * (z * K(x * y,z)) = (y \ T(x * y,z)) * z
    ]]></literal>
    <justification jstring="[para(14031(a,1),6351(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14031 6351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14430">
    <literal><![CDATA[
      (x \ y) / (x \ T(y,z)) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,8507,a(flip),b,14061,a),flip(a)].">
      <j1 rule="hyper" parents="334 8507 14061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14431">
    <literal><![CDATA[
      T(1 / (x * K(y,z)),K(z,y)) = (1 / x) * K(z,y)
    ]]></literal>
    <justification jstring="[para(14215(a,2),14081(a,1,1))].">
      <j1 rule="para" parents="14215 14081"/>
    </justification>
  </clause>

  <clause id="14435">
    <literal><![CDATA[
      T(x,T((y \ 1) * z,u)) = T(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,4812,a(flip),b,14129,a)].">
      <j1 rule="hyper" parents="58 4812 14129"/>
    </justification>
  </clause>

  <clause id="14436">
    <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,12402,a(flip),b,14139,a)].">
      <j1 rule="hyper" parents="58 12402 14139"/>
    </justification>
  </clause>

  <clause id="14437">
    <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(4564(a,1),14207(a,1,1,2,1))].">
      <j1 rule="para" parents="4564 14207"/>
    </justification>
  </clause>

  <clause id="14438">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = y \ T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(12516(a,1),14207(a,1,1,2))].">
      <j1 rule="para" parents="12516 14207"/>
    </justification>
  </clause>

  <clause id="14439">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(14263(a,2),8552(a,1))].">
      <j1 rule="para" parents="14263 8552"/>
    </justification>
  </clause>

  <clause id="14441">
    <literal><![CDATA[
      K(x,y / (T(z \ (u \ w),x) * K(u,u \ w))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[para(14302(a,1),9255(a,2,2,2))].">
      <j1 rule="para" parents="14302 9255"/>
    </justification>
  </clause>

  <clause id="14443">
    <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(14307(a,1),11171(a,2,2,1))].">
      <j1 rule="para" parents="14307 11171"/>
    </justification>
  </clause>

  <clause id="14445">
    <literal><![CDATA[
      (x \ 1) \ K(y,T(z,x)) = (x \ K(z,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8162(a,1),14334(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8162 14334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14446">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(14356(a,2),8552(a,1))].">
      <j1 rule="para" parents="14356 8552"/>
    </justification>
  </clause>

  <clause id="14448">
    <literal><![CDATA[
      ((x \ y) * z) \ ((x \ y) * x) = ((y / x) * z) \ y
    ]]></literal>
    <justification jstring="[para(5682(a,1),14367(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5682 14367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14449">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ z) * K(x,K(z,y \ u)) = K(x,z / ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(14368(a,1),8664(a,1,2))].">
      <j1 rule="para" parents="14368 8664"/>
    </justification>
  </clause>

  <clause id="14450">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((z \ y) * u)) = K(x,((z \ y) * u) / y)
    ]]></literal>
    <justification jstring="[para(14368(a,1),8682(a,1,1))].">
      <j1 rule="para" parents="14368 8682"/>
    </justification>
  </clause>

  <clause id="14451">
    <literal><![CDATA[
      ((x * T(y,x)) / z) \ T(x,T(y,x)) = ((y * ((y * x) / y)) / z) \ x
    ]]></literal>
    <justification jstring="[para(4121(a,1),14372(a,2,1,1))].">
      <j1 rule="para" parents="4121 14372"/>
    </justification>
  </clause>

  <clause id="14452">
    <literal><![CDATA[
      K(x,(((y * z) / u) \ T(K(y,z),x)) \ w) = K(x,(((z * y) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(14373(a,1),8831(a,2,2,1))].">
      <j1 rule="para" parents="14373 8831"/>
    </justification>
  </clause>

  <clause id="14453">
    <literal><![CDATA[
      T(x,T((y \ 1) * z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(14435(a,2),4597(a,1))].">
      <j1 rule="para" parents="14435 4597"/>
    </justification>
  </clause>

  <clause id="14454">
    <literal><![CDATA[
      ((x \ 1) \ K(y,z)) * K(x,K(y,z)) = (x \ K(z,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,12635,a,b,14445,a)].">
      <j1 rule="hyper" parents="58 12635 14445"/>
    </justification>
  </clause>

  <clause id="14455">
    <literal><![CDATA[
      L(x,x \ y,z) \ (z * y) = T(z * (y / x),x)
    ]]></literal>
    <justification jstring="[para(10684(a,1),14290(a,1,1))].">
      <j1 rule="para" parents="10684 14290"/>
    </justification>
  </clause>

  <clause id="14456">
    <literal><![CDATA[
      K(x,T(y * z,z \ u)) = K(x,T(y * z,y * u))
    ]]></literal>
    <justification jstring="[para(14291(a,1),7386(a,1,2))].">
      <j1 rule="para" parents="14291 7386"/>
    </justification>
  </clause>

  <clause id="14457">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(14332,a,10601,a)].">
      <j1 rule="hyper" parents="14332 10601"/>
    </justification>
  </clause>

  <clause id="14458">
    <literal><![CDATA[
      K(x,(y \ x) * z) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(10805,a,14457,a),flip(a)].">
      <j1 rule="hyper" parents="10805 14457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14460">
    <literal><![CDATA[
      T(x,(y \ x) * z) = T(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,14458,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 14458 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14462">
    <literal><![CDATA[
      (K(x,y) / x) * (y * x) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(13618,a,14366,a)].">
      <j1 rule="hyper" parents="13618 14366"/>
    </justification>
  </clause>

  <clause id="14463">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,T(w,v5)) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(14376(a,1),7189(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14376 7189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14464">
    <literal><![CDATA[
      a(x,T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,235,a(flip),b,14382,a)].">
      <j1 rule="hyper" parents="334 235 14382"/>
    </justification>
  </clause>

  <clause id="14466">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,9,a(flip),b,14464,a)].">
      <j1 rule="hyper" parents="334 9 14464"/>
    </justification>
  </clause>

  <clause id="14467">
    <literal><![CDATA[
      a(x,y * x,z) = a(x,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,13631,a(flip),b,14464,a)].">
      <j1 rule="hyper" parents="58 13631 14464"/>
    </justification>
  </clause>

  <clause id="14468">
    <literal><![CDATA[
      a(x / y,y,z) = a(y \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4929,a(flip),b,14464,a)].">
      <j1 rule="hyper" parents="58 4929 14464"/>
    </justification>
  </clause>

  <clause id="14469">
    <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(14407(a,1),286(a,1))].">
      <j1 rule="para" parents="14407 286"/>
    </justification>
  </clause>

  <clause id="14470">
    <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(2223(a,1),14424(a,1,2,1))].">
      <j1 rule="para" parents="2223 14424"/>
    </justification>
  </clause>

  <clause id="14471">
    <literal><![CDATA[
      T(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(4473(a,1),14453(a,1))].">
      <j1 rule="para" parents="4473 14453"/>
    </justification>
  </clause>

  <clause id="14472">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(14130(a,2),14471(a,1))].">
      <j1 rule="para" parents="14130 14471"/>
    </justification>
  </clause>

  <clause id="14473">
    <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(14267(a,1),14471(a,1,2,1))].">
      <j1 rule="para" parents="14267 14471"/>
    </justification>
  </clause>

  <clause id="14474">
    <literal><![CDATA[
      L(x,x \ (x * y),z) \ (z * (x * y)) = T(z * (y * K(x,y)),x)
    ]]></literal>
    <justification jstring="[para(5017(a,1),14455(a,2,1,2))].">
      <j1 rule="para" parents="5017 14455"/>
    </justification>
  </clause>

  <clause id="14475">
    <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(6685(a,1),14455(a,1,2))].">
      <j1 rule="para" parents="6685 14455"/>
    </justification>
  </clause>

  <clause id="14476">
    <literal><![CDATA[
      a(x,T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(14466(a,1),709(a,1))].">
      <j1 rule="para" parents="14466 709"/>
    </justification>
  </clause>

  <clause id="14477">
    <literal><![CDATA[
      a(x / y,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(y \ x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4929(a,1),14476(a,1))].">
      <j1 rule="para" parents="4929 14476"/>
    </justification>
  </clause>

  <clause id="14478">
    <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(2982(a,1),14472(a,1,2,1))].">
      <j1 rule="para" parents="2982 14472"/>
    </justification>
  </clause>

  <clause id="14479">
    <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(3228(a,2),14472(a,1,2,1))].">
      <j1 rule="para" parents="3228 14472"/>
    </justification>
  </clause>

  <clause id="14480">
    <literal><![CDATA[
      K(x,y * (z * K(u,y * z))) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(14006(a,1),8189(a,1,2))].">
      <j1 rule="para" parents="14006 8189"/>
    </justification>
  </clause>

  <clause id="14481">
    <literal><![CDATA[
      L(x \ y,x,z / T(y,z)) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(4515,a,14042,a)].">
      <j1 rule="hyper" parents="4515 14042"/>
    </justification>
  </clause>

  <clause id="14482">
    <literal><![CDATA[
      L(x \ y,x,y \ z) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,12907,a(flip),b,14481,a)].">
      <j1 rule="hyper" parents="58 12907 14481"/>
    </justification>
  </clause>

  <clause id="14483">
    <literal><![CDATA[
      x / L(y \ z,y,z \ x) = (x / z) * y
    ]]></literal>
    <justification jstring="[hyper(201,a,14482,a(flip))].">
      <j1 rule="hyper" parents="201 14482"/>
    </justification>
  </clause>

  <clause id="14485">
    <literal><![CDATA[
      x / L(y,z,(z * y) \ x) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(4(a,1),14483(a,1,2,1))].">
      <j1 rule="para" parents="4 14483"/>
    </justification>
  </clause>

  <clause id="14486">
    <literal><![CDATA[
      (x \ y) / (K(z,x) \ y) = ((x \ y) / y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(13615(a,1),14483(a,1,2))].">
      <j1 rule="para" parents="13615 14483"/>
    </justification>
  </clause>

  <clause id="14487">
    <literal><![CDATA[
      x / K(y,L(z,u,(u * K(y,z)) \ x)) = (x / (u * K(y,z))) * u
    ]]></literal>
    <justification jstring="[para(11089(a,1),14485(a,1,2))].">
      <j1 rule="para" parents="11089 14485"/>
    </justification>
  </clause>

  <clause id="14488">
    <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(2224(a,1),14107(a,1,2,1,1))].">
      <j1 rule="para" parents="2224 14107"/>
    </justification>
  </clause>

  <clause id="14489">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,z \ 1) = R(x,z,z \ 1) * y
    ]]></literal>
    <justification jstring="[para(230(a,1),14116(a,1,2)),flip(a)].">
      <j1 rule="para" parents="230 14116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14490">
    <literal><![CDATA[
      ((x * y) / x) * L(x,z,z \ 1) = L(x,z,z \ 1) * y
    ]]></literal>
    <justification jstring="[para(230(a,1),14127(a,1,2)),flip(a)].">
      <j1 rule="para" parents="230 14127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14491">
    <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,11128,a(flip),b,14140,a),flip(a)].">
      <j1 rule="hyper" parents="58 11128 14140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14492">
    <literal><![CDATA[
      T(x,(y / z) \ K(u,y)) = T(x,z / T(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,4716,a(flip),b,14164,a),flip(a)].">
      <j1 rule="hyper" parents="58 4716 14164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14493">
    <literal><![CDATA[
      T(x,(y \ z) / T(z,u)) = T(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),14492(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 14492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14494">
    <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(14192(a,2),11132(a,1))].">
      <j1 rule="para" parents="14192 11132"/>
    </justification>
  </clause>

  <clause id="14495">
    <literal><![CDATA[
      (x \ (y * z)) * K(x * (y \ (x \ (y * z))),y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(30,a,4895,a(flip),b,14211,a),flip(a)].">
      <j1 rule="hyper" parents="30 4895 14211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14496">
    <literal><![CDATA[
      (K(x,y) * z) \ K(x,K(y,u)) = z \ K(y,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,12634,a(flip),b,14239,a),flip(a)].">
      <j1 rule="hyper" parents="334 12634 14239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14497">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u)) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(8214,a,14246,a),flip(a)].">
      <j1 rule="hyper" parents="8214 14246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14498">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(14246(a,1),8214(a,1))].">
      <j1 rule="para" parents="14246 8214"/>
    </justification>
  </clause>

  <clause id="14499">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),u)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),14497(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 14497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14500">
    <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(14250(a,2),11132(a,1))].">
      <j1 rule="para" parents="14250 11132"/>
    </justification>
  </clause>

  <clause id="14501">
    <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(14255(a,2),11132(a,1))].">
      <j1 rule="para" parents="14255 11132"/>
    </justification>
  </clause>

  <clause id="14504">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(14286(a,2),7609(a,1))].">
      <j1 rule="para" parents="14286 7609"/>
    </justification>
  </clause>

  <clause id="14505">
    <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(6463(a,1),14504(a,1,1,2))].">
      <j1 rule="para" parents="6463 14504"/>
    </justification>
  </clause>

  <clause id="14506">
    <literal><![CDATA[
      (x \ T(y * x,z)) / T(y,x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(17(a,2),14320(a,1,2))].">
      <j1 rule="para" parents="17 14320"/>
    </justification>
  </clause>

  <clause id="14507">
    <literal><![CDATA[
      K(x * y,z) * T(y,x) = x \ T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,14506,a)].">
      <j1 rule="hyper" parents="133 14506"/>
    </justification>
  </clause>

  <clause id="14508">
    <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(14506(a,1),543(a,1,1))].">
      <j1 rule="para" parents="14506 543"/>
    </justification>
  </clause>

  <clause id="14509">
    <literal><![CDATA[
      T(x,y * (T(z,u) \ K(w,u * z))) = T(x,y / (u \ T(z * u,w)))
    ]]></literal>
    <justification jstring="[para(14507(a,1),14196(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14507 14196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14510">
    <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(8170(a,1),14405(a,1,1,2))].">
      <j1 rule="para" parents="8170 14405"/>
    </justification>
  </clause>

  <clause id="14511">
    <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(11463(a,1),14405(a,1,2,1))].">
      <j1 rule="para" parents="11463 14405"/>
    </justification>
  </clause>

  <clause id="14512">
    <literal><![CDATA[
      1 / (K(x,y) * z) = (1 / z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8497,a(flip),b,14431,a)].">
      <j1 rule="hyper" parents="58 8497 14431"/>
    </justification>
  </clause>

  <clause id="14513">
    <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(14512(a,1),14067(a,1,2))].">
      <j1 rule="para" parents="14512 14067"/>
    </justification>
  </clause>

  <clause id="14514">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) \ x = K(u,L(z,y,y \ x))
    ]]></literal>
    <justification jstring="[hyper(11168,a,14448,a),flip(a)].">
      <j1 rule="hyper" parents="11168 14448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14515">
    <literal><![CDATA[
      K(x,y * (((z * y) \ u) * K(z,z \ u))) = K(x,T(y * ((z * y) \ u),z))
    ]]></literal>
    <justification jstring="[para(12735(a,1),14480(a,1,2,2,2))].">
      <j1 rule="para" parents="12735 14480"/>
    </justification>
  </clause>

  <clause id="14516">
    <literal><![CDATA[
      (x \ y) / (K(x,z) * y) = ((x \ y) / y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(5391(a,1),14486(a,1,2))].">
      <j1 rule="para" parents="5391 14486"/>
    </justification>
  </clause>

  <clause id="14517">
    <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(3700(a,1),14343(a,1,1,2))].">
      <j1 rule="para" parents="3700 14343"/>
    </justification>
  </clause>

  <clause id="14518">
    <literal><![CDATA[
      L(a(x,y,z),u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(14384(a,1),10176(a,1)),flip(b)].">
      <j1 rule="para" parents="14384 10176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14519">
    <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(11050(a,2),14518(a,1))].">
      <j1 rule="para" parents="11050 14518"/>
    </justification>
  </clause>

  <clause id="14521">
    <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(14514(a,1),345(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14514 345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14522">
    <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(6469(a,1),14146(a,1,2,1))].">
      <j1 rule="para" parents="6469 14146"/>
    </justification>
  </clause>

  <clause id="14523">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,z \ y)) = K(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(334,a,14175,a(flip),b,14187,a),flip(a)].">
      <j1 rule="hyper" parents="334 14175 14187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14524">
    <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),14523(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="180 14523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14525">
    <literal><![CDATA[
      K(x,y * (T(1 / y,z) * u)) = K(x,K(y \ 1,z) * u)
    ]]></literal>
    <justification jstring="[para(3442(a,1),14220(a,2,2,1))].">
      <j1 rule="para" parents="3442 14220"/>
    </justification>
  </clause>

  <clause id="14526">
    <literal><![CDATA[
      (K(x,y) * (z \ 1)) \ K(z,K(y,x)) = (z \ K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,14239,a,b,14454,a)].">
      <j1 rule="hyper" parents="58 14239 14454"/>
    </justification>
  </clause>

  <clause id="14527">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,z \ 1) = y * R(T(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,245,a,b,14489,a),flip(a)].">
      <j1 rule="hyper" parents="334 245 14489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14528">
    <literal><![CDATA[
      (L(x,y,y \ 1) * z) / L(x,y,y \ 1) = (x * z) / x
    ]]></literal>
    <justification jstring="[hyper(130,a,14490,a)].">
      <j1 rule="hyper" parents="130 14490"/>
    </justification>
  </clause>

  <clause id="14529">
    <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(14046(a,1),14528(a,2,1))].">
      <j1 rule="para" parents="14046 14528"/>
    </justification>
  </clause>

  <clause id="14531">
    <literal><![CDATA[
      K(x,y) * ((y / z) * (z * x)) = L(x,z,z \ y) * y
    ]]></literal>
    <justification jstring="[hyper(14181,a,14120,a)].">
      <j1 rule="hyper" parents="14181 14120"/>
    </justification>
  </clause>

  <clause id="14533">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(x,y,T(z,x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,228,a(flip),b,14295,a)].">
      <j1 rule="hyper" parents="58 228 14295"/>
    </justification>
  </clause>

  <clause id="14534">
    <literal><![CDATA[
      a(x,y,T(z,x * y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(709,a,14533,a),flip(a)].">
      <j1 rule="hyper" parents="709 14533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14535">
    <literal><![CDATA[
      L(x \ (T(y,z) \ z),x,K(y,z)) = x \ (y \ T(z,y))
    ]]></literal>
    <justification jstring="[para(5230(a,1),14388(a,1,3))].">
      <j1 rule="para" parents="5230 14388"/>
    </justification>
  </clause>

  <clause id="14536">
    <literal><![CDATA[
      (K(x,y) * z) \ (x \ y) = z \ (x \ T(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5489,a(flip),b,14535,a)].">
      <j1 rule="hyper" parents="58 5489 14535"/>
    </justification>
  </clause>

  <clause id="14537">
    <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(10414(a,1),14500(a,1,2,1,2))].">
      <j1 rule="para" parents="10414 14500"/>
    </justification>
  </clause>

  <clause id="14538">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * u) = K(x,z * ((z \ T(u,y)) * y))
    ]]></literal>
    <justification jstring="[para(11260(a,1),14027(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11260 14027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14539">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(x,K(y,z \ x)) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8019(a,1),14056(a,1,2))].">
      <j1 rule="para" parents="8019 14056"/>
    </justification>
  </clause>

  <clause id="14540">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,x / z)) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8019(a,1),14072(a,1,2))].">
      <j1 rule="para" parents="8019 14072"/>
    </justification>
  </clause>

  <clause id="14541">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = (z * K(x,y)) \ y
    ]]></literal>
    <justification jstring="[para(8131(a,1),14148(a,2,1))].">
      <j1 rule="para" parents="8131 14148"/>
    </justification>
  </clause>

  <clause id="14542">
    <literal><![CDATA[
      ((x * K(y,z)) \ 1) \ K(x,K(y,z)) = (x \ K(z,y)) \ 1
    ]]></literal>
    <justification jstring="[para(14103(a,1),14171(a,2,1))].">
      <j1 rule="para" parents="14103 14171"/>
    </justification>
  </clause>

  <clause id="14543">
    <literal><![CDATA[
      (x * K(y,z)) \ 1 = K(z,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,14526,a,b,14542,a),flip(a)].">
      <j1 rule="hyper" parents="34 14526 14542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14544">
    <literal><![CDATA[
      T(K(x,y) / z,z * K(y,x)) = K(x,y) * (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,14268,a,b,14543,a)].">
      <j1 rule="hyper" parents="58 14268 14543"/>
    </justification>
  </clause>

  <clause id="14546">
    <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(14248(a,2),14498(a,1))].">
      <j1 rule="para" parents="14248 14498"/>
    </justification>
  </clause>

  <clause id="14547">
    <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(14308(a,1),5283(a,1))].">
      <j1 rule="para" parents="14308 5283"/>
    </justification>
  </clause>

  <clause id="14548">
    <literal><![CDATA[
      K(x \ (y * z),T(x,y)) = K(z / (y \ x),x)
    ]]></literal>
    <justification jstring="[hyper(14547,a,8519,a)].">
      <j1 rule="hyper" parents="14547 8519"/>
    </justification>
  </clause>

  <clause id="14549">
    <literal><![CDATA[
      K(x / (y \ z),z) = K(z \ (x * y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,13452,a(flip),b,14548,a),flip(a)].">
      <j1 rule="hyper" parents="58 13452 14548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14550">
    <literal><![CDATA[
      K(x \ (y * (x / z)),x) = K(y / z,x)
    ]]></literal>
    <justification jstring="[para(75(a,1),14549(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 14549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14551">
    <literal><![CDATA[
      K(x / (y \ z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (z \ y),z) = u
    ]]></literal>
    <justification jstring="[para(14549(a,2),10697(a,1))].">
      <j1 rule="para" parents="14549 10697"/>
    </justification>
  </clause>

  <clause id="14552">
    <literal><![CDATA[
      T(K(x,y) * T(y / z,K(x,y)),z) = z \ (y * T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(8635(a,1),14362(a,1,1,2))].">
      <j1 rule="para" parents="8635 14362"/>
    </justification>
  </clause>

  <clause id="14554">
    <literal><![CDATA[
      (x \ (y * z)) * K(y \ (y * z),y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(10698(a,1),14495(a,1,2))].">
      <j1 rule="para" parents="10698 14495"/>
    </justification>
  </clause>

  <clause id="14555">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),14554(a,1,2,1))].">
      <j1 rule="para" parents="4 14554"/>
    </justification>
  </clause>

  <clause id="14557">
    <literal><![CDATA[
      ((x * y) / z) \ (y * x) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(638,a,14555,a),flip(a)].">
      <j1 rule="hyper" parents="638 14555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14558">
    <literal><![CDATA[
      (x \ (y * z)) / (y * z) = (x \ (z * y)) / (z * y)
    ]]></literal>
    <justification jstring="[hyper(117,a,14555,a(flip),b,10646,a)].">
      <j1 rule="hyper" parents="117 14555 10646"/>
    </justification>
  </clause>

  <clause id="14559">
    <literal><![CDATA[
      (x \ y) * K(z \ y,z) = x \ ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),14555(a,1,1,2))].">
      <j1 rule="para" parents="5 14555"/>
    </justification>
  </clause>

  <clause id="14561">
    <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(13763(a,1),14555(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13763 14555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14562">
    <literal><![CDATA[
      (x * y) / (z * K(x,y)) = (y * x) / z
    ]]></literal>
    <justification jstring="[hyper(201,a,14557,a)].">
      <j1 rule="hyper" parents="201 14557"/>
    </justification>
  </clause>

  <clause id="14563">
    <literal><![CDATA[
      x / (y * K(x / z,z)) = (z * (x / z)) / y
    ]]></literal>
    <justification jstring="[para(14557(a,1),338(a,1,2))].">
      <j1 rule="para" parents="14557 338"/>
    </justification>
  </clause>

  <clause id="14564">
    <literal><![CDATA[
      (x * y) / (z * K(y,x)) = K(x,y) * ((x * y) / z)
    ]]></literal>
    <justification jstring="[para(14557(a,1),14365(a,1,2))].">
      <j1 rule="para" parents="14557 14365"/>
    </justification>
  </clause>

  <clause id="14565">
    <literal><![CDATA[
      (x * y) / (z * K(y,T(x,y))) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[para(105(a,1),14562(a,1,1))].">
      <j1 rule="para" parents="105 14562"/>
    </justification>
  </clause>

  <clause id="14566">
    <literal><![CDATA[
      (x * y) / (z * T(x,y)) = (y * x) / (z * x)
    ]]></literal>
    <justification jstring="[para(6374(a,1),14562(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6374 14562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14567">
    <literal><![CDATA[
      x / (y * K(z \ x,z)) = (z * (x / z)) / y
    ]]></literal>
    <justification jstring="[para(5235(a,1),14563(a,1,2,2))].">
      <j1 rule="para" parents="5235 14563"/>
    </justification>
  </clause>

  <clause id="14568">
    <literal><![CDATA[
      R(x,y,z) = (z * (x * y)) / (y * T(z,x * y))
    ]]></literal>
    <justification jstring="[hyper(334,a,15,a,b,14566,a)].">
      <j1 rule="hyper" parents="334 15 14566"/>
    </justification>
  </clause>

  <clause id="14569">
    <literal><![CDATA[
      (x * (y / x)) / (z * (y / x)) = y / (z * (x \ y))
    ]]></literal>
    <justification jstring="[para(6747(a,1),14567(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6747 14567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14570">
    <literal><![CDATA[
      R(x,y,z) \ (z * (x * y)) = y * T(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,14568,a,b,154,a)].">
      <j1 rule="hyper" parents="118 14568 154"/>
    </justification>
  </clause>

  <clause id="14571">
    <literal><![CDATA[
      (x * y) / (z * K(y,x)) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[para(5182(a,1),14565(a,1,2,2))].">
      <j1 rule="para" parents="5182 14565"/>
    </justification>
  </clause>

  <clause id="14572">
    <literal><![CDATA[
      K(x,y) * ((x * y) / z) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[hyper(58,a,14564,a(flip),b,14571,a)].">
      <j1 rule="hyper" parents="58 14564 14571"/>
    </justification>
  </clause>

  <clause id="14573">
    <literal><![CDATA[
      T(x,y) * a(x,z,z \ 1) = R(T(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(7045,a,14527,a)].">
      <j1 rule="hyper" parents="7045 14527"/>
    </justification>
  </clause>

  <clause id="14574">
    <literal><![CDATA[
      a(T(x,y),z,z \ 1) = a(x,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(29,a,726,a,b,14573,a)].">
      <j1 rule="hyper" parents="29 726 14573"/>
    </justification>
  </clause>

  <clause id="14575">
    <literal><![CDATA[
      a(x / y,z,z \ 1) = a(y \ x,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,13088,a(flip),b,14574,a),flip(a)].">
      <j1 rule="hyper" parents="58 13088 14574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14576">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(x,K(y,z)) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8429(a,1),14539(a,1,2))].">
      <j1 rule="para" parents="8429 14539"/>
    </justification>
  </clause>

  <clause id="14577">
    <literal><![CDATA[
      (x \ y) \ K(z,T(y,x)) = (x \ T(y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,14496,a(flip),b,14576,a)].">
      <j1 rule="hyper" parents="58 14496 14576"/>
    </justification>
  </clause>

  <clause id="14578">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8422(a,1),14540(a,1,2))].">
      <j1 rule="para" parents="8422 14540"/>
    </justification>
  </clause>

  <clause id="14579">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) = K(y,x) * ((x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,14543,a(flip),b,14578,a),flip(a)].">
      <j1 rule="hyper" parents="334 14543 14578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14580">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = y \ (x * T(K(z,x),y))
    ]]></literal>
    <justification jstring="[para(105(a,1),14552(a,1,1))].">
      <j1 rule="para" parents="105 14552"/>
    </justification>
  </clause>

  <clause id="14581">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = y \ (x * K(z,T(x,y)))
    ]]></literal>
    <justification jstring="[para(7401(a,2),14580(a,2,2,2))].">
      <j1 rule="para" parents="7401 14580"/>
    </justification>
  </clause>

  <clause id="14583">
    <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(1697(a,2),14381(a,1,1,2))].">
      <j1 rule="para" parents="1697 14381"/>
    </justification>
  </clause>

  <clause id="14584">
    <literal><![CDATA[
      L(x,y,z) \ (z * (x * y)) = T(z * (y * K(x,y)),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),14474(a,1,1,2))].">
      <j1 rule="para" parents="4 14474"/>
    </justification>
  </clause>

  <clause id="14585">
    <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(14006(a,2),14584(a,1,2))].">
      <j1 rule="para" parents="14006 14584"/>
    </justification>
  </clause>

  <clause id="14586">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(9991,a,13993,a),flip(a)].">
      <j1 rule="hyper" parents="9991 13993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14587">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(13993(a,1),9991(a,1))].">
      <j1 rule="para" parents="13993 9991"/>
    </justification>
  </clause>

  <clause id="14588">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(13994,a,14586,a),flip(a)].">
      <j1 rule="hyper" parents="13994 14586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14589">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(K(u,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,13987,a,b,14586,a),flip(a)].">
      <j1 rule="hyper" parents="334 13987 14586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14590">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = a(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,12118,a,b,14586,a)].">
      <j1 rule="hyper" parents="334 12118 14586"/>
    </justification>
  </clause>

  <clause id="14591">
    <literal><![CDATA[
      a(K(x,a(y,z,u)),w,v5) = 1
    ]]></literal>
    <justification jstring="[hyper(334,a,13707,a(flip),b,14586,a),flip(a)].">
      <j1 rule="hyper" parents="334 13707 14586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14592">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13987,a(flip),b,14586,a),flip(a)].">
      <j1 rule="hyper" parents="58 13987 14586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14593">
    <literal><![CDATA[
      (K(x,y) * (z * u)) * a(x,z,K(u,y)) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(119,a,14586,a(flip),b,9,a(flip))].">
      <j1 rule="hyper" parents="119 14586 9"/>
    </justification>
  </clause>

  <clause id="14594">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) = x * a(w,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(14586(a,1),13990(a,1,2))].">
      <j1 rule="para" parents="14586 13990"/>
    </justification>
  </clause>

  <clause id="14595">
    <literal><![CDATA[
      K(x,a(a(y,z,u),w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(13994,a,14591,a)].">
      <j1 rule="hyper" parents="13994 14591"/>
    </justification>
  </clause>

  <clause id="14596">
    <literal><![CDATA[
      a(a(x,y,z),u,K(w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,13987,a(flip),b,14591,a)].">
      <j1 rule="hyper" parents="58 13987 14591"/>
    </justification>
  </clause>

  <clause id="14597">
    <literal><![CDATA[
      a(a(x,y,K(z,u)),w,v5) = 1
    ]]></literal>
    <justification jstring="[para(13702(a,2),14591(a,1,1))].">
      <j1 rule="para" parents="13702 14591"/>
    </justification>
  </clause>

  <clause id="14598">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * v5 = v5 * a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(552,a,14595,a)].">
      <j1 rule="hyper" parents="552 14595"/>
    </justification>
  </clause>

  <clause id="14599">
    <literal><![CDATA[
      T(x,a(a(y,z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,14595,a)].">
      <j1 rule="hyper" parents="51 14595"/>
    </justification>
  </clause>

  <clause id="14600">
    <literal><![CDATA[
      x / a(a(y,z,u),w,v5) = a(a(y,z,u),w,v5) \ x
    ]]></literal>
    <justification jstring="[hyper(171,a,5275,a,b,14595,a(flip))].">
      <j1 rule="hyper" parents="171 5275 14595"/>
    </justification>
  </clause>

  <clause id="14601">
    <literal><![CDATA[
      T(x,L(y,z,a(u,w,v5))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(11200,a,14596,a)].">
      <j1 rule="hyper" parents="11200 14596"/>
    </justification>
  </clause>

  <clause id="14602">
    <literal><![CDATA[
      L(K(x,y),z,a(u,w,v5)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6202,a,14596,a)].">
      <j1 rule="hyper" parents="6202 14596"/>
    </justification>
  </clause>

  <clause id="14603">
    <literal><![CDATA[
      (a(x,y,z) * u) * K(w,v5) = a(x,y,z) * (u * K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(214,a,14596,a)].">
      <j1 rule="hyper" parents="214 14596"/>
    </justification>
  </clause>

  <clause id="14604">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) * v5 = a(x,y,K(z,u)) * (w * v5)
    ]]></literal>
    <justification jstring="[hyper(6922,a,14597,a)].">
      <j1 rule="hyper" parents="6922 14597"/>
    </justification>
  </clause>

  <clause id="14605">
    <literal><![CDATA[
      L(x,y,a(z,u,K(w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,14597,a)].">
      <j1 rule="hyper" parents="47 14597"/>
    </justification>
  </clause>

  <clause id="14606">
    <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(14599(a,1),431(a,1))].">
      <j1 rule="para" parents="14599 431"/>
    </justification>
  </clause>

  <clause id="14607">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) \ v5 = w \ (a(x,y,K(z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,311,a(flip),b,14605,a)].">
      <j1 rule="hyper" parents="58 311 14605"/>
    </justification>
  </clause>

  <clause id="14608">
    <literal><![CDATA[
      L(x,y,a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      x = v6
    ]]></literal>
    <justification jstring="[para(14605(a,1),45(a,2))].">
      <j1 rule="para" parents="14605 45"/>
    </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="[para(14605(a,1),556(a,1,2))].">
      <j1 rule="para" parents="14605 556"/>
    </justification>
  </clause>

  <clause id="14610">
    <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(14605(a,1),490(a,1,2,2,1))].">
      <j1 rule="para" parents="14605 490"/>
    </justification>
  </clause>

  <clause id="14612">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,13676,a,b,14588,a)].">
      <j1 rule="hyper" parents="334 13676 14588"/>
    </justification>
  </clause>

  <clause id="14613">
    <literal><![CDATA[
      (x * y) * a(y,z,K(u,w)) = x * T(y,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,14588,a,b,6470,a)].">
      <j1 rule="hyper" parents="119 14588 6470"/>
    </justification>
  </clause>

  <clause id="14614">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,14588,a,b,4995,a(flip))].">
      <j1 rule="hyper" parents="119 14588 4995"/>
    </justification>
  </clause>

  <clause id="14615">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) / x = T(1 / x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(117,a,14588,a,b,5093,a)].">
      <j1 rule="hyper" parents="117 14588 5093"/>
    </justification>
  </clause>

  <clause id="14616">
    <literal><![CDATA[
      K(x * y,(x * y) \ (z \ ((z * x) * y))) = a(x * y,x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(10693,a,14588,a(flip))].">
      <j1 rule="hyper" parents="10693 14588"/>
    </justification>
  </clause>

  <clause id="14617">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(14588(a,2),5034(a,2,1)),flip(a)].">
      <j1 rule="para" parents="14588 5034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14618">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(14588(a,2),5030(a,1,2))].">
      <j1 rule="para" parents="14588 5030"/>
    </justification>
  </clause>

  <clause id="14619">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (x * w) = T(x,a(u,y,z)) * w
    ]]></literal>
    <justification jstring="[para(14588(a,2),5047(a,1,1))].">
      <j1 rule="para" parents="14588 5047"/>
    </justification>
  </clause>

  <clause id="14620">
    <literal><![CDATA[
      (x / y) \ (x * a(y,z,K(u,w))) = T(y,a(w,z,u))
    ]]></literal>
    <justification jstring="[para(14588(a,2),6465(a,1,2,2))].">
      <j1 rule="para" parents="14588 6465"/>
    </justification>
  </clause>

  <clause id="14621">
    <literal><![CDATA[
      L(a(x,y,K(z,u)),w,v5) = K(x,L(a(u,y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(14588(a,2),11089(a,1,1))].">
      <j1 rule="para" parents="14588 11089"/>
    </justification>
  </clause>

  <clause id="14622">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(z,K(x,a(w,y,u)))
    ]]></literal>
    <justification jstring="[para(14588(a,1),13702(a,2,2))].">
      <j1 rule="para" parents="14588 13702"/>
    </justification>
  </clause>

  <clause id="14623">
    <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(14588(a,2),14348(a,1,2,2))].">
      <j1 rule="para" parents="14588 14348"/>
    </justification>
  </clause>

  <clause id="14624">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,14586,a(flip),b,14589,a),flip(a)].">
      <j1 rule="hyper" parents="334 14586 14589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14625">
    <literal><![CDATA[
      a(x \ y,x,K(z,u)) = a(u,x,K(y / x,z))
    ]]></literal>
    <justification jstring="[hyper(14477,a,14592,a)].">
      <j1 rule="hyper" parents="14477 14592"/>
    </justification>
  </clause>

  <clause id="14626">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,K(w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(13754,a,14592,a),flip(a)].">
      <j1 rule="hyper" parents="13754 14592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14627">
    <literal><![CDATA[
      a(L(x,y,z),x,K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(13722,a,14592,a),flip(a)].">
      <j1 rule="hyper" parents="13722 14592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14628">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(11331,a,14592,a)].">
      <j1 rule="hyper" parents="11331 14592"/>
    </justification>
  </clause>

  <clause id="14629">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(11189,a,14592,a)].">
      <j1 rule="hyper" parents="11189 14592"/>
    </justification>
  </clause>

  <clause id="14630">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(11180,a,14592,a)].">
      <j1 rule="hyper" parents="11180 14592"/>
    </justification>
  </clause>

  <clause id="14631">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(11177,a,14592,a)].">
      <j1 rule="hyper" parents="11177 14592"/>
    </justification>
  </clause>

  <clause id="14632">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,13692,a,b,14592,a)].">
      <j1 rule="hyper" parents="334 13692 14592"/>
    </justification>
  </clause>

  <clause id="14633">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,11333,a,b,14592,a)].">
      <j1 rule="hyper" parents="334 11333 14592"/>
    </justification>
  </clause>

  <clause id="14634">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * x) = a(w,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,10187,a,b,14592,a)].">
      <j1 rule="hyper" parents="334 10187 14592"/>
    </justification>
  </clause>

  <clause id="14635">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,x) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,6199,a,b,14592,a)].">
      <j1 rule="hyper" parents="334 6199 14592"/>
    </justification>
  </clause>

  <clause id="14636">
    <literal><![CDATA[
      a((x \ y) \ z,u,K(w,v5)) = a(v5,u,K(y \ (x * z),w))
    ]]></literal>
    <justification jstring="[hyper(334,a,12121,a(flip),b,14592,a),flip(a)].">
      <j1 rule="hyper" parents="334 12121 14592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14637">
    <literal><![CDATA[
      a(x \ y,z,K(u,w)) = a(w,z,K(u,y \ x))
    ]]></literal>
    <justification jstring="[hyper(334,a,11338,a(flip),b,14592,a),flip(a)].">
      <j1 rule="hyper" parents="334 11338 14592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14638">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,11337,a(flip),b,14592,a),flip(a)].">
      <j1 rule="hyper" parents="334 11337 14592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14639">
    <literal><![CDATA[
      a(x,y \ z,K(y,u)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,11222,a(flip),b,14592,a),flip(a)].">
      <j1 rule="hyper" parents="334 11222 14592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14640">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,14592,a,b,6204,a)].">
      <j1 rule="hyper" parents="119 14592 6204"/>
    </justification>
  </clause>

  <clause id="14641">
    <literal><![CDATA[
      a(x \ y,z,K(u,w)) = a(u,z,K(y \ x,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,11338,a,b,14592,a),flip(a)].">
      <j1 rule="hyper" parents="58 11338 14592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14642">
    <literal><![CDATA[
      a(x,y,K(z,u \ z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11335,a,b,14592,a)].">
      <j1 rule="hyper" parents="58 11335 14592"/>
    </justification>
  </clause>

  <clause id="14643">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,11333,a,b,14592,a)].">
      <j1 rule="hyper" parents="58 11333 14592"/>
    </justification>
  </clause>

  <clause id="14644">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11321,a,b,14592,a)].">
      <j1 rule="hyper" parents="58 11321 14592"/>
    </justification>
  </clause>

  <clause id="14645">
    <literal><![CDATA[
      a((x * y) \ z,u,K(w,v5)) = a(w,u,K(v5,y \ (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,12120,a(flip),b,14592,a),flip(a)].">
      <j1 rule="hyper" parents="58 12120 14592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14646">
    <literal><![CDATA[
      a(L(x,y,z),u,K(w,v5)) = a(w,u,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,12118,a(flip),b,14592,a),flip(a)].">
      <j1 rule="hyper" parents="58 12118 14592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14647">
    <literal><![CDATA[
      a(x * y,z,K(u,x)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,11332,a(flip),b,14592,a),flip(a)].">
      <j1 rule="hyper" parents="58 11332 14592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14648">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,11222,a(flip),b,14592,a),flip(a)].">
      <j1 rule="hyper" parents="58 11222 14592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14649">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,14592,a(flip),b,13701,a)].">
      <j1 rule="hyper" parents="119 14592 13701"/>
    </justification>
  </clause>

  <clause id="14650">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (a(z,y,K(x,u)) * w) = w
    ]]></literal>
    <justification jstring="[hyper(118,a,14592,a(flip),b,10187,a),flip(a)].">
      <j1 rule="hyper" parents="118 14592 10187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14651">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(w,y,K(x,K(z,u)))
    ]]></literal>
    <justification jstring="[para(8019(a,1),14592(a,1,3))].">
      <j1 rule="para" parents="8019 14592"/>
    </justification>
  </clause>

  <clause id="14652">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,y,K(x,K(w,z)))
    ]]></literal>
    <justification jstring="[para(8049(a,1),14592(a,1,3))].">
      <j1 rule="para" parents="8049 14592"/>
    </justification>
  </clause>

  <clause id="14653">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(z,y,K(x,K(u,w)))
    ]]></literal>
    <justification jstring="[para(8066(a,1),14592(a,1,3))].">
      <j1 rule="para" parents="8066 14592"/>
    </justification>
  </clause>

  <clause id="14654">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = a(u,y,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(14592(a,2),10186(a,1,1))].">
      <j1 rule="para" parents="14592 10186"/>
    </justification>
  </clause>

  <clause id="14655">
    <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(14592(a,2),10190(a,1,1))].">
      <j1 rule="para" parents="14592 10190"/>
    </justification>
  </clause>

  <clause id="14656">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u,y)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14592(a,1),11102(a,1,2))].">
      <j1 rule="para" parents="14592 11102"/>
    </justification>
  </clause>

  <clause id="14657">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14592(a,2),11102(a,1,2))].">
      <j1 rule="para" parents="14592 11102"/>
    </justification>
  </clause>

  <clause id="14658">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,L(z,y,u)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(14592(a,2),11118(a,1,1))].">
      <j1 rule="para" parents="14592 11118"/>
    </justification>
  </clause>

  <clause id="14659">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[para(14592(a,1),11173(a,1,1))].">
      <j1 rule="para" parents="14592 11173"/>
    </justification>
  </clause>

  <clause id="14660">
    <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(14592(a,1),11165(a,1,2))].">
      <j1 rule="para" parents="14592 11165"/>
    </justification>
  </clause>

  <clause id="14661">
    <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(14592(a,2),11165(a,1,2))].">
      <j1 rule="para" parents="14592 11165"/>
    </justification>
  </clause>

  <clause id="14662">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(14592(a,1),13709(a,1,1))].">
      <j1 rule="para" parents="14592 13709"/>
    </justification>
  </clause>

  <clause id="14663">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x * a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(14592(a,1),13920(a,2,2))].">
      <j1 rule="para" parents="14592 13920"/>
    </justification>
  </clause>

  <clause id="14664">
    <literal><![CDATA[
      L(K(x,y),z,L(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6202,a,14627,a)].">
      <j1 rule="hyper" parents="6202 14627"/>
    </justification>
  </clause>

  <clause id="14665">
    <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,14601,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 14601 17"/>
    </justification>
  </clause>

  <clause id="14666">
    <literal><![CDATA[
      K((a(x,y,z) * u) \ w,v5) = K(u \ (a(x,y,z) \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(11248,a,14602,a)].">
      <j1 rule="hyper" parents="11248 14602"/>
    </justification>
  </clause>

  <clause id="14667">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11132,a,14602,a)].">
      <j1 rule="hyper" parents="11132 14602"/>
    </justification>
  </clause>

  <clause id="14668">
    <literal><![CDATA[
      K(x,(a(y,z,u) \ w) \ v5) = K(x,w \ (a(y,z,u) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,11114,a(flip),b,14602,a),flip(a)].">
      <j1 rule="hyper" parents="58 11114 14602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14669">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,a(w,v5,v6))) = z
    ]]></literal>
    <justification jstring="[para(14602(a,1),6956(a,1))].">
      <j1 rule="para" parents="14602 6956"/>
    </justification>
  </clause>

  <clause id="14671">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(x,y) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,1990,a,b,14624,a)].">
      <j1 rule="hyper" parents="334 1990 14624"/>
    </justification>
  </clause>

  <clause id="14672">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) * K(w,v5) = (x \ L(x,y,z)) * (u * K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(214,a,14626,a)].">
      <j1 rule="hyper" parents="214 14626"/>
    </justification>
  </clause>

  <clause id="14673">
    <literal><![CDATA[
      K(x,L(y,z,L(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11132,a,14664,a)].">
      <j1 rule="hyper" parents="11132 14664"/>
    </justification>
  </clause>

  <clause id="14674">
    <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(14612(a,1),6677(a,1,1,1))].">
      <j1 rule="para" parents="14612 6677"/>
    </justification>
  </clause>

  <clause id="14675">
    <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(14612(a,1),5822(a,1,1,1))].">
      <j1 rule="para" parents="14612 5822"/>
    </justification>
  </clause>

  <clause id="14676">
    <literal><![CDATA[
      T(x,a(y * z,u,y)) = x * a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[para(11332(a,1),14614(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11332 14614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14677">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(14629(a,1),11236(a,1))].">
      <j1 rule="para" parents="14629 11236"/>
    </justification>
  </clause>

  <clause id="14678">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) = x * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(14629(a,1),14614(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14629 14614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14679">
    <literal><![CDATA[
      a(x,y,K(z \ (u * x),w)) = a(w,y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[para(10604(a,1),14633(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10604 14633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14680">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,14592,a(flip),b,14638,a),flip(a)].">
      <j1 rule="hyper" parents="334 14592 14638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14681">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[para(14638(a,1),11102(a,1,2))].">
      <j1 rule="para" parents="14638 11102"/>
    </justification>
  </clause>

  <clause id="14682">
    <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(14638(a,1),11165(a,1,2))].">
      <j1 rule="para" parents="14638 11165"/>
    </justification>
  </clause>

  <clause id="14683">
    <literal><![CDATA[
      a(x,y \ z,K(y,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,14592,a,b,14639,a),flip(a)].">
      <j1 rule="hyper" parents="334 14592 14639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14684">
    <literal><![CDATA[
      a(x,y,K(z,x * u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14592,a(flip),b,14644,a)].">
      <j1 rule="hyper" parents="58 14592 14644"/>
    </justification>
  </clause>

  <clause id="14685">
    <literal><![CDATA[
      a(x * y,z,K(u,x)) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,14592,a(flip),b,14647,a),flip(a)].">
      <j1 rule="hyper" parents="334 14592 14647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14686">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,14592,a,b,14648,a),flip(a)].">
      <j1 rule="hyper" parents="334 14592 14648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14687">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,14592,a(flip),b,14648,a),flip(a)].">
      <j1 rule="hyper" parents="334 14592 14648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14688">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,y)) = x \ T(y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,14649,a(flip),b,723,a),flip(a)].">
      <j1 rule="hyper" parents="116 14649 723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14689">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),y) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14649(a,1),11229(a,1,1))].">
      <j1 rule="para" parents="14649 11229"/>
    </justification>
  </clause>

  <clause id="14690">
    <literal><![CDATA[
      T(x * (y * z),a(x,y,z)) = (x * (y * z)) * 1
    ]]></literal>
    <justification jstring="[para(14016(a,1),14649(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14016 14649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14691">
    <literal><![CDATA[
      T(x,a(x * y,z,u)) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14644(a,1),14649(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14644 14649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14692">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = a(y,z,K(u,x)) * x
    ]]></literal>
    <justification jstring="[hyper(334,a,13677,a,b,14662,a)].">
      <j1 rule="hyper" parents="334 13677 14662"/>
    </justification>
  </clause>

  <clause id="14693">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u * z) = T(u * z,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(11334(a,1),14662(a,1,1))].">
      <j1 rule="para" parents="11334 14662"/>
    </justification>
  </clause>

  <clause id="14694">
    <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(12118(a,1),14662(a,1,1))].">
      <j1 rule="para" parents="12118 14662"/>
    </justification>
  </clause>

  <clause id="14695">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u * w) = T(u,a(z,y,x)) * w
    ]]></literal>
    <justification jstring="[para(14662(a,1),13664(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14662 13664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14696">
    <literal><![CDATA[
      a(K(x,y) / z,u,K(w,v5)) = a(z * K(y,x),u,K(v5,w))
    ]]></literal>
    <justification jstring="[para(14267(a,1),14680(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14267 14680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14697">
    <literal><![CDATA[
      a(x,y * z,K(y,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),14683(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 14683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14698">
    <literal><![CDATA[
      (x * y) * a(y,z,K(u,x)) = T(x * y,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(14685(a,1),14614(a,1,2))].">
      <j1 rule="para" parents="14685 14614"/>
    </justification>
  </clause>

  <clause id="14699">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(y,x) \ a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(116,a,14687,a(flip),b,11120,a),flip(a)].">
      <j1 rule="hyper" parents="116 14687 11120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14700">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(x,y) * a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[para(14687(a,1),11102(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14687 11102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14701">
    <literal><![CDATA[
      T(x,a(y,x \ z,u)) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14687(a,1),14614(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14687 14614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14702">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = x * a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[para(14687(a,1),14649(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14687 14649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14703">
    <literal><![CDATA[
      T(T(x,y),a(y,z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(447,a,14689,a)].">
      <j1 rule="hyper" parents="447 14689"/>
    </justification>
  </clause>

  <clause id="14704">
    <literal><![CDATA[
      T(x,a(y,z,u)) * y = y * T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,14689,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 14689 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14705">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,y))) = a(x,z,K(y,K(u,w)))
    ]]></literal>
    <justification jstring="[para(8053(a,2),14697(a,1,3))].">
      <j1 rule="para" parents="8053 14697"/>
    </justification>
  </clause>

  <clause id="14706">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(14589(a,2),14587(a,1))].">
      <j1 rule="para" parents="14589 14587"/>
    </justification>
  </clause>

  <clause id="14707">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(x,z)) = w
    ]]></literal>
    <justification jstring="[para(14624(a,1),14587(a,1))].">
      <j1 rule="para" parents="14624 14587"/>
    </justification>
  </clause>

  <clause id="14708">
    <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(14590(a,2),14587(a,1))].">
      <j1 rule="para" parents="14590 14587"/>
    </justification>
  </clause>

  <clause id="14709">
    <literal><![CDATA[
      a(L(x,y,z),u,K(w,v5)) = a(x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(334,a,14592,a(flip),b,14646,a),flip(a)].">
      <j1 rule="hyper" parents="334 14592 14646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14710">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,v5))) = K(x,y) * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(14646(a,1),11102(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14646 11102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14711">
    <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(11338(a,1),14677(a,1))].">
      <j1 rule="para" parents="11338 14677"/>
    </justification>
  </clause>

  <clause id="14712">
    <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(13604(a,1),14677(a,1))].">
      <j1 rule="para" parents="13604 14677"/>
    </justification>
  </clause>

  <clause id="14713">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(14628(a,2),14677(a,1))].">
      <j1 rule="para" parents="14628 14677"/>
    </justification>
  </clause>

  <clause id="14714">
    <literal><![CDATA[
      a(x,y \ z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(14639(a,2),14677(a,1))].">
      <j1 rule="para" parents="14639 14677"/>
    </justification>
  </clause>

  <clause id="14715">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(14680(a,2),14677(a,1))].">
      <j1 rule="para" parents="14680 14677"/>
    </justification>
  </clause>

  <clause id="14716">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(14687(a,2),14677(a,1))].">
      <j1 rule="para" parents="14687 14677"/>
    </justification>
  </clause>

  <clause id="14717">
    <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(8049(a,1),14707(a,1,3))].">
      <j1 rule="para" parents="8049 14707"/>
    </justification>
  </clause>

  <clause id="14718">
    <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(13688(a,2),14707(a,1))].">
      <j1 rule="para" parents="13688 14707"/>
    </justification>
  </clause>

  <clause id="14719">
    <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(14550(a,1),14707(a,1,3))].">
      <j1 rule="para" parents="14550 14707"/>
    </justification>
  </clause>

  <clause id="14720">
    <literal><![CDATA[
      a((x * y) \ z,u,K(w,v5)) = a(y \ (x \ z),u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(311(a,1),14709(a,1,1))].">
      <j1 rule="para" parents="311 14709"/>
    </justification>
  </clause>

  <clause id="14721">
    <literal><![CDATA[
      a((x \ y) \ z,u,K(w,v5)) = a(y \ (x * z),u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(502(a,1),14709(a,1,1)),flip(a)].">
      <j1 rule="para" parents="502 14709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14722">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(u,K(x,a(w,y,z)))
    ]]></literal>
    <justification jstring="[para(8048(a,1),14622(a,1,3))].">
      <j1 rule="para" parents="8048 14622"/>
    </justification>
  </clause>

  <clause id="14723">
    <literal><![CDATA[
      a(x,y,K((y * z) / y,u)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[para(4(a,1),14625(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 14625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14724">
    <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,14632,a(flip),b,9172,a)].">
      <j1 rule="hyper" parents="119 14632 9172"/>
    </justification>
  </clause>

  <clause id="14725">
    <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(14634(a,1),260(a,1,1))].">
      <j1 rule="para" parents="14634 260"/>
    </justification>
  </clause>

  <clause id="14726">
    <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(14634(a,1),276(a,1,1)),flip(b)].">
      <j1 rule="para" parents="14634 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14727">
    <literal><![CDATA[
      K(L(x,y,z),u) * K(u,x) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[para(11131(a,1),14635(a,1,1))].">
      <j1 rule="para" parents="11131 14635"/>
    </justification>
  </clause>

  <clause id="14728">
    <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(14637(a,2),14707(a,1))].">
      <j1 rule="para" parents="14637 14707"/>
    </justification>
  </clause>

  <clause id="14729">
    <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(8496(a,1),14640(a,1,2,3))].">
      <j1 rule="para" parents="8496 14640"/>
    </justification>
  </clause>

  <clause id="14730">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(3968,a,14650,a),flip(a)].">
      <j1 rule="hyper" parents="3968 14650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14731">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,y,K(z,K(x,w)))
    ]]></literal>
    <justification jstring="[para(8053(a,1),14652(a,2,3))].">
      <j1 rule="para" parents="8053 14652"/>
    </justification>
  </clause>

  <clause id="14732">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) / w)) = K(x,y) * a(x,z,K(u \ 1,y))
    ]]></literal>
    <justification jstring="[para(5709(a,1),14656(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="5709 14656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14733">
    <literal><![CDATA[
      K(x,L(y,z,K(y,u) * w)) = K(x,y) * a(x,z,K(w,y))
    ]]></literal>
    <justification jstring="[para(7595(a,1),14656(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="7595 14656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14734">
    <literal><![CDATA[
      K(x,L(y,R(z,u,w),z)) = K(x,y) * 1
    ]]></literal>
    <justification jstring="[para(10996(a,1),14656(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10996 14656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14735">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,z,u \ y))
    ]]></literal>
    <justification jstring="[para(11336(a,1),14656(a,1,2))].">
      <j1 rule="para" parents="11336 14656"/>
    </justification>
  </clause>

  <clause id="14736">
    <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(11412(a,1),14656(a,1,2,3))].">
      <j1 rule="para" parents="11412 14656"/>
    </justification>
  </clause>

  <clause id="14737">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u * w,y)) = K(x,L(y,z,u / (w \ 1)))
    ]]></literal>
    <justification jstring="[para(14178(a,1),14656(a,1,2,3))].">
      <j1 rule="para" parents="14178 14656"/>
    </justification>
  </clause>

  <clause id="14738">
    <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(14060(a,1),14656(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="14060 14656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14739">
    <literal><![CDATA[
      K(x,L(y,R(z,u,w),z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(14734(a,2),127(a,1)),flip(b)].">
      <j1 rule="para" parents="14734 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14740">
    <literal><![CDATA[
      K(x,L(y,z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(391(a,1),14739(a,1,2,2))].">
      <j1 rule="para" parents="391 14739"/>
    </justification>
  </clause>

  <clause id="14741">
    <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(9255(a,1),14657(a,1,2,3))].">
      <j1 rule="para" parents="9255 14657"/>
    </justification>
  </clause>

  <clause id="14742">
    <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(14657(a,2),11091(a,1))].">
      <j1 rule="para" parents="14657 11091"/>
    </justification>
  </clause>

  <clause id="14743">
    <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(11219(a,1),14657(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="11219 14657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14744">
    <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(14277(a,1),14657(a,1,2,3))].">
      <j1 rule="para" parents="14277 14657"/>
    </justification>
  </clause>

  <clause id="14745">
    <literal><![CDATA[
      K(x,a(y,z,u) \ x) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(5109,a,14663,a)].">
      <j1 rule="hyper" parents="5109 14663"/>
    </justification>
  </clause>

  <clause id="14746">
    <literal><![CDATA[
      a(x,y,K(z,a(x,y,z) \ u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13734,a(flip),b,14745,a)].">
      <j1 rule="hyper" parents="58 13734 14745"/>
    </justification>
  </clause>

  <clause id="14747">
    <literal><![CDATA[
      T(x,a(y * z,u,y)) = T(x,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,14614,a(flip),b,14676,a),flip(a)].">
      <j1 rule="hyper" parents="334 14614 14676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14748">
    <literal><![CDATA[
      T(x,a(y \ z,u,y)) = T(x,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(5(a,1),14747(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 14747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14749">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,13705,a(flip),b,14678,a),flip(a)].">
      <j1 rule="hyper" parents="334 13705 14678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14750">
    <literal><![CDATA[
      T(x,a(y,y * z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(14467(a,1),14749(a,1,2))].">
      <j1 rule="para" parents="14467 14749"/>
    </justification>
  </clause>

  <clause id="14751">
    <literal><![CDATA[
      T(x,a(y,(z \ y) * u,z)) = T(x,a(z \ y,u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14748,a(flip),b,14750,a)].">
      <j1 rule="hyper" parents="58 14748 14750"/>
    </justification>
  </clause>

  <clause id="14752">
    <literal><![CDATA[
      T(x,a(x * y,z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,14614,a(flip),b,14691,a),flip(a)].">
      <j1 rule="hyper" parents="334 14614 14691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14753">
    <literal><![CDATA[
      T(x,a(x \ y,z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),14752(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 14752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14754">
    <literal><![CDATA[
      T(x,a(y,x \ z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,14614,a(flip),b,14701,a),flip(a)].">
      <j1 rule="hyper" parents="334 14614 14701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14755">
    <literal><![CDATA[
      T(T(x,y),a(z,x \ u,w)) = T(T(x,a(z,u,w)),y)
    ]]></literal>
    <justification jstring="[para(14754(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14754 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14756">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,14649,a(flip),b,14702,a),flip(a)].">
      <j1 rule="hyper" parents="334 14649 14702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14757">
    <literal><![CDATA[
      T(x,a(y,z * u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),14756(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 14756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14758">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(z,K(w,a(u,y,x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14651,a,b,14722,a)].">
      <j1 rule="hyper" parents="58 14651 14722"/>
    </justification>
  </clause>

  <clause id="14759">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(x,K(z,a(u,y,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14652,a(flip),b,14722,a)].">
      <j1 rule="hyper" parents="58 14652 14722"/>
    </justification>
  </clause>

  <clause id="14760">
    <literal><![CDATA[
      a(x,y,K(z,T(u,y))) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[para(8181(a,1),14723(a,1,3))].">
      <j1 rule="para" parents="8181 14723"/>
    </justification>
  </clause>

  <clause id="14761">
    <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(14727(a,1),5410(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14727 5410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14762">
    <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(334,a,11135,a(flip),b,14730,a),flip(a)].">
      <j1 rule="hyper" parents="334 11135 14730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14763">
    <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(14730(a,1),39(a,1))].">
      <j1 rule="para" parents="14730 39"/>
    </justification>
  </clause>

  <clause id="14764">
    <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(14730(a,2),11144(a,1))].">
      <j1 rule="para" parents="14730 11144"/>
    </justification>
  </clause>

  <clause id="14765">
    <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(11272,a,14731,a)].">
      <j1 rule="hyper" parents="11272 14731"/>
    </justification>
  </clause>

  <clause id="14766">
    <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,14709,a,b,14758,a)].">
      <j1 rule="hyper" parents="58 14709 14758"/>
    </justification>
  </clause>

  <clause id="14767">
    <literal><![CDATA[
      T(x * (y * z),a(x,y,z)) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(334,a,3,a(flip),b,14690,a),flip(a)].">
      <j1 rule="hyper" parents="334 3 14690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14769">
    <literal><![CDATA[
      a(x,y,z) * (x * (y * z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,14767,a(flip),b,702,a(flip))].">
      <j1 rule="hyper" parents="119 14767 702"/>
    </justification>
  </clause>

  <clause id="14770">
    <literal><![CDATA[
      a(x,y,z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(14767(a,1),703(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14767 703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14771">
    <literal><![CDATA[
      ((x * y) * z) / (y * (T(x,y) * z)) = a(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(117,a,229,a(flip),b,14769,a)].">
      <j1 rule="hyper" parents="117 229 14769"/>
    </justification>
  </clause>

  <clause id="14772">
    <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(5522(a,1),14769(a,2,1))].">
      <j1 rule="para" parents="5522 14769"/>
    </justification>
  </clause>

  <clause id="14773">
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,x) = a(x,y,z) * ((y * z) * x)
    ]]></literal>
    <justification jstring="[para(14769(a,1),10624(a,1,1))].">
      <j1 rule="para" parents="14769 10624"/>
    </justification>
  </clause>

  <clause id="14775">
    <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(13831,a,14770,a(flip))].">
      <j1 rule="hyper" parents="13831 14770"/>
    </justification>
  </clause>

  <clause id="14777">
    <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(10641(a,2),14713(a,1,3))].">
      <j1 rule="para" parents="10641 14713"/>
    </justification>
  </clause>

  <clause id="14778">
    <literal><![CDATA[
      a(x,y,K(z,x \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(14592(a,1),14713(a,1))].">
      <j1 rule="para" parents="14592 14713"/>
    </justification>
  </clause>

  <clause id="14779">
    <literal><![CDATA[
      a(x,y \ z,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(14592(a,2),14716(a,1))].">
      <j1 rule="para" parents="14592 14716"/>
    </justification>
  </clause>

  <clause id="14780">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = a(z,y,u) * (x / a(z,y,u))
    ]]></literal>
    <justification jstring="[para(14746(a,1),13737(a,1,1))].">
      <j1 rule="para" parents="14746 13737"/>
    </justification>
  </clause>

  <clause id="14781">
    <literal><![CDATA[
      T(1 / x,a(y,z,u)) = a(x,z,K(y,u)) / x
    ]]></literal>
    <justification jstring="[para(14680(a,1),14615(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14680 14615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14782">
    <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,12117,a,b,14621,a)].">
      <j1 rule="hyper" parents="58 12117 14621"/>
    </justification>
  </clause>

  <clause id="14783">
    <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(7297(a,1),14681(a,1,2,3))].">
      <j1 rule="para" parents="7297 14681"/>
    </justification>
  </clause>

  <clause id="14784">
    <literal><![CDATA[
      T(x * y,a(y,z,u)) = T(x,a(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,14693,a(flip),b,14695,a)].">
      <j1 rule="hyper" parents="58 14693 14695"/>
    </justification>
  </clause>

  <clause id="14785">
    <literal><![CDATA[
      T(x,a(y,z,u)) * a(u,z,y) = a(u,z,y) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,13735,a(flip),b,14695,a),flip(a)].">
      <j1 rule="hyper" parents="58 13735 14695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14786">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),a(u,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(246,a,14695,a(flip),b,13735,a(flip))].">
      <j1 rule="hyper" parents="246 14695 13735"/>
    </justification>
  </clause>

  <clause id="14787">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),L(u,z,y)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(14786(a,1),14689(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14786 14689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14788">
    <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(14787(a,1),12538(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14787 12538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14789">
    <literal><![CDATA[
      T(x * y,a(y,z,u)) = y * T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,14704,a(flip),b,14784,a),flip(a)].">
      <j1 rule="hyper" parents="334 14704 14784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14790">
    <literal><![CDATA[
      T(x * y,a(x,z,u)) = x * T(y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14613,a(flip),b,14698,a),flip(a)].">
      <j1 rule="hyper" parents="58 14613 14698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14791">
    <literal><![CDATA[
      T(x,a(y,z,u)) / y = T(x / y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(4835,a,14790,a)].">
      <j1 rule="hyper" parents="4835 14790"/>
    </justification>
  </clause>

  <clause id="14792">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,11102,a(flip),b,14700,a),flip(a)].">
      <j1 rule="hyper" parents="334 11102 14700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14793">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(14700(a,2),11165(a,1))].">
      <j1 rule="para" parents="14700 11165"/>
    </justification>
  </clause>

  <clause id="14794">
    <literal><![CDATA[
      K(x,(y * ((y \ z) / u)) \ z) = K(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(11125,a,14792,a)].">
      <j1 rule="hyper" parents="11125 14792"/>
    </justification>
  </clause>

  <clause id="14795">
    <literal><![CDATA[
      K(x,L(y \ (z \ u),u,z)) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(11124,a,14792,a),flip(a)].">
      <j1 rule="hyper" parents="11124 14792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14796">
    <literal><![CDATA[
      T(x,L(y,z \ u,z)) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,14792,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 14792 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14797">
    <literal><![CDATA[
      K(x,L(y,z * u,z)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),14792(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 14792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14798">
    <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(725(a,1),14792(a,1,2,2))].">
      <j1 rule="para" parents="725 14792"/>
    </justification>
  </clause>

  <clause id="14799">
    <literal><![CDATA[
      K(x,L((y \ z) \ u,z,y)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(502(a,1),14792(a,1,2)),flip(a)].">
      <j1 rule="para" parents="502 14792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14800">
    <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(4357(a,1),14792(a,1,2,2))].">
      <j1 rule="para" parents="4357 14792"/>
    </justification>
  </clause>

  <clause id="14801">
    <literal><![CDATA[
      K(x,L(y \ z,u,y \ u)) = K(x,u \ ((u / y) * z))
    ]]></literal>
    <justification jstring="[para(7251(a,1),14792(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7251 14792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14802">
    <literal><![CDATA[
      x * K(y,L(z,x,u)) = u * ((u \ x) * K(y,z))
    ]]></literal>
    <justification jstring="[para(14792(a,1),11109(a,1,2))].">
      <j1 rule="para" parents="14792 11109"/>
    </justification>
  </clause>

  <clause id="14803">
    <literal><![CDATA[
      K(x,L(y,z,u \ z)) = K(x,L(y,u,u \ z))
    ]]></literal>
    <justification jstring="[para(11476(a,1),14792(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11476 14792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14804">
    <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(14156(a,1),14796(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14156 14796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14805">
    <literal><![CDATA[
      K(x,L(y,z * u,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(13571(a,2),14797(a,1,2))].">
      <j1 rule="para" parents="13571 14797"/>
    </justification>
  </clause>

  <clause id="14806">
    <literal><![CDATA[
      K(x,y \ ((y / z) * (u * z))) = K(x,L(T(u,z),y,z \ y))
    ]]></literal>
    <justification jstring="[para(11441(a,1),14803(a,2,2)),flip(a)].">
      <j1 rule="para" parents="11441 14803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14807">
    <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(14357(a,1),14803(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="14357 14803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14808">
    <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(11476(a,1),14793(a,1,2))].">
      <j1 rule="para" parents="11476 14793"/>
    </justification>
  </clause>

  <clause id="14809">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(14794(a,1),11167(a,1))].">
      <j1 rule="para" parents="14794 11167"/>
    </justification>
  </clause>

  <clause id="14810">
    <literal><![CDATA[
      K(x,(y \ R(y,z,u)) \ w) = K(x,R(y,z,u) \ (y * w))
    ]]></literal>
    <justification jstring="[hyper(14739,a,14799,a)].">
      <j1 rule="hyper" parents="14739 14799"/>
    </justification>
  </clause>

  <clause id="14811">
    <literal><![CDATA[
      x \ (K(y,L(z,u,x)) * u) = (x \ u) * K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(8801,a,14802,a)].">
      <j1 rule="hyper" parents="8801 14802"/>
    </justification>
  </clause>

  <clause id="14812">
    <literal><![CDATA[
      x \ (y * K(z,L(u,y,x))) = (x \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(549,a,14802,a)].">
      <j1 rule="hyper" parents="549 14802"/>
    </justification>
  </clause>

  <clause id="14813">
    <literal><![CDATA[
      x \ (y * K(z,T(y,u))) = (x \ y) * K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(11104(a,1),14812(a,1,2,2))].">
      <j1 rule="para" parents="11104 14812"/>
    </justification>
  </clause>

  <clause id="14814">
    <literal><![CDATA[
      L(x,y,z) \ (x * K(u,w)) = (L(x,y,z) \ x) * K(u,w)
    ]]></literal>
    <justification jstring="[para(14673(a,1),14812(a,1,2,2))].">
      <j1 rule="para" parents="14673 14812"/>
    </justification>
  </clause>

  <clause id="14815">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,y))) = a(x,z,K(u,K(w,y)))
    ]]></literal>
    <justification jstring="[para(8053(a,2),14705(a,2,3))].">
      <j1 rule="para" parents="8053 14705"/>
    </justification>
  </clause>

  <clause id="14816">
    <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(12117(a,1),14708(a,1))].">
      <j1 rule="para" parents="12117 14708"/>
    </justification>
  </clause>

  <clause id="14817">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = K(x,L(y,z,u \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,14681,a(flip),b,14735,a)].">
      <j1 rule="hyper" parents="58 14681 14735"/>
    </justification>
  </clause>

  <clause id="14818">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u \ w,y)) = K(x,L(y,z,(w \ u) \ y))
    ]]></literal>
    <justification jstring="[para(11338(a,2),14735(a,1,2))].">
      <j1 rule="para" parents="11338 14735"/>
    </justification>
  </clause>

  <clause id="14819">
    <literal><![CDATA[
      T(x,a(y,(z \ y) * u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,14748,a(flip),b,14751,a),flip(a)].">
      <j1 rule="hyper" parents="334 14748 14751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14820">
    <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(14782(a,1),14708(a,1))].">
      <j1 rule="para" parents="14782 14708"/>
    </justification>
  </clause>

  <clause id="14821">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = (y \ x) * K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,14581,a,b,14813,a)].">
      <j1 rule="hyper" parents="58 14581 14813"/>
    </justification>
  </clause>

  <clause id="14822">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = K(z,x) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,8520,a(flip),b,14821,a),flip(a)].">
      <j1 rule="hyper" parents="334 8520 14821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14823">
    <literal><![CDATA[
      T(x * K(y,z),x \ z) = K(y,z) * ((x \ z) \ z)
    ]]></literal>
    <justification jstring="[para(72(a,1),14822(a,1,1,1))].">
      <j1 rule="para" parents="72 14822"/>
    </justification>
  </clause>

  <clause id="14824">
    <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(11336(a,1),14660(a,1,2))].">
      <j1 rule="para" parents="11336 14660"/>
    </justification>
  </clause>

  <clause id="14825">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,v5))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,14657,a(flip),b,14710,a),flip(a)].">
      <j1 rule="hyper" parents="334 14657 14710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14826">
    <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(14710(a,2),14661(a,1))].">
      <j1 rule="para" parents="14710 14661"/>
    </justification>
  </clause>

  <clause id="14827">
    <literal><![CDATA[
      K(x,L(y,z \ 1,L(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,14105,a(flip),b,14825,a),flip(a)].">
      <j1 rule="hyper" parents="334 14105 14825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14828">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ u)) = K(x,L(y,z,w \ 1))
    ]]></literal>
    <justification jstring="[para(221(a,1),14825(a,1,2,3))].">
      <j1 rule="para" parents="221 14825"/>
    </justification>
  </clause>

  <clause id="14829">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ v5)) = K(x,L(y,z,w \ (u \ v5)))
    ]]></literal>
    <justification jstring="[para(311(a,1),14825(a,1,2,3))].">
      <j1 rule="para" parents="311 14825"/>
    </justification>
  </clause>

  <clause id="14830">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ 1)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[para(401(a,1),14825(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="401 14825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14831">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(14825(a,1),14740(a,1))].">
      <j1 rule="para" parents="14825 14740"/>
    </justification>
  </clause>

  <clause id="14832">
    <literal><![CDATA[
      K(x,L(y,z,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(14825(a,2),14740(a,1))].">
      <j1 rule="para" parents="14825 14740"/>
    </justification>
  </clause>

  <clause id="14833">
    <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(2752(a,1),14827(a,1,2))].">
      <j1 rule="para" parents="2752 14827"/>
    </justification>
  </clause>

  <clause id="14834">
    <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(14795(a,1),14831(a,1))].">
      <j1 rule="para" parents="14795 14831"/>
    </justification>
  </clause>

  <clause id="14835">
    <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(221(a,1),14826(a,1,2,3))].">
      <j1 rule="para" parents="221 14826"/>
    </justification>
  </clause>

  <clause id="14836">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ y)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14817,a(flip),b,14830,a)].">
      <j1 rule="hyper" parents="58 14817 14830"/>
    </justification>
  </clause>

  <clause id="14837">
    <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(14653(a,1),14717(a,1))].">
      <j1 rule="para" parents="14653 14717"/>
    </justification>
  </clause>

  <clause id="14838">
    <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(14718,a,14374,a),flip(a)].">
      <j1 rule="hyper" parents="14718 14374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14839">
    <literal><![CDATA[
      a(x,y,z) = ((y * x) * z) / (x * (T(y,x) * z))
    ]]></literal>
    <justification jstring="[hyper(334,a,14464,a(flip),b,14771,a)].">
      <j1 rule="hyper" parents="334 14464 14771"/>
    </justification>
  </clause>

  <clause id="14840">
    <literal><![CDATA[
      a(x,y,z) \ ((y * x) * z) = x * (T(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(118,a,14839,a,b,154,a)].">
      <j1 rule="hyper" parents="118 14839 154"/>
    </justification>
  </clause>

  <clause id="14841">
    <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(334,a,649,a(flip),b,14840,a),flip(a)].">
      <j1 rule="hyper" parents="334 649 14840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14842">
    <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(14840(a,1),3096(a,2,2))].">
      <j1 rule="para" parents="14840 3096"/>
    </justification>
  </clause>

  <clause id="14843">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (K(u,z) * w) = K(u,L(z,y,x)) * w
    ]]></literal>
    <justification jstring="[para(11173(a,1),14604(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11173 14604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14844">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) \ v5 = w \ (a(u,y,K(z,x)) * v5)
    ]]></literal>
    <justification jstring="[para(14654(a,1),14607(a,2,2))].">
      <j1 rule="para" parents="14654 14607"/>
    </justification>
  </clause>

  <clause id="14845">
    <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(14636(a,2),14677(a,1))].">
      <j1 rule="para" parents="14636 14677"/>
    </justification>
  </clause>

  <clause id="14846">
    <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(14645(a,2),14707(a,1))].">
      <j1 rule="para" parents="14645 14707"/>
    </justification>
  </clause>

  <clause id="14847">
    <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(334,a,20,a,b,14694,a),flip(a)].">
      <j1 rule="hyper" parents="334 20 14694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14848">
    <literal><![CDATA[
      K(x,L(y,z,K(y,u) * w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,14656,a(flip),b,14733,a),flip(a)].">
      <j1 rule="hyper" parents="334 14656 14733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14849">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ (y * u)) = K(x,a(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(725(a,1),14810(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="725 14810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14850">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(u,w) = x * (L(x,y,z) \ K(u,w))
    ]]></literal>
    <justification jstring="[hyper(1521,a,14814,a),flip(a)].">
      <j1 rule="hyper" parents="1521 14814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14851">
    <literal><![CDATA[
      x / K(y,L(z,u,K(y,z) \ (u \ x))) = (x / (u * K(y,z))) * u
    ]]></literal>
    <justification jstring="[para(14829(a,1),14487(a,1,2))].">
      <j1 rule="para" parents="14829 14487"/>
    </justification>
  </clause>

  <clause id="14852">
    <literal><![CDATA[
      K(x,y) \ L(T(y,a(x,z,u)),z,u) = T(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(14847(a,1),11174(a,1,2))].">
      <j1 rule="para" parents="14847 11174"/>
    </justification>
  </clause>

  <clause id="14853">
    <literal><![CDATA[
      K(x,y) * L(T(x,a(y,z,u)),z,u) = T(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(5426,a,14852,a)].">
      <j1 rule="hyper" parents="5426 14852"/>
    </justification>
  </clause>

  <clause id="14854">
    <literal><![CDATA[
      K(x,y) * L(T(x,a(y,z,u)),z,u) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,20,a,b,14853,a),flip(a)].">
      <j1 rule="hyper" parents="334 20 14853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14855">
    <literal><![CDATA[
      K(x,y) / (z * (L(z,u,w) \ K(x,y))) = (L(z,u,w) \ z) \ 1
    ]]></literal>
    <justification jstring="[para(14850(a,1),14212(a,1,2))].">
      <j1 rule="para" parents="14850 14212"/>
    </justification>
  </clause>

  <clause id="14856">
    <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(14593(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="14593 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14857">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u \ x)) = (x / u) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(14806(a,1),11527(a,1,2))].">
      <j1 rule="para" parents="14806 11527"/>
    </justification>
  </clause>

  <clause id="14858">
    <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(14803(a,1),14835(a,1))].">
      <j1 rule="para" parents="14803 14835"/>
    </justification>
  </clause>

  <clause id="14859">
    <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(14075(a,1),14857(a,2,2))].">
      <j1 rule="para" parents="14075 14857"/>
    </justification>
  </clause>

  <clause id="14860">
    <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(14732(a,2),14660(a,1))].">
      <j1 rule="para" parents="14732 14660"/>
    </justification>
  </clause>

  <clause id="14861">
    <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(14737(a,1),14660(a,1))].">
      <j1 rule="para" parents="14737 14660"/>
    </justification>
  </clause>

  <clause id="14862">
    <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),14762(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="91 14762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14863">
    <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(8048(a,1),14762(a,1,1,3))].">
      <j1 rule="para" parents="8048 14762"/>
    </justification>
  </clause>

  <clause id="14864">
    <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(8443(a,1),14762(a,1,1,3))].">
      <j1 rule="para" parents="8443 14762"/>
    </justification>
  </clause>

  <clause id="14865">
    <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(8067(a,1),14765(a,1,2))].">
      <j1 rule="para" parents="8067 14765"/>
    </justification>
  </clause>

  <clause id="14866">
    <literal><![CDATA[
      K(x,L(y,a(z,u,u \ 1),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14739,a,14798,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14739 14798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14867">
    <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(11122,a,14866,a)].">
      <j1 rule="hyper" parents="11122 14866"/>
    </justification>
  </clause>

  <clause id="14868">
    <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(14818(a,1),14660(a,1))].">
      <j1 rule="para" parents="14818 14660"/>
    </justification>
  </clause>

  <clause id="14869">
    <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(14817(a,2),14868(a,1))].">
      <j1 rule="para" parents="14817 14868"/>
    </justification>
  </clause>

  <clause id="14870">
    <literal><![CDATA[
      a(T(x,y),z,K(u,x * y)) = K(L(x,z,u) * y,x * y)
    ]]></literal>
    <justification jstring="[para(244(a,1),14838(a,1,1)),flip(a)].">
      <j1 rule="para" parents="244 14838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14871">
    <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,11838,a(flip),b,14865,a)].">
      <j1 rule="hyper" parents="58 11838 14865"/>
    </justification>
  </clause>

  <clause id="14872">
    <literal><![CDATA[
      K(a(x,y * z,K(z,u)),w) = a(z,y,K(w,K(x,u)))
    ]]></literal>
    <justification jstring="[para(6878(a,1),14871(a,1,1))].">
      <j1 rule="para" parents="6878 14871"/>
    </justification>
  </clause>

  <clause id="14873">
    <literal><![CDATA[
      K(a(x,y * z,K(z,u)),w) = a(z,y,K(w,K(u,x)))
    ]]></literal>
    <justification jstring="[para(8067(a,1),14872(a,2,3))].">
      <j1 rule="para" parents="8067 14872"/>
    </justification>
  </clause>

  <clause id="14874">
    <literal><![CDATA[
      K(x * y,(x * y) \ (z \ ((z * x) * y))) = 1
    ]]></literal>
    <justification jstring="[hyper(334,a,13995,a(flip),b,14616,a),flip(a)].">
      <j1 rule="hyper" parents="334 13995 14616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14876">
    <literal><![CDATA[
      K(x * y,z \ R(z,x,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,10608,a(flip),b,14874,a)].">
      <j1 rule="hyper" parents="58 10608 14874"/>
    </justification>
  </clause>

  <clause id="14877">
    <literal><![CDATA[
      T(x \ R(x,y,z),y * z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(5077,a,14876,a)].">
      <j1 rule="hyper" parents="5077 14876"/>
    </justification>
  </clause>

  <clause id="14878">
    <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(14876(a,1),14656(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="14876 14656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14879">
    <literal><![CDATA[
      x / K(y,L(z,u,K(z,y) * (u \ x))) = (x / (u * K(y,z))) * u
    ]]></literal>
    <justification jstring="[para(5391(a,1),14851(a,1,2,2,3))].">
      <j1 rule="para" parents="5391 14851"/>
    </justification>
  </clause>

  <clause id="14880">
    <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(14828(a,1),14858(a,1))].">
      <j1 rule="para" parents="14828 14858"/>
    </justification>
  </clause>

  <clause id="14881">
    <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(13592(a,1),14880(a,1,2))].">
      <j1 rule="para" parents="13592 14880"/>
    </justification>
  </clause>

  <clause id="14882">
    <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(14817(a,1),14880(a,1))].">
      <j1 rule="para" parents="14817 14880"/>
    </justification>
  </clause>

  <clause id="14883">
    <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(14828(a,2),14880(a,1))].">
      <j1 rule="para" parents="14828 14880"/>
    </justification>
  </clause>

  <clause id="14884">
    <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(14881,a,13803,a)].">
      <j1 rule="hyper" parents="14881 13803"/>
    </justification>
  </clause>

  <clause id="14885">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,L((y * z) \ u,z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(14881,a,11100,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14881 11100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14886">
    <literal><![CDATA[
      K(x,L(y,z * u,z \ 1)) = K(x,L(y,u,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(14881,a,xx),flip(a)].">
      <j1 rule="hyper" parents="14881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14887">
    <literal><![CDATA[
      K(x,L(y,z \ u,z \ 1)) = K(x,L(y,u,z \ 1))
    ]]></literal>
    <justification jstring="[para(5(a,1),14886(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 14886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14888">
    <literal><![CDATA[
      K(x,(y * z) \ R(y,u,u \ 1)) = K(x,z \ a(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[para(727(a,1),14867(a,1,2))].">
      <j1 rule="para" parents="727 14867"/>
    </justification>
  </clause>

  <clause id="14889">
    <literal><![CDATA[
      x / K(y,L(z,u,u \ x)) = (x / (u * K(y,z))) * u
    ]]></literal>
    <justification jstring="[para(14848(a,1),14879(a,1,2))].">
      <j1 rule="para" parents="14848 14879"/>
    </justification>
  </clause>

  <clause id="14890">
    <literal><![CDATA[
      (x / (y * K(z,u))) * y = (x / y) * (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(14521,a,14889,a),flip(a)].">
      <j1 rule="hyper" parents="14521 14889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14892">
    <literal><![CDATA[
      ((x * y) / (y * K(z,u))) * y = x * (y * K(u,z))
    ]]></literal>
    <justification jstring="[para(6(a,1),14890(a,2,1))].">
      <j1 rule="para" parents="6 14890"/>
    </justification>
  </clause>

  <clause id="14893">
    <literal><![CDATA[
      (x / y) * (y * K(z,T(u,y))) = (x / (K(u,z) * y)) * y
    ]]></literal>
    <justification jstring="[para(7393(a,1),14890(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7393 14890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14894">
    <literal><![CDATA[
      (x / ((y \ 1) * K(z,u))) * (y \ 1) = (x / (y \ 1)) * (y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(14141(a,1),14890(a,2,2))].">
      <j1 rule="para" parents="14141 14890"/>
    </justification>
  </clause>

  <clause id="14895">
    <literal><![CDATA[
      (x * (y * K(z,u))) / y = (x * y) / (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(130,a,14892,a)].">
      <j1 rule="hyper" parents="130 14892"/>
    </justification>
  </clause>

  <clause id="14896">
    <literal><![CDATA[
      (x * (y * K(z,u))) / y != w
    ]]></literal>
    <literal><![CDATA[
      (x * y) / (y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(14892(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="14892 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14897">
    <literal><![CDATA[
      (x / (K(y,z) * u)) * u = (x / u) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7551,a(flip),b,14893,a),flip(a)].">
      <j1 rule="hyper" parents="58 7551 14893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14898">
    <literal><![CDATA[
      (x / (K(y,z) * (1 / u))) * (1 / u) = (x / (1 / u)) * (K(z,y) / u)
    ]]></literal>
    <justification jstring="[para(14038(a,1),14897(a,2,2))].">
      <j1 rule="para" parents="14038 14897"/>
    </justification>
  </clause>

  <clause id="14899">
    <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(14186(a,1),14420(a,1))].">
      <j1 rule="para" parents="14186 14420"/>
    </justification>
  </clause>

  <clause id="14900">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) * (v5 \ 1)))) = K(x,y * (z / (K(u,w) / v5)))
    ]]></literal>
    <justification jstring="[para(14543(a,1),14273(a,1,2,2,2))].">
      <j1 rule="para" parents="14543 14273"/>
    </justification>
  </clause>

  <clause id="14901">
    <literal><![CDATA[
      T(x,T((y / z) \ K(y,u),w)) = T(x,T((z / y) * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(14103(a,1),14341(a,1,2,1))].">
      <j1 rule="para" parents="14103 14341"/>
    </justification>
  </clause>

  <clause id="14902">
    <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),14436(a,1,2)),flip(a)].">
      <j1 rule="para" parents="60 14436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14903">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) * x,u)) = K(x,x * ((y * T(z,u)) \ y))
    ]]></literal>
    <justification jstring="[hyper(334,a,5649,a(flip),b,14902,a),flip(a)].">
      <j1 rule="hyper" parents="334 5649 14902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14904">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) * x,u)) = K(x,T(z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,10779,a(flip),b,14903,a),flip(a)].">
      <j1 rule="hyper" parents="334 10779 14903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14906">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) * x,u)) = K(x,T(z \ x,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,8842,a,b,14904,a),flip(a)].">
      <j1 rule="hyper" parents="334 8842 14904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14907">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,u)) = K(x,T((z \ y) * x,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),14906(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 14906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14908">
    <literal><![CDATA[
      K(x,T((y \ z) * x,z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(9484,a,14907,a),flip(a)].">
      <j1 rule="hyper" parents="9484 14907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14909">
    <literal><![CDATA[
      K(x,T(x * (y \ z),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(12603,a,14908,a)].">
      <j1 rule="hyper" parents="12603 14908"/>
    </justification>
  </clause>

  <clause id="14910">
    <literal><![CDATA[
      K(x,T((y \ z) * x,y)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9973,a(flip),b,14908,a)].">
      <j1 rule="hyper" parents="58 9973 14908"/>
    </justification>
  </clause>

  <clause id="14911">
    <literal><![CDATA[
      K(x,T(x * T(y,z),z)) = K(x,((y \ z) / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11782,a(flip),b,14909,a)].">
      <j1 rule="hyper" parents="58 11782 14909"/>
    </justification>
  </clause>

  <clause id="14912">
    <literal><![CDATA[
      K(x,(y / (y * z)) \ x) = K(x,T(z * x,y))
    ]]></literal>
    <justification jstring="[para(4(a,1),14910(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4 14910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14913">
    <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(9425,a,14912,a)].">
      <j1 rule="hyper" parents="9425 14912"/>
    </justification>
  </clause>

  <clause id="14914">
    <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(14911(a,2),7052(a,1,1))].">
      <j1 rule="para" parents="14911 7052"/>
    </justification>
  </clause>

  <clause id="14915">
    <literal><![CDATA[
      ((x * ((x * y) / x)) / z) \ y = ((x * y) / z) \ T(y,T(x,y))
    ]]></literal>
    <justification jstring="[para(105(a,1),14451(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="105 14451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14916">
    <literal><![CDATA[
      ((x * ((x * y) / x)) / z) \ y = ((x * y) / z) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4473(a,1),14915(a,2,2))].">
      <j1 rule="para" parents="4473 14915"/>
    </justification>
  </clause>

  <clause id="14917">
    <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(9839(a,2),14524(a,1,2,2))].">
      <j1 rule="para" parents="9839 14524"/>
    </justification>
  </clause>

  <clause id="14918">
    <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(10413(a,1),14524(a,1,2,1,1))].">
      <j1 rule="para" parents="10413 14524"/>
    </justification>
  </clause>

  <clause id="14919">
    <literal><![CDATA[
      K(x,L(y,z,u \ L(u,w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11204,a,14672,a)].">
      <j1 rule="hyper" parents="11204 14672"/>
    </justification>
  </clause>

  <clause id="14920">
    <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(14919(a,2),14669(a,1))].">
      <j1 rule="para" parents="14919 14669"/>
    </justification>
  </clause>

  <clause id="14921">
    <literal><![CDATA[
      K(x,y \ L(y,z,u)) = 1 * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(13550(a,1),14724(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13550 14724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14923">
    <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(14729(a,1),14742(a,1))].">
      <j1 rule="para" parents="14729 14742"/>
    </justification>
  </clause>

  <clause id="14924">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u / w,y)) = K(x,L(y,z,u / (y * w)))
    ]]></literal>
    <justification jstring="[para(11318(a,1),14736(a,1,2))].">
      <j1 rule="para" parents="11318 14736"/>
    </justification>
  </clause>

  <clause id="14925">
    <literal><![CDATA[
      K(x,L(L(y,z,u),z,u \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14761,a,14783,a),flip(a)].">
      <j1 rule="hyper" parents="14761 14783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14926">
    <literal><![CDATA[
      K(x,L(L(y,z,u \ 1),z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(25(a,1),14925(a,1,2))].">
      <j1 rule="para" parents="25 14925"/>
    </justification>
  </clause>

  <clause id="14927">
    <literal><![CDATA[
      K(x,L((y * z) \ u,z,y \ 1)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(311(a,1),14925(a,1,2,1))].">
      <j1 rule="para" parents="311 14925"/>
    </justification>
  </clause>

  <clause id="14928">
    <literal><![CDATA[
      x * (y * K(z,L(u,y,x \ 1))) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14925(a,1),11203(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14925 11203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14929">
    <literal><![CDATA[
      (x \ y) * K(z,L(u,y,x \ 1)) = x \ (y * K(z,u))
    ]]></literal>
    <justification jstring="[para(14926(a,1),14812(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14926 14812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14930">
    <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),14927(a,1,2,1))].">
      <j1 rule="para" parents="17 14927"/>
    </justification>
  </clause>

  <clause id="14931">
    <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),14927(a,1,2,1))].">
      <j1 rule="para" parents="81 14927"/>
    </justification>
  </clause>

  <clause id="14932">
    <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,7423,a(flip),b,14928,a),flip(a)].">
      <j1 rule="hyper" parents="116 7423 14928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14934">
    <literal><![CDATA[
      x * (y * K(z,L(u,y,x \ u))) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14817(a,1),14928(a,1,2,2))].">
      <j1 rule="para" parents="14817 14928"/>
    </justification>
  </clause>

  <clause id="14935">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(29,a,11235,a(flip),b,14929,a),flip(a)].">
      <j1 rule="hyper" parents="29 11235 14929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14937">
    <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(14462(a,1),14934(a,2,1))].">
      <j1 rule="para" parents="14462 14934"/>
    </justification>
  </clause>

  <clause id="14938">
    <literal><![CDATA[
      x * K(y,x \ (z \ (u * (z * x)))) = z \ (K(y,u) * (z * x))
    ]]></literal>
    <justification jstring="[para(14930(a,1),14932(a,1,2))].">
      <j1 rule="para" parents="14930 14932"/>
    </justification>
  </clause>

  <clause id="14939">
    <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),14938(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="101 14938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14940">
    <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(9988(a,1),14856(a,1))].">
      <j1 rule="para" parents="9988 14856"/>
    </justification>
  </clause>

  <clause id="14941">
    <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,14863,a(flip),b,14864,a),flip(a)].">
      <j1 rule="hyper" parents="58 14863 14864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14942">
    <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),14941(a,1,2,2,3)),flip(a)].">
      <j1 rule="para" parents="75 14941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14943">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(334,a,14927,a(flip),b,14885,a),flip(a)].">
      <j1 rule="hyper" parents="334 14927 14885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14944">
    <literal><![CDATA[
      (x / (K(y,z) / u)) * (1 / u) = (x / (1 / u)) * (K(z,y) / u)
    ]]></literal>
    <justification jstring="[para(14038(a,1),14898(a,1,1,2))].">
      <j1 rule="para" parents="14038 14898"/>
    </justification>
  </clause>

  <clause id="14946">
    <literal><![CDATA[
      ((x * (y * z)) * K(z,u)) \ ((x * y) * T(z,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(9520(a,1),14380(a,1,1))].">
      <j1 rule="para" parents="9520 14380"/>
    </justification>
  </clause>

  <clause id="14947">
    <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(11089(a,1),14409(a,1,1))].">
      <j1 rule="para" parents="11089 14409"/>
    </justification>
  </clause>

  <clause id="14948">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),T(x,z)) = K(y * K((x \ 1) \ y,z),x)
    ]]></literal>
    <justification jstring="[hyper(14505,a,11547,a),flip(a)].">
      <j1 rule="hyper" parents="14505 11547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14949">
    <literal><![CDATA[
      K(x * K((y \ 1) \ x,z),y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(14504,a,14948,a),flip(a)].">
      <j1 rule="hyper" parents="14504 14948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14951">
    <literal><![CDATA[
      K(x * K(y * x,z),y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(14124(a,1),14949(a,1,1,2))].">
      <j1 rule="para" parents="14124 14949"/>
    </justification>
  </clause>

  <clause id="14952">
    <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,14951,a(flip),b,5548,a(flip))].">
      <j1 rule="hyper" parents="119 14951 5548"/>
    </justification>
  </clause>

  <clause id="14953">
    <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(8048(a,1),14764(a,1,1,3))].">
      <j1 rule="para" parents="8048 14764"/>
    </justification>
  </clause>

  <clause id="14954">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) \ w) = K(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(14392,a,14833,a)].">
      <j1 rule="hyper" parents="14392 14833"/>
    </justification>
  </clause>

  <clause id="14956">
    <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(3654(a,1),14954(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3654 14954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14957">
    <literal><![CDATA[
      x * K(y,x \ (z \ ((u * z) * x))) = z \ ((K(y,u) * z) * x)
    ]]></literal>
    <justification jstring="[para(12796(a,1),14939(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12796 14939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14958">
    <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,14957,a(flip),b,4487,a)].">
      <j1 rule="hyper" parents="116 14957 4487"/>
    </justification>
  </clause>

  <clause id="14959">
    <literal><![CDATA[
      K(x,L(y,z,u)) * T(u * (z / y),K(x,y)) = u * (z / T(y,x))
    ]]></literal>
    <justification jstring="[para(11099(a,1),14947(a,1,1))].">
      <j1 rule="para" parents="11099 14947"/>
    </justification>
  </clause>

  <clause id="14960">
    <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(7689(a,1),14043(a,1,3,2))].">
      <j1 rule="para" parents="7689 14043"/>
    </justification>
  </clause>

  <clause id="14961">
    <literal><![CDATA[
      K(x,(((y * z) / u) \ K(y,T(z,x))) \ w) = K(x,(((z * y) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(7401(a,2),14452(a,1,2,1,2))].">
      <j1 rule="para" parents="7401 14452"/>
    </justification>
  </clause>

  <clause id="14962">
    <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(14488(a,2),14501(a,1))].">
      <j1 rule="para" parents="14488 14501"/>
    </justification>
  </clause>

  <clause id="14963">
    <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(14643(a,1),14743(a,2,2))].">
      <j1 rule="para" parents="14643 14743"/>
    </justification>
  </clause>

  <clause id="14964">
    <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(14963(a,2),11165(a,1))].">
      <j1 rule="para" parents="14963 11165"/>
    </justification>
  </clause>

  <clause id="14965">
    <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),14964(a,1,2,3,1,2))].">
      <j1 rule="para" parents="104 14964"/>
    </justification>
  </clause>

  <clause id="14966">
    <literal><![CDATA[
      K(x,L(y,z,(u * x) \ w)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(14965,a,xx),flip(a)].">
      <j1 rule="hyper" parents="14965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14967">
    <literal><![CDATA[
      K(x \ 1,L(y,z,x \ u)) = K(x \ 1,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(164(a,1),14966(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="164 14966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14968">
    <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),14878(a,2,2))].">
      <j1 rule="para" parents="112 14878"/>
    </justification>
  </clause>

  <clause id="14970">
    <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(14968(a,2),127(a,1)),flip(b)].">
      <j1 rule="para" parents="14968 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14971">
    <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,9325,a(flip),b,14913,a),flip(a)].">
      <j1 rule="hyper" parents="58 9325 14913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14972">
    <literal><![CDATA[
      K(x,T(T(y * T(x,z),u),z)) = K(x,T((u / (u * y)) \ x,z))
    ]]></literal>
    <justification jstring="[hyper(7970,a,14971,a)].">
      <j1 rule="hyper" parents="7970 14971"/>
    </justification>
  </clause>

  <clause id="14974">
    <literal><![CDATA[
      K(x,T((y / (y * z)) \ x,u)) = K(x,T(T(x * z,y),u))
    ]]></literal>
    <justification jstring="[hyper(58,a,10574,a(flip),b,14972,a),flip(a)].">
      <j1 rule="hyper" parents="58 10574 14972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14976">
    <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),14974(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="105 14974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14977">
    <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(334,a,9487,a(flip),b,14976,a),flip(a)].">
      <j1 rule="hyper" parents="334 9487 14976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14978">
    <literal><![CDATA[
      K(x,T(x * T(y,z),z)) = K(x,R(1 / (1 / (1 / y)),y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(9089,a,14977,a)].">
      <j1 rule="hyper" parents="9089 14977"/>
    </justification>
  </clause>

  <clause id="14979">
    <literal><![CDATA[
      K(x,T(x * T(y,z),z)) = K(x,R((1 / (1 / y)) \ 1,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,5607,a(flip),b,14978,a),flip(a)].">
      <j1 rule="hyper" parents="334 5607 14978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14980">
    <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),14979(a,2,2,1,1))].">
      <j1 rule="para" parents="75 14979"/>
    </justification>
  </clause>

  <clause id="14981">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,T(x * T(y,z),z))
    ]]></literal>
    <justification jstring="[hyper(334,a,11991,a(flip),b,14980,a)].">
      <j1 rule="hyper" parents="334 11991 14980"/>
    </justification>
  </clause>

  <clause id="14983">
    <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(14981(a,2),7052(a,1,1))].">
      <j1 rule="para" parents="14981 7052"/>
    </justification>
  </clause>

  <clause id="14984">
    <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,7054,a(flip),b,14983,a)].">
      <j1 rule="hyper" parents="58 7054 14983"/>
    </justification>
  </clause>

  <clause id="14985">
    <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,7052,a(flip),b,14914,a)].">
      <j1 rule="hyper" parents="58 7052 14914"/>
    </justification>
  </clause>

  <clause id="14986">
    <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(334,a,13001,a(flip),b,14985,a),flip(a)].">
      <j1 rule="hyper" parents="334 13001 14985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14987">
    <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),14986(a,2,2,2))].">
      <j1 rule="para" parents="72 14986"/>
    </justification>
  </clause>

  <clause id="14989">
    <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,14984,a,b,14987,a)].">
      <j1 rule="hyper" parents="58 14984 14987"/>
    </justification>
  </clause>

  <clause id="14991">
    <literal><![CDATA[
      R(K(x,R(x * y,z,u)),y,w) = K(R(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(12795(a,1),14989(a,1,1))].">
      <j1 rule="para" parents="12795 14989"/>
    </justification>
  </clause>

  <clause id="14992">
    <literal><![CDATA[
      K(x,R(R(x * y,z,u),y,w)) = K(R(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(12802,a,14991,a)].">
      <j1 rule="hyper" parents="12802 14991"/>
    </justification>
  </clause>

  <clause id="14993">
    <literal><![CDATA[
      K(x,R(R(x * y,z,u),y,w)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,12795,a(flip),b,14992,a),flip(a)].">
      <j1 rule="hyper" parents="334 12795 14992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14994">
    <literal><![CDATA[
      K(x,R(x * y,y * z,u)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12825,a(flip),b,14993,a),flip(a)].">
      <j1 rule="hyper" parents="58 12825 14993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14996">
    <literal><![CDATA[
      K(x,R(x * y,z,u)) = K(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,13010,a(flip),b,14994,a),flip(a)].">
      <j1 rule="hyper" parents="58 13010 14994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14997">
    <literal><![CDATA[
      T(x,R(x * y,z,u)) = T(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,14996,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 14996 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14998">
    <literal><![CDATA[
      L(T(x,R(y,z,u)),y,T(x,w)) = T(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,12862,a,b,14997,a)].">
      <j1 rule="hyper" parents="334 12862 14997"/>
    </justification>
  </clause>

  <clause id="14999">
    <literal><![CDATA[
      L(T(x,R(y,z,u)),y,x) = T(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(11483,a,14998,a)].">
      <j1 rule="hyper" parents="11483 14998"/>
    </justification>
  </clause>

  <clause id="15000">
    <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,12803,a,b,14999,a)].">
      <j1 rule="hyper" parents="58 12803 14999"/>
    </justification>
  </clause>

  <clause id="15001">
    <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(3301(a,2),14999(a,2,2,1))].">
      <j1 rule="para" parents="3301 14999"/>
    </justification>
  </clause>

  <clause id="15002">
    <literal><![CDATA[
      T(x,x * y) * a(x,z,K(u,y)) = T(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[para(14586(a,1),15000(a,1,2))].">
      <j1 rule="para" parents="14586 15000"/>
    </justification>
  </clause>

  <clause id="15003">
    <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,13914,a,b,15002,a)].">
      <j1 rule="hyper" parents="58 13914 15002"/>
    </justification>
  </clause>

  <clause id="15004">
    <literal><![CDATA[
      T(x * a(x,y,K(z,u)),u * x) = T(x,R(x * u,y,z))
    ]]></literal>
    <justification jstring="[para(13149(a,1),15003(a,1,1))].">
      <j1 rule="para" parents="13149 15003"/>
    </justification>
  </clause>

  <clause id="15005">
    <literal><![CDATA[
      T(T(x,a(y,z,u) \ x),u * x) = T(x,R(x * u,z,y))
    ]]></literal>
    <justification jstring="[para(14663(a,2),15004(a,1,1))].">
      <j1 rule="para" parents="14663 15004"/>
    </justification>
  </clause>

  <clause id="15006">
    <literal><![CDATA[
      T(T(x,x * y),a(z,u,y) \ x) = T(x,R(x * y,u,z))
    ]]></literal>
    <justification jstring="[hyper(4661,a,15005,a)].">
      <j1 rule="hyper" parents="4661 15005"/>
    </justification>
  </clause>

  <clause id="15007">
    <literal><![CDATA[
      T(x,R(x * y,z,u)) = T(x,L(y * x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,13922,a(flip),b,15006,a),flip(a)].">
      <j1 rule="hyper" parents="58 13922 15006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15008">
    <literal><![CDATA[
      K(x,(y * L(y \ 1,z,u)) \ w) = K(x,y \ (L(y \ 1,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(14417,a,14956,a),flip(a)].">
      <j1 rule="hyper" parents="14417 14956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15009">
    <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(4553(a,1),14437(a,1,1,1))].">
      <j1 rule="para" parents="4553 14437"/>
    </justification>
  </clause>

  <clause id="15010">
    <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(14586(a,1),14772(a,1,1))].">
      <j1 rule="para" parents="14586 14772"/>
    </justification>
  </clause>

  <clause id="15011">
    <literal><![CDATA[
      K(x,L(y,a(z \ 1,z,u),L(u,z,z \ 1))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,14673,a(flip),b,14800,a),flip(a)].">
      <j1 rule="hyper" parents="334 14673 14800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15012">
    <literal><![CDATA[
      K(x,L(y,a(z \ 1,z,u),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14826,a,15011,a)].">
      <j1 rule="hyper" parents="14826 15011"/>
    </justification>
  </clause>

  <clause id="15014">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) * (y \ u)) = K(x,a(z \ 1,z,y) \ u)
    ]]></literal>
    <justification jstring="[para(4365(a,1),15011(a,1,2))].">
      <j1 rule="para" parents="4365 15011"/>
    </justification>
  </clause>

  <clause id="15016">
    <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(14032(a,1),14952(a,1,1,2))].">
      <j1 rule="para" parents="14032 14952"/>
    </justification>
  </clause>

  <clause id="15017">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,y * K(x * y,u),x)
    ]]></literal>
    <justification jstring="[hyper(13598,a,15016,a)].">
      <j1 rule="hyper" parents="13598 15016"/>
    </justification>
  </clause>

  <clause id="15019">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,x \ T(x * y,u),x)
    ]]></literal>
    <justification jstring="[para(14052(a,2),15017(a,2,2))].">
      <j1 rule="para" parents="14052 15017"/>
    </justification>
  </clause>

  <clause id="15020">
    <literal><![CDATA[
      L(x,x \ T(x * y,z),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(12973,a,15019,a),flip(a)].">
      <j1 rule="hyper" parents="12973 15019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15021">
    <literal><![CDATA[
      L(x,x \ T(y,z),x) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),15020(a,1,2,2,1))].">
      <j1 rule="para" parents="5 15020"/>
    </justification>
  </clause>

  <clause id="15023">
    <literal><![CDATA[
      L(x,x \ (y / z),x) = L(x,x \ (z \ y),x)
    ]]></literal>
    <justification jstring="[para(107(a,1),15021(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 15021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15024">
    <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(15023(a,1),12713(a,1,2))].">
      <j1 rule="para" parents="15023 12713"/>
    </justification>
  </clause>

  <clause id="15025">
    <literal><![CDATA[
      T(T(x,x * y) * K(x * y,z),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(13338(a,1),15009(a,1,1,2))].">
      <j1 rule="para" parents="13338 15009"/>
    </justification>
  </clause>

  <clause id="15026">
    <literal><![CDATA[
      T(T(x * K(x * y,z),x * y),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(7687(a,2),15025(a,1,1))].">
      <j1 rule="para" parents="7687 15025"/>
    </justification>
  </clause>

  <clause id="15028">
    <literal><![CDATA[
      T(T(x * K(x * y,z),y),x * y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[hyper(447,a,15026,a)].">
      <j1 rule="hyper" parents="447 15026"/>
    </justification>
  </clause>

  <clause id="15029">
    <literal><![CDATA[
      T(T(x * K(x * y,z),y),x * y) = y \ T(T(x,x * y) * y,z)
    ]]></literal>
    <justification jstring="[para(4553(a,1),15028(a,2,2,1,1))].">
      <j1 rule="para" parents="4553 15028"/>
    </justification>
  </clause>

  <clause id="15030">
    <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),14491(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 14491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15031">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,z,u)) = K(x,L(y,(y / z) \ 1,u))
    ]]></literal>
    <justification jstring="[para(10682(a,1),15030(a,2,2))].">
      <j1 rule="para" parents="10682 15030"/>
    </justification>
  </clause>

  <clause id="15032">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,z,u)) = K(x,L(y,(z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(13594(a,1),15031(a,2,2))].">
      <j1 rule="para" parents="13594 15031"/>
    </justification>
  </clause>

  <clause id="15033">
    <literal><![CDATA[
      K(x,L((y / z) * z,z,u)) = K(x,L(y,(z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(14494,a,15032,a)].">
      <j1 rule="hyper" parents="14494 15032"/>
    </justification>
  </clause>

  <clause id="15034">
    <literal><![CDATA[
      K(x,L(y,(z \ y) \ 1,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),15033(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15035">
    <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(334,a,14141,a(flip),b,14561,a),flip(a)].">
      <j1 rule="hyper" parents="334 14141 14561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15036">
    <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(14468(a,1),14227(a,1,2))].">
      <j1 rule="para" parents="14468 14227"/>
    </justification>
  </clause>

  <clause id="15037">
    <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(14683(a,1),14862(a,2,1))].">
      <j1 rule="para" parents="14683 14862"/>
    </justification>
  </clause>

  <clause id="15038">
    <literal><![CDATA[
      K(x,K(y,z \ (u * ((u \ z) * w)))) = K(x,K(y,L(w,z,u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,14762,a(flip),b,15037,a),flip(a)].">
      <j1 rule="hyper" parents="334 14762 15037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15039">
    <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),15038(a,1,2,2))].">
      <j1 rule="para" parents="91 15038"/>
    </justification>
  </clause>

  <clause id="15040">
    <literal><![CDATA[
      K(x,K(y,L(z,u / w,w))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(11478(a,2),15039(a,1,2,2))].">
      <j1 rule="para" parents="11478 15039"/>
    </justification>
  </clause>

  <clause id="15041">
    <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(14034(a,1),14327(a,2,1))].">
      <j1 rule="para" parents="14034 14327"/>
    </justification>
  </clause>

  <clause id="15042">
    <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(14071(a,1),15041(a,1,2,2))].">
      <j1 rule="para" parents="14071 15041"/>
    </justification>
  </clause>

  <clause id="15043">
    <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(8048(a,1),15042(a,1,2))].">
      <j1 rule="para" parents="8048 15042"/>
    </justification>
  </clause>

  <clause id="15044">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(z \ x,y)) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(7457(a,1),15043(a,1,2,2))].">
      <j1 rule="para" parents="7457 15043"/>
    </justification>
  </clause>

  <clause id="15045">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(z,y)) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(8436(a,1),15044(a,1,2))].">
      <j1 rule="para" parents="8436 15044"/>
    </justification>
  </clause>

  <clause id="15046">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(8067(a,1),15045(a,1,2))].">
      <j1 rule="para" parents="8067 15045"/>
    </justification>
  </clause>

  <clause id="15047">
    <literal><![CDATA[
      (T(x,T(y,z)) / z) \ 1 = K(y,x) * ((x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,14579,a(flip),b,15046,a),flip(a)].">
      <j1 rule="hyper" parents="58 14579 15046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15048">
    <literal><![CDATA[
      K(x * y,L(z,u,u \ 1)) = (x \ T(y * x,z)) * (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(14508,a,14098,a),flip(a)].">
      <j1 rule="hyper" parents="14508 14098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15049">
    <literal><![CDATA[
      (x \ T(y * x,z)) * (T(y,x) \ 1) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(14508,a,14078,a)].">
      <j1 rule="hyper" parents="14508 14078"/>
    </justification>
  </clause>

  <clause id="15050">
    <literal><![CDATA[
      (x \ T(y * x,z)) * (T(y,x) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(15048(a,1),6670(a,1))].">
      <j1 rule="para" parents="15048 6670"/>
    </justification>
  </clause>

  <clause id="15051">
    <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(13522,a,14884,a)].">
      <j1 rule="hyper" parents="13522 14884"/>
    </justification>
  </clause>

  <clause id="15052">
    <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(13626,a,15051,a)].">
      <j1 rule="hyper" parents="13626 15051"/>
    </justification>
  </clause>

  <clause id="15053">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ ((z \ 1) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14927,a(flip),b,15052,a),flip(a)].">
      <j1 rule="hyper" parents="58 14927 15052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15054">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ ((z \ 1) * u)) = K(x,(y / z) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(536(a,1),15053(a,1,2,1))].">
      <j1 rule="para" parents="536 15053"/>
    </justification>
  </clause>

  <clause id="15055">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ ((z \ 1) * (z * u))) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(4(a,1),15054(a,2,2,2))].">
      <j1 rule="para" parents="4 15054"/>
    </justification>
  </clause>

  <clause id="15056">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ L(u,z,z \ 1)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6006,a(flip),b,15055,a)].">
      <j1 rule="hyper" parents="58 6006 15055"/>
    </justification>
  </clause>

  <clause id="15057">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (y \ (z * u))) = a(x,y \ z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(14820,a,14931,a),flip(a)].">
      <j1 rule="hyper" parents="14820 14931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15058">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (y \ (z * u))) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,11222,a(flip),b,15057,a),flip(a)].">
      <j1 rule="hyper" parents="334 11222 15057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15059">
    <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(9720(a,1),15058(a,1,2,1))].">
      <j1 rule="para" parents="9720 15058"/>
    </justification>
  </clause>

  <clause id="15060">
    <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(4349(a,1),14329(a,1,2))].">
      <j1 rule="para" parents="4349 14329"/>
    </justification>
  </clause>

  <clause id="15061">
    <literal><![CDATA[
      ((x * ((y * (x / y)) \ y)) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(10417(a,1),14288(a,1,1,1,2))].">
      <j1 rule="para" parents="10417 14288"/>
    </justification>
  </clause>

  <clause id="15062">
    <literal><![CDATA[
      x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(5652(a,1),15061(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5652 15061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15063">
    <literal><![CDATA[
      x / (x * ((1 / ((x / ((x \ y) \ 1)) / x)) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(2977(a,2),15062(a,1,2,2,1))].">
      <j1 rule="para" parents="2977 15062"/>
    </justification>
  </clause>

  <clause id="15064">
    <literal><![CDATA[
      x / (x * ((x / ((x \ y) \ 1)) / x)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),15063(a,1,2,2))].">
      <j1 rule="para" parents="75 15063"/>
    </justification>
  </clause>

  <clause id="15066">
    <literal><![CDATA[
      x / (x / ((y / x) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(11667(a,1),15064(a,1,2))].">
      <j1 rule="para" parents="11667 15064"/>
    </justification>
  </clause>

  <clause id="15067">
    <literal><![CDATA[
      1 / (x / (x / ((y / x) \ 1))) = (x / (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(201,a,15066,a(flip))].">
      <j1 rule="hyper" parents="201 15066"/>
    </justification>
  </clause>

  <clause id="15068">
    <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(13000(a,1),14807(a,2,2))].">
      <j1 rule="para" parents="13000 14807"/>
    </justification>
  </clause>

  <clause id="15069">
    <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(14357(a,1),15068(a,1,2,3))].">
      <j1 rule="para" parents="14357 15068"/>
    </justification>
  </clause>

  <clause id="15070">
    <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(11470(a,1),14841(a,2,1))].">
      <j1 rule="para" parents="11470 14841"/>
    </justification>
  </clause>

  <clause id="15071">
    <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),15070(a,2,2))].">
      <j1 rule="para" parents="105 15070"/>
    </justification>
  </clause>

  <clause id="15072">
    <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),15071(a,1,1,3,2))].">
      <j1 rule="para" parents="105 15071"/>
    </justification>
  </clause>

  <clause id="15073">
    <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),15024(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="62 15024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15074">
    <literal><![CDATA[
      ((x * (y * z)) / x) \ L(z,y,z) = T((x * (z * y)) / x,z) \ z
    ]]></literal>
    <justification jstring="[para(5(a,1),15073(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 15073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15076">
    <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(13132(a,1),14842(a,1,1,2,1,2))].">
      <j1 rule="para" parents="13132 14842"/>
    </justification>
  </clause>

  <clause id="15077">
    <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),15076(a,1,1,2,1))].">
      <j1 rule="para" parents="72 15076"/>
    </justification>
  </clause>

  <clause id="15079">
    <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(14840(a,1),15077(a,1,1,2))].">
      <j1 rule="para" parents="14840 15077"/>
    </justification>
  </clause>

  <clause id="15080">
    <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(13760(a,1),14775(a,1,2))].">
      <j1 rule="para" parents="13760 14775"/>
    </justification>
  </clause>

  <clause id="15081">
    <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(1426(a,1),15080(a,1,2,2))].">
      <j1 rule="para" parents="1426 15080"/>
    </justification>
  </clause>

  <clause id="15082">
    <literal><![CDATA[
      a(x,y,z * a(u,w,a(v5,v6,v7))) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(13717(a,1),15081(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13717 15081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15083">
    <literal><![CDATA[
      a(x,y,z * a(u,w,a(v5,v6,v7))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,14770,a,b,15082,a),flip(a)].">
      <j1 rule="hyper" parents="334 14770 15082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15085">
    <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(15083(a,2),214(a,1))].">
      <j1 rule="para" parents="15083 214"/>
    </justification>
  </clause>

  <clause id="15086">
    <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(6520(a,1),14310(a,1,1,2))].">
      <j1 rule="para" parents="6520 14310"/>
    </justification>
  </clause>

  <clause id="15087">
    <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(11961(a,1),15001(a,1,1))].">
      <j1 rule="para" parents="11961 15001"/>
    </justification>
  </clause>

  <clause id="15088">
    <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),15087(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="75 15087"/>
    </justification>
  </clause>

  <clause id="15089">
    <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(10572(a,1),15088(a,1,1))].">
      <j1 rule="para" parents="10572 15088"/>
    </justification>
  </clause>

  <clause id="15090">
    <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,4325,a(flip),b,15089,a)].">
      <j1 rule="hyper" parents="58 4325 15089"/>
    </justification>
  </clause>

  <clause id="15092">
    <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),15090(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="75 15090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15093">
    <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(334,a,10849,a(flip),b,15092,a),flip(a)].">
      <j1 rule="hyper" parents="334 10849 15092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15095">
    <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(334,a,14999,a(flip),b,15093,a),flip(a)].">
      <j1 rule="hyper" parents="334 14999 15093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15096">
    <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),15095(a,2,2,1))].">
      <j1 rule="para" parents="5 15095"/>
    </justification>
  </clause>

  <clause id="15098">
    <literal><![CDATA[
      T(x,R(x * (y / T(1 / (1 / x),z)),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(3301(a,1),15096(a,1,2,1))].">
      <j1 rule="para" parents="3301 15096"/>
    </justification>
  </clause>

  <clause id="15099">
    <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,15007,a(flip),b,15098,a)].">
      <j1 rule="hyper" parents="58 15007 15098"/>
    </justification>
  </clause>

  <clause id="15100">
    <literal><![CDATA[
      T(x,L(y * (x * (1 / T(x,z))),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(9969(a,1),15099(a,1,2,1))].">
      <j1 rule="para" parents="9969 15099"/>
    </justification>
  </clause>

  <clause id="15101">
    <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,3946,a(flip),b,15100,a)].">
      <j1 rule="hyper" parents="58 3946 15100"/>
    </justification>
  </clause>

  <clause id="15102">
    <literal><![CDATA[
      T(x,L(y * K(z,x),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(5064(a,2),15101(a,1,2,1,2))].">
      <j1 rule="para" parents="5064 15101"/>
    </justification>
  </clause>

  <clause id="15103">
    <literal><![CDATA[
      T(x,R(y,z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(181(a,1),15102(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="181 15102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15104">
    <literal><![CDATA[
      R(x,y,z) * T(u,L(x,y,z)) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,15103,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 15103 17"/>
    </justification>
  </clause>

  <clause id="15105">
    <literal><![CDATA[
      T(x,L(y / z,z,u)) = T(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[para(102(a,1),15103(a,1,2)),flip(a)].">
      <j1 rule="para" parents="102 15103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15106">
    <literal><![CDATA[
      T(x,L((y / z) / u,u,z)) = T(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(314(a,1),15103(a,1,2)),flip(a)].">
      <j1 rule="para" parents="314 15103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15107">
    <literal><![CDATA[
      x / T(x,L(y,z,u)) = K(R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(15103(a,1),5062(a,2,2)),flip(a)].">
      <j1 rule="para" parents="15103 5062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15108">
    <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(15103(a,1),8543(a,1,2))].">
      <j1 rule="para" parents="15103 8543"/>
    </justification>
  </clause>

  <clause id="15109">
    <literal><![CDATA[
      T(x,L(y / (z / u),u \ z,u)) = T(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(10662(a,1),15103(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10662 15103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15110">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(5133,a,15107,a),flip(a)].">
      <j1 rule="hyper" parents="5133 15107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15111">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,11137,a(flip),b,15110,a),flip(a)].">
      <j1 rule="hyper" parents="334 11137 15110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15112">
    <literal><![CDATA[
      K(L(x / y,y,z),u) = K((x * z) / (y * z),u)
    ]]></literal>
    <justification jstring="[para(102(a,1),15110(a,1,1)),flip(a)].">
      <j1 rule="para" parents="102 15110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15113">
    <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(15110(a,1),7991(a,1))].">
      <j1 rule="para" parents="15110 7991"/>
    </justification>
  </clause>

  <clause id="15114">
    <literal><![CDATA[
      K(x,R(y,z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12805,a,15111,a)].">
      <j1 rule="hyper" parents="12805 15111"/>
    </justification>
  </clause>

  <clause id="15115">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12804,a,15111,a)].">
      <j1 rule="hyper" parents="12804 15111"/>
    </justification>
  </clause>

  <clause id="15116">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,11089,a,b,15114,a)].">
      <j1 rule="hyper" parents="334 11089 15114"/>
    </justification>
  </clause>

  <clause id="15117">
    <literal><![CDATA[
      ((x * y) * z) / ((T(x,u) * y) * z) = K(u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6277,a,b,15114,a)].">
      <j1 rule="hyper" parents="58 6277 15114"/>
    </justification>
  </clause>

  <clause id="15118">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[para(102(a,1),15114(a,1,2)),flip(a)].">
      <j1 rule="para" parents="102 15114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15119">
    <literal><![CDATA[
      K(x,L((y / z) / u,u,z)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(314(a,1),15114(a,1,2)),flip(a)].">
      <j1 rule="para" parents="314 15114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15120">
    <literal><![CDATA[
      K(x,L(y \ (z / u),y,u)) = K(x,T(z / (y * u),y))
    ]]></literal>
    <justification jstring="[para(667(a,1),15114(a,1,2)),flip(a)].">
      <j1 rule="para" parents="667 15114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15121">
    <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(15114(a,1),10041(a,1,2))].">
      <j1 rule="para" parents="15114 10041"/>
    </justification>
  </clause>

  <clause id="15122">
    <literal><![CDATA[
      K(x,L(y / (z / u),u \ z,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(10662(a,1),15114(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10662 15114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15123">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(15114(a,1),12796(a,1,1))].">
      <j1 rule="para" parents="15114 12796"/>
    </justification>
  </clause>

  <clause id="15124">
    <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(15114(a,1),14657(a,1,2,3))].">
      <j1 rule="para" parents="15114 14657"/>
    </justification>
  </clause>

  <clause id="15125">
    <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(15114(a,1),14363(a,1,1))].">
      <j1 rule="para" parents="15114 14363"/>
    </justification>
  </clause>

  <clause id="15126">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(6285,a,15115,a)].">
      <j1 rule="hyper" parents="6285 15115"/>
    </justification>
  </clause>

  <clause id="15127">
    <literal><![CDATA[
      K(x,L(y / z,y,u)) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[hyper(6284,a,15115,a),flip(a)].">
      <j1 rule="hyper" parents="6284 15115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15128">
    <literal><![CDATA[
      R(K(x,y),z,u) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,11089,a,b,15115,a),flip(a)].">
      <j1 rule="hyper" parents="334 11089 15115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15129">
    <literal><![CDATA[
      K(x,L(y / (z / u),y,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6160,a(flip),b,15115,a),flip(a)].">
      <j1 rule="hyper" parents="58 6160 15115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15130">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u)) = K(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,6150,a(flip),b,15115,a),flip(a)].">
      <j1 rule="hyper" parents="58 6150 15115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15131">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) = K(x \ 1,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5975,a(flip),b,15115,a)].">
      <j1 rule="hyper" parents="58 5975 15115"/>
    </justification>
  </clause>

  <clause id="15132">
    <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(15115(a,1),721(a,1,1))].">
      <j1 rule="para" parents="15115 721"/>
    </justification>
  </clause>

  <clause id="15133">
    <literal><![CDATA[
      (K(x,T(y,z * u)) * z) * u = (z * u) * K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(15115(a,1),8176(a,2,2))].">
      <j1 rule="para" parents="15115 8176"/>
    </justification>
  </clause>

  <clause id="15134">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (u * z) = (K(x,y) * z) * T(u,z)
    ]]></literal>
    <justification jstring="[para(15115(a,1),10656(a,1,1))].">
      <j1 rule="para" parents="15115 10656"/>
    </justification>
  </clause>

  <clause id="15135">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) * u = (K(x,y) * (u / z)) * z
    ]]></literal>
    <justification jstring="[para(15115(a,1),10665(a,1,1))].">
      <j1 rule="para" parents="15115 10665"/>
    </justification>
  </clause>

  <clause id="15136">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(15115(a,2),11091(a,1))].">
      <j1 rule="para" parents="15115 11091"/>
    </justification>
  </clause>

  <clause id="15137">
    <literal><![CDATA[
      K(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(15116(a,1),11132(a,1))].">
      <j1 rule="para" parents="15116 11132"/>
    </justification>
  </clause>

  <clause id="15138">
    <literal><![CDATA[
      L(K(x,y),z,u) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(15116(a,2),12796(a,1,1))].">
      <j1 rule="para" parents="15116 12796"/>
    </justification>
  </clause>

  <clause id="15139">
    <literal><![CDATA[
      L(K(x / (y / z),u),x,z) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7062,a(flip),b,15128,a),flip(a)].">
      <j1 rule="hyper" parents="58 7062 15128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15141">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(15128(a,2),11132(a,1))].">
      <j1 rule="para" parents="15128 11132"/>
    </justification>
  </clause>

  <clause id="15142">
    <literal><![CDATA[
      L(K(x,y),z,u) \ (u * (K(x,y) * z)) = z * T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(15128(a,1),14570(a,1,1))].">
      <j1 rule="para" parents="15128 14570"/>
    </justification>
  </clause>

  <clause id="15143">
    <literal><![CDATA[
      K(x,(y * z) / (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y / u),y,z) = w
    ]]></literal>
    <justification jstring="[para(6156(a,1),15136(a,1))].">
      <j1 rule="para" parents="6156 15136"/>
    </justification>
  </clause>

  <clause id="15144">
    <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),15137(a,1,2))].">
      <j1 rule="para" parents="102 15137"/>
    </justification>
  </clause>

  <clause id="15145">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(6161(a,2),15141(a,1))].">
      <j1 rule="para" parents="6161 15141"/>
    </justification>
  </clause>

  <clause id="15146">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,11108,a(flip),b,15130,a),flip(a)].">
      <j1 rule="hyper" parents="58 11108 15130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15147">
    <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,7831,a(flip),b,15131,a),flip(a)].">
      <j1 rule="hyper" parents="58 7831 15131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15148">
    <literal><![CDATA[
      K(T(x / y,z) \ 1,L(u,y,y \ z)) = K((z \ (x * (y \ z))) \ 1,u)
    ]]></literal>
    <justification jstring="[para(1003(a,1),15131(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1003 15131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15149">
    <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(790(a,1),15146(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="790 15146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15151">
    <literal><![CDATA[
      R(x,y,z) * T(y * z,x) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(14020(a,1),15104(a,1,2))].">
      <j1 rule="para" parents="14020 15104"/>
    </justification>
  </clause>

  <clause id="15152">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(((x \ z) * x) / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(8531,a,15112,a)].">
      <j1 rule="hyper" parents="8531 15112"/>
    </justification>
  </clause>

  <clause id="15153">
    <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(15112(a,1),8531(a,1))].">
      <j1 rule="para" parents="15112 8531"/>
    </justification>
  </clause>

  <clause id="15154">
    <literal><![CDATA[
      K(x,T((y * z) \ u,z)) = K(x,((y \ u) * y) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8285,a(flip),b,15118,a)].">
      <j1 rule="hyper" parents="58 8285 15118"/>
    </justification>
  </clause>

  <clause id="15155">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,y / z,z))) = K(x,K(w,y / (u * z)))
    ]]></literal>
    <justification jstring="[para(15119(a,1),11195(a,2,2))].">
      <j1 rule="para" parents="15119 11195"/>
    </justification>
  </clause>

  <clause id="15156">
    <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(15123(a,1),6447(a,2,2,1))].">
      <j1 rule="para" parents="15123 6447"/>
    </justification>
  </clause>

  <clause id="15157">
    <literal><![CDATA[
      (K(x,L(y,z,u \ 1)) * z) * u = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(14926(a,1),15123(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14926 15123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15158">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,((y * z) * (z \ 1)) / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(14880,a,15127,a)].">
      <j1 rule="hyper" parents="14880 15127"/>
    </justification>
  </clause>

  <clause id="15159">
    <literal><![CDATA[
      K(x,(y * (y \ z)) / (u * (y \ z))) = K(x,L(y / u,z,y \ z))
    ]]></literal>
    <justification jstring="[hyper(14808,a,15127,a),flip(a)].">
      <j1 rule="hyper" parents="14808 15127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15160">
    <literal><![CDATA[
      K(x,L(y * z,y,u)) = K(x,(y * u) / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(14500,a,15127,a)].">
      <j1 rule="hyper" parents="14500 15127"/>
    </justification>
  </clause>

  <clause id="15161">
    <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,15129,a(flip),b,14659,a)].">
      <j1 rule="hyper" parents="116 15129 14659"/>
    </justification>
  </clause>

  <clause id="15162">
    <literal><![CDATA[
      L(K(x,y),z,u) * (z * u) = (K(y,x) \ z) * u
    ]]></literal>
    <justification jstring="[para(5391(a,2),15138(a,2,1))].">
      <j1 rule="para" parents="5391 15138"/>
    </justification>
  </clause>

  <clause id="15164">
    <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(7429,a,15139,a)].">
      <j1 rule="hyper" parents="7429 15139"/>
    </justification>
  </clause>

  <clause id="15165">
    <literal><![CDATA[
      L(K(x,y),z,u) \ (z * u) = (K(x,y) \ z) * u
    ]]></literal>
    <justification jstring="[hyper(58,a,6198,a,b,15162,a)].">
      <j1 rule="hyper" parents="58 6198 15162"/>
    </justification>
  </clause>

  <clause id="15166">
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,x) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(6757,a,15151,a)].">
      <j1 rule="hyper" parents="6757 15151"/>
    </justification>
  </clause>

  <clause id="15167">
    <literal><![CDATA[
      ((x * y) * z) * a(z,x,y) = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11533,a,b,15151,a)].">
      <j1 rule="hyper" parents="58 11533 15151"/>
    </justification>
  </clause>

  <clause id="15168">
    <literal><![CDATA[
      ((x * y) * R(z,x,y)) / a(z,x,y) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(117,a,15151,a(flip),b,11533,a)].">
      <j1 rule="hyper" parents="117 15151 11533"/>
    </justification>
  </clause>

  <clause id="15169">
    <literal><![CDATA[
      x * a(x,y,a(z,u,w)) = R(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(933,a,15167,a)].">
      <j1 rule="hyper" parents="933 15167"/>
    </justification>
  </clause>

  <clause id="15170">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = R(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(859,a,15167,a)].">
      <j1 rule="hyper" parents="859 15167"/>
    </justification>
  </clause>

  <clause id="15171">
    <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(7423(a,1),15167(a,1,1,1))].">
      <j1 rule="para" parents="7423 15167"/>
    </justification>
  </clause>

  <clause id="15172">
    <literal><![CDATA[
      R(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(15170(a,1),14618(a,1))].">
      <j1 rule="para" parents="15170 14618"/>
    </justification>
  </clause>

  <clause id="15173">
    <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,4039,a,b,15169,a)].">
      <j1 rule="hyper" parents="29 4039 15169"/>
    </justification>
  </clause>

  <clause id="15174">
    <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(15169(a,1),92(a,2,1))].">
      <j1 rule="para" parents="15169 92"/>
    </justification>
  </clause>

  <clause id="15175">
    <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(15169(a,1),490(a,1,2,2))].">
      <j1 rule="para" parents="15169 490"/>
    </justification>
  </clause>

  <clause id="15176">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * x) = v5 * R(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(15169(a,1),13745(a,2,2))].">
      <j1 rule="para" parents="15169 13745"/>
    </justification>
  </clause>

  <clause id="15177">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,y * z)
    ]]></literal>
    <justification jstring="[hyper(618,a,15168,a),flip(a)].">
      <j1 rule="hyper" parents="618 15168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15178">
    <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(15177(a,2),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15177 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15179">
    <literal><![CDATA[
      K(x,L(y \ R(y,z,u),y,z * u)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(15177(a,1),14588(a,2,2)),flip(a)].">
      <j1 rule="para" parents="15177 14588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15181">
    <literal><![CDATA[
      T(x,L(y / (z / u),z,u)) = T(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,14796,a(flip),b,15109,a)].">
      <j1 rule="hyper" parents="58 14796 15109"/>
    </justification>
  </clause>

  <clause id="15182">
    <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(14506(a,1),15181(a,1,2,1,2))].">
      <j1 rule="para" parents="14506 15181"/>
    </justification>
  </clause>

  <clause id="15183">
    <literal><![CDATA[
      K(L(x,y,z),u) * ((x * y) * z) = (T(x,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(31,a,5403,a,b,15117,a)].">
      <j1 rule="hyper" parents="31 5403 15117"/>
    </justification>
  </clause>

  <clause id="15184">
    <literal><![CDATA[
      K(x,L(y,z,(T(y,x) * z) \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(15117(a,1),337(a,1,1))].">
      <j1 rule="para" parents="15117 337"/>
    </justification>
  </clause>

  <clause id="15185">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),z \ u)) = K(x,u \ (z * (y / z)))
    ]]></literal>
    <justification jstring="[para(502(a,1),15120(a,1,2)),flip(a)].">
      <j1 rule="para" parents="502 15120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15186">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,(z * y) \ K(z,1 / z))
    ]]></literal>
    <justification jstring="[para(509(a,1),15120(a,1,2)),flip(a)].">
      <j1 rule="para" parents="509 15120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15187">
    <literal><![CDATA[
      K(x,L(y / (z / u),z,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(14793,a,15122,a)].">
      <j1 rule="hyper" parents="14793 15122"/>
    </justification>
  </clause>

  <clause id="15188">
    <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,15012,a(flip),b,15187,a),flip(a)].">
      <j1 rule="hyper" parents="58 15012 15187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15189">
    <literal><![CDATA[
      K(x,L(y,z,u)) * z = (K(x,y) * (z / u)) * u
    ]]></literal>
    <justification jstring="[para(14792(a,1),15135(a,1,1))].">
      <j1 rule="para" parents="14792 15135"/>
    </justification>
  </clause>

  <clause id="15190">
    <literal><![CDATA[
      (x * K(y,L(z,x,u))) / u = K(y,T(z,x)) * (x / u)
    ]]></literal>
    <justification jstring="[hyper(8884,a,15189,a)].">
      <j1 rule="hyper" parents="8884 15189"/>
    </justification>
  </clause>

  <clause id="15191">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * z) / u = K(x,y) * (z / u)
    ]]></literal>
    <justification jstring="[hyper(550,a,15189,a)].">
      <j1 rule="hyper" parents="550 15189"/>
    </justification>
  </clause>

  <clause id="15192">
    <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(15189(a,1),550(a,1))].">
      <j1 rule="para" parents="15189 550"/>
    </justification>
  </clause>

  <clause id="15193">
    <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(14469,a,15191,a)].">
      <j1 rule="hyper" parents="14469 15191"/>
    </justification>
  </clause>

  <clause id="15194">
    <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(14895(a,1),15191(a,2,2))].">
      <j1 rule="para" parents="14895 15191"/>
    </justification>
  </clause>

  <clause id="15195">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) * (z / u) = (K(x,y) * z) / u
    ]]></literal>
    <justification jstring="[para(14926(a,1),15191(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14926 15191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15197">
    <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(10382(a,1),15157(a,2,2))].">
      <j1 rule="para" parents="10382 15157"/>
    </justification>
  </clause>

  <clause id="15198">
    <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(5526(a,1),15160(a,2,2,1))].">
      <j1 rule="para" parents="5526 15160"/>
    </justification>
  </clause>

  <clause id="15199">
    <literal><![CDATA[
      a(x,y,K(y * z,u)) * K(x,(y * u) / ((z \ 1) * u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(15160(a,1),14658(a,1,2))].">
      <j1 rule="para" parents="15160 14658"/>
    </justification>
  </clause>

  <clause id="15200">
    <literal><![CDATA[
      a(x,y,z) * ((y * z) * x) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,14773,a(flip),b,15166,a)].">
      <j1 rule="hyper" parents="58 14773 15166"/>
    </justification>
  </clause>

  <clause id="15201">
    <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(334,a,1101,a(flip),b,15200,a),flip(a)].">
      <j1 rule="hyper" parents="334 1101 15200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15202">
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(14970,a,15179,a)].">
      <j1 rule="hyper" parents="14970 15179"/>
    </justification>
  </clause>

  <clause id="15203">
    <literal><![CDATA[
      T(x,y \ R(y,z,u)) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,15202,a(flip),b,4995,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 15202 4995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15204">
    <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(15202(a,1),10143(a,1,1,2))].">
      <j1 rule="para" parents="15202 10143"/>
    </justification>
  </clause>

  <clause id="15205">
    <literal><![CDATA[
      T(x,y \ R(y,z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,14614,a(flip),b,15203,a),flip(a)].">
      <j1 rule="hyper" parents="334 14614 15203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15206">
    <literal><![CDATA[
      K(x,y) * ((x * y) * z) = (T(x,y) * y) * z
    ]]></literal>
    <justification jstring="[para(10619(a,1),15183(a,1,1))].">
      <j1 rule="para" parents="10619 15183"/>
    </justification>
  </clause>

  <clause id="15207">
    <literal><![CDATA[
      K(x,L(y,z,u)) * ((x * z) * u) = (T(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(11137(a,1),15183(a,1,1))].">
      <j1 rule="para" parents="11137 15183"/>
    </justification>
  </clause>

  <clause id="15208">
    <literal><![CDATA[
      ((x * y) / x) \ ((y * x) * z) = y \ ((T(y,x) * x) * z)
    ]]></literal>
    <justification jstring="[hyper(116,a,15206,a(flip),b,5083,a),flip(a)].">
      <j1 rule="hyper" parents="116 15206 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15209">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(T(z,x) / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,13451,a(flip),b,15152,a),flip(a)].">
      <j1 rule="hyper" parents="334 13451 15152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15210">
    <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,14282,a(flip),b,15209,a)].">
      <j1 rule="hyper" parents="58 14282 15209"/>
    </justification>
  </clause>

  <clause id="15211">
    <literal><![CDATA[
      K(T(x,y),(z * y) \ u) = K(x,((z \ u) * z) / (y * z))
    ]]></literal>
    <justification jstring="[hyper(7561,a,15154,a)].">
      <j1 rule="hyper" parents="7561 15154"/>
    </justification>
  </clause>

  <clause id="15212">
    <literal><![CDATA[
      K(x,T((y * z) \ u,z)) = K(x,T(u,y) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(334,a,13443,a(flip),b,15154,a),flip(a)].">
      <j1 rule="hyper" parents="334 13443 15154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15213">
    <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(5870(a,1),15212(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5870 15212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15214">
    <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(7234(a,2),15212(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7234 15212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15215">
    <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(334,a,3749,a(flip),b,15176,a),flip(a)].">
      <j1 rule="hyper" parents="334 3749 15176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15216">
    <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,15176,a(flip),b,13716,a(flip))].">
      <j1 rule="hyper" parents="116 15176 13716"/>
    </justification>
  </clause>

  <clause id="15217">
    <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(15176(a,1),11153(a,2,1,1))].">
      <j1 rule="para" parents="15176 11153"/>
    </justification>
  </clause>

  <clause id="15218">
    <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(15211(a,1),7970(a,1))].">
      <j1 rule="para" parents="15211 7970"/>
    </justification>
  </clause>

  <clause id="15219">
    <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(15216(a,1),92(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15216 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15220">
    <literal><![CDATA[
      T(K(x,T(y,z * u)) * z,u) = T(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(246,a,15133,a,b,11511,a(flip))].">
      <j1 rule="hyper" parents="246 15133 11511"/>
    </justification>
  </clause>

  <clause id="15221">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,x * y)) = T(K(z,u) * x,y)
    ]]></literal>
    <justification jstring="[para(8157(a,1),15220(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8157 15220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15222">
    <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(15221(a,2),791(a,1))].">
      <j1 rule="para" parents="15221 791"/>
    </justification>
  </clause>

  <clause id="15223">
    <literal><![CDATA[
      K(x,y * T(K(x,z) * u,w)) = K(x,y * T(u,w))
    ]]></literal>
    <justification jstring="[para(15221(a,1),7657(a,1,2,2))].">
      <j1 rule="para" parents="15221 7657"/>
    </justification>
  </clause>

  <clause id="15224">
    <literal><![CDATA[
      L(a(x,y,z),u,x \ 1) = L(x \ R(x,y,z),x,y * z)
    ]]></literal>
    <justification jstring="[para(13790(a,1),15178(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13790 15178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15225">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,y * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(15224(a,1),385(a,1)),flip(b)].">
      <j1 rule="para" parents="15224 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15226">
    <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(15124(a,1),14661(a,1))].">
      <j1 rule="para" parents="15124 14661"/>
    </justification>
  </clause>

  <clause id="15227">
    <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(15226,a,11302,a)].">
      <j1 rule="hyper" parents="15226 11302"/>
    </justification>
  </clause>

  <clause id="15228">
    <literal><![CDATA[
      L(K(x,y),z,u) * (u * (K(y,x) * z)) = z * T(u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(6203,a,15142,a)].">
      <j1 rule="hyper" parents="6203 15142"/>
    </justification>
  </clause>

  <clause id="15229">
    <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(13451(a,1),15153(a,1))].">
      <j1 rule="para" parents="13451 15153"/>
    </justification>
  </clause>

  <clause id="15230">
    <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(14179(a,1),15155(a,1,2))].">
      <j1 rule="para" parents="14179 15155"/>
    </justification>
  </clause>

  <clause id="15231">
    <literal><![CDATA[
      K(x,L(y / z,u,y \ u)) = K(x,u / (z * (y \ u)))
    ]]></literal>
    <justification jstring="[para(5(a,1),15159(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 15159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15233">
    <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(4595(a,2),15231(a,2,2,2,2))].">
      <j1 rule="para" parents="4595 15231"/>
    </justification>
  </clause>

  <clause id="15234">
    <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(13443(a,1),15218(a,1))].">
      <j1 rule="para" parents="13443 15218"/>
    </justification>
  </clause>

  <clause id="15235">
    <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,11282,a,b,15228,a)].">
      <j1 rule="hyper" parents="58 11282 15228"/>
    </justification>
  </clause>

  <clause id="15236">
    <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),15125(a,1,2,2))].">
      <j1 rule="para" parents="22 15125"/>
    </justification>
  </clause>

  <clause id="15237">
    <literal><![CDATA[
      K(T(x / y,z) \ 1,L(u,y,y \ z)) = K((x * (y \ z)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,6615,a(flip),b,15148,a),flip(a)].">
      <j1 rule="hyper" parents="334 6615 15148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15238">
    <literal><![CDATA[
      K((x / y) \ 1,T(L(z,y,y \ u),u)) = K((x * (y \ u)) \ u,z)
    ]]></literal>
    <justification jstring="[hyper(7978,a,15237,a)].">
      <j1 rule="hyper" parents="7978 15237"/>
    </justification>
  </clause>

  <clause id="15239">
    <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),15238(a,1,2))].">
      <j1 rule="para" parents="20 15238"/>
    </justification>
  </clause>

  <clause id="15240">
    <literal><![CDATA[
      a(x,y,K(z,(u / y) \ z)) \ K(x,(y * z) / u) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(8755(a,1),15161(a,1,1,3))].">
      <j1 rule="para" parents="8755 15161"/>
    </justification>
  </clause>

  <clause id="15241">
    <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(4473(a,1),15236(a,1,2,2,1))].">
      <j1 rule="para" parents="4473 15236"/>
    </justification>
  </clause>

  <clause id="15242">
    <literal><![CDATA[
      T(x,L(y,z,u)) \ R(T(x,y),z,u) = R(x,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(11155,a,15241,a)].">
      <j1 rule="hyper" parents="11155 15241"/>
    </justification>
  </clause>

  <clause id="15243">
    <literal><![CDATA[
      T(x,L(y,z,u)) \ R(T(x,y),z,u) = x \ R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,1274,a(flip),b,15242,a),flip(a)].">
      <j1 rule="hyper" parents="334 1274 15242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15244">
    <literal><![CDATA[
      a(x,y,K(z,u / y)) \ K(z,(y * x) / u) = K(z,y / (u / x))
    ]]></literal>
    <justification jstring="[para(14642(a,1),15240(a,1,1))].">
      <j1 rule="para" parents="14642 15240"/>
    </justification>
  </clause>

  <clause id="15245">
    <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(334,a,7412,a,b,15149,a),flip(a)].">
      <j1 rule="hyper" parents="334 7412 15149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15246">
    <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(269(a,1),15158(a,2,2,1))].">
      <j1 rule="para" parents="269 15158"/>
    </justification>
  </clause>

  <clause id="15247">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,z \ (R(1 / y,y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(14826,a,15227,a)].">
      <j1 rule="hyper" parents="14826 15227"/>
    </justification>
  </clause>

  <clause id="15249">
    <literal><![CDATA[
      K(x,y \ (R(1 / z,z,y) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14943,a(flip),b,15247,a),flip(a)].">
      <j1 rule="hyper" parents="58 14943 15247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15250">
    <literal><![CDATA[
      K(x,y \ ((y / (z * y)) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(223(a,1),15249(a,1,2,2,1))].">
      <j1 rule="para" parents="223 15249"/>
    </justification>
  </clause>

  <clause id="15251">
    <literal><![CDATA[
      K(x,y \ ((z / y) \ u)) = K(x,y \ ((y / z) * u))
    ]]></literal>
    <justification jstring="[para(418(a,1),15249(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="418 15249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15252">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z \ ((z / u) * w)) = K(y,T(z \ ((u / z) \ w),x))
    ]]></literal>
    <justification jstring="[hyper(14439,a,15251,a),flip(a)].">
      <j1 rule="hyper" parents="14439 15251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15253">
    <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(15252(a,1),14439(a,1))].">
      <j1 rule="para" parents="15252 14439"/>
    </justification>
  </clause>

  <clause id="15254">
    <literal><![CDATA[
      K(x,L((y / z) \ u,y / z,z) \ 1) = K(x,T(y / (u * z),y / z))
    ]]></literal>
    <justification jstring="[hyper(334,a,10063,a(flip),b,15245,a),flip(a)].">
      <j1 rule="hyper" parents="334 10063 15245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15255">
    <literal><![CDATA[
      K(x,T(y / (z * u),y / u)) = K(x,(u * z) \ (u * (y / u)))
    ]]></literal>
    <justification jstring="[hyper(6758,a,15254,a),flip(a)].">
      <j1 rule="hyper" parents="6758 15254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15256">
    <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(334,a,13409,a(flip),b,15255,a),flip(a)].">
      <j1 rule="hyper" parents="334 13409 15255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15257">
    <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(6015(a,1),15255(a,2,2,1))].">
      <j1 rule="para" parents="6015 15255"/>
    </justification>
  </clause>

  <clause id="15258">
    <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(334,a,146,a(flip),b,15219,a),flip(a)].">
      <j1 rule="hyper" parents="334 146 15219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15260">
    <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(1696(a,1),15258(a,1,2))].">
      <j1 rule="para" parents="1696 15258"/>
    </justification>
  </clause>

  <clause id="15261">
    <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(15201(a,1),356(a,1))].">
      <j1 rule="para" parents="15201 356"/>
    </justification>
  </clause>

  <clause id="15262">
    <literal><![CDATA[
      ((x / (y * z)) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      a((y * z) \ x,y,z) * x = u
    ]]></literal>
    <justification jstring="[para(1695(a,1),15261(a,1))].">
      <j1 rule="para" parents="1695 15261"/>
    </justification>
  </clause>

  <clause id="15263">
    <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(12069(a,1),15235(a,1,1))].">
      <j1 rule="para" parents="12069 15235"/>
    </justification>
  </clause>

  <clause id="15264">
    <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(8100(a,1),15263(a,1,1,2))].">
      <j1 rule="para" parents="8100 15263"/>
    </justification>
  </clause>

  <clause id="15265">
    <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(13879,a,15264,a)].">
      <j1 rule="hyper" parents="13879 15264"/>
    </justification>
  </clause>

  <clause id="15266">
    <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(791,a,15264,a)].">
      <j1 rule="hyper" parents="791 15264"/>
    </justification>
  </clause>

  <clause id="15267">
    <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(8353(a,2),15265(a,1,2,2))].">
      <j1 rule="para" parents="8353 15265"/>
    </justification>
  </clause>

  <clause id="15268">
    <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(9138(a,2),15267(a,1,2))].">
      <j1 rule="para" parents="9138 15267"/>
    </justification>
  </clause>

  <clause id="15269">
    <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(8145(a,2),15268(a,1,2,2,2))].">
      <j1 rule="para" parents="8145 15268"/>
    </justification>
  </clause>

  <clause id="15270">
    <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),15256(a,1,2,1,2))].">
      <j1 rule="para" parents="5 15256"/>
    </justification>
  </clause>

  <clause id="15271">
    <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(3812(a,1),15198(a,1,2))].">
      <j1 rule="para" parents="3812 15198"/>
    </justification>
  </clause>

  <clause id="15272">
    <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(13600(a,1),15271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13600 15271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15273">
    <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,5845,a(flip),b,15272,a)].">
      <j1 rule="hyper" parents="58 5845 15272"/>
    </justification>
  </clause>

  <clause id="15274">
    <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(14760(a,1),15171(a,1,2))].">
      <j1 rule="para" parents="14760 15171"/>
    </justification>
  </clause>

  <clause id="15275">
    <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(14940,a,15274,a),flip(a)].">
      <j1 rule="hyper" parents="14940 15274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15276">
    <literal><![CDATA[
      (K(x,y) * z) * R(u,z,K(x,T(y,z))) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(7423(a,1),15275(a,1,1))].">
      <j1 rule="para" parents="7423 15275"/>
    </justification>
  </clause>

  <clause id="15277">
    <literal><![CDATA[
      (K(x,y) * z) * R(u,z,K(x,y)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(10658(a,1),15276(a,1,2))].">
      <j1 rule="para" parents="10658 15276"/>
    </justification>
  </clause>

  <clause id="15278">
    <literal><![CDATA[
      R(x,y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(493,a,15277,a),flip(a)].">
      <j1 rule="hyper" parents="493 15277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15279">
    <literal><![CDATA[
      L(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(15172,a,15278,a),flip(a)].">
      <j1 rule="hyper" parents="15172 15278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15280">
    <literal><![CDATA[
      L((x * K(y,z)) / u,u,K(z,y)) = x / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6541,a,15278,a),flip(a)].">
      <j1 rule="hyper" parents="6541 15278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15281">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) = (y * K(z,u)) / ((x \ y) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(912,a,15278,a),flip(a)].">
      <j1 rule="hyper" parents="912 15278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15282">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15170,a,b,15278,a)].">
      <j1 rule="hyper" parents="58 15170 15278"/>
    </justification>
  </clause>

  <clause id="15283">
    <literal><![CDATA[
      x \ L(x,y,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,15278,a(flip),b,15170,a)].">
      <j1 rule="hyper" parents="116 15278 15170"/>
    </justification>
  </clause>

  <clause id="15284">
    <literal><![CDATA[
      L(x,y,K(z,u)) * (y * K(z,u)) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(15278(a,1),101(a,1,1))].">
      <j1 rule="para" parents="15278 101"/>
    </justification>
  </clause>

  <clause id="15285">
    <literal><![CDATA[
      L(x,x \ y,K(z,z \ y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(15278(a,1),5481(a,1,1))].">
      <j1 rule="para" parents="15278 5481"/>
    </justification>
  </clause>

  <clause id="15286">
    <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(15278(a,1),7213(a,1))].">
      <j1 rule="para" parents="15278 7213"/>
    </justification>
  </clause>

  <clause id="15287">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(15278(a,1),15172(a,1))].">
      <j1 rule="para" parents="15278 15172"/>
    </justification>
  </clause>

  <clause id="15288">
    <literal><![CDATA[
      T(x,a(y,(z \ y) * u,z)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,14819,a,b,15279,a)].">
      <j1 rule="hyper" parents="334 14819 15279"/>
    </justification>
  </clause>

  <clause id="15289">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,14756,a,b,15279,a)].">
      <j1 rule="hyper" parents="334 14756 15279"/>
    </justification>
  </clause>

  <clause id="15290">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u = L(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,14662,a,b,15279,a)].">
      <j1 rule="hyper" parents="334 14662 15279"/>
    </justification>
  </clause>

  <clause id="15291">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,14649,a,b,15279,a)].">
      <j1 rule="hyper" parents="334 14649 15279"/>
    </justification>
  </clause>

  <clause id="15292">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,14617,a,b,15279,a)].">
      <j1 rule="hyper" parents="334 14617 15279"/>
    </justification>
  </clause>

  <clause id="15293">
    <literal><![CDATA[
      a(x,y,K(z,u)) * z = L(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,13709,a,b,15279,a)].">
      <j1 rule="hyper" parents="334 13709 15279"/>
    </justification>
  </clause>

  <clause id="15294">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,13705,a,b,15279,a)].">
      <j1 rule="hyper" parents="334 13705 15279"/>
    </justification>
  </clause>

  <clause id="15295">
    <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(334,a,15079,a(flip),b,15279,a),flip(a)].">
      <j1 rule="hyper" parents="334 15079 15279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15296">
    <literal><![CDATA[
      L(1 / x,y,K(z,u)) = a(x,y,K(u,z)) / x
    ]]></literal>
    <justification jstring="[hyper(334,a,14781,a(flip),b,15279,a),flip(a)].">
      <j1 rule="hyper" parents="334 14781 15279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15297">
    <literal><![CDATA[
      L(T(x,y),x \ z,K(u,w)) = T(T(x,a(w,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,14755,a(flip),b,15279,a),flip(a)].">
      <j1 rule="hyper" parents="334 14755 15279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15298">
    <literal><![CDATA[
      L(T(x,y),z,K(u,y)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,14703,a(flip),b,15279,a),flip(a)].">
      <j1 rule="hyper" parents="334 14703 15279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15299">
    <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(334,a,14289,a(flip),b,15279,a)].">
      <j1 rule="hyper" parents="334 14289 15279"/>
    </justification>
  </clause>

  <clause id="15300">
    <literal><![CDATA[
      L(x / a(y,z,u),z,K(u,y)) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(334,a,107,a(flip),b,15279,a),flip(a)].">
      <j1 rule="hyper" parents="334 107 15279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15301">
    <literal><![CDATA[
      (x / y) * L(y,z,K(u,w)) = x * a(y,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,15279,a,b,14620,a)].">
      <j1 rule="hyper" parents="119 15279 14620"/>
    </justification>
  </clause>

  <clause id="15302">
    <literal><![CDATA[
      a(x,y,z) * L(u,y,K(z,x)) = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,15279,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="119 15279 17"/>
    </justification>
  </clause>

  <clause id="15303">
    <literal><![CDATA[
      x \ L(x,y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,15279,a,b,13705,a)].">
      <j1 rule="hyper" parents="116 15279 13705"/>
    </justification>
  </clause>

  <clause id="15304">
    <literal><![CDATA[
      T(L(x,y,K(z,u)),a(z,y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,14786,a(flip),b,15279,a),flip(a)].">
      <j1 rule="hyper" parents="36 14786 15279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15305">
    <literal><![CDATA[
      L(x,y,K(L(z,u,w),v5)) = T(x,a(v5,y,z))
    ]]></literal>
    <justification jstring="[hyper(13744,a,15279,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="13744 15279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15306">
    <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(15279(a,2),431(a,1))].">
      <j1 rule="para" parents="15279 431"/>
    </justification>
  </clause>

  <clause id="15307">
    <literal><![CDATA[
      (x * y) * a(z,u,K(y,w)) = x * L(y,u,K(w,z))
    ]]></literal>
    <justification jstring="[para(15279(a,2),13704(a,2,2))].">
      <j1 rule="para" parents="15279 13704"/>
    </justification>
  </clause>

  <clause id="15308">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,y)) = x \ L(y,u,K(z,w))
    ]]></literal>
    <justification jstring="[para(15279(a,2),14688(a,2,2))].">
      <j1 rule="para" parents="15279 14688"/>
    </justification>
  </clause>

  <clause id="15309">
    <literal><![CDATA[
      L(x,y,K(z,u)) * a(z,y,u) = a(z,y,u) * x
    ]]></literal>
    <justification jstring="[para(15279(a,2),14785(a,1,1))].">
      <j1 rule="para" parents="15279 14785"/>
    </justification>
  </clause>

  <clause id="15310">
    <literal><![CDATA[
      L(x,y,K(z,u)) / u = T(x / u,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(15279(a,2),14791(a,1,1))].">
      <j1 rule="para" parents="15279 14791"/>
    </justification>
  </clause>

  <clause id="15311">
    <literal><![CDATA[
      K(x,y) * L(L(x,z,K(u,y)),z,u) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(15279(a,2),14854(a,1,2,1))].">
      <j1 rule="para" parents="15279 14854"/>
    </justification>
  </clause>

  <clause id="15312">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,K(u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,15279,a,b,15304,a)].">
      <j1 rule="hyper" parents="58 15279 15304"/>
    </justification>
  </clause>

  <clause id="15313">
    <literal><![CDATA[
      T((K(x,y) * z) \ u,a(x,z,y)) = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(5415(a,1),15304(a,1,1))].">
      <j1 rule="para" parents="5415 15304"/>
    </justification>
  </clause>

  <clause id="15314">
    <literal><![CDATA[
      L((K(x,y) * z) \ u,z,K(y,x)) = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(6042,a,15312,a),flip(a)].">
      <j1 rule="hyper" parents="6042 15312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15315">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15283(a,1),263(a,1,2)),flip(b)].">
      <j1 rule="para" parents="15283 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15316">
    <literal><![CDATA[
      L(x,y \ z,K(y,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15279,a,b,15289,a)].">
      <j1 rule="hyper" parents="58 15279 15289"/>
    </justification>
  </clause>

  <clause id="15317">
    <literal><![CDATA[
      a(x,y,z) * (u / a(x,y,z)) = L(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14780,a(flip),b,15292,a)].">
      <j1 rule="hyper" parents="58 14780 15292"/>
    </justification>
  </clause>

  <clause id="15318">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (z * w) = L(z,y,K(u,x)) * w
    ]]></literal>
    <justification jstring="[para(15293(a,1),14604(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15293 14604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15319">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ x = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(15294(a,1),9989(a,1,1))].">
      <j1 rule="para" parents="15294 9989"/>
    </justification>
  </clause>

  <clause id="15320">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * L(z,y,K(u,x))) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(15294(a,1),13767(a,1,2,2))].">
      <j1 rule="para" parents="15294 13767"/>
    </justification>
  </clause>

  <clause id="15321">
    <literal><![CDATA[
      L(x,y * z,K(y,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),15316(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 15316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15322">
    <literal><![CDATA[
      L(L(x,y,z),y,K(z,u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(7188,a,15321,a),flip(a)].">
      <j1 rule="hyper" parents="7188 15321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15323">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,z) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(15321(a,1),7189(a,1,1))].">
      <j1 rule="para" parents="15321 7189"/>
    </justification>
  </clause>

  <clause id="15324">
    <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(15321(a,1),7188(a,1))].">
      <j1 rule="para" parents="15321 7188"/>
    </justification>
  </clause>

  <clause id="15325">
    <literal><![CDATA[
      L(x,y,K(z,L(u,w,v5))) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(10878(a,1),15305(a,1,3))].">
      <j1 rule="para" parents="10878 15305"/>
    </justification>
  </clause>

  <clause id="15326">
    <literal><![CDATA[
      L(x,T(y,z),T(u,y)) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(6180,a,15322,a),flip(a)].">
      <j1 rule="hyper" parents="6180 15322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15328">
    <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(15322(a,1),1503(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15322 1503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15329">
    <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(15322(a,1),15319(a,1,1))].">
      <j1 rule="para" parents="15322 15319"/>
    </justification>
  </clause>

  <clause id="15330">
    <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(15326(a,1),13578(a,1))].">
      <j1 rule="para" parents="15326 13578"/>
    </justification>
  </clause>

  <clause id="15331">
    <literal><![CDATA[
      L(L(x,y,K(z * u,u \ 1)),y,z * u) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(334,a,12940,a(flip),b,15323,a),flip(a)].">
      <j1 rule="hyper" parents="334 12940 15323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15332">
    <literal><![CDATA[
      L(x,y,K(z,L(u,w,v5))) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,15279,a,b,15325,a),flip(a)].">
      <j1 rule="hyper" parents="334 15279 15325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15333">
    <literal><![CDATA[
      L(x,(y \ z) * u,K(y,z)) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15279,a,b,15288,a)].">
      <j1 rule="hyper" parents="58 15279 15288"/>
    </justification>
  </clause>

  <clause id="15335">
    <literal><![CDATA[
      L(x / y,z,K(u,y)) = L(x,z,K(u,y)) / y
    ]]></literal>
    <justification jstring="[hyper(334,a,15279,a,b,15310,a)].">
      <j1 rule="hyper" parents="334 15279 15310"/>
    </justification>
  </clause>

  <clause id="15336">
    <literal><![CDATA[
      L(L(x,y,z \ u),y,K(z,u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,13050,a(flip),b,15333,a),flip(a)].">
      <j1 rule="hyper" parents="58 13050 15333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15337">
    <literal><![CDATA[
      L(x * y,z,K(u,x)) = x * L(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(914,a,15335,a),flip(a)].">
      <j1 rule="hyper" parents="914 15335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15338">
    <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(451,a,15300,a,b,14812,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="451 15300 14812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15339">
    <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,15309,a,b,14603,a)].">
      <j1 rule="hyper" parents="117 15309 14603"/>
    </justification>
  </clause>

  <clause id="15340">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(14592(a,2),15315(a,1,2))].">
      <j1 rule="para" parents="14592 15315"/>
    </justification>
  </clause>

  <clause id="15341">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(14614(a,1),15315(a,1))].">
      <j1 rule="para" parents="14614 15315"/>
    </justification>
  </clause>

  <clause id="15342">
    <literal><![CDATA[
      R(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15170(a,1),15315(a,1))].">
      <j1 rule="para" parents="15170 15315"/>
    </justification>
  </clause>

  <clause id="15343">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(14749(a,2),15341(a,1))].">
      <j1 rule="para" parents="14749 15341"/>
    </justification>
  </clause>

  <clause id="15344">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z \ y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15289(a,1),15341(a,1))].">
      <j1 rule="para" parents="15289 15341"/>
    </justification>
  </clause>

  <clause id="15345">
    <literal><![CDATA[
      L(x,y,K(z,u)) / a(u,y,z) = a(u,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,15312,a(flip),b,15317,a),flip(a)].">
      <j1 rule="hyper" parents="116 15312 15317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15346">
    <literal><![CDATA[
      x / a(y,z,x) = a(y,z,x) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,7775,a(flip),b,15317,a),flip(a)].">
      <j1 rule="hyper" parents="116 7775 15317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15347">
    <literal><![CDATA[
      L(T(x,y),x \ z,K(u,w)) = T(L(x,z,K(u,w)),y)
    ]]></literal>
    <justification jstring="[para(15279(a,2),15297(a,2,1))].">
      <j1 rule="para" parents="15279 15297"/>
    </justification>
  </clause>

  <clause id="15348">
    <literal><![CDATA[
      L(T(x,y),x \ z,K(u,w)) = L(T(x,y),z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,20,a,b,15347,a),flip(a)].">
      <j1 rule="hyper" parents="334 20 15347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15349">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,15347,a(flip))].">
      <j1 rule="hyper" parents="139 15347"/>
    </justification>
  </clause>

  <clause id="15350">
    <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(15349(a,1),14475(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15349 14475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15351">
    <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(7114(a,1),15284(a,1,2))].">
      <j1 rule="para" parents="7114 15284"/>
    </justification>
  </clause>

  <clause id="15352">
    <literal><![CDATA[
      x \ (K(y,z) * ((K(z,y) * x) * u)) = T(u,a(z,x,y))
    ]]></literal>
    <justification jstring="[para(4(a,1),15313(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 15313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15353">
    <literal><![CDATA[
      (K(x,y) * (x * y)) \ z = (x * y) \ (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(11473,a,15314,a)].">
      <j1 rule="hyper" parents="11473 15314"/>
    </justification>
  </clause>

  <clause id="15354">
    <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(725(a,1),15314(a,1,1)),flip(a)].">
      <j1 rule="para" parents="725 15314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15355">
    <literal><![CDATA[
      (x * y) \ (K(y,x) * z) = (T(x,y) * y) \ z
    ]]></literal>
    <justification jstring="[para(5047(a,1),15353(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5047 15353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15356">
    <literal><![CDATA[
      K(x,y) * ((K(y,x) * z) * u) = z * L(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,15279,a,b,15352,a),flip(a)].">
      <j1 rule="hyper" parents="119 15279 15352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15357">
    <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(451,a,15356,a,b,1706,a)].">
      <j1 rule="hyper" parents="451 15356 1706"/>
    </justification>
  </clause>

  <clause id="15358">
    <literal><![CDATA[
      (x * y) * (z * L(u,z,K(y,x))) = (y * x) * ((K(x,y) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(119,a,15356,a(flip),b,11464,a)].">
      <j1 rule="hyper" parents="119 15356 11464"/>
    </justification>
  </clause>

  <clause id="15359">
    <literal><![CDATA[
      L(x,y,T(z,u)) \ L(x,y,z) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,12118,a(flip),b,15329,a),flip(a)].">
      <j1 rule="hyper" parents="334 12118 15329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15361">
    <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(15359(a,1),502(a,1,1,1))].">
      <j1 rule="para" parents="15359 502"/>
    </justification>
  </clause>

  <clause id="15362">
    <literal><![CDATA[
      (x * K(y,z)) / ((u \ x) * K(y,z)) = L(u,x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15349,a(flip),b,15281,a),flip(a)].">
      <j1 rule="hyper" parents="58 15349 15281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15363">
    <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(15281(a,2),276(a,1,1)),flip(b)].">
      <j1 rule="para" parents="15281 276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15364">
    <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(4361(a,1),15362(a,1,2,1))].">
      <j1 rule="para" parents="4361 15362"/>
    </justification>
  </clause>

  <clause id="15365">
    <literal><![CDATA[
      L(L(x,y,K(z,u * z)),y,u * z) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(13015(a,1),15331(a,1,1))].">
      <j1 rule="para" parents="13015 15331"/>
    </justification>
  </clause>

  <clause id="15366">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,u * z) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(12888(a,1),15365(a,1,1))].">
      <j1 rule="para" parents="12888 15365"/>
    </justification>
  </clause>

  <clause id="15367">
    <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,14294,a(flip),b,15366,a)].">
      <j1 rule="hyper" parents="58 14294 15366"/>
    </justification>
  </clause>

  <clause id="15368">
    <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,13801,a(flip),b,15299,a),flip(a)].">
      <j1 rule="hyper" parents="58 13801 15299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15369">
    <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(7780(a,1),15363(a,1,1))].">
      <j1 rule="para" parents="7780 15363"/>
    </justification>
  </clause>

  <clause id="15370">
    <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(14475(a,1),15363(a,1))].">
      <j1 rule="para" parents="14475 15363"/>
    </justification>
  </clause>

  <clause id="15371">
    <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(7884(a,2),15369(a,1))].">
      <j1 rule="para" parents="7884 15369"/>
    </justification>
  </clause>

  <clause id="15372">
    <literal><![CDATA[
      L(x,x \ y,K(z,y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(12873(a,1),15285(a,1,1))].">
      <j1 rule="para" parents="12873 15285"/>
    </justification>
  </clause>

  <clause id="15373">
    <literal><![CDATA[
      (x \ y) * K(z,z \ y) = x \ (z * (y / z))
    ]]></literal>
    <justification jstring="[para(14021(a,1),15372(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14021 15372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15374">
    <literal><![CDATA[
      K(x,y * ((z * y) \ (z * (u / z)))) = K(x,T(y * ((z * y) \ u),z))
    ]]></literal>
    <justification jstring="[para(15373(a,1),14515(a,1,2,2))].">
      <j1 rule="para" parents="15373 14515"/>
    </justification>
  </clause>

  <clause id="15375">
    <literal><![CDATA[
      T(x * a(y,x,K(z,u)),y) = y \ (K(z,u) * ((K(u,z) * x) * y))
    ]]></literal>
    <justification jstring="[para(15301(a,1),15357(a,1,1))].">
      <j1 rule="para" parents="15301 15357"/>
    </justification>
  </clause>

  <clause id="15376">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) * u)) / u = z * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(257,a,15375,a)].">
      <j1 rule="hyper" parents="257 15375"/>
    </justification>
  </clause>

  <clause id="15377">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) * (u \ 1))) / (u \ 1) = z * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(14680(a,1),15376(a,2,2))].">
      <j1 rule="para" parents="14680 15376"/>
    </justification>
  </clause>

  <clause id="15378">
    <literal><![CDATA[
      T(K(x,y) * ((x \ y) / z),z) = z \ ((x \ y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(12890(a,1),15350(a,2,1))].">
      <j1 rule="para" parents="12890 15350"/>
    </justification>
  </clause>

  <clause id="15379">
    <literal><![CDATA[
      T(K(x,y) * ((x \ y) / z),z) = z \ (K(x,y) * (x \ y))
    ]]></literal>
    <justification jstring="[para(6685(a,2),15378(a,2,2))].">
      <j1 rule="para" parents="6685 15378"/>
    </justification>
  </clause>

  <clause id="15380">
    <literal><![CDATA[
      x \ (K(y,z) * (y \ z)) = (x \ (y \ z)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(15370,a,15379,a),flip(a)].">
      <j1 rule="hyper" parents="15370 15379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15381">
    <literal><![CDATA[
      x \ (y \ ((y * z) / y)) = (x \ (y \ z)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5653,a,b,15380,a)].">
      <j1 rule="hyper" parents="58 5653 15380"/>
    </justification>
  </clause>

  <clause id="15382">
    <literal><![CDATA[
      (K(x,y) * z) \ (x \ ((x * y) / x)) = (z \ (x \ T(y,x))) * K(x,y)
    ]]></literal>
    <justification jstring="[para(14536(a,1),15381(a,2,1))].">
      <j1 rule="para" parents="14536 15381"/>
    </justification>
  </clause>

  <clause id="15383">
    <literal><![CDATA[
      (x \ (y \ T(z,y))) * K(y,z) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,14387,a(flip),b,15382,a),flip(a)].">
      <j1 rule="hyper" parents="58 14387 15382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15384">
    <literal><![CDATA[
      (x \ (y \ z)) * K(z,y) = x \ (y \ T(z,y))
    ]]></literal>
    <justification jstring="[hyper(6527,a,15383,a)].">
      <j1 rule="hyper" parents="6527 15383"/>
    </justification>
  </clause>

  <clause id="15385">
    <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(15322(a,1),15328(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15322 15328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15386">
    <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(4320(a,1),15351(a,1,1))].">
      <j1 rule="para" parents="4320 15351"/>
    </justification>
  </clause>

  <clause id="15387">
    <literal><![CDATA[
      (x * (1 / T(y,z))) * K(y,u) = x * (K(y,u) / T(y,z))
    ]]></literal>
    <justification jstring="[para(10478(a,1),15386(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10478 15386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15388">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = x * (K(y,z) / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7050,a,b,15387,a)].">
      <j1 rule="hyper" parents="58 7050 15387"/>
    </justification>
  </clause>

  <clause id="15389">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(5021(a,1),15388(a,2,2))].">
      <j1 rule="para" parents="5021 15388"/>
    </justification>
  </clause>

  <clause id="15390">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2943,a,15389,a),flip(a)].">
      <j1 rule="hyper" parents="2943 15389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15392">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,T(y,z)) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(7051,a,15390,a)].">
      <j1 rule="hyper" parents="7051 15390"/>
    </justification>
  </clause>

  <clause id="15393">
    <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(15392(a,1),11804(a,2,2))].">
      <j1 rule="para" parents="15392 11804"/>
    </justification>
  </clause>

  <clause id="15394">
    <literal><![CDATA[
      x / (T(y,z) \ R(x,y \ 1,y)) = (x * (1 / T(T(y,1),z))) \ x
    ]]></literal>
    <justification jstring="[para(15393(a,1),8653(a,1,2))].">
      <j1 rule="para" parents="15393 8653"/>
    </justification>
  </clause>

  <clause id="15396">
    <literal><![CDATA[
      (x * (1 / T(T(y,1),z))) \ x = T((x * (1 / y)) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11780,a(flip),b,15394,a),flip(a)].">
      <j1 rule="hyper" parents="58 11780 15394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15397">
    <literal><![CDATA[
      T((x * (1 / y)) \ x,z) = (x * (1 / T(y,z))) \ x
    ]]></literal>
    <justification jstring="[para(202(a,1),15396(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="202 15396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15398">
    <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(15397(a,2),13363(a,1,2,2,1))].">
      <j1 rule="para" parents="15397 13363"/>
    </justification>
  </clause>

  <clause id="15399">
    <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(334,a,14375,a(flip),b,15354,a),flip(a)].">
      <j1 rule="hyper" parents="334 14375 15354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15401">
    <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(15358(a,1),15367(a,1,1))].">
      <j1 rule="para" parents="15358 15367"/>
    </justification>
  </clause>

  <clause id="15402">
    <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),15214(a,2,2,1,1))].">
      <j1 rule="para" parents="7 15214"/>
    </justification>
  </clause>

  <clause id="15403">
    <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(334,a,14139,a(flip),b,15402,a),flip(a)].">
      <j1 rule="hyper" parents="334 14139 15402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15405">
    <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(14279(a,1),15403(a,1,2,1))].">
      <j1 rule="para" parents="14279 15403"/>
    </justification>
  </clause>

  <clause id="15406">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) / (u * ((z \ 1) / u))) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(7234(a,1),15405(a,1,2,2))].">
      <j1 rule="para" parents="7234 15405"/>
    </justification>
  </clause>

  <clause id="15407">
    <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(7406(a,2),15269(a,1,2,2))].">
      <j1 rule="para" parents="7406 15269"/>
    </justification>
  </clause>

  <clause id="15408">
    <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(5262(a,2),15197(a,1,1,1,2,3))].">
      <j1 rule="para" parents="5262 15197"/>
    </justification>
  </clause>

  <clause id="15409">
    <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),15260(a,1,1))].">
      <j1 rule="para" parents="68 15260"/>
    </justification>
  </clause>

  <clause id="15410">
    <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(15173(a,1),15409(a,1,2,1))].">
      <j1 rule="para" parents="15173 15409"/>
    </justification>
  </clause>

  <clause id="15411">
    <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(298,a,15410,a)].">
      <j1 rule="hyper" parents="298 15410"/>
    </justification>
  </clause>

  <clause id="15412">
    <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,13715,a(flip),b,15411,a),flip(a)].">
      <j1 rule="hyper" parents="58 13715 15411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15414">
    <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(3839(a,1),15408(a,1,1,1,2))].">
      <j1 rule="para" parents="3839 15408"/>
    </justification>
  </clause>

  <clause id="15415">
    <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(12896(a,1),15414(a,1,1,1,2))].">
      <j1 rule="para" parents="12896 15414"/>
    </justification>
  </clause>

  <clause id="15416">
    <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(14797(a,1),15415(a,1,1,1))].">
      <j1 rule="para" parents="14797 15415"/>
    </justification>
  </clause>

  <clause id="15417">
    <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(15134(a,1),15416(a,1,1))].">
      <j1 rule="para" parents="15134 15416"/>
    </justification>
  </clause>

  <clause id="15418">
    <literal><![CDATA[
      R(K(x,y) * z,u,u \ 1) = K(x,y) * R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,10374,a(flip),b,15417,a)].">
      <j1 rule="hyper" parents="58 10374 15417"/>
    </justification>
  </clause>

  <clause id="15420">
    <literal><![CDATA[
      R(K(x,y) * (z / u),u,u \ 1) = K(x,y) * (z * (u \ 1))
    ]]></literal>
    <justification jstring="[para(536(a,1),15418(a,2,2))].">
      <j1 rule="para" parents="536 15418"/>
    </justification>
  </clause>

  <clause id="15421">
    <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(15418(a,2),15399(a,1,2))].">
      <j1 rule="para" parents="15418 15399"/>
    </justification>
  </clause>

  <clause id="15422">
    <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(15420(a,1),572(a,1,1))].">
      <j1 rule="para" parents="15420 572"/>
    </justification>
  </clause>

  <clause id="15423">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) / u)) * u = z * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(15422,a,15377,a)].">
      <j1 rule="hyper" parents="15422 15377"/>
    </justification>
  </clause>

  <clause id="15424">
    <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(14365(a,1),15423(a,1,1,2))].">
      <j1 rule="para" parents="14365 15423"/>
    </justification>
  </clause>

  <clause id="15425">
    <literal><![CDATA[
      a(K(x,y) * z,u,u \ 1) = z \ R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(5394(a,1),15421(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5394 15421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15426">
    <literal><![CDATA[
      a(K(x,y) * z,u,u \ 1) = a(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,725,a(flip),b,15425,a),flip(a)].">
      <j1 rule="hyper" parents="334 725 15425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15427">
    <literal><![CDATA[
      a(x * K(y,z),u,u \ 1) = a(x,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(7538(a,1),15426(a,1,1))].">
      <j1 rule="para" parents="7538 15426"/>
    </justification>
  </clause>

  <clause id="15428">
    <literal><![CDATA[
      a(x \ (y / z),u,u \ 1) = a(x \ (z \ y),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(14302(a,1),15427(a,1,1))].">
      <j1 rule="para" parents="14302 15427"/>
    </justification>
  </clause>

  <clause id="15429">
    <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(8052(a,1),15424(a,1,1,2,1))].">
      <j1 rule="para" parents="8052 15424"/>
    </justification>
  </clause>

  <clause id="15430">
    <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(6520(a,1),15182(a,1,2,1))].">
      <j1 rule="para" parents="6520 15182"/>
    </justification>
  </clause>

  <clause id="15431">
    <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(15190(a,1),15338(a,1,2,1))].">
      <j1 rule="para" parents="15190 15338"/>
    </justification>
  </clause>

  <clause id="15432">
    <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(5426,a,15431,a)].">
      <j1 rule="hyper" parents="5426 15431"/>
    </justification>
  </clause>

  <clause id="15433">
    <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(459(a,1),15175(a,1,2)),flip(a)].">
      <j1 rule="para" parents="459 15175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15434">
    <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(334,a,15258,a(flip),b,15433,a),flip(a)].">
      <j1 rule="hyper" parents="334 15258 15433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15435">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,v5,v6)) = a(x,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(931,a,15434,a),flip(a)].">
      <j1 rule="hyper" parents="931 15434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15438">
    <literal><![CDATA[
      a((x * y) \ z,u,a(w,v5,v6)) = a(y \ (x \ z),u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(311(a,1),15435(a,1,1))].">
      <j1 rule="para" parents="311 15435"/>
    </justification>
  </clause>

  <clause id="15439">
    <literal><![CDATA[
      a((x \ y) \ 1,z,a(u,w,v5)) = a(y \ x,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(401(a,1),15435(a,1,1)),flip(a)].">
      <j1 rule="para" parents="401 15435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15440">
    <literal><![CDATA[
      a(x \ ((x / y) * z),u,a(w,v5,v6)) = a(y \ z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(505(a,1),15435(a,1,1))].">
      <j1 rule="para" parents="505 15435"/>
    </justification>
  </clause>

  <clause id="15441">
    <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(2862(a,1),15435(a,1,1))].">
      <j1 rule="para" parents="2862 15435"/>
    </justification>
  </clause>

  <clause id="15442">
    <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(14340(a,2),15440(a,1,1))].">
      <j1 rule="para" parents="14340 15440"/>
    </justification>
  </clause>

  <clause id="15443">
    <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,15435,a(flip),b,15441,a),flip(a)].">
      <j1 rule="hyper" parents="58 15435 15441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15445">
    <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(334,a,15438,a(flip),b,15443,a),flip(a)].">
      <j1 rule="hyper" parents="334 15438 15443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15446">
    <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),15445(a,2,1,2))].">
      <j1 rule="para" parents="4 15445"/>
    </justification>
  </clause>

  <clause id="15447">
    <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(334,a,15438,a(flip),b,15446,a),flip(a)].">
      <j1 rule="hyper" parents="334 15438 15446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15448">
    <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),15447(a,2,1,2))].">
      <j1 rule="para" parents="61 15447"/>
    </justification>
  </clause>

  <clause id="15449">
    <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),15448(a,1,1,1))].">
      <j1 rule="para" parents="2 15448"/>
    </justification>
  </clause>

  <clause id="15451">
    <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(12545(a,1),15213(a,2,2))].">
      <j1 rule="para" parents="12545 15213"/>
    </justification>
  </clause>

  <clause id="15452">
    <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(7960(a,1),15451(a,1,2,1))].">
      <j1 rule="para" parents="7960 15451"/>
    </justification>
  </clause>

  <clause id="15453">
    <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(5869(a,1),15452(a,1,2,2))].">
      <j1 rule="para" parents="5869 15452"/>
    </justification>
  </clause>

  <clause id="15454">
    <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(9722(a,2),15453(a,1,2,2))].">
      <j1 rule="para" parents="9722 15453"/>
    </justification>
  </clause>

  <clause id="15455">
    <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(12515(a,1),15454(a,1,2,2,1))].">
      <j1 rule="para" parents="12515 15454"/>
    </justification>
  </clause>

  <clause id="15456">
    <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(14207(a,1),15455(a,1,2,2))].">
      <j1 rule="para" parents="14207 15455"/>
    </justification>
  </clause>

  <clause id="15457">
    <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(14654(a,1),15361(a,1,1))].">
      <j1 rule="para" parents="14654 15361"/>
    </justification>
  </clause>

  <clause id="15458">
    <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(15359(a,1),15457(a,1,2))].">
      <j1 rule="para" parents="15359 15457"/>
    </justification>
  </clause>

  <clause id="15459">
    <literal><![CDATA[
      L(x,y,z) \ (L(x,y,T(z,u)) * w) = a(x,y,K(z,u)) * w
    ]]></literal>
    <justification jstring="[hyper(13694,a,15458,a),flip(a)].">
      <j1 rule="hyper" parents="13694 15458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15460">
    <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,15385,a(flip),b,15459,a)].">
      <j1 rule="hyper" parents="58 15385 15459"/>
    </justification>
  </clause>

  <clause id="15461">
    <literal><![CDATA[
      L(x,y,T(z,u)) * (L(x,y,z) \ u) = T(u,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(334,a,14692,a,b,15460,a),flip(a)].">
      <j1 rule="hyper" parents="334 14692 15460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15462">
    <literal><![CDATA[
      T(L(x,y,z) \ x,u) \ x = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(30,a,14312,a,b,15461,a)].">
      <j1 rule="hyper" parents="30 14312 15461"/>
    </justification>
  </clause>

  <clause id="15463">
    <literal><![CDATA[
      T(L(x,y,z) \ x,u) = L(x,y,T(z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(34,a,3960,a,b,15462,a),flip(a)].">
      <j1 rule="hyper" parents="34 3960 15462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15464">
    <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),15257(a,1,2,1,2))].">
      <j1 rule="para" parents="7 15257"/>
    </justification>
  </clause>

  <clause id="15465">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(5868(a,2),15407(a,1,2))].">
      <j1 rule="para" parents="5868 15407"/>
    </justification>
  </clause>

  <clause id="15466">
    <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),15465(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15467">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(u,z)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[para(8100(a,1),15465(a,1,2,1,2))].">
      <j1 rule="para" parents="8100 15465"/>
    </justification>
  </clause>

  <clause id="15468">
    <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(8455(a,1),15465(a,1,2,1,2))].">
      <j1 rule="para" parents="8455 15465"/>
    </justification>
  </clause>

  <clause id="15469">
    <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(8478(a,1),15465(a,1,2,1,2))].">
      <j1 rule="para" parents="8478 15465"/>
    </justification>
  </clause>

  <clause id="15470">
    <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(15465(a,1),8918(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15465 8918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15471">
    <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(15465(a,1),13367(a,2,1,2))].">
      <j1 rule="para" parents="15465 13367"/>
    </justification>
  </clause>

  <clause id="15472">
    <literal><![CDATA[
      T(x / T(y,K(z,u)),K(z,u) \ y) = y \ T(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(5391(a,2),15466(a,1,2))].">
      <j1 rule="para" parents="5391 15466"/>
    </justification>
  </clause>

  <clause id="15473">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[para(8100(a,1),15467(a,1,2))].">
      <j1 rule="para" parents="8100 15467"/>
    </justification>
  </clause>

  <clause id="15474">
    <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(6600(a,2),15472(a,1,1))].">
      <j1 rule="para" parents="6600 15472"/>
    </justification>
  </clause>

  <clause id="15475">
    <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,15473,a),flip(a)].">
      <j1 rule="hyper" parents="134 15473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15476">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15465,a(flip),b,15473,a)].">
      <j1 rule="hyper" parents="58 15465 15473"/>
    </justification>
  </clause>

  <clause id="15477">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,u) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(11815,a,15476,a)].">
      <j1 rule="hyper" parents="11815 15476"/>
    </justification>
  </clause>

  <clause id="15478">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(334,a,13372,a,b,15476,a)].">
      <j1 rule="hyper" parents="334 13372 15476"/>
    </justification>
  </clause>

  <clause id="15479">
    <literal><![CDATA[
      T(x,K(y,y * z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(334,a,13352,a(flip),b,15476,a),flip(a)].">
      <j1 rule="hyper" parents="334 13352 15476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15480">
    <literal><![CDATA[
      x \ T(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(116,a,15476,a,b,5020,a(flip))].">
      <j1 rule="hyper" parents="116 15476 5020"/>
    </justification>
  </clause>

  <clause id="15481">
    <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),15476(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 15476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15482">
    <literal><![CDATA[
      T(x,K(y,z) * (z * u)) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5047(a,1),15476(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5047 15476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15483">
    <literal><![CDATA[
      T(x,K(y,z) * (K(y,z) * u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(5394(a,1),15476(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5394 15476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15484">
    <literal><![CDATA[
      T(x,K(y,z) * (y \ u)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5392(a,1),15476(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5392 15476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15485">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * (((y \ u) / u) \ w)) = T(x,T((y \ u) / u,z) \ w)
    ]]></literal>
    <justification jstring="[para(5616(a,1),15476(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5616 15476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15486">
    <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(15476(a,1),13436(a,1,2,1))].">
      <j1 rule="para" parents="15476 13436"/>
    </justification>
  </clause>

  <clause id="15487">
    <literal><![CDATA[
      T(x,K(y,z) * (z / u)) = T(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(14034(a,1),15476(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14034 15476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15488">
    <literal><![CDATA[
      T(x,y * (T(T(y,z),z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(6146(a,1),15483(a,1,2))].">
      <j1 rule="para" parents="6146 15483"/>
    </justification>
  </clause>

  <clause id="15489">
    <literal><![CDATA[
      T(x,T(T(y,z),z) * u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(4(a,1),15488(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 15488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15490">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,y * T(T(z,u),u))
    ]]></literal>
    <justification jstring="[hyper(12612,a,15489,a),flip(a)].">
      <j1 rule="hyper" parents="12612 15489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15491">
    <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(12611,a,15479,a),flip(a)].">
      <j1 rule="hyper" parents="12611 15479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15492">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(5110,a,15480,a)].">
      <j1 rule="hyper" parents="5110 15480"/>
    </justification>
  </clause>

  <clause id="15493">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15480(a,1),5110(a,1))].">
      <j1 rule="para" parents="15480 5110"/>
    </justification>
  </clause>

  <clause id="15494">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(13488,a,15492,a),flip(a)].">
      <j1 rule="hyper" parents="13488 15492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15495">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * w) = K(x,K(y \ z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(334,a,13408,a(flip),b,15492,a),flip(a)].">
      <j1 rule="hyper" parents="334 13408 15492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15496">
    <literal><![CDATA[
      K(x,K(y,z) * (z * u)) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5047(a,1),15492(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5047 15492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15497">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(5391(a,2),15492(a,1,2))].">
      <j1 rule="para" parents="5391 15492"/>
    </justification>
  </clause>

  <clause id="15498">
    <literal><![CDATA[
      K(x,K(y,z) * (T(z,y) \ u)) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(5337(a,1),15492(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5337 15492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15499">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ u)) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5392(a,1),15492(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5392 15492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15500">
    <literal><![CDATA[
      K(x,K(y,z \ u) * (u / z)) = K(x,T(u / z,T(y,z)))
    ]]></literal>
    <justification jstring="[para(7568(a,1),15492(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7568 15492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15501">
    <literal><![CDATA[
      K(x,K(y,z) * (z / u)) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(14034(a,1),15492(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14034 15492"/>
      <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="[para(5391(a,2),15497(a,2,2))].">
      <j1 rule="para" parents="5391 15497"/>
    </justification>
  </clause>

  <clause id="15503">
    <literal><![CDATA[
      K(x,K(y,y \ z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(334,a,13448,a(flip),b,15502,a),flip(a)].">
      <j1 rule="hyper" parents="334 13448 15502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15504">
    <literal><![CDATA[
      T(x,K(y,z) \ u) = T(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15502,a,b,5664,a)].">
      <j1 rule="hyper" parents="118 15502 5664"/>
    </justification>
  </clause>

  <clause id="15505">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = K(x,K(L(z,u,w),y) \ v5)
    ]]></literal>
    <justification jstring="[para(11089(a,2),15502(a,1,2,1))].">
      <j1 rule="para" parents="11089 15502"/>
    </justification>
  </clause>

  <clause id="15506">
    <literal><![CDATA[
      T(x,K(y,z) \ (y / u)) = T(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(14068(a,1),15504(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14068 15504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15507">
    <literal><![CDATA[
      T(x,((y * z) / y) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5350(a,2),15484(a,1,2))].">
      <j1 rule="para" parents="5350 15484"/>
    </justification>
  </clause>

  <clause id="15508">
    <literal><![CDATA[
      T(x,T(y \ z,y) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(5656(a,1),15484(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5656 15484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15509">
    <literal><![CDATA[
      T(x,T(y \ z,y) / u) = T(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[para(14361(a,1),15487(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14361 15487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15510">
    <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),15494(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 15494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15511">
    <literal><![CDATA[
      K(x,((y * z) / y) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5493(a,1),15496(a,1,2))].">
      <j1 rule="para" parents="5493 15496"/>
    </justification>
  </clause>

  <clause id="15512">
    <literal><![CDATA[
      K(x,T(y \ z,y) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(5682(a,1),15496(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5682 15496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15513">
    <literal><![CDATA[
      K(x,T(T(y,z),z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(5504(a,1),15498(a,1,2))].">
      <j1 rule="para" parents="5504 15498"/>
    </justification>
  </clause>

  <clause id="15514">
    <literal><![CDATA[
      K(x,T(y * z,z) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13458,a(flip),b,15513,a)].">
      <j1 rule="hyper" parents="58 13458 15513"/>
    </justification>
  </clause>

  <clause id="15515">
    <literal><![CDATA[
      K(x,T(y \ z,y) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(107(a,1),15513(a,1,2,1,1))].">
      <j1 rule="para" parents="107 15513"/>
    </justification>
  </clause>

  <clause id="15516">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,(z / (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(4544(a,1),15513(a,1,2,1,1))].">
      <j1 rule="para" parents="4544 15513"/>
    </justification>
  </clause>

  <clause id="15517">
    <literal><![CDATA[
      K(x,(y * K(z,y)) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(14306(a,2),15501(a,1,2))].">
      <j1 rule="para" parents="14306 15501"/>
    </justification>
  </clause>

  <clause id="15518">
    <literal><![CDATA[
      K(x,T(y \ z,y) / u) = K(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[para(14361(a,1),15501(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14361 15501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15519">
    <literal><![CDATA[
      T(x,K(y,y \ z) \ u) = T(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15503,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 15503 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15520">
    <literal><![CDATA[
      K(x,K(y,z \ y) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13447,a,b,15503,a)].">
      <j1 rule="hyper" parents="58 13447 15503"/>
    </justification>
  </clause>

  <clause id="15521">
    <literal><![CDATA[
      K(x,K(y \ z,z) \ u) = K(x,K(z,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(5271(a,1),15503(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5271 15503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15522">
    <literal><![CDATA[
      T(x,K(y,z) \ (z / u)) = T(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15504,a,b,15506,a)].">
      <j1 rule="hyper" parents="58 15504 15506"/>
    </justification>
  </clause>

  <clause id="15523">
    <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(14165(a,1),15507(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="14165 15507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15524">
    <literal><![CDATA[
      T(x,T((y / (z \ 1)) / y,y) \ u) = T(x,((y / (z \ K(z,y))) / y) \ u)
    ]]></literal>
    <justification jstring="[para(10405(a,1),15508(a,1,2,1,1))].">
      <j1 rule="para" parents="10405 15508"/>
    </justification>
  </clause>

  <clause id="15525">
    <literal><![CDATA[
      K(x,T(T(y,z),z) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(231(a,1),15511(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="231 15511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15526">
    <literal><![CDATA[
      K(x,T(L(y \ z,u,w),y) * v5) = K(x,L(z / y,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(662(a,1),15511(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="662 15511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15527">
    <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),15525(a,2,2))].">
      <j1 rule="para" parents="101 15525"/>
    </justification>
  </clause>

  <clause id="15528">
    <literal><![CDATA[
      K(x,T(y,z * u) / (z * u)) = K(x,T(u * z,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,13301,a,b,15514,a)].">
      <j1 rule="hyper" parents="334 13301 15514"/>
    </justification>
  </clause>

  <clause id="15529">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(7(a,1),15514(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 15514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15530">
    <literal><![CDATA[
      K(x,T(T(y,z),z) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(5016(a,1),15517(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5016 15517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15531">
    <literal><![CDATA[
      K(x,((y * z) / y) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(5017(a,2),15517(a,1,2,1))].">
      <j1 rule="para" parents="5017 15517"/>
    </justification>
  </clause>

  <clause id="15532">
    <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(12942(a,1),15518(a,1,2,1,1))].">
      <j1 rule="para" parents="12942 15518"/>
    </justification>
  </clause>

  <clause id="15533">
    <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(13037(a,1),15518(a,1,2,1))].">
      <j1 rule="para" parents="13037 15518"/>
    </justification>
  </clause>

  <clause id="15534">
    <literal><![CDATA[
      K(x,K(y \ z,z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15502,a,b,15520,a)].">
      <j1 rule="hyper" parents="58 15502 15520"/>
    </justification>
  </clause>

  <clause id="15535">
    <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(7931(a,2),15522(a,2,2,1))].">
      <j1 rule="para" parents="7931 15522"/>
    </justification>
  </clause>

  <clause id="15536">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,w,v5)) = K(L(x,w,v5),T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(11169,a,15529,a)].">
      <j1 rule="hyper" parents="11169 15529"/>
    </justification>
  </clause>

  <clause id="15537">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ u) = K(x,(y * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(334,a,13409,a,b,15529,a)].">
      <j1 rule="hyper" parents="334 13409 15529"/>
    </justification>
  </clause>

  <clause id="15538">
    <literal><![CDATA[
      K(x,T(y \ z,z) \ u) = K(x,(y \ T(z,y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(4089(a,2),15529(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4089 15529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15539">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15494(a,2),15493(a,1))].">
      <j1 rule="para" parents="15494 15493"/>
    </justification>
  </clause>

  <clause id="15540">
    <literal><![CDATA[
      T(x,K(y,z) * K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(8120,a,15477,a),flip(a)].">
      <j1 rule="hyper" parents="8120 15477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15541">
    <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(15540(a,1),13376(a,1,2,2))].">
      <j1 rule="para" parents="15540 13376"/>
    </justification>
  </clause>

  <clause id="15542">
    <literal><![CDATA[
      T(x,y * K(z,u)) = T(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(8116(a,1),15481(a,1,2))].">
      <j1 rule="para" parents="8116 15481"/>
    </justification>
  </clause>

  <clause id="15543">
    <literal><![CDATA[
      x / T(x,y * K(z,u)) = K(y * K(u,z),x)
    ]]></literal>
    <justification jstring="[para(15542(a,1),5062(a,2,2)),flip(a)].">
      <j1 rule="para" parents="15542 5062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15544">
    <literal><![CDATA[
      T(x,(y / z) * K(z,u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(6368(a,1),15542(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6368 15542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15545">
    <literal><![CDATA[
      K(x * K(y,z),u) = K(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(5133,a,15543,a)].">
      <j1 rule="hyper" parents="5133 15543"/>
    </justification>
  </clause>

  <clause id="15546">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(15543(a,1),5133(a,1))].">
      <j1 rule="para" parents="15543 5133"/>
    </justification>
  </clause>

  <clause id="15547">
    <literal><![CDATA[
      K((1 / x) * K(y,z),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(14403,a,15545,a),flip(a)].">
      <j1 rule="hyper" parents="14403 15545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15548">
    <literal><![CDATA[
      K((x / y) * K(y,z),u) = K(x / T(y,z),u)
    ]]></literal>
    <justification jstring="[para(6368(a,1),15545(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6368 15545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15549">
    <literal><![CDATA[
      K((x * K(y,z)) * K(y,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(6516(a,1),15545(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6516 15545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15550">
    <literal><![CDATA[
      K((x \ y) * K(z,y),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(14025(a,1),15545(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14025 15545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15551">
    <literal><![CDATA[
      K(x * (K(y,z) * K(y,z)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(9209(a,1),15549(a,1,1))].">
      <j1 rule="para" parents="9209 15549"/>
    </justification>
  </clause>

  <clause id="15552">
    <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(15551(a,1),5034(a,2,1)),flip(a)].">
      <j1 rule="para" parents="15551 5034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15553">
    <literal><![CDATA[
      T(x,y / ((z * u) / z)) = T(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(6694(a,2),15544(a,1,2))].">
      <j1 rule="para" parents="6694 15544"/>
    </justification>
  </clause>

  <clause id="15554">
    <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(6556(a,1),15544(a,1,2,1))].">
      <j1 rule="para" parents="6556 15544"/>
    </justification>
  </clause>

  <clause id="15556">
    <literal><![CDATA[
      K(x \ K(y,z),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(14403,a,15547,a)].">
      <j1 rule="hyper" parents="14403 15547"/>
    </justification>
  </clause>

  <clause id="15557">
    <literal><![CDATA[
      K(x \ K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(15547(a,1),14403(a,1))].">
      <j1 rule="para" parents="15547 14403"/>
    </justification>
  </clause>

  <clause id="15558">
    <literal><![CDATA[
      K(x \ K(y \ z,y),u) = K(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(13496,a,15556,a),flip(a)].">
      <j1 rule="hyper" parents="13496 15556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15559">
    <literal><![CDATA[
      (x \ K(y \ K(z,u),w)) \ (x \ 1) = K(w,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(15556(a,1),14233(a,1,1,2))].">
      <j1 rule="para" parents="15556 14233"/>
    </justification>
  </clause>

  <clause id="15560">
    <literal><![CDATA[
      K((x \ y) \ K(z,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ T(x,z),u) = w
    ]]></literal>
    <justification jstring="[para(15556(a,1),14343(a,1))].">
      <j1 rule="para" parents="15556 14343"/>
    </justification>
  </clause>

  <clause id="15561">
    <literal><![CDATA[
      K(x / ((y * z) / y),u) = K(x / T(z,y),u)
    ]]></literal>
    <justification jstring="[para(6694(a,2),15548(a,1,1))].">
      <j1 rule="para" parents="6694 15548"/>
    </justification>
  </clause>

  <clause id="15563">
    <literal><![CDATA[
      K(x \ (y * K(z,y)),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(14299(a,2),15550(a,1,1))].">
      <j1 rule="para" parents="14299 15550"/>
    </justification>
  </clause>

  <clause id="15565">
    <literal><![CDATA[
      T(x,y / T(T(z \ u,w),z)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[para(469(a,1),15553(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="469 15553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15566">
    <literal><![CDATA[
      T(x,y / ((z * u) / T(z,w))) = T(x,y / T(u * K(w,z),z))
    ]]></literal>
    <justification jstring="[para(7708(a,1),15553(a,1,2,2))].">
      <j1 rule="para" parents="7708 15553"/>
    </justification>
  </clause>

  <clause id="15567">
    <literal><![CDATA[
      T(x,y / (((z * u) / z) * K(z,w))) = T(x,y / T(u * K(z,w),z))
    ]]></literal>
    <justification jstring="[para(7278(a,1),15553(a,1,2,2))].">
      <j1 rule="para" parents="7278 15553"/>
    </justification>
  </clause>

  <clause id="15568">
    <literal><![CDATA[
      K(x \ K(y \ z,z),u) = K(x \ K(y,y \ z),u)
    ]]></literal>
    <justification jstring="[para(5236(a,1),15558(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5236 15558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15571">
    <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(15561(a,1),7688(a,1,2))].">
      <j1 rule="para" parents="15561 7688"/>
    </justification>
  </clause>

  <clause id="15572">
    <literal><![CDATA[
      K(x \ T(T(y,z),z),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(5016(a,1),15563(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5016 15563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15573">
    <literal><![CDATA[
      K(x \ T(y * z,z),u) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13463,a(flip),b,15572,a)].">
      <j1 rule="hyper" parents="58 13463 15572"/>
    </justification>
  </clause>

  <clause id="15574">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) = 1 / K(y \ z,x)
    ]]></literal>
    <justification jstring="[para(15572(a,1),5243(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15572 5243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15575">
    <literal><![CDATA[
      K(x \ (y * (z / y)),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[para(7(a,1),15573(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15576">
    <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(15573(a,1),11102(a,1,2,3))].">
      <j1 rule="para" parents="15573 11102"/>
    </justification>
  </clause>

  <clause id="15577">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(334,a,5243,a(flip),b,15574,a),flip(a)].">
      <j1 rule="hyper" parents="334 5243 15574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15578">
    <literal><![CDATA[
      T(x,y \ T(T(z,u),u)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(118,a,15577,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 15577 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15579">
    <literal><![CDATA[
      K(x,y \ T(z \ u,z)) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[para(107(a,1),15577(a,1,2,2,1))].">
      <j1 rule="para" parents="107 15577"/>
    </justification>
  </clause>

  <clause id="15580">
    <literal><![CDATA[
      K(x,y \ T(z * (u / T(z,u)),z)) = K(x,y \ (z * (u / z)))
    ]]></literal>
    <justification jstring="[para(4524(a,1),15577(a,1,2,2,1))].">
      <j1 rule="para" parents="4524 15577"/>
    </justification>
  </clause>

  <clause id="15581">
    <literal><![CDATA[
      K(x,y \ (z * K(u,z))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(5086(a,1),15577(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5086 15577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15582">
    <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(15577(a,1),12614(a,1,1,2))].">
      <j1 rule="para" parents="15577 12614"/>
    </justification>
  </clause>

  <clause id="15583">
    <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(7823(a,1),15579(a,1,2,2,1))].">
      <j1 rule="para" parents="7823 15579"/>
    </justification>
  </clause>

  <clause id="15584">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(6871,a,15581,a)].">
      <j1 rule="hyper" parents="6871 15581"/>
    </justification>
  </clause>

  <clause id="15585">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u \ 1,y)) = K(x,z \ T(y,1 / u))
    ]]></literal>
    <justification jstring="[para(3105(a,2),15584(a,2,2,2))].">
      <j1 rule="para" parents="3105 15584"/>
    </justification>
  </clause>

  <clause id="15586">
    <literal><![CDATA[
      T(x,y * T(T(z,u),u)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(12586,a,15490,a),flip(a)].">
      <j1 rule="hyper" parents="12586 15490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15587">
    <literal><![CDATA[
      T(x,y * ((z * u) / z)) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(230(a,1),15586(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="230 15586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15588">
    <literal><![CDATA[
      T(x,y * (z * K(u,z))) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(5086(a,1),15586(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5086 15586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15589">
    <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(15586(a,1),12576(a,1,2,1))].">
      <j1 rule="para" parents="15586 12576"/>
    </justification>
  </clause>

  <clause id="15590">
    <literal><![CDATA[
      T(x,y * ((z * u) / z)) = x * K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,5020,a(flip),b,15587,a),flip(a)].">
      <j1 rule="hyper" parents="334 5020 15587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15591">
    <literal><![CDATA[
      K(x * ((y * z) / y),u) = u / T(u,x * T(z,y))
    ]]></literal>
    <justification jstring="[para(15587(a,1),5062(a,2,2))].">
      <j1 rule="para" parents="15587 5062"/>
    </justification>
  </clause>

  <clause id="15592">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(13517,a,15516,a),flip(a)].">
      <j1 rule="hyper" parents="13517 15516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15593">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(15516(a,1),13517(a,1))].">
      <j1 rule="para" parents="15516 13517"/>
    </justification>
  </clause>

  <clause id="15594">
    <literal><![CDATA[
      T(x,(y / (y / z)) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15592,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 15592 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15595">
    <literal><![CDATA[
      K(x,T(y \ z,z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(72(a,1),15592(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 15592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15596">
    <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(15594(a,1),12589(a,1,2,1))].">
      <j1 rule="para" parents="15594 12589"/>
    </justification>
  </clause>

  <clause id="15597">
    <literal><![CDATA[
      K(x,(y / z) \ T(u,y / z)) = K(x,u / T(z \ y,y))
    ]]></literal>
    <justification jstring="[hyper(13438,a,15595,a),flip(a)].">
      <j1 rule="hyper" parents="13438 15595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15598">
    <literal><![CDATA[
      K(x,K(y,z \ 1) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15534,a(flip),b,15521,a),flip(a)].">
      <j1 rule="hyper" parents="58 15534 15521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15599">
    <literal><![CDATA[
      K(x,T(y,z \ 1) \ u) = K(x,K(y,z) \ (y \ u))
    ]]></literal>
    <justification jstring="[para(5348(a,1),15598(a,1,2))].">
      <j1 rule="para" parents="5348 15598"/>
    </justification>
  </clause>

  <clause id="15600">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ u) \ 1 = K(((y \ z) * y) \ u,x)
    ]]></literal>
    <justification jstring="[para(15537(a,1),5232(a,1,1))].">
      <j1 rule="para" parents="15537 5232"/>
    </justification>
  </clause>

  <clause id="15601">
    <literal><![CDATA[
      K(x \ K(y \ z,z),u) = K(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,13402,a(flip),b,15568,a),flip(a)].">
      <j1 rule="hyper" parents="334 13402 15568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15602">
    <literal><![CDATA[
      K(x \ K(y,z \ y),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(15557,a,15601,a)].">
      <j1 rule="hyper" parents="15557 15601"/>
    </justification>
  </clause>

  <clause id="15603">
    <literal><![CDATA[
      K(x \ K(y,z \ 1),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13454,a,b,15602,a)].">
      <j1 rule="hyper" parents="58 13454 15602"/>
    </justification>
  </clause>

  <clause id="15604">
    <literal><![CDATA[
      K((x \ y) \ K(z,x),u) = K(y \ T(x,1 / z),u)
    ]]></literal>
    <justification jstring="[hyper(14517,a,15603,a),flip(a)].">
      <j1 rule="hyper" parents="14517 15603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15605">
    <literal><![CDATA[
      K(x,y * ((z * u) / z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(5109,a,15590,a)].">
      <j1 rule="hyper" parents="5109 15590"/>
    </justification>
  </clause>

  <clause id="15606">
    <literal><![CDATA[
      K(x,y * T(z \ u,z)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(5(a,1),15605(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 15605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15607">
    <literal><![CDATA[
      K(x,y * T(T(z,u),u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(231(a,1),15605(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="231 15605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15608">
    <literal><![CDATA[
      K(x,y * (z * K(u,z))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(5017(a,1),15605(a,1,2,2))].">
      <j1 rule="para" parents="5017 15605"/>
    </justification>
  </clause>

  <clause id="15609">
    <literal><![CDATA[
      K(x,(y / (z * u)) * T(u,z)) = K(x,(y / (u * z)) * u)
    ]]></literal>
    <justification jstring="[para(10921(a,1),15605(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10921 15605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15610">
    <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(14165(a,1),15605(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14165 15605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15611">
    <literal><![CDATA[
      K(x,T(y,z \ u) * (u \ z)) = K(x,(u \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,14523,a(flip),b,15607,a)].">
      <j1 rule="hyper" parents="58 14523 15607"/>
    </justification>
  </clause>

  <clause id="15612">
    <literal><![CDATA[
      K(x,y * T(z * u,u)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13501,a(flip),b,15607,a)].">
      <j1 rule="hyper" parents="58 13501 15607"/>
    </justification>
  </clause>

  <clause id="15613">
    <literal><![CDATA[
      K(x,y * T(z \ u,u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13426,a(flip),b,15607,a)].">
      <j1 rule="hyper" parents="58 13426 15607"/>
    </justification>
  </clause>

  <clause id="15614">
    <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),15607(a,2,2))].">
      <j1 rule="para" parents="90 15607"/>
    </justification>
  </clause>

  <clause id="15615">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) \ u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(4480(a,1),15606(a,1,2,2))].">
      <j1 rule="para" parents="4480 15606"/>
    </justification>
  </clause>

  <clause id="15616">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ (u \ z))) = K(x,y * ((u \ z) / z))
    ]]></literal>
    <justification jstring="[para(4595(a,1),15606(a,1,2,2))].">
      <j1 rule="para" parents="4595 15606"/>
    </justification>
  </clause>

  <clause id="15617">
    <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(14789(a,2),15606(a,1,2))].">
      <j1 rule="para" parents="14789 15606"/>
    </justification>
  </clause>

  <clause id="15618">
    <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(4443(a,1),15608(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4443 15608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15619">
    <literal><![CDATA[
      K(x,y * (z * (u / z))) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),15612(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15620">
    <literal><![CDATA[
      K(x,L(y * T(z \ u,u),w,v5)) = K(L(x,w,v5),y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(11169,a,15613,a)].">
      <j1 rule="hyper" parents="11169 15613"/>
    </justification>
  </clause>

  <clause id="15621">
    <literal><![CDATA[
      K(x,y * (z * ((z * u) / z))) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(334,a,13376,a(flip),b,15619,a),flip(a)].">
      <j1 rule="hyper" parents="334 13376 15619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15622">
    <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),15619(a,2,2,2))].">
      <j1 rule="para" parents="18 15619"/>
    </justification>
  </clause>

  <clause id="15623">
    <literal><![CDATA[
      K(x * ((y * z) / y),u) = K(x * T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,5062,a,b,15591,a),flip(a)].">
      <j1 rule="hyper" parents="334 5062 15591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15624">
    <literal><![CDATA[
      K(x * (y * K(z,y)),u) = K(x * T(y,z),u)
    ]]></literal>
    <justification jstring="[para(5017(a,1),15623(a,1,1,2))].">
      <j1 rule="para" parents="5017 15623"/>
    </justification>
  </clause>

  <clause id="15625">
    <literal><![CDATA[
      K(x,T(y,z \ 1) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5348(a,1),15599(a,2,2))].">
      <j1 rule="para" parents="5348 15599"/>
    </justification>
  </clause>

  <clause id="15626">
    <literal><![CDATA[
      K(x,T(y * (z \ 1),z) \ u) = K(x,((z \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15514,a(flip),b,15625,a),flip(a)].">
      <j1 rule="hyper" parents="58 15514 15625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15627">
    <literal><![CDATA[
      K(x,y * (T(z,u) \ u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13468,a(flip),b,15615,a)].">
      <j1 rule="hyper" parents="58 13468 15615"/>
    </justification>
  </clause>

  <clause id="15628">
    <literal><![CDATA[
      K(x,y * (z \ T(u,z))) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(4490(a,1),15627(a,1,2,2))].">
      <j1 rule="para" parents="4490 15627"/>
    </justification>
  </clause>

  <clause id="15629">
    <literal><![CDATA[
      K(x,x * (((y * x) * z) \ T(u,(y * x) * z))) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(334,a,12937,a(flip),b,15628,a),flip(a)].">
      <j1 rule="hyper" parents="334 12937 15628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15630">
    <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(5432(a,1),15628(a,2,2,2))].">
      <j1 rule="para" parents="5432 15628"/>
    </justification>
  </clause>

  <clause id="15631">
    <literal><![CDATA[
      K(x,y * (T(z,u) * u)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(231(a,1),15621(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="231 15621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15632">
    <literal><![CDATA[
      K(x,T((y * z) * u,y * z)) = K(x,u * (T(z,y) * y))
    ]]></literal>
    <justification jstring="[hyper(334,a,12551,a,b,15631,a)].">
      <j1 rule="hyper" parents="334 12551 15631"/>
    </justification>
  </clause>

  <clause id="15633">
    <literal><![CDATA[
      T(x,y * (T(z,u) * u)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(118,a,15631,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 15631 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15634">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * ((w * u) / w))) = K(x,y * (((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[para(8219(a,1),15631(a,1,2,2,1))].">
      <j1 rule="para" parents="8219 15631"/>
    </justification>
  </clause>

  <clause id="15635">
    <literal><![CDATA[
      T(x,y * (T(z \ u,w) * z)) = T(x,y * (z * T(u / z,w)))
    ]]></literal>
    <justification jstring="[para(254(a,1),15633(a,1,2,2,1))].">
      <j1 rule="para" parents="254 15633"/>
    </justification>
  </clause>

  <clause id="15636">
    <literal><![CDATA[
      K(x \ T(y,1 / z),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(15560,a,15604,a),flip(a)].">
      <j1 rule="hyper" parents="15560 15604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15637">
    <literal><![CDATA[
      K(x \ T(y,z \ 1),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(72(a,1),15636(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 15636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15638">
    <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(15637(a,1),11102(a,1,2,3))].">
      <j1 rule="para" parents="15637 11102"/>
    </justification>
  </clause>

  <clause id="15639">
    <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(15475(a,2),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="15475 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15640">
    <literal><![CDATA[
      K(x,T(y * z,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(15528(a,1),13368(a,1))].">
      <j1 rule="para" parents="15528 13368"/>
    </justification>
  </clause>

  <clause id="15641">
    <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(13430(a,1),15640(a,1))].">
      <j1 rule="para" parents="13430 15640"/>
    </justification>
  </clause>

  <clause id="15642">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15595,a(flip),b,15538,a),flip(a)].">
      <j1 rule="hyper" parents="58 15595 15538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15643">
    <literal><![CDATA[
      K(x,y \ K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15559(a,1),6664(a,1))].">
      <j1 rule="para" parents="15559 6664"/>
    </justification>
  </clause>

  <clause id="15644">
    <literal><![CDATA[
      T(x,y / T(((z \ u) \ u) \ u,w)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[para(4592(a,1),15565(a,1,2,2))].">
      <j1 rule="para" parents="4592 15565"/>
    </justification>
  </clause>

  <clause id="15645">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(15597(a,1),13435(a,1))].">
      <j1 rule="para" parents="15597 13435"/>
    </justification>
  </clause>

  <clause id="15646">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,u) = K((x * (y / x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(5241,a,15600,a),flip(a)].">
      <j1 rule="hyper" parents="5241 15600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15647">
    <literal><![CDATA[
      K((x * (y / x)) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13411,a(flip),b,15646,a),flip(a)].">
      <j1 rule="hyper" parents="58 13411 15646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15648">
    <literal><![CDATA[
      K(K(x,y) * (x \ z),u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(13503,a,15647,a)].">
      <j1 rule="hyper" parents="13503 15647"/>
    </justification>
  </clause>

  <clause id="15649">
    <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,15210,a(flip),b,15647,a),flip(a)].">
      <j1 rule="hyper" parents="58 15210 15647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15650">
    <literal><![CDATA[
      K(K(x,x \ y) * (x \ z),u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,13515,a(flip),b,15648,a),flip(a)].">
      <j1 rule="hyper" parents="334 13515 15648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15652">
    <literal><![CDATA[
      K((x / (x / y)) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(5659(a,2),15650(a,1,1))].">
      <j1 rule="para" parents="5659 15650"/>
    </justification>
  </clause>

  <clause id="15653">
    <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,15512,a,b,15609,a)].">
      <j1 rule="hyper" parents="58 15512 15609"/>
    </justification>
  </clause>

  <clause id="15654">
    <literal><![CDATA[
      K(x,y * T(z * (u / z),w)) = K(x,y * T(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(4821(a,2),15622(a,1,2,2))].">
      <j1 rule="para" parents="4821 15622"/>
    </justification>
  </clause>

  <clause id="15655">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) \ u) = K(x,R(z,y,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(810(a,1),15626(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="810 15626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15656">
    <literal><![CDATA[
      K(x,y * (T(z,u) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (u * z)) = w
    ]]></literal>
    <justification jstring="[para(15632(a,1),12587(a,1))].">
      <j1 rule="para" parents="15632 12587"/>
    </justification>
  </clause>

  <clause id="15657">
    <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(12567(a,1),15656(a,1,2,2,1))].">
      <j1 rule="para" parents="12567 15656"/>
    </justification>
  </clause>

  <clause id="15658">
    <literal><![CDATA[
      T(x,y * T(z * (u / z),w)) = T(x,y * T(T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(118,a,15654,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 15654 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15659">
    <literal><![CDATA[
      K(x,R(T(T(y,z),z),u,w) * (u * w)) = K(x,(y * u) * w)
    ]]></literal>
    <justification jstring="[para(850(a,2),15527(a,1,2,1))].">
      <j1 rule="para" parents="850 15527"/>
    </justification>
  </clause>

  <clause id="15660">
    <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),15614(a,1,2,2,1))].">
      <j1 rule="para" parents="20 15614"/>
    </justification>
  </clause>

  <clause id="15661">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ u) = K(x,L(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5840,a(flip),b,15655,a),flip(a)].">
      <j1 rule="hyper" parents="58 5840 15655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15662">
    <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,14849,a(flip),b,15661,a),flip(a)].">
      <j1 rule="hyper" parents="58 14849 15661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15663">
    <literal><![CDATA[
      K(x,(T(T(y,z),z) * u) * w) = K(x,(y * u) * w)
    ]]></literal>
    <justification jstring="[para(101(a,1),15659(a,1,2))].">
      <j1 rule="para" parents="101 15659"/>
    </justification>
  </clause>

  <clause id="15664">
    <literal><![CDATA[
      K(x,(((y * z) / y) * u) * w) = K(x,(T(z,y) * u) * w)
    ]]></literal>
    <justification jstring="[para(230(a,1),15663(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="230 15663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15665">
    <literal><![CDATA[
      K(x,(T(y,z) * z) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(7(a,1),15664(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15666">
    <literal><![CDATA[
      K(x,(y * (K(z,y) * u)) * w) = K(x,(T(y,z) * u) * w)
    ]]></literal>
    <justification jstring="[para(5444(a,1),15664(a,1,2,1))].">
      <j1 rule="para" parents="5444 15664"/>
    </justification>
  </clause>

  <clause id="15667">
    <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(7693(a,1),15665(a,1,2,1,1))].">
      <j1 rule="para" parents="7693 15665"/>
    </justification>
  </clause>

  <clause id="15668">
    <literal><![CDATA[
      K(x,(y * (K(z,y) * (u / y))) * w) = K(x,((T(y,z) \ u) * y) * w)
    ]]></literal>
    <justification jstring="[para(7882(a,1),15665(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7882 15665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15669">
    <literal><![CDATA[
      K(x,((y \ z) * (y * K(u,y))) * w) = K(x,(y * (z / T(y,u))) * w)
    ]]></literal>
    <justification jstring="[para(7865(a,1),15665(a,1,2,1))].">
      <j1 rule="para" parents="7865 15665"/>
    </justification>
  </clause>

  <clause id="15670">
    <literal><![CDATA[
      K(x,y * (z * T(T(u,w),w))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(461(a,1),15660(a,1,2))].">
      <j1 rule="para" parents="461 15660"/>
    </justification>
  </clause>

  <clause id="15671">
    <literal><![CDATA[
      K(x,y * (z * T(u \ w,w))) = K(x,y * (z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13521,a(flip),b,15670,a)].">
      <j1 rule="hyper" parents="58 13521 15670"/>
    </justification>
  </clause>

  <clause id="15672">
    <literal><![CDATA[
      K(x,y * (z * ((u * w) / u))) = K(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[para(230(a,1),15670(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="230 15670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15673">
    <literal><![CDATA[
      T(x,y * K(z,z * u)) = T(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(12610,a,15491,a),flip(a)].">
      <j1 rule="hyper" parents="12610 15491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15674">
    <literal><![CDATA[
      K(x,K(y,z) * T(u,K(z,y))) = K(x,u * K(z,z \ y))
    ]]></literal>
    <justification jstring="[para(8236(a,1),15510(a,1,2,2))].">
      <j1 rule="para" parents="8236 15510"/>
    </justification>
  </clause>

  <clause id="15675">
    <literal><![CDATA[
      K(x,y * K(z,z \ u)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(8116(a,1),15674(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8116 15674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15676">
    <literal><![CDATA[
      K(x,y * K(z,u)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13377,a(flip),b,15675,a)].">
      <j1 rule="hyper" parents="58 13377 15675"/>
    </justification>
  </clause>

  <clause id="15678">
    <literal><![CDATA[
      K(x,(y / z) * K(z,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(6368(a,1),15676(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6368 15676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15679">
    <literal><![CDATA[
      K(x,(y \ z) * K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15676(a,1),14416(a,1))].">
      <j1 rule="para" parents="15676 14416"/>
    </justification>
  </clause>

  <clause id="15680">
    <literal><![CDATA[
      K(x,y / ((z * u) / z)) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(6694(a,2),15678(a,1,2))].">
      <j1 rule="para" parents="6694 15678"/>
    </justification>
  </clause>

  <clause id="15681">
    <literal><![CDATA[
      K(x,y / T(z \ u,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(6743(a,1),15678(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6743 15678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15683">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,T(y,z))) = K(x,u / ((z * y) / z))
    ]]></literal>
    <justification jstring="[hyper(334,a,13434,a,b,15680,a)].">
      <j1 rule="hyper" parents="334 13434 15680"/>
    </justification>
  </clause>

  <clause id="15685">
    <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(4293(a,1),15679(a,1,2,2))].">
      <j1 rule="para" parents="4293 15679"/>
    </justification>
  </clause>

  <clause id="15686">
    <literal><![CDATA[
      K(x,y \ (z * K(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(14299(a,2),15679(a,1,2))].">
      <j1 rule="para" parents="14299 15679"/>
    </justification>
  </clause>

  <clause id="15687">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(6868(a,2),15686(a,1))].">
      <j1 rule="para" parents="6868 15686"/>
    </justification>
  </clause>

  <clause id="15688">
    <literal><![CDATA[
      K(x,y / ((z * u) / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15683(a,1),13435(a,1))].">
      <j1 rule="para" parents="15683 13435"/>
    </justification>
  </clause>

  <clause id="15689">
    <literal><![CDATA[
      K(x,(y / z) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(6694(a,1),15688(a,1,2))].">
      <j1 rule="para" parents="6694 15688"/>
    </justification>
  </clause>

  <clause id="15690">
    <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(15536(a,2),11169(a,1))].">
      <j1 rule="para" parents="15536 11169"/>
    </justification>
  </clause>

  <clause id="15691">
    <literal><![CDATA[
      K(x,y \ ((z / T(u,z)) * u)) = K(x,y \ (u * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13383,a(flip),b,15580,a)].">
      <j1 rule="hyper" parents="58 13383 15580"/>
    </justification>
  </clause>

  <clause id="15692">
    <literal><![CDATA[
      K(x,y \ (z * (u / z))) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(4484(a,1),15691(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4484 15691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15693">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),z \ u)) = K(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15185,a,b,15692,a)].">
      <j1 rule="hyper" parents="58 15185 15692"/>
    </justification>
  </clause>

  <clause id="15694">
    <literal><![CDATA[
      K(x,y \ T(z * u,u)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(6(a,1),15692(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6 15692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15695">
    <literal><![CDATA[
      K(x,y \ T(z * u,z)) = K(x,y \ (T(z,u) * u))
    ]]></literal>
    <justification jstring="[para(4121(a,2),15692(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4121 15692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15696">
    <literal><![CDATA[
      K(x,y \ T(z \ u,u)) = K(x,y \ (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(4089(a,2),15692(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4089 15692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15697">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * u)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13383,a(flip),b,15695,a),flip(a)].">
      <j1 rule="hyper" parents="58 13383 15695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15698">
    <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(12562(a,1),15697(a,1,2,2,1))].">
      <j1 rule="para" parents="12562 15697"/>
    </justification>
  </clause>

  <clause id="15699">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * ((u \ 1) \ w))) = K(x,y \ (((u \ 1) \ w) * z))
    ]]></literal>
    <justification jstring="[para(14130(a,1),15697(a,1,2,2,1))].">
      <j1 rule="para" parents="14130 15697"/>
    </justification>
  </clause>

  <clause id="15700">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * ((1 / u) \ w))) = K(x,y \ (((1 / u) \ w) * z))
    ]]></literal>
    <justification jstring="[para(14216(a,1),15697(a,1,2,2,1))].">
      <j1 rule="para" parents="14216 15697"/>
    </justification>
  </clause>

  <clause id="15701">
    <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(15620(a,2),11169(a,1))].">
      <j1 rule="para" parents="15620 11169"/>
    </justification>
  </clause>

  <clause id="15702">
    <literal><![CDATA[
      T(x,y / T(T(z \ u,w),u)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13417,a(flip),b,15644,a)].">
      <j1 rule="hyper" parents="58 13417 15644"/>
    </justification>
  </clause>

  <clause id="15703">
    <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),15702(a,1,2,2))].">
      <j1 rule="para" parents="18 15702"/>
    </justification>
  </clause>

  <clause id="15704">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,a(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1509(a,1),15662(a,1,2))].">
      <j1 rule="para" parents="1509 15662"/>
    </justification>
  </clause>

  <clause id="15705">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15465(a,1),15639(a,1))].">
      <j1 rule="para" parents="15465 15639"/>
    </justification>
  </clause>

  <clause id="15706">
    <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(15473(a,2),15705(a,1))].">
      <j1 rule="para" parents="15473 15705"/>
    </justification>
  </clause>

  <clause id="15707">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15478(a,2),15705(a,1))].">
      <j1 rule="para" parents="15478 15705"/>
    </justification>
  </clause>

  <clause id="15709">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u \ 1,z) * x)
    ]]></literal>
    <justification jstring="[para(8455(a,1),15468(a,1,2))].">
      <j1 rule="para" parents="8455 15468"/>
    </justification>
  </clause>

  <clause id="15710">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(15706,a,15709,a),flip(a)].">
      <j1 rule="hyper" parents="15706 15709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15711">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15709(a,1),15706(a,1))].">
      <j1 rule="para" parents="15709 15706"/>
    </justification>
  </clause>

  <clause id="15712">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = x \ T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(116,a,15710,a(flip),b,5020,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 15710 5020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15713">
    <literal><![CDATA[
      K(K(x \ 1,y) * z,u) = u / T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(15710(a,1),5062(a,2,2))].">
      <j1 rule="para" parents="15710 5062"/>
    </justification>
  </clause>

  <clause id="15714">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(334,a,4995,a,b,15712,a),flip(a)].">
      <j1 rule="hyper" parents="334 4995 15712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15715">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15712(a,2),5110(a,1))].">
      <j1 rule="para" parents="15712 5110"/>
    </justification>
  </clause>

  <clause id="15716">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(15493,a,15714,a)].">
      <j1 rule="hyper" parents="15493 15714"/>
    </justification>
  </clause>

  <clause id="15717">
    <literal><![CDATA[
      K(x,y * (T(1 / y,z) * u)) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,14525,a,b,15714,a)].">
      <j1 rule="hyper" parents="58 14525 15714"/>
    </justification>
  </clause>

  <clause id="15718">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[para(6615(a,1),15714(a,1,2,1))].">
      <j1 rule="para" parents="6615 15714"/>
    </justification>
  </clause>

  <clause id="15719">
    <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(15714(a,1),7033(a,1,1))].">
      <j1 rule="para" parents="15714 7033"/>
    </justification>
  </clause>

  <clause id="15720">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(334,a,15492,a,b,15716,a),flip(a)].">
      <j1 rule="hyper" parents="334 15492 15716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15721">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(u,z \ y) * w)
    ]]></literal>
    <justification jstring="[para(6423(a,1),15716(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6423 15716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15722">
    <literal><![CDATA[
      K(x,K(y,z) * T(u,K(z,y))) = K(x,u * K(z,y \ 1))
    ]]></literal>
    <justification jstring="[para(8477(a,1),15716(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8477 15716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15723">
    <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(15716(a,1),7034(a,1,1))].">
      <j1 rule="para" parents="15716 7034"/>
    </justification>
  </clause>

  <clause id="15724">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) = K(x,K(z,y) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(14396,a,15720,a)].">
      <j1 rule="hyper" parents="14396 15720"/>
    </justification>
  </clause>

  <clause id="15725">
    <literal><![CDATA[
      T(x,K(y,z \ 1) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15720,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 15720 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15726">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,u) = u / T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(15725(a,1),5062(a,2,2))].">
      <j1 rule="para" parents="15725 5062"/>
    </justification>
  </clause>

  <clause id="15727">
    <literal><![CDATA[
      K(K(x \ 1,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(x,y) * z,u) = w
    ]]></literal>
    <justification jstring="[para(15713(a,2),5133(a,1))].">
      <j1 rule="para" parents="15713 5133"/>
    </justification>
  </clause>

  <clause id="15728">
    <literal><![CDATA[
      K(x,y * (K(1 / z,y) * u)) = K(x,K(z,y) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(14415,a,15717,a)].">
      <j1 rule="hyper" parents="14415 15717"/>
    </justification>
  </clause>

  <clause id="15729">
    <literal><![CDATA[
      K(x,K(y \ z,z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(13488,a,15718,a),flip(a)].">
      <j1 rule="hyper" parents="13488 15718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15730">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * w) = K(x,K(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(334,a,15495,a,b,15718,a)].">
      <j1 rule="hyper" parents="334 15495 15718"/>
    </justification>
  </clause>

  <clause id="15731">
    <literal><![CDATA[
      K(x,K(y \ z,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15718(a,1),13488(a,1))].">
      <j1 rule="para" parents="15718 13488"/>
    </justification>
  </clause>

  <clause id="15732">
    <literal><![CDATA[
      T(x,K(y \ z,z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15729,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 15729 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15733">
    <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,15500,a(flip),b,15729,a)].">
      <j1 rule="hyper" parents="58 15500 15729"/>
    </justification>
  </clause>

  <clause id="15734">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ u) = K(x,K(z,y) * (y \ u))
    ]]></literal>
    <justification jstring="[para(5392(a,1),15729(a,1,2))].">
      <j1 rule="para" parents="5392 15729"/>
    </justification>
  </clause>

  <clause id="15735">
    <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(15732(a,1),13436(a,1,2,1))].">
      <j1 rule="para" parents="15732 13436"/>
    </justification>
  </clause>

  <clause id="15736">
    <literal><![CDATA[
      K(x,K(y,z \ y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15721(a,1),13488(a,1))].">
      <j1 rule="para" parents="15721 13488"/>
    </justification>
  </clause>

  <clause id="15737">
    <literal><![CDATA[
      K(x,K(y \ (z \ 1),u) * w) = K(x,K(u,z * y) * w)
    ]]></literal>
    <justification jstring="[para(14106(a,1),15721(a,2,2,1))].">
      <j1 rule="para" parents="14106 15721"/>
    </justification>
  </clause>

  <clause id="15738">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(334,a,15496,a(flip),b,15724,a),flip(a)].">
      <j1 rule="hyper" parents="334 15496 15724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15739">
    <literal><![CDATA[
      K(x,T(1 / y,z) \ u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(14470,a,15738,a)].">
      <j1 rule="hyper" parents="14470 15738"/>
    </justification>
  </clause>

  <clause id="15740">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z) \ u,w,v5)) = K(L(x,w,v5),T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(11169,a,15738,a)].">
      <j1 rule="hyper" parents="11169 15738"/>
    </justification>
  </clause>

  <clause id="15741">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) = K(x,(T(y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(334,a,14106,a,b,15738,a),flip(a)].">
      <j1 rule="hyper" parents="334 14106 15738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15742">
    <literal><![CDATA[
      T(x,T(y \ 1,z) \ u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15738,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 15738 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15743">
    <literal><![CDATA[
      T(x,T(1 / y,z) \ u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15739,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 15739 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15744">
    <literal><![CDATA[
      K(x,T(y \ 1,z) * u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(72(a,1),15739(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="72 15739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15745">
    <literal><![CDATA[
      T(x,T(y \ 1,z) * u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(72(a,1),15743(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="72 15743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15746">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w) \ v5) = T(x,T(u \ K(z,y),w) * v5)
    ]]></literal>
    <justification jstring="[para(14147(a,1),15743(a,1,2,1,1))].">
      <j1 rule="para" parents="14147 15743"/>
    </justification>
  </clause>

  <clause id="15747">
    <literal><![CDATA[
      T(x,T(K(y,z) / u,w) \ v5) = T(x,T(u * K(z,y),w) * v5)
    ]]></literal>
    <justification jstring="[para(14215(a,1),15743(a,1,2,1,1))].">
      <j1 rule="para" parents="14215 15743"/>
    </justification>
  </clause>

  <clause id="15748">
    <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(14169(a,1),15745(a,1,2,1,1))].">
      <j1 rule="para" parents="14169 15745"/>
    </justification>
  </clause>

  <clause id="15749">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,u) = K(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,5062,a,b,15726,a),flip(a)].">
      <j1 rule="hyper" parents="334 5062 15726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15750">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(K(y,x) * (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(14397,a,15749,a)].">
      <j1 rule="hyper" parents="14397 15749"/>
    </justification>
  </clause>

  <clause id="15751">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5392(a,1),15734(a,2,2))].">
      <j1 rule="para" parents="5392 15734"/>
    </justification>
  </clause>

  <clause id="15752">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15741(a,2),14346(a,1))].">
      <j1 rule="para" parents="15741 14346"/>
    </justification>
  </clause>

  <clause id="15753">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(x * (K(y,x) * z),u)
    ]]></literal>
    <justification jstring="[para(5522(a,1),15750(a,2,1))].">
      <j1 rule="para" parents="5522 15750"/>
    </justification>
  </clause>

  <clause id="15754">
    <literal><![CDATA[
      K(x,K(y,z) * (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15724(a,1),15752(a,1))].">
      <j1 rule="para" parents="15724 15752"/>
    </justification>
  </clause>

  <clause id="15755">
    <literal><![CDATA[
      K(x,y * (K(z,y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(5522(a,1),15754(a,1,2))].">
      <j1 rule="para" parents="5522 15754"/>
    </justification>
  </clause>

  <clause id="15756">
    <literal><![CDATA[
      K(x,y * K(z,u \ 1)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(8116(a,1),15722(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8116 15722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15757">
    <literal><![CDATA[
      K(x,y * K(z \ 1,u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15676,a,b,15756,a)].">
      <j1 rule="hyper" parents="58 15676 15756"/>
    </justification>
  </clause>

  <clause id="15758">
    <literal><![CDATA[
      K(x * K(y,z \ 1),u) = 1 / K(u,x * K(z,y))
    ]]></literal>
    <justification jstring="[para(15756(a,1),5243(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15756 5243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15759">
    <literal><![CDATA[
      T(x,y * K(z \ 1,u)) = T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,15757,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 15757 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15760">
    <literal><![CDATA[
      K(x * K(y,z \ 1),u) = K(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,5243,a(flip),b,15758,a),flip(a)].">
      <j1 rule="hyper" parents="334 5243 15758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15761">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) = K(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(15546,a,15760,a)].">
      <j1 rule="hyper" parents="15546 15760"/>
    </justification>
  </clause>

  <clause id="15762">
    <literal><![CDATA[
      K(((x * (y \ z)) / x) * y,u) = K(z * K(z \ y,x),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(12583,a,15760,a)].">
      <j1 rule="hyper" parents="12583 15760"/>
    </justification>
  </clause>

  <clause id="15763">
    <literal><![CDATA[
      K(x * K(x \ y,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12533,a(flip),b,15761,a),flip(a)].">
      <j1 rule="hyper" parents="58 12533 15761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15764">
    <literal><![CDATA[
      K(x,y * (K(1 / z,y) * u)) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(334,a,15496,a(flip),b,15728,a),flip(a)].">
      <j1 rule="hyper" parents="334 15496 15728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15765">
    <literal><![CDATA[
      K(x,y * (K(z \ 1,y) * u)) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(3442(a,1),15764(a,1,2,2,1))].">
      <j1 rule="para" parents="3442 15764"/>
    </justification>
  </clause>

  <clause id="15766">
    <literal><![CDATA[
      K(x,T(y,z \ 1) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(15755,a,15765,a)].">
      <j1 rule="hyper" parents="15755 15765"/>
    </justification>
  </clause>

  <clause id="15767">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) * w) = K(x,T(y,u * z) * w)
    ]]></literal>
    <justification jstring="[para(14333(a,1),15766(a,1,2,1))].">
      <j1 rule="para" parents="14333 15766"/>
    </justification>
  </clause>

  <clause id="15768">
    <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(334,a,11137,a(flip),b,15740,a),flip(a)].">
      <j1 rule="hyper" parents="334 11137 15740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15769">
    <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(15740(a,2),11169(a,1))].">
      <j1 rule="para" parents="15740 11169"/>
    </justification>
  </clause>

  <clause id="15770">
    <literal><![CDATA[
      K(((x * (y \ z)) / x) * y,u) = K(y * T(z / y,x),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,15763,a(flip),b,15762,a),flip(a)].">
      <j1 rule="hyper" parents="334 15763 15762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15771">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) = K((z \ 1) * T((z \ y) / (z \ 1),x),u)
    ]]></literal>
    <justification jstring="[hyper(13117,a,15770,a)].">
      <j1 rule="hyper" parents="13117 15770"/>
    </justification>
  </clause>

  <clause id="15772">
    <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),15768(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 15768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15773">
    <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(15772(a,1),14962(a,1))].">
      <j1 rule="para" parents="15772 14962"/>
    </justification>
  </clause>

  <clause id="15774">
    <literal><![CDATA[
      T(x * (K(y,z) * K(y,z)),u) = T(x,u) * (K(y,z) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5299,a,15552,a),flip(a)].">
      <j1 rule="hyper" parents="5299 15552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15775">
    <literal><![CDATA[
      K(x,(y * z) \ T(u,(y * x) * z)) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(12831,a,15629,a)].">
      <j1 rule="hyper" parents="12831 15629"/>
    </justification>
  </clause>

  <clause id="15776">
    <literal><![CDATA[
      K(x,((T(y,z) \ u) * y) * w) = K(x,(T(y,z) * (u / y)) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15666,a(flip),b,15668,a),flip(a)].">
      <j1 rule="hyper" parents="58 15666 15668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15777">
    <literal><![CDATA[
      K(x,T(y / z,T(u \ (z \ y),z))) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(334,a,15500,a(flip),b,15733,a),flip(a)].">
      <j1 rule="hyper" parents="334 15500 15733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15778">
    <literal><![CDATA[
      K(x,T(y / z,y / (z * u))) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[para(9878(a,1),15777(a,1,2))].">
      <j1 rule="para" parents="9878 15777"/>
    </justification>
  </clause>

  <clause id="15779">
    <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,15464,a(flip),b,15778,a)].">
      <j1 rule="hyper" parents="58 15464 15778"/>
    </justification>
  </clause>

  <clause id="15780">
    <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(6230(a,1),15778(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6230 15778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15781">
    <literal><![CDATA[
      K(x \ T((x \ y) * x,z),u) = K(((z * y) / z) / x,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,12667,a(flip),b,15771,a)].">
      <j1 rule="hyper" parents="334 12667 15771"/>
    </justification>
  </clause>

  <clause id="15782">
    <literal><![CDATA[
      K(T(x \ T(y,z),x),u) = K(((z * y) / z) / x,u)
    ]]></literal>
    <justification jstring="[para(4844(a,1),15781(a,1,1))].">
      <j1 rule="para" parents="4844 15781"/>
    </justification>
  </clause>

  <clause id="15783">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(8539,a,15782,a),flip(a)].">
      <j1 rule="hyper" parents="8539 15782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15784">
    <literal><![CDATA[
      K(T(T(x,y),y) / z,u) = K(x / z,u)
    ]]></literal>
    <justification jstring="[para(231(a,1),15783(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="231 15783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15785">
    <literal><![CDATA[
      K((x * y) \ T(z,x),T(u,y)) = K(z / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(15229,a,15784,a)].">
      <j1 rule="hyper" parents="15229 15784"/>
    </justification>
  </clause>

  <clause id="15786">
    <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(14326(a,1),15785(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14326 15785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15787">
    <literal><![CDATA[
      T(x,K(y,z) * (((y \ u) / u) \ w)) = T(x,T((y \ u) / u,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(15711,a,15485,a)].">
      <j1 rule="hyper" parents="15711 15485"/>
    </justification>
  </clause>

  <clause id="15788">
    <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),15524(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 15524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15789">
    <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,15670,a(flip),b,15589,a)].">
      <j1 rule="hyper" parents="58 15670 15589"/>
    </justification>
  </clause>

  <clause id="15790">
    <literal><![CDATA[
      K(x,(y * T(T(z,u),u)) * w) = K(x,(y * z) * w)
    ]]></literal>
    <justification jstring="[hyper(12589,a,15789,a),flip(a)].">
      <j1 rule="hyper" parents="12589 15789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15792">
    <literal><![CDATA[
      K(x,(y * (z * K(u,z))) * w) = K(x,(y * T(z,u)) * w)
    ]]></literal>
    <justification jstring="[para(5086(a,1),15790(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5086 15790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15793">
    <literal><![CDATA[
      T(x,(y * (z * K(u,z))) * w) = T(x,(y * T(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(118,a,15792,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 15792 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15794">
    <literal><![CDATA[
      K(x,((y \ z) * T(y,u)) * w) = K(x,(y * (z / T(y,u))) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15669,a(flip),b,15792,a),flip(a)].">
      <j1 rule="hyper" parents="58 15669 15792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15795">
    <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,15672,a(flip),b,15634,a)].">
      <j1 rule="hyper" parents="58 15672 15634"/>
    </justification>
  </clause>

  <clause id="15796">
    <literal><![CDATA[
      K(x,y * (((z * u) / z) * w)) = K(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(15656,a,15795,a),flip(a)].">
      <j1 rule="hyper" parents="15656 15795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15797">
    <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(15795(a,1),15656(a,1))].">
      <j1 rule="para" parents="15795 15656"/>
    </justification>
  </clause>

  <clause id="15798">
    <literal><![CDATA[
      K(x,y * (T(T(z,u),u) * w)) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(231(a,1),15796(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="231 15796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15799">
    <literal><![CDATA[
      K(x,y * (z * (T(T(z,u),u) \ w))) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(5(a,1),15798(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 15798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15800">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (K(z,u) * w))) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(6146(a,2),15799(a,1,2,2))].">
      <j1 rule="para" parents="6146 15799"/>
    </justification>
  </clause>

  <clause id="15801">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (z \ w))) = K(x,y * (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[para(5337(a,1),15800(a,1,2,2,2))].">
      <j1 rule="para" parents="5337 15800"/>
    </justification>
  </clause>

  <clause id="15802">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * K(z,u)) * w)) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(11742(a,2),15800(a,1,2,2))].">
      <j1 rule="para" parents="11742 15800"/>
    </justification>
  </clause>

  <clause id="15803">
    <literal><![CDATA[
      K(x,y * (z * (K(u,w) * K(u,w)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15541,a(flip),b,15802,a)].">
      <j1 rule="hyper" parents="58 15541 15802"/>
    </justification>
  </clause>

  <clause id="15805">
    <literal><![CDATA[
      K(x,y * (z * K(u,w))) = K(x,y * (z * K(w,u)))
    ]]></literal>
    <justification jstring="[para(9210(a,1),15803(a,1,2,2))].">
      <j1 rule="para" parents="9210 15803"/>
    </justification>
  </clause>

  <clause id="15806">
    <literal><![CDATA[
      K(x,y * ((z / u) * K(u,w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[para(6368(a,1),15805(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6368 15805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15807">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(w,u))) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(14025(a,1),15805(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14025 15805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15808">
    <literal><![CDATA[
      K(x,y * ((z / (z / u)) \ w)) = K(x,y * (T(u,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13507,a,b,15801,a)].">
      <j1 rule="hyper" parents="58 13507 15801"/>
    </justification>
  </clause>

  <clause id="15809">
    <literal><![CDATA[
      K(x,y * (z / T(u,u \ w))) = K(x,y * (z / (w / (w / u))))
    ]]></literal>
    <justification jstring="[para(6745(a,2),15806(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6745 15806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15810">
    <literal><![CDATA[
      K(x,y * (z \ ((u * w) / u))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[para(14300(a,2),15807(a,1,2,2))].">
      <j1 rule="para" parents="14300 15807"/>
    </justification>
  </clause>

  <clause id="15811">
    <literal><![CDATA[
      K(x,y * (z \ (L(u,w,u) * w))) = K(x,y * (z \ T(w * u,u)))
    ]]></literal>
    <justification jstring="[para(14359(a,1),15807(a,1,2,2))].">
      <j1 rule="para" parents="14359 15807"/>
    </justification>
  </clause>

  <clause id="15812">
    <literal><![CDATA[
      K(x,y * (z \ T(T(u,w),w))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(231(a,1),15810(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="231 15810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15813">
    <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(334,a,12614,a,b,15812,a),flip(a)].">
      <j1 rule="hyper" parents="334 12614 15812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15814">
    <literal><![CDATA[
      K(x,y * (z \ T(u * w,w))) = K(x,y * (z \ (w * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13484,a(flip),b,15811,a),flip(a)].">
      <j1 rule="hyper" parents="58 13484 15811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15816">
    <literal><![CDATA[
      K(x,y * (z \ (u * (w / u)))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[para(7(a,1),15814(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15817">
    <literal><![CDATA[
      K(x,T(y * ((z * y) \ u),z)) = K(x,y * ((z * y) \ T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15374,a(flip),b,15816,a)].">
      <j1 rule="hyper" parents="58 15374 15816"/>
    </justification>
  </clause>

  <clause id="15818">
    <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,5603,a(flip),b,15700,a)].">
      <j1 rule="hyper" parents="58 5603 15700"/>
    </justification>
  </clause>

  <clause id="15819">
    <literal><![CDATA[
      K(x,y \ (((1 / z) \ u) * w)) = K(x,y \ (((z \ 1) \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15699,a(flip),b,15818,a),flip(a)].">
      <j1 rule="hyper" parents="58 15699 15818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15820">
    <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(8019(a,1),15474(a,1,1,1,2))].">
      <j1 rule="para" parents="8019 15474"/>
    </justification>
  </clause>

  <clause id="15821">
    <literal><![CDATA[
      K(x,(K(y,z \ K(z,u)) * u) \ w) = K(x,(u * K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(7176,a,15719,a),flip(a)].">
      <j1 rule="hyper" parents="7176 15719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15822">
    <literal><![CDATA[
      K(x,(y * K(z,u \ 1)) \ w) = K(x,(y * K(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(6232(a,1),15821(a,1,2,1))].">
      <j1 rule="para" parents="6232 15821"/>
    </justification>
  </clause>

  <clause id="15823">
    <literal><![CDATA[
      K(x,(K(y \ K(y,z),u) * z) \ w) = K(x,(z * K(u,y)) \ w)
    ]]></literal>
    <justification jstring="[hyper(7176,a,15723,a),flip(a)].">
      <j1 rule="hyper" parents="7176 15723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15824">
    <literal><![CDATA[
      K(x,(y * K(z \ 1,u)) \ w) = K(x,(y * K(u,z)) \ w)
    ]]></literal>
    <justification jstring="[para(6954(a,1),15823(a,1,2,1))].">
      <j1 rule="para" parents="6954 15823"/>
    </justification>
  </clause>

  <clause id="15825">
    <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(8060(a,1),15824(a,2,2))].">
      <j1 rule="para" parents="8060 15824"/>
    </justification>
  </clause>

  <clause id="15826">
    <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(15553(a,1),15571(a,1,1))].">
      <j1 rule="para" parents="15553 15571"/>
    </justification>
  </clause>

  <clause id="15827">
    <literal><![CDATA[
      T(x,T(y / ((z * u) / z),w)) = T(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(7969,a,15826,a),flip(a)].">
      <j1 rule="hyper" parents="7969 15826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15828">
    <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,12660,a(flip),b,15827,a)].">
      <j1 rule="hyper" parents="58 12660 15827"/>
    </justification>
  </clause>

  <clause id="15829">
    <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,14901,a,b,15828,a)].">
      <j1 rule="hyper" parents="58 14901 15828"/>
    </justification>
  </clause>

  <clause id="15830">
    <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(6520(a,1),15523(a,2,2,1))].">
      <j1 rule="para" parents="6520 15523"/>
    </justification>
  </clause>

  <clause id="15831">
    <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(7527(a,1),15535(a,1,2,1))].">
      <j1 rule="para" parents="7527 15535"/>
    </justification>
  </clause>

  <clause id="15832">
    <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,15519,a(flip),b,15831,a),flip(a)].">
      <j1 rule="hyper" parents="58 15519 15831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15834">
    <literal><![CDATA[
      K(x,(y \ T(T(z,u),u)) * w) = K(x,(y \ z) * w)
    ]]></literal>
    <justification jstring="[hyper(29,a,15813,a(flip),b,15582,a),flip(a)].">
      <j1 rule="hyper" parents="29 15813 15582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15835">
    <literal><![CDATA[
      K(x,(y \ ((z * u) / z)) * w) = K(x,(y \ T(u,z)) * w)
    ]]></literal>
    <justification jstring="[para(230(a,1),15834(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="230 15834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15837">
    <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(6520(a,1),15610(a,2,2,2))].">
      <j1 rule="para" parents="6520 15610"/>
    </justification>
  </clause>

  <clause id="15838">
    <literal><![CDATA[
      K(x,y * ((((1 / z) * u) \ u) \ u)) = K(x,y * (((1 / z) * u) * K(z,z \ u)))
    ]]></literal>
    <justification jstring="[para(14104(a,1),15618(a,2,2,2,2))].">
      <j1 rule="para" parents="14104 15618"/>
    </justification>
  </clause>

  <clause id="15839">
    <literal><![CDATA[
      K(x,y * ((((1 / z) * u) \ u) \ u)) = K(x,y * ((1 / z) * (z * (u / z))))
    ]]></literal>
    <justification jstring="[para(10611(a,1),15838(a,2,2,2))].">
      <j1 rule="para" parents="10611 15838"/>
    </justification>
  </clause>

  <clause id="15840">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * ((((1 / u) * z) \ z) \ z))
    ]]></literal>
    <justification jstring="[para(3146(a,1),15839(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3146 15839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15841">
    <literal><![CDATA[
      K(x,y * T((1 / z) * u,u)) = K(x,y * L(u / z,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(334,a,13354,a(flip),b,15840,a)].">
      <j1 rule="hyper" parents="334 13354 15840"/>
    </justification>
  </clause>

  <clause id="15842">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * (z * (1 / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15612,a(flip),b,15841,a),flip(a)].">
      <j1 rule="hyper" parents="58 15612 15841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15843">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(334,a,5596,a(flip),b,15842,a),flip(a)].">
      <j1 rule="hyper" parents="334 5596 15842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15844">
    <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,15822,a(flip),b,15779,a)].">
      <j1 rule="hyper" parents="58 15822 15779"/>
    </justification>
  </clause>

  <clause id="15845">
    <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,13500,a(flip),b,15844,a)].">
      <j1 rule="hyper" parents="58 13500 15844"/>
    </justification>
  </clause>

  <clause id="15846">
    <literal><![CDATA[
      K(x,T(y,z) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y)))
    ]]></literal>
    <justification jstring="[para(5020(a,2),15845(a,1,2,1))].">
      <j1 rule="para" parents="5020 15845"/>
    </justification>
  </clause>

  <clause id="15847">
    <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(4473(a,1),15846(a,1,2,1))].">
      <j1 rule="para" parents="4473 15846"/>
    </justification>
  </clause>

  <clause id="15848">
    <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(7836(a,1),15786(a,2,1,2))].">
      <j1 rule="para" parents="7836 15786"/>
    </justification>
  </clause>

  <clause id="15850">
    <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),15847(a,1,2,2,1))].">
      <j1 rule="para" parents="105 15847"/>
    </justification>
  </clause>

  <clause id="15851">
    <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),15850(a,1,2,2,2,2))].">
      <j1 rule="para" parents="105 15850"/>
    </justification>
  </clause>

  <clause id="15852">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z * y) * (u / (z * y)))) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[para(8182(a,1),15851(a,2,2))].">
      <j1 rule="para" parents="8182 15851"/>
    </justification>
  </clause>

  <clause id="15853">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,z * y)) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15692,a(flip),b,15852,a)].">
      <j1 rule="hyper" parents="58 15692 15852"/>
    </justification>
  </clause>

  <clause id="15855">
    <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(6104(a,1),15853(a,1,2,2,2))].">
      <j1 rule="para" parents="6104 15853"/>
    </justification>
  </clause>

  <clause id="15856">
    <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(15596,a,15808,a),flip(a)].">
      <j1 rule="hyper" parents="15596 15808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15857">
    <literal><![CDATA[
      K(x,((y / (y / z)) \ u) * w) = K(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(12589,a,15856,a),flip(a)].">
      <j1 rule="hyper" parents="12589 15856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15858">
    <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(15856(a,1),12589(a,1))].">
      <j1 rule="para" parents="15856 12589"/>
    </justification>
  </clause>

  <clause id="15859">
    <literal><![CDATA[
      K(x,(T(y,y \ z) \ u) * w) = K(x,((z / (z / y)) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(334,a,13474,a,b,15857,a)].">
      <j1 rule="hyper" parents="334 13474 15857"/>
    </justification>
  </clause>

  <clause id="15860">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(75(a,1),15857(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 15857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15861">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(4490(a,1),15860(a,1,2,1))].">
      <j1 rule="para" parents="4490 15860"/>
    </justification>
  </clause>

  <clause id="15862">
    <literal><![CDATA[
      K(x,(T(y,T(z,u)) \ (u * (z / u))) * w) = K(x,((u * (z / u)) / y) * w)
    ]]></literal>
    <justification jstring="[para(12567(a,1),15860(a,1,2,1,1))].">
      <j1 rule="para" parents="12567 15860"/>
    </justification>
  </clause>

  <clause id="15863">
    <literal><![CDATA[
      K(x,(T(y,z) / z) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15834,a(flip),b,15861,a),flip(a)].">
      <j1 rule="hyper" parents="58 15834 15861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15864">
    <literal><![CDATA[
      K(x,(y / T(z,y)) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(4488(a,1),15863(a,1,2,1))].">
      <j1 rule="para" parents="4488 15863"/>
    </justification>
  </clause>

  <clause id="15865">
    <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(14196(a,1),15864(a,1,2,1,2))].">
      <j1 rule="para" parents="14196 15864"/>
    </justification>
  </clause>

  <clause id="15866">
    <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(15859(a,2),15858(a,1))].">
      <j1 rule="para" parents="15859 15858"/>
    </justification>
  </clause>

  <clause id="15867">
    <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),15866(a,1,2,1,1))].">
      <j1 rule="para" parents="106 15866"/>
    </justification>
  </clause>

  <clause id="15868">
    <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(334,a,9618,a(flip),b,15470,a),flip(a)].">
      <j1 rule="hyper" parents="334 9618 15470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15870">
    <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(15476(a,1),15868(a,2,2))].">
      <j1 rule="para" parents="15476 15868"/>
    </justification>
  </clause>

  <clause id="15871">
    <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(15694(a,1),15576(a,1,1))].">
      <j1 rule="para" parents="15694 15576"/>
    </justification>
  </clause>

  <clause id="15872">
    <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(15871(a,1),11165(a,1))].">
      <j1 rule="para" parents="15871 11165"/>
    </justification>
  </clause>

  <clause id="15873">
    <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(10208(a,1),15780(a,2,2))].">
      <j1 rule="para" parents="10208 15780"/>
    </justification>
  </clause>

  <clause id="15874">
    <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(8220(a,1),15873(a,1,2))].">
      <j1 rule="para" parents="8220 15873"/>
    </justification>
  </clause>

  <clause id="15875">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(y / z,u \ 1))
    ]]></literal>
    <justification jstring="[para(9886(a,1),15874(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9886 15874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15876">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,8499,a(flip),b,15875,a),flip(a)].">
      <j1 rule="hyper" parents="334 8499 15875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15878">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z \ y) * (u / (z \ y)))) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15270,a(flip),b,15876,a)].">
      <j1 rule="hyper" parents="58 15270 15876"/>
    </justification>
  </clause>

  <clause id="15879">
    <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(4522(a,1),15878(a,1,2,2,1))].">
      <j1 rule="para" parents="4522 15878"/>
    </justification>
  </clause>

  <clause id="15880">
    <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(7584(a,1),15825(a,1,2,2,2))].">
      <j1 rule="para" parents="7584 15825"/>
    </justification>
  </clause>

  <clause id="15882">
    <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(8053(a,2),15880(a,1,2,2))].">
      <j1 rule="para" parents="8053 15880"/>
    </justification>
  </clause>

  <clause id="15883">
    <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(8462(a,1),15882(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8462 15882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15884">
    <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(334,a,6455,a(flip),b,15883,a),flip(a)].">
      <j1 rule="hyper" parents="334 6455 15883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15885">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,13391,a(flip),b,15884,a)].">
      <j1 rule="hyper" parents="58 13391 15884"/>
    </justification>
  </clause>

  <clause id="15886">
    <literal><![CDATA[
      K(x,y \ K(z,u \ 1)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(6760,a,15885,a),flip(a)].">
      <j1 rule="hyper" parents="6760 15885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15890">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(15643,a,15886,a)].">
      <j1 rule="hyper" parents="15643 15886"/>
    </justification>
  </clause>

  <clause id="15891">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(3696(a,1),15886(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3696 15886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15892">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,1 / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15585,a(flip),b,15890,a),flip(a)].">
      <j1 rule="hyper" parents="58 15585 15890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15893">
    <literal><![CDATA[
      K(x,y \ K(z \ u,u)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13397,a(flip),b,15891,a)].">
      <j1 rule="hyper" parents="58 13397 15891"/>
    </justification>
  </clause>

  <clause id="15894">
    <literal><![CDATA[
      K(x,y \ K(z,u \ z)) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(15643,a,15893,a)].">
      <j1 rule="hyper" parents="15643 15893"/>
    </justification>
  </clause>

  <clause id="15895">
    <literal><![CDATA[
      K(x,y \ T(z,1 / u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(15687,a,15892,a),flip(a)].">
      <j1 rule="hyper" parents="15687 15892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15896">
    <literal><![CDATA[
      K(x,y \ T(z,u \ 1)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),15895(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="72 15895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15897">
    <literal><![CDATA[
      K(x,y \ T(z * (u \ 1),u)) = K(x,y \ ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15694,a(flip),b,15896,a),flip(a)].">
      <j1 rule="hyper" parents="58 15694 15896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15898">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w \ u))) = K(x,y \ T(z,T(w,u)))
    ]]></literal>
    <justification jstring="[para(7936(a,1),15896(a,1,2,2))].">
      <j1 rule="para" parents="7936 15896"/>
    </justification>
  </clause>

  <clause id="15899">
    <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(15896(a,1),15638(a,1,1))].">
      <j1 rule="para" parents="15896 15638"/>
    </justification>
  </clause>

  <clause id="15900">
    <literal><![CDATA[
      K(x,y \ ((z \ 1) * (z * u))) = K(x,y \ R(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(810(a,1),15897(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="810 15897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15901">
    <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(6960,a,15900,a)].">
      <j1 rule="hyper" parents="6960 15900"/>
    </justification>
  </clause>

  <clause id="15902">
    <literal><![CDATA[
      K(x,y \ R(z,u,u \ 1)) = K(x,y \ L(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,6006,a(flip),b,15900,a),flip(a)].">
      <j1 rule="hyper" parents="58 6006 15900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15903">
    <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,14888,a(flip),b,15902,a),flip(a)].">
      <j1 rule="hyper" parents="58 14888 15902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15904">
    <literal><![CDATA[
      K(x,y \ L(z / u,u,u \ 1)) = K(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(536(a,1),15902(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="536 15902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15905">
    <literal><![CDATA[
      K(x,y \ (z \ L(z,u,u \ 1))) = K(x,y \ a(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(14834,a,15903,a)].">
      <j1 rule="hyper" parents="14834 15903"/>
    </justification>
  </clause>

  <clause id="15906">
    <literal><![CDATA[
      K(x,(y \ 1) \ a(z,u,u \ 1)) = K(x,y * (z \ L(z,u,u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(14346,a,15905,a),flip(a)].">
      <j1 rule="hyper" parents="14346 15905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15907">
    <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(15906(a,1),14346(a,1))].">
      <j1 rule="para" parents="15906 14346"/>
    </justification>
  </clause>

  <clause id="15908">
    <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(15899(a,1),11165(a,1))].">
      <j1 rule="para" parents="15899 11165"/>
    </justification>
  </clause>

  <clause id="15909">
    <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(8844(a,1),15879(a,1,2,1))].">
      <j1 rule="para" parents="8844 15879"/>
    </justification>
  </clause>

  <clause id="15910">
    <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(4522(a,1),15909(a,1,2,2,2,2))].">
      <j1 rule="para" parents="4522 15909"/>
    </justification>
  </clause>

  <clause id="15912">
    <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,15751,a(flip),b,15910,a)].">
      <j1 rule="hyper" parents="58 15751 15910"/>
    </justification>
  </clause>

  <clause id="15913">
    <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(13043(a,1),15912(a,2,2))].">
      <j1 rule="para" parents="13043 15912"/>
    </justification>
  </clause>

  <clause id="15914">
    <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,15692,a(flip),b,15913,a)].">
      <j1 rule="hyper" parents="58 15692 15913"/>
    </justification>
  </clause>

  <clause id="15915">
    <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,13356,a(flip),b,15855,a)].">
      <j1 rule="hyper" parents="58 13356 15855"/>
    </justification>
  </clause>

  <clause id="15916">
    <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(15759(a,1),15915(a,1,2,2))].">
      <j1 rule="para" parents="15759 15915"/>
    </justification>
  </clause>

  <clause id="15917">
    <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(5649(a,1),15916(a,1,2,2,2,2))].">
      <j1 rule="para" parents="5649 15916"/>
    </justification>
  </clause>

  <clause id="15918">
    <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(15673(a,1),15917(a,1,2,2))].">
      <j1 rule="para" parents="15673 15917"/>
    </justification>
  </clause>

  <clause id="15919">
    <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(5020(a,2),15918(a,1,2,2,2))].">
      <j1 rule="para" parents="5020 15918"/>
    </justification>
  </clause>

  <clause id="15920">
    <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(13516,a,15919,a),flip(a)].">
      <j1 rule="hyper" parents="13516 15919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15921">
    <literal><![CDATA[
      K(x,T(y / (z * u),(z * u) \ u)) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(334,a,15514,a(flip),b,15920,a),flip(a)].">
      <j1 rule="hyper" parents="334 15514 15920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15922">
    <literal><![CDATA[
      K(x,T(y / (z * u),u \ (z \ u))) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[para(7960(a,1),15921(a,1,2))].">
      <j1 rule="para" parents="7960 15921"/>
    </justification>
  </clause>

  <clause id="15923">
    <literal><![CDATA[
      K(x,T(y / (z * u),T(z,u))) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(8558,a,15922,a)].">
      <j1 rule="hyper" parents="8558 15922"/>
    </justification>
  </clause>

  <clause id="15924">
    <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(5310(a,1),15923(a,2,2,1))].">
      <j1 rule="para" parents="5310 15923"/>
    </justification>
  </clause>

  <clause id="15925">
    <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(14604(a,1),14610(a,1,2))].">
      <j1 rule="para" parents="14604 14610"/>
    </justification>
  </clause>

  <clause id="15926">
    <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(861,a,15925,a)].">
      <j1 rule="hyper" parents="861 15925"/>
    </justification>
  </clause>

  <clause id="15927">
    <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(14608,a,15926,a),flip(a)].">
      <j1 rule="hyper" parents="14608 15926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15929">
    <literal><![CDATA[
      L(x,y,a(z,u,K(w,v5)) * v6) = L(x,y,v6)
    ]]></literal>
    <justification jstring="[para(14605(a,1),15927(a,1,2))].">
      <j1 rule="para" parents="14605 15927"/>
    </justification>
  </clause>

  <clause id="15930">
    <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(13536(a,1),14917(a,1,2))].">
      <j1 rule="para" parents="13536 14917"/>
    </justification>
  </clause>

  <clause id="15931">
    <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(15074(a,1),15930(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="15074 15930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15932">
    <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(230(a,1),15931(a,2,2,1,1,1))].">
      <j1 rule="para" parents="230 15931"/>
    </justification>
  </clause>

  <clause id="15934">
    <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(15932(a,2),14422(a,1))].">
      <j1 rule="para" parents="15932 14422"/>
    </justification>
  </clause>

  <clause id="15935">
    <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),14918(a,1,2,2))].">
      <j1 rule="para" parents="60 14918"/>
    </justification>
  </clause>

  <clause id="15936">
    <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(15332(a,1),15193(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15332 15193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15937">
    <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(14805(a,1),15936(a,2,2,2,1))].">
      <j1 rule="para" parents="14805 15936"/>
    </justification>
  </clause>

  <clause id="15939">
    <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(14811(a,1),15937(a,2,2))].">
      <j1 rule="para" parents="14811 15937"/>
    </justification>
  </clause>

  <clause id="15940">
    <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(8218(a,1),15924(a,2,2,2))].">
      <j1 rule="para" parents="8218 15924"/>
    </justification>
  </clause>

  <clause id="15941">
    <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(8484(a,1),15940(a,2,2,2))].">
      <j1 rule="para" parents="8484 15940"/>
    </justification>
  </clause>

  <clause id="15942">
    <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(334,a,15898,a(flip),b,15941,a),flip(a)].">
      <j1 rule="hyper" parents="334 15898 15941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15943">
    <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(334,a,15824,a(flip),b,15942,a),flip(a)].">
      <j1 rule="hyper" parents="334 15824 15942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15944">
    <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(334,a,13500,a(flip),b,15943,a),flip(a)].">
      <j1 rule="hyper" parents="334 13500 15943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15945">
    <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(5020(a,2),15944(a,2,2,1))].">
      <j1 rule="para" parents="5020 15944"/>
    </justification>
  </clause>

  <clause id="15946">
    <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(334,a,15914,a(flip),b,15945,a),flip(a)].">
      <j1 rule="hyper" parents="334 15914 15945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15947">
    <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),15946(a,1,2,1,2))].">
      <j1 rule="para" parents="5 15946"/>
    </justification>
  </clause>

  <clause id="15948">
    <literal><![CDATA[
      K(x,T(y / z,T(z * u,z))) = K(x,T(y / z,u \ z))
    ]]></literal>
    <justification jstring="[para(7350(a,1),15947(a,1,2))].">
      <j1 rule="para" parents="7350 15947"/>
    </justification>
  </clause>

  <clause id="15949">
    <literal><![CDATA[
      K(x,T(y / z,u \ z)) = K(x,T(y / z,u * z))
    ]]></literal>
    <justification jstring="[para(12541(a,1),15948(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12541 15948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15950">
    <literal><![CDATA[
      K(x,T((y * z) / z,u * z)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6(a,1),15949(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6 15949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15951">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(6(a,1),15950(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6 15950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15952">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8553,a,15951,a)].">
      <j1 rule="hyper" parents="8553 15951"/>
    </justification>
  </clause>

  <clause id="15953">
    <literal><![CDATA[
      K(x \ y,T(z,y * x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(8332,a,15951,a),flip(a)].">
      <j1 rule="hyper" parents="8332 15951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15955">
    <literal><![CDATA[
      K(x,T(y,z * u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15951,a(flip),b,15952,a)].">
      <j1 rule="hyper" parents="58 15951 15952"/>
    </justification>
  </clause>

  <clause id="15956">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),u * z)) = K(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15693,a(flip),b,15952,a),flip(a)].">
      <j1 rule="hyper" parents="58 15693 15952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15957">
    <literal><![CDATA[
      T(x * K(y,T(x,z * u)),y) = T(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(15952(a,1),8404(a,1,1,2))].">
      <j1 rule="para" parents="15952 8404"/>
    </justification>
  </clause>

  <clause id="15958">
    <literal><![CDATA[
      K(x,T((y \ z) * u,z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (y \ z)) = w
    ]]></literal>
    <justification jstring="[para(15952(a,1),12587(a,1))].">
      <j1 rule="para" parents="15952 12587"/>
    </justification>
  </clause>

  <clause id="15959">
    <literal><![CDATA[
      K(x,T(y * (z \ u),u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ u) * y) = w
    ]]></literal>
    <justification jstring="[para(15952(a,1),12588(a,1))].">
      <j1 rule="para" parents="15952 12588"/>
    </justification>
  </clause>

  <clause id="15960">
    <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(15952(a,1),14280(a,1))].">
      <j1 rule="para" parents="15952 14280"/>
    </justification>
  </clause>

  <clause id="15961">
    <literal><![CDATA[
      K(x * (y * z),T(u,z * y)) = K((y * z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(12531,a,15955,a),flip(a)].">
      <j1 rule="hyper" parents="12531 15955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15962">
    <literal><![CDATA[
      K(x,T(y,z * (u * y))) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(334,a,9395,a,b,15955,a)].">
      <j1 rule="hyper" parents="334 9395 15955"/>
    </justification>
  </clause>

  <clause id="15963">
    <literal><![CDATA[
      x * K(y,T(z,u * w)) = x * K(y,T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(119,a,15955,a,b,4,a)].">
      <j1 rule="hyper" parents="119 15955 4"/>
    </justification>
  </clause>

  <clause id="15965">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * z)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),15955(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 15955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15968">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,y * x)) = T(K(z,u) * x,y)
    ]]></literal>
    <justification jstring="[para(15955(a,1),15221(a,1,2))].">
      <j1 rule="para" parents="15955 15221"/>
    </justification>
  </clause>

  <clause id="15970">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(12540(a,1),15965(a,1,2))].">
      <j1 rule="para" parents="12540 15965"/>
    </justification>
  </clause>

  <clause id="15971">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,y)) = K(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(12587,a,15970,a),flip(a)].">
      <j1 rule="hyper" parents="12587 15970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15972">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8549,a,15970,a)].">
      <j1 rule="hyper" parents="8549 15970"/>
    </justification>
  </clause>

  <clause id="15975">
    <literal><![CDATA[
      K(x \ y,T(z,T(y,u))) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,8163,a(flip),b,15970,a),flip(a)].">
      <j1 rule="hyper" parents="334 8163 15970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15976">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,7401,a(flip),b,15970,a),flip(a)].">
      <j1 rule="hyper" parents="334 7401 15970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15977">
    <literal><![CDATA[
      T(x,T(y,T(z,u))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,15970,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 15970 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15978">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(107(a,1),15970(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 15970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15980">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,x)) = K(z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(15970(a,1),7423(a,1,2))].">
      <j1 rule="para" parents="15970 7423"/>
    </justification>
  </clause>

  <clause id="15981">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(x,T(y,T(z,u))) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(15970(a,1),9917(a,1,1))].">
      <j1 rule="para" parents="15970 9917"/>
    </justification>
  </clause>

  <clause id="15982">
    <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(15970(a,1),12526(a,1))].">
      <j1 rule="para" parents="15970 12526"/>
    </justification>
  </clause>

  <clause id="15983">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = T(K(x,y),T(z,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,15972,a,b,15972,a)].">
      <j1 rule="hyper" parents="334 15972 15972"/>
    </justification>
  </clause>

  <clause id="15986">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,7401,a(flip),b,15972,a),flip(a)].">
      <j1 rule="hyper" parents="334 7401 15972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15987">
    <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(15972(a,1),11977(a,1,2))].">
      <j1 rule="para" parents="15972 11977"/>
    </justification>
  </clause>

  <clause id="15989">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15976(a,2),7974(a,1))].">
      <j1 rule="para" parents="15976 7974"/>
    </justification>
  </clause>

  <clause id="15990">
    <literal><![CDATA[
      T(x,T(T(y,z) / u,y)) = T(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7506,a,15977,a),flip(a)].">
      <j1 rule="hyper" parents="7506 15977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15992">
    <literal><![CDATA[
      T(x,T(T(y,z) \ u,y)) = T(x,u / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8218,a(flip),b,15977,a),flip(a)].">
      <j1 rule="hyper" parents="58 8218 15977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15993">
    <literal><![CDATA[
      T(x,T(y,z / u)) = T(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(107(a,1),15977(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 15977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15995">
    <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(15977(a,1),7695(a,1))].">
      <j1 rule="para" parents="15977 7695"/>
    </justification>
  </clause>

  <clause id="15996">
    <literal><![CDATA[
      T(x,y) * K(x / T(y,x),z) = y * T(y \ T(x,y),T(z,x))
    ]]></literal>
    <justification jstring="[para(15977(a,1),8611(a,2,2))].">
      <j1 rule="para" parents="15977 8611"/>
    </justification>
  </clause>

  <clause id="15998">
    <literal><![CDATA[
      T(K(x,y),K(z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8228,a,15986,a)].">
      <j1 rule="hyper" parents="8228 15986"/>
    </justification>
  </clause>

  <clause id="16001">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15986(a,2),7974(a,1))].">
      <j1 rule="para" parents="15986 7974"/>
    </justification>
  </clause>

  <clause id="16002">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(12565,a,15998,a),flip(a)].">
      <j1 rule="hyper" parents="12565 15998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16003">
    <literal><![CDATA[
      K(x,T(T(y,K(z,u)),w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(8376,a,15998,a)].">
      <j1 rule="hyper" parents="8376 15998"/>
    </justification>
  </clause>

  <clause id="16004">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8256,a,15998,a),flip(a)].">
      <j1 rule="hyper" parents="8256 15998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16005">
    <literal><![CDATA[
      K(T(x,K(y,z)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(7664,a,15998,a)].">
      <j1 rule="hyper" parents="7664 15998"/>
    </justification>
  </clause>

  <clause id="16007">
    <literal><![CDATA[
      K(x,K(y,z) / u) = K(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6761,a,15998,a),flip(a)].">
      <j1 rule="hyper" parents="6761 15998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16010">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ K(z,u) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6731,a,b,15998,a)].">
      <j1 rule="hyper" parents="58 6731 15998"/>
    </justification>
  </clause>

  <clause id="16011">
    <literal><![CDATA[
      K(x,y) \ K(z,u) = K(z,u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,15998,a(flip),b,5393,a),flip(a)].">
      <j1 rule="hyper" parents="119 15998 5393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16012">
    <literal><![CDATA[
      K(x,y) * K(z,u) = K(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,15998,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 15998 17"/>
    </justification>
  </clause>

  <clause id="16013">
    <literal><![CDATA[
      K(x,y) / (K(x,y) * K(z,u)) = K(u,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,15998,a(flip),b,8113,a)].">
      <j1 rule="hyper" parents="117 15998 8113"/>
    </justification>
  </clause>

  <clause id="16014">
    <literal><![CDATA[
      T(x \ K(y,z),K(u,x)) = x \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,15998,a(flip),b,8406,a),flip(a)].">
      <j1 rule="hyper" parents="116 15998 8406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16015">
    <literal><![CDATA[
      K(x,K(y,K(z,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,15998,a(flip),b,10864,a),flip(a)].">
      <j1 rule="hyper" parents="115 15998 10864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16016">
    <literal><![CDATA[
      K(x,K(K(y,z),u)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,15998,a(flip),b,8078,a),flip(a)].">
      <j1 rule="hyper" parents="115 15998 8078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16018">
    <literal><![CDATA[
      T(L(K(x,y),z,u),K(w,v5)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(15998(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15998 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16028">
    <literal><![CDATA[
      x * (K(y,z) * K(x,u)) = T(x,u) * K(y,z)
    ]]></literal>
    <justification jstring="[para(15998(a,1),5339(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15998 5339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16029">
    <literal><![CDATA[
      T(K(x,y),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(15998(a,1),5897(a,1,1))].">
      <j1 rule="para" parents="15998 5897"/>
    </justification>
  </clause>

  <clause id="16031">
    <literal><![CDATA[
      T(x * K(y,z),K(x,u)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(15998(a,1),7857(a,2,2))].">
      <j1 rule="para" parents="15998 7857"/>
    </justification>
  </clause>

  <clause id="16032">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(15998(a,1),8256(a,1))].">
      <j1 rule="para" parents="15998 8256"/>
    </justification>
  </clause>

  <clause id="16034">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15998(a,1),12565(a,1))].">
      <j1 rule="para" parents="15998 12565"/>
    </justification>
  </clause>

  <clause id="16036">
    <literal><![CDATA[
      T(K(x,K(y,z)),u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5077,a,16015,a)].">
      <j1 rule="hyper" parents="5077 16015"/>
    </justification>
  </clause>

  <clause id="16037">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(552,a,16015,a)].">
      <j1 rule="hyper" parents="552 16015"/>
    </justification>
  </clause>

  <clause id="16039">
    <literal><![CDATA[
      T(x,K(y,K(z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,16015,a)].">
      <j1 rule="hyper" parents="51 16015"/>
    </justification>
  </clause>

  <clause id="16040">
    <literal><![CDATA[
      K(x,T(K(y,z),u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8339,a,16016,a)].">
      <j1 rule="hyper" parents="8339 16016"/>
    </justification>
  </clause>

  <clause id="16041">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(12581,a,16039,a)].">
      <j1 rule="hyper" parents="12581 16039"/>
    </justification>
  </clause>

  <clause id="16042">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * x) = u * T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8655,a,16039,a)].">
      <j1 rule="hyper" parents="8655 16039"/>
    </justification>
  </clause>

  <clause id="16043">
    <literal><![CDATA[
      T(x,K(y,z) / u) = T(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8600,a,16039,a)].">
      <j1 rule="hyper" parents="8600 16039"/>
    </justification>
  </clause>

  <clause id="16044">
    <literal><![CDATA[
      x * (y * K(x,K(z,u))) = T(x,K(z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(8585,a,16039,a)].">
      <j1 rule="hyper" parents="8585 16039"/>
    </justification>
  </clause>

  <clause id="16045">
    <literal><![CDATA[
      T(x,T(K(y,z),u)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8127,a,16039,a)].">
      <j1 rule="hyper" parents="8127 16039"/>
    </justification>
  </clause>

  <clause id="16046">
    <literal><![CDATA[
      T(x,T(y,K(z,u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(7969,a,16039,a)].">
      <j1 rule="hyper" parents="7969 16039"/>
    </justification>
  </clause>

  <clause id="16047">
    <literal><![CDATA[
      (x * y) * K(x,K(z,u)) = T(x,K(z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(6814,a,16039,a)].">
      <j1 rule="hyper" parents="6814 16039"/>
    </justification>
  </clause>

  <clause id="16048">
    <literal><![CDATA[
      T(x,K(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(16039(a,1),44(a,2))].">
      <j1 rule="para" parents="16039 44"/>
    </justification>
  </clause>

  <clause id="16049">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * K(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16039(a,1),294(a,1,2))].">
      <j1 rule="para" parents="16039 294"/>
    </justification>
  </clause>

  <clause id="16050">
    <literal><![CDATA[
      L(x,y,z) * K(u,K(w,v5)) = K(u,K(w,v5)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(16039(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16039 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16052">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16039(a,1),12586(a,1,1))].">
      <j1 rule="para" parents="16039 12586"/>
    </justification>
  </clause>

  <clause id="16053">
    <literal><![CDATA[
      x \ T(y * x,K(z,K(u,w))) = T(y,K(K(u,w),z) * x)
    ]]></literal>
    <justification jstring="[para(16039(a,1),15465(a,1,2,1,2))].">
      <j1 rule="para" parents="16039 15465"/>
    </justification>
  </clause>

  <clause id="16054">
    <literal><![CDATA[
      K(K(x,y) * (z * x),u) = K(z * T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(12584,a,16004,a)].">
      <j1 rule="hyper" parents="12584 16004"/>
    </justification>
  </clause>

  <clause id="16055">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(12531,a,16004,a)].">
      <j1 rule="hyper" parents="12531 16004"/>
    </justification>
  </clause>

  <clause id="16059">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(6519(a,1),16004(a,1,2))].">
      <j1 rule="para" parents="6519 16004"/>
    </justification>
  </clause>

  <clause id="16061">
    <literal><![CDATA[
      K(x,y * (z * K(y,u))) = K(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[para(7275(a,1),16004(a,1,2))].">
      <j1 rule="para" parents="7275 16004"/>
    </justification>
  </clause>

  <clause id="16062">
    <literal><![CDATA[
      x * (K(y,z) * K(u,w)) = x * (K(u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[para(16004(a,1),7551(a,1,2,2))].">
      <j1 rule="para" parents="16004 7551"/>
    </justification>
  </clause>

  <clause id="16063">
    <literal><![CDATA[
      K(x,K(y,z) * (u * y)) = K(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[para(8362(a,1),16004(a,1,2))].">
      <j1 rule="para" parents="8362 16004"/>
    </justification>
  </clause>

  <clause id="16066">
    <literal><![CDATA[
      K(K(x,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * K(x,y),u) = w
    ]]></literal>
    <justification jstring="[para(16004(a,1),12526(a,1))].">
      <j1 rule="para" parents="16004 12526"/>
    </justification>
  </clause>

  <clause id="16067">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * x,u) = w
    ]]></literal>
    <justification jstring="[para(16004(a,1),12531(a,1))].">
      <j1 rule="para" parents="16004 12531"/>
    </justification>
  </clause>

  <clause id="16068">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(16004(a,1),12588(a,1))].">
      <j1 rule="para" parents="16004 12588"/>
    </justification>
  </clause>

  <clause id="16069">
    <literal><![CDATA[
      K(T(1 / x,K(y,z)),u) = K(1 / L(x,w,x),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,9025,a,b,16005,a),flip(a)].">
      <j1 rule="hyper" parents="334 9025 16005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16070">
    <literal><![CDATA[
      K(K(x,y) \ z,u) = K(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(6519(a,1),16005(a,1,1))].">
      <j1 rule="para" parents="6519 16005"/>
    </justification>
  </clause>

  <clause id="16073">
    <literal><![CDATA[
      T(x * K(y,z),T(u,x)) = T(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(9005,a,16046,a)].">
      <j1 rule="hyper" parents="9005 16046"/>
    </justification>
  </clause>

  <clause id="16075">
    <literal><![CDATA[
      T(x,T(T(y,K(z,u)),w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(18(a,1),16046(a,1,2))].">
      <j1 rule="para" parents="18 16046"/>
    </justification>
  </clause>

  <clause id="16076">
    <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(666(a,1),16046(a,1,2))].">
      <j1 rule="para" parents="666 16046"/>
    </justification>
  </clause>

  <clause id="16077">
    <literal><![CDATA[
      T(x,K(y,z) * (u / z)) = T(x,u / T(z,y))
    ]]></literal>
    <justification jstring="[para(6578(a,1),16046(a,1,2))].">
      <j1 rule="para" parents="6578 16046"/>
    </justification>
  </clause>

  <clause id="16078">
    <literal><![CDATA[
      T(x,K(y,z) * (u * y)) = T(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[para(8362(a,1),16046(a,1,2))].">
      <j1 rule="para" parents="8362 16046"/>
    </justification>
  </clause>

  <clause id="16079">
    <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(16046(a,1),10307(a,2,2))].">
      <j1 rule="para" parents="16046 10307"/>
    </justification>
  </clause>

  <clause id="16081">
    <literal><![CDATA[
      x * K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,u)) * x = w
    ]]></literal>
    <justification jstring="[para(6535(a,1),16048(a,1))].">
      <j1 rule="para" parents="6535 16048"/>
    </justification>
  </clause>

  <clause id="16082">
    <literal><![CDATA[
      T(x,T(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(7688(a,1),16048(a,1))].">
      <j1 rule="para" parents="7688 16048"/>
    </justification>
  </clause>

  <clause id="16083">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8327,a,16036,a)].">
      <j1 rule="hyper" parents="8327 16036"/>
    </justification>
  </clause>

  <clause id="16084">
    <literal><![CDATA[
      K(T(x,y),K(z,u)) = K(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(7664,a,16036,a)].">
      <j1 rule="hyper" parents="7664 16036"/>
    </justification>
  </clause>

  <clause id="16088">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(8317,a,16040,a)].">
      <j1 rule="hyper" parents="8317 16040"/>
    </justification>
  </clause>

  <clause id="16089">
    <literal><![CDATA[
      K(x,T(K(y,z),u)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,8053,a,b,16040,a),flip(a)].">
      <j1 rule="hyper" parents="334 8053 16040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16090">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) * K(x,K(y,z)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(119,a,16040,a(flip),b,8003,a)].">
      <j1 rule="hyper" parents="119 16040 8003"/>
    </justification>
  </clause>

  <clause id="16091">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6440(a,1),16040(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6440 16040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16092">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7388(a,2),16040(a,1,2))].">
      <j1 rule="para" parents="7388 16040"/>
    </justification>
  </clause>

  <clause id="16093">
    <literal><![CDATA[
      K(x,K(y,z * u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[para(12550(a,1),16040(a,1,2))].">
      <j1 rule="para" parents="12550 16040"/>
    </justification>
  </clause>

  <clause id="16094">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ x) = u \ T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(16040(a,1),14044(a,1,1))].">
      <j1 rule="para" parents="16040 14044"/>
    </justification>
  </clause>

  <clause id="16095">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,w) = T(u,w) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(16040(a,1),15220(a,1,1,1))].">
      <j1 rule="para" parents="16040 15220"/>
    </justification>
  </clause>

  <clause id="16096">
    <literal><![CDATA[
      T(x,K(y,z / u)) = T(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6440(a,1),16045(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6440 16045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16097">
    <literal><![CDATA[
      T(x,K(y,T(z,u))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6577(a,1),16045(a,1,2))].">
      <j1 rule="para" parents="6577 16045"/>
    </justification>
  </clause>

  <clause id="16098">
    <literal><![CDATA[
      T(x,K(T(y,z),u)) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7388(a,2),16045(a,1,2))].">
      <j1 rule="para" parents="7388 16045"/>
    </justification>
  </clause>

  <clause id="16099">
    <literal><![CDATA[
      T(x,K(y,z * u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[para(12550(a,1),16045(a,1,2))].">
      <j1 rule="para" parents="12550 16045"/>
    </justification>
  </clause>

  <clause id="16100">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(8050,a,16083,a)].">
      <j1 rule="hyper" parents="8050 16083"/>
    </justification>
  </clause>

  <clause id="16101">
    <literal><![CDATA[
      K(K(x,y),T(z,u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8028,a,16083,a)].">
      <j1 rule="hyper" parents="8028 16083"/>
    </justification>
  </clause>

  <clause id="16103">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,8053,a(flip),b,16083,a),flip(a)].">
      <j1 rule="hyper" parents="334 8053 16083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16104">
    <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,8359,a(flip),b,16083,a)].">
      <j1 rule="hyper" parents="58 8359 16083"/>
    </justification>
  </clause>

  <clause id="16105">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(16083(a,2),8069(a,1))].">
      <j1 rule="para" parents="16083 8069"/>
    </justification>
  </clause>

  <clause id="16106">
    <literal><![CDATA[
      K(x,K(y,L(z / u,u,w))) = K(x,K(y,(w * u) \ (w * z)))
    ]]></literal>
    <justification jstring="[para(8284(a,1),16083(a,1,2))].">
      <j1 rule="para" parents="8284 16083"/>
    </justification>
  </clause>

  <clause id="16107">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ (u * (y / u)),z) = K((u * (y / u)) / x,z)
    ]]></literal>
    <justification jstring="[para(16083(a,1),12535(a,1,1))].">
      <j1 rule="para" parents="16083 12535"/>
    </justification>
  </clause>

  <clause id="16109">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,K(x,u)) = K(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(16084(a,1),8086(a,1,2))].">
      <j1 rule="para" parents="16084 8086"/>
    </justification>
  </clause>

  <clause id="16111">
    <literal><![CDATA[
      T(x,K(y,T(z,u))) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,16088,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 16088 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16112">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z / y))
    ]]></literal>
    <justification jstring="[para(7414(a,1),16088(a,1,2))].">
      <j1 rule="para" parents="7414 16088"/>
    </justification>
  </clause>

  <clause id="16113">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(16088(a,1),7557(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16088 7557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16114">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16088(a,2),8099(a,1))].">
      <j1 rule="para" parents="16088 8099"/>
    </justification>
  </clause>

  <clause id="16115">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ T(y,u),z) = K(T(y,u) / x,z)
    ]]></literal>
    <justification jstring="[para(16088(a,1),8657(a,1,1))].">
      <j1 rule="para" parents="16088 8657"/>
    </justification>
  </clause>

  <clause id="16116">
    <literal><![CDATA[
      K(x,K(y,(z \ u) * z)) = K(x,K(u,y))
    ]]></literal>
    <justification jstring="[para(12559(a,2),16088(a,1,2))].">
      <j1 rule="para" parents="12559 16088"/>
    </justification>
  </clause>

  <clause id="16118">
    <literal><![CDATA[
      K(x * y,K(z,u)) = K(z,K(u,y * x))
    ]]></literal>
    <justification jstring="[hyper(12531,a,16089,a)].">
      <j1 rule="hyper" parents="12531 16089"/>
    </justification>
  </clause>

  <clause id="16119">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) * K(y,K(z,x)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(119,a,16089,a(flip),b,8003,a)].">
      <j1 rule="hyper" parents="119 16089 8003"/>
    </justification>
  </clause>

  <clause id="16121">
    <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(16092(a,1),10937(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="16092 10937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16125">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,u) \ y) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(16097(a,1),8601(a,1,1))].">
      <j1 rule="para" parents="16097 8601"/>
    </justification>
  </clause>

  <clause id="16127">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,u) * y) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(16097(a,1),12544(a,1,1))].">
      <j1 rule="para" parents="16097 12544"/>
    </justification>
  </clause>

  <clause id="16128">
    <literal><![CDATA[
      T(K(x,T(y,z)) * u,K(y,x)) = u * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8123,a,16098,a),flip(a)].">
      <j1 rule="hyper" parents="8123 16098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16129">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u,K(y,x)) = u * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(16098(a,1),8116(a,1,2))].">
      <j1 rule="para" parents="16098 8116"/>
    </justification>
  </clause>

  <clause id="16131">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(16100(a,1),7557(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16100 7557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16132">
    <literal><![CDATA[
      K(x,y) * (K(z,K(y,u)) * w) = y * (T(T(y,K(z,u)),x) \ w)
    ]]></literal>
    <justification jstring="[para(16100(a,1),10206(a,1,2,1))].">
      <j1 rule="para" parents="16100 10206"/>
    </justification>
  </clause>

  <clause id="16136">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(y,K(z,x))) = u
    ]]></literal>
    <justification jstring="[para(16101(a,1),7541(a,1,2,2))].">
      <j1 rule="para" parents="16101 7541"/>
    </justification>
  </clause>

  <clause id="16137">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,y)) = u * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(16101(a,1),8216(a,1,1))].">
      <j1 rule="para" parents="16101 8216"/>
    </justification>
  </clause>

  <clause id="16138">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) = K(y,K(u,T(x,w)))
    ]]></literal>
    <justification jstring="[hyper(334,a,16092,a,b,16103,a)].">
      <j1 rule="hyper" parents="334 16092 16103"/>
    </justification>
  </clause>

  <clause id="16140">
    <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(16111(a,1),8737(a,1,1))].">
      <j1 rule="para" parents="16111 8737"/>
    </justification>
  </clause>

  <clause id="16141">
    <literal><![CDATA[
      K(x,y / K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) \ y) = w
    ]]></literal>
    <justification jstring="[para(8172(a,1),16029(a,1))].">
      <j1 rule="para" parents="8172 16029"/>
    </justification>
  </clause>

  <clause id="16142">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) \ y) = w
    ]]></literal>
    <justification jstring="[para(6536(a,1),16032(a,1,2))].">
      <j1 rule="para" parents="6536 16032"/>
    </justification>
  </clause>

  <clause id="16143">
    <literal><![CDATA[
      K(x,y * (z * K(y,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) * z) = w
    ]]></literal>
    <justification jstring="[para(7275(a,1),16032(a,1,2))].">
      <j1 rule="para" parents="7275 16032"/>
    </justification>
  </clause>

  <clause id="16144">
    <literal><![CDATA[
      K(x,y) / (K(x,y) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,z) = w
    ]]></literal>
    <justification jstring="[para(8271(a,2),16032(a,1))].">
      <j1 rule="para" parents="8271 16032"/>
    </justification>
  </clause>

  <clause id="16145">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(8223(a,1),16032(a,1,2))].">
      <j1 rule="para" parents="8223 16032"/>
    </justification>
  </clause>

  <clause id="16146">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(8597(a,1),16032(a,1,2))].">
      <j1 rule="para" parents="8597 16032"/>
    </justification>
  </clause>

  <clause id="16147">
    <literal><![CDATA[
      K(x,K(y,z) * (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(8362(a,1),16032(a,1,2))].">
      <j1 rule="para" parents="8362 16032"/>
    </justification>
  </clause>

  <clause id="16148">
    <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(7992(a,1),16032(a,1,2))].">
      <j1 rule="para" parents="7992 16032"/>
    </justification>
  </clause>

  <clause id="16149">
    <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(10745(a,1),16032(a,1,2))].">
      <j1 rule="para" parents="10745 16032"/>
    </justification>
  </clause>

  <clause id="16150">
    <literal><![CDATA[
      K(x,T(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(12572(a,1),16032(a,1,2))].">
      <j1 rule="para" parents="12572 16032"/>
    </justification>
  </clause>

  <clause id="16151">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(14059(a,1),16032(a,1,2))].">
      <j1 rule="para" parents="14059 16032"/>
    </justification>
  </clause>

  <clause id="16152">
    <literal><![CDATA[
      K(x,(y / z) * K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) / z) = w
    ]]></literal>
    <justification jstring="[para(14073(a,1),16032(a,1,2))].">
      <j1 rule="para" parents="14073 16032"/>
    </justification>
  </clause>

  <clause id="16153">
    <literal><![CDATA[
      T(x,K(y,z) * (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u / T(z,y)) = w
    ]]></literal>
    <justification jstring="[para(6578(a,1),16082(a,1,2))].">
      <j1 rule="para" parents="6578 16082"/>
    </justification>
  </clause>

  <clause id="16154">
    <literal><![CDATA[
      T(x,T(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(7688(a,1),16082(a,1,2))].">
      <j1 rule="para" parents="7688 16082"/>
    </justification>
  </clause>

  <clause id="16155">
    <literal><![CDATA[
      T(x,K(y,z) * (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(8362(a,1),16082(a,1,2))].">
      <j1 rule="para" parents="8362 16082"/>
    </justification>
  </clause>

  <clause id="16156">
    <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(8106(a,1),16082(a,1,2))].">
      <j1 rule="para" parents="8106 16082"/>
    </justification>
  </clause>

  <clause id="16157">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(14059(a,1),16082(a,1,2))].">
      <j1 rule="para" parents="14059 16082"/>
    </justification>
  </clause>

  <clause id="16158">
    <literal><![CDATA[
      T(x,y) * K(z \ x,u) = K(x / z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(15975(a,1),8170(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15975 8170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16159">
    <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(334,a,15164,a,b,15978,a)].">
      <j1 rule="hyper" parents="334 15164 15978"/>
    </justification>
  </clause>

  <clause id="16160">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(334,a,15951,a(flip),b,15978,a),flip(a)].">
      <j1 rule="hyper" parents="334 15951 15978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16167">
    <literal><![CDATA[
      T(K(x \ T(y,z),u),T(y,w)) = K((x / y) \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,9945,a(flip),b,15983,a),flip(a)].">
      <j1 rule="hyper" parents="334 9945 15983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16173">
    <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(15993(a,1),7697(a,1))].">
      <j1 rule="para" parents="15993 7697"/>
    </justification>
  </clause>

  <clause id="16174">
    <literal><![CDATA[
      K(x,(y * z) * K(u,y)) = K(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(15754,a,16002,a),flip(a)].">
      <j1 rule="hyper" parents="15754 16002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16175">
    <literal><![CDATA[
      K(x,y * K(z,u \ z)) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(15736,a,16002,a),flip(a)].">
      <j1 rule="hyper" parents="15736 16002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16176">
    <literal><![CDATA[
      K(x,y * K(z \ 1,u)) = K(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(15715,a,16002,a),flip(a)].">
      <j1 rule="hyper" parents="15715 16002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16177">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(15493,a,16002,a)].">
      <j1 rule="hyper" parents="15493 16002"/>
    </justification>
  </clause>

  <clause id="16178">
    <literal><![CDATA[
      K(x,K(y,z) * (u / y)) = K(x,u / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,15678,a(flip),b,16002,a),flip(a)].">
      <j1 rule="hyper" parents="334 15678 16002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16179">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,13377,a(flip),b,16002,a),flip(a)].">
      <j1 rule="hyper" parents="334 13377 16002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16180">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15497,a,b,16002,a)].">
      <j1 rule="hyper" parents="58 15497 16002"/>
    </justification>
  </clause>

  <clause id="16181">
    <literal><![CDATA[
      K(x,y * K(z * u,z)) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,13365,a(flip),b,16002,a),flip(a)].">
      <j1 rule="hyper" parents="58 13365 16002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16182">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (w * u)) = K(x,w * (u * K(y,z)))
    ]]></literal>
    <justification jstring="[para(11110(a,1),16002(a,2,2))].">
      <j1 rule="para" parents="11110 16002"/>
    </justification>
  </clause>

  <clause id="16183">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(16002(a,1),15493(a,1))].">
      <j1 rule="para" parents="16002 15493"/>
    </justification>
  </clause>

  <clause id="16184">
    <literal><![CDATA[
      K(x,K(y,z) * (u / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16002(a,2),15689(a,1))].">
      <j1 rule="para" parents="16002 15689"/>
    </justification>
  </clause>

  <clause id="16185">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u / z),w)) = K(x,T(u / T(z,y),w))
    ]]></literal>
    <justification jstring="[para(6578(a,1),16003(a,1,2,1))].">
      <j1 rule="para" parents="6578 16003"/>
    </justification>
  </clause>

  <clause id="16186">
    <literal><![CDATA[
      K(x,T(K(y,y \ z) * (u / z),w)) = K(x,T(u / ((y \ z) * y),w))
    ]]></literal>
    <justification jstring="[para(10918(a,1),16003(a,1,2,1))].">
      <j1 rule="para" parents="10918 16003"/>
    </justification>
  </clause>

  <clause id="16187">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,K(z,1 / z) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(334,a,15186,a,b,16007,a)].">
      <j1 rule="hyper" parents="334 15186 16007"/>
    </justification>
  </clause>

  <clause id="16188">
    <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(16007(a,2),11243(a,2,2))].">
      <j1 rule="para" parents="16007 11243"/>
    </justification>
  </clause>

  <clause id="16189">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ w != K(y,x)
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = w
    ]]></literal>
    <justification jstring="[para(16010(a,1),42(a,1)),flip(a)].">
      <j1 rule="para" parents="16010 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16191">
    <literal><![CDATA[
      K(x,y) \ K(z,u) = K(u,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(334,a,5391,a,b,16011,a)].">
      <j1 rule="hyper" parents="334 5391 16011"/>
    </justification>
  </clause>

  <clause id="16194">
    <literal><![CDATA[
      K(x,y) * K(z / (z / u),w) = K(u,T(w,z)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8191(a,1),16012(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8191 16012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16198">
    <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(16014(a,1),15467(a,1,2,1,2))].">
      <j1 rule="para" parents="16014 15467"/>
    </justification>
  </clause>

  <clause id="16199">
    <literal><![CDATA[
      T((x * K(y,z)) * u,K(x,u)) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(16031(a,1),8383(a,2,1))].">
      <j1 rule="para" parents="16031 8383"/>
    </justification>
  </clause>

  <clause id="16200">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,K(y,u)) = K(x,T(y,u)) * z
    ]]></literal>
    <justification jstring="[hyper(8872,a,16037,a),flip(a)].">
      <j1 rule="hyper" parents="8872 16037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16201">
    <literal><![CDATA[
      K(x,K(y,z)) \ u = u * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8098,a,16037,a)].">
      <j1 rule="hyper" parents="8098 16037"/>
    </justification>
  </clause>

  <clause id="16202">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[hyper(8096,a,16037,a),flip(a)].">
      <j1 rule="hyper" parents="8096 16037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16203">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,K(y,z))) = u
    ]]></literal>
    <justification jstring="[hyper(8095,a,16037,a)].">
      <j1 rule="hyper" parents="8095 16037"/>
    </justification>
  </clause>

  <clause id="16204">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ K(y,z)) = u \ K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,12635,a(flip),b,16037,a),flip(a)].">
      <j1 rule="hyper" parents="334 12635 16037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16205">
    <literal><![CDATA[
      x \ (y * K(x,K(z,u))) = T(x,K(z,u)) \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,16037,a(flip),b,8093,a)].">
      <j1 rule="hyper" parents="116 16037 8093"/>
    </justification>
  </clause>

  <clause id="16206">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * K(x,K(y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(16037(a,1),8096(a,1))].">
      <j1 rule="para" parents="16037 8096"/>
    </justification>
  </clause>

  <clause id="16208">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(15705,a,16041,a)].">
      <j1 rule="hyper" parents="15705 16041"/>
    </justification>
  </clause>

  <clause id="16209">
    <literal><![CDATA[
      T(x,(y / z) * K(u,y)) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15487,a(flip),b,16041,a),flip(a)].">
      <j1 rule="hyper" parents="58 15487 16041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16210">
    <literal><![CDATA[
      T(x,(y \ z) * K(y,u)) = T(x,T(y,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15484,a(flip),b,16041,a),flip(a)].">
      <j1 rule="hyper" parents="58 15484 16041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16211">
    <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,16041,a(flip),b,15473,a),flip(a)].">
      <j1 rule="hyper" parents="119 16041 15473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16212">
    <literal><![CDATA[
      T(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(16041(a,1),15705(a,1))].">
      <j1 rule="para" parents="16041 15705"/>
    </justification>
  </clause>

  <clause id="16213">
    <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(16043(a,1),14859(a,1,2,2,1))].">
      <j1 rule="para" parents="16043 14859"/>
    </justification>
  </clause>

  <clause id="16214">
    <literal><![CDATA[
      K(x * K(y \ z,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(9046,a,16055,a),flip(a)].">
      <j1 rule="hyper" parents="9046 16055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16215">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,15545,a,b,16055,a),flip(a)].">
      <j1 rule="hyper" parents="334 15545 16055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16216">
    <literal><![CDATA[
      K(x * K(y * z,y),u) = K(K(z,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13404,a(flip),b,16055,a),flip(a)].">
      <j1 rule="hyper" parents="58 13404 16055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16217">
    <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(16055(a,1),7980(a,1))].">
      <j1 rule="para" parents="16055 7980"/>
    </justification>
  </clause>

  <clause id="16218">
    <literal><![CDATA[
      K(x * K(y \ z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) * x,u) = w
    ]]></literal>
    <justification jstring="[para(16055(a,1),13489(a,1))].">
      <j1 rule="para" parents="16055 13489"/>
    </justification>
  </clause>

  <clause id="16219">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * x,u) = w
    ]]></literal>
    <justification jstring="[para(16055(a,1),15727(a,1))].">
      <j1 rule="para" parents="16055 15727"/>
    </justification>
  </clause>

  <clause id="16220">
    <literal><![CDATA[
      K(x / (y / z),y) = K(x / (z \ y),y)
    ]]></literal>
    <justification jstring="[para(6743(a,1),16214(a,1,1))].">
      <j1 rule="para" parents="6743 16214"/>
    </justification>
  </clause>

  <clause id="16221">
    <literal><![CDATA[
      K(x * (y / z),y) = K(x * (z \ y),y)
    ]]></literal>
    <justification jstring="[para(6747(a,1),16214(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6747 16214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16222">
    <literal><![CDATA[
      K(x,K(y,y \ z) \ (u / z)) = K(x,u / (y * (z / y)))
    ]]></literal>
    <justification jstring="[para(10920(a,1),16059(a,2,2))].">
      <j1 rule="para" parents="10920 16059"/>
    </justification>
  </clause>

  <clause id="16223">
    <literal><![CDATA[
      K(x,K(y \ K(z,u),w) * v5) = K(x,K(w,y * K(u,z)) * v5)
    ]]></literal>
    <justification jstring="[para(16059(a,1),15721(a,2,2,1))].">
      <j1 rule="para" parents="16059 15721"/>
    </justification>
  </clause>

  <clause id="16224">
    <literal><![CDATA[
      K(K(x,y) \ z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,15545,a,b,16070,a),flip(a)].">
      <j1 rule="hyper" parents="334 15545 16070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16225">
    <literal><![CDATA[
      T(x,T(T(y,T(z,u)) * u,w)) = T(x,T(T(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(8226(a,1),16075(a,1,2,1))].">
      <j1 rule="para" parents="8226 16075"/>
    </justification>
  </clause>

  <clause id="16226">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(8545,a,16091,a)].">
      <j1 rule="hyper" parents="8545 16091"/>
    </justification>
  </clause>

  <clause id="16228">
    <literal><![CDATA[
      x * K(x,K(y,z * u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(119,a,16093,a,b,4995,a(flip))].">
      <j1 rule="hyper" parents="119 16093 4995"/>
    </justification>
  </clause>

  <clause id="16229">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,u * z)) = w
    ]]></literal>
    <justification jstring="[para(16093(a,1),8050(a,1))].">
      <j1 rule="para" parents="16093 8050"/>
    </justification>
  </clause>

  <clause id="16230">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,y * x))
    ]]></literal>
    <justification jstring="[para(16093(a,1),12599(a,2,2))].">
      <j1 rule="para" parents="16093 12599"/>
    </justification>
  </clause>

  <clause id="16231">
    <literal><![CDATA[
      T(x,K(y,(z * u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16096(a,1),8546(a,1))].">
      <j1 rule="para" parents="16096 8546"/>
    </justification>
  </clause>

  <clause id="16232">
    <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(16099(a,1),15706(a,1,2,1,2))].">
      <j1 rule="para" parents="16099 15706"/>
    </justification>
  </clause>

  <clause id="16233">
    <literal><![CDATA[
      K(x,K(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(16112(a,1),8099(a,1))].">
      <j1 rule="para" parents="16112 8099"/>
    </justification>
  </clause>

  <clause id="16234">
    <literal><![CDATA[
      K(x,K(y \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z / y,u)) = w
    ]]></literal>
    <justification jstring="[para(16112(a,2),8099(a,1))].">
      <j1 rule="para" parents="16112 8099"/>
    </justification>
  </clause>

  <clause id="16235">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(w,y,z))) = K(x,K(w,u / (z * y)))
    ]]></literal>
    <justification jstring="[para(11151(a,2),16112(a,1,2))].">
      <j1 rule="para" parents="11151 16112"/>
    </justification>
  </clause>

  <clause id="16236">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,K(x,u)) = K(x,T(y,u)) * z
    ]]></literal>
    <justification jstring="[hyper(9451,a,16113,a),flip(a)].">
      <j1 rule="hyper" parents="9451 16113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16237">
    <literal><![CDATA[
      K(x,K(y / z,(z \ u) * y)) = K(x,K(u,y / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,10672,a(flip),b,16116,a)].">
      <j1 rule="hyper" parents="58 10672 16116"/>
    </justification>
  </clause>

  <clause id="16239">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(16118(a,1),8089(a,1))].">
      <j1 rule="para" parents="16118 8089"/>
    </justification>
  </clause>

  <clause id="16240">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * K(y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(16136(a,1),8096(a,1,2))].">
      <j1 rule="para" parents="16136 8096"/>
    </justification>
  </clause>

  <clause id="16241">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (y \ z))) = K(x,u / (z / y))
    ]]></literal>
    <justification jstring="[hyper(334,a,13450,a(flip),b,16177,a),flip(a)].">
      <j1 rule="hyper" parents="334 13450 16177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16243">
    <literal><![CDATA[
      K(x,K(y,z) * (u * z)) = K(x,u * T(z,y))
    ]]></literal>
    <justification jstring="[para(6432(a,1),16177(a,2,2))].">
      <j1 rule="para" parents="6432 16177"/>
    </justification>
  </clause>

  <clause id="16244">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16180(a,2),15689(a,1))].">
      <j1 rule="para" parents="16180 15689"/>
    </justification>
  </clause>

  <clause id="16245">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(w,v5) = K(v5,w) \ K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(11089(a,2),16191(a,1,1))].">
      <j1 rule="para" parents="11089 16191"/>
    </justification>
  </clause>

  <clause id="16246">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,x) = x \ (u * T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(334,a,7284,a,b,16201,a),flip(a)].">
      <j1 rule="hyper" parents="334 7284 16201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16247">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u / T(x,K(y,z))) != w
    ]]></literal>
    <literal><![CDATA[
      u / x = w
    ]]></literal>
    <justification jstring="[para(16201(a,2),6559(a,1))].">
      <j1 rule="para" parents="16201 6559"/>
    </justification>
  </clause>

  <clause id="16248">
    <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(16201(a,2),15820(a,1,1,1))].">
      <j1 rule="para" parents="16201 15820"/>
    </justification>
  </clause>

  <clause id="16249">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      w * K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(16203(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="16203 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16251">
    <literal><![CDATA[
      x \ T(y,K(z,u) * w) = x \ T(y,w * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,16208,a,b,5,a)].">
      <j1 rule="hyper" parents="116 16208 5"/>
    </justification>
  </clause>

  <clause id="16252">
    <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(16208(a,2),431(a,1))].">
      <j1 rule="para" parents="16208 431"/>
    </justification>
  </clause>

  <clause id="16253">
    <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(6430(a,2),16208(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6430 16208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16254">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ z)) = T(x,u \ T(z,y))
    ]]></literal>
    <justification jstring="[para(14025(a,1),16208(a,2,2))].">
      <j1 rule="para" parents="14025 16208"/>
    </justification>
  </clause>

  <clause id="16256">
    <literal><![CDATA[
      K(x * K(y,z),x \ z) = K(x,T(x \ z,y))
    ]]></literal>
    <justification jstring="[hyper(11554,a,16215,a),flip(a)].">
      <j1 rule="hyper" parents="11554 16215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16257">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,16055,a,b,16215,a)].">
      <j1 rule="hyper" parents="334 16055 16215"/>
    </justification>
  </clause>

  <clause id="16258">
    <literal><![CDATA[
      K(K(x \ y,x) * z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,13399,a(flip),b,16215,a),flip(a)].">
      <j1 rule="hyper" parents="334 13399 16215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16259">
    <literal><![CDATA[
      K(K(x,y) * (z * (x * y)),u) = K(z * (y * x),u)
    ]]></literal>
    <justification jstring="[para(10624(a,1),16215(a,2,1))].">
      <j1 rule="para" parents="10624 16215"/>
    </justification>
  </clause>

  <clause id="16260">
    <literal><![CDATA[
      K(x / ((y \ z) \ z),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),16220(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 16220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16261">
    <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),16226(a,2,2,2))].">
      <j1 rule="para" parents="13 16226"/>
    </justification>
  </clause>

  <clause id="16262">
    <literal><![CDATA[
      K(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(16226(a,1),8545(a,1))].">
      <j1 rule="para" parents="16226 8545"/>
    </justification>
  </clause>

  <clause id="16263">
    <literal><![CDATA[
      K(K(x,y) * (T(x,y) * z),u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(5091(a,1),16257(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5091 16257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16264">
    <literal><![CDATA[
      K(x * (y \ (z \ y)),y) = K(x / z,y)
    ]]></literal>
    <justification jstring="[hyper(14551,a,16260,a)].">
      <j1 rule="hyper" parents="14551 16260"/>
    </justification>
  </clause>

  <clause id="16265">
    <literal><![CDATA[
      x / (K(y / z,u) * x) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,y * (u \ (z \ u))) = w
    ]]></literal>
    <justification jstring="[para(16264(a,1),5412(a,1,2,1))].">
      <j1 rule="para" parents="16264 5412"/>
    </justification>
  </clause>

  <clause id="16266">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(12540(a,2),15989(a,1,2))].">
      <j1 rule="para" parents="12540 15989"/>
    </justification>
  </clause>

  <clause id="16267">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(16138(a,2),16105(a,1))].">
      <j1 rule="para" parents="16138 16105"/>
    </justification>
  </clause>

  <clause id="16268">
    <literal><![CDATA[
      K(x,K(y * z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z * y,u)) = w
    ]]></literal>
    <justification jstring="[para(12516(a,1),16114(a,1,2))].">
      <j1 rule="para" parents="12516 16114"/>
    </justification>
  </clause>

  <clause id="16270">
    <literal><![CDATA[
      T(x * K(y,T(x,z * u)),y) = T(x,K(y,u * (x * z)))
    ]]></literal>
    <justification jstring="[para(15962(a,1),8416(a,1,1,2))].">
      <j1 rule="para" parents="15962 8416"/>
    </justification>
  </clause>

  <clause id="16271">
    <literal><![CDATA[
      T(x,y) * K(z / x,u) = K(x \ z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(8180(a,1),15980(a,1,2))].">
      <j1 rule="para" parents="8180 15980"/>
    </justification>
  </clause>

  <clause id="16272">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) * T(z,w) = T(z,w) * K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(8169(a,1),15980(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8169 15980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16273">
    <literal><![CDATA[
      T(x,y) * K(z * x,u) = K(x * z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(12517(a,1),15980(a,1,2))].">
      <j1 rule="para" parents="12517 15980"/>
    </justification>
  </clause>

  <clause id="16274">
    <literal><![CDATA[
      T(x,T(y * z,u) / T(y,w)) = T(x,T(y,w) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[para(8563(a,1),15992(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8563 15992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16275">
    <literal><![CDATA[
      T(L(K(x,y),z,u),w / v5) = T(L(K(x,y),z,u),v5 \ w)
    ]]></literal>
    <justification jstring="[para(16018(a,1),8598(a,1,1))].">
      <j1 rule="para" parents="16018 8598"/>
    </justification>
  </clause>

  <clause id="16276">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u * x) = x \ (u * T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(116,a,16042,a(flip),b,8093,a),flip(a)].">
      <j1 rule="hyper" parents="116 16042 8093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16277">
    <literal><![CDATA[
      T(x,K(y,z)) * (u / T(x,K(y,z))) = x * (u / x)
    ]]></literal>
    <justification jstring="[para(6517(a,1),16044(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6517 16044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16279">
    <literal><![CDATA[
      K(K(x,y) * (z * (x * y)),u) = K(z * T(x * y,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13456,a(flip),b,16054,a)].">
      <j1 rule="hyper" parents="58 13456 16054"/>
    </justification>
  </clause>

  <clause id="16281">
    <literal><![CDATA[
      K(x,y * (z * K(u,y))) = K(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15805,a,b,16061,a)].">
      <j1 rule="hyper" parents="58 15805 16061"/>
    </justification>
  </clause>

  <clause id="16282">
    <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(8604(a,1),16063(a,2,2,2))].">
      <j1 rule="para" parents="8604 16063"/>
    </justification>
  </clause>

  <clause id="16284">
    <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,8220,a(flip),b,16073,a)].">
      <j1 rule="hyper" parents="58 8220 16073"/>
    </justification>
  </clause>

  <clause id="16286">
    <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(7493(a,1),16077(a,1,2,1))].">
      <j1 rule="para" parents="7493 16077"/>
    </justification>
  </clause>

  <clause id="16287">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (w * u)) = K(x,w * (u * K(y \ 1,z)))
    ]]></literal>
    <justification jstring="[para(11110(a,1),16176(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11110 16176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16288">
    <literal><![CDATA[
      K(x,K(y,z \ (y \ u)) * w) = K(x,w * K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(10603(a,2),16179(a,1,2,1))].">
      <j1 rule="para" parents="10603 16179"/>
    </justification>
  </clause>

  <clause id="16289">
    <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(7708(a,1),16209(a,1,2,1))].">
      <j1 rule="para" parents="7708 16209"/>
    </justification>
  </clause>

  <clause id="16290">
    <literal><![CDATA[
      K(x * K(y * (z * u),z),w) = K(K(y * u,z) * x,w)
    ]]></literal>
    <justification jstring="[para(10744(a,2),16216(a,1,1,2))].">
      <j1 rule="para" parents="10744 16216"/>
    </justification>
  </clause>

  <clause id="16291">
    <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(5187(a,1),16243(a,1,2,1))].">
      <j1 rule="para" parents="5187 16243"/>
    </justification>
  </clause>

  <clause id="16292">
    <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(16256(a,1),15544(a,1,2,2))].">
      <j1 rule="para" parents="16256 15544"/>
    </justification>
  </clause>

  <clause id="16293">
    <literal><![CDATA[
      K(((x \ y) \ z) * K(x,y),u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[para(5656(a,1),16258(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5656 16258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16294">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) * x,u) = w
    ]]></literal>
    <justification jstring="[para(16258(a,1),13489(a,1))].">
      <j1 rule="para" parents="16258 13489"/>
    </justification>
  </clause>

  <clause id="16295">
    <literal><![CDATA[
      K(T(T(x,y),y) * z,u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(5387(a,1),16263(a,1,1))].">
      <j1 rule="para" parents="5387 16263"/>
    </justification>
  </clause>

  <clause id="16296">
    <literal><![CDATA[
      K(((x * y) / x) * z,u) = K(T(y,x) * z,u)
    ]]></literal>
    <justification jstring="[para(230(a,1),16295(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="230 16295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16297">
    <literal><![CDATA[
      K(x,T(y,z) * (u * z)) = K(x,y * (u * T(z,y)))
    ]]></literal>
    <justification jstring="[para(6432(a,1),16281(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6432 16281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16298">
    <literal><![CDATA[
      K(x * (K(y,x) * z),u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5444(a,1),16296(a,1,1))].">
      <j1 rule="para" parents="5444 16296"/>
    </justification>
  </clause>

  <clause id="16299">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15753,a,b,16298,a)].">
      <j1 rule="hyper" parents="58 15753 16298"/>
    </justification>
  </clause>

  <clause id="16300">
    <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,15649,a(flip),b,16299,a)].">
      <j1 rule="hyper" parents="58 15649 16299"/>
    </justification>
  </clause>

  <clause id="16301">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(16177(a,1),16034(a,1))].">
      <j1 rule="para" parents="16177 16034"/>
    </justification>
  </clause>

  <clause id="16302">
    <literal><![CDATA[
      K(x,y * K(z,u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(16175(a,2),16034(a,1))].">
      <j1 rule="para" parents="16175 16034"/>
    </justification>
  </clause>

  <clause id="16303">
    <literal><![CDATA[
      K(x,y * K(z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(16181(a,2),16034(a,1))].">
      <j1 rule="para" parents="16181 16034"/>
    </justification>
  </clause>

  <clause id="16304">
    <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(13440(a,1),16052(a,1))].">
      <j1 rule="para" parents="13440 16052"/>
    </justification>
  </clause>

  <clause id="16305">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(15476(a,1),16052(a,1))].">
      <j1 rule="para" parents="15476 16052"/>
    </justification>
  </clause>

  <clause id="16306">
    <literal><![CDATA[
      K(K(x,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) * z,u) = w
    ]]></literal>
    <justification jstring="[para(16215(a,2),16067(a,1))].">
      <j1 rule="para" parents="16215 16067"/>
    </justification>
  </clause>

  <clause id="16307">
    <literal><![CDATA[
      K(T(1 / (x \ y),K(z,u)),w) = K(1 / L(x \ y,v5,y / x),w)
    ]]></literal>
    <justification jstring="[para(9337(a,2),16069(a,2,1,2))].">
      <j1 rule="para" parents="9337 16069"/>
    </justification>
  </clause>

  <clause id="16308">
    <literal><![CDATA[
      x * K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,u)) * x = w
    ]]></literal>
    <justification jstring="[para(8048(a,1),16081(a,1,2))].">
      <j1 rule="para" parents="8048 16081"/>
    </justification>
  </clause>

  <clause id="16309">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(16177(a,2),16142(a,1))].">
      <j1 rule="para" parents="16177 16142"/>
    </justification>
  </clause>

  <clause id="16310">
    <literal><![CDATA[
      K(x,T(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(15951(a,1),16145(a,1))].">
      <j1 rule="para" parents="15951 16145"/>
    </justification>
  </clause>

  <clause id="16311">
    <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(11434(a,1),16150(a,1,2,2))].">
      <j1 rule="para" parents="11434 16150"/>
    </justification>
  </clause>

  <clause id="16312">
    <literal><![CDATA[
      K(x,T(y,z / (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(14144(a,2),16150(a,1,2))].">
      <j1 rule="para" parents="14144 16150"/>
    </justification>
  </clause>

  <clause id="16313">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(15952(a,2),16150(a,1))].">
      <j1 rule="para" parents="15952 16150"/>
    </justification>
  </clause>

  <clause id="16314">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(16160(a,2),16150(a,1))].">
      <j1 rule="para" parents="16160 16150"/>
    </justification>
  </clause>

  <clause id="16315">
    <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(537(a,2),16233(a,1,2,2))].">
      <j1 rule="para" parents="537 16233"/>
    </justification>
  </clause>

  <clause id="16316">
    <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),16239(a,1,2,2))].">
      <j1 rule="para" parents="101 16239"/>
    </justification>
  </clause>

  <clause id="16317">
    <literal><![CDATA[
      K(x,K(y,(1 / z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(14104(a,2),16262(a,1,2))].">
      <j1 rule="para" parents="14104 16262"/>
    </justification>
  </clause>

  <clause id="16320">
    <literal><![CDATA[
      K(x,y * K(z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(13375(a,2),16301(a,1))].">
      <j1 rule="para" parents="13375 16301"/>
    </justification>
  </clause>

  <clause id="16321">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8632,a,15957,a),flip(a)].">
      <j1 rule="hyper" parents="8632 15957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16322">
    <literal><![CDATA[
      T(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(15957(a,1),8632(a,1))].">
      <j1 rule="para" parents="15957 8632"/>
    </justification>
  </clause>

  <clause id="16323">
    <literal><![CDATA[
      T(x,K(y,z * (u * z))) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(16231,a,16321,a),flip(a)].">
      <j1 rule="hyper" parents="16231 16321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16324">
    <literal><![CDATA[
      x * K(x,K(y,z * u)) = T(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(334,a,16228,a,b,16321,a)].">
      <j1 rule="hyper" parents="334 16228 16321"/>
    </justification>
  </clause>

  <clause id="16325">
    <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(16321(a,1),15469(a,1,2,1,2))].">
      <j1 rule="para" parents="16321 15469"/>
    </justification>
  </clause>

  <clause id="16326">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(29,a,5020,a(flip),b,16324,a)].">
      <j1 rule="hyper" parents="29 5020 16324"/>
    </justification>
  </clause>

  <clause id="16327">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8487,a,16326,a)].">
      <j1 rule="hyper" parents="8487 16326"/>
    </justification>
  </clause>

  <clause id="16328">
    <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(16327(a,1),8041(a,1,1))].">
      <j1 rule="para" parents="16327 8041"/>
    </justification>
  </clause>

  <clause id="16329">
    <literal><![CDATA[
      K((x * y) * T(z,y),T(u,y * z)) = K((z * y) * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(10656(a,1),15961(a,1,1))].">
      <j1 rule="para" parents="10656 15961"/>
    </justification>
  </clause>

  <clause id="16330">
    <literal><![CDATA[
      T(x,y) \ T(K(z,u) * x,y) = K(z,T(u,y * x))
    ]]></literal>
    <justification jstring="[hyper(15222,a,15963,a)].">
      <j1 rule="hyper" parents="15222 15963"/>
    </justification>
  </clause>

  <clause id="16331">
    <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(15968(a,1),297(a,1,2)),flip(b)].">
      <j1 rule="para" parents="15968 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16332">
    <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(15192,a,16062,a)].">
      <j1 rule="hyper" parents="15192 16062"/>
    </justification>
  </clause>

  <clause id="16333">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,w) = K(x,K(y,z)) * T(u,w)
    ]]></literal>
    <justification jstring="[hyper(334,a,16037,a,b,16095,a),flip(a)].">
      <j1 rule="hyper" parents="334 16037 16095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16334">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),w) = T(x,w) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(16037(a,1),16095(a,1,1))].">
      <j1 rule="para" parents="16037 16095"/>
    </justification>
  </clause>

  <clause id="16335">
    <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),16109(a,2,2))].">
      <j1 rule="para" parents="18 16109"/>
    </justification>
  </clause>

  <clause id="16336">
    <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(7894(a,1),16125(a,2,2))].">
      <j1 rule="para" parents="7894 16125"/>
    </justification>
  </clause>

  <clause id="16337">
    <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,12579,a(flip),b,16127,a)].">
      <j1 rule="hyper" parents="58 12579 16127"/>
    </justification>
  </clause>

  <clause id="16338">
    <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(16128(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16128 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16339">
    <literal><![CDATA[
      K(x,T(y,z)) * (u * K(y,T(x,z))) = T(u,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,16129,a(flip),b,7469,a)].">
      <j1 rule="hyper" parents="119 16129 7469"/>
    </justification>
  </clause>

  <clause id="16340">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,y)) = u * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,7422,a,b,16137,a),flip(a)].">
      <j1 rule="hyper" parents="334 7422 16137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16341">
    <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(451,a,16199,a,b,14249,a)].">
      <j1 rule="hyper" parents="451 16199 14249"/>
    </justification>
  </clause>

  <clause id="16342">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) * K(y,K(x,z)) = z \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,14044,a(flip),b,16236,a),flip(a)].">
      <j1 rule="hyper" parents="334 14044 16236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16343">
    <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),16246(a,2,2,2))].">
      <j1 rule="para" parents="107 16246"/>
    </justification>
  </clause>

  <clause id="16344">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,z) = z \ (u * T(z,K(x,y)))
    ]]></literal>
    <justification jstring="[para(8053(a,2),16246(a,1,1))].">
      <j1 rule="para" parents="8053 16246"/>
    </justification>
  </clause>

  <clause id="16345">
    <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(16251(a,1),7818(a,2,2,1))].">
      <j1 rule="para" parents="16251 7818"/>
    </justification>
  </clause>

  <clause id="16346">
    <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(16271(a,2),15105(a,2,2,2))].">
      <j1 rule="para" parents="16271 15105"/>
    </justification>
  </clause>

  <clause id="16347">
    <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(8111(a,1),16276(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8111 16276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16348">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),w) / y = y \ T(T(y,K(z,u)) * x,w)
    ]]></literal>
    <justification jstring="[hyper(4857,a,16277,a),flip(a)].">
      <j1 rule="hyper" parents="4857 16277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16349">
    <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(16297(a,2),7656(a,1))].">
      <j1 rule="para" parents="16297 7656"/>
    </justification>
  </clause>

  <clause id="16350">
    <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(15337(a,2),16330(a,2,2,2))].">
      <j1 rule="para" parents="15337 16330"/>
    </justification>
  </clause>

  <clause id="16352">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),w) = K(y,K(z,u)) * T(x,w)
    ]]></literal>
    <justification jstring="[para(16037(a,1),16333(a,1,1))].">
      <j1 rule="para" parents="16037 16333"/>
    </justification>
  </clause>

  <clause id="16353">
    <literal><![CDATA[
      T(K(x,K(y,z)) \ u,w) = K(x,K(y,z)) \ T(u,w)
    ]]></literal>
    <justification jstring="[hyper(4848,a,16334,a),flip(a)].">
      <j1 rule="hyper" parents="4848 16334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16354">
    <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(16334(a,2),8080(a,1,1))].">
      <j1 rule="para" parents="16334 8080"/>
    </justification>
  </clause>

  <clause id="16355">
    <literal><![CDATA[
      K(x,T(y,z)) * K(x,K(y,u)) = K(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[para(8048(a,1),16335(a,1,2))].">
      <j1 rule="para" parents="8048 16335"/>
    </justification>
  </clause>

  <clause id="16356">
    <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(16339(a,1),11514(a,1,2,2))].">
      <j1 rule="para" parents="16339 11514"/>
    </justification>
  </clause>

  <clause id="16357">
    <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(16340(a,2),38(a,1))].">
      <j1 rule="para" parents="16340 38"/>
    </justification>
  </clause>

  <clause id="16358">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(z,y) = K(z,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(30,a,16119,a,b,16342,a)].">
      <j1 rule="hyper" parents="30 16119 16342"/>
    </justification>
  </clause>

  <clause id="16359">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = K(y,x) * (z \ y)
    ]]></literal>
    <justification jstring="[para(8129(a,2),16358(a,1,1))].">
      <j1 rule="para" parents="8129 16358"/>
    </justification>
  </clause>

  <clause id="16360">
    <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(8165(a,1),15981(a,1,1))].">
      <j1 rule="para" parents="8165 15981"/>
    </justification>
  </clause>

  <clause id="16361">
    <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),15982(a,1,2))].">
      <j1 rule="para" parents="18 15982"/>
    </justification>
  </clause>

  <clause id="16362">
    <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(15995,a,14435,a)].">
      <j1 rule="hyper" parents="15995 14435"/>
    </justification>
  </clause>

  <clause id="16363">
    <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(7597(a,1),16147(a,1,2,1))].">
      <j1 rule="para" parents="7597 16147"/>
    </justification>
  </clause>

  <clause id="16364">
    <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(9691(a,1),16147(a,1,2,1))].">
      <j1 rule="para" parents="9691 16147"/>
    </justification>
  </clause>

  <clause id="16365">
    <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(14349(a,1),16155(a,1,2,2))].">
      <j1 rule="para" parents="14349 16155"/>
    </justification>
  </clause>

  <clause id="16366">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(z,y)) = w
    ]]></literal>
    <justification jstring="[para(15476(a,1),16157(a,1))].">
      <j1 rule="para" parents="15476 16157"/>
    </justification>
  </clause>

  <clause id="16367">
    <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(14131(a,1),16302(a,1,2,2))].">
      <j1 rule="para" parents="14131 16302"/>
    </justification>
  </clause>

  <clause id="16368">
    <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(13624(a,2),16303(a,1))].">
      <j1 rule="para" parents="13624 16303"/>
    </justification>
  </clause>

  <clause id="16369">
    <literal><![CDATA[
      K(x,K(y,z * (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z / u)) = w
    ]]></literal>
    <justification jstring="[para(16093(a,1),16317(a,1))].">
      <j1 rule="para" parents="16093 16317"/>
    </justification>
  </clause>

  <clause id="16370">
    <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(12774(a,2),16320(a,1,2,2))].">
      <j1 rule="para" parents="12774 16320"/>
    </justification>
  </clause>

  <clause id="16371">
    <literal><![CDATA[
      T(x,K(K(y,z),u) * w) = w \ (x * w)
    ]]></literal>
    <justification jstring="[para(16039(a,1),16053(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16039 16053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16372">
    <literal><![CDATA[
      T(x,K(K(y,z),u) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(334,a,17,a,b,16371,a),flip(a)].">
      <j1 rule="hyper" parents="334 17 16371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16374">
    <literal><![CDATA[
      T(x,y \ T(z,K(u,w))) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(16366,a,16372,a)].">
      <j1 rule="hyper" parents="16366 16372"/>
    </justification>
  </clause>

  <clause id="16375">
    <literal><![CDATA[
      T(x,y * K(z,K(u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(16305,a,16372,a)].">
      <j1 rule="hyper" parents="16305 16372"/>
    </justification>
  </clause>

  <clause id="16376">
    <literal><![CDATA[
      T(x,y / T(z,K(u,w))) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(16153,a,16372,a)].">
      <j1 rule="hyper" parents="16153 16372"/>
    </justification>
  </clause>

  <clause id="16377">
    <literal><![CDATA[
      T(x,K(y,K(z,u)) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(15705,a,16372,a)].">
      <j1 rule="hyper" parents="15705 16372"/>
    </justification>
  </clause>

  <clause id="16378">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) / w) = T(x,y / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15487,a(flip),b,16372,a)].">
      <j1 rule="hyper" parents="58 15487 16372"/>
    </justification>
  </clause>

  <clause id="16379">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) * w) = T(x,y * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15482,a(flip),b,16372,a)].">
      <j1 rule="hyper" parents="58 15482 16372"/>
    </justification>
  </clause>

  <clause id="16380">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) \ w) = T(x,y \ w)
    ]]></literal>
    <justification jstring="[para(5392(a,1),16372(a,1,2))].">
      <j1 rule="para" parents="5392 16372"/>
    </justification>
  </clause>

  <clause id="16381">
    <literal><![CDATA[
      T(x,y * (K(z,K(u,w)) * v5)) = T(x,y * v5)
    ]]></literal>
    <justification jstring="[para(6333(a,1),16372(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6333 16372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16382">
    <literal><![CDATA[
      T(x,y * (K(z,u) * w)) = T(x,y * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(10647(a,1),16372(a,1,2))].">
      <j1 rule="para" parents="10647 16372"/>
    </justification>
  </clause>

  <clause id="16383">
    <literal><![CDATA[
      T(x,(K(y,z) * u) * w) = T(x,(u * K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(11459(a,1),16372(a,1,2))].">
      <j1 rule="para" parents="11459 16372"/>
    </justification>
  </clause>

  <clause id="16384">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) = x \ T(x,w)
    ]]></literal>
    <justification jstring="[para(16372(a,1),15480(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16372 15480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16385">
    <literal><![CDATA[
      T(x,y * T(z,K(u,w))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(1532(a,1),16375(a,1,2))].">
      <j1 rule="para" parents="1532 16375"/>
    </justification>
  </clause>

  <clause id="16386">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) = w / T(w,x)
    ]]></literal>
    <justification jstring="[para(16375(a,1),5062(a,2,2))].">
      <j1 rule="para" parents="16375 5062"/>
    </justification>
  </clause>

  <clause id="16387">
    <literal><![CDATA[
      T(x,y * (z * T(u,K(w,v5)))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(6288(a,1),16375(a,1,2))].">
      <j1 rule="para" parents="6288 16375"/>
    </justification>
  </clause>

  <clause id="16388">
    <literal><![CDATA[
      T(x,y / (K(z,u) * w)) = T(x,y / (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(10910(a,1),16375(a,1,2))].">
      <j1 rule="para" parents="10910 16375"/>
    </justification>
  </clause>

  <clause id="16389">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) = T(x,K(y,z) * w)
    ]]></literal>
    <justification jstring="[para(16200(a,1),16375(a,1,2))].">
      <j1 rule="para" parents="16200 16375"/>
    </justification>
  </clause>

  <clause id="16390">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w))) = T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(16340(a,1),16377(a,1,2))].">
      <j1 rule="para" parents="16340 16377"/>
    </justification>
  </clause>

  <clause id="16391">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w))) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(7688(a,1),16374(a,1,2,2))].">
      <j1 rule="para" parents="7688 16374"/>
    </justification>
  </clause>

  <clause id="16392">
    <literal><![CDATA[
      T(x,y / T(z,T(u,w))) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(7688(a,1),16376(a,1,2,2))].">
      <j1 rule="para" parents="7688 16376"/>
    </justification>
  </clause>

  <clause id="16393">
    <literal><![CDATA[
      T(x,y / T(T(z,T(u,w)),v5)) = T(x,y / T(T(z,u),v5))
    ]]></literal>
    <justification jstring="[para(7692(a,1),16376(a,1,2,2))].">
      <j1 rule="para" parents="7692 16376"/>
    </justification>
  </clause>

  <clause id="16394">
    <literal><![CDATA[
      T(x,T(y,T(z,u)) / w) = T(x,T(y,z) / w)
    ]]></literal>
    <justification jstring="[para(7688(a,1),16378(a,1,2,1))].">
      <j1 rule="para" parents="7688 16378"/>
    </justification>
  </clause>

  <clause id="16396">
    <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,13510,a(flip),b,16379,a),flip(a)].">
      <j1 rule="hyper" parents="58 13510 16379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16397">
    <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,14522,a(flip),b,16380,a),flip(a)].">
      <j1 rule="hyper" parents="58 14522 16380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16398">
    <literal><![CDATA[
      T(x,T(y,T(z,u)) \ w) = T(x,T(y,z) \ w)
    ]]></literal>
    <justification jstring="[para(7688(a,1),16380(a,1,2,1))].">
      <j1 rule="para" parents="7688 16380"/>
    </justification>
  </clause>

  <clause id="16399">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(334,a,4995,a,b,16384,a),flip(a)].">
      <j1 rule="hyper" parents="334 4995 16384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16400">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(16384(a,2),5110(a,1))].">
      <j1 rule="para" parents="16384 5110"/>
    </justification>
  </clause>

  <clause id="16401">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) \ w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(16309,a,16399,a)].">
      <j1 rule="hyper" parents="16309 16399"/>
    </justification>
  </clause>

  <clause id="16402">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(16184,a,16399,a)].">
      <j1 rule="hyper" parents="16184 16399"/>
    </justification>
  </clause>

  <clause id="16403">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(16151,a,16399,a)].">
      <j1 rule="hyper" parents="16151 16399"/>
    </justification>
  </clause>

  <clause id="16404">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(16147,a,16399,a)].">
      <j1 rule="hyper" parents="16147 16399"/>
    </justification>
  </clause>

  <clause id="16405">
    <literal><![CDATA[
      K(x,y * K(z,K(u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(16034,a,16399,a)].">
      <j1 rule="hyper" parents="16034 16399"/>
    </justification>
  </clause>

  <clause id="16406">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ w) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15499,a(flip),b,16399,a)].">
      <j1 rule="hyper" parents="58 15499 16399"/>
    </justification>
  </clause>

  <clause id="16407">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) * w) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(5047(a,1),16399(a,1,2))].">
      <j1 rule="para" parents="5047 16399"/>
    </justification>
  </clause>

  <clause id="16408">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) / w) = K(x,y / w)
    ]]></literal>
    <justification jstring="[para(5921(a,1),16399(a,1,2))].">
      <j1 rule="para" parents="5921 16399"/>
    </justification>
  </clause>

  <clause id="16409">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,(u * K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(9888(a,1),16399(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9888 16399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16410">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,(u * K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(11459(a,1),16399(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11459 16399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16411">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,(u * K(y,z)) / w)
    ]]></literal>
    <justification jstring="[para(14370(a,1),16399(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14370 16399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16412">
    <literal><![CDATA[
      K(x,y \ K(z,T(u,w))) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[para(16204(a,1),16399(a,1,2))].">
      <j1 rule="para" parents="16204 16399"/>
    </justification>
  </clause>

  <clause id="16413">
    <literal><![CDATA[
      K(x,y * K(z,T(u,w))) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(16340(a,1),16399(a,1,2))].">
      <j1 rule="para" parents="16340 16399"/>
    </justification>
  </clause>

  <clause id="16414">
    <literal><![CDATA[
      K(x,y * (z * T(u,K(w,v5)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(6288(a,1),16405(a,1,2))].">
      <j1 rule="para" parents="6288 16405"/>
    </justification>
  </clause>

  <clause id="16415">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(8401(a,1),16405(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8401 16405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16416">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,y / (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(10910(a,1),16405(a,1,2))].">
      <j1 rule="para" parents="10910 16405"/>
    </justification>
  </clause>

  <clause id="16417">
    <literal><![CDATA[
      K(x,y * (z * K(u,K(w,v5)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(11183(a,1),16405(a,1,2))].">
      <j1 rule="para" parents="11183 16405"/>
    </justification>
  </clause>

  <clause id="16418">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,y \ (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(14495(a,1),16405(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14495 16405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16419">
    <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,13413,a(flip),b,16385,a),flip(a)].">
      <j1 rule="hyper" parents="58 13413 16385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16422">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(334,a,5062,a,b,16386,a),flip(a)].">
      <j1 rule="hyper" parents="334 5062 16386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16423">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(16386(a,2),5133(a,1))].">
      <j1 rule="para" parents="16386 5133"/>
    </justification>
  </clause>

  <clause id="16424">
    <literal><![CDATA[
      K(K(x,K(y,z)) * u,w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(16219,a,16422,a)].">
      <j1 rule="hyper" parents="16219 16422"/>
    </justification>
  </clause>

  <clause id="16425">
    <literal><![CDATA[
      K(K(x,K(y,z)) \ u,w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,16224,a,b,16422,a)].">
      <j1 rule="hyper" parents="58 16224 16422"/>
    </justification>
  </clause>

  <clause id="16426">
    <literal><![CDATA[
      K(x \ T(y,K(z,u)),w) = K(x \ y,w)
    ]]></literal>
    <justification jstring="[para(1529(a,1),16422(a,1,1))].">
      <j1 rule="para" parents="1529 16422"/>
    </justification>
  </clause>

  <clause id="16427">
    <literal><![CDATA[
      K(x * (K(y,z) * u),w) = K(x * (u * K(y,z)),w)
    ]]></literal>
    <justification jstring="[para(8401(a,1),16422(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8401 16422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16428">
    <literal><![CDATA[
      K(x \ K(y,T(z,u)),w) = K(x \ K(y,z),w)
    ]]></literal>
    <justification jstring="[para(12627(a,1),16422(a,1,1))].">
      <j1 rule="para" parents="12627 16422"/>
    </justification>
  </clause>

  <clause id="16429">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K(x \ (u * K(y,z)),w)
    ]]></literal>
    <justification jstring="[para(14495(a,1),16422(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14495 16422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16430">
    <literal><![CDATA[
      K(x * K(y,T(z,u)),w) = K(x * K(y,z),w)
    ]]></literal>
    <justification jstring="[para(16340(a,1),16424(a,1,1))].">
      <j1 rule="para" parents="16340 16424"/>
    </justification>
  </clause>

  <clause id="16431">
    <literal><![CDATA[
      K(K(x,K(y,z)) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,w) = v5
    ]]></literal>
    <justification jstring="[para(16425(a,1),6663(a,1))].">
      <j1 rule="para" parents="16425 6663"/>
    </justification>
  </clause>

  <clause id="16432">
    <literal><![CDATA[
      K(x,y \ T(z,y)) = K(x,z / T(y,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(334,a,13434,a,b,16402,a)].">
      <j1 rule="hyper" parents="334 13434 16402"/>
    </justification>
  </clause>

  <clause id="16433">
    <literal><![CDATA[
      K(x,y / T(z,u / w)) = K(x,y / T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(8223(a,1),16402(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8223 16402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16434">
    <literal><![CDATA[
      K(x,y \ T(z,u / w)) = K(x,y \ T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(8223(a,1),16403(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8223 16403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16436">
    <literal><![CDATA[
      K(x,y * T(z,T(u,w))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(7688(a,1),16404(a,1,2,2))].">
      <j1 rule="para" parents="7688 16404"/>
    </justification>
  </clause>

  <clause id="16437">
    <literal><![CDATA[
      K(x,y * T(z,u / w)) = K(x,y * T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(8223(a,1),16404(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8223 16404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16438">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ z))) = K(x,y * (w \ T(z,u)))
    ]]></literal>
    <justification jstring="[para(14059(a,1),16404(a,1,2,2))].">
      <j1 rule="para" parents="14059 16404"/>
    </justification>
  </clause>

  <clause id="16439">
    <literal><![CDATA[
      K(x,y * ((z / u) * K(z,w))) = K(x,y * (T(z,w) / u))
    ]]></literal>
    <justification jstring="[para(14073(a,1),16404(a,1,2,2))].">
      <j1 rule="para" parents="14073 16404"/>
    </justification>
  </clause>

  <clause id="16440">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * w) = K(x,T(y,z) * w)
    ]]></literal>
    <justification jstring="[para(7688(a,1),16407(a,1,2,1))].">
      <j1 rule="para" parents="7688 16407"/>
    </justification>
  </clause>

  <clause id="16441">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) / w) = K(x,T(y,z) / w)
    ]]></literal>
    <justification jstring="[para(7688(a,1),16408(a,1,2,1))].">
      <j1 rule="para" parents="7688 16408"/>
    </justification>
  </clause>

  <clause id="16442">
    <literal><![CDATA[
      K(x,T(y,z / u) / w) = K(x,T(y,u \ z) / w)
    ]]></literal>
    <justification jstring="[para(8223(a,1),16408(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8223 16408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16443">
    <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,15870,a(flip),b,16426,a),flip(a)].">
      <j1 rule="hyper" parents="58 15870 16426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16444">
    <literal><![CDATA[
      K(x \ T(y,T(z,u)),w) = K(x \ T(y,z),w)
    ]]></literal>
    <justification jstring="[para(7688(a,1),16426(a,1,1,2))].">
      <j1 rule="para" parents="7688 16426"/>
    </justification>
  </clause>

  <clause id="16445">
    <literal><![CDATA[
      K(x \ T(y,z * u),w) = K(x \ T(y,u * z),w)
    ]]></literal>
    <justification jstring="[para(12572(a,1),16426(a,1,1,2))].">
      <j1 rule="para" parents="12572 16426"/>
    </justification>
  </clause>

  <clause id="16446">
    <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(16426(a,1),14266(a,1,1,1,2))].">
      <j1 rule="para" parents="16426 14266"/>
    </justification>
  </clause>

  <clause id="16447">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * w) = v5
    ]]></literal>
    <justification jstring="[para(5047(a,1),16400(a,1,2))].">
      <j1 rule="para" parents="5047 16400"/>
    </justification>
  </clause>

  <clause id="16448">
    <literal><![CDATA[
      K(x,K(K(y,z),u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(5886(a,2),16400(a,1,2,1))].">
      <j1 rule="para" parents="5886 16400"/>
    </justification>
  </clause>

  <clause id="16449">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v5
    ]]></literal>
    <justification jstring="[para(5820(a,1),16400(a,1,2))].">
      <j1 rule="para" parents="5820 16400"/>
    </justification>
  </clause>

  <clause id="16450">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = v5
    ]]></literal>
    <justification jstring="[para(5818(a,1),16400(a,1,2))].">
      <j1 rule="para" parents="5818 16400"/>
    </justification>
  </clause>

  <clause id="16451">
    <literal><![CDATA[
      K(x,y * K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(7538(a,1),16400(a,1,2))].">
      <j1 rule="para" parents="7538 16400"/>
    </justification>
  </clause>

  <clause id="16452">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ w) = v5
    ]]></literal>
    <justification jstring="[para(8040(a,1),16400(a,1,2))].">
      <j1 rule="para" parents="8040 16400"/>
    </justification>
  </clause>

  <clause id="16453">
    <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(14370(a,1),16400(a,1,2))].">
      <j1 rule="para" parents="14370 16400"/>
    </justification>
  </clause>

  <clause id="16454">
    <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(15183(a,1),16400(a,1,2))].">
      <j1 rule="para" parents="15183 16400"/>
    </justification>
  </clause>

  <clause id="16455">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = v5
    ]]></literal>
    <justification jstring="[para(16178(a,1),16400(a,1))].">
      <j1 rule="para" parents="16178 16400"/>
    </justification>
  </clause>

  <clause id="16456">
    <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(16204(a,1),16400(a,1,2))].">
      <j1 rule="para" parents="16204 16400"/>
    </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(1529(a,1),16423(a,1,1))].">
      <j1 rule="para" parents="1529 16423"/>
    </justification>
  </clause>

  <clause id="16458">
    <literal><![CDATA[
      K(T(x,K(y,z)) / u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x / u,w) = v5
    ]]></literal>
    <justification jstring="[para(1542(a,1),16423(a,1,1))].">
      <j1 rule="para" parents="1542 16423"/>
    </justification>
  </clause>

  <clause id="16459">
    <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(9888(a,1),16431(a,1,1))].">
      <j1 rule="para" parents="9888 16431"/>
    </justification>
  </clause>

  <clause id="16460">
    <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(11497(a,1),16431(a,1,1))].">
      <j1 rule="para" parents="11497 16431"/>
    </justification>
  </clause>

  <clause id="16461">
    <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(16259(a,1),16431(a,1))].">
      <j1 rule="para" parents="16259 16431"/>
    </justification>
  </clause>

  <clause id="16462">
    <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(10647(a,1),16448(a,1,2))].">
      <j1 rule="para" parents="10647 16448"/>
    </justification>
  </clause>

  <clause id="16463">
    <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(11459(a,1),16448(a,1,2))].">
      <j1 rule="para" parents="11459 16448"/>
    </justification>
  </clause>

  <clause id="16464">
    <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(6288(a,1),16451(a,1,2))].">
      <j1 rule="para" parents="6288 16451"/>
    </justification>
  </clause>

  <clause id="16465">
    <literal><![CDATA[
      K(x,y * (z * K(u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v6
    ]]></literal>
    <justification jstring="[para(11183(a,1),16451(a,1,2))].">
      <j1 rule="para" parents="11183 16451"/>
    </justification>
  </clause>

  <clause id="16466">
    <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(14495(a,1),16451(a,1,2))].">
      <j1 rule="para" parents="14495 16451"/>
    </justification>
  </clause>

  <clause id="16467">
    <literal><![CDATA[
      T(x,y * K(z / u,w)) = T(x,y * K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(6646(a,1),16381(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6646 16381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16468">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) = T(x,K(z,y) * w)
    ]]></literal>
    <justification jstring="[hyper(334,a,15476,a,b,16389,a),flip(a)].">
      <j1 rule="hyper" parents="334 15476 16389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16469">
    <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(16389(a,1),16366(a,1))].">
      <j1 rule="para" parents="16389 16366"/>
    </justification>
  </clause>

  <clause id="16470">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w))) = T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,16208,a,b,16390,a),flip(a)].">
      <j1 rule="hyper" parents="334 16208 16390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16471">
    <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(16390(a,2),16212(a,1))].">
      <j1 rule="para" parents="16390 16212"/>
    </justification>
  </clause>

  <clause id="16472">
    <literal><![CDATA[
      T(x,T(y * K(y * z,u),z)) = T(x,z \ T(y * z,u))
    ]]></literal>
    <justification jstring="[para(14438(a,2),16391(a,1,2))].">
      <j1 rule="para" parents="14438 16391"/>
    </justification>
  </clause>

  <clause id="16473">
    <literal><![CDATA[
      T(x,y / T(z,T(u,w))) = T(x,y / T(z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(334,a,13346,a,b,16392,a),flip(a)].">
      <j1 rule="hyper" parents="334 13346 16392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16474">
    <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(16392(a,1),13042(a,1))].">
      <j1 rule="para" parents="16392 13042"/>
    </justification>
  </clause>

  <clause id="16475">
    <literal><![CDATA[
      T(x,T(T(y,z) \ u,y) / w) = T(x,(u / T(y,z)) / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15509,a(flip),b,16394,a),flip(a)].">
      <j1 rule="hyper" parents="58 15509 16394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16476">
    <literal><![CDATA[
      K(x,y \ K(z / u,w)) = K(x,y \ K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(7414(a,1),16412(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7414 16412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16477">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * w) = K(x,w * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(16068,a,16413,a)].">
      <j1 rule="hyper" parents="16068 16413"/>
    </justification>
  </clause>

  <clause id="16478">
    <literal><![CDATA[
      K(x,y * K(z,u / w)) = K(x,y * K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(107(a,1),16413(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="107 16413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16479">
    <literal><![CDATA[
      K(x,y * K(z,u * w)) = K(x,y * K(z,w * u))
    ]]></literal>
    <justification jstring="[para(12551(a,1),16413(a,1,2,2))].">
      <j1 rule="para" parents="12551 16413"/>
    </justification>
  </clause>

  <clause id="16480">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,w)) = K(x,T(u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[para(15221(a,1),16413(a,1,2))].">
      <j1 rule="para" parents="15221 16413"/>
    </justification>
  </clause>

  <clause id="16481">
    <literal><![CDATA[
      K(x,y * (z / T(u,K(w,v5)))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15806,a(flip),b,16417,a)].">
      <j1 rule="hyper" parents="58 15806 16417"/>
    </justification>
  </clause>

  <clause id="16482">
    <literal><![CDATA[
      K(x,y * (z \ T(u,K(w,v5)))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(1529(a,1),16417(a,1,2,2))].">
      <j1 rule="para" parents="1529 16417"/>
    </justification>
  </clause>

  <clause id="16483">
    <literal><![CDATA[
      K(x,y * (T(z,K(u,w)) / v5)) = K(x,y * (z / v5))
    ]]></literal>
    <justification jstring="[para(1542(a,1),16417(a,1,2,2))].">
      <j1 rule="para" parents="1542 16417"/>
    </justification>
  </clause>

  <clause id="16484">
    <literal><![CDATA[
      K(x,y * (T(z,K(u,w)) * v5)) = K(x,y * (z * v5))
    ]]></literal>
    <justification jstring="[para(5803(a,1),16417(a,1,2,2))].">
      <j1 rule="para" parents="5803 16417"/>
    </justification>
  </clause>

  <clause id="16486">
    <literal><![CDATA[
      K(x,y * (K(z,T(u,w)) * v5)) = K(x,y * (K(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(16200(a,1),16417(a,1,2,2))].">
      <j1 rule="para" parents="16200 16417"/>
    </justification>
  </clause>

  <clause id="16487">
    <literal><![CDATA[
      K(x \ K(y,z * u),w) = K(x \ K(y,u * z),w)
    ]]></literal>
    <justification jstring="[para(12551(a,1),16428(a,1,1,2))].">
      <j1 rule="para" parents="12551 16428"/>
    </justification>
  </clause>

  <clause id="16488">
    <literal><![CDATA[
      K(x * K(y,T(z,u)),w) = K(K(z,y) * x,w)
    ]]></literal>
    <justification jstring="[hyper(334,a,16215,a,b,16430,a),flip(a)].">
      <j1 rule="hyper" parents="334 16215 16430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16489">
    <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,13829,a(flip),b,16436,a),flip(a)].">
      <j1 rule="hyper" parents="58 13829 16436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16490">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,12576,a(flip),b,16440,a),flip(a)].">
      <j1 rule="hyper" parents="334 12576 16440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16491">
    <literal><![CDATA[
      K(x,T(T(y,z) / u,y) * w) = K(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,13364,a(flip),b,16440,a),flip(a)].">
      <j1 rule="hyper" parents="58 13364 16440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16492">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * z)) = K(x,(u * z) * y)
    ]]></literal>
    <justification jstring="[para(12541(a,1),16490(a,1,2,1))].">
      <j1 rule="para" parents="12541 16490"/>
    </justification>
  </clause>

  <clause id="16493">
    <literal><![CDATA[
      K(x,T(T(y,z) / u,y) / w) = K(x,(u \ T(y,z)) / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,13366,a(flip),b,16441,a),flip(a)].">
      <j1 rule="hyper" parents="58 13366 16441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16494">
    <literal><![CDATA[
      K(T(x * K(x * y,z),y),u) = K(y \ T(x * y,z),u)
    ]]></literal>
    <justification jstring="[para(14438(a,2),16444(a,1,1))].">
      <j1 rule="para" parents="14438 16444"/>
    </justification>
  </clause>

  <clause id="16495">
    <literal><![CDATA[
      T(x,K(y * z,u) * w) = T(x,K(u,z * y) * w)
    ]]></literal>
    <justification jstring="[para(12516(a,1),16468(a,1,2,1))].">
      <j1 rule="para" parents="12516 16468"/>
    </justification>
  </clause>

  <clause id="16496">
    <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,15939,a,b,16470,a)].">
      <j1 rule="hyper" parents="58 15939 16470"/>
    </justification>
  </clause>

  <clause id="16497">
    <literal><![CDATA[
      K(x,K(y * z,u) * w) = K(x,w * K(z * y,u))
    ]]></literal>
    <justification jstring="[para(12516(a,1),16477(a,1,2,1))].">
      <j1 rule="para" parents="12516 16477"/>
    </justification>
  </clause>

  <clause id="16498">
    <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(16477(a,2),16183(a,1))].">
      <j1 rule="para" parents="16477 16183"/>
    </justification>
  </clause>

  <clause id="16499">
    <literal><![CDATA[
      K(K(x * y,z) * u,w) = K(u * K(z,y * x),w)
    ]]></literal>
    <justification jstring="[para(12551(a,1),16488(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12551 16488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16500">
    <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(8223(a,1),16447(a,1,2,1))].">
      <j1 rule="para" parents="8223 16447"/>
    </justification>
  </clause>

  <clause id="16501">
    <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(8597(a,1),16449(a,1,2,2))].">
      <j1 rule="para" parents="8597 16449"/>
    </justification>
  </clause>

  <clause id="16502">
    <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(8362(a,1),16449(a,1,2,2))].">
      <j1 rule="para" parents="8362 16449"/>
    </justification>
  </clause>

  <clause id="16503">
    <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(14059(a,1),16449(a,1,2,2))].">
      <j1 rule="para" parents="14059 16449"/>
    </justification>
  </clause>

  <clause id="16504">
    <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(14073(a,1),16449(a,1,2,2))].">
      <j1 rule="para" parents="14073 16449"/>
    </justification>
  </clause>

  <clause id="16505">
    <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(15613(a,1),16449(a,1))].">
      <j1 rule="para" parents="15613 16449"/>
    </justification>
  </clause>

  <clause id="16506">
    <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(8597(a,1),16450(a,1,2,2))].">
      <j1 rule="para" parents="8597 16450"/>
    </justification>
  </clause>

  <clause id="16507">
    <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(12572(a,1),16450(a,1,2,2))].">
      <j1 rule="para" parents="12572 16450"/>
    </justification>
  </clause>

  <clause id="16508">
    <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),16455(a,1,2,2))].">
      <j1 rule="para" parents="20 16455"/>
    </justification>
  </clause>

  <clause id="16509">
    <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(14059(a,1),16455(a,1,2,2))].">
      <j1 rule="para" parents="14059 16455"/>
    </justification>
  </clause>

  <clause id="16510">
    <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(7688(a,1),16457(a,1,1,2))].">
      <j1 rule="para" parents="7688 16457"/>
    </justification>
  </clause>

  <clause id="16511">
    <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(8597(a,1),16458(a,1,1,1))].">
      <j1 rule="para" parents="8597 16458"/>
    </justification>
  </clause>

  <clause id="16512">
    <literal><![CDATA[
      T(x,y * (z * T(u,w / v5))) = T(x,y * (z * T(u,v5 \ w)))
    ]]></literal>
    <justification jstring="[para(8223(a,1),16387(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8223 16387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16513">
    <literal><![CDATA[
      T(x,y / (z * K(u,w))) = T(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14196,a(flip),b,16388,a),flip(a)].">
      <j1 rule="hyper" parents="58 14196 16388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16515">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(16409(a,1),6760(a,1))].">
      <j1 rule="para" parents="16409 6760"/>
    </justification>
  </clause>

  <clause id="16516">
    <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(15123(a,1),16411(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15123 16411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16517">
    <literal><![CDATA[
      K(x,y * (z * (K(u,w) / v5))) = K(x,y * (z * (v5 \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(58,a,15671,a(flip),b,16414,a)].">
      <j1 rule="hyper" parents="58 15671 16414"/>
    </justification>
  </clause>

  <clause id="16518">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(334,a,15805,a,b,16415,a),flip(a)].">
      <j1 rule="hyper" parents="334 15805 16415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16519">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w / z))) = K(x,y * (w / T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,15806,a(flip),b,16415,a),flip(a)].">
      <j1 rule="hyper" parents="334 15806 16415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16520">
    <literal><![CDATA[
      K(x,y * (z * K(u,u \ w))) = K(x,y * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13386,a(flip),b,16415,a),flip(a)].">
      <j1 rule="hyper" parents="58 13386 16415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16521">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14185,a(flip),b,16416,a),flip(a)].">
      <j1 rule="hyper" parents="58 14185 16416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16522">
    <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(15123(a,1),16418(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15123 16418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16523">
    <literal><![CDATA[
      K(x * (((y * z) / y) \ u),w) = K(x * ((z \ u) * K(z,y)),w)
    ]]></literal>
    <justification jstring="[para(5350(a,2),16427(a,1,1,2))].">
      <j1 rule="para" parents="5350 16427"/>
    </justification>
  </clause>

  <clause id="16524">
    <literal><![CDATA[
      K(x,(y / z) / T(u,z \ y)) = K(x,u \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(13370,a,16433,a),flip(a)].">
      <j1 rule="hyper" parents="13370 16433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16525">
    <literal><![CDATA[
      K(x,(y / z) / T(u,z \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (y / z)) = w
    ]]></literal>
    <justification jstring="[para(16433(a,1),13370(a,1))].">
      <j1 rule="para" parents="16433 13370"/>
    </justification>
  </clause>

  <clause id="16527">
    <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,15533,a(flip),b,16442,a),flip(a)].">
      <j1 rule="hyper" parents="58 15533 16442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16528">
    <literal><![CDATA[
      K(x,T(y,z \ u) / (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u / z) \ y) = w
    ]]></literal>
    <justification jstring="[para(16442(a,1),13368(a,1))].">
      <j1 rule="para" parents="16442 13368"/>
    </justification>
  </clause>

  <clause id="16529">
    <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(16445(a,1),6987(a,1))].">
      <j1 rule="para" parents="16445 6987"/>
    </justification>
  </clause>

  <clause id="16530">
    <literal><![CDATA[
      T(x,((y / z) \ u) * K(z \ y,w)) = T(x,T(y / z,w) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16210,a(flip),b,16467,a),flip(a)].">
      <j1 rule="hyper" parents="58 16210 16467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16531">
    <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,15554,a(flip),b,16467,a),flip(a)].">
      <j1 rule="hyper" parents="58 15554 16467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16532">
    <literal><![CDATA[
      T(x,y \ K(z / u,w)) = T(x,y \ K(u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(118,a,16476,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 16476 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16533">
    <literal><![CDATA[
      K(x,(y * z) * K(u,z * y)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(8295,a,16479,a),flip(a)].">
      <j1 rule="hyper" parents="8295 16479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16534">
    <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(16479(a,1),16183(a,1))].">
      <j1 rule="para" parents="16479 16183"/>
    </justification>
  </clause>

  <clause id="16535">
    <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(16479(a,1),16301(a,1))].">
      <j1 rule="para" parents="16479 16301"/>
    </justification>
  </clause>

  <clause id="16536">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,w)) = K(x,K(y,z) * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,16002,a,b,16480,a),flip(a)].">
      <j1 rule="hyper" parents="334 16002 16480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16537">
    <literal><![CDATA[
      K(x,y * (z / T(u,u \ w))) = K(x,y * (z / ((u \ w) \ w)))
    ]]></literal>
    <justification jstring="[para(3474(a,1),16481(a,1,2,2,2))].">
      <j1 rule="para" parents="3474 16481"/>
    </justification>
  </clause>

  <clause id="16538">
    <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(15266(a,1),16482(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15266 16482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16539">
    <literal><![CDATA[
      K(x,y * (T(z,u / w) / v5)) = K(x,y * (T(z,w \ u) / v5))
    ]]></literal>
    <justification jstring="[para(8223(a,1),16483(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8223 16483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16540">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * v5)) = K(x,y * (T(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(7688(a,1),16484(a,1,2,2,1))].">
      <j1 rule="para" parents="7688 16484"/>
    </justification>
  </clause>

  <clause id="16541">
    <literal><![CDATA[
      K(x,y * (T(z,u / w) * v5)) = K(x,y * (T(z,w \ u) * v5))
    ]]></literal>
    <justification jstring="[para(8223(a,1),16484(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8223 16484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16542">
    <literal><![CDATA[
      K(x \ K(y,z * (u * y)),w) = K(x \ K(y,u * z),w)
    ]]></literal>
    <justification jstring="[hyper(334,a,13455,a(flip),b,16487,a),flip(a)].">
      <j1 rule="hyper" parents="334 13455 16487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16543">
    <literal><![CDATA[
      K(x,T(y,(z / y) * u) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[para(10665(a,2),16492(a,2,2))].">
      <j1 rule="para" parents="10665 16492"/>
    </justification>
  </clause>

  <clause id="16544">
    <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(16495(a,2),15705(a,1))].">
      <j1 rule="para" parents="16495 15705"/>
    </justification>
  </clause>

  <clause id="16545">
    <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(16497(a,2),16183(a,1))].">
      <j1 rule="para" parents="16497 16183"/>
    </justification>
  </clause>

  <clause id="16546">
    <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(16499(a,1),16066(a,1))].">
      <j1 rule="para" parents="16499 16066"/>
    </justification>
  </clause>

  <clause id="16547">
    <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,15567,a(flip),b,16513,a),flip(a)].">
      <j1 rule="hyper" parents="58 15567 16513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16548">
    <literal><![CDATA[
      T(x,y * (z \ K(y,u))) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[para(14063(a,1),16513(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14063 16513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16549">
    <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(15624(a,1),16548(a,1,2,2,2))].">
      <j1 rule="para" parents="15624 16548"/>
    </justification>
  </clause>

  <clause id="16550">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w * u))) = K(x,y * (w * T(u,z)))
    ]]></literal>
    <justification jstring="[para(6432(a,1),16518(a,2,2,2))].">
      <j1 rule="para" parents="6432 16518"/>
    </justification>
  </clause>

  <clause id="16551">
    <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,14441,a(flip),b,16521,a),flip(a)].">
      <j1 rule="hyper" parents="58 14441 16521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16552">
    <literal><![CDATA[
      K(x,y * ((z / u) \ K(u,w))) = K(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[para(6368(a,1),16521(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6368 16521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16553">
    <literal><![CDATA[
      K(x,y * ((z * u) \ K(w,u))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(6432(a,1),16521(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6432 16521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16554">
    <literal><![CDATA[
      K(x,y / (z * ((u * w) / u))) = K(x,y * ((z * w) \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(6413(a,1),16521(a,1,2,2))].">
      <j1 rule="para" parents="6413 16521"/>
    </justification>
  </clause>

  <clause id="16555">
    <literal><![CDATA[
      K(x,y * ((z \ (u \ w)) \ K(u,w))) = K(x,y / (z \ (u \ T(w,u))))
    ]]></literal>
    <justification jstring="[para(15384(a,1),16521(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15384 16521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16556">
    <literal><![CDATA[
      K(x,y * (z * K(u,z * y))) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(14015(a,1),16533(a,1,2))].">
      <j1 rule="para" parents="14015 16533"/>
    </justification>
  </clause>

  <clause id="16557">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,K(y,z) * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(118,a,16536,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 16536 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16558">
    <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(14559(a,1),16556(a,1,2,2))].">
      <j1 rule="para" parents="14559 16556"/>
    </justification>
  </clause>

  <clause id="16559">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,T(u,w) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,16208,a(flip),b,16557,a),flip(a)].">
      <j1 rule="hyper" parents="334 16208 16557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16560">
    <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(8164(a,1),16456(a,1,2,2))].">
      <j1 rule="para" parents="8164 16456"/>
    </justification>
  </clause>

  <clause id="16561">
    <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(1529(a,1),16465(a,1,2,2))].">
      <j1 rule="para" parents="1529 16465"/>
    </justification>
  </clause>

  <clause id="16562">
    <literal><![CDATA[
      K(x,y * (K(z,K(u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * v5) = v6
    ]]></literal>
    <justification jstring="[para(7393(a,1),16465(a,1,2,2))].">
      <j1 rule="para" parents="7393 16465"/>
    </justification>
  </clause>

  <clause id="16563">
    <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(8037(a,1),16465(a,1,2,2))].">
      <j1 rule="para" parents="8037 16465"/>
    </justification>
  </clause>

  <clause id="16564">
    <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(12627(a,1),16465(a,1,2,2))].">
      <j1 rule="para" parents="12627 16465"/>
    </justification>
  </clause>

  <clause id="16565">
    <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(16334(a,2),16465(a,1,2,2))].">
      <j1 rule="para" parents="16334 16465"/>
    </justification>
  </clause>

  <clause id="16566">
    <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(15588(a,1),16474(a,1,2,2))].">
      <j1 rule="para" parents="15588 16474"/>
    </justification>
  </clause>

  <clause id="16567">
    <literal><![CDATA[
      K(x,((y * z) / y) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u / z) \ K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(6746(a,1),16515(a,1))].">
      <j1 rule="para" parents="6746 16515"/>
    </justification>
  </clause>

  <clause id="16568">
    <literal><![CDATA[
      K((x / y) \ K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(y,z) / x,u) = w
    ]]></literal>
    <justification jstring="[para(16167(a,1),8325(a,1))].">
      <j1 rule="para" parents="16167 8325"/>
    </justification>
  </clause>

  <clause id="16569">
    <literal><![CDATA[
      K((x / y) \ K(z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(y,z) / x,u) = w
    ]]></literal>
    <justification jstring="[para(15556(a,1),16568(a,1))].">
      <j1 rule="para" parents="15556 16568"/>
    </justification>
  </clause>

  <clause id="16570">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,1 / (z * y))
    ]]></literal>
    <justification jstring="[hyper(334,a,5608,a(flip),b,16187,a),flip(a)].">
      <j1 rule="hyper" parents="334 5608 16187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16571">
    <literal><![CDATA[
      K(x,y / (y * (y * z))) = K(x,1 / (z * y))
    ]]></literal>
    <justification jstring="[hyper(8738,a,16570,a)].">
      <j1 rule="hyper" parents="8738 16570"/>
    </justification>
  </clause>

  <clause id="16573">
    <literal><![CDATA[
      K(x / (x / y),z * ((x / y) / x)) = K(y,T(((x / y) / x) * z,x))
    ]]></literal>
    <justification jstring="[hyper(12656,a,16194,a)].">
      <j1 rule="hyper" parents="12656 16194"/>
    </justification>
  </clause>

  <clause id="16574">
    <literal><![CDATA[
      T(x * T(y,x * K(z,u)),K(z,u)) = y * T(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(8121,a,16211,a)].">
      <j1 rule="hyper" parents="8121 16211"/>
    </justification>
  </clause>

  <clause id="16576">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / y)) = K(x,u / (z * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15503,a(flip),b,16222,a)].">
      <j1 rule="hyper" parents="58 15503 16222"/>
    </justification>
  </clause>

  <clause id="16577">
    <literal><![CDATA[
      K(x,y / (z * (u / z))) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(16244,a,16576,a),flip(a)].">
      <j1 rule="hyper" parents="16244 16576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16578">
    <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,15406,a(flip),b,16577,a),flip(a)].">
      <j1 rule="hyper" parents="58 15406 16577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16579">
    <literal><![CDATA[
      K(x,y / T(z * u,u)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(6(a,1),16577(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6 16577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16580">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) = K(x,y / (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(4089(a,2),16577(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4089 16577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16581">
    <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,12606,a,b,16225,a)].">
      <j1 rule="hyper" parents="58 12606 16225"/>
    </justification>
  </clause>

  <clause id="16582">
    <literal><![CDATA[
      K(x,y) \ K(L(x,z,u),y) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,14671,a(flip),b,16245,a),flip(a)].">
      <j1 rule="hyper" parents="58 14671 16245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16583">
    <literal><![CDATA[
      T(x,K(y,z * (x * u))) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8632,a,16270,a),flip(a)].">
      <j1 rule="hyper" parents="8632 16270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16584">
    <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(334,a,15963,a,b,16272,a),flip(a)].">
      <j1 rule="hyper" parents="334 15963 16272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16585">
    <literal><![CDATA[
      T(L(K(x,y),z \ u,z),u / z) = u \ (z * (K(x,y) * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,814,a(flip),b,16275,a),flip(a)].">
      <j1 rule="hyper" parents="334 814 16275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16586">
    <literal><![CDATA[
      K(x * T(y * z,z),u) = K(x * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16259,a(flip),b,16279,a),flip(a)].">
      <j1 rule="hyper" parents="58 16259 16279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16587">
    <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,15848,a,b,16290,a)].">
      <j1 rule="hyper" parents="58 15848 16290"/>
    </justification>
  </clause>

  <clause id="16588">
    <literal><![CDATA[
      (x * K(y,z)) \ z = K(z,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,14541,a(flip),b,16359,a)].">
      <j1 rule="hyper" parents="58 14541 16359"/>
    </justification>
  </clause>

  <clause id="16589">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ z = K(z,T(y,u)) * (x \ z)
    ]]></literal>
    <justification jstring="[para(7403(a,1),16588(a,1,1,2))].">
      <j1 rule="para" parents="7403 16588"/>
    </justification>
  </clause>

  <clause id="16590">
    <literal><![CDATA[
      K(x,y) * ((z \ T(x,y)) \ x) = (z \ x) \ x
    ]]></literal>
    <justification jstring="[para(14046(a,1),16588(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14046 16588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16591">
    <literal><![CDATA[
      K(x,y) * ((z \ y) \ y) = (z \ T(y,x)) \ y
    ]]></literal>
    <justification jstring="[hyper(5409,a,16590,a)].">
      <j1 rule="hyper" parents="5409 16590"/>
    </justification>
  </clause>

  <clause id="16592">
    <literal><![CDATA[
      T(x * K(y,z),x \ z) = (x \ T(z,y)) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,14823,a,b,16591,a)].">
      <j1 rule="hyper" parents="58 14823 16591"/>
    </justification>
  </clause>

  <clause id="16593">
    <literal><![CDATA[
      (x * K(y,T(z \ u,z))) \ (z \ u) = K(u / z,y) * (x \ (z \ u))
    ]]></literal>
    <justification jstring="[para(8180(a,1),16589(a,2,1))].">
      <j1 rule="para" parents="8180 16589"/>
    </justification>
  </clause>

  <clause id="16594">
    <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,13046,a(flip),b,16393,a),flip(a)].">
      <j1 rule="hyper" parents="58 13046 16393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16595">
    <literal><![CDATA[
      K(x,y * (K(z / u,w) * v5)) = K(x,y * (K(u \ z,w) * v5))
    ]]></literal>
    <justification jstring="[para(7414(a,1),16486(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7414 16486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16596">
    <literal><![CDATA[
      K(x,T(y * ((y / z) / y),y) / u) = K(x,(z \ T(y,z \ 1)) / u)
    ]]></literal>
    <justification jstring="[para(4096(a,1),16493(a,1,2,1,1))].">
      <j1 rule="para" parents="4096 16493"/>
    </justification>
  </clause>

  <clause id="16597">
    <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(16494(a,1),7970(a,1))].">
      <j1 rule="para" parents="16494 7970"/>
    </justification>
  </clause>

  <clause id="16598">
    <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,15837,a,b,16520,a)].">
      <j1 rule="hyper" parents="58 15837 16520"/>
    </justification>
  </clause>

  <clause id="16599">
    <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,14152,a,b,16520,a)].">
      <j1 rule="hyper" parents="58 14152 16520"/>
    </justification>
  </clause>

  <clause id="16600">
    <literal><![CDATA[
      K(x,y * (z / (u / (u / w)))) = K(x,y * (K(w,u) * (z / w)))
    ]]></literal>
    <justification jstring="[para(6745(a,2),16520(a,1,2,2))].">
      <j1 rule="para" parents="6745 16520"/>
    </justification>
  </clause>

  <clause id="16601">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w * u))) = K(x,y * (w * (z * (u / z))))
    ]]></literal>
    <justification jstring="[para(10611(a,1),16520(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10611 16520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16602">
    <literal><![CDATA[
      K(x,y * (T(z,u) * (w * (u / w)))) = K(x,y * ((w * (u / w)) * z))
    ]]></literal>
    <justification jstring="[hyper(15657,a,16540,a),flip(a)].">
      <j1 rule="hyper" parents="15657 16540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16603">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(u,w))) = K(x,y * (T(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(15656,a,16540,a),flip(a)].">
      <j1 rule="hyper" parents="15656 16540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16604">
    <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(16540(a,1),15656(a,1))].">
      <j1 rule="para" parents="16540 15656"/>
    </justification>
  </clause>

  <clause id="16605">
    <literal><![CDATA[
      K(x,y * T((z / u) \ 1,z)) = K(x,y / (z / T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13520,a,b,16552,a)].">
      <j1 rule="hyper" parents="58 13520 16552"/>
    </justification>
  </clause>

  <clause id="16606">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z \ 1))) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(15645,a,16580,a),flip(a)].">
      <j1 rule="hyper" parents="15645 16580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16607">
    <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,15456,a(flip),b,16606,a),flip(a)].">
      <j1 rule="hyper" parents="58 15456 16606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16608">
    <literal><![CDATA[
      K(x,K(y,L(z / u,u,w))) = K(x,K(y,(w * z) / (w * u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,16091,a,b,16106,a),flip(a)].">
      <j1 rule="hyper" parents="334 16091 16106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16609">
    <literal><![CDATA[
      K(x,K((y \ z) / u,L(w,u,y))) = K(x,K(w,z / (y * u)))
    ]]></literal>
    <justification jstring="[hyper(16234,a,16235,a)].">
      <j1 rule="hyper" parents="16234 16235"/>
    </justification>
  </clause>

  <clause id="16610">
    <literal><![CDATA[
      K(x,y * (x \ (z \ x))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(16265,a,16013,a)].">
      <j1 rule="hyper" parents="16265 16013"/>
    </justification>
  </clause>

  <clause id="16611">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(12745,a,16610,a),flip(a)].">
      <j1 rule="hyper" parents="12745 16610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16612">
    <literal><![CDATA[
      K(x,y / (x \ z)) = K(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(8741,a,16611,a)].">
      <j1 rule="hyper" parents="8741 16611"/>
    </justification>
  </clause>

  <clause id="16613">
    <literal><![CDATA[
      T(x,y / (x \ z)) = T(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(118,a,16612,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 16612 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16614">
    <literal><![CDATA[
      x / (K(y,z * (u \ y)) * x) = K(z / (y \ u),y)
    ]]></literal>
    <justification jstring="[para(16612(a,1),5403(a,1,2,1))].">
      <j1 rule="para" parents="16612 5403"/>
    </justification>
  </clause>

  <clause id="16615">
    <literal><![CDATA[
      T(x,(x * y) / z) = T(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,8761,a,b,16613,a)].">
      <j1 rule="hyper" parents="58 8761 16613"/>
    </justification>
  </clause>

  <clause id="16616">
    <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(16615(a,1),15442(a,1,1,1,1))].">
      <j1 rule="para" parents="16615 15442"/>
    </justification>
  </clause>

  <clause id="16617">
    <literal><![CDATA[
      K(x / (y \ z),y) = K(x * (z \ y),y)
    ]]></literal>
    <justification jstring="[hyper(16144,a,16614,a),flip(a)].">
      <j1 rule="hyper" parents="16144 16614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16618">
    <literal><![CDATA[
      K(x * (y \ z),z) * ((z * x) / y) = T((z * x) / y,z)
    ]]></literal>
    <justification jstring="[para(16617(a,1),8822(a,1,1))].">
      <j1 rule="para" parents="16617 8822"/>
    </justification>
  </clause>

  <clause id="16619">
    <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(6522(a,1),16454(a,1,2,1,1))].">
      <j1 rule="para" parents="6522 16454"/>
    </justification>
  </clause>

  <clause id="16620">
    <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(15667(a,1),16454(a,1))].">
      <j1 rule="para" parents="15667 16454"/>
    </justification>
  </clause>

  <clause id="16621">
    <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(16518(a,1),16462(a,1))].">
      <j1 rule="para" parents="16518 16462"/>
    </justification>
  </clause>

  <clause id="16622">
    <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(8223(a,1),16464(a,1,2,2,2))].">
      <j1 rule="para" parents="8223 16464"/>
    </justification>
  </clause>

  <clause id="16623">
    <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(14276(a,2),16505(a,1))].">
      <j1 rule="para" parents="14276 16505"/>
    </justification>
  </clause>

  <clause id="16624">
    <literal><![CDATA[
      K(x,(y * z) \ T(u,z * (y * x))) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(16507,a,15775,a)].">
      <j1 rule="hyper" parents="16507 15775"/>
    </justification>
  </clause>

  <clause id="16625">
    <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(16398(a,1),16525(a,1,2,2))].">
      <j1 rule="para" parents="16398 16525"/>
    </justification>
  </clause>

  <clause id="16627">
    <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(6522(a,1),16561(a,1,2,2,2))].">
      <j1 rule="para" parents="6522 16561"/>
    </justification>
  </clause>

  <clause id="16628">
    <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(7688(a,1),16561(a,1,2,2,2))].">
      <j1 rule="para" parents="7688 16561"/>
    </justification>
  </clause>

  <clause id="16629">
    <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(14236(a,1),16561(a,1,2,2,2))].">
      <j1 rule="para" parents="14236 16561"/>
    </justification>
  </clause>

  <clause id="16630">
    <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(7688(a,1),16563(a,1,2,2,2))].">
      <j1 rule="para" parents="7688 16563"/>
    </justification>
  </clause>

  <clause id="16631">
    <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(14236(a,1),16563(a,1,2,2,2))].">
      <j1 rule="para" parents="14236 16563"/>
    </justification>
  </clause>

  <clause id="16632">
    <literal><![CDATA[
      K(x,(y / z) \ K(u,z)) = K(x,T(z,u) / y)
    ]]></literal>
    <justification jstring="[hyper(16567,a,15531,a)].">
      <j1 rule="hyper" parents="16567 15531"/>
    </justification>
  </clause>

  <clause id="16633">
    <literal><![CDATA[
      K(x,(y / z) \ K(z,u)) = K(x,T(z,u) / y)
    ]]></literal>
    <justification jstring="[hyper(15643,a,16632,a)].">
      <j1 rule="hyper" parents="15643 16632"/>
    </justification>
  </clause>

  <clause id="16634">
    <literal><![CDATA[
      K(x,(y / z) \ K(z,u \ w)) = K(x,T(z,w / u) / y)
    ]]></literal>
    <justification jstring="[hyper(16560,a,16633,a)].">
      <j1 rule="hyper" parents="16560 16633"/>
    </justification>
  </clause>

  <clause id="16635">
    <literal><![CDATA[
      K(x,T(y,y / z) / u) = K(x,(u / y) \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15894,a(flip),b,16634,a),flip(a)].">
      <j1 rule="hyper" parents="58 15894 16634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16636">
    <literal><![CDATA[
      K(x,T(y,y / z) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(334,a,16633,a(flip),b,16635,a),flip(a)].">
      <j1 rule="hyper" parents="334 16633 16635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16637">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,u)) = K(x,T(y,z) / (u * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(15234,a,16636,a)].">
      <j1 rule="hyper" parents="15234 16636"/>
    </justification>
  </clause>

  <clause id="16638">
    <literal><![CDATA[
      K(x,T(y,z \ y) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16442,a(flip),b,16636,a)].">
      <j1 rule="hyper" parents="58 16442 16636"/>
    </justification>
  </clause>

  <clause id="16639">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ y)) / w) = K(x,T(y,u * z) / w)
    ]]></literal>
    <justification jstring="[para(14331(a,1),16638(a,1,2,1))].">
      <j1 rule="para" parents="14331 16638"/>
    </justification>
  </clause>

  <clause id="16640">
    <literal><![CDATA[
      K(x,T(y,z \ (y / u)) / w) = K(x,T(y,u * z) / w)
    ]]></literal>
    <justification jstring="[para(10974(a,2),16639(a,1,2,1))].">
      <j1 rule="para" parents="10974 16639"/>
    </justification>
  </clause>

  <clause id="16641">
    <literal><![CDATA[
      K(x,T(y,z * u) / ((y / z) / u)) = K(x,((y / z) / u) \ y)
    ]]></literal>
    <justification jstring="[hyper(16528,a,16640,a),flip(a)].">
      <j1 rule="hyper" parents="16528 16640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16642">
    <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),16608(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6 16608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16643">
    <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(8286(a,2),16608(a,1,2))].">
      <j1 rule="para" parents="8286 16608"/>
    </justification>
  </clause>

  <clause id="16644">
    <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),16609(a,1,2,1,1))].">
      <j1 rule="para" parents="17 16609"/>
    </justification>
  </clause>

  <clause id="16645">
    <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(16416(a,2),16623(a,1))].">
      <j1 rule="para" parents="16416 16623"/>
    </justification>
  </clause>

  <clause id="16646">
    <literal><![CDATA[
      K(x,K(y * z,y * (u * z))) = K(x,K(y * z,L(u,z,y)))
    ]]></literal>
    <justification jstring="[hyper(8535,a,16642,a)].">
      <j1 rule="hyper" parents="8535 16642"/>
    </justification>
  </clause>

  <clause id="16647">
    <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(16646(a,1),8690(a,1,1))].">
      <j1 rule="para" parents="16646 8690"/>
    </justification>
  </clause>

  <clause id="16648">
    <literal><![CDATA[
      T(x * T(x \ y,T(z,y)),x) = T(y,x) * K(y / T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,1617,a,b,15996,a)].">
      <j1 rule="hyper" parents="334 1617 15996"/>
    </justification>
  </clause>

  <clause id="16651">
    <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(5963(a,1),16104(a,2,2))].">
      <j1 rule="para" parents="5963 16104"/>
    </justification>
  </clause>

  <clause id="16652">
    <literal><![CDATA[
      K(x,T(L(K(y,z),u,w),v5)) = K(x,L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,11227,a(flip),b,16651,a),flip(a)].">
      <j1 rule="hyper" parents="334 11227 16651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16653">
    <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(16652(a,2),11145(a,1))].">
      <j1 rule="para" parents="16652 11145"/>
    </justification>
  </clause>

  <clause id="16654">
    <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(16132(a,1),15429(a,1,1))].">
      <j1 rule="para" parents="16132 15429"/>
    </justification>
  </clause>

  <clause id="16656">
    <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(16284(a,1),15583(a,1,2,2))].">
      <j1 rule="para" parents="16284 15583"/>
    </justification>
  </clause>

  <clause id="16657">
    <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(16348(a,1),15471(a,1,1,2,1))].">
      <j1 rule="para" parents="16348 15471"/>
    </justification>
  </clause>

  <clause id="16658">
    <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(16200(a,1),16354(a,1,1,1))].">
      <j1 rule="para" parents="16200 16354"/>
    </justification>
  </clause>

  <clause id="16659">
    <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,14082,a,b,16517,a)].">
      <j1 rule="hyper" parents="58 14082 16517"/>
    </justification>
  </clause>

  <clause id="16660">
    <literal><![CDATA[
      K(x * (((y * z) / y) \ u),w) = K(x * (K(z,y) * (z \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(334,a,16427,a,b,16523,a),flip(a)].">
      <j1 rule="hyper" parents="334 16427 16523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16661">
    <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(16541(a,1),15656(a,1))].">
      <j1 rule="para" parents="16541 15656"/>
    </justification>
  </clause>

  <clause id="16662">
    <literal><![CDATA[
      K(x,y * (z / (u / (u / w)))) = K(x,y * (z / T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,16519,a(flip),b,16600,a),flip(a)].">
      <j1 rule="hyper" parents="334 16519 16600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16663">
    <literal><![CDATA[
      K(x,y * (z / T(u,u \ w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15809,a,b,16662,a)].">
      <j1 rule="hyper" parents="58 15809 16662"/>
    </justification>
  </clause>

  <clause id="16664">
    <literal><![CDATA[
      K(x,y * (z / ((u \ w) \ w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16537,a(flip),b,16663,a)].">
      <j1 rule="hyper" parents="58 16537 16663"/>
    </justification>
  </clause>

  <clause id="16665">
    <literal><![CDATA[
      T(x,y * (z / ((u \ w) \ w))) = T(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(118,a,16664,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 16664 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16666">
    <literal><![CDATA[
      K(x,y * (z * (u * (w / u)))) = K(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16550,a(flip),b,16601,a),flip(a)].">
      <j1 rule="hyper" parents="58 16550 16601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16667">
    <literal><![CDATA[
      K(x,y * (z * T(u * w,w))) = K(x,y * (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(6(a,1),16666(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6 16666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16668">
    <literal><![CDATA[
      K(x,y * ((z * u) * u)) = K(x,y * (u * (u * z)))
    ]]></literal>
    <justification jstring="[para(105(a,1),16667(a,1,2,2))].">
      <j1 rule="para" parents="105 16667"/>
    </justification>
  </clause>

  <clause id="16669">
    <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(7782(a,2),16668(a,2,2,2,2))].">
      <j1 rule="para" parents="7782 16668"/>
    </justification>
  </clause>

  <clause id="16670">
    <literal><![CDATA[
      T(x,y) * K(x / T(y,x),z) = T(x * K(x / y,z),y)
    ]]></literal>
    <justification jstring="[para(8249(a,1),16648(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8249 16648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16671">
    <literal><![CDATA[
      T(x * K(x / y,z),y) = T(x,y) * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(13022(a,1),16670(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13022 16670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16672">
    <literal><![CDATA[
      T(x * K(x / y,z),y) = K(x / y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,16158,a(flip),b,16671,a),flip(a)].">
      <j1 rule="hyper" parents="334 16158 16671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16673">
    <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(5391(a,1),16076(a,1,2,1))].">
      <j1 rule="para" parents="5391 16076"/>
    </justification>
  </clause>

  <clause id="16674">
    <literal><![CDATA[
      K(x,y * (z * K(u \ 1,w))) = K(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16182,a(flip),b,16287,a),flip(a)].">
      <j1 rule="hyper" parents="58 16182 16287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16675">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * (u * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,7194,a,b,16674,a)].">
      <j1 rule="hyper" parents="58 7194 16674"/>
    </justification>
  </clause>

  <clause id="16676">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(5020(a,2),16675(a,2,2,2))].">
      <j1 rule="para" parents="5020 16675"/>
    </justification>
  </clause>

  <clause id="16677">
    <literal><![CDATA[
      K(x,y / ((z * (u \ 1)) / z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(14400,a,16676,a)].">
      <j1 rule="hyper" parents="14400 16676"/>
    </justification>
  </clause>

  <clause id="16678">
    <literal><![CDATA[
      K(x,y / T(z \ 1,u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(15688,a,16677,a)].">
      <j1 rule="hyper" parents="15688 16677"/>
    </justification>
  </clause>

  <clause id="16679">
    <literal><![CDATA[
      K(x,y * T(z,z * (x * y))) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(14413,a,16678,a),flip(a)].">
      <j1 rule="hyper" parents="14413 16678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16680">
    <literal><![CDATA[
      K(x,L(y / T(z \ 1,u),w,v5)) = K(L(x,w,v5),y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(11169,a,16678,a)].">
      <j1 rule="hyper" parents="11169 16678"/>
    </justification>
  </clause>

  <clause id="16681">
    <literal><![CDATA[
      T(x,y / T(z \ 1,u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,16678,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 16678 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16682">
    <literal><![CDATA[
      K(x,y / T(1 / z,u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,5593,a,b,16678,a)].">
      <j1 rule="hyper" parents="58 5593 16678"/>
    </justification>
  </clause>

  <clause id="16683">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) * T(z,u)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16578,a(flip),b,16678,a),flip(a)].">
      <j1 rule="hyper" parents="58 16578 16678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16684">
    <literal><![CDATA[
      K(x,y * T(1 / z,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(75(a,1),16678(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="75 16678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16685">
    <literal><![CDATA[
      K(x,y * T(z,x * y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(13486,a,16679,a)].">
      <j1 rule="hyper" parents="13486 16679"/>
    </justification>
  </clause>

  <clause id="16686">
    <literal><![CDATA[
      T(x,y * T(z,x * y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,16685,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 16685 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16687">
    <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,15467,a,b,16686,a)].">
      <j1 rule="hyper" parents="58 15467 16686"/>
    </justification>
  </clause>

  <clause id="16688">
    <literal><![CDATA[
      T(x,y / T(1 / z,u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,3993,a,b,16681,a)].">
      <j1 rule="hyper" parents="58 3993 16681"/>
    </justification>
  </clause>

  <clause id="16689">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),v5)) = T(x,y * T(K(w,u) / z,v5))
    ]]></literal>
    <justification jstring="[para(14267(a,1),16681(a,1,2,2,1))].">
      <j1 rule="para" parents="14267 16681"/>
    </justification>
  </clause>

  <clause id="16690">
    <literal><![CDATA[
      K(x,y * T(z \ 1,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),16682(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="72 16682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16691">
    <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,15935,a(flip),b,16684,a),flip(a)].">
      <j1 rule="hyper" parents="58 15935 16684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16692">
    <literal><![CDATA[
      T(x,y / T(K(z,u) * w,v5)) = T(x,y * T(w \ K(u,z),v5))
    ]]></literal>
    <justification jstring="[para(14147(a,1),16688(a,1,2,2,1))].">
      <j1 rule="para" parents="14147 16688"/>
    </justification>
  </clause>

  <clause id="16693">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y / T(z / u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16605,a(flip),b,16690,a)].">
      <j1 rule="hyper" parents="58 16605 16690"/>
    </justification>
  </clause>

  <clause id="16694">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(334,a,13353,a(flip),b,16693,a),flip(a)].">
      <j1 rule="hyper" parents="334 13353 16693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16695">
    <literal><![CDATA[
      K(x,y / (T(z,u) / u)) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9056,a,b,16694,a)].">
      <j1 rule="hyper" parents="58 9056 16694"/>
    </justification>
  </clause>

  <clause id="16696">
    <literal><![CDATA[
      K(x,T(y,z * u) * T(u,z)) = K(x,T(u * y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15767,a(flip),b,16683,a)].">
      <j1 rule="hyper" parents="58 15767 16683"/>
    </justification>
  </clause>

  <clause id="16697">
    <literal><![CDATA[
      K(x,T(y * ((z * y) \ u),z)) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15653,a(flip),b,16696,a),flip(a)].">
      <j1 rule="hyper" parents="58 15653 16696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16698">
    <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(6108(a,1),16696(a,1,2,1))].">
      <j1 rule="para" parents="6108 16696"/>
    </justification>
  </clause>

  <clause id="16699">
    <literal><![CDATA[
      K(x,y * ((z * y) \ T(u,z))) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15817,a(flip),b,16697,a)].">
      <j1 rule="hyper" parents="58 15817 16697"/>
    </justification>
  </clause>

  <clause id="16700">
    <literal><![CDATA[
      K(x,y * ((T(z,u) * y) \ u)) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[para(14041(a,2),16699(a,1,2,2))].">
      <j1 rule="para" parents="14041 16699"/>
    </justification>
  </clause>

  <clause id="16701">
    <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(334,a,11137,a(flip),b,16680,a),flip(a)].">
      <j1 rule="hyper" parents="334 11137 16680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16702">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),v5)) = T(x,y * T(z \ K(w,u),v5))
    ]]></literal>
    <justification jstring="[hyper(334,a,16419,a(flip),b,16689,a),flip(a)].">
      <j1 rule="hyper" parents="334 16419 16689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16703">
    <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(14537,a,16701,a)].">
      <j1 rule="hyper" parents="14537 16701"/>
    </justification>
  </clause>

  <clause id="16704">
    <literal><![CDATA[
      T(x,((y \ z) * y) * K(u,w)) = T(x,T(K(u,w) * z,y))
    ]]></literal>
    <justification jstring="[hyper(16304,a,16557,a(flip))].">
      <j1 rule="hyper" parents="16304 16557"/>
    </justification>
  </clause>

  <clause id="16705">
    <literal><![CDATA[
      L(K(x \ y,z),u,x / y) = K(T(1 / (y \ x),K(w,v5)),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,6645,a(flip),b,16307,a)].">
      <j1 rule="hyper" parents="334 6645 16307"/>
    </justification>
  </clause>

  <clause id="16706">
    <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),16705(a,1,1,1))].">
      <j1 rule="para" parents="4 16705"/>
    </justification>
  </clause>

  <clause id="16707">
    <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(16595(a,1),16502(a,1))].">
      <j1 rule="para" parents="16595 16502"/>
    </justification>
  </clause>

  <clause id="16708">
    <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(16518(a,1),16503(a,1))].">
      <j1 rule="para" parents="16518 16503"/>
    </justification>
  </clause>

  <clause id="16709">
    <literal><![CDATA[
      T(L(K(x,y),z / u,u),z / u) = z \ (u * (K(x,y) * (u \ z)))
    ]]></literal>
    <justification jstring="[para(11478(a,2),16585(a,1,1))].">
      <j1 rule="para" parents="11478 16585"/>
    </justification>
  </clause>

  <clause id="16710">
    <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(8218(a,1),16604(a,1,2,2,2))].">
      <j1 rule="para" parents="8218 16604"/>
    </justification>
  </clause>

  <clause id="16711">
    <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(16666(a,2),16604(a,1))].">
      <j1 rule="para" parents="16666 16604"/>
    </justification>
  </clause>

  <clause id="16712">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ T(z / u,z))) = K(x,y * (z \ (z / u)))
    ]]></literal>
    <justification jstring="[hyper(16628,a,15630,a)].">
      <j1 rule="hyper" parents="16628 15630"/>
    </justification>
  </clause>

  <clause id="16713">
    <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(14326(a,1),16628(a,1,2,2))].">
      <j1 rule="para" parents="14326 16628"/>
    </justification>
  </clause>

  <clause id="16714">
    <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,15103,a(flip),b,16673,a)].">
      <j1 rule="hyper" parents="58 15103 16673"/>
    </justification>
  </clause>

  <clause id="16715">
    <literal><![CDATA[
      L(K(x,y),z,u / (u * x)) = K(1 / ((u * x) \ u),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,16005,a(flip),b,16706,a),flip(a)].">
      <j1 rule="hyper" parents="334 16005 16706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16716">
    <literal><![CDATA[
      L(K(x,y),z,u / (u * x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(16715(a,2),6673(a,1))].">
      <j1 rule="para" parents="16715 6673"/>
    </justification>
  </clause>

  <clause id="16717">
    <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(334,a,5391,a(flip),b,16079,a),flip(a)].">
      <j1 rule="hyper" parents="334 5391 16079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16719">
    <literal><![CDATA[
      K((x * (y / x)) / z,u) = K(z,K(y,u)) * K(z \ T(y,x),u)
    ]]></literal>
    <justification jstring="[para(15575(a,1),16107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15575 16107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16721">
    <literal><![CDATA[
      K((x * (y / x)) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,16115,a(flip),b,16719,a),flip(a)].">
      <j1 rule="hyper" parents="334 16115 16719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16722">
    <literal><![CDATA[
      K(T(x * y,y) / z,u) = K((y * x) / z,u)
    ]]></literal>
    <justification jstring="[para(6(a,1),16721(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6 16721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16723">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) = (w * K((z * y) / u,x)) \ w
    ]]></literal>
    <justification jstring="[para(16722(a,1),6523(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="16722 6523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16724">
    <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(14462(a,1),16722(a,2,1,1))].">
      <j1 rule="para" parents="14462 16722"/>
    </justification>
  </clause>

  <clause id="16725">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[hyper(334,a,16010,a(flip),b,16723,a),flip(a)].">
      <j1 rule="hyper" parents="334 16010 16723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16726">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) / u) = w
    ]]></literal>
    <justification jstring="[para(16723(a,2),6528(a,1))].">
      <j1 rule="para" parents="16723 6528"/>
    </justification>
  </clause>

  <clause id="16727">
    <literal><![CDATA[
      K(x,(y * (z / y)) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(7(a,1),16725(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 16725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16728">
    <literal><![CDATA[
      K(x,(y * ((y * z) / y)) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[hyper(334,a,13373,a(flip),b,16727,a),flip(a)].">
      <j1 rule="hyper" parents="334 13373 16727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16729">
    <literal><![CDATA[
      K(x,T(y,z) / (u * (y / z))) = K(x,y / (u * (z \ y)))
    ]]></literal>
    <justification jstring="[para(14569(a,1),16727(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14569 16727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16730">
    <literal><![CDATA[
      K(x,(T(y,z) * z) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[para(231(a,1),16728(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="231 16728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16731">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,u,z)) = K(x,(z * y) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(15144,a,16730,a)].">
      <j1 rule="hyper" parents="15144 16730"/>
    </justification>
  </clause>

  <clause id="16732">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,u)) = K(x,y / (u * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16637,a,b,16729,a)].">
      <j1 rule="hyper" parents="58 16637 16729"/>
    </justification>
  </clause>

  <clause id="16733">
    <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,13483,a(flip),b,16186,a),flip(a)].">
      <j1 rule="hyper" parents="58 13483 16186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16734">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),w)) = K(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(334,a,16185,a(flip),b,16733,a),flip(a)].">
      <j1 rule="hyper" parents="334 16185 16733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16735">
    <literal><![CDATA[
      K(x,T(y / T(z,u),z * u)) = K(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15956,a(flip),b,16734,a),flip(a)].">
      <j1 rule="hyper" parents="58 15956 16734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16736">
    <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),16300(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 16300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16737">
    <literal><![CDATA[
      K(T(x,y) * z,T(u,y * x)) = K(T(z,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,14178,a(flip),b,16736,a),flip(a)].">
      <j1 rule="hyper" parents="334 14178 16736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16739">
    <literal><![CDATA[
      K(x * T(y,z),T(u,z * y)) = K(T(x,z) * y,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(16361,a,16737,a)].">
      <j1 rule="hyper" parents="16361 16737"/>
    </justification>
  </clause>

  <clause id="16740">
    <literal><![CDATA[
      K(x * T(y,z),T(u,z * y)) = K(y * T(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,12516,a(flip),b,16739,a),flip(a)].">
      <j1 rule="hyper" parents="334 12516 16739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16741">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) = K(x * T(z * y,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16329,a(flip),b,16740,a)].">
      <j1 rule="hyper" parents="58 16329 16740"/>
    </justification>
  </clause>

  <clause id="16742">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) = K(x * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,16586,a(flip),b,16741,a),flip(a)].">
      <j1 rule="hyper" parents="334 16586 16741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16743">
    <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,16742,a(flip),b,8338,a)].">
      <j1 rule="hyper" parents="116 16742 8338"/>
    </justification>
  </clause>

  <clause id="16744">
    <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),16742(a,1,1,2))].">
      <j1 rule="para" parents="99 16742"/>
    </justification>
  </clause>

  <clause id="16745">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z \ y,u) \ y) = T(x,T(y / z,u) \ y)
    ]]></literal>
    <justification jstring="[para(8440(a,1),16336(a,1,1))].">
      <j1 rule="para" parents="8440 16336"/>
    </justification>
  </clause>

  <clause id="16746">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y \ z,u) \ z) = T(x,T(z / y,u) \ z)
    ]]></literal>
    <justification jstring="[para(8100(a,1),16745(a,1,1))].">
      <j1 rule="para" parents="8100 16745"/>
    </justification>
  </clause>

  <clause id="16747">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z / y,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(8236(a,1),16337(a,1,1))].">
      <j1 rule="para" parents="8236 16337"/>
    </justification>
  </clause>

  <clause id="16748">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * T(y / z,u)) = T(x,z * T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(8100(a,1),16747(a,1,1))].">
      <j1 rule="para" parents="8100 16747"/>
    </justification>
  </clause>

  <clause id="16750">
    <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,10586,a(flip),b,16443,a)].">
      <j1 rule="hyper" parents="58 10586 16443"/>
    </justification>
  </clause>

  <clause id="16751">
    <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(6558(a,2),16538(a,1,2,2))].">
      <j1 rule="para" parents="6558 16538"/>
    </justification>
  </clause>

  <clause id="16752">
    <literal><![CDATA[
      K(x,T(((y / x) / y) * z,y)) = K(x,T(z * ((y / x) / y),y))
    ]]></literal>
    <justification jstring="[hyper(8214,a,16573,a),flip(a)].">
      <j1 rule="hyper" parents="8214 16573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16753">
    <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(334,a,12653,a(flip),b,16581,a),flip(a)].">
      <j1 rule="hyper" parents="334 12653 16581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16754">
    <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(8188(a,1),16584(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8188 16584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16755">
    <literal><![CDATA[
      (x * K(y,z / u)) \ (u \ z) = K(z / u,y) * (x \ (u \ z))
    ]]></literal>
    <justification jstring="[para(8186(a,1),16593(a,1,1,2))].">
      <j1 rule="para" parents="8186 16593"/>
    </justification>
  </clause>

  <clause id="16756">
    <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(16755(a,1),13418(a,1,2,2,1))].">
      <j1 rule="para" parents="16755 13418"/>
    </justification>
  </clause>

  <clause id="16757">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) / u) = K(x,(((z / y) / z) * z) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13373,a(flip),b,16596,a),flip(a)].">
      <j1 rule="hyper" parents="58 13373 16596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16758">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) / u) = K(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[para(7(a,1),16757(a,2,2,1))].">
      <j1 rule="para" parents="7 16757"/>
    </justification>
  </clause>

  <clause id="16760">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ (u \ z))) = K(x,y * (z \ (z / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13473,a(flip),b,16712,a)].">
      <j1 rule="hyper" parents="58 13473 16712"/>
    </justification>
  </clause>

  <clause id="16761">
    <literal><![CDATA[
      K(x,y * ((z \ u) / u)) = K(x,y * (u \ (u / z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15616,a(flip),b,16760,a)].">
      <j1 rule="hyper" parents="58 15616 16760"/>
    </justification>
  </clause>

  <clause id="16762">
    <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(8134,a,16717,a)].">
      <j1 rule="hyper" parents="8134 16717"/>
    </justification>
  </clause>

  <clause id="16763">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(16423,a,16750,a),flip(a)].">
      <j1 rule="hyper" parents="16423 16750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16764">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16750(a,1),16423(a,1))].">
      <j1 rule="para" parents="16750 16423"/>
    </justification>
  </clause>

  <clause id="16766">
    <literal><![CDATA[
      K(x,T(y,z / K(u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(16310,a,16763,a)].">
      <j1 rule="hyper" parents="16310 16763"/>
    </justification>
  </clause>

  <clause id="16767">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(16150,a,16763,a)].">
      <j1 rule="hyper" parents="16150 16763"/>
    </justification>
  </clause>

  <clause id="16770">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = T(K(x,y),w)
    ]]></literal>
    <justification jstring="[hyper(334,a,7401,a(flip),b,16763,a),flip(a)].">
      <j1 rule="hyper" parents="334 7401 16763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16771">
    <literal><![CDATA[
      T(x,T(y,K(z,u) * w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(118,a,16763,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 16763 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16772">
    <literal><![CDATA[
      K(x,T(y,T(z,u) * w)) = K(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(5047(a,1),16763(a,1,2,2))].">
      <j1 rule="para" parents="5047 16763"/>
    </justification>
  </clause>

  <clause id="16773">
    <literal><![CDATA[
      K(x,T(y,T(z,u) \ w)) = K(x,T(y,z \ w))
    ]]></literal>
    <justification jstring="[para(5337(a,1),16763(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5337 16763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16774">
    <literal><![CDATA[
      K(x,T(y,(z / u) * w)) = K(x,T(y,(u \ z) * w))
    ]]></literal>
    <justification jstring="[para(5680(a,1),16763(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5680 16763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16775">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(5666(a,1),16763(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5666 16763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16776">
    <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(16763(a,1),7427(a,1,2))].">
      <j1 rule="para" parents="16763 7427"/>
    </justification>
  </clause>

  <clause id="16779">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w)) = K(x,T(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[para(11459(a,1),16763(a,1,2,2))].">
      <j1 rule="para" parents="11459 16763"/>
    </justification>
  </clause>

  <clause id="16780">
    <literal><![CDATA[
      K(x,T(y,K(z,u) / w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(8557,a,16766,a)].">
      <j1 rule="hyper" parents="8557 16766"/>
    </justification>
  </clause>

  <clause id="16781">
    <literal><![CDATA[
      T(K(x,y),z * K(u,w)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8549,a,16767,a)].">
      <j1 rule="hyper" parents="8549 16767"/>
    </justification>
  </clause>

  <clause id="16786">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) = K(x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(6579(a,1),16767(a,1,2,2))].">
      <j1 rule="para" parents="6579 16767"/>
    </justification>
  </clause>

  <clause id="16787">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,w)) * v5)) = K(x,T(y,z * v5))
    ]]></literal>
    <justification jstring="[para(7105(a,1),16767(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7105 16767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16788">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(u,w)) = (z * K(u,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(16767(a,1),8170(a,1,1))].">
      <j1 rule="para" parents="16767 8170"/>
    </justification>
  </clause>

  <clause id="16792">
    <literal><![CDATA[
      K(x,T(y,z \ (u / w))) = K(x,T(y,z \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(14302(a,1),16767(a,1,2,2))].">
      <j1 rule="para" parents="14302 16767"/>
    </justification>
  </clause>

  <clause id="16793">
    <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(16767(a,1),15113(a,1))].">
      <j1 rule="para" parents="16767 15113"/>
    </justification>
  </clause>

  <clause id="16794">
    <literal><![CDATA[
      K(x,T(y,K(z,u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16767(a,1),16266(a,1))].">
      <j1 rule="para" parents="16767 16266"/>
    </justification>
  </clause>

  <clause id="16795">
    <literal><![CDATA[
      T(K(x,y),K(z,u) * w) = T(K(x,y),w)
    ]]></literal>
    <justification jstring="[hyper(8549,a,16770,a)].">
      <j1 rule="hyper" parents="8549 16770"/>
    </justification>
  </clause>

  <clause id="16796">
    <literal><![CDATA[
      T(x,T(y,K(z,u) \ w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),16771(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 16771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16797">
    <literal><![CDATA[
      T(x,T(y,T(z,u) * w)) = T(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(5047(a,1),16771(a,1,2,2))].">
      <j1 rule="para" parents="5047 16771"/>
    </justification>
  </clause>

  <clause id="16798">
    <literal><![CDATA[
      T(x,T(y,(z * u) * w)) = T(x,T(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[para(11459(a,1),16771(a,1,2,2))].">
      <j1 rule="para" parents="11459 16771"/>
    </justification>
  </clause>

  <clause id="16799">
    <literal><![CDATA[
      T(x,T(y,(T(z,u) * w) * v5)) = T(x,T(y,(z * w) * v5))
    ]]></literal>
    <justification jstring="[para(15183(a,1),16771(a,1,2,2))].">
      <j1 rule="para" parents="15183 16771"/>
    </justification>
  </clause>

  <clause id="16800">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(u,w) / z) = (K(u,w) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(16780(a,1),8170(a,1,1))].">
      <j1 rule="para" parents="16780 8170"/>
    </justification>
  </clause>

  <clause id="16801">
    <literal><![CDATA[
      T(K(x,y),z * K(u,w)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(334,a,7401,a(flip),b,16781,a),flip(a)].">
      <j1 rule="hyper" parents="334 7401 16781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16803">
    <literal><![CDATA[
      (K(x,T(y,z)) * z) * K(x,y) = (x * y) * ((y * x) \ (K(x,y) * z))
    ]]></literal>
    <justification jstring="[para(16781(a,1),11494(a,1,1,1))].">
      <j1 rule="para" parents="16781 11494"/>
    </justification>
  </clause>

  <clause id="16805">
    <literal><![CDATA[
      (K(x,T(y,z)) * u) \ (z * K(x,y)) = (K(x,y) * u) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(16781(a,1),14315(a,1,1,1))].">
      <j1 rule="para" parents="16781 14315"/>
    </justification>
  </clause>

  <clause id="16806">
    <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(16781(a,1),15086(a,1,2,2))].">
      <j1 rule="para" parents="16781 15086"/>
    </justification>
  </clause>

  <clause id="16809">
    <literal><![CDATA[
      T(K(x,y),K(z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16795(a,2),7974(a,1))].">
      <j1 rule="para" parents="16795 7974"/>
    </justification>
  </clause>

  <clause id="16811">
    <literal><![CDATA[
      T(x,T(y,z \ K(u,w))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8548,a,16796,a)].">
      <j1 rule="hyper" parents="8548 16796"/>
    </justification>
  </clause>

  <clause id="16812">
    <literal><![CDATA[
      T(x,T((K(y,z) \ u) \ w,u)) = T(x,w / (K(y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8218,a(flip),b,16796,a),flip(a)].">
      <j1 rule="hyper" parents="58 8218 16796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16815">
    <literal><![CDATA[
      T(K(x,y),z * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(16801(a,2),7974(a,1))].">
      <j1 rule="para" parents="16801 7974"/>
    </justification>
  </clause>

  <clause id="16818">
    <literal><![CDATA[
      T(x * K(y,x),T(y,z)) = T(x,K(y,K(u,w) / z))
    ]]></literal>
    <justification jstring="[hyper(16173,a,16811,a),flip(a)].">
      <j1 rule="hyper" parents="16173 16811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16819">
    <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(16773(a,1),12526(a,1))].">
      <j1 rule="para" parents="16773 12526"/>
    </justification>
  </clause>

  <clause id="16820">
    <literal><![CDATA[
      K(x,T(y,z \ (u / (u / w)))) = K(x,T(y,z \ w))
    ]]></literal>
    <justification jstring="[para(252(a,1),16775(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="252 16775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16821">
    <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(1648(a,1),16764(a,1,2,2))].">
      <j1 rule="para" parents="1648 16764"/>
    </justification>
  </clause>

  <clause id="16822">
    <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(5047(a,1),16764(a,1,2,2))].">
      <j1 rule="para" parents="5047 16764"/>
    </justification>
  </clause>

  <clause id="16823">
    <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(5820(a,1),16764(a,1,2,2))].">
      <j1 rule="para" parents="5820 16764"/>
    </justification>
  </clause>

  <clause id="16824">
    <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(5818(a,1),16764(a,1,2,2))].">
      <j1 rule="para" parents="5818 16764"/>
    </justification>
  </clause>

  <clause id="16825">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(7538(a,1),16764(a,1,2,2))].">
      <j1 rule="para" parents="7538 16764"/>
    </justification>
  </clause>

  <clause id="16826">
    <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(12516(a,1),16764(a,1))].">
      <j1 rule="para" parents="12516 16764"/>
    </justification>
  </clause>

  <clause id="16827">
    <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(6579(a,1),16825(a,1,2,2))].">
      <j1 rule="para" parents="6579 16825"/>
    </justification>
  </clause>

  <clause id="16828">
    <literal><![CDATA[
      K(x,T(y,T(z * u,w) * v5)) = K(x,T(y,(u * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(334,a,16772,a,b,16779,a)].">
      <j1 rule="hyper" parents="334 16772 16779"/>
    </justification>
  </clause>

  <clause id="16829">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z / (u / w))) = K(x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(8345,a,16786,a)].">
      <j1 rule="hyper" parents="8345 16786"/>
    </justification>
  </clause>

  <clause id="16830">
    <literal><![CDATA[
      T(x,K(y,K(z,u) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16818(a,1),7697(a,1))].">
      <j1 rule="para" parents="16818 7697"/>
    </justification>
  </clause>

  <clause id="16831">
    <literal><![CDATA[
      T(x,K(y,z \ K(u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(16830,a,16096,a),flip(a)].">
      <j1 rule="hyper" parents="16830 16096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16832">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) = T(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(16322,a,16831,a)].">
      <j1 rule="hyper" parents="16322 16831"/>
    </justification>
  </clause>

  <clause id="16833">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,K(w,v5) * z)) = u
    ]]></literal>
    <justification jstring="[para(16831(a,1),16322(a,1))].">
      <j1 rule="para" parents="16831 16322"/>
    </justification>
  </clause>

  <clause id="16834">
    <literal><![CDATA[
      T(x,K(y,z \ K(u,w))) = T(x,K(y,K(v5,v6) * z))
    ]]></literal>
    <justification jstring="[hyper(334,a,16831,a,b,16832,a)].">
      <j1 rule="hyper" parents="334 16831 16832"/>
    </justification>
  </clause>

  <clause id="16835">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) = T(x,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,8100,a,b,16832,a),flip(a)].">
      <j1 rule="hyper" parents="334 8100 16832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16836">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) = x * K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,5020,a(flip),b,16832,a),flip(a)].">
      <j1 rule="hyper" parents="334 5020 16832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16837">
    <literal><![CDATA[
      T(x,K(y,(z / u) \ w)) = T(x,K(y,(u \ z) \ w))
    ]]></literal>
    <justification jstring="[para(5656(a,1),16832(a,1,2,2))].">
      <j1 rule="para" parents="5656 16832"/>
    </justification>
  </clause>

  <clause id="16838">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(16832(a,2),8134(a,1))].">
      <j1 rule="para" parents="16832 8134"/>
    </justification>
  </clause>

  <clause id="16839">
    <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(16832(a,1),15465(a,1,2,1,2))].">
      <j1 rule="para" parents="16832 15465"/>
    </justification>
  </clause>

  <clause id="16840">
    <literal><![CDATA[
      T(x,K(y,z * (u * K(w,v5)))) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(16182(a,1),16832(a,1,2))].">
      <j1 rule="para" parents="16182 16832"/>
    </justification>
  </clause>

  <clause id="16841">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(5109,a,16836,a)].">
      <j1 rule="hyper" parents="5109 16836"/>
    </justification>
  </clause>

  <clause id="16842">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(29,a,16228,a,b,16836,a(flip))].">
      <j1 rule="hyper" parents="29 16228 16836"/>
    </justification>
  </clause>

  <clause id="16845">
    <literal><![CDATA[
      K(x,K(y,K(z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,16326,a,b,16841,a)].">
      <j1 rule="hyper" parents="58 16326 16841"/>
    </justification>
  </clause>

  <clause id="16846">
    <literal><![CDATA[
      K(x,K(y,((z * u) / z) * w)) = K(x,K(y,u * w))
    ]]></literal>
    <justification jstring="[para(5490(a,1),16841(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5490 16841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16849">
    <literal><![CDATA[
      K(x,K(y,z / T(u,w))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(8615(a,1),16841(a,1,2,2))].">
      <j1 rule="para" parents="8615 16841"/>
    </justification>
  </clause>

  <clause id="16850">
    <literal><![CDATA[
      K(x,K(y,(z * u) * w)) = K(x,K(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[para(11459(a,1),16841(a,1,2,2))].">
      <j1 rule="para" parents="11459 16841"/>
    </justification>
  </clause>

  <clause id="16851">
    <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(16841(a,1),12616(a,1,1))].">
      <j1 rule="para" parents="16841 12616"/>
    </justification>
  </clause>

  <clause id="16852">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[para(14370(a,1),16841(a,1,2,2))].">
      <j1 rule="para" parents="14370 16841"/>
    </justification>
  </clause>

  <clause id="16853">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) * w) * v5)) = K(x,K(y,(z * w) * v5))
    ]]></literal>
    <justification jstring="[para(15183(a,1),16841(a,1,2,2))].">
      <j1 rule="para" parents="15183 16841"/>
    </justification>
  </clause>

  <clause id="16854">
    <literal><![CDATA[
      K(x,K(y,(K(z,u) * w) / v5)) = K(x,K(y,w / v5))
    ]]></literal>
    <justification jstring="[para(15195(a,1),16841(a,1,2,2))].">
      <j1 rule="para" parents="15195 16841"/>
    </justification>
  </clause>

  <clause id="16855">
    <literal><![CDATA[
      K(x,K(y,z / (u / w))) = K(x,K(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(16241(a,1),16841(a,1,2))].">
      <j1 rule="para" parents="16241 16841"/>
    </justification>
  </clause>

  <clause id="16856">
    <literal><![CDATA[
      K(x,K(y,K(z,u) / w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(8547,a,16842,a)].">
      <j1 rule="hyper" parents="8547 16842"/>
    </justification>
  </clause>

  <clause id="16857">
    <literal><![CDATA[
      K(x,K(y,z / ((u * w) / u))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[para(6410(a,1),16842(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6410 16842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16858">
    <literal><![CDATA[
      K(x,K(y,z / (u / (u / w)))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[para(6744(a,2),16842(a,1,2,2))].">
      <j1 rule="para" parents="6744 16842"/>
    </justification>
  </clause>

  <clause id="16859">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) * v5)) = K(x,K(y,z * v5))
    ]]></literal>
    <justification jstring="[para(7105(a,1),16842(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7105 16842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16860">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * K(u,w)) = T(z * K(u,w),K(x,y))
    ]]></literal>
    <justification jstring="[para(16842(a,1),8064(a,1,1))].">
      <j1 rule="para" parents="16842 8064"/>
    </justification>
  </clause>

  <clause id="16861">
    <literal><![CDATA[
      K(x,K(y,z \ (u / w))) = K(x,K(y,z \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(14302(a,1),16842(a,1,2,2))].">
      <j1 rule="para" parents="14302 16842"/>
    </justification>
  </clause>

  <clause id="16863">
    <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(16845(a,1),16344(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16845 16344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16864">
    <literal><![CDATA[
      K(x,K(y,K(z,u) / w)) = K(x,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,8067,a,b,16856,a),flip(a)].">
      <j1 rule="hyper" parents="334 8067 16856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16865">
    <literal><![CDATA[
      K(x,K(y * K(z,u),w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(8488,a,16864,a),flip(a)].">
      <j1 rule="hyper" parents="8488 16864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16866">
    <literal><![CDATA[
      K(x,K(K(y,z) / u,w)) = K(x,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(8099,a,16864,a)].">
      <j1 rule="hyper" parents="8099 16864"/>
    </justification>
  </clause>

  <clause id="16867">
    <literal><![CDATA[
      K(x,K(y * K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16864(a,1),8488(a,1))].">
      <j1 rule="para" parents="16864 8488"/>
    </justification>
  </clause>

  <clause id="16868">
    <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(11137(a,1),16864(a,1,2))].">
      <j1 rule="para" parents="11137 16864"/>
    </justification>
  </clause>

  <clause id="16869">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w)) = K(x,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(16268,a,16865,a)].">
      <j1 rule="hyper" parents="16268 16865"/>
    </justification>
  </clause>

  <clause id="16870">
    <literal><![CDATA[
      K(x,K(T(y,z) / u,w)) = K(x,K(y / u,w))
    ]]></literal>
    <justification jstring="[para(1542(a,1),16865(a,1,2,1))].">
      <j1 rule="para" parents="1542 16865"/>
    </justification>
  </clause>

  <clause id="16873">
    <literal><![CDATA[
      K(x,K(K(y,z) / u,w)) = K(x,K(u * K(v5,v6),w))
    ]]></literal>
    <justification jstring="[hyper(334,a,16865,a,b,16866,a),flip(a)].">
      <j1 rule="hyper" parents="334 16865 16866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16874">
    <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(11161,a,16869,a)].">
      <j1 rule="hyper" parents="11161 16869"/>
    </justification>
  </clause>

  <clause id="16875">
    <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,16644,a(flip),b,16870,a),flip(a)].">
      <j1 rule="hyper" parents="58 16644 16870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16876">
    <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(16831(a,2),16833(a,1))].">
      <j1 rule="para" parents="16831 16833"/>
    </justification>
  </clause>

  <clause id="16877">
    <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,16834,a(flip),b,8406,a),flip(a)].">
      <j1 rule="hyper" parents="116 16834 8406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16878">
    <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(16834(a,1),8127(a,1))].">
      <j1 rule="para" parents="16834 8127"/>
    </justification>
  </clause>

  <clause id="16879">
    <literal><![CDATA[
      T(x,K(y,z * (u \ T(w,v5)))) = T(x,K(y,z * (u \ w)))
    ]]></literal>
    <justification jstring="[para(1529(a,1),16840(a,1,2,2,2))].">
      <j1 rule="para" parents="1529 16840"/>
    </justification>
  </clause>

  <clause id="16880">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,w / (u * z)))
    ]]></literal>
    <justification jstring="[hyper(8545,a,16852,a),flip(a)].">
      <j1 rule="hyper" parents="8545 16852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16881">
    <literal><![CDATA[
      K(x,K(y,((z * u) * w) / (w * u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(334,a,16642,a(flip),b,16852,a),flip(a)].">
      <j1 rule="hyper" parents="334 16642 16852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16882">
    <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(996(a,1),16852(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="996 16852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16883">
    <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(16852(a,1),8545(a,1))].">
      <j1 rule="para" parents="16852 8545"/>
    </justification>
  </clause>

  <clause id="16884">
    <literal><![CDATA[
      K(x,K(y,z / (K(u,w) * v5))) = K(x,K(y,v5 / z))
    ]]></literal>
    <justification jstring="[hyper(8545,a,16854,a)].">
      <j1 rule="hyper" parents="8545 16854"/>
    </justification>
  </clause>

  <clause id="16885">
    <literal><![CDATA[
      K(x,K(y,(z * T(u,w)) / v5)) = K(x,K(y,(z * u) / v5))
    ]]></literal>
    <justification jstring="[para(5820(a,1),16854(a,1,2,2,1))].">
      <j1 rule="para" parents="5820 16854"/>
    </justification>
  </clause>

  <clause id="16886">
    <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(16855(a,2),11135(a,1,1))].">
      <j1 rule="para" parents="16855 11135"/>
    </justification>
  </clause>

  <clause id="16887">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) / w) * v5)) = K(x,K(y,(z / w) * v5))
    ]]></literal>
    <justification jstring="[para(1542(a,1),16859(a,1,2,2,1))].">
      <j1 rule="para" parents="1542 16859"/>
    </justification>
  </clause>

  <clause id="16888">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * v5)) = K(x,K(y,((u \ z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(6790(a,1),16859(a,1,2,2,1))].">
      <j1 rule="para" parents="6790 16859"/>
    </justification>
  </clause>

  <clause id="16889">
    <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(16859(a,2),16239(a,1))].">
      <j1 rule="para" parents="16859 16239"/>
    </justification>
  </clause>

  <clause id="16890">
    <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,11195,a(flip),b,16873,a),flip(a)].">
      <j1 rule="hyper" parents="58 11195 16873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16891">
    <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(16880(a,1),8545(a,1))].">
      <j1 rule="para" parents="16880 8545"/>
    </justification>
  </clause>

  <clause id="16892">
    <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(16880(a,2),8545(a,1))].">
      <j1 rule="para" parents="16880 8545"/>
    </justification>
  </clause>

  <clause id="16893">
    <literal><![CDATA[
      K(x,K(y,z / ((K(u,w) * v5) * v6))) = K(x,K(y,(v5 * v6) / z))
    ]]></literal>
    <justification jstring="[para(7057(a,1),16884(a,1,2,2,2))].">
      <j1 rule="para" parents="7057 16884"/>
    </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="[para(8213(a,1),16884(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8213 16884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16895">
    <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(16894(a,1),16340(a,1,1))].">
      <j1 rule="para" parents="16894 16340"/>
    </justification>
  </clause>

  <clause id="16896">
    <literal><![CDATA[
      K(x,y) * ((1 / y) * K(z,u)) = ((1 / y) * K(z,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(3702(a,1),16788(a,1,1))].">
      <j1 rule="para" parents="3702 16788"/>
    </justification>
  </clause>

  <clause id="16897">
    <literal><![CDATA[
      T(x,T(y,(z * T(u,w)) * v5)) = T(x,T(y,(u * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,16798,a,b,16799,a)].">
      <j1 rule="hyper" parents="58 16798 16799"/>
    </justification>
  </clause>

  <clause id="16898">
    <literal><![CDATA[
      K(x,T(y,z)) / T(z,u) = (K(u,z) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14389,a,16800,a)].">
      <j1 rule="hyper" parents="14389 16800"/>
    </justification>
  </clause>

  <clause id="16899">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = (K(u,x) / x) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,14330,a,b,16898,a)].">
      <j1 rule="hyper" parents="58 14330 16898"/>
    </justification>
  </clause>

  <clause id="16900">
    <literal><![CDATA[
      K(x,K(y,z * (T(u,w) * v5))) = K(x,K(y,(u * v5) * z))
    ]]></literal>
    <justification jstring="[hyper(16239,a,16853,a)].">
      <j1 rule="hyper" parents="16239 16853"/>
    </justification>
  </clause>

  <clause id="16901">
    <literal><![CDATA[
      T(x * K(y,z),K(u,w)) = T(x,K(u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(8077,a,16860,a),flip(a)].">
      <j1 rule="hyper" parents="8077 16860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16902">
    <literal><![CDATA[
      T(K(x,y) * z,K(u,w)) = K(x,y) * T(z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(6330,a,16901,a),flip(a)].">
      <j1 rule="hyper" parents="6330 16901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16908">
    <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(334,a,11159,a,b,16868,a),flip(a)].">
      <j1 rule="hyper" parents="334 11159 16868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16909">
    <literal><![CDATA[
      K(x,K(y,z / (T(u,w) * v5))) = K(x,K(y,(v5 * u) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16880,a(flip),b,16885,a)].">
      <j1 rule="hyper" parents="58 16880 16885"/>
    </justification>
  </clause>

  <clause id="16910">
    <literal><![CDATA[
      K(x,K(y,((z / (z / u)) / w) * v5)) = K(x,K(y,(u / w) * v5))
    ]]></literal>
    <justification jstring="[para(252(a,1),16887(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="252 16887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16911">
    <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,8573,a(flip),b,16897,a),flip(a)].">
      <j1 rule="hyper" parents="58 8573 16897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16912">
    <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),16909(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="107 16909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16914">
    <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,15039,a(flip),b,16875,a)].">
      <j1 rule="hyper" parents="58 15039 16875"/>
    </justification>
  </clause>

  <clause id="16915">
    <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(8128(a,1),16875(a,1,2,1))].">
      <j1 rule="para" parents="8128 16875"/>
    </justification>
  </clause>

  <clause id="16916">
    <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(6368(a,1),16889(a,1,2,2,1))].">
      <j1 rule="para" parents="6368 16889"/>
    </justification>
  </clause>

  <clause id="16917">
    <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(6532(a,1),16889(a,1,2,2))].">
      <j1 rule="para" parents="6532 16889"/>
    </justification>
  </clause>

  <clause id="16918">
    <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(16093(a,1),16889(a,1))].">
      <j1 rule="para" parents="16093 16889"/>
    </justification>
  </clause>

  <clause id="16919">
    <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),16918(a,1,2,2,2))].">
      <j1 rule="para" parents="84 16918"/>
    </justification>
  </clause>

  <clause id="16920">
    <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(8812(a,1),16918(a,1,2,2,2))].">
      <j1 rule="para" parents="8812 16918"/>
    </justification>
  </clause>

  <clause id="16921">
    <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(891(a,1),16888(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="891 16888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16922">
    <literal><![CDATA[
      K(x,K(y,z / ((K(u,w) * v5) * v6))) = K(x,K(y,z / (v5 * v6)))
    ]]></literal>
    <justification jstring="[hyper(334,a,8458,a,b,16893,a),flip(a)].">
      <j1 rule="hyper" parents="334 8458 16893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16923">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = K(u,x) / (K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(14513,a,16896,a),flip(a)].">
      <j1 rule="hyper" parents="14513 16896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16924">
    <literal><![CDATA[
      K(x,y) / (K(z,u) * y) = (K(x,y) / y) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,16899,a(flip),b,16923,a),flip(a)].">
      <j1 rule="hyper" parents="58 16899 16923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16925">
    <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(16924(a,2),6878(a,2,2))].">
      <j1 rule="para" parents="16924 6878"/>
    </justification>
  </clause>

  <clause id="16926">
    <literal><![CDATA[
      K(x,K(y,z * ((u / (u / w)) / v5))) = K(x,K(y,(w / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(16239,a,16910,a)].">
      <j1 rule="hyper" parents="16239 16910"/>
    </justification>
  </clause>

  <clause id="16927">
    <literal><![CDATA[
      K(x,K(y,z / (u * (K(w,v5) * v6)))) = K(x,K(y,z / (v6 * u)))
    ]]></literal>
    <justification jstring="[hyper(16891,a,16922,a)].">
      <j1 rule="hyper" parents="16891 16922"/>
    </justification>
  </clause>

  <clause id="16928">
    <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),16926(a,1,2,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 16926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16929">
    <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(16926(a,1),16239(a,1))].">
      <j1 rule="para" parents="16926 16239"/>
    </justification>
  </clause>

  <clause id="16930">
    <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(16927(a,2),16891(a,1))].">
      <j1 rule="para" parents="16927 16891"/>
    </justification>
  </clause>

  <clause id="16931">
    <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(16751(a,1),16565(a,1))].">
      <j1 rule="para" parents="16751 16565"/>
    </justification>
  </clause>

  <clause id="16932">
    <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(5820(a,1),16931(a,1,2,2,2))].">
      <j1 rule="para" parents="5820 16931"/>
    </justification>
  </clause>

  <clause id="16933">
    <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(7538(a,1),16931(a,1,2,2,2))].">
      <j1 rule="para" parents="7538 16931"/>
    </justification>
  </clause>

  <clause id="16934">
    <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(14302(a,1),16933(a,1,2,2,2))].">
      <j1 rule="para" parents="14302 16933"/>
    </justification>
  </clause>

  <clause id="16935">
    <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,15221,a(flip),b,16754,a),flip(a)].">
      <j1 rule="hyper" parents="58 15221 16754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16936">
    <literal><![CDATA[
      K(x,T(y,z * u)) * T(u,z) = T(u * K(x,y),z)
    ]]></literal>
    <justification jstring="[para(8170(a,1),16935(a,2,1))].">
      <j1 rule="para" parents="8170 16935"/>
    </justification>
  </clause>

  <clause id="16937">
    <literal><![CDATA[
      T(x * K(x \ y,z),y) = K(x \ y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(15953(a,1),16936(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15953 16936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16938">
    <literal><![CDATA[
      K(x,T(y,z * u)) * T(z,u) = T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(15955(a,1),16936(a,1,1))].">
      <j1 rule="para" parents="15955 16936"/>
    </justification>
  </clause>

  <clause id="16939">
    <literal><![CDATA[
      T(x * K(x \ y,z),y) = T(x,y) * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,16271,a,b,16937,a),flip(a)].">
      <j1 rule="hyper" parents="334 16271 16937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16940">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = K(x * y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5182(a,1),16938(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5182 16938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16941">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = T(x,y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,16273,a,b,16940,a),flip(a)].">
      <j1 rule="hyper" parents="334 16273 16940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16942">
    <literal><![CDATA[
      T(x * y,z) / T(y,x) = T(x * K(x * y,z),y)
    ]]></literal>
    <justification jstring="[hyper(14402,a,16940,a(flip))].">
      <j1 rule="hyper" parents="14402 16940"/>
    </justification>
  </clause>

  <clause id="16943">
    <literal><![CDATA[
      T(x * K(x * y,y \ 1),y) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[hyper(334,a,12595,a(flip),b,16941,a),flip(a)].">
      <j1 rule="hyper" parents="334 12595 16941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16944">
    <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(16942(a,2),7470(a,2,2))].">
      <j1 rule="para" parents="16942 7470"/>
    </justification>
  </clause>

  <clause id="16945">
    <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(16942(a,1),15990(a,1,2,1))].">
      <j1 rule="para" parents="16942 15990"/>
    </justification>
  </clause>

  <clause id="16946">
    <literal><![CDATA[
      x \ T(y * x,x \ 1) = (y * x) * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6844,a(flip),b,16943,a)].">
      <j1 rule="hyper" parents="58 6844 16943"/>
    </justification>
  </clause>

  <clause id="16947">
    <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(16946(a,2),15127(a,2,2,1))].">
      <j1 rule="para" parents="16946 15127"/>
    </justification>
  </clause>

  <clause id="16948">
    <literal><![CDATA[
      (x * y) * ((y * x) \ (K(x,y) * z)) = (z * K(x,y)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8170(a,1),16803(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8170 16803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16950">
    <literal><![CDATA[
      (x * y) * ((y * x) \ (K(x,y) * z)) = z * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,9209,a(flip),b,16948,a),flip(a)].">
      <j1 rule="hyper" parents="334 9209 16948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16951">
    <literal><![CDATA[
      (x * y) * ((T(y,x) * x) \ z) = z * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(15355(a,1),16950(a,1,2))].">
      <j1 rule="para" parents="15355 16950"/>
    </justification>
  </clause>

  <clause id="16952">
    <literal><![CDATA[
      (x * (K(y,z) * K(y,z))) / (y * z) = x / (T(z,y) * y)
    ]]></literal>
    <justification jstring="[para(16951(a,1),12659(a,1,1))].">
      <j1 rule="para" parents="16951 12659"/>
    </justification>
  </clause>

  <clause id="16954">
    <literal><![CDATA[
      K(x,(y * (T(z,y) * K(u,w))) / v5) = K(x,((K(u,w) * z) * y) / v5)
    ]]></literal>
    <justification jstring="[para(11511(a,1),16516(a,1,2,1))].">
      <j1 rule="para" parents="11511 16516"/>
    </justification>
  </clause>

  <clause id="16955">
    <literal><![CDATA[
      K(x,y \ (z * (T(u,z) * K(w,v5)))) = K(x,y \ ((K(w,v5) * u) * z))
    ]]></literal>
    <justification jstring="[para(11511(a,1),16522(a,1,2,2))].">
      <j1 rule="para" parents="11511 16522"/>
    </justification>
  </clause>

  <clause id="16956">
    <literal><![CDATA[
      K(x,T(y,z * (y \ u)) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[para(12743(a,1),16543(a,1,2,1))].">
      <j1 rule="para" parents="12743 16543"/>
    </justification>
  </clause>

  <clause id="16957">
    <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(16602(a,1),16711(a,1))].">
      <j1 rule="para" parents="16602 16711"/>
    </justification>
  </clause>

  <clause id="16958">
    <literal><![CDATA[
      K(x,T(y,z * u) * z) = K(x,y * (u \ T(u * z,y)))
    ]]></literal>
    <justification jstring="[hyper(16713,a,16281,a),flip(a)].">
      <j1 rule="hyper" parents="16713 16281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16959">
    <literal><![CDATA[
      K(x,T(y,z * x) * z) = K(x,(x \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,12746,a(flip),b,16958,a),flip(a)].">
      <j1 rule="hyper" parents="334 12746 16958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16960">
    <literal><![CDATA[
      K(x,T(y,z * x) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),16959(a,2,2,1))].">
      <j1 rule="para" parents="4 16959"/>
    </justification>
  </clause>

  <clause id="16961">
    <literal><![CDATA[
      K(x,y * T(z,y * x)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15525,a(flip),b,16960,a),flip(a)].">
      <j1 rule="hyper" parents="58 15525 16960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16962">
    <literal><![CDATA[
      K(T(x,y),z * T(u,z * x)) = K(T(x,y),u * z)
    ]]></literal>
    <justification jstring="[hyper(16932,a,16961,a)].">
      <j1 rule="hyper" parents="16932 16961"/>
    </justification>
  </clause>

  <clause id="16963">
    <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(5264(a,1),16930(a,1,2,2,2,2))].">
      <j1 rule="para" parents="5264 16930"/>
    </justification>
  </clause>

  <clause id="16964">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[hyper(13502,a,16956,a)].">
      <j1 rule="hyper" parents="13502 16956"/>
    </justification>
  </clause>

  <clause id="16965">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * (z / y))) = K(x,(u * (z / y)) * y)
    ]]></literal>
    <justification jstring="[para(10665(a,1),16964(a,2,2))].">
      <j1 rule="para" parents="10665 16964"/>
    </justification>
  </clause>

  <clause id="16966">
    <literal><![CDATA[
      K(x,T(y,L(z,u,u \ w) * w)) = K(x,T(y,(u \ w) * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(16311,a,16774,a)].">
      <j1 rule="hyper" parents="16311 16774"/>
    </justification>
  </clause>

  <clause id="16967">
    <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(16321(a,1),16325(a,1,2))].">
      <j1 rule="para" parents="16321 16325"/>
    </justification>
  </clause>

  <clause id="16969">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),(x * y) \ y) = T(x * y,K(y,z)) \ y
    ]]></literal>
    <justification jstring="[para(6469(a,1),16397(a,2,1))].">
      <j1 rule="para" parents="6469 16397"/>
    </justification>
  </clause>

  <clause id="16970">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),(x * y) \ y) = T((x * y) \ y,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8640,a,b,16969,a),flip(a)].">
      <j1 rule="hyper" parents="334 8640 16969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16971">
    <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,15532,a(flip),b,16527,a)].">
      <j1 rule="hyper" parents="58 15532 16527"/>
    </justification>
  </clause>

  <clause id="16972">
    <literal><![CDATA[
      K(x,(K(y,z) * (u / (y \ z))) / w) = K(x,(u / (T(y,z) \ z)) / w)
    ]]></literal>
    <justification jstring="[para(12895(a,1),16971(a,1,2,1))].">
      <j1 rule="para" parents="12895 16971"/>
    </justification>
  </clause>

  <clause id="16973">
    <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(12515(a,1),16587(a,2,1))].">
      <j1 rule="para" parents="12515 16587"/>
    </justification>
  </clause>

  <clause id="16974">
    <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),16607(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 16607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16975">
    <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(6529,a,16658,a),flip(a)].">
      <j1 rule="hyper" parents="6529 16658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16976">
    <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(16703(a,2),15701(a,1))].">
      <j1 rule="para" parents="16703 15701"/>
    </justification>
  </clause>

  <clause id="16977">
    <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(334,a,16908,a(flip),b,16890,a),flip(a)].">
      <j1 rule="hyper" parents="334 16908 16890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16979">
    <literal><![CDATA[
      K(x,K(y * K(z,u),L(w,K(v5,v6),v7))) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,11194,a(flip),b,16977,a),flip(a)].">
      <j1 rule="hyper" parents="334 11194 16977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16980">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w),v5))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(16867,a,16979,a)].">
      <j1 rule="hyper" parents="16867 16979"/>
    </justification>
  </clause>

  <clause id="16982">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,w)) / v5)) = K(x,T(y,v5 / z))
    ]]></literal>
    <justification jstring="[hyper(16357,a,16895,a),flip(a)].">
      <j1 rule="hyper" parents="16357 16895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16983">
    <literal><![CDATA[
      K(x,T(y,(z / T(u,w)) / v5)) = K(x,T(y,v5 / (z / u)))
    ]]></literal>
    <justification jstring="[para(6368(a,1),16982(a,1,2,2,1))].">
      <j1 rule="para" parents="6368 16982"/>
    </justification>
  </clause>

  <clause id="16984">
    <literal><![CDATA[
      K(x,T(y,z / (u / T(w,v5)))) = K(x,T(y,z / (u / w)))
    ]]></literal>
    <justification jstring="[hyper(8557,a,16983,a)].">
      <j1 rule="hyper" parents="8557 16983"/>
    </justification>
  </clause>

  <clause id="16985">
    <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(334,a,8751,a(flip),b,16984,a),flip(a)].">
      <j1 rule="hyper" parents="334 8751 16984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16986">
    <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),16984(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="107 16984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16987">
    <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(16984(a,1),5178(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16984 5178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16988">
    <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(13509(a,1),16911(a,1,2))].">
      <j1 rule="para" parents="13509 16911"/>
    </justification>
  </clause>

  <clause id="16989">
    <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(15029(a,1),16945(a,1,2))].">
      <j1 rule="para" parents="15029 16945"/>
    </justification>
  </clause>

  <clause id="16990">
    <literal><![CDATA[
      K(((T(x,y) * z) * y) / (z * T(x,y)),u) = K(z \ T(y * z,x),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,14325,a(flip),b,16973,a),flip(a)].">
      <j1 rule="hyper" parents="334 14325 16973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16991">
    <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(11500,a,16990,a)].">
      <j1 rule="hyper" parents="11500 16990"/>
    </justification>
  </clause>

  <clause id="16992">
    <literal><![CDATA[
      K(x * K(y,z),T(u,z * T(y,x))) = K(z \ T(x * z,y),u)
    ]]></literal>
    <justification jstring="[para(8212(a,1),16991(a,1,1))].">
      <j1 rule="para" parents="8212 16991"/>
    </justification>
  </clause>

  <clause id="16993">
    <literal><![CDATA[
      K(x * K(y,z),T(u,z * y)) = K(z \ T(x * z,y),u)
    ]]></literal>
    <justification jstring="[hyper(16823,a,16992,a)].">
      <j1 rule="hyper" parents="16823 16992"/>
    </justification>
  </clause>

  <clause id="16994">
    <literal><![CDATA[
      K(T(K(x,y) * z,x * y),u) = K(y \ T(z * y,x),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12620,a,b,16993,a)].">
      <j1 rule="hyper" parents="58 12620 16993"/>
    </justification>
  </clause>

  <clause id="16995">
    <literal><![CDATA[
      K(K(x,y) * z,T(u,x * y)) = K(y \ T(z * y,x),u)
    ]]></literal>
    <justification jstring="[hyper(7970,a,16994,a)].">
      <j1 rule="hyper" parents="7970 16994"/>
    </justification>
  </clause>

  <clause id="16996">
    <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(7401(a,2),16975(a,1,2))].">
      <j1 rule="para" parents="7401 16975"/>
    </justification>
  </clause>

  <clause id="16997">
    <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(7477,a,16996,a),flip(a)].">
      <j1 rule="hyper" parents="7477 16996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16998">
    <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,16338,a(flip),b,16997,a),flip(a)].">
      <j1 rule="hyper" parents="58 16338 16997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16999">
    <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(334,a,5391,a,b,16998,a)].">
      <j1 rule="hyper" parents="334 5391 16998"/>
    </justification>
  </clause>

  <clause id="17000">
    <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(16999(a,1),5426(a,1))].">
      <j1 rule="para" parents="16999 5426"/>
    </justification>
  </clause>

  <clause id="17001">
    <literal><![CDATA[
      T(K(x,K(y,z)) \ u,K(x,y) \ z) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(395(a,1),16248(a,1,1))].">
      <j1 rule="para" parents="395 16248"/>
    </justification>
  </clause>

  <clause id="17002">
    <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,16353,a(flip),b,17001,a)].">
      <j1 rule="hyper" parents="58 16353 17001"/>
    </justification>
  </clause>

  <clause id="17003">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) / v5))) = K(x,y * (z / (v5 \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(16631,a,14900,a),flip(a)].">
      <j1 rule="hyper" parents="16631 14900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17004">
    <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(3659(a,2),17003(a,1,2))].">
      <j1 rule="para" parents="3659 17003"/>
    </justification>
  </clause>

  <clause id="17005">
    <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(7440(a,1),16643(a,1,2))].">
      <j1 rule="para" parents="7440 16643"/>
    </justification>
  </clause>

  <clause id="17006">
    <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(17005(a,1),16653(a,1))].">
      <j1 rule="para" parents="17005 16653"/>
    </justification>
  </clause>

  <clause id="17007">
    <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(16835(a,1),16878(a,1))].">
      <j1 rule="para" parents="16835 16878"/>
    </justification>
  </clause>

  <clause id="17008">
    <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(5392(a,1),16198(a,2,2))].">
      <j1 rule="para" parents="5392 16198"/>
    </justification>
  </clause>

  <clause id="17009">
    <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,7818,a(flip),b,16345,a)].">
      <j1 rule="hyper" parents="58 7818 16345"/>
    </justification>
  </clause>

  <clause id="17010">
    <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,16559,a,b,16531,a)].">
      <j1 rule="hyper" parents="58 16559 16531"/>
    </justification>
  </clause>

  <clause id="17012">
    <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,15703,a(flip),b,16594,a)].">
      <j1 rule="hyper" parents="58 15703 16594"/>
    </justification>
  </clause>

  <clause id="17013">
    <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(14034(a,1),16598(a,2,2,2))].">
      <j1 rule="para" parents="14034 16598"/>
    </justification>
  </clause>

  <clause id="17014">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) / w)) = K(x,y * (T(z,u) / w))
    ]]></literal>
    <justification jstring="[hyper(16449,a,17013,a)].">
      <j1 rule="hyper" parents="16449 17013"/>
    </justification>
  </clause>

  <clause id="17015">
    <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(13419,a,17014,a),flip(a)].">
      <j1 rule="hyper" parents="13419 17014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17017">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) / u) * w) = K(x,(T(y,z) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(12589,a,17015,a),flip(a)].">
      <j1 rule="hyper" parents="12589 17015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17018">
    <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(7700(a,1),16656(a,1,2,2))].">
      <j1 rule="para" parents="7700 16656"/>
    </justification>
  </clause>

  <clause id="17019">
    <literal><![CDATA[
      K(x,y \ (z / T(z / u,w))) = K(x,y \ (T(u \ z,w) \ z))
    ]]></literal>
    <justification jstring="[para(7879(a,1),17018(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7879 17018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17020">
    <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(16832(a,1),16839(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16832 16839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17021">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) = T(x,K(u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(334,a,15465,a(flip),b,17020,a),flip(a)].">
      <j1 rule="hyper" parents="334 15465 17020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17022">
    <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(17020(a,2),15706(a,1))].">
      <j1 rule="para" parents="17020 15706"/>
    </justification>
  </clause>

  <clause id="17024">
    <literal><![CDATA[
      T(x,K(y * K(z,u),w) * v5) = T(x,K(y,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(16544,a,17021,a)].">
      <j1 rule="hyper" parents="16544 17021"/>
    </justification>
  </clause>

  <clause id="17025">
    <literal><![CDATA[
      T(x,y * K(z,K(u,w) * v5)) = T(x,K(v5,z) * y)
    ]]></literal>
    <justification jstring="[hyper(16305,a,17021,a)].">
      <j1 rule="hyper" parents="16305 17021"/>
    </justification>
  </clause>

  <clause id="17026">
    <literal><![CDATA[
      T(x,y * K(K(z,u) * w,v5)) = T(x,K(w,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(16052,a,17021,a)].">
      <j1 rule="hyper" parents="16052 17021"/>
    </justification>
  </clause>

  <clause id="17027">
    <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,15484,a(flip),b,17021,a),flip(a)].">
      <j1 rule="hyper" parents="58 15484 17021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17028">
    <literal><![CDATA[
      T(x,K(T(y,z) \ u,w) * v5) = T(x,K(y \ u,w) * v5)
    ]]></literal>
    <justification jstring="[para(5337(a,1),17021(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5337 17021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17029">
    <literal><![CDATA[
      T(x,y * K(z,u * K(w,v5))) = T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(16305,a,17024,a)].">
      <j1 rule="hyper" parents="16305 17024"/>
    </justification>
  </clause>

  <clause id="17031">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w) * v5)) = T(x,K(u * v5,z) * y)
    ]]></literal>
    <justification jstring="[para(5047(a,1),17025(a,1,2,2,2))].">
      <j1 rule="para" parents="5047 17025"/>
    </justification>
  </clause>

  <clause id="17032">
    <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,17026,a(flip),b,14877,a(flip))].">
      <j1 rule="hyper" parents="119 17026 14877"/>
    </justification>
  </clause>

  <clause id="17033">
    <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(17029(a,1),5110(a,1,2))].">
      <j1 rule="para" parents="17029 5110"/>
    </justification>
  </clause>

  <clause id="17034">
    <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(17029(a,1),5133(a,1,2))].">
      <j1 rule="para" parents="17029 5133"/>
    </justification>
  </clause>

  <clause id="17035">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w) \ v5)) = T(x,K(u \ v5,z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(16366,a,17028,a)].">
      <j1 rule="hyper" parents="16366 17028"/>
    </justification>
  </clause>

  <clause id="17036">
    <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(17028(a,1),16366(a,1))].">
      <j1 rule="para" parents="17028 16366"/>
    </justification>
  </clause>

  <clause id="17037">
    <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(17035(a,2),16366(a,1))].">
      <j1 rule="para" parents="17035 16366"/>
    </justification>
  </clause>

  <clause id="17038">
    <literal><![CDATA[
      K(x,y * K(z,u * K(w,v5))) = K(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(17033,a,15480,a)].">
      <j1 rule="hyper" parents="17033 15480"/>
    </justification>
  </clause>

  <clause id="17039">
    <literal><![CDATA[
      K(x,y * K(z,u * K(w,v5))) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(17033,a,4995,a(flip))].">
      <j1 rule="hyper" parents="17033 4995"/>
    </justification>
  </clause>

  <clause id="17040">
    <literal><![CDATA[
      K(x,y * K(K(z,u) * w,v5)) = K(x,K(v5,w) * y)
    ]]></literal>
    <justification jstring="[hyper(16535,a,17038,a)].">
      <j1 rule="hyper" parents="16535 17038"/>
    </justification>
  </clause>

  <clause id="17041">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) = K(x,K(w,u) * v5)
    ]]></literal>
    <justification jstring="[hyper(16534,a,17038,a)].">
      <j1 rule="hyper" parents="16534 17038"/>
    </justification>
  </clause>

  <clause id="17042">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * v5) = K(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(16068,a,17038,a)].">
      <j1 rule="hyper" parents="16068 17038"/>
    </justification>
  </clause>

  <clause id="17043">
    <literal><![CDATA[
      K(x,y * K(K(z,u) * w,v5)) = K(x,K(w,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(16535,a,17039,a)].">
      <j1 rule="hyper" parents="16535 17039"/>
    </justification>
  </clause>

  <clause id="17044">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) = K(x,K(u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(16534,a,17039,a)].">
      <j1 rule="hyper" parents="16534 17039"/>
    </justification>
  </clause>

  <clause id="17045">
    <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(17039(a,1),16068(a,1))].">
      <j1 rule="para" parents="17039 16068"/>
    </justification>
  </clause>

  <clause id="17046">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w) * v5) = K(x,v5 * K(w,y))
    ]]></literal>
    <justification jstring="[para(5394(a,1),17040(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5394 17040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17047">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * v5) = K(x,v5 * K(z,y))
    ]]></literal>
    <justification jstring="[para(8213(a,1),17040(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8213 17040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17048">
    <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(17041(a,2),15493(a,1))].">
      <j1 rule="para" parents="17041 15493"/>
    </justification>
  </clause>

  <clause id="17049">
    <literal><![CDATA[
      K(x,K(y \ K(z,u),w) * v5) = K(x,K(w,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,16223,a,b,17042,a)].">
      <j1 rule="hyper" parents="58 16223 17042"/>
    </justification>
  </clause>

  <clause id="17051">
    <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(17046(a,2),16183(a,1))].">
      <j1 rule="para" parents="17046 16183"/>
    </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(15493,a,17049,a)].">
      <j1 rule="hyper" parents="15493 17049"/>
    </justification>
  </clause>

  <clause id="17054">
    <literal><![CDATA[
      T(x,K(y,z \ K(u,w)) * v5) = T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(118,a,17052,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 17052 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17055">
    <literal><![CDATA[
      T(x,y * K(z \ K(u,w),v5)) = T(x,K(v5,z) * y)
    ]]></literal>
    <justification jstring="[hyper(16305,a,17054,a)].">
      <j1 rule="hyper" parents="16305 17054"/>
    </justification>
  </clause>

  <clause id="17056">
    <literal><![CDATA[
      T(x,y * K(z \ K(u,w),v5)) = T(x,K(z,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,15476,a,b,17055,a),flip(a)].">
      <j1 rule="hyper" parents="334 15476 17055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17057">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) = T(x,v5 * K(u \ K(v6,v7),w))
    ]]></literal>
    <justification jstring="[hyper(334,a,17021,a,b,17056,a)].">
      <j1 rule="hyper" parents="334 17021 17056"/>
    </justification>
  </clause>

  <clause id="17058">
    <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,16530,a(flip),b,17056,a),flip(a)].">
      <j1 rule="hyper" parents="58 16530 17056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17059">
    <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(5129(a,1),17048(a,1,2,1,1))].">
      <j1 rule="para" parents="5129 17048"/>
    </justification>
  </clause>

  <clause id="17060">
    <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(5391(a,2),17059(a,1,2))].">
      <j1 rule="para" parents="5391 17059"/>
    </justification>
  </clause>

  <clause id="17061">
    <literal><![CDATA[
      T(x,K(y \ K(z,u),w) * v5) = T(x,K(K(v6,v7) * y,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(334,a,16041,a,b,17057,a)].">
      <j1 rule="hyper" parents="334 16041 17057"/>
    </justification>
  </clause>

  <clause id="17062">
    <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,16253,a(flip),b,17061,a),flip(a)].">
      <j1 rule="hyper" parents="58 16253 17061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17063">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w)),v5) = K(K(z,y) * x,v5)
    ]]></literal>
    <justification jstring="[hyper(17034,a,5062,a(flip))].">
      <j1 rule="hyper" parents="17034 5062"/>
    </justification>
  </clause>

  <clause id="17064">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w)),v5) = K(x * K(y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(334,a,16215,a(flip),b,17063,a),flip(a)].">
      <j1 rule="hyper" parents="334 16215 17063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17065">
    <literal><![CDATA[
      K(x * K(y,T(z,u) * w),v5) = K(x * K(y,z * w),v5)
    ]]></literal>
    <justification jstring="[para(5803(a,1),17064(a,1,1,2,2))].">
      <j1 rule="para" parents="5803 17064"/>
    </justification>
  </clause>

  <clause id="17066">
    <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(334,a,15746,a(flip),b,17027,a),flip(a)].">
      <j1 rule="hyper" parents="334 15746 17027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17068">
    <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(17062(a,1),17022(a,1))].">
      <j1 rule="para" parents="17062 17022"/>
    </justification>
  </clause>

  <clause id="17069">
    <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(8614(a,1),17010(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8614 17010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17070">
    <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(334,a,11359,a(flip),b,17069,a),flip(a)].">
      <j1 rule="hyper" parents="334 11359 17069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17072">
    <literal><![CDATA[
      K(x,K(y \ (1 / z),L(y / u,u,z))) = K(x,K(z * y,y / u))
    ]]></literal>
    <justification jstring="[hyper(334,a,16864,a(flip),b,16188,a),flip(a)].">
      <j1 rule="hyper" parents="334 16864 16188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17073">
    <literal><![CDATA[
      K(x,K((1 / y) / z,L(z / u,u,y))) = K(x,K(y * z,z / u))
    ]]></literal>
    <justification jstring="[hyper(16234,a,17072,a)].">
      <j1 rule="hyper" parents="16234 17072"/>
    </justification>
  </clause>

  <clause id="17075">
    <literal><![CDATA[
      K(x,K((y \ z) * u,u / y)) = K(x,K(z,(1 / (y \ z)) / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15121,a(flip),b,17073,a),flip(a)].">
      <j1 rule="hyper" parents="58 15121 17073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17076">
    <literal><![CDATA[
      K(x,K(y / z,(z \ u) * y)) = K(x,K(u,(1 / (z \ u)) / y))
    ]]></literal>
    <justification jstring="[hyper(8099,a,17075,a)].">
      <j1 rule="hyper" parents="8099 17075"/>
    </justification>
  </clause>

  <clause id="17077">
    <literal><![CDATA[
      K(x,K(y,(1 / (z \ y)) / u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16237,a(flip),b,17076,a),flip(a)].">
      <j1 rule="hyper" parents="58 16237 17076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17078">
    <literal><![CDATA[
      K(x,K(y,(1 / z) / u)) = K(x,K(y,u / (y / z)))
    ]]></literal>
    <justification jstring="[para(75(a,1),17077(a,1,2,2,1,2))].">
      <j1 rule="para" parents="75 17077"/>
    </justification>
  </clause>

  <clause id="17079">
    <literal><![CDATA[
      K(x,K(y,z / (y / u))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12152,a(flip),b,17078,a),flip(a)].">
      <j1 rule="hyper" parents="58 12152 17078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17080">
    <literal><![CDATA[
      K(x,K(y,z * (y / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16858,a(flip),b,17079,a),flip(a)].">
      <j1 rule="hyper" parents="58 16858 17079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17081">
    <literal><![CDATA[
      K(x,K(y,z * x)) * K(y / x,(y / x) \ z) = K(x \ y,z / (y / x))
    ]]></literal>
    <justification jstring="[para(17079(a,1),8659(a,1,1))].">
      <j1 rule="para" parents="17079 8659"/>
    </justification>
  </clause>

  <clause id="17082">
    <literal><![CDATA[
      K(x,K(y,z * (x / u))) = K(y,K(x,z / u))
    ]]></literal>
    <justification jstring="[hyper(8050,a,17080,a)].">
      <j1 rule="hyper" parents="8050 17080"/>
    </justification>
  </clause>

  <clause id="17083">
    <literal><![CDATA[
      K(x,K(y,z * (x / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(334,a,8048,a,b,17082,a),flip(a)].">
      <j1 rule="hyper" parents="334 8048 17082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17084">
    <literal><![CDATA[
      K(x,K(y,z / y)) * K(y / x,(x / y) * z) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[para(17083(a,1),12655(a,1,1))].">
      <j1 rule="para" parents="17083 12655"/>
    </justification>
  </clause>

  <clause id="17085">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,(z / x) \ y) = K(x \ z,y / (z / x))
    ]]></literal>
    <justification jstring="[para(8151(a,1),17081(a,1,1))].">
      <j1 rule="para" parents="8151 17081"/>
    </justification>
  </clause>

  <clause id="17086">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,y / (z / x)) = K(x \ z,y / (z / x))
    ]]></literal>
    <justification jstring="[para(5186(a,2),17085(a,1,2))].">
      <j1 rule="para" parents="5186 17085"/>
    </justification>
  </clause>

  <clause id="17087">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y / x,(x / y) * z) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[para(8136(a,1),17084(a,1,1))].">
      <j1 rule="para" parents="8136 17084"/>
    </justification>
  </clause>

  <clause id="17088">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,(x / z) * y) = K(x \ z,y * (x / z))
    ]]></literal>
    <justification jstring="[para(8067(a,1),17087(a,1,1))].">
      <j1 rule="para" parents="8067 17087"/>
    </justification>
  </clause>

  <clause id="17089">
    <literal><![CDATA[
      T(x,K(y \ z,u) * w) = T(x,K(z * y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(16232,a,16967,a),flip(a)].">
      <j1 rule="hyper" parents="16232 16967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17090">
    <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(16967(a,1),16232(a,1))].">
      <j1 rule="para" parents="16967 16232"/>
    </justification>
  </clause>

  <clause id="17091">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w) \ v5)) = T(x,K(v5 * u,z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(17036,a,17089,a)].">
      <j1 rule="hyper" parents="17036 17089"/>
    </justification>
  </clause>

  <clause id="17092">
    <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(17089(a,1),15049(a,1,1,2))].">
      <j1 rule="para" parents="17089 15049"/>
    </justification>
  </clause>

  <clause id="17093">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w) \ v5)) = T(x,y \ T(z,v5 * u))
    ]]></literal>
    <justification jstring="[hyper(334,a,16254,a(flip),b,17091,a),flip(a)].">
      <j1 rule="hyper" parents="334 16254 17091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17094">
    <literal><![CDATA[
      T(x,y \ T(z,u \ w)) = T(x,y \ T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(17037,a,17093,a)].">
      <j1 rule="hyper" parents="17037 17093"/>
    </justification>
  </clause>

  <clause id="17095">
    <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(17094(a,1),15049(a,1,1,2))].">
      <j1 rule="para" parents="17094 15049"/>
    </justification>
  </clause>

  <clause id="17096">
    <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(14079(a,1),16724(a,1,1,1,1))].">
      <j1 rule="para" parents="14079 16724"/>
    </justification>
  </clause>

  <clause id="17097">
    <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(16511,a,17096,a)].">
      <j1 rule="hyper" parents="16511 17096"/>
    </justification>
  </clause>

  <clause id="17098">
    <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(15987(a,1),17000(a,1))].">
      <j1 rule="para" parents="15987 17000"/>
    </justification>
  </clause>

  <clause id="17099">
    <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(6649(a,1),16159(a,1,2,2))].">
      <j1 rule="para" parents="6649 16159"/>
    </justification>
  </clause>

  <clause id="17100">
    <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(16471,a,16292,a)].">
      <j1 rule="hyper" parents="16471 16292"/>
    </justification>
  </clause>

  <clause id="17101">
    <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(15707,a,17100,a),flip(a)].">
      <j1 rule="hyper" parents="15707 17100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17103">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * (z * K(y,x))) = (z * K(y,x)) \ (u * (K(x,y) \ z))
    ]]></literal>
    <justification jstring="[para(8111(a,1),16347(a,1,2,2))].">
      <j1 rule="para" parents="8111 16347"/>
    </justification>
  </clause>

  <clause id="17104">
    <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(334,a,8218,a(flip),b,16362,a),flip(a)].">
      <j1 rule="hyper" parents="334 8218 16362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17105">
    <literal><![CDATA[
      T(((x \ 1) * y) \ z,K(y * (x \ 1),x)) = T(z / ((x \ 1) * y),y / x)
    ]]></literal>
    <justification jstring="[para(12516(a,1),17104(a,1,2))].">
      <j1 rule="para" parents="12516 17104"/>
    </justification>
  </clause>

  <clause id="17106">
    <literal><![CDATA[
      T(((x \ 1) * y) \ z,K(x \ y,x)) = T(z / ((x \ 1) * y),y / x)
    ]]></literal>
    <justification jstring="[para(6123(a,1),17105(a,1,2))].">
      <j1 rule="para" parents="6123 17105"/>
    </justification>
  </clause>

  <clause id="17107">
    <literal><![CDATA[
      T(x / ((y \ 1) * z),z / y) = T(((y \ 1) * z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8544,a,17106,a),flip(a)].">
      <j1 rule="hyper" parents="8544 17106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17108">
    <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(6518(a,2),16599(a,1,2))].">
      <j1 rule="para" parents="6518 16599"/>
    </justification>
  </clause>

  <clause id="17109">
    <literal><![CDATA[
      K(x,y * (((z * (u / z)) / z) * (w \ 1))) = K(x,y * ((u / z) * (w \ K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(334,a,13498,a(flip),b,16659,a),flip(a)].">
      <j1 rule="hyper" parents="334 13498 16659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17110">
    <literal><![CDATA[
      K(x,y * (T(z / u,u) * (w \ 1))) = K(x,y * ((z / u) * (w \ K(u,z))))
    ]]></literal>
    <justification jstring="[hyper(15797,a,17109,a)].">
      <j1 rule="hyper" parents="15797 17109"/>
    </justification>
  </clause>

  <clause id="17111">
    <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),17110(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="107 17110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17112">
    <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(13487,a,16698,a)].">
      <j1 rule="hyper" parents="13487 16698"/>
    </justification>
  </clause>

  <clause id="17113">
    <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,15744,a(flip),b,17112,a),flip(a)].">
      <j1 rule="hyper" parents="58 15744 17112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17114">
    <literal><![CDATA[
      K(x,T(y * ((z \ (u * y)) \ 1),u)) = K(x,((u * y) / z) \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,15515,a(flip),b,17113,a),flip(a)].">
      <j1 rule="hyper" parents="334 15515 17113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17115">
    <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(17114(a,1),14401(a,1))].">
      <j1 rule="para" parents="17114 14401"/>
    </justification>
  </clause>

  <clause id="17116">
    <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,12527,a(flip),b,16744,a)].">
      <j1 rule="hyper" parents="58 12527 16744"/>
    </justification>
  </clause>

  <clause id="17117">
    <literal><![CDATA[
      T(x,y / ((z \ T(z \ u,w)) \ (z \ u))) = T(x,y / (T(z \ u,w) \ u))
    ]]></literal>
    <justification jstring="[para(14316(a,1),16756(a,1,2,2,1))].">
      <j1 rule="para" parents="14316 16756"/>
    </justification>
  </clause>

  <clause id="17118">
    <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(8111(a,1),16863(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8111 16863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17119">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * (z * K(y,x))) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,17002,a(flip),b,17118,a),flip(a)].">
      <j1 rule="hyper" parents="58 17002 17118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17120">
    <literal><![CDATA[
      (x * K(y,z)) \ (u * (K(z,y) \ x)) = x \ T(u * x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,17103,a(flip),b,17119,a)].">
      <j1 rule="hyper" parents="58 17103 17119"/>
    </justification>
  </clause>

  <clause id="17121">
    <literal><![CDATA[
      (x * K(y,z)) \ (u * (K(z,y) \ x)) = x \ T(u * x,K(y,z))
    ]]></literal>
    <justification jstring="[para(8100(a,1),17120(a,2,2))].">
      <j1 rule="para" parents="8100 17120"/>
    </justification>
  </clause>

  <clause id="17122">
    <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(16876,a,16877,a)].">
      <j1 rule="hyper" parents="16876 16877"/>
    </justification>
  </clause>

  <clause id="17123">
    <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,16797,a(flip),b,16988,a)].">
      <j1 rule="hyper" parents="58 16797 16988"/>
    </justification>
  </clause>

  <clause id="17125">
    <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,12608,a(flip),b,17123,a),flip(a)].">
      <j1 rule="hyper" parents="58 12608 17123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17126">
    <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(15278(a,1),17032(a,1,2,1,2))].">
      <j1 rule="para" parents="15278 17032"/>
    </justification>
  </clause>

  <clause id="17127">
    <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(17092(a,1),15050(a,1))].">
      <j1 rule="para" parents="17092 15050"/>
    </justification>
  </clause>

  <clause id="17128">
    <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(17095(a,1),15050(a,1))].">
      <j1 rule="para" parents="17095 15050"/>
    </justification>
  </clause>

  <clause id="17129">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,y / x)) = y \ (y * K((x * (z / x)) \ y,u))
    ]]></literal>
    <justification jstring="[para(6928(a,1),17099(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6928 17099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17130">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,y / x)) = K((x * (z / x)) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(334,a,4,a(flip),b,17129,a),flip(a)].">
      <j1 rule="hyper" parents="334 4 17129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17131">
    <literal><![CDATA[
      K((x * ((y * ((x \ z) * x)) / x)) \ z,u) = K(1 / y,T(u,z / x))
    ]]></literal>
    <justification jstring="[hyper(5716,a,17130,a),flip(a)].">
      <j1 rule="hyper" parents="5716 17130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17133">
    <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(17130(a,1),5716(a,1))].">
      <j1 rule="para" parents="17130 5716"/>
    </justification>
  </clause>

  <clause id="17134">
    <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(10615(a,1),17116(a,1,1,2))].">
      <j1 rule="para" parents="10615 17116"/>
    </justification>
  </clause>

  <clause id="17136">
    <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(16835(a,1),17122(a,2,2))].">
      <j1 rule="para" parents="16835 17122"/>
    </justification>
  </clause>

  <clause id="17137">
    <literal><![CDATA[
      T((x \ K(y,z)) \ u,K(x,w)) = (x \ K(y,z)) \ T(u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(16838,a,17136,a)].">
      <j1 rule="hyper" parents="16838 17136"/>
    </justification>
  </clause>

  <clause id="17138">
    <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(334,a,17008,a(flip),b,17137,a),flip(a)].">
      <j1 rule="hyper" parents="334 17008 17137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17139">
    <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),17138(a,1,1))].">
      <j1 rule="para" parents="17 17138"/>
    </justification>
  </clause>

  <clause id="17140">
    <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(17139(a,1),17007(a,1))].">
      <j1 rule="para" parents="17139 17007"/>
    </justification>
  </clause>

  <clause id="17141">
    <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(15303(a,1),17126(a,1,2,1))].">
      <j1 rule="para" parents="15303 17126"/>
    </justification>
  </clause>

  <clause id="17142">
    <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(8703(a,1),16213(a,1,2,2,1))].">
      <j1 rule="para" parents="8703 16213"/>
    </justification>
  </clause>

  <clause id="17144">
    <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(255(a,1),16291(a,2,2,2))].">
      <j1 rule="para" parents="255 16291"/>
    </justification>
  </clause>

  <clause id="17145">
    <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(16364,a,15720,a),flip(a)].">
      <j1 rule="hyper" parents="16364 15720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17146">
    <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(16363,a,17145,a),flip(a)].">
      <j1 rule="hyper" parents="16363 17145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17147">
    <literal><![CDATA[
      K(x,y * T(K(x,z) * u,z)) = K(x,y * T(u,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,15223,a(flip),b,17146,a),flip(a)].">
      <j1 rule="hyper" parents="58 15223 17146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17148">
    <literal><![CDATA[
      K(x,y * T(z,u \ 1)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15223,a(flip),b,17147,a),flip(a)].">
      <j1 rule="hyper" parents="58 15223 17147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17150">
    <literal><![CDATA[
      T(x,y * T(z,u \ 1)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,17148,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 17148 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17151">
    <literal><![CDATA[
      K(x,y * T((z \ 1) \ u,z)) = K(x,y * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15606,a(flip),b,17148,a),flip(a)].">
      <j1 rule="hyper" parents="58 15606 17148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17152">
    <literal><![CDATA[
      T(x,(y * ((z \ 1) * K(u,z \ 1))) * u) = T(x,(y * (z \ 1)) * T(u,z))
    ]]></literal>
    <justification jstring="[para(6599(a,2),17150(a,1,2))].">
      <j1 rule="para" parents="6599 17150"/>
    </justification>
  </clause>

  <clause id="17153">
    <literal><![CDATA[
      K(x,y * ((z \ K(z,u)) \ u)) = K(x,y * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13462,a(flip),b,17151,a)].">
      <j1 rule="hyper" parents="58 13462 17151"/>
    </justification>
  </clause>

  <clause id="17154">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,(y * (z \ 1)) * T(u,z))
    ]]></literal>
    <justification jstring="[para(2563(a,1),17152(a,1,2,1,2))].">
      <j1 rule="para" parents="2563 17152"/>
    </justification>
  </clause>

  <clause id="17155">
    <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(16365,a,15658,a),flip(a)].">
      <j1 rule="hyper" parents="16365 15658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17156">
    <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,16557,a,b,17155,a)].">
      <j1 rule="hyper" parents="58 16557 17155"/>
    </justification>
  </clause>

  <clause id="17157">
    <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(16672(a,2),17156(a,1,2,1))].">
      <j1 rule="para" parents="16672 17156"/>
    </justification>
  </clause>

  <clause id="17158">
    <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,16753,a(flip),b,17157,a),flip(a)].">
      <j1 rule="hyper" parents="58 16753 17157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17159">
    <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(12755(a,1),16282(a,1,2,1))].">
      <j1 rule="para" parents="12755 16282"/>
    </justification>
  </clause>

  <clause id="17160">
    <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(16281(a,1),16289(a,1,2,2))].">
      <j1 rule="para" parents="16281 16289"/>
    </justification>
  </clause>

  <clause id="17161">
    <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,17031,a(flip),b,17160,a)].">
      <j1 rule="hyper" parents="58 17031 17160"/>
    </justification>
  </clause>

  <clause id="17163">
    <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(14034(a,1),17161(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14034 17161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17164">
    <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(334,a,16274,a(flip),b,17163,a),flip(a)].">
      <j1 rule="hyper" parents="334 16274 17163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17165">
    <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,8297,a(flip),b,17164,a)].">
      <j1 rule="hyper" parents="58 8297 17164"/>
    </justification>
  </clause>

  <clause id="17166">
    <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(6351(a,1),17165(a,1,2,2,1))].">
      <j1 rule="para" parents="6351 17165"/>
    </justification>
  </clause>

  <clause id="17167">
    <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,15793,a(flip),b,16549,a)].">
      <j1 rule="hyper" parents="58 15793 16549"/>
    </justification>
  </clause>

  <clause id="17168">
    <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,16548,a(flip),b,17167,a),flip(a)].">
      <j1 rule="hyper" parents="58 16548 17167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17169">
    <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,15438,a(flip),b,16616,a)].">
      <j1 rule="hyper" parents="58 15438 16616"/>
    </justification>
  </clause>

  <clause id="17170">
    <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),16687(a,1,2,1,2))].">
      <j1 rule="para" parents="18 16687"/>
    </justification>
  </clause>

  <clause id="17171">
    <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(16742(a,1),16743(a,1,1))].">
      <j1 rule="para" parents="16742 16743"/>
    </justification>
  </clause>

  <clause id="17172">
    <literal><![CDATA[
      K(x,(y * z) * R(u,z,y)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(8346,a,17171,a),flip(a)].">
      <j1 rule="hyper" parents="8346 17171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17173">
    <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(768(a,1),17172(a,2,2))].">
      <j1 rule="para" parents="768 17172"/>
    </justification>
  </clause>

  <clause id="17174">
    <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(11436(a,1),17172(a,2,2))].">
      <j1 rule="para" parents="11436 17172"/>
    </justification>
  </clause>

  <clause id="17175">
    <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),17173(a,1,2,1))].">
      <j1 rule="para" parents="5 17173"/>
    </justification>
  </clause>

  <clause id="17177">
    <literal><![CDATA[
      K(x,R(y,z \ u,z) * u) = K(x,L(y,z \ u,z) * u)
    ]]></literal>
    <justification jstring="[para(245(a,1),17175(a,1,2))].">
      <j1 rule="para" parents="245 17175"/>
    </justification>
  </clause>

  <clause id="17178">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * u) = K(x,(y * (u / z)) * z)
    ]]></literal>
    <justification jstring="[para(10665(a,1),17177(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10665 17177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17179">
    <literal><![CDATA[
      K(x,y * ((y \ T(z,u)) * u)) = K(x,(u * (z / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,14538,a(flip),b,17178,a)].">
      <j1 rule="hyper" parents="58 14538 17178"/>
    </justification>
  </clause>

  <clause id="17180">
    <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),17174(a,1,2,1))].">
      <j1 rule="para" parents="7 17174"/>
    </justification>
  </clause>

  <clause id="17182">
    <literal><![CDATA[
      K(x,y * R(T(z,y),u,u \ y)) = K(x,L(z,u,u \ y) * y)
    ]]></literal>
    <justification jstring="[para(10654(a,1),17180(a,1,2,2))].">
      <j1 rule="para" parents="10654 17180"/>
    </justification>
  </clause>

  <clause id="17183">
    <literal><![CDATA[
      K(x,L(y,z,z \ u) * u) = K(x,(y * z) * (z \ u))
    ]]></literal>
    <justification jstring="[para(751(a,1),17182(a,1,2)),flip(a)].">
      <j1 rule="para" parents="751 17182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17184">
    <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(334,a,14622,a,b,16882,a),flip(a)].">
      <j1 rule="hyper" parents="334 14622 16882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17185">
    <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,15730,a(flip),b,17159,a)].">
      <j1 rule="hyper" parents="58 15730 17159"/>
    </justification>
  </clause>

  <clause id="17186">
    <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(5441(a,1),17169(a,1,1,2))].">
      <j1 rule="para" parents="5441 17169"/>
    </justification>
  </clause>

  <clause id="17187">
    <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(16618(a,1),17186(a,1,1,2))].">
      <j1 rule="para" parents="16618 17186"/>
    </justification>
  </clause>

  <clause id="17188">
    <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(8100(a,1),17170(a,1,2))].">
      <j1 rule="para" parents="8100 17170"/>
    </justification>
  </clause>

  <clause id="17189">
    <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(16112(a,1),17184(a,2,3))].">
      <j1 rule="para" parents="16112 17184"/>
    </justification>
  </clause>

  <clause id="17190">
    <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(16574(a,1),17188(a,1,2))].">
      <j1 rule="para" parents="16574 17188"/>
    </justification>
  </clause>

  <clause id="17191">
    <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,10101,a(flip),b,17190,a)].">
      <j1 rule="hyper" parents="58 10101 17190"/>
    </justification>
  </clause>

  <clause id="17192">
    <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(16902(a,2),17191(a,1,2))].">
      <j1 rule="para" parents="16902 17191"/>
    </justification>
  </clause>

  <clause id="17193">
    <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(12515(a,1),17192(a,1,2,1))].">
      <j1 rule="para" parents="12515 17192"/>
    </justification>
  </clause>

  <clause id="17194">
    <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(14207(a,1),17193(a,1,2))].">
      <j1 rule="para" parents="14207 17193"/>
    </justification>
  </clause>

  <clause id="17195">
    <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(5391(a,1),17194(a,1,2))].">
      <j1 rule="para" parents="5391 17194"/>
    </justification>
  </clause>

  <clause id="17196">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u * K(y,x),z) = T(u,z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(8746,a,17195,a)].">
      <j1 rule="hyper" parents="8746 17195"/>
    </justification>
  </clause>

  <clause id="17197">
    <literal><![CDATA[
      K(x,y) * T(z * K(y,T(x,u)),u) = T(z,u * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(17098,a,17196,a)].">
      <j1 rule="hyper" parents="17098 17196"/>
    </justification>
  </clause>

  <clause id="17198">
    <literal><![CDATA[
      T(x * K(y,T(z,u)),u) = K(y,z) * T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5409,a,17197,a),flip(a)].">
      <j1 rule="hyper" parents="5409 17197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17199">
    <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(17198(a,2),14568(a,2,2)),flip(a)].">
      <j1 rule="para" parents="17198 14568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17200">
    <literal><![CDATA[
      L(x,K(y,T(z,x)),u) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(14510,a,17199,a)].">
      <j1 rule="hyper" parents="14510 17199"/>
    </justification>
  </clause>

  <clause id="17201">
    <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,16849,a(flip),b,17189,a)].">
      <j1 rule="hyper" parents="58 16849 17189"/>
    </justification>
  </clause>

  <clause id="17203">
    <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),16350(a,1,1))].">
      <j1 rule="para" parents="20 16350"/>
    </justification>
  </clause>

  <clause id="17204">
    <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(7690(a,1),16654(a,1,1,2,1))].">
      <j1 rule="para" parents="7690 16654"/>
    </justification>
  </clause>

  <clause id="17205">
    <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(5090(a,1),17204(a,1,1))].">
      <j1 rule="para" parents="5090 17204"/>
    </justification>
  </clause>

  <clause id="17206">
    <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),16921(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4 16921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17207">
    <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(16316,a,17206,a)].">
      <j1 rule="hyper" parents="16316 17206"/>
    </justification>
  </clause>

  <clause id="17209">
    <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),17207(a,1,2,2,2))].">
      <j1 rule="para" parents="24 17207"/>
    </justification>
  </clause>

  <clause id="17210">
    <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(15298(a,1),17203(a,1,1))].">
      <j1 rule="para" parents="15298 17203"/>
    </justification>
  </clause>

  <clause id="17212">
    <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,8912,a(flip),b,16489,a),flip(a)].">
      <j1 rule="hyper" parents="58 8912 16489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17214">
    <literal><![CDATA[
      K((x * y) / x,z * ((x / y) / T(x,y))) = K(y,((x / y) / x) * T(z,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,8393,a(flip),b,17212,a),flip(a)].">
      <j1 rule="hyper" parents="334 8393 17212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17215">
    <literal><![CDATA[
      K(x,T(y * ((z / x) / T(z,x)),z)) = K(x,((z / x) / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8190,a,17214,a)].">
      <j1 rule="hyper" parents="8190 17214"/>
    </justification>
  </clause>

  <clause id="17216">
    <literal><![CDATA[
      K(x,T(y * ((z / x) / z),z)) = K(x,((z / x) / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8952,a(flip),b,17215,a)].">
      <j1 rule="hyper" parents="58 8952 17215"/>
    </justification>
  </clause>

  <clause id="17217">
    <literal><![CDATA[
      K(x,T(((y / x) / y) * z,y)) = K(x,((y / x) / y) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16752,a,b,17216,a)].">
      <j1 rule="hyper" parents="58 16752 17216"/>
    </justification>
  </clause>

  <clause id="17218">
    <literal><![CDATA[
      K(x,((y / x) / y) * T(T(z,y),y)) = K(x,z * ((y / x) / y))
    ]]></literal>
    <justification jstring="[hyper(13830,a,17217,a),flip(a)].">
      <j1 rule="hyper" parents="13830 17217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17219">
    <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(4121(a,1),17218(a,2,2))].">
      <j1 rule="para" parents="4121 17218"/>
    </justification>
  </clause>

  <clause id="17220">
    <literal><![CDATA[
      K(x,T(T(y,z),z) * ((z / x) / z)) = K(x,y * ((y * ((z / x) / z)) / y))
    ]]></literal>
    <justification jstring="[para(464(a,1),17219(a,1,2))].">
      <j1 rule="para" parents="464 17219"/>
    </justification>
  </clause>

  <clause id="17221">
    <literal><![CDATA[
      K(x,T(y * ((z / x) / z),y)) = K(x,T(T(y,z),z) * ((z / x) / z))
    ]]></literal>
    <justification jstring="[hyper(334,a,12564,a(flip),b,17220,a)].">
      <j1 rule="hyper" parents="334 12564 17220"/>
    </justification>
  </clause>

  <clause id="17222">
    <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(17221(a,1),12587(a,1))].">
      <j1 rule="para" parents="17221 12587"/>
    </justification>
  </clause>

  <clause id="17223">
    <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(14133(a,1),16647(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="14133 16647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17224">
    <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(11244(a,1),17223(a,2,1))].">
      <j1 rule="para" parents="11244 17223"/>
    </justification>
  </clause>

  <clause id="17225">
    <literal><![CDATA[
      K(x,(y * z) \ (y * (L(y,u,w) * z))) = K(x,T(L(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8083,a(flip),b,17224,a),flip(a)].">
      <j1 rule="hyper" parents="334 8083 17224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17226">
    <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(730(a,1),17225(a,1,2))].">
      <j1 rule="para" parents="730 17225"/>
    </justification>
  </clause>

  <clause id="17227">
    <literal><![CDATA[
      K(x,T(L(y,z,u),y * w)) = K(x,T(L(y,z,u),w))
    ]]></literal>
    <justification jstring="[para(1014(a,1),17226(a,1,2))].">
      <j1 rule="para" parents="1014 17226"/>
    </justification>
  </clause>

  <clause id="17228">
    <literal><![CDATA[
      K(x,T(L(y,z,u),w / y)) = K(x,T(L(y,z,u),w))
    ]]></literal>
    <justification jstring="[hyper(16310,a,17227,a)].">
      <j1 rule="hyper" parents="16310 17227"/>
    </justification>
  </clause>

  <clause id="17229">
    <literal><![CDATA[
      K(x,L(y / (y / z),u,w)) = K(x,T(L(z,u,w),y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8286,a(flip),b,17228,a)].">
      <j1 rule="hyper" parents="58 8286 17228"/>
    </justification>
  </clause>

  <clause id="17230">
    <literal><![CDATA[
      K(x,T(L(y,z / y,u),z)) = K(x,(z * u) / ((z / y) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15118,a(flip),b,17229,a),flip(a)].">
      <j1 rule="hyper" parents="58 15118 17229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17231">
    <literal><![CDATA[
      K(x,(y * z) / ((y / u) * z)) = T(L(K(x,u),y,z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7440,a(flip),b,17230,a),flip(a)].">
      <j1 rule="hyper" parents="58 7440 17230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17232">
    <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),17231(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 17231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17233">
    <literal><![CDATA[
      K(x,y / (((y / z) / u) * z)) = y \ (z * (K(x,u) * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16709,a(flip),b,17232,a),flip(a)].">
      <j1 rule="hyper" parents="58 16709 17232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17234">
    <literal><![CDATA[
      K(x,(y / x) / ((((y / x) / y) / z) * y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,10495,a(flip),b,17233,a),flip(a)].">
      <j1 rule="hyper" parents="334 10495 17233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17235">
    <literal><![CDATA[
      K(x,y / (((((y / x) / y) / z) * y) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7340,a(flip),b,17234,a)].">
      <j1 rule="hyper" parents="58 7340 17234"/>
    </justification>
  </clause>

  <clause id="17236">
    <literal><![CDATA[
      K(x,1 / ((((y / x) / y) / z) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(11390,a,17235,a)].">
      <j1 rule="hyper" parents="11390 17235"/>
    </justification>
  </clause>

  <clause id="17238">
    <literal><![CDATA[
      K(x,y / (((z / x) / z) * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11391,a(flip),b,17236,a)].">
      <j1 rule="hyper" parents="58 11391 17236"/>
    </justification>
  </clause>

  <clause id="17239">
    <literal><![CDATA[
      K(x,y / (x * ((z / x) / z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10916,a,17238,a)].">
      <j1 rule="hyper" parents="10916 17238"/>
    </justification>
  </clause>

  <clause id="17240">
    <literal><![CDATA[
      L(K(x,y / x),y,(z / x) / z) = K(x,y * ((z / x) / z))
    ]]></literal>
    <justification jstring="[hyper(15143,a,17239,a)].">
      <j1 rule="hyper" parents="15143 17239"/>
    </justification>
  </clause>

  <clause id="17241">
    <literal><![CDATA[
      L(K(x,y / x),y,z / (z * x)) = K(x,y * ((z / x) / z))
    ]]></literal>
    <justification jstring="[hyper(14923,a,17240,a)].">
      <j1 rule="hyper" parents="14923 17240"/>
    </justification>
  </clause>

  <clause id="17242">
    <literal><![CDATA[
      K(x,y * ((z / x) / z)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(16716,a,17241,a),flip(a)].">
      <j1 rule="hyper" parents="16716 17241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17243">
    <literal><![CDATA[
      K(x,T(T(y,z),z) / x) = K(x,((z / x) / z) * y)
    ]]></literal>
    <justification jstring="[hyper(17222,a,17242,a),flip(a)].">
      <j1 rule="hyper" parents="17222 17242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17244">
    <literal><![CDATA[
      K(x,((y / x) / y) * z) = K(x,z / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,15530,a(flip),b,17243,a),flip(a)].">
      <j1 rule="hyper" parents="58 15530 17243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17246">
    <literal><![CDATA[
      K(x / y,z / (x / y)) = K(x / y,(y / x) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8561,a(flip),b,17244,a),flip(a)].">
      <j1 rule="hyper" parents="58 8561 17244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17247">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,(x / z) * y) = K(x \ z,y / (z / x))
    ]]></literal>
    <justification jstring="[para(17246(a,1),17086(a,1,2))].">
      <j1 rule="para" parents="17246 17086"/>
    </justification>
  </clause>

  <clause id="17248">
    <literal><![CDATA[
      K(x \ y,z / (y / x)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,17088,a(flip),b,17247,a),flip(a)].">
      <j1 rule="hyper" parents="58 17088 17247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17249">
    <literal><![CDATA[
      x * K(y \ z,x * (y / z)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[para(17248(a,1),8798(a,1,2))].">
      <j1 rule="para" parents="17248 8798"/>
    </justification>
  </clause>

  <clause id="17250">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = (y \ x) * (z / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,9716,a,b,17249,a)].">
      <j1 rule="hyper" parents="58 9716 17249"/>
    </justification>
  </clause>

  <clause id="17251">
    <literal><![CDATA[
      x * K(y \ z,x * (z \ y)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[para(9703(a,1),17249(a,1,2))].">
      <j1 rule="para" parents="9703 17249"/>
    </justification>
  </clause>

  <clause id="17252">
    <literal><![CDATA[
      x * K(y \ z,(z \ y) * x) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[para(9702(a,2),17251(a,1,2))].">
      <j1 rule="para" parents="9702 17251"/>
    </justification>
  </clause>

  <clause id="17253">
    <literal><![CDATA[
      (((x \ y) * z) \ z) * ((x \ y) * z) = (y \ x) * (z / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6637,a,b,17252,a)].">
      <j1 rule="hyper" parents="58 6637 17252"/>
    </justification>
  </clause>

  <clause id="17254">
    <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(7577(a,1),16669(a,1,2,2,1))].">
      <j1 rule="para" parents="7577 16669"/>
    </justification>
  </clause>

  <clause id="17255">
    <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(11143(a,1),16925(a,1,1))].">
      <j1 rule="para" parents="11143 16925"/>
    </justification>
  </clause>

  <clause id="17256">
    <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(6520(a,1),16346(a,1,2,1))].">
      <j1 rule="para" parents="6520 16346"/>
    </justification>
  </clause>

  <clause id="17257">
    <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(10071(a,1),16360(a,1,1))].">
      <j1 rule="para" parents="10071 16360"/>
    </justification>
  </clause>

  <clause id="17258">
    <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(6615(a,1),17257(a,1,2))].">
      <j1 rule="para" parents="6615 17257"/>
    </justification>
  </clause>

  <clause id="17259">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(15975(a,1),17258(a,1,2))].">
      <j1 rule="para" parents="15975 17258"/>
    </justification>
  </clause>

  <clause id="17260">
    <literal><![CDATA[
      a((x \ y) \ 1,z,(x \ y) \ 1) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,13155,a(flip),b,17259,a),flip(a)].">
      <j1 rule="hyper" parents="58 13155 17259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17261">
    <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(17260(a,1),13868(a,1,1))].">
      <j1 rule="para" parents="17260 13868"/>
    </justification>
  </clause>

  <clause id="17262">
    <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(13491(a,1),16947(a,1,2))].">
      <j1 rule="para" parents="13491 16947"/>
    </justification>
  </clause>

  <clause id="17263">
    <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(14883,a,17262,a),flip(a)].">
      <j1 rule="hyper" parents="14883 17262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17264">
    <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,16758,a(flip),b,17263,a)].">
      <j1 rule="hyper" parents="58 16758 17263"/>
    </justification>
  </clause>

  <clause id="17265">
    <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),17264(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6 17264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17267">
    <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(334,a,20,a,b,16496,a),flip(a)].">
      <j1 rule="hyper" parents="334 20 16496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17268">
    <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(7475(a,1),16806(a,1,2))].">
      <j1 rule="para" parents="7475 16806"/>
    </justification>
  </clause>

  <clause id="17270">
    <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(14805(a,1),17267(a,1,1,2,1))].">
      <j1 rule="para" parents="14805 17267"/>
    </justification>
  </clause>

  <clause id="17271">
    <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(14811(a,1),17270(a,1,1))].">
      <j1 rule="para" parents="14811 17270"/>
    </justification>
  </clause>

  <clause id="17272">
    <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),17271(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 17271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17273">
    <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(16471,a,17268,a)].">
      <j1 rule="hyper" parents="16471 17268"/>
    </justification>
  </clause>

  <clause id="17274">
    <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(16252,a,17273,a),flip(a)].">
      <j1 rule="hyper" parents="16252 17273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17276">
    <literal><![CDATA[
      (x / K(y,T(z,u))) \ (K(z,y) * u) = (x * K(z,y)) \ (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(16781(a,1),17274(a,1,1,2))].">
      <j1 rule="para" parents="16781 17274"/>
    </justification>
  </clause>

  <clause id="17277">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ (K(y,z) * u) = (x * K(y,z)) \ (u * K(y,z))
    ]]></literal>
    <justification jstring="[para(7475(a,1),17276(a,1,1))].">
      <j1 rule="para" parents="7475 17276"/>
    </justification>
  </clause>

  <clause id="17279">
    <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,17272,a,b,17277,a)].">
      <j1 rule="hyper" parents="58 17272 17277"/>
    </justification>
  </clause>

  <clause id="17280">
    <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(16510,a,16657,a)].">
      <j1 rule="hyper" parents="16510 16657"/>
    </justification>
  </clause>

  <clause id="17282">
    <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(16385(a,1),17280(a,1,1,2))].">
      <j1 rule="para" parents="16385 17280"/>
    </justification>
  </clause>

  <clause id="17284">
    <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),17261(a,1,1,1))].">
      <j1 rule="para" parents="4 17261"/>
    </justification>
  </clause>

  <clause id="17285">
    <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),17284(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="4 17284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17286">
    <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(6438(a,1),17285(a,2,2))].">
      <j1 rule="para" parents="6438 17285"/>
    </justification>
  </clause>

  <clause id="17287">
    <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),17286(a,2,2,2))].">
      <j1 rule="para" parents="4 17286"/>
    </justification>
  </clause>

  <clause id="17288">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = a(z,x,z) * K(x,z)
    ]]></literal>
    <justification jstring="[para(5230(a,1),17287(a,2,2))].">
      <j1 rule="para" parents="5230 17287"/>
    </justification>
  </clause>

  <clause id="17289">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,9180,a(flip),b,17288,a),flip(a)].">
      <j1 rule="hyper" parents="334 9180 17288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17290">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),y \ (y * z)) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(6759,a,17289,a)].">
      <j1 rule="hyper" parents="6759 17289"/>
    </justification>
  </clause>

  <clause id="17291">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),z) = K(z * x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),17290(a,1,2))].">
      <j1 rule="para" parents="4 17290"/>
    </justification>
  </clause>

  <clause id="17292">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(14428,a,17291,a)].">
      <j1 rule="hyper" parents="14428 17291"/>
    </justification>
  </clause>

  <clause id="17293">
    <literal><![CDATA[
      K(((x * y) \ x) \ z,y) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(9955,a,17292,a)].">
      <j1 rule="hyper" parents="9955 17292"/>
    </justification>
  </clause>

  <clause id="17294">
    <literal><![CDATA[
      K(((x * y) \ x) \ (y \ z),y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),17293(a,2,1))].">
      <j1 rule="para" parents="5 17293"/>
    </justification>
  </clause>

  <clause id="17295">
    <literal><![CDATA[
      K(((x * y) \ x) * z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,10614,a(flip),b,17294,a),flip(a)].">
      <j1 rule="hyper" parents="58 10614 17294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17296">
    <literal><![CDATA[
      K(x * ((y * z) \ y),z) = K(z \ x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9700,a(flip),b,17295,a)].">
      <j1 rule="hyper" parents="58 9700 17295"/>
    </justification>
  </clause>

  <clause id="17297">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K((y \ x) * z,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),17295(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 17295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17299">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(z * (y \ x),x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),17296(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 17296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17300">
    <literal><![CDATA[
      x * K((y \ z) * x,z \ y) = ((z \ y) \ x) * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,17297,a(flip),b,85,a)].">
      <j1 rule="hyper" parents="119 17297 85"/>
    </justification>
  </clause>

  <clause id="17301">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(z * (x / y),x \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,9705,a,b,17299,a),flip(a)].">
      <j1 rule="hyper" parents="334 9705 17299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17302">
    <literal><![CDATA[
      x * K(x * (y / z),y \ z) = ((y \ z) \ x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,17301,a(flip),b,85,a)].">
      <j1 rule="hyper" parents="119 17301 85"/>
    </justification>
  </clause>

  <clause id="17303">
    <literal><![CDATA[
      (((x \ y) \ 1) \ z) * ((x \ y) \ 1) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6452,a,b,17300,a)].">
      <j1 rule="hyper" parents="58 6452 17300"/>
    </justification>
  </clause>

  <clause id="17304">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9717,a,b,17302,a)].">
      <j1 rule="hyper" parents="58 9717 17302"/>
    </justification>
  </clause>

  <clause id="17305">
    <literal><![CDATA[
      ((x \ y) * z) * (z / ((x \ y) * z)) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4186,a(flip),b,17303,a)].">
      <j1 rule="hyper" parents="58 4186 17303"/>
    </justification>
  </clause>

  <clause id="17306">
    <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(17304(a,1),17131(a,1,1,1,2,1,2))].">
      <j1 rule="para" parents="17304 17131"/>
    </justification>
  </clause>

  <clause id="17307">
    <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(17250(a,1),17306(a,1,1,1))].">
      <j1 rule="para" parents="17250 17306"/>
    </justification>
  </clause>

  <clause id="17308">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u \ w)))) = K(1 / x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(17133,a,17307,a),flip(a)].">
      <j1 rule="hyper" parents="17133 17307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17309">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u \ w)))) = K(1 / x,T(y,z / (u / w)))
    ]]></literal>
    <justification jstring="[hyper(334,a,16786,a,b,17308,a),flip(a)].">
      <j1 rule="hyper" parents="334 16786 17308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17310">
    <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,16986,a,b,17309,a)].">
      <j1 rule="hyper" parents="58 16986 17309"/>
    </justification>
  </clause>

  <clause id="17311">
    <literal><![CDATA[
      K(1 / x,T(y,z / (u / w))) = K(1 / x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(16312,a,17310,a),flip(a)].">
      <j1 rule="hyper" parents="16312 17310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17312">
    <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(17311(a,1),16987(a,2,1))].">
      <j1 rule="para" parents="17311 16987"/>
    </justification>
  </clause>

  <clause id="17313">
    <literal><![CDATA[
      T(1 / x,T(y,z / (u / T(w,v5)))) = T(1 / x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(334,a,5178,a(flip),b,17312,a),flip(a)].">
      <j1 rule="hyper" parents="334 5178 17312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17314">
    <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(17313(a,1),3454(a,1,1))].">
      <j1 rule="para" parents="17313 3454"/>
    </justification>
  </clause>

  <clause id="17315">
    <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,3454,a(flip),b,17314,a),flip(a)].">
      <j1 rule="hyper" parents="58 3454 17314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17316">
    <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(17315(a,1),13936(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="17315 13936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17317">
    <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(334,a,13936,a(flip),b,17316,a),flip(a)].">
      <j1 rule="hyper" parents="334 13936 17316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17318">
    <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(334,a,7403,a(flip),b,17317,a),flip(a)].">
      <j1 rule="hyper" parents="334 7403 17317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17319">
    <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(7970,a,17318,a)].">
      <j1 rule="hyper" parents="7970 17318"/>
    </justification>
  </clause>

  <clause id="17320">
    <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,16984,a(flip),b,17319,a)].">
      <j1 rule="hyper" parents="58 16984 17319"/>
    </justification>
  </clause>

  <clause id="17321">
    <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,16985,a(flip),b,17320,a),flip(a)].">
      <j1 rule="hyper" parents="58 16985 17320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17322">
    <literal><![CDATA[
      K(x,T(y,(T(z,u) / w) * v5)) = K(x,T(y,v5 / (w / z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8751,a(flip),b,17321,a)].">
      <j1 rule="hyper" parents="58 8751 17321"/>
    </justification>
  </clause>

  <clause id="17323">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) = K(x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[para(104(a,1),17322(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="104 17322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17324">
    <literal><![CDATA[
      K(x,T(y,z / (u \ w))) = K(x,T(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(16827,a,17323,a)].">
      <j1 rule="hyper" parents="16827 17323"/>
    </justification>
  </clause>

  <clause id="17326">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,(z / u) * w)) = K(x,T(y,w / (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,8033,a,b,17324,a)].">
      <j1 rule="hyper" parents="334 8033 17324"/>
    </justification>
  </clause>

  <clause id="17327">
    <literal><![CDATA[
      K(x,K(y,z / (u / w))) = K(x,K(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(29,a,16829,a,b,17326,a)].">
      <j1 rule="hyper" parents="29 16829 17326"/>
    </justification>
  </clause>

  <clause id="17328">
    <literal><![CDATA[
      K(x,K(y,(z / u) / w)) = K(x,K(y,(u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(8545,a,17327,a)].">
      <j1 rule="hyper" parents="8545 17327"/>
    </justification>
  </clause>

  <clause id="17329">
    <literal><![CDATA[
      K(x,K(y,((z / u) / z) * w)) = K(x,K(y,w / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16858,a(flip),b,17327,a),flip(a)].">
      <j1 rule="hyper" parents="58 16858 17327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17330">
    <literal><![CDATA[
      K(x,K(y,(z / (z * u)) * w)) = K(x,K(y,w / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16857,a(flip),b,17327,a),flip(a)].">
      <j1 rule="hyper" parents="58 16857 17327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17331">
    <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(17327(a,1),16886(a,1,1))].">
      <j1 rule="para" parents="17327 16886"/>
    </justification>
  </clause>

  <clause id="17332">
    <literal><![CDATA[
      K(x,K(y,z * (u / (u * w)))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[hyper(16239,a,17330,a)].">
      <j1 rule="hyper" parents="16239 17330"/>
    </justification>
  </clause>

  <clause id="17333">
    <literal><![CDATA[
      K(x,K(y,z / (u \ w))) = K(x,K(y,z * (u / w)))
    ]]></literal>
    <justification jstring="[para(5(a,1),17332(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 17332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17334">
    <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(11144,a,17331,a),flip(a)].">
      <j1 rule="hyper" parents="11144 17331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17335">
    <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,16914,a(flip),b,17334,a),flip(a)].">
      <j1 rule="hyper" parents="58 16914 17334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17336">
    <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),17334(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="75 17334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17337">
    <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(16268,a,17336,a)].">
      <j1 rule="hyper" parents="16268 17336"/>
    </justification>
  </clause>

  <clause id="17338">
    <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),17335(a,2,2,2,2))].">
      <j1 rule="para" parents="5 17335"/>
    </justification>
  </clause>

  <clause id="17339">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(y * u) / z))
    ]]></literal>
    <justification jstring="[hyper(334,a,16852,a,b,17338,a),flip(a)].">
      <j1 rule="hyper" parents="334 16852 17338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17340">
    <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(17338(a,2),16892(a,1))].">
      <j1 rule="para" parents="17338 16892"/>
    </justification>
  </clause>

  <clause id="17341">
    <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,17337,a(flip),b,17339,a)].">
      <j1 rule="hyper" parents="58 17337 17339"/>
    </justification>
  </clause>

  <clause id="17342">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,z,y))) = K(x,K(w,(y * (1 / u)) / z))
    ]]></literal>
    <justification jstring="[para(14177(a,1),17339(a,1,2))].">
      <j1 rule="para" parents="14177 17339"/>
    </justification>
  </clause>

  <clause id="17343">
    <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(17339(a,2),16892(a,1))].">
      <j1 rule="para" parents="17339 16892"/>
    </justification>
  </clause>

  <clause id="17344">
    <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,17342,a(flip),b,17341,a),flip(a)].">
      <j1 rule="hyper" parents="58 17342 17341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17345">
    <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(4145(a,2),17341(a,2,2,2,1))].">
      <j1 rule="para" parents="4145 17341"/>
    </justification>
  </clause>

  <clause id="17346">
    <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(14179(a,1),17345(a,1,2))].">
      <j1 rule="para" parents="14179 17345"/>
    </justification>
  </clause>

  <clause id="17347">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) / (1 / u)) / w)) = K(x,K(y,(z * u) / w))
    ]]></literal>
    <justification jstring="[hyper(17340,a,17346,a),flip(a)].">
      <j1 rule="hyper" parents="17340 17346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17348">
    <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,17328,a(flip),b,17347,a)].">
      <j1 rule="hyper" parents="58 17328 17347"/>
    </justification>
  </clause>

  <clause id="17349">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) / w))) = K(x,K(y,(w * u) / z))
    ]]></literal>
    <justification jstring="[hyper(16916,a,17348,a)].">
      <j1 rule="hyper" parents="16916 17348"/>
    </justification>
  </clause>

  <clause id="17350">
    <literal><![CDATA[
      K(x,K(y,((z \ 1) / u) * w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,16928,a,b,17349,a)].">
      <j1 rule="hyper" parents="58 16928 17349"/>
    </justification>
  </clause>

  <clause id="17351">
    <literal><![CDATA[
      K(x,K(y,(z * (1 / u)) / w)) = K(x,K(y,(u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,16926,a(flip),b,17349,a),flip(a)].">
      <j1 rule="hyper" parents="58 16926 17349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17352">
    <literal><![CDATA[
      K(x,K(y,((z / (z / (u \ 1))) / w) * v5)) = K(x,K(y,(w * u) / v5))
    ]]></literal>
    <justification jstring="[hyper(16929,a,17350,a)].">
      <j1 rule="hyper" parents="16929 17350"/>
    </justification>
  </clause>

  <clause id="17353">
    <literal><![CDATA[
      K(x,K(y,z / ((1 / u) * w))) = K(x,K(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(16883,a,17351,a)].">
      <j1 rule="hyper" parents="16883 17351"/>
    </justification>
  </clause>

  <clause id="17354">
    <literal><![CDATA[
      K(x,K(y,(z * ((u / w) / u)) / v5)) = K(x,K(y,(w / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,17344,a,b,17351,a)].">
      <j1 rule="hyper" parents="58 17344 17351"/>
    </justification>
  </clause>

  <clause id="17355">
    <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,16261,a(flip),b,17351,a),flip(a)].">
      <j1 rule="hyper" parents="58 16261 17351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17356">
    <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,15230,a,b,17353,a)].">
      <j1 rule="hyper" parents="58 15230 17353"/>
    </justification>
  </clause>

  <clause id="17357">
    <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(8496(a,1),17353(a,1,2))].">
      <j1 rule="para" parents="8496 17353"/>
    </justification>
  </clause>

  <clause id="17358">
    <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(15067(a,1),17353(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="15067 17353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17359">
    <literal><![CDATA[
      K(x,K(y,z / (((u / w) / u) * v5))) = K(x,K(y,(w / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(16883,a,17354,a)].">
      <j1 rule="hyper" parents="16883 17354"/>
    </justification>
  </clause>

  <clause id="17360">
    <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,15040,a(flip),b,17356,a)].">
      <j1 rule="hyper" parents="58 15040 17356"/>
    </justification>
  </clause>

  <clause id="17361">
    <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(16571(a,1),17357(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16571 17357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17362">
    <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(334,a,17359,a(flip),b,17358,a),flip(a)].">
      <j1 rule="hyper" parents="334 17359 17358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17364">
    <literal><![CDATA[
      K(x,K(y,(z * (u / w)) / v5)) = K(x,K(y,((w / u) / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,17352,a(flip),b,17362,a)].">
      <j1 rule="hyper" parents="58 17352 17362"/>
    </justification>
  </clause>

  <clause id="17365">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) / v5)) = K(x,K(y,((u / z) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(16892,a,17364,a)].">
      <j1 rule="hyper" parents="16892 17364"/>
    </justification>
  </clause>

  <clause id="17367">
    <literal><![CDATA[
      K(x,K(y,z / ((u \ w) * v5))) = K(x,K(y,((u / w) / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16912,a(flip),b,17364,a)].">
      <j1 rule="hyper" parents="58 16912 17364"/>
    </justification>
  </clause>

  <clause id="17368">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * w) / v5)) = K(x,K(y,((z / u) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(8545,a,17367,a)].">
      <j1 rule="hyper" parents="8545 17367"/>
    </justification>
  </clause>

  <clause id="17369">
    <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),17367(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="105 17367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17370">
    <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,17201,a(flip),b,17368,a),flip(a)].">
      <j1 rule="hyper" parents="58 17201 17368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17371">
    <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(16229,a,17370,a)].">
      <j1 rule="hyper" parents="16229 17370"/>
    </justification>
  </clause>

  <clause id="17372">
    <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(334,a,14815,a,b,17370,a),flip(a)].">
      <j1 rule="hyper" parents="334 14815 17370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17373">
    <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(17370(a,1),8050(a,1))].">
      <j1 rule="para" parents="17370 8050"/>
    </justification>
  </clause>

  <clause id="17374">
    <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),17371(a,1,2,2,2,2))].">
      <j1 rule="para" parents="7 17371"/>
    </justification>
  </clause>

  <clause id="17375">
    <literal><![CDATA[
      K(x,K(y,z / (u * (w \ v5)))) = K(x,K(y,z * ((w / v5) / u)))
    ]]></literal>
    <justification jstring="[hyper(16916,a,17369,a),flip(a)].">
      <j1 rule="hyper" parents="16916 17369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17376">
    <literal><![CDATA[
      K(x,K(y,z / (u * (w / v5)))) = K(x,K(y,z * ((v5 / w) / u)))
    ]]></literal>
    <justification jstring="[hyper(16963,a,17375,a)].">
      <j1 rule="hyper" parents="16963 17375"/>
    </justification>
  </clause>

  <clause id="17377">
    <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(17376(a,1),17006(a,1))].">
      <j1 rule="para" parents="17376 17006"/>
    </justification>
  </clause>

  <clause id="17378">
    <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),17372(a,2,2))].">
      <j1 rule="para" parents="7 17372"/>
    </justification>
  </clause>

  <clause id="17379">
    <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(334,a,8456,a(flip),b,17361,a),flip(a)].">
      <j1 rule="hyper" parents="334 8456 17361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17380">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) * w))) = K(x,K(y,(u / w) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,17332,a(flip),b,17379,a),flip(a)].">
      <j1 rule="hyper" parents="58 17332 17379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17382">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) * w))) = K(x,K(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(334,a,17328,a(flip),b,17380,a),flip(a)].">
      <j1 rule="hyper" parents="334 17328 17380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17383">
    <literal><![CDATA[
      K(x,K(y,z * (u * (1 / w)))) = K(x,K(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(16919,a,17382,a)].">
      <j1 rule="hyper" parents="16919 17382"/>
    </justification>
  </clause>

  <clause id="17384">
    <literal><![CDATA[
      K(x,K(y,z * L(u,w,1 / w))) = K(x,K(y,((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[para(267(a,1),17382(a,1,2,2,2))].">
      <j1 rule="para" parents="267 17382"/>
    </justification>
  </clause>

  <clause id="17385">
    <literal><![CDATA[
      K(x,K(y,z * L(u,w,1 / w))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(334,a,16846,a(flip),b,17384,a),flip(a)].">
      <j1 rule="hyper" parents="334 16846 17384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17387">
    <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,17209,a(flip),b,17385,a),flip(a)].">
      <j1 rule="hyper" parents="58 17209 17385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17389">
    <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),17387(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="101 17387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17390">
    <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,16850,a,b,17389,a)].">
      <j1 rule="hyper" parents="58 16850 17389"/>
    </justification>
  </clause>

  <clause id="17391">
    <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(16917,a,17390,a),flip(a)].">
      <j1 rule="hyper" parents="16917 17390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17392">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((w / u) * z) * (1 / v5)))
    ]]></literal>
    <justification jstring="[hyper(16369,a,17390,a)].">
      <j1 rule="hyper" parents="16369 17390"/>
    </justification>
  </clause>

  <clause id="17393">
    <literal><![CDATA[
      K(x,K(y,z * (u * ((1 / w) * v5)))) = K(x,K(y,z * ((v5 / w) * u)))
    ]]></literal>
    <justification jstring="[hyper(16917,a,17391,a),flip(a)].">
      <j1 rule="hyper" parents="16917 17391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17394">
    <literal><![CDATA[
      K(x,K(y,z * (((u / (1 / w)) / w) * v5))) = K(x,K(y,z * (v5 * u)))
    ]]></literal>
    <justification jstring="[hyper(16920,a,17393,a),flip(a)].">
      <j1 rule="hyper" parents="16920 17393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17395">
    <literal><![CDATA[
      K(x,K(y,z * (((1 / u) * w) * v5))) = K(x,K(y,z * ((w / u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(16919,a,17393,a)].">
      <j1 rule="hyper" parents="16919 17393"/>
    </justification>
  </clause>

  <clause id="17396">
    <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,17355,a(flip),b,17393,a),flip(a)].">
      <j1 rule="hyper" parents="58 17355 17393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17397">
    <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,17383,a(flip),b,17396,a)].">
      <j1 rule="hyper" parents="58 17383 17396"/>
    </justification>
  </clause>

  <clause id="17398">
    <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(334,a,16900,a(flip),b,17394,a),flip(a)].">
      <j1 rule="hyper" parents="334 16900 17394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17399">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((w / u) * z) / v5))
    ]]></literal>
    <justification jstring="[hyper(334,a,12148,a(flip),b,17392,a),flip(a)].">
      <j1 rule="hyper" parents="334 12148 17392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17400">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((u / w) / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(334,a,17365,a(flip),b,17399,a),flip(a)].">
      <j1 rule="hyper" parents="334 17365 17399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17401">
    <literal><![CDATA[
      K(x,K(y,z / (u * ((1 / w) * v5)))) = K(x,K(y,((w / v5) / u) * z))
    ]]></literal>
    <justification jstring="[hyper(8545,a,17400,a)].">
      <j1 rule="hyper" parents="8545 17400"/>
    </justification>
  </clause>

  <clause id="17402">
    <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(13979(a,1),17401(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13979 17401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17403">
    <literal><![CDATA[
      K(x,K(y,z * ((u / (1 / w)) * K(w,v5)))) = K(x,K(y,(w * u) * z))
    ]]></literal>
    <justification jstring="[para(6467(a,1),17398(a,1,2,2,2))].">
      <j1 rule="para" parents="6467 17398"/>
    </justification>
  </clause>

  <clause id="17404">
    <literal><![CDATA[
      K(x,K(y,z * (u / (1 / w)))) = K(x,K(y,(w * u) * z))
    ]]></literal>
    <justification jstring="[hyper(16918,a,17403,a)].">
      <j1 rule="hyper" parents="16918 17403"/>
    </justification>
  </clause>

  <clause id="17405">
    <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,17404,a(flip),b,17397,a)].">
      <j1 rule="hyper" parents="58 17404 17397"/>
    </justification>
  </clause>

  <clause id="17406">
    <literal><![CDATA[
      K(x,K(y,L(z,1 / u,1 / w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(17377,a,17405,a),flip(a)].">
      <j1 rule="hyper" parents="17377 17405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17407">
    <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,14942,a(flip),b,17406,a)].">
      <j1 rule="hyper" parents="58 14942 17406"/>
    </justification>
  </clause>

  <clause id="17408">
    <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(334,a,14759,a,b,17402,a),flip(a)].">
      <j1 rule="hyper" parents="334 14759 17402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17409">
    <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,13353,a(flip),b,16691,a),flip(a)].">
      <j1 rule="hyper" parents="58 13353 16691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17410">
    <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),17409(a,1,2,1))].">
      <j1 rule="para" parents="60 17409"/>
    </justification>
  </clause>

  <clause id="17411">
    <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(16267,a,16915,a),flip(a)].">
      <j1 rule="hyper" parents="16267 16915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17413">
    <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(15111(a,1),17411(a,2,2))].">
      <j1 rule="para" parents="15111 17411"/>
    </justification>
  </clause>

  <clause id="17414">
    <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(334,a,16980,a(flip),b,17413,a),flip(a)].">
      <j1 rule="hyper" parents="334 16980 17413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17415">
    <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(16930,a,17414,a)].">
      <j1 rule="hyper" parents="16930 17414"/>
    </justification>
  </clause>

  <clause id="17417">
    <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,16881,a(flip),b,17415,a)].">
      <j1 rule="hyper" parents="58 16881 17415"/>
    </justification>
  </clause>

  <clause id="17418">
    <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,16874,a(flip),b,17417,a),flip(a)].">
      <j1 rule="hyper" parents="58 16874 17417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17419">
    <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(11170,a,17418,a)].">
      <j1 rule="hyper" parents="11170 17418"/>
    </justification>
  </clause>

  <clause id="17421">
    <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(14038(a,1),17418(a,1,2,2,2))].">
      <j1 rule="para" parents="14038 17418"/>
    </justification>
  </clause>

  <clause id="17422">
    <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(334,a,14762,a,b,17419,a),flip(a)].">
      <j1 rule="hyper" parents="334 14762 17419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17423">
    <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(334,a,17407,a(flip),b,17421,a),flip(a)].">
      <j1 rule="hyper" parents="334 17407 17421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17424">
    <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(17423(a,1),17255(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17423 17255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17425">
    <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(14763,a,17422,a)].">
      <j1 rule="hyper" parents="14763 17422"/>
    </justification>
  </clause>

  <clause id="17426">
    <literal><![CDATA[
      a(x,y * (z / y),K(u,K(w,v5))) = a(x,z,K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(4976(a,1),17425(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4976 17425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17427">
    <literal><![CDATA[
      a(x,y / z,K(u,K(w,v5))) = a(x,z \ y,K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(5129(a,1),17425(a,1,2))].">
      <j1 rule="para" parents="5129 17425"/>
    </justification>
  </clause>

  <clause id="17428">
    <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,12157,a(flip),b,17426,a),flip(a)].">
      <j1 rule="hyper" parents="58 12157 17426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17429">
    <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(8053(a,2),17428(a,2,3))].">
      <j1 rule="para" parents="8053 17428"/>
    </justification>
  </clause>

  <clause id="17430">
    <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(12152(a,1),17429(a,2,3))].">
      <j1 rule="para" parents="12152 17429"/>
    </justification>
  </clause>

  <clause id="17431">
    <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),17430(a,1,3,2,2))].">
      <j1 rule="para" parents="5 17430"/>
    </justification>
  </clause>

  <clause id="17432">
    <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(8053(a,1),17431(a,1,3))].">
      <j1 rule="para" parents="8053 17431"/>
    </justification>
  </clause>

  <clause id="17433">
    <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),17432(a,2,3,2,2))].">
      <j1 rule="para" parents="5 17432"/>
    </justification>
  </clause>

  <clause id="17434">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(z,K(u,w))) = a(x,y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(8053(a,1),17433(a,2,3))].">
      <j1 rule="para" parents="8053 17433"/>
    </justification>
  </clause>

  <clause id="17435">
    <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),17434(a,1,2,2))].">
      <j1 rule="para" parents="75 17434"/>
    </justification>
  </clause>

  <clause id="17436">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,w / y,K(w,K(z,u)))
    ]]></literal>
    <justification jstring="[para(8053(a,2),17435(a,1,3))].">
      <j1 rule="para" parents="8053 17435"/>
    </justification>
  </clause>

  <clause id="17437">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,w / y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(8053(a,2),17436(a,2,3))].">
      <j1 rule="para" parents="8053 17436"/>
    </justification>
  </clause>

  <clause id="17438">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,u / y,K(z,K(x,u)))
    ]]></literal>
    <justification jstring="[hyper(14837,a,17437,a)].">
      <j1 rule="hyper" parents="14837 17437"/>
    </justification>
  </clause>

  <clause id="17439">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,u / y,K(z,K(u,x)))
    ]]></literal>
    <justification jstring="[para(8067(a,1),17438(a,2,3))].">
      <j1 rule="para" parents="8067 17438"/>
    </justification>
  </clause>

  <clause id="17440">
    <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(8066(a,1),17424(a,2,2))].">
      <j1 rule="para" parents="8066 17424"/>
    </justification>
  </clause>

  <clause id="17442">
    <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(334,a,11838,a(flip),b,17440,a),flip(a)].">
      <j1 rule="hyper" parents="334 11838 17440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17443">
    <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(6878(a,1),17442(a,2,1))].">
      <j1 rule="para" parents="6878 17442"/>
    </justification>
  </clause>

  <clause id="17444">
    <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(334,a,14873,a(flip),b,17443,a),flip(a)].">
      <j1 rule="hyper" parents="334 14873 17443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17445">
    <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(16924(a,1),17444(a,1,2))].">
      <j1 rule="para" parents="16924 17444"/>
    </justification>
  </clause>

  <clause id="17446">
    <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(8066(a,1),17445(a,1,3))].">
      <j1 rule="para" parents="8066 17445"/>
    </justification>
  </clause>

  <clause id="17447">
    <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(11236,a,17446,a)].">
      <j1 rule="hyper" parents="11236 17446"/>
    </justification>
  </clause>

  <clause id="17448">
    <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),17447(a,1,2,1))].">
      <j1 rule="para" parents="167 17447"/>
    </justification>
  </clause>

  <clause id="17449">
    <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,17408,a,b,17448,a)].">
      <j1 rule="hyper" parents="58 17408 17448"/>
    </justification>
  </clause>

  <clause id="17450">
    <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,17439,a(flip),b,17448,a)].">
      <j1 rule="hyper" parents="58 17439 17448"/>
    </justification>
  </clause>

  <clause id="17451">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) = a(y,z,K(u,K(x,w)))
    ]]></literal>
    <justification jstring="[hyper(334,a,14731,a,b,17450,a),flip(a)].">
      <j1 rule="hyper" parents="334 14731 17450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17452">
    <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(8053(a,1),17449(a,2,3))].">
      <j1 rule="para" parents="8053 17449"/>
    </justification>
  </clause>

  <clause id="17453">
    <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(5783(a,1),17452(a,1,2,2,2,1))].">
      <j1 rule="para" parents="5783 17452"/>
    </justification>
  </clause>

  <clause id="17454">
    <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(14267(a,1),17004(a,1,2,2,1,2))].">
      <j1 rule="para" parents="14267 17004"/>
    </justification>
  </clause>

  <clause id="17455">
    <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(14544(a,1),17454(a,1,2,2,1))].">
      <j1 rule="para" parents="14544 17454"/>
    </justification>
  </clause>

  <clause id="17456">
    <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(10199(a,1),17453(a,1,2))].">
      <j1 rule="para" parents="10199 17453"/>
    </justification>
  </clause>

  <clause id="17457">
    <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(14274(a,1),17456(a,1,2))].">
      <j1 rule="para" parents="14274 17456"/>
    </justification>
  </clause>

  <clause id="17458">
    <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(6729(a,1),17457(a,1,2,2,1))].">
      <j1 rule="para" parents="6729 17457"/>
    </justification>
  </clause>

  <clause id="17459">
    <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,17395,a(flip),b,17458,a)].">
      <j1 rule="hyper" parents="58 17395 17458"/>
    </justification>
  </clause>

  <clause id="17460">
    <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(16889,a,17459,a)].">
      <j1 rule="hyper" parents="16889 17459"/>
    </justification>
  </clause>

  <clause id="17461">
    <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(6545(a,1),17460(a,2,3,2))].">
      <j1 rule="para" parents="6545 17460"/>
    </justification>
  </clause>

  <clause id="17462">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * ((u / w) / z))) = a(w,u,K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(16842(a,1),17461(a,2,3))].">
      <j1 rule="para" parents="16842 17461"/>
    </justification>
  </clause>

  <clause id="17463">
    <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,17374,a(flip),b,17462,a)].">
      <j1 rule="hyper" parents="58 17374 17462"/>
    </justification>
  </clause>

  <clause id="17465">
    <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),17463(a,1,3,2,1))].">
      <j1 rule="para" parents="72 17463"/>
    </justification>
  </clause>

  <clause id="17466">
    <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(17333(a,1),17465(a,1,3))].">
      <j1 rule="para" parents="17333 17465"/>
    </justification>
  </clause>

  <clause id="17467">
    <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(8048(a,1),17466(a,1,3))].">
      <j1 rule="para" parents="8048 17466"/>
    </justification>
  </clause>

  <clause id="17468">
    <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(17083(a,1),17467(a,1,3))].">
      <j1 rule="para" parents="17083 17467"/>
    </justification>
  </clause>

  <clause id="17469">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(w,z))) = a(u,z,K(y,K(w,x / z)))
    ]]></literal>
    <justification jstring="[hyper(14714,a,17468,a),flip(a)].">
      <j1 rule="hyper" parents="14714 17468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17470">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(z,w))) = a(u,z,K(y,K(w,x / z)))
    ]]></literal>
    <justification jstring="[para(8067(a,1),17469(a,1,3))].">
      <j1 rule="para" parents="8067 17469"/>
    </justification>
  </clause>

  <clause id="17471">
    <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,17427,a,b,17470,a)].">
      <j1 rule="hyper" parents="58 17427 17470"/>
    </justification>
  </clause>

  <clause id="17472">
    <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,17451,a(flip),b,17471,a),flip(a)].">
      <j1 rule="hyper" parents="58 17451 17471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17473">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(y,z,K(w,K(x,u)))
    ]]></literal>
    <justification jstring="[para(8048(a,1),17472(a,2,3))].">
      <j1 rule="para" parents="8048 17472"/>
    </justification>
  </clause>

  <clause id="17474">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(z,y,K(u,K(x,w)))
    ]]></literal>
    <justification jstring="[hyper(17373,a,17473,a)].">
      <j1 rule="hyper" parents="17373 17473"/>
    </justification>
  </clause>

  <clause id="17475">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(z,y,K(x,K(w,u)))
    ]]></literal>
    <justification jstring="[para(8053(a,2),17474(a,2,3))].">
      <j1 rule="para" parents="8053 17474"/>
    </justification>
  </clause>

  <clause id="17476">
    <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,17378,a(flip),b,17475,a)].">
      <j1 rule="hyper" parents="58 17378 17475"/>
    </justification>
  </clause>

  <clause id="17477">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(w,x,K(z,K(u,y)))
    ]]></literal>
    <justification jstring="[para(8458(a,1),17476(a,1,3))].">
      <j1 rule="para" parents="8458 17476"/>
    </justification>
  </clause>

  <clause id="17478">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(w,x,K(z,K(y,u)))
    ]]></literal>
    <justification jstring="[para(8067(a,1),17477(a,2,3))].">
      <j1 rule="para" parents="8067 17477"/>
    </justification>
  </clause>

  <clause id="17479">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,z,K(x,K(y,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17473,a(flip),b,17478,a),flip(a)].">
      <j1 rule="hyper" parents="58 17473 17478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17480">
    <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(17479(a,1),14730(a,1,1))].">
      <j1 rule="para" parents="17479 14730"/>
    </justification>
  </clause>

  <clause id="17481">
    <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(8048(a,1),17480(a,1,2))].">
      <j1 rule="para" parents="8048 17480"/>
    </justification>
  </clause>

  <clause id="17482">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(z,L(y,w,u)))
    ]]></literal>
    <justification jstring="[hyper(14953,a,17481,a),flip(a)].">
      <j1 rule="hyper" parents="14953 17481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17483">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,L(z,w,u)))
    ]]></literal>
    <justification jstring="[hyper(11237,a,17482,a)].">
      <j1 rule="hyper" parents="11237 17482"/>
    </justification>
  </clause>

  <clause id="17484">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(334,a,17360,a(flip),b,17483,a),flip(a)].">
      <j1 rule="hyper" parents="334 17360 17483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17485">
    <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(717(a,1),17483(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="717 17483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17486">
    <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(6974(a,1),17483(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6974 17483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17487">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,(z / w) * u))
    ]]></literal>
    <justification jstring="[hyper(17343,a,17484,a)].">
      <j1 rule="hyper" parents="17343 17484"/>
    </justification>
  </clause>

  <clause id="17488">
    <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(17486(a,2),8473(a,1))].">
      <j1 rule="para" parents="17486 8473"/>
    </justification>
  </clause>

  <clause id="17489">
    <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(334,a,16091,a,b,17485,a),flip(a)].">
      <j1 rule="hyper" parents="334 16091 17485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17490">
    <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(334,a,17487,a(flip),b,17489,a),flip(a)].">
      <j1 rule="hyper" parents="334 17487 17489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17491">
    <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(334,a,17329,a(flip),b,17490,a),flip(a)].">
      <j1 rule="hyper" parents="334 17329 17490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17494">
    <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(8283(a,1),17491(a,2,2))].">
      <j1 rule="para" parents="8283 17491"/>
    </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,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(334,a,16083,a(flip),b,17494,a),flip(a)].">
      <j1 rule="hyper" parents="334 16083 17494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17498">
    <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,15040,a(flip),b,17495,a)].">
      <j1 rule="hyper" parents="58 15040 17495"/>
    </justification>
  </clause>

  <clause id="17499">
    <literal><![CDATA[
      K(x,K(y,L(1 / z,z,u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(17488,a,17498,a),flip(a)].">
      <j1 rule="hyper" parents="17488 17498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17502">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,1 / z))
    ]]></literal>
    <justification jstring="[para(6671(a,1),17499(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6671 17499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17504">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,8469,a(flip),b,17502,a),flip(a)].">
      <j1 rule="hyper" parents="334 8469 17502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17505">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,8456,a(flip),b,17502,a),flip(a)].">
      <j1 rule="hyper" parents="334 8456 17502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17508">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(11170,a,17504,a)].">
      <j1 rule="hyper" parents="11170 17504"/>
    </justification>
  </clause>

  <clause id="17511">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = x * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(17504(a,1),11160(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17504 11160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17512">
    <literal><![CDATA[
      (x * y) * K(z,K(u,w)) = x * (y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(17504(a,1),11183(a,1,2))].">
      <j1 rule="para" parents="17504 11183"/>
    </justification>
  </clause>

  <clause id="17521">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,17505,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 17505 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17522">
    <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(17505(a,1),8686(a,1,1))].">
      <j1 rule="para" parents="17505 8686"/>
    </justification>
  </clause>

  <clause id="17524">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(15114(a,2),17505(a,1,2))].">
      <j1 rule="para" parents="15114 17505"/>
    </justification>
  </clause>

  <clause id="17527">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,17508,a,b,1992,a),flip(a)].">
      <j1 rule="hyper" parents="115 17508 1992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17529">
    <literal><![CDATA[
      a(K(x,y),z,K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,17508,a(flip),b,14640,a),flip(a)].">
      <j1 rule="hyper" parents="115 17508 14640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17530">
    <literal><![CDATA[
      x \ (y * K(z,K(u,w))) = (x \ y) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[para(17508(a,1),487(a,1,2,2))].">
      <j1 rule="para" parents="17508 487"/>
    </justification>
  </clause>

  <clause id="17531">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * w = K(x,K(y,z)) * (u * w)
    ]]></literal>
    <justification jstring="[para(17508(a,1),15138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17508 15138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17532">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * w) = (K(x,K(y,z)) \ u) * w
    ]]></literal>
    <justification jstring="[para(17508(a,1),15165(a,1,1))].">
      <j1 rule="para" parents="17508 15165"/>
    </justification>
  </clause>

  <clause id="17533">
    <literal><![CDATA[
      L(K(x,y),z,K(u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(13992,a,17527,a)].">
      <j1 rule="hyper" parents="13992 17527"/>
    </justification>
  </clause>

  <clause id="17534">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(13708,a,17527,a)].">
      <j1 rule="hyper" parents="13708 17527"/>
    </justification>
  </clause>

  <clause id="17538">
    <literal><![CDATA[
      K(x,K(y,a(z,u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,14766,a(flip),b,17527,a)].">
      <j1 rule="hyper" parents="58 14766 17527"/>
    </justification>
  </clause>

  <clause id="17540">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(168,a,15283,a,b,17527,a(flip))].">
      <j1 rule="hyper" parents="168 15283 17527"/>
    </justification>
  </clause>

  <clause id="17542">
    <literal><![CDATA[
      L(K(x,y),z,K(u,w)) = K(x,y) * 1
    ]]></literal>
    <justification jstring="[para(17527(a,1),14640(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17527 14640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17544">
    <literal><![CDATA[
      T(x,L(y,z,K(u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(11200,a,17529,a)].">
      <j1 rule="hyper" parents="11200 17529"/>
    </justification>
  </clause>

  <clause id="17545">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,w) = K(x,y) * (z * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(214,a,17529,a)].">
      <j1 rule="hyper" parents="214 17529"/>
    </justification>
  </clause>

  <clause id="17547">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(168,a,16582,a,b,17529,a(flip))].">
      <j1 rule="hyper" parents="168 16582 17529"/>
    </justification>
  </clause>

  <clause id="17548">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(168,a,15359,a,b,17529,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="168 15359 17529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17549">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = w * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(2420,a,17534,a),flip(a)].">
      <j1 rule="hyper" parents="2420 17534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17551">
    <literal><![CDATA[
      T(a(x,y,K(z,u)),w) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(49,a,17534,a)].">
      <j1 rule="hyper" parents="49 17534"/>
    </justification>
  </clause>

  <clause id="17552">
    <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(17534(a,1),294(a,1,2))].">
      <j1 rule="para" parents="17534 294"/>
    </justification>
  </clause>

  <clause id="17553">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w))) = x
    ]]></literal>
    <justification jstring="[para(13702(a,1),17534(a,1,2))].">
      <j1 rule="para" parents="13702 17534"/>
    </justification>
  </clause>

  <clause id="17554">
    <literal><![CDATA[
      T(x,K(a(y,z,u),w)) = x
    ]]></literal>
    <justification jstring="[para(13729(a,1),17534(a,1,2))].">
      <j1 rule="para" parents="13729 17534"/>
    </justification>
  </clause>

  <clause id="17555">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w) \ z)) = x
    ]]></literal>
    <justification jstring="[para(14612(a,2),17534(a,1,2))].">
      <j1 rule="para" parents="14612 17534"/>
    </justification>
  </clause>

  <clause id="17559">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8339,a,17538,a)].">
      <j1 rule="hyper" parents="8339 17538"/>
    </justification>
  </clause>

  <clause id="17565">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ (K(x,K(y,z)) * w) = u \ w
    ]]></literal>
    <justification jstring="[hyper(13603,a,17540,a)].">
      <j1 rule="hyper" parents="13603 17540"/>
    </justification>
  </clause>

  <clause id="17566">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = u \ (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(782,a,17540,a)].">
      <j1 rule="hyper" parents="782 17540"/>
    </justification>
  </clause>

  <clause id="17568">
    <literal><![CDATA[
      L(x,y,K(z,u) / w) = L(x,y,w \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15336,a(flip),b,17540,a)].">
      <j1 rule="hyper" parents="58 15336 17540"/>
    </justification>
  </clause>

  <clause id="17569">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      v5 = x
    ]]></literal>
    <justification jstring="[para(17540(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="17540 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17570">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(17540(a,1),45(a,2))].">
      <j1 rule="para" parents="17540 45"/>
    </justification>
  </clause>

  <clause id="17571">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) / w = K(x,K(y,z)) * (u / w)
    ]]></literal>
    <justification jstring="[para(17540(a,1),556(a,1,2))].">
      <j1 rule="para" parents="17540 556"/>
    </justification>
  </clause>

  <clause id="17572">
    <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(17540(a,1),491(a,2,1))].">
      <j1 rule="para" parents="17540 491"/>
    </justification>
  </clause>

  <clause id="17573">
    <literal><![CDATA[
      K(x,K(y,z)) * L(x,u,w) = L(T(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(17540(a,1),15311(a,1,2,1))].">
      <j1 rule="para" parents="17540 15311"/>
    </justification>
  </clause>

  <clause id="17574">
    <literal><![CDATA[
      L(x,y,K(z,u) * w) = L(x,y,w * K(z,u))
    ]]></literal>
    <justification jstring="[para(17540(a,1),15366(a,1,1))].">
      <j1 rule="para" parents="17540 15366"/>
    </justification>
  </clause>

  <clause id="17575">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) = T(x,w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12581,a,17553,a)].">
      <j1 rule="hyper" parents="12581 17553"/>
    </justification>
  </clause>

  <clause id="17577">
    <literal><![CDATA[
      T(x,T(y,a(z,u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(7969,a,17553,a)].">
      <j1 rule="hyper" parents="7969 17553"/>
    </justification>
  </clause>

  <clause id="17578">
    <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(17553(a,1),15467(a,1,2,1,2))].">
      <j1 rule="para" parents="17553 15467"/>
    </justification>
  </clause>

  <clause id="17580">
    <literal><![CDATA[
      T(K(x,y),a(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15287,a,17533,a)].">
      <j1 rule="hyper" parents="15287 17533"/>
    </justification>
  </clause>

  <clause id="17581">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11132,a,17533,a)].">
      <j1 rule="hyper" parents="11132 17533"/>
    </justification>
  </clause>

  <clause id="17583">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K(z \ (K(y,x) * u),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,6904,a(flip),b,17533,a),flip(a)].">
      <j1 rule="hyper" parents="58 6904 17533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17584">
    <literal><![CDATA[
      L(x * K(y,z),u,K(w,x)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(17533(a,1),15337(a,2,2))].">
      <j1 rule="para" parents="17533 15337"/>
    </justification>
  </clause>

  <clause id="17585">
    <literal><![CDATA[
      K(x,y) * a(z,u,w) = a(z,u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[para(17533(a,1),15302(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17533 15302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17588">
    <literal><![CDATA[
      T(x,T((K(y,z) * u) \ w,v5)) = T(x,T(u \ (K(y,z) \ w),v5))
    ]]></literal>
    <justification jstring="[para(577(a,1),17544(a,1,2))].">
      <j1 rule="para" parents="577 17544"/>
    </justification>
  </clause>

  <clause id="17589">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) = T(x,u \ (K(z,y) * w))
    ]]></literal>
    <justification jstring="[para(5415(a,1),17544(a,1,2))].">
      <j1 rule="para" parents="5415 17544"/>
    </justification>
  </clause>

  <clause id="17590">
    <literal><![CDATA[
      T(x,L(y,z,T(u,w))) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(7187(a,1),17544(a,1,2))].">
      <j1 rule="para" parents="7187 17544"/>
    </justification>
  </clause>

  <clause id="17591">
    <literal><![CDATA[
      ((x * y) * ((K(y,x) * z) * u)) / T((y * x) * z,u) = L(u,z,x * y)
    ]]></literal>
    <justification jstring="[para(17544(a,1),15401(a,1,2))].">
      <j1 rule="para" parents="17544 15401"/>
    </justification>
  </clause>

  <clause id="17592">
    <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(16793,a,17547,a)].">
      <j1 rule="hyper" parents="16793 17547"/>
    </justification>
  </clause>

  <clause id="17593">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w) \ z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8631,a,17555,a)].">
      <j1 rule="hyper" parents="8631 17555"/>
    </justification>
  </clause>

  <clause id="17594">
    <literal><![CDATA[
      T(x,K(y,z \ L(z,u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(8490,a,17555,a)].">
      <j1 rule="hyper" parents="8490 17555"/>
    </justification>
  </clause>

  <clause id="17595">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      T(y,K(z,L(u,w,v5) \ u)) = x
    ]]></literal>
    <justification jstring="[para(17555(a,1),8121(a,1))].">
      <j1 rule="para" parents="17555 8121"/>
    </justification>
  </clause>

  <clause id="17598">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ w) * y) = K(x,y * (w / L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15617,a(flip),b,17559,a),flip(a)].">
      <j1 rule="hyper" parents="58 15617 17559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17599">
    <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(17559(a,1),7427(a,1,2))].">
      <j1 rule="para" parents="17559 7427"/>
    </justification>
  </clause>

  <clause id="17600">
    <literal><![CDATA[
      T(K(x,y),a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(17559(a,1),8256(a,1,1))].">
      <j1 rule="para" parents="17559 8256"/>
    </justification>
  </clause>

  <clause id="17601">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(17559(a,1),8281(a,1))].">
      <j1 rule="para" parents="17559 8281"/>
    </justification>
  </clause>

  <clause id="17602">
    <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(17559(a,1),12526(a,1))].">
      <j1 rule="para" parents="17559 12526"/>
    </justification>
  </clause>

  <clause id="17603">
    <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(17559(a,1),12588(a,1))].">
      <j1 rule="para" parents="17559 12588"/>
    </justification>
  </clause>

  <clause id="17604">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(14703(a,1),17559(a,1,2))].">
      <j1 rule="para" parents="14703 17559"/>
    </justification>
  </clause>

  <clause id="17605">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,u \ (K(z,y) * w))
    ]]></literal>
    <justification jstring="[para(15313(a,1),17559(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15313 17559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17606">
    <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,7882,a(flip),b,17577,a),flip(a)].">
      <j1 rule="hyper" parents="58 7882 17577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17607">
    <literal><![CDATA[
      K(x,y) * ((a(z,u,w) \ y) * x) = (a(z,u,w) \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(17577(a,1),8522(a,2,2))].">
      <j1 rule="para" parents="17577 8522"/>
    </justification>
  </clause>

  <clause id="17608">
    <literal><![CDATA[
      T(a(x,y,z),K(u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(49,a,17580,a)].">
      <j1 rule="hyper" parents="49 17580"/>
    </justification>
  </clause>

  <clause id="17609">
    <literal><![CDATA[
      T(K(x,y) * z,a(z,u,w)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(17580(a,1),14784(a,2,1))].">
      <j1 rule="para" parents="17580 14784"/>
    </justification>
  </clause>

  <clause id="17611">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(7187(a,1),17581(a,1,2))].">
      <j1 rule="para" parents="7187 17581"/>
    </justification>
  </clause>

  <clause id="17612">
    <literal><![CDATA[
      K(x,L(y,z,u / w)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[para(13050(a,1),17581(a,1,2))].">
      <j1 rule="para" parents="13050 17581"/>
    </justification>
  </clause>

  <clause id="17613">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,y / (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(15280(a,1),17581(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15280 17581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17614">
    <literal><![CDATA[
      K(x,T(y,z \ L(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8631,a,17594,a)].">
      <j1 rule="hyper" parents="8631 17594"/>
    </justification>
  </clause>

  <clause id="17615">
    <literal><![CDATA[
      L(x,y,(y * x) \ z) = L(x,y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11523,a(flip),b,17548,a),flip(a)].">
      <j1 rule="hyper" parents="58 11523 17548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17616">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(7187(a,1),17569(a,1)),flip(b)].">
      <j1 rule="para" parents="7187 17569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17617">
    <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(13050(a,1),17569(a,1)),flip(b)].">
      <j1 rule="para" parents="13050 17569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17619">
    <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(17521(a,1),294(a,1,2))].">
      <j1 rule="para" parents="17521 294"/>
    </justification>
  </clause>

  <clause id="17620">
    <literal><![CDATA[
      T(x,K(y,(z \ u) \ w)) = T(x,K(y,u \ (z * w)))
    ]]></literal>
    <justification jstring="[para(502(a,1),17521(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="502 17521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17622">
    <literal><![CDATA[
      K(x,K(y,z \ (u * (w \ z)))) = K(x,K(y,u / w))
    ]]></literal>
    <justification jstring="[hyper(16315,a,17524,a)].">
      <j1 rule="hyper" parents="16315 17524"/>
    </justification>
  </clause>

  <clause id="17629">
    <literal><![CDATA[
      L(K(x,y),z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(17542(a,2),127(a,1)),flip(b)].">
      <j1 rule="para" parents="17542 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17630">
    <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,14456,a(flip),b,17593,a)].">
      <j1 rule="hyper" parents="58 14456 17593"/>
    </justification>
  </clause>

  <clause id="17631">
    <literal><![CDATA[
      K(x,T(y \ R(z,u,w),z)) = K(x,R(z,u,w) / y)
    ]]></literal>
    <justification jstring="[hyper(15108,a,17604,a),flip(a)].">
      <j1 rule="hyper" parents="15108 17604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17632">
    <literal><![CDATA[
      K(x,T(y * (L(y,z,u) \ w),y)) = K(x,(y * w) / L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8540,a,17604,a),flip(a)].">
      <j1 rule="hyper" parents="8540 17604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17634">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ w)) = K(x,T(y,u \ (z \ w)))
    ]]></literal>
    <justification jstring="[para(311(a,1),17604(a,1,2,2))].">
      <j1 rule="para" parents="311 17604"/>
    </justification>
  </clause>

  <clause id="17636">
    <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(17604(a,1),12591(a,1))].">
      <j1 rule="para" parents="17604 12591"/>
    </justification>
  </clause>

  <clause id="17637">
    <literal><![CDATA[
      K(x,T(y,(z / u) / w)) = K(x,T(y,z / (w * u)))
    ]]></literal>
    <justification jstring="[para(15106(a,1),17604(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15106 17604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17638">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) = K(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(12588,a,17614,a)].">
      <j1 rule="hyper" parents="12588 17614"/>
    </justification>
  </clause>

  <clause id="17639">
    <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(17614(a,1),12587(a,1))].">
      <j1 rule="para" parents="17614 12587"/>
    </justification>
  </clause>

  <clause id="17640">
    <literal><![CDATA[
      T(a(x,y,K(z,u)),w) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,14592,a(flip),b,17551,a),flip(a)].">
      <j1 rule="hyper" parents="334 14592 17551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17641">
    <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,15430,a(flip),b,17590,a),flip(a)].">
      <j1 rule="hyper" parents="58 15430 17590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17642">
    <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,14804,a(flip),b,17590,a),flip(a)].">
      <j1 rule="hyper" parents="58 14804 17590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17643">
    <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(8172(a,1),17600(a,1))].">
      <j1 rule="para" parents="8172 17600"/>
    </justification>
  </clause>

  <clause id="17644">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(14703(a,1),17601(a,1,2))].">
      <j1 rule="para" parents="14703 17601"/>
    </justification>
  </clause>

  <clause id="17645">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(15279(a,2),17601(a,1,2))].">
      <j1 rule="para" parents="15279 17601"/>
    </justification>
  </clause>

  <clause id="17646">
    <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,13806,a(flip),b,17611,a),flip(a)].">
      <j1 rule="hyper" parents="58 13806 17611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17647">
    <literal><![CDATA[
      K(x,L(y,z,u * w)) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[para(12872(a,1),17611(a,1,2))].">
      <j1 rule="para" parents="12872 17611"/>
    </justification>
  </clause>

  <clause id="17649">
    <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(6459(a,2),17629(a,1))].">
      <j1 rule="para" parents="6459 17629"/>
    </justification>
  </clause>

  <clause id="17650">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = w * a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,17640,a(flip),b,16371,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 17640 16371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17651">
    <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(7136(a,1),17645(a,1,2))].">
      <j1 rule="para" parents="7136 17645"/>
    </justification>
  </clause>

  <clause id="17652">
    <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(7187(a,1),17645(a,1,2))].">
      <j1 rule="para" parents="7187 17645"/>
    </justification>
  </clause>

  <clause id="17653">
    <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(13050(a,1),17645(a,1,2))].">
      <j1 rule="para" parents="13050 17645"/>
    </justification>
  </clause>

  <clause id="17654">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(17511(a,2),5030(a,1))].">
      <j1 rule="para" parents="17511 5030"/>
    </justification>
  </clause>

  <clause id="17656">
    <literal><![CDATA[
      T(x * K(y,z),a(u,w,x)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(17584(a,1),15304(a,1,1))].">
      <j1 rule="para" parents="17584 15304"/>
    </justification>
  </clause>

  <clause id="17657">
    <literal><![CDATA[
      L(K(x,y) * z,u,K(w,z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(15343,a,17609,a)].">
      <j1 rule="hyper" parents="15343 17609"/>
    </justification>
  </clause>

  <clause id="17658">
    <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),17616(a,1,3))].">
      <j1 rule="para" parents="18 17616"/>
    </justification>
  </clause>

  <clause id="17659">
    <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(8362(a,1),17616(a,1,3))].">
      <j1 rule="para" parents="8362 17616"/>
    </justification>
  </clause>

  <clause id="17660">
    <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(12572(a,1),17616(a,1,3))].">
      <j1 rule="para" parents="12572 17616"/>
    </justification>
  </clause>

  <clause id="17661">
    <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(17656(a,1),14275(a,2,2))].">
      <j1 rule="para" parents="17656 14275"/>
    </justification>
  </clause>

  <clause id="17662">
    <literal><![CDATA[
      (K(x,y) * z) / a(u,w,z) = a(u,w,z) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(116,a,17657,a(flip),b,15317,a),flip(a)].">
      <j1 rule="hyper" parents="116 17657 15317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17663">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * a(u,y,K(z,x))) = w
    ]]></literal>
    <justification jstring="[hyper(14655,a,17549,a)].">
      <j1 rule="hyper" parents="14655 17549"/>
    </justification>
  </clause>

  <clause id="17664">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,x)) = T(x,a(z,u,w)) \ y
    ]]></literal>
    <justification jstring="[hyper(13738,a,17549,a),flip(a)].">
      <j1 rule="hyper" parents="13738 17549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17665">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = w * a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,14594,a,b,17549,a),flip(a)].">
      <j1 rule="hyper" parents="334 14594 17549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17666">
    <literal><![CDATA[
      x \ (y * a(z,u,K(w,v5))) = a(z,u,K(w,v5)) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,778,a,b,17549,a)].">
      <j1 rule="hyper" parents="334 778 17549"/>
    </justification>
  </clause>

  <clause id="17667">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * x) = w * T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,14613,a(flip),b,17549,a),flip(a)].">
      <j1 rule="hyper" parents="334 14613 17549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17668">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * v5) = w * (v5 * a(x,y,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,358,a(flip),b,17549,a),flip(a)].">
      <j1 rule="hyper" parents="334 358 17549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17670">
    <literal><![CDATA[
      K(x,a(y,z,u)) * w = w * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14588(a,1),17549(a,1,1))].">
      <j1 rule="para" parents="14588 17549"/>
    </justification>
  </clause>

  <clause id="17671">
    <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(17549(a,1),14725(a,1))].">
      <j1 rule="para" parents="17549 14725"/>
    </justification>
  </clause>

  <clause id="17672">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * v5 = a(y,z,K(u,w)) * (x * v5)
    ]]></literal>
    <justification jstring="[para(17549(a,1),14604(a,1,1))].">
      <j1 rule="para" parents="17549 14604"/>
    </justification>
  </clause>

  <clause id="17673">
    <literal><![CDATA[
      L(x,y,z * a(u,w,K(v5,v6))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(17549(a,1),15929(a,1,3))].">
      <j1 rule="para" parents="17549 15929"/>
    </justification>
  </clause>

  <clause id="17674">
    <literal><![CDATA[
      L(x,y,T(a(z,u,w),v5)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(13732(a,1),17673(a,1,3))].">
      <j1 rule="para" parents="13732 17673"/>
    </justification>
  </clause>

  <clause id="17675">
    <literal><![CDATA[
      L(x,y,z \ L(u,w,K(v5,v6))) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(15308(a,1),17673(a,1,3))].">
      <j1 rule="para" parents="15308 17673"/>
    </justification>
  </clause>

  <clause id="17676">
    <literal><![CDATA[
      L(x,y,z \ K(z,z \ u)) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,13782,a,b,17568,a),flip(a)].">
      <j1 rule="hyper" parents="58 13782 17568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17677">
    <literal><![CDATA[
      L(x,y,z * K(u,u \ w)) = L(x,y,K(u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(334,a,13000,a,b,17574,a)].">
      <j1 rule="hyper" parents="334 13000 17574"/>
    </justification>
  </clause>

  <clause id="17678">
    <literal><![CDATA[
      x * L(y,K(z,u),K(u,z) * x) = (x * K(u,z)) * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(17574(a,2),6530(a,1,2))].">
      <j1 rule="para" parents="17574 6530"/>
    </justification>
  </clause>

  <clause id="17679">
    <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(17575(a,1),16735(a,1,2,1,2))].">
      <j1 rule="para" parents="17575 16735"/>
    </justification>
  </clause>

  <clause id="17680">
    <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(17585(a,2),5416(a,2,1))].">
      <j1 rule="para" parents="17585 5416"/>
    </justification>
  </clause>

  <clause id="17682">
    <literal><![CDATA[
      K(x,L(y,z,(u \ 1) \ w)) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[hyper(14861,a,17612,a),flip(a)].">
      <j1 rule="hyper" parents="14861 17612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17683">
    <literal><![CDATA[
      K(x,L(y,z,u \ (w \ u))) = K(x,L(y,z,w \ 1))
    ]]></literal>
    <justification jstring="[hyper(14860,a,17612,a),flip(a)].">
      <j1 rule="hyper" parents="14860 17612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17684">
    <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(17612(a,1),14860(a,1))].">
      <j1 rule="para" parents="17612 14860"/>
    </justification>
  </clause>

  <clause id="17686">
    <literal><![CDATA[
      x / L(y,z,(y * z) \ x) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(17615(a,1),14485(a,1,2))].">
      <j1 rule="para" parents="17615 14485"/>
    </justification>
  </clause>

  <clause id="17687">
    <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(311(a,1),17644(a,1,2,2))].">
      <j1 rule="para" parents="311 17644"/>
    </justification>
  </clause>

  <clause id="17688">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w \ z) = w \ L(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,15308,a(flip),b,17650,a),flip(a)].">
      <j1 rule="hyper" parents="334 15308 17650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17689">
    <literal><![CDATA[
      (x * y) * a(z,u,K(x,w)) = T(x,a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,14619,a(flip),b,17650,a),flip(a)].">
      <j1 rule="hyper" parents="58 14619 17650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17690">
    <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(14935(a,1),17654(a,1,2))].">
      <j1 rule="para" parents="14935 17654"/>
    </justification>
  </clause>

  <clause id="17691">
    <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,14847,a(flip),b,17665,a),flip(a)].">
      <j1 rule="hyper" parents="58 14847 17665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17692">
    <literal><![CDATA[
      (x / y) * a(x,z,K(u,w)) = T(x,a(w,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(14166,a,17670,a),flip(a)].">
      <j1 rule="hyper" parents="14166 17670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17693">
    <literal><![CDATA[
      T(L(x,y,a(z,u,w)) \ x,v5) = L(x,y,a(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(17674(a,1),15463(a,2,1))].">
      <j1 rule="para" parents="17674 15463"/>
    </justification>
  </clause>

  <clause id="17694">
    <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(11093(a,2),17651(a,1))].">
      <j1 rule="para" parents="11093 17651"/>
    </justification>
  </clause>

  <clause id="17695">
    <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(4924(a,1),17652(a,1,2))].">
      <j1 rule="para" parents="4924 17652"/>
    </justification>
  </clause>

  <clause id="17696">
    <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(12872(a,1),17652(a,1,2))].">
      <j1 rule="para" parents="12872 17652"/>
    </justification>
  </clause>

  <clause id="17697">
    <literal><![CDATA[
      L(x,y,z \ (u / a(w,v5,v6))) = L(x,y,z \ (a(w,v5,v6) \ u))
    ]]></literal>
    <justification jstring="[para(15300(a,1),17675(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="15300 17675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17698">
    <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(15047(a,2),17686(a,1,2,3,1))].">
      <j1 rule="para" parents="15047 17686"/>
    </justification>
  </clause>

  <clause id="17699">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (w * K(y,K(x,z)))
    ]]></literal>
    <justification jstring="[hyper(16308,a,17512,a)].">
      <j1 rule="hyper" parents="16308 17512"/>
    </justification>
  </clause>

  <clause id="17700">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (w * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(16081,a,17512,a)].">
      <j1 rule="hyper" parents="16081 17512"/>
    </justification>
  </clause>

  <clause id="17703">
    <literal><![CDATA[
      x \ (y * K(z,K(u,w))) = K(z,K(u,w)) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,16037,a,b,17530,a),flip(a)].">
      <j1 rule="hyper" parents="334 16037 17530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17704">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,K(u,w)) = x \ (y * T(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(6432(a,1),17530(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6432 17530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17705">
    <literal><![CDATA[
      (x \ (y * z)) * K(y,K(u,w)) = x \ (T(y,K(u,w)) * z)
    ]]></literal>
    <justification jstring="[para(16047(a,1),17530(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16047 17530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17706">
    <literal><![CDATA[
      x \ T(K(y,K(z,u)) * w,v5) = (x \ T(w,v5)) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(16095(a,2),17530(a,1,2))].">
      <j1 rule="para" parents="16095 17530"/>
    </justification>
  </clause>

  <clause id="17707">
    <literal><![CDATA[
      x \ (y * (z * K(u,K(w,v5)))) = (x \ (y * z)) * K(u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(17512(a,1),17530(a,1,2))].">
      <j1 rule="para" parents="17512 17530"/>
    </justification>
  </clause>

  <clause id="17708">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,y) * u) = T(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[para(7799(a,1),17531(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7799 17531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17709">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = K(y,K(z,u)) * (x * w)
    ]]></literal>
    <justification jstring="[para(16037(a,1),17531(a,1,1))].">
      <j1 rule="para" parents="16037 17531"/>
    </justification>
  </clause>

  <clause id="17710">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,T(w,z)) = K(x,y) * (K(u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(334,a,7551,a(flip),b,17545,a),flip(a)].">
      <j1 rule="hyper" parents="334 7551 17545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17712">
    <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(17545(a,1),15(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="17545 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17716">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ w = u \ (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(8091(a,1),17565(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8091 17565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17717">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ (K(x,K(y,z)) \ w) = u \ w
    ]]></literal>
    <justification jstring="[para(5(a,1),17566(a,2,2))].">
      <j1 rule="para" parents="5 17566"/>
    </justification>
  </clause>

  <clause id="17718">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) / w = K(x,K(y,z)) * (u / w)
    ]]></literal>
    <justification jstring="[para(8092(a,2),17571(a,1,1))].">
      <j1 rule="para" parents="8092 17571"/>
    </justification>
  </clause>

  <clause id="17719">
    <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,17573,a(flip),b,8093,a),flip(a)].">
      <j1 rule="hyper" parents="116 17573 8093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17720">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K(x \ (K(z,y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(16460,a,17583,a)].">
      <j1 rule="hyper" parents="16460 17583"/>
    </justification>
  </clause>

  <clause id="17722">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,u \ (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(334,a,16418,a(flip),b,17605,a),flip(a)].">
      <j1 rule="hyper" parents="334 16418 17605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17723">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,u / (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(16453,a,17613,a)].">
      <j1 rule="hyper" parents="16453 17613"/>
    </justification>
  </clause>

  <clause id="17724">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,y * (w \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,16521,a(flip),b,17613,a),flip(a)].">
      <j1 rule="hyper" parents="334 16521 17613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17725">
    <literal><![CDATA[
      T(T(x,(y \ z) \ u),K(w,z \ (y * u))) = T(x,T((y \ z) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(8127,a,17620,a),flip(a)].">
      <j1 rule="hyper" parents="8127 17620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17726">
    <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(17620(a,1),8490(a,1))].">
      <j1 rule="para" parents="17620 8490"/>
    </justification>
  </clause>

  <clause id="17727">
    <literal><![CDATA[
      K(x,K(y,z \ (u * (w \ z)))) = K(x,K(y,w \ u))
    ]]></literal>
    <justification jstring="[hyper(334,a,16091,a(flip),b,17622,a),flip(a)].">
      <j1 rule="hyper" parents="334 16091 17622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17728">
    <literal><![CDATA[
      K(x,T(y,z / (u * w))) = K(x,T(y,u \ (z / w)))
    ]]></literal>
    <justification jstring="[hyper(16146,a,17637,a),flip(a)].">
      <j1 rule="hyper" parents="16146 17637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17729">
    <literal><![CDATA[
      T(x \ 1,a(y,z,u)) = T(x,a(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(13743,a,17664,a)].">
      <j1 rule="hyper" parents="13743 17664"/>
    </justification>
  </clause>

  <clause id="17730">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(29,a,13730,a,b,17664,a)].">
      <j1 rule="hyper" parents="29 13730 17664"/>
    </justification>
  </clause>

  <clause id="17731">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,x)) = L(x,u,K(w,z)) \ y
    ]]></literal>
    <justification jstring="[para(15279(a,2),17664(a,2,1))].">
      <j1 rule="para" parents="15279 17664"/>
    </justification>
  </clause>

  <clause id="17732">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,14592,a,b,17730,a),flip(a)].">
      <j1 rule="hyper" parents="334 14592 17730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17733">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,14592,a(flip),b,17730,a),flip(a)].">
      <j1 rule="hyper" parents="334 14592 17730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17734">
    <literal><![CDATA[
      a(x,y,K(z,u / w)) = a(x,y,K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(107(a,1),17730(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="107 17730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17735">
    <literal><![CDATA[
      a(x,y,K(z / u,w)) = a(x,y,K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(7414(a,1),17730(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7414 17730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17736">
    <literal><![CDATA[
      a(x,y,K(z * u,w)) = a(x,y,K(u * z,w))
    ]]></literal>
    <justification jstring="[para(12516(a,1),17730(a,1,3))].">
      <j1 rule="para" parents="12516 17730"/>
    </justification>
  </clause>

  <clause id="17737">
    <literal><![CDATA[
      a(x,y,K(z,u * w)) = a(x,y,K(z,w * u))
    ]]></literal>
    <justification jstring="[para(12551(a,1),17730(a,1,3))].">
      <j1 rule="para" parents="12551 17730"/>
    </justification>
  </clause>

  <clause id="17739">
    <literal><![CDATA[
      T(x,a(y,z,T(u,w))) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,17732,a(flip),b,13701,a),flip(a)].">
      <j1 rule="hyper" parents="119 17732 13701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17742">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(w,z,K(y * x,u))
    ]]></literal>
    <justification jstring="[para(12516(a,1),17732(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12516 17732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17744">
    <literal><![CDATA[
      a(T(x,y),z,K(u,w)) = a(x,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(14707,a,17733,a)].">
      <j1 rule="hyper" parents="14707 17733"/>
    </justification>
  </clause>

  <clause id="17746">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(u,z,K(w,y * x))
    ]]></literal>
    <justification jstring="[para(12551(a,1),17733(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12551 17733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17747">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = a(x,y,K(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14870,a(flip),b,17744,a)].">
      <j1 rule="hyper" parents="58 14870 17744"/>
    </justification>
  </clause>

  <clause id="17748">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(y * x,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13103,a(flip),b,17744,a)].">
      <j1 rule="hyper" parents="58 13103 17744"/>
    </justification>
  </clause>

  <clause id="17749">
    <literal><![CDATA[
      a(x / y,z,K(u,w)) = a(y \ x,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13088,a(flip),b,17744,a),flip(a)].">
      <j1 rule="hyper" parents="58 13088 17744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17750">
    <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(17729(a,2),14080(a,1,2))].">
      <j1 rule="para" parents="17729 14080"/>
    </justification>
  </clause>

  <clause id="17751">
    <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(17734(a,1),14741(a,1,2))].">
      <j1 rule="para" parents="17734 14741"/>
    </justification>
  </clause>

  <clause id="17752">
    <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(17734(a,1),15199(a,1,1))].">
      <j1 rule="para" parents="17734 15199"/>
    </justification>
  </clause>

  <clause id="17753">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) \ K(z,(y * x) / u) = K(z,y / (u / x))
    ]]></literal>
    <justification jstring="[para(17734(a,1),15244(a,1,1))].">
      <j1 rule="para" parents="17734 15244"/>
    </justification>
  </clause>

  <clause id="17754">
    <literal><![CDATA[
      a(x,y,K(z,x \ (u * (x / w)))) = a(z,y,K(w \ u,x))
    ]]></literal>
    <justification jstring="[hyper(14719,a,17735,a)].">
      <j1 rule="hyper" parents="14719 17735"/>
    </justification>
  </clause>

  <clause id="17755">
    <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(17735(a,1),14681(a,1,2))].">
      <j1 rule="para" parents="17735 14681"/>
    </justification>
  </clause>

  <clause id="17756">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u \ w,y)) = K(x,L(y,z,w / (y * u)))
    ]]></literal>
    <justification jstring="[para(17735(a,1),14924(a,1,2))].">
      <j1 rule="para" parents="17735 14924"/>
    </justification>
  </clause>

  <clause id="17757">
    <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(17736(a,1),14677(a,1))].">
      <j1 rule="para" parents="17736 14677"/>
    </justification>
  </clause>

  <clause id="17758">
    <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(17737(a,1),14707(a,1))].">
      <j1 rule="para" parents="17737 14707"/>
    </justification>
  </clause>

  <clause id="17759">
    <literal><![CDATA[
      T(x,a(y,z,T(u,w))) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,14614,a(flip),b,17739,a),flip(a)].">
      <j1 rule="hyper" parents="334 14614 17739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17760">
    <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(17739(a,2),14618(a,1))].">
      <j1 rule="para" parents="17739 14618"/>
    </justification>
  </clause>

  <clause id="17761">
    <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,17656,a(flip),b,17759,a),flip(a)].">
      <j1 rule="hyper" parents="58 17656 17759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17762">
    <literal><![CDATA[
      T(x,a(y,T(z,u),u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(6921(a,1),17759(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6921 17759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17763">
    <literal><![CDATA[
      T(x,a(y,z * u,u)) = T(x,a(y,u * z,u))
    ]]></literal>
    <justification jstring="[para(13631(a,1),17762(a,1,2))].">
      <j1 rule="para" parents="13631 17762"/>
    </justification>
  </clause>

  <clause id="17764">
    <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(17742(a,2),14677(a,1))].">
      <j1 rule="para" parents="17742 14677"/>
    </justification>
  </clause>

  <clause id="17765">
    <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(17742(a,2),14707(a,1))].">
      <j1 rule="para" parents="17742 14707"/>
    </justification>
  </clause>

  <clause id="17766">
    <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(17746(a,1),14677(a,1))].">
      <j1 rule="para" parents="17746 14677"/>
    </justification>
  </clause>

  <clause id="17767">
    <literal><![CDATA[
      a(K(x,y),z,u \ w) = a(w / u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,14624,a,b,17749,a)].">
      <j1 rule="hyper" parents="334 14624 17749"/>
    </justification>
  </clause>

  <clause id="17768">
    <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(17749(a,1),15060(a,1,2))].">
      <j1 rule="para" parents="17749 15060"/>
    </justification>
  </clause>

  <clause id="17769">
    <literal><![CDATA[
      T(x,a(y,z * u,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,14757,a(flip),b,17763,a),flip(a)].">
      <j1 rule="hyper" parents="334 14757 17763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17770">
    <literal><![CDATA[
      L(x,y * z,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(15341,a,17769,a)].">
      <j1 rule="hyper" parents="15341 17769"/>
    </justification>
  </clause>

  <clause id="17771">
    <literal><![CDATA[
      L(x,y * z,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,15279,a,b,17770,a),flip(a)].">
      <j1 rule="hyper" parents="334 15279 17770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17773">
    <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,7951,a(flip),b,17771,a)].">
      <j1 rule="hyper" parents="58 7951 17771"/>
    </justification>
  </clause>

  <clause id="17774">
    <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(17771(a,1),15286(a,1))].">
      <j1 rule="para" parents="17771 15286"/>
    </justification>
  </clause>

  <clause id="17776">
    <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(17767(a,1),14706(a,1))].">
      <j1 rule="para" parents="17767 14706"/>
    </justification>
  </clause>

  <clause id="17777">
    <literal><![CDATA[
      L(x,y,K(z,u) * (w * (z \ u))) = L(x,y,w * (u / z))
    ]]></literal>
    <justification jstring="[para(6417(a,1),17677(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6417 17677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17778">
    <literal><![CDATA[
      L(x,y,K(z,u) * (w / (u / z))) = L(x,y,w / (z \ u))
    ]]></literal>
    <justification jstring="[para(6695(a,1),17677(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6695 17677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17779">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,u * y)) = K(x,u \ ((u / (y \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14801,a(flip),b,17682,a),flip(a)].">
      <j1 rule="hyper" parents="58 14801 17682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17780">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ w)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,14829,a,b,17683,a)].">
      <j1 rule="hyper" parents="58 14829 17683"/>
    </justification>
  </clause>

  <clause id="17781">
    <literal><![CDATA[
      (x \ y) * K(z,L(u,y,x \ 1)) = ((x \ y) / y) * (y * K(z,u))
    ]]></literal>
    <justification jstring="[para(17683(a,1),11440(a,1,2))].">
      <j1 rule="para" parents="17683 11440"/>
    </justification>
  </clause>

  <clause id="17782">
    <literal><![CDATA[
      (x / y) * a(x,z,K(u,w)) = L(x,z,K(u,w)) / y
    ]]></literal>
    <justification jstring="[para(15279(a,2),17692(a,2,1))].">
      <j1 rule="para" parents="15279 17692"/>
    </justification>
  </clause>

  <clause id="17783">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(16131(a,2),17699(a,2,2))].">
      <j1 rule="para" parents="16131 17699"/>
    </justification>
  </clause>

  <clause id="17784">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * w = u * (w * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17531,a,b,17700,a)].">
      <j1 rule="hyper" parents="58 17531 17700"/>
    </justification>
  </clause>

  <clause id="17785">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * (w \ x)) = u * (w \ T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(12642(a,1),17700(a,2,2))].">
      <j1 rule="para" parents="12642 17700"/>
    </justification>
  </clause>

  <clause id="17786">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * (w * v5)) = u * (w * (v5 * K(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(17512(a,1),17700(a,2,2))].">
      <j1 rule="para" parents="17512 17700"/>
    </justification>
  </clause>

  <clause id="17787">
    <literal><![CDATA[
      x \ (K(y,K(z,u)) * w) = K(y,K(z,u)) * (x \ w)
    ]]></literal>
    <justification jstring="[para(16037(a,2),17703(a,1,2))].">
      <j1 rule="para" parents="16037 17703"/>
    </justification>
  </clause>

  <clause id="17788">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ (K(x,K(y,z)) * w)) = u \ w
    ]]></literal>
    <justification jstring="[para(16202(a,1),17703(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16202 17703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17789">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ (T(x,K(y,z)) \ w)) = u \ (x \ w)
    ]]></literal>
    <justification jstring="[para(16090(a,1),17703(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16090 17703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17790">
    <literal><![CDATA[
      x \ T(K(y,K(z,u)) * w,v5) = K(y,K(z,u)) * (x \ T(w,v5))
    ]]></literal>
    <justification jstring="[para(16095(a,2),17703(a,1,2))].">
      <j1 rule="para" parents="16095 17703"/>
    </justification>
  </clause>

  <clause id="17791">
    <literal><![CDATA[
      x \ T(y * K(z,K(u,w)),v5) = K(z,K(u,w)) * (x \ T(y,v5))
    ]]></literal>
    <justification jstring="[para(16334(a,2),17703(a,1,2))].">
      <j1 rule="para" parents="16334 17703"/>
    </justification>
  </clause>

  <clause id="17792">
    <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(17708(a,1),16562(a,1,2,2))].">
      <j1 rule="para" parents="17708 16562"/>
    </justification>
  </clause>

  <clause id="17793">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = x * (w * K(y,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,17700,a(flip),b,17709,a),flip(a)].">
      <j1 rule="hyper" parents="334 17700 17709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17794">
    <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(17718(a,2),8098(a,1))].">
      <j1 rule="para" parents="17718 8098"/>
    </justification>
  </clause>

  <clause id="17795">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K(x \ (u * K(z,y)),w)
    ]]></literal>
    <justification jstring="[hyper(334,a,16429,a(flip),b,17720,a),flip(a)].">
      <j1 rule="hyper" parents="334 16429 17720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17796">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,y \ (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16409,a(flip),b,17722,a)].">
      <j1 rule="hyper" parents="58 16409 17722"/>
    </justification>
  </clause>

  <clause id="17797">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(334,a,16521,a(flip),b,17723,a),flip(a)].">
      <j1 rule="hyper" parents="334 16521 17723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17798">
    <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(17723(a,2),16623(a,1))].">
      <j1 rule="para" parents="17723 16623"/>
    </justification>
  </clause>

  <clause id="17799">
    <literal><![CDATA[
      T(x,(y * K(z,u)) / w) = T(x,y * (w \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(118,a,17724,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 17724 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17800">
    <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,11208,a(flip),b,17724,a),flip(a)].">
      <j1 rule="hyper" parents="58 11208 17724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17801">
    <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,9241,a(flip),b,17724,a),flip(a)].">
      <j1 rule="hyper" parents="58 9241 17724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17802">
    <literal><![CDATA[
      K(x,(y / z) * (u \ K(w,z))) = K(x,(y / T(z,w)) / u)
    ]]></literal>
    <justification jstring="[para(6368(a,1),17724(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6368 17724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17803">
    <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(17724(a,1),16453(a,1))].">
      <j1 rule="para" parents="17724 16453"/>
    </justification>
  </clause>

  <clause id="17804">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ (w * u))) = K(x,K(y,z \ w))
    ]]></literal>
    <justification jstring="[para(4(a,1),17727(a,1,2,2,2,2))].">
      <j1 rule="para" parents="4 17727"/>
    </justification>
  </clause>

  <clause id="17805">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ w)) = K(x,T(y,z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(16146,a,17728,a)].">
      <j1 rule="hyper" parents="16146 17728"/>
    </justification>
  </clause>

  <clause id="17806">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (z \ w) = L(z,y,K(x,u)) \ w
    ]]></literal>
    <justification jstring="[hyper(58,a,17650,a,b,17731,a)].">
      <j1 rule="hyper" parents="58 17650 17731"/>
    </justification>
  </clause>

  <clause id="17807">
    <literal><![CDATA[
      L(x,y,L(z,u,K(w,v5)) \ v6) = L(x,y,z \ v6)
    ]]></literal>
    <justification jstring="[para(17731(a,1),17673(a,1,3))].">
      <j1 rule="para" parents="17731 17673"/>
    </justification>
  </clause>

  <clause id="17809">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,14684,a(flip),b,17747,a),flip(a)].">
      <j1 rule="hyper" parents="334 14684 17747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17813">
    <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,13593,a(flip),b,17780,a),flip(a)].">
      <j1 rule="hyper" parents="58 13593 17780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17814">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,((u / (z * u)) * y) \ u)
    ]]></literal>
    <justification jstring="[para(14482(a,1),17780(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14482 17780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17815">
    <literal><![CDATA[
      ((x * y) \ y) * ((((x * y) \ y) \ z) * K(u,w)) = z * K(u,L(w,z,x \ 1))
    ]]></literal>
    <justification jstring="[para(17780(a,1),14802(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17780 14802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17817">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * w) = u * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(8098,a,17783,a)].">
      <j1 rule="hyper" parents="8098 17783"/>
    </justification>
  </clause>

  <clause id="17819">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = x * (K(y,K(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17709,a,b,17783,a)].">
      <j1 rule="hyper" parents="58 17709 17783"/>
    </justification>
  </clause>

  <clause id="17821">
    <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(17783(a,1),16562(a,1,2,2))].">
      <j1 rule="para" parents="17783 16562"/>
    </justification>
  </clause>

  <clause id="17822">
    <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(17784(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="17784 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17823">
    <literal><![CDATA[
      (K(x,y) * z) * (u * K(x,K(y,w))) = (K(x,T(y,w)) * z) * u
    ]]></literal>
    <justification jstring="[para(8792(a,1),17784(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8792 17784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17824">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (K(x,K(y,z)) * w) = u * w
    ]]></literal>
    <justification jstring="[para(16202(a,1),17784(a,2,2))].">
      <j1 rule="para" parents="16202 17784"/>
    </justification>
  </clause>

  <clause id="17825">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ w = K(x,K(y,z)) * (u \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17716,a,b,17787,a)].">
      <j1 rule="hyper" parents="58 17716 17787"/>
    </justification>
  </clause>

  <clause id="17826">
    <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(17793(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17793 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17827">
    <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(17793(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="17793 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17828">
    <literal><![CDATA[
      (x * T(K(y,z),u)) * (w * K(u,K(y,z))) = (x * K(y,z)) * w
    ]]></literal>
    <justification jstring="[para(6374(a,1),17793(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6374 17793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17829">
    <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(16355(a,1),17793(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16355 17793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17830">
    <literal><![CDATA[
      K((x \ 1) \ (y * K(z,u)),w) = K((x \ K(u,z)) \ y,w)
    ]]></literal>
    <justification jstring="[para(14141(a,1),17795(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14141 17795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17831">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / w) = T(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(118,a,17797,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 17797 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17832">
    <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,16972,a(flip),b,17797,a),flip(a)].">
      <j1 rule="hyper" parents="58 16972 17797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17833">
    <literal><![CDATA[
      K(x,(y * z) * (u \ K(y,w))) = K(x,(T(y,w) * z) / u)
    ]]></literal>
    <justification jstring="[para(5047(a,1),17797(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5047 17797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17834">
    <literal><![CDATA[
      K(x,(y \ z) * (u \ K(w,y))) = K(x,(T(y,w) \ z) / u)
    ]]></literal>
    <justification jstring="[para(5392(a,1),17797(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5392 17797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17835">
    <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,17070,a(flip),b,17799,a),flip(a)].">
      <j1 rule="hyper" parents="58 17070 17799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17836">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ w)) = K(x,K(y,z \ (w / u)))
    ]]></literal>
    <justification jstring="[para(7(a,1),17804(a,1,2,2,2))].">
      <j1 rule="para" parents="7 17804"/>
    </justification>
  </clause>

  <clause id="17837">
    <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(16217,a,17805,a),flip(a)].">
      <j1 rule="hyper" parents="16217 17805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17838">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ w))) = K(x,T(y,u \ (w / z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17634,a(flip),b,17805,a)].">
      <j1 rule="hyper" parents="58 17634 17805"/>
    </justification>
  </clause>

  <clause id="17839">
    <literal><![CDATA[
      R(x,K(y,K(z,u)),w) = x
    ]]></literal>
    <justification jstring="[hyper(3617,a,17819,a)].">
      <j1 rule="hyper" parents="3617 17819"/>
    </justification>
  </clause>

  <clause id="17840">
    <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,17819,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 17819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17841">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) * v5 = (x * y) * (K(z,K(u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(17512(a,1),17819(a,1,1))].">
      <j1 rule="para" parents="17512 17819"/>
    </justification>
  </clause>

  <clause id="17842">
    <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(17839(a,1),523(a,1,1,1,2))].">
      <j1 rule="para" parents="17839 523"/>
    </justification>
  </clause>

  <clause id="17843">
    <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,17824,a)].">
      <j1 rule="hyper" parents="117 7 17824"/>
    </justification>
  </clause>

  <clause id="17844">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = K(x,K(y,z)) \ (u \ w)
    ]]></literal>
    <justification jstring="[hyper(600,a,17825,a),flip(a)].">
      <j1 rule="hyper" parents="600 17825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17845">
    <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(17825(a,2),16049(a,1))].">
      <j1 rule="para" parents="17825 16049"/>
    </justification>
  </clause>

  <clause id="17846">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) \ v5 = K(y,K(z,u)) * ((x * w) \ v5)
    ]]></literal>
    <justification jstring="[para(17783(a,1),17825(a,1,1))].">
      <j1 rule="para" parents="17783 17825"/>
    </justification>
  </clause>

  <clause id="17847">
    <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,17012,a(flip),b,17831,a)].">
      <j1 rule="hyper" parents="58 17012 17831"/>
    </justification>
  </clause>

  <clause id="17848">
    <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(17831(a,1),15864(a,1,2,1,2))].">
      <j1 rule="para" parents="17831 15864"/>
    </justification>
  </clause>

  <clause id="17849">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ w)) = K(x,K(y,z \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(334,a,16861,a(flip),b,17836,a),flip(a)].">
      <j1 rule="hyper" parents="334 16861 17836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17850">
    <literal><![CDATA[
      K(x,T(y,(z / u) \ w)) = K(x,T(y,u \ (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(334,a,8512,a,b,17838,a)].">
      <j1 rule="hyper" parents="334 8512 17838"/>
    </justification>
  </clause>

  <clause id="17851">
    <literal><![CDATA[
      K(x,T(y,(z / u) \ (w \ z))) = K(x,T(y,w \ u))
    ]]></literal>
    <justification jstring="[hyper(334,a,16820,a(flip),b,17838,a),flip(a)].">
      <j1 rule="hyper" parents="334 16820 17838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17852">
    <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),17838(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="17 17838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17853">
    <literal><![CDATA[
      x / (K(y,K(z,u)) * w) = K(y,K(z,u)) \ (x / w)
    ]]></literal>
    <justification jstring="[hyper(116,a,17840,a(flip),b,16037,a),flip(a)].">
      <j1 rule="hyper" parents="116 17840 16037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17854">
    <literal><![CDATA[
      K(x,K(y,z)) * (u / (w \ x)) = u / (w \ T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(16094(a,1),17843(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16094 17843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17855">
    <literal><![CDATA[
      x / T(y * K(z,K(u,w)),v5) = K(z,K(u,w)) * (x / T(y,v5))
    ]]></literal>
    <justification jstring="[para(16352(a,2),17843(a,1,2))].">
      <j1 rule="para" parents="16352 17843"/>
    </justification>
  </clause>

  <clause id="17856">
    <literal><![CDATA[
      K(x,(K(y,K(z,u)) \ w) \ v5) = K(x,w \ v5)
    ]]></literal>
    <justification jstring="[para(17844(a,2),16401(a,1,2))].">
      <j1 rule="para" parents="17844 16401"/>
    </justification>
  </clause>

  <clause id="17857">
    <literal><![CDATA[
      K(x,y \ (K(z,K(u,w)) \ v5)) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[para(17717(a,1),17856(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17717 17856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17858">
    <literal><![CDATA[
      K(x,y \ (T(z,K(u,w)) * v5)) = K(x,y \ (z * v5))
    ]]></literal>
    <justification jstring="[para(5049(a,1),17857(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5049 17857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17859">
    <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(16343(a,1),17857(a,1,2,2))].">
      <j1 rule="para" parents="16343 17857"/>
    </justification>
  </clause>

  <clause id="17860">
    <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(17849(a,1),8680(a,1,1))].">
      <j1 rule="para" parents="17849 8680"/>
    </justification>
  </clause>

  <clause id="17861">
    <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(17849(a,1),13410(a,1,1))].">
      <j1 rule="para" parents="17849 13410"/>
    </justification>
  </clause>

  <clause id="17862">
    <literal><![CDATA[
      K(x,T(y,z \ ((u \ w) \ w))) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,17850,a(flip),b,17851,a)].">
      <j1 rule="hyper" parents="58 17850 17851"/>
    </justification>
  </clause>

  <clause id="17863">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ (z * w)))) = K(x,T(y,u \ w))
    ]]></literal>
    <justification jstring="[para(6(a,1),17851(a,1,2,2,1))].">
      <j1 rule="para" parents="6 17851"/>
    </justification>
  </clause>

  <clause id="17864">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u / (K(x,K(y,z)) \ w)) = u / w
    ]]></literal>
    <justification jstring="[para(5(a,1),17853(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 17853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17865">
    <literal><![CDATA[
      K(x,y \ (T(z,T(u,w)) * v5)) = K(x,y \ (T(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(7688(a,1),17858(a,1,2,2,1))].">
      <j1 rule="para" parents="7688 17858"/>
    </justification>
  </clause>

  <clause id="17866">
    <literal><![CDATA[
      K(x,T(y,z \ (K(u,w) * v5))) = K(x,T(y,z \ v5))
    ]]></literal>
    <justification jstring="[hyper(16794,a,17863,a)].">
      <j1 rule="hyper" parents="16794 17863"/>
    </justification>
  </clause>

  <clause id="17867">
    <literal><![CDATA[
      K(x,T(y,z \ (T(u,w) \ v5))) = K(x,T(y,z \ (u \ v5)))
    ]]></literal>
    <justification jstring="[para(5337(a,1),17866(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5337 17866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17868">
    <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(14592(a,2),17552(a,1,1))].">
      <j1 rule="para" parents="14592 17552"/>
    </justification>
  </clause>

  <clause id="17869">
    <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(17650(a,1),17552(a,1))].">
      <j1 rule="para" parents="17650 17552"/>
    </justification>
  </clause>

  <clause id="17870">
    <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(17665(a,1),17552(a,1))].">
      <j1 rule="para" parents="17665 17552"/>
    </justification>
  </clause>

  <clause id="17871">
    <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(15188(a,1),17643(a,1))].">
      <j1 rule="para" parents="15188 17643"/>
    </justification>
  </clause>

  <clause id="17872">
    <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(14696(a,1),17776(a,1))].">
      <j1 rule="para" parents="14696 17776"/>
    </justification>
  </clause>

  <clause id="17874">
    <literal><![CDATA[
      K(x,L(y,z,u) * T(w,y)) = K(x,w * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(13648(a,1),17630(a,1,2))].">
      <j1 rule="para" parents="13648 17630"/>
    </justification>
  </clause>

  <clause id="17875">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) * T(y,z)) = K(x,y * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(13512,a,17874,a)].">
      <j1 rule="hyper" parents="13512 17874"/>
    </justification>
  </clause>

  <clause id="17877">
    <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(17638(a,2),15907(a,1))].">
      <j1 rule="para" parents="17638 15907"/>
    </justification>
  </clause>

  <clause id="17878">
    <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(15156(a,1),17649(a,1))].">
      <j1 rule="para" parents="15156 17649"/>
    </justification>
  </clause>

  <clause id="17879">
    <literal><![CDATA[
      a(x,y,z) \ (K(u,w) * z) = K(u,w) * (z / a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14385,a(flip),b,17662,a),flip(a)].">
      <j1 rule="hyper" parents="58 14385 17662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17880">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w \ a(x,y,z)) = w \ T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(13732(a,1),17666(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13732 17666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17881">
    <literal><![CDATA[
      x \ (a(y,z,K(u,w)) * v5) = a(y,z,K(u,w)) * (x \ v5)
    ]]></literal>
    <justification jstring="[para(17549(a,2),17666(a,1,2))].">
      <j1 rule="para" parents="17549 17666"/>
    </justification>
  </clause>

  <clause id="17882">
    <literal><![CDATA[
      x * (y * a(z,u,K(x,w))) = L(x,u,K(w,z)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,15318,a(flip),b,17668,a),flip(a)].">
      <j1 rule="hyper" parents="58 15318 17668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17883">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * (v5 * x)) = w * (v5 * T(x,a(u,y,z)))
    ]]></literal>
    <justification jstring="[para(14613(a,1),17668(a,2,2))].">
      <j1 rule="para" parents="14613 17668"/>
    </justification>
  </clause>

  <clause id="17884">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * v5) = w * (a(x,y,K(z,u)) * v5)
    ]]></literal>
    <justification jstring="[para(17549(a,2),17668(a,2,2))].">
      <j1 rule="para" parents="17549 17668"/>
    </justification>
  </clause>

  <clause id="17885">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * v5) = w * (a(u,y,K(x,z)) * v5)
    ]]></literal>
    <justification jstring="[para(17665(a,2),17668(a,2,2))].">
      <j1 rule="para" parents="17665 17668"/>
    </justification>
  </clause>

  <clause id="17886">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1) / u) = L(x,y,u \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13495,a(flip),b,17676,a),flip(a)].">
      <j1 rule="hyper" parents="58 13495 17676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17887">
    <literal><![CDATA[
      L(x,y,z \ K(u,z \ 1)) = L(x,y,z \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(17617,a,17886,a)].">
      <j1 rule="hyper" parents="17617 17886"/>
    </justification>
  </clause>

  <clause id="17888">
    <literal><![CDATA[
      L(x,y,z \ K(z,y)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,11485,a(flip),b,17887,a),flip(a)].">
      <j1 rule="hyper" parents="58 11485 17887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17889">
    <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(14577(a,1),17888(a,1,3))].">
      <j1 rule="para" parents="14577 17888"/>
    </justification>
  </clause>

  <clause id="17890">
    <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(14638(a,1),17691(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14638 17691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17891">
    <literal><![CDATA[
      ((L(x,y,a(z,u,w)) \ x) \ v5) \ v5 = L(x,y,a(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[hyper(4536,a,17693,a)].">
      <j1 rule="hyper" parents="4536 17693"/>
    </justification>
  </clause>

  <clause id="17892">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u \ (w * x)) = x \ (u \ (w * T(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(17704(a,1),16205(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17704 16205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17893">
    <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(17704(a,1),16451(a,1,2))].">
      <j1 rule="para" parents="17704 16451"/>
    </justification>
  </clause>

  <clause id="17894">
    <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(17705(a,1),16465(a,1,2,2))].">
      <j1 rule="para" parents="17705 16465"/>
    </justification>
  </clause>

  <clause id="17895">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * w) = K(z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[hyper(16776,a,17710,a)].">
      <j1 rule="hyper" parents="16776 17710"/>
    </justification>
  </clause>

  <clause id="17900">
    <literal><![CDATA[
      (K(x,y) * z) / (K(x,y) * (K(u,w) * z)) = K(w,u)
    ]]></literal>
    <justification jstring="[para(17895(a,1),5403(a,1,2))].">
      <j1 rule="para" parents="17895 5403"/>
    </justification>
  </clause>

  <clause id="17902">
    <literal><![CDATA[
      a(x,y,K(z * (u / w),u)) = a(x,y,K(w \ z,u))
    ]]></literal>
    <justification jstring="[hyper(14778,a,17754,a)].">
      <j1 rule="hyper" parents="14778 17754"/>
    </justification>
  </clause>

  <clause id="17903">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),w)) = a(x,y,K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(16221(a,1),17902(a,1,3))].">
      <j1 rule="para" parents="16221 17902"/>
    </justification>
  </clause>

  <clause id="17904">
    <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(17903(a,1),14738(a,2,2))].">
      <j1 rule="para" parents="17903 14738"/>
    </justification>
  </clause>

  <clause id="17905">
    <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(17785(a,1),16431(a,1,1))].">
      <j1 rule="para" parents="17785 16431"/>
    </justification>
  </clause>

  <clause id="17906">
    <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(17830(a,1),14414(a,1))].">
      <j1 rule="para" parents="17830 14414"/>
    </justification>
  </clause>

  <clause id="17907">
    <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(17852(a,2),16824(a,1))].">
      <j1 rule="para" parents="17852 16824"/>
    </justification>
  </clause>

  <clause id="17908">
    <literal><![CDATA[
      K(x,y / (z \ T(u,K(w,v5)))) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[para(17854(a,1),16399(a,1,2))].">
      <j1 rule="para" parents="17854 16399"/>
    </justification>
  </clause>

  <clause id="17909">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * v5))) = K(x,y / (z \ (v5 * K(u,w))))
    ]]></literal>
    <justification jstring="[para(6522(a,1),17908(a,1,2,2,2))].">
      <j1 rule="para" parents="6522 17908"/>
    </justification>
  </clause>

  <clause id="17910">
    <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(15266(a,1),17908(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15266 17908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17911">
    <literal><![CDATA[
      K(x,(y * T(z,u)) \ (T(y,z) * w)) = K(x,(T(z,u) * y) \ (y * w))
    ]]></literal>
    <justification jstring="[para(11492(a,1),17865(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11492 17865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17912">
    <literal><![CDATA[
      a(x,y,z) \ (K(u,w) * z) = K(u,w) * (a(x,y,z) \ z)
    ]]></literal>
    <justification jstring="[para(15346(a,1),17879(a,2,2))].">
      <j1 rule="para" parents="15346 17879"/>
    </justification>
  </clause>

  <clause id="17913">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) \ v5 = a(u,y,K(z,x)) * (w \ v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,14844,a,b,17881,a)].">
      <j1 rule="hyper" parents="58 14844 17881"/>
    </justification>
  </clause>

  <clause id="17914">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * v5 = x * (a(y,z,K(u,w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,17672,a,b,17884,a)].">
      <j1 rule="hyper" parents="58 17672 17884"/>
    </justification>
  </clause>

  <clause id="17915">
    <literal><![CDATA[
      (x * (a(y,z,K(u,w)) * v5)) / v6 = a(u,z,K(w,y)) * ((x * v5) / v6)
    ]]></literal>
    <justification jstring="[para(17885(a,1),14609(a,1,1))].">
      <j1 rule="para" parents="17885 14609"/>
    </justification>
  </clause>

  <clause id="17916">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) \ v5 = a(w,z,K(u,y)) * (x \ v5)
    ]]></literal>
    <justification jstring="[para(17549(a,1),17913(a,1,1))].">
      <j1 rule="para" parents="17549 17913"/>
    </justification>
  </clause>

  <clause id="17917">
    <literal><![CDATA[
      (x * (y * a(z,u,K(w,v5)))) \ v6 = a(v5,u,K(w,z)) * ((x * y) \ v6)
    ]]></literal>
    <justification jstring="[para(17668(a,1),17913(a,1,1))].">
      <j1 rule="para" parents="17668 17913"/>
    </justification>
  </clause>

  <clause id="17918">
    <literal><![CDATA[
      R(x,a(y,z,K(u,w)),v5) = x
    ]]></literal>
    <justification jstring="[hyper(3617,a,17914,a)].">
      <j1 rule="hyper" parents="3617 17914"/>
    </justification>
  </clause>

  <clause id="17919">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)),v5) = x
    ]]></literal>
    <justification jstring="[hyper(493,a,17914,a)].">
      <j1 rule="hyper" parents="493 17914"/>
    </justification>
  </clause>

  <clause id="17920">
    <literal><![CDATA[
      (x * (y * a(z,u,K(w,v5)))) * v6 = (x * y) * (a(z,u,K(w,v5)) * v6)
    ]]></literal>
    <justification jstring="[para(358(a,1),17914(a,1,1))].">
      <j1 rule="para" parents="358 17914"/>
    </justification>
  </clause>

  <clause id="17921">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (((x * y) * K(z,u)) \ w) = (x * (y * K(z,u))) \ w
    ]]></literal>
    <justification jstring="[para(17918(a,1),784(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17918 784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17924">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) \ v5) = (x / v5) * a(y,z,K(u,w))
    ]]></literal>
    <justification jstring="[para(17919(a,1),510(a,1,2))].">
      <j1 rule="para" parents="17919 510"/>
    </justification>
  </clause>

  <clause id="17925">
    <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(17919(a,1),490(a,1,2,2,1))].">
      <j1 rule="para" parents="17919 490"/>
    </justification>
  </clause>

  <clause id="17926">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * v5) = (x / v5) * a(w,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14654(a,1),17924(a,1,2))].">
      <j1 rule="para" parents="14654 17924"/>
    </justification>
  </clause>

  <clause id="17927">
    <literal><![CDATA[
      (x / y) * a(z,u,K(y,w)) = x / L(y,u,K(z,w))
    ]]></literal>
    <justification jstring="[para(15293(a,1),17926(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15293 17926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17928">
    <literal><![CDATA[
      x / (y * (a(z,u,K(w,v5)) * v6)) = (x / (y * v6)) * a(z,u,K(v5,w))
    ]]></literal>
    <justification jstring="[para(17885(a,1),17926(a,1,2))].">
      <j1 rule="para" parents="17885 17926"/>
    </justification>
  </clause>

  <clause id="17929">
    <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(16837(a,2),17690(a,1))].">
      <j1 rule="para" parents="16837 17690"/>
    </justification>
  </clause>

  <clause id="17930">
    <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(17905,a,16446,a),flip(a)].">
      <j1 rule="hyper" parents="17905 16446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17931">
    <literal><![CDATA[
      K(((x \ K(y,z)) \ 1) * u,w) = K(x * (u * K(z,y)),w)
    ]]></literal>
    <justification jstring="[hyper(17906,a,14197,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="17906 14197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17932">
    <literal><![CDATA[
      K((K(x,y) * z) * u,w) = K(z * (u * K(x,y)),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,14182,a(flip),b,17931,a)].">
      <j1 rule="hyper" parents="58 14182 17931"/>
    </justification>
  </clause>

  <clause id="17933">
    <literal><![CDATA[
      K((x \ y) * (z * K(u,x)),w) = K((T(x,u) \ y) * z,w)
    ]]></literal>
    <justification jstring="[para(5392(a,1),17932(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5392 17932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17934">
    <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(16792(a,1),17907(a,1))].">
      <j1 rule="para" parents="16792 17907"/>
    </justification>
  </clause>

  <clause id="17935">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) = v5 \ (x * v5)
    ]]></literal>
    <justification jstring="[para(17554(a,1),17578(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17554 17578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17936">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) = T(x,v5)
    ]]></literal>
    <justification jstring="[hyper(334,a,17,a,b,17935,a),flip(a)].">
      <j1 rule="hyper" parents="334 17 17935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17937">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(17935(a,2),298(a,1))].">
      <j1 rule="para" parents="17935 298"/>
    </justification>
  </clause>

  <clause id="17939">
    <literal><![CDATA[
      T(x,T(a(y,z,u),w) * v5) = T(x,a(y,z,u) * v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,15482,a(flip),b,17936,a)].">
      <j1 rule="hyper" parents="58 15482 17936"/>
    </justification>
  </clause>

  <clause id="17940">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w)) * v5) = T(x,v5)
    ]]></literal>
    <justification jstring="[para(13702(a,2),17936(a,1,2,1))].">
      <j1 rule="para" parents="13702 17936"/>
    </justification>
  </clause>

  <clause id="17941">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) = v5 / T(v5,w)
    ]]></literal>
    <justification jstring="[para(17940(a,1),5062(a,2,2))].">
      <j1 rule="para" parents="17940 5062"/>
    </justification>
  </clause>

  <clause id="17942">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) * v5) = T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(10184(a,1),17940(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10184 17940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17943">
    <literal><![CDATA[
      T(x,(y * z) * K(u,w)) = T(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(14769(a,1),17940(a,1,2))].">
      <j1 rule="para" parents="14769 17940"/>
    </justification>
  </clause>

  <clause id="17944">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) * v5) = T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(14843(a,1),17940(a,1,2))].">
      <j1 rule="para" parents="14843 17940"/>
    </justification>
  </clause>

  <clause id="17945">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) = K(w,v5)
    ]]></literal>
    <justification jstring="[hyper(334,a,5062,a,b,17941,a),flip(a)].">
      <j1 rule="hyper" parents="334 5062 17941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17946">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(w,v5) = v6
    ]]></literal>
    <justification jstring="[para(17941(a,2),5133(a,1))].">
      <j1 rule="para" parents="17941 5133"/>
    </justification>
  </clause>

  <clause id="17947">
    <literal><![CDATA[
      K(x * a(y,z,K(u,w)),v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(17602,a,17945,a)].">
      <j1 rule="hyper" parents="17602 17945"/>
    </justification>
  </clause>

  <clause id="17948">
    <literal><![CDATA[
      K((x * y) * K(z,u),w) = K(x * (y * K(z,u)),w)
    ]]></literal>
    <justification jstring="[para(14769(a,1),17945(a,1,1))].">
      <j1 rule="para" parents="14769 17945"/>
    </justification>
  </clause>

  <clause id="17949">
    <literal><![CDATA[
      K(x * T(y,a(z,u,w)),v5) = K(x * y,v5)
    ]]></literal>
    <justification jstring="[para(17667(a,1),17945(a,1,1))].">
      <j1 rule="para" parents="17667 17945"/>
    </justification>
  </clause>

  <clause id="17950">
    <literal><![CDATA[
      K(x \ (y * a(z,u,K(w,v5))),v6) = K(x \ y,v6)
    ]]></literal>
    <justification jstring="[para(17666(a,2),17945(a,1,1))].">
      <j1 rule="para" parents="17666 17945"/>
    </justification>
  </clause>

  <clause id="17951">
    <literal><![CDATA[
      K(x * a(y,z,K(u,w)),v5) = (v6 * K(v5,x)) \ v6
    ]]></literal>
    <justification jstring="[hyper(334,a,6523,a,b,17947,a),flip(a)].">
      <j1 rule="hyper" parents="334 6523 17947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17952">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),w) = K((x \ y) * K(z,u),w)
    ]]></literal>
    <justification jstring="[para(1414(a,1),17947(a,1,1))].">
      <j1 rule="para" parents="1414 17947"/>
    </justification>
  </clause>

  <clause id="17953">
    <literal><![CDATA[
      K(T(x,y) * L(y,z,u),w) = K(L(y,z,u) * x,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,14788,a(flip),b,17949,a)].">
      <j1 rule="hyper" parents="58 14788 17949"/>
    </justification>
  </clause>

  <clause id="17954">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(13702(a,2),17937(a,1,2,1))].">
      <j1 rule="para" parents="13702 17937"/>
    </justification>
  </clause>

  <clause id="17955">
    <literal><![CDATA[
      K(K(x,a(y,z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(w,v5) = v6
    ]]></literal>
    <justification jstring="[para(13702(a,1),17946(a,1,1,1))].">
      <j1 rule="para" parents="13702 17946"/>
    </justification>
  </clause>

  <clause id="17956">
    <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(14769(a,1),17954(a,1,2))].">
      <j1 rule="para" parents="14769 17954"/>
    </justification>
  </clause>

  <clause id="17957">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ v5) = T(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[para(6198(a,2),17942(a,1,2))].">
      <j1 rule="para" parents="6198 17942"/>
    </justification>
  </clause>

  <clause id="17958">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) * v5) = T(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(334,a,15476,a,b,17944,a),flip(a)].">
      <j1 rule="hyper" parents="334 15476 17944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17959">
    <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),17950(a,1,1,2))].">
      <j1 rule="para" parents="80 17950"/>
    </justification>
  </clause>

  <clause id="17960">
    <literal><![CDATA[
      K(x,y * a(z,u,K(w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(16189,a,17951,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16189 17951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17961">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) * v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(17603,a,17960,a)].">
      <j1 rule="hyper" parents="17603 17960"/>
    </justification>
  </clause>

  <clause id="17962">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) = K(x,y * a(v5,v6,K(v7,v8)))
    ]]></literal>
    <justification jstring="[hyper(334,a,17559,a,b,17960,a)].">
      <j1 rule="hyper" parents="334 17559 17960"/>
    </justification>
  </clause>

  <clause id="17963">
    <literal><![CDATA[
      K(x,(y * z) * K(u,w)) = K(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(80(a,1),17960(a,1,2))].">
      <j1 rule="para" parents="80 17960"/>
    </justification>
  </clause>

  <clause id="17964">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,K(v5,v6)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(358(a,1),17960(a,1,2))].">
      <j1 rule="para" parents="358 17960"/>
    </justification>
  </clause>

  <clause id="17965">
    <literal><![CDATA[
      K(x,y \ (z * K(u,w))) = K(x,(y \ z) * K(u,w))
    ]]></literal>
    <justification jstring="[para(1414(a,1),17960(a,1,2))].">
      <j1 rule="para" parents="1414 17960"/>
    </justification>
  </clause>

  <clause id="17966">
    <literal><![CDATA[
      K(x,y * T(z,a(u,w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(13704(a,1),17960(a,1,2))].">
      <j1 rule="para" parents="13704 17960"/>
    </justification>
  </clause>

  <clause id="17967">
    <literal><![CDATA[
      K(x,y / T(z,a(u,w,v5))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(13731(a,1),17960(a,1,2))].">
      <j1 rule="para" parents="13731 17960"/>
    </justification>
  </clause>

  <clause id="17968">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[para(14593(a,1),17960(a,1,2))].">
      <j1 rule="para" parents="14593 17960"/>
    </justification>
  </clause>

  <clause id="17969">
    <literal><![CDATA[
      K(x,y * L(z,u,K(w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(15307(a,1),17960(a,1,2))].">
      <j1 rule="para" parents="15307 17960"/>
    </justification>
  </clause>

  <clause id="17970">
    <literal><![CDATA[
      K(x,y \ L(z,u,K(w,v5))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(15308(a,1),17960(a,1,2))].">
      <j1 rule="para" parents="15308 17960"/>
    </justification>
  </clause>

  <clause id="17971">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w)) \ v5) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[para(17731(a,1),17960(a,1,2))].">
      <j1 rule="para" parents="17731 17960"/>
    </justification>
  </clause>

  <clause id="17972">
    <literal><![CDATA[
      K(x,y / L(z,u,K(w,v5))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(17927(a,1),17960(a,1,2))].">
      <j1 rule="para" parents="17927 17960"/>
    </justification>
  </clause>

  <clause id="17973">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) * v6) = K(x,v5 * v6)
    ]]></literal>
    <justification jstring="[para(14604(a,2),17961(a,1,2))].">
      <j1 rule="para" parents="14604 17961"/>
    </justification>
  </clause>

  <clause id="17974">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * v5) = K(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(14843(a,1),17961(a,1,2))].">
      <j1 rule="para" parents="14843 17961"/>
    </justification>
  </clause>

  <clause id="17975">
    <literal><![CDATA[
      K(x,(y * a(z,u,K(w,v5))) * v6) = K(x,y * v6)
    ]]></literal>
    <justification jstring="[para(17672(a,2),17961(a,1,2))].">
      <j1 rule="para" parents="17672 17961"/>
    </justification>
  </clause>

  <clause id="17976">
    <literal><![CDATA[
      K(x,y * (a(z,u,K(w,v5)) * v6)) = K(x,y * v6)
    ]]></literal>
    <justification jstring="[para(17884(a,1),17961(a,1,2))].">
      <j1 rule="para" parents="17884 17961"/>
    </justification>
  </clause>

  <clause id="17977">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) \ v6) = K(x,v5 \ v6)
    ]]></literal>
    <justification jstring="[para(17913(a,2),17961(a,1,2))].">
      <j1 rule="para" parents="17913 17961"/>
    </justification>
  </clause>

  <clause id="17978">
    <literal><![CDATA[
      K(x,y * T(z,L(u,w,v5))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(14703(a,1),17966(a,1,2,2))].">
      <j1 rule="para" parents="14703 17966"/>
    </justification>
  </clause>

  <clause id="17979">
    <literal><![CDATA[
      K(x,y / (a(z,u,w) / v5)) = K(x,y / (v5 \ a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(15645,a,17967,a)].">
      <j1 rule="hyper" parents="15645 17967"/>
    </justification>
  </clause>

  <clause id="17980">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) \ v5)) = K(x,y / (w \ (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[para(15313(a,1),17967(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15313 17967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17981">
    <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(579(a,1),17969(a,1,2,2))].">
      <j1 rule="para" parents="579 17969"/>
    </justification>
  </clause>

  <clause id="17982">
    <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(14321(a,1),17969(a,1,2,2))].">
      <j1 rule="para" parents="14321 17969"/>
    </justification>
  </clause>

  <clause id="17983">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ (K(z,w) * v5))) = K(x,y \ ((T(z,w) \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(5488(a,1),17970(a,1,2,2))].">
      <j1 rule="para" parents="5488 17970"/>
    </justification>
  </clause>

  <clause id="17984">
    <literal><![CDATA[
      K(x,y \ T(z,L(u,w,v5))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(15298(a,1),17970(a,1,2,2))].">
      <j1 rule="para" parents="15298 17970"/>
    </justification>
  </clause>

  <clause id="17985">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w)) \ v5) = K(x,T(y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(15298(a,1),17971(a,1,2,1))].">
      <j1 rule="para" parents="15298 17971"/>
    </justification>
  </clause>

  <clause id="17986">
    <literal><![CDATA[
      K(x,y / ((z * ((K(u,w) * z) \ v5)) / z)) = K(x,y / ((K(u,w) \ v5) / z))
    ]]></literal>
    <justification jstring="[para(890(a,1),17972(a,1,2,2))].">
      <j1 rule="para" parents="890 17972"/>
    </justification>
  </clause>

  <clause id="17987">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ v5) = T(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(5391(a,2),17957(a,2,2))].">
      <j1 rule="para" parents="5391 17957"/>
    </justification>
  </clause>

  <clause id="17988">
    <literal><![CDATA[
      T(x,(K(y,z) * u) * w) = T(x,K(z,y) * (u * w))
    ]]></literal>
    <justification jstring="[para(15123(a,1),17958(a,1,2))].">
      <j1 rule="para" parents="15123 17958"/>
    </justification>
  </clause>

  <clause id="17990">
    <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),17964(a,1,2,2))].">
      <j1 rule="para" parents="80 17964"/>
    </justification>
  </clause>

  <clause id="17991">
    <literal><![CDATA[
      K(x,y * (z * (u * a(w,v5,K(v6,v7))))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(358(a,1),17964(a,1,2,2))].">
      <j1 rule="para" parents="358 17964"/>
    </justification>
  </clause>

  <clause id="17992">
    <literal><![CDATA[
      K(x,y * (z / L(u,w,K(v5,v6)))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(17927(a,1),17964(a,1,2,2))].">
      <j1 rule="para" parents="17927 17964"/>
    </justification>
  </clause>

  <clause id="17993">
    <literal><![CDATA[
      K(x,(y \ L(z,u,K(w,v5))) * v6) = K(x,(y \ z) * v6)
    ]]></literal>
    <justification jstring="[para(17688(a,1),17973(a,1,2,1))].">
      <j1 rule="para" parents="17688 17973"/>
    </justification>
  </clause>

  <clause id="17994">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * v5) = K(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(334,a,15492,a,b,17974,a),flip(a)].">
      <j1 rule="hyper" parents="334 15492 17974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17995">
    <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,17144,a(flip),b,17974,a),flip(a)].">
      <j1 rule="hyper" parents="58 17144 17974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17996">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (w * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16182,a(flip),b,17974,a),flip(a)].">
      <j1 rule="hyper" parents="58 16182 17974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17997">
    <literal><![CDATA[
      K(x,K((y \ z) \ u,w) * v5) = K(x,K(z \ (y * u),w) * v5)
    ]]></literal>
    <justification jstring="[para(11106(a,1),17974(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11106 17974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17998">
    <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(17974(a,2),15493(a,1))].">
      <j1 rule="para" parents="17974 15493"/>
    </justification>
  </clause>

  <clause id="17999">
    <literal><![CDATA[
      K(x,(L(y,z,K(u,w)) / v5) * v6) = K(x,(y / v5) * v6)
    ]]></literal>
    <justification jstring="[para(17782(a,1),17975(a,1,2,1))].">
      <j1 rule="para" parents="17782 17975"/>
    </justification>
  </clause>

  <clause id="18000">
    <literal><![CDATA[
      K(x,y * (z \ (a(u,w,K(v5,v6)) * v7))) = K(x,y * (z \ v7))
    ]]></literal>
    <justification jstring="[para(17881(a,2),17976(a,1,2,2))].">
      <j1 rule="para" parents="17881 17976"/>
    </justification>
  </clause>

  <clause id="18001">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = K(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(3966(a,1),17977(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3966 17977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18002">
    <literal><![CDATA[
      K(x,y * T(z,L(u / w,v5,v6))) = K(x,y * T(z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(334,a,16437,a(flip),b,17978,a),flip(a)].">
      <j1 rule="hyper" parents="334 16437 17978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18003">
    <literal><![CDATA[
      K(x,y \ T(z,L(u / w,v5,v6))) = K(x,y \ T(z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(334,a,16434,a(flip),b,17984,a),flip(a)].">
      <j1 rule="hyper" parents="334 16434 17984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18004">
    <literal><![CDATA[
      K(x,T(y,z) \ L(z,u,w)) = K(x,L(z,u,w) / y)
    ]]></literal>
    <justification jstring="[hyper(13436,a,17985,a),flip(a)].">
      <j1 rule="hyper" parents="13436 17985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18005">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = x \ T(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(116,a,17987,a(flip),b,5020,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 17987 5020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18006">
    <literal><![CDATA[
      K(x,y * K(z,L(u,w,v5))) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(16034,a,17994,a)].">
      <j1 rule="hyper" parents="16034 17994"/>
    </justification>
  </clause>

  <clause id="18007">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16182,a(flip),b,17994,a),flip(a)].">
      <j1 rule="hyper" parents="58 16182 17994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18008">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,K(z,y) * (u * w))
    ]]></literal>
    <justification jstring="[para(15123(a,1),17994(a,1,2))].">
      <j1 rule="para" parents="15123 17994"/>
    </justification>
  </clause>

  <clause id="18009">
    <literal><![CDATA[
      K(x,K(y,z) * ((z * u) * w)) = K(x,(T(z,y) * u) * w)
    ]]></literal>
    <justification jstring="[para(15207(a,1),17994(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15207 17994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18010">
    <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(17994(a,2),15493(a,1))].">
      <j1 rule="para" parents="17994 15493"/>
    </justification>
  </clause>

  <clause id="18011">
    <literal><![CDATA[
      K(x,y * K(z,L(u,w,v5))) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,16002,a(flip),b,18006,a),flip(a)].">
      <j1 rule="hyper" parents="334 16002 18006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18012">
    <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(18006(a,2),16034(a,1))].">
      <j1 rule="para" parents="18006 16034"/>
    </justification>
  </clause>

  <clause id="18013">
    <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(18011(a,2),16068(a,1))].">
      <j1 rule="para" parents="18011 16068"/>
    </justification>
  </clause>

  <clause id="18014">
    <literal><![CDATA[
      T(x,T(a(y,z,u),w) * v5) = T(x,v5 * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,17575,a(flip),b,17939,a),flip(a)].">
      <j1 rule="hyper" parents="334 17575 17939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18015">
    <literal><![CDATA[
      T(x,(y \ z) * (y * K(u,w))) = T(x,T(K(u,w) * z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16704,a(flip),b,17943,a),flip(a)].">
      <j1 rule="hyper" parents="58 16704 17943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18016">
    <literal><![CDATA[
      K(K(x,y) * (z * u),w) = K(z * (u * K(y,x)),w)
    ]]></literal>
    <justification jstring="[hyper(16294,a,17948,a)].">
      <j1 rule="hyper" parents="16294 17948"/>
    </justification>
  </clause>

  <clause id="18017">
    <literal><![CDATA[
      K(K(x,y) * (z * u),w) = K(z * (u * K(x,y)),w)
    ]]></literal>
    <justification jstring="[hyper(16067,a,17948,a)].">
      <j1 rule="hyper" parents="16067 17948"/>
    </justification>
  </clause>

  <clause id="18018">
    <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(17948(a,1),16067(a,1))].">
      <j1 rule="para" parents="17948 16067"/>
    </justification>
  </clause>

  <clause id="18019">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),w) = K(K(u,z) * (x \ y),w)
    ]]></literal>
    <justification jstring="[hyper(334,a,16215,a,b,17952,a),flip(a)].">
      <j1 rule="hyper" parents="334 16215 17952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18020">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K((x \ u) * K(z,y),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17795,a,b,17952,a)].">
      <j1 rule="hyper" parents="58 17795 17952"/>
    </justification>
  </clause>

  <clause id="18022">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = K(u * L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9050,a(flip),b,17953,a),flip(a)].">
      <j1 rule="hyper" parents="58 9050 17953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18023">
    <literal><![CDATA[
      K(x,y * a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v6
    ]]></literal>
    <justification jstring="[para(17962(a,1),17601(a,1))].">
      <j1 rule="para" parents="17962 17601"/>
    </justification>
  </clause>

  <clause id="18024">
    <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),18023(a,1,2))].">
      <j1 rule="para" parents="80 18023"/>
    </justification>
  </clause>

  <clause id="18025">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) = K(x,u * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(16142,a,17963,a)].">
      <j1 rule="hyper" parents="16142 17963"/>
    </justification>
  </clause>

  <clause id="18026">
    <literal><![CDATA[
      K(x,y * ((1 / z) * K(u,y / z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(14546,a,17963,a),flip(a)].">
      <j1 rule="hyper" parents="14546 17963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18027">
    <literal><![CDATA[
      K(x,(y * z) * K(u,w)) = K(x,y * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(334,a,16415,a,b,17963,a),flip(a)].">
      <j1 rule="hyper" parents="334 16415 17963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18028">
    <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(17299(a,1),17963(a,1,2,2))].">
      <j1 rule="para" parents="17299 17963"/>
    </justification>
  </clause>

  <clause id="18029">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,(y \ w) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(16466,a,17965,a)].">
      <j1 rule="hyper" parents="16466 17965"/>
    </justification>
  </clause>

  <clause id="18030">
    <literal><![CDATA[
      K(x,y \ (z * K(u,w))) = K(x,K(u,w) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(334,a,16002,a,b,17965,a),flip(a)].">
      <j1 rule="hyper" parents="334 16002 17965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18031">
    <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(11110(a,1),17965(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11110 17965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18032">
    <literal><![CDATA[
      K(x,(K(y,L(z,u,w)) * v5) * v6) = K(x,K(y,z) * (v5 * v6))
    ]]></literal>
    <justification jstring="[hyper(334,a,17974,a(flip),b,17968,a),flip(a)].">
      <j1 rule="hyper" parents="334 17974 17968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18033">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) * w)) = K(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[para(5392(a,1),17968(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5392 17968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18034">
    <literal><![CDATA[
      K(x,K(y,z) * ((y / u) * w)) = K(x,(T(y,z) / u) * w)
    ]]></literal>
    <justification jstring="[para(14034(a,1),17968(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14034 17968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18035">
    <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(17968(a,2),15493(a,1))].">
      <j1 rule="para" parents="17968 15493"/>
    </justification>
  </clause>

  <clause id="18036">
    <literal><![CDATA[
      T(x,(y \ K(z,u)) \ w) = T(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,14218,a,b,17988,a)].">
      <j1 rule="hyper" parents="58 14218 17988"/>
    </justification>
  </clause>

  <clause id="18037">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * w) = T(x,K(u,z) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,16383,a(flip),b,17988,a)].">
      <j1 rule="hyper" parents="58 16383 17988"/>
    </justification>
  </clause>

  <clause id="18038">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (K(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(334,a,16518,a,b,17996,a),flip(a)].">
      <j1 rule="hyper" parents="334 16518 17996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18039">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (K(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(334,a,16415,a,b,17996,a),flip(a)].">
      <j1 rule="hyper" parents="334 16415 17996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18040">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (1 / w))) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(334,a,14232,a(flip),b,17996,a),flip(a)].">
      <j1 rule="hyper" parents="334 14232 17996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18042">
    <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(17996(a,2),16621(a,1))].">
      <j1 rule="para" parents="17996 16621"/>
    </justification>
  </clause>

  <clause id="18043">
    <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(607(a,1),18004(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="607 18004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18044">
    <literal><![CDATA[
      K(x,K(y,z * u) * (w * v5)) = K(x,w * (v5 * K(y,u * z)))
    ]]></literal>
    <justification jstring="[hyper(16545,a,18007,a)].">
      <j1 rule="hyper" parents="16545 18007"/>
    </justification>
  </clause>

  <clause id="18045">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (z / w))) = K(x,u * (T(z,y) / w))
    ]]></literal>
    <justification jstring="[hyper(334,a,16439,a(flip),b,18007,a),flip(a)].">
      <j1 rule="hyper" parents="334 16439 18007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18046">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (1 / w))) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(334,a,14232,a(flip),b,18007,a),flip(a)].">
      <j1 rule="hyper" parents="334 14232 18007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18047">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * w) = K(x,K(u,z) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(16463,a,18008,a)].">
      <j1 rule="hyper" parents="16463 18008"/>
    </justification>
  </clause>

  <clause id="18048">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) \ w) = K(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(14418,a,18008,a)].">
      <j1 rule="hyper" parents="14418 18008"/>
    </justification>
  </clause>

  <clause id="18049">
    <literal><![CDATA[
      K(x,K(y,z) * ((z / u) * w)) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[para(14034(a,1),18008(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14034 18008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18050">
    <literal><![CDATA[
      K(x,K(y,z) * (((z * y) / u) * w)) = K(x,((T(z,y) * y) / u) * w)
    ]]></literal>
    <justification jstring="[para(14572(a,1),18008(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14572 18008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18051">
    <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(18008(a,1),16851(a,1,2))].">
      <j1 rule="para" parents="18008 16851"/>
    </justification>
  </clause>

  <clause id="18052">
    <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(18014(a,1),16140(a,1,2,1))].">
      <j1 rule="para" parents="18014 16140"/>
    </justification>
  </clause>

  <clause id="18053">
    <literal><![CDATA[
      K((K(x,y) * z) * u,w) = K(K(y,x) * (z * u),w)
    ]]></literal>
    <justification jstring="[hyper(334,a,17932,a,b,18016,a)].">
      <j1 rule="hyper" parents="334 17932 18016"/>
    </justification>
  </clause>

  <clause id="18054">
    <literal><![CDATA[
      K(K(x,y) * ((y \ z) * u),w) = K((T(y,x) \ z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(334,a,17933,a(flip),b,18017,a),flip(a)].">
      <j1 rule="hyper" parents="334 17933 18017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18055">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K(K(z,y) * (x \ u),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,16429,a,b,18019,a)].">
      <j1 rule="hyper" parents="58 16429 18019"/>
    </justification>
  </clause>

  <clause id="18056">
    <literal><![CDATA[
      K(K(x,y) * (z \ (u * K(x,y))),w) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[para(6516(a,1),18019(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6516 18019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18057">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K((z \ u) * K(y,x),w)
    ]]></literal>
    <justification jstring="[hyper(16459,a,18020,a)].">
      <j1 rule="hyper" parents="16459 18020"/>
    </justification>
  </clause>

  <clause id="18059">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K(K(z,y) * (x \ u),w)
    ]]></literal>
    <justification jstring="[hyper(334,a,16055,a,b,18020,a),flip(a)].">
      <j1 rule="hyper" parents="334 16055 18020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18060">
    <literal><![CDATA[
      K(((x * y) \ z) * K(u,y),w) = K((x * T(y,u)) \ z,w)
    ]]></literal>
    <justification jstring="[para(6432(a,1),18020(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6432 18020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18061">
    <literal><![CDATA[
      K(((x \ y) \ z) * K(u,y),w) = K((x \ T(y,u)) \ z,w)
    ]]></literal>
    <justification jstring="[para(14025(a,1),18020(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14025 18020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18062">
    <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(18020(a,1),14641(a,2,3))].">
      <j1 rule="para" parents="18020 14641"/>
    </justification>
  </clause>

  <clause id="18063">
    <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(11089(a,2),18025(a,2,2,2,2))].">
      <j1 rule="para" parents="11089 18025"/>
    </justification>
  </clause>

  <clause id="18064">
    <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,18006,a(flip),b,18027,a),flip(a)].">
      <j1 rule="hyper" parents="58 18006 18027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18065">
    <literal><![CDATA[
      K(x,y * (K(z,x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * u) = w
    ]]></literal>
    <justification jstring="[para(18027(a,1),8694(a,1))].">
      <j1 rule="para" parents="18027 8694"/>
    </justification>
  </clause>

  <clause id="18066">
    <literal><![CDATA[
      K(x,y * (T(z,x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * u)) = w
    ]]></literal>
    <justification jstring="[para(5047(a,1),18065(a,1,2,2))].">
      <j1 rule="para" parents="5047 18065"/>
    </justification>
  </clause>

  <clause id="18067">
    <literal><![CDATA[
      K(x,y * (T(z,x) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ u)) = w
    ]]></literal>
    <justification jstring="[para(15801(a,1),18065(a,1))].">
      <j1 rule="para" parents="15801 18065"/>
    </justification>
  </clause>

  <clause id="18068">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(334,a,16177,a,b,18029,a),flip(a)].">
      <j1 rule="hyper" parents="334 16177 18029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18069">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(334,a,16002,a,b,18029,a),flip(a)].">
      <j1 rule="hyper" parents="334 16002 18029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18070">
    <literal><![CDATA[
      T(x,y \ (z * K(u,w))) = T(x,K(u,w) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,18030,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 18030 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18071">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17796,a,b,18030,a)].">
      <j1 rule="hyper" parents="58 17796 18030"/>
    </justification>
  </clause>

  <clause id="18072">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17722,a,b,18030,a)].">
      <j1 rule="hyper" parents="58 17722 18030"/>
    </justification>
  </clause>

  <clause id="18073">
    <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,12521,a(flip),b,18030,a)].">
      <j1 rule="hyper" parents="58 12521 18030"/>
    </justification>
  </clause>

  <clause id="18074">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * y))) = K(x,u \ (w * T(y,z)))
    ]]></literal>
    <justification jstring="[para(6432(a,1),18030(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6432 18030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18075">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u \ (w / (y \ z)))) = K(x,u \ (w / (z / y)))
    ]]></literal>
    <justification jstring="[para(6743(a,1),18030(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6743 18030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18076">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (u \ (w * z))) = K(x,u \ (w * (y * (z / y))))
    ]]></literal>
    <justification jstring="[para(10611(a,1),18030(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10611 18030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18077">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u \ (w * z))) = K(x,u \ (w * ((y \ z) * y)))
    ]]></literal>
    <justification jstring="[para(10617(a,1),18030(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10617 18030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18078">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w \ y))) = K(x,u \ (w \ T(y,z)))
    ]]></literal>
    <justification jstring="[para(14025(a,1),18030(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14025 18030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18079">
    <literal><![CDATA[
      T(x,(K(y,z) / u) \ w) = T(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(14473,a,18037,a)].">
      <j1 rule="hyper" parents="14473 18037"/>
    </justification>
  </clause>

  <clause id="18080">
    <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,17158,a(flip),b,18037,a),flip(a)].">
      <j1 rule="hyper" parents="58 17158 18037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18081">
    <literal><![CDATA[
      T(x,K(y,z) * (u * w)) = T(x,u * (K(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(118,a,18038,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 18038 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18082">
    <literal><![CDATA[
      K(x,(K(y,z) / u) \ w) = K(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(14425,a,18047,a)].">
      <j1 rule="hyper" parents="14425 18047"/>
    </justification>
  </clause>

  <clause id="18083">
    <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,11207,a(flip),b,18047,a),flip(a)].">
      <j1 rule="hyper" parents="58 11207 18047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18084">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ z) * w)) = K(x,(u \ T(z,y)) * w)
    ]]></literal>
    <justification jstring="[para(14025(a,1),18047(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14025 18047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18085">
    <literal><![CDATA[
      K(x,K(y \ z,y) * ((u \ z) * w)) = K(x,(u \ (y * (z / y))) * w)
    ]]></literal>
    <justification jstring="[para(15373(a,1),18047(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15373 18047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18086">
    <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(18047(a,1),17766(a,1,3))].">
      <j1 rule="para" parents="18047 17766"/>
    </justification>
  </clause>

  <clause id="18087">
    <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,14961,a(flip),b,18048,a),flip(a)].">
      <j1 rule="hyper" parents="58 14961 18048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18088">
    <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(18048(a,1),15602(a,1,1,2))].">
      <j1 rule="para" parents="18048 15602"/>
    </justification>
  </clause>

  <clause id="18089">
    <literal><![CDATA[
      K(x * (K(y,z) * u),T(w,u)) = K(K(z,y) * (u * x),w)
    ]]></literal>
    <justification jstring="[hyper(16826,a,18053,a)].">
      <j1 rule="hyper" parents="16826 18053"/>
    </justification>
  </clause>

  <clause id="18090">
    <literal><![CDATA[
      K(K(x,y) * (z \ (K(x,y) * u)),w) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[para(5394(a,1),18055(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5394 18055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18091">
    <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(18056(a,2),8694(a,1))].">
      <j1 rule="para" parents="18056 8694"/>
    </justification>
  </clause>

  <clause id="18092">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K(K(y,x) * (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(334,a,16055,a,b,18057,a),flip(a)].">
      <j1 rule="hyper" parents="334 16055 18057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18094">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (z * w))) = K(x,u \ (T(z,y) * w))
    ]]></literal>
    <justification jstring="[para(5047(a,1),18068(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5047 18068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18095">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (u \ (z * w))) = K(x,u \ (((y \ z) * y) * w))
    ]]></literal>
    <justification jstring="[para(11426(a,1),18068(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11426 18068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18096">
    <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(15735,a,18069,a),flip(a)].">
      <j1 rule="hyper" parents="15735 18069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18097">
    <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(15486,a,18069,a),flip(a)].">
      <j1 rule="hyper" parents="15486 18069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18098">
    <literal><![CDATA[
      x * K(x,K(y,z) * (u \ w)) = T(x,u \ (K(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(119,a,18069,a(flip),b,4995,a(flip))].">
      <j1 rule="hyper" parents="119 18069 4995"/>
    </justification>
  </clause>

  <clause id="18099">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (y * w))) = K(x,u \ (T(y,z) * w))
    ]]></literal>
    <justification jstring="[para(5047(a,1),18069(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5047 18069"/>
      <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(5392(a,1),18069(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5392 18069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18101">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,z) * w))) = K(x,K(u,z) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[para(5522(a,1),18069(a,1,2,2))].">
      <j1 rule="para" parents="5522 18069"/>
    </justification>
  </clause>

  <clause id="18102">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u \ ((z / y) * w))) = K(x,u \ ((y \ z) * w))
    ]]></literal>
    <justification jstring="[para(5680(a,1),18069(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5680 18069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18103">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((z * y) * w))) = K(x,u \ ((y * z) * w))
    ]]></literal>
    <justification jstring="[para(11459(a,1),18069(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11459 18069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18104">
    <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(18070(a,1),16432(a,1,2,2))].">
      <j1 rule="para" parents="18070 16432"/>
    </justification>
  </clause>

  <clause id="18105">
    <literal><![CDATA[
      T(x,(y * K(z,u)) \ w) = T(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(118,a,18071,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 18071 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18106">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,K(z,u) \ (y \ w))
    ]]></literal>
    <justification jstring="[para(5391(a,2),18071(a,2,2))].">
      <j1 rule="para" parents="5391 18071"/>
    </justification>
  </clause>

  <clause id="18107">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ z) \ w)) = K(x,(u \ T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(14025(a,1),18071(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14025 18071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18108">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) = T(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(118,a,18072,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 18072 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18109">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,z) * x))) = K(x,K(u,z) * ((z \ y) \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6990,a(flip),b,18072,a)].">
      <j1 rule="hyper" parents="58 6990 18072"/>
    </justification>
  </clause>

  <clause id="18110">
    <literal><![CDATA[
      K(x,K(y,z) * ((y \ u) \ w)) = K(x,(T(y,z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(5392(a,1),18072(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5392 18072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18111">
    <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(18079(a,1),14443(a,1,2,1,1))].">
      <j1 rule="para" parents="18079 14443"/>
    </justification>
  </clause>

  <clause id="18112">
    <literal><![CDATA[
      T(x,(y \ K(z,u)) \ w) = T(x,y * (K(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,18036,a,b,18081,a)].">
      <j1 rule="hyper" parents="58 18036 18081"/>
    </justification>
  </clause>

  <clause id="18113">
    <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,17455,a(flip),b,18082,a)].">
      <j1 rule="hyper" parents="58 17455 18082"/>
    </justification>
  </clause>

  <clause id="18114">
    <literal><![CDATA[
      K(K(x,y) * (((x * y) * z) \ u),w) = K(((y * x) * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(11459(a,1),18092(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11459 18092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18115">
    <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,15830,a,b,18105,a)].">
      <j1 rule="hyper" parents="58 15830 18105"/>
    </justification>
  </clause>

  <clause id="18116">
    <literal><![CDATA[
      T(x,K(y,z) * ((u / y) \ w)) = T(x,(u / T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(6368(a,1),18105(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6368 18105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18117">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * z) \ w)) = T(x,(u * T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(6432(a,1),18105(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6432 18105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18118">
    <literal><![CDATA[
      T(x,K(y \ z,y) * ((u \ (y \ z)) \ w)) = T(x,(u \ (z / y)) \ w)
    ]]></literal>
    <justification jstring="[para(14302(a,1),18105(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14302 18105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18119">
    <literal><![CDATA[
      K(x,K(y,z) \ ((u / z) \ w)) = K(x,(u / T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(6368(a,1),18106(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6368 18106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18120">
    <literal><![CDATA[
      T(x,K(y,z) * ((z / u) \ w)) = T(x,(T(z,y) / u) \ w)
    ]]></literal>
    <justification jstring="[para(14034(a,1),18108(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14034 18108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18121">
    <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(18108(a,1),16473(a,2,2,2))].">
      <j1 rule="para" parents="18108 16473"/>
    </justification>
  </clause>

  <clause id="18122">
    <literal><![CDATA[
      T(x,(y \ z) * (K(u,z \ y) * w)) = T(x,T((y \ z) \ 1,u) \ w)
    ]]></literal>
    <justification jstring="[para(6628(a,1),18112(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6628 18112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18123">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * w) / v5)) = K(x,y * (K(z,u) * (w / v5)))
    ]]></literal>
    <justification jstring="[para(556(a,1),17992(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="556 17992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18124">
    <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(5210(a,1),17993(a,1,2,1,2))].">
      <j1 rule="para" parents="5210 17993"/>
    </justification>
  </clause>

  <clause id="18125">
    <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(577(a,1),17999(a,1,2,1,1))].">
      <j1 rule="para" parents="577 17999"/>
    </justification>
  </clause>

  <clause id="18126">
    <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(18005(a,2),5110(a,1))].">
      <j1 rule="para" parents="18005 5110"/>
    </justification>
  </clause>

  <clause id="18127">
    <literal><![CDATA[
      K(x,(T(y,z) * (u / y)) * w) = K(x,K(z,y) * (T(u,y) * w))
    ]]></literal>
    <justification jstring="[hyper(16957,a,18009,a),flip(a)].">
      <j1 rule="hyper" parents="16957 18009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18128">
    <literal><![CDATA[
      K(x * L(y,z,u),y * x) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,17809,a(flip),b,18022,a),flip(a)].">
      <j1 rule="hyper" parents="58 17809 18022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18129">
    <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(2489(a,1),18128(a,1,1,2))].">
      <j1 rule="para" parents="2489 18128"/>
    </justification>
  </clause>

  <clause id="18130">
    <literal><![CDATA[
      K(x,y * (K(z,u \ y) / u)) = K(x,T(y / u,z))
    ]]></literal>
    <justification jstring="[para(14328(a,1),18026(a,1,2,2))].">
      <j1 rule="para" parents="14328 18026"/>
    </justification>
  </clause>

  <clause id="18131">
    <literal><![CDATA[
      K(x,y * (z \ K(u,z \ y))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(16505,a,18130,a)].">
      <j1 rule="hyper" parents="16505 18130"/>
    </justification>
  </clause>

  <clause id="18132">
    <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(8942(a,1),18131(a,1,2,2,2))].">
      <j1 rule="para" parents="8942 18131"/>
    </justification>
  </clause>

  <clause id="18133">
    <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(11540(a,1),18131(a,1,2,2,2))].">
      <j1 rule="para" parents="11540 18131"/>
    </justification>
  </clause>

  <clause id="18134">
    <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(11552(a,1),18131(a,1,2,2,2))].">
      <j1 rule="para" parents="11552 18131"/>
    </justification>
  </clause>

  <clause id="18135">
    <literal><![CDATA[
      K(x,(y \ z) * (u * K(w,y))) = K(x,(T(y,w) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,17996,a(flip),b,18033,a)].">
      <j1 rule="hyper" parents="58 17996 18033"/>
    </justification>
  </clause>

  <clause id="18136">
    <literal><![CDATA[
      K(x,K(y,z) * ((y / u) * w)) = K(x,(T(y,K(v5,v6) * z) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(17051,a,18034,a)].">
      <j1 rule="hyper" parents="17051 18034"/>
    </justification>
  </clause>

  <clause id="18137">
    <literal><![CDATA[
      K(x,(K(y,z) * (z / u)) * w) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18008,a,b,18034,a)].">
      <j1 rule="hyper" parents="58 18008 18034"/>
    </justification>
  </clause>

  <clause id="18138">
    <literal><![CDATA[
      K(x,y * (z \ K(u,L(w,v5,v6)))) = K(x,K(w,u) * (y * (1 / z)))
    ]]></literal>
    <justification jstring="[hyper(17998,a,18040,a),flip(a)].">
      <j1 rule="hyper" parents="17998 18040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18139">
    <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,17185,a(flip),b,18045,a),flip(a)].">
      <j1 rule="hyper" parents="58 17185 18045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18140">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18040,a(flip),b,18046,a)].">
      <j1 rule="hyper" parents="58 18040 18046"/>
    </justification>
  </clause>

  <clause id="18141">
    <literal><![CDATA[
      K(x,y * (z \ K(z,u))) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(14419,a,18140,a),flip(a)].">
      <j1 rule="hyper" parents="14419 18140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18142">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,u))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(334,a,13499,a,b,18140,a)].">
      <j1 rule="hyper" parents="334 13499 18140"/>
    </justification>
  </clause>

  <clause id="18143">
    <literal><![CDATA[
      K(x,(y \ z) * (u \ K(y,w))) = K(x,(T(y,w) \ z) / u)
    ]]></literal>
    <justification jstring="[hyper(334,a,17834,a(flip),b,18140,a),flip(a)].">
      <j1 rule="hyper" parents="334 17834 18140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18144">
    <literal><![CDATA[
      K(x,(y * z) * (u \ K(w,y))) = K(x,(T(y,w) * z) / u)
    ]]></literal>
    <justification jstring="[hyper(334,a,17833,a(flip),b,18140,a),flip(a)].">
      <j1 rule="hyper" parents="334 17833 18140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18145">
    <literal><![CDATA[
      K(x,(y / z) * (u \ K(z,w))) = K(x,(y / T(z,w)) / u)
    ]]></literal>
    <justification jstring="[hyper(334,a,17802,a(flip),b,18140,a),flip(a)].">
      <j1 rule="hyper" parents="334 17802 18140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18146">
    <literal><![CDATA[
      K(x,y * ((z * u) \ K(u,w))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(334,a,16553,a(flip),b,18140,a),flip(a)].">
      <j1 rule="hyper" parents="334 16553 18140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18147">
    <literal><![CDATA[
      K(x,y * ((z / u) \ K(w,u))) = K(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(334,a,16552,a(flip),b,18140,a),flip(a)].">
      <j1 rule="hyper" parents="334 16552 18140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18148">
    <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(6228(a,2),18141(a,2,2,2))].">
      <j1 rule="para" parents="6228 18141"/>
    </justification>
  </clause>

  <clause id="18149">
    <literal><![CDATA[
      K(x,(T(y,x) / z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / z) * u) = w
    ]]></literal>
    <justification jstring="[para(18049(a,1),7613(a,1))].">
      <j1 rule="para" parents="18049 7613"/>
    </justification>
  </clause>

  <clause id="18150">
    <literal><![CDATA[
      K(x,L(y,z,z \ u) * u) = K(x,(T(u,y) / z) * (z * y))
    ]]></literal>
    <justification jstring="[para(14531(a,1),18049(a,1,2))].">
      <j1 rule="para" parents="14531 18049"/>
    </justification>
  </clause>

  <clause id="18151">
    <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),18149(a,1,2,1,1))].">
      <j1 rule="para" parents="18 18149"/>
    </justification>
  </clause>

  <clause id="18152">
    <literal><![CDATA[
      K(K(x,y) * ((z * x) \ u),w) = K((z * T(x,y)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(16294,a,18060,a)].">
      <j1 rule="hyper" parents="16294 18060"/>
    </justification>
  </clause>

  <clause id="18153">
    <literal><![CDATA[
      K((x \ T(y,x)) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16293,a(flip),b,18061,a),flip(a)].">
      <j1 rule="hyper" parents="58 16293 18061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18154">
    <literal><![CDATA[
      K((T(x,y) \ y) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9321,a,b,18153,a)].">
      <j1 rule="hyper" parents="58 9321 18153"/>
    </justification>
  </clause>

  <clause id="18155">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * z))) = K(x,u \ (w * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(15493,a,18074,a)].">
      <j1 rule="hyper" parents="15493 18074"/>
    </justification>
  </clause>

  <clause id="18156">
    <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(18078(a,1),16400(a,1))].">
      <j1 rule="para" parents="18078 16400"/>
    </justification>
  </clause>

  <clause id="18157">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) * w)) = K(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(15493,a,18084,a)].">
      <j1 rule="hyper" parents="15493 18084"/>
    </justification>
  </clause>

  <clause id="18158">
    <literal><![CDATA[
      K(x,(y \ T(z,x)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ z) * u) = w
    ]]></literal>
    <justification jstring="[para(18084(a,1),7613(a,1))].">
      <j1 rule="para" parents="18084 7613"/>
    </justification>
  </clause>

  <clause id="18159">
    <literal><![CDATA[
      K(K(x,y) * (z * u),T(w,z)) = K(u * (K(y,x) * z),w)
    ]]></literal>
    <justification jstring="[hyper(8281,a,18089,a),flip(a)].">
      <j1 rule="hyper" parents="8281 18089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18160">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (z * x))) = K(x,u \ (x * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(334,a,7686,a(flip),b,18094,a),flip(a)].">
      <j1 rule="hyper" parents="334 7686 18094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18161">
    <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(18098(a,1),5030(a,1))].">
      <j1 rule="para" parents="18098 5030"/>
    </justification>
  </clause>

  <clause id="18162">
    <literal><![CDATA[
      K(x,T(y,z) \ (z \ u)) = K(x,y \ (T(z,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15499,a(flip),b,18100,a)].">
      <j1 rule="hyper" parents="58 15499 18100"/>
    </justification>
  </clause>

  <clause id="18163">
    <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(18162(a,2),8415(a,1,2))].">
      <j1 rule="para" parents="18162 8415"/>
    </justification>
  </clause>

  <clause id="18164">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) \ w)) = K(x,(u \ T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(15493,a,18107,a)].">
      <j1 rule="hyper" parents="15493 18107"/>
    </justification>
  </clause>

  <clause id="18165">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ w)) = K(x,(T(z,y) \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(15493,a,18110,a)].">
      <j1 rule="hyper" parents="15493 18110"/>
    </justification>
  </clause>

  <clause id="18166">
    <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,17058,a(flip),b,18116,a),flip(a)].">
      <j1 rule="hyper" parents="58 17058 18116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18167">
    <literal><![CDATA[
      T(x,(y * T(z,u)) \ T(z,w)) = T(x,(y * z) \ T(T(z,w),u))
    ]]></literal>
    <justification jstring="[hyper(16469,a,18117,a),flip(a)].">
      <j1 rule="hyper" parents="16469 18117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18168">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * y) \ w)) = T(x,(u * T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(15705,a,18117,a)].">
      <j1 rule="hyper" parents="15705 18117"/>
    </justification>
  </clause>

  <clause id="18169">
    <literal><![CDATA[
      K(x,(y / T(z,z \ u)) \ w) = K(x,K(u,z) \ ((y / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13448,a(flip),b,18119,a),flip(a)].">
      <j1 rule="hyper" parents="58 13448 18119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18170">
    <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(15505(a,1),18126(a,1))].">
      <j1 rule="para" parents="15505 18126"/>
    </justification>
  </clause>

  <clause id="18171">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * (w \ (y * z))) = K(x,(y \ u) * (w \ (z * y)))
    ]]></literal>
    <justification jstring="[para(14555(a,1),18135(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14555 18135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18172">
    <literal><![CDATA[
      K(x,(T(y,z) / (u \ 1)) * w) = K(x,(y / (u \ K(y,z))) * w)
    ]]></literal>
    <justification jstring="[para(14342(a,1),18137(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14342 18137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18173">
    <literal><![CDATA[
      K(x,(T(y \ z,y) / u) * w) = K(x,((z / y) / u) * w)
    ]]></literal>
    <justification jstring="[para(14361(a,1),18137(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14361 18137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18174">
    <literal><![CDATA[
      K(x,(K(y \ z,y) * u) / w) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(17803,a,18142,a)].">
      <j1 rule="hyper" parents="17803 18142"/>
    </justification>
  </clause>

  <clause id="18175">
    <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,16551,a(flip),b,18142,a),flip(a)].">
      <j1 rule="hyper" parents="58 16551 18142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18176">
    <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(334,a,16725,a,b,18144,a)].">
      <j1 rule="hyper" parents="334 16725 18144"/>
    </justification>
  </clause>

  <clause id="18177">
    <literal><![CDATA[
      K(x,y / (z * ((u * w) / u))) = K(x,y / (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16554,a,b,18146,a)].">
      <j1 rule="hyper" parents="58 16554 18146"/>
    </justification>
  </clause>

  <clause id="18178">
    <literal><![CDATA[
      T(x,y * ((z / u) \ K(w,u))) = T(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(118,a,18147,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 18147 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18179">
    <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,18054,a(flip),b,18159,a)].">
      <j1 rule="hyper" parents="58 18054 18159"/>
    </justification>
  </clause>

  <clause id="18180">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ y) \ w)) = T(x,(u \ T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(118,a,18164,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 18164 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18181">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13449,a(flip),b,18165,a),flip(a)].">
      <j1 rule="hyper" parents="58 13449 18165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18182">
    <literal><![CDATA[
      K(x,(y / z) \ T(u,y / z)) = K(x,u / (T(z,y) \ y))
    ]]></literal>
    <justification jstring="[hyper(13439,a,18181,a),flip(a)].">
      <j1 rule="hyper" parents="13439 18181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18183">
    <literal><![CDATA[
      T(x,(T(y,z) \ z) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,18181,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 18181 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18184">
    <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(8218(a,1),18183(a,1,2,1,1))].">
      <j1 rule="para" parents="8218 18183"/>
    </justification>
  </clause>

  <clause id="18185">
    <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(18183(a,1),16524(a,1,2,2))].">
      <j1 rule="para" parents="18183 16524"/>
    </justification>
  </clause>

  <clause id="18186">
    <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,17066,a(flip),b,18168,a),flip(a)].">
      <j1 rule="hyper" parents="58 17066 18168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18187">
    <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(15476(a,1),18173(a,1,2,1,1))].">
      <j1 rule="para" parents="15476 18173"/>
    </justification>
  </clause>

  <clause id="18188">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (u \ K(z,y))) = K(x,T(y * (1 / z),z) / u)
    ]]></literal>
    <justification jstring="[para(6125(a,1),18174(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6125 18174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18189">
    <literal><![CDATA[
      K(x,y / (z * T(u \ w,u))) = K(x,y / (z * (w / u)))
    ]]></literal>
    <justification jstring="[para(5(a,1),18177(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 18177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18190">
    <literal><![CDATA[
      K(x,y / (z * T(T(u,w),w))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(231(a,1),18177(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="231 18177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18191">
    <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,16547,a(flip),b,18178,a),flip(a)].">
      <j1 rule="hyper" parents="58 16547 18178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18192">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ y) \ w)) = T(x,((u \ T(y,z)) \ 1) * w)
    ]]></literal>
    <justification jstring="[hyper(334,a,14217,a,b,18180,a),flip(a)].">
      <j1 rule="hyper" parents="334 14217 18180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18193">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ u)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(13435,a,18182,a),flip(a)].">
      <j1 rule="hyper" parents="13435 18182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18194">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(18182(a,1),13435(a,1))].">
      <j1 rule="para" parents="18182 13435"/>
    </justification>
  </clause>

  <clause id="18195">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z))) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(4490(a,1),18193(a,1,2,2))].">
      <j1 rule="para" parents="4490 18193"/>
    </justification>
  </clause>

  <clause id="18196">
    <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(13038(a,1),18194(a,1,2,2,1))].">
      <j1 rule="para" parents="13038 18194"/>
    </justification>
  </clause>

  <clause id="18197">
    <literal><![CDATA[
      K(x,y * (z * ((K(u,w) * v5) * v6))) = K(x,y * (z * (K(u,w) * (v5 * v6))))
    ]]></literal>
    <justification jstring="[para(14593(a,1),17991(a,1,2,2,2))].">
      <j1 rule="para" parents="14593 17991"/>
    </justification>
  </clause>

  <clause id="18198">
    <literal><![CDATA[
      K(x,y * (z \ ((u * w) * K(v5,v6)))) = K(x,y * (z \ (u * (w * K(v5,v6)))))
    ]]></literal>
    <justification jstring="[para(14769(a,1),18000(a,1,2,2,2))].">
      <j1 rule="para" parents="14769 18000"/>
    </justification>
  </clause>

  <clause id="18199">
    <literal><![CDATA[
      K(x,y * T(z,u / (w * v5))) = K(x,y * T(z,w \ (u / v5)))
    ]]></literal>
    <justification jstring="[para(15106(a,1),18002(a,1,2,2))].">
      <j1 rule="para" parents="15106 18002"/>
    </justification>
  </clause>

  <clause id="18200">
    <literal><![CDATA[
      K(x,y \ T(z,u / (w * v5))) = K(x,y \ T(z,w \ (u / v5)))
    ]]></literal>
    <justification jstring="[para(15106(a,1),18003(a,1,2,2))].">
      <j1 rule="para" parents="15106 18003"/>
    </justification>
  </clause>

  <clause id="18201">
    <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(18090(a,1),18024(a,1,2,2))].">
      <j1 rule="para" parents="18090 18024"/>
    </justification>
  </clause>

  <clause id="18202">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) * v5) = K(x,K(y,z) * ((u * w) * v5))
    ]]></literal>
    <justification jstring="[para(15123(a,1),18032(a,1,2,1))].">
      <j1 rule="para" parents="15123 18032"/>
    </justification>
  </clause>

  <clause id="18203">
    <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(16410(a,1),18035(a,1))].">
      <j1 rule="para" parents="16410 18035"/>
    </justification>
  </clause>

  <clause id="18204">
    <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(17047(a,1),18042(a,1))].">
      <j1 rule="para" parents="17047 18042"/>
    </justification>
  </clause>

  <clause id="18205">
    <literal><![CDATA[
      K(x,y * (K(z,L(u,w,v5)) * v6)) = K(x,y * (K(u,z) * v6))
    ]]></literal>
    <justification jstring="[hyper(334,a,18039,a(flip),b,18064,a),flip(a)].">
      <j1 rule="hyper" parents="334 18039 18064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18206">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * (u * z)) = K(x,(z * u) * (u \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,17183,a(flip),b,18150,a),flip(a)].">
      <j1 rule="hyper" parents="58 17183 18150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18207">
    <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(10408(a,2),18206(a,1,2,2))].">
      <j1 rule="para" parents="10408 18206"/>
    </justification>
  </clause>

  <clause id="18208">
    <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(17589(a,2),18161(a,1))].">
      <j1 rule="para" parents="17589 18161"/>
    </justification>
  </clause>

  <clause id="18209">
    <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(11196(a,1),18205(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11196 18205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18210">
    <literal><![CDATA[
      T(x,T((K(y,z) \ u) \ w,v5)) = T(x,T(u \ (K(z,y) \ w),v5))
    ]]></literal>
    <justification jstring="[para(5391(a,2),17588(a,1,2,1,1))].">
      <j1 rule="para" parents="5391 17588"/>
    </justification>
  </clause>

  <clause id="18211">
    <literal><![CDATA[
      K(x,(y * z) / L(y,u,w)) = K(x,(L(y,u,w) \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(12587,a,17632,a),flip(a)].">
      <j1 rule="hyper" parents="12587 17632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18212">
    <literal><![CDATA[
      K(x,(y * z) / L(y,u,w)) = K(x,y * (z / L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(334,a,17598,a(flip),b,18211,a),flip(a)].">
      <j1 rule="hyper" parents="334 17598 18211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18213">
    <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(17706(a,2),16081(a,1))].">
      <j1 rule="para" parents="17706 16081"/>
    </justification>
  </clause>

  <clause id="18214">
    <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(709,a,17707,a),flip(a)].">
      <j1 rule="hyper" parents="709 17707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18215">
    <literal><![CDATA[
      x \ (y * (K(z,K(u,w)) * v5)) = (x \ (y * v5)) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[para(16037(a,2),17707(a,1,2,2))].">
      <j1 rule="para" parents="16037 17707"/>
    </justification>
  </clause>

  <clause id="18216">
    <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(15279(a,2),17750(a,1,2))].">
      <j1 rule="para" parents="15279 17750"/>
    </justification>
  </clause>

  <clause id="18217">
    <literal><![CDATA[
      K(x,L(y,z,u / (y * w))) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(14660,a,17756,a),flip(a)].">
      <j1 rule="hyper" parents="14660 17756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18218">
    <literal><![CDATA[
      K(x,L(y,z,(y * u) \ w)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(17653,a,18217,a)].">
      <j1 rule="hyper" parents="17653 18217"/>
    </justification>
  </clause>

  <clause id="18219">
    <literal><![CDATA[
      (x * (y * (z * K(u,K(w,v5))))) \ v6 = K(u,K(w,v5)) * ((x * (y * z)) \ v6)
    ]]></literal>
    <justification jstring="[para(17786(a,1),17825(a,1,1))].">
      <j1 rule="para" parents="17786 17825"/>
    </justification>
  </clause>

  <clause id="18220">
    <literal><![CDATA[
      (K(x,T(y,z)) * u) * z = (K(x,y) * u) * T(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(8022(a,1),17823(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8022 17823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18221">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * (w * K(u,K(y,z))) = (x * K(y,z)) * w
    ]]></literal>
    <justification jstring="[para(7401(a,2),17828(a,1,1,2))].">
      <j1 rule="para" parents="7401 17828"/>
    </justification>
  </clause>

  <clause id="18222">
    <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),17846(a,2,2,1))].">
      <j1 rule="para" parents="90 17846"/>
    </justification>
  </clause>

  <clause id="18223">
    <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(17855(a,2),16400(a,1,2))].">
      <j1 rule="para" parents="17855 16400"/>
    </justification>
  </clause>

  <clause id="18224">
    <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(10381(a,1),17875(a,1,2,1,1))].">
      <j1 rule="para" parents="10381 17875"/>
    </justification>
  </clause>

  <clause id="18225">
    <literal><![CDATA[
      T(x,a(y \ 1,z,u)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,17691,a(flip),b,17890,a),flip(a)].">
      <j1 rule="hyper" parents="36 17691 17890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18226">
    <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,17254,a(flip),b,17990,a)].">
      <j1 rule="hyper" parents="58 17254 17990"/>
    </justification>
  </clause>

  <clause id="18227">
    <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(17990(a,1),16143(a,1))].">
      <j1 rule="para" parents="17990 16143"/>
    </justification>
  </clause>

  <clause id="18228">
    <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,15737,a(flip),b,17997,a),flip(a)].">
      <j1 rule="hyper" parents="58 15737 17997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18229">
    <literal><![CDATA[
      K(x,y * (z * K((u * w) \ y,u * w))) = K(x,(((w * u) \ y) * (w * u)) * z)
    ]]></literal>
    <justification jstring="[para(13476(a,1),18044(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13476 18044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18230">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * (v5 \ ((y * z) * v6))) = K(x,v5 \ ((z * y) * v6))
    ]]></literal>
    <justification jstring="[hyper(17045,a,18103,a)].">
      <j1 rule="hyper" parents="17045 18103"/>
    </justification>
  </clause>

  <clause id="18231">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ x)) = K(x,K(y,z) * (u \ (z * x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18101,a(flip),b,18109,a),flip(a)].">
      <j1 rule="hyper" parents="58 18101 18109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18232">
    <literal><![CDATA[
      K(((a(x,y,z) * u) * w) \ v5,v6) = K(((u * a(x,y,z)) * w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(17955,a,18114,a),flip(a)].">
      <j1 rule="hyper" parents="17955 18114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18233">
    <literal><![CDATA[
      K(x,((y \ z) * T(y,u)) * w) = K(x,K(u,y) * (T(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(16620,a,18127,a)].">
      <j1 rule="hyper" parents="16620 18127"/>
    </justification>
  </clause>

  <clause id="18234">
    <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,15776,a,b,18127,a)].">
      <j1 rule="hyper" parents="58 15776 18127"/>
    </justification>
  </clause>

  <clause id="18235">
    <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,18079,a(flip),b,18166,a),flip(a)].">
      <j1 rule="hyper" parents="58 18079 18166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18236">
    <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,13422,a(flip),b,18167,a),flip(a)].">
      <j1 rule="hyper" parents="58 13422 18167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18237">
    <literal><![CDATA[
      K(x,(y / T(z,z \ u)) \ w) = K(x,(y / T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(334,a,18119,a(flip),b,18169,a),flip(a)].">
      <j1 rule="hyper" parents="334 18119 18169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18238">
    <literal><![CDATA[
      K(x,(y / T(z,y)) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(273(a,1),18237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="273 18237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18239">
    <literal><![CDATA[
      T(x,(y / T(z,y)) \ u) = T(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,18238,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 18238 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18240">
    <literal><![CDATA[
      K(x,(T(y,z) / z) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4488(a,2),18238(a,1,2,1))].">
      <j1 rule="para" parents="4488 18238"/>
    </justification>
  </clause>

  <clause id="18241">
    <literal><![CDATA[
      T(x,(T(y,z) / z) \ u) = T(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4488(a,2),18239(a,1,2,1))].">
      <j1 rule="para" parents="4488 18239"/>
    </justification>
  </clause>

  <clause id="18242">
    <literal><![CDATA[
      T(x,T(y \ K(z,u),w) * v5) = T(x,K(z,u) * (T(y,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(18208,a,18186,a),flip(a)].">
      <j1 rule="hyper" parents="18208 18186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18243">
    <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,15566,a(flip),b,18191,a)].">
      <j1 rule="hyper" parents="58 15566 18191"/>
    </justification>
  </clause>

  <clause id="18244">
    <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(18192(a,2),14471(a,1))].">
      <j1 rule="para" parents="18192 14471"/>
    </justification>
  </clause>

  <clause id="18245">
    <literal><![CDATA[
      K(x,y * T(z,(u * w) \ v5)) = K(x,y * T(z,u \ (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(16501,a,18199,a)].">
      <j1 rule="hyper" parents="16501 18199"/>
    </justification>
  </clause>

  <clause id="18246">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) \ v5)) = K(x,y \ T(z,u \ (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(16506,a,18200,a)].">
      <j1 rule="hyper" parents="16506 18200"/>
    </justification>
  </clause>

  <clause id="18247">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) * v5) = K(x,K(z,y) * ((u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(334,a,15492,a,b,18202,a),flip(a)].">
      <j1 rule="hyper" parents="334 15492 18202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18248">
    <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),18209(a,2,2,1))].">
      <j1 rule="para" parents="20 18209"/>
    </justification>
  </clause>

  <clause id="18249">
    <literal><![CDATA[
      T(x,T(y \ (K(z,u) \ w),y)) = T(x,w / (K(u,z) \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16812,a(flip),b,18210,a),flip(a)].">
      <j1 rule="hyper" parents="58 16812 18210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18250">
    <literal><![CDATA[
      T(x,(K(y,z) \ u) / w) = T(x,u / (K(z,y) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,8218,a(flip),b,18249,a)].">
      <j1 rule="hyper" parents="58 8218 18249"/>
    </justification>
  </clause>

  <clause id="18251">
    <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(15279(a,2),18216(a,2,2))].">
      <j1 rule="para" parents="15279 18216"/>
    </justification>
  </clause>

  <clause id="18252">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * (w * K(y,K(z,u))) = (x * K(y,z)) * w
    ]]></literal>
    <justification jstring="[para(8053(a,2),18221(a,1,2,2))].">
      <j1 rule="para" parents="8053 18221"/>
    </justification>
  </clause>

  <clause id="18253">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ x)) = K(x,u \ (x * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(334,a,18160,a(flip),b,18231,a),flip(a)].">
      <j1 rule="hyper" parents="334 18160 18231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18254">
    <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,15794,a(flip),b,18233,a)].">
      <j1 rule="hyper" parents="58 15794 18233"/>
    </justification>
  </clause>

  <clause id="18255">
    <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,15747,a(flip),b,18235,a)].">
      <j1 rule="hyper" parents="58 15747 18235"/>
    </justification>
  </clause>

  <clause id="18256">
    <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,15748,a(flip),b,18242,a),flip(a)].">
      <j1 rule="hyper" parents="58 15748 18242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18257">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),w)) = T(x,y * T(K(u,w) / z,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,16689,a(flip),b,18243,a),flip(a)].">
      <j1 rule="hyper" parents="334 16689 18243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18258">
    <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(18245(a,2),16934(a,1))].">
      <j1 rule="para" parents="18245 16934"/>
    </justification>
  </clause>

  <clause id="18259">
    <literal><![CDATA[
      K(x,((y * K(z,u)) * w) * v5) = K(x,K(u,z) * ((y * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(16619,a,18247,a)].">
      <j1 rule="hyper" parents="16619 18247"/>
    </justification>
  </clause>

  <clause id="18260">
    <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,13386,a(flip),b,18248,a)].">
      <j1 rule="hyper" parents="58 13386 18248"/>
    </justification>
  </clause>

  <clause id="18261">
    <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(15262,a,18252,a)].">
      <j1 rule="hyper" parents="15262 18252"/>
    </justification>
  </clause>

  <clause id="18263">
    <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,16396,a,b,18255,a)].">
      <j1 rule="hyper" parents="58 16396 18255"/>
    </justification>
  </clause>

  <clause id="18264">
    <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,16286,a,b,18257,a)].">
      <j1 rule="hyper" parents="58 16286 18257"/>
    </justification>
  </clause>

  <clause id="18265">
    <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,14319,a(flip),b,18263,a),flip(a)].">
      <j1 rule="hyper" parents="58 14319 18263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18266">
    <literal><![CDATA[
      (x * (y / z)) * K(u,L(z,y,x)) = x * (y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(17619,a,14959,a)].">
      <j1 rule="hyper" parents="17619 14959"/>
    </justification>
  </clause>

  <clause id="18267">
    <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(18266(a,1),15805(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18266 15805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18268">
    <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(18266(a,1),17043(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18266 17043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18269">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,y,z)) = K(x,(z * y) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(17694,a,16731,a)].">
      <j1 rule="hyper" parents="17694 16731"/>
    </justification>
  </clause>

  <clause id="18270">
    <literal><![CDATA[
      a(x \ y,x,K(z,u)) * K(z,(x * u) / y) = K(z,x / (y / u))
    ]]></literal>
    <justification jstring="[hyper(14726,a,17753,a)].">
      <j1 rule="hyper" parents="14726 17753"/>
    </justification>
  </clause>

  <clause id="18271">
    <literal><![CDATA[
      K(x,L(y * z,u,u * y)) = K(x,u \ ((u / (y \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(14494,a,17779,a)].">
      <j1 rule="hyper" parents="14494 17779"/>
    </justification>
  </clause>

  <clause id="18272">
    <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(6323(a,1),17779(a,2,2,2,1))].">
      <j1 rule="para" parents="6323 17779"/>
    </justification>
  </clause>

  <clause id="18273">
    <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),18271(a,1,2,3))].">
      <j1 rule="para" parents="105 18271"/>
    </justification>
  </clause>

  <clause id="18274">
    <literal><![CDATA[
      ((x \ y) / y) * (y * K(z,u)) = x \ (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14929,a(flip),b,17781,a),flip(a)].">
      <j1 rule="hyper" parents="58 14929 17781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18275">
    <literal><![CDATA[
      (x \ (y * K(z,u))) / (y * K(z,u)) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,14929,a(flip),b,17781,a(flip))].">
      <j1 rule="hyper" parents="117 14929 17781"/>
    </justification>
  </clause>

  <clause id="18276">
    <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(18274(a,1),7817(a,2,2,1))].">
      <j1 rule="para" parents="18274 7817"/>
    </justification>
  </clause>

  <clause id="18277">
    <literal><![CDATA[
      (x \ (K(y,z) * u)) / (K(y,z) * u) = (x \ u) / u
    ]]></literal>
    <justification jstring="[hyper(58,a,14558,a,b,18275,a)].">
      <j1 rule="hyper" parents="58 14558 18275"/>
    </justification>
  </clause>

  <clause id="18278">
    <literal><![CDATA[
      (x \ y) / (K(x,z) * y) = (T(x,z) \ y) / y
    ]]></literal>
    <justification jstring="[para(5344(a,1),18277(a,1,1))].">
      <j1 rule="para" parents="5344 18277"/>
    </justification>
  </clause>

  <clause id="18279">
    <literal><![CDATA[
      ((x \ y) / y) * K(z,x) = (T(x,z) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(58,a,14516,a(flip),b,18278,a)].">
      <j1 rule="hyper" parents="58 14516 18278"/>
    </justification>
  </clause>

  <clause id="18280">
    <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(18279(a,1),5416(a,2,1))].">
      <j1 rule="para" parents="18279 5416"/>
    </justification>
  </clause>

  <clause id="18281">
    <literal><![CDATA[
      K(x,((y / (z * y)) * u) \ y) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,14935,a(flip),b,17814,a),flip(a)].">
      <j1 rule="hyper" parents="58 14935 17814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18282">
    <literal><![CDATA[
      K(x,((y / z) \ u) \ z) = K(x,((z / y) * u) \ z)
    ]]></literal>
    <justification jstring="[para(7(a,1),18281(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 18281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18283">
    <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(18282(a,2),14446(a,1))].">
      <j1 rule="para" parents="18282 14446"/>
    </justification>
  </clause>

  <clause id="18284">
    <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(8685(a,1),17821(a,1,2,2,2))].">
      <j1 rule="para" parents="8685 17821"/>
    </justification>
  </clause>

  <clause id="18285">
    <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(8559(a,1),18151(a,1))].">
      <j1 rule="para" parents="8559 18151"/>
    </justification>
  </clause>

  <clause id="18286">
    <literal><![CDATA[
      a(x,y,K(z \ y,u)) * K(x,(y * u) / z) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[para(14641(a,1),18270(a,1,1))].">
      <j1 rule="para" parents="14641 18270"/>
    </justification>
  </clause>

  <clause id="18287">
    <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(17732(a,1),18270(a,1,1))].">
      <j1 rule="para" parents="17732 18270"/>
    </justification>
  </clause>

  <clause id="18288">
    <literal><![CDATA[
      K(x,(y * z) / u) * a(z,y,K(x,u \ y)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(17868,a,18286,a)].">
      <j1 rule="hyper" parents="17868 18286"/>
    </justification>
  </clause>

  <clause id="18289">
    <literal><![CDATA[
      K(x,(y * z) / u) * a(x,y,K(u \ y,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(17599,a,18286,a)].">
      <j1 rule="hyper" parents="17599 18286"/>
    </justification>
  </clause>

  <clause id="18290">
    <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(12942(a,1),18286(a,1,1,3,1))].">
      <j1 rule="para" parents="12942 18286"/>
    </justification>
  </clause>

  <clause id="18291">
    <literal><![CDATA[
      K((x * K(y,z)) \ ((x * u) * K(y,z)),w) = K(u,T(T(w,x),x))
    ]]></literal>
    <justification jstring="[hyper(334,a,8205,a(flip),b,17592,a),flip(a)].">
      <j1 rule="hyper" parents="334 8205 17592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18292">
    <literal><![CDATA[
      K((x * K(y,z)) \ ((x * u) * K(y,z)),w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(334,a,8157,a(flip),b,18291,a),flip(a)].">
      <j1 rule="hyper" parents="334 8157 18291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18294">
    <literal><![CDATA[
      K((x * K(y,z)) \ (x * (u * K(y,z))),w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17959,a(flip),b,18292,a)].">
      <j1 rule="hyper" parents="58 17959 18292"/>
    </justification>
  </clause>

  <clause id="18295">
    <literal><![CDATA[
      K(L(T(x,K(y,z)),K(y,z),u),w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(239(a,1),18294(a,1,1))].">
      <j1 rule="para" parents="239 18294"/>
    </justification>
  </clause>

  <clause id="18296">
    <literal><![CDATA[
      K(L(x,K(y,z),u),T(w,K(y,z))) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(7972,a,18295,a)].">
      <j1 rule="hyper" parents="7972 18295"/>
    </justification>
  </clause>

  <clause id="18297">
    <literal><![CDATA[
      K(L(x,K(y,z),u),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(16032,a,18296,a)].">
      <j1 rule="hyper" parents="16032 18296"/>
    </justification>
  </clause>

  <clause id="18298">
    <literal><![CDATA[
      K(x,L(y,K(z,u),w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11169,a,18297,a)].">
      <j1 rule="hyper" parents="11169 18297"/>
    </justification>
  </clause>

  <clause id="18299">
    <literal><![CDATA[
      L(K(x,y),K(z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11164,a,18297,a)].">
      <j1 rule="hyper" parents="11164 18297"/>
    </justification>
  </clause>

  <clause id="18303">
    <literal><![CDATA[
      a(x,K(y,z),K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,18297,a,b,11139,a),flip(a)].">
      <j1 rule="hyper" parents="115 18297 11139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18305">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) * K(w,u) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,18297,a(flip),b,11136,a)].">
      <j1 rule="hyper" parents="119 18297 11136"/>
    </justification>
  </clause>

  <clause id="18307">
    <literal><![CDATA[
      L(x,K(y,z),K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(13992,a,18303,a)].">
      <j1 rule="hyper" parents="13992 18303"/>
    </justification>
  </clause>

  <clause id="18308">
    <literal><![CDATA[
      T(x,a(y,K(z,u),w)) = x
    ]]></literal>
    <justification jstring="[hyper(13708,a,18303,a)].">
      <j1 rule="hyper" parents="13708 18303"/>
    </justification>
  </clause>

  <clause id="18309">
    <literal><![CDATA[
      T(x,L(y,K(z,u),w)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(11200,a,18303,a)].">
      <j1 rule="hyper" parents="11200 18303"/>
    </justification>
  </clause>

  <clause id="18310">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = x * (K(y,z) * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(214,a,18303,a)].">
      <j1 rule="hyper" parents="214 18303"/>
    </justification>
  </clause>

  <clause id="18312">
    <literal><![CDATA[
      L(x,K(y,z),T(u,w)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(168,a,15359,a,b,18303,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="168 15359 18303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18318">
    <literal><![CDATA[
      L(x,K(y,z),u / w) = L(x,K(y,z),w \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15336,a(flip),b,18307,a)].">
      <j1 rule="hyper" parents="58 15336 18307"/>
    </justification>
  </clause>

  <clause id="18321">
    <literal><![CDATA[
      L(x,K(y,z),K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      v5 = x
    ]]></literal>
    <justification jstring="[para(18307(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="18307 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18324">
    <literal><![CDATA[
      T(x,y \ R(y,K(z,u),w)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,15205,a,b,18308,a)].">
      <j1 rule="hyper" parents="58 15205 18308"/>
    </justification>
  </clause>

  <clause id="18328">
    <literal><![CDATA[
      K(x,(y / z) / K(u,w)) = K(x,y / (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15119,a(flip),b,18298,a),flip(a)].">
      <j1 rule="hyper" parents="58 15119 18298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18329">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,w)) = K(x,z \ (y * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,11107,a(flip),b,18298,a),flip(a)].">
      <j1 rule="hyper" parents="58 11107 18298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18335">
    <literal><![CDATA[
      L(K(x,y),L(K(z,u),w,v5),v6) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5949(a,1),18299(a,1,2))].">
      <j1 rule="para" parents="5949 18299"/>
    </justification>
  </clause>

  <clause id="18337">
    <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,17256,a(flip),b,18309,a)].">
      <j1 rule="hyper" parents="58 17256 18309"/>
    </justification>
  </clause>

  <clause id="18338">
    <literal><![CDATA[
      L(x,K(y,z),u) * T(w,x) = w * L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(119,a,18309,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 18309 17"/>
    </justification>
  </clause>

  <clause id="18339">
    <literal><![CDATA[
      T(x,L(y,K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(15298(a,1),18321(a,1)),flip(b)].">
      <j1 rule="para" parents="15298 18321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18340">
    <literal><![CDATA[
      L(x,K(y,z),(u \ w) \ w) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(12897,a,18312,a)].">
      <j1 rule="hyper" parents="12897 18312"/>
    </justification>
  </clause>

  <clause id="18341">
    <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,11113,a(flip),b,18335,a)].">
      <j1 rule="hyper" parents="58 11113 18335"/>
    </justification>
  </clause>

  <clause id="18344">
    <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(16714(a,1),18339(a,1))].">
      <j1 rule="para" parents="16714 18339"/>
    </justification>
  </clause>

  <clause id="18345">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) / (u * w) = (x * K(y,z)) / (w * u)
    ]]></literal>
    <justification jstring="[hyper(117,a,18305,a(flip),b,10646,a),flip(a)].">
      <j1 rule="hyper" parents="117 18305 10646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18346">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) * K(z,y) = x * K(u,w)
    ]]></literal>
    <justification jstring="[para(16012(a,1),18305(a,1,1,2))].">
      <j1 rule="para" parents="16012 18305"/>
    </justification>
  </clause>

  <clause id="18348">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(u,w)) = z * (K(u,w) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16788,a,b,18310,a)].">
      <j1 rule="hyper" parents="58 16788 18310"/>
    </justification>
  </clause>

  <clause id="18350">
    <literal><![CDATA[
      K(x,(y / z) / K(u,w)) = K(x,y / (K(w,u) \ z))
    ]]></literal>
    <justification jstring="[para(5391(a,2),18328(a,2,2,2))].">
      <j1 rule="para" parents="5391 18328"/>
    </justification>
  </clause>

  <clause id="18351">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,(y / w) * K(u,z))
    ]]></literal>
    <justification jstring="[para(6520(a,1),18328(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6520 18328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18352">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,w)) = K(x,K(u,w) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(334,a,18030,a(flip),b,18329,a),flip(a)].">
      <j1 rule="hyper" parents="334 18030 18329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18353">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) * (K(z,y) * K(w,u)) = x
    ]]></literal>
    <justification jstring="[hyper(30,a,18305,a(flip),b,18346,a),flip(a)].">
      <j1 rule="hyper" parents="30 18305 18346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18355">
    <literal><![CDATA[
      K(x,y / (K(z,u) \ w)) = K(x,K(u,z) \ (y / w))
    ]]></literal>
    <justification jstring="[hyper(16141,a,18350,a),flip(a)].">
      <j1 rule="hyper" parents="16141 18350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18356">
    <literal><![CDATA[
      K(x,(y / z) * K(u,w)) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(16645,a,18351,a),flip(a)].">
      <j1 rule="hyper" parents="16645 18351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18357">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,K(u,z) * (y / w))
    ]]></literal>
    <justification jstring="[hyper(334,a,16002,a,b,18351,a),flip(a)].">
      <j1 rule="hyper" parents="334 16002 18351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18358">
    <literal><![CDATA[
      K(x,(y \ z) \ K(z,u)) = K(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,15499,a(flip),b,18352,a),flip(a)].">
      <j1 rule="hyper" parents="334 15499 18352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18359">
    <literal><![CDATA[
      T(x,(y \ z) \ K(z,u)) = T(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(118,a,18358,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 18358 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18360">
    <literal><![CDATA[
      T(x,(y \ (z / u)) \ K(u \ z,w)) = T(x,T(z / u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16532,a(flip),b,18359,a)].">
      <j1 rule="hyper" parents="58 16532 18359"/>
    </justification>
  </clause>

  <clause id="18361">
    <literal><![CDATA[
      x / (K(y,z) * K(u,w)) = x * (K(z,y) * K(w,u))
    ]]></literal>
    <justification jstring="[hyper(341,a,18353,a),flip(a)].">
      <j1 rule="hyper" parents="341 18353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18363">
    <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(18353(a,1),342(a,1,1)),flip(b)].">
      <j1 rule="para" parents="18353 342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18364">
    <literal><![CDATA[
      T(x,y / (K(z,u) \ w)) = T(x,K(u,z) \ (y / w))
    ]]></literal>
    <justification jstring="[hyper(118,a,18355,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 18355 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18365">
    <literal><![CDATA[
      K(x,y * (z \ K(u,K(w,v5)))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(16451,a,18356,a),flip(a)].">
      <j1 rule="hyper" parents="16451 18356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18366">
    <literal><![CDATA[
      K(x,K(y,z) * (u / w)) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(16183,a,18356,a)].">
      <j1 rule="hyper" parents="16183 18356"/>
    </justification>
  </clause>

  <clause id="18367">
    <literal><![CDATA[
      K(x,K(y,z) * (u / w)) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(16068,a,18356,a)].">
      <j1 rule="hyper" parents="16068 18356"/>
    </justification>
  </clause>

  <clause id="18368">
    <literal><![CDATA[
      K(x,y * (z \ K(y,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) / z) = w
    ]]></literal>
    <justification jstring="[para(18356(a,1),16152(a,1))].">
      <j1 rule="para" parents="18356 16152"/>
    </justification>
  </clause>

  <clause id="18369">
    <literal><![CDATA[
      K(x,(y / T(z,K(u,w))) / v5) = K(x,(y / z) / v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,18145,a(flip),b,18365,a)].">
      <j1 rule="hyper" parents="58 18145 18365"/>
    </justification>
  </clause>

  <clause id="18370">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (w \ z))) = K(x,u / (w \ T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(16509,a,18357,a),flip(a)].">
      <j1 rule="hyper" parents="16509 18357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18371">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (y \ w))) = K(x,u / (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[para(5392(a,1),18357(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5392 18357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18372">
    <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(18357(a,1),16645(a,1))].">
      <j1 rule="para" parents="18357 16645"/>
    </justification>
  </clause>

  <clause id="18373">
    <literal><![CDATA[
      T(x,(K(y,z) \ u) / w) = T(x,K(y,z) \ (u / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,18250,a,b,18364,a)].">
      <j1 rule="hyper" parents="58 18250 18364"/>
    </justification>
  </clause>

  <clause id="18374">
    <literal><![CDATA[
      T(x,K(y,z) * (u / w)) = T(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(118,a,18366,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 18366 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18375">
    <literal><![CDATA[
      T(x,K(y,z) * (u / w)) = T(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(118,a,18367,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 18367 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18377">
    <literal><![CDATA[
      K(x,(y / T(z,T(u,w))) / v5) = K(x,(y / T(z,u)) / v5)
    ]]></literal>
    <justification jstring="[para(7688(a,1),18369(a,1,2,1,2))].">
      <j1 rule="para" parents="7688 18369"/>
    </justification>
  </clause>

  <clause id="18378">
    <literal><![CDATA[
      T(x,K(y,z) \ ((T(z,y) \ u) / w)) = T(x,(z \ u) / w)
    ]]></literal>
    <justification jstring="[para(5390(a,1),18373(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5390 18373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18379">
    <literal><![CDATA[
      T(x,K(y * z,u) * (w / T(z,y))) = T(x,w / (y \ T(z * y,u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,14509,a(flip),b,18374,a),flip(a)].">
      <j1 rule="hyper" parents="334 14509 18374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18380">
    <literal><![CDATA[
      T(x,K(y,z) * (u / (y \ w))) = T(x,u / (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(334,a,14345,a(flip),b,18375,a),flip(a)].">
      <j1 rule="hyper" parents="334 14345 18375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18381">
    <literal><![CDATA[
      K(x,y * (z \ K(u,y))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) / z) = w
    ]]></literal>
    <justification jstring="[para(18140(a,1),18368(a,1))].">
      <j1 rule="para" parents="18140 18368"/>
    </justification>
  </clause>

  <clause id="18382">
    <literal><![CDATA[
      x * (y * (K(x,z) * K(x,z))) = T(x,z) * (K(x,z) * y)
    ]]></literal>
    <justification jstring="[para(18348(a,1),7436(a,1,2))].">
      <j1 rule="para" parents="18348 7436"/>
    </justification>
  </clause>

  <clause id="18383">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (y \ z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (z / y)) = w
    ]]></literal>
    <justification jstring="[para(18371(a,2),18194(a,1))].">
      <j1 rule="para" parents="18371 18194"/>
    </justification>
  </clause>

  <clause id="18384">
    <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(16625,a,18377,a)].">
      <j1 rule="hyper" parents="16625 18377"/>
    </justification>
  </clause>

  <clause id="18385">
    <literal><![CDATA[
      T(x,(((y \ T(z,y)) \ z) \ z) / u) = T(x,(y \ z) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15832,a,b,18378,a)].">
      <j1 rule="hyper" parents="58 15832 18378"/>
    </justification>
  </clause>

  <clause id="18386">
    <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,16665,a(flip),b,18380,a)].">
      <j1 rule="hyper" parents="58 16665 18380"/>
    </justification>
  </clause>

  <clause id="18387">
    <literal><![CDATA[
      x * (y * (K(x,z) * K(x,z))) = T(T(x,z),z) * y
    ]]></literal>
    <justification jstring="[hyper(334,a,5358,a(flip),b,18382,a),flip(a)].">
      <j1 rule="hyper" parents="334 5358 18382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18388">
    <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(18387(a,1),12085(a,2,2,1))].">
      <j1 rule="para" parents="18387 12085"/>
    </justification>
  </clause>

  <clause id="18390">
    <literal><![CDATA[
      T(x,T(T(y,z) \ z,y) / u) = T(x,(y \ z) / u)
    ]]></literal>
    <justification jstring="[para(7931(a,1),18385(a,1,2,1))].">
      <j1 rule="para" parents="7931 18385"/>
    </justification>
  </clause>

  <clause id="18391">
    <literal><![CDATA[
      T(x,(y / T(z,y)) / u) = T(x,(z \ y) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16475,a(flip),b,18390,a)].">
      <j1 rule="hyper" parents="58 16475 18390"/>
    </justification>
  </clause>

  <clause id="18392">
    <literal><![CDATA[
      T(x,(y \ z) / T(u,y \ z)) = T(x,u \ (z / T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(13045,a,18391,a),flip(a)].">
      <j1 rule="hyper" parents="13045 18391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18393">
    <literal><![CDATA[
      T(x,y \ (z / T(u,z))) = T(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(13042,a,18392,a),flip(a)].">
      <j1 rule="hyper" parents="13042 18392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18394">
    <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(18393(a,1),5301(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="18393 5301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18395">
    <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(14196(a,1),18344(a,1))].">
      <j1 rule="para" parents="14196 18344"/>
    </justification>
  </clause>

  <clause id="18396">
    <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(15628(a,2),18372(a,1))].">
      <j1 rule="para" parents="15628 18372"/>
    </justification>
  </clause>

  <clause id="18397">
    <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(18366(a,1),18372(a,1))].">
      <j1 rule="para" parents="18366 18372"/>
    </justification>
  </clause>

  <clause id="18398">
    <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(17044(a,1),18383(a,1))].">
      <j1 rule="para" parents="17044 18383"/>
    </justification>
  </clause>

  <clause id="18399">
    <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(13499(a,2),18397(a,1))].">
      <j1 rule="para" parents="13499 18397"/>
    </justification>
  </clause>

  <clause id="18400">
    <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(18040(a,2),18397(a,1))].">
      <j1 rule="para" parents="18040 18397"/>
    </justification>
  </clause>

  <clause id="18401">
    <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(18142(a,2),18397(a,1))].">
      <j1 rule="para" parents="18142 18397"/>
    </justification>
  </clause>

  <clause id="18402">
    <literal><![CDATA[
      (x * K(y,z)) / (z * y) = x / (T(z,y) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16952,a(flip),b,18345,a),flip(a)].">
      <j1 rule="hyper" parents="58 16952 18345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18403">
    <literal><![CDATA[
      (x / (y * z)) * K(z,y) = x / (T(y,z) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10909,a(flip),b,18402,a)].">
      <j1 rule="hyper" parents="58 10909 18402"/>
    </justification>
  </clause>

  <clause id="18404">
    <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(451,a,14895,a,b,18403,a),flip(a)].">
      <j1 rule="hyper" parents="451 14895 18403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18405">
    <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(18138(a,2),18400(a,1))].">
      <j1 rule="para" parents="18138 18400"/>
    </justification>
  </clause>

  <clause id="18406">
    <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(18140(a,1),18401(a,1))].">
      <j1 rule="para" parents="18140 18401"/>
    </justification>
  </clause>

  <clause id="18409">
    <literal><![CDATA[
      T(x,L(y,z \ T(u * z,w),u)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(17642(a,2),18339(a,1))].">
      <j1 rule="para" parents="17642 18339"/>
    </justification>
  </clause>

  <clause id="18410">
    <literal><![CDATA[
      T(T(x,y \ (z * z)),K(u,y \ (z * z))) = T(x,T((z \ y) \ z,u))
    ]]></literal>
    <justification jstring="[para(14296(a,1),17725(a,1,1))].">
      <j1 rule="para" parents="14296 17725"/>
    </justification>
  </clause>

  <clause id="18411">
    <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(11325(a,1),17755(a,1,2))].">
      <j1 rule="para" parents="11325 17755"/>
    </justification>
  </clause>

  <clause id="18412">
    <literal><![CDATA[
      K(x * K(y,z),T(u,w / x)) = K(K(y,z) * x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(16794,a,17837,a)].">
      <j1 rule="hyper" parents="16794 17837"/>
    </justification>
  </clause>

  <clause id="18413">
    <literal><![CDATA[
      K(x * K(y,z),T(u,x \ w)) = K(K(y,z) * x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(16146,a,18412,a)].">
      <j1 rule="hyper" parents="16146 18412"/>
    </justification>
  </clause>

  <clause id="18414">
    <literal><![CDATA[
      L(x,T(y,z),(y / z) \ 1) = L(x,T(y,z),(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,12909,a(flip),b,17889,a)].">
      <j1 rule="hyper" parents="58 12909 17889"/>
    </justification>
  </clause>

  <clause id="18415">
    <literal><![CDATA[
      L(x,T(y,z),(z \ y) \ 1) = L(x,y,(y / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(15330,a,18414,a),flip(a)].">
      <j1 rule="hyper" parents="15330 18414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18416">
    <literal><![CDATA[
      L(x,y,(y / z) \ 1) = L(x,y,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(13579,a,18415,a),flip(a)].">
      <j1 rule="hyper" parents="13579 18415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18417">
    <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(844(a,1),18416(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="844 18416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18418">
    <literal><![CDATA[
      K(x,L(y,z,u * (w \ T(y,v5)))) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(334,a,14656,a(flip),b,17904,a),flip(a)].">
      <j1 rule="hyper" parents="334 14656 17904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18419">
    <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(6558(a,2),17910(a,1,2,2))].">
      <j1 rule="para" parents="6558 17910"/>
    </justification>
  </clause>

  <clause id="18420">
    <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(17920(a,1),14770(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="17920 14770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18421">
    <literal><![CDATA[
      (x * (a(y,z,K(u,w)) * v5)) * v6 = (x * v5) * (a(y,z,K(u,w)) * v6)
    ]]></literal>
    <justification jstring="[para(17549(a,2),17920(a,1,1,2))].">
      <j1 rule="para" parents="17549 17920"/>
    </justification>
  </clause>

  <clause id="18422">
    <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(16240,a,18051,a)].">
      <j1 rule="hyper" parents="16240 18051"/>
    </justification>
  </clause>

  <clause id="18423">
    <literal><![CDATA[
      K(x,y * (z * L(K(u,w),v5,v6))) = K(x,K(u,w) \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(18170,a,18063,a),flip(a)].">
      <j1 rule="hyper" parents="18170 18063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18424">
    <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(18423(a,2),8699(a,1))].">
      <j1 rule="para" parents="18423 8699"/>
    </justification>
  </clause>

  <clause id="18425">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ K(u,x))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = w
    ]]></literal>
    <justification jstring="[para(11671(a,1),18424(a,1))].">
      <j1 rule="para" parents="11671 18424"/>
    </justification>
  </clause>

  <clause id="18426">
    <literal><![CDATA[
      K(x,y / (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(14173(a,1),18425(a,1))].">
      <j1 rule="para" parents="14173 18425"/>
    </justification>
  </clause>

  <clause id="18427">
    <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(4359(a,1),18426(a,1,2,2))].">
      <j1 rule="para" parents="4359 18426"/>
    </justification>
  </clause>

  <clause id="18428">
    <literal><![CDATA[
      K(x,y / (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(5576(a,2),18426(a,1))].">
      <j1 rule="para" parents="5576 18426"/>
    </justification>
  </clause>

  <clause id="18429">
    <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(14189(a,1),18426(a,1))].">
      <j1 rule="para" parents="14189 18426"/>
    </justification>
  </clause>

  <clause id="18430">
    <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(14215(a,1),18428(a,1,2,2))].">
      <j1 rule="para" parents="14215 18428"/>
    </justification>
  </clause>

  <clause id="18431">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ (u / (z \ y)))
    ]]></literal>
    <justification jstring="[para(5688(a,1),18075(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5688 18075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18432">
    <literal><![CDATA[
      K(x,y \ (z * (u * (w / u)))) = K(x,K(u,w) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(15539,a,18076,a),flip(a)].">
      <j1 rule="hyper" parents="15539 18076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18433">
    <literal><![CDATA[
      K(x,y \ (z * (u * (w / u)))) = K(x,y \ (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,18155,a(flip),b,18432,a),flip(a)].">
      <j1 rule="hyper" parents="334 18155 18432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18434">
    <literal><![CDATA[
      K(x,y \ (z * T(u * w,w))) = K(x,y \ (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(6(a,1),18433(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6 18433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18435">
    <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,15698,a(flip),b,18434,a),flip(a)].">
      <j1 rule="hyper" parents="58 15698 18434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18436">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) * u))) = K(x,K(w,u) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(13488,a,18077,a),flip(a)].">
      <j1 rule="hyper" parents="13488 18077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18437">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) * u))) = K(x,y \ (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,18074,a(flip),b,18436,a),flip(a)].">
      <j1 rule="hyper" parents="334 18074 18436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18438">
    <literal><![CDATA[
      K(x,y \ (z * T(u * w,u))) = K(x,y \ (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(4(a,1),18437(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 18437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18439">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) * w)) = K(x,(u \ (z * (y / z))) * w)
    ]]></literal>
    <justification jstring="[hyper(13488,a,18085,a)].">
      <j1 rule="hyper" parents="13488 18085"/>
    </justification>
  </clause>

  <clause id="18440">
    <literal><![CDATA[
      K(x,(y \ (z * (u / z))) * w) = K(x,(y \ T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18157,a(flip),b,18439,a),flip(a)].">
      <j1 rule="hyper" parents="58 18157 18439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18441">
    <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,15862,a(flip),b,18440,a),flip(a)].">
      <j1 rule="hyper" parents="58 15862 18440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18442">
    <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,16542,a(flip),b,18088,a),flip(a)].">
      <j1 rule="hyper" parents="58 16542 18088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18443">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * z) * w)) = K(x,K(z,u) * (y \ (u * w)))
    ]]></literal>
    <justification jstring="[hyper(15539,a,18095,a),flip(a)].">
      <j1 rule="hyper" parents="15539 18095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18444">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * z) * w)) = K(x,y \ (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(334,a,18094,a(flip),b,18443,a),flip(a)].">
      <j1 rule="hyper" parents="334 18094 18443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18445">
    <literal><![CDATA[
      K(x,y \ ((z / (T(u,z) \ 1)) * w)) = K(x,y \ (T(z / (u \ 1),z) * w))
    ]]></literal>
    <justification jstring="[para(10376(a,1),18444(a,1,2,2,1))].">
      <j1 rule="para" parents="10376 18444"/>
    </justification>
  </clause>

  <clause id="18446">
    <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(334,a,17797,a(flip),b,18097,a),flip(a)].">
      <j1 rule="hyper" parents="334 17797 18097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18447">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y / z) * w))) = K(x,u \ ((z \ y) * w))
    ]]></literal>
    <justification jstring="[hyper(13488,a,18102,a)].">
      <j1 rule="hyper" parents="13488 18102"/>
    </justification>
  </clause>

  <clause id="18448">
    <literal><![CDATA[
      T(x,(y \ T(z \ u,z)) \ w) = T(x,(y \ (u / z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(18244,a,18118,a)].">
      <j1 rule="hyper" parents="18244 18118"/>
    </justification>
  </clause>

  <clause id="18449">
    <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,16382,a(flip),b,18122,a)].">
      <j1 rule="hyper" parents="58 16382 18122"/>
    </justification>
  </clause>

  <clause id="18450">
    <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,18034,a(flip),b,18136,a),flip(a)].">
      <j1 rule="hyper" parents="58 18034 18136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18451">
    <literal><![CDATA[
      K(x,y * ((z \ (u \ w)) \ K(u,w))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(18067,a,18175,a)].">
      <j1 rule="hyper" parents="18067 18175"/>
    </justification>
  </clause>

  <clause id="18452">
    <literal><![CDATA[
      K(x,y / (z \ (u \ T(w,u)))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16555,a(flip),b,18451,a)].">
      <j1 rule="hyper" parents="58 16555 18451"/>
    </justification>
  </clause>

  <clause id="18453">
    <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(18176(a,1),16726(a,1))].">
      <j1 rule="para" parents="18176 16726"/>
    </justification>
  </clause>

  <clause id="18454">
    <literal><![CDATA[
      K(x * (K(y,z) * (y \ u)),w) = K(x * (T(y,z) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(16819,a,18179,a),flip(a)].">
      <j1 rule="hyper" parents="16819 18179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18455">
    <literal><![CDATA[
      K(x * ((y \ z) * K(y,u)),w) = K(x * (T(y,u) \ z),w)
    ]]></literal>
    <justification jstring="[hyper(16461,a,18454,a)].">
      <j1 rule="hyper" parents="16461 18454"/>
    </justification>
  </clause>

  <clause id="18456">
    <literal><![CDATA[
      K(x * (((y * z) / y) \ u),w) = K(x * (T(z,y) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,16660,a,b,18454,a)].">
      <j1 rule="hyper" parents="58 16660 18454"/>
    </justification>
  </clause>

  <clause id="18457">
    <literal><![CDATA[
      K(K(x,y) * (z * (x \ u)),w) = K(z * (T(x,y) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(18018,a,18455,a)].">
      <j1 rule="hyper" parents="18018 18455"/>
    </justification>
  </clause>

  <clause id="18458">
    <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(18456(a,1),17757(a,1,3))].">
      <j1 rule="para" parents="18456 17757"/>
    </justification>
  </clause>

  <clause id="18459">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (u \ K(z,y))) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(334,a,13525,a(flip),b,18188,a),flip(a)].">
      <j1 rule="hyper" parents="334 13525 18188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18460">
    <literal><![CDATA[
      K(x,(T(y,z) * (1 / z)) / u) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(18453,a,18459,a)].">
      <j1 rule="hyper" parents="18453 18459"/>
    </justification>
  </clause>

  <clause id="18461">
    <literal><![CDATA[
      K(x,(y * (1 / T(z,y))) / u) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[para(5526(a,1),18460(a,1,2,1))].">
      <j1 rule="para" parents="5526 18460"/>
    </justification>
  </clause>

  <clause id="18462">
    <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,15273,a(flip),b,18461,a)].">
      <j1 rule="hyper" parents="58 15273 18461"/>
    </justification>
  </clause>

  <clause id="18463">
    <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,18228,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 18228 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18464">
    <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(4969(a,2),18232(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4969 18232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18465">
    <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(334,a,16419,a(flip),b,18264,a),flip(a)].">
      <j1 rule="hyper" parents="334 16419 18264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18466">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) \ v6) = K(x,K(z,u) \ (y \ v6))
    ]]></literal>
    <justification jstring="[hyper(334,a,18001,a(flip),b,18341,a),flip(a)].">
      <j1 rule="hyper" parents="334 18001 18341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18468">
    <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),18466(a,1,2,1))].">
      <j1 rule="para" parents="90 18466"/>
    </justification>
  </clause>

  <clause id="18469">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) \ v5) = K(x,((y * z) \ v5) * K(w,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,16059,a(flip),b,18468,a),flip(a)].">
      <j1 rule="hyper" parents="334 16059 18468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18470">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) \ v5) = K(x,K(w,u) * ((y * z) \ v5))
    ]]></literal>
    <justification jstring="[para(5391(a,1),18468(a,2,2))].">
      <j1 rule="para" parents="5391 18468"/>
    </justification>
  </clause>

  <clause id="18471">
    <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(18469(a,2),16068(a,1))].">
      <j1 rule="para" parents="18469 16068"/>
    </justification>
  </clause>

  <clause id="18472">
    <literal><![CDATA[
      T(x,K(y * z,u) * (w / T(z,y))) = T(x,w / (T(z \ y,u) \ y))
    ]]></literal>
    <justification jstring="[hyper(17090,a,18386,a)].">
      <j1 rule="hyper" parents="17090 18386"/>
    </justification>
  </clause>

  <clause id="18473">
    <literal><![CDATA[
      T(x,T((y \ z) \ y,u)) = T(x,T(z \ (y * y),u))
    ]]></literal>
    <justification jstring="[hyper(8127,a,18410,a),flip(a)].">
      <j1 rule="hyper" parents="8127 18410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18474">
    <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(14052(a,1),18473(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="14052 18473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18475">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w) * v5)) = K(x,y / T(z,v5))
    ]]></literal>
    <justification jstring="[hyper(18223,a,18419,a),flip(a)].">
      <j1 rule="hyper" parents="18223 18419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18477">
    <literal><![CDATA[
      T(x,y / T(z,K(u,w) * v5)) = T(x,y / T(z,v5))
    ]]></literal>
    <justification jstring="[hyper(118,a,18475,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 18475 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18478">
    <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,15681,a(flip),b,18475,a),flip(a)].">
      <j1 rule="hyper" parents="58 15681 18475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18479">
    <literal><![CDATA[
      T(x,y \ K(K(z,u) * w,v5)) = T(x,(y \ v5) / T(v5,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,14493,a(flip),b,18477,a)].">
      <j1 rule="hyper" parents="58 14493 18477"/>
    </justification>
  </clause>

  <clause id="18480">
    <literal><![CDATA[
      T(x,y / T(z,u * T(w,v5))) = T(x,y / T(z,u * w))
    ]]></literal>
    <justification jstring="[para(5820(a,1),18477(a,1,2,2,2))].">
      <j1 rule="para" parents="5820 18477"/>
    </justification>
  </clause>

  <clause id="18481">
    <literal><![CDATA[
      T(x,y \ K(K(z,u) * w,v5)) = T(x,y \ K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(334,a,14493,a(flip),b,18479,a),flip(a)].">
      <j1 rule="hyper" parents="334 14493 18479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18482">
    <literal><![CDATA[
      T(x,y \ K(T(z,u) \ w,v5)) = T(x,y \ K(z \ w,v5))
    ]]></literal>
    <justification jstring="[para(5337(a,1),18481(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5337 18481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18483">
    <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(16566,a,18480,a),flip(a)].">
      <j1 rule="hyper" parents="16566 18480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18484">
    <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(18480(a,1),16474(a,1))].">
      <j1 rule="para" parents="18480 16474"/>
    </justification>
  </clause>

  <clause id="18485">
    <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,18360,a(flip),b,18482,a),flip(a)].">
      <j1 rule="hyper" parents="58 18360 18482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18486">
    <literal><![CDATA[
      K(x,y \ (T(z * u,u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15697,a(flip),b,18435,a),flip(a)].">
      <j1 rule="hyper" parents="58 15697 18435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18487">
    <literal><![CDATA[
      K(x,((y * (z / y)) / u) * w) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15860,a(flip),b,18441,a),flip(a)].">
      <j1 rule="hyper" parents="58 15860 18441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18488">
    <literal><![CDATA[
      K(x,(T(y * z,y) / u) * w) = K(x,((T(y,z) * z) / u) * w)
    ]]></literal>
    <justification jstring="[para(4121(a,2),18487(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4121 18487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18489">
    <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(15493,a,18446,a)].">
      <j1 rule="hyper" parents="15493 18446"/>
    </justification>
  </clause>

  <clause id="18490">
    <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,18015,a(flip),b,18449,a)].">
      <j1 rule="hyper" parents="58 18015 18449"/>
    </justification>
  </clause>

  <clause id="18491">
    <literal><![CDATA[
      T(x,T(y * K(z,y \ u),u)) = T(x,T((u \ y) \ 1,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(16156,a,18490,a)].">
      <j1 rule="hyper" parents="16156 18490"/>
    </justification>
  </clause>

  <clause id="18492">
    <literal><![CDATA[
      T(x,T((y \ z) \ 1,u) \ y) = T(x,T(z \ y,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(7982,a,18491,a),flip(a)].">
      <j1 rule="hyper" parents="7982 18491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18493">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ z) = T(x,T(z \ y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15742,a(flip),b,18492,a),flip(a)].">
      <j1 rule="hyper" parents="58 15742 18492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18494">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ z) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,12579,a(flip),b,18493,a),flip(a)].">
      <j1 rule="hyper" parents="334 12579 18493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18495">
    <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,16746,a(flip),b,18494,a),flip(a)].">
      <j1 rule="hyper" parents="58 16746 18494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18496">
    <literal><![CDATA[
      T(x,T(y / z,u) \ y) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16748,a(flip),b,18495,a),flip(a)].">
      <j1 rule="hyper" parents="58 16748 18495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18497">
    <literal><![CDATA[
      T(x,y * K(z,u \ (w * (v5 \ 1)))) = T(x,K(z,v5 * (w \ u)) * y)
    ]]></literal>
    <justification jstring="[hyper(16305,a,18463,a)].">
      <j1 rule="hyper" parents="16305 18463"/>
    </justification>
  </clause>

  <clause id="18498">
    <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,17101,a,b,18465,a)].">
      <j1 rule="hyper" parents="58 17101 18465"/>
    </justification>
  </clause>

  <clause id="18499">
    <literal><![CDATA[
      T(x,y / (T(z \ u,w) \ u)) = T(x,y / (u \ T(z * u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18379,a(flip),b,18472,a),flip(a)].">
      <j1 rule="hyper" parents="58 18379 18472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18500">
    <literal><![CDATA[
      T(x,y / ((z \ T(u,w)) \ u)) = T(x,y * T(z \ K(w,u),u))
    ]]></literal>
    <justification jstring="[para(16592(a,1),18498(a,1,2,2))].">
      <j1 rule="para" parents="16592 18498"/>
    </justification>
  </clause>

  <clause id="18501">
    <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,17117,a(flip),b,18500,a),flip(a)].">
      <j1 rule="hyper" parents="58 17117 18500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18502">
    <literal><![CDATA[
      L(x,K(y,z) * u,z * y) = L(x,u,z * y)
    ]]></literal>
    <justification jstring="[hyper(14511,a,17591,a)].">
      <j1 rule="hyper" parents="14511 17591"/>
    </justification>
  </clause>

  <clause id="18504">
    <literal><![CDATA[
      L(x,K(y,z / y) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[para(7(a,1),18502(a,1,3))].">
      <j1 rule="para" parents="7 18502"/>
    </justification>
  </clause>

  <clause id="18505">
    <literal><![CDATA[
      L(x,K(y,y \ z) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[para(5186(a,1),18504(a,1,2,1))].">
      <j1 rule="para" parents="5186 18504"/>
    </justification>
  </clause>

  <clause id="18506">
    <literal><![CDATA[
      L(x,K(y,z) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,13563,a(flip),b,18505,a)].">
      <j1 rule="hyper" parents="58 13563 18505"/>
    </justification>
  </clause>

  <clause id="18507">
    <literal><![CDATA[
      L(x,K(y,z) * u,z) = L(x,u,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),18506(a,2,3))].">
      <j1 rule="para" parents="7 18506"/>
    </justification>
  </clause>

  <clause id="18508">
    <literal><![CDATA[
      L(x,K(y,z) * u,y) = L(x,u,y)
    ]]></literal>
    <justification jstring="[para(5394(a,1),18507(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5394 18507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18513">
    <literal><![CDATA[
      L(x,y \ K(z,u),z) = L(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(14222(a,1),18508(a,1,2))].">
      <j1 rule="para" parents="14222 18508"/>
    </justification>
  </clause>

  <clause id="18514">
    <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(6432(a,1),17921(a,2,1,2))].">
      <j1 rule="para" parents="6432 17921"/>
    </justification>
  </clause>

  <clause id="18515">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,v5)))) = K(x,K(v5,w) * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(18013,a,18031,a),flip(a)].">
      <j1 rule="hyper" parents="18013 18031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18516">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,v5)))) = K(x,(y \ (z * u)) * K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(18012,a,18031,a),flip(a)].">
      <j1 rule="hyper" parents="18012 18031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18518">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,v5)))) = K(x,K(w,v5) * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,15492,a,b,18515,a),flip(a)].">
      <j1 rule="hyper" parents="334 15492 18515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18519">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * (v5 \ z)))) = K(x,u \ (w * (v5 \ T(z,y))))
    ]]></literal>
    <justification jstring="[para(14025(a,1),18515(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="14025 18515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18520">
    <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,16955,a(flip),b,18516,a),flip(a)].">
      <j1 rule="hyper" parents="58 16955 18516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18521">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * (w \ (v5 * u))) = K(x,w \ (v5 * (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[para(7423(a,1),18518(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7423 18518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18522">
    <literal><![CDATA[
      K(x,T(y,z) \ (u * (w \ y))) = K(x,y \ (u * (w \ T(y,z))))
    ]]></literal>
    <justification jstring="[para(5392(a,1),18519(a,1,2))].">
      <j1 rule="para" parents="5392 18519"/>
    </justification>
  </clause>

  <clause id="18523">
    <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),18520(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="105 18520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18524">
    <literal><![CDATA[
      K(x,y \ ((K(z,u) * w) * v5)) = K(x,K(z,u) * (y \ (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(334,a,16177,a,b,18523,a),flip(a)].">
      <j1 rule="hyper" parents="334 16177 18523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18525">
    <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),18523(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13 18523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18526">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y * w) * v5))) = K(x,u \ ((T(y,z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(5047(a,1),18524(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5047 18524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18527">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y / z) * w))) = K(x,u \ ((T(y,z) / z) * w))
    ]]></literal>
    <justification jstring="[para(5515(a,1),18524(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5515 18524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18529">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,w) * v5))) = K(x,K(w,u) * (y \ (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(16498,a,18521,a),flip(a)].">
      <j1 rule="hyper" parents="16498 18521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18530">
    <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(18521(a,1),16498(a,1))].">
      <j1 rule="para" parents="18521 16498"/>
    </justification>
  </clause>

  <clause id="18532">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) / u) * w)) = K(x,y \ ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,18447,a(flip),b,18527,a),flip(a)].">
      <j1 rule="hyper" parents="58 18447 18527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18533">
    <literal><![CDATA[
      K(x,L(y,z,u / (T(w,x) * v5))) = K(x,L(y,z,(w * v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(14661,a,17751,a),flip(a)].">
      <j1 rule="hyper" parents="14661 17751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18534">
    <literal><![CDATA[
      K(x,L(y,z,(T(u,x) * w) \ v5)) = K(x,L(y,z,(u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(17653,a,18533,a)].">
      <j1 rule="hyper" parents="17653 18533"/>
    </justification>
  </clause>

  <clause id="18535">
    <literal><![CDATA[
      K(x,L(y,z,(y * z) \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(18534(a,1),15184(a,1,1))].">
      <j1 rule="para" parents="18534 15184"/>
    </justification>
  </clause>

  <clause id="18536">
    <literal><![CDATA[
      K(x,L(y,z,z \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(18218(a,1),18535(a,1,1))].">
      <j1 rule="para" parents="18218 18535"/>
    </justification>
  </clause>

  <clause id="18537">
    <literal><![CDATA[
      (x * y) * ((T(x,z) * y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      (K(z,x) * y) * (y \ u) = w
    ]]></literal>
    <justification jstring="[para(18536(a,1),15132(a,1))].">
      <j1 rule="para" parents="18536 15132"/>
    </justification>
  </clause>

  <clause id="18538">
    <literal><![CDATA[
      K(x,T(y / (z \ u),x) * (w \ K(z,u))) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(18399,a,17801,a)].">
      <j1 rule="hyper" parents="18399 17801"/>
    </justification>
  </clause>

  <clause id="18539">
    <literal><![CDATA[
      K(x,(y / (z \ u)) * (w \ K(z,u))) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(8697,a,18538,a)].">
      <j1 rule="hyper" parents="8697 18538"/>
    </justification>
  </clause>

  <clause id="18540">
    <literal><![CDATA[
      K(x,(y / (T(z,u) \ u)) / w) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17832,a(flip),b,18539,a)].">
      <j1 rule="hyper" parents="58 17832 18539"/>
    </justification>
  </clause>

  <clause id="18541">
    <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(334,a,17835,a(flip),b,17847,a),flip(a)].">
      <j1 rule="hyper" parents="334 17835 17847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18542">
    <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(18161,a,18541,a)].">
      <j1 rule="hyper" parents="18161 18541"/>
    </justification>
  </clause>

  <clause id="18543">
    <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,18256,a(flip),b,18542,a),flip(a)].">
      <j1 rule="hyper" parents="58 18256 18542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18544">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,w)) = T(x,z * T(T(y,w) / z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,18494,a(flip),b,18543,a),flip(a)].">
      <j1 rule="hyper" parents="334 18494 18543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18545">
    <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(17930(a,2),14404(a,1))].">
      <j1 rule="para" parents="17930 14404"/>
    </justification>
  </clause>

  <clause id="18546">
    <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(18545,a,17282,a)].">
      <j1 rule="hyper" parents="18545 17282"/>
    </justification>
  </clause>

  <clause id="18547">
    <literal><![CDATA[
      K(x,y / T((K(z,u) * w) \ v5,w)) = K(x,y / ((K(z,u) \ v5) / w))
    ]]></literal>
    <justification jstring="[hyper(15688,a,17986,a)].">
      <j1 rule="hyper" parents="15688 17986"/>
    </justification>
  </clause>

  <clause id="18548">
    <literal><![CDATA[
      K(x,y / ((K(z,u) \ w) / v5)) = K(x,y / (w / (K(z,u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18478,a(flip),b,18547,a),flip(a)].">
      <j1 rule="hyper" parents="58 18478 18547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18549">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) / v5)) = K(x,y / (w / (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[para(5391(a,1),18548(a,1,2,2,1))].">
      <j1 rule="para" parents="5391 18548"/>
    </justification>
  </clause>

  <clause id="18550">
    <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(15539,a,17995,a)].">
      <j1 rule="hyper" parents="15539 17995"/>
    </justification>
  </clause>

  <clause id="18552">
    <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,18033,a(flip),b,18550,a)].">
      <j1 rule="hyper" parents="58 18033 18550"/>
    </justification>
  </clause>

  <clause id="18553">
    <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(6742(a,1),18550(a,1,2,2,2,1))].">
      <j1 rule="para" parents="6742 18550"/>
    </justification>
  </clause>

  <clause id="18554">
    <literal><![CDATA[
      K(x,K(y,z) * (((z * y) / u) * w)) = K(x,(((y * z) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[hyper(16498,a,18087,a)].">
      <j1 rule="hyper" parents="16498 18087"/>
    </justification>
  </clause>

  <clause id="18555">
    <literal><![CDATA[
      K(x,(((y * z) / u) \ 1) \ w) = K(x,((T(z,y) * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18050,a(flip),b,18554,a),flip(a)].">
      <j1 rule="hyper" parents="58 18050 18554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18556">
    <literal><![CDATA[
      K(x,((T(y,z) * z) / u) * w) = K(x,((z * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(14346,a,18555,a),flip(a)].">
      <j1 rule="hyper" parents="14346 18555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18557">
    <literal><![CDATA[
      K(x,(T(y * z,y) / u) * w) = K(x,((z * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18488,a,b,18556,a)].">
      <j1 rule="hyper" parents="58 18488 18556"/>
    </justification>
  </clause>

  <clause id="18558">
    <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(18139(a,2),16449(a,1))].">
      <j1 rule="para" parents="18139 16449"/>
    </justification>
  </clause>

  <clause id="18559">
    <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,18448,a(flip),b,18184,a)].">
      <j1 rule="hyper" parents="58 18448 18184"/>
    </justification>
  </clause>

  <clause id="18560">
    <literal><![CDATA[
      T(x,(T(y \ z,y) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18183,a(flip),b,18559,a),flip(a)].">
      <j1 rule="hyper" parents="58 18183 18559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18561">
    <literal><![CDATA[
      T(x,((((y \ z) \ z) \ z) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[para(4480(a,1),18560(a,1,2,1,1))].">
      <j1 rule="para" parents="4480 18560"/>
    </justification>
  </clause>

  <clause id="18563">
    <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,18526,a(flip),b,18230,a)].">
      <j1 rule="hyper" parents="58 18526 18230"/>
    </justification>
  </clause>

  <clause id="18564">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) * u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(181(a,1),18563(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="181 18563"/>
    </justification>
  </clause>

  <clause id="18565">
    <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(16562,a,18260,a),flip(a)].">
      <j1 rule="hyper" parents="16562 18260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18566">
    <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,15635,a(flip),b,18265,a)].">
      <j1 rule="hyper" parents="58 15635 18265"/>
    </justification>
  </clause>

  <clause id="18568">
    <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(16939(a,2),18337(a,1,2,2))].">
      <j1 rule="para" parents="16939 18337"/>
    </justification>
  </clause>

  <clause id="18569">
    <literal><![CDATA[
      K(x,y \ (z / T(u,T(w,v5)))) = K(x,y \ (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(334,a,16524,a(flip),b,18384,a),flip(a)].">
      <j1 rule="hyper" parents="334 16524 18384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18570">
    <literal><![CDATA[
      K(x,y \ ((z / (T(u,z) \ 1)) * w)) = K(x,y \ (((u \ 1) \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(334,a,13471,a(flip),b,18445,a),flip(a)].">
      <j1 rule="hyper" parents="334 13471 18445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18571">
    <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,18273,a,b,18570,a)].">
      <j1 rule="hyper" parents="58 18273 18570"/>
    </justification>
  </clause>

  <clause id="18572">
    <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(14151(a,1),18474(a,2,2,1))].">
      <j1 rule="para" parents="14151 18474"/>
    </justification>
  </clause>

  <clause id="18573">
    <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(4553(a,1),18572(a,2,2,1,2))].">
      <j1 rule="para" parents="4553 18572"/>
    </justification>
  </clause>

  <clause id="18574">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ (y * y),u)) = T(x,T(z \ T(y,z),u))
    ]]></literal>
    <justification jstring="[hyper(334,a,13540,a(flip),b,18573,a),flip(a)].">
      <j1 rule="hyper" parents="334 13540 18573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18575">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ (y * y),u)) = T(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,13047,a(flip),b,18574,a),flip(a)].">
      <j1 rule="hyper" parents="334 13047 18574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18576">
    <literal><![CDATA[
      T(x,T((y * z) \ (z * z),u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(13539,a,18575,a)].">
      <j1 rule="hyper" parents="13539 18575"/>
    </justification>
  </clause>

  <clause id="18577">
    <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(451,a,18576,a,b,14249,a)].">
      <j1 rule="hyper" parents="451 18576 14249"/>
    </justification>
  </clause>

  <clause id="18578">
    <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,15860,a(flip),b,18552,a)].">
      <j1 rule="hyper" parents="58 15860 18552"/>
    </justification>
  </clause>

  <clause id="18579">
    <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,15526,a(flip),b,18565,a)].">
      <j1 rule="hyper" parents="58 15526 18565"/>
    </justification>
  </clause>

  <clause id="18580">
    <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,18080,a(flip),b,18566,a),flip(a)].">
      <j1 rule="hyper" parents="58 18080 18566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18581">
    <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,18544,a,b,18580,a)].">
      <j1 rule="hyper" parents="58 18544 18580"/>
    </justification>
  </clause>

  <clause id="18582">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,w)) = T(x,T(z * T(y / z,u),w))
    ]]></literal>
    <justification jstring="[hyper(16154,a,18581,a)].">
      <j1 rule="hyper" parents="16154 18581"/>
    </justification>
  </clause>

  <clause id="18584">
    <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,18544,a(flip),b,18582,a),flip(a)].">
      <j1 rule="hyper" parents="58 18544 18582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18586">
    <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(18584(a,1),16154(a,1))].">
      <j1 rule="para" parents="18584 16154"/>
    </justification>
  </clause>

  <clause id="18587">
    <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,16702,a(flip),b,18568,a)].">
      <j1 rule="hyper" parents="58 16702 18568"/>
    </justification>
  </clause>

  <clause id="18588">
    <literal><![CDATA[
      K(x,T(y * z,x) * (u \ K(w,v5))) = K(x,(y * (z * K(w,v5))) / u)
    ]]></literal>
    <justification jstring="[hyper(18405,a,17800,a)].">
      <j1 rule="hyper" parents="18405 17800"/>
    </justification>
  </clause>

  <clause id="18589">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) / v5) = K(x,(y * z) * (v5 \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(8697,a,18588,a),flip(a)].">
      <j1 rule="hyper" parents="8697 18588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18590">
    <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,16954,a(flip),b,18589,a),flip(a)].">
      <j1 rule="hyper" parents="58 16954 18589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18591">
    <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),18590(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="105 18590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18592">
    <literal><![CDATA[
      (x / (y * x)) * ((y * x) * K(z,u)) = x * K(z,L(u,x,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(6069,a,17815,a)].">
      <j1 rule="hyper" parents="6069 17815"/>
    </justification>
  </clause>

  <clause id="18593">
    <literal><![CDATA[
      K(x,y / (z \ a(u \ 1,u,z))) = K(x,a(u \ 1,u,z) \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(17871,a,17979,a),flip(a)].">
      <j1 rule="hyper" parents="17871 17979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18594">
    <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(18593(a,1),18427(a,1))].">
      <j1 rule="para" parents="18593 18427"/>
    </justification>
  </clause>

  <clause id="18595">
    <literal><![CDATA[
      K(x,(x * y) \ (x * T(z,y * x))) = K(x,R(z,z \ (x * y),z) / y)
    ]]></literal>
    <justification jstring="[hyper(334,a,18253,a(flip),b,18073,a)].">
      <j1 rule="hyper" parents="334 18253 18073"/>
    </justification>
  </clause>

  <clause id="18596">
    <literal><![CDATA[
      K(x,R(y,y \ (x * z),y) / z) = K(x,z \ T(y,z * x))
    ]]></literal>
    <justification jstring="[hyper(7646,a,18595,a),flip(a)].">
      <j1 rule="hyper" parents="7646 18595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18597">
    <literal><![CDATA[
      K(x,y \ T(z,y * x)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(13369,a,18596,a),flip(a)].">
      <j1 rule="hyper" parents="13369 18596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18599">
    <literal><![CDATA[
      K(x,(1 / y) \ T(T(z,y),(1 / y) * x)) = K(x,z / (K(y,z) / y))
    ]]></literal>
    <justification jstring="[para(14157(a,1),18597(a,2,2))].">
      <j1 rule="para" parents="14157 18597"/>
    </justification>
  </clause>

  <clause id="18600">
    <literal><![CDATA[
      K(x,(1 / y) \ T(T(z,y),y \ x)) = K(x,z / (K(y,z) / y))
    ]]></literal>
    <justification jstring="[para(14128(a,1),18599(a,1,2,2))].">
      <j1 rule="para" parents="14128 18599"/>
    </justification>
  </clause>

  <clause id="18601">
    <literal><![CDATA[
      K(x,y / (K(z,y) / z)) = K(x,z * T(T(y,z),z \ x))
    ]]></literal>
    <justification jstring="[hyper(14412,a,18600,a),flip(a)].">
      <j1 rule="hyper" parents="14412 18600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18602">
    <literal><![CDATA[
      K(x,y / (K(z,y) / z)) = K(x,T(y,z \ x) * z)
    ]]></literal>
    <justification jstring="[para(243(a,1),18601(a,2,2))].">
      <j1 rule="para" parents="243 18601"/>
    </justification>
  </clause>

  <clause id="18603">
    <literal><![CDATA[
      K(x,T(y,z \ x) * z) = K(x,y * (z * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(18430,a,18602,a),flip(a)].">
      <j1 rule="hyper" parents="18430 18602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18604">
    <literal><![CDATA[
      K(x,T(y,z \ x) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,12578,a(flip),b,18603,a),flip(a)].">
      <j1 rule="hyper" parents="334 12578 18603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18605">
    <literal><![CDATA[
      K(x,T(y,(x * z) \ x) * (x * z)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,7816,a,b,18604,a),flip(a)].">
      <j1 rule="hyper" parents="334 7816 18604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18606">
    <literal><![CDATA[
      K(x,T(y,z \ 1) * (x * z)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[para(6501(a,1),18605(a,1,2,1))].">
      <j1 rule="para" parents="6501 18605"/>
    </justification>
  </clause>

  <clause id="18607">
    <literal><![CDATA[
      K(x,T(y,z) * (x * z)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15766,a(flip),b,18606,a)].">
      <j1 rule="hyper" parents="58 15766 18606"/>
    </justification>
  </clause>

  <clause id="18609">
    <literal><![CDATA[
      K(x,y * (T(z,y) * x)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(16349,a,18607,a)].">
      <j1 rule="hyper" parents="16349 18607"/>
    </justification>
  </clause>

  <clause id="18610">
    <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(18609(a,1),8189(a,1,2,2))].">
      <j1 rule="para" parents="18609 8189"/>
    </justification>
  </clause>

  <clause id="18611">
    <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(11137(a,1),18083(a,1,2,1))].">
      <j1 rule="para" parents="11137 18083"/>
    </justification>
  </clause>

  <clause id="18612">
    <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(181(a,1),18091(a,1,2))].">
      <j1 rule="para" parents="181 18091"/>
    </justification>
  </clause>

  <clause id="18613">
    <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(11137(a,1),18267(a,1,2,2,2))].">
      <j1 rule="para" parents="11137 18267"/>
    </justification>
  </clause>

  <clause id="18614">
    <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(11311(a,1),18268(a,1,2))].">
      <j1 rule="para" parents="11311 18268"/>
    </justification>
  </clause>

  <clause id="18615">
    <literal><![CDATA[
      K(x,y * (z / T(u,K(w,v5) * v6))) = K(x,y * (z / T(u,v6)))
    ]]></literal>
    <justification jstring="[hyper(16630,a,18614,a),flip(a)].">
      <j1 rule="hyper" parents="16630 18614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18616">
    <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,13446,a(flip),b,18615,a),flip(a)].">
      <j1 rule="hyper" parents="58 13446 18615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18617">
    <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,18123,a(flip),b,18616,a)].">
      <j1 rule="hyper" parents="58 18123 18616"/>
    </justification>
  </clause>

  <clause id="18618">
    <literal><![CDATA[
      K(x,y * (z \ (K(u,w) * v5))) = K(x,y * (K(u,w) * (z \ v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13519,a(flip),b,18617,a),flip(a)].">
      <j1 rule="hyper" parents="58 13519 18617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18619">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ (v5 \ 1)))) = K(x,y * (w \ (v5 \ K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(16629,a,18618,a),flip(a)].">
      <j1 rule="hyper" parents="16629 18618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18620">
    <literal><![CDATA[
      K(x,y * (z \ (u * K(w,v5)))) = K(x,y * (K(w,v5) * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(16627,a,18618,a)].">
      <j1 rule="hyper" parents="16627 18618"/>
    </justification>
  </clause>

  <clause id="18621">
    <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,18198,a(flip),b,18620,a)].">
      <j1 rule="hyper" parents="58 18198 18620"/>
    </justification>
  </clause>

  <clause id="18622">
    <literal><![CDATA[
      K(x,y * ((T(z,u) \ u) \ (w \ K(u,z)))) = K(x,y * ((z \ u) \ (w \ 1)))
    ]]></literal>
    <justification jstring="[para(13590(a,1),18619(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13590 18619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18623">
    <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),18586(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="104 18586"/>
    </justification>
  </clause>

  <clause id="18624">
    <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(18566(a,2),18586(a,1))].">
      <j1 rule="para" parents="18566 18586"/>
    </justification>
  </clause>

  <clause id="18625">
    <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(18066,a,18611,a)].">
      <j1 rule="hyper" parents="18066 18611"/>
    </justification>
  </clause>

  <clause id="18626">
    <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(18625(a,1),18010(a,1))].">
      <j1 rule="para" parents="18625 18010"/>
    </justification>
  </clause>

  <clause id="18627">
    <literal><![CDATA[
      K(x,y * (z * ((u / w) * K(w,v5)))) = K(x,y * (z * (u / T(w,v5))))
    ]]></literal>
    <justification jstring="[para(11210(a,1),18613(a,1,2,2))].">
      <j1 rule="para" parents="11210 18613"/>
    </justification>
  </clause>

  <clause id="18628">
    <literal><![CDATA[
      K(x,T(y,z) * (u * (w / y))) = K(x,y * (u * (w / T(y,z))))
    ]]></literal>
    <justification jstring="[hyper(18227,a,18627,a)].">
      <j1 rule="hyper" parents="18227 18627"/>
    </justification>
  </clause>

  <clause id="18629">
    <literal><![CDATA[
      K(x,y * (z * (u / T(y,u * z)))) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16965,a(flip),b,18628,a),flip(a)].">
      <j1 rule="hyper" parents="58 16965 18628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18630">
    <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(18037(a,2),18624(a,1))].">
      <j1 rule="para" parents="18037 18624"/>
    </justification>
  </clause>

  <clause id="18631">
    <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(17157(a,2),18630(a,1))].">
      <j1 rule="para" parents="17157 18630"/>
    </justification>
  </clause>

  <clause id="18632">
    <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(16581(a,1),18631(a,1))].">
      <j1 rule="para" parents="16581 18631"/>
    </justification>
  </clause>

  <clause id="18633">
    <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(12596(a,2),18632(a,1))].">
      <j1 rule="para" parents="12596 18632"/>
    </justification>
  </clause>

  <clause id="18634">
    <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(17125(a,1),18633(a,1))].">
      <j1 rule="para" parents="17125 18633"/>
    </justification>
  </clause>

  <clause id="18635">
    <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(6520(a,1),17859(a,1,2,2,1))].">
      <j1 rule="para" parents="6520 17859"/>
    </justification>
  </clause>

  <clause id="18636">
    <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(18029(a,1),17878(a,1))].">
      <j1 rule="para" parents="18029 17878"/>
    </justification>
  </clause>

  <clause id="18637">
    <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(5391(a,1),17981(a,2,2,2,1,2))].">
      <j1 rule="para" parents="5391 17981"/>
    </justification>
  </clause>

  <clause id="18638">
    <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(334,a,14190,a(flip),b,18043,a),flip(a)].">
      <j1 rule="hyper" parents="334 14190 18043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18639">
    <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(18638(a,1),18428(a,1))].">
      <j1 rule="para" parents="18638 18428"/>
    </justification>
  </clause>

  <clause id="18640">
    <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(18578(a,1),18639(a,1))].">
      <j1 rule="para" parents="18578 18639"/>
    </justification>
  </clause>

  <clause id="18641">
    <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(15731,a,18096,a)].">
      <j1 rule="hyper" parents="15731 18096"/>
    </justification>
  </clause>

  <clause id="18642">
    <literal><![CDATA[
      K(x,(K(y \ z,z) * u) / w) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18489,a(flip),b,18641,a),flip(a)].">
      <j1 rule="hyper" parents="58 18489 18641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18643">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(17798,a,18642,a)].">
      <j1 rule="hyper" parents="17798 18642"/>
    </justification>
  </clause>

  <clause id="18644">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w \ u))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(6652(a,1),18643(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6652 18643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18645">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * (u \ K(z,y \ z))) = K(x,T((y \ (z * u)) / u,z))
    ]]></literal>
    <justification jstring="[hyper(16564,a,18132,a)].">
      <j1 rule="hyper" parents="16564 18132"/>
    </justification>
  </clause>

  <clause id="18646">
    <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,18644,a(flip),b,18645,a)].">
      <j1 rule="hyper" parents="58 18644 18645"/>
    </justification>
  </clause>

  <clause id="18647">
    <literal><![CDATA[
      K(x,(T(y,z) \ (z * u)) / u) = K(x,T((y \ (z * u)) / u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18143,a(flip),b,18646,a)].">
      <j1 rule="hyper" parents="58 18143 18646"/>
    </justification>
  </clause>

  <clause id="18648">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * (u \ K(y,y \ z))) = K(x,T((y \ (z * u)) / u,y))
    ]]></literal>
    <justification jstring="[hyper(16564,a,18133,a)].">
      <j1 rule="hyper" parents="16564 18133"/>
    </justification>
  </clause>

  <clause id="18649">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * (u \ K(z,y))) = K(x,T((y \ (z * u)) / u,y))
    ]]></literal>
    <justification jstring="[hyper(18406,a,18648,a)].">
      <j1 rule="hyper" parents="18406 18648"/>
    </justification>
  </clause>

  <clause id="18650">
    <literal><![CDATA[
      K(x,T((y \ (z * u)) / u,y)) = K(x,(T(y,z) \ (z * u)) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,17834,a(flip),b,18649,a),flip(a)].">
      <j1 rule="hyper" parents="58 17834 18649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18651">
    <literal><![CDATA[
      K(x,T((y \ (z * u)) / u,z)) = K(x,T((y \ (z * u)) / u,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,18647,a(flip),b,18650,a)].">
      <j1 rule="hyper" parents="334 18647 18650"/>
    </justification>
  </clause>

  <clause id="18652">
    <literal><![CDATA[
      K(x,y * ((z \ (u * y)) \ K(u,u \ z))) = K(x,T(y / (z \ (u * y)),u))
    ]]></literal>
    <justification jstring="[hyper(16564,a,18134,a)].">
      <j1 rule="hyper" parents="16564 18134"/>
    </justification>
  </clause>

  <clause id="18653">
    <literal><![CDATA[
      K(x,y * ((z \ (u * y)) \ K(z,u))) = K(x,T(y / (z \ (u * y)),u))
    ]]></literal>
    <justification jstring="[hyper(18406,a,18652,a)].">
      <j1 rule="hyper" parents="18406 18652"/>
    </justification>
  </clause>

  <clause id="18654">
    <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(18653(a,1),14421(a,1))].">
      <j1 rule="para" parents="18653 14421"/>
    </justification>
  </clause>

  <clause id="18655">
    <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,18540,a(flip),b,18185,a)].">
      <j1 rule="hyper" parents="58 18540 18185"/>
    </justification>
  </clause>

  <clause id="18656">
    <literal><![CDATA[
      K(x,y \ (z / (T(u,w) \ w))) = K(x,y \ (z / (w / u)))
    ]]></literal>
    <justification jstring="[hyper(16525,a,18655,a),flip(a)].">
      <j1 rule="hyper" parents="16525 18655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18657">
    <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(18655(a,1),16525(a,1))].">
      <j1 rule="para" parents="18655 16525"/>
    </justification>
  </clause>

  <clause id="18658">
    <literal><![CDATA[
      K(x,y \ (z / (z / u))) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),18656(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 18656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18659">
    <literal><![CDATA[
      K(x,y \ T(z \ u,u)) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[para(72(a,1),18658(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="72 18658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18660">
    <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(10387(a,1),18658(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10387 18658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18661">
    <literal><![CDATA[
      K(x,y \ (z \ T(u,z \ 1))) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15696,a(flip),b,18659,a)].">
      <j1 rule="hyper" parents="58 15696 18659"/>
    </justification>
  </clause>

  <clause id="18662">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ ((z \ y) \ T(u,(y / z) \ 1)))
    ]]></literal>
    <justification jstring="[para(5875(a,1),18661(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5875 18661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18663">
    <literal><![CDATA[
      K(x,y * (z * K((u * w) \ y,u * w))) = K(x,T(y,w * u) * z)
    ]]></literal>
    <justification jstring="[hyper(334,a,13518,a(flip),b,18229,a),flip(a)].">
      <j1 rule="hyper" parents="334 13518 18229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18664">
    <literal><![CDATA[
      K(x,y * (z * K(u \ (w \ y),w * u))) = K(x,T(y,u * w) * z)
    ]]></literal>
    <justification jstring="[para(14304(a,1),18663(a,1,2,2,2))].">
      <j1 rule="para" parents="14304 18663"/>
    </justification>
  </clause>

  <clause id="18665">
    <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(18626,a,18276,a)].">
      <j1 rule="hyper" parents="18626 18276"/>
    </justification>
  </clause>

  <clause id="18666">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18289,a(flip),b,18411,a),flip(a)].">
      <j1 rule="hyper" parents="58 18289 18411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18667">
    <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(14537,a,18666,a)].">
      <j1 rule="hyper" parents="14537 18666"/>
    </justification>
  </clause>

  <clause id="18668">
    <literal><![CDATA[
      K(x,L((y * z) * u,y,z \ 1)) = K(x,y / ((u \ 1) / z))
    ]]></literal>
    <justification jstring="[hyper(14500,a,18666,a)].">
      <j1 rule="hyper" parents="14500 18666"/>
    </justification>
  </clause>

  <clause id="18669">
    <literal><![CDATA[
      K(x,y / (z * (y / (u * y)))) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,17265,a(flip),b,18666,a)].">
      <j1 rule="hyper" parents="58 17265 18666"/>
    </justification>
  </clause>

  <clause id="18670">
    <literal><![CDATA[
      K(x,(y \ z) / (u * ((y \ z) / z))) = K(x,(y \ z) / (u / y))
    ]]></literal>
    <justification jstring="[para(5(a,1),18669(a,1,2,2,2,2))].">
      <j1 rule="para" parents="5 18669"/>
    </justification>
  </clause>

  <clause id="18671">
    <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(5043(a,1),18546(a,1,1,2,1))].">
      <j1 rule="para" parents="5043 18546"/>
    </justification>
  </clause>

  <clause id="18672">
    <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(17790(a,1),18671(a,1,1))].">
      <j1 rule="para" parents="17790 18671"/>
    </justification>
  </clause>

  <clause id="18673">
    <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,13475,a(flip),b,18672,a)].">
      <j1 rule="hyper" parents="58 13475 18672"/>
    </justification>
  </clause>

  <clause id="18674">
    <literal><![CDATA[
      K(x \ T(y,K(z,u) * w),v5) = K(x \ T(y,w),v5)
    ]]></literal>
    <justification jstring="[hyper(16431,a,18673,a),flip(a)].">
      <j1 rule="hyper" parents="16431 18673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18675">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) = K(y \ K(x,z * K(w,v5)),u)
    ]]></literal>
    <justification jstring="[hyper(16529,a,18674,a),flip(a)].">
      <j1 rule="hyper" parents="16529 18674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18677">
    <literal><![CDATA[
      K(x \ K(y,z * K(u,w)),v5) = K(x \ K(y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(6987,a,18675,a),flip(a)].">
      <j1 rule="hyper" parents="6987 18675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18678">
    <literal><![CDATA[
      K(x \ K(y \ K(z,u),w),v5) = K(x \ K(w,y),v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,18442,a,b,18677,a)].">
      <j1 rule="hyper" parents="58 18442 18677"/>
    </justification>
  </clause>

  <clause id="18679">
    <literal><![CDATA[
      K((x / y) \ K(y,z),u) = K(T(y,z \ K(w,v5)) / x,u)
    ]]></literal>
    <justification jstring="[hyper(16569,a,18678,a),flip(a)].">
      <j1 rule="hyper" parents="16569 18678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18681">
    <literal><![CDATA[
      K(T(x,y \ K(z,u)) / w,v5) = K(T(x,y) / w,v5)
    ]]></literal>
    <justification jstring="[hyper(16568,a,18679,a),flip(a)].">
      <j1 rule="hyper" parents="16568 18679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18682">
    <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,17097,a(flip),b,18681,a),flip(a)].">
      <j1 rule="hyper" parents="58 17097 18681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18683">
    <literal><![CDATA[
      K(T(x,y \ T(z,u)) / w,v5) = K(T(x,z \ y) / w,v5)
    ]]></literal>
    <justification jstring="[para(6827(a,1),18681(a,1,1,1))].">
      <j1 rule="para" parents="6827 18681"/>
    </justification>
  </clause>

  <clause id="18684">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w)) / v5) = (v6 * K(T(y,u \ z) / v5,x)) \ v6
    ]]></literal>
    <justification jstring="[para(18683(a,1),6523(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="18683 6523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18686">
    <literal><![CDATA[
      K(((x * y) * (1 / y)) / z,u) = K(L(x,y,y \ 1) / z,u)
    ]]></literal>
    <justification jstring="[para(2418(a,1),18682(a,1,1,1))].">
      <j1 rule="para" parents="2418 18682"/>
    </justification>
  </clause>

  <clause id="18687">
    <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(18686(a,1),13924(a,1,2,2))].">
      <j1 rule="para" parents="18686 13924"/>
    </justification>
  </clause>

  <clause id="18688">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w)) / v5) = K(x,T(y,u \ z) / v5)
    ]]></literal>
    <justification jstring="[hyper(334,a,16010,a(flip),b,18684,a),flip(a)].">
      <j1 rule="hyper" parents="334 16010 18684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18689">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / w) = K(x,T(y,u) / w)
    ]]></literal>
    <justification jstring="[para(7349(a,1),18688(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7349 18688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18690">
    <literal><![CDATA[
      K(x,T(T(y,z) \ u,z * y)) = K(x,T(u,z) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16974,a,b,18689,a)].">
      <j1 rule="hyper" parents="58 16974 18689"/>
    </justification>
  </clause>

  <clause id="18692">
    <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(5859(a,1),18690(a,1,2,1))].">
      <j1 rule="para" parents="5859 18690"/>
    </justification>
  </clause>

  <clause id="18693">
    <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(16370,a,18610,a)].">
      <j1 rule="hyper" parents="16370 18610"/>
    </justification>
  </clause>

  <clause id="18694">
    <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(18024,a,18693,a)].">
      <j1 rule="hyper" parents="18024 18693"/>
    </justification>
  </clause>

  <clause id="18695">
    <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,17990,a(flip),b,18694,a)].">
      <j1 rule="hyper" parents="58 17990 18694"/>
    </justification>
  </clause>

  <clause id="18696">
    <literal><![CDATA[
      K(x,y * ((y \ T(z * y,u)) * u)) = K(x,T(y * (T(z,y) * u),u))
    ]]></literal>
    <justification jstring="[para(14429(a,1),18695(a,1,2,2))].">
      <j1 rule="para" parents="14429 18695"/>
    </justification>
  </clause>

  <clause id="18697">
    <literal><![CDATA[
      K(x,T(y * (T(z,y) * u),u)) = K(x,(u * ((z * y) / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,17179,a(flip),b,18696,a),flip(a)].">
      <j1 rule="hyper" parents="58 17179 18696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18698">
    <literal><![CDATA[
      K(x,T(y * (T(z,y) * u),u)) = K(x,(u * z) * y)
    ]]></literal>
    <justification jstring="[para(6(a,1),18697(a,2,2,1,2))].">
      <j1 rule="para" parents="6 18697"/>
    </justification>
  </clause>

  <clause id="18699">
    <literal><![CDATA[
      K(x,L(y,z,u) * (z * u)) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(17636,a,18698,a)].">
      <j1 rule="hyper" parents="17636 18698"/>
    </justification>
  </clause>

  <clause id="18700">
    <literal><![CDATA[
      T(x,L(y,z,u) * (z * u)) = T(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(118,a,18699,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 18699 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18701">
    <literal><![CDATA[
      K(x,((y * z) \ (z * u)) * (y * z)) = K(x,((T(y,z) \ u) * y) * z)
    ]]></literal>
    <justification jstring="[para(11477(a,1),18699(a,1,2,1))].">
      <j1 rule="para" parents="11477 18699"/>
    </justification>
  </clause>

  <clause id="18702">
    <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(5221(a,1),18700(a,1,2,2))].">
      <j1 rule="para" parents="5221 18700"/>
    </justification>
  </clause>

  <clause id="18703">
    <literal><![CDATA[
      K(x,((T(y,z) \ u) * y) * z) = K(x,T(z * u,y * z))
    ]]></literal>
    <justification jstring="[hyper(12580,a,18701,a),flip(a)].">
      <j1 rule="hyper" parents="12580 18701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18704">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,z) * y)) = K(x,T(y * u,z * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,18234,a(flip),b,18703,a)].">
      <j1 rule="hyper" parents="58 18234 18703"/>
    </justification>
  </clause>

  <clause id="18705">
    <literal><![CDATA[
      K(x,T(y * z,u * y)) = K(x,T(z,u) * T(y,u))
    ]]></literal>
    <justification jstring="[hyper(16147,a,18704,a),flip(a)].">
      <j1 rule="hyper" parents="16147 18704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18706">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z * y)) = K(x,(u / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,15512,a(flip),b,18705,a),flip(a)].">
      <j1 rule="hyper" parents="334 15512 18705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18707">
    <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(17121(a,1),18635(a,1,2,2))].">
      <j1 rule="para" parents="17121 18635"/>
    </justification>
  </clause>

  <clause id="18708">
    <literal><![CDATA[
      K(x,y \ T(z,u / K(w,v5))) = K(x,y \ (u \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(18156,a,18707,a),flip(a)].">
      <j1 rule="hyper" parents="18156 18707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18709">
    <literal><![CDATA[
      K(x,y \ T(z,u / K(w,v5))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(17(a,2),18708(a,2,2,2))].">
      <j1 rule="para" parents="17 18708"/>
    </justification>
  </clause>

  <clause id="18710">
    <literal><![CDATA[
      K(x,y \ T(z,u * T(w,v5))) = K(x,y \ T(z,u * w))
    ]]></literal>
    <justification jstring="[para(6401(a,1),18709(a,1,2,2,2))].">
      <j1 rule="para" parents="6401 18709"/>
    </justification>
  </clause>

  <clause id="18711">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w / v5))) = K(x,y \ T(z,u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(6778(a,1),18709(a,1,2,2,2))].">
      <j1 rule="para" parents="6778 18709"/>
    </justification>
  </clause>

  <clause id="18712">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w) * v5)) = K(x,y \ T(z,v5))
    ]]></literal>
    <justification jstring="[para(7535(a,1),18709(a,1,2,2,2))].">
      <j1 rule="para" parents="7535 18709"/>
    </justification>
  </clause>

  <clause id="18713">
    <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(515(a,1),18712(a,1,2)),flip(a)].">
      <j1 rule="para" parents="515 18712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18714">
    <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(18710(a,2),16507(a,1))].">
      <j1 rule="para" parents="18710 16507"/>
    </justification>
  </clause>

  <clause id="18715">
    <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(18011(a,1),18636(a,1))].">
      <j1 rule="para" parents="18011 18636"/>
    </justification>
  </clause>

  <clause id="18717">
    <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(334,a,17019,a(flip),b,18660,a),flip(a)].">
      <j1 rule="hyper" parents="334 17019 18660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18718">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ ((z \ y) \ T(u,z / y)))
    ]]></literal>
    <justification jstring="[para(4716(a,1),18662(a,2,2,2,2))].">
      <j1 rule="para" parents="4716 18662"/>
    </justification>
  </clause>

  <clause id="18719">
    <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(465(a,1),18665(a,1,2,2,1))].">
      <j1 rule="para" parents="465 18665"/>
    </justification>
  </clause>

  <clause id="18720">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,y \ z) / y) = K(x,T(y \ ((z / y) \ u),z))
    ]]></literal>
    <justification jstring="[hyper(16266,a,18692,a),flip(a)].">
      <j1 rule="hyper" parents="16266 18692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18722">
    <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(18720(a,2),15253(a,1))].">
      <j1 rule="para" parents="18720 15253"/>
    </justification>
  </clause>

  <clause id="18723">
    <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,13383,a(flip),b,18717,a),flip(a)].">
      <j1 rule="hyper" parents="58 13383 18717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18724">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,y \ (u * (K(w,u \ 1) * z)))
    ]]></literal>
    <justification jstring="[para(12948(a,1),18723(a,2,2,2))].">
      <j1 rule="para" parents="12948 18723"/>
    </justification>
  </clause>

  <clause id="18725">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,K(u \ 1,w) * (y \ (u * z)))
    ]]></literal>
    <justification jstring="[hyper(334,a,18529,a(flip),b,18724,a),flip(a)].">
      <j1 rule="hyper" parents="334 18529 18724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18726">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,K(u,w) * (y \ (u * z)))
    ]]></literal>
    <justification jstring="[hyper(334,a,15714,a(flip),b,18725,a),flip(a)].">
      <j1 rule="hyper" parents="334 15714 18725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18727">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,y \ (T(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(334,a,18099,a(flip),b,18726,a),flip(a)].">
      <j1 rule="hyper" parents="334 18099 18726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18728">
    <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,15398,a(flip),b,18727,a)].">
      <j1 rule="hyper" parents="58 15398 18727"/>
    </justification>
  </clause>

  <clause id="18729">
    <literal><![CDATA[
      K(x,y \ T(z * (1 / T(u,w)),z)) = K(x,y \ (T(u \ 1,w) * z))
    ]]></literal>
    <justification jstring="[hyper(334,a,6017,a(flip),b,18728,a),flip(a)].">
      <j1 rule="hyper" parents="334 6017 18728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18730">
    <literal><![CDATA[
      K(x,y \ ((1 / T(z,u)) * w)) = K(x,y \ (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13383,a(flip),b,18729,a)].">
      <j1 rule="hyper" parents="58 13383 18729"/>
    </justification>
  </clause>

  <clause id="18731">
    <literal><![CDATA[
      K(x,y \ (T(z \ 1,u) * w)) = K(x,y \ ((T(z,u) \ 1) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,5602,a(flip),b,18730,a),flip(a)].">
      <j1 rule="hyper" parents="58 5602 18730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18732">
    <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(334,a,11232,a(flip),b,18731,a),flip(a)].">
      <j1 rule="hyper" parents="334 11232 18731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18733">
    <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(17559(a,1),17606(a,1,1,1))].">
      <j1 rule="para" parents="17559 17606"/>
    </justification>
  </clause>

  <clause id="18734">
    <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(15371,a,18733,a)].">
      <j1 rule="hyper" parents="15371 18733"/>
    </justification>
  </clause>

  <clause id="18736">
    <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(13729(a,2),18734(a,1,2))].">
      <j1 rule="para" parents="13729 18734"/>
    </justification>
  </clause>

  <clause id="18737">
    <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(18736(a,1),15204(a,1,1))].">
      <j1 rule="para" parents="18736 15204"/>
    </justification>
  </clause>

  <clause id="18738">
    <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(14689(a,1),18737(a,1,1,1))].">
      <j1 rule="para" parents="14689 18737"/>
    </justification>
  </clause>

  <clause id="18739">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,u) = T(x \ R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(15243(a,1),18738(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15243 18738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18740">
    <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(18739(a,1),15177(a,2,1)),flip(a)].">
      <j1 rule="para" parents="18739 15177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18742">
    <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(16762(a,2),18740(a,1,3))].">
      <j1 rule="para" parents="16762 18740"/>
    </justification>
  </clause>

  <clause id="18743">
    <literal><![CDATA[
      K(x * (1 / (1 / (y \ z))),(z \ y) \ x) = a(1 / (z \ y),z \ y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(14398,a,18129,a)].">
      <j1 rule="hyper" parents="14398 18129"/>
    </justification>
  </clause>

  <clause id="18744">
    <literal><![CDATA[
      K(x * (y \ z),(z \ y) \ x) = a(1 / (z \ y),z \ y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(14427,a,18743,a)].">
      <j1 rule="hyper" parents="14427 18743"/>
    </justification>
  </clause>

  <clause id="18745">
    <literal><![CDATA[
      K(x * (y \ z),(z \ y) \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(334,a,14110,a(flip),b,18744,a),flip(a)].">
      <j1 rule="hyper" parents="334 14110 18744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18746">
    <literal><![CDATA[
      K(x * (y \ z),x / (z \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(14899,a,18745,a)].">
      <j1 rule="hyper" parents="14899 18745"/>
    </justification>
  </clause>

  <clause id="18748">
    <literal><![CDATA[
      K(x,y / (T(z,u / w) \ (u / w))) = K(x,y / ((w \ T(u,w)) / z))
    ]]></literal>
    <justification jstring="[hyper(18196,a,18452,a),flip(a)].">
      <j1 rule="hyper" parents="18196 18452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18749">
    <literal><![CDATA[
      K(x,y / ((z \ T(u,z)) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(18194,a,18748,a),flip(a)].">
      <j1 rule="hyper" parents="18194 18748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18750">
    <literal><![CDATA[
      K(x,y / ((T(z,u) \ u) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9951,a,b,18749,a)].">
      <j1 rule="hyper" parents="58 9951 18749"/>
    </justification>
  </clause>

  <clause id="18751">
    <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,18219,a,b,18222,a),flip(a)].">
      <j1 rule="hyper" parents="34 18219 18222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18752">
    <literal><![CDATA[
      L(x * K(y,K(z,u)),w,v5) = K(y,K(z,u)) * L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(493,a,18751,a)].">
      <j1 rule="hyper" parents="493 18751"/>
    </justification>
  </clause>

  <clause id="18753">
    <literal><![CDATA[
      L(x * K(y,K(z,u)),w,v5) = L(x,w,v5) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,16050,a,b,18752,a),flip(a)].">
      <j1 rule="hyper" parents="334 16050 18752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18754">
    <literal><![CDATA[
      L(x * K(y,K(z,u)),w,v5) * K(y,K(z,u)) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(16249,a,18752,a(flip))].">
      <j1 rule="hyper" parents="16249 18752"/>
    </justification>
  </clause>

  <clause id="18755">
    <literal><![CDATA[
      K(x,L(y * K(z,K(u,w)),v5,v6)) = K(x,L(y,v5,v6))
    ]]></literal>
    <justification jstring="[para(18752(a,2),16399(a,1,2))].">
      <j1 rule="para" parents="18752 16399"/>
    </justification>
  </clause>

  <clause id="18756">
    <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(18752(a,2),16562(a,1,2,2))].">
      <j1 rule="para" parents="18752 16562"/>
    </justification>
  </clause>

  <clause id="18757">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)) \ w,v5,v6)) = K(x,L(y \ w,v5,v6))
    ]]></literal>
    <justification jstring="[para(16090(a,1),18755(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16090 18755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18759">
    <literal><![CDATA[
      L(K(x,K(y,z)) * u,w,v5) = L(u,w,v5) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(16037(a,2),18753(a,1,1))].">
      <j1 rule="para" parents="16037 18753"/>
    </justification>
  </clause>

  <clause id="18760">
    <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),18754(a,1,1))].">
      <j1 rule="para" parents="13 18754"/>
    </justification>
  </clause>

  <clause id="18761">
    <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(7688(a,1),18757(a,1,2,1,1))].">
      <j1 rule="para" parents="7688 18757"/>
    </justification>
  </clause>

  <clause id="18762">
    <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(18759(a,2),16417(a,1,2,2))].">
      <j1 rule="para" parents="18759 16417"/>
    </justification>
  </clause>

  <clause id="18763">
    <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(5656(a,1),18762(a,1,2,2,1))].">
      <j1 rule="para" parents="5656 18762"/>
    </justification>
  </clause>

  <clause id="18764">
    <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(6520(a,1),18763(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6520 18763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18765">
    <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,13494,a(flip),b,18280,a)].">
      <j1 rule="hyper" parents="58 13494 18280"/>
    </justification>
  </clause>

  <clause id="18766">
    <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(18370(a,1),18398(a,1))].">
      <j1 rule="para" parents="18370 18398"/>
    </justification>
  </clause>

  <clause id="18767">
    <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(17980(a,1),18766(a,1))].">
      <j1 rule="para" parents="17980 18766"/>
    </justification>
  </clause>

  <clause id="18768">
    <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(334,a,9,a,b,18514,a),flip(a)].">
      <j1 rule="hyper" parents="334 9 18514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18769">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,(v5 * z) \ (v5 * (z * y)))
    ]]></literal>
    <justification jstring="[hyper(18715,a,18525,a),flip(a)].">
      <j1 rule="hyper" parents="18715 18525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18770">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,L(y,z,v5))
    ]]></literal>
    <justification jstring="[para(13(a,2),18769(a,2,2))].">
      <j1 rule="para" parents="13 18769"/>
    </justification>
  </clause>

  <clause id="18771">
    <literal><![CDATA[
      K(x,L(y,z,u * K(w,v5))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(17696,a,18770,a)].">
      <j1 rule="hyper" parents="17696 18770"/>
    </justification>
  </clause>

  <clause id="18772">
    <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(14809,a,18770,a)].">
      <j1 rule="hyper" parents="14809 18770"/>
    </justification>
  </clause>

  <clause id="18773">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,(z * v5) / ((y \ z) * v5))
    ]]></literal>
    <justification jstring="[hyper(334,a,15126,a,b,18770,a),flip(a)].">
      <j1 rule="hyper" parents="334 15126 18770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18775">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w) \ v5)) = K(x,L(y,z,u \ v5))
    ]]></literal>
    <justification jstring="[para(5337(a,1),18770(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="5337 18770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18776">
    <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(18770(a,1),11110(a,1,2))].">
      <j1 rule="para" parents="18770 11110"/>
    </justification>
  </clause>

  <clause id="18778">
    <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(18770(a,1),15123(a,1,1))].">
      <j1 rule="para" parents="18770 15123"/>
    </justification>
  </clause>

  <clause id="18779">
    <literal><![CDATA[
      K(x,L(y,z,u * (w / v5))) = K(x,L(y,z,u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(17777(a,1),18770(a,1,2))].">
      <j1 rule="para" parents="17777 18770"/>
    </justification>
  </clause>

  <clause id="18780">
    <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,15069,a(flip),b,18771,a),flip(a)].">
      <j1 rule="hyper" parents="58 15069 18771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18781">
    <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(14054(a,1),18771(a,1,2,3))].">
      <j1 rule="para" parents="14054 18771"/>
    </justification>
  </clause>

  <clause id="18782">
    <literal><![CDATA[
      a(x,y,K(z * K(u,w),v5)) = K(v5,x) * K(x,L(v5,y,z))
    ]]></literal>
    <justification jstring="[para(18771(a,1),14631(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18771 14631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18783">
    <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(18771(a,1),15123(a,1,1))].">
      <j1 rule="para" parents="18771 15123"/>
    </justification>
  </clause>

  <clause id="18784">
    <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(18771(a,1),16332(a,1,1,1))].">
      <j1 rule="para" parents="18771 16332"/>
    </justification>
  </clause>

  <clause id="18785">
    <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,15233,a(flip),b,18775,a),flip(a)].">
      <j1 rule="hyper" parents="58 15233 18775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18786">
    <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,10435,a(flip),b,18775,a),flip(a)].">
      <j1 rule="hyper" parents="58 10435 18775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18787">
    <literal><![CDATA[
      a(x,y,K(z * K(u,w),v5)) = a(x,y,K(z,v5))
    ]]></literal>
    <justification jstring="[hyper(334,a,14631,a(flip),b,18782,a),flip(a)].">
      <j1 rule="hyper" parents="334 14631 18782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18788">
    <literal><![CDATA[
      a(x * K(y,z),u,K(w,v5)) = a(v5,u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(14677,a,18787,a)].">
      <j1 rule="hyper" parents="14677 18787"/>
    </justification>
  </clause>

  <clause id="18789">
    <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,18062,a,b,18787,a)].">
      <j1 rule="hyper" parents="58 18062 18787"/>
    </justification>
  </clause>

  <clause id="18790">
    <literal><![CDATA[
      a(x,y,K(z \ (u / w),v5)) = a(x,y,K(z \ (w \ u),v5))
    ]]></literal>
    <justification jstring="[para(14302(a,1),18787(a,1,3,1))].">
      <j1 rule="para" parents="14302 18787"/>
    </justification>
  </clause>

  <clause id="18791">
    <literal><![CDATA[
      a(x,y,K((z / u) \ w,v5)) = a(x,y,K((u \ z) \ w,v5))
    ]]></literal>
    <justification jstring="[para(16293(a,1),18787(a,1,3))].">
      <j1 rule="para" parents="16293 18787"/>
    </justification>
  </clause>

  <clause id="18792">
    <literal><![CDATA[
      a(x \ K(y,z),u,K(w,v5)) = a(w,u,K(x,v5))
    ]]></literal>
    <justification jstring="[hyper(17872,a,18788,a)].">
      <j1 rule="hyper" parents="17872 18788"/>
    </justification>
  </clause>

  <clause id="18793">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w) * v5)) = a(z,y,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(17765,a,18788,a)].">
      <j1 rule="hyper" parents="17765 18788"/>
    </justification>
  </clause>

  <clause id="18794">
    <literal><![CDATA[
      a(x * K(y,z),u,K(w,v5)) = a(w,u,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,14592,a(flip),b,18788,a),flip(a)].">
      <j1 rule="hyper" parents="334 14592 18788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18795">
    <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(18788(a,1),15296(a,2,1))].">
      <j1 rule="para" parents="18788 15296"/>
    </justification>
  </clause>

  <clause id="18796">
    <literal><![CDATA[
      a(x,y,K(z,u * (w * K(v5,v6)))) = a(z,y,K(w * u,x))
    ]]></literal>
    <justification jstring="[hyper(18086,a,18793,a)].">
      <j1 rule="hyper" parents="18086 18793"/>
    </justification>
  </clause>

  <clause id="18797">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w) * v5)) = a(x,y,K(z,v5))
    ]]></literal>
    <justification jstring="[hyper(334,a,14592,a(flip),b,18793,a),flip(a)].">
      <j1 rule="hyper" parents="334 14592 18793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18798">
    <literal><![CDATA[
      T(x,a(K(y,z) * u,w,v5)) = x * a(v5,w,K(u,x))
    ]]></literal>
    <justification jstring="[para(18793(a,1),14614(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18793 14614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18799">
    <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(18793(a,1),17141(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18793 17141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18800">
    <literal><![CDATA[
      T(x,a(y * K(z,u),w,v5)) = x * a(x,w,K(v5,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,18794,a(flip),b,13701,a),flip(a)].">
      <j1 rule="hyper" parents="119 18794 13701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18801">
    <literal><![CDATA[
      a(x,y,K(z,u * K(w,v5))) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[para(6516(a,1),18794(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6516 18794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18802">
    <literal><![CDATA[
      a(x,y,K(z,(u / w) * v5)) = a(x,y,K(z,(w \ u) * v5))
    ]]></literal>
    <justification jstring="[para(5680(a,1),18797(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5680 18797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18803">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,v5)) = a(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(17758,a,18801,a)].">
      <j1 rule="hyper" parents="17758 18801"/>
    </justification>
  </clause>

  <clause id="18804">
    <literal><![CDATA[
      a(T(x,y) \ z,u,K(w,v5)) = a(x \ z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(5337(a,1),18803(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5337 18803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18805">
    <literal><![CDATA[
      a(x \ T(y,z),u,K(w,v5)) = a(x \ y,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(5666(a,1),18803(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5666 18803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18806">
    <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(18803(a,2),14707(a,1))].">
      <j1 rule="para" parents="18803 14707"/>
    </justification>
  </clause>

  <clause id="18807">
    <literal><![CDATA[
      T(x * y,a(K(z,u) * y,w,v5)) = (x * y) * a(v5,w,K(y,x))
    ]]></literal>
    <justification jstring="[para(11334(a,1),18798(a,2,2))].">
      <j1 rule="para" parents="11334 18798"/>
    </justification>
  </clause>

  <clause id="18808">
    <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(18800(a,2),14618(a,1))].">
      <j1 rule="para" parents="18800 14618"/>
    </justification>
  </clause>

  <clause id="18809">
    <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),18804(a,1,1,1))].">
      <j1 rule="para" parents="20 18804"/>
    </justification>
  </clause>

  <clause id="18810">
    <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),18805(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 18805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18811">
    <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(14302(a,1),18808(a,1,2,1))].">
      <j1 rule="para" parents="14302 18808"/>
    </justification>
  </clause>

  <clause id="18813">
    <literal><![CDATA[
      x * a(y,z,K(u \ (w \ v5),x)) = T(x,a(u \ (v5 / w),z,y))
    ]]></literal>
    <justification jstring="[para(18790(a,1),14649(a,1,2))].">
      <j1 rule="para" parents="18790 14649"/>
    </justification>
  </clause>

  <clause id="18814">
    <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(18796(a,1),14744(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18796 14744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18815">
    <literal><![CDATA[
      a((x * y) \ (z \ u),w,K(v5,v6)) = a(y \ (x \ (u / z)),w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(14846,a,18810,a),flip(a)].">
      <j1 rule="hyper" parents="14846 18810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18816">
    <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(18773(a,2),15145(a,1))].">
      <j1 rule="para" parents="18773 15145"/>
    </justification>
  </clause>

  <clause id="18817">
    <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(5392(a,1),18816(a,1,2,3))].">
      <j1 rule="para" parents="5392 18816"/>
    </justification>
  </clause>

  <clause id="18818">
    <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(7538(a,1),18816(a,1,2,3))].">
      <j1 rule="para" parents="7538 18816"/>
    </justification>
  </clause>

  <clause id="18819">
    <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(11497(a,1),18816(a,1,2,3))].">
      <j1 rule="para" parents="11497 18816"/>
    </justification>
  </clause>

  <clause id="18820">
    <literal><![CDATA[
      K(x,L(y,(K(z,u) * w) \ v5,w)) = K(x,L(y,v5,w))
    ]]></literal>
    <justification jstring="[hyper(18816,a,18772,a)].">
      <j1 rule="hyper" parents="18816 18772"/>
    </justification>
  </clause>

  <clause id="18822">
    <literal><![CDATA[
      K(x,L(y,z \ (u \ w),z)) = K(x,L(y,w / u,z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(17695,a,18780,a)].">
      <j1 rule="hyper" parents="17695 18780"/>
    </justification>
  </clause>

  <clause id="18824">
    <literal><![CDATA[
      T(x * y,a(K(z,u) * y,w,v5)) = x * T(y,a(v5,w,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,13704,a(flip),b,18807,a),flip(a)].">
      <j1 rule="hyper" parents="334 13704 18807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18825">
    <literal><![CDATA[
      T(x,a(x \ ((y * x) / z),u,w)) = x * a(w,u,K(z \ y,x))
    ]]></literal>
    <justification jstring="[para(10642(a,1),18813(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="10642 18813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18826">
    <literal><![CDATA[
      K(x,L(y,z / u,w * K(u,z))) = K(x,L(y,u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(14793,a,18822,a),flip(a)].">
      <j1 rule="hyper" parents="14793 18822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18827">
    <literal><![CDATA[
      K(x,L(y,z / u,w)) = K(x,L(y,u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(18818,a,18826,a)].">
      <j1 rule="hyper" parents="18818 18826"/>
    </justification>
  </clause>

  <clause id="18829">
    <literal><![CDATA[
      K(x,L(y,(z * u) / z,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(4(a,1),18827(a,2,2,2))].">
      <j1 rule="para" parents="4 18827"/>
    </justification>
  </clause>

  <clause id="18830">
    <literal><![CDATA[
      K(x,L(y,T(z,u),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[para(231(a,1),18829(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="231 18829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18834">
    <literal><![CDATA[
      K(x,L(y,z * u,w)) = K(x,L(y,u * z,w))
    ]]></literal>
    <justification jstring="[para(13558(a,1),18830(a,1,2))].">
      <j1 rule="para" parents="13558 18830"/>
    </justification>
  </clause>

  <clause id="18835">
    <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(15313(a,1),18830(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15313 18830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18836">
    <literal><![CDATA[
      T(x,a(x \ ((y * x) / z),u,w)) = T(x,a(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,14649,a(flip),b,18825,a),flip(a)].">
      <j1 rule="hyper" parents="334 14649 18825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18837">
    <literal><![CDATA[
      T(x,a(x \ (y \ (z * x)),u,w)) = T(x,a(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(18811,a,18836,a)].">
      <j1 rule="hyper" parents="18811 18836"/>
    </justification>
  </clause>

  <clause id="18838">
    <literal><![CDATA[
      T(x,a(y \ (z * x),u,w)) = T(x,a(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,14753,a(flip),b,18837,a)].">
      <j1 rule="hyper" parents="58 14753 18837"/>
    </justification>
  </clause>

  <clause id="18839">
    <literal><![CDATA[
      T(x,a(y \ 1,z,u)) = T(x,a(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(2(a,1),18838(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2 18838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18840">
    <literal><![CDATA[
      T(x,a(y \ x,z,u)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,18225,a(flip),b,18839,a),flip(a)].">
      <j1 rule="hyper" parents="58 18225 18839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18841">
    <literal><![CDATA[
      L(x,y,K(z,u \ x)) = T(x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(15341,a,18840,a)].">
      <j1 rule="hyper" parents="15341 18840"/>
    </justification>
  </clause>

  <clause id="18842">
    <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(5441(a,1),18840(a,1,2,1))].">
      <j1 rule="para" parents="5441 18840"/>
    </justification>
  </clause>

  <clause id="18843">
    <literal><![CDATA[
      L(x,y,K(z,u \ x)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,15279,a,b,18841,a),flip(a)].">
      <j1 rule="hyper" parents="334 15279 18841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18844">
    <literal><![CDATA[
      L(x,y,K(x \ z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,13016,a,b,18843,a)].">
      <j1 rule="hyper" parents="58 13016 18843"/>
    </justification>
  </clause>

  <clause id="18845">
    <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(18842(a,2),17760(a,1))].">
      <j1 rule="para" parents="18842 17760"/>
    </justification>
  </clause>

  <clause id="18846">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ v5)) = K(x,L(y,z,u \ (w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(18819,a,14829,a)].">
      <j1 rule="hyper" parents="18819 14829"/>
    </justification>
  </clause>

  <clause id="18847">
    <literal><![CDATA[
      K(x \ 1,L(y,z,(x * u) \ w)) = K(x \ 1,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(334,a,14967,a(flip),b,18846,a),flip(a)].">
      <j1 rule="hyper" parents="334 14967 18846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18848">
    <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,15147,a(flip),b,18847,a),flip(a)].">
      <j1 rule="hyper" parents="58 15147 18847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18849">
    <literal><![CDATA[
      T(x * y,a(z,u,x)) = x * T(y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(18845,a,18824,a)].">
      <j1 rule="hyper" parents="18845 18824"/>
    </justification>
  </clause>

  <clause id="18850">
    <literal><![CDATA[
      T(x * y,a(z,u,x)) = x * L(y,u,K(x,z))
    ]]></literal>
    <justification jstring="[para(15279(a,2),18849(a,2,2))].">
      <j1 rule="para" parents="15279 18849"/>
    </justification>
  </clause>

  <clause id="18851">
    <literal><![CDATA[
      L(x * y,z,K(x,u)) = x * L(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(15341,a,18850,a)].">
      <j1 rule="hyper" parents="15341 18850"/>
    </justification>
  </clause>

  <clause id="18852">
    <literal><![CDATA[
      K(x \ (y * (((z / y) * y) \ x)),u) = K((z * (y \ x)) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15239,a(flip),b,18848,a),flip(a)].">
      <j1 rule="hyper" parents="58 15239 18848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18853">
    <literal><![CDATA[
      K((x * (y \ z)) \ z,u) = K(z \ (y * (x \ z)),u)
    ]]></literal>
    <justification jstring="[para(7(a,1),18852(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 18852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18855">
    <literal><![CDATA[
      x / (K(y \ (z * (u \ y)),w) * x) = K(w,(u * (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[para(18853(a,1),5403(a,1,2,1))].">
      <j1 rule="para" parents="18853 5403"/>
    </justification>
  </clause>

  <clause id="18856">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (z * (y \ u))) = w
    ]]></literal>
    <justification jstring="[para(18855(a,1),5412(a,1))].">
      <j1 rule="para" parents="18855 5412"/>
    </justification>
  </clause>

  <clause id="18857">
    <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,15231,a(flip),b,18781,a),flip(a)].">
      <j1 rule="hyper" parents="58 15231 18781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18858">
    <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(14215(a,1),18795(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14215 18795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18859">
    <literal><![CDATA[
      R(x,y,K(K(z,u) * w,v5)) = x * a(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[para(17551(a,1),18799(a,2,2))].">
      <j1 rule="para" parents="17551 18799"/>
    </justification>
  </clause>

  <clause id="18861">
    <literal><![CDATA[
      R(x,y,K(K(z,u) * w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(334,a,15282,a(flip),b,18859,a),flip(a)].">
      <j1 rule="hyper" parents="334 15282 18859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18863">
    <literal><![CDATA[
      L(x,y,K(K(z,u) * w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(15342,a,18861,a)].">
      <j1 rule="hyper" parents="15342 18861"/>
    </justification>
  </clause>

  <clause id="18864">
    <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(15344,a,18863,a)].">
      <j1 rule="hyper" parents="15344 18863"/>
    </justification>
  </clause>

  <clause id="18865">
    <literal><![CDATA[
      L(x,y,K(z / u,w)) = L(x,y,K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(5129(a,1),18863(a,1,3,1))].">
      <j1 rule="para" parents="5129 18863"/>
    </justification>
  </clause>

  <clause id="18866">
    <literal><![CDATA[
      L(x,y,K(z,T(u,w))) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(8207(a,1),18863(a,1,3))].">
      <j1 rule="para" parents="8207 18863"/>
    </justification>
  </clause>

  <clause id="18867">
    <literal><![CDATA[
      L(x,y,K(z,u / w)) = L(x,y,K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(107(a,1),18866(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="107 18866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18869">
    <literal><![CDATA[
      L(x,y,K(z / x,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,18844,a(flip),b,18865,a),flip(a)].">
      <j1 rule="hyper" parents="334 18844 18865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18870">
    <literal><![CDATA[
      L(x,y,K(z * x,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(6(a,1),18869(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="6 18869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18871">
    <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,6341,a(flip),b,18867,a),flip(a)].">
      <j1 rule="hyper" parents="58 6341 18867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18872">
    <literal><![CDATA[
      L(x,(K(y,z) * u) \ w,K(u,v5)) = L(x,w,K(u,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,18863,a(flip),b,18864,a)].">
      <j1 rule="hyper" parents="58 18863 18864"/>
    </justification>
  </clause>

  <clause id="18874">
    <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(333(a,1),18809(a,1,1,1,1))].">
      <j1 rule="para" parents="333 18809"/>
    </justification>
  </clause>

  <clause id="18875">
    <literal><![CDATA[
      K(x,L(y,z,u / (K(w,v5) / v6))) = K(x,L(y,z,v6 * u))
    ]]></literal>
    <justification jstring="[hyper(334,a,14656,a(flip),b,18814,a),flip(a)].">
      <j1 rule="hyper" parents="334 14656 18814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18877">
    <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(18815(a,1),14846(a,1))].">
      <j1 rule="para" parents="18815 14846"/>
    </justification>
  </clause>

  <clause id="18878">
    <literal><![CDATA[
      K(x,L(y,z \ (K(u,w) * v5),z)) = K(x,L(y,v5,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18820,a(flip),b,18835,a),flip(a)].">
      <j1 rule="hyper" parents="58 18820 18835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18879">
    <literal><![CDATA[
      K(x,L(y,K(z,u) * w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(14793,a,18878,a)].">
      <j1 rule="hyper" parents="14793 18878"/>
    </justification>
  </clause>

  <clause id="18880">
    <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,18878,a(flip),b,14699,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 18878 14699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18886">
    <literal><![CDATA[
      K(x,L(y,z * (K(u,w) * v5),v6)) = K(x,L(y,z * v5,v6))
    ]]></literal>
    <justification jstring="[para(6333(a,1),18879(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6333 18879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18887">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = a(v5,u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,14631,a(flip),b,18880,a),flip(a)].">
      <j1 rule="hyper" parents="334 14631 18880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18888">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = a(x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(334,a,11120,a(flip),b,18880,a),flip(a)].">
      <j1 rule="hyper" parents="334 11120 18880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18889">
    <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,18887,a)].">
      <j1 rule="hyper" parents="52 18887"/>
    </justification>
  </clause>

  <clause id="18891">
    <literal><![CDATA[
      a(x,y * z,K(u,w)) = a(x,z * y,K(u,w))
    ]]></literal>
    <justification jstring="[para(4990(a,1),18888(a,1,2))].">
      <j1 rule="para" parents="4990 18888"/>
    </justification>
  </clause>

  <clause id="18894">
    <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(18888(a,1),14677(a,1))].">
      <j1 rule="para" parents="18888 14677"/>
    </justification>
  </clause>

  <clause id="18896">
    <literal><![CDATA[
      x * a(x,y * z,K(u,w)) = L(x,z * y,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,18891,a,b,15283,a)].">
      <j1 rule="hyper" parents="119 18891 15283"/>
    </justification>
  </clause>

  <clause id="18897">
    <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(18896(a,1),15315(a,1))].">
      <j1 rule="para" parents="18896 15315"/>
    </justification>
  </clause>

  <clause id="18898">
    <literal><![CDATA[
      L(x,y * (y \ z),K(u,w)) = L(x,T(z,y),K(u,w))
    ]]></literal>
    <justification jstring="[hyper(18897,a,13572,a)].">
      <j1 rule="hyper" parents="18897 13572"/>
    </justification>
  </clause>

  <clause id="18899">
    <literal><![CDATA[
      L(x,T(y,z),K(u,w)) = L(x,y,K(u,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),18898(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 18898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18900">
    <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(15313(a,1),18899(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15313 18899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18901">
    <literal><![CDATA[
      K(x,L(y,z * (K(u,w) * v5),v6)) = K(x,L(y,v5 * z,v6))
    ]]></literal>
    <justification jstring="[hyper(334,a,18834,a,b,18886,a),flip(a)].">
      <j1 rule="hyper" parents="334 18834 18886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18902">
    <literal><![CDATA[
      K(x,L(y,z * (u * K(w,v5)),v6)) = K(x,L(y,u * z,v6))
    ]]></literal>
    <justification jstring="[para(7538(a,1),18901(a,1,2,2,2))].">
      <j1 rule="para" parents="7538 18901"/>
    </justification>
  </clause>

  <clause id="18903">
    <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(18902(a,1),15194(a,1,1,1))].">
      <j1 rule="para" parents="18902 15194"/>
    </justification>
  </clause>

  <clause id="18904">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),K(y,v5)) = L(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,18872,a(flip),b,18900,a),flip(a)].">
      <j1 rule="hyper" parents="58 18872 18900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18905">
    <literal><![CDATA[
      L(x,K(y,z) * u,K(w,v5)) = L(x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,15316,a(flip),b,18904,a)].">
      <j1 rule="hyper" parents="58 15316 18904"/>
    </justification>
  </clause>

  <clause id="18906">
    <literal><![CDATA[
      L(x,y * K(z,u),K(w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(18897,a,18905,a)].">
      <j1 rule="hyper" parents="18897 18905"/>
    </justification>
  </clause>

  <clause id="18908">
    <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,11529,a(flip),b,18906,a),flip(a)].">
      <j1 rule="hyper" parents="58 11529 18906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18909">
    <literal><![CDATA[
      L(x,y \ (z * K(u,w)),K(v5,v6)) = L(x,y \ z,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(14929(a,1),18906(a,1,2))].">
      <j1 rule="para" parents="14929 18906"/>
    </justification>
  </clause>

  <clause id="18910">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),K(v5,v6)) = L(x,y \ w,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(7391(a,1),18909(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7391 18909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18911">
    <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,10673,a(flip),b,18910,a),flip(a)].">
      <j1 rule="hyper" parents="58 10673 18910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18913">
    <literal><![CDATA[
      K(x,y) * (((x \ z) / z) \ u) = ((T(x,y) \ z) / z) \ u
    ]]></literal>
    <justification jstring="[hyper(12958,a,18765,a)].">
      <j1 rule="hyper" parents="12958 18765"/>
    </justification>
  </clause>

  <clause id="18915">
    <literal><![CDATA[
      T(x,((T(y,z) \ u) / u) \ w) = T(x,T((y \ u) / u,z) \ w)
    ]]></literal>
    <justification jstring="[para(18913(a,1),15787(a,1,2))].">
      <j1 rule="para" parents="18913 15787"/>
    </justification>
  </clause>

  <clause id="18916">
    <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(11166,a,18786,a),flip(a)].">
      <j1 rule="hyper" parents="11166 18786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18918">
    <literal><![CDATA[
      K(x,((T(y,z) \ 1) * u) \ ((y \ 1) * (z * y))) = K(x,(y \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,14935,a(flip),b,18786,a),flip(a)].">
      <j1 rule="hyper" parents="58 14935 18786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18920">
    <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,15348,a(flip),b,18911,a)].">
      <j1 rule="hyper" parents="58 15348 18911"/>
    </justification>
  </clause>

  <clause id="18921">
    <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,17279,a(flip),b,18920,a),flip(a)].">
      <j1 rule="hyper" parents="58 17279 18920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18922">
    <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(18921(a,1),15314(a,1,1))].">
      <j1 rule="para" parents="18921 15314"/>
    </justification>
  </clause>

  <clause id="18923">
    <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,18620,a(flip),b,17982,a)].">
      <j1 rule="hyper" parents="58 18620 17982"/>
    </justification>
  </clause>

  <clause id="18924">
    <literal><![CDATA[
      K(x,y * (z * K((u \ w) \ v5,u \ w))) = K(x,(y * z) * K(w \ u,v5))
    ]]></literal>
    <justification jstring="[hyper(16368,a,18028,a),flip(a)].">
      <j1 rule="hyper" parents="16368 18028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18925">
    <literal><![CDATA[
      K(x,y * (z * K((u \ w) \ y,u \ w))) = K(x,T(y,w \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(334,a,16174,a(flip),b,18924,a),flip(a)].">
      <j1 rule="hyper" parents="334 16174 18924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18926">
    <literal><![CDATA[
      K(x,y * (z * K(u * (w \ y),u \ w))) = K(x,T(y,w \ u) * z)
    ]]></literal>
    <justification jstring="[para(12752(a,1),18925(a,1,2,2,2))].">
      <j1 rule="para" parents="12752 18925"/>
    </justification>
  </clause>

  <clause id="18927">
    <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(334,a,13372,a(flip),b,18115,a),flip(a)].">
      <j1 rule="hyper" parents="334 13372 18115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18928">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) / u) \ w) = T(x,K(z,y) * ((y / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,16380,a(flip),b,18927,a)].">
      <j1 rule="hyper" parents="58 16380 18927"/>
    </justification>
  </clause>

  <clause id="18929">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) / u) \ w) = T(x,(T(y,z) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(334,a,18120,a(flip),b,18928,a),flip(a)].">
      <j1 rule="hyper" parents="334 18120 18928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18931">
    <literal><![CDATA[
      T(x,(T(y \ z,z) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18561,a(flip),b,18929,a),flip(a)].">
      <j1 rule="hyper" parents="58 18561 18929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18932">
    <literal><![CDATA[
      T(x,((y / z) / y) \ u) = T(x,(y \ (z \ y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,18241,a(flip),b,18931,a),flip(a)].">
      <j1 rule="hyper" parents="58 18241 18931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18933">
    <literal><![CDATA[
      T(x,(y \ ((z \ K(z,y)) \ y)) \ u) = T(x,(y \ (y / (z \ 1))) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15788,a(flip),b,18932,a),flip(a)].">
      <j1 rule="hyper" parents="58 15788 18932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18934">
    <literal><![CDATA[
      T(x,(((y \ 1) \ z) / z) \ u) = T(x,(z \ (z / (y \ 1))) \ u)
    ]]></literal>
    <justification jstring="[para(10409(a,1),18933(a,1,2,1))].">
      <j1 rule="para" parents="10409 18933"/>
    </justification>
  </clause>

  <clause id="18935">
    <literal><![CDATA[
      T(x,(y \ (y / ((z \ 1) \ 1))) \ u) = T(x,((z \ y) / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(14479,a,18934,a),flip(a)].">
      <j1 rule="hyper" parents="14479 18934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18936">
    <literal><![CDATA[
      T(x,((y \ z) / z) \ u) = T(x,(z \ (z / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(14478,a,18935,a),flip(a)].">
      <j1 rule="hyper" parents="14478 18935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18937">
    <literal><![CDATA[
      T(x,T((y \ z) / z,u) \ w) = T(x,(z \ (z / T(y,u))) \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18915,a(flip),b,18936,a)].">
      <j1 rule="hyper" parents="58 18915 18936"/>
    </justification>
  </clause>

  <clause id="18938">
    <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(334,a,18485,a(flip),b,18937,a),flip(a)].">
      <j1 rule="hyper" parents="334 18485 18937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18939">
    <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(17140,a,18938,a)].">
      <j1 rule="hyper" parents="17140 18938"/>
    </justification>
  </clause>

  <clause id="18940">
    <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,15829,a(flip),b,18939,a)].">
      <j1 rule="hyper" parents="58 15829 18939"/>
    </justification>
  </clause>

  <clause id="18941">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,T(y / T(z,w),u) \ y)
    ]]></literal>
    <justification jstring="[para(7894(a,1),18940(a,1,2,1))].">
      <j1 rule="para" parents="7894 18940"/>
    </justification>
  </clause>

  <clause id="18942">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,y * T(y \ T(z,w),u))
    ]]></literal>
    <justification jstring="[hyper(334,a,18496,a(flip),b,18941,a),flip(a)].">
      <j1 rule="hyper" parents="334 18496 18941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18943">
    <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(334,a,12665,a,b,18942,a)].">
      <j1 rule="hyper" parents="334 12665 18942"/>
    </justification>
  </clause>

  <clause id="18944">
    <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(18623,a,18943,a)].">
      <j1 rule="hyper" parents="18623 18943"/>
    </justification>
  </clause>

  <clause id="18945">
    <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,12652,a(flip),b,18944,a),flip(a)].">
      <j1 rule="hyper" parents="58 12652 18944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18946">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,T(y * T(y \ z,u),w))
    ]]></literal>
    <justification jstring="[para(465(a,1),18945(a,2,2,1))].">
      <j1 rule="para" parents="465 18945"/>
    </justification>
  </clause>

  <clause id="18947">
    <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,18942,a(flip),b,18946,a),flip(a)].">
      <j1 rule="hyper" parents="58 18942 18946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18948">
    <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(334,a,18477,a(flip),b,18121,a),flip(a)].">
      <j1 rule="hyper" parents="334 18477 18121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18950">
    <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(334,a,16692,a(flip),b,18948,a),flip(a)].">
      <j1 rule="hyper" parents="334 16692 18948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18951">
    <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,16392,a(flip),b,18950,a),flip(a)].">
      <j1 rule="hyper" parents="58 16392 18950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18952">
    <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(334,a,16692,a(flip),b,18951,a),flip(a)].">
      <j1 rule="hyper" parents="334 16692 18951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18953">
    <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,18501,a(flip),b,18952,a),flip(a)].">
      <j1 rule="hyper" parents="58 18501 18952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18954">
    <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,18587,a(flip),b,18953,a),flip(a)].">
      <j1 rule="hyper" parents="58 18587 18953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18955">
    <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,18499,a(flip),b,18954,a)].">
      <j1 rule="hyper" parents="58 18499 18954"/>
    </justification>
  </clause>

  <clause id="18956">
    <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(5391(a,1),18125(a,2,2,1,1,1,2))].">
      <j1 rule="para" parents="5391 18125"/>
    </justification>
  </clause>

  <clause id="18957">
    <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(5629(a,1),18148(a,1,2,2,2))].">
      <j1 rule="para" parents="5629 18148"/>
    </justification>
  </clause>

  <clause id="18958">
    <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,18643,a(flip),b,18957,a),flip(a)].">
      <j1 rule="hyper" parents="58 18643 18957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18959">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K(u,z))) = K(x,y / T((z \ 1) * u,u))
    ]]></literal>
    <justification jstring="[para(6228(a,1),18958(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6228 18958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18960">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(334,a,16579,a(flip),b,18959,a),flip(a)].">
      <j1 rule="hyper" parents="334 16579 18959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18961">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * T(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18146,a(flip),b,18960,a)].">
      <j1 rule="hyper" parents="58 18146 18960"/>
    </justification>
  </clause>

  <clause id="18962">
    <literal><![CDATA[
      K(x,y / (T(z,u) * (u \ 1))) = K(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18190,a(flip),b,18961,a),flip(a)].">
      <j1 rule="hyper" parents="58 18190 18961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18963">
    <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(334,a,13588,a(flip),b,18417,a),flip(a)].">
      <j1 rule="hyper" parents="334 13588 18417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18964">
    <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,17168,a(flip),b,18483,a)].">
      <j1 rule="hyper" parents="58 17168 18483"/>
    </justification>
  </clause>

  <clause id="18965">
    <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(18964(a,1),18484(a,1))].">
      <j1 rule="para" parents="18964 18484"/>
    </justification>
  </clause>

  <clause id="18966">
    <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(17166(a,1),18965(a,1))].">
      <j1 rule="para" parents="17166 18965"/>
    </justification>
  </clause>

  <clause id="18967">
    <literal><![CDATA[
      L(x,(y * z) / y,(y \ z) \ 1) = L(x,y * (z / y),(z / y) \ 1)
    ]]></literal>
    <justification jstring="[para(4102(a,1),18963(a,1,3,1))].">
      <j1 rule="para" parents="4102 18963"/>
    </justification>
  </clause>

  <clause id="18968">
    <literal><![CDATA[
      L(x,y * (z / y),(z / y) \ 1) = L(x,y * (z / y),(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,13588,a(flip),b,18967,a),flip(a)].">
      <j1 rule="hyper" parents="58 13588 18967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18969">
    <literal><![CDATA[
      L(x,y * (z / y),(z / y) \ 1) = L(x,z,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(334,a,13602,a(flip),b,18968,a),flip(a)].">
      <j1 rule="hyper" parents="334 13602 18968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18970">
    <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(18969(a,1),10421(a,1,2))].">
      <j1 rule="para" parents="18969 10421"/>
    </justification>
  </clause>

  <clause id="18971">
    <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(17817(a,2),17572(a,1,1))].">
      <j1 rule="para" parents="17817 17572"/>
    </justification>
  </clause>

  <clause id="18972">
    <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(13729(a,2),17661(a,1,2,1,2))].">
      <j1 rule="para" parents="13729 17661"/>
    </justification>
  </clause>

  <clause id="18973">
    <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(12754(a,1),17752(a,1,1))].">
      <j1 rule="para" parents="12754 17752"/>
    </justification>
  </clause>

  <clause id="18974">
    <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(4356(a,1),17768(a,1,2))].">
      <j1 rule="para" parents="4356 17768"/>
    </justification>
  </clause>

  <clause id="18975">
    <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(14881,a,17813,a)].">
      <j1 rule="hyper" parents="14881 17813"/>
    </justification>
  </clause>

  <clause id="18977">
    <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(15908,a,18975,a)].">
      <j1 rule="hyper" parents="15908 18975"/>
    </justification>
  </clause>

  <clause id="18978">
    <literal><![CDATA[
      K(x,(((y * z) \ z) * u) \ T(z,y)) = K(x,L(u \ (y * z),z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(15872,a,18977,a),flip(a)].">
      <j1 rule="hyper" parents="15872 18977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18979">
    <literal><![CDATA[
      K(x,L(y \ (z * u),u,z \ 1)) = K(x,(((u * z) \ u) * y) \ u)
    ]]></literal>
    <justification jstring="[para(14150(a,1),18978(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14150 18978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18980">
    <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(17784(a,1),17822(a,1,2))].">
      <j1 rule="para" parents="17784 17822"/>
    </justification>
  </clause>

  <clause id="18981">
    <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(18285,a,18254,a),flip(a)].">
      <j1 rule="hyper" parents="18285 18254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18982">
    <literal><![CDATA[
      K(x,T(T(y,x) / (z \ 1),y) * u) = K(x,(T(y,z) / (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(7613,a,18981,a)].">
      <j1 rule="hyper" parents="7613 18981"/>
    </justification>
  </clause>

  <clause id="18984">
    <literal><![CDATA[
      K(x,((y \ 1) \ T(z,x)) * u) = K(x,(T(z,y) / (y \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16491,a(flip),b,18982,a)].">
      <j1 rule="hyper" parents="58 16491 18982"/>
    </justification>
  </clause>

  <clause id="18985">
    <literal><![CDATA[
      K(x,(T(y,z) / (z \ 1)) * u) = K(x,((z \ 1) \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(18158,a,18984,a),flip(a)].">
      <j1 rule="hyper" parents="18158 18984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18986">
    <literal><![CDATA[
      K(x,(y / (z \ K(y,z))) * u) = K(x,((z \ 1) \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,18172,a(flip),b,18985,a)].">
      <j1 rule="hyper" parents="58 18172 18985"/>
    </justification>
  </clause>

  <clause id="18987">
    <literal><![CDATA[
      K(x,y \ (z / T(u,z))) = K(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(334,a,5301,a(flip),b,18394,a),flip(a)].">
      <j1 rule="hyper" parents="334 5301 18394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18988">
    <literal><![CDATA[
      K(x,y \ (T(z,u) / u)) = K(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[para(4488(a,2),18987(a,1,2,2))].">
      <j1 rule="para" parents="4488 18987"/>
    </justification>
  </clause>

  <clause id="18989">
    <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(13037(a,1),18988(a,1,2,2,1))].">
      <j1 rule="para" parents="13037 18988"/>
    </justification>
  </clause>

  <clause id="18990">
    <literal><![CDATA[
      K(x,y \ (T(z,u / w) / (u / w))) = K(x,y \ ((T(w,u) \ u) \ z))
    ]]></literal>
    <justification jstring="[hyper(18657,a,18989,a)].">
      <j1 rule="hyper" parents="18657 18989"/>
    </justification>
  </clause>

  <clause id="18991">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) \ u) \ w)) = K(x,y \ ((u / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,18988,a(flip),b,18990,a),flip(a)].">
      <j1 rule="hyper" parents="58 18988 18990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18992">
    <literal><![CDATA[
      K(x,(y \ 1) \ ((z / u) \ w)) = K(x,y * ((u \ T(z,u)) \ w))
    ]]></literal>
    <justification jstring="[hyper(14411,a,18991,a),flip(a)].">
      <j1 rule="hyper" parents="14411 18991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18993">
    <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(18992(a,1),14346(a,1))].">
      <j1 rule="para" parents="18992 14346"/>
    </justification>
  </clause>

  <clause id="18994">
    <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(4490(a,2),18993(a,1,2,2,1))].">
      <j1 rule="para" parents="4490 18993"/>
    </justification>
  </clause>

  <clause id="18995">
    <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(18622(a,1),18994(a,1))].">
      <j1 rule="para" parents="18622 18994"/>
    </justification>
  </clause>

  <clause id="18996">
    <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(16976,a,18667,a)].">
      <j1 rule="hyper" parents="16976 18667"/>
    </justification>
  </clause>

  <clause id="18997">
    <literal><![CDATA[
      K(x,y / (T((z \ u) \ 1,u) / w)) = K(x,y / (((u / z) \ 1) / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,18668,a(flip),b,18996,a),flip(a)].">
      <j1 rule="hyper" parents="58 18668 18996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18998">
    <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(455,a,18288,a,b,18997,a)].">
      <j1 rule="hyper" parents="455 18288 18997"/>
    </justification>
  </clause>

  <clause id="18999">
    <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(18513(a,1),18702(a,1,2,1))].">
      <j1 rule="para" parents="18513 18702"/>
    </justification>
  </clause>

  <clause id="19000">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,u * ((z \ 1) * T(y,u / z)))
    ]]></literal>
    <justification jstring="[para(14195(a,1),18999(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14195 18999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19002">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,u * ((z \ 1) * T(y,z \ u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,16512,a(flip),b,19000,a),flip(a)].">
      <j1 rule="hyper" parents="334 16512 19000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19003">
    <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,17154,a(flip),b,19002,a),flip(a)].">
      <j1 rule="hyper" parents="58 17154 19002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19004">
    <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(17581(a,1),18784(a,1,1,1))].">
      <j1 rule="para" parents="17581 18784"/>
    </justification>
  </clause>

  <clause id="19006">
    <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(18363,a,19004,a)].">
      <j1 rule="hyper" parents="18363 19004"/>
    </justification>
  </clause>

  <clause id="19008">
    <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(18361(a,1),19006(a,2,2))].">
      <j1 rule="para" parents="18361 19006"/>
    </justification>
  </clause>

  <clause id="19009">
    <literal><![CDATA[
      L(K(x,y) * K(z,u),w,K(v5,v6)) = K(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4329,a,19008,a)].">
      <j1 rule="hyper" parents="4329 19008"/>
    </justification>
  </clause>

  <clause id="19010">
    <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(19009(a,1),15339(a,1,1,1))].">
      <j1 rule="para" parents="19009 15339"/>
    </justification>
  </clause>

  <clause id="19011">
    <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(14383(a,1),19010(a,1,1))].">
      <j1 rule="para" parents="14383 19010"/>
    </justification>
  </clause>

  <clause id="19012">
    <literal><![CDATA[
      T(K(x,y) * a(z,u,w),K(v5,v6)) = a(z,u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8132,a,19011,a)].">
      <j1 rule="hyper" parents="8132 19011"/>
    </justification>
  </clause>

  <clause id="19013">
    <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(14797(a,1),18903(a,1,1,1))].">
      <j1 rule="para" parents="14797 18903"/>
    </justification>
  </clause>

  <clause id="19015">
    <literal><![CDATA[
      ((K(x,y) * z) * (u * K(w,v5))) / u = K(x,y) * ((z * u) / (u * K(v5,w)))
    ]]></literal>
    <justification jstring="[para(18783(a,1),19013(a,1,1))].">
      <j1 rule="para" parents="18783 19013"/>
    </justification>
  </clause>

  <clause id="19016">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (u * K(w,v5)) = K(x,y) * ((z * u) / (u * K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(14896,a,19015,a)].">
      <j1 rule="hyper" parents="14896 19015"/>
    </justification>
  </clause>

  <clause id="19017">
    <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(334,a,14886,a(flip),b,18916,a),flip(a)].">
      <j1 rule="hyper" parents="334 14886 18916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19018">
    <literal><![CDATA[
      K(x,L(y \ (z * u),u,z \ 1)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,18918,a(flip),b,19017,a),flip(a)].">
      <j1 rule="hyper" parents="58 18918 19017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19019">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * u) \ y) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,18979,a(flip),b,19018,a)].">
      <j1 rule="hyper" parents="58 18979 19018"/>
    </justification>
  </clause>

  <clause id="19020">
    <literal><![CDATA[
      K(x,y \ (z * (((y * u) \ y) \ y))) = K(x,(u \ (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(18856,a,19019,a)].">
      <j1 rule="hyper" parents="18856 19019"/>
    </justification>
  </clause>

  <clause id="19021">
    <literal><![CDATA[
      K(x,T(y \ z,K(u,w)) \ v5) = K(x,(((v5 * y) \ v5) * z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(334,a,16406,a,b,19019,a)].">
      <j1 rule="hyper" parents="334 16406 19019"/>
    </justification>
  </clause>

  <clause id="19022">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * T(u,z \ 1)) \ y) = K(x,(u / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,15642,a(flip),b,19019,a),flip(a)].">
      <j1 rule="hyper" parents="334 15642 19019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19023">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ y) = K(x,((z \ y) * u) \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),19019(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 19019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19024">
    <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(14812(a,1),19019(a,2,2,1))].">
      <j1 rule="para" parents="14812 19019"/>
    </justification>
  </clause>

  <clause id="19025">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ z) * K(x,K(z,y \ u)) = K(x,z / ((z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(19023(a,1),10210(a,1,1))].">
      <j1 rule="para" parents="19023 10210"/>
    </justification>
  </clause>

  <clause id="19026">
    <literal><![CDATA[
      K(x,y \ (z * T(y * u,y))) = K(x,(u \ (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,13470,a(flip),b,19020,a)].">
      <j1 rule="hyper" parents="58 13470 19020"/>
    </justification>
  </clause>

  <clause id="19027">
    <literal><![CDATA[
      K(x,(y \ (z \ u)) \ u) = K(x,u \ (z * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18438,a(flip),b,19026,a),flip(a)].">
      <j1 rule="hyper" parents="58 18438 19026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19028">
    <literal><![CDATA[
      K(x,y \ ((y / z) * (u * y))) = K(x,(u \ z) \ y)
    ]]></literal>
    <justification jstring="[para(75(a,1),19027(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="75 19027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19029">
    <literal><![CDATA[
      K(x,(y \ (z * u)) \ u) = K(x,u \ (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15250,a(flip),b,19028,a),flip(a)].">
      <j1 rule="hyper" parents="58 15250 19028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19031">
    <literal><![CDATA[
      K(x,((y / z) \ u) \ z) = K(x,z \ ((z / u) * y))
    ]]></literal>
    <justification jstring="[para(7(a,1),19028(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7 19028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19032">
    <literal><![CDATA[
      T(K(x,y \ (z \ (u * y))),y) = K(x,y / (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(19029(a,1),8155(a,1,1))].">
      <j1 rule="para" parents="19029 8155"/>
    </justification>
  </clause>

  <clause id="19033">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z \ ((z / u) * w)) = K(y,T(((z / w) * u) \ z,x))
    ]]></literal>
    <justification jstring="[hyper(18283,a,19031,a),flip(a)].">
      <j1 rule="hyper" parents="18283 19031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19034">
    <literal><![CDATA[
      K(x,(y \ (z * u)) / u) = K(x,u / (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(8321,a,19032,a)].">
      <j1 rule="hyper" parents="8321 19032"/>
    </justification>
  </clause>

  <clause id="19035">
    <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,14958,a,b,19032,a)].">
      <j1 rule="hyper" parents="58 14958 19032"/>
    </justification>
  </clause>

  <clause id="19036">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z / (u \ (w * z))) = K(y,T((w \ (u * z)) / z,x))
    ]]></literal>
    <justification jstring="[hyper(14446,a,19034,a),flip(a)].">
      <j1 rule="hyper" parents="14446 19034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19037">
    <literal><![CDATA[
      K(x,y / (z \ (T(u,z) * y))) = K(x,T((u \ (z * y)) / y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18647,a(flip),b,19034,a),flip(a)].">
      <j1 rule="hyper" parents="58 18647 19034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19038">
    <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(334,a,18470,a(flip),b,19021,a),flip(a)].">
      <j1 rule="hyper" parents="334 18470 19021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19039">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * u) \ y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ u) \ y) = w
    ]]></literal>
    <justification jstring="[para(19021(a,1),16452(a,1))].">
      <j1 rule="para" parents="19021 16452"/>
    </justification>
  </clause>

  <clause id="19040">
    <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(18979(a,2),19039(a,1))].">
      <j1 rule="para" parents="18979 19039"/>
    </justification>
  </clause>

  <clause id="19041">
    <literal><![CDATA[
      K(x,(y * ((z * u) \ z)) \ z) = K(x,(y / u) \ z)
    ]]></literal>
    <justification jstring="[para(6567(a,1),19022(a,1,2,1))].">
      <j1 rule="para" parents="6567 19022"/>
    </justification>
  </clause>

  <clause id="19042">
    <literal><![CDATA[
      K(x,y \ ((y * z) * (u \ y))) = K(x,(u / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(18856,a,19041,a)].">
      <j1 rule="hyper" parents="18856 19041"/>
    </justification>
  </clause>

  <clause id="19043">
    <literal><![CDATA[
      K(x,((y / z) / u) \ y) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[para(75(a,1),19042(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="75 19042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19044">
    <literal><![CDATA[
      K(x,y \ ((z * y) * (u \ y))) = K(x,(u / T(z,y)) \ y)
    ]]></literal>
    <justification jstring="[para(105(a,1),19042(a,1,2,2,1))].">
      <j1 rule="para" parents="105 19042"/>
    </justification>
  </clause>

  <clause id="19045">
    <literal><![CDATA[
      K(x,((y * ((y * z) / y)) / u) \ z) = K(x,z \ ((z * u) * ((y * z) \ T(z,y))))
    ]]></literal>
    <justification jstring="[para(14314(a,1),19042(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="14314 19042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19046">
    <literal><![CDATA[
      K(x,T(y,z * u) / ((y / z) / u)) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16641,a,b,19043,a)].">
      <j1 rule="hyper" parents="58 16641 19043"/>
    </justification>
  </clause>

  <clause id="19047">
    <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(4360(a,1),19044(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4360 19044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19049">
    <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(19017(a,2),19040(a,1))].">
      <j1 rule="para" parents="19017 19040"/>
    </justification>
  </clause>

  <clause id="19050">
    <literal><![CDATA[
      K(x,y / ((y \ z) \ u)) = K(x,y / ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14449,a(flip),b,19025,a),flip(a)].">
      <j1 rule="hyper" parents="58 14449 19025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19051">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,w)) = K(x,T(y \ ((y / u) * z),w))
    ]]></literal>
    <justification jstring="[hyper(14446,a,19033,a),flip(a)].">
      <j1 rule="hyper" parents="14446 19033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19052">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,y / (z * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16732,a(flip),b,19051,a),flip(a)].">
      <j1 rule="hyper" parents="58 16732 19051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19053">
    <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(19036(a,1),14446(a,1))].">
      <j1 rule="para" parents="19036 14446"/>
    </justification>
  </clause>

  <clause id="19054">
    <literal><![CDATA[
      K(x,T((y \ (z * u)) / u,y)) = K(x,T(u / (z \ (y * u)),z))
    ]]></literal>
    <justification jstring="[hyper(19053,a,18651,a),flip(a)].">
      <j1 rule="hyper" parents="19053 18651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19055">
    <literal><![CDATA[
      K(x,y / (z \ (T(u,z) * y))) = K(x,T(y / (z \ (u * y)),z))
    ]]></literal>
    <justification jstring="[hyper(19053,a,19037,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19053 19037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19056">
    <literal><![CDATA[
      K(x,T(y / (z \ (u * y)),u)) = K(x,T(y / (z \ (u * y)),z))
    ]]></literal>
    <justification jstring="[hyper(19053,a,19054,a)].">
      <j1 rule="hyper" parents="19053 19054"/>
    </justification>
  </clause>

  <clause id="19057">
    <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(18786(a,2),19049(a,1))].">
      <j1 rule="para" parents="18786 19049"/>
    </justification>
  </clause>

  <clause id="19058">
    <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(15901(a,1),19057(a,1))].">
      <j1 rule="para" parents="15901 19057"/>
    </justification>
  </clause>

  <clause id="19059">
    <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(15902(a,1),19058(a,1))].">
      <j1 rule="para" parents="15902 19058"/>
    </justification>
  </clause>

  <clause id="19060">
    <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(18471,a,19024,a)].">
      <j1 rule="hyper" parents="18471 19024"/>
    </justification>
  </clause>

  <clause id="19061">
    <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(11137(a,1),19060(a,1,2,1))].">
      <j1 rule="para" parents="11137 19060"/>
    </justification>
  </clause>

  <clause id="19062">
    <literal><![CDATA[
      K(x,K(y,z) * ((((u * w) \ u) * v5) \ u)) = K(x,((w \ v5) * K(z,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(18010,a,19061,a)].">
      <j1 rule="hyper" parents="18010 19061"/>
    </justification>
  </clause>

  <clause id="19063">
    <literal><![CDATA[
      K(x,K(y,z) * ((((u * w) \ u) * v5) \ u)) = K(x,K(y,z) * ((w \ v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(334,a,18071,a(flip),b,19062,a),flip(a)].">
      <j1 rule="hyper" parents="334 18071 19062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19065">
    <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(334,a,19063,a(flip),b,19038,a),flip(a)].">
      <j1 rule="hyper" parents="334 19063 19038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19066">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ v5) = K(x,K(w,u) * ((y \ z) \ v5))
    ]]></literal>
    <justification jstring="[hyper(16452,a,19065,a)].">
      <j1 rule="hyper" parents="16452 19065"/>
    </justification>
  </clause>

  <clause id="19067">
    <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(17817(a,2),18971(a,1,2))].">
      <j1 rule="para" parents="17817 18971"/>
    </justification>
  </clause>

  <clause id="19068">
    <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(17689(a,1),18972(a,1,2,1))].">
      <j1 rule="para" parents="17689 18972"/>
    </justification>
  </clause>

  <clause id="19069">
    <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(17761(a,1),19068(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17761 19068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19070">
    <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(334,a,14215,a(flip),b,19069,a),flip(a)].">
      <j1 rule="hyper" parents="334 14215 19069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19072">
    <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(14588(a,2),19070(a,1,1))].">
      <j1 rule="para" parents="14588 19070"/>
    </justification>
  </clause>

  <clause id="19073">
    <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(15279(a,2),19072(a,2,2))].">
      <j1 rule="para" parents="15279 19072"/>
    </justification>
  </clause>

  <clause id="19074">
    <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,18858,a(flip),b,19073,a)].">
      <j1 rule="hyper" parents="58 18858 19073"/>
    </justification>
  </clause>

  <clause id="19075">
    <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(334,a,18251,a(flip),b,19074,a),flip(a)].">
      <j1 rule="hyper" parents="334 18251 19074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19076">
    <literal><![CDATA[
      L(K(x,y) * z,u,K(w,v5)) = K(x,y) * L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(14080(a,1),19075(a,1,1))].">
      <j1 rule="para" parents="14080 19075"/>
    </justification>
  </clause>

  <clause id="19077">
    <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(334,a,15432,a(flip),b,19076,a),flip(a)].">
      <j1 rule="hyper" parents="334 15432 19076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19078">
    <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(19076(a,2),17210(a,1,2,1))].">
      <j1 rule="para" parents="19076 17210"/>
    </justification>
  </clause>

  <clause id="19079">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,T(u,y)) / y) = (x / (y \ 1)) * (y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15036,a(flip),b,18974,a),flip(a)].">
      <j1 rule="hyper" parents="58 15036 18974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19080">
    <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(17512(a,1),18980(a,1,2,2))].">
      <j1 rule="para" parents="17512 18980"/>
    </justification>
  </clause>

  <clause id="19081">
    <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,6080,a(flip),b,19067,a)].">
      <j1 rule="hyper" parents="58 6080 19067"/>
    </justification>
  </clause>

  <clause id="19082">
    <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(8019(a,1),19081(a,1,3))].">
      <j1 rule="para" parents="8019 19081"/>
    </justification>
  </clause>

  <clause id="19083">
    <literal><![CDATA[
      L(x,K(y,K(z,u)) * w,v5) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(17570,a,19082,a),flip(a)].">
      <j1 rule="hyper" parents="17570 19082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19084">
    <literal><![CDATA[
      L(x,K(y,K(z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(19082(a,1),17569(a,1)),flip(b)].">
      <j1 rule="para" parents="19082 17569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19087">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),w) = L(x,K(y,z),w)
    ]]></literal>
    <justification jstring="[para(7409(a,1),19083(a,1,2))].">
      <j1 rule="para" parents="7409 19083"/>
    </justification>
  </clause>

  <clause id="19088">
    <literal><![CDATA[
      R(x,K(y,z),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,17200,a(flip),b,19087,a)].">
      <j1 rule="hyper" parents="58 17200 19087"/>
    </justification>
  </clause>

  <clause id="19089">
    <literal><![CDATA[
      L((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(6542,a,19088,a),flip(a)].">
      <j1 rule="hyper" parents="6542 19088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19091">
    <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,16121,a,b,19088,a)].">
      <j1 rule="hyper" parents="58 16121 19088"/>
    </justification>
  </clause>

  <clause id="19092">
    <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,9770,a(flip),b,19088,a),flip(a)].">
      <j1 rule="hyper" parents="58 9770 19088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19093">
    <literal><![CDATA[
      L(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(19088(a,1),10141(a,1,1))].">
      <j1 rule="para" parents="19088 10141"/>
    </justification>
  </clause>

  <clause id="19094">
    <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(19088(a,1),15177(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="19088 15177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19095">
    <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(19088(a,1),15225(a,1,1,2))].">
      <j1 rule="para" parents="19088 15225"/>
    </justification>
  </clause>

  <clause id="19096">
    <literal><![CDATA[
      T(x,y \ L(y,K(z,u),w)) = x
    ]]></literal>
    <justification jstring="[para(19088(a,1),18324(a,1,2,2))].">
      <j1 rule="para" parents="19088 18324"/>
    </justification>
  </clause>

  <clause id="19097">
    <literal><![CDATA[
      T(x \ L(x,K(y,z),u),w) = x \ L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(49,a,19096,a)].">
      <j1 rule="hyper" parents="49 19096"/>
    </justification>
  </clause>

  <clause id="19098">
    <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(7409(a,1),19084(a,1,2))].">
      <j1 rule="para" parents="7409 19084"/>
    </justification>
  </clause>

  <clause id="19099">
    <literal><![CDATA[
      R(x,K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(17200(a,1),19098(a,1))].">
      <j1 rule="para" parents="17200 19098"/>
    </justification>
  </clause>

  <clause id="19100">
    <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(17712(a,2),19099(a,1))].">
      <j1 rule="para" parents="17712 19099"/>
    </justification>
  </clause>

  <clause id="19101">
    <literal><![CDATA[
      L(x * K(y,z),K(z,y),u) = (x * u) / (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(6(a,1),19089(a,1,1,1))].">
      <j1 rule="para" parents="6 19089"/>
    </justification>
  </clause>

  <clause id="19102">
    <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(19101(a,1),6725(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19101 6725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19103">
    <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(18312(a,1),19094(a,1,1,2))].">
      <j1 rule="para" parents="18312 19094"/>
    </justification>
  </clause>

  <clause id="19104">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,y),u) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(19098,a,19092,a)].">
      <j1 rule="hyper" parents="19098 19092"/>
    </justification>
  </clause>

  <clause id="19105">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,y),u) = (x * (u * K(y,z))) / u
    ]]></literal>
    <justification jstring="[hyper(334,a,14895,a,b,19104,a),flip(a)].">
      <j1 rule="hyper" parents="334 14895 19104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19107">
    <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(19105(a,2),14896(a,1))].">
      <j1 rule="para" parents="19105 14896"/>
    </justification>
  </clause>

  <clause id="19108">
    <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(16356(a,2),19107(a,1))].">
      <j1 rule="para" parents="16356 19107"/>
    </justification>
  </clause>

  <clause id="19109">
    <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(334,a,19087,a(flip),b,19091,a),flip(a)].">
      <j1 rule="hyper" parents="334 19087 19091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19111">
    <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,19016,a(flip),b,19109,a)].">
      <j1 rule="hyper" parents="58 19016 19109"/>
    </justification>
  </clause>

  <clause id="19112">
    <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(10109(a,1),19077(a,1,1))].">
      <j1 rule="para" parents="10109 19077"/>
    </justification>
  </clause>

  <clause id="19113">
    <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(12165(a,1),19112(a,1,1))].">
      <j1 rule="para" parents="12165 19112"/>
    </justification>
  </clause>

  <clause id="19114">
    <literal><![CDATA[
      T(a(x,y,z) \ u,K(w,v5)) = a(x,y,z) \ T(u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(15306,a,19113,a),flip(a)].">
      <j1 rule="hyper" parents="15306 19113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19115">
    <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(334,a,16230,a(flip),b,19114,a),flip(a)].">
      <j1 rule="hyper" parents="334 16230 19114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19116">
    <literal><![CDATA[
      x * K(y,K(z,x * a(u,w,v5))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),19115(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 19115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19117">
    <literal><![CDATA[
      K(x,K(y,z * a(u,w,v5))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(29,a,8063,a,b,19116,a),flip(a)].">
      <j1 rule="hyper" parents="29 8063 19116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19118">
    <literal><![CDATA[
      K(x,K(y,a(z,u,w) * v5)) = K(x,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(16239,a,19117,a)].">
      <j1 rule="hyper" parents="16239 19117"/>
    </justification>
  </clause>

  <clause id="19119">
    <literal><![CDATA[
      T(x,K(y,z * a(u,w,v5))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,19117,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 19117 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19120">
    <literal><![CDATA[
      K(x,K(y,a(z,u,w) * v5)) = K(x,y) * K(y,T(x,v5))
    ]]></literal>
    <justification jstring="[hyper(334,a,8072,a,b,19118,a),flip(a)].">
      <j1 rule="hyper" parents="334 8072 19118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19121">
    <literal><![CDATA[
      T(x,K(y,(z * u) * w)) = T(x,K(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(80(a,1),19119(a,1,2,2))].">
      <j1 rule="para" parents="80 19119"/>
    </justification>
  </clause>

  <clause id="19122">
    <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(19119(a,1),15465(a,1,2,1,2))].">
      <j1 rule="para" parents="19119 15465"/>
    </justification>
  </clause>

  <clause id="19123">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w) * v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(8354,a,19120,a)].">
      <j1 rule="hyper" parents="8354 19120"/>
    </justification>
  </clause>

  <clause id="19124">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w)) = K(x,T(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(14769(a,1),19123(a,1,2,2))].">
      <j1 rule="para" parents="14769 19123"/>
    </justification>
  </clause>

  <clause id="19125">
    <literal><![CDATA[
      K(x,T(y,T(z * u,w) * v5)) = K(x,T(y,u * (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16828,a,b,19124,a)].">
      <j1 rule="hyper" parents="58 16828 19124"/>
    </justification>
  </clause>

  <clause id="19127">
    <literal><![CDATA[
      K(x,T(y,T(z * a(u,w,v5),v6) * v7)) = K(x,T(y,z * v7))
    ]]></literal>
    <justification jstring="[hyper(334,a,19123,a(flip),b,19125,a),flip(a)].">
      <j1 rule="hyper" parents="334 19123 19125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19128">
    <literal><![CDATA[
      K(x,T(y,(z * a(u,w,v5)) * v6)) = K(x,T(y,z * v6))
    ]]></literal>
    <justification jstring="[hyper(16822,a,19127,a)].">
      <j1 rule="hyper" parents="16822 19127"/>
    </justification>
  </clause>

  <clause id="19129">
    <literal><![CDATA[
      K(x,T(y,z * (a(u,w,v5) * v6))) = K(x,T(y,z * v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,19124,a(flip),b,19128,a)].">
      <j1 rule="hyper" parents="58 19124 19128"/>
    </justification>
  </clause>

  <clause id="19130">
    <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(19119(a,1),19122(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19119 19122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19131">
    <literal><![CDATA[
      T(x,K(y * a(z,u,w),v5) * v6) = T(x,K(y,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(334,a,15465,a(flip),b,19130,a),flip(a)].">
      <j1 rule="hyper" parents="334 15465 19130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19133">
    <literal><![CDATA[
      T(x,K(a(y,z,u) \ w,v5) * v6) = T(x,K(w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,17089,a,b,19131,a)].">
      <j1 rule="hyper" parents="58 17089 19131"/>
    </justification>
  </clause>

  <clause id="19134">
    <literal><![CDATA[
      T(x,T(y,z * a(u,w,v5)) \ v6) = T(x,K(z,y) * (y \ v6))
    ]]></literal>
    <justification jstring="[para(5392(a,1),19131(a,1,2))].">
      <j1 rule="para" parents="5392 19131"/>
    </justification>
  </clause>

  <clause id="19135">
    <literal><![CDATA[
      K(K(a(x,y,z) \ u,w) * v5,v6) = v6 / T(v6,K(u,w) * v5)
    ]]></literal>
    <justification jstring="[para(19133(a,1),5062(a,2,2))].">
      <j1 rule="para" parents="19133 5062"/>
    </justification>
  </clause>

  <clause id="19136">
    <literal><![CDATA[
      T(x,T(y,z * a(u,w,v5)) \ v6) = T(x,T(y,z) \ v6)
    ]]></literal>
    <justification jstring="[para(5392(a,1),19134(a,2,2))].">
      <j1 rule="para" parents="5392 19134"/>
    </justification>
  </clause>

  <clause id="19137">
    <literal><![CDATA[
      K(K(a(x,y,z) \ u,w) * v5,v6) = K(K(u,w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(334,a,5062,a,b,19135,a),flip(a)].">
      <j1 rule="hyper" parents="334 5062 19135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19138">
    <literal><![CDATA[
      K(K(a(x,y,z) \ u,w) * v5,v6) = K(v5 * K(w,u),v6)
    ]]></literal>
    <justification jstring="[hyper(334,a,16215,a(flip),b,19137,a),flip(a)].">
      <j1 rule="hyper" parents="334 16215 19137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19139">
    <literal><![CDATA[
      K(K(x,a(y,z,u) \ w) * v5,v6) = K(v5 * K(x,w),v6)
    ]]></literal>
    <justification jstring="[hyper(16306,a,19138,a)].">
      <j1 rule="hyper" parents="16306 19138"/>
    </justification>
  </clause>

  <clause id="19140">
    <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),19138(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 19138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19141">
    <literal><![CDATA[
      K(x * K(y * a(z,u,w),v5),v6) = K(K(y,v5) * x,v6)
    ]]></literal>
    <justification jstring="[hyper(16546,a,19140,a)].">
      <j1 rule="hyper" parents="16546 19140"/>
    </justification>
  </clause>

  <clause id="19142">
    <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),19078(a,1,2))].">
      <j1 rule="para" parents="20 19078"/>
    </justification>
  </clause>

  <clause id="19143">
    <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(17700(a,2),19080(a,1,1))].">
      <j1 rule="para" parents="17700 19080"/>
    </justification>
  </clause>

  <clause id="19144">
    <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(15298(a,1),19142(a,1,2))].">
      <j1 rule="para" parents="15298 19142"/>
    </justification>
  </clause>

  <clause id="19145">
    <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(16331,a,19144,a),flip(a)].">
      <j1 rule="hyper" parents="16331 19144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19146">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w) * v5)) = K(x,T(y,z * v5))
    ]]></literal>
    <justification jstring="[hyper(17644,a,19145,a),flip(a)].">
      <j1 rule="hyper" parents="17644 19145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19147">
    <literal><![CDATA[
      K(x,T(y,z * L(u,w,v5))) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(16150,a,19146,a)].">
      <j1 rule="hyper" parents="16150 19146"/>
    </justification>
  </clause>

  <clause id="19149">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * (z * w))) = K(x,T(y,w * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16966,a(flip),b,19146,a)].">
      <j1 rule="hyper" parents="58 16966 19146"/>
    </justification>
  </clause>

  <clause id="19150">
    <literal><![CDATA[
      K(x,T(y,z * L(u,w,v5))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(334,a,15955,a,b,19147,a),flip(a)].">
      <j1 rule="hyper" parents="334 15955 19147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19151">
    <literal><![CDATA[
      T(x * K(y,T(x,z * u)),y) = T(x,K(y,z * L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(19150(a,1),8404(a,1,1,2))].">
      <j1 rule="para" parents="19150 8404"/>
    </justification>
  </clause>

  <clause id="19152">
    <literal><![CDATA[
      K(x,T(y,(z * u) * (z \ w))) = K(x,T(y,u * w))
    ]]></literal>
    <justification jstring="[hyper(16150,a,19149,a)].">
      <j1 rule="hyper" parents="16150 19149"/>
    </justification>
  </clause>

  <clause id="19154">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * w)) = K(x,T(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[para(5(a,1),19152(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 19152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19155">
    <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,17134,a(flip),b,19154,a),flip(a)].">
      <j1 rule="hyper" parents="58 17134 19154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19156">
    <literal><![CDATA[
      T(x,K(y,z * L(u,w,v5))) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(8632,a,19151,a),flip(a)].">
      <j1 rule="hyper" parents="8632 19151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19157">
    <literal><![CDATA[
      T(x,K(y,z * ((u * w) \ v5))) = T(x,K(y,z * (w \ (u \ v5))))
    ]]></literal>
    <justification jstring="[para(311(a,1),19156(a,1,2,2,2))].">
      <j1 rule="para" parents="311 19156"/>
    </justification>
  </clause>

  <clause id="19158">
    <literal><![CDATA[
      T(x,K(y,z * ((u * z) \ w))) = T(x,K(y,u \ w))
    ]]></literal>
    <justification jstring="[para(5(a,1),19157(a,2,2,2))].">
      <j1 rule="para" parents="5 19157"/>
    </justification>
  </clause>

  <clause id="19159">
    <literal><![CDATA[
      T(x,K(y,(z / u) \ w)) = T(x,K(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[para(7(a,1),19158(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 19158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19160">
    <literal><![CDATA[
      T(x,K(y,z \ (u * w))) = T(x,K(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(17929,a,19159,a)].">
      <j1 rule="hyper" parents="17929 19159"/>
    </justification>
  </clause>

  <clause id="19161">
    <literal><![CDATA[
      T(x,K(y,z \ (u \ w))) = T(x,K(y,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(17726,a,19160,a)].">
      <j1 rule="hyper" parents="17726 19160"/>
    </justification>
  </clause>

  <clause id="19162">
    <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,18163,a(flip),b,19161,a),flip(a)].">
      <j1 rule="hyper" parents="58 18163 19161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19163">
    <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,16879,a(flip),b,19162,a)].">
      <j1 rule="hyper" parents="58 16879 19162"/>
    </justification>
  </clause>

  <clause id="19165">
    <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,8415,a(flip),b,19163,a),flip(a)].">
      <j1 rule="hyper" parents="58 8415 19163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19166">
    <literal><![CDATA[
      x * K(y,T(x,z \ (u \ w))) = x * K(y,T(x,u * (w \ z)))
    ]]></literal>
    <justification jstring="[para(17867(a,1),19165(a,1,2))].">
      <j1 rule="para" parents="17867 19165"/>
    </justification>
  </clause>

  <clause id="19167">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ w))) = K(x,T(y,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(287,a,19166,a),flip(a)].">
      <j1 rule="hyper" parents="287 19166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19170">
    <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(19167(a,1),17934(a,1))].">
      <j1 rule="para" parents="19167 17934"/>
    </justification>
  </clause>

  <clause id="19171">
    <literal><![CDATA[
      K(x * K(y \ (z \ x),y),T(u,x \ z)) = K(((z * y) \ x) * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(19170,a,19155,a)].">
      <j1 rule="hyper" parents="19170 19155"/>
    </justification>
  </clause>

  <clause id="19172">
    <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,18413,a(flip),b,19171,a)].">
      <j1 rule="hyper" parents="58 18413 19171"/>
    </justification>
  </clause>

  <clause id="19173">
    <literal><![CDATA[
      K(x * K(y \ (x / z),y),T(u,z)) = K(((z * y) \ x) * (y * z),u)
    ]]></literal>
    <justification jstring="[para(11422(a,1),19172(a,1,1))].">
      <j1 rule="para" parents="11422 19172"/>
    </justification>
  </clause>

  <clause id="19174">
    <literal><![CDATA[
      K(K(x / y,z) * x,T(u,y)) = K(((y * z) \ x) * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(16218,a,19173,a)].">
      <j1 rule="hyper" parents="16218 19173"/>
    </justification>
  </clause>

  <clause id="19175">
    <literal><![CDATA[
      K(((x * y) \ z) * (y * x),u) = K(z * K(x \ z,y),T(u,x))
    ]]></literal>
    <justification jstring="[para(6649(a,1),19174(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6649 19174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19176">
    <literal><![CDATA[
      K(((x * y) \ z) * (y * x),u) = K(x * T(z / x,y),u)
    ]]></literal>
    <justification jstring="[hyper(334,a,12534,a(flip),b,19175,a),flip(a)].">
      <j1 rule="hyper" parents="334 12534 19175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19177">
    <literal><![CDATA[
      K(K(x,y) * z,T(u,x * y)) = K(y * T(z / y,x),u)
    ]]></literal>
    <justification jstring="[hyper(12585,a,19176,a)].">
      <j1 rule="hyper" parents="12585 19176"/>
    </justification>
  </clause>

  <clause id="19178">
    <literal><![CDATA[
      K(x \ T(y * x,z),u) = K(x * T(y / x,z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16995,a(flip),b,19177,a)].">
      <j1 rule="hyper" parents="58 16995 19177"/>
    </justification>
  </clause>

  <clause id="19179">
    <literal><![CDATA[
      K(x * K(x * y,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[hyper(16597,a,19178,a)].">
      <j1 rule="hyper" parents="16597 19178"/>
    </justification>
  </clause>

  <clause id="19180">
    <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(19179(a,1),16944(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="19179 16944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19181">
    <literal><![CDATA[
      T(x,T(y * z,u) / T(z,y)) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,5518,a(flip),b,19180,a),flip(a)].">
      <j1 rule="hyper" parents="334 5518 19180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19182">
    <literal><![CDATA[
      T(x,T(y * K(y * z,u),z)) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[para(16942(a,1),19181(a,1,2))].">
      <j1 rule="para" parents="16942 19181"/>
    </justification>
  </clause>

  <clause id="19183">
    <literal><![CDATA[
      T(x,y \ T(z * y,u)) = T(x,y * T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16472,a(flip),b,19182,a)].">
      <j1 rule="hyper" parents="58 16472 19182"/>
    </justification>
  </clause>

  <clause id="19184">
    <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,16989,a(flip),b,19183,a),flip(a)].">
      <j1 rule="hyper" parents="58 16989 19183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19185">
    <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(18623,a,19184,a)].">
      <j1 rule="hyper" parents="18623 19184"/>
    </justification>
  </clause>

  <clause id="19186">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),y)) = T(x,T(y,z) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(18634,a,19185,a)].">
      <j1 rule="hyper" parents="18634 19185"/>
    </justification>
  </clause>

  <clause id="19187">
    <literal><![CDATA[
      T(x,T(y,z) \ T(z * y,u)) = T(x,T(z / y,u) * y)
    ]]></literal>
    <justification jstring="[hyper(12552,a,19186,a),flip(a)].">
      <j1 rule="hyper" parents="12552 19186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19188">
    <literal><![CDATA[
      T(x,T(y,z) \ T(z * y,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(465(a,1),19187(a,2,2))].">
      <j1 rule="para" parents="465 19187"/>
    </justification>
  </clause>

  <clause id="19189">
    <literal><![CDATA[
      T(x,y \ T(z * T(y,z),u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(18966,a,19188,a)].">
      <j1 rule="hyper" parents="18966 19188"/>
    </justification>
  </clause>

  <clause id="19190">
    <literal><![CDATA[
      T(x,y \ T(y * z,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(105(a,1),19189(a,1,2,2,1))].">
      <j1 rule="para" parents="105 19189"/>
    </justification>
  </clause>

  <clause id="19191">
    <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(17845,a,19143,a)].">
      <j1 rule="hyper" parents="17845 19143"/>
    </justification>
  </clause>

  <clause id="19192">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w)) * v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,18760,a(flip),b,19191,a),flip(a)].">
      <j1 rule="hyper" parents="58 18760 19191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19193">
    <literal><![CDATA[
      L(x,y,z * T(u,K(w,v5))) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(17659,a,19192,a)].">
      <j1 rule="hyper" parents="17659 19192"/>
    </justification>
  </clause>

  <clause id="19195">
    <literal><![CDATA[
      L(x,y,z / (K(u,w) / v5)) = L(x,y,z / (v5 \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17778,a(flip),b,19192,a),flip(a)].">
      <j1 rule="hyper" parents="58 17778 19192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19196">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w)) \ v5) = L(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(5337(a,1),19192(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5337 19192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19197">
    <literal><![CDATA[
      L(x,y,z * K(u,T(w,v5))) = L(x,y,z * K(u,w))
    ]]></literal>
    <justification jstring="[para(16340(a,1),19192(a,1,3))].">
      <j1 rule="para" parents="16340 19192"/>
    </justification>
  </clause>

  <clause id="19198">
    <literal><![CDATA[
      L(x,y,z * (T(u,T(w,v5)) / v5)) = L(x,y,z * (T(u,w) / v5))
    ]]></literal>
    <justification jstring="[para(8417(a,1),19193(a,1,3,2))].">
      <j1 rule="para" parents="8417 19193"/>
    </justification>
  </clause>

  <clause id="19199">
    <literal><![CDATA[
      L(x,y,(K(z,u) / w) \ v5) = L(x,y,(w \ K(z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,12911,a(flip),b,19196,a),flip(a)].">
      <j1 rule="hyper" parents="58 12911 19196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19200">
    <literal><![CDATA[
      L(x,y,T(K(z,u) * w,v5)) = L(x,y,T(w,v5) * K(z,u))
    ]]></literal>
    <justification jstring="[para(15221(a,1),19197(a,1,3))].">
      <j1 rule="para" parents="15221 19197"/>
    </justification>
  </clause>

  <clause id="19201">
    <literal><![CDATA[
      K(x,L(y,z,u / (w \ K(v5,v6)))) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[para(19195(a,1),18875(a,1,2))].">
      <j1 rule="para" parents="19195 18875"/>
    </justification>
  </clause>

  <clause id="19202">
    <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(19199(a,1),14937(a,1,2,2,2))].">
      <j1 rule="para" parents="19199 14937"/>
    </justification>
  </clause>

  <clause id="19203">
    <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(19199(a,1),17142(a,1,2,2))].">
      <j1 rule="para" parents="19199 17142"/>
    </justification>
  </clause>

  <clause id="19204">
    <literal><![CDATA[
      L(x,y,T(K(z,u) * w,v5)) = L(x,y,K(z,u) * T(w,v5))
    ]]></literal>
    <justification jstring="[hyper(334,a,17574,a,b,19200,a),flip(a)].">
      <j1 rule="hyper" parents="334 17574 19200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19205">
    <literal><![CDATA[
      K(x,L(y,z,(u \ K(w,v5)) \ v6)) = K(x,L(y,z,u * v6))
    ]]></literal>
    <justification jstring="[hyper(17653,a,19201,a)].">
      <j1 rule="hyper" parents="17653 19201"/>
    </justification>
  </clause>

  <clause id="19206">
    <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(334,a,19103,a(flip),b,19204,a),flip(a)].">
      <j1 rule="hyper" parents="334 19103 19204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19207">
    <literal><![CDATA[
      K(x,L(y,z,(u \ K(w,v5)) \ v6)) = K(x,L(y,z,v6 * u))
    ]]></literal>
    <justification jstring="[hyper(334,a,17647,a,b,19205,a),flip(a)].">
      <j1 rule="hyper" parents="334 17647 19205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19208">
    <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(19207(a,2),17696(a,1))].">
      <j1 rule="para" parents="19207 17696"/>
    </justification>
  </clause>

  <clause id="19209">
    <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,14463,a(flip),b,19206,a)].">
      <j1 rule="hyper" parents="58 14463 19206"/>
    </justification>
  </clause>

  <clause id="19210">
    <literal><![CDATA[
      a(x,K(y,z),T(u,w)) = a(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(19095,a,19209,a),flip(a)].">
      <j1 rule="hyper" parents="19095 19209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19212">
    <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(19209(a,1),19095(a,1))].">
      <j1 rule="para" parents="19209 19095"/>
    </justification>
  </clause>

  <clause id="19213">
    <literal><![CDATA[
      x * K(y,L(T(z,u \ 1),x,u * x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(19205(a,1),19203(a,1,2))].">
      <j1 rule="para" parents="19205 19203"/>
    </justification>
  </clause>

  <clause id="19214">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u * x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(8901(a,1),19213(a,1,2))].">
      <j1 rule="para" parents="8901 19213"/>
    </justification>
  </clause>

  <clause id="19216">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u * x)) = (x / (1 / u)) * (K(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(334,a,14944,a(flip),b,19214,a),flip(a)].">
      <j1 rule="hyper" parents="334 14944 19214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19217">
    <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(13392(a,1),17861(a,1,2))].">
      <j1 rule="para" parents="13392 17861"/>
    </justification>
  </clause>

  <clause id="19218">
    <literal><![CDATA[
      K(x,y / (T(z * u,z) \ w)) = K(x,y / ((u * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17860,a(flip),b,19217,a),flip(a)].">
      <j1 rule="hyper" parents="58 17860 19217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19219">
    <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,18956,a(flip),b,18187,a)].">
      <j1 rule="hyper" parents="58 18956 18187"/>
    </justification>
  </clause>

  <clause id="19220">
    <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,13421,a(flip),b,18236,a)].">
      <j1 rule="hyper" parents="58 13421 18236"/>
    </justification>
  </clause>

  <clause id="19221">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) * a(x,y,z) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(14946(a,1),18768(a,1,2))].">
      <j1 rule="para" parents="14946 18768"/>
    </justification>
  </clause>

  <clause id="19222">
    <literal><![CDATA[
      a(x,y,K(z,u)) * a(x,y,z) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(11175(a,1),19221(a,1,1))].">
      <j1 rule="para" parents="11175 19221"/>
    </justification>
  </clause>

  <clause id="19224">
    <literal><![CDATA[
      a(x,y,z) * a(x,y,K(z,u)) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(17552,a,19222,a)].">
      <j1 rule="hyper" parents="17552 19222"/>
    </justification>
  </clause>

  <clause id="19225">
    <literal><![CDATA[
      a(x,y,T(z,u)) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(13736,a,19222,a),flip(a)].">
      <j1 rule="hyper" parents="13736 19222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19226">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,T(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,19222,a(flip),b,17549,a(flip))].">
      <j1 rule="hyper" parents="116 19222 17549"/>
    </justification>
  </clause>

  <clause id="19227">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * L(z,y,K(u,x))) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,15320,a,b,19225,a)].">
      <j1 rule="hyper" parents="334 15320 19225"/>
    </justification>
  </clause>

  <clause id="19228">
    <literal><![CDATA[
      a(x,y,T(z,K(u,w))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,17608,a(flip),b,19225,a),flip(a)].">
      <j1 rule="hyper" parents="334 17608 19225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19229">
    <literal><![CDATA[
      a(x,y,T(z,a(u,w,v5) \ 1)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,13741,a(flip),b,19225,a),flip(a)].">
      <j1 rule="hyper" parents="334 13741 19225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19231">
    <literal><![CDATA[
      T(x,a(y,z,u)) / a(y,z,u) = x / a(y,z,T(u,x))
    ]]></literal>
    <justification jstring="[para(19225(a,2),4488(a,2,2))].">
      <j1 rule="para" parents="19225 4488"/>
    </justification>
  </clause>

  <clause id="19232">
    <literal><![CDATA[
      a(x,y,T(z,T(u,w))) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(7688(a,1),19228(a,1,3))].">
      <j1 rule="para" parents="7688 19228"/>
    </justification>
  </clause>

  <clause id="19233">
    <literal><![CDATA[
      a(x,y,T(z,T(x * y,u))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,14534,a(flip),b,19232,a),flip(a)].">
      <j1 rule="hyper" parents="334 14534 19232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19234">
    <literal><![CDATA[
      a(x,y,T(z,y * x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(12541(a,1),19233(a,1,3))].">
      <j1 rule="para" parents="12541 19233"/>
    </justification>
  </clause>

  <clause id="19235">
    <literal><![CDATA[
      a(x,y,z) \ ((y * x) * T(z,x * T(y,x))) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(19234(a,1),15072(a,1,1))].">
      <j1 rule="para" parents="19234 15072"/>
    </justification>
  </clause>

  <clause id="19236">
    <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),19235(a,1,2,2,2))].">
      <j1 rule="para" parents="105 19235"/>
    </justification>
  </clause>

  <clause id="19237">
    <literal><![CDATA[
      a(x,y,z) \ (z * (y * x)) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,228,a(flip),b,19236,a)].">
      <j1 rule="hyper" parents="58 228 19236"/>
    </justification>
  </clause>

  <clause id="19238">
    <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,18450,a(flip),b,19219,a)].">
      <j1 rule="hyper" parents="58 18450 19219"/>
    </justification>
  </clause>

  <clause id="19240">
    <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,18173,a(flip),b,19238,a)].">
      <j1 rule="hyper" parents="58 18173 19238"/>
    </justification>
  </clause>

  <clause id="19242">
    <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(17641(a,1),18409(a,1))].">
      <j1 rule="para" parents="17641 18409"/>
    </justification>
  </clause>

  <clause id="19243">
    <literal><![CDATA[
      T(x,y * K(z,u \ w)) = T(x,y * K(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(19242,a,18955,a),flip(a)].">
      <j1 rule="hyper" parents="19242 18955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19244">
    <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(19243(a,1),15049(a,1,1,2))].">
      <j1 rule="para" parents="19243 15049"/>
    </justification>
  </clause>

  <clause id="19245">
    <literal><![CDATA[
      K(x * y,z * K(u,w \ v5)) = K(x * y,z * K(u,v5 * w))
    ]]></literal>
    <justification jstring="[hyper(15050,a,19244,a),flip(a)].">
      <j1 rule="hyper" parents="15050 19244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19246">
    <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(19244(a,1),15050(a,1))].">
      <j1 rule="para" parents="19244 15050"/>
    </justification>
  </clause>

  <clause id="19247">
    <literal><![CDATA[
      K(K(x,y) * (z \ (u * K(x,y))),w * K(v5,u * z)) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[hyper(18091,a,19245,a),flip(a)].">
      <j1 rule="hyper" parents="18091 19245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19248">
    <literal><![CDATA[
      K(x \ y,z * K(u,y * x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(18612,a,19247,a)].">
      <j1 rule="hyper" parents="18612 19247"/>
    </justification>
  </clause>

  <clause id="19249">
    <literal><![CDATA[
      K(x * K(y,z * u),u \ z) = w / (K(u \ z,x) * w)
    ]]></literal>
    <justification jstring="[para(19248(a,1),5403(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="19248 5403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19250">
    <literal><![CDATA[
      K(x * K(y,z * u),u \ z) = K(x,u \ z)
    ]]></literal>
    <justification jstring="[hyper(334,a,17900,a(flip),b,19249,a),flip(a)].">
      <j1 rule="hyper" parents="334 17900 19249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19251">
    <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(17128,a,19250,a)].">
      <j1 rule="hyper" parents="17128 19250"/>
    </justification>
  </clause>

  <clause id="19252">
    <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(16507,a,19250,a)].">
      <j1 rule="hyper" parents="16507 19250"/>
    </justification>
  </clause>

  <clause id="19253">
    <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(10667(a,1),19250(a,1,1,2,2))].">
      <j1 rule="para" parents="10667 19250"/>
    </justification>
  </clause>

  <clause id="19254">
    <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(16478(a,1),19250(a,1,1,2))].">
      <j1 rule="para" parents="16478 19250"/>
    </justification>
  </clause>

  <clause id="19255">
    <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,17065,a(flip),b,19251,a)].">
      <j1 rule="hyper" parents="58 17065 19251"/>
    </justification>
  </clause>

  <clause id="19258">
    <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,17065,a(flip),b,19252,a)].">
      <j1 rule="hyper" parents="58 17065 19252"/>
    </justification>
  </clause>

  <clause id="19260">
    <literal><![CDATA[
      K(x,y \ T(z,u \ w)) = K(x,y \ T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,19255,a(flip),b,19258,a)].">
      <j1 rule="hyper" parents="58 19255 19258"/>
    </justification>
  </clause>

  <clause id="19261">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w / v5))) = K(x,y \ T(z,(u * v5) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,18246,a(flip),b,19260,a)].">
      <j1 rule="hyper" parents="58 18246 19260"/>
    </justification>
  </clause>

  <clause id="19262">
    <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(19237(a,1),19260(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="19237 19260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19263">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) * v5)) = K(x,y \ T(z,u * (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19260,a(flip),b,19261,a),flip(a)].">
      <j1 rule="hyper" parents="58 19260 19261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19264">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) * v5)) = K(x,y \ T(z,u * (w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(334,a,18711,a(flip),b,19263,a),flip(a)].">
      <j1 rule="hyper" parents="334 18711 19263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19265">
    <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(18700(a,1),19262(a,2,2,2))].">
      <j1 rule="para" parents="18700 19262"/>
    </justification>
  </clause>

  <clause id="19266">
    <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(334,a,19264,a(flip),b,19265,a),flip(a)].">
      <j1 rule="hyper" parents="334 19264 19265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19267">
    <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,19129,a(flip),b,17679,a)].">
      <j1 rule="hyper" parents="58 19129 17679"/>
    </justification>
  </clause>

  <clause id="19269">
    <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(17793(a,2),17826(a,1,2,1))].">
      <j1 rule="para" parents="17793 17826"/>
    </justification>
  </clause>

  <clause id="19270">
    <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(17841(a,1),17826(a,1,2))].">
      <j1 rule="para" parents="17841 17826"/>
    </justification>
  </clause>

  <clause id="19271">
    <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(17512(a,1),17827(a,1,1,2))].">
      <j1 rule="para" parents="17512 17827"/>
    </justification>
  </clause>

  <clause id="19272">
    <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(18052,a,19136,a),flip(a)].">
      <j1 rule="hyper" parents="18052 19136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19273">
    <literal><![CDATA[
      T(x,y / T(z,T(a(u,w,v5),v6) * v7)) = T(x,y / T(z,v7))
    ]]></literal>
    <justification jstring="[hyper(16140,a,19272,a),flip(a)].">
      <j1 rule="hyper" parents="16140 19272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19274">
    <literal><![CDATA[
      T(x,y / T(z,u * a(w,v5,v6))) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(12577(a,1),19273(a,1,2,2))].">
      <j1 rule="para" parents="12577 19273"/>
    </justification>
  </clause>

  <clause id="19275">
    <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(19274(a,1),7446(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="19274 7446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19276">
    <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(19275(a,2),7973(a,1))].">
      <j1 rule="para" parents="19275 7973"/>
    </justification>
  </clause>

  <clause id="19277">
    <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(19276,a,19267,a)].">
      <j1 rule="hyper" parents="19276 19267"/>
    </justification>
  </clause>

  <clause id="19278">
    <literal><![CDATA[
      K(x,y \ T(z,a(u,w,v5) * v6)) = K(x,y \ T(z,v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,16735,a(flip),b,19277,a),flip(a)].">
      <j1 rule="hyper" parents="58 16735 19277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19279">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w \ v5))) = K(x,y \ T(z,u * (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19266,a(flip),b,19278,a)].">
      <j1 rule="hyper" parents="58 19266 19278"/>
    </justification>
  </clause>

  <clause id="19281">
    <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,18215,a,b,18214,a)].">
      <j1 rule="hyper" parents="58 18215 18214"/>
    </justification>
  </clause>

  <clause id="19282">
    <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(18219(a,1),18214(a,1,1))].">
      <j1 rule="para" parents="18219 18214"/>
    </justification>
  </clause>

  <clause id="19283">
    <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(17684,a,18785,a)].">
      <j1 rule="hyper" parents="17684 18785"/>
    </justification>
  </clause>

  <clause id="19286">
    <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,14887,a(flip),b,19283,a),flip(a)].">
      <j1 rule="hyper" parents="58 14887 19283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19287">
    <literal><![CDATA[
      K(x,(y \ z) / (u * T(z \ (y \ z),z))) = K(x,((y \ 1) * z) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(334,a,18269,a(flip),b,19286,a),flip(a)].">
      <j1 rule="hyper" parents="334 18269 19286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19288">
    <literal><![CDATA[
      K(x,(y \ z) / (u * ((y \ z) / z))) = K(x,((y \ 1) * z) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18189,a(flip),b,19287,a)].">
      <j1 rule="hyper" parents="58 18189 19287"/>
    </justification>
  </clause>

  <clause id="19289">
    <literal><![CDATA[
      K(x,((y \ 1) * z) / (u * (y \ 1))) = K(x,(y \ z) / (u / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,18670,a(flip),b,19288,a),flip(a)].">
      <j1 rule="hyper" parents="58 18670 19288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19290">
    <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,18462,a,b,19289,a)].">
      <j1 rule="hyper" parents="58 18462 19289"/>
    </justification>
  </clause>

  <clause id="19291">
    <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(14869,a,18970,a)].">
      <j1 rule="hyper" parents="14869 18970"/>
    </justification>
  </clause>

  <clause id="19292">
    <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(15690,a,19291,a),flip(a)].">
      <j1 rule="hyper" parents="15690 19291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19293">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u)) = K(x,y \ ((T(y,z) / z) * u))
    ]]></literal>
    <justification jstring="[para(13586(a,1),19292(a,2,2))].">
      <j1 rule="para" parents="13586 19292"/>
    </justification>
  </clause>

  <clause id="19294">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(334,a,18532,a(flip),b,19293,a),flip(a)].">
      <j1 rule="hyper" parents="334 18532 19293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19295">
    <literal><![CDATA[
      K(x,(y * ((y / z) \ 1)) \ (((y / z) \ 1) * u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(15641,a,19294,a)].">
      <j1 rule="hyper" parents="15641 19294"/>
    </justification>
  </clause>

  <clause id="19296">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ ((y / z) \ u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15054,a(flip),b,19295,a)].">
      <j1 rule="hyper" parents="58 15054 19295"/>
    </justification>
  </clause>

  <clause id="19297">
    <literal><![CDATA[
      K(x,y \ ((y \ z) \ u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[para(5875(a,1),19296(a,1,2))].">
      <j1 rule="para" parents="5875 19296"/>
    </justification>
  </clause>

  <clause id="19298">
    <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,18718,a,b,19297,a)].">
      <j1 rule="hyper" parents="58 18718 19297"/>
    </justification>
  </clause>

  <clause id="19299">
    <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,17983,a(flip),b,19297,a),flip(a)].">
      <j1 rule="hyper" parents="58 17983 19297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19300">
    <literal><![CDATA[
      K(x,y \ (((K(z,y) * u) \ y) * w)) = K(x,y \ ((T(y,z) \ u) \ w))
    ]]></literal>
    <justification jstring="[para(5367(a,1),19297(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5367 19297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19301">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((z \ y) * u)) = K(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(19297(a,1),10211(a,1,2))].">
      <j1 rule="para" parents="19297 10211"/>
    </justification>
  </clause>

  <clause id="19302">
    <literal><![CDATA[
      K(x,K(y,z) * (z \ ((u \ z) * w))) = K(x,z \ ((T(z,y) \ u) \ w))
    ]]></literal>
    <justification jstring="[hyper(18530,a,19299,a)].">
      <j1 rule="hyper" parents="18530 19299"/>
    </justification>
  </clause>

  <clause id="19303">
    <literal><![CDATA[
      K(x,y \ ((T(y,z) \ u) \ w)) = K(x,y \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[para(14040(a,1),19300(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14040 19300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19304">
    <literal><![CDATA[
      K(x,T(y,z) \ ((u \ y) * w)) = K(x,y \ ((T(y,z) \ u) \ w))
    ]]></literal>
    <justification jstring="[para(5392(a,1),19302(a,1,2))].">
      <j1 rule="para" parents="5392 19302"/>
    </justification>
  </clause>

  <clause id="19305">
    <literal><![CDATA[
      K(x,T(y,z) \ ((u \ y) * w)) = K(x,y \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[hyper(334,a,19303,a(flip),b,19304,a),flip(a)].">
      <j1 rule="hyper" parents="334 19303 19304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19306">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ T(u * (y \ z),K(y,z)))
    ]]></literal>
    <justification jstring="[para(9315(a,2),19298(a,2,2,2))].">
      <j1 rule="para" parents="9315 19298"/>
    </justification>
  </clause>

  <clause id="19307">
    <literal><![CDATA[
      K(x,((y \ z) \ u) / y) = K(x,((z \ y) * u) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,14450,a(flip),b,19301,a),flip(a)].">
      <j1 rule="hyper" parents="58 14450 19301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19308">
    <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(4441(a,1),19307(a,2,2,1))].">
      <j1 rule="para" parents="4441 19307"/>
    </justification>
  </clause>

  <clause id="19309">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ (u * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(334,a,16403,a(flip),b,19306,a),flip(a)].">
      <j1 rule="hyper" parents="334 16403 19306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19311">
    <literal><![CDATA[
      K(x,y \ (z / (y \ u))) = K(x,y \ (z * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18431,a(flip),b,19309,a)].">
      <j1 rule="hyper" parents="58 18431 19309"/>
    </justification>
  </clause>

  <clause id="19312">
    <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(8800(a,1),19311(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8800 19311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19313">
    <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(14569(a,1),18973(a,1,2,2))].">
      <j1 rule="para" parents="14569 18973"/>
    </justification>
  </clause>

  <clause id="19314">
    <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,19269,a(flip),b,19271,a),flip(a)].">
      <j1 rule="hyper" parents="58 19269 19271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19315">
    <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(334,a,19270,a,b,19314,a)].">
      <j1 rule="hyper" parents="334 19270 19314"/>
    </justification>
  </clause>

  <clause id="19316">
    <literal><![CDATA[
      a(x,y,z * K(u,K(w,v5))) = (x * (y * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(16206,a,19282,a),flip(a)].">
      <j1 rule="hyper" parents="16206 19282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19318">
    <literal><![CDATA[
      a(x,y,z * K(u,K(w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(334,a,9,a,b,19316,a),flip(a)].">
      <j1 rule="hyper" parents="334 9 19316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19319">
    <literal><![CDATA[
      a(x,y,z * K(u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(19316(a,2),709(a,1))].">
      <j1 rule="para" parents="19316 709"/>
    </justification>
  </clause>

  <clause id="19320">
    <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),19319(a,1,3))].">
      <j1 rule="para" parents="84 19319"/>
    </justification>
  </clause>

  <clause id="19321">
    <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(8038(a,1),19319(a,1,3))].">
      <j1 rule="para" parents="8038 19319"/>
    </justification>
  </clause>

  <clause id="19322">
    <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(13640(a,2),19320(a,1))].">
      <j1 rule="para" parents="13640 19320"/>
    </justification>
  </clause>

  <clause id="19323">
    <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,19281,a(flip),b,19315,a),flip(a)].">
      <j1 rule="hyper" parents="58 19281 19315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19324">
    <literal><![CDATA[
      a(x * K(y,K(z,u)),w,v5) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(334,a,19318,a(flip),b,19323,a),flip(a)].">
      <j1 rule="hyper" parents="334 19318 19323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19326">
    <literal><![CDATA[
      a(x,y * K(z,K(u,w)),v5) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,19314,a(flip),b,19324,a)].">
      <j1 rule="hyper" parents="58 19314 19324"/>
    </justification>
  </clause>

  <clause id="19327">
    <literal><![CDATA[
      a(K(x,y) * z,u,w) = a(z * K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(84(a,1),19324(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 19324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19328">
    <literal><![CDATA[
      a(T(x,K(y,z)),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(1067(a,2),19324(a,1,1))].">
      <j1 rule="para" parents="1067 19324"/>
    </justification>
  </clause>

  <clause id="19329">
    <literal><![CDATA[
      a(T(x,T(y,z)),u,w) = a(T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(8016(a,1),19324(a,1,1))].">
      <j1 rule="para" parents="8016 19324"/>
    </justification>
  </clause>

  <clause id="19330">
    <literal><![CDATA[
      a(T(x,K(y,z)) \ u,w,v5) = a(x \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(16090(a,1),19324(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16090 19324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19331">
    <literal><![CDATA[
      a(K(x,y) * (z \ x),u,w) = a(z \ T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(16342(a,1),19324(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16342 19324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19332">
    <literal><![CDATA[
      a(T(x / T(y,z),y),u,w) = a(T(y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(8227(a,1),19328(a,1,1))].">
      <j1 rule="para" parents="8227 19328"/>
    </justification>
  </clause>

  <clause id="19333">
    <literal><![CDATA[
      a(K(x,y) * (z \ 1),u,w) = a(z \ K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(14236(a,1),19328(a,1,1))].">
      <j1 rule="para" parents="14236 19328"/>
    </justification>
  </clause>

  <clause id="19335">
    <literal><![CDATA[
      a(x,K(y,z) * u,w) = a(x,u * K(y,z),w)
    ]]></literal>
    <justification jstring="[para(84(a,1),19326(a,1,2)),flip(a)].">
      <j1 rule="para" parents="84 19326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19336">
    <literal><![CDATA[
      a(x,K(y,T(z,u)),w) = a(x,K(y,z),w)
    ]]></literal>
    <justification jstring="[para(7410(a,1),19326(a,1,2))].">
      <j1 rule="para" parents="7410 19326"/>
    </justification>
  </clause>

  <clause id="19338">
    <literal><![CDATA[
      a(T(x * ((x / y) / x),x),z,u) = a(x * ((y \ x) / x),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13196,a(flip),b,19329,a),flip(a)].">
      <j1 rule="hyper" parents="58 13196 19329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19339">
    <literal><![CDATA[
      a(K(x,x \ y) * z,u,w) = a(z * K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(334,a,13281,a(flip),b,19327,a),flip(a)].">
      <j1 rule="hyper" parents="334 13281 19327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19340">
    <literal><![CDATA[
      a(L(x \ 1,x,y) \ z,u,w) = a(((y * x) \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(1348(a,1),19330(a,1,1,1))].">
      <j1 rule="para" parents="1348 19330"/>
    </justification>
  </clause>

  <clause id="19341">
    <literal><![CDATA[
      a(K(x * y,y \ 1) * z,u,w) = a(z * K(x * y,x),u,w)
    ]]></literal>
    <justification jstring="[para(6441(a,1),19339(a,1,1,1))].">
      <j1 rule="para" parents="6441 19339"/>
    </justification>
  </clause>

  <clause id="19343">
    <literal><![CDATA[
      a(x * ((y \ x) / x),z,u) = a(x / y,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13082,a(flip),b,19338,a),flip(a)].">
      <j1 rule="hyper" parents="58 13082 19338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19345">
    <literal><![CDATA[
      a(T(x,y) * ((z \ x) / x),u,w) = a(T(x,y) / z,u,w)
    ]]></literal>
    <justification jstring="[para(14051(a,1),19343(a,1,1,2))].">
      <j1 rule="para" parents="14051 19343"/>
    </justification>
  </clause>

  <clause id="19346">
    <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,13094,a(flip),b,19345,a)].">
      <j1 rule="hyper" parents="58 13094 19345"/>
    </justification>
  </clause>

  <clause id="19347">
    <literal><![CDATA[
      a(K(x * y,y \ 1) * z,u,w) = a(z * K(y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(334,a,13280,a(flip),b,19341,a),flip(a)].">
      <j1 rule="hyper" parents="334 13280 19341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19348">
    <literal><![CDATA[
      a(K(x * y,x \ 1) * z,u,w) = a(z * K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(6133(a,1),19347(a,1,1,1))].">
      <j1 rule="para" parents="6133 19347"/>
    </justification>
  </clause>

  <clause id="19349">
    <literal><![CDATA[
      a(T(x,x \ y) / z,u,w) = a(T(x,y) / z,u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,19345,a(flip),b,19346,a),flip(a)].">
      <j1 rule="hyper" parents="58 19345 19346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19350">
    <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(19349(a,1),13635(a,1,2))].">
      <j1 rule="para" parents="19349 13635"/>
    </justification>
  </clause>

  <clause id="19351">
    <literal><![CDATA[
      (x * y) / a(z \ x,T(z,x),y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(13090(a,1),19350(a,1,2))].">
      <j1 rule="para" parents="13090 19350"/>
    </justification>
  </clause>

  <clause id="19352">
    <literal><![CDATA[
      (x * y) / a(x / z,z,y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(13634(a,1),19351(a,1,2))].">
      <j1 rule="para" parents="13634 19351"/>
    </justification>
  </clause>

  <clause id="19353">
    <literal><![CDATA[
      (x / ((x \ y) * x)) * (((x \ y) * x) * z) = (x / y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(929,a,19352,a),flip(a)].">
      <j1 rule="hyper" parents="929 19352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19354">
    <literal><![CDATA[
      ((x / ((x \ y) * x)) * (((x \ y) * x) * z)) * u = ((x / y) * (y * z)) * u
    ]]></literal>
    <justification jstring="[hyper(52,a,19353,a)].">
      <j1 rule="hyper" parents="52 19353"/>
    </justification>
  </clause>

  <clause id="19355">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * w = (x * K(z,L(u,x,(x \ y) \ 1))) * w
    ]]></literal>
    <justification jstring="[para(18592(a,1),19354(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18592 19354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19356">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * w = (x * K(z,L(u,x,y \ x))) * w
    ]]></literal>
    <justification jstring="[para(14830(a,1),19355(a,2,1,2))].">
      <j1 rule="para" parents="14830 19355"/>
    </justification>
  </clause>

  <clause id="19357">
    <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(334,a,18310,a(flip),b,19356,a),flip(a)].">
      <j1 rule="hyper" parents="334 18310 19356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19358">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = x * a(z,x,K(y \ x,u))
    ]]></literal>
    <justification jstring="[para(14630(a,1),19357(a,2,2))].">
      <j1 rule="para" parents="14630 19357"/>
    </justification>
  </clause>

  <clause id="19359">
    <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,19240,a(flip),b,17848,a)].">
      <j1 rule="hyper" parents="58 19240 17848"/>
    </justification>
  </clause>

  <clause id="19360">
    <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,18712,a(flip),b,18104,a)].">
      <j1 rule="hyper" parents="58 18712 18104"/>
    </justification>
  </clause>

  <clause id="19362">
    <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(19360(a,2),16455(a,1))].">
      <j1 rule="para" parents="19360 16455"/>
    </justification>
  </clause>

  <clause id="19363">
    <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(19260(a,1),19362(a,1))].">
      <j1 rule="para" parents="19260 19362"/>
    </justification>
  </clause>

  <clause id="19364">
    <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(19066(a,1),19363(a,1))].">
      <j1 rule="para" parents="19066 19363"/>
    </justification>
  </clause>

  <clause id="19365">
    <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(5725(a,1),18226(a,2,2,2,2))].">
      <j1 rule="para" parents="5725 18226"/>
    </justification>
  </clause>

  <clause id="19366">
    <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(8240(a,1),19035(a,1,1))].">
      <j1 rule="para" parents="8240 19035"/>
    </justification>
  </clause>

  <clause id="19367">
    <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(16321(a,1),19366(a,1,1))].">
      <j1 rule="para" parents="16321 19366"/>
    </justification>
  </clause>

  <clause id="19368">
    <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(19121(a,1),19367(a,1,1))].">
      <j1 rule="para" parents="19121 19367"/>
    </justification>
  </clause>

  <clause id="19369">
    <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(16583(a,1),19368(a,1,1))].">
      <j1 rule="para" parents="16583 19368"/>
    </justification>
  </clause>

  <clause id="19370">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u \ ((K(y,z) * u) * x)) = K(y,x / ((z * u) \ (u * x)))
    ]]></literal>
    <justification jstring="[para(16323(a,1),19369(a,1,1))].">
      <j1 rule="para" parents="16323 19369"/>
    </justification>
  </clause>

  <clause id="19371">
    <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,17892,a(flip),b,19370,a)].">
      <j1 rule="hyper" parents="58 17892 19370"/>
    </justification>
  </clause>

  <clause id="19373">
    <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(14836(a,1),19202(a,1,2,2))].">
      <j1 rule="para" parents="14836 19202"/>
    </justification>
  </clause>

  <clause id="19374">
    <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(5240(a,1),19373(a,1,2,2,2,3))].">
      <j1 rule="para" parents="5240 19373"/>
    </justification>
  </clause>

  <clause id="19375">
    <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(12923(a,1),19374(a,1,2,2,2))].">
      <j1 rule="para" parents="12923 19374"/>
    </justification>
  </clause>

  <clause id="19376">
    <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(14805(a,1),19375(a,1,2,2))].">
      <j1 rule="para" parents="14805 19375"/>
    </justification>
  </clause>

  <clause id="19378">
    <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(11511(a,1),19376(a,1,2))].">
      <j1 rule="para" parents="11511 19376"/>
    </justification>
  </clause>

  <clause id="19379">
    <literal><![CDATA[
      L(x * K(y,z),u,u \ 1) = L(x,u,u \ 1) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(13619,a,19378,a)].">
      <j1 rule="hyper" parents="13619 19378"/>
    </justification>
  </clause>

  <clause id="19380">
    <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(19379(a,2),14529(a,1,1))].">
      <j1 rule="para" parents="19379 14529"/>
    </justification>
  </clause>

  <clause id="19381">
    <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(19379(a,2),15364(a,1,2))].">
      <j1 rule="para" parents="19379 15364"/>
    </justification>
  </clause>

  <clause id="19382">
    <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(3963,a,19381,a)].">
      <j1 rule="hyper" parents="3963 19381"/>
    </justification>
  </clause>

  <clause id="19383">
    <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(19382(a,1),4362(a,1))].">
      <j1 rule="para" parents="19382 4362"/>
    </justification>
  </clause>

  <clause id="19384">
    <literal><![CDATA[
      a(x \ 1,x,y * K(z,u)) = a(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(19383,a,14375,a)].">
      <j1 rule="hyper" parents="19383 14375"/>
    </justification>
  </clause>

  <clause id="19385">
    <literal><![CDATA[
      a(x \ 1,x,K(y,z) * u) = a(x \ 1,x,u)
    ]]></literal>
    <justification jstring="[hyper(19322,a,19384,a)].">
      <j1 rule="hyper" parents="19322 19384"/>
    </justification>
  </clause>

  <clause id="19387">
    <literal><![CDATA[
      a(x \ 1,x,y) \ (K(z,u) * y) = L(K(z,u) * y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(19385(a,1),4361(a,1,1))].">
      <j1 rule="para" parents="19385 4361"/>
    </justification>
  </clause>

  <clause id="19388">
    <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,17912,a(flip),b,19387,a)].">
      <j1 rule="hyper" parents="58 17912 19387"/>
    </justification>
  </clause>

  <clause id="19389">
    <literal><![CDATA[
      L(K(x,y) * z,u,u \ 1) = K(x,y) * L(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(4361(a,1),19388(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4361 19388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19390">
    <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,19389,a,b,5441,a)].">
      <j1 rule="hyper" parents="119 19389 5441"/>
    </justification>
  </clause>

  <clause id="19391">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ z,u,u \ 1) = x * L(x \ z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(5392(a,1),19390(a,1,2,1))].">
      <j1 rule="para" parents="5392 19390"/>
    </justification>
  </clause>

  <clause id="19392">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,z \ 1),u) = L(x \ T(y,u),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(2199,a,19391,a)].">
      <j1 rule="hyper" parents="2199 19391"/>
    </justification>
  </clause>

  <clause id="19393">
    <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(19392(a,1),14430(a,1,2))].">
      <j1 rule="para" parents="19392 14430"/>
    </justification>
  </clause>

  <clause id="19394">
    <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(13396(a,1),19253(a,1,1,2))].">
      <j1 rule="para" parents="13396 19253"/>
    </justification>
  </clause>

  <clause id="19395">
    <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(5391(a,1),19394(a,1,2))].">
      <j1 rule="para" parents="5391 19394"/>
    </justification>
  </clause>

  <clause id="19396">
    <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,16288,a(flip),b,19395,a)].">
      <j1 rule="hyper" parents="58 16288 19395"/>
    </justification>
  </clause>

  <clause id="19397">
    <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(19246,a,19396,a)].">
      <j1 rule="hyper" parents="19246 19396"/>
    </justification>
  </clause>

  <clause id="19398">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),z) \ w) = K(x,w * K(z,u * y))
    ]]></literal>
    <justification jstring="[hyper(8267,a,19397,a),flip(a)].">
      <j1 rule="hyper" parents="8267 19397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19399">
    <literal><![CDATA[
      K(x,K(y,z \ (y \ u)) * w) = K(x,w * K(y,u * z))
    ]]></literal>
    <justification jstring="[para(5391(a,1),19398(a,1,2))].">
      <j1 rule="para" parents="5391 19398"/>
    </justification>
  </clause>

  <clause id="19400">
    <literal><![CDATA[
      K(x,y * K(z,u \ w)) = K(x,y * K(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16288,a(flip),b,19399,a)].">
      <j1 rule="hyper" parents="58 16288 19399"/>
    </justification>
  </clause>

  <clause id="19401">
    <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(18204,a,19400,a)].">
      <j1 rule="hyper" parents="18204 19400"/>
    </justification>
  </clause>

  <clause id="19402">
    <literal><![CDATA[
      K(x,y * K(z,(u \ z) * w)) = K(x,y * K(u * w,z))
    ]]></literal>
    <justification jstring="[hyper(16367,a,19400,a),flip(a)].">
      <j1 rule="hyper" parents="16367 19400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19403">
    <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(19400(a,1),19254(a,1,1,2))].">
      <j1 rule="para" parents="19400 19254"/>
    </justification>
  </clause>

  <clause id="19404">
    <literal><![CDATA[
      K(x,y * K(z,z * (u \ w))) = K(x,y * K(u * w,z))
    ]]></literal>
    <justification jstring="[para(14458(a,1),19402(a,1,2,2))].">
      <j1 rule="para" parents="14458 19402"/>
    </justification>
  </clause>

  <clause id="19405">
    <literal><![CDATA[
      K(x,y * K(z \ u,w)) = K(x,y * K(z * u,w))
    ]]></literal>
    <justification jstring="[hyper(16320,a,19404,a)].">
      <j1 rule="hyper" parents="16320 19404"/>
    </justification>
  </clause>

  <clause id="19406">
    <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(18201,a,19405,a)].">
      <j1 rule="hyper" parents="18201 19405"/>
    </justification>
  </clause>

  <clause id="19407">
    <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(334,a,17963,a(flip),b,19401,a),flip(a)].">
      <j1 rule="hyper" parents="334 17963 19401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19408">
    <literal><![CDATA[
      K(x,y * (z * K(u,w \ v5))) = K(x,y * (z * K(u,v5 * w)))
    ]]></literal>
    <justification jstring="[para(181(a,1),19407(a,1,2,2,2,1))].">
      <j1 rule="para" parents="181 19407"/>
    </justification>
  </clause>

  <clause id="19409">
    <literal><![CDATA[
      K(x,y * (z * K(u,w / v5))) = K(x,y * (z * K(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(18284,a,19408,a)].">
      <j1 rule="hyper" parents="18284 19408"/>
    </justification>
  </clause>

  <clause id="19410">
    <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,18926,a(flip),b,19408,a),flip(a)].">
      <j1 rule="hyper" parents="58 18926 19408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19411">
    <literal><![CDATA[
      K(x,y * ((z / u) * K(z,w * v5))) = K(x,y * (T(z,w / v5) / u))
    ]]></literal>
    <justification jstring="[hyper(16504,a,19409,a),flip(a)].">
      <j1 rule="hyper" parents="16504 19409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19412">
    <literal><![CDATA[
      K(x,y * (T(z,u / w) / v5)) = K(x,y * (T(z,u * w) / v5))
    ]]></literal>
    <justification jstring="[hyper(16504,a,19411,a),flip(a)].">
      <j1 rule="hyper" parents="16504 19411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19413">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) / v5)) = K(x,y * (T(z,w * u) / v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,16539,a(flip),b,19412,a)].">
      <j1 rule="hyper" parents="58 16539 19412"/>
    </justification>
  </clause>

  <clause id="19414">
    <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(19413(a,1),18558(a,1))].">
      <j1 rule="para" parents="19413 18558"/>
    </justification>
  </clause>

  <clause id="19415">
    <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(17060,a,19403,a)].">
      <j1 rule="hyper" parents="17060 19403"/>
    </justification>
  </clause>

  <clause id="19416">
    <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(17127,a,19415,a)].">
      <j1 rule="hyper" parents="17127 19415"/>
    </justification>
  </clause>

  <clause id="19417">
    <literal><![CDATA[
      K(x,K(y,z / u) \ w) = K(x,K(z * u,y) * w)
    ]]></literal>
    <justification jstring="[hyper(8267,a,19416,a),flip(a)].">
      <j1 rule="hyper" parents="8267 19416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19418">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(z * y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(17060,a,19417,a)].">
      <j1 rule="hyper" parents="17060 19417"/>
    </justification>
  </clause>

  <clause id="19419">
    <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(19418(a,1),18422(a,1,1))].">
      <j1 rule="para" parents="19418 18422"/>
    </justification>
  </clause>

  <clause id="19420">
    <literal><![CDATA[
      K(x,y * (K(z,u \ w) * v5)) = K(x,y * (K(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,18422,a(flip),b,19419,a),flip(a)].">
      <j1 rule="hyper" parents="58 18422 19419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19421">
    <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(16707,a,19420,a),flip(a)].">
      <j1 rule="hyper" parents="16707 19420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19422">
    <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(334,a,17963,a(flip),b,19406,a),flip(a)].">
      <j1 rule="hyper" parents="334 17963 19406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19423">
    <literal><![CDATA[
      K(x,y * (z * T(u / w,v5 \ v6))) = K(x,y * (z * T(u / w,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(16707,a,19421,a),flip(a)].">
      <j1 rule="hyper" parents="16707 19421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19424">
    <literal><![CDATA[
      K(x,y * (z * K(u \ w,v5))) = K(x,y * (z * K(u * w,v5)))
    ]]></literal>
    <justification jstring="[para(17788(a,1),19422(a,1,2,2,2,1))].">
      <j1 rule="para" parents="17788 19422"/>
    </justification>
  </clause>

  <clause id="19425">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(w * v5,u))) = K(x,y * (z \ T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(16708,a,19424,a),flip(a)].">
      <j1 rule="hyper" parents="16708 19424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19426">
    <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,18664,a(flip),b,19424,a),flip(a)].">
      <j1 rule="hyper" parents="58 18664 19424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19427">
    <literal><![CDATA[
      K(x,y * (z \ T(u,w \ v5))) = K(x,y * (z \ T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(16708,a,19425,a),flip(a)].">
      <j1 rule="hyper" parents="16708 19425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19428">
    <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(18396,a,19427,a),flip(a)].">
      <j1 rule="hyper" parents="18396 19427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19429">
    <literal><![CDATA[
      K(x,T(y,z \ u) * w) = K(x,T(y,u * z) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,19410,a(flip),b,19426,a)].">
      <j1 rule="hyper" parents="58 19410 19426"/>
    </justification>
  </clause>

  <clause id="19430">
    <literal><![CDATA[
      K(x,T(y,z / u) * w) = K(x,T(y,z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(16500,a,19429,a)].">
      <j1 rule="hyper" parents="16500 19429"/>
    </justification>
  </clause>

  <clause id="19431">
    <literal><![CDATA[
      K(x,T(y,z * u) * (z \ u)) = K(x,(z \ u) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15611,a(flip),b,19429,a),flip(a)].">
      <j1 rule="hyper" parents="58 15611 19429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19432">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,y * z)) = K(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15525,a(flip),b,19431,a),flip(a)].">
      <j1 rule="hyper" parents="58 15525 19431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19433">
    <literal><![CDATA[
      K(x,y / (z \ (u * K(w,v5)))) = K(x,y * ((z \ u) \ K(v5,w)))
    ]]></literal>
    <justification jstring="[hyper(19364,a,19428,a)].">
      <j1 rule="hyper" parents="19364 19428"/>
    </justification>
  </clause>

  <clause id="19434">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * v5))) = K(x,y * ((z \ v5) \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17909,a,b,19433,a)].">
      <j1 rule="hyper" parents="58 17909 19433"/>
    </justification>
  </clause>

  <clause id="19436">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,z)) \ K(w,v5))) = K(x,y / (u / (K(w,v5) * z)))
    ]]></literal>
    <justification jstring="[hyper(18767,a,19434,a),flip(a)].">
      <j1 rule="hyper" parents="18767 19434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19437">
    <literal><![CDATA[
      K(x,y / (z / (K(u,w) * v5))) = K(x,y * ((z / v5) \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(18993,a,19436,a),flip(a)].">
      <j1 rule="hyper" parents="18993 19436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19438">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) / v5)) = K(x,y * ((w / v5) \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18549,a,b,19437,a)].">
      <j1 rule="hyper" parents="58 18549 19437"/>
    </justification>
  </clause>

  <clause id="19439">
    <literal><![CDATA[
      K(x,y * (((z \ u) / w) \ K(z,v5))) = K(x,y / ((T(z,v5) \ u) / w))
    ]]></literal>
    <justification jstring="[para(5392(a,1),19438(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5392 19438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19440">
    <literal><![CDATA[
      K(x,y * (((z / u) / w) \ K(v5,z))) = K(x,y / ((T(z,v5) / u) / w))
    ]]></literal>
    <justification jstring="[para(14034(a,1),19438(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14034 19438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19441">
    <literal><![CDATA[
      K(x,T(y,z) / ((y / u) / w)) = K(x,y / ((T(y,z) / u) / w))
    ]]></literal>
    <justification jstring="[hyper(18381,a,19440,a)].">
      <j1 rule="hyper" parents="18381 19440"/>
    </justification>
  </clause>

  <clause id="19442">
    <literal><![CDATA[
      K(x,y / ((T(y,z * u) / z) / u)) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19046,a(flip),b,19441,a),flip(a)].">
      <j1 rule="hyper" parents="58 19046 19441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19443">
    <literal><![CDATA[
      K(x,((((y \ z) * u) \ u) \ u) / z) = K(x,((z \ y) \ (((z \ y) \ u) * (z \ y))) / z)
    ]]></literal>
    <justification jstring="[para(17305(a,1),19308(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17305 19308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19444">
    <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),19443(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="17 19443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19445">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,((((z \ y) * u) \ u) \ u) / y)
    ]]></literal>
    <justification jstring="[hyper(18722,a,19444,a)].">
      <j1 rule="hyper" parents="18722 19444"/>
    </justification>
  </clause>

  <clause id="19446">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,T((z \ y) * u,u) / y)
    ]]></literal>
    <justification jstring="[hyper(334,a,13361,a(flip),b,19445,a),flip(a)].">
      <j1 rule="hyper" parents="334 13361 19445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19447">
    <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(19446(a,2),16726(a,1))].">
      <j1 rule="para" parents="19446 16726"/>
    </justification>
  </clause>

  <clause id="19448">
    <literal><![CDATA[
      K(x,(y * (z \ u)) / u) = K(x,u / (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(19447,a,19052,a)].">
      <j1 rule="hyper" parents="19447 19052"/>
    </justification>
  </clause>

  <clause id="19449">
    <literal><![CDATA[
      K(x,y / ((z \ y) * (u \ y))) = K(x,(u * T(z,y)) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,13466,a(flip),b,19448,a),flip(a)].">
      <j1 rule="hyper" parents="58 13466 19448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19450">
    <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(17719(a,2),19448(a,2,2,2,2))].">
      <j1 rule="para" parents="17719 19448"/>
    </justification>
  </clause>

  <clause id="19451">
    <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(14855(a,1),19449(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14855 19449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19452">
    <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,15865,a(flip),b,19359,a),flip(a)].">
      <j1 rule="hyper" parents="58 15865 19359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19453">
    <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(15774(a,2),19365(a,2,2,2,2))].">
      <j1 rule="para" parents="15774 19365"/>
    </justification>
  </clause>

  <clause id="19454">
    <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(14046(a,1),19380(a,1,1,1))].">
      <j1 rule="para" parents="14046 19380"/>
    </justification>
  </clause>

  <clause id="19455">
    <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(334,a,14430,a(flip),b,19454,a),flip(a)].">
      <j1 rule="hyper" parents="334 14430 19454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19457">
    <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(6787(a,1),19453(a,2,2,2,2,1))].">
      <j1 rule="para" parents="6787 19453"/>
    </justification>
  </clause>

  <clause id="19458">
    <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,18197,a(flip),b,19457,a)].">
      <j1 rule="hyper" parents="58 18197 19457"/>
    </justification>
  </clause>

  <clause id="19459">
    <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,15800,a(flip),b,19458,a),flip(a)].">
      <j1 rule="hyper" parents="58 15800 19458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19461">
    <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(5143(a,2),19459(a,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5143 19459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19462">
    <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(334,a,19423,a(flip),b,19461,a),flip(a)].">
      <j1 rule="hyper" parents="334 19423 19461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19463">
    <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(334,a,19459,a(flip),b,19462,a),flip(a)].">
      <j1 rule="hyper" parents="334 19459 19462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19464">
    <literal><![CDATA[
      K(x,y * (z * T(u,w \ v5))) = K(x,y * (z * T(u,v5 * w)))
    ]]></literal>
    <justification jstring="[para(5086(a,1),19463(a,1,2,2,2,1))].">
      <j1 rule="para" parents="5086 19463"/>
    </justification>
  </clause>

  <clause id="19465">
    <literal><![CDATA[
      K(x,y * (z * T(u,w / v5))) = K(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(16622,a,19464,a)].">
      <j1 rule="hyper" parents="16622 19464"/>
    </justification>
  </clause>

  <clause id="19466">
    <literal><![CDATA[
      T(x,y * (z * T(u,w \ v5))) = T(x,y * (z * T(u,v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(118,a,19464,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 19464 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19467">
    <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(16710,a,19465,a)].">
      <j1 rule="hyper" parents="16710 19465"/>
    </justification>
  </clause>

  <clause id="19468">
    <literal><![CDATA[
      T(x,y * (z * T(u,w / v5))) = T(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(118,a,19465,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 19465 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19469">
    <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,19003,a(flip),b,19466,a),flip(a)].">
      <j1 rule="hyper" parents="58 19003 19466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19470">
    <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(19468(a,1),16624(a,1,2,2))].">
      <j1 rule="para" parents="19468 16624"/>
    </justification>
  </clause>

  <clause id="19471">
    <literal><![CDATA[
      K(x,y * (T(z,T(u \ w,u)) * v5)) = K(x,y * (T(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(334,a,16603,a(flip),b,19467,a),flip(a)].">
      <j1 rule="hyper" parents="334 16603 19467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19472">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) * v5)) = K(x,y * (T(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(17792,a,19471,a)].">
      <j1 rule="hyper" parents="17792 19471"/>
    </justification>
  </clause>

  <clause id="19474">
    <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(19472(a,1),16661(a,1))].">
      <j1 rule="para" parents="19472 16661"/>
    </justification>
  </clause>

  <clause id="19475">
    <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(19469(a,1),19470(a,1,2,2))].">
      <j1 rule="para" parents="19469 19470"/>
    </justification>
  </clause>

  <clause id="19476">
    <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(15769,a,17646,a)].">
      <j1 rule="hyper" parents="15769 17646"/>
    </justification>
  </clause>

  <clause id="19478">
    <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(4553(a,1),19476(a,1,2,1,1))].">
      <j1 rule="para" parents="4553 19476"/>
    </justification>
  </clause>

  <clause id="19479">
    <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(13523,a,19478,a)].">
      <j1 rule="hyper" parents="13523 19478"/>
    </justification>
  </clause>

  <clause id="19480">
    <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,17911,a(flip),b,18732,a),flip(a)].">
      <j1 rule="hyper" parents="58 17911 18732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19481">
    <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(334,a,15054,a(flip),b,19480,a),flip(a)].">
      <j1 rule="hyper" parents="334 15054 19480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19482">
    <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(334,a,18240,a(flip),b,19481,a),flip(a)].">
      <j1 rule="hyper" parents="334 18240 19481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19483">
    <literal><![CDATA[
      K(x,(y \ (z \ u)) \ (y \ u)) = K(x,L(T(z,u),u,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(18817,a,19482,a),flip(a)].">
      <j1 rule="hyper" parents="18817 19482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19484">
    <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(455,a,11271,a(flip),b,19483,a)].">
      <j1 rule="hyper" parents="455 11271 19483"/>
    </justification>
  </clause>

  <clause id="19486">
    <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(14147(a,1),18113(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14147 18113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19487">
    <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(334,a,18579,a(flip),b,19486,a),flip(a)].">
      <j1 rule="hyper" parents="334 18579 19486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19488">
    <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(4713(a,1),18207(a,1,2,1,1))].">
      <j1 rule="para" parents="4713 18207"/>
    </justification>
  </clause>

  <clause id="19489">
    <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(3106(a,1),19488(a,1,2,1,1))].">
      <j1 rule="para" parents="3106 19488"/>
    </justification>
  </clause>

  <clause id="19491">
    <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,17153,a(flip),b,19489,a)].">
      <j1 rule="hyper" parents="58 17153 19489"/>
    </justification>
  </clause>

  <clause id="19492">
    <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),19491(a,2,2,1))].">
      <j1 rule="para" parents="7 19491"/>
    </justification>
  </clause>

  <clause id="19493">
    <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,10228,a(flip),b,19492,a)].">
      <j1 rule="hyper" parents="58 10228 19492"/>
    </justification>
  </clause>

  <clause id="19495">
    <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,5598,a(flip),b,19493,a),flip(a)].">
      <j1 rule="hyper" parents="58 5598 19493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19496">
    <literal><![CDATA[
      K(x,(((y \ 1) \ 1) \ z) * (z \ (u * y))) = K(x,(T(u * y,u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(334,a,17017,a(flip),b,19495,a),flip(a)].">
      <j1 rule="hyper" parents="334 17017 19495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19497">
    <literal><![CDATA[
      K(x,(((y \ 1) \ 1) \ z) * (z \ (u * y))) = K(x,((y * u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(334,a,18557,a(flip),b,19496,a),flip(a)].">
      <j1 rule="hyper" parents="334 18557 19496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19498">
    <literal><![CDATA[
      K(x,(T(y,1) \ z) * (z \ (u * y))) = K(x,((y * u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(15867,a,19497,a)].">
      <j1 rule="hyper" parents="15867 19497"/>
    </justification>
  </clause>

  <clause id="19499">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,(y \ u) * (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(202(a,1),19498(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="202 19498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19500">
    <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(18537,a,18388,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18537 18388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19501">
    <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(5182(a,1),19500(a,2,1,1))].">
      <j1 rule="para" parents="5182 19500"/>
    </justification>
  </clause>

  <clause id="19502">
    <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(5047(a,1),19501(a,1,2,1))].">
      <j1 rule="para" parents="5047 19501"/>
    </justification>
  </clause>

  <clause id="19503">
    <literal><![CDATA[
      (K(x,y) * (z * K(y,x))) * ((z * K(y,x)) \ u) = (K(x,y) * z) * (z \ u)
    ]]></literal>
    <justification jstring="[hyper(18537,a,19502,a)].">
      <j1 rule="hyper" parents="18537 19502"/>
    </justification>
  </clause>

  <clause id="19504">
    <literal><![CDATA[
      T(x,K(y,z)) * ((x * K(y,z)) \ u) = (K(z,y) * x) * (x \ u)
    ]]></literal>
    <justification jstring="[para(5402(a,1),19503(a,1,1))].">
      <j1 rule="para" parents="5402 19503"/>
    </justification>
  </clause>

  <clause id="19505">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * ((K(y,x) * z) \ u)) = z \ u
    ]]></literal>
    <justification jstring="[hyper(11518,a,19504,a)].">
      <j1 rule="hyper" parents="11518 19504"/>
    </justification>
  </clause>

  <clause id="19506">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ u) != w
    ]]></literal>
    <literal><![CDATA[
      z * ((K(y,x) * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(19504(a,1),11508(a,1))].">
      <j1 rule="para" parents="19504 11508"/>
    </justification>
  </clause>

  <clause id="19507">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * u) = z \ ((K(y,x) * z) * u)
    ]]></literal>
    <justification jstring="[para(4(a,1),19505(a,1,2,2))].">
      <j1 rule="para" parents="4 19505"/>
    </justification>
  </clause>

  <clause id="19508">
    <literal><![CDATA[
      x \ ((K(y,z) * x) * T(u,K(z,y))) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(19108,a,19507,a),flip(a)].">
      <j1 rule="hyper" parents="19108 19507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19509">
    <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,11514,a(flip),b,19507,a),flip(a)].">
      <j1 rule="hyper" parents="58 11514 19507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19510">
    <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(19507(a,1),18923(a,1,2,2,2))].">
      <j1 rule="para" parents="19507 18923"/>
    </justification>
  </clause>

  <clause id="19511">
    <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(19506,a,17205,a),flip(a)].">
      <j1 rule="hyper" parents="19506 17205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19512">
    <literal><![CDATA[
      x \ ((x * K(y,z)) * (K(z,y) * u)) = L(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[para(11501(a,1),19509(a,1,2))].">
      <j1 rule="para" parents="11501 19509"/>
    </justification>
  </clause>

  <clause id="19513">
    <literal><![CDATA[
      L(x,K(y,z),u * K(z,y)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(6531,a,19512,a)].">
      <j1 rule="hyper" parents="6531 19512"/>
    </justification>
  </clause>

  <clause id="19514">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * u) = x * L(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(134,a,19512,a),flip(a)].">
      <j1 rule="hyper" parents="134 19512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19515">
    <literal><![CDATA[
      L(x,K(y,z),u \ T(z,y)) = L(x,K(y,z),u \ z)
    ]]></literal>
    <justification jstring="[para(14025(a,1),19513(a,1,3))].">
      <j1 rule="para" parents="14025 19513"/>
    </justification>
  </clause>

  <clause id="19516">
    <literal><![CDATA[
      L(x,K(y,z),u) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(19513(a,1),19093(a,1,1))].">
      <j1 rule="para" parents="19513 19093"/>
    </justification>
  </clause>

  <clause id="19517">
    <literal><![CDATA[
      x * L(K(y,z) * u,K(z,y),x) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(5394(a,1),19514(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5394 19514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19518">
    <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(6524(a,1),19516(a,2,1))].">
      <j1 rule="para" parents="6524 19516"/>
    </justification>
  </clause>

  <clause id="19519">
    <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(19517(a,1),15814(a,1,2,2,2,1))].">
      <j1 rule="para" parents="19517 15814"/>
    </justification>
  </clause>

  <clause id="19520">
    <literal><![CDATA[
      x \ ((K(y,z) * x) * T(u,K(y,z))) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(8100(a,1),19508(a,1,2,2))].">
      <j1 rule="para" parents="8100 19508"/>
    </justification>
  </clause>

  <clause id="19521">
    <literal><![CDATA[
      x \ ((K(y,T(z,u)) * x) * u) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(18220(a,2),19508(a,1,2))].">
      <j1 rule="para" parents="18220 19508"/>
    </justification>
  </clause>

  <clause id="19522">
    <literal><![CDATA[
      (x * y) / (y * K(z,T(u,x))) = y \ ((K(u,z) * y) * x)
    ]]></literal>
    <justification jstring="[para(8162(a,1),19521(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="8162 19521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19523">
    <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(19522(a,1),19111(a,1,2))].">
      <j1 rule="para" parents="19522 19111"/>
    </justification>
  </clause>

  <clause id="19524">
    <literal><![CDATA[
      K(x,y / ((z * u) \ (u * y))) = y \ ((y * u) / (u * K(z,x)))
    ]]></literal>
    <justification jstring="[para(19520(a,1),19371(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19520 19371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19525">
    <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(16805(a,1),19511(a,2,2))].">
      <j1 rule="para" parents="16805 19511"/>
    </justification>
  </clause>

  <clause id="19526">
    <literal><![CDATA[
      x * a(y,x,K(x \ z,u)) = z * ((K(y,u) * z) \ (K(y,u) * x))
    ]]></literal>
    <justification jstring="[para(18789(a,1),19525(a,1,2))].">
      <j1 rule="para" parents="18789 19525"/>
    </justification>
  </clause>

  <clause id="19527">
    <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(7934(a,1),19526(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7934 19526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19529">
    <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(14679(a,1),19527(a,2,2))].">
      <j1 rule="para" parents="14679 19527"/>
    </justification>
  </clause>

  <clause id="19530">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,x,K(y,u)) = z * a(u,z,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(17773(a,1),19529(a,1,2))].">
      <j1 rule="para" parents="17773 19529"/>
    </justification>
  </clause>

  <clause id="19531">
    <literal><![CDATA[
      x * a(y,x,K(z,x \ u)) = u * (z * L(z \ (u \ x),u,K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(1130,a,19530,a),flip(a)].">
      <j1 rule="hyper" parents="1130 19530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19532">
    <literal><![CDATA[
      x * L(y * (y \ (x \ z)),x,K(y,u)) = z * a(u,z,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(18851(a,2),19531(a,2,2)),flip(a)].">
      <j1 rule="para" parents="18851 19531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19533">
    <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),19532(a,1,2,1))].">
      <j1 rule="para" parents="5 19532"/>
    </justification>
  </clause>

  <clause id="19535">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = y * a(u,y,K(x \ y,z))
    ]]></literal>
    <justification jstring="[para(11338(a,2),19533(a,2,2))].">
      <j1 rule="para" parents="11338 19533"/>
    </justification>
  </clause>

  <clause id="19536">
    <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(19523(a,1),19510(a,1,2,2))].">
      <j1 rule="para" parents="19523 19510"/>
    </justification>
  </clause>

  <clause id="19537">
    <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(18756,a,19536,a),flip(a)].">
      <j1 rule="hyper" parents="18756 19536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19538">
    <literal><![CDATA[
      K(x,y * L(z,K(u,w),v5)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(16465,a,19537,a),flip(a)].">
      <j1 rule="hyper" parents="16465 19537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19539">
    <literal><![CDATA[
      K(x,y * L(z,K(u,w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v6
    ]]></literal>
    <justification jstring="[para(19537(a,1),16465(a,1))].">
      <j1 rule="para" parents="19537 16465"/>
    </justification>
  </clause>

  <clause id="19541">
    <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(579(a,1),19538(a,1,2,2))].">
      <j1 rule="para" parents="579 19538"/>
    </justification>
  </clause>

  <clause id="19542">
    <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(6530(a,1),19539(a,1,2))].">
      <j1 rule="para" parents="6530 19539"/>
    </justification>
  </clause>

  <clause id="19543">
    <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(5391(a,1),19541(a,2,2,2,1))].">
      <j1 rule="para" parents="5391 19541"/>
    </justification>
  </clause>

  <clause id="19544">
    <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,18764,a,b,19543,a)].">
      <j1 rule="hyper" parents="58 18764 19543"/>
    </justification>
  </clause>

  <clause id="19545">
    <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(5391(a,1),19544(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5391 19544"/>
    </justification>
  </clause>

  <clause id="19546">
    <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,18637,a(flip),b,19545,a)].">
      <j1 rule="hyper" parents="58 18637 19545"/>
    </justification>
  </clause>

  <clause id="19547">
    <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(16149,a,19546,a),flip(a)].">
      <j1 rule="hyper" parents="16149 19546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19548">
    <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),19547(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4 19547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19549">
    <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(17059,a,18553,a)].">
      <j1 rule="hyper" parents="17059 18553"/>
    </justification>
  </clause>

  <clause id="19550">
    <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,15578,a(flip),b,19220,a)].">
      <j1 rule="hyper" parents="58 15578 19220"/>
    </justification>
  </clause>

  <clause id="19551">
    <literal><![CDATA[
      T((x * y) \ y,K(y,y \ z)) = (x * T(y,y \ z)) \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,16970,a(flip),b,19550,a)].">
      <j1 rule="hyper" parents="58 16970 19550"/>
    </justification>
  </clause>

  <clause id="19552">
    <literal><![CDATA[
      (x * T(y,y \ z)) \ ((y \ z) \ z) = T((x * y) \ y,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8386,a,19551,a),flip(a)].">
      <j1 rule="hyper" parents="8386 19551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19553">
    <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(18714,a,19475,a)].">
      <j1 rule="hyper" parents="18714 19475"/>
    </justification>
  </clause>

  <clause id="19554">
    <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),19549(a,1,2,1,1))].">
      <j1 rule="para" parents="4 19549"/>
    </justification>
  </clause>

  <clause id="19556">
    <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(14920,a,18857,a)].">
      <j1 rule="hyper" parents="14920 18857"/>
    </justification>
  </clause>

  <clause id="19557">
    <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(19556(a,1),6670(a,1))].">
      <j1 rule="para" parents="19556 6670"/>
    </justification>
  </clause>

  <clause id="19558">
    <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,18910,a(flip),b,18922,a)].">
      <j1 rule="hyper" parents="58 18910 18922"/>
    </justification>
  </clause>

  <clause id="19560">
    <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,18908,a(flip),b,19558,a)].">
      <j1 rule="hyper" parents="58 18908 19558"/>
    </justification>
  </clause>

  <clause id="19561">
    <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(15952(a,1),19560(a,1,2,1))].">
      <j1 rule="para" parents="15952 19560"/>
    </justification>
  </clause>

  <clause id="19562">
    <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(9743(a,2),19561(a,1,2))].">
      <j1 rule="para" parents="9743 19561"/>
    </justification>
  </clause>

  <clause id="19563">
    <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(8053(a,2),19562(a,1,2,1,1))].">
      <j1 rule="para" parents="8053 19562"/>
    </justification>
  </clause>

  <clause id="19564">
    <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(18213,a,19563,a)].">
      <j1 rule="hyper" parents="18213 19563"/>
    </justification>
  </clause>

  <clause id="19565">
    <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(16328,a,19564,a)].">
      <j1 rule="hyper" parents="16328 19564"/>
    </justification>
  </clause>

  <clause id="19566">
    <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(19565(a,2),13778(a,1,3,2))].">
      <j1 rule="para" parents="19565 13778"/>
    </justification>
  </clause>

  <clause id="19567">
    <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(15476(a,1),19566(a,2,3,2))].">
      <j1 rule="para" parents="15476 19566"/>
    </justification>
  </clause>

  <clause id="19568">
    <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),19393(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 19393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19569">
    <literal><![CDATA[
      K(x,T(y * L(y \ z,u,u \ 1),y)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,19455,a(flip),b,19568,a),flip(a)].">
      <j1 rule="hyper" parents="334 19455 19568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19571">
    <literal><![CDATA[
      K(x,y * L(z / y,u,u \ 1)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(12590,a,19569,a)].">
      <j1 rule="hyper" parents="12590 19569"/>
    </justification>
  </clause>

  <clause id="19573">
    <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(17817(a,2),17842(a,1,1))].">
      <j1 rule="para" parents="17817 17842"/>
    </justification>
  </clause>

  <clause id="19574">
    <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(14259(a,1),18224(a,1,2,2))].">
      <j1 rule="para" parents="14259 18224"/>
    </justification>
  </clause>

  <clause id="19575">
    <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),18272(a,1,2,3))].">
      <j1 rule="para" parents="5 18272"/>
    </justification>
  </clause>

  <clause id="19576">
    <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(14832,a,19575,a),flip(a)].">
      <j1 rule="hyper" parents="14832 19575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19579">
    <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(334,a,14106,a(flip),b,19576,a),flip(a)].">
      <j1 rule="hyper" parents="334 14106 19576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19580">
    <literal><![CDATA[
      K(x,y \ (((L(y,z,u) \ y) \ y) * w)) = K(x,(y \ L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(3729(a,1),19579(a,1,2,2,1,1))].">
      <j1 rule="para" parents="3729 19579"/>
    </justification>
  </clause>

  <clause id="19581">
    <literal><![CDATA[
      K(x,y \ (L(y,z,u) * w)) = K(x,(y \ L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(3960(a,1),19580(a,1,2,2,1))].">
      <j1 rule="para" parents="3960 19580"/>
    </justification>
  </clause>

  <clause id="19582">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) = K(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[para(1503(a,1),19581(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1503 19581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19583">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) * (y \ u)) = K(x,u * a(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(17877,a,19582,a),flip(a)].">
      <j1 rule="hyper" parents="17877 19582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19584">
    <literal><![CDATA[
      K(x,L(y,z,u) * (y \ w)) = K(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(17639,a,19582,a),flip(a)].">
      <j1 rule="hyper" parents="17639 19582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19585">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) * w) = T(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(118,a,19582,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 19582 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19586">
    <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,19432,a(flip),b,19582,a),flip(a)].">
      <j1 rule="hyper" parents="58 19432 19582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19587">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ w)) = T(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(118,a,19584,a,b,5664,a),flip(a)].">
      <j1 rule="hyper" parents="118 19584 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19588">
    <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(19585(a,1),825(a,1,1))].">
      <j1 rule="para" parents="19585 825"/>
    </justification>
  </clause>

  <clause id="19589">
    <literal><![CDATA[
      K(x,a(y \ 1,y,z) \ u) = K(x,u * a(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,15014,a(flip),b,19583,a)].">
      <j1 rule="hyper" parents="58 15014 19583"/>
    </justification>
  </clause>

  <clause id="19590">
    <literal><![CDATA[
      K(x,(y * z) * a(z,u,u \ 1)) = K(x,y * L(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(18594,a,19589,a),flip(a)].">
      <j1 rule="hyper" parents="18594 19589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19591">
    <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(19589(a,1),18594(a,1))].">
      <j1 rule="para" parents="19589 18594"/>
    </justification>
  </clause>

  <clause id="19592">
    <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(10380(a,2),19590(a,1,2,1))].">
      <j1 rule="para" parents="10380 19590"/>
    </justification>
  </clause>

  <clause id="19593">
    <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(334,a,18569,a(flip),b,19312,a),flip(a)].">
      <j1 rule="hyper" parents="334 18569 19312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19595">
    <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(334,a,13357,a(flip),b,19593,a),flip(a)].">
      <j1 rule="hyper" parents="334 13357 19593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19596">
    <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(19552(a,1),19595(a,1,2,2,2))].">
      <j1 rule="para" parents="19552 19595"/>
    </justification>
  </clause>

  <clause id="19597">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * ((w * y) \ y))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(17893,a,19596,a)].">
      <j1 rule="hyper" parents="17893 19596"/>
    </justification>
  </clause>

  <clause id="19598">
    <literal><![CDATA[
      K(x,T(y,z) \ (u * ((w * y) \ y))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(13516,a,19597,a)].">
      <j1 rule="hyper" parents="13516 19597"/>
    </justification>
  </clause>

  <clause id="19599">
    <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,18522,a(flip),b,19598,a)].">
      <j1 rule="hyper" parents="58 18522 19598"/>
    </justification>
  </clause>

  <clause id="19600">
    <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,19045,a,b,19599,a),flip(a)].">
      <j1 rule="hyper" parents="58 19045 19599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19601">
    <literal><![CDATA[
      K(x,((y * ((y * z) / y)) / u) \ z) = K(x,z \ ((z * u) / y))
    ]]></literal>
    <justification jstring="[hyper(16148,a,19600,a),flip(a)].">
      <j1 rule="hyper" parents="16148 19600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19602">
    <literal><![CDATA[
      K(x,((y * z) / u) \ T(z,y)) = K(x,z \ ((z * u) / y))
    ]]></literal>
    <justification jstring="[para(14916(a,1),19601(a,1,2))].">
      <j1 rule="para" parents="14916 19601"/>
    </justification>
  </clause>

  <clause id="19603">
    <literal><![CDATA[
      K(x,T(y / (z \ (u * y)),u)) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(17115,a,19602,a)].">
      <j1 rule="hyper" parents="17115 19602"/>
    </justification>
  </clause>

  <clause id="19604">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ (u * y))) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(18654,a,19603,a)].">
      <j1 rule="hyper" parents="18654 19603"/>
    </justification>
  </clause>

  <clause id="19605">
    <literal><![CDATA[
      K(x,T(y / (z \ (u * y)),z)) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19056,a(flip),b,19603,a)].">
      <j1 rule="hyper" parents="58 19056 19603"/>
    </justification>
  </clause>

  <clause id="19606">
    <literal><![CDATA[
      K(x,y / ((z * u) \ (u * y))) = K(x,y \ ((y * (u * z)) / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19218,a(flip),b,19604,a)].">
      <j1 rule="hyper" parents="58 19218 19604"/>
    </justification>
  </clause>

  <clause id="19607">
    <literal><![CDATA[
      K(x,y / (z \ (T(u,z) * y))) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19055,a,b,19605,a)].">
      <j1 rule="hyper" parents="58 19055 19605"/>
    </justification>
  </clause>

  <clause id="19608">
    <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(334,a,6423,a(flip),b,19451,a),flip(a)].">
      <j1 rule="hyper" parents="334 6423 19451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19609">
    <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,14921,a(flip),b,19608,a),flip(a)].">
      <j1 rule="hyper" parents="114 14921 19608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19610">
    <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(334,a,18792,a(flip),b,19609,a),flip(a)].">
      <j1 rule="hyper" parents="334 18792 19609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19612">
    <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(6520(a,1),19610(a,1,2))].">
      <j1 rule="para" parents="6520 19610"/>
    </justification>
  </clause>

  <clause id="19613">
    <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(18024,a,19612,a)].">
      <j1 rule="hyper" parents="18024 19612"/>
    </justification>
  </clause>

  <clause id="19614">
    <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(5896(a,1),19613(a,1,2,2))].">
      <j1 rule="para" parents="5896 19613"/>
    </justification>
  </clause>

  <clause id="19615">
    <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,19487,a,b,19614,a)].">
      <j1 rule="hyper" parents="58 19487 19614"/>
    </justification>
  </clause>

  <clause id="19617">
    <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(16201(a,2),19573(a,1,2,1))].">
      <j1 rule="para" parents="16201 19573"/>
    </justification>
  </clause>

  <clause id="19618">
    <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(7814(a,1),19574(a,1,2,2))].">
      <j1 rule="para" parents="7814 19574"/>
    </justification>
  </clause>

  <clause id="19620">
    <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(10375(a,1),19618(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10375 19618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19621">
    <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(334,a,14175,a(flip),b,19620,a),flip(a)].">
      <j1 rule="hyper" parents="334 14175 19620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19622">
    <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(334,a,13425,a(flip),b,19621,a),flip(a)].">
      <j1 rule="hyper" parents="334 13425 19621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19623">
    <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(334,a,17874,a(flip),b,19622,a),flip(a)].">
      <j1 rule="hyper" parents="334 17874 19622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19624">
    <literal><![CDATA[
      K(x,y * L((z / (y \ 1)) / y,u,w)) = K(x,y * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(10381(a,1),19623(a,1,2,2,1))].">
      <j1 rule="para" parents="10381 19623"/>
    </justification>
  </clause>

  <clause id="19625">
    <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(19392(a,2),19624(a,2,2,2))].">
      <j1 rule="para" parents="19392 19624"/>
    </justification>
  </clause>

  <clause id="19626">
    <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(14575(a,1),19592(a,1,2,2))].">
      <j1 rule="para" parents="14575 19592"/>
    </justification>
  </clause>

  <clause id="19627">
    <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(17532(a,2),19617(a,1,2))].">
      <j1 rule="para" parents="17532 19617"/>
    </justification>
  </clause>

  <clause id="19628">
    <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,19571,a(flip),b,19625,a)].">
      <j1 rule="hyper" parents="58 19571 19625"/>
    </justification>
  </clause>

  <clause id="19630">
    <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,14499,a(flip),b,19628,a)].">
      <j1 rule="hyper" parents="58 14499 19628"/>
    </justification>
  </clause>

  <clause id="19631">
    <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(12588,a,19630,a),flip(a)].">
      <j1 rule="hyper" parents="12588 19630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19632">
    <literal><![CDATA[
      K(x,y * L(z \ T(u,w),v5,v5 \ 1)) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(19392(a,1),19631(a,1,2,2))].">
      <j1 rule="para" parents="19392 19631"/>
    </justification>
  </clause>

  <clause id="19633">
    <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(15428(a,1),19626(a,1,2,2))].">
      <j1 rule="para" parents="15428 19626"/>
    </justification>
  </clause>

  <clause id="19634">
    <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(17794,a,19627,a)].">
      <j1 rule="hyper" parents="17794 19627"/>
    </justification>
  </clause>

  <clause id="19635">
    <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,18986,a(flip),b,19633,a)].">
      <j1 rule="hyper" parents="58 18986 19633"/>
    </justification>
  </clause>

  <clause id="19636">
    <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(334,a,19624,a(flip),b,19635,a),flip(a)].">
      <j1 rule="hyper" parents="334 19624 19635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19637">
    <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,17864,a(flip),b,19634,a),flip(a)].">
      <j1 rule="hyper" parents="58 17864 19634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19639">
    <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(334,a,15,a,b,19637,a),flip(a)].">
      <j1 rule="hyper" parents="334 15 19637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19640">
    <literal><![CDATA[
      R(x,y,K(z,K(u,w)) * v5) = R(x,y,v5)
    ]]></literal>
    <justification jstring="[para(17839(a,1),19639(a,1,2))].">
      <j1 rule="para" parents="17839 19639"/>
    </justification>
  </clause>

  <clause id="19642">
    <literal><![CDATA[
      R(x,y,z \ (T(u,K(w,v5)) \ v6)) = R(x,y,z \ (u \ v6))
    ]]></literal>
    <justification jstring="[para(17789(a,1),19640(a,1,3)),flip(a)].">
      <j1 rule="para" parents="17789 19640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19643">
    <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,19567,a(flip),b,19642,a),flip(a)].">
      <j1 rule="hyper" parents="58 19567 19642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19645">
    <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,14960,a,b,19643,a)].">
      <j1 rule="hyper" parents="58 14960 19643"/>
    </justification>
  </clause>

  <clause id="19646">
    <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(17791(a,1),19645(a,1,3))].">
      <j1 rule="para" parents="17791 19645"/>
    </justification>
  </clause>

  <clause id="19647">
    <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,19640,a(flip),b,19646,a),flip(a)].">
      <j1 rule="hyper" parents="58 19640 19646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19649">
    <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(19647(a,1),18713(a,1,2,1))].">
      <j1 rule="para" parents="19647 18713"/>
    </justification>
  </clause>

  <clause id="19650">
    <literal><![CDATA[
      K(x,y * (z \ T(u,K(w,v5) * v6))) = K(x,y * (z \ T(u,v6)))
    ]]></literal>
    <justification jstring="[para(515(a,1),19649(a,1,2)),flip(a)].">
      <j1 rule="para" parents="515 19649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19652">
    <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(11089(a,1),17698(a,1,2))].">
      <j1 rule="para" parents="11089 17698"/>
    </justification>
  </clause>

  <clause id="19653">
    <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(13594(a,1),19652(a,1,2,2))].">
      <j1 rule="para" parents="13594 19652"/>
    </justification>
  </clause>

  <clause id="19654">
    <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(17682(a,1),19653(a,1,2))].">
      <j1 rule="para" parents="17682 19653"/>
    </justification>
  </clause>

  <clause id="19655">
    <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(19198(a,1),19654(a,1,2,2))].">
      <j1 rule="para" parents="19198 19654"/>
    </justification>
  </clause>

  <clause id="19656">
    <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(18779(a,1),19655(a,1,2))].">
      <j1 rule="para" parents="18779 19655"/>
    </justification>
  </clause>

  <clause id="19657">
    <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(18418(a,1),19656(a,1,2))].">
      <j1 rule="para" parents="18418 19656"/>
    </justification>
  </clause>

  <clause id="19658">
    <literal><![CDATA[
      x / K(y,L(z,u,u \ x)) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(15034(a,1),19657(a,1,2))].">
      <j1 rule="para" parents="15034 19657"/>
    </justification>
  </clause>

  <clause id="19660">
    <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(19658(a,1),14521(a,1))].">
      <j1 rule="para" parents="19658 14521"/>
    </justification>
  </clause>

  <clause id="19661">
    <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(14894(a,1),19660(a,1))].">
      <j1 rule="para" parents="14894 19660"/>
    </justification>
  </clause>

  <clause id="19662">
    <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(14304(a,1),18464(a,2,1,1,2))].">
      <j1 rule="para" parents="14304 18464"/>
    </justification>
  </clause>

  <clause id="19663">
    <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(334,a,18059,a(flip),b,19662,a),flip(a)].">
      <j1 rule="hyper" parents="334 18059 19662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19664">
    <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(334,a,19139,a(flip),b,19663,a),flip(a)].">
      <j1 rule="hyper" parents="334 19139 19663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19666">
    <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(334,a,19141,a(flip),b,19664,a),flip(a)].">
      <j1 rule="hyper" parents="334 19141 19664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19668">
    <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(334,a,18152,a(flip),b,19666,a),flip(a)].">
      <j1 rule="hyper" parents="334 18152 19666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19669">
    <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(334,a,13477,a(flip),b,19668,a),flip(a)].">
      <j1 rule="hyper" parents="334 13477 19668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19670">
    <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(334,a,14666,a(flip),b,19669,a),flip(a)].">
      <j1 rule="hyper" parents="334 14666 19669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19671">
    <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,15652,a(flip),b,19670,a)].">
      <j1 rule="hyper" parents="58 15652 19670"/>
    </justification>
  </clause>

  <clause id="19672">
    <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(16078(a,1),18111(a,1,2,1,1))].">
      <j1 rule="para" parents="16078 18111"/>
    </justification>
  </clause>

  <clause id="19673">
    <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(12630(a,2),19672(a,1,2,1,1))].">
      <j1 rule="para" parents="12630 19672"/>
    </justification>
  </clause>

  <clause id="19674">
    <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(19199(a,1),19673(a,1,2))].">
      <j1 rule="para" parents="19199 19673"/>
    </justification>
  </clause>

  <clause id="19675">
    <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(19208,a,19674,a)].">
      <j1 rule="hyper" parents="19208 19674"/>
    </justification>
  </clause>

  <clause id="19677">
    <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,18761,a(flip),b,19675,a)].">
      <j1 rule="hyper" parents="58 18761 19675"/>
    </justification>
  </clause>

  <clause id="19678">
    <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(15773,a,19677,a)].">
      <j1 rule="hyper" parents="15773 19677"/>
    </justification>
  </clause>

  <clause id="19680">
    <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(4553(a,1),19678(a,1,2,1,1))].">
      <j1 rule="para" parents="4553 19678"/>
    </justification>
  </clause>

  <clause id="19681">
    <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(13523,a,19680,a)].">
      <j1 rule="hyper" parents="13523 19680"/>
    </justification>
  </clause>

  <clause id="19682">
    <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(334,a,18071,a(flip),b,19681,a),flip(a)].">
      <j1 rule="hyper" parents="334 18071 19681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19683">
    <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(334,a,15499,a(flip),b,19682,a),flip(a)].">
      <j1 rule="hyper" parents="334 15499 19682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19684">
    <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(334,a,19305,a(flip),b,19683,a),flip(a)].">
      <j1 rule="hyper" parents="334 19305 19683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19685">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,z \ (((1 / y) \ z) * u))
    ]]></literal>
    <justification jstring="[para(11906(a,1),19684(a,2,2,2,1))].">
      <j1 rule="para" parents="11906 19684"/>
    </justification>
  </clause>

  <clause id="19686">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(334,a,15819,a(flip),b,19685,a),flip(a)].">
      <j1 rule="hyper" parents="334 15819 19685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19687">
    <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,19479,a(flip),b,19686,a)].">
      <j1 rule="hyper" parents="58 19479 19686"/>
    </justification>
  </clause>

  <clause id="19688">
    <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,13472,a(flip),b,19687,a)].">
      <j1 rule="hyper" parents="58 13472 19687"/>
    </justification>
  </clause>

  <clause id="19689">
    <literal><![CDATA[
      K(x,((y * z) * (y \ 1)) \ ((z * y) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18486,a(flip),b,19688,a)].">
      <j1 rule="hyper" parents="58 18486 19688"/>
    </justification>
  </clause>

  <clause id="19690">
    <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(17914(a,1),17925(a,1,2))].">
      <j1 rule="para" parents="17914 17925"/>
    </justification>
  </clause>

  <clause id="19691">
    <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(10669(a,1),18404(a,2,1))].">
      <j1 rule="para" parents="10669 18404"/>
    </justification>
  </clause>

  <clause id="19692">
    <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(334,a,8100,a,b,19691,a),flip(a)].">
      <j1 rule="hyper" parents="334 8100 19691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19693">
    <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(334,a,16039,a(flip),b,19692,a),flip(a)].">
      <j1 rule="hyper" parents="334 16039 19692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19695">
    <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(8066(a,1),19693(a,1,1))].">
      <j1 rule="para" parents="8066 19693"/>
    </justification>
  </clause>

  <clause id="19696">
    <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(5896(a,1),19695(a,1,2,1,2))].">
      <j1 rule="para" parents="5896 19695"/>
    </justification>
  </clause>

  <clause id="19697">
    <literal><![CDATA[
      (x * (K(y,z) * u)) / u = (x * u) / (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(16247,a,19696,a)].">
      <j1 rule="hyper" parents="16247 19696"/>
    </justification>
  </clause>

  <clause id="19698">
    <literal><![CDATA[
      (x * (y / z)) / (K(u,y) * (y / z)) = (x * (T(y,u) / z)) / (y / z)
    ]]></literal>
    <justification jstring="[para(14034(a,1),19697(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="14034 19697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19699">
    <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(19697(a,1),15191(a,2,2))].">
      <j1 rule="para" parents="19697 15191"/>
    </justification>
  </clause>

  <clause id="19700">
    <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(18901(a,1),19699(a,1,1,1))].">
      <j1 rule="para" parents="18901 19699"/>
    </justification>
  </clause>

  <clause id="19701">
    <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(14797(a,1),19700(a,1,1,1))].">
      <j1 rule="para" parents="14797 19700"/>
    </justification>
  </clause>

  <clause id="19703">
    <literal><![CDATA[
      ((K(x,y) * z) * (K(u,w) * v5)) / v5 = K(x,y) * ((z * v5) / (K(w,u) * v5))
    ]]></literal>
    <justification jstring="[para(18778(a,1),19701(a,1,1))].">
      <j1 rule="para" parents="18778 19701"/>
    </justification>
  </clause>

  <clause id="19704">
    <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,19697,a(flip),b,19703,a)].">
      <j1 rule="hyper" parents="58 19697 19703"/>
    </justification>
  </clause>

  <clause id="19705">
    <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(19100,a,19704,a),flip(a)].">
      <j1 rule="hyper" parents="19100 19704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19706">
    <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),19705(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15 19705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19707">
    <literal><![CDATA[
      L(K(x,y) * z,K(u,w),v5) = K(x,y) * L(z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[para(19088(a,1),19706(a,2,2))].">
      <j1 rule="para" parents="19088 19706"/>
    </justification>
  </clause>

  <clause id="19708">
    <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(334,a,19102,a(flip),b,19707,a),flip(a)].">
      <j1 rule="hyper" parents="334 19102 19707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19709">
    <literal><![CDATA[
      ((x * y) / (K(z,u) * y)) * K(z,u) = L(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(5394(a,1),19708(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5394 19708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19710">
    <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(14069(a,1),19709(a,1,1,2))].">
      <j1 rule="para" parents="14069 19709"/>
    </justification>
  </clause>

  <clause id="19711">
    <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(334,a,18318,a(flip),b,19710,a),flip(a)].">
      <j1 rule="hyper" parents="334 18318 19710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19712">
    <literal><![CDATA[
      ((x * (T(y,z) / u)) / (y / u)) * K(z,y) = L(x,K(z,y),u \ y)
    ]]></literal>
    <justification jstring="[hyper(334,a,19515,a(flip),b,19711,a),flip(a)].">
      <j1 rule="hyper" parents="334 19515 19711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19713">
    <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(18421(a,1),18420(a,1,1))].">
      <j1 rule="para" parents="18421 18420"/>
    </justification>
  </clause>

  <clause id="19714">
    <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(18309(a,1),19519(a,1,2,2,2))].">
      <j1 rule="para" parents="18309 19519"/>
    </justification>
  </clause>

  <clause id="19715">
    <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,19650,a(flip),b,19714,a)].">
      <j1 rule="hyper" parents="58 19650 19714"/>
    </justification>
  </clause>

  <clause id="19718">
    <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,15814,a(flip),b,19715,a),flip(a)].">
      <j1 rule="hyper" parents="58 15814 19715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19719">
    <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(334,a,18621,a(flip),b,19718,a),flip(a)].">
      <j1 rule="hyper" parents="334 18621 19718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19720">
    <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(19518(a,1),19719(a,1,2,2,2))].">
      <j1 rule="para" parents="19518 19719"/>
    </justification>
  </clause>

  <clause id="19721">
    <literal><![CDATA[
      K(x,y * (z \ (u * (K(w,v5) * v6)))) = K(x,y * (K(w,v5) * (z \ (u * v6))))
    ]]></literal>
    <justification jstring="[hyper(17894,a,19720,a)].">
      <j1 rule="hyper" parents="17894 19720"/>
    </justification>
  </clause>

  <clause id="19722">
    <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,19548,a(flip),b,19721,a),flip(a)].">
      <j1 rule="hyper" parents="58 19548 19721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19723">
    <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),19722(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13 19722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19724">
    <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(19542,a,19723,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19542 19723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19725">
    <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(18203,a,19724,a)].">
      <j1 rule="hyper" parents="18203 19724"/>
    </justification>
  </clause>

  <clause id="19726">
    <literal><![CDATA[
      K(x,y * L(y \ 1,z,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19615,a(flip),b,19725,a),flip(a)].">
      <j1 rule="hyper" parents="58 19615 19725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19727">
    <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,19554,a(flip),b,19725,a)].">
      <j1 rule="hyper" parents="58 19554 19725"/>
    </justification>
  </clause>

  <clause id="19728">
    <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,17410,a(flip),b,19726,a)].">
      <j1 rule="hyper" parents="58 17410 19726"/>
    </justification>
  </clause>

  <clause id="19729">
    <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(15934,a,19727,a),flip(a)].">
      <j1 rule="hyper" parents="15934 19727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19731">
    <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(7403(a,1),19728(a,2,3))].">
      <j1 rule="para" parents="7403 19728"/>
    </justification>
  </clause>

  <clause id="19732">
    <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(5704(a,1),19731(a,2,3))].">
      <j1 rule="para" parents="5704 19731"/>
    </justification>
  </clause>

  <clause id="19733">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / (z \ y)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[para(7457(a,1),19732(a,2,3))].">
      <j1 rule="para" parents="7457 19732"/>
    </justification>
  </clause>

  <clause id="19734">
    <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,15835,a(flip),b,19729,a)].">
      <j1 rule="hyper" parents="58 15835 19729"/>
    </justification>
  </clause>

  <clause id="19735">
    <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,15861,a(flip),b,19734,a)].">
      <j1 rule="hyper" parents="58 15861 19734"/>
    </justification>
  </clause>

  <clause id="19736">
    <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),19735(a,1,2,1))].">
      <j1 rule="para" parents="6 19735"/>
    </justification>
  </clause>

  <clause id="19737">
    <literal><![CDATA[
      K(x,L(y / (z * y),u,w) * z) = K(x,z * L((y * z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(18429,a,19736,a)].">
      <j1 rule="hyper" parents="18429 19736"/>
    </justification>
  </clause>

  <clause id="19738">
    <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(861,a,19690,a)].">
      <j1 rule="hyper" parents="861 19690"/>
    </justification>
  </clause>

  <clause id="19739">
    <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(14605(a,1),19738(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14605 19738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19740">
    <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(17919(a,1),19739(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17919 19739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19741">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)) * v5,v6) = L(x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(334,a,17673,a(flip),b,19740,a),flip(a)].">
      <j1 rule="hyper" parents="334 17673 19740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19743">
    <literal><![CDATA[
      L(x,L(y,z,K(u,w)),v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[para(15290(a,1),19741(a,1,2))].">
      <j1 rule="para" parents="15290 19741"/>
    </justification>
  </clause>

  <clause id="19744">
    <literal><![CDATA[
      L(x,y * a(z,u,K(w,v5)),v6) = L(x,y,v6)
    ]]></literal>
    <justification jstring="[para(17549(a,1),19741(a,1,2))].">
      <j1 rule="para" parents="17549 19741"/>
    </justification>
  </clause>

  <clause id="19746">
    <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(13605,a,19744,a),flip(a)].">
      <j1 rule="hyper" parents="13605 19744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19747">
    <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(334,a,17917,a(flip),b,19746,a),flip(a)].">
      <j1 rule="hyper" parents="334 17917 19746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19748">
    <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),19747(a,2,2))].">
      <j1 rule="para" parents="13 19747"/>
    </justification>
  </clause>

  <clause id="19749">
    <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(14654(a,1),19748(a,1,1,1))].">
      <j1 rule="para" parents="14654 19748"/>
    </justification>
  </clause>

  <clause id="19750">
    <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(17919(a,1),19749(a,1,1))].">
      <j1 rule="para" parents="17919 19749"/>
    </justification>
  </clause>

  <clause id="19751">
    <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(19750(a,2),17884(a,2,2))].">
      <j1 rule="para" parents="19750 17884"/>
    </justification>
  </clause>

  <clause id="19753">
    <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(17920(a,1),19713(a,1,2))].">
      <j1 rule="para" parents="17920 19713"/>
    </justification>
  </clause>

  <clause id="19754">
    <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,17928,a(flip),b,19753,a)].">
      <j1 rule="hyper" parents="58 17928 19753"/>
    </justification>
  </clause>

  <clause id="19755">
    <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(17915(a,1),19754(a,1,1))].">
      <j1 rule="para" parents="17915 19754"/>
    </justification>
  </clause>

  <clause id="19756">
    <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(14770(a,2),19755(a,1,1,2))].">
      <j1 rule="para" parents="14770 19755"/>
    </justification>
  </clause>

  <clause id="19757">
    <literal><![CDATA[
      a(x * (y * a(z,u,K(w,v5))),v6,v7) = a(x * y,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(17671,a,19756,a),flip(a)].">
      <j1 rule="hyper" parents="17671 19756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19758">
    <literal><![CDATA[
      a(a(x,y,K(z,u)) * w,v5,v6) = a(w,v5,v6)
    ]]></literal>
    <justification jstring="[para(17663(a,1),19757(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17663 19757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19759">
    <literal><![CDATA[
      a(L(x,y,K(z,u)),w,v5) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[para(15290(a,1),19758(a,1,1))].">
      <j1 rule="para" parents="15290 19758"/>
    </justification>
  </clause>

  <clause id="19760">
    <literal><![CDATA[
      a(x \ L(y,z,K(u,w)),v5,v6) = a(x \ y,v5,v6)
    ]]></literal>
    <justification jstring="[para(17688(a,1),19758(a,1,1))].">
      <j1 rule="para" parents="17688 19758"/>
    </justification>
  </clause>

  <clause id="19761">
    <literal><![CDATA[
      a(L(x,y,K(z,u)) \ w,v5,v6) = a(x \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(17806(a,1),19758(a,1,1))].">
      <j1 rule="para" parents="17806 19758"/>
    </justification>
  </clause>

  <clause id="19762">
    <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),19759(a,1,1))].">
      <j1 rule="para" parents="25 19759"/>
    </justification>
  </clause>

  <clause id="19763">
    <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(18154(a,1),18290(a,1,1,3))].">
      <j1 rule="para" parents="18154 18290"/>
    </justification>
  </clause>

  <clause id="19764">
    <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(18791(a,1),19763(a,1,1))].">
      <j1 rule="para" parents="18791 19763"/>
    </justification>
  </clause>

  <clause id="19765">
    <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,18889,a(flip),b,19764,a)].">
      <j1 rule="hyper" parents="58 18889 19764"/>
    </justification>
  </clause>

  <clause id="19767">
    <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(18591(a,1),19765(a,1,2))].">
      <j1 rule="para" parents="18591 19765"/>
    </justification>
  </clause>

  <clause id="19768">
    <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(14344(a,1),19767(a,1,2))].">
      <j1 rule="para" parents="14344 19767"/>
    </justification>
  </clause>

  <clause id="19769">
    <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(18193(a,1),19768(a,1,2))].">
      <j1 rule="para" parents="18193 19768"/>
    </justification>
  </clause>

  <clause id="19770">
    <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(334,a,17797,a(flip),b,19769,a),flip(a)].">
      <j1 rule="hyper" parents="334 17797 19769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19771">
    <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(334,a,19439,a(flip),b,19770,a),flip(a)].">
      <j1 rule="hyper" parents="334 19439 19770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19772">
    <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(334,a,18750,a(flip),b,19771,a),flip(a)].">
      <j1 rule="hyper" parents="334 18750 19771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19773">
    <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(9754(a,1),19484(a,1,1))].">
      <j1 rule="para" parents="9754 19484"/>
    </justification>
  </clause>

  <clause id="19774">
    <literal><![CDATA[
      K(x,(y \ (z \ (u * z))) \ (y \ (u * z))) = K(x,L(T(z,u),u,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(16029,a,19773,a),flip(a)].">
      <j1 rule="hyper" parents="16029 19773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19776">
    <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),19774(a,1,2,1,2))].">
      <j1 rule="para" parents="17 19774"/>
    </justification>
  </clause>

  <clause id="19777">
    <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(16508,a,19450,a),flip(a)].">
      <j1 rule="hyper" parents="16508 19450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19778">
    <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(334,a,18212,a(flip),b,19777,a),flip(a)].">
      <j1 rule="hyper" parents="334 18212 19777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19779">
    <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(17719(a,1),19778(a,1,2,2,2))].">
      <j1 rule="para" parents="17719 19778"/>
    </justification>
  </clause>

  <clause id="19780">
    <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(19557,a,19779,a),flip(a)].">
      <j1 rule="hyper" parents="19557 19779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19781">
    <literal><![CDATA[
      K(x,y * ((z \ L(y,u,w)) / L(y,u,w))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(1306(a,1),19780(a,1,2,2,1,2,1))].">
      <j1 rule="para" parents="1306 19780"/>
    </justification>
  </clause>

  <clause id="19782">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ (L(y,z,u) / w))) = K(x,y / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,16761,a(flip),b,19781,a)].">
      <j1 rule="hyper" parents="58 16761 19781"/>
    </justification>
  </clause>

  <clause id="19783">
    <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(17253(a,1),15059(a,1,2,2,2,2))].">
      <j1 rule="para" parents="17253 15059"/>
    </justification>
  </clause>

  <clause id="19784">
    <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),19783(a,1,2,2))].">
      <j1 rule="para" parents="91 19783"/>
    </justification>
  </clause>

  <clause id="19785">
    <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(15593,a,19784,a)].">
      <j1 rule="hyper" parents="15593 19784"/>
    </justification>
  </clause>

  <clause id="19786">
    <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(15640,a,19785,a)].">
      <j1 rule="hyper" parents="15640 19785"/>
    </justification>
  </clause>

  <clause id="19787">
    <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(17253(a,1),19786(a,2,3,1))].">
      <j1 rule="para" parents="17253 19786"/>
    </justification>
  </clause>

  <clause id="19788">
    <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(12524(a,1),19787(a,2,3))].">
      <j1 rule="para" parents="12524 19787"/>
    </justification>
  </clause>

  <clause id="19789">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ L(y / (u \ z),u \ z,u)) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,17730,a(flip),b,19788,a),flip(a)].">
      <j1 rule="hyper" parents="334 17730 19788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19791">
    <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,17522,a,b,19789,a)].">
      <j1 rule="hyper" parents="58 17522 19789"/>
    </justification>
  </clause>

  <clause id="19792">
    <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(18746(a,1),19791(a,1,1,2))].">
      <j1 rule="para" parents="18746 19791"/>
    </justification>
  </clause>

  <clause id="19793">
    <literal><![CDATA[
      K(x,L(y / (z \ u),z \ u,z) / (y * (u \ z))) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(208,a,19792,a)].">
      <j1 rule="hyper" parents="208 19792"/>
    </justification>
  </clause>

  <clause id="19795">
    <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(13719(a,1),15217(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13719 15217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19796">
    <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(334,a,14667,a(flip),b,19795,a),flip(a)].">
      <j1 rule="hyper" parents="334 14667 19795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19798">
    <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(932(a,1),19796(a,1,1))].">
      <j1 rule="para" parents="932 19796"/>
    </justification>
  </clause>

  <clause id="19799">
    <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(19088(a,1),18742(a,1,1,1,2))].">
      <j1 rule="para" parents="19088 18742"/>
    </justification>
  </clause>

  <clause id="19800">
    <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(18312(a,1),19799(a,1,1,1,2))].">
      <j1 rule="para" parents="18312 19799"/>
    </justification>
  </clause>

  <clause id="19802">
    <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(19513(a,1),19800(a,1,1,1,2))].">
      <j1 rule="para" parents="19513 19800"/>
    </justification>
  </clause>

  <clause id="19803">
    <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(19097(a,1),19802(a,1,1))].">
      <j1 rule="para" parents="19097 19802"/>
    </justification>
  </clause>

  <clause id="19804">
    <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(16762(a,1),19803(a,1,3))].">
      <j1 rule="para" parents="16762 19803"/>
    </justification>
  </clause>

  <clause id="19806">
    <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,19204,a,b,19804,a)].">
      <j1 rule="hyper" parents="58 19204 19804"/>
    </justification>
  </clause>

  <clause id="19807">
    <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(8113(a,1),19806(a,1,3,1))].">
      <j1 rule="para" parents="8113 19806"/>
    </justification>
  </clause>

  <clause id="19808">
    <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(19807(a,1),17658(a,1))].">
      <j1 rule="para" parents="19807 17658"/>
    </justification>
  </clause>

  <clause id="19809">
    <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(19210(a,1),19808(a,1))].">
      <j1 rule="para" parents="19210 19808"/>
    </justification>
  </clause>

  <clause id="19811">
    <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(18047(a,1),14352(a,1,1))].">
      <j1 rule="para" parents="18047 14352"/>
    </justification>
  </clause>

  <clause id="19812">
    <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(18047(a,1),14353(a,1,1))].">
      <j1 rule="para" parents="18047 14353"/>
    </justification>
  </clause>

  <clause id="19813">
    <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(11134(a,1),18871(a,1,3))].">
      <j1 rule="para" parents="11134 18871"/>
    </justification>
  </clause>

  <clause id="19814">
    <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,18866,a(flip),b,19813,a)].">
      <j1 rule="hyper" parents="58 18866 19813"/>
    </justification>
  </clause>

  <clause id="19816">
    <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(11137(a,1),19814(a,1,3))].">
      <j1 rule="para" parents="11137 19814"/>
    </justification>
  </clause>

  <clause id="19817">
    <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(7423(a,2),19816(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7423 19816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19818">
    <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(13317(a,1),19811(a,1,1))].">
      <j1 rule="para" parents="13317 19811"/>
    </justification>
  </clause>

  <clause id="19819">
    <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(7974,a,19818,a)].">
      <j1 rule="hyper" parents="7974 19818"/>
    </justification>
  </clause>

  <clause id="19820">
    <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(16824,a,19819,a)].">
      <j1 rule="hyper" parents="16824 19819"/>
    </justification>
  </clause>

  <clause id="19822">
    <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),19820(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 19820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19823">
    <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(334,a,16767,a(flip),b,19822,a),flip(a)].">
      <j1 rule="hyper" parents="334 16767 19822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19826">
    <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(13394(a,1),19812(a,1,1))].">
      <j1 rule="para" parents="13394 19812"/>
    </justification>
  </clause>

  <clause id="19827">
    <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(7974,a,19826,a)].">
      <j1 rule="hyper" parents="7974 19826"/>
    </justification>
  </clause>

  <clause id="19828">
    <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(16824,a,19827,a)].">
      <j1 rule="hyper" parents="16824 19827"/>
    </justification>
  </clause>

  <clause id="19830">
    <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),19828(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 19828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19831">
    <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(334,a,16767,a(flip),b,19830,a),flip(a)].">
      <j1 rule="hyper" parents="334 16767 19830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19834">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),u)) = K(x,w * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,17108,a(flip),b,19831,a),flip(a)].">
      <j1 rule="hyper" parents="58 17108 19831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19835">
    <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,19823,a,b,19834,a)].">
      <j1 rule="hyper" parents="58 19823 19834"/>
    </justification>
  </clause>

  <clause id="19836">
    <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(6749(a,1),19835(a,1,2))].">
      <j1 rule="para" parents="6749 19835"/>
    </justification>
  </clause>

  <clause id="19837">
    <literal><![CDATA[
      K(x,y * (z * K(u \ w,u))) = K(x,y * (K(w,u) * z))
    ]]></literal>
    <justification jstring="[hyper(14323,a,19836,a)].">
      <j1 rule="hyper" parents="14323 19836"/>
    </justification>
  </clause>

  <clause id="19838">
    <literal><![CDATA[
      K(x,y * (z \ ((u \ w) * u))) = K(x,y * (K(w,u) * (z \ w)))
    ]]></literal>
    <justification jstring="[para(14559(a,1),19837(a,1,2,2))].">
      <j1 rule="para" parents="14559 19837"/>
    </justification>
  </clause>

  <clause id="19839">
    <literal><![CDATA[
      K(x,y * (z \ ((u \ w) * u))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,16438,a(flip),b,19838,a),flip(a)].">
      <j1 rule="hyper" parents="334 16438 19838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19840">
    <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,16558,a(flip),b,19839,a)].">
      <j1 rule="hyper" parents="58 16558 19839"/>
    </justification>
  </clause>

  <clause id="19841">
    <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(14460(a,1),19840(a,2,2,2,2))].">
      <j1 rule="para" parents="14460 19840"/>
    </justification>
  </clause>

  <clause id="19842">
    <literal><![CDATA[
      K(x,T(y * (z \ u),((z \ u) * y) \ u)) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(334,a,13469,a(flip),b,19841,a),flip(a)].">
      <j1 rule="hyper" parents="334 13469 19841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19843">
    <literal><![CDATA[
      K(x,T(y * (z \ u),y \ ((z \ u) \ u))) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(17687,a,19842,a)].">
      <j1 rule="hyper" parents="17687 19842"/>
    </justification>
  </clause>

  <clause id="19844">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z \ y)) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17862,a(flip),b,19843,a)].">
      <j1 rule="hyper" parents="58 17862 19843"/>
    </justification>
  </clause>

  <clause id="19845">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z * y)) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(16313,a,19844,a)].">
      <j1 rule="hyper" parents="16313 19844"/>
    </justification>
  </clause>

  <clause id="19847">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z * y)) = K(x,y * (z \ T(u,z * y)))
    ]]></literal>
    <justification jstring="[hyper(334,a,19427,a(flip),b,19845,a),flip(a)].">
      <j1 rule="hyper" parents="334 19427 19845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19848">
    <literal><![CDATA[
      K(x,y * (z \ T(u,z * y))) = K(x,(u / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18706,a(flip),b,19847,a),flip(a)].">
      <j1 rule="hyper" parents="58 18706 19847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19849">
    <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,19586,a(flip),b,19848,a),flip(a)].">
      <j1 rule="hyper" parents="58 19586 19848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19850">
    <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),19849(a,1,2,2))].">
      <j1 rule="para" parents="180 19849"/>
    </justification>
  </clause>

  <clause id="19851">
    <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,19632,a(flip),b,19850,a),flip(a)].">
      <j1 rule="hyper" parents="58 19632 19850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19852">
    <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),19851(a,2,2))].">
      <j1 rule="para" parents="7 19851"/>
    </justification>
  </clause>

  <clause id="19853">
    <literal><![CDATA[
      K(x,y * a(z \ T(u,w),v5,v5 \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15907,a,19852,a)].">
      <j1 rule="hyper" parents="15907 19852"/>
    </justification>
  </clause>

  <clause id="19856">
    <literal><![CDATA[
      K(x,y * a(z,u,u \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),19853(a,1,2,2,1))].">
      <j1 rule="para" parents="75 19853"/>
    </justification>
  </clause>

  <clause id="19857">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(19591,a,19856,a)].">
      <j1 rule="hyper" parents="19591 19856"/>
    </justification>
  </clause>

  <clause id="19858">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,19636,a(flip),b,19856,a)].">
      <j1 rule="hyper" parents="58 19636 19856"/>
    </justification>
  </clause>

  <clause id="19859">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(13727(a,1),19856(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13727 19856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19861">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15704,a,b,19859,a)].">
      <j1 rule="hyper" parents="58 15704 19859"/>
    </justification>
  </clause>

  <clause id="19864">
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15843,a(flip),b,19857,a)].">
      <j1 rule="hyper" parents="58 15843 19857"/>
    </justification>
  </clause>

  <clause id="19866">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ u) = K(x,w * (L(w,v5,v5 \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(334,a,19859,a,b,19861,a)].">
      <j1 rule="hyper" parents="334 19859 19861"/>
    </justification>
  </clause>

  <clause id="19867">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,19782,a(flip),b,19861,a),flip(a)].">
      <j1 rule="hyper" parents="58 19782 19861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19869">
    <literal><![CDATA[
      K(x,y * (z / (u \ 1))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,5599,a(flip),b,19864,a),flip(a)].">
      <j1 rule="hyper" parents="58 5599 19864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19871">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = w
    ]]></literal>
    <justification jstring="[para(19858(a,2),14346(a,1))].">
      <j1 rule="para" parents="19858 14346"/>
    </justification>
  </clause>

  <clause id="19872">
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z / u)) = w
    ]]></literal>
    <justification jstring="[para(15843(a,1),19871(a,1))].">
      <j1 rule="para" parents="15843 19871"/>
    </justification>
  </clause>

  <clause id="19873">
    <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(17111(a,2),19872(a,1))].">
      <j1 rule="para" parents="17111 19872"/>
    </justification>
  </clause>

  <clause id="19874">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) \ (y * u)) = K(x,a(w,v5,v5 \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1509(a,2),19866(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1509 19866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19875">
    <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,19047,a,b,19874,a),flip(a)].">
      <j1 rule="hyper" parents="58 19047 19874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19880">
    <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(3975(a,1),19875(a,2,2,1,2))].">
      <j1 rule="para" parents="3975 19875"/>
    </justification>
  </clause>

  <clause id="19881">
    <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(14112(a,1),19880(a,2,2,1))].">
      <j1 rule="para" parents="14112 19880"/>
    </justification>
  </clause>

  <clause id="19882">
    <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(334,a,14668,a(flip),b,19881,a),flip(a)].">
      <j1 rule="hyper" parents="334 14668 19881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19883">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ (u \ L(w,v5,v5 \ 1))) = K(x,u \ w)
    ]]></literal>
    <justification jstring="[para(4360(a,1),19882(a,2,2,2))].">
      <j1 rule="para" parents="4360 19882"/>
    </justification>
  </clause>

  <clause id="19884">
    <literal><![CDATA[
      K(x,y \ L(z,u,u \ 1)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,19859,a(flip),b,19883,a)].">
      <j1 rule="hyper" parents="58 19859 19883"/>
    </justification>
  </clause>

  <clause id="19886">
    <literal><![CDATA[
      K(x,y \ (z * (u \ 1))) = K(x,y \ (z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15904,a(flip),b,19884,a)].">
      <j1 rule="hyper" parents="58 15904 19884"/>
    </justification>
  </clause>

  <clause id="19887">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ u) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15056,a(flip),b,19884,a),flip(a)].">
      <j1 rule="hyper" parents="58 15056 19884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19888">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ z) \ u) = w
    ]]></literal>
    <justification jstring="[para(19884(a,1),19059(a,1))].">
      <j1 rule="para" parents="19884 19059"/>
    </justification>
  </clause>

  <clause id="19891">
    <literal><![CDATA[
      K(x,((y * z) / y) \ ((z * y) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19689,a(flip),b,19887,a),flip(a)].">
      <j1 rule="hyper" parents="58 19689 19887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19893">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,y \ ((T(y,z) * z) * u))
    ]]></literal>
    <justification jstring="[para(15208(a,1),19891(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15208 19891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19894">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,y \ ((z * y) * u))
    ]]></literal>
    <justification jstring="[hyper(334,a,18564,a(flip),b,19893,a),flip(a)].">
      <j1 rule="hyper" parents="334 18564 19893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19895">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y * z)) = K(x,z \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18571,a,b,19894,a)].">
      <j1 rule="hyper" parents="58 18571 19894"/>
    </justification>
  </clause>

  <clause id="19896">
    <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(18259(a,1),16341(a,1,1))].">
      <j1 rule="para" parents="18259 16341"/>
    </justification>
  </clause>

  <clause id="19897">
    <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(16440(a,1),18577(a,1,1))].">
      <j1 rule="para" parents="16440 18577"/>
    </justification>
  </clause>

  <clause id="19899">
    <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(19430(a,1),19897(a,1,1))].">
      <j1 rule="para" parents="19430 19897"/>
    </justification>
  </clause>

  <clause id="19900">
    <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,19190,a(flip),b,19899,a)].">
      <j1 rule="hyper" parents="58 19190 19899"/>
    </justification>
  </clause>

  <clause id="19901">
    <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,18947,a,b,19900,a)].">
      <j1 rule="hyper" parents="58 18947 19900"/>
    </justification>
  </clause>

  <clause id="19902">
    <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(16001,a,19901,a)].">
      <j1 rule="hyper" parents="16001 19901"/>
    </justification>
  </clause>

  <clause id="19904">
    <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(16821,a,19902,a),flip(a)].">
      <j1 rule="hyper" parents="16821 19902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19905">
    <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(334,a,15971,a(flip),b,19904,a),flip(a)].">
      <j1 rule="hyper" parents="334 15971 19904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19906">
    <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(18576(a,1),19905(a,1,2))].">
      <j1 rule="para" parents="18576 19905"/>
    </justification>
  </clause>

  <clause id="19907">
    <literal><![CDATA[
      K(x,y * T(z,T(u / w,v5))) = K(x,y * T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(14323,a,19906,a)].">
      <j1 rule="hyper" parents="14323 19906"/>
    </justification>
  </clause>

  <clause id="19908">
    <literal><![CDATA[
      K(x,y * T(z,u \ w)) = K(x,y * T(z,w * u))
    ]]></literal>
    <justification jstring="[para(107(a,1),19907(a,1,2,2,2))].">
      <j1 rule="para" parents="107 19907"/>
    </justification>
  </clause>

  <clause id="19909">
    <literal><![CDATA[
      K(x,y * T(z,u \ (w \ v5))) = K(x,y * T(z,v5 * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(18258,a,19908,a)].">
      <j1 rule="hyper" parents="18258 19908"/>
    </justification>
  </clause>

  <clause id="19910">
    <literal><![CDATA[
      K(x,y * T(z,(u \ w) * v5)) = K(x,y * T(z,w * (v5 * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19908,a(flip),b,19909,a)].">
      <j1 rule="hyper" parents="58 19908 19909"/>
    </justification>
  </clause>

  <clause id="19911">
    <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,16962,a(flip),b,19910,a),flip(a)].">
      <j1 rule="hyper" parents="58 16962 19910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19912">
    <literal><![CDATA[
      K(x,T((y \ z) * T(u,z * (x * y)),w)) = K(T(x,w),u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(7970,a,19911,a)].">
      <j1 rule="hyper" parents="7970 19911"/>
    </justification>
  </clause>

  <clause id="19913">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(T(x,z * u),y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(15958,a,19912,a)].">
      <j1 rule="hyper" parents="15958 19912"/>
    </justification>
  </clause>

  <clause id="19914">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(x,T(y * (u \ z),z * u))
    ]]></literal>
    <justification jstring="[hyper(334,a,7403,a(flip),b,19913,a),flip(a)].">
      <j1 rule="hyper" parents="334 7403 19913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19915">
    <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(19914(a,2),15959(a,1))].">
      <j1 rule="para" parents="19914 15959"/>
    </justification>
  </clause>

  <clause id="19916">
    <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(7974,a,19896,a)].">
      <j1 rule="hyper" parents="7974 19896"/>
    </justification>
  </clause>

  <clause id="19917">
    <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(16824,a,19916,a)].">
      <j1 rule="hyper" parents="16824 19916"/>
    </justification>
  </clause>

  <clause id="19919">
    <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),19917(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 19917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19920">
    <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(334,a,16787,a(flip),b,19919,a),flip(a)].">
      <j1 rule="hyper" parents="334 16787 19919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19923">
    <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(334,a,19834,a(flip),b,19920,a),flip(a)].">
      <j1 rule="hyper" parents="334 19834 19920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19924">
    <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(16199(a,1),19923(a,1,2))].">
      <j1 rule="para" parents="16199 19923"/>
    </justification>
  </clause>

  <clause id="19925">
    <literal><![CDATA[
      K(x,y * ((z * K(u,w)) * v5)) = K(x,y * (K(u,w) * (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(14323,a,19924,a)].">
      <j1 rule="hyper" parents="14323 19924"/>
    </justification>
  </clause>

  <clause id="19926">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((w * z) * v5))) = K(x,y * ((w * T(z,u)) * v5))
    ]]></literal>
    <justification jstring="[para(6432(a,1),19925(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6432 19925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19927">
    <literal><![CDATA[
      K(x,y * ((z * T(u,x)) * w)) = K(x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[hyper(18065,a,19926,a),flip(a)].">
      <j1 rule="hyper" parents="18065 19926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19928">
    <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,18719,a(flip),b,19927,a),flip(a)].">
      <j1 rule="hyper" parents="58 18719 19927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19929">
    <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),19928(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 19928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19930">
    <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,18124,a,b,19929,a),flip(a)].">
      <j1 rule="hyper" parents="58 18124 19929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19932">
    <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,18157,a(flip),b,19930,a),flip(a)].">
      <j1 rule="hyper" parents="58 18157 19930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19933">
    <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,19452,a(flip),b,19932,a)].">
      <j1 rule="hyper" parents="58 19452 19932"/>
    </justification>
  </clause>

  <clause id="19934">
    <literal><![CDATA[
      K(x,(y \ T(z,K(u,w) * v5)) * v6) = K(x,(y \ ((v5 * z) / v5)) * v6)
    ]]></literal>
    <justification jstring="[para(5394(a,1),19933(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5394 19933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19935">
    <literal><![CDATA[
      K(x,(y \ T(z,K(u,w) * v5)) * v6) = K(x,(y \ T(z,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(334,a,15835,a(flip),b,19934,a),flip(a)].">
      <j1 rule="hyper" parents="334 15835 19934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19936">
    <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,17009,a(flip),b,19935,a)].">
      <j1 rule="hyper" parents="58 17009 19935"/>
    </justification>
  </clause>

  <clause id="19938">
    <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(17829(a,1),18261(a,1,1,1,1))].">
      <j1 rule="para" parents="17829 18261"/>
    </justification>
  </clause>

  <clause id="19939">
    <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(8157(a,1),19938(a,1,1,1,1,1))].">
      <j1 rule="para" parents="8157 19938"/>
    </justification>
  </clause>

  <clause id="19941">
    <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(19318(a,1),19939(a,1,1))].">
      <j1 rule="para" parents="19318 19939"/>
    </justification>
  </clause>

  <clause id="19943">
    <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(14175(a,1),18998(a,1,1,1))].">
      <j1 rule="para" parents="14175 18998"/>
    </justification>
  </clause>

  <clause id="19944">
    <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(14106(a,1),19943(a,1,1,2,3))].">
      <j1 rule="para" parents="14106 19943"/>
    </justification>
  </clause>

  <clause id="19945">
    <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(18802(a,1),19944(a,1,1,2))].">
      <j1 rule="para" parents="18802 19944"/>
    </justification>
  </clause>

  <clause id="19946">
    <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,19012,a(flip),b,19945,a)].">
      <j1 rule="hyper" parents="58 19012 19945"/>
    </justification>
  </clause>

  <clause id="19947">
    <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(334,a,18997,a(flip),b,19946,a),flip(a)].">
      <j1 rule="hyper" parents="334 18997 19946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19949">
    <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(334,a,14375,a(flip),b,19817,a),flip(a)].">
      <j1 rule="hyper" parents="334 14375 19817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19951">
    <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(7889(a,1),19949(a,1,2,2))].">
      <j1 rule="para" parents="7889 19949"/>
    </justification>
  </clause>

  <clause id="19952">
    <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(7314(a,1),19951(a,1,2,2))].">
      <j1 rule="para" parents="7314 19951"/>
    </justification>
  </clause>

  <clause id="19955">
    <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(11134(a,1),19952(a,1,2,2))].">
      <j1 rule="para" parents="11134 19952"/>
    </justification>
  </clause>

  <clause id="19956">
    <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(7423(a,1),19955(a,1,2,1,1))].">
      <j1 rule="para" parents="7423 19955"/>
    </justification>
  </clause>

  <clause id="19957">
    <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(7455(a,1),19956(a,1,2,2))].">
      <j1 rule="para" parents="7455 19956"/>
    </justification>
  </clause>

  <clause id="19958">
    <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(334,a,19336,a(flip),b,19957,a),flip(a)].">
      <j1 rule="hyper" parents="334 19336 19957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19960">
    <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(11137(a,1),19958(a,1,2,2))].">
      <j1 rule="para" parents="11137 19958"/>
    </justification>
  </clause>

  <clause id="19961">
    <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(18776(a,1),19960(a,1,2))].">
      <j1 rule="para" parents="18776 19960"/>
    </justification>
  </clause>

  <clause id="19962">
    <literal><![CDATA[
      (x * y) \ ((K(z,u) * x) * (K(u,T(z,x)) * y)) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(7553(a,1),19961(a,1,2,2))].">
      <j1 rule="para" parents="7553 19961"/>
    </justification>
  </clause>

  <clause id="19963">
    <literal><![CDATA[
      (x * y) \ ((x * K(z,u)) * (K(u,z) * y)) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(11501(a,1),19962(a,1,2))].">
      <j1 rule="para" parents="11501 19962"/>
    </justification>
  </clause>

  <clause id="19964">
    <literal><![CDATA[
      a(x,K(y,z),K(z,y) * u) = a(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(5428,a,19963,a)].">
      <j1 rule="hyper" parents="5428 19963"/>
    </justification>
  </clause>

  <clause id="19965">
    <literal><![CDATA[
      a(x,K(y,z),u * K(z,y)) = a(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(19321,a,19964,a)].">
      <j1 rule="hyper" parents="19321 19964"/>
    </justification>
  </clause>

  <clause id="19966">
    <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,11532,a(flip),b,19964,a)].">
      <j1 rule="hyper" parents="58 11532 19964"/>
    </justification>
  </clause>

  <clause id="19967">
    <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(19965(a,1),19809(a,1))].">
      <j1 rule="para" parents="19965 19809"/>
    </justification>
  </clause>

  <clause id="19968">
    <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(5394(a,1),19966(a,1,1,1))].">
      <j1 rule="para" parents="5394 19966"/>
    </justification>
  </clause>

  <clause id="19969">
    <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(19088(a,1),19968(a,1,2,1))].">
      <j1 rule="para" parents="19088 19968"/>
    </justification>
  </clause>

  <clause id="19970">
    <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(5394(a,1),19969(a,1,2,2,1))].">
      <j1 rule="para" parents="5394 19969"/>
    </justification>
  </clause>

  <clause id="19971">
    <literal><![CDATA[
      (x * y) \ (x * L(y,K(z,u),K(u,z) * x)) = a(y,K(z,u),x)
    ]]></literal>
    <justification jstring="[para(18338(a,1),19970(a,1,2))].">
      <j1 rule="para" parents="18338 19970"/>
    </justification>
  </clause>

  <clause id="19972">
    <literal><![CDATA[
      (x * y) \ ((x * K(z,u)) * (K(u,z) * y)) = a(y,K(u,z),x)
    ]]></literal>
    <justification jstring="[para(17678(a,1),19971(a,1,2))].">
      <j1 rule="para" parents="17678 19971"/>
    </justification>
  </clause>

  <clause id="19973">
    <literal><![CDATA[
      a(x,K(y,z),u) = a(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,19963,a(flip),b,19972,a)].">
      <j1 rule="hyper" parents="58 19963 19972"/>
    </justification>
  </clause>

  <clause id="19974">
    <literal><![CDATA[
      a(T(x,y),K(z,u),w) = a(w,K(u,z),x)
    ]]></literal>
    <justification jstring="[hyper(19212,a,19973,a),flip(a)].">
      <j1 rule="hyper" parents="19212 19973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19975">
    <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(19967,a,19974,a)].">
      <j1 rule="hyper" parents="19967 19974"/>
    </justification>
  </clause>

  <clause id="19976">
    <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(18228(a,1),14354(a,1,1))].">
      <j1 rule="para" parents="18228 14354"/>
    </justification>
  </clause>

  <clause id="19977">
    <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,19190,a(flip),b,19976,a)].">
      <j1 rule="hyper" parents="58 19190 19976"/>
    </justification>
  </clause>

  <clause id="19978">
    <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(17068,a,19977,a)].">
      <j1 rule="hyper" parents="17068 19977"/>
    </justification>
  </clause>

  <clause id="19979">
    <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,18497,a(flip),b,19978,a)].">
      <j1 rule="hyper" parents="58 18497 19978"/>
    </justification>
  </clause>

  <clause id="19980">
    <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(16815,a,19979,a),flip(a)].">
      <j1 rule="hyper" parents="16815 19979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19982">
    <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(334,a,12551,a(flip),b,19980,a),flip(a)].">
      <j1 rule="hyper" parents="334 12551 19980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19983">
    <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(4293(a,1),19982(a,1,2))].">
      <j1 rule="para" parents="4293 19982"/>
    </justification>
  </clause>

  <clause id="19984">
    <literal><![CDATA[
      K(x,y * K(z \ (u * (w \ 1)),v5)) = K(x,y * K(v5,w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(14323,a,19983,a)].">
      <j1 rule="hyper" parents="14323 19983"/>
    </justification>
  </clause>

  <clause id="19985">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (1 / v5)))) = K(x,(y \ z) * K(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(15685,a,19984,a)].">
      <j1 rule="hyper" parents="15685 19984"/>
    </justification>
  </clause>

  <clause id="19986">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (1 / v5)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,14221,a(flip),b,19985,a),flip(a)].">
      <j1 rule="hyper" parents="334 14221 19985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19987">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (v5 \ 1)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[para(3938(a,1),19986(a,1,2,2))].">
      <j1 rule="para" parents="3938 19986"/>
    </justification>
  </clause>

  <clause id="19988">
    <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,19260,a(flip),b,19987,a)].">
      <j1 rule="hyper" parents="58 19260 19987"/>
    </justification>
  </clause>

  <clause id="19989">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w * (v5 \ 1)))) = K(x,y \ T(z,v5 * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(334,a,19279,a(flip),b,19988,a),flip(a)].">
      <j1 rule="hyper" parents="334 19279 19988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19990">
    <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,19553,a(flip),b,19989,a),flip(a)].">
      <j1 rule="hyper" parents="58 19553 19989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19991">
    <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(7970,a,19990,a)].">
      <j1 rule="hyper" parents="7970 19990"/>
    </justification>
  </clause>

  <clause id="19992">
    <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(16314,a,19991,a)].">
      <j1 rule="hyper" parents="16314 19991"/>
    </justification>
  </clause>

  <clause id="19993">
    <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(15960,a,19992,a)].">
      <j1 rule="hyper" parents="15960 19992"/>
    </justification>
  </clause>

  <clause id="19994">
    <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(334,a,7403,a(flip),b,19993,a),flip(a)].">
      <j1 rule="hyper" parents="334 7403 19993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19995">
    <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(17107(a,1),19994(a,2,2))].">
      <j1 rule="para" parents="17107 19994"/>
    </justification>
  </clause>

  <clause id="19996">
    <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(19995(a,2),16032(a,1))].">
      <j1 rule="para" parents="19995 16032"/>
    </justification>
  </clause>

  <clause id="19997">
    <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,16467,a(flip),b,18687,a)].">
      <j1 rule="hyper" parents="58 16467 18687"/>
    </justification>
  </clause>

  <clause id="19998">
    <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(17956,a,19997,a)].">
      <j1 rule="hyper" parents="17956 19997"/>
    </justification>
  </clause>

  <clause id="19999">
    <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,14230,a(flip),b,19998,a)].">
      <j1 rule="hyper" parents="58 14230 19998"/>
    </justification>
  </clause>

  <clause id="20000">
    <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(18395,a,19999,a)].">
      <j1 rule="hyper" parents="18395 19999"/>
    </justification>
  </clause>

  <clause id="20001">
    <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(16809,a,20000,a),flip(a)].">
      <j1 rule="hyper" parents="16809 20000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20002">
    <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(334,a,17631,a(flip),b,20001,a),flip(a)].">
      <j1 rule="hyper" parents="334 17631 20001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20003">
    <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(18686(a,1),20002(a,1,1,2))].">
      <j1 rule="para" parents="18686 20002"/>
    </justification>
  </clause>

  <clause id="20004">
    <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(2418(a,1),20003(a,1,2))].">
      <j1 rule="para" parents="2418 20003"/>
    </justification>
  </clause>

  <clause id="20005">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) / u) = K(x,L(y,z,z \ 1) / u)
    ]]></literal>
    <justification jstring="[hyper(6528,a,20004,a),flip(a)].">
      <j1 rule="hyper" parents="6528 20004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20007">
    <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,15246,a,b,20005,a)].">
      <j1 rule="hyper" parents="58 15246 20005"/>
    </justification>
  </clause>

  <clause id="20008">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / (u * (z \ 1))) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18666,a(flip),b,20007,a),flip(a)].">
      <j1 rule="hyper" parents="58 18666 20007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20009">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19867,a(flip),b,20008,a)].">
      <j1 rule="hyper" parents="58 19867 20008"/>
    </justification>
  </clause>

  <clause id="20010">
    <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,18962,a(flip),b,20008,a)].">
      <j1 rule="hyper" parents="58 18962 20008"/>
    </justification>
  </clause>

  <clause id="20011">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(334,a,18195,a,b,20009,a)].">
      <j1 rule="hyper" parents="334 18195 20009"/>
    </justification>
  </clause>

  <clause id="20013">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / ((z \ 1) * u)) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(334,a,16695,a(flip),b,20010,a),flip(a)].">
      <j1 rule="hyper" parents="334 16695 20010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20014">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19867,a(flip),b,20013,a)].">
      <j1 rule="hyper" parents="58 19867 20013"/>
    </justification>
  </clause>

  <clause id="20016">
    <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(20014(a,1),19313(a,1,2))].">
      <j1 rule="para" parents="20014 19313"/>
    </justification>
  </clause>

  <clause id="20017">
    <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(20014(a,1),19996(a,1))].">
      <j1 rule="para" parents="20014 19996"/>
    </justification>
  </clause>

  <clause id="20018">
    <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(19050(a,1),20016(a,1,2))].">
      <j1 rule="para" parents="19050 20016"/>
    </justification>
  </clause>

  <clause id="20019">
    <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(19449(a,1),20018(a,1,2))].">
      <j1 rule="para" parents="19449 20018"/>
    </justification>
  </clause>

  <clause id="20020">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18287,a(flip),b,20019,a)].">
      <j1 rule="hyper" parents="58 18287 20019"/>
    </justification>
  </clause>

  <clause id="20021">
    <literal><![CDATA[
      K(x,y / (z \ u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16694,a(flip),b,20020,a)].">
      <j1 rule="hyper" parents="58 16694 20020"/>
    </justification>
  </clause>

  <clause id="20022">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(x,((z \ 1) * u) \ y)
    ]]></literal>
    <justification jstring="[hyper(20017,a,20021,a),flip(a)].">
      <j1 rule="hyper" parents="20017 20021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20024">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,20014,a,b,20021,a)].">
      <j1 rule="hyper" parents="58 20014 20021"/>
    </justification>
  </clause>

  <clause id="20025">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y * (T(z,u) \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,20011,a(flip),b,20021,a)].">
      <j1 rule="hyper" parents="58 20011 20021"/>
    </justification>
  </clause>

  <clause id="20026">
    <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,19733,a(flip),b,20021,a),flip(a)].">
      <j1 rule="hyper" parents="58 19733 20021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20027">
    <literal><![CDATA[
      K(x,y * ((T(z,u) * y) \ u)) = K(x,y \ ((y * u) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19607,a(flip),b,20021,a),flip(a)].">
      <j1 rule="hyper" parents="58 19607 20021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20030">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ v5)) = a(x,y,K(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[para(20021(a,1),17734(a,1,3)),flip(a)].">
      <j1 rule="para" parents="20021 17734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20031">
    <literal><![CDATA[
      K(x,y * (z \ (u \ 1))) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5846,a(flip),b,20024,a),flip(a)].">
      <j1 rule="hyper" parents="58 5846 20024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20032">
    <literal><![CDATA[
      K(x,y * ((z / u) \ (w \ K(z,u)))) = K(x,y / (w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(18995,a,20031,a)].">
      <j1 rule="hyper" parents="18995 20031"/>
    </justification>
  </clause>

  <clause id="20033">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(334,a,15627,a(flip),b,20025,a),flip(a)].">
      <j1 rule="hyper" parents="334 15627 20025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20034">
    <literal><![CDATA[
      K(x,y / (z / u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,20009,a(flip),b,20033,a)].">
      <j1 rule="hyper" parents="58 20009 20033"/>
    </justification>
  </clause>

  <clause id="20035">
    <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,19290,a,b,20034,a)].">
      <j1 rule="hyper" parents="58 19290 20034"/>
    </justification>
  </clause>

  <clause id="20037">
    <literal><![CDATA[
      K(x,y \ ((y * z) / u)) = K(x,(z / (y * u)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16700,a(flip),b,20027,a),flip(a)].">
      <j1 rule="hyper" parents="58 16700 20027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20038">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(19915,a,20022,a),flip(a)].">
      <j1 rule="hyper" parents="19915 20022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20039">
    <literal><![CDATA[
      K(x,(y \ z) \ u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(19888,a,20038,a)].">
      <j1 rule="hyper" parents="19888 20038"/>
    </justification>
  </clause>

  <clause id="20040">
    <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,19776,a(flip),b,20039,a),flip(a)].">
      <j1 rule="hyper" parents="58 19776 20039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20041">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a(v5,u,K(w,(z \ y) * x))
    ]]></literal>
    <justification jstring="[para(20039(a,1),14637(a,2,3))].">
      <j1 rule="para" parents="20039 14637"/>
    </justification>
  </clause>

  <clause id="20042">
    <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(20039(a,1),14711(a,1,3))].">
      <j1 rule="para" parents="20039 14711"/>
    </justification>
  </clause>

  <clause id="20043">
    <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(20039(a,1),19772(a,1,1,3))].">
      <j1 rule="para" parents="20039 19772"/>
    </justification>
  </clause>

  <clause id="20044">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a(x * (z \ y),u,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,17746,a,b,20041,a),flip(a)].">
      <j1 rule="hyper" parents="334 17746 20041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20045">
    <literal><![CDATA[
      a((x * y) \ z,u,K(w,v5)) = a(y * (z \ x),u,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,14720,a,b,20044,a)].">
      <j1 rule="hyper" parents="58 14720 20044"/>
    </justification>
  </clause>

  <clause id="20046">
    <literal><![CDATA[
      a(x \ (y * z),u,K(w,v5)) = a(z * (x \ y),u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(14728,a,20045,a)].">
      <j1 rule="hyper" parents="14728 20045"/>
    </justification>
  </clause>

  <clause id="20047">
    <literal><![CDATA[
      a(x \ (y * z),u,K(w,v5)) = a((x \ y) * z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(334,a,17748,a,b,20046,a),flip(a)].">
      <j1 rule="hyper" parents="334 17748 20046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20048">
    <literal><![CDATA[
      a(x * (y \ 1),z,K(u,w)) = a(y \ x,z,K(u,w))
    ]]></literal>
    <justification jstring="[para(2(a,1),20046(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2 20046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20049">
    <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(20046(a,2),17764(a,1))].">
      <j1 rule="para" parents="20046 17764"/>
    </justification>
  </clause>

  <clause id="20050">
    <literal><![CDATA[
      a((x \ 1) * y,z,K(u,w)) = a(x \ y,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(17764,a,20048,a)].">
      <j1 rule="hyper" parents="17764 20048"/>
    </justification>
  </clause>

  <clause id="20051">
    <literal><![CDATA[
      a((x \ y) \ z,u,K(w,v5)) = a((y \ x) * z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,14721,a,b,20047,a)].">
      <j1 rule="hyper" parents="58 14721 20047"/>
    </justification>
  </clause>

  <clause id="20052">
    <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(20047(a,2),17764(a,1))].">
      <j1 rule="para" parents="20047 17764"/>
    </justification>
  </clause>

  <clause id="20053">
    <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),20051(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 20051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20054">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,(z \ y) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(334,a,19869,a(flip),b,20035,a),flip(a)].">
      <j1 rule="hyper" parents="334 19869 20035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20055">
    <literal><![CDATA[
      K(x,(y \ z) * (z \ (u * y))) = K(x,L(T(u,y),y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,18171,a(flip),b,20040,a)].">
      <j1 rule="hyper" parents="58 18171 20040"/>
    </justification>
  </clause>

  <clause id="20056">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,L(T(z,y),y,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,19499,a,b,20055,a)].">
      <j1 rule="hyper" parents="58 19499 20055"/>
    </justification>
  </clause>

  <clause id="20057">
    <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,19737,a(flip),b,20026,a)].">
      <j1 rule="hyper" parents="58 19737 20026"/>
    </justification>
  </clause>

  <clause id="20058">
    <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),20057(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5 20057"/>
    </justification>
  </clause>

  <clause id="20059">
    <literal><![CDATA[
      K(x,L(y / z,u,w) * (z / y)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[hyper(18640,a,20058,a)].">
      <j1 rule="hyper" parents="18640 20058"/>
    </justification>
  </clause>

  <clause id="20061">
    <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(20034(a,1),20043(a,1,2))].">
      <j1 rule="para" parents="20034 20043"/>
    </justification>
  </clause>

  <clause id="20062">
    <literal><![CDATA[
      K(x,y / (((z / u) \ 1) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,19947,a(flip),b,20061,a)].">
      <j1 rule="hyper" parents="58 19947 20061"/>
    </justification>
  </clause>

  <clause id="20063">
    <literal><![CDATA[
      K(x,y * (z / ((u / w) \ 1))) = K(x,y / ((w / u) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,20034,a(flip),b,20062,a)].">
      <j1 rule="hyper" parents="58 20034 20062"/>
    </justification>
  </clause>

  <clause id="20064">
    <literal><![CDATA[
      K(x,y / ((z / u) / w)) = K(x,y * (w * (u / z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19869,a(flip),b,20063,a),flip(a)].">
      <j1 rule="hyper" parents="58 19869 20063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20065">
    <literal><![CDATA[
      K(x,y * (z / (u / w))) = K(x,y * (z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,20034,a(flip),b,20064,a)].">
      <j1 rule="hyper" parents="58 20034 20064"/>
    </justification>
  </clause>

  <clause id="20066">
    <literal><![CDATA[
      K(x,y * (z * (u / T(y,u * z)))) = K(x,y \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19442,a(flip),b,20064,a),flip(a)].">
      <j1 rule="hyper" parents="58 19442 20064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20067">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) * (u / w))) = K(x,y * ((w / u) \ z))
    ]]></literal>
    <justification jstring="[hyper(19414,a,20065,a),flip(a)].">
      <j1 rule="hyper" parents="19414 20065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20068">
    <literal><![CDATA[
      K(x,y \ ((y * z) * u)) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,18629,a(flip),b,20066,a),flip(a)].">
      <j1 rule="hyper" parents="58 18629 20066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20069">
    <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,18563,a,b,20068,a)].">
      <j1 rule="hyper" parents="58 18563 20068"/>
    </justification>
  </clause>

  <clause id="20070">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) / u)) * u) = K(x,u \ ((u * y) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19886,a(flip),b,20068,a),flip(a)].">
      <j1 rule="hyper" parents="58 19886 20068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20071">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) / u)) * u) = K(x,(y / (u * z)) * u)
    ]]></literal>
    <justification jstring="[hyper(334,a,20037,a(flip),b,20070,a),flip(a)].">
      <j1 rule="hyper" parents="334 20037 20070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20072">
    <literal><![CDATA[
      K(x,y * ((z / u) \ w)) = K(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(19474,a,20067,a),flip(a)].">
      <j1 rule="hyper" parents="19474 20067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20073">
    <literal><![CDATA[
      K(x,y * ((z / u) * (w \ K(u,z)))) = K(x,y / (w * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,20032,a(flip),b,20072,a),flip(a)].">
      <j1 rule="hyper" parents="58 20032 20072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20074">
    <literal><![CDATA[
      K(x,y / (z * (u \ w))) = K(x,y * ((w \ u) / z))
    ]]></literal>
    <justification jstring="[hyper(19873,a,20073,a),flip(a)].">
      <j1 rule="hyper" parents="19873 20073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20075">
    <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,19793,a(flip),b,20074,a),flip(a)].">
      <j1 rule="hyper" parents="58 19793 20074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20076">
    <literal><![CDATA[
      a(x,y \ z,K(u \ (y \ z),y)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,20059,a(flip),b,20075,a)].">
      <j1 rule="hyper" parents="58 20059 20075"/>
    </justification>
  </clause>

  <clause id="20077">
    <literal><![CDATA[
      a(x,y \ z,K(u \ z,y)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(14777,a,20076,a)].">
      <j1 rule="hyper" parents="14777 20076"/>
    </justification>
  </clause>

  <clause id="20078">
    <literal><![CDATA[
      a(x,a(y,z,u),K(w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(13752,a,20076,a),flip(a)].">
      <j1 rule="hyper" parents="13752 20076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20079">
    <literal><![CDATA[
      L(x,a(y,z,u),K(w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(13992,a,20078,a)].">
      <j1 rule="hyper" parents="13992 20078"/>
    </justification>
  </clause>

  <clause id="20080">
    <literal><![CDATA[
      L(K(x,y),a(z,u,w),v5) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6202,a,20078,a)].">
      <j1 rule="hyper" parents="6202 20078"/>
    </justification>
  </clause>

  <clause id="20082">
    <literal><![CDATA[
      K(x,L(y,a(z,u,w),v5)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11132,a,20080,a)].">
      <j1 rule="hyper" parents="11132 20080"/>
    </justification>
  </clause>

  <clause id="20084">
    <literal><![CDATA[
      R(K(x,y),a(z,u,w),v5) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15128,a,b,20080,a)].">
      <j1 rule="hyper" parents="58 15128 20080"/>
    </justification>
  </clause>

  <clause id="20085">
    <literal><![CDATA[
      K(x,L(y,a(z,u,w),v5)) = K(x,L(y,v6,L(v6,v7,v8)))
    ]]></literal>
    <justification jstring="[hyper(334,a,14673,a,b,20082,a),flip(a)].">
      <j1 rule="hyper" parents="334 14673 20082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20087">
    <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(334,a,19123,a(flip),b,20084,a),flip(a)].">
      <j1 rule="hyper" parents="334 19123 20084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20089">
    <literal><![CDATA[
      a(x,y,K(z \ y,u)) = a(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(14779,a,20077,a)].">
      <j1 rule="hyper" parents="14779 20077"/>
    </justification>
  </clause>

  <clause id="20090">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,20076,a(flip),b,20089,a),flip(a)].">
      <j1 rule="hyper" parents="58 20076 20089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20091">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = x * a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[para(20089(a,1),19358(a,2,2))].">
      <j1 rule="para" parents="20089 19358"/>
    </justification>
  </clause>

  <clause id="20092">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = y * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(20089(a,1),19535(a,2,2))].">
      <j1 rule="para" parents="20089 19535"/>
    </justification>
  </clause>

  <clause id="20093">
    <literal><![CDATA[
      K(x,L(y,a(z,u,w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v6
    ]]></literal>
    <justification jstring="[para(20085(a,2),6670(a,1))].">
      <j1 rule="para" parents="20085 6670"/>
    </justification>
  </clause>

  <clause id="20094">
    <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(11154(a,1),20093(a,1))].">
      <j1 rule="para" parents="11154 20093"/>
    </justification>
  </clause>

  <clause id="20095">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = L(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,15291,a(flip),b,20092,a),flip(a)].">
      <j1 rule="hyper" parents="334 15291 20092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20096">
    <literal><![CDATA[
      x * a(y,x,K(z,x \ u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19533,a(flip),b,20095,a)].">
      <j1 rule="hyper" parents="58 19533 20095"/>
    </justification>
  </clause>

  <clause id="20097">
    <literal><![CDATA[
      x * a(y,x,K(z,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(20090(a,1),20096(a,1,2))].">
      <j1 rule="para" parents="20090 20096"/>
    </justification>
  </clause>

  <clause id="20098">
    <literal><![CDATA[
      x * a(y,x,K(z,u)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(17870,a,20097,a)].">
      <j1 rule="hyper" parents="17870 20097"/>
    </justification>
  </clause>

  <clause id="20099">
    <literal><![CDATA[
      x * a(y,x,K(z,u)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(17869,a,20097,a)].">
      <j1 rule="hyper" parents="17869 20097"/>
    </justification>
  </clause>

  <clause id="20100">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(29,a,15294,a,b,20097,a)].">
      <j1 rule="hyper" parents="29 15294 20097"/>
    </justification>
  </clause>

  <clause id="20101">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(29,a,15291,a,b,20097,a)].">
      <j1 rule="hyper" parents="29 15291 20097"/>
    </justification>
  </clause>

  <clause id="20102">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(z,x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(29,a,15282,a,b,20097,a)].">
      <j1 rule="hyper" parents="29 15282 20097"/>
    </justification>
  </clause>

  <clause id="20103">
    <literal><![CDATA[
      a(x \ y,z,K(u,w)) = a(u,w,K(z,y \ x))
    ]]></literal>
    <justification jstring="[hyper(14728,a,20100,a)].">
      <j1 rule="hyper" parents="14728 20100"/>
    </justification>
  </clause>

  <clause id="20104">
    <literal><![CDATA[
      a(x,y,K(z,u \ 1)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(14715,a,20100,a),flip(a)].">
      <j1 rule="hyper" parents="14715 20100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20105">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,20100,a,b,15283,a)].">
      <j1 rule="hyper" parents="119 20100 15283"/>
    </justification>
  </clause>

  <clause id="20106">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(x,u)) = w
    ]]></literal>
    <justification jstring="[para(20100(a,1),14677(a,1))].">
      <j1 rule="para" parents="20100 14677"/>
    </justification>
  </clause>

  <clause id="20107">
    <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(20100(a,1),17766(a,1))].">
      <j1 rule="para" parents="20100 17766"/>
    </justification>
  </clause>

  <clause id="20108">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,14592,a,b,20101,a)].">
      <j1 rule="hyper" parents="334 14592 20101"/>
    </justification>
  </clause>

  <clause id="20109">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(z,u,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,14592,a(flip),b,20101,a)].">
      <j1 rule="hyper" parents="334 14592 20101"/>
    </justification>
  </clause>

  <clause id="20110">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,v5)) = a(w,v5,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(18806,a,20101,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18806 20101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20111">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(20101(a,1),14677(a,1))].">
      <j1 rule="para" parents="20101 14677"/>
    </justification>
  </clause>

  <clause id="20112">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,u,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(20101(a,2),14677(a,1))].">
      <j1 rule="para" parents="20101 14677"/>
    </justification>
  </clause>

  <clause id="20113">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,u,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(20101(a,2),14707(a,1))].">
      <j1 rule="para" parents="20101 14707"/>
    </justification>
  </clause>

  <clause id="20114">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(20101(a,2),14656(a,1,2))].">
      <j1 rule="para" parents="20101 14656"/>
    </justification>
  </clause>

  <clause id="20115">
    <literal><![CDATA[
      a(x \ y,z,K(x,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,14686,a(flip),b,20102,a),flip(a)].">
      <j1 rule="hyper" parents="334 14686 20102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20116">
    <literal><![CDATA[
      a(x,y,z) * a(y,z,K(x,u)) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,20102,a,b,19226,a)].">
      <j1 rule="hyper" parents="119 20102 19226"/>
    </justification>
  </clause>

  <clause id="20117">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,x,K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(20102(a,2),14707(a,1))].">
      <j1 rule="para" parents="20102 14707"/>
    </justification>
  </clause>

  <clause id="20118">
    <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(20102(a,2),17758(a,1))].">
      <j1 rule="para" parents="20102 17758"/>
    </justification>
  </clause>

  <clause id="20119">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a((z \ y) * x,v5,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(20042,a,20108,a)].">
      <j1 rule="hyper" parents="20042 20108"/>
    </justification>
  </clause>

  <clause id="20120">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = a(w,v5,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(18894,a,20108,a)].">
      <j1 rule="hyper" parents="18894 20108"/>
    </justification>
  </clause>

  <clause id="20121">
    <literal><![CDATA[
      a(((x * y) \ x) * z,u,K(w,v5)) = a(u,v5,K(w,y \ z))
    ]]></literal>
    <justification jstring="[hyper(334,a,20053,a,b,20108,a)].">
      <j1 rule="hyper" parents="334 20053 20108"/>
    </justification>
  </clause>

  <clause id="20122">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) = a(y,x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,14638,a,b,20108,a)].">
      <j1 rule="hyper" parents="334 14638 20108"/>
    </justification>
  </clause>

  <clause id="20123">
    <literal><![CDATA[
      a(x,y,K(z,(u \ 1) * w)) = a(u \ w,x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,20050,a(flip),b,20108,a),flip(a)].">
      <j1 rule="hyper" parents="334 20050 20108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20124">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(20108(a,2),14677(a,1))].">
      <j1 rule="para" parents="20108 14677"/>
    </justification>
  </clause>

  <clause id="20125">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,u,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(20108(a,1),14707(a,1))].">
      <j1 rule="para" parents="20108 14707"/>
    </justification>
  </clause>

  <clause id="20126">
    <literal><![CDATA[
      a(x,y * z,K(u,y)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,11223,a,b,20109,a)].">
      <j1 rule="hyper" parents="334 11223 20109"/>
    </justification>
  </clause>

  <clause id="20127">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w \ x) = w \ L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[para(20109(a,1),17688(a,1,1))].">
      <j1 rule="para" parents="20109 17688"/>
    </justification>
  </clause>

  <clause id="20128">
    <literal><![CDATA[
      x * (y * a(x,z,K(u,w))) = L(x,w,K(z,u)) * y
    ]]></literal>
    <justification jstring="[para(20109(a,1),17882(a,1,2,2))].">
      <j1 rule="para" parents="20109 17882"/>
    </justification>
  </clause>

  <clause id="20129">
    <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(18457(a,1),20109(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18457 20109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20130">
    <literal><![CDATA[
      L(x,y,K(z,u)) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,20097,a(flip),b,20098,a)].">
      <j1 rule="hyper" parents="58 20097 20098"/>
    </justification>
  </clause>

  <clause id="20131">
    <literal><![CDATA[
      L(L(x,y,z),u,K(y,z)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(15324,a,20130,a),flip(a)].">
      <j1 rule="hyper" parents="15324 20130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20132">
    <literal><![CDATA[
      L(x,y,K(z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(15287,a,20130,a),flip(a)].">
      <j1 rule="hyper" parents="15287 20130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20133">
    <literal><![CDATA[
      L(x,y,K(z * u,z)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(13018,a,20130,a)].">
      <j1 rule="hyper" parents="13018 20130"/>
    </justification>
  </clause>

  <clause id="20134">
    <literal><![CDATA[
      L(x,T(y,z),K(u,w)) = L(x,u,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,18899,a,b,20130,a)].">
      <j1 rule="hyper" parents="334 18899 20130"/>
    </justification>
  </clause>

  <clause id="20135">
    <literal><![CDATA[
      a(x,y,z) * (u / a(x,y,z)) = L(u,x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,15317,a,b,20130,a)].">
      <j1 rule="hyper" parents="334 15317 20130"/>
    </justification>
  </clause>

  <clause id="20136">
    <literal><![CDATA[
      L(x,y * x,K(z,u)) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,18870,a(flip),b,20130,a),flip(a)].">
      <j1 rule="hyper" parents="334 18870 20130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20137">
    <literal><![CDATA[
      L(x * y,x,K(z,u)) = x * L(y,u,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,18851,a(flip),b,20130,a),flip(a)].">
      <j1 rule="hyper" parents="334 18851 20130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20138">
    <literal><![CDATA[
      x * L(y,z,K(u,w)) = x * L(y,w,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,20130,a,b,4,a)].">
      <j1 rule="hyper" parents="119 20130 4"/>
    </justification>
  </clause>

  <clause id="20139">
    <literal><![CDATA[
      (K(x,y) * z) * L(u,x,K(y,z)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(119,a,20130,a,b,13,a(flip))].">
      <j1 rule="hyper" parents="119 20130 13"/>
    </justification>
  </clause>

  <clause id="20140">
    <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,15368,a(flip),b,20130,a),flip(a)].">
      <j1 rule="hyper" parents="58 15368 20130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20141">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),z,u) = L(x,z,T(u,y))
    ]]></literal>
    <justification jstring="[para(20130(a,1),15323(a,1,1))].">
      <j1 rule="para" parents="20130 15323"/>
    </justification>
  </clause>

  <clause id="20142">
    <literal><![CDATA[
      L(x,y,K(z,u)) / a(y,z,u) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(20130(a,1),15345(a,1,1))].">
      <j1 rule="para" parents="20130 15345"/>
    </justification>
  </clause>

  <clause id="20143">
    <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(20130(a,1),15324(a,1))].">
      <j1 rule="para" parents="20130 15324"/>
    </justification>
  </clause>

  <clause id="20144">
    <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(20130(a,2),18897(a,1))].">
      <j1 rule="para" parents="20130 18897"/>
    </justification>
  </clause>

  <clause id="20145">
    <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(334,a,2197,a,b,20132,a)].">
      <j1 rule="hyper" parents="334 2197 20132"/>
    </justification>
  </clause>

  <clause id="20146">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * (v5 * x)) = w * (v5 * L(x,u,K(y,z)))
    ]]></literal>
    <justification jstring="[para(20132(a,2),17883(a,2,2,2))].">
      <j1 rule="para" parents="20132 17883"/>
    </justification>
  </clause>

  <clause id="20147">
    <literal><![CDATA[
      L(x,y,K(z,u)) / a(y,z,u) = x / a(y,z,T(u,x))
    ]]></literal>
    <justification jstring="[para(20132(a,2),19231(a,1,1))].">
      <j1 rule="para" parents="20132 19231"/>
    </justification>
  </clause>

  <clause id="20148">
    <literal><![CDATA[
      T(x,x * (y \ L(y,z,u))) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(13695,a,20105,a)].">
      <j1 rule="hyper" parents="13695 20105"/>
    </justification>
  </clause>

  <clause id="20149">
    <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(20122(a,1),14674(a,1,1,1))].">
      <j1 rule="para" parents="20122 14674"/>
    </justification>
  </clause>

  <clause id="20150">
    <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(20122(a,1),14675(a,1,1,1))].">
      <j1 rule="para" parents="20122 14675"/>
    </justification>
  </clause>

  <clause id="20151">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (K(z,y) * ((y * u) * x)) = (y * (K(z,y) * u)) * x
    ]]></literal>
    <justification jstring="[para(20126(a,1),15010(a,1,1))].">
      <j1 rule="para" parents="20126 15010"/>
    </justification>
  </clause>

  <clause id="20152">
    <literal><![CDATA[
      L(x,y,K(z,y * u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,20130,a(flip),b,20133,a)].">
      <j1 rule="hyper" parents="58 20130 20133"/>
    </justification>
  </clause>

  <clause id="20153">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,u,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(20134(a,1),11486(a,1))].">
      <j1 rule="para" parents="20134 11486"/>
    </justification>
  </clause>

  <clause id="20154">
    <literal><![CDATA[
      L(R(x,y,z),y,K(z,u)) = R(x,y,T(z,y * u))
    ]]></literal>
    <justification jstring="[hyper(17774,a,20152,a),flip(a)].">
      <j1 rule="hyper" parents="17774 20152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20155">
    <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(20041(a,2),20117(a,1))].">
      <j1 rule="para" parents="20041 20117"/>
    </justification>
  </clause>

  <clause id="20156">
    <literal><![CDATA[
      L((x * y) \ z,u,K(y,x)) = L(y \ (x \ z),y,T(x,u))
    ]]></literal>
    <justification jstring="[para(311(a,1),20131(a,1,1))].">
      <j1 rule="para" parents="311 20131"/>
    </justification>
  </clause>

  <clause id="20157">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),z,u) = T(L(x,z,u) \ x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(334,a,15462,a,b,20141,a),flip(a)].">
      <j1 rule="hyper" parents="334 15462 20141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20158">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u != w
    ]]></literal>
    <literal><![CDATA[
      L(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(15290(a,2),20153(a,1))].">
      <j1 rule="para" parents="15290 20153"/>
    </justification>
  </clause>

  <clause id="20159">
    <literal><![CDATA[
      a(x \ (y * z),u,K(w,v5)) = a(w,v5,K(u,z \ (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(14845,a,20103,a)].">
      <j1 rule="hyper" parents="14845 20103"/>
    </justification>
  </clause>

  <clause id="20160">
    <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,18809,a,b,20103,a)].">
      <j1 rule="hyper" parents="58 18809 20103"/>
    </justification>
  </clause>

  <clause id="20161">
    <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(20110(a,2),20113(a,1))].">
      <j1 rule="para" parents="20110 20113"/>
    </justification>
  </clause>

  <clause id="20162">
    <literal><![CDATA[
      K(x,L(y,z,u \ y)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(14824,a,20114,a)].">
      <j1 rule="hyper" parents="14824 20114"/>
    </justification>
  </clause>

  <clause id="20163">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(14682,a,20114,a)].">
      <j1 rule="hyper" parents="14682 20114"/>
    </justification>
  </clause>

  <clause id="20164">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = K(x,L(y,u,z * u))
    ]]></literal>
    <justification jstring="[hyper(14882,a,20162,a)].">
      <j1 rule="hyper" parents="14882 20162"/>
    </justification>
  </clause>

  <clause id="20165">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,L(T(z,y),u,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,20056,a,b,20163,a)].">
      <j1 rule="hyper" parents="58 20056 20163"/>
    </justification>
  </clause>

  <clause id="20166">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y)) = K(x,(z \ y) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,20054,a(flip),b,20163,a),flip(a)].">
      <j1 rule="hyper" parents="58 20054 20163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20167">
    <literal><![CDATA[
      L(x * y,x,K(z,u)) = x * L(y,x,K(z,u))
    ]]></literal>
    <justification jstring="[para(20130(a,2),20137(a,2,2))].">
      <j1 rule="para" parents="20130 20137"/>
    </justification>
  </clause>

  <clause id="20168">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ x)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19587,a,b,20148,a)].">
      <j1 rule="hyper" parents="58 19587 20148"/>
    </justification>
  </clause>

  <clause id="20169">
    <literal><![CDATA[
      K(x,L(y,z,u * z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,20163,a(flip),b,20164,a),flip(a)].">
      <j1 rule="hyper" parents="58 20163 20164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20170">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y)) = K(x,z \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19895,a(flip),b,20169,a),flip(a)].">
      <j1 rule="hyper" parents="58 19895 20169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20171">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,u) / y) = x * K(z,L(T(u,y),x,y))
    ]]></literal>
    <justification jstring="[para(20169(a,1),19216(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20169 19216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20172">
    <literal><![CDATA[
      L(x * y,x,K(z,u)) = K(z,u) * ((K(u,z) * x) * y)
    ]]></literal>
    <justification jstring="[hyper(334,a,15356,a,b,20167,a),flip(a)].">
      <j1 rule="hyper" parents="334 15356 20167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20173">
    <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,15321,a(flip),b,20167,a),flip(a)].">
      <j1 rule="hyper" parents="58 15321 20167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20174">
    <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,13549,a,b,20168,a)].">
      <j1 rule="hyper" parents="58 13549 20168"/>
    </justification>
  </clause>

  <clause id="20175">
    <literal><![CDATA[
      a(x,y,z) * (a(y,z,K(x,u)) * w) = a(x,y,T(z,u)) * w
    ]]></literal>
    <justification jstring="[para(20116(a,1),17914(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20116 17914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20176">
    <literal><![CDATA[
      L(x * a(y,z,u),y,K(u,z)) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(6(a,1),20135(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 20135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20177">
    <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(20142(a,1),259(a,1,1)),flip(b)].">
      <j1 rule="para" parents="20142 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20178">
    <literal><![CDATA[
      R(x,y,T(z,y * x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7781,a(flip),b,20154,a),flip(a)].">
      <j1 rule="hyper" parents="58 7781 20154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20179">
    <literal><![CDATA[
      R(x,y,z) \ (z * (y * x)) = T(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(20178(a,1),12823(a,1,1))].">
      <j1 rule="para" parents="20178 12823"/>
    </justification>
  </clause>

  <clause id="20182">
    <literal><![CDATA[
      L(x,y,(a(z,u,w) * v5) \ v6) = L(x,y,(v5 * a(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[para(20176(a,1),17807(a,1,3,1))].">
      <j1 rule="para" parents="20176 17807"/>
    </justification>
  </clause>

  <clause id="20183">
    <literal><![CDATA[
      a((a(x,y,z) * u) \ w,v5,v6) = a((u * a(x,y,z)) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(20176(a,1),19761(a,1,1,1))].">
      <j1 rule="para" parents="20176 19761"/>
    </justification>
  </clause>

  <clause id="20184">
    <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(20127(a,1),19751(a,2,2,1))].">
      <j1 rule="para" parents="20127 19751"/>
    </justification>
  </clause>

  <clause id="20185">
    <literal><![CDATA[
      x / a(y,z,T(u,x)) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,20142,a(flip),b,20147,a),flip(a)].">
      <j1 rule="hyper" parents="58 20142 20147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20186">
    <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(20185(a,1),1760(a,1,1))].">
      <j1 rule="para" parents="20185 1760"/>
    </justification>
  </clause>

  <clause id="20187">
    <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(5680(a,1),20161(a,1,1))].">
      <j1 rule="para" parents="5680 20161"/>
    </justification>
  </clause>

  <clause id="20188">
    <literal><![CDATA[
      K(x,y \ ((z * y) * u)) = K(x,(y \ z) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,20166,a(flip),b,20170,a),flip(a)].">
      <j1 rule="hyper" parents="58 20166 20170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20189">
    <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,20069,a(flip),b,20188,a),flip(a)].">
      <j1 rule="hyper" parents="58 20069 20188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20190">
    <literal><![CDATA[
      K(x,y) * L(z * u,z,K(y,x)) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(119,a,20172,a,b,5391,a)].">
      <j1 rule="hyper" parents="119 20172 5391"/>
    </justification>
  </clause>

  <clause id="20191">
    <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(20179(a,1),15412(a,1,1,2))].">
      <j1 rule="para" parents="20179 15412"/>
    </justification>
  </clause>

  <clause id="20192">
    <literal><![CDATA[
      K(x,y) * L(z * u,y,K(x,z)) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(58,a,20138,a,b,20190,a)].">
      <j1 rule="hyper" parents="58 20138 20190"/>
    </justification>
  </clause>

  <clause id="20193">
    <literal><![CDATA[
      L(K(x,y) * (z * u),y,K(x,z)) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(58,a,19076,a,b,20192,a)].">
      <j1 rule="hyper" parents="58 19076 20192"/>
    </justification>
  </clause>

  <clause id="20194">
    <literal><![CDATA[
      a(x \ (y \ (z \ u)),w,K(v5,v6)) = a(((u / z) \ y) * x,v6,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(18877,a,20119,a)].">
      <j1 rule="hyper" parents="18877 20119"/>
    </justification>
  </clause>

  <clause id="20195">
    <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(14712,a,20119,a),flip(a)].">
      <j1 rule="hyper" parents="14712 20119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20196">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a(z \ (y * x),v5,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,20047,a,b,20119,a),flip(a)].">
      <j1 rule="hyper" parents="334 20047 20119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20197">
    <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(20121(a,2),20117(a,1))].">
      <j1 rule="para" parents="20121 20117"/>
    </justification>
  </clause>

  <clause id="20198">
    <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,20152,a(flip),b,20156,a),flip(a)].">
      <j1 rule="hyper" parents="58 20152 20156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20199">
    <literal><![CDATA[
      a(x \ (y * (z \ 1)),u,K(w,v5)) = a(w,v5,K(u,z * (y \ x)))
    ]]></literal>
    <justification jstring="[para(14106(a,1),20159(a,2,3))].">
      <j1 rule="para" parents="14106 20159"/>
    </justification>
  </clause>

  <clause id="20200">
    <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(20159(a,2),14707(a,1))].">
      <j1 rule="para" parents="20159 14707"/>
    </justification>
  </clause>

  <clause id="20201">
    <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(20159(a,2),20124(a,1))].">
      <j1 rule="para" parents="20159 20124"/>
    </justification>
  </clause>

  <clause id="20202">
    <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(10624(a,1),20196(a,2,1,2))].">
      <j1 rule="para" parents="10624 20196"/>
    </justification>
  </clause>

  <clause id="20203">
    <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(7401(a,1),20087(a,1,1))].">
      <j1 rule="para" parents="7401 20087"/>
    </justification>
  </clause>

  <clause id="20204">
    <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(20091(a,2),15340(a,1))].">
      <j1 rule="para" parents="20091 15340"/>
    </justification>
  </clause>

  <clause id="20205">
    <literal><![CDATA[
      T(a(a(x,y,z),u,w) \ 1,v5) = a(a(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(246,a,20140,a(flip),b,20079,a(flip))].">
      <j1 rule="hyper" parents="246 20140 20079"/>
    </justification>
  </clause>

  <clause id="20206">
    <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,20175,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 20175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20207">
    <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(19750(a,2),20175(a,1,2))].">
      <j1 rule="para" parents="19750 20175"/>
    </justification>
  </clause>

  <clause id="20208">
    <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(334,a,14602,a,b,20203,a),flip(a)].">
      <j1 rule="hyper" parents="334 14602 20203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20209">
    <literal><![CDATA[
      L((x * y) * z,y,K(x,u)) = (x * y) * L(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[para(15321(a,1),20173(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15321 20173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20210">
    <literal><![CDATA[
      L((x * y) * z,u,K(y,x)) = (x * y) * L(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(20153,a,20209,a)].">
      <j1 rule="hyper" parents="20153 20209"/>
    </justification>
  </clause>

  <clause id="20211">
    <literal><![CDATA[
      L((x * y) * z,u,K(y,x)) = (x * y) * L(z,x,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,20138,a,b,20210,a),flip(a)].">
      <j1 rule="hyper" parents="334 20138 20210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20212">
    <literal><![CDATA[
      a(x \ (y * (z \ 1)),u,K(w,v5)) = a(z * (y \ x),v5,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,14592,a(flip),b,20199,a),flip(a)].">
      <j1 rule="hyper" parents="334 14592 20199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20213">
    <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(20212(a,2),14677(a,1))].">
      <j1 rule="para" parents="20212 14677"/>
    </justification>
  </clause>

  <clause id="20214">
    <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,18874,a(flip),b,20160,a)].">
      <j1 rule="hyper" parents="58 18874 20160"/>
    </justification>
  </clause>

  <clause id="20215">
    <literal><![CDATA[
      T(x,y \ L(y,z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19588,a(flip),b,20174,a)].">
      <j1 rule="hyper" parents="58 19588 20174"/>
    </justification>
  </clause>

  <clause id="20216">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(13684,a,20215,a)].">
      <j1 rule="hyper" parents="13684 20215"/>
    </justification>
  </clause>

  <clause id="20218">
    <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(20216(a,2),14518(a,1))].">
      <j1 rule="para" parents="20216 14518"/>
    </justification>
  </clause>

  <clause id="20219">
    <literal><![CDATA[
      a(x,y,L(z,u,K(w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(20216(a,1),19229(a,1,3))].">
      <j1 rule="para" parents="20216 19229"/>
    </justification>
  </clause>

  <clause id="20220">
    <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,11785,a(flip),b,20219,a),flip(a)].">
      <j1 rule="hyper" parents="58 11785 20219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20221">
    <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(19225(a,2),20218(a,1))].">
      <j1 rule="para" parents="19225 20218"/>
    </justification>
  </clause>

  <clause id="20222">
    <literal><![CDATA[
      a(x,y,L(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(20216(a,1),20221(a,1,3))].">
      <j1 rule="para" parents="20216 20221"/>
    </justification>
  </clause>

  <clause id="20223">
    <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(13843(a,1),20222(a,1))].">
      <j1 rule="para" parents="13843 20222"/>
    </justification>
  </clause>

  <clause id="20224">
    <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(13843(a,2),20223(a,1))].">
      <j1 rule="para" parents="13843 20223"/>
    </justification>
  </clause>

  <clause id="20225">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) * (y * u)) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,19936,a(flip),b,20189,a)].">
      <j1 rule="hyper" parents="58 19936 20189"/>
    </justification>
  </clause>

  <clause id="20226">
    <literal><![CDATA[
      K(x,(y * (z / u)) * u) = K(x,(y / u) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15861,a(flip),b,20225,a),flip(a)].">
      <j1 rule="hyper" parents="58 15861 20225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20227">
    <literal><![CDATA[
      K(x,(y / z) * (z * (u \ 1))) = K(x,(y / (z * u)) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,20071,a(flip),b,20226,a),flip(a)].">
      <j1 rule="hyper" parents="58 20071 20226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20228">
    <literal><![CDATA[
      K(x,(y / (z * u)) * z) = K(x,(y / z) * (z / u))
    ]]></literal>
    <justification jstring="[hyper(19872,a,20227,a),flip(a)].">
      <j1 rule="hyper" parents="19872 20227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20229">
    <literal><![CDATA[
      K(x,y \ ((y * z) / u)) = K(x,(z / y) * (y / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,20037,a,b,20228,a)].">
      <j1 rule="hyper" parents="58 20037 20228"/>
    </justification>
  </clause>

  <clause id="20230">
    <literal><![CDATA[
      K(x,y \ ((y * (z * u)) / z)) = K(x,L(T(u,z),y,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,20165,a(flip),b,20229,a),flip(a)].">
      <j1 rule="hyper" parents="334 20165 20229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20231">
    <literal><![CDATA[
      K(x,y / ((z * u) \ (u * y))) = K(x,L(T(z,u),y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19606,a,b,20230,a)].">
      <j1 rule="hyper" parents="58 19606 20230"/>
    </justification>
  </clause>

  <clause id="20232">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u)) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,20231,a(flip),b,19524,a(flip))].">
      <j1 rule="hyper" parents="119 20231 19524"/>
    </justification>
  </clause>

  <clause id="20233">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,u) / y) = (x * y) / (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,20171,a,b,20232,a)].">
      <j1 rule="hyper" parents="58 20171 20232"/>
    </justification>
  </clause>

  <clause id="20234">
    <literal><![CDATA[
      (x * y) / (y * K(T(z,y),u)) = (x / (y \ 1)) * (y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19079,a(flip),b,20233,a),flip(a)].">
      <j1 rule="hyper" parents="58 19079 20233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20235">
    <literal><![CDATA[
      (x / (y \ 1)) * (y \ K(z,u)) = (x * y) / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(7393(a,1),20234(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7393 20234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20236">
    <literal><![CDATA[
      (x * (y / z)) / (K(u,y) * (y / z)) = (x / z) * (z * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(19661,a,20235,a),flip(a)].">
      <j1 rule="hyper" parents="19661 20235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20237">
    <literal><![CDATA[
      (x * (T(y,z) / u)) / (y / u) = (x / u) * (u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19698,a(flip),b,20236,a)].">
      <j1 rule="hyper" parents="58 19698 20236"/>
    </justification>
  </clause>

  <clause id="20238">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = L(x,K(u,z),y \ z)
    ]]></literal>
    <justification jstring="[para(20237(a,1),19712(a,1,1))].">
      <j1 rule="para" parents="20237 19712"/>
    </justification>
  </clause>

  <clause id="20239">
    <literal><![CDATA[
      L(x,K(y,z),u \ z) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(20204,a,20238,a),flip(a)].">
      <j1 rule="hyper" parents="20204 20238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20240">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,18340,a(flip),b,20239,a),flip(a)].">
      <j1 rule="hyper" parents="58 18340 20239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20241">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(12999,a,20240,a),flip(a)].">
      <j1 rule="hyper" parents="12999 20240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20242">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(334,a,20130,a(flip),b,20241,a),flip(a)].">
      <j1 rule="hyper" parents="334 20130 20241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20244">
    <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(20241(a,1),19975(a,1,1,2))].">
      <j1 rule="para" parents="20241 19975"/>
    </justification>
  </clause>

  <clause id="20245">
    <literal><![CDATA[
      R(x,K(y,z),u) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19088,a,b,20242,a)].">
      <j1 rule="hyper" parents="58 19088 20242"/>
    </justification>
  </clause>

  <clause id="20246">
    <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(20242(a,1),14585(a,1,1))].">
      <j1 rule="para" parents="20242 14585"/>
    </justification>
  </clause>

  <clause id="20248">
    <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(15303(a,1),20244(a,1,1))].">
      <j1 rule="para" parents="15303 20244"/>
    </justification>
  </clause>

  <clause id="20249">
    <literal><![CDATA[
      a(x,K(y,z),u) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(14816,a,20248,a),flip(a)].">
      <j1 rule="hyper" parents="14816 20248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20251">
    <literal><![CDATA[
      a(x,K(y,z),u) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(334,a,20108,a(flip),b,20249,a),flip(a)].">
      <j1 rule="hyper" parents="334 20108 20249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20252">
    <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(20251(a,1),19941(a,1,1))].">
      <j1 rule="para" parents="20251 19941"/>
    </justification>
  </clause>

  <clause id="20253">
    <literal><![CDATA[
      a(((x / y) \ z) * u,w,K(v5,v6)) = a(((y \ x) \ z) * u,w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(20155,a,20194,a),flip(a)].">
      <j1 rule="hyper" parents="20155 20194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20254">
    <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,20146,a(flip),b,20151,a)].">
      <j1 rule="hyper" parents="58 20146 20151"/>
    </justification>
  </clause>

  <clause id="20255">
    <literal><![CDATA[
      K(x,y) * L((y * z) * u,x,K(z,y)) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[para(20210(a,2),20254(a,1,2))].">
      <j1 rule="para" parents="20210 20254"/>
    </justification>
  </clause>

  <clause id="20257">
    <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(18232(a,1),20094(a,1))].">
      <j1 rule="para" parents="18232 20094"/>
    </justification>
  </clause>

  <clause id="20258">
    <literal><![CDATA[
      a(x,y,K(z * (T(u,w) \ v5),v6)) = a(z * (u \ v5),v6,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(20161,a,20129,a),flip(a)].">
      <j1 rule="hyper" parents="20161 20129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20259">
    <literal><![CDATA[
      a((((x * y) / x) \ z) * u,w,K(v5,v6)) = a(u * (y \ z),v5,K(v6,w))
    ]]></literal>
    <justification jstring="[hyper(18458,a,20258,a)].">
      <j1 rule="hyper" parents="18458 20258"/>
    </justification>
  </clause>

  <clause id="20261">
    <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,12872,a(flip),b,20198,a),flip(a)].">
      <j1 rule="hyper" parents="58 12872 20198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20262">
    <literal><![CDATA[
      L(((x * y) * z) \ u,x,K(z,y)) = ((y * x) * z) \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(334,a,11491,a(flip),b,20261,a),flip(a)].">
      <j1 rule="hyper" parents="334 11491 20261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20263">
    <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,15295,a(flip),b,20262,a),flip(a)].">
      <j1 rule="hyper" parents="58 15295 20262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20265">
    <literal><![CDATA[
      a(T(x,y),K(y,x) * z,u) = a(x,z,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(334,a,19227,a(flip),b,20220,a),flip(a)].">
      <j1 rule="hyper" parents="334 19227 20220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20267">
    <literal><![CDATA[
      a(T(x,y),z * K(y,x),u) = a(x,z,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,19335,a(flip),b,20265,a)].">
      <j1 rule="hyper" parents="58 19335 20265"/>
    </justification>
  </clause>

  <clause id="20268">
    <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(6370(a,1),20267(a,1,2))].">
      <j1 rule="para" parents="6370 20267"/>
    </justification>
  </clause>

  <clause id="20269">
    <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,19326,a(flip),b,20268,a),flip(a)].">
      <j1 rule="hyper" parents="58 19326 20268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20271">
    <literal><![CDATA[
      a(x,y / K(z,T(x,u)),T(w,z)) = a(T(x,z),y,w)
    ]]></literal>
    <justification jstring="[para(6577(a,1),20269(a,1,2,2))].">
      <j1 rule="para" parents="6577 20269"/>
    </justification>
  </clause>

  <clause id="20272">
    <literal><![CDATA[
      a(x,y * K(x,T(z,u)),T(w,z)) = a(T(x,z),y,w)
    ]]></literal>
    <justification jstring="[para(7475(a,1),20271(a,1,2))].">
      <j1 rule="para" parents="7475 20271"/>
    </justification>
  </clause>

  <clause id="20273">
    <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(20206(a,1),20207(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="20206 20207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20274">
    <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(7401(a,1),20208(a,2,1))].">
      <j1 rule="para" parents="7401 20208"/>
    </justification>
  </clause>

  <clause id="20275">
    <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(334,a,239,a,b,20274,a),flip(a)].">
      <j1 rule="hyper" parents="334 239 20274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20276">
    <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(5391(a,1),20202(a,1,1))].">
      <j1 rule="para" parents="5391 20202"/>
    </justification>
  </clause>

  <clause id="20277">
    <literal><![CDATA[
      a((x * (y * z)) \ u,w,K(v5,v6)) = a(u \ (x * (z * y)),v6,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(20161,a,20276,a)].">
      <j1 rule="hyper" parents="20161 20276"/>
    </justification>
  </clause>

  <clause id="20278">
    <literal><![CDATA[
      a((x * y) \ (z \ u),w,K(v5,v6)) = a(u \ (z * (y * x)),v6,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(14846,a,20277,a)].">
      <j1 rule="hyper" parents="14846 20277"/>
    </justification>
  </clause>

  <clause id="20280">
    <literal><![CDATA[
      a(x \ (y \ (z \ u)),w,K(v5,v6)) = a(u \ (z * (x * y)),v6,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(14846,a,20278,a)].">
      <j1 rule="hyper" parents="14846 20278"/>
    </justification>
  </clause>

  <clause id="20281">
    <literal><![CDATA[
      a(x \ (y * (z * u)),w,K(v5,v6)) = a(((y \ x) \ u) * z,w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(20155,a,20280,a),flip(a)].">
      <j1 rule="hyper" parents="20155 20280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20282">
    <literal><![CDATA[
      a(((x \ y) \ z) * u,w,K(v5,v6)) = a((y \ x) * (u * z),w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(20049,a,20281,a),flip(a)].">
      <j1 rule="hyper" parents="20049 20281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20283">
    <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,20253,a,b,20282,a)].">
      <j1 rule="hyper" parents="58 20253 20282"/>
    </justification>
  </clause>

  <clause id="20284">
    <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,20259,a(flip),b,20283,a),flip(a)].">
      <j1 rule="hyper" parents="58 20259 20283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20285">
    <literal><![CDATA[
      a(x \ (y * z),u,K(w,v5)) = a(y * (x \ z),w,K(v5,u))
    ]]></literal>
    <justification jstring="[hyper(20197,a,20284,a)].">
      <j1 rule="hyper" parents="20197 20284"/>
    </justification>
  </clause>

  <clause id="20286">
    <literal><![CDATA[
      a(x * (y \ (z \ 1)),u,K(w,v5)) = a(u,w,K(v5,z * (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(20213,a,20285,a),flip(a)].">
      <j1 rule="hyper" parents="20213 20285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20287">
    <literal><![CDATA[
      a(x * (y \ z),u,K(w,v5)) = a(v5,u,K(w,z \ (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(20201,a,20285,a),flip(a)].">
      <j1 rule="hyper" parents="20201 20285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20288">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a(y * (z \ x),w,K(u,v5))
    ]]></literal>
    <justification jstring="[hyper(20200,a,20285,a)].">
      <j1 rule="hyper" parents="20200 20285"/>
    </justification>
  </clause>

  <clause id="20289">
    <literal><![CDATA[
      a(x * (y \ z),u,K(w,v5)) = a(z * (y \ x),v5,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(20052,a,20285,a),flip(a)].">
      <j1 rule="hyper" parents="20052 20285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20290">
    <literal><![CDATA[
      a((x \ y) * z,u,K(w,v5)) = a(y * (x \ z),w,K(v5,u))
    ]]></literal>
    <justification jstring="[hyper(20049,a,20285,a)].">
      <j1 rule="hyper" parents="20049 20285"/>
    </justification>
  </clause>

  <clause id="20291">
    <literal><![CDATA[
      a(x * (y \ z),u,K(w,v5)) = a(u,v5,K(w,y \ (x * z)))
    ]]></literal>
    <justification jstring="[hyper(14677,a,20285,a),flip(a)].">
      <j1 rule="hyper" parents="14677 20285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20292">
    <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(20285(a,2),20125(a,1))].">
      <j1 rule="para" parents="20285 20125"/>
    </justification>
  </clause>

  <clause id="20293">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a(y * (z \ x),u,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,14592,a(flip),b,20287,a)].">
      <j1 rule="hyper" parents="334 14592 20287"/>
    </justification>
  </clause>

  <clause id="20294">
    <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),20287(a,2,3,2,2))].">
      <j1 rule="para" parents="4 20287"/>
    </justification>
  </clause>

  <clause id="20295">
    <literal><![CDATA[
      a(x * (y \ z),u,K(w,v5)) = a(w,u,K(v5,z * (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(20112,a,20289,a),flip(a)].">
      <j1 rule="hyper" parents="20112 20289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20296">
    <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(20289(a,2),20111(a,1))].">
      <j1 rule="para" parents="20289 20111"/>
    </justification>
  </clause>

  <clause id="20297">
    <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(20289(a,2),20125(a,1))].">
      <j1 rule="para" parents="20289 20125"/>
    </justification>
  </clause>

  <clause id="20298">
    <literal><![CDATA[
      a((x / y) * z,u,K(w,v5)) = a(x * (y \ z),w,K(v5,u))
    ]]></literal>
    <justification jstring="[hyper(20187,a,20290,a)].">
      <j1 rule="hyper" parents="20187 20290"/>
    </justification>
  </clause>

  <clause id="20299">
    <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),20291(a,2,3,2,2))].">
      <j1 rule="para" parents="5 20291"/>
    </justification>
  </clause>

  <clause id="20300">
    <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(20293(a,2),20125(a,1))].">
      <j1 rule="para" parents="20293 20125"/>
    </justification>
  </clause>

  <clause id="20301">
    <literal><![CDATA[
      a(x * (y \ (x \ z)),u,K(w,v5)) = a(w,u,K(v5,y \ z))
    ]]></literal>
    <justification jstring="[hyper(20125,a,20299,a)].">
      <j1 rule="hyper" parents="20125 20299"/>
    </justification>
  </clause>

  <clause id="20302">
    <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(20301(a,2),20106(a,1))].">
      <j1 rule="para" parents="20301 20106"/>
    </justification>
  </clause>

  <clause id="20303">
    <literal><![CDATA[
      a(x * (y \ (z \ 1)),u,K(w,v5)) = a(z * (x \ y),u,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,20108,a(flip),b,20286,a),flip(a)].">
      <j1 rule="hyper" parents="334 20108 20286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20304">
    <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(3732(a,1),20296(a,1,1,2))].">
      <j1 rule="para" parents="3732 20296"/>
    </justification>
  </clause>

  <clause id="20305">
    <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(17748(a,1),20297(a,1))].">
      <j1 rule="para" parents="17748 20297"/>
    </justification>
  </clause>

  <clause id="20306">
    <literal><![CDATA[
      ((x * y) * z) \ (y * (T(x,y) * z)) = ((y * x) * z) \ (y * (x * z))
    ]]></literal>
    <justification jstring="[para(5378(a,1),20263(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5378 20263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20307">
    <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,15438,a(flip),b,20191,a)].">
      <j1 rule="hyper" parents="58 15438 20191"/>
    </justification>
  </clause>

  <clause id="20308">
    <literal><![CDATA[
      (K(x,y) * a(z,u,w)) * v5 = a(z,u,w) * (K(x,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(988,a,20275,a)].">
      <j1 rule="hyper" parents="988 20275"/>
    </justification>
  </clause>

  <clause id="20309">
    <literal><![CDATA[
      (a(x,y,z) * K(u,w)) * v5 = a(x,y,z) * (K(u,w) * v5)
    ]]></literal>
    <justification jstring="[para(17585(a,1),20308(a,1,1))].">
      <j1 rule="para" parents="17585 20308"/>
    </justification>
  </clause>

  <clause id="20310">
    <literal><![CDATA[
      L(x,K(y,z),a(u,w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(493,a,20309,a)].">
      <j1 rule="hyper" parents="493 20309"/>
    </justification>
  </clause>

  <clause id="20311">
    <literal><![CDATA[
      L(x,K(y,z),a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      x = v6
    ]]></literal>
    <justification jstring="[para(20310(a,1),45(a,2))].">
      <j1 rule="para" parents="20310 45"/>
    </justification>
  </clause>

  <clause id="20313">
    <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(17680(a,1),20311(a,1))].">
      <j1 rule="para" parents="17680 20311"/>
    </justification>
  </clause>

  <clause id="20314">
    <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(14339(a,1),20313(a,1))].">
      <j1 rule="para" parents="14339 20313"/>
    </justification>
  </clause>

  <clause id="20315">
    <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(6558(a,2),20307(a,1,1,2))].">
      <j1 rule="para" parents="6558 20307"/>
    </justification>
  </clause>

  <clause id="20316">
    <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,15438,a(flip),b,20315,a)].">
      <j1 rule="hyper" parents="58 15438 20315"/>
    </justification>
  </clause>

  <clause id="20317">
    <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(20136(a,1),20246(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20136 20246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20318">
    <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(4450(a,1),20317(a,2,1))].">
      <j1 rule="para" parents="4450 20317"/>
    </justification>
  </clause>

  <clause id="20319">
    <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(334,a,14299,a(flip),b,20318,a),flip(a)].">
      <j1 rule="hyper" parents="334 14299 20318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20320">
    <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),20319(a,2,1))].">
      <j1 rule="para" parents="17 20319"/>
    </justification>
  </clause>

  <clause id="20321">
    <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(8151(a,1),20320(a,1,1,2,2))].">
      <j1 rule="para" parents="8151 20320"/>
    </justification>
  </clause>

  <clause id="20322">
    <literal><![CDATA[
      T(x * K(y,z * x),z) = T(x,z) * K(y,x * z)
    ]]></literal>
    <justification jstring="[para(12617(a,1),20321(a,1,1,2))].">
      <j1 rule="para" parents="12617 20321"/>
    </justification>
  </clause>

  <clause id="20323">
    <literal><![CDATA[
      x \ T(x * K(y,z * x),z) = K(y,x * z) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,20322,a,b,16028,a)].">
      <j1 rule="hyper" parents="116 20322 16028"/>
    </justification>
  </clause>

  <clause id="20324">
    <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(20322(a,2),20316(a,1,1,2,2,1))].">
      <j1 rule="para" parents="20322 20316"/>
    </justification>
  </clause>

  <clause id="20325">
    <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(20132(a,2),20145(a,1,1))].">
      <j1 rule="para" parents="20132 20145"/>
    </justification>
  </clause>

  <clause id="20326">
    <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(20132(a,2),20325(a,1,2,1,1))].">
      <j1 rule="para" parents="20132 20325"/>
    </justification>
  </clause>

  <clause id="20327">
    <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(20132(a,2),20326(a,1,2,1,2))].">
      <j1 rule="para" parents="20132 20326"/>
    </justification>
  </clause>

  <clause id="20328">
    <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(17730(a,1),20252(a,1,1))].">
      <j1 rule="para" parents="17730 20252"/>
    </justification>
  </clause>

  <clause id="20329">
    <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(14720(a,1),20328(a,1,1))].">
      <j1 rule="para" parents="14720 20328"/>
    </justification>
  </clause>

  <clause id="20331">
    <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(5391(a,1),20329(a,1,1,1,2))].">
      <j1 rule="para" parents="5391 20329"/>
    </justification>
  </clause>

  <clause id="20332">
    <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(20115(a,1),20331(a,1,1))].">
      <j1 rule="para" parents="20115 20331"/>
    </justification>
  </clause>

  <clause id="20333">
    <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(20120(a,1),20332(a,1,1))].">
      <j1 rule="para" parents="20120 20332"/>
    </justification>
  </clause>

  <clause id="20334">
    <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(20158,a,20333,a),flip(a)].">
      <j1 rule="hyper" parents="20158 20333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20336">
    <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(17829(a,1),20334(a,1,1,1,2))].">
      <j1 rule="para" parents="17829 20334"/>
    </justification>
  </clause>

  <clause id="20337">
    <literal><![CDATA[
      ((x / (K(y,z) * u)) * K(y,z)) * u = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(5895(a,1),20336(a,1,1,1,2,1,2))].">
      <j1 rule="para" parents="5895 20336"/>
    </justification>
  </clause>

  <clause id="20338">
    <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(20337(a,1),14583(a,1,1,2))].">
      <j1 rule="para" parents="20337 14583"/>
    </justification>
  </clause>

  <clause id="20339">
    <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(20303(a,1),20304(a,1))].">
      <j1 rule="para" parents="20303 20304"/>
    </justification>
  </clause>

  <clause id="20340">
    <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(20193(a,1),20338(a,1,1,2))].">
      <j1 rule="para" parents="20193 20338"/>
    </justification>
  </clause>

  <clause id="20341">
    <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(20245(a,1),20340(a,1,2,2,2))].">
      <j1 rule="para" parents="20245 20340"/>
    </justification>
  </clause>

  <clause id="20342">
    <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(20211(a,2),20341(a,1,2,2))].">
      <j1 rule="para" parents="20211 20341"/>
    </justification>
  </clause>

  <clause id="20343">
    <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(20255(a,1),20342(a,1,2))].">
      <j1 rule="para" parents="20255 20342"/>
    </justification>
  </clause>

  <clause id="20344">
    <literal><![CDATA[
      a(x,y,R(z,K(u,x),y)) = a(x,K(u,x) * y,z)
    ]]></literal>
    <justification jstring="[hyper(709,a,20343,a),flip(a)].">
      <j1 rule="hyper" parents="709 20343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20345">
    <literal><![CDATA[
      a(x,y,L(z,x,K(u,y))) = a(x,K(u,x) * y,z)
    ]]></literal>
    <justification jstring="[para(20245(a,1),20344(a,1,3))].">
      <j1 rule="para" parents="20245 20344"/>
    </justification>
  </clause>

  <clause id="20346">
    <literal><![CDATA[
      a(x,K(y,x) * z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(20222,a,20345,a),flip(a)].">
      <j1 rule="hyper" parents="20222 20345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20348">
    <literal><![CDATA[
      a(x,K(x,y) * z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(5394(a,1),20346(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5394 20346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20350">
    <literal><![CDATA[
      a(x,y * K(x,z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,19335,a(flip),b,20348,a)].">
      <j1 rule="hyper" parents="58 19335 20348"/>
    </justification>
  </clause>

  <clause id="20352">
    <literal><![CDATA[
      a(T(x,y),z,u) = a(x,z,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,20272,a(flip),b,20350,a)].">
      <j1 rule="hyper" parents="58 20272 20350"/>
    </justification>
  </clause>

  <clause id="20355">
    <literal><![CDATA[
      a(T(x,y),z,u) = T(a(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(334,a,19225,a(flip),b,20352,a),flip(a)].">
      <j1 rule="hyper" parents="334 19225 20352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20356">
    <literal><![CDATA[
      a(x,y,z) \ a(T(x,u),y,z) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,20352,a,b,19224,a)].">
      <j1 rule="hyper" parents="116 20352 19224"/>
    </justification>
  </clause>

  <clause id="20357">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w \ a(x,y,z)) = w \ a(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(20355(a,2),17880(a,2,2))].">
      <j1 rule="para" parents="20355 17880"/>
    </justification>
  </clause>

  <clause id="20358">
    <literal><![CDATA[
      a(x \ a(T(y,z),u,w),v5,v6) = a(x \ a(y,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(20357(a,1),19758(a,1,1))].">
      <j1 rule="para" parents="20357 19758"/>
    </justification>
  </clause>

  <clause id="20359">
    <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(20185(a,1),20186(a,1,2,2,1,2,1))].">
      <j1 rule="para" parents="20185 20186"/>
    </justification>
  </clause>

  <clause id="20360">
    <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(20273(a,1),20359(a,1,2))].">
      <j1 rule="para" parents="20273 20359"/>
    </justification>
  </clause>

  <clause id="20361">
    <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,13783,a(flip),b,20360,a)].">
      <j1 rule="hyper" parents="58 13783 20360"/>
    </justification>
  </clause>

  <clause id="20363">
    <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(20132(a,2),20361(a,1,1))].">
      <j1 rule="para" parents="20132 20361"/>
    </justification>
  </clause>

  <clause id="20364">
    <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(20132(a,2),20363(a,1,2,1,1))].">
      <j1 rule="para" parents="20132 20363"/>
    </justification>
  </clause>

  <clause id="20365">
    <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,20327,a(flip),b,20364,a)].">
      <j1 rule="hyper" parents="58 20327 20364"/>
    </justification>
  </clause>

  <clause id="20367">
    <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(334,a,20184,a,b,20365,a)].">
      <j1 rule="hyper" parents="334 20184 20365"/>
    </justification>
  </clause>

  <clause id="20368">
    <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,15290,a,b,20367,a)].">
      <j1 rule="hyper" parents="30 15290 20367"/>
    </justification>
  </clause>

  <clause id="20369">
    <literal><![CDATA[
      a(x,y,K(z,u * L(u \ w,v5,v6))) = a(z,x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(334,a,14592,a,b,20368,a),flip(a)].">
      <j1 rule="hyper" parents="334 14592 20368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20370">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5) * v6)) = a(u * v6,x,K(z,y))
    ]]></literal>
    <justification jstring="[para(651(a,1),20368(a,1,3,2))].">
      <j1 rule="para" parents="651 20368"/>
    </justification>
  </clause>

  <clause id="20371">
    <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(1763(a,1),20369(a,1,3,2))].">
      <j1 rule="para" parents="1763 20369"/>
    </justification>
  </clause>

  <clause id="20372">
    <literal><![CDATA[
      a(x * L(y,z,u),w,K(v5,v6)) = a(y * x,w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(20118,a,20370,a)].">
      <j1 rule="hyper" parents="20118 20370"/>
    </justification>
  </clause>

  <clause id="20373">
    <literal><![CDATA[
      a(L(x,y,z) * u,w,K(v5,v6)) = a(x * u,v6,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(20111,a,20370,a)].">
      <j1 rule="hyper" parents="20111 20370"/>
    </justification>
  </clause>

  <clause id="20374">
    <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(20305,a,20372,a)].">
      <j1 rule="hyper" parents="20305 20372"/>
    </justification>
  </clause>

  <clause id="20375">
    <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(20373(a,1),20339(a,1))].">
      <j1 rule="para" parents="20373 20339"/>
    </justification>
  </clause>

  <clause id="20376">
    <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(20117,a,20371,a)].">
      <j1 rule="hyper" parents="20117 20371"/>
    </justification>
  </clause>

  <clause id="20377">
    <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(334,a,20289,a(flip),b,20374,a),flip(a)].">
      <j1 rule="hyper" parents="334 20289 20374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20378">
    <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(20376(a,1),20292(a,1))].">
      <j1 rule="para" parents="20376 20292"/>
    </justification>
  </clause>

  <clause id="20379">
    <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(20377(a,2),20297(a,1))].">
      <j1 rule="para" parents="20377 20297"/>
    </justification>
  </clause>

  <clause id="20380">
    <literal><![CDATA[
      a(x * (y \ L(x \ 1,z,u)),w,K(v5,v6)) = a(v5,v6,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(20378,a,20104,a)].">
      <j1 rule="hyper" parents="20378 20104"/>
    </justification>
  </clause>

  <clause id="20381">
    <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,20294,a(flip),b,20380,a)].">
      <j1 rule="hyper" parents="58 20294 20380"/>
    </justification>
  </clause>

  <clause id="20382">
    <literal><![CDATA[
      a(L(x \ 1,y,z) \ u,w,K(v5,v6)) = a(v6,v5,K(w,x * u))
    ]]></literal>
    <justification jstring="[hyper(14707,a,20381,a)].">
      <j1 rule="hyper" parents="14707 20381"/>
    </justification>
  </clause>

  <clause id="20383">
    <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,20214,a(flip),b,20382,a)].">
      <j1 rule="hyper" parents="58 20214 20382"/>
    </justification>
  </clause>

  <clause id="20384">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(w,v5,v6))) = a(w \ u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(334,a,20123,a(flip),b,20383,a),flip(a)].">
      <j1 rule="hyper" parents="334 20123 20383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20385">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(w,v5,v6))) = a(y,x,K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(14159(a,1),20383(a,2,3))].">
      <j1 rule="para" parents="14159 20383"/>
    </justification>
  </clause>

  <clause id="20386">
    <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(20384(a,2),20112(a,1))].">
      <j1 rule="para" parents="20384 20112"/>
    </justification>
  </clause>

  <clause id="20387">
    <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,20195,a,b,20385,a)].">
      <j1 rule="hyper" parents="58 20195 20385"/>
    </justification>
  </clause>

  <clause id="20389">
    <literal><![CDATA[
      a(((x * y) \ (x * z)) * u,w,K(v5,v6)) = a(v6,v5,K(w,u * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(334,a,20030,a(flip),b,20387,a),flip(a)].">
      <j1 rule="hyper" parents="334 20030 20387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20390">
    <literal><![CDATA[
      a(x,y,K(z,u * ((w * v5) \ (w * v6)))) = a(x,y,K(z,u * (v5 \ v6)))
    ]]></literal>
    <justification jstring="[hyper(20107,a,20389,a)].">
      <j1 rule="hyper" parents="20107 20389"/>
    </justification>
  </clause>

  <clause id="20391">
    <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(14379(a,1),20390(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="14379 20390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20392">
    <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(20375,a,20298,a)].">
      <j1 rule="hyper" parents="20375 20298"/>
    </justification>
  </clause>

  <clause id="20394">
    <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),20392(a,2,1))].">
      <j1 rule="para" parents="2 20392"/>
    </justification>
  </clause>

  <clause id="20395">
    <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(334,a,20288,a(flip),b,20394,a),flip(a)].">
      <j1 rule="hyper" parents="334 20288 20394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20396">
    <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),20395(a,2,1,2))].">
      <j1 rule="para" parents="61 20395"/>
    </justification>
  </clause>

  <clause id="20397">
    <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),20396(a,2,1))].">
      <j1 rule="para" parents="3 20396"/>
    </justification>
  </clause>

  <clause id="20399">
    <literal><![CDATA[
      a(x,y,K(z,u \ (L(u \ 1,w,v5) \ v6))) = a(v6,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(14159(a,1),20397(a,1,3))].">
      <j1 rule="para" parents="14159 20397"/>
    </justification>
  </clause>

  <clause id="20400">
    <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(20149(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="20149 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20401">
    <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(14654(a,1),20150(a,1,1))].">
      <j1 rule="para" parents="14654 20150"/>
    </justification>
  </clause>

  <clause id="20402">
    <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(19750(a,2),20401(a,1,1))].">
      <j1 rule="para" parents="19750 20401"/>
    </justification>
  </clause>

  <clause id="20403">
    <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(15293(a,1),20402(a,1,1,1))].">
      <j1 rule="para" parents="15293 20402"/>
    </justification>
  </clause>

  <clause id="20404">
    <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(5728,a,20403,a),flip(a)].">
      <j1 rule="hyper" parents="5728 20403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20406">
    <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,20157,a(flip),b,20404,a),flip(a)].">
      <j1 rule="hyper" parents="34 20157 20404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20407">
    <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(17595,a,20406,a)].">
      <j1 rule="hyper" parents="17595 20406"/>
    </justification>
  </clause>

  <clause id="20408">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (L(z,x,u) \ z) = T(L(z,x,u) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(20400,a,20407,a)].">
      <j1 rule="hyper" parents="20400 20407"/>
    </justification>
  </clause>

  <clause id="20409">
    <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(307,a,20408,a)].">
      <j1 rule="hyper" parents="307 20408"/>
    </justification>
  </clause>

  <clause id="20411">
    <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,17916,a,b,20409,a)].">
      <j1 rule="hyper" parents="58 17916 20409"/>
    </justification>
  </clause>

  <clause id="20412">
    <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(20115(a,2),20411(a,1,1,2))].">
      <j1 rule="para" parents="20115 20411"/>
    </justification>
  </clause>

  <clause id="20413">
    <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(14612(a,2),20412(a,1,1,2))].">
      <j1 rule="para" parents="14612 20412"/>
    </justification>
  </clause>

  <clause id="20414">
    <literal><![CDATA[
      T(L(x,y,z) \ x,x \ u) = T(L(x,y,z) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(6375,a,20413,a)].">
      <j1 rule="hyper" parents="6375 20413"/>
    </justification>
  </clause>

  <clause id="20415">
    <literal><![CDATA[
      T(L(x,y,z) \ x,x * u) = T(L(x,y,z) \ x,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),20414(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 20414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20416">
    <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(20414(a,1),12076(a,1))].">
      <j1 rule="para" parents="20414 12076"/>
    </justification>
  </clause>

  <clause id="20417">
    <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(13667(a,1),20416(a,1))].">
      <j1 rule="para" parents="13667 20416"/>
    </justification>
  </clause>

  <clause id="20419">
    <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(20415(a,1),20417(a,1))].">
      <j1 rule="para" parents="20415 20417"/>
    </justification>
  </clause>

  <clause id="20420">
    <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(13667(a,1),20419(a,1))].">
      <j1 rule="para" parents="13667 20419"/>
    </justification>
  </clause>

  <clause id="20421">
    <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(20420,a,7007,a)].">
      <j1 rule="hyper" parents="20420 7007"/>
    </justification>
  </clause>

  <clause id="20423">
    <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(12075(a,1),20421(a,1,1))].">
      <j1 rule="para" parents="12075 20421"/>
    </justification>
  </clause>

  <clause id="20424">
    <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(20423(a,1),20295(a,2,3,2,2))].">
      <j1 rule="para" parents="20423 20295"/>
    </justification>
  </clause>

  <clause id="20425">
    <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,20373,a(flip),b,20424,a)].">
      <j1 rule="hyper" parents="58 20373 20424"/>
    </justification>
  </clause>

  <clause id="20426">
    <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(20305,a,20425,a)].">
      <j1 rule="hyper" parents="20305 20425"/>
    </justification>
  </clause>

  <clause id="20428">
    <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),20426(a,1,1))].">
      <j1 rule="para" parents="2 20426"/>
    </justification>
  </clause>

  <clause id="20429">
    <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(20300,a,20428,a)].">
      <j1 rule="hyper" parents="20300 20428"/>
    </justification>
  </clause>

  <clause id="20430">
    <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(20379,a,20429,a)].">
      <j1 rule="hyper" parents="20379 20429"/>
    </justification>
  </clause>

  <clause id="20431">
    <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(20302,a,20430,a)].">
      <j1 rule="hyper" parents="20302 20430"/>
    </justification>
  </clause>

  <clause id="20433">
    <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(20386,a,20431,a)].">
      <j1 rule="hyper" parents="20386 20431"/>
    </justification>
  </clause>

  <clause id="20436">
    <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(15008(a,1),20433(a,1,3))].">
      <j1 rule="para" parents="15008 20433"/>
    </justification>
  </clause>

  <clause id="20437">
    <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,20399,a(flip),b,20436,a),flip(a)].">
      <j1 rule="hyper" parents="58 20399 20436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20439">
    <literal><![CDATA[
      a(x,y,K(z,u * a(w,v5,v6))) = a(u,x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,20391,a(flip),b,20437,a)].">
      <j1 rule="hyper" parents="58 20391 20437"/>
    </justification>
  </clause>

  <clause id="20440">
    <literal><![CDATA[
      a(a(x,y,z) * u,w,K(v5,v6)) = a(u,w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(20118,a,20439,a)].">
      <j1 rule="hyper" parents="20118 20439"/>
    </justification>
  </clause>

  <clause id="20442">
    <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(20439(a,1),15315(a,1,2))].">
      <j1 rule="para" parents="20439 15315"/>
    </justification>
  </clause>

  <clause id="20443">
    <literal><![CDATA[
      a(x * (y \ a(z,u,w)),v5,K(v6,v7)) = a(y \ x,v7,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(20297,a,20440,a)].">
      <j1 rule="hyper" parents="20297 20440"/>
    </justification>
  </clause>

  <clause id="20444">
    <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),20440(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 20440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20446">
    <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(20443(a,1),14623(a,1,2,2))].">
      <j1 rule="para" parents="20443 14623"/>
    </justification>
  </clause>

  <clause id="20447">
    <literal><![CDATA[
      L(x,y,K(z,u * a(w,v5,v6))) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(20442,a,20099,a)].">
      <j1 rule="hyper" parents="20442 20099"/>
    </justification>
  </clause>

  <clause id="20448">
    <literal><![CDATA[
      L(x,a(y,z,u) * w,K(v5,v6)) = L(x,w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(20144,a,20447,a)].">
      <j1 rule="hyper" parents="20144 20447"/>
    </justification>
  </clause>

  <clause id="20449">
    <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(20143,a,20448,a),flip(a)].">
      <j1 rule="hyper" parents="20143 20448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20450">
    <literal><![CDATA[
      L(x,y,T(z,a(u,w,v5) * v6)) = L(x,y,T(z,v6))
    ]]></literal>
    <justification jstring="[hyper(20143,a,20449,a),flip(a)].">
      <j1 rule="hyper" parents="20143 20449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20451">
    <literal><![CDATA[
      L(x,y,T(z,u * a(w,v5,v6))) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(17660,a,20450,a)].">
      <j1 rule="hyper" parents="17660 20450"/>
    </justification>
  </clause>

  <clause id="20452">
    <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),20451(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 20451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20453">
    <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(20444(a,1),20446(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="20444 20446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20454">
    <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(334,a,20128,a(flip),b,20453,a),flip(a)].">
      <j1 rule="hyper" parents="334 20128 20453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20456">
    <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(20177,a,20454,a)].">
      <j1 rule="hyper" parents="20177 20454"/>
    </justification>
  </clause>

  <clause id="20457">
    <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(20456(a,2),490(a,1,2,2))].">
      <j1 rule="para" parents="20456 490"/>
    </justification>
  </clause>

  <clause id="20458">
    <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(20139(a,1),20457(a,1,2))].">
      <j1 rule="para" parents="20139 20457"/>
    </justification>
  </clause>

  <clause id="20459">
    <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(861,a,20458,a)].">
      <j1 rule="hyper" parents="861 20458"/>
    </justification>
  </clause>

  <clause id="20460">
    <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,14384,a(flip),b,20459,a),flip(a)].">
      <j1 rule="hyper" parents="58 14384 20459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20462">
    <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,19743,a(flip),b,20460,a)].">
      <j1 rule="hyper" parents="58 19743 20460"/>
    </justification>
  </clause>

  <clause id="20464">
    <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(20462(a,1),489(a,1,1,2,2))].">
      <j1 rule="para" parents="20462 489"/>
    </justification>
  </clause>

  <clause id="20465">
    <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,12421,a(flip),b,20464,a),flip(a)].">
      <j1 rule="hyper" parents="58 12421 20464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20466">
    <literal><![CDATA[
      a(K(x,y) * z,u,a(w,v5,v6)) = a(z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(20224,a,20465,a)].">
      <j1 rule="hyper" parents="20224 20465"/>
    </justification>
  </clause>

  <clause id="20469">
    <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,19348,a(flip),b,20466,a)].">
      <j1 rule="hyper" parents="58 19348 20466"/>
    </justification>
  </clause>

  <clause id="20470">
    <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,19333,a(flip),b,20466,a)].">
      <j1 rule="hyper" parents="58 19333 20466"/>
    </justification>
  </clause>

  <clause id="20471">
    <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,19331,a(flip),b,20466,a)].">
      <j1 rule="hyper" parents="58 19331 20466"/>
    </justification>
  </clause>

  <clause id="20472">
    <literal><![CDATA[
      a(T(x,y) \ z,u,a(w,v5,v6)) = a(x \ z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(5337(a,1),20466(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5337 20466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20473">
    <literal><![CDATA[
      a(x \ (y / z),u,a(w,v5,v6)) = a(x \ (z \ y),u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(14302(a,1),20469(a,1,1))].">
      <j1 rule="para" parents="14302 20469"/>
    </justification>
  </clause>

  <clause id="20474">
    <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,17187,a(flip),b,20471,a),flip(a)].">
      <j1 rule="hyper" parents="58 17187 20471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20476">
    <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,20473,a(flip),b,20474,a)].">
      <j1 rule="hyper" parents="58 20473 20474"/>
    </justification>
  </clause>

  <clause id="20477">
    <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(14046(a,1),20476(a,1,1,2,2))].">
      <j1 rule="para" parents="14046 20476"/>
    </justification>
  </clause>

  <clause id="20478">
    <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(5391(a,1),20477(a,1,1))].">
      <j1 rule="para" parents="5391 20477"/>
    </justification>
  </clause>

  <clause id="20479">
    <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,20466,a(flip),b,20478,a),flip(a)].">
      <j1 rule="hyper" parents="58 20466 20478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20481">
    <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,20324,a(flip),b,20479,a),flip(a)].">
      <j1 rule="hyper" parents="58 20324 20479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20483">
    <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(20323(a,1),20481(a,1,1,2))].">
      <j1 rule="para" parents="20323 20481"/>
    </justification>
  </clause>

  <clause id="20484">
    <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(6378(a,2),20483(a,1,1))].">
      <j1 rule="para" parents="6378 20483"/>
    </justification>
  </clause>

  <clause id="20485">
    <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,19332,a(flip),b,20484,a)].">
      <j1 rule="hyper" parents="58 19332 20484"/>
    </justification>
  </clause>

  <clause id="20486">
    <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,20470,a(flip),b,20485,a),flip(a)].">
      <j1 rule="hyper" parents="58 20470 20485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20488">
    <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(334,a,20472,a(flip),b,20486,a),flip(a)].">
      <j1 rule="hyper" parents="334 20472 20486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20490">
    <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(20488(a,1),15215(a,1,1))].">
      <j1 rule="para" parents="20488 15215"/>
    </justification>
  </clause>

  <clause id="20491">
    <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(210,a,20490,a),flip(a)].">
      <j1 rule="hyper" parents="210 20490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20494">
    <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(15173(a,1),20491(a,1,1))].">
      <j1 rule="para" parents="15173 20491"/>
    </justification>
  </clause>

  <clause id="20495">
    <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(334,a,19340,a(flip),b,20494,a),flip(a)].">
      <j1 rule="hyper" parents="334 19340 20494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20496">
    <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(15449(a,1),20495(a,1,1))].">
      <j1 rule="para" parents="15449 20495"/>
    </justification>
  </clause>

  <clause id="20497">
    <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(4355(a,1),20496(a,1,1))].">
      <j1 rule="para" parents="4355 20496"/>
    </justification>
  </clause>

  <clause id="20499">
    <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(334,a,15439,a(flip),b,20497,a),flip(a)].">
      <j1 rule="hyper" parents="334 15439 20497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20500">
    <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),20499(a,2,1))].">
      <j1 rule="para" parents="4 20499"/>
    </justification>
  </clause>

  <clause id="20502">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) * v6 = a(x,y,a(z,u,w)) * (v5 * v6)
    ]]></literal>
    <justification jstring="[para(20500(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20500 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20503">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6))) = x
    ]]></literal>
    <justification jstring="[hyper(4329,a,20502,a)].">
      <j1 rule="hyper" parents="4329 20502"/>
    </justification>
  </clause>

  <clause id="20504">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) * v6 = v5 * (v6 * a(x,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(334,a,13745,a(flip),b,20502,a),flip(a)].">
      <j1 rule="hyper" parents="334 13745 20502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20505">
    <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,20502,a)].">
      <j1 rule="hyper" parents="116 151 20502"/>
    </justification>
  </clause>

  <clause id="20506">
    <literal><![CDATA[
      a(a(x,y,a(z,u,w)),v5,v6) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,20502,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="115 20502 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20507">
    <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(20502(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="20502 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20508">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      x = v7
    ]]></literal>
    <justification jstring="[para(20503(a,1),45(a,2))].">
      <j1 rule="para" parents="20503 45"/>
    </justification>
  </clause>

  <clause id="20509">
    <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(20503(a,1),782(a,1)),flip(a)].">
      <j1 rule="para" parents="20503 782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20510">
    <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(20503(a,1),490(a,1,2,2,1))].">
      <j1 rule="para" parents="20503 490"/>
    </justification>
  </clause>

  <clause id="20511">
    <literal><![CDATA[
      a(x,a(y,z,a(u,w,v5)),v6) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,13804,a(flip),b,20506,a)].">
      <j1 rule="hyper" parents="58 13804 20506"/>
    </justification>
  </clause>

  <clause id="20512">
    <literal><![CDATA[
      (x * a(y,z,a(u,w,v5))) * v6 = x * (a(y,z,a(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(15085,a,20511,a)].">
      <j1 rule="hyper" parents="15085 20511"/>
    </justification>
  </clause>

  <clause id="20514">
    <literal><![CDATA[
      L(x,a(y,z,a(u,w,v5)),v6) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,20511,a)].">
      <j1 rule="hyper" parents="47 20511"/>
    </justification>
  </clause>

  <clause id="20515">
    <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,15174,a(flip),b,20514,a)].">
      <j1 rule="hyper" parents="58 15174 20514"/>
    </justification>
  </clause>

  <clause id="20517">
    <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(13745(a,1),20504(a,1,1))].">
      <j1 rule="para" parents="13745 20504"/>
    </justification>
  </clause>

  <clause id="20518">
    <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(20512(a,1),13757(a,1,2))].">
      <j1 rule="para" parents="20512 13757"/>
    </justification>
  </clause>

  <clause id="20519">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) \ v5) \ v6 = (v5 \ v6) * a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(20509,a,13746,a)].">
      <j1 rule="hyper" parents="20509 13746"/>
    </justification>
  </clause>

  <clause id="20520">
    <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(15169(a,1),20517(a,2,2))].">
      <j1 rule="para" parents="15169 20517"/>
    </justification>
  </clause>

  <clause id="20521">
    <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(20520(a,1),13459(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="20520 13459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20522">
    <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,19671,a(flip),b,20521,a)].">
      <j1 rule="hyper" parents="58 19671 20521"/>
    </justification>
  </clause>

  <clause id="20523">
    <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,13339,a(flip),b,20522,a),flip(a)].">
      <j1 rule="hyper" parents="58 13339 20522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20524">
    <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,13750,a(flip),b,20518,a)].">
      <j1 rule="hyper" parents="58 13750 20518"/>
    </justification>
  </clause>

  <clause id="20525">
    <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(15035(a,1),20524(a,1,1))].">
      <j1 rule="para" parents="15035 20524"/>
    </justification>
  </clause>

  <clause id="20526">
    <literal><![CDATA[
      K(x * a(y,z,a(u,w,v5)),v6) = K(x,v6)
    ]]></literal>
    <justification jstring="[hyper(13748,a,20525,a),flip(a)].">
      <j1 rule="hyper" parents="13748 20525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20528">
    <literal><![CDATA[
      K((x * R(y,z,a(u,w,v5))) \ v6,v7) = K((x * y) \ v6,v7)
    ]]></literal>
    <justification jstring="[hyper(58,a,19798,a(flip),b,20526,a),flip(a)].">
      <j1 rule="hyper" parents="58 19798 20526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20530">
    <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,20523,a(flip),b,20528,a),flip(a)].">
      <j1 rule="hyper" parents="58 20523 20528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20531">
    <literal><![CDATA[
      K(((x * a(y,z,u)) * w) \ v5,v6) = K((a(y,z,u) * (x * w)) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(334,a,14666,a,b,20530,a),flip(a)].">
      <j1 rule="hyper" parents="334 14666 20530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20533">
    <literal><![CDATA[
      K(((x * a(y,z,u)) * w) \ ((a(y,z,u) * (x * w)) * v5),v6) = K(v5,v6)
    ]]></literal>
    <justification jstring="[hyper(334,a,691,a(flip),b,20531,a),flip(a)].">
      <j1 rule="hyper" parents="334 691 20531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20534">
    <literal><![CDATA[
      K(a(a(x,y,z),u,w) \ v5,v6) = K(v5,v6)
    ]]></literal>
    <justification jstring="[hyper(20257,a,20533,a)].">
      <j1 rule="hyper" parents="20257 20533"/>
    </justification>
  </clause>

  <clause id="20535">
    <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(20534(a,1),5523(a,1,2,1))].">
      <j1 rule="para" parents="20534 5523"/>
    </justification>
  </clause>

  <clause id="20536">
    <literal><![CDATA[
      T(x,a(a(y,z,u),w,v5) \ v6) = T(x,v6)
    ]]></literal>
    <justification jstring="[hyper(20535,a,5518,a)].">
      <j1 rule="hyper" parents="20535 5518"/>
    </justification>
  </clause>

  <clause id="20537">
    <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(20536(a,1),294(a,1,2))].">
      <j1 rule="para" parents="20536 294"/>
    </justification>
  </clause>

  <clause id="20538">
    <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(20502(a,1),20507(a,1,2,1))].">
      <j1 rule="para" parents="20502 20507"/>
    </justification>
  </clause>

  <clause id="20539">
    <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(20502(a,1),20538(a,1,2))].">
      <j1 rule="para" parents="20502 20538"/>
    </justification>
  </clause>

  <clause id="20540">
    <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,20505,a(flip),b,20539,a),flip(a)].">
      <j1 rule="hyper" parents="58 20505 20539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20542">
    <literal><![CDATA[
      a(a(x,y,a(z,u,w)) * v5,v6,v7) = a(v5,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(334,a,9,a,b,20540,a),flip(a)].">
      <j1 rule="hyper" parents="334 9 20540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20543">
    <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(20540(a,2),709(a,1))].">
      <j1 rule="para" parents="20540 709"/>
    </justification>
  </clause>

  <clause id="20544">
    <literal><![CDATA[
      a(a(x,y,a(z,u,w)) \ v5,v6,v7) = a(v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(5(a,1),20542(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 20542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20545">
    <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(13716(a,1),20543(a,1,1))].">
      <j1 rule="para" parents="13716 20543"/>
    </justification>
  </clause>

  <clause id="20546">
    <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(20502(a,1),20510(a,1,2))].">
      <j1 rule="para" parents="20502 20510"/>
    </justification>
  </clause>

  <clause id="20547">
    <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(861,a,20546,a)].">
      <j1 rule="hyper" parents="861 20546"/>
    </justification>
  </clause>

  <clause id="20548">
    <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(20508,a,20547,a),flip(a)].">
      <j1 rule="hyper" parents="20508 20547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20550">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6)) * v7) = L(x,y,v7)
    ]]></literal>
    <justification jstring="[para(20503(a,1),20548(a,1,2))].">
      <j1 rule="para" parents="20503 20548"/>
    </justification>
  </clause>

  <clause id="20551">
    <literal><![CDATA[
      L(x,y,L(a(z,u,w),v5,v6)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(3965(a,1),20550(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3965 20550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20552">
    <literal><![CDATA[
      L(x,y,z * a(u,w,a(v5,v6,v7))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(13716(a,1),20550(a,1,3))].">
      <j1 rule="para" parents="13716 20550"/>
    </justification>
  </clause>

  <clause id="20553">
    <literal><![CDATA[
      L(x,y,R(z,u,a(w,v5,v6))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(15169(a,1),20552(a,1,3))].">
      <j1 rule="para" parents="15169 20552"/>
    </justification>
  </clause>

  <clause id="20554">
    <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(667(a,1),20553(a,1,3))].">
      <j1 rule="para" parents="667 20553"/>
    </justification>
  </clause>

  <clause id="20555">
    <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(20551(a,1),13837(a,1,1))].">
      <j1 rule="para" parents="20551 13837"/>
    </justification>
  </clause>

  <clause id="20556">
    <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,20452,a(flip),b,20554,a)].">
      <j1 rule="hyper" parents="58 20452 20554"/>
    </justification>
  </clause>

  <clause id="20557">
    <literal><![CDATA[
      L(x,y,(z * a(u,w,v5)) \ v6) = L(x,y,z \ (a(u,w,v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(334,a,17697,a(flip),b,20556,a),flip(a)].">
      <j1 rule="hyper" parents="334 17697 20556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20558">
    <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,20182,a,b,20557,a)].">
      <j1 rule="hyper" parents="58 20182 20557"/>
    </justification>
  </clause>

  <clause id="20559">
    <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),20558(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13 20558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20560">
    <literal><![CDATA[
      L(x,y,L(z,u,a(w,v5,v6))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(62(a,1),20559(a,1,3)),flip(a)].">
      <j1 rule="para" parents="62 20559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20561">
    <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,3343,a(flip),b,20560,a),flip(a)].">
      <j1 rule="hyper" parents="36 3343 20560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20562">
    <literal><![CDATA[
      (L(x,y,a(z,u,w)) \ x) \ v5 = x \ (L(x,y,a(z,u,w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(782,a,20561,a)].">
      <j1 rule="hyper" parents="782 20561"/>
    </justification>
  </clause>

  <clause id="20563">
    <literal><![CDATA[
      (L(x,y,a(z,u,w)) \ x) \ v5 = L(x,y,a(z,u,w)) * (x \ v5)
    ]]></literal>
    <justification jstring="[hyper(334,a,1503,a(flip),b,20562,a),flip(a)].">
      <j1 rule="hyper" parents="334 1503 20562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20564">
    <literal><![CDATA[
      (L(x,y,a(z,u,w)) * (x \ v5)) \ v5 = L(x,y,a(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(20563(a,1),17891(a,1,1))].">
      <j1 rule="para" parents="20563 17891"/>
    </justification>
  </clause>

  <clause id="20565">
    <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),20564(a,1,1,2))].">
      <j1 rule="para" parents="17 20564"/>
    </justification>
  </clause>

  <clause id="20566">
    <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),20564(a,1,1))].">
      <j1 rule="para" parents="67 20564"/>
    </justification>
  </clause>

  <clause id="20567">
    <literal><![CDATA[
      (x * L(y,z,a(u,w,v5))) \ (x * y) = L(y,z,a(u,w,v5)) \ y
    ]]></literal>
    <justification jstring="[para(14665(a,1),20565(a,1,1))].">
      <j1 rule="para" parents="14665 20565"/>
    </justification>
  </clause>

  <clause id="20568">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ x = a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(14519,a,20567,a),flip(a)].">
      <j1 rule="hyper" parents="14519 20567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20569">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * a(a(z,u,w),y,x) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,14379,a(flip),b,20567,a(flip))].">
      <j1 rule="hyper" parents="119 14379 20567"/>
    </justification>
  </clause>

  <clause id="20570">
    <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,20568,a(flip),b,20566,a),flip(a)].">
      <j1 rule="hyper" parents="119 20568 20566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20571">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ w = L(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(20568(a,1),3960(a,1,1))].">
      <j1 rule="para" parents="20568 3960"/>
    </justification>
  </clause>

  <clause id="20572">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ 1 = w \ L(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(20568(a,1),12379(a,1,1))].">
      <j1 rule="para" parents="20568 12379"/>
    </justification>
  </clause>

  <clause id="20573">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (x \ v5) = a(a(z,u,w),y,x) \ v5
    ]]></literal>
    <justification jstring="[para(20568(a,1),20563(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20568 20563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20574">
    <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(20573(a,1),502(a,2,2))].">
      <j1 rule="para" parents="20573 502"/>
    </justification>
  </clause>

  <clause id="20575">
    <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,20560,a(flip),b,20574,a)].">
      <j1 rule="hyper" parents="58 20560 20574"/>
    </justification>
  </clause>

  <clause id="20577">
    <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,311,a(flip),b,20575,a)].">
      <j1 rule="hyper" parents="58 311 20575"/>
    </justification>
  </clause>

  <clause id="20578">
    <literal><![CDATA[
      (x * a(a(y,z,u),w,v5)) \ v6 = x \ (a(a(y,z,u),w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(20570(a,1),20577(a,1,1))].">
      <j1 rule="para" parents="20570 20577"/>
    </justification>
  </clause>

  <clause id="20579">
    <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,20578,a)].">
      <j1 rule="hyper" parents="119 62 20578"/>
    </justification>
  </clause>

  <clause id="20580">
    <literal><![CDATA[
      (a(a(x,y,z),u,w) * v5) \ v6 = v5 \ (a(a(x,y,z),u,w) \ v6)
    ]]></literal>
    <justification jstring="[para(14598(a,2),20578(a,1,1))].">
      <j1 rule="para" parents="14598 20578"/>
    </justification>
  </clause>

  <clause id="20581">
    <literal><![CDATA[
      (a(a(x,y,z),u,w) * v5) * v6 = a(a(x,y,z),u,w) * (v5 * v6)
    ]]></literal>
    <justification jstring="[para(14598(a,2),20579(a,1,1))].">
      <j1 rule="para" parents="14598 20579"/>
    </justification>
  </clause>

  <clause id="20582">
    <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,20580,a(flip))].">
      <j1 rule="hyper" parents="119 164 20580"/>
    </justification>
  </clause>

  <clause id="20583">
    <literal><![CDATA[
      L(x,y,a(a(z,u,w),v5,v6)) = x
    ]]></literal>
    <justification jstring="[hyper(4329,a,20581,a)].">
      <j1 rule="hyper" parents="4329 20581"/>
    </justification>
  </clause>

  <clause id="20584">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ (v5 * v6) = (a(a(x,y,z),u,w) \ v5) * v6
    ]]></literal>
    <justification jstring="[hyper(630,a,20581,a)].">
      <j1 rule="hyper" parents="630 20581"/>
    </justification>
  </clause>

  <clause id="20585">
    <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(20581(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="20581 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20586">
    <literal><![CDATA[
      L(x,y,a(a(z,u,w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      x = v7
    ]]></literal>
    <justification jstring="[para(20583(a,1),45(a,2))].">
      <j1 rule="para" parents="20583 45"/>
    </justification>
  </clause>

  <clause id="20587">
    <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(451,a,20584,a(flip),b,20582,a),flip(a)].">
      <j1 rule="hyper" parents="451 20584 20582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20588">
    <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(334,a,20205,a(flip),b,20587,a),flip(a)].">
      <j1 rule="hyper" parents="334 20205 20587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20590">
    <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,3903,a(flip),b,20588,a)].">
      <j1 rule="hyper" parents="58 3903 20588"/>
    </justification>
  </clause>

  <clause id="20591">
    <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,20572,a(flip),b,20590,a)].">
      <j1 rule="hyper" parents="119 20572 20590"/>
    </justification>
  </clause>

  <clause id="20592">
    <literal><![CDATA[
      x * (y \ L(y,z,a(u,w,v5))) = x / a(a(u,w,v5),z,y)
    ]]></literal>
    <justification jstring="[hyper(334,a,14600,a,b,20591,a),flip(a)].">
      <j1 rule="hyper" parents="334 14600 20591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20593">
    <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(20314,a,20591,a(flip))].">
      <j1 rule="hyper" parents="20314 20591"/>
    </justification>
  </clause>

  <clause id="20594">
    <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(20592(a,2),14606(a,1))].">
      <j1 rule="para" parents="20592 14606"/>
    </justification>
  </clause>

  <clause id="20595">
    <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(20584(a,1),20593(a,1,2))].">
      <j1 rule="para" parents="20584 20593"/>
    </justification>
  </clause>

  <clause id="20596">
    <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,17607,a(flip),b,20595,a)].">
      <j1 rule="hyper" parents="58 17607 20595"/>
    </justification>
  </clause>

  <clause id="20597">
    <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(20537,a,20596,a),flip(a)].">
      <j1 rule="hyper" parents="20537 20596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20598">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ (v5 * v6) = v5 * (a(a(x,y,z),u,w) \ v6)
    ]]></literal>
    <justification jstring="[hyper(20594,a,20597,a)].">
      <j1 rule="hyper" parents="20594 20597"/>
    </justification>
  </clause>

  <clause id="20599">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * (v5 * v6) = v5 * (a(a(x,y,z),u,w) * v6)
    ]]></literal>
    <justification jstring="[hyper(978,a,20598,a)].">
      <j1 rule="hyper" parents="978 20598"/>
    </justification>
  </clause>

  <clause id="20600">
    <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,20579,a,b,20599,a)].">
      <j1 rule="hyper" parents="58 20579 20599"/>
    </justification>
  </clause>

  <clause id="20601">
    <literal><![CDATA[
      R(x,a(a(y,z,u),w,v5),v6) = x
    ]]></literal>
    <justification jstring="[hyper(3617,a,20600,a)].">
      <j1 rule="hyper" parents="3617 20600"/>
    </justification>
  </clause>

  <clause id="20602">
    <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(20581(a,1),20585(a,1,2,1))].">
      <j1 rule="para" parents="20581 20585"/>
    </justification>
  </clause>

  <clause id="20603">
    <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(20581(a,1),20602(a,1,2))].">
      <j1 rule="para" parents="20581 20602"/>
    </justification>
  </clause>

  <clause id="20604">
    <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(863,a,20603,a)].">
      <j1 rule="hyper" parents="863 20603"/>
    </justification>
  </clause>

  <clause id="20605">
    <literal><![CDATA[
      a(a(a(x,y,z),u,w) * v5,v6,v7) = a(v5,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(20586,a,20604,a),flip(a)].">
      <j1 rule="hyper" parents="20586 20604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20607">
    <literal><![CDATA[
      a(a(a(x,y,z),u,w) \ v5,v6,v7) = a(v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(5(a,1),20605(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 20605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20608">
    <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(784(a,2),20605(a,1,1))].">
      <j1 rule="para" parents="784 20605"/>
    </justification>
  </clause>

  <clause id="20609">
    <literal><![CDATA[
      a(L(x,y,a(z,u,w)),v5,v6) = a(x,v5,v6)
    ]]></literal>
    <justification jstring="[para(20571(a,1),20607(a,1,1))].">
      <j1 rule="para" parents="20571 20607"/>
    </justification>
  </clause>

  <clause id="20610">
    <literal><![CDATA[
      a((a(x,y,z) * u) \ w,v5,v6) = a(u \ (a(x,y,z) \ w),v5,v6)
    ]]></literal>
    <justification jstring="[para(311(a,1),20609(a,1,1))].">
      <j1 rule="para" parents="311 20609"/>
    </justification>
  </clause>

  <clause id="20611">
    <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,20183,a(flip),b,20610,a)].">
      <j1 rule="hyper" parents="58 20183 20610"/>
    </justification>
  </clause>

  <clause id="20612">
    <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(733(a,1),20611(a,1,1)),flip(a)].">
      <j1 rule="para" parents="733 20611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20613">
    <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(502(a,1),20555(a,1,1)),flip(a)].">
      <j1 rule="para" parents="502 20555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20615">
    <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(20519(a,1),20613(a,1,1))].">
      <j1 rule="para" parents="20519 20613"/>
    </justification>
  </clause>

  <clause id="20616">
    <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(20545,a,20615,a)].">
      <j1 rule="hyper" parents="20545 20615"/>
    </justification>
  </clause>

  <clause id="20617">
    <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),20616(a,1,1,2))].">
      <j1 rule="para" parents="3 20616"/>
    </justification>
  </clause>

  <clause id="20618">
    <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),20617(a,2,1,2))].">
      <j1 rule="para" parents="3 20617"/>
    </justification>
  </clause>

  <clause id="20619">
    <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(20601(a,1),20608(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="20601 20608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20620">
    <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(334,a,20610,a(flip),b,20619,a),flip(a)].">
      <j1 rule="hyper" parents="334 20610 20619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20622">
    <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(20306(a,1),20620(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20306 20620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20623">
    <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(15279(a,2),20612(a,2,1,1))].">
      <j1 rule="para" parents="15279 20612"/>
    </justification>
  </clause>

  <clause id="20624">
    <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(20553(a,1),20623(a,2,1))].">
      <j1 rule="para" parents="20553 20623"/>
    </justification>
  </clause>

  <clause id="20625">
    <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(334,a,19762,a(flip),b,20624,a),flip(a)].">
      <j1 rule="hyper" parents="334 19762 20624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20628">
    <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),20625(a,1,1,2))].">
      <j1 rule="para" parents="17 20625"/>
    </justification>
  </clause>

  <clause id="20629">
    <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(15279(a,2),20628(a,1,1,2))].">
      <j1 rule="para" parents="15279 20628"/>
    </justification>
  </clause>

  <clause id="20630">
    <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,19760,a(flip),b,20629,a)].">
      <j1 rule="hyper" parents="58 19760 20629"/>
    </justification>
  </clause>

  <clause id="20632">
    <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(20515(a,1),20630(a,1,1))].">
      <j1 rule="para" parents="20515 20630"/>
    </justification>
  </clause>

  <clause id="20633">
    <literal><![CDATA[
      a(L(x,a(y,z,u),w),v5,v6) = a(x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,20544,a(flip),b,20632,a),flip(a)].">
      <j1 rule="hyper" parents="58 20544 20632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20635">
    <literal><![CDATA[
      a((x * a(y,z,u)) \ w,v5,v6) = a(a(y,z,u) \ (x \ w),v5,v6)
    ]]></literal>
    <justification jstring="[para(311(a,1),20633(a,1,1))].">
      <j1 rule="para" parents="311 20633"/>
    </justification>
  </clause>

  <clause id="20636">
    <literal><![CDATA[
      a(x \ (x / a(y,z,u)),w,v5) = a(a(y,z,u) \ 1,w,v5)
    ]]></literal>
    <justification jstring="[para(409(a,1),20633(a,1,1))].">
      <j1 rule="para" parents="409 20633"/>
    </justification>
  </clause>

  <clause id="20637">
    <literal><![CDATA[
      a(((x * y) * z) \ (x * (y * z)),u,w) = a(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(188(a,1),20636(a,1,1,2))].">
      <j1 rule="para" parents="188 20636"/>
    </justification>
  </clause>

  <clause id="20638">
    <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,20611,a(flip),b,20635,a),flip(a)].">
      <j1 rule="hyper" parents="58 20611 20635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20639">
    <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(239(a,1),20638(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="239 20638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20640">
    <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,20622,a,b,20637,a)].">
      <j1 rule="hyper" parents="58 20622 20637"/>
    </justification>
  </clause>

  <clause id="20641">
    <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(20355(a,2),20640(a,1,1,2,2,2,1))].">
      <j1 rule="para" parents="20355 20640"/>
    </justification>
  </clause>

  <clause id="20642">
    <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,20639,a(flip),b,20641,a)].">
      <j1 rule="hyper" parents="58 20639 20641"/>
    </justification>
  </clause>

  <clause id="20643">
    <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(20355(a,2),20642(a,1,1,2,1))].">
      <j1 rule="para" parents="20355 20642"/>
    </justification>
  </clause>

  <clause id="20644">
    <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,20618,a(flip),b,20643,a)].">
      <j1 rule="hyper" parents="58 20618 20643"/>
    </justification>
  </clause>

  <clause id="20646">
    <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,20358,a(flip),b,20644,a),flip(a)].">
      <j1 rule="hyper" parents="58 20358 20644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20648">
    <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(20356(a,1),20646(a,2,1))].">
      <j1 rule="para" parents="20356 20646"/>
    </justification>
  </clause>

  <clause id="20649">
    <literal><![CDATA[
      a(a(x,a(y,z,u),w) \ 1,v5,v6) = 1
    ]]></literal>
    <justification jstring="[hyper(334,a,14597,a(flip),b,20648,a),flip(a)].">
      <j1 rule="hyper" parents="334 14597 20648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20651">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,v5),v6) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,20649,a)].">
      <j1 rule="hyper" parents="47 20649"/>
    </justification>
  </clause>

  <clause id="20652">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,v5),v6) \ 1) != v7
    ]]></literal>
    <literal><![CDATA[
      x = v7
    ]]></literal>
    <justification jstring="[para(20651(a,1),45(a,2))].">
      <j1 rule="para" parents="20651 45"/>
    </justification>
  </clause>

  <clause id="20653">
    <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(20651(a,1),3834(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20651 3834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20654">
    <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(20651(a,1),20653(a,2,2))].">
      <j1 rule="para" parents="20651 20653"/>
    </justification>
  </clause>

  <clause id="20655">
    <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(334,a,4,a(flip),b,20654,a),flip(a)].">
      <j1 rule="hyper" parents="334 4 20654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20657">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,v5),v6)) = x
    ]]></literal>
    <justification jstring="[hyper(20652,a,20655,a)].">
      <j1 rule="hyper" parents="20652 20655"/>
    </justification>
  </clause>

  <clause id="20659">
    <literal><![CDATA[
      a(a(x,a(y,z,u),w),v5,v6) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,20657,a,b,20569,a),flip(a)].">
      <j1 rule="hyper" parents="115 20657 20569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20660">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer("nil3 25, aa2-Nl")
    ]]></attribute>
    <justification jstring="[resolve(20659,a,59,a)].">
      <j1 rule="resolve" parents="20659 59"/>
    </justification>
  </clause>

</proof>

</proofs>
