<?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_29.out</source>

<heading><![CDATA[
Prover9 (64) version 2022-12A (+ restricted para), January 2023.
Process 3860276 was started by veroff on b146-16,
Wed Jan 14 12:17:54 2026
The command was "prover9 -f nil3_23_32_to_29.in".
]]></heading>

<proof number="1" length="17846" max_count="65">

<comments><![CDATA[
% Proof 1 at 4334.54 (+ 252.97) seconds: "nil3 29, aa3-Nm".
% Length of proof: 17846 (0 new hints)
% Level of proof: 887
% Maximum clause weight: 65.000
% Given clauses in run: 17834
% Given clauses in proof: 17834 (0 new hints)
]]></comments>

  <clause id="1" type="goal">
    <literal><![CDATA[
      a(x,a(y,z,a(u,w,v5)),v6) = 1
    ]]></literal>
    <attribute><![CDATA[
      label("nil3 29, aa3-Nm")
    ]]></attribute>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <attribute><![CDATA[
      label(goal)
    ]]></attribute>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

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

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

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

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

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

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

  <clause id="8" type="assumption">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(x,y,z)
    ]]></literal>
    <attribute><![CDATA[
      label("associator")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="10" type="assumption">
    <literal><![CDATA[
      (x * y) \ (y * x) = K(y,x)
    ]]></literal>
    <attribute><![CDATA[
      label("commutator")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

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

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

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

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

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

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

  <clause id="18" type="assumption">
    <literal><![CDATA[
      T(T(x,y),z) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="19" type="assumption">
    <literal><![CDATA[
      T(L(x,y,z),u) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="21" type="assumption">
    <literal><![CDATA[
      T(R(x,y,z),u) = R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="23" type="assumption">
    <literal><![CDATA[
      L(R(x,y,z),u,w) = R(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="25" type="assumption">
    <literal><![CDATA[
      L(L(x,y,z),u,w) = L(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="26" type="assumption">
    <literal><![CDATA[
      R(R(x,y,z),u,w) = R(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="27" type="assumption">
    <literal><![CDATA[
      a(x,y,a(z,u,K(w,v5))) = 1
    ]]></literal>
    <attribute><![CDATA[
      label("nil3 23, aK3-Nr")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="29" type="assumption">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      x * u != z
    ]]></literal>
    <literal><![CDATA[
      y = u
    ]]></literal>
    <attribute><![CDATA[
      label("*-Cancellation 1")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="30" type="assumption">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      u * y != z
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <attribute><![CDATA[
      label("*-Cancellation 2")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="32" type="assumption">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      u / y != z
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <attribute><![CDATA[
      label("/-Cancellation 2")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="34" type="assumption">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      u \ y != z
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <attribute><![CDATA[
      label("\-Cancellation 2")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="36" type="assumption">
    <literal><![CDATA[
      L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(w,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <attribute><![CDATA[
      label("L-Cancellation 1")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37" type="assumption">
    <literal><![CDATA[
      R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(w,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <attribute><![CDATA[
      label("R-Cancellation 1")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="38" type="assumption">
    <literal><![CDATA[
      x * y != x * z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <attribute><![CDATA[
      label("*-Cancellation 3")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="39" type="assumption">
    <literal><![CDATA[
      x * y != z * y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <attribute><![CDATA[
      label("*-Cancellation 4")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="40" type="assumption">
    <literal><![CDATA[
      x / y != x / z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <attribute><![CDATA[
      label("/-Cancellation 3")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="41" type="assumption">
    <literal><![CDATA[
      x / y != z / y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <attribute><![CDATA[
      label("/-Cancellation 4")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="43" type="assumption">
    <literal><![CDATA[
      x \ y != z \ y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <attribute><![CDATA[
      label("\-Cancellation 4")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="44" type="assumption">
    <literal><![CDATA[
      T(x,y) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <attribute><![CDATA[
      label("T-Cancellation 2")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="45" type="assumption">
    <literal><![CDATA[
      L(x,y,z) != L(u,y,z)
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <attribute><![CDATA[
      label("L-Cancellation 2")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="46" type="assumption">
    <literal><![CDATA[
      R(x,y,z) != R(u,y,z)
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <attribute><![CDATA[
      label("R-Cancellation 2")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

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

  <clause id="48" type="assumption">
    <literal><![CDATA[
      L(x,y,z) != x
    ]]></literal>
    <literal><![CDATA[
      a(z,y,x) = 1
    ]]></literal>
    <attribute><![CDATA[
      label("Compat 2")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="49" type="assumption">
    <literal><![CDATA[
      T(x,y) != x
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = y
    ]]></literal>
    <attribute><![CDATA[
      label("Compat 3")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="50" type="assumption">
    <literal><![CDATA[
      T(x,y) != x
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = 1
    ]]></literal>
    <attribute><![CDATA[
      label("Compat 4")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="51" type="assumption">
    <literal><![CDATA[
      K(x,y) != 1
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = x
    ]]></literal>
    <attribute><![CDATA[
      label("Compat 5")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="52" type="assumption">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      x * z = y * z
    ]]></literal>
    <attribute><![CDATA[
      label("Aux 1")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="53" type="assumption">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * x = z * y
    ]]></literal>
    <attribute><![CDATA[
      label("Aux 2")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="54" type="assumption">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      x / z = y / z
    ]]></literal>
    <attribute><![CDATA[
      label("Aux 3")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="55" type="assumption">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z / x = z / y
    ]]></literal>
    <attribute><![CDATA[
      label("Aux 4")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="56" type="assumption">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      x \ z = y \ z
    ]]></literal>
    <attribute><![CDATA[
      label("Aux 5")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="57" type="assumption">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z \ x = z \ y
    ]]></literal>
    <attribute><![CDATA[
      label("Aux 6")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="58" type="assumption">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <attribute><![CDATA[
      label("Transitivity =")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="59" type="deny">
    <literal><![CDATA[
      a(c1,a(c2,c3,a(c4,c5,c6)),c7) != 1
    ]]></literal>
    <attribute><![CDATA[
      label("nil3 29, aa3-Nm")
    ]]></attribute>
    <attribute><![CDATA[
      answer("nil3 29, aa3-Nm")
    ]]></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) != z
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(5(a,1),39(a,2))].">
      <j1 rule="para" parents="5 39"/>
    </justification>
  </clause>

  <clause id="131">
    <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="132">
    <literal><![CDATA[
      ((x * y) / z) * z != u * y
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(7(a,2),39(a,2)),flip(a)].">
      <j1 rule="para" parents="7 39"/>
      <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 \ ((y * z) * u) != a(y,z,u)
    ]]></literal>
    <literal><![CDATA[
      y * (z * u) = x
    ]]></literal>
    <justification jstring="[para(9(a,2),43(a,1)),flip(a)].">
      <j1 rule="para" parents="9 43"/>
      <j2 rule="flip"/>
    </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[
      R(L(x,y,z),u,w) != L(v5,y,z)
    ]]></literal>
    <literal><![CDATA[
      R(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(24(a,2),45(a,1))].">
      <j1 rule="para" parents="24 45"/>
    </justification>
  </clause>

  <clause id="142">
    <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="143">
    <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="144">
    <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="145">
    <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="146">
    <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="147">
    <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="148">
    <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="149">
    <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="150">
    <literal><![CDATA[
      x * T(T(y,z),u) = x * T(T(y,u),z)
    ]]></literal>
    <justification jstring="[hyper(53,a,18,a)].">
      <j1 rule="hyper" parents="53 18"/>
    </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[
      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="155">
    <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="156">
    <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="157">
    <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="158">
    <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="159">
    <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="160">
    <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="161">
    <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="162">
    <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="163">
    <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="164">
    <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="165">
    <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="166">
    <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="167">
    <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="168">
    <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="169">
    <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="170">
    <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="171">
    <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="172">
    <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="173">
    <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="174">
    <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="175">
    <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="176">
    <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="177">
    <literal><![CDATA[
      T(x,y) != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(104(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="104 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="178">
    <literal><![CDATA[
      x * K(y,y) = x
    ]]></literal>
    <justification jstring="[para(166(a,2),3(a,1,2))].">
      <j1 rule="para" parents="166 3"/>
    </justification>
  </clause>

  <clause id="179">
    <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="180">
    <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="181">
    <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="182">
    <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="183">
    <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="184">
    <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="185">
    <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="186">
    <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="187">
    <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="188">
    <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="189">
    <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="190">
    <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="191">
    <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="192">
    <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="193">
    <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="194">
    <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="195">
    <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="196">
    <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="197">
    <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="198">
    <literal><![CDATA[
      T(x,1) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,17,a,b,162,a)].">
      <j1 rule="hyper" parents="58 17 162"/>
    </justification>
  </clause>

  <clause id="199">
    <literal><![CDATA[
      K(x,1) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,198,a)].">
      <j1 rule="hyper" parents="50 198"/>
    </justification>
  </clause>

  <clause id="200">
    <literal><![CDATA[
      T(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(49,a,198,a)].">
      <j1 rule="hyper" parents="49 198"/>
    </justification>
  </clause>

  <clause id="201">
    <literal><![CDATA[
      K(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,200,a)].">
      <j1 rule="hyper" parents="50 200"/>
    </justification>
  </clause>

  <clause id="202">
    <literal><![CDATA[
      T(x,T(T(x,y),z)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,18,a,b,174,a(flip))].">
      <j1 rule="hyper" parents="35 18 174"/>
    </justification>
  </clause>

  <clause id="203">
    <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="204">
    <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="205">
    <literal><![CDATA[
      K(x,1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(199(a,2),120(a,1,1))].">
      <j1 rule="para" parents="199 120"/>
    </justification>
  </clause>

  <clause id="206">
    <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="207">
    <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="208">
    <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="209">
    <literal><![CDATA[
      (x * (x \ 1)) \ y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(5(a,2),165(a,1,1))].">
      <j1 rule="para" parents="5 165"/>
    </justification>
  </clause>

  <clause id="210">
    <literal><![CDATA[
      ((1 / x) * x) \ y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(7(a,2),165(a,1,1))].">
      <j1 rule="para" parents="7 165"/>
    </justification>
  </clause>

  <clause id="211">
    <literal><![CDATA[
      x / (y * (y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(5(a,2),171(a,1,2))].">
      <j1 rule="para" parents="5 171"/>
    </justification>
  </clause>

  <clause id="212">
    <literal><![CDATA[
      T(x,R(T(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,18,a,b,172,a(flip))].">
      <j1 rule="hyper" parents="35 18 172"/>
    </justification>
  </clause>

  <clause id="213">
    <literal><![CDATA[
      T(x,L(L(x,y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,20,a,b,173,a(flip))].">
      <j1 rule="hyper" parents="36 20 173"/>
    </justification>
  </clause>

  <clause id="214">
    <literal><![CDATA[
      T(x,L(T(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,18,a,b,173,a(flip))].">
      <j1 rule="hyper" parents="35 18 173"/>
    </justification>
  </clause>

  <clause id="215">
    <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="216">
    <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="217">
    <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="218">
    <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="219">
    <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="220">
    <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="221">
    <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="222">
    <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="223">
    <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="224">
    <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="225">
    <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="226">
    <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="227">
    <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="228">
    <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="229">
    <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="230">
    <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="231">
    <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="232">
    <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="233">
    <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="234">
    <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="235">
    <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="236">
    <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="237">
    <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="238">
    <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="239">
    <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="240">
    <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="241">
    <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="242">
    <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="243">
    <literal><![CDATA[
      T(x,y) * x = x * T(x,y)
    ]]></literal>
    <justification jstring="[para(174(a,1),105(a,1,2))].">
      <j1 rule="para" parents="174 105"/>
    </justification>
  </clause>

  <clause id="244">
    <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="245">
    <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="246">
    <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="247">
    <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="248">
    <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="249">
    <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="250">
    <literal><![CDATA[
      x * 1 != y * z
    ]]></literal>
    <literal><![CDATA[
      x / z = y
    ]]></literal>
    <justification jstring="[para(158(a,1),39(a,1))].">
      <j1 rule="para" parents="158 39"/>
    </justification>
  </clause>

  <clause id="251">
    <literal><![CDATA[
      (x / y) * y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(158(a,2),127(a,1))].">
      <j1 rule="para" parents="158 127"/>
    </justification>
  </clause>

  <clause id="252">
    <literal><![CDATA[
      (x / y) * y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(158(a,2),128(a,1))].">
      <j1 rule="para" parents="158 128"/>
    </justification>
  </clause>

  <clause id="253">
    <literal><![CDATA[
      1 * x != 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="254">
    <literal><![CDATA[
      x * 1 != y * z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(161(a,1),38(a,1))].">
      <j1 rule="para" parents="161 38"/>
    </justification>
  </clause>

  <clause id="255">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(161(a,2),127(a,1))].">
      <j1 rule="para" parents="161 127"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(161(a,2),128(a,1))].">
      <j1 rule="para" parents="161 128"/>
    </justification>
  </clause>

  <clause id="257">
    <literal><![CDATA[
      x * ((x \ 1) * y) = L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,13,a,b,163,a),flip(a)].">
      <j1 rule="hyper" parents="58 13 163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      K(x \ 1,x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,11,a,b,163,a)].">
      <j1 rule="hyper" parents="58 11 163"/>
    </justification>
  </clause>

  <clause id="259">
    <literal><![CDATA[
      (1 / x) * (x * 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="260">
    <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="261">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,15,a,b,169,a),flip(a)].">
      <j1 rule="hyper" parents="58 15 169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="262">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,1 / y,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15,a,b,170,a),flip(a)].">
      <j1 rule="hyper" parents="58 15 170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="263">
    <literal><![CDATA[
      K(T(x,y),x) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,175,a)].">
      <j1 rule="hyper" parents="50 175"/>
    </justification>
  </clause>

  <clause id="264">
    <literal><![CDATA[
      K(x \ y,y / x) = 1
    ]]></literal>
    <justification jstring="[para(107(a,1),263(a,1,1))].">
      <j1 rule="para" parents="107 263"/>
    </justification>
  </clause>

  <clause id="265">
    <literal><![CDATA[
      x / T(y,y \ x) = y \ x
    ]]></literal>
    <justification jstring="[para(5(a,1),187(a,1,1))].">
      <j1 rule="para" parents="5 187"/>
    </justification>
  </clause>

  <clause id="266">
    <literal><![CDATA[
      (x * y) / z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(187(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="187 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="267">
    <literal><![CDATA[
      (x / y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(191(a,2),171(a,1))].">
      <j1 rule="para" parents="191 171"/>
    </justification>
  </clause>

  <clause id="268">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      T(z / x,x) = y
    ]]></literal>
    <justification jstring="[para(222(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="222 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="269">
    <literal><![CDATA[
      (x * T(T(y,x),z)) / x = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,18,a,b,224,a),flip(a)].">
      <j1 rule="hyper" parents="35 18 224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="270">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(224(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="224 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="271">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * z) / y = x
    ]]></literal>
    <justification jstring="[para(224(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="224 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="272">
    <literal><![CDATA[
      K(x,(y * x) / y) = 1
    ]]></literal>
    <justification jstring="[para(224(a,1),263(a,1,1))].">
      <j1 rule="para" parents="224 263"/>
    </justification>
  </clause>

  <clause id="273">
    <literal><![CDATA[
      T((x * y) / x,T(y,z)) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(224(a,1),202(a,1,2,1))].">
      <j1 rule="para" parents="224 202"/>
    </justification>
  </clause>

  <clause id="274">
    <literal><![CDATA[
      L(x,y,z) \ (u * L(T(x,u),y,z)) = u
    ]]></literal>
    <justification jstring="[para(20(a,2),226(a,1,2,2))].">
      <j1 rule="para" parents="20 226"/>
    </justification>
  </clause>

  <clause id="275">
    <literal><![CDATA[
      T(x \ y,y / x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(51,a,264,a)].">
      <j1 rule="hyper" parents="51 264"/>
    </justification>
  </clause>

  <clause id="276">
    <literal><![CDATA[
      T(x,(y * x) / y) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,272,a)].">
      <j1 rule="hyper" parents="51 272"/>
    </justification>
  </clause>

  <clause id="277">
    <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="278">
    <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="279">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      z / T(x,y) = y
    ]]></literal>
    <justification jstring="[para(105(a,1),131(a,1))].">
      <j1 rule="para" parents="105 131"/>
    </justification>
  </clause>

  <clause id="280">
    <literal><![CDATA[
      1 != x
    ]]></literal>
    <literal><![CDATA[
      x \ y = y
    ]]></literal>
    <justification jstring="[para(69(a,1),188(a,1))].">
      <j1 rule="para" parents="69 188"/>
    </justification>
  </clause>

  <clause id="281">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      x * (y \ z) = z
    ]]></literal>
    <justification jstring="[para(6(a,1),189(a,1)),flip(b)].">
      <j1 rule="para" parents="6 189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="282">
    <literal><![CDATA[
      T(x / y,L(y \ x,z,u)) = x / y
    ]]></literal>
    <justification jstring="[para(107(a,1),214(a,1,2,1))].">
      <j1 rule="para" parents="107 214"/>
    </justification>
  </clause>

  <clause id="283">
    <literal><![CDATA[
      R(x,y,z) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(15(a,2),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="15 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="284">
    <literal><![CDATA[
      x * T(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(187(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="187 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="285">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      y * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(225(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="225 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="286">
    <literal><![CDATA[
      (x * y) * L(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(13(a,2),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="287">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(6(a,1),267(a,1,1))].">
      <j1 rule="para" parents="6 267"/>
    </justification>
  </clause>

  <clause id="288">
    <literal><![CDATA[
      x \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(187(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="187 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="289">
    <literal><![CDATA[
      ((x / y) \ x) * (y \ z) = z
    ]]></literal>
    <justification jstring="[hyper(281,a,75,a)].">
      <j1 rule="hyper" parents="281 75"/>
    </justification>
  </clause>

  <clause id="290">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * (L(L(x,u,w),y,z) \ v5) = v5
    ]]></literal>
    <justification jstring="[hyper(281,a,25,a)].">
      <j1 rule="hyper" parents="281 25"/>
    </justification>
  </clause>

  <clause id="291">
    <literal><![CDATA[
      ((x / y) * y) * (x \ z) = z
    ]]></literal>
    <justification jstring="[hyper(281,a,7,a)].">
      <j1 rule="hyper" parents="281 7"/>
    </justification>
  </clause>

  <clause id="292">
    <literal><![CDATA[
      T((x * y) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(107(a,2),287(a,1))].">
      <j1 rule="para" parents="107 287"/>
    </justification>
  </clause>

  <clause id="293">
    <literal><![CDATA[
      x \ (y * 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(161(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="161 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="294">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      x * (u \ (u * y)) = z
    ]]></literal>
    <justification jstring="[para(63(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="63 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="295">
    <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="296">
    <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="297">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * (z \ x) = y
    ]]></literal>
    <justification jstring="[para(67(a,1),255(a,1)),flip(b)].">
      <j1 rule="para" parents="67 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="298">
    <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="299">
    <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="300">
    <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="301">
    <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="302">
    <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="303">
    <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="304">
    <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="305">
    <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="306">
    <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="307">
    <literal><![CDATA[
      (x * y) \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(84(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="84 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="308">
    <literal><![CDATA[
      (x \ y) \ y = z * (z \ T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(297,a,106,a),flip(a)].">
      <j1 rule="hyper" parents="297 106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="309">
    <literal><![CDATA[
      T(x,x \ y) * (((x \ y) \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(281,a,106,a)].">
      <j1 rule="hyper" parents="281 106"/>
    </justification>
  </clause>

  <clause id="310">
    <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="311">
    <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="312">
    <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="313">
    <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="314">
    <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="315">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,x \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(281,a,106,a(flip))].">
      <j1 rule="hyper" parents="281 106"/>
    </justification>
  </clause>

  <clause id="316">
    <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="317">
    <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="318">
    <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="319">
    <literal><![CDATA[
      T((x \ y) \ y,x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(106(a,1),175(a,1,1))].">
      <j1 rule="para" parents="106 175"/>
    </justification>
  </clause>

  <clause id="320">
    <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="321">
    <literal><![CDATA[
      ((x / y) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x \ u = z
    ]]></literal>
    <justification jstring="[para(147(a,2),123(a,1))].">
      <j1 rule="para" parents="147 123"/>
    </justification>
  </clause>

  <clause id="322">
    <literal><![CDATA[
      (x * (x \ y)) * z != y * u
    ]]></literal>
    <literal><![CDATA[
      u = z
    ]]></literal>
    <justification jstring="[para(148(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="148 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="323">
    <literal><![CDATA[
      (x / (y * (y \ z))) * z = x
    ]]></literal>
    <justification jstring="[hyper(252,a,151,a),flip(a)].">
      <j1 rule="hyper" parents="252 151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="324">
    <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="325">
    <literal><![CDATA[
      x / y != (z / u) * u
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(156(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="156 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="326">
    <literal><![CDATA[
      ((x / y) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(156(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="156 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="327">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(156(a,2),251(a,1))].">
      <j1 rule="para" parents="156 251"/>
    </justification>
  </clause>

  <clause id="328">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(156(a,2),252(a,1))].">
      <j1 rule="para" parents="156 252"/>
    </justification>
  </clause>

  <clause id="329">
    <literal><![CDATA[
      x / x != y
    ]]></literal>
    <literal><![CDATA[
      1 = y
    ]]></literal>
    <justification jstring="[para(2(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="330">
    <literal><![CDATA[
      x / (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(5(a,1),327(a,1,1))].">
      <j1 rule="para" parents="5 327"/>
    </justification>
  </clause>

  <clause id="331">
    <literal><![CDATA[
      (x * T(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(105(a,2),327(a,1,1))].">
      <j1 rule="para" parents="105 327"/>
    </justification>
  </clause>

  <clause id="332">
    <literal><![CDATA[
      x / (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(5(a,1),328(a,1,1))].">
      <j1 rule="para" parents="5 328"/>
    </justification>
  </clause>

  <clause id="333">
    <literal><![CDATA[
      (x * T(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(105(a,2),328(a,1,1))].">
      <j1 rule="para" parents="105 328"/>
    </justification>
  </clause>

  <clause id="334">
    <literal><![CDATA[
      (x * (y * z)) / L(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      x * y = u
    ]]></literal>
    <justification jstring="[para(13(a,2),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="335">
    <literal><![CDATA[
      x / K(y,y \ x) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(30,a,84,a,b,157,a),flip(a)].">
      <j1 rule="hyper" parents="30 84 157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="336">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(157(a,2),38(a,1))].">
      <j1 rule="para" parents="157 38"/>
    </justification>
  </clause>

  <clause id="337">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(157(a,1),39(a,1))].">
      <j1 rule="para" parents="157 39"/>
    </justification>
  </clause>

  <clause id="338">
    <literal><![CDATA[
      (x * (x \ y)) / z != u
    ]]></literal>
    <literal><![CDATA[
      y / z = u
    ]]></literal>
    <justification jstring="[para(157(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="157 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="339">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(160(a,2),38(a,1))].">
      <j1 rule="para" parents="160 38"/>
    </justification>
  </clause>

  <clause id="340">
    <literal><![CDATA[
      x \ y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      x * u = y
    ]]></literal>
    <justification jstring="[para(160(a,1),42(a,1)),flip(a)].">
      <j1 rule="para" parents="160 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="341">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(160(a,2),208(a,1))].">
      <j1 rule="para" parents="160 208"/>
    </justification>
  </clause>

  <clause id="342">
    <literal><![CDATA[
      x * (y * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(160(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="160 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="343">
    <literal><![CDATA[
      (x / y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(7(a,1),341(a,1,2))].">
      <j1 rule="para" parents="7 341"/>
    </justification>
  </clause>

  <clause id="344">
    <literal><![CDATA[
      T(x,x) != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(17(a,2),341(a,1))].">
      <j1 rule="para" parents="17 341"/>
    </justification>
  </clause>

  <clause id="345">
    <literal><![CDATA[
      T((x * y) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(107(a,2),341(a,1))].">
      <j1 rule="para" parents="107 341"/>
    </justification>
  </clause>

  <clause id="346">
    <literal><![CDATA[
      (x * y) * a(z,u,a(w,v5,v6)) = x * (y * a(z,u,a(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(167,a,9,a(flip),b,28,a(flip))].">
      <j1 rule="hyper" parents="167 9 28"/>
    </justification>
  </clause>

  <clause id="347">
    <literal><![CDATA[
      (x * y) * a(z,u,K(w,v5)) = x * (y * a(z,u,K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(167,a,9,a(flip),b,27,a(flip))].">
      <j1 rule="hyper" parents="167 9 27"/>
    </justification>
  </clause>

  <clause id="348">
    <literal><![CDATA[
      (x / (y \ x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(181(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="181 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="349">
    <literal><![CDATA[
      x / y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      u \ x = y
    ]]></literal>
    <justification jstring="[para(182(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="182 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="350">
    <literal><![CDATA[
      (x * (x \ y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      y \ z = u
    ]]></literal>
    <justification jstring="[para(182(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="182 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="351">
    <literal><![CDATA[
      x \ y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      y / u = x
    ]]></literal>
    <justification jstring="[para(192(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="192 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="352">
    <literal><![CDATA[
      (x / y) * ((z / y) \ z) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,7,a(flip),b,193,a),flip(a)].">
      <j1 rule="hyper" parents="320 7 193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="353">
    <literal><![CDATA[
      x * ((y / z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      u / z = x
    ]]></literal>
    <justification jstring="[para(193(a,2),131(a,1))].">
      <j1 rule="para" parents="193 131"/>
    </justification>
  </clause>

  <clause id="354">
    <literal><![CDATA[
      ((x / y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y \ u = z
    ]]></literal>
    <justification jstring="[para(194(a,2),123(a,1))].">
      <j1 rule="para" parents="194 123"/>
    </justification>
  </clause>

  <clause id="355">
    <literal><![CDATA[
      (x \ y) * z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(223(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="223 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="356">
    <literal><![CDATA[
      (x \ y) \ y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(223(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="223 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="357">
    <literal><![CDATA[
      T(x / (x / y),(z / (x / y)) \ z) = y
    ]]></literal>
    <justification jstring="[para(75(a,2),244(a,1,2))].">
      <j1 rule="para" parents="75 244"/>
    </justification>
  </clause>

  <clause id="358">
    <literal><![CDATA[
      x * T(x \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,105,a,b,258,a)].">
      <j1 rule="hyper" parents="320 105 258"/>
    </justification>
  </clause>

  <clause id="359">
    <literal><![CDATA[
      K(x \ 1,x) / x = x \ 1
    ]]></literal>
    <justification jstring="[hyper(131,a,258,a(flip))].">
      <j1 rule="hyper" parents="131 258"/>
    </justification>
  </clause>

  <clause id="360">
    <literal><![CDATA[
      (x \ 1) \ K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(123,a,258,a(flip))].">
      <j1 rule="hyper" parents="123 258"/>
    </justification>
  </clause>

  <clause id="361">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ ((x * (y \ 1)) * y) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(258(a,2),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="258 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="362">
    <literal><![CDATA[
      x \ K(x \ 1,x) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(258(a,2),17(a,2,2)),flip(a)].">
      <j1 rule="para" parents="258 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="363">
    <literal><![CDATA[
      K(x,1 / x) \ (x * ((1 / x) * y)) = L(y,1 / x,x)
    ]]></literal>
    <justification jstring="[para(260(a,2),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="260 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="364">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      (z / x) \ z = y
    ]]></literal>
    <justification jstring="[para(289(a,1),208(a,1))].">
      <j1 rule="para" parents="289 208"/>
    </justification>
  </clause>

  <clause id="365">
    <literal><![CDATA[
      R(x / y,y,x \ z) = z / (y * (x \ z))
    ]]></literal>
    <justification jstring="[para(291(a,1),15(a,2,1))].">
      <j1 rule="para" parents="291 15"/>
    </justification>
  </clause>

  <clause id="366">
    <literal><![CDATA[
      x \ (y * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      z / u = x
    ]]></literal>
    <justification jstring="[para(295(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="295 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="367">
    <literal><![CDATA[
      R(x,y,(x * y) \ z) \ z = y * ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(15(a,2),300(a,1,1))].">
      <j1 rule="para" parents="15 300"/>
    </justification>
  </clause>

  <clause id="368">
    <literal><![CDATA[
      R(x,y,y \ z) * z = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(15(a,2),323(a,1,1))].">
      <j1 rule="para" parents="15 323"/>
    </justification>
  </clause>

  <clause id="369">
    <literal><![CDATA[
      (x / T(y,y \ z)) * ((y \ z) \ z) = x
    ]]></literal>
    <justification jstring="[para(265(a,1),352(a,1,2,1))].">
      <j1 rule="para" parents="265 352"/>
    </justification>
  </clause>

  <clause id="370">
    <literal><![CDATA[
      (x \ 1) * x != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(359(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="359 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="371">
    <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="372">
    <literal><![CDATA[
      L(x,1,y) = x
    ]]></literal>
    <justification jstring="[hyper(341,a,371,a),flip(a)].">
      <j1 rule="hyper" parents="341 371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="373">
    <literal><![CDATA[
      L(x,1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(371(a,1),287(a,1))].">
      <j1 rule="para" parents="371 287"/>
    </justification>
  </clause>

  <clause id="375">
    <literal><![CDATA[
      a(x,1,y) = 1
    ]]></literal>
    <justification jstring="[hyper(48,a,372,a)].">
      <j1 rule="hyper" parents="48 372"/>
    </justification>
  </clause>

  <clause id="376">
    <literal><![CDATA[
      R(1,x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(329,a,95,a),flip(a)].">
      <j1 rule="hyper" parents="329 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="378">
    <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="379">
    <literal><![CDATA[
      R(x,1,y) = x
    ]]></literal>
    <justification jstring="[hyper(328,a,378,a),flip(a)].">
      <j1 rule="hyper" parents="328 378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="380">
    <literal><![CDATA[
      R(x,1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(378(a,1),327(a,1))].">
      <j1 rule="para" parents="378 327"/>
    </justification>
  </clause>

  <clause id="382">
    <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="383">
    <literal><![CDATA[
      R(x,y,1) = x
    ]]></literal>
    <justification jstring="[hyper(328,a,382,a),flip(a)].">
      <j1 rule="hyper" parents="328 382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="384">
    <literal><![CDATA[
      R(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(382(a,1),327(a,1))].">
      <j1 rule="para" parents="382 327"/>
    </justification>
  </clause>

  <clause id="386">
    <literal><![CDATA[
      K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(11(a,2),210(a,1))].">
      <j1 rule="para" parents="11 210"/>
    </justification>
  </clause>

  <clause id="387">
    <literal><![CDATA[
      L(x,y,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * (y * x) = z
    ]]></literal>
    <justification jstring="[para(13(a,2),210(a,1))].">
      <j1 rule="para" parents="13 210"/>
    </justification>
  </clause>

  <clause id="388">
    <literal><![CDATA[
      R(x,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (x * y) * (y \ 1) = z
    ]]></literal>
    <justification jstring="[para(15(a,2),211(a,1)),flip(b)].">
      <j1 rule="para" parents="15 211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="389">
    <literal><![CDATA[
      L(x \ 1,x,1 / x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(320,a,164,a(flip),b,217,a),flip(a)].">
      <j1 rule="hyper" parents="320 164 217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="390">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(320,a,155,a(flip),b,217,a),flip(a)].">
      <j1 rule="hyper" parents="320 155 217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="391">
    <literal><![CDATA[
      L(x \ 1,x,y) * (((y * x) \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(281,a,217,a)].">
      <j1 rule="hyper" parents="281 217"/>
    </justification>
  </clause>

  <clause id="392">
    <literal><![CDATA[
      x \ L(y \ 1,y,z) = x \ ((z * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(57,a,217,a)].">
      <j1 rule="hyper" parents="57 217"/>
    </justification>
  </clause>

  <clause id="393">
    <literal><![CDATA[
      L(x \ 1,x,y) \ z = ((y * x) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(56,a,217,a)].">
      <j1 rule="hyper" parents="56 217"/>
    </justification>
  </clause>

  <clause id="394">
    <literal><![CDATA[
      x / L(y \ 1,y,z) = x / ((z * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(55,a,217,a)].">
      <j1 rule="hyper" parents="55 217"/>
    </justification>
  </clause>

  <clause id="395">
    <literal><![CDATA[
      x * L(y \ 1,y,z) = x * ((z * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(53,a,217,a)].">
      <j1 rule="hyper" parents="53 217"/>
    </justification>
  </clause>

  <clause id="396">
    <literal><![CDATA[
      L(x \ 1,x,y) * z = ((y * x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(52,a,217,a)].">
      <j1 rule="hyper" parents="52 217"/>
    </justification>
  </clause>

  <clause id="397">
    <literal><![CDATA[
      x / L(y \ 1,y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(197,a,217,a(flip))].">
      <j1 rule="hyper" parents="197 217"/>
    </justification>
  </clause>

  <clause id="398">
    <literal><![CDATA[
      (x * y) * L(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(134,a,217,a(flip))].">
      <j1 rule="hyper" parents="134 217"/>
    </justification>
  </clause>

  <clause id="399">
    <literal><![CDATA[
      L(x \ 1,x,y / x) = y \ (y / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),217(a,2,1))].">
      <j1 rule="para" parents="7 217"/>
    </justification>
  </clause>

  <clause id="400">
    <literal><![CDATA[
      T((x * y) \ x,z) = L(T(y \ 1,z),y,x)
    ]]></literal>
    <justification jstring="[para(217(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="217 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="401">
    <literal><![CDATA[
      R((x * y) \ x,z,u) = L(R(y \ 1,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(217(a,1),24(a,1,1))].">
      <j1 rule="para" parents="217 24"/>
    </justification>
  </clause>

  <clause id="402">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,u) = L((u * x) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(217(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="217 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="403">
    <literal><![CDATA[
      R(1 / x,x,x \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,169,a(flip),b,219,a),flip(a)].">
      <j1 rule="hyper" parents="320 169 219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="404">
    <literal><![CDATA[
      x * R(1 / y,y,z) = x * (z / (y * z))
    ]]></literal>
    <justification jstring="[hyper(53,a,219,a)].">
      <j1 rule="hyper" parents="53 219"/>
    </justification>
  </clause>

  <clause id="405">
    <literal><![CDATA[
      R(1 / x,x,y) * z = (y / (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(52,a,219,a)].">
      <j1 rule="hyper" parents="52 219"/>
    </justification>
  </clause>

  <clause id="406">
    <literal><![CDATA[
      (x / (y * x)) * (R(1 / y,y,x) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(281,a,219,a(flip))].">
      <j1 rule="hyper" parents="281 219"/>
    </justification>
  </clause>

  <clause id="407">
    <literal><![CDATA[
      R(1 / x,x,y) \ y = x * y
    ]]></literal>
    <justification jstring="[hyper(188,a,219,a(flip))].">
      <j1 rule="hyper" parents="188 219"/>
    </justification>
  </clause>

  <clause id="408">
    <literal><![CDATA[
      R(1 / x,x,x \ y) = (x \ y) / y
    ]]></literal>
    <justification jstring="[para(5(a,1),219(a,2,2))].">
      <j1 rule="para" parents="5 219"/>
    </justification>
  </clause>

  <clause id="409">
    <literal><![CDATA[
      R(1 / (x / y),x / y,y) = y / x
    ]]></literal>
    <justification jstring="[para(7(a,1),219(a,2,2))].">
      <j1 rule="para" parents="7 219"/>
    </justification>
  </clause>

  <clause id="410">
    <literal><![CDATA[
      T(x / (y * x),z) = R(T(1 / y,z),y,x)
    ]]></literal>
    <justification jstring="[para(219(a,1),22(a,2,1)),flip(a)].">
      <j1 rule="para" parents="219 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="411">
    <literal><![CDATA[
      R(R(1 / x,y,z),x,u) = R(u / (x * u),y,z)
    ]]></literal>
    <justification jstring="[para(219(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="219 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="412">
    <literal><![CDATA[
      T(x,y) * z != x * y
    ]]></literal>
    <literal><![CDATA[
      T(y,T(x,y)) = z
    ]]></literal>
    <justification jstring="[para(105(a,1),240(a,2))].">
      <j1 rule="para" parents="105 240"/>
    </justification>
  </clause>

  <clause id="413">
    <literal><![CDATA[
      x * T(T(y,x),z) != u * x
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(18(a,1),241(a,1,2))].">
      <j1 rule="para" parents="18 241"/>
    </justification>
  </clause>

  <clause id="414">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(158(a,2),250(a,1))].">
      <j1 rule="para" parents="158 250"/>
    </justification>
  </clause>

  <clause id="415">
    <literal><![CDATA[
      ((1 / x) * x) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(7(a,2),253(a,1,1))].">
      <j1 rule="para" parents="7 253"/>
    </justification>
  </clause>

  <clause id="416">
    <literal><![CDATA[
      x * (y * (y \ 1)) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(5(a,2),254(a,1,2))].">
      <j1 rule="para" parents="5 254"/>
    </justification>
  </clause>

  <clause id="417">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(161(a,2),254(a,1))].">
      <j1 rule="para" parents="161 254"/>
    </justification>
  </clause>

  <clause id="418">
    <literal><![CDATA[
      x * T(T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(18(a,1),284(a,1,2))].">
      <j1 rule="para" parents="18 284"/>
    </justification>
  </clause>

  <clause id="419">
    <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),284(a,1,2))].">
      <j1 rule="para" parents="20 284"/>
    </justification>
  </clause>

  <clause id="420">
    <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),284(a,1,2))].">
      <j1 rule="para" parents="22 284"/>
    </justification>
  </clause>

  <clause id="421">
    <literal><![CDATA[
      T(x / y,y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(5(a,1),292(a,1,1,1)),flip(b)].">
      <j1 rule="para" parents="5 292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="422">
    <literal><![CDATA[
      L(T(x \ 1,y),x,1 / x) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(389(a,1),20(a,2,1))].">
      <j1 rule="para" parents="389 20"/>
    </justification>
  </clause>

  <clause id="423">
    <literal><![CDATA[
      x / L(y,1 / y,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),397(a,1,2,1))].">
      <j1 rule="para" parents="75 397"/>
    </justification>
  </clause>

  <clause id="424">
    <literal><![CDATA[
      (x * y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(397(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="397 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="425">
    <literal><![CDATA[
      L(L(x \ 1,x,y),y * x,z) = (z * (y * x)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(398(a,1),13(a,2,2,2))].">
      <j1 rule="para" parents="398 13"/>
    </justification>
  </clause>

  <clause id="426">
    <literal><![CDATA[
      R(x,x \ 1,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(72(a,1),407(a,1,1,1))].">
      <j1 rule="para" parents="72 407"/>
    </justification>
  </clause>

  <clause id="427">
    <literal><![CDATA[
      x / (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,y,x) = z
    ]]></literal>
    <justification jstring="[para(407(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="407 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="428">
    <literal><![CDATA[
      T(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(72(a,1),421(a,1,1))].">
      <j1 rule="para" parents="72 421"/>
    </justification>
  </clause>

  <clause id="429">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ (y * x) = z
    ]]></literal>
    <justification jstring="[para(187(a,1),421(a,1,1))].">
      <j1 rule="para" parents="187 421"/>
    </justification>
  </clause>

  <clause id="430">
    <literal><![CDATA[
      T(x * y,L(y \ 1,y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) \ x = z
    ]]></literal>
    <justification jstring="[para(397(a,1),421(a,1,1))].">
      <j1 rule="para" parents="397 421"/>
    </justification>
  </clause>

  <clause id="431">
    <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="432">
    <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="433">
    <literal><![CDATA[
      K(x \ 1,x) \ 1 = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(258(a,2),86(a,1,1))].">
      <j1 rule="para" parents="258 86"/>
    </justification>
  </clause>

  <clause id="434">
    <literal><![CDATA[
      K(x,1 / x) \ 1 = K(1 / x,x)
    ]]></literal>
    <justification jstring="[para(260(a,2),88(a,1,1))].">
      <j1 rule="para" parents="260 88"/>
    </justification>
  </clause>

  <clause id="435">
    <literal><![CDATA[
      T(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(108(a,1),288(a,1))].">
      <j1 rule="para" parents="108 288"/>
    </justification>
  </clause>

  <clause id="436">
    <literal><![CDATA[
      (x * y) \ R(x,y,y \ 1) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,15,a,b,169,a(flip))].">
      <j1 rule="hyper" parents="116 15 169"/>
    </justification>
  </clause>

  <clause id="437">
    <literal><![CDATA[
      (1 / x) \ L(y,x,1 / x) = x * y
    ]]></literal>
    <justification jstring="[hyper(116,a,13,a,b,164,a(flip))].">
      <j1 rule="hyper" parents="116 13 164"/>
    </justification>
  </clause>

  <clause id="438">
    <literal><![CDATA[
      x \ L(y,x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(116,a,13,a,b,163,a(flip))].">
      <j1 rule="hyper" parents="116 13 163"/>
    </justification>
  </clause>

  <clause id="439">
    <literal><![CDATA[
      (T(x,x \ y) / z) \ ((x \ y) \ y) = z
    ]]></literal>
    <justification jstring="[hyper(116,a,106,a(flip),b,7,a)].">
      <j1 rule="hyper" parents="116 106 7"/>
    </justification>
  </clause>

  <clause id="440">
    <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="441">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(117,a,15,a,b,169,a(flip))].">
      <j1 rule="hyper" parents="117 15 169"/>
    </justification>
  </clause>

  <clause id="442">
    <literal><![CDATA[
      L(x,y \ 1,y) / ((y \ 1) * x) = y
    ]]></literal>
    <justification jstring="[hyper(117,a,13,a,b,163,a(flip))].">
      <j1 rule="hyper" parents="117 13 163"/>
    </justification>
  </clause>

  <clause id="443">
    <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="444">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = z
    ]]></literal>
    <justification jstring="[para(187(a,1),118(b,1)),flip(c)].">
      <j1 rule="para" parents="187 118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="445">
    <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="446">
    <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="447">
    <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="448">
    <literal><![CDATA[
      x * L(y,z \ x,z) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,13,a,b,155,a(flip))].">
      <j1 rule="hyper" parents="119 13 155"/>
    </justification>
  </clause>

  <clause id="449">
    <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="450">
    <literal><![CDATA[
      L(x \ T(y,z),x,z) = (z * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(227(a,1),13(a,2,2))].">
      <j1 rule="para" parents="227 13"/>
    </justification>
  </clause>

  <clause id="451">
    <literal><![CDATA[
      x * T(x \ (y * x),z) = T(y,z) * x
    ]]></literal>
    <justification jstring="[para(17(a,1),236(a,1,2,1))].">
      <j1 rule="para" parents="17 236"/>
    </justification>
  </clause>

  <clause id="452">
    <literal><![CDATA[
      x * T(T(T(y,x),z),u) = T(T(y,z),u) * x
    ]]></literal>
    <justification jstring="[para(18(a,1),236(a,1,2,1))].">
      <j1 rule="para" parents="18 236"/>
    </justification>
  </clause>

  <clause id="453">
    <literal><![CDATA[
      T(x / y,z) * y = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),236(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="454">
    <literal><![CDATA[
      T((x * y) / x,z) * x = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(224(a,1),236(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="224 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="455">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(106(a,1),236(a,1,2,1))].">
      <j1 rule="para" parents="106 236"/>
    </justification>
  </clause>

  <clause id="456">
    <literal><![CDATA[
      T(x / (x / y),z) * (x / y) = (x / y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(244(a,1),236(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="244 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="457">
    <literal><![CDATA[
      (x * T(x \ y,z)) / x = T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(271,a,246,a)].">
      <j1 rule="hyper" parents="271 246"/>
    </justification>
  </clause>

  <clause id="458">
    <literal><![CDATA[
      T(x \ y,z) != T(u,x)
    ]]></literal>
    <literal><![CDATA[
      T(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(246(a,1),44(a,1))].">
      <j1 rule="para" parents="246 44"/>
    </justification>
  </clause>

  <clause id="459">
    <literal><![CDATA[
      x * T(x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,z) * x = u
    ]]></literal>
    <justification jstring="[para(246(a,1),284(a,1,2))].">
      <j1 rule="para" parents="246 284"/>
    </justification>
  </clause>

  <clause id="460">
    <literal><![CDATA[
      (x * T(y,z)) / x = T((x * y) / x,z)
    ]]></literal>
    <justification jstring="[para(224(a,1),269(a,1,1,2,1))].">
      <j1 rule="para" parents="224 269"/>
    </justification>
  </clause>

  <clause id="461">
    <literal><![CDATA[
      T(x,y) != T(z,u)
    ]]></literal>
    <literal><![CDATA[
      T((y * z) / y,u) = x
    ]]></literal>
    <justification jstring="[para(270(a,1),44(a,2)),flip(b)].">
      <j1 rule="para" parents="270 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="462">
    <literal><![CDATA[
      (x * T(y,z)) / x != u
    ]]></literal>
    <literal><![CDATA[
      T((x * y) / x,z) = u
    ]]></literal>
    <justification jstring="[para(270(a,1),331(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="270 331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="463">
    <literal><![CDATA[
      (x * y) \ (x * ((z \ y) * z)) = L(K(z \ y,z),y,x)
    ]]></literal>
    <justification jstring="[para(302(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="302 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="464">
    <literal><![CDATA[
      (x \ y) * x != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,x) = z
    ]]></literal>
    <justification jstring="[para(302(a,1),38(a,1))].">
      <j1 rule="para" parents="302 38"/>
    </justification>
  </clause>

  <clause id="465">
    <literal><![CDATA[
      x \ ((y \ x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,y) = z
    ]]></literal>
    <justification jstring="[para(302(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="302 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="466">
    <literal><![CDATA[
      K(x \ y,x) * z != (x \ y) * x
    ]]></literal>
    <literal><![CDATA[
      T(y,K(x \ y,x)) = z
    ]]></literal>
    <justification jstring="[para(302(a,1),240(a,2))].">
      <j1 rule="para" parents="302 240"/>
    </justification>
  </clause>

  <clause id="467">
    <literal><![CDATA[
      x \ (y * (x / y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x / y) = z
    ]]></literal>
    <justification jstring="[para(303(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="303 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="468">
    <literal><![CDATA[
      1 / K(x,x \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,258,a,b,335,a),flip(a)].">
      <j1 rule="hyper" parents="320 258 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="469">
    <literal><![CDATA[
      (x * (y * z)) / T(x * y,L(z,y,x)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(279,a,90,a)].">
      <j1 rule="hyper" parents="279 90"/>
    </justification>
  </clause>

  <clause id="470">
    <literal><![CDATA[
      L(x,y,z) \ (z * (y * x)) = T(z * y,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(277,a,90,a),flip(a)].">
      <j1 rule="hyper" parents="277 90"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="471">
    <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="472">
    <literal><![CDATA[
      x * L(y,z,x / z) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,147,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="58 147 90"/>
    </justification>
  </clause>

  <clause id="473">
    <literal><![CDATA[
      L(x \ T(y * x,y),x,y) = y
    ]]></literal>
    <justification jstring="[hyper(29,a,227,a(flip),b,90,a),flip(a)].">
      <j1 rule="hyper" parents="29 227 90"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="474">
    <literal><![CDATA[
      x \ (y * L(z,x \ y,x)) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(116,a,148,a(flip),b,90,a(flip))].">
      <j1 rule="hyper" parents="116 148 90"/>
    </justification>
  </clause>

  <clause id="475">
    <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="476">
    <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="477">
    <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="478">
    <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="479">
    <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="480">
    <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="481">
    <literal><![CDATA[
      (x * y) * L(z,T(x,y),y) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(105(a,1),90(a,1,1))].">
      <j1 rule="para" parents="105 90"/>
    </justification>
  </clause>

  <clause id="482">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(90(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="90 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="483">
    <literal><![CDATA[
      (x * (y * z)) * K(L(z,y,x),x * y) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(90(a,1),84(a,1,1))].">
      <j1 rule="para" parents="90 84"/>
    </justification>
  </clause>

  <clause id="484">
    <literal><![CDATA[
      K(x \ 1,x) * L(y,x,x \ 1) = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(258(a,2),90(a,1,1))].">
      <j1 rule="para" parents="258 90"/>
    </justification>
  </clause>

  <clause id="485">
    <literal><![CDATA[
      x * ((x \ 1) * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(90(a,1),203(a,1))].">
      <j1 rule="para" parents="90 203"/>
    </justification>
  </clause>

  <clause id="486">
    <literal><![CDATA[
      (1 / x) * (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,1 / x) = z
    ]]></literal>
    <justification jstring="[para(90(a,1),204(a,1))].">
      <j1 rule="para" parents="90 204"/>
    </justification>
  </clause>

  <clause id="487">
    <literal><![CDATA[
      (x * y) * L(K(z \ y,z),y,x) = x * ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(302(a,1),90(a,2,2))].">
      <j1 rule="para" parents="302 90"/>
    </justification>
  </clause>

  <clause id="488">
    <literal><![CDATA[
      L(x \ y,x,1 / x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,164,a(flip),b,92,a),flip(a)].">
      <j1 rule="hyper" parents="320 164 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="489">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(320,a,163,a(flip),b,92,a),flip(a)].">
      <j1 rule="hyper" parents="320 163 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="490">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,155,a(flip),b,92,a),flip(a)].">
      <j1 rule="hyper" parents="320 155 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="491">
    <literal><![CDATA[
      L(x \ ((y * x) / y),x,y) = K(y,(y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,87,a(flip),b,92,a),flip(a)].">
      <j1 rule="hyper" parents="320 87 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="492">
    <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="493">
    <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="494">
    <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="495">
    <literal><![CDATA[
      L(L(x \ y,z,u),x,w) = L((w * x) \ (w * y),z,u)
    ]]></literal>
    <justification jstring="[para(92(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="92 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="496">
    <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="497">
    <literal><![CDATA[
      L(x \ (1 / y),x,y) = (y * x) \ K(y,1 / y)
    ]]></literal>
    <justification jstring="[para(260(a,2),92(a,2,2))].">
      <j1 rule="para" parents="260 92"/>
    </justification>
  </clause>

  <clause id="498">
    <literal><![CDATA[
      x / L(y \ z,y,x / z) = (x / z) * y
    ]]></literal>
    <justification jstring="[para(92(a,2),324(a,1,2))].">
      <j1 rule="para" parents="92 324"/>
    </justification>
  </clause>

  <clause id="499">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(92(a,2),209(a,1))].">
      <j1 rule="para" parents="92 209"/>
    </justification>
  </clause>

  <clause id="500">
    <literal><![CDATA[
      L(x \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) \ y = z
    ]]></literal>
    <justification jstring="[para(92(a,2),293(a,1))].">
      <j1 rule="para" parents="92 293"/>
    </justification>
  </clause>

  <clause id="501">
    <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="502">
    <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="503">
    <literal><![CDATA[
      L(L(x \ y,x,z),z * x,u) = (u * (z * x)) \ (u * (z * y))
    ]]></literal>
    <justification jstring="[para(92(a,2),92(a,1,1))].">
      <j1 rule="para" parents="92 92"/>
    </justification>
  </clause>

  <clause id="504">
    <literal><![CDATA[
      R(x / y,y,x \ z) \ z = y * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,291,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="116 291 101"/>
    </justification>
  </clause>

  <clause id="505">
    <literal><![CDATA[
      R(x,x \ y,z) \ (y * z) = (x \ 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="506">
    <literal><![CDATA[
      R(x / y,y,z) \ (x * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(116,a,147,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="116 147 101"/>
    </justification>
  </clause>

  <clause id="507">
    <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="508">
    <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="509">
    <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="510">
    <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="511">
    <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="512">
    <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="513">
    <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="514">
    <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="515">
    <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="516">
    <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="517">
    <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="518">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(101(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="101 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="519">
    <literal><![CDATA[
      (R(x,y,z) * (y * z)) / z != u
    ]]></literal>
    <literal><![CDATA[
      x * y = u
    ]]></literal>
    <justification jstring="[para(101(a,2),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="101 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="520">
    <literal><![CDATA[
      R(x,y \ 1,y) * K(y \ 1,y) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[para(258(a,2),101(a,1,2))].">
      <j1 rule="para" parents="258 101"/>
    </justification>
  </clause>

  <clause id="521">
    <literal><![CDATA[
      (x * y) * (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(101(a,1),206(a,1)),flip(b)].">
      <j1 rule="para" parents="101 206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="522">
    <literal><![CDATA[
      R(x / (1 / y),1 / y,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(320,a,170,a(flip),b,102,a),flip(a)].">
      <j1 rule="hyper" parents="320 170 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="523">
    <literal><![CDATA[
      R(x / y,y,y \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,169,a(flip),b,102,a),flip(a)].">
      <j1 rule="hyper" parents="320 169 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="524">
    <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="525">
    <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="526">
    <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="527">
    <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="528">
    <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="529">
    <literal><![CDATA[
      R(x / T(y,z),T(y,z),y) = (x * y) / (y * T(y,z))
    ]]></literal>
    <justification jstring="[para(243(a,1),102(a,2,2))].">
      <j1 rule="para" parents="243 102"/>
    </justification>
  </clause>

  <clause id="530">
    <literal><![CDATA[
      R(x / y,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * (y \ 1) = z
    ]]></literal>
    <justification jstring="[para(102(a,2),211(a,1)),flip(b)].">
      <j1 rule="para" parents="102 211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="531">
    <literal><![CDATA[
      R(R(1 / x,x,y),x * y,z) = (y * z) / ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(219(a,2),102(a,1,1))].">
      <j1 rule="para" parents="219 102"/>
    </justification>
  </clause>

  <clause id="532">
    <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="533">
    <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="534">
    <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="535">
    <literal><![CDATA[
      x \ (y * x) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(y,x) = u
    ]]></literal>
    <justification jstring="[para(227(a,1),122(a,1,2)),flip(b)].">
      <j1 rule="para" parents="227 122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="536">
    <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="537">
    <literal><![CDATA[
      x * y != z * u
    ]]></literal>
    <literal><![CDATA[
      (x * y) / u = z
    ]]></literal>
    <justification jstring="[para(78(a,1),132(a,1,1)),flip(b)].">
      <j1 rule="para" parents="78 132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="538">
    <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="539">
    <literal><![CDATA[
      R(x,y,z) \ u != y * z
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(184(a,1),42(a,1)),flip(a)].">
      <j1 rule="para" parents="184 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="540">
    <literal><![CDATA[
      R(x,T(y,x),z) \ ((y * x) * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[para(105(a,1),184(a,1,2,1))].">
      <j1 rule="para" parents="105 184"/>
    </justification>
  </clause>

  <clause id="541">
    <literal><![CDATA[
      R(x * y,K(y,x),z) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(84(a,1),184(a,1,2,1))].">
      <j1 rule="para" parents="84 184"/>
    </justification>
  </clause>

  <clause id="542">
    <literal><![CDATA[
      R(x,K(y \ x,y),z) \ (((y \ x) * y) * z) = K(y \ x,y) * z
    ]]></literal>
    <justification jstring="[para(302(a,1),184(a,1,2,1))].">
      <j1 rule="para" parents="302 184"/>
    </justification>
  </clause>

  <clause id="543">
    <literal><![CDATA[
      R(x * y,L(z,y,x),u) \ ((x * (y * z)) * u) = L(z,y,x) * u
    ]]></literal>
    <justification jstring="[para(90(a,1),184(a,1,2,1))].">
      <j1 rule="para" parents="90 184"/>
    </justification>
  </clause>

  <clause id="544">
    <literal><![CDATA[
      (x * y) / L(z,y / z,x) = x * (y / z)
    ]]></literal>
    <justification jstring="[para(7(a,1),186(a,1,1,2))].">
      <j1 rule="para" parents="7 186"/>
    </justification>
  </clause>

  <clause id="545">
    <literal><![CDATA[
      (x * (y * z)) / L(T(y,z),z,x) = x * z
    ]]></literal>
    <justification jstring="[para(105(a,1),186(a,1,1,2))].">
      <j1 rule="para" parents="105 186"/>
    </justification>
  </clause>

  <clause id="546">
    <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(186(a,1),421(a,1,1))].">
      <j1 rule="para" parents="186 421"/>
    </justification>
  </clause>

  <clause id="547">
    <literal><![CDATA[
      K(x,1 / x) \ x = L(x,1 / x,x)
    ]]></literal>
    <justification jstring="[para(260(a,2),221(a,2,1)),flip(a)].">
      <j1 rule="para" parents="260 221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="548">
    <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,257,a)].">
      <j1 rule="hyper" parents="116 25 257"/>
    </justification>
  </clause>

  <clause id="549">
    <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,257,a)].">
      <j1 rule="hyper" parents="116 20 257"/>
    </justification>
  </clause>

  <clause id="550">
    <literal><![CDATA[
      L(x,y \ 1,y) != y * z
    ]]></literal>
    <literal><![CDATA[
      (y \ 1) * x = z
    ]]></literal>
    <justification jstring="[para(257(a,1),38(a,1))].">
      <j1 rule="para" parents="257 38"/>
    </justification>
  </clause>

  <clause id="551">
    <literal><![CDATA[
      L(T(x,y \ 1),y \ 1,y) = y * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(105(a,1),257(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="552">
    <literal><![CDATA[
      x \ L(y,x \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(257(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="257 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="553">
    <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,259,a)].">
      <j1 rule="hyper" parents="116 25 259"/>
    </justification>
  </clause>

  <clause id="554">
    <literal><![CDATA[
      L(T(x,y),y,1 / y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[para(105(a,1),259(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="555">
    <literal><![CDATA[
      (1 / x) \ L(y,x,1 / x) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(259(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="259 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="556">
    <literal><![CDATA[
      (x \ 1) \ R(y,x,x \ 1) = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(277,a,261,a),flip(a)].">
      <j1 rule="hyper" parents="277 261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="557">
    <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,261,a)].">
      <j1 rule="hyper" parents="117 24 261"/>
    </justification>
  </clause>

  <clause id="558">
    <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,261,a)].">
      <j1 rule="hyper" parents="117 22 261"/>
    </justification>
  </clause>

  <clause id="559">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(261(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="261 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="560">
    <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),261(a,1,1)),flip(a)].">
      <j1 rule="para" parents="101 261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="561">
    <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,262,a)].">
      <j1 rule="hyper" parents="117 26 262"/>
    </justification>
  </clause>

  <clause id="562">
    <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,262,a)].">
      <j1 rule="hyper" parents="117 24 262"/>
    </justification>
  </clause>

  <clause id="563">
    <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,262,a)].">
      <j1 rule="hyper" parents="117 22 262"/>
    </justification>
  </clause>

  <clause id="564">
    <literal><![CDATA[
      L(T(x \ (y \ z),u),x,y) = T((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(298(a,1),20(a,2,1))].">
      <j1 rule="para" parents="298 20"/>
    </justification>
  </clause>

  <clause id="565">
    <literal><![CDATA[
      L(R(x \ (y \ z),u,w),x,y) = R((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(298(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="298 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="566">
    <literal><![CDATA[
      L(L(x \ (y \ z),u,w),x,y) = L((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(298(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="298 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="567">
    <literal><![CDATA[
      L(x,(y \ z) / x,y) = (y * ((y \ z) / x)) \ z
    ]]></literal>
    <justification jstring="[para(75(a,1),298(a,1,1))].">
      <j1 rule="para" parents="75 298"/>
    </justification>
  </clause>

  <clause id="568">
    <literal><![CDATA[
      (x * (x \ y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(72(a,1),326(a,1,1,1))].">
      <j1 rule="para" parents="72 326"/>
    </justification>
  </clause>

  <clause id="569">
    <literal><![CDATA[
      (x * T(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) * z = u
    ]]></literal>
    <justification jstring="[para(187(a,1),326(a,1,1,1))].">
      <j1 rule="para" parents="187 326"/>
    </justification>
  </clause>

  <clause id="570">
    <literal><![CDATA[
      ((x \ 1) * x) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) * y = z
    ]]></literal>
    <justification jstring="[para(359(a,1),326(a,1,1,1))].">
      <j1 rule="para" parents="359 326"/>
    </justification>
  </clause>

  <clause id="571">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(156(a,1),336(a,1,1))].">
      <j1 rule="para" parents="156 336"/>
    </justification>
  </clause>

  <clause id="572">
    <literal><![CDATA[
      (x * y) / y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(156(a,2),336(a,1))].">
      <j1 rule="para" parents="156 336"/>
    </justification>
  </clause>

  <clause id="573">
    <literal><![CDATA[
      x * (y \ (y * (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      z / w = u
    ]]></literal>
    <justification jstring="[para(4(a,2),337(a,1,2))].">
      <j1 rule="para" parents="4 337"/>
    </justification>
  </clause>

  <clause id="574">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(160(a,1),337(a,1,2))].">
      <j1 rule="para" parents="160 337"/>
    </justification>
  </clause>

  <clause id="575">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(160(a,2),337(a,1))].">
      <j1 rule="para" parents="160 337"/>
    </justification>
  </clause>

  <clause id="576">
    <literal><![CDATA[
      ((x / y) * y) / z != u
    ]]></literal>
    <literal><![CDATA[
      x / z = u
    ]]></literal>
    <justification jstring="[para(75(a,1),338(a,1,1,2))].">
      <j1 rule="para" parents="75 338"/>
    </justification>
  </clause>

  <clause id="577">
    <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),339(a,1,2))].">
      <j1 rule="para" parents="90 339"/>
    </justification>
  </clause>

  <clause id="578">
    <literal><![CDATA[
      x \ y != z * (u \ (u * (z \ w)))
    ]]></literal>
    <literal><![CDATA[
      x * w = y
    ]]></literal>
    <justification jstring="[para(4(a,2),340(a,2,2))].">
      <j1 rule="para" parents="4 340"/>
    </justification>
  </clause>

  <clause id="579">
    <literal><![CDATA[
      x \ y != z * T(u,z)
    ]]></literal>
    <literal><![CDATA[
      x * (u * z) = y
    ]]></literal>
    <justification jstring="[para(17(a,2),340(a,2,2))].">
      <j1 rule="para" parents="17 340"/>
    </justification>
  </clause>

  <clause id="580">
    <literal><![CDATA[
      x \ y != (z / u) * u
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></literal>
    <justification jstring="[para(75(a,1),340(a,2,2))].">
      <j1 rule="para" parents="75 340"/>
    </justification>
  </clause>

  <clause id="581">
    <literal><![CDATA[
      x \ (x * y) != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * y = u
    ]]></literal>
    <justification jstring="[para(160(a,2),340(a,2)),flip(a)].">
      <j1 rule="para" parents="160 340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="582">
    <literal><![CDATA[
      (x / y) \ x != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * y = u
    ]]></literal>
    <justification jstring="[para(192(a,2),340(a,2)),flip(a)].">
      <j1 rule="para" parents="192 340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="583">
    <literal><![CDATA[
      x \ y != (z \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      x * K(z \ 1,z) = y
    ]]></literal>
    <justification jstring="[para(360(a,1),340(a,2,2))].">
      <j1 rule="para" parents="360 340"/>
    </justification>
  </clause>

  <clause id="584">
    <literal><![CDATA[
      x * (y \ (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(160(a,2),342(a,1,2))].">
      <j1 rule="para" parents="160 342"/>
    </justification>
  </clause>

  <clause id="585">
    <literal><![CDATA[
      x * ((y / z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(192(a,2),342(a,1,2))].">
      <j1 rule="para" parents="192 342"/>
    </justification>
  </clause>

  <clause id="586">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) != u
    ]]></literal>
    <literal><![CDATA[
      y \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(92(a,2),350(a,1))].">
      <j1 rule="para" parents="92 350"/>
    </justification>
  </clause>

  <clause id="587">
    <literal><![CDATA[
      T((x \ y) \ 1,y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(390(a,1),173(a,1,2))].">
      <j1 rule="para" parents="390 173"/>
    </justification>
  </clause>

  <clause id="588">
    <literal><![CDATA[
      T(1 / (x \ y),y \ x) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[para(390(a,1),282(a,1,2))].">
      <j1 rule="para" parents="390 282"/>
    </justification>
  </clause>

  <clause id="589">
    <literal><![CDATA[
      T(x \ (x / y),z) = L(T(y \ 1,z),y,x / y)
    ]]></literal>
    <justification jstring="[para(399(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="399 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="590">
    <literal><![CDATA[
      x * R(1 / y,y,y \ z) = x * ((y \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(119,a,408,a,b,4,a)].">
      <j1 rule="hyper" parents="119 408 4"/>
    </justification>
  </clause>

  <clause id="591">
    <literal><![CDATA[
      ((x \ y) / y) * (R(1 / x,x,x \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(281,a,408,a(flip))].">
      <j1 rule="hyper" parents="281 408"/>
    </justification>
  </clause>

  <clause id="592">
    <literal><![CDATA[
      T((x \ y) / y,z) = R(T(1 / x,z),x,x \ y)
    ]]></literal>
    <justification jstring="[para(408(a,1),22(a,2,1)),flip(a)].">
      <j1 rule="para" parents="408 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="593">
    <literal><![CDATA[
      T(1 / (x / y),y / x) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[para(409(a,1),172(a,1,2))].">
      <j1 rule="para" parents="409 172"/>
    </justification>
  </clause>

  <clause id="594">
    <literal><![CDATA[
      (((x / y) / z) * z) * y != u * w
    ]]></literal>
    <literal><![CDATA[
      x / w = u
    ]]></literal>
    <justification jstring="[para(7(a,2),414(a,1,1))].">
      <j1 rule="para" parents="7 414"/>
    </justification>
  </clause>

  <clause id="595">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(156(a,1),414(a,1,1))].">
      <j1 rule="para" parents="156 414"/>
    </justification>
  </clause>

  <clause id="596">
    <literal><![CDATA[
      x * (y \ (y * (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ z = w
    ]]></literal>
    <justification jstring="[para(4(a,2),417(a,1,2))].">
      <j1 rule="para" parents="4 417"/>
    </justification>
  </clause>

  <clause id="597">
    <literal><![CDATA[
      x * (y * (y \ (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ z = w
    ]]></literal>
    <justification jstring="[para(5(a,2),417(a,1,2))].">
      <j1 rule="para" parents="5 417"/>
    </justification>
  </clause>

  <clause id="598">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(160(a,1),417(a,1,2))].">
      <j1 rule="para" parents="160 417"/>
    </justification>
  </clause>

  <clause id="599">
    <literal><![CDATA[
      x \ y != (z \ 1) * y
    ]]></literal>
    <literal><![CDATA[
      R(z,z \ 1,y) = x
    ]]></literal>
    <justification jstring="[para(426(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="426 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="600">
    <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),428(a,1))].">
      <j1 rule="para" parents="22 428"/>
    </justification>
  </clause>

  <clause id="601">
    <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),428(a,1,2))].">
      <j1 rule="para" parents="106 428"/>
    </justification>
  </clause>

  <clause id="602">
    <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),435(a,1,1))].">
      <j1 rule="para" parents="106 435"/>
    </justification>
  </clause>

  <clause id="603">
    <literal><![CDATA[
      x \ L(y,x \ 1,x) != (x \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(438(a,2),38(a,1))].">
      <j1 rule="para" parents="438 38"/>
    </justification>
  </clause>

  <clause id="604">
    <literal><![CDATA[
      (x * y) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ z,y,x) = u
    ]]></literal>
    <justification jstring="[para(471(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="471 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="605">
    <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(471(a,1),421(a,1,1))].">
      <j1 rule="para" parents="471 421"/>
    </justification>
  </clause>

  <clause id="606">
    <literal><![CDATA[
      L(T(x \ y,z),x,1 / x) = T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(488(a,1),20(a,2,1))].">
      <j1 rule="para" parents="488 20"/>
    </justification>
  </clause>

  <clause id="607">
    <literal><![CDATA[
      L(T((x \ 1) \ y,z),x \ 1,x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(489(a,1),20(a,2,1))].">
      <j1 rule="para" parents="489 20"/>
    </justification>
  </clause>

  <clause id="608">
    <literal><![CDATA[
      L(R((x \ 1) \ y,z,u),x \ 1,x) = R(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(489(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="489 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="609">
    <literal><![CDATA[
      T((x \ 1) \ y,x * y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(489(a,1),173(a,1,2))].">
      <j1 rule="para" parents="489 173"/>
    </justification>
  </clause>

  <clause id="610">
    <literal><![CDATA[
      R(T(x / (1 / y),z),1 / y,y) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(522(a,1),22(a,2,1))].">
      <j1 rule="para" parents="522 22"/>
    </justification>
  </clause>

  <clause id="611">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ 1) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(523(a,1),22(a,2,1))].">
      <j1 rule="para" parents="523 22"/>
    </justification>
  </clause>

  <clause id="612">
    <literal><![CDATA[
      R(R(x / y,z,u),y,y \ 1) = R(x * (y \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(523(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="523 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="613">
    <literal><![CDATA[
      (x * (x \ y)) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y * z) = w
    ]]></literal>
    <justification jstring="[para(148(a,2),536(a,1))].">
      <j1 rule="para" parents="148 536"/>
    </justification>
  </clause>

  <clause id="614">
    <literal><![CDATA[
      x * (y \ (y * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(152(a,2),536(a,1))].">
      <j1 rule="para" parents="152 536"/>
    </justification>
  </clause>

  <clause id="615">
    <literal><![CDATA[
      (x * (x \ y)) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      (y * z) / w = u
    ]]></literal>
    <justification jstring="[para(148(a,2),537(a,1))].">
      <j1 rule="para" parents="148 537"/>
    </justification>
  </clause>

  <clause id="616">
    <literal><![CDATA[
      x * (y \ (y * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(152(a,2),537(a,1))].">
      <j1 rule="para" parents="152 537"/>
    </justification>
  </clause>

  <clause id="617">
    <literal><![CDATA[
      R(x,y,z) \ ((x * y) * z) != u * w
    ]]></literal>
    <literal><![CDATA[
      (y * z) / w = u
    ]]></literal>
    <justification jstring="[para(184(a,2),537(a,1))].">
      <j1 rule="para" parents="184 537"/>
    </justification>
  </clause>

  <clause id="618">
    <literal><![CDATA[
      K(x,1 / x) * L(x,1 / x,x) = x
    ]]></literal>
    <justification jstring="[hyper(134,a,547,a)].">
      <j1 rule="hyper" parents="134 547"/>
    </justification>
  </clause>

  <clause id="619">
    <literal><![CDATA[
      ((x / y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(192(a,2),568(a,1,1))].">
      <j1 rule="para" parents="192 568"/>
    </justification>
  </clause>

  <clause id="620">
    <literal><![CDATA[
      (x * y) \ x != z * u
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) / u = z
    ]]></literal>
    <justification jstring="[para(398(a,1),575(a,1,2))].">
      <j1 rule="para" parents="398 575"/>
    </justification>
  </clause>

  <clause id="621">
    <literal><![CDATA[
      R((x / y) / z,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / (z * y) = u
    ]]></literal>
    <justification jstring="[para(102(a,2),576(a,1))].">
      <j1 rule="para" parents="102 576"/>
    </justification>
  </clause>

  <clause id="622">
    <literal><![CDATA[
      x \ y != (z * u) / u
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></literal>
    <justification jstring="[para(156(a,2),580(a,2))].">
      <j1 rule="para" parents="156 580"/>
    </justification>
  </clause>

  <clause id="623">
    <literal><![CDATA[
      x \ y != (z / (u \ z)) * w
    ]]></literal>
    <literal><![CDATA[
      x * (u * w) = y
    ]]></literal>
    <justification jstring="[para(181(a,1),580(a,2,1))].">
      <j1 rule="para" parents="181 580"/>
    </justification>
  </clause>

  <clause id="624">
    <literal><![CDATA[
      x \ (y * (y \ (x * z))) != u \ w
    ]]></literal>
    <literal><![CDATA[
      u * z = w
    ]]></literal>
    <justification jstring="[para(5(a,2),581(a,1,2))].">
      <j1 rule="para" parents="5 581"/>
    </justification>
  </clause>

  <clause id="625">
    <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),581(a,1,2))].">
      <j1 rule="para" parents="90 581"/>
    </justification>
  </clause>

  <clause id="626">
    <literal><![CDATA[
      x * ((y * z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      x * L(z \ 1,z,y) = u
    ]]></literal>
    <justification jstring="[para(398(a,1),584(a,1,2,2))].">
      <j1 rule="para" parents="398 584"/>
    </justification>
  </clause>

  <clause id="627">
    <literal><![CDATA[
      K(x,1 / x) * y != x
    ]]></literal>
    <literal><![CDATA[
      L(x,1 / x,x) = y
    ]]></literal>
    <justification jstring="[para(618(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="618 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="628">
    <literal><![CDATA[
      x \ y != (z * T(u,z)) / z
    ]]></literal>
    <literal><![CDATA[
      x * u = y
    ]]></literal>
    <justification jstring="[para(105(a,2),622(a,2,1))].">
      <j1 rule="para" parents="105 622"/>
    </justification>
  </clause>

  <clause id="629">
    <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),288(a,1))].">
      <j1 rule="para" parents="110 288"/>
    </justification>
  </clause>

  <clause id="630">
    <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="631">
    <literal><![CDATA[
      x * (y * T(z,x * y)) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,90,a(flip),b,237,a)].">
      <j1 rule="hyper" parents="58 90 237"/>
    </justification>
  </clause>

  <clause id="632">
    <literal><![CDATA[
      x \ (L(y,z,x) * (x * z)) = z * T(y,x * z)
    ]]></literal>
    <justification jstring="[hyper(116,a,237,a(flip),b,90,a(flip))].">
      <j1 rule="hyper" parents="116 237 90"/>
    </justification>
  </clause>

  <clause id="633">
    <literal><![CDATA[
      x * L(x \ (y * x),z,u) = L(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(17(a,1),237(a,1,2,1))].">
      <j1 rule="para" parents="17 237"/>
    </justification>
  </clause>

  <clause id="634">
    <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),237(a,1,2,1))].">
      <j1 rule="para" parents="22 237"/>
    </justification>
  </clause>

  <clause id="635">
    <literal><![CDATA[
      L(x / y,z,u) * y = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(107(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="636">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(224(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="224 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="637">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ y,z,u) = L(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(106(a,1),237(a,1,2,1))].">
      <j1 rule="para" parents="106 237"/>
    </justification>
  </clause>

  <clause id="638">
    <literal><![CDATA[
      (x * y) * R(T(z,x * y),x,y) = (z * x) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,101,a(flip),b,238,a),flip(a)].">
      <j1 rule="hyper" parents="320 101 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="639">
    <literal><![CDATA[
      R(x / y,z,u) * y = y * R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(107(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="640">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(224(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="224 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="641">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(106(a,1),238(a,1,2,1))].">
      <j1 rule="para" parents="106 238"/>
    </justification>
  </clause>

  <clause id="642">
    <literal><![CDATA[
      T(x / y,(z / y) \ z) = y \ x
    ]]></literal>
    <justification jstring="[hyper(239,a,352,a,b,289,a)].">
      <j1 rule="hyper" parents="239 352 289"/>
    </justification>
  </clause>

  <clause id="643">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) / x = L(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(271,a,247,a)].">
      <j1 rule="hyper" parents="271 247"/>
    </justification>
  </clause>

  <clause id="644">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) / x = R(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(271,a,248,a)].">
      <j1 rule="hyper" parents="271 248"/>
    </justification>
  </clause>

  <clause id="645">
    <literal><![CDATA[
      T(x / (y * x),y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(219(a,1),248(a,1,1))].">
      <j1 rule="para" parents="219 248"/>
    </justification>
  </clause>

  <clause id="646">
    <literal><![CDATA[
      x * R(x \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(y / x,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(248(a,1),284(a,1,2))].">
      <j1 rule="para" parents="248 284"/>
    </justification>
  </clause>

  <clause id="647">
    <literal><![CDATA[
      T((x * y) / (z * y),z) = R(z \ x,z,y)
    ]]></literal>
    <justification jstring="[para(102(a,1),248(a,1,1))].">
      <j1 rule="para" parents="102 248"/>
    </justification>
  </clause>

  <clause id="648">
    <literal><![CDATA[
      R(x \ (y / z),x,z) = T(y / (x * z),x)
    ]]></literal>
    <justification jstring="[para(301(a,1),248(a,1,1)),flip(a)].">
      <j1 rule="para" parents="301 248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="649">
    <literal><![CDATA[
      R((x / y) \ 1,x / y,y) = T(y / x,x / y)
    ]]></literal>
    <justification jstring="[para(409(a,1),248(a,1,1)),flip(a)].">
      <j1 rule="para" parents="409 248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="650">
    <literal><![CDATA[
      R(x \ y,x,x \ 1) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[para(523(a,1),248(a,1,1)),flip(a)].">
      <j1 rule="para" parents="523 248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="651">
    <literal><![CDATA[
      (x / (y * x)) * y = y * R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,645,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 645 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="652">
    <literal><![CDATA[
      x * R(x \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y / (x * y)) * x = z
    ]]></literal>
    <justification jstring="[para(645(a,1),284(a,1,2))].">
      <j1 rule="para" parents="645 284"/>
    </justification>
  </clause>

  <clause id="653">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      T(u,w) = w \ (x * z)
    ]]></literal>
    <justification jstring="[para(299(a,1),240(a,1))].">
      <j1 rule="para" parents="299 240"/>
    </justification>
  </clause>

  <clause id="654">
    <literal><![CDATA[
      x * (y \ T(z,z \ u)) = x * (y \ ((z \ u) \ u))
    ]]></literal>
    <justification jstring="[para(308(a,2),152(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="308 152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="655">
    <literal><![CDATA[
      T(x,x \ y) * z != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) \ u = z
    ]]></literal>
    <justification jstring="[para(309(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="309 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="656">
    <literal><![CDATA[
      T(x,x \ y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) \ z = u
    ]]></literal>
    <justification jstring="[para(309(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="309 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="657">
    <literal><![CDATA[
      T(x \ T(y,y \ z),x \ ((y \ z) \ z)) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(444,a,310,a,b,xx)].">
      <j1 rule="hyper" parents="444 310"/>
    </justification>
  </clause>

  <clause id="658">
    <literal><![CDATA[
      (x \ T(y,y \ z)) \ u = (x \ ((y \ z) \ z)) \ u
    ]]></literal>
    <justification jstring="[hyper(56,a,310,a)].">
      <j1 rule="hyper" parents="56 310"/>
    </justification>
  </clause>

  <clause id="659">
    <literal><![CDATA[
      T(x,x \ y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) * u = z
    ]]></literal>
    <justification jstring="[para(311(a,2),134(a,1))].">
      <j1 rule="para" parents="311 134"/>
    </justification>
  </clause>

  <clause id="660">
    <literal><![CDATA[
      (x * T(y,y \ z)) / ((y \ z) \ z) = x
    ]]></literal>
    <justification jstring="[hyper(328,a,312,a),flip(a)].">
      <j1 rule="hyper" parents="328 312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="661">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) = K(z,T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(116,a,313,a(flip),b,84,a)].">
      <j1 rule="hyper" parents="116 313 84"/>
    </justification>
  </clause>

  <clause id="662">
    <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(313(a,1),307(a,1,2))].">
      <j1 rule="para" parents="313 307"/>
    </justification>
  </clause>

  <clause id="663">
    <literal><![CDATA[
      T(T(x,x \ y),z) = T((x \ y) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(239,a,314,a,b,105,a)].">
      <j1 rule="hyper" parents="239 314 105"/>
    </justification>
  </clause>

  <clause id="664">
    <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,314,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="116 314 90"/>
    </justification>
  </clause>

  <clause id="665">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) = K(z,(x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(314(a,2),11(a,2,1)),flip(a)].">
      <j1 rule="para" parents="314 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="666">
    <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(314(a,2),307(a,1,1))].">
      <j1 rule="para" parents="314 307"/>
    </justification>
  </clause>

  <clause id="667">
    <literal><![CDATA[
      T(x,x \ y) * z != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) * z = u
    ]]></literal>
    <justification jstring="[para(315(a,1),584(a,1))].">
      <j1 rule="para" parents="315 584"/>
    </justification>
  </clause>

  <clause id="668">
    <literal><![CDATA[
      (x \ y) * L(T((x \ y) \ y,z),u,w) = L(T(x,z),u,w) * (x \ y)
    ]]></literal>
    <justification jstring="[para(316(a,1),237(a,1,2,1))].">
      <j1 rule="para" parents="316 237"/>
    </justification>
  </clause>

  <clause id="669">
    <literal><![CDATA[
      x \ (x / y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x / y) = z
    ]]></literal>
    <justification jstring="[para(7(a,1),424(a,1,1))].">
      <j1 rule="para" parents="7 424"/>
    </justification>
  </clause>

  <clause id="670">
    <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),427(a,1,2))].">
      <j1 rule="para" parents="105 427"/>
    </justification>
  </clause>

  <clause id="671">
    <literal><![CDATA[
      (1 / x) / K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      R(1 / x,x,1 / x) = y
    ]]></literal>
    <justification jstring="[para(260(a,2),427(a,1,2))].">
      <j1 rule="para" parents="260 427"/>
    </justification>
  </clause>

  <clause id="672">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,85,a(flip),b,431,a)].">
      <j1 rule="hyper" parents="320 85 431"/>
    </justification>
  </clause>

  <clause id="673">
    <literal><![CDATA[
      K(x \ (x * y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(63(a,1),672(a,1,1)),flip(a)].">
      <j1 rule="para" parents="63 672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="674">
    <literal><![CDATA[
      K((x / y) \ x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),673(a,1,1,2))].">
      <j1 rule="para" parents="7 673"/>
    </justification>
  </clause>

  <clause id="675">
    <literal><![CDATA[
      x / T(y,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x / ((y \ z) \ z) = u
    ]]></literal>
    <justification jstring="[para(445(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="445 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="676">
    <literal><![CDATA[
      T((x * y) / x,z) * x != x * u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(454(a,2),38(a,1))].">
      <j1 rule="para" parents="454 38"/>
    </justification>
  </clause>

  <clause id="677">
    <literal><![CDATA[
      T(x / y,z) * y != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(457(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="457 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="678">
    <literal><![CDATA[
      T(T(x / y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(457(a,1),292(a,1,1)),flip(b)].">
      <j1 rule="para" parents="457 292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="679">
    <literal><![CDATA[
      T((x * (y / z)) / x,z) = (x * (z \ y)) / x
    ]]></literal>
    <justification jstring="[para(107(a,1),460(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="680">
    <literal><![CDATA[
      T((x * y) / x,z) * x != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(460(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="460 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="681">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(460(a,1),292(a,1,1)),flip(b)].">
      <j1 rule="para" parents="460 292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="682">
    <literal><![CDATA[
      T(1 / ((x * y) \ x),y) = 1 / ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),588(a,1,2))].">
      <j1 rule="para" parents="4 588"/>
    </justification>
  </clause>

  <clause id="683">
    <literal><![CDATA[
      T(x * y,(x \ 1) \ y) = x * y
    ]]></literal>
    <justification jstring="[hyper(49,a,609,a)].">
      <j1 rule="hyper" parents="49 609"/>
    </justification>
  </clause>

  <clause id="684">
    <literal><![CDATA[
      T(x * (y * z),a(x,y,z)) = a(x,y,z) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(440,a,xx,b,80,a)].">
      <j1 rule="hyper" parents="440 80"/>
    </justification>
  </clause>

  <clause id="685">
    <literal><![CDATA[
      ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(279,a,80,a)].">
      <j1 rule="hyper" parents="279 80"/>
    </justification>
  </clause>

  <clause id="686">
    <literal><![CDATA[
      (x * y) / a(z,z \ x,y) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(117,a,148,a(flip),b,80,a)].">
      <j1 rule="hyper" parents="117 148 80"/>
    </justification>
  </clause>

  <clause id="687">
    <literal><![CDATA[
      (x * y) / a(x / z,z,y) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(117,a,147,a(flip),b,80,a)].">
      <j1 rule="hyper" parents="117 147 80"/>
    </justification>
  </clause>

  <clause id="688">
    <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="689">
    <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="690">
    <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="691">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(80(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="80 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="692">
    <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="693">
    <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),581(a,1,2))].">
      <j1 rule="para" parents="80 581"/>
    </justification>
  </clause>

  <clause id="694">
    <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="695">
    <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="696">
    <literal><![CDATA[
      x * L(y,z,x / z) != u
    ]]></literal>
    <literal><![CDATA[
      (x / z) * (z * y) = u
    ]]></literal>
    <justification jstring="[para(93(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="93 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="697">
    <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="698">
    <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="699">
    <literal><![CDATA[
      R(x,x \ y,y \ z) \ z = (x \ y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(98(a,2),300(a,1,1))].">
      <j1 rule="para" parents="98 300"/>
    </justification>
  </clause>

  <clause id="700">
    <literal><![CDATA[
      R(x,y,y \ z) * z != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * (y \ z) = u
    ]]></literal>
    <justification jstring="[para(100(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="100 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="701">
    <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),143(a,1)),flip(a)].">
      <j1 rule="para" parents="106 143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="702">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,K(w,v5))) = y * a(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(119,a,146,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="119 146 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="703">
    <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(146(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="146 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="704">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(261(a,1),216(a,1,2))].">
      <j1 rule="para" parents="261 216"/>
    </justification>
  </clause>

  <clause id="705">
    <literal><![CDATA[
      x * a(x,y,y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,704,a)].">
      <j1 rule="hyper" parents="134 704"/>
    </justification>
  </clause>

  <clause id="706">
    <literal><![CDATA[
      L(x \ a(y,z,z \ 1),x,y) = (y * x) \ R(y,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(704(a,1),298(a,1,1,2))].">
      <j1 rule="para" parents="704 298"/>
    </justification>
  </clause>

  <clause id="707">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(705(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="705 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="708">
    <literal><![CDATA[
      x \ R(x,1 / y,y) = a(x,1 / y,y)
    ]]></literal>
    <justification jstring="[para(262(a,1),220(a,1,2))].">
      <j1 rule="para" parents="262 220"/>
    </justification>
  </clause>

  <clause id="709">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) = T(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,20,a(flip),b,232,a),flip(a)].">
      <j1 rule="hyper" parents="320 20 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="710">
    <literal><![CDATA[
      L(T(x,y),y,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(288,a,232,a),flip(a)].">
      <j1 rule="hyper" parents="288 232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="711">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,20,a(flip),b,710,a)].">
      <j1 rule="hyper" parents="58 20 710"/>
    </justification>
  </clause>

  <clause id="712">
    <literal><![CDATA[
      L(T(T(x,y),z),y,x) = T(T(x,x * y),z)
    ]]></literal>
    <justification jstring="[para(710(a,1),20(a,2,1))].">
      <j1 rule="para" parents="710 20"/>
    </justification>
  </clause>

  <clause id="713">
    <literal><![CDATA[
      L(R(T(x,y),z,u),y,x) = R(T(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(710(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="710 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="714">
    <literal><![CDATA[
      x * T(y,y * x) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[para(710(a,1),237(a,1,2))].">
      <j1 rule="para" parents="710 237"/>
    </justification>
  </clause>

  <clause id="715">
    <literal><![CDATA[
      (x * y) * R(L(T(x,y),y,x),z,u) = R(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[para(710(a,2),238(a,1,2,1))].">
      <j1 rule="para" parents="710 238"/>
    </justification>
  </clause>

  <clause id="716">
    <literal><![CDATA[
      (x * T(y,y * x)) / x = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(271,a,711,a)].">
      <j1 rule="hyper" parents="271 711"/>
    </justification>
  </clause>

  <clause id="717">
    <literal><![CDATA[
      T((x * y) / x,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,270,a,b,711,a)].">
      <j1 rule="hyper" parents="35 270 711"/>
    </justification>
  </clause>

  <clause id="718">
    <literal><![CDATA[
      T(L(L(x,y,x),z,u),y) = L(T(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(711(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="711 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="719">
    <literal><![CDATA[
      x * L(T(y,y * x),z,u) = L(L(y,x,y),z,u) * x
    ]]></literal>
    <justification jstring="[para(711(a,1),237(a,1,2,1))].">
      <j1 rule="para" parents="711 237"/>
    </justification>
  </clause>

  <clause id="720">
    <literal><![CDATA[
      L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),714(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="721">
    <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),714(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="105 714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="722">
    <literal><![CDATA[
      T(((x \ y) * x) / (x \ y),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),717(a,1,2))].">
      <j1 rule="para" parents="5 717"/>
    </justification>
  </clause>

  <clause id="723">
    <literal><![CDATA[
      T(T((x * y) / x,z),y * x) = T(L(y,x,y),z)
    ]]></literal>
    <justification jstring="[para(717(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="717 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="724">
    <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(305(a,1),453(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="305 453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="725">
    <literal><![CDATA[
      T(R(x / y,y,y \ z),z) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(440,a,147,a(flip),b,368,a)].">
      <j1 rule="hyper" parents="440 147 368"/>
    </justification>
  </clause>

  <clause id="726">
    <literal><![CDATA[
      x * R(T(y,x),z,z \ x) = (y * z) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,238,a,b,368,a)].">
      <j1 rule="hyper" parents="58 238 368"/>
    </justification>
  </clause>

  <clause id="727">
    <literal><![CDATA[
      x \ ((y * z) * (z \ x)) = R(T(y,x),z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(116,a,368,a(flip),b,238,a)].">
      <j1 rule="hyper" parents="116 368 238"/>
    </justification>
  </clause>

  <clause id="728">
    <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),368(a,1,1))].">
      <j1 rule="para" parents="24 368"/>
    </justification>
  </clause>

  <clause id="729">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (z * ((y * x) \ y)) = T(z,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(239,a,67,a(flip),b,391,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="239 67 391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="730">
    <literal><![CDATA[
      ((x * y) \ x) * T(z,L(y \ 1,y,x)) = z * L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,17,a,b,393,a(flip))].">
      <j1 rule="hyper" parents="119 17 393"/>
    </justification>
  </clause>

  <clause id="731">
    <literal><![CDATA[
      L(x \ 1,x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      ((y * x) \ y) * u = z
    ]]></literal>
    <justification jstring="[para(393(a,2),134(a,1))].">
      <j1 rule="para" parents="393 134"/>
    </justification>
  </clause>

  <clause id="732">
    <literal><![CDATA[
      x * (y * L(z \ 1,z,u)) = x * (y * ((u * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(119,a,395,a,b,4,a)].">
      <j1 rule="hyper" parents="119 395 4"/>
    </justification>
  </clause>

  <clause id="733">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,400,a,b,13,a(flip))].">
      <j1 rule="hyper" parents="119 400 13"/>
    </justification>
  </clause>

  <clause id="734">
    <literal><![CDATA[
      R(1 / x,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      y / (x * y) = z
    ]]></literal>
    <justification jstring="[para(406(a,1),208(a,1))].">
      <j1 rule="para" parents="406 208"/>
    </justification>
  </clause>

  <clause id="735">
    <literal><![CDATA[
      R(T(1 / x,x * y),x,y) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(421,a,410,a),flip(a)].">
      <j1 rule="hyper" parents="421 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="736">
    <literal><![CDATA[
      T(x / (y * x),z) * (y * x) = (T(1 / y,z) * y) * x
    ]]></literal>
    <justification jstring="[para(410(a,2),101(a,1,1))].">
      <j1 rule="para" parents="410 101"/>
    </justification>
  </clause>

  <clause id="737">
    <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),413(a,1,2))].">
      <j1 rule="para" parents="106 413"/>
    </justification>
  </clause>

  <clause id="738">
    <literal><![CDATA[
      x * T(x \ (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(17(a,1),418(a,1,2,1))].">
      <j1 rule="para" parents="17 418"/>
    </justification>
  </clause>

  <clause id="739">
    <literal><![CDATA[
      L(T(x \ 1,x),x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,107,a(flip),b,422,a),flip(a)].">
      <j1 rule="hyper" parents="320 107 422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="740">
    <literal><![CDATA[
      (1 / x) \ T(1 / x,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,422,a(flip),b,259,a)].">
      <j1 rule="hyper" parents="116 422 259"/>
    </justification>
  </clause>

  <clause id="741">
    <literal><![CDATA[
      x * ((x \ y) * T(z,y)) = L(z,x \ y,x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,237,a(flip),b,448,a),flip(a)].">
      <j1 rule="hyper" parents="58 237 448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="742">
    <literal><![CDATA[
      x \ (L(y,x \ z,x) * z) = (x \ z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,237,a(flip),b,448,a(flip))].">
      <j1 rule="hyper" parents="116 237 448"/>
    </justification>
  </clause>

  <clause id="743">
    <literal><![CDATA[
      x \ (y * ((y \ x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y \ x,y) = u
    ]]></literal>
    <justification jstring="[para(448(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="448 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="744">
    <literal><![CDATA[
      x * L(y,T(z,z \ x),z \ x) = (z \ x) * (((z \ x) \ x) * y)
    ]]></literal>
    <justification jstring="[para(106(a,2),448(a,1,2,2))].">
      <j1 rule="para" parents="106 448"/>
    </justification>
  </clause>

  <clause id="745">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,11,a,b,450,a)].">
      <j1 rule="hyper" parents="320 11 450"/>
    </justification>
  </clause>

  <clause id="746">
    <literal><![CDATA[
      L(T(x \ T(y,z),u),x,z) = T((z * x) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(450(a,1),20(a,2,1))].">
      <j1 rule="para" parents="450 20"/>
    </justification>
  </clause>

  <clause id="747">
    <literal><![CDATA[
      L(x \ T(x,y),x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(450(a,2),307(a,1))].">
      <j1 rule="para" parents="450 307"/>
    </justification>
  </clause>

  <clause id="748">
    <literal><![CDATA[
      L(x \ y,x,y / x) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(239,a,151,a(flip),b,472,a),flip(a)].">
      <j1 rule="hyper" parents="239 151 472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="749">
    <literal><![CDATA[
      (x / y) * (y * T(z,x)) = L(z,y,x / y) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,237,a(flip),b,472,a),flip(a)].">
      <j1 rule="hyper" parents="58 237 472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="750">
    <literal><![CDATA[
      (x / y) \ (L(z,y,x / y) * x) = y * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,237,a(flip),b,472,a(flip))].">
      <j1 rule="hyper" parents="116 237 472"/>
    </justification>
  </clause>

  <clause id="751">
    <literal><![CDATA[
      x \ (y * L(z,x \ y,x)) != (x \ y) * u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(474(a,2),38(a,1))].">
      <j1 rule="para" parents="474 38"/>
    </justification>
  </clause>

  <clause id="752">
    <literal><![CDATA[
      x \ (y * a(z,u,K(w,v5))) = (x \ y) * a(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(146(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="146 474"/>
    </justification>
  </clause>

  <clause id="753">
    <literal><![CDATA[
      L(T((x \ y) \ z,u),x \ y,x) = T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(490(a,1),20(a,2,1))].">
      <j1 rule="para" parents="490 20"/>
    </justification>
  </clause>

  <clause id="754">
    <literal><![CDATA[
      L(R((x \ y) \ z,u,w),x \ y,x) = R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(490(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="490 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="755">
    <literal><![CDATA[
      L(L((x \ y) \ z,u,w),x \ y,x) = L(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(490(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="490 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="756">
    <literal><![CDATA[
      L(x,y \ z,y) != z \ (y * u)
    ]]></literal>
    <literal><![CDATA[
      (y \ z) \ u = x
    ]]></literal>
    <justification jstring="[para(490(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="490 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="757">
    <literal><![CDATA[
      L(x \ y,x,y / x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y / x,y) = z
    ]]></literal>
    <justification jstring="[para(492(a,2),288(a,1))].">
      <j1 rule="para" parents="492 288"/>
    </justification>
  </clause>

  <clause id="758">
    <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(185(a,1),504(a,1,1,1))].">
      <j1 rule="para" parents="185 504"/>
    </justification>
  </clause>

  <clause id="759">
    <literal><![CDATA[
      (x * y) / ((z \ x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      R(z,z \ x,y) = u
    ]]></literal>
    <justification jstring="[para(505(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="505 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="760">
    <literal><![CDATA[
      L(R(x,y / z,z),u,w) * y = (L(x,u,w) * (y / z)) * z
    ]]></literal>
    <justification jstring="[para(24(a,1),508(a,1,1))].">
      <j1 rule="para" parents="24 508"/>
    </justification>
  </clause>

  <clause id="761">
    <literal><![CDATA[
      R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(525(a,1),22(a,2,1))].">
      <j1 rule="para" parents="525 22"/>
    </justification>
  </clause>

  <clause id="762">
    <literal><![CDATA[
      R(R(x / (y / z),u,w),y / z,z) = R((x * z) / y,u,w)
    ]]></literal>
    <justification jstring="[para(525(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="525 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="763">
    <literal><![CDATA[
      R(x / R(1 / y,y,z),z / (y * z),y * z) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[para(219(a,2),525(a,1,1,2))].">
      <j1 rule="para" parents="219 525"/>
    </justification>
  </clause>

  <clause id="764">
    <literal><![CDATA[
      R(x / (y / (z * y)),R(1 / z,z,y),z * y) = (x * (z * y)) / y
    ]]></literal>
    <justification jstring="[para(219(a,2),525(a,1,2))].">
      <j1 rule="para" parents="219 525"/>
    </justification>
  </clause>

  <clause id="765">
    <literal><![CDATA[
      R((x / y) \ z,x / y,y) = T((z * y) / x,x / y)
    ]]></literal>
    <justification jstring="[para(525(a,1),248(a,1,1)),flip(a)].">
      <j1 rule="para" parents="525 248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="766">
    <literal><![CDATA[
      T(x,y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(x,y) = u
    ]]></literal>
    <justification jstring="[para(17(a,2),535(a,1))].">
      <j1 rule="para" parents="17 535"/>
    </justification>
  </clause>

  <clause id="767">
    <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(544(a,1),421(a,1,1))].">
      <j1 rule="para" parents="544 421"/>
    </justification>
  </clause>

  <clause id="768">
    <literal><![CDATA[
      (x * (y * z)) / u != x * z
    ]]></literal>
    <literal><![CDATA[
      L(T(y,z),z,x) = u
    ]]></literal>
    <justification jstring="[para(545(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="545 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="769">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(z,y),y,x) = u
    ]]></literal>
    <justification jstring="[para(545(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="545 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="770">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) * x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,739,a(flip),b,554,a),flip(a)].">
      <j1 rule="hyper" parents="58 739 554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="771">
    <literal><![CDATA[
      T(L(x,y,1 / y),y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,20,a(flip),b,554,a)].">
      <j1 rule="hyper" parents="58 20 554"/>
    </justification>
  </clause>

  <clause id="772">
    <literal><![CDATA[
      (1 / x) \ T(L(y,x,1 / x),x) = y * x
    ]]></literal>
    <justification jstring="[hyper(116,a,20,a(flip),b,554,a(flip))].">
      <j1 rule="hyper" parents="116 20 554"/>
    </justification>
  </clause>

  <clause id="773">
    <literal><![CDATA[
      (1 / (1 / x)) * (x * (1 / x)) = (1 / x) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),770(a,1,2,1))].">
      <j1 rule="para" parents="75 770"/>
    </justification>
  </clause>

  <clause id="774">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,x) = x \ 1
    ]]></literal>
    <justification jstring="[para(258(a,2),770(a,1,2))].">
      <j1 rule="para" parents="258 770"/>
    </justification>
  </clause>

  <clause id="775">
    <literal><![CDATA[
      (1 / x) \ (x \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,774,a)].">
      <j1 rule="hyper" parents="123 774"/>
    </justification>
  </clause>

  <clause id="776">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = x \ ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,774,a(flip),b,183,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 774 183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="777">
    <literal><![CDATA[
      (x \ 1) \ ((1 / x) * (K(x \ 1,x) * y)) = L(y,K(x \ 1,x),1 / x)
    ]]></literal>
    <justification jstring="[para(774(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="774 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="778">
    <literal><![CDATA[
      (x * (y \ 1)) / L(K(y \ 1,y),1 / y,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(774(a,1),186(a,1,1,2))].">
      <j1 rule="para" parents="774 186"/>
    </justification>
  </clause>

  <clause id="779">
    <literal><![CDATA[
      x / L(K(y \ 1,y),1 / y,x / (y \ 1)) = (x / (y \ 1)) * (1 / y)
    ]]></literal>
    <justification jstring="[para(775(a,1),498(a,1,2,1))].">
      <j1 rule="para" parents="775 498"/>
    </justification>
  </clause>

  <clause id="780">
    <literal><![CDATA[
      T(x / y,y) != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * (y \ x) = u
    ]]></literal>
    <justification jstring="[para(457(a,1),628(a,2)),flip(a)].">
      <j1 rule="para" parents="457 628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="781">
    <literal><![CDATA[
      R(x,y,z) = T(((y * x) * z) / (y * z),y)
    ]]></literal>
    <justification jstring="[para(4(a,1),647(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4 647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="782">
    <literal><![CDATA[
      T(x / (y * z),y) * (y * z) = ((y \ (x / z)) * y) * z
    ]]></literal>
    <justification jstring="[para(648(a,1),101(a,1,1))].">
      <j1 rule="para" parents="648 101"/>
    </justification>
  </clause>

  <clause id="783">
    <literal><![CDATA[
      ((x \ y) * x) * (x \ 1) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,261,a,b,650,a)].">
      <j1 rule="hyper" parents="58 261 650"/>
    </justification>
  </clause>

  <clause id="784">
    <literal><![CDATA[
      T((x * y) * (x \ 1),x) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),650(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="785">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,x / y,y) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),651(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="786">
    <literal><![CDATA[
      (x * R(x \ 1,x,y)) \ (x * (y / (x * y))) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x * y)) = z
    ]]></literal>
    <justification jstring="[para(651(a,1),307(a,1,1))].">
      <j1 rule="para" parents="651 307"/>
    </justification>
  </clause>

  <clause id="787">
    <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(647(a,1),678(a,1,1))].">
      <j1 rule="para" parents="647 678"/>
    </justification>
  </clause>

  <clause id="788">
    <literal><![CDATA[
      T((((x * y) / x) \ z) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,((x * y) / x) \ z) = u
    ]]></literal>
    <justification jstring="[para(106(a,1),681(a,1,1))].">
      <j1 rule="para" parents="106 681"/>
    </justification>
  </clause>

  <clause id="789">
    <literal><![CDATA[
      (x * y) * (y \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(689(a,1),38(a,1))].">
      <j1 rule="para" parents="689 38"/>
    </justification>
  </clause>

  <clause id="790">
    <literal><![CDATA[
      x \ ((x * y) * (y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(689(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="689 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="791">
    <literal><![CDATA[
      T(L(x,y \ z,y),y \ z) = z \ (y * (x * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(350,a,709,a),flip(a)].">
      <j1 rule="hyper" parents="350 709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="792">
    <literal><![CDATA[
      T(L(x,y,z / y),y) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[para(7(a,1),709(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="793">
    <literal><![CDATA[
      T(L(x,y \ z,y),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      z \ (y * (x * (y \ z))) = u
    ]]></literal>
    <justification jstring="[para(709(a,1),350(a,1))].">
      <j1 rule="para" parents="709 350"/>
    </justification>
  </clause>

  <clause id="794">
    <literal><![CDATA[
      (x * y) * T(T(x,x * y),z) = x * (y * T(T(x,y),z))
    ]]></literal>
    <justification jstring="[hyper(119,a,712,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 712 13"/>
    </justification>
  </clause>

  <clause id="795">
    <literal><![CDATA[
      T((1 / x) * (x * y),x) = (1 / x) * (y * x)
    ]]></literal>
    <justification jstring="[para(259(a,2),771(a,1,1))].">
      <j1 rule="para" parents="259 771"/>
    </justification>
  </clause>

  <clause id="796">
    <literal><![CDATA[
      (1 / x) * ((x \ y) * x) = T((1 / x) * y,x)
    ]]></literal>
    <justification jstring="[para(488(a,1),771(a,1,1)),flip(a)].">
      <j1 rule="para" parents="488 771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="797">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) * y,x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(488(a,1),772(a,1,2,1))].">
      <j1 rule="para" parents="488 772"/>
    </justification>
  </clause>

  <clause id="798">
    <literal><![CDATA[
      (((x * y) * z) / (x * z)) * x = x * R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,781,a,b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 781 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="799">
    <literal><![CDATA[
      T(x,y) != R(z,y,u)
    ]]></literal>
    <literal><![CDATA[
      ((y * z) * u) / (y * u) = x
    ]]></literal>
    <justification jstring="[para(781(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="781 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="800">
    <literal><![CDATA[
      T(((1 / x) * y) * x,1 / x) = R(y,1 / x,x)
    ]]></literal>
    <justification jstring="[para(170(a,1),781(a,2,1)),flip(a)].">
      <j1 rule="para" parents="170 781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="801">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = T(R(z,x,y),x * y)
    ]]></literal>
    <justification jstring="[para(781(a,2),246(a,1,1)),flip(a)].">
      <j1 rule="para" parents="781 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="802">
    <literal><![CDATA[
      T(R(x,y,x),y * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(781(a,2),270(a,1,1))].">
      <j1 rule="para" parents="781 270"/>
    </justification>
  </clause>

  <clause id="803">
    <literal><![CDATA[
      R(T(x,y * x),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,22,a,b,802,a)].">
      <j1 rule="hyper" parents="58 22 802"/>
    </justification>
  </clause>

  <clause id="804">
    <literal><![CDATA[
      L(R(x,y,x),z,u) * (y * x) = (y * x) * L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(802(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="802 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="805">
    <literal><![CDATA[
      R(R(x,y,x),z,u) * (y * x) = (y * x) * R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(802(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="802 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="806">
    <literal><![CDATA[
      R(x,y,z) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      T(z,y * z) = x
    ]]></literal>
    <justification jstring="[para(802(a,1),143(a,1)),flip(a)].">
      <j1 rule="para" parents="802 143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="807">
    <literal><![CDATA[
      ((x * T(y,x * y)) * y) / (x * y) = y
    ]]></literal>
    <justification jstring="[hyper(35,a,781,a(flip),b,803,a(flip))].">
      <j1 rule="hyper" parents="35 781 803"/>
    </justification>
  </clause>

  <clause id="808">
    <literal><![CDATA[
      R(T(x,y),y / x,x) = T(x,y / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),803(a,1,1,2))].">
      <j1 rule="para" parents="7 803"/>
    </justification>
  </clause>

  <clause id="809">
    <literal><![CDATA[
      (T(x,y * x) * y) * x = T(x,y) * (y * x)
    ]]></literal>
    <justification jstring="[para(803(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="803 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="810">
    <literal><![CDATA[
      R(x,y / z,z) != T(z,y / z)
    ]]></literal>
    <literal><![CDATA[
      T(z,y) = x
    ]]></literal>
    <justification jstring="[para(808(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="808 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="811">
    <literal><![CDATA[
      R(x,1 / x,x) = T(x,1 / x)
    ]]></literal>
    <justification jstring="[para(198(a,1),808(a,1,1))].">
      <j1 rule="para" parents="198 808"/>
    </justification>
  </clause>

  <clause id="812">
    <literal><![CDATA[
      T(x,1 / x) / x = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,811,a(flip),b,262,a)].">
      <j1 rule="hyper" parents="117 811 262"/>
    </justification>
  </clause>

  <clause id="813">
    <literal><![CDATA[
      R(R(x,y,z),1 / x,x) = R(T(x,1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(811(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="811 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="814">
    <literal><![CDATA[
      T(x,1 / x) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,260,a,b,812,a),flip(a)].">
      <j1 rule="hyper" parents="320 260 812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="815">
    <literal><![CDATA[
      K(x,1 / x) * x = T(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(133,a,814,a)].">
      <j1 rule="hyper" parents="133 814"/>
    </justification>
  </clause>

  <clause id="816">
    <literal><![CDATA[
      T(x * T(y,x * y),y) = x * y
    ]]></literal>
    <justification jstring="[hyper(266,a,807,a)].">
      <j1 rule="hyper" parents="266 807"/>
    </justification>
  </clause>

  <clause id="817">
    <literal><![CDATA[
      (x * (y * x)) / x = y * T(x,y * x)
    ]]></literal>
    <justification jstring="[para(807(a,1),78(a,1,1,1))].">
      <j1 rule="para" parents="807 78"/>
    </justification>
  </clause>

  <clause id="818">
    <literal><![CDATA[
      (x * R(y,x,x \ 1)) / x = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(271,a,784,a)].">
      <j1 rule="hyper" parents="271 784"/>
    </justification>
  </clause>

  <clause id="819">
    <literal><![CDATA[
      R(T(T(x,y),z),u,w) = T(T(R(x,u,w),z),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,22,a,b,111,a)].">
      <j1 rule="hyper" parents="320 22 111"/>
    </justification>
  </clause>

  <clause id="820">
    <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),283(a,1,2))].">
      <j1 rule="para" parents="105 283"/>
    </justification>
  </clause>

  <clause id="821">
    <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),286(a,1,2))].">
      <j1 rule="para" parents="24 286"/>
    </justification>
  </clause>

  <clause id="822">
    <literal><![CDATA[
      K(x \ 1,x) * L(y,x,x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * (x * y) = z
    ]]></literal>
    <justification jstring="[para(258(a,2),286(a,1,1))].">
      <j1 rule="para" parents="258 286"/>
    </justification>
  </clause>

  <clause id="823">
    <literal><![CDATA[
      L(T(x,x \ y),z,u) = L((x \ y) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,20,a,b,317,a)].">
      <j1 rule="hyper" parents="58 20 317"/>
    </justification>
  </clause>

  <clause id="824">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = R((x \ y) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,22,a,b,318,a)].">
      <j1 rule="hyper" parents="58 22 318"/>
    </justification>
  </clause>

  <clause id="825">
    <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),334(a,1,1))].">
      <j1 rule="para" parents="7 334"/>
    </justification>
  </clause>

  <clause id="826">
    <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(146(a,1),480(a,1,2))].">
      <j1 rule="para" parents="146 480"/>
    </justification>
  </clause>

  <clause id="827">
    <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),482(a,1,1))].">
      <j1 rule="para" parents="105 482"/>
    </justification>
  </clause>

  <clause id="828">
    <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),482(a,1,2,2))].">
      <j1 rule="para" parents="90 482"/>
    </justification>
  </clause>

  <clause id="829">
    <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(314(a,2),482(a,1,1))].">
      <j1 rule="para" parents="314 482"/>
    </justification>
  </clause>

  <clause id="830">
    <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),482(a,1,2,2))].">
      <j1 rule="para" parents="80 482"/>
    </justification>
  </clause>

  <clause id="831">
    <literal><![CDATA[
      x * K(x \ 1,x) != y
    ]]></literal>
    <literal><![CDATA[
      L(x,x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(258(a,2),485(a,1,2))].">
      <j1 rule="para" parents="258 485"/>
    </justification>
  </clause>

  <clause id="832">
    <literal><![CDATA[
      L(x,x \ 1,x) != y
    ]]></literal>
    <literal><![CDATA[
      x * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(360(a,1),499(a,1,1))].">
      <j1 rule="para" parents="360 499"/>
    </justification>
  </clause>

  <clause id="833">
    <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),515(a,2,2))].">
      <j1 rule="para" parents="84 515"/>
    </justification>
  </clause>

  <clause id="834">
    <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(774(a,1),515(a,2,2))].">
      <j1 rule="para" parents="774 515"/>
    </justification>
  </clause>

  <clause id="835">
    <literal><![CDATA[
      x / (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      R((x / z) / y,y,z) = u
    ]]></literal>
    <justification jstring="[para(79(a,1),518(a,1,1))].">
      <j1 rule="para" parents="79 518"/>
    </justification>
  </clause>

  <clause id="836">
    <literal><![CDATA[
      x * y != 1
    ]]></literal>
    <literal><![CDATA[
      (z * x) * y = R(z,x,y)
    ]]></literal>
    <justification jstring="[para(61(a,1),539(a,1)),flip(a)].">
      <j1 rule="para" parents="61 539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="837">
    <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),552(a,1,2))].">
      <j1 rule="para" parents="20 552"/>
    </justification>
  </clause>

  <clause id="838">
    <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),603(a,1,2))].">
      <j1 rule="para" parents="25 603"/>
    </justification>
  </clause>

  <clause id="839">
    <literal><![CDATA[
      R(x / y,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) / (y * z) = u
    ]]></literal>
    <justification jstring="[para(6(a,1),621(a,1,1,1))].">
      <j1 rule="para" parents="6 621"/>
    </justification>
  </clause>

  <clause id="840">
    <literal><![CDATA[
      (x * ((y * x) \ y)) / x = L(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,395,a(flip),b,635,a)].">
      <j1 rule="hyper" parents="117 395 635"/>
    </justification>
  </clause>

  <clause id="841">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) * (x \ y) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(390(a,1),635(a,2,2))].">
      <j1 rule="para" parents="390 635"/>
    </justification>
  </clause>

  <clause id="842">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) / (x \ y) = L(1 / (x \ y),x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),840(a,1,1,2,1))].">
      <j1 rule="para" parents="5 840"/>
    </justification>
  </clause>

  <clause id="843">
    <literal><![CDATA[
      L((x * y) / x,z,u) = (x * L(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,636,a),flip(a)].">
      <j1 rule="hyper" parents="131 636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="844">
    <literal><![CDATA[
      L((x * (y \ 1)) / x,y,z) = (x * ((z * y) \ z)) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,395,a(flip),b,636,a),flip(a)].">
      <j1 rule="hyper" parents="117 395 636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="845">
    <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,636,a),flip(a)].">
      <j1 rule="hyper" parents="117 90 636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="846">
    <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(305(a,1),639(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="305 639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="847">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,x,y) != u
    ]]></literal>
    <literal><![CDATA[
      ((z / (x * y)) * x) * y = u
    ]]></literal>
    <justification jstring="[para(639(a,1),283(a,1))].">
      <j1 rule="para" parents="639 283"/>
    </justification>
  </clause>

  <clause id="848">
    <literal><![CDATA[
      ((((x * y) * z) / (x * y)) * x) * y = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(283,a,640,a)].">
      <j1 rule="hyper" parents="283 640"/>
    </justification>
  </clause>

  <clause id="849">
    <literal><![CDATA[
      R((x * y) / x,z,u) = (x * R(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,640,a),flip(a)].">
      <j1 rule="hyper" parents="131 640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="850">
    <literal><![CDATA[
      R((x * (1 / y)) / x,y,z) = (x * (z / (y * z))) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,404,a(flip),b,640,a),flip(a)].">
      <j1 rule="hyper" parents="117 404 640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="851">
    <literal><![CDATA[
      (((x * y) / x) * z) * (z \ x) = x * R(y,z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,368,a(flip),b,640,a)].">
      <j1 rule="hyper" parents="58 368 640"/>
    </justification>
  </clause>

  <clause id="852">
    <literal><![CDATA[
      ((x * y) * R(z,x,y)) / y = (((x * y) * z) / (x * y)) * x
    ]]></literal>
    <justification jstring="[hyper(117,a,640,a(flip),b,101,a(flip))].">
      <j1 rule="hyper" parents="117 640 101"/>
    </justification>
  </clause>

  <clause id="853">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) / (x / y) = L(x / (x / y),z,u)
    ]]></literal>
    <justification jstring="[para(75(a,1),643(a,1,1,2,1))].">
      <j1 rule="para" parents="75 643"/>
    </justification>
  </clause>

  <clause id="854">
    <literal><![CDATA[
      L(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(643(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="643 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="855">
    <literal><![CDATA[
      T(L(x / y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(643(a,1),292(a,1,1)),flip(b)].">
      <j1 rule="para" parents="643 292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="856">
    <literal><![CDATA[
      (x * ((y * x) \ (y * z))) / x = L(z / x,x,y)
    ]]></literal>
    <justification jstring="[para(92(a,1),643(a,1,1,2))].">
      <j1 rule="para" parents="92 643"/>
    </justification>
  </clause>

  <clause id="857">
    <literal><![CDATA[
      L((x \ y) / z,z,x) = (z * ((x * z) \ y)) / z
    ]]></literal>
    <justification jstring="[para(298(a,1),643(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="298 643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="858">
    <literal><![CDATA[
      (x * ((1 / x) * y)) / x = L(y / x,x,1 / x)
    ]]></literal>
    <justification jstring="[para(488(a,1),643(a,1,1,2))].">
      <j1 rule="para" parents="488 643"/>
    </justification>
  </clause>

  <clause id="859">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) / (x \ 1) = L(y / (x \ 1),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(489(a,1),643(a,1,1,2))].">
      <j1 rule="para" parents="489 643"/>
    </justification>
  </clause>

  <clause id="860">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[para(745(a,2),643(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="745 643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="861">
    <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),644(a,1,1,2,1))].">
      <j1 rule="para" parents="13 644"/>
    </justification>
  </clause>

  <clause id="862">
    <literal><![CDATA[
      R(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * R(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(644(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="644 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="863">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / x = (y * (z / x)) / y
    ]]></literal>
    <justification jstring="[hyper(271,a,679,a)].">
      <j1 rule="hyper" parents="271 679"/>
    </justification>
  </clause>

  <clause id="864">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,679,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 679 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="865">
    <literal><![CDATA[
      ((x * (y / z)) / x) \ (z * ((x * (z \ y)) / x)) = z
    ]]></literal>
    <justification jstring="[para(679(a,1),226(a,1,2,2))].">
      <j1 rule="para" parents="679 226"/>
    </justification>
  </clause>

  <clause id="866">
    <literal><![CDATA[
      T(T(1 / ((x * y) \ x),z),y) = T(1 / ((x * y) \ x),z)
    ]]></literal>
    <justification jstring="[para(682(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="682 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="867">
    <literal><![CDATA[
      (1 / (1 / x)) * (x * (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,75,a(flip),b,773,a),flip(a)].">
      <j1 rule="hyper" parents="320 75 773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="869">
    <literal><![CDATA[
      (1 / (1 / x)) * K(x,1 / x) = x
    ]]></literal>
    <justification jstring="[para(260(a,2),867(a,1,2))].">
      <j1 rule="para" parents="260 867"/>
    </justification>
  </clause>

  <clause id="870">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) * x = (1 / x) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),797(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="871">
    <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),819(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="107 819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="872">
    <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,824,a,b,309,a)].">
      <j1 rule="hyper" parents="116 824 309"/>
    </justification>
  </clause>

  <clause id="873">
    <literal><![CDATA[
      x \ R(T(y,y \ z),u,w) = x \ R((y \ z) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(116,a,824,a,b,5,a)].">
      <j1 rule="hyper" parents="116 824 5"/>
    </justification>
  </clause>

  <clause id="874">
    <literal><![CDATA[
      R(x,x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * z) / ((x \ y) * z) = u
    ]]></literal>
    <justification jstring="[para(72(a,1),839(a,1,1))].">
      <j1 rule="para" parents="72 839"/>
    </justification>
  </clause>

  <clause id="875">
    <literal><![CDATA[
      (x * y) * ((z * L(u,y,x)) / z) = x * (y * ((z * u) / z))
    ]]></literal>
    <justification jstring="[hyper(119,a,843,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 843 13"/>
    </justification>
  </clause>

  <clause id="876">
    <literal><![CDATA[
      L((x * y) / x,z,u) != w / x
    ]]></literal>
    <literal><![CDATA[
      x * L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(843(a,2),41(a,1))].">
      <j1 rule="para" parents="843 41"/>
    </justification>
  </clause>

  <clause id="877">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x != w
    ]]></literal>
    <literal><![CDATA[
      x * L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(843(a,2),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="843 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="878">
    <literal><![CDATA[
      L((x * (y \ z)) / x,y,u) = (x * ((u * y) \ (u * z))) / x
    ]]></literal>
    <justification jstring="[para(92(a,1),843(a,2,1,2))].">
      <j1 rule="para" parents="92 843"/>
    </justification>
  </clause>

  <clause id="879">
    <literal><![CDATA[
      L((x * (y \ (z \ u))) / x,y,z) = (x * ((z * y) \ u)) / x
    ]]></literal>
    <justification jstring="[para(298(a,1),843(a,2,1,2))].">
      <j1 rule="para" parents="298 843"/>
    </justification>
  </clause>

  <clause id="880">
    <literal><![CDATA[
      L((x * (y \ 1)) / x,y,z / y) = (x * (z \ (z / y))) / x
    ]]></literal>
    <justification jstring="[para(399(a,1),843(a,2,1,2))].">
      <j1 rule="para" parents="399 843"/>
    </justification>
  </clause>

  <clause id="881">
    <literal><![CDATA[
      L((x * (y \ z)) / x,y,1 / y) = (x * ((1 / y) * z)) / x
    ]]></literal>
    <justification jstring="[para(488(a,1),843(a,2,1,2))].">
      <j1 rule="para" parents="488 843"/>
    </justification>
  </clause>

  <clause id="882">
    <literal><![CDATA[
      L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x
    ]]></literal>
    <justification jstring="[para(490(a,1),843(a,2,1,2))].">
      <j1 rule="para" parents="490 843"/>
    </justification>
  </clause>

  <clause id="883">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x != w
    ]]></literal>
    <literal><![CDATA[
      x * R(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(849(a,2),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="849 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="884">
    <literal><![CDATA[
      R((x * ((y / z) / u)) / x,u,z) = (x * (y / (u * z))) / x
    ]]></literal>
    <justification jstring="[para(301(a,1),849(a,2,1,2))].">
      <j1 rule="para" parents="301 849"/>
    </justification>
  </clause>

  <clause id="885">
    <literal><![CDATA[
      R((x * (y / (1 / z))) / x,1 / z,z) = (x * (y * z)) / x
    ]]></literal>
    <justification jstring="[para(522(a,1),849(a,2,1,2))].">
      <j1 rule="para" parents="522 849"/>
    </justification>
  </clause>

  <clause id="886">
    <literal><![CDATA[
      R((x * (y / z)) / x,z,z \ 1) = (x * (y * (z \ 1))) / x
    ]]></literal>
    <justification jstring="[para(523(a,1),849(a,2,1,2))].">
      <j1 rule="para" parents="523 849"/>
    </justification>
  </clause>

  <clause id="887">
    <literal><![CDATA[
      ((x * R(y,z,u)) / x) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      (((x * y) / x) * z) * u = w
    ]]></literal>
    <justification jstring="[para(849(a,1),283(a,1,1))].">
      <j1 rule="para" parents="849 283"/>
    </justification>
  </clause>

  <clause id="888">
    <literal><![CDATA[
      ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((1 / x) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(116,a,870,a(flip),b,302,a)].">
      <j1 rule="hyper" parents="116 870 302"/>
    </justification>
  </clause>

  <clause id="889">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,a(w,v5,v6))) = y * a(z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(167,a,81,a,b,28,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 81 28"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="890">
    <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),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="83 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="891">
    <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),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="99 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="892">
    <literal><![CDATA[
      L(R(a(x,y,a(z,u,w)),v5,v6),v7,v8) = R(a(x,y,a(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(145(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="145 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="893">
    <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(145(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="145 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="894">
    <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(145(a,1),480(a,1,2))].">
      <j1 rule="para" parents="145 480"/>
    </justification>
  </clause>

  <clause id="895">
    <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,231,a)].">
      <j1 rule="hyper" parents="119 25 231"/>
    </justification>
  </clause>

  <clause id="896">
    <literal><![CDATA[
      T(((x * y) * x) / (x * y),y) = R(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,460,a(flip),b,234,a)].">
      <j1 rule="hyper" parents="58 460 234"/>
    </justification>
  </clause>

  <clause id="897">
    <literal><![CDATA[
      T(R(x,y,T(x,y)),x * y) = T(x,y)
    ]]></literal>
    <justification jstring="[para(234(a,1),224(a,1,1))].">
      <j1 rule="para" parents="234 224"/>
    </justification>
  </clause>

  <clause id="898">
    <literal><![CDATA[
      T(R(x,y,T(x,y)),z) * (x * y) = (x * y) * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(234(a,1),454(a,1,1,1))].">
      <j1 rule="para" parents="234 454"/>
    </justification>
  </clause>

  <clause id="899">
    <literal><![CDATA[
      R(T(x,x * y),y,T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,22,a,b,897,a)].">
      <j1 rule="hyper" parents="58 22 897"/>
    </justification>
  </clause>

  <clause id="900">
    <literal><![CDATA[
      T(x,y * z) != T(y,z)
    ]]></literal>
    <literal><![CDATA[
      R(y,z,T(y,z)) = x
    ]]></literal>
    <justification jstring="[para(897(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="897 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="901">
    <literal><![CDATA[
      (x * y) * T(y,x) = (y * x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,802,a(flip),b,245,a)].">
      <j1 rule="hyper" parents="119 802 245"/>
    </justification>
  </clause>

  <clause id="902">
    <literal><![CDATA[
      (x * (y / x)) * x = y * T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(326,a,901,a),flip(a)].">
      <j1 rule="hyper" parents="326 901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="903">
    <literal><![CDATA[
      (x * (y / x)) \ (y * (y / x)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,147,a(flip),b,901,a)].">
      <j1 rule="hyper" parents="116 147 901"/>
    </justification>
  </clause>

  <clause id="904">
    <literal><![CDATA[
      ((x \ 1) * x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,64,a(flip),b,901,a)].">
      <j1 rule="hyper" parents="116 64 901"/>
    </justification>
  </clause>

  <clause id="905">
    <literal><![CDATA[
      (T(x,y) * (y * x)) \ ((x * y) * x) = K(y * x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,901,a(flip),b,84,a)].">
      <j1 rule="hyper" parents="116 901 84"/>
    </justification>
  </clause>

  <clause id="906">
    <literal><![CDATA[
      K(x \ 1,x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(258(a,2),904(a,1,1))].">
      <j1 rule="para" parents="258 904"/>
    </justification>
  </clause>

  <clause id="907">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,106,a(flip),b,906,a)].">
      <j1 rule="hyper" parents="119 106 906"/>
    </justification>
  </clause>

  <clause id="908">
    <literal><![CDATA[
      (x * y) \ (y * T(x,y / x)) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[para(902(a,1),82(a,1,2))].">
      <j1 rule="para" parents="902 82"/>
    </justification>
  </clause>

  <clause id="909">
    <literal><![CDATA[
      ((x / y) * (x / (x / y))) * y = x * (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(119,a,244,a(flip),b,903,a)].">
      <j1 rule="hyper" parents="119 244 903"/>
    </justification>
  </clause>

  <clause id="910">
    <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,401,a,b,231,a)].">
      <j1 rule="hyper" parents="119 401 231"/>
    </justification>
  </clause>

  <clause id="911">
    <literal><![CDATA[
      (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,401,a,b,13,a(flip))].">
      <j1 rule="hyper" parents="119 401 13"/>
    </justification>
  </clause>

  <clause id="912">
    <literal><![CDATA[
      L(L(x \ 1,y * x,z),x,y) = (z * (y * x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,92,a(flip),b,402,a),flip(a)].">
      <j1 rule="hyper" parents="320 92 402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="913">
    <literal><![CDATA[
      (x * y) * L((x * y) \ x,z,u) = x * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,402,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 402 13"/>
    </justification>
  </clause>

  <clause id="914">
    <literal><![CDATA[
      L((x * (y \ z)) \ x,y \ z,y) = L(z \ y,y \ z,x)
    ]]></literal>
    <justification jstring="[para(390(a,1),402(a,1,1)),flip(a)].">
      <j1 rule="para" parents="390 402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="915">
    <literal><![CDATA[
      R(x / (y * x),z,u) * (y * x) = (R(1 / y,z,u) * y) * x
    ]]></literal>
    <justification jstring="[para(411(a,1),101(a,1,1))].">
      <j1 rule="para" parents="411 101"/>
    </justification>
  </clause>

  <clause id="916">
    <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),419(a,1,2,1))].">
      <j1 rule="para" parents="17 419"/>
    </justification>
  </clause>

  <clause id="917">
    <literal><![CDATA[
      (x / y) * R(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x / (x / y),z,u) * (x / y) = w
    ]]></literal>
    <justification jstring="[para(244(a,1),420(a,1,2,1))].">
      <j1 rule="para" parents="244 420"/>
    </justification>
  </clause>

  <clause id="918">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(92(a,1),449(a,1,2,1))].">
      <j1 rule="para" parents="92 449"/>
    </justification>
  </clause>

  <clause id="919">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,u) = x * (y * T(y \ (x \ z),u))
    ]]></literal>
    <justification jstring="[para(298(a,1),449(a,1,2,1))].">
      <j1 rule="para" parents="298 449"/>
    </justification>
  </clause>

  <clause id="920">
    <literal><![CDATA[
      x * (T(y,x) * T(z,y * x)) = L(z,T(y,x),x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(419,a,481,a),flip(a)].">
      <j1 rule="hyper" parents="419 481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="921">
    <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),494(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="105 494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="922">
    <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(494(a,2),286(a,1,2))].">
      <j1 rule="para" parents="494 286"/>
    </justification>
  </clause>

  <clause id="923">
    <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(496(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="496 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="924">
    <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(496(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="496 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="925">
    <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),512(a,1,2))].">
      <j1 rule="para" parents="105 512"/>
    </justification>
  </clause>

  <clause id="926">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = T(x / (z * y),u) * (z * y)
    ]]></literal>
    <justification jstring="[para(301(a,1),512(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="301 512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="927">
    <literal><![CDATA[
      (T(x,x * y) * y) * T(x,y) = T(x,y) * (x * y)
    ]]></literal>
    <justification jstring="[para(899(a,1),516(a,1,1)),flip(a)].">
      <j1 rule="para" parents="899 516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="928">
    <literal><![CDATA[
      R(T(x / y,y * z),y,z) = (y * z) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(421,a,526,a),flip(a)].">
      <j1 rule="hyper" parents="421 526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="929">
    <literal><![CDATA[
      R(T(x / y,y * z),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * z) \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(526(a,1),421(a,1))].">
      <j1 rule="para" parents="526 421"/>
    </justification>
  </clause>

  <clause id="930">
    <literal><![CDATA[
      R(T(T(x / y,z),y * u),y,u) = T((y * u) \ (x * u),z)
    ]]></literal>
    <justification jstring="[para(528(a,1),819(a,2,1))].">
      <j1 rule="para" parents="528 819"/>
    </justification>
  </clause>

  <clause id="931">
    <literal><![CDATA[
      R(x,T(y,x),T(z,y * x)) \ (z * (y * x)) = T(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(105(a,1),540(a,1,2))].">
      <j1 rule="para" parents="105 540"/>
    </justification>
  </clause>

  <clause id="932">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(489(a,1),549(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="489 549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="933">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = T(x / y,z) * y
    ]]></literal>
    <justification jstring="[para(523(a,1),558(a,1,1,1))].">
      <j1 rule="para" parents="523 558"/>
    </justification>
  </clause>

  <clause id="934">
    <literal><![CDATA[
      T(x / (1 / y),z) * (1 / y) = T(x * y,z) / y
    ]]></literal>
    <justification jstring="[para(522(a,1),563(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="522 563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="935">
    <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(564(a,1),286(a,1,2))].">
      <j1 rule="para" parents="564 286"/>
    </justification>
  </clause>

  <clause id="936">
    <literal><![CDATA[
      R(1 / x,x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) / y = z
    ]]></literal>
    <justification jstring="[para(591(a,1),208(a,1))].">
      <j1 rule="para" parents="591 208"/>
    </justification>
  </clause>

  <clause id="937">
    <literal><![CDATA[
      T((x \ y) / y,z) * y = (T(1 / x,z) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(592(a,2),368(a,1,1))].">
      <j1 rule="para" parents="592 368"/>
    </justification>
  </clause>

  <clause id="938">
    <literal><![CDATA[
      (1 / x) * (x * T(x \ y,z)) = T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[hyper(387,a,606,a)].">
      <j1 rule="hyper" parents="387 606"/>
    </justification>
  </clause>

  <clause id="939">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) * y,z) = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,606,a(flip),b,259,a)].">
      <j1 rule="hyper" parents="116 606 259"/>
    </justification>
  </clause>

  <clause id="940">
    <literal><![CDATA[
      x * (((x \ 1) \ y) * (x \ 1)) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,551,a(flip),b,607,a)].">
      <j1 rule="hyper" parents="58 551 607"/>
    </justification>
  </clause>

  <clause id="941">
    <literal><![CDATA[
      x \ T(x * y,x \ 1) = ((x \ 1) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,607,a(flip),b,551,a(flip))].">
      <j1 rule="hyper" parents="116 607 551"/>
    </justification>
  </clause>

  <clause id="942">
    <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),630(a,1,2)),flip(a)].">
      <j1 rule="para" parents="80 630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="943">
    <literal><![CDATA[
      x \ (((x * y) \ x) * (x * y)) = y * T(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(116,a,396,a(flip),b,631,a)].">
      <j1 rule="hyper" parents="116 396 631"/>
    </justification>
  </clause>

  <clause id="944">
    <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),676(a,1,1))].">
      <j1 rule="para" parents="106 676"/>
    </justification>
  </clause>

  <clause id="945">
    <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),677(a,1,1,1))].">
      <j1 rule="para" parents="72 677"/>
    </justification>
  </clause>

  <clause id="946">
    <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),680(a,1,1,1,1))].">
      <j1 rule="para" parents="7 680"/>
    </justification>
  </clause>

  <clause id="947">
    <literal><![CDATA[
      (x * y) / a(z,z \ y,T(x,y)) = z * ((z \ y) * T(x,y))
    ]]></literal>
    <justification jstring="[para(105(a,1),686(a,1,1))].">
      <j1 rule="para" parents="105 686"/>
    </justification>
  </clause>

  <clause id="948">
    <literal><![CDATA[
      ((x * y) * (y \ z)) / T(x * z,a(x,y,y \ z)) = a(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(279,a,688,a)].">
      <j1 rule="hyper" parents="279 688"/>
    </justification>
  </clause>

  <clause id="949">
    <literal><![CDATA[
      (x / y) * ((y \ 1) * y) = x * T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[hyper(119,a,589,a,b,695,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 589 695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="950">
    <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),713(a,1,1))].">
      <j1 rule="para" parents="22 713"/>
    </justification>
  </clause>

  <clause id="951">
    <literal><![CDATA[
      T(L(L(x,y,x),z,u),y) = T(L(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,20,a(flip),b,718,a),flip(a)].">
      <j1 rule="hyper" parents="320 20 718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="952">
    <literal><![CDATA[
      ((x \ T(x,y)) * x) / (x \ T(x,y)) = L(x,x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,273,a(flip),b,722,a)].">
      <j1 rule="hyper" parents="58 273 722"/>
    </justification>
  </clause>

  <clause id="953">
    <literal><![CDATA[
      L(x,x \ y,x) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(722(a,1),680(a,1,1))].">
      <j1 rule="para" parents="722 680"/>
    </justification>
  </clause>

  <clause id="954">
    <literal><![CDATA[
      T(T((x * y) / x,z),y * x) = L(T(y,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,20,a,b,723,a),flip(a)].">
      <j1 rule="hyper" parents="320 20 723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="955">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ z) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,22,a,b,725,a)].">
      <j1 rule="hyper" parents="58 22 725"/>
    </justification>
  </clause>

  <clause id="956">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,y) = x \ ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(390(a,1),742(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="390 742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="957">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ z,y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[para(490(a,1),742(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="490 742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="958">
    <literal><![CDATA[
      (x / y) \ ((x \ (x / y)) * x) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(399(a,1),750(a,1,2,1))].">
      <j1 rule="para" parents="399 750"/>
    </justification>
  </clause>

  <clause id="959">
    <literal><![CDATA[
      x \ ((x / y) * ((y \ z) * y)) = T(x \ ((x / y) * z),y)
    ]]></literal>
    <justification jstring="[para(492(a,1),792(a,1,1)),flip(a)].">
      <j1 rule="para" parents="492 792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="960">
    <literal><![CDATA[
      (x * y) * ((y * ((x * y) \ z)) / y) = x * (y * ((x \ z) / y))
    ]]></literal>
    <justification jstring="[hyper(119,a,857,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 857 13"/>
    </justification>
  </clause>

  <clause id="961">
    <literal><![CDATA[
      L((x \ (y * (x * z))) / z,z,x) = (z * T(y,x * z)) / z
    ]]></literal>
    <justification jstring="[para(17(a,2),857(a,2,1,2))].">
      <j1 rule="para" parents="17 857"/>
    </justification>
  </clause>

  <clause id="962">
    <literal><![CDATA[
      L((x \ (T(x,y) * y)) / y,y,x) = (y * K(T(x,y),y)) / y
    ]]></literal>
    <justification jstring="[para(230(a,1),857(a,2,1,2))].">
      <j1 rule="para" parents="230 857"/>
    </justification>
  </clause>

  <clause id="963">
    <literal><![CDATA[
      (x * y) * ((y * ((x * y) \ z)) / y) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * ((x \ z) / y)) = u
    ]]></literal>
    <justification jstring="[para(857(a,1),286(a,1,2))].">
      <j1 rule="para" parents="857 286"/>
    </justification>
  </clause>

  <clause id="964">
    <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(950(a,2),46(a,1)),flip(a)].">
      <j1 rule="para" parents="950 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="965">
    <literal><![CDATA[
      x * R(T(y,y * x),z,u) = L(R(y,z,u),x,y) * x
    ]]></literal>
    <justification jstring="[para(950(a,1),237(a,1,2))].">
      <j1 rule="para" parents="950 237"/>
    </justification>
  </clause>

  <clause id="966">
    <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),951(a,1,1))].">
      <j1 rule="para" parents="25 951"/>
    </justification>
  </clause>

  <clause id="967">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (T(y / z,x) * z) * (z \ x)
    ]]></literal>
    <justification jstring="[para(955(a,1),368(a,1,1))].">
      <j1 rule="para" parents="955 368"/>
    </justification>
  </clause>

  <clause id="968">
    <literal><![CDATA[
      (x * y) * T(L(x,z,u),x * y) = x * (y * T(L(x,z,u),y))
    ]]></literal>
    <justification jstring="[para(966(a,1),449(a,1,2))].">
      <j1 rule="para" parents="966 449"/>
    </justification>
  </clause>

  <clause id="969">
    <literal><![CDATA[
      a(x,y,z) != 1
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = x * (y * z)
    ]]></literal>
    <justification jstring="[para(61(a,1),135(a,1)),flip(a),flip(b)].">
      <j1 rule="para" parents="61 135"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="970">
    <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(290(a,1),208(a,1))].">
      <j1 rule="para" parents="290 208"/>
    </justification>
  </clause>

  <clause id="971">
    <literal><![CDATA[
      (x * ((y * z) / y)) / x = (y * ((x * z) / x)) / y
    ]]></literal>
    <justification jstring="[para(4(a,1),863(a,1,1,2,1,2))].">
      <j1 rule="para" parents="4 863"/>
    </justification>
  </clause>

  <clause id="972">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x * (z \ y)) / x) = u
    ]]></literal>
    <justification jstring="[para(863(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="863 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="973">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ y)) / z) = ((z * x) / z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(72(a,1),864(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="974">
    <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),864(a,1,1,1,2))].">
      <j1 rule="para" parents="102 864"/>
    </justification>
  </clause>

  <clause id="975">
    <literal><![CDATA[
      ((x * (y / (y / z))) / x) \ ((y / z) * ((x * z) / x)) = y / z
    ]]></literal>
    <justification jstring="[para(75(a,1),865(a,1,2,2,1,2))].">
      <j1 rule="para" parents="75 865"/>
    </justification>
  </clause>

  <clause id="976">
    <literal><![CDATA[
      T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y)
    ]]></literal>
    <justification jstring="[para(102(a,1),871(a,1,1,1))].">
      <j1 rule="para" parents="102 871"/>
    </justification>
  </clause>

  <clause id="977">
    <literal><![CDATA[
      R(T(x \ y,z),x,x \ z) = T(z \ (y * (x \ z)),x)
    ]]></literal>
    <justification jstring="[para(725(a,1),871(a,1,1)),flip(a)].">
      <j1 rule="para" parents="725 871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="978">
    <literal><![CDATA[
      T(T(x,x * y) * y,T(x,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(239,a,927,a,b,xx)].">
      <j1 rule="hyper" parents="239 927"/>
    </justification>
  </clause>

  <clause id="979">
    <literal><![CDATA[
      T(T(x / y,(x / y) * y) * y,T(x / y,y)) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,7,a(flip),b,978,a),flip(a)].">
      <j1 rule="hyper" parents="320 7 978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="980">
    <literal><![CDATA[
      x \ T(x * (y * (x \ 1)),z) = T(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(738,a,932,a),flip(a)].">
      <j1 rule="hyper" parents="738 932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="981">
    <literal><![CDATA[
      (x \ 1) \ (x \ T(x * y,z)) = T((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,932,a)].">
      <j1 rule="hyper" parents="123 932"/>
    </justification>
  </clause>

  <clause id="982">
    <literal><![CDATA[
      T(x * (y * (x \ 1)),z) = x * (T(y,z) * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(119,a,451,a(flip),b,932,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 451 932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="983">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3(a,1),932(a,2,2,1))].">
      <j1 rule="para" parents="3 932"/>
    </justification>
  </clause>

  <clause id="984">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),932(a,2,2,1))].">
      <j1 rule="para" parents="5 932"/>
    </justification>
  </clause>

  <clause id="985">
    <literal><![CDATA[
      T(x,y) * (x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,455,a(flip),b,983,a)].">
      <j1 rule="hyper" parents="58 455 983"/>
    </justification>
  </clause>

  <clause id="986">
    <literal><![CDATA[
      T(x,y) \ (x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,983,a(flip),b,455,a(flip))].">
      <j1 rule="hyper" parents="116 983 455"/>
    </justification>
  </clause>

  <clause id="987">
    <literal><![CDATA[
      (x * y) \ (y * (x \ T(x,y))) = L(x \ 1,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(985(a,1),231(a,1,2,2))].">
      <j1 rule="para" parents="985 231"/>
    </justification>
  </clause>

  <clause id="988">
    <literal><![CDATA[
      T(x,y) * (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(986(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="986 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="989">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(455(a,2),988(a,1))].">
      <j1 rule="para" parents="455 988"/>
    </justification>
  </clause>

  <clause id="990">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,453,a(flip),b,933,a),flip(a)].">
      <j1 rule="hyper" parents="320 453 933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="991">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(933(a,2),677(a,1))].">
      <j1 rule="para" parents="933 677"/>
    </justification>
  </clause>

  <clause id="992">
    <literal><![CDATA[
      T(((1 / x) * y) * x,z) / x = (1 / x) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(680,a,934,a),flip(a)].">
      <j1 rule="hyper" parents="680 934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="993">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(677,a,934,a)].">
      <j1 rule="hyper" parents="677 934"/>
    </justification>
  </clause>

  <clause id="994">
    <literal><![CDATA[
      (1 / x) \ (T(y * x,z) / x) = T((1 / x) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,934,a(flip),b,453,a(flip))].">
      <j1 rule="hyper" parents="116 934 453"/>
    </justification>
  </clause>

  <clause id="995">
    <literal><![CDATA[
      T(1 / (1 / x),y) * (1 / x) = T(x,y) / x
    ]]></literal>
    <justification jstring="[para(2(a,1),934(a,2,1,1))].">
      <j1 rule="para" parents="2 934"/>
    </justification>
  </clause>

  <clause id="996">
    <literal><![CDATA[
      x / y != T(z / (1 / y),u) * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      T(z * y,u) = x
    ]]></literal>
    <justification jstring="[para(934(a,2),41(a,1)),flip(a)].">
      <j1 rule="para" parents="934 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="997">
    <literal><![CDATA[
      T(x * y,1 / y) / y = ((1 / y) \ x) * (1 / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),934(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="998">
    <literal><![CDATA[
      T(x * y,z) / y != u
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * T((1 / y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(934(a,1),677(a,1))].">
      <j1 rule="para" parents="934 677"/>
    </justification>
  </clause>

  <clause id="999">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(677,a,995,a)].">
      <j1 rule="hyper" parents="677 995"/>
    </justification>
  </clause>

  <clause id="1000">
    <literal><![CDATA[
      (1 / x) * T(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,456,a(flip),b,995,a)].">
      <j1 rule="hyper" parents="58 456 995"/>
    </justification>
  </clause>

  <clause id="1001">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) / x) = T(1 / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(440,a,995,a(flip),b,456,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="440 995 456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1002">
    <literal><![CDATA[
      (T(x,y) / x) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(117,a,995,a(flip),b,456,a(flip))].">
      <j1 rule="hyper" parents="117 995 456"/>
    </justification>
  </clause>

  <clause id="1003">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(995(a,1),677(a,1))].">
      <j1 rule="para" parents="995 677"/>
    </justification>
  </clause>

  <clause id="1004">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(348,a,1000,a),flip(a)].">
      <j1 rule="hyper" parents="348 1000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1005">
    <literal><![CDATA[
      T(x,x \ y) / x = (1 / x) * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,313,a(flip),b,1000,a),flip(a)].">
      <j1 rule="hyper" parents="58 313 1000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1006">
    <literal><![CDATA[
      T(x / y,y) / (x / y) = (1 / (x / y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),1000(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1007">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * T(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(1000(a,1),348(a,1))].">
      <j1 rule="para" parents="1000 348"/>
    </justification>
  </clause>

  <clause id="1008">
    <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(1000(a,1),717(a,1,2))].">
      <j1 rule="para" parents="1000 717"/>
    </justification>
  </clause>

  <clause id="1009">
    <literal><![CDATA[
      L(x \ 1,x,T(x,y) / x) = T(1 / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(669,a,1001,a)].">
      <j1 rule="hyper" parents="669 1001"/>
    </justification>
  </clause>

  <clause id="1010">
    <literal><![CDATA[
      T(x * T(x \ 1,y),x \ 1) = (x \ 1) \ T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1004(a,1),107(a,1,1))].">
      <j1 rule="para" parents="1004 107"/>
    </justification>
  </clause>

  <clause id="1011">
    <literal><![CDATA[
      (1 / x) * ((x \ y) \ y) = ((x \ y) \ y) / x
    ]]></literal>
    <justification jstring="[para(106(a,1),1005(a,1,1)),flip(a)].">
      <j1 rule="para" parents="106 1005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1012">
    <literal><![CDATA[
      ((x \ 1) \ (x \ y)) * (x \ 1) = x \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(5(a,1),941(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1013">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) = (((x / y) \ 1) \ y) * ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),941(a,1,2,1))].">
      <j1 rule="para" parents="7 941"/>
    </justification>
  </clause>

  <clause id="1014">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x * T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[para(258(a,2),949(a,1,2))].">
      <j1 rule="para" parents="258 949"/>
    </justification>
  </clause>

  <clause id="1015">
    <literal><![CDATA[
      K(x,y) = ((y * x) \ y) * T(((y * x) \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,431,a,b,956,a)].">
      <j1 rule="hyper" parents="320 431 956"/>
    </justification>
  </clause>

  <clause id="1016">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,x) = ((x * y) \ x) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,431,a,b,956,a),flip(a)].">
      <j1 rule="hyper" parents="116 431 956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1017">
    <literal><![CDATA[
      K(x \ (x / y),x) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(465,a,958,a)].">
      <j1 rule="hyper" parents="465 958"/>
    </justification>
  </clause>

  <clause id="1018">
    <literal><![CDATA[
      x \ K(y \ (y / x),y) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,85,a(flip),b,958,a(flip))].">
      <j1 rule="hyper" parents="116 85 958"/>
    </justification>
  </clause>

  <clause id="1019">
    <literal><![CDATA[
      K(x \ (x / (1 / y)),x) = T(y,x) / y
    ]]></literal>
    <justification jstring="[hyper(320,a,999,a(flip),b,1017,a),flip(a)].">
      <j1 rule="hyper" parents="320 999 1017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1020">
    <literal><![CDATA[
      K(x \ (x / (y \ 1)),x) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,983,a(flip),b,1017,a),flip(a)].">
      <j1 rule="hyper" parents="320 983 1017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1021">
    <literal><![CDATA[
      T(x,y) = x * K(y \ (y / (x \ 1)),y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1017,a,b,983,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1017 983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1022">
    <literal><![CDATA[
      K(x \ (x / y),x) / y = T(1 / y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,1017,a,b,453,a)].">
      <j1 rule="hyper" parents="117 1017 453"/>
    </justification>
  </clause>

  <clause id="1023">
    <literal><![CDATA[
      K(T(1 / x,T(x,y)),T(x,y)) = x * T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(1001(a,1),1017(a,1,1))].">
      <j1 rule="para" parents="1001 1017"/>
    </justification>
  </clause>

  <clause id="1024">
    <literal><![CDATA[
      T(x,y) = K(y \ (y / (1 / x)),y) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,1019,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 1019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1025">
    <literal><![CDATA[
      K(x \ (x / (1 / (y / (x * y)))),x) = R(x \ 1,x,y) / (y / (x * y))
    ]]></literal>
    <justification jstring="[para(645(a,1),1019(a,2,1))].">
      <j1 rule="para" parents="645 1019"/>
    </justification>
  </clause>

  <clause id="1026">
    <literal><![CDATA[
      K(x \ (x / (((x * y) / x) \ 1)),x) = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[para(224(a,1),1020(a,2,2))].">
      <j1 rule="para" parents="224 1020"/>
    </justification>
  </clause>

  <clause id="1027">
    <literal><![CDATA[
      K((x * y) \ x,x * y) / y = T(1 / y,x * y)
    ]]></literal>
    <justification jstring="[para(6(a,1),1022(a,1,1,1,2))].">
      <j1 rule="para" parents="6 1022"/>
    </justification>
  </clause>

  <clause id="1028">
    <literal><![CDATA[
      T((x \ 1) \ (x \ y),z) = (x \ 1) \ (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),981(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1029">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(981(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="981 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1030">
    <literal><![CDATA[
      (x \ T(y,z)) / (x \ 1) = T((x \ y) / (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(117,a,984,a(flip),b,453,a)].">
      <j1 rule="hyper" parents="117 984 453"/>
    </justification>
  </clause>

  <clause id="1031">
    <literal><![CDATA[
      (x * T(x \ y,z)) * (x \ 1) = T(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(133,a,990,a)].">
      <j1 rule="hyper" parents="133 990"/>
    </justification>
  </clause>

  <clause id="1032">
    <literal><![CDATA[
      T(x * y,1 / y) / y != z
    ]]></literal>
    <literal><![CDATA[
      ((1 / y) \ x) * (1 / y) = z
    ]]></literal>
    <justification jstring="[para(993(a,1),284(a,1))].">
      <j1 rule="para" parents="993 284"/>
    </justification>
  </clause>

  <clause id="1033">
    <literal><![CDATA[
      T((1 / x) \ (y / x),z) = (1 / x) \ (T(y,z) / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),994(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1034">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y * x,z) / x = u
    ]]></literal>
    <justification jstring="[para(994(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="994 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1035">
    <literal><![CDATA[
      ((1 / x) \ (y / x)) * (1 / x) = T(y,1 / x) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),997(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7 997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1036">
    <literal><![CDATA[
      (1 / (x / y)) * (y \ x) = (y \ x) / (x / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),1006(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 1006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1037">
    <literal><![CDATA[
      (x \ y) \ ((x \ y) / (y / x)) = T(1 / (y / x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(440,a,xx,b,1036,a),flip(a)].">
      <j1 rule="hyper" parents="440 1036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1038">
    <literal><![CDATA[
      (x \ y) / (y / x) != (x \ y) * z
    ]]></literal>
    <literal><![CDATA[
      T(1 / (y / x),x \ y) = z
    ]]></literal>
    <justification jstring="[para(1036(a,1),240(a,2)),flip(a)].">
      <j1 rule="para" parents="1036 240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1039">
    <literal><![CDATA[
      ((x * y) \ x) * T(((x * y) \ x) \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(1016(a,2),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1016 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1040">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,y) = ((y * x) \ y) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(217(a,2),1016(a,1,1,1))].">
      <j1 rule="para" parents="217 1016"/>
    </justification>
  </clause>

  <clause id="1041">
    <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(1016(a,1),1004(a,1,1))].">
      <j1 rule="para" parents="1016 1004"/>
    </justification>
  </clause>

  <clause id="1042">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(1028(a,2),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1028 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1043">
    <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(1028(a,2),340(a,2,2))].">
      <j1 rule="para" parents="1028 340"/>
    </justification>
  </clause>

  <clause id="1044">
    <literal><![CDATA[
      T((x * y) * (x \ 1),z) = (x * T(y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),1031(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1045">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ (y / x)) = (T(y,1 / x) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[para(1035(a,1),86(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1035 86"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1046">
    <literal><![CDATA[
      T((x * y) * (x \ 1),y) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(104(a,1),1044(a,2,1,2))].">
      <j1 rule="para" parents="104 1044"/>
    </justification>
  </clause>

  <clause id="1047">
    <literal><![CDATA[
      K((x * y) * (x \ 1),y) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,1046,a)].">
      <j1 rule="hyper" parents="50 1046"/>
    </justification>
  </clause>

  <clause id="1048">
    <literal><![CDATA[
      K(((1 / x) * y) * x,y) = 1
    ]]></literal>
    <justification jstring="[para(75(a,1),1047(a,1,1,2))].">
      <j1 rule="para" parents="75 1047"/>
    </justification>
  </clause>

  <clause id="1049">
    <literal><![CDATA[
      K(x * y,(1 / y) \ x) = 1
    ]]></literal>
    <justification jstring="[para(5(a,1),1048(a,1,1,1))].">
      <j1 rule="para" parents="5 1048"/>
    </justification>
  </clause>

  <clause id="1050">
    <literal><![CDATA[
      T(x * y,(1 / y) \ x) = x * y
    ]]></literal>
    <justification jstring="[hyper(51,a,1049,a)].">
      <j1 rule="hyper" parents="51 1049"/>
    </justification>
  </clause>

  <clause id="1051">
    <literal><![CDATA[
      K(x,1 / x) \ (x * (T(x,y) / x)) = L(T(x,y),1 / x,x)
    ]]></literal>
    <justification jstring="[para(1000(a,1),363(a,1,2,2))].">
      <j1 rule="para" parents="1000 363"/>
    </justification>
  </clause>

  <clause id="1052">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(298(a,1),446(a,1,2,1))].">
      <j1 rule="para" parents="298 446"/>
    </justification>
  </clause>

  <clause id="1053">
    <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),447(a,1,2,1))].">
      <j1 rule="para" parents="92 447"/>
    </justification>
  </clause>

  <clause id="1054">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(298(a,1),447(a,1,2,1))].">
      <j1 rule="para" parents="298 447"/>
    </justification>
  </clause>

  <clause id="1055">
    <literal><![CDATA[
      K(x \ 1,x) * L(x \ y,x,x \ 1) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,151,a(flip),b,484,a),flip(a)].">
      <j1 rule="hyper" parents="320 151 484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1056">
    <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(564(a,1),484(a,1,2))].">
      <j1 rule="para" parents="564 484"/>
    </justification>
  </clause>

  <clause id="1057">
    <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),513(a,1,1,1))].">
      <j1 rule="para" parents="102 513"/>
    </justification>
  </clause>

  <clause id="1058">
    <literal><![CDATA[
      (L((x / y) / z,u,w) * z) * y = L(x / (z * y),u,w) * (z * y)
    ]]></literal>
    <justification jstring="[para(301(a,1),513(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="301 513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1059">
    <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),514(a,1,1,1))].">
      <j1 rule="para" parents="102 514"/>
    </justification>
  </clause>

  <clause id="1060">
    <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,520,a(flip),b,238,a)].">
      <j1 rule="hyper" parents="116 520 238"/>
    </justification>
  </clause>

  <clause id="1061">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(489(a,1),548(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="489 548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1062">
    <literal><![CDATA[
      (1 / x) \ L(1 / x,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(389(a,1),553(a,1,2,1))].">
      <j1 rule="para" parents="389 553"/>
    </justification>
  </clause>

  <clause id="1063">
    <literal><![CDATA[
      (1 / x) \ L((1 / x) * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(488(a,1),553(a,1,2,1))].">
      <j1 rule="para" parents="488 553"/>
    </justification>
  </clause>

  <clause id="1064">
    <literal><![CDATA[
      (1 / x) \ L(x \ 1,y,z) = x * L(T(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(739(a,1),553(a,1,2,1))].">
      <j1 rule="para" parents="739 553"/>
    </justification>
  </clause>

  <clause id="1065">
    <literal><![CDATA[
      L(x \ 1,y,z) / (x \ 1) = L(1 / x,y,z) * x
    ]]></literal>
    <justification jstring="[para(403(a,1),557(a,1,1,1))].">
      <j1 rule="para" parents="403 557"/>
    </justification>
  </clause>

  <clause id="1066">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = L(x / y,z,u) * y
    ]]></literal>
    <justification jstring="[para(523(a,1),557(a,1,1,1))].">
      <j1 rule="para" parents="523 557"/>
    </justification>
  </clause>

  <clause id="1067">
    <literal><![CDATA[
      L(x \ 1,y,z) / (x \ 1) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,635,a(flip),b,1065,a),flip(a)].">
      <j1 rule="hyper" parents="320 635 1065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1068">
    <literal><![CDATA[
      L(x \ 1,x,y) / (x \ 1) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,395,a(flip),b,1067,a),flip(a)].">
      <j1 rule="hyper" parents="320 395 1067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1069">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * (x \ 1) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,1068,a)].">
      <j1 rule="hyper" parents="133 1068"/>
    </justification>
  </clause>

  <clause id="1070">
    <literal><![CDATA[
      (x \ y) * ((x * (x \ y)) \ x) = (y \ x) / ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(390(a,1),1068(a,1,1)),flip(a)].">
      <j1 rule="para" parents="390 1068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1071">
    <literal><![CDATA[
      L(x \ 1,x,y) \ ((x \ 1) * (x * ((y * x) \ y))) = K(x \ 1,x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[para(1069(a,1),11(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1069 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1072">
    <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(561(a,2),39(a,1))].">
      <j1 rule="para" parents="561 39"/>
    </justification>
  </clause>

  <clause id="1073">
    <literal><![CDATA[
      L(T(x,1 / x),y,z) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(811(a,1),562(a,1,1,1))].">
      <j1 rule="para" parents="811 562"/>
    </justification>
  </clause>

  <clause id="1074">
    <literal><![CDATA[
      T(L(x,y,z),1 / x) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(20(a,1),1073(a,1,1))].">
      <j1 rule="para" parents="20 1073"/>
    </justification>
  </clause>

  <clause id="1075">
    <literal><![CDATA[
      (1 / x) \ (L(x,y,z) / x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,1035,a,b,1074,a(flip))].">
      <j1 rule="hyper" parents="30 1035 1074"/>
    </justification>
  </clause>

  <clause id="1076">
    <literal><![CDATA[
      (L(x,y,z) / x) / L(x,y,z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(197,a,1075,a)].">
      <j1 rule="hyper" parents="197 1075"/>
    </justification>
  </clause>

  <clause id="1077">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(134,a,1075,a)].">
      <j1 rule="hyper" parents="134 1075"/>
    </justification>
  </clause>

  <clause id="1078">
    <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(1077(a,1),717(a,1,2))].">
      <j1 rule="para" parents="1077 717"/>
    </justification>
  </clause>

  <clause id="1079">
    <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(565(a,1),484(a,1,2))].">
      <j1 rule="para" parents="565 484"/>
    </justification>
  </clause>

  <clause id="1080">
    <literal><![CDATA[
      L((x * (y \ z)) \ u,y \ z,y) = L(z \ (y * (x \ u)),y \ z,x)
    ]]></literal>
    <justification jstring="[para(490(a,1),566(a,1,1)),flip(a)].">
      <j1 rule="para" parents="490 566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1081">
    <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(566(a,1),286(a,1,2))].">
      <j1 rule="para" parents="566 286"/>
    </justification>
  </clause>

  <clause id="1082">
    <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(566(a,1),484(a,1,2))].">
      <j1 rule="para" parents="566 484"/>
    </justification>
  </clause>

  <clause id="1083">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,608,a(flip),b,257,a),flip(a)].">
      <j1 rule="hyper" parents="116 608 257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1084">
    <literal><![CDATA[
      (R(x / y,z,u) * y) * (y \ 1) = R(x * (y \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(388,a,612,a)].">
      <j1 rule="hyper" parents="388 612"/>
    </justification>
  </clause>

  <clause id="1085">
    <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(721(a,2),38(a,1)),flip(a)].">
      <j1 rule="para" parents="721 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1086">
    <literal><![CDATA[
      x * ((x \ y) * T((x \ y) \ z,u)) = y * T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(119,a,753,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="119 753 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1087">
    <literal><![CDATA[
      (T(x / (y / z),u) * (y / z)) * z = T((x * z) / y,u) * y
    ]]></literal>
    <justification jstring="[para(761(a,1),508(a,1,1)),flip(a)].">
      <j1 rule="para" parents="761 508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1088">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,22,a,b,801,a),flip(a)].">
      <j1 rule="hyper" parents="320 22 801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1089">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * (y * ((z * (y \ 1)) / z))
    ]]></literal>
    <justification jstring="[hyper(119,a,844,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 844 13"/>
    </justification>
  </clause>

  <clause id="1090">
    <literal><![CDATA[
      ((x * (y / (z * y))) / x) * (z * y) = (((x * (1 / z)) / x) * z) * y
    ]]></literal>
    <justification jstring="[para(850(a,1),101(a,1,1))].">
      <j1 rule="para" parents="850 101"/>
    </justification>
  </clause>

  <clause id="1091">
    <literal><![CDATA[
      ((x * ((y \ z) / (y * (y \ z)))) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(850(a,1),368(a,1,1))].">
      <j1 rule="para" parents="850 368"/>
    </justification>
  </clause>

  <clause id="1092">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = ((x * (1 / y)) / x) * y
    ]]></literal>
    <justification jstring="[hyper(117,a,590,a(flip),b,851,a)].">
      <j1 rule="hyper" parents="117 590 851"/>
    </justification>
  </clause>

  <clause id="1093">
    <literal><![CDATA[
      ((x \ y) * x) * (x \ z) = z * T(z \ (y * (x \ z)),x)
    ]]></literal>
    <justification jstring="[hyper(119,a,977,a(flip),b,727,a),flip(a)].">
      <j1 rule="hyper" parents="119 977 727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1094">
    <literal><![CDATA[
      K(x,y) = L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1040,a,b,393,a),flip(a)].">
      <j1 rule="hyper" parents="119 1040 393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1095">
    <literal><![CDATA[
      K(x \ 1,x) * y != (x \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      L(x \ z,x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(1055(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="1055 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1096">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = (T(1 / x,z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(677,a,736,a)].">
      <j1 rule="hyper" parents="677 736"/>
    </justification>
  </clause>

  <clause id="1097">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[hyper(677,a,782,a)].">
      <j1 rule="hyper" parents="677 782"/>
    </justification>
  </clause>

  <clause id="1098">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) * T((x * z) \ y,x) = u
    ]]></literal>
    <justification jstring="[para(782(a,1),677(a,1))].">
      <j1 rule="para" parents="782 677"/>
    </justification>
  </clause>

  <clause id="1099">
    <literal><![CDATA[
      x * (y * T(T(x,y),z)) = T(x,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(418,a,794,a),flip(a)].">
      <j1 rule="hyper" parents="418 794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1100">
    <literal><![CDATA[
      T(x,y) * (x * z) = x * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(236(a,1),1099(a,1,2)),flip(a)].">
      <j1 rule="para" parents="236 1099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1101">
    <literal><![CDATA[
      x \ (T(x,y) * z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(598,a,1100,a)].">
      <j1 rule="hyper" parents="598 1100"/>
    </justification>
  </clause>

  <clause id="1102">
    <literal><![CDATA[
      T(x,y) * (x \ (T(x,y) \ z)) = x \ z
    ]]></literal>
    <justification jstring="[hyper(597,a,1100,a),flip(a)].">
      <j1 rule="hyper" parents="597 1100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1103">
    <literal><![CDATA[
      (T(x,y) * z) / (T(x,y) * (x \ z)) = x
    ]]></literal>
    <justification jstring="[hyper(574,a,1100,a)].">
      <j1 rule="hyper" parents="574 1100"/>
    </justification>
  </clause>

  <clause id="1104">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,y) \ z)) = (x * (T(x,y) \ z)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(440,a,151,a(flip),b,1100,a)].">
      <j1 rule="hyper" parents="440 151 1100"/>
    </justification>
  </clause>

  <clause id="1105">
    <literal><![CDATA[
      x * (T(x,y) * (x \ z)) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(342,a,1100,a),flip(a)].">
      <j1 rule="hyper" parents="342 1100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1106">
    <literal><![CDATA[
      T(x,y) * (x * (T(x,y) \ z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(320,a,151,a(flip),b,1100,a),flip(a)].">
      <j1 rule="hyper" parents="320 151 1100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1107">
    <literal><![CDATA[
      (x * (T(x,y) * z)) / (x * z) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,1100,a)].">
      <j1 rule="hyper" parents="131 1100"/>
    </justification>
  </clause>

  <clause id="1108">
    <literal><![CDATA[
      T(x,y) \ (x * z) = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,1100,a)].">
      <j1 rule="hyper" parents="116 151 1100"/>
    </justification>
  </clause>

  <clause id="1109">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,68,a(flip),b,1100,a),flip(a)].">
      <j1 rule="hyper" parents="116 68 1100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1110">
    <literal><![CDATA[
      x * (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,65,a(flip),b,1100,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 1100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1111">
    <literal><![CDATA[
      (x / y) * (T(x / y,z) * y) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(7(a,1),1100(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 1100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1112">
    <literal><![CDATA[
      T(x,y) * (x * z) != x * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(1100(a,2),38(a,1))].">
      <j1 rule="para" parents="1100 38"/>
    </justification>
  </clause>

  <clause id="1113">
    <literal><![CDATA[
      x * (T(x,y) * T(z,x)) = T(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(105(a,1),1100(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 1100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1114">
    <literal><![CDATA[
      (x / y) * (T(x / y,y) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),1100(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 1100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1115">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(268,a,1110,a)].">
      <j1 rule="hyper" parents="268 1110"/>
    </justification>
  </clause>

  <clause id="1116">
    <literal><![CDATA[
      (T(x,y) \ x) / (T(x,y) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(131,a,1110,a)].">
      <j1 rule="hyper" parents="131 1110"/>
    </justification>
  </clause>

  <clause id="1117">
    <literal><![CDATA[
      x \ (T(x,y) \ x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,1110,a)].">
      <j1 rule="hyper" parents="123 1110"/>
    </justification>
  </clause>

  <clause id="1118">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,1 / x) = (1 / x) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1110,a(flip),b,437,a),flip(a)].">
      <j1 rule="hyper" parents="119 1110 437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1119">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ 1 = z
    ]]></literal>
    <justification jstring="[para(1110(a,1),292(a,1,1,1)),flip(b)].">
      <j1 rule="para" parents="1110 292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1120">
    <literal><![CDATA[
      T((1 / x) * (T(x,y) \ x),x) = (1 / x) * ((T(x,y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(1110(a,1),795(a,1,1,2))].">
      <j1 rule="para" parents="1110 795"/>
    </justification>
  </clause>

  <clause id="1121">
    <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(1116(a,1),421(a,1,1))].">
      <j1 rule="para" parents="1116 421"/>
    </justification>
  </clause>

  <clause id="1122">
    <literal><![CDATA[
      (T(x,y) \ T(x,z)) / (T(x,y) \ 1) = T(x,z)
    ]]></literal>
    <justification jstring="[para(1116(a,1),1030(a,2,1))].">
      <j1 rule="para" parents="1116 1030"/>
    </justification>
  </clause>

  <clause id="1123">
    <literal><![CDATA[
      T(x,y) \ (x \ z) = x \ (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(123,a,1102,a)].">
      <j1 rule="hyper" parents="123 1102"/>
    </justification>
  </clause>

  <clause id="1124">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (T(x,y) \ z) = w
    ]]></literal>
    <justification jstring="[para(1102(a,1),596(a,1,2,2))].">
      <j1 rule="para" parents="1102 596"/>
    </justification>
  </clause>

  <clause id="1125">
    <literal><![CDATA[
      (T(x,y) * z) / u != x
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(1103(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="1103 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1126">
    <literal><![CDATA[
      T(x,y) * z != x * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(1103(a,1),125(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1103 125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1127">
    <literal><![CDATA[
      x \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(1103(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1103 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1128">
    <literal><![CDATA[
      x * (T(x,y) \ y) = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(412,a,1106,a),flip(a)].">
      <j1 rule="hyper" parents="412 1106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1129">
    <literal><![CDATA[
      x * (T(x,y) \ ((x \ T(x,y)) * z)) = L(z,x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(29,a,448,a,b,1106,a),flip(a)].">
      <j1 rule="hyper" parents="29 448 1106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1130">
    <literal><![CDATA[
      x * (T(x,y) \ (T(x,y) / x)) = K(x,T(x,y) / x)
    ]]></literal>
    <justification jstring="[hyper(29,a,303,a,b,1106,a),flip(a)].">
      <j1 rule="hyper" parents="29 303 1106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1131">
    <literal><![CDATA[
      T(x,y) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(1106(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1106 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1132">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ y) = T(y,T(x / y,y))
    ]]></literal>
    <justification jstring="[para(107(a,1),1128(a,1,2,1))].">
      <j1 rule="para" parents="107 1128"/>
    </justification>
  </clause>

  <clause id="1133">
    <literal><![CDATA[
      x \ y != T(z,u) * (z \ (T(z,u) \ w))
    ]]></literal>
    <literal><![CDATA[
      x * (z \ w) = y
    ]]></literal>
    <justification jstring="[para(1109(a,1),578(a,2,2,2))].">
      <j1 rule="para" parents="1109 578"/>
    </justification>
  </clause>

  <clause id="1134">
    <literal><![CDATA[
      T(x,y) * (x \ (T(x,y) \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      x \ z = u
    ]]></literal>
    <justification jstring="[para(1123(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1123 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1135">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(1123(a,2),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1123 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1136">
    <literal><![CDATA[
      T(T(x,y * x) * y,x) = T(x,y) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(239,a,809,a,b,1113,a)].">
      <j1 rule="hyper" parents="239 809 1113"/>
    </justification>
  </clause>

  <clause id="1137">
    <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,448,a,b,1113,a),flip(a)].">
      <j1 rule="hyper" parents="29 448 1113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1138">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * x) = x * K(x \ (x / T(x,y)),x)
    ]]></literal>
    <justification jstring="[para(1017(a,2),1113(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1017 1113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1139">
    <literal><![CDATA[
      T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,1122,a)].">
      <j1 rule="hyper" parents="133 1122"/>
    </justification>
  </clause>

  <clause id="1140">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ y) = T(y,y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),1132(a,2,2))].">
      <j1 rule="para" parents="107 1132"/>
    </justification>
  </clause>

  <clause id="1141">
    <literal><![CDATA[
      ((x * y) / x) * (y \ x) = T(x,x \ (x * y))
    ]]></literal>
    <justification jstring="[para(4(a,1),1140(a,1,2,1))].">
      <j1 rule="para" parents="4 1140"/>
    </justification>
  </clause>

  <clause id="1142">
    <literal><![CDATA[
      T(x / y,z) \ T(x / y,y) = (y \ x) * (T(x / y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,1),1139(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 1139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1143">
    <literal><![CDATA[
      T(x,y) = ((x * y) / x) * (y \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1141(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4 1141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1144">
    <literal><![CDATA[
      ((x * y) / x) \ T(x,y) = y \ x
    ]]></literal>
    <justification jstring="[hyper(766,a,1143,a)].">
      <j1 rule="hyper" parents="766 1143"/>
    </justification>
  </clause>

  <clause id="1145">
    <literal><![CDATA[
      T((x * y) / x,y \ x) = (y \ x) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(440,a,1143,a,b,xx)].">
      <j1 rule="hyper" parents="440 1143"/>
    </justification>
  </clause>

  <clause id="1146">
    <literal><![CDATA[
      ((x * (x / y)) / x) * y = T(x,x / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,193,a(flip),b,1143,a)].">
      <j1 rule="hyper" parents="320 193 1143"/>
    </justification>
  </clause>

  <clause id="1147">
    <literal><![CDATA[
      T(x,x / y) / y = (x * (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,1143,a,b,193,a(flip))].">
      <j1 rule="hyper" parents="117 1143 193"/>
    </justification>
  </clause>

  <clause id="1148">
    <literal><![CDATA[
      ((x * y) * x) / (x * y) = T(x * y,x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,1143,a,b,152,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="117 1143 152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1149">
    <literal><![CDATA[
      T(x,y) / (y \ x) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,1143,a,b,xx)].">
      <j1 rule="hyper" parents="117 1143"/>
    </justification>
  </clause>

  <clause id="1150">
    <literal><![CDATA[
      (x / (x / y)) * (y \ (x / y)) = T(x / y,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),1143(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 1143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1151">
    <literal><![CDATA[
      ((x * R(y,y \ 1,x)) / x) * ((y \ 1) * x) = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[para(426(a,1),1143(a,2,2)),flip(a)].">
      <j1 rule="para" parents="426 1143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1152">
    <literal><![CDATA[
      T(T(x,y) / (y \ x),x) = y
    ]]></literal>
    <justification jstring="[para(1149(a,2),224(a,1,1))].">
      <j1 rule="para" parents="1149 224"/>
    </justification>
  </clause>

  <clause id="1153">
    <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(1149(a,1),1018(a,1,2,1,2))].">
      <j1 rule="para" parents="1149 1018"/>
    </justification>
  </clause>

  <clause id="1154">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(1152(a,1),246(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1152 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1155">
    <literal><![CDATA[
      T(T(R(x,y,y \ 1),x * y) / (y \ 1),R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(436(a,1),1152(a,1,1,2))].">
      <j1 rule="para" parents="436 1152"/>
    </justification>
  </clause>

  <clause id="1156">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) = T(y,y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,864,a(flip),b,1146,a)].">
      <j1 rule="hyper" parents="58 864 1146"/>
    </justification>
  </clause>

  <clause id="1157">
    <literal><![CDATA[
      x \ T(y,y / x) = (y * (x \ y)) / y
    ]]></literal>
    <justification jstring="[hyper(116,a,1146,a(flip),b,864,a(flip))].">
      <j1 rule="hyper" parents="116 1146 864"/>
    </justification>
  </clause>

  <clause id="1158">
    <literal><![CDATA[
      ((x * (x / y)) / x) * y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x / y) = z
    ]]></literal>
    <justification jstring="[para(1147(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1147 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1159">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),y) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,106,a(flip),b,1154,a),flip(a)].">
      <j1 rule="hyper" parents="320 106 1154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1160">
    <literal><![CDATA[
      (x / y) * ((x * y) / x) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[para(75(a,1),1156(a,1,2,1,2))].">
      <j1 rule="para" parents="75 1156"/>
    </justification>
  </clause>

  <clause id="1161">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(y,y / x) = u
    ]]></literal>
    <justification jstring="[para(1156(a,2),766(a,1))].">
      <j1 rule="para" parents="1156 766"/>
    </justification>
  </clause>

  <clause id="1162">
    <literal><![CDATA[
      (x * y) * L((x \ y) / y,y,x) = T(y,y / (x * y))
    ]]></literal>
    <justification jstring="[para(857(a,2),1156(a,1,2))].">
      <j1 rule="para" parents="857 1156"/>
    </justification>
  </clause>

  <clause id="1163">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,y / x) = z
    ]]></literal>
    <justification jstring="[para(1157(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1157 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1164">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),x * y) = L(T(x,x \ y),y,x)
    ]]></literal>
    <justification jstring="[para(1145(a,1),954(a,1,1))].">
      <j1 rule="para" parents="1145 954"/>
    </justification>
  </clause>

  <clause id="1165">
    <literal><![CDATA[
      T(T(x * y,x) / y,y) = R(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[para(1148(a,1),896(a,1,1))].">
      <j1 rule="para" parents="1148 896"/>
    </justification>
  </clause>

  <clause id="1166">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(421,a,1165,a)].">
      <j1 rule="hyper" parents="421 1165"/>
    </justification>
  </clause>

  <clause id="1167">
    <literal><![CDATA[
      R(x,y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      y \ T(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(1165(a,1),421(a,1))].">
      <j1 rule="para" parents="1165 421"/>
    </justification>
  </clause>

  <clause id="1168">
    <literal><![CDATA[
      L(R(x,y,T(x,y)),y,x) = x
    ]]></literal>
    <justification jstring="[para(1166(a,1),473(a,1,1))].">
      <j1 rule="para" parents="1166 473"/>
    </justification>
  </clause>

  <clause id="1169">
    <literal><![CDATA[
      (x * y) / ((x * y) / x) = y / (x \ ((x * y) / x))
    ]]></literal>
    <justification jstring="[hyper(117,a,224,a(flip),b,1150,a),flip(a)].">
      <j1 rule="hyper" parents="117 224 1150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1170">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(225(a,1),1160(a,1,2)),flip(a)].">
      <j1 rule="para" parents="225 1160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1171">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      y * (T(y,x) \ x) = z
    ]]></literal>
    <justification jstring="[para(235(a,1),1131(a,1))].">
      <j1 rule="para" parents="235 1131"/>
    </justification>
  </clause>

  <clause id="1172">
    <literal><![CDATA[
      x * (T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(4(a,1),1135(a,1,2,2))].">
      <j1 rule="para" parents="4 1135"/>
    </justification>
  </clause>

  <clause id="1173">
    <literal><![CDATA[
      (x / y) * (y * T(y \ x,z)) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(453(a,1),1111(a,1,2))].">
      <j1 rule="para" parents="453 1111"/>
    </justification>
  </clause>

  <clause id="1174">
    <literal><![CDATA[
      x * T(1 / x,T(x,y)) = K(x,T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(1001(a,1),1130(a,1,2))].">
      <j1 rule="para" parents="1001 1130"/>
    </justification>
  </clause>

  <clause id="1175">
    <literal><![CDATA[
      x * (y * ((x \ y) / y)) = T(y,y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(286,a,1162,a)].">
      <j1 rule="hyper" parents="286 1162"/>
    </justification>
  </clause>

  <clause id="1176">
    <literal><![CDATA[
      T(x,x / (y * x)) != z
    ]]></literal>
    <literal><![CDATA[
      y * (x * ((y \ x) / x)) = z
    ]]></literal>
    <justification jstring="[para(1162(a,1),286(a,1))].">
      <j1 rule="para" parents="1162 286"/>
    </justification>
  </clause>

  <clause id="1177">
    <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(873(a,2),656(a,1))].">
      <j1 rule="para" parents="873 656"/>
    </justification>
  </clause>

  <clause id="1178">
    <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(914(a,1),45(a,1))].">
      <j1 rule="para" parents="914 45"/>
    </justification>
  </clause>

  <clause id="1179">
    <literal><![CDATA[
      (T(1 / x,y) * x) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(677,a,937,a),flip(a)].">
      <j1 rule="hyper" parents="677 937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1180">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (z * T(z \ y,x)) * (z \ x)
    ]]></literal>
    <justification jstring="[para(453(a,1),967(a,2,1))].">
      <j1 rule="para" parents="453 967"/>
    </justification>
  </clause>

  <clause id="1181">
    <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,1010,a(flip),b,938,a)].">
      <j1 rule="hyper" parents="116 1010 938"/>
    </justification>
  </clause>

  <clause id="1182">
    <literal><![CDATA[
      T((x * y) / x,K(x \ (x / (((x * y) / x) \ 1)),x)) = (((x * y) / x) \ y) \ y
    ]]></literal>
    <justification jstring="[para(1026(a,2),106(a,1,2))].">
      <j1 rule="para" parents="1026 106"/>
    </justification>
  </clause>

  <clause id="1183">
    <literal><![CDATA[
      T((x * y) / x,K(x \ (x / (((x * y) / x) \ 1)),x)) != z
    ]]></literal>
    <literal><![CDATA[
      (((x * y) / x) \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(1026(a,2),428(a,1,2))].">
      <j1 rule="para" parents="1026 428"/>
    </justification>
  </clause>

  <clause id="1184">
    <literal><![CDATA[
      K(T(1 / (1 / x),x \ 1),x \ 1) = T(x,x \ 1) / x
    ]]></literal>
    <justification jstring="[para(1037(a,1),1019(a,1,1))].">
      <j1 rule="para" parents="1037 1019"/>
    </justification>
  </clause>

  <clause id="1185">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3(a,1),1061(a,2,2,1))].">
      <j1 rule="para" parents="3 1061"/>
    </justification>
  </clause>

  <clause id="1186">
    <literal><![CDATA[
      L(x,y,z) * (x \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,637,a(flip),b,1185,a)].">
      <j1 rule="hyper" parents="58 637 1185"/>
    </justification>
  </clause>

  <clause id="1187">
    <literal><![CDATA[
      L(x,y,z) \ (x \ L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,1185,a(flip),b,637,a(flip))].">
      <j1 rule="hyper" parents="116 1185 637"/>
    </justification>
  </clause>

  <clause id="1188">
    <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(1186(a,1),651(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1186 651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1189">
    <literal><![CDATA[
      x \ T(x * (x \ L(x,y,z)),u) = T(L(x,y,z),u) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1186(a,1),980(a,1,2,1,2))].">
      <j1 rule="para" parents="1186 980"/>
    </justification>
  </clause>

  <clause id="1190">
    <literal><![CDATA[
      x * L(x \ ((1 / x) \ y),z,u) = (1 / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),1063(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1191">
    <literal><![CDATA[
      (1 / x) \ L(x \ 1,y,z) = L(x \ 1,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,237,a(flip),b,1064,a),flip(a)].">
      <j1 rule="hyper" parents="320 237 1064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1192">
    <literal><![CDATA[
      (x * y) \ x = (1 / y) * (L(y \ 1,y,x) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1191,a(flip),b,392,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1191 392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1193">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) * (x \ y) = (1 / (x \ y)) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(390(a,1),1191(a,1,2)),flip(a)].">
      <j1 rule="para" parents="390 1191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1194">
    <literal><![CDATA[
      (1 / x) * (((y * x) \ y) * x) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(217(a,1),1192(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="217 1192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1195">
    <literal><![CDATA[
      x * L(x \ (((y * x) \ y) * x),z,u) = (1 / x) \ L((y * x) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(1194(a,1),1063(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1194 1063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1196">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,635,a(flip),b,1066,a),flip(a)].">
      <j1 rule="hyper" parents="320 635 1066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1197">
    <literal><![CDATA[
      (x \ y) / ((y \ x) \ 1) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),1070(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1199">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3(a,1),1083(a,2,2,1))].">
      <j1 rule="para" parents="3 1083"/>
    </justification>
  </clause>

  <clause id="1200">
    <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),1083(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="17 1083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1201">
    <literal><![CDATA[
      R(x,y,z) * (x \ 1) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,641,a(flip),b,1199,a)].">
      <j1 rule="hyper" parents="58 641 1199"/>
    </justification>
  </clause>

  <clause id="1202">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,y,z) = R(1 / x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(585,a,1201,a),flip(a)].">
      <j1 rule="hyper" parents="585 1201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1203">
    <literal><![CDATA[
      (x \ R(x,y,z)) / R(T(x,x \ 1),y,z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(117,a,1201,a(flip),b,238,a)].">
      <j1 rule="hyper" parents="117 1201 238"/>
    </justification>
  </clause>

  <clause id="1204">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(x \ 1,R(x,y,z)) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1201(a,1),84(a,1,1))].">
      <j1 rule="para" parents="1201 84"/>
    </justification>
  </clause>

  <clause id="1205">
    <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(1201(a,1),651(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1201 651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1206">
    <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(1201(a,1),679(a,2,1))].">
      <j1 rule="para" parents="1201 679"/>
    </justification>
  </clause>

  <clause id="1207">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,639,a(flip),b,1202,a),flip(a)].">
      <j1 rule="hyper" parents="320 639 1202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1208">
    <literal><![CDATA[
      (1 / x) * ((y / (x * y)) * x) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,405,a(flip),b,1202,a)].">
      <j1 rule="hyper" parents="119 405 1202"/>
    </justification>
  </clause>

  <clause id="1209">
    <literal><![CDATA[
      ((x / (y * x)) * y) \ (x / (y * x)) = T(1 / y,(x / (y * x)) * y)
    ]]></literal>
    <justification jstring="[hyper(440,a,219,a(flip),b,1208,a),flip(a)].">
      <j1 rule="hyper" parents="440 219 1208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1210">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,x / y,y) = (1 / (x / y)) \ (y / x)
    ]]></literal>
    <justification jstring="[para(409(a,1),1207(a,1,2)),flip(a)].">
      <j1 rule="para" parents="409 1207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1211">
    <literal><![CDATA[
      x * R(x \ 1,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(1 / x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(1207(a,1),707(a,1))].">
      <j1 rule="para" parents="1207 707"/>
    </justification>
  </clause>

  <clause id="1212">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) * (x \ 1) = R(y * (x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(639(a,1),1084(a,1,1))].">
      <j1 rule="para" parents="639 1084"/>
    </justification>
  </clause>

  <clause id="1213">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,864,a(flip),b,1092,a),flip(a)].">
      <j1 rule="hyper" parents="320 864 1092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1214">
    <literal><![CDATA[
      ((x \ 1) * x) * (x \ y) = y * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(2(a,1),1093(a,2,2,1,2))].">
      <j1 rule="para" parents="2 1093"/>
    </justification>
  </clause>

  <clause id="1215">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(570,a,1214,a)].">
      <j1 rule="hyper" parents="570 1214"/>
    </justification>
  </clause>

  <clause id="1216">
    <literal><![CDATA[
      (x * T(x \ (y \ x),y)) / (y \ x) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,1215,a)].">
      <j1 rule="hyper" parents="131 1215"/>
    </justification>
  </clause>

  <clause id="1217">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ (x \ y),x) = z
    ]]></literal>
    <justification jstring="[para(1216(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1216 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1218">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[para(453(a,1),1096(a,2,1))].">
      <j1 rule="para" parents="453 1096"/>
    </justification>
  </clause>

  <clause id="1219">
    <literal><![CDATA[
      ((x \ (x / y)) * x) * y = x * (y * T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,733,a(flip),b,1097,a),flip(a)].">
      <j1 rule="hyper" parents="58 733 1097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1220">
    <literal><![CDATA[
      x * ((y \ x) * T((y \ x) \ 1,x)) = ((x \ y) * x) * (y \ x)
    ]]></literal>
    <justification jstring="[para(72(a,1),1219(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 1219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1221">
    <literal><![CDATA[
      (x / y) * ((y \ x) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),1114(a,1,2,1))].">
      <j1 rule="para" parents="107 1114"/>
    </justification>
  </clause>

  <clause id="1222">
    <literal><![CDATA[
      (x \ (x * y)) * (((x * y) / x) * z) = ((x * y) / x) * (y * z)
    ]]></literal>
    <justification jstring="[para(224(a,1),1114(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="224 1114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1223">
    <literal><![CDATA[
      ((x / y) \ x) * ((x / (x / y)) * z) = (x / (x / y)) * (y * z)
    ]]></literal>
    <justification jstring="[para(244(a,1),1114(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="244 1114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1224">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ 1) = (y \ x) \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(416,a,1221,a),flip(a)].">
      <j1 rule="hyper" parents="416 1221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1225">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = (x \ 1) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1011,a(flip),b,1224,a)].">
      <j1 rule="hyper" parents="58 1011 1224"/>
    </justification>
  </clause>

  <clause id="1226">
    <literal><![CDATA[
      (x \ (x * y)) \ ((x * y) / x) = ((x * y) / x) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),1224(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1227">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(453(a,1),1179(a,1,1))].">
      <j1 rule="para" parents="453 1179"/>
    </justification>
  </clause>

  <clause id="1228">
    <literal><![CDATA[
      (x \ (y \ x)) * x = (y * T(y \ 1,x)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(2(a,1),1180(a,1,1,2))].">
      <j1 rule="para" parents="2 1180"/>
    </justification>
  </clause>

  <clause id="1229">
    <literal><![CDATA[
      T(x * T(x \ 1,y),x \ y) = K(y \ (x \ y),y)
    ]]></literal>
    <justification jstring="[hyper(239,a,1228,a(flip),b,302,a)].">
      <j1 rule="hyper" parents="239 1228 302"/>
    </justification>
  </clause>

  <clause id="1230">
    <literal><![CDATA[
      L(x \ ((1 / x) \ y),z,u) = x \ ((1 / x) \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(123,a,1190,a),flip(a)].">
      <j1 rule="hyper" parents="123 1190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1231">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) * (x \ 1) = L(y * (x \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,1196,a)].">
      <j1 rule="hyper" parents="133 1196"/>
    </justification>
  </clause>

  <clause id="1232">
    <literal><![CDATA[
      x * L(x \ (y / (x \ 1)),z,u) = L(y,z,u) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),1196(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7 1196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1233">
    <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),1196(a,1,1,1,2))].">
      <j1 rule="para" parents="75 1196"/>
    </justification>
  </clause>

  <clause id="1234">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) * (x \ 1) = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(2(a,1),1212(a,2,1))].">
      <j1 rule="para" parents="2 1212"/>
    </justification>
  </clause>

  <clause id="1235">
    <literal><![CDATA[
      R(x \ 1,y,z) / (x \ 1) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,1234,a)].">
      <j1 rule="hyper" parents="131 1234"/>
    </justification>
  </clause>

  <clause id="1236">
    <literal><![CDATA[
      K(R(x \ 1,y,z) \ (x * R(x \ 1,y,z)),R(x \ 1,y,z)) = x \ T(x,R(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(1235(a,1),1020(a,1,1,2))].">
      <j1 rule="para" parents="1235 1020"/>
    </justification>
  </clause>

  <clause id="1237">
    <literal><![CDATA[
      T(x,x * T(x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(239,a,733,a(flip),b,1218,a(flip))].">
      <j1 rule="hyper" parents="239 733 1218"/>
    </justification>
  </clause>

  <clause id="1238">
    <literal><![CDATA[
      T(x,(x \ 1) * x) = x
    ]]></literal>
    <justification jstring="[para(105(a,1),1237(a,1,2))].">
      <j1 rule="para" parents="105 1237"/>
    </justification>
  </clause>

  <clause id="1239">
    <literal><![CDATA[
      R(x,(x * T(x \ 1,y)) / x,x) = T(x,(x * T(x \ 1,y)) / x)
    ]]></literal>
    <justification jstring="[para(1237(a,1),808(a,1,1))].">
      <j1 rule="para" parents="1237 808"/>
    </justification>
  </clause>

  <clause id="1240">
    <literal><![CDATA[
      T(x \ 1,T(x,y) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(455(a,1),1237(a,1,2))].">
      <j1 rule="para" parents="455 1237"/>
    </justification>
  </clause>

  <clause id="1241">
    <literal><![CDATA[
      T(x \ 1,x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[para(983(a,1),1237(a,1,2))].">
      <j1 rule="para" parents="983 1237"/>
    </justification>
  </clause>

  <clause id="1242">
    <literal><![CDATA[
      T(1 / x,T(x,y) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(999(a,1),1237(a,1,2))].">
      <j1 rule="para" parents="999 1237"/>
    </justification>
  </clause>

  <clause id="1243">
    <literal><![CDATA[
      R(x,x \ 1,x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1238(a,1),803(a,1,1))].">
      <j1 rule="para" parents="1238 803"/>
    </justification>
  </clause>

  <clause id="1244">
    <literal><![CDATA[
      T(x,x \ 1) \ x = (x \ 1) * x
    ]]></literal>
    <justification jstring="[para(1243(a,1),426(a,1,1))].">
      <j1 rule="para" parents="1243 426"/>
    </justification>
  </clause>

  <clause id="1245">
    <literal><![CDATA[
      T(x \ T(x,y),x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,1241,a)].">
      <j1 rule="hyper" parents="49 1241"/>
    </justification>
  </clause>

  <clause id="1246">
    <literal><![CDATA[
      (x \ T(x,y)) * (x \ 1) = (x \ 1) * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,1241,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 1241 17"/>
    </justification>
  </clause>

  <clause id="1247">
    <literal><![CDATA[
      T((x * (1 / y)) / x,T(y,z) / y) = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(1242(a,1),460(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1242 460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1248">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ x = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(656,a,1244,a)].">
      <j1 rule="hyper" parents="656 1244"/>
    </justification>
  </clause>

  <clause id="1249">
    <literal><![CDATA[
      T(x,x \ 1) \ 1 = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(239,a,1244,a(flip),b,1110,a),flip(a)].">
      <j1 rule="hyper" parents="239 1244 1110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1250">
    <literal><![CDATA[
      ((x \ 1) \ 1) * K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(583,a,1248,a)].">
      <j1 rule="hyper" parents="583 1248"/>
    </justification>
  </clause>

  <clause id="1251">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ x != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(1248(a,2),370(a,1))].">
      <j1 rule="para" parents="1248 370"/>
    </justification>
  </clause>

  <clause id="1252">
    <literal><![CDATA[
      T(x \ 1,x) = ((x \ 1) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(656,a,1249,a),flip(a)].">
      <j1 rule="hyper" parents="656 1249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1253">
    <literal><![CDATA[
      1 / T(x \ 1,x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(197,a,1249,a)].">
      <j1 rule="hyper" parents="197 1249"/>
    </justification>
  </clause>

  <clause id="1254">
    <literal><![CDATA[
      T((1 / x) \ 1,1 / x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(642(a,1),1249(a,1,1)),flip(a)].">
      <j1 rule="para" parents="642 1249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1255">
    <literal><![CDATA[
      T(x \ 1,(x \ 1) \ 1) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,106,a,b,1252,a)].">
      <j1 rule="hyper" parents="320 106 1252"/>
    </justification>
  </clause>

  <clause id="1256">
    <literal><![CDATA[
      T((x \ 1) \ 1,x \ 1) = T(x \ 1,x) \ 1
    ]]></literal>
    <justification jstring="[para(1252(a,2),1252(a,2,1))].">
      <j1 rule="para" parents="1252 1252"/>
    </justification>
  </clause>

  <clause id="1257">
    <literal><![CDATA[
      R(x \ 1,T(x,y),x \ 1) = T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(1240(a,1),803(a,1,1))].">
      <j1 rule="para" parents="1240 803"/>
    </justification>
  </clause>

  <clause id="1258">
    <literal><![CDATA[
      T((x * y) \ (y * x),y \ 1) = L(y \ T(y,x),y,x)
    ]]></literal>
    <justification jstring="[para(1245(a,1),746(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1245 746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1259">
    <literal><![CDATA[
      T(x,1 / x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),1254(a,1,1))].">
      <j1 rule="para" parents="75 1254"/>
    </justification>
  </clause>

  <clause id="1260">
    <literal><![CDATA[
      T(x,1 / x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,106,a,b,1259,a),flip(a)].">
      <j1 rule="hyper" parents="320 106 1259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1261">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,1259,a(flip),b,815,a)].">
      <j1 rule="hyper" parents="117 1259 815"/>
    </justification>
  </clause>

  <clause id="1262">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(1259(a,1),1073(a,1,1,1))].">
      <j1 rule="para" parents="1259 1073"/>
    </justification>
  </clause>

  <clause id="1263">
    <literal><![CDATA[
      K(x,1 / x) * x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,815,a,b,1260,a)].">
      <j1 rule="hyper" parents="58 815 1260"/>
    </justification>
  </clause>

  <clause id="1264">
    <literal><![CDATA[
      (x * T(y,y \ 1)) / x = T((x * y) / x,1 / y)
    ]]></literal>
    <justification jstring="[para(1260(a,1),460(a,1,1,2))].">
      <j1 rule="para" parents="1260 460"/>
    </justification>
  </clause>

  <clause id="1265">
    <literal><![CDATA[
      R(R(x,y,z),1 / x,x) = R(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1260(a,1),813(a,2,1))].">
      <j1 rule="para" parents="1260 813"/>
    </justification>
  </clause>

  <clause id="1266">
    <literal><![CDATA[
      (x \ 1) \ (1 / x) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1225,a(flip),b,1261,a)].">
      <j1 rule="hyper" parents="58 1225 1261"/>
    </justification>
  </clause>

  <clause id="1267">
    <literal><![CDATA[
      T(x,x \ 1) / x != y
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / x) = y
    ]]></literal>
    <justification jstring="[para(1263(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1263 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1268">
    <literal><![CDATA[
      (1 / x) / K(x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(197,a,1266,a)].">
      <j1 rule="hyper" parents="197 1266"/>
    </justification>
  </clause>

  <clause id="1269">
    <literal><![CDATA[
      R(1 / x,x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(671,a,1268,a)].">
      <j1 rule="hyper" parents="671 1268"/>
    </justification>
  </clause>

  <clause id="1270">
    <literal><![CDATA[
      R(x / (y * x),y,1 / y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(1269(a,1),411(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1269 411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1271">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x != y
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / x) = y
    ]]></literal>
    <justification jstring="[para(106(a,1),1267(a,1,1))].">
      <j1 rule="para" parents="106 1267"/>
    </justification>
  </clause>

  <clause id="1272">
    <literal><![CDATA[
      (x \ 1) / (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) = y
    ]]></literal>
    <justification jstring="[para(642(a,1),1267(a,1,1))].">
      <j1 rule="para" parents="642 1267"/>
    </justification>
  </clause>

  <clause id="1273">
    <literal><![CDATA[
      R(x \ 1,x,y) \ (((y / (x * y)) * x) * (1 / x)) = x * (1 / x)
    ]]></literal>
    <justification jstring="[para(1270(a,1),184(a,1,1))].">
      <j1 rule="para" parents="1270 184"/>
    </justification>
  </clause>

  <clause id="1274">
    <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(1265(a,1),708(a,1,2))].">
      <j1 rule="para" parents="1265 708"/>
    </justification>
  </clause>

  <clause id="1275">
    <literal><![CDATA[
      L(1 / x,y,z) * (1 / (1 / x)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(75(a,1),1262(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 1262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1276">
    <literal><![CDATA[
      T(L(x,y,z) * (1 / x),x) = x \ L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1262(a,1),107(a,1,1))].">
      <j1 rule="para" parents="1262 107"/>
    </justification>
  </clause>

  <clause id="1277">
    <literal><![CDATA[
      T((x * y) / x,1 / y) = T((x * y) / x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(462,a,1264,a),flip(a)].">
      <j1 rule="hyper" parents="462 1264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1278">
    <literal><![CDATA[
      T((x * T(y,x)) / x,T(y,x) \ 1) = T(y,1 / T(y,x))
    ]]></literal>
    <justification jstring="[para(225(a,1),1277(a,1,1)),flip(a)].">
      <j1 rule="para" parents="225 1277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1279">
    <literal><![CDATA[
      K(x,y) = T((y * x) \ (x * y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,745,a,b,1258,a)].">
      <j1 rule="hyper" parents="320 745 1258"/>
    </justification>
  </clause>

  <clause id="1280">
    <literal><![CDATA[
      T(K(x,y),x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,2),1279(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11 1279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1281">
    <literal><![CDATA[
      T(x \ 1,K(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(49,a,1280,a)].">
      <j1 rule="hyper" parents="49 1280"/>
    </justification>
  </clause>

  <clause id="1282">
    <literal><![CDATA[
      K(x,y) * (x \ 1) = (x \ 1) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1280,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1280 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1283">
    <literal><![CDATA[
      (x \ 1) * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ 1) = z
    ]]></literal>
    <justification jstring="[para(1280(a,1),284(a,1,2))].">
      <j1 rule="para" parents="1280 284"/>
    </justification>
  </clause>

  <clause id="1284">
    <literal><![CDATA[
      T((x * y) \ x,K(y,z)) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(1281(a,1),400(a,2,1))].">
      <j1 rule="para" parents="1281 400"/>
    </justification>
  </clause>

  <clause id="1285">
    <literal><![CDATA[
      T((x * y) \ x,K(y,z)) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(320,a,217,a(flip),b,1284,a),flip(a)].">
      <j1 rule="hyper" parents="320 217 1284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1286">
    <literal><![CDATA[
      T(K(x,y),(z * x) \ z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,1285,a)].">
      <j1 rule="hyper" parents="49 1285"/>
    </justification>
  </clause>

  <clause id="1287">
    <literal><![CDATA[
      T(K(x \ 1,y),x) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(163(a,1),1286(a,1,2))].">
      <j1 rule="para" parents="163 1286"/>
    </justification>
  </clause>

  <clause id="1288">
    <literal><![CDATA[
      T(K(x,y),1 / x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(164(a,1),1286(a,1,2))].">
      <j1 rule="para" parents="164 1286"/>
    </justification>
  </clause>

  <clause id="1289">
    <literal><![CDATA[
      T(1 / x,K(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(49,a,1288,a)].">
      <j1 rule="hyper" parents="49 1288"/>
    </justification>
  </clause>

  <clause id="1290">
    <literal><![CDATA[
      (1 / x) * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (1 / x) = z
    ]]></literal>
    <justification jstring="[para(1288(a,1),284(a,1,2))].">
      <j1 rule="para" parents="1288 284"/>
    </justification>
  </clause>

  <clause id="1291">
    <literal><![CDATA[
      T((1 * x) / y,K(y / x,z)) = R(1 / (y / x),y / x,x)
    ]]></literal>
    <justification jstring="[para(1289(a,1),761(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1289 761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1292">
    <literal><![CDATA[
      T(x,K(x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,1287,a)].">
      <j1 rule="hyper" parents="49 1287"/>
    </justification>
  </clause>

  <clause id="1293">
    <literal><![CDATA[
      x * K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) * x = z
    ]]></literal>
    <justification jstring="[para(1287(a,1),284(a,1,2))].">
      <j1 rule="para" parents="1287 284"/>
    </justification>
  </clause>

  <clause id="1294">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1226(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 1226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1295">
    <literal><![CDATA[
      (x * T(x \ (y \ x),z)) / (y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(1227(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1227 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1296">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ z) = z * T(z \ ((x \ 1) \ z),y)
    ]]></literal>
    <justification jstring="[para(983(a,1),1227(a,1,1))].">
      <j1 rule="para" parents="983 1227"/>
    </justification>
  </clause>

  <clause id="1297">
    <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),1230(a,2,2,1))].">
      <j1 rule="para" parents="72 1230"/>
    </justification>
  </clause>

  <clause id="1298">
    <literal><![CDATA[
      T(x,1 / T(x,y)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(225(a,1),1278(a,1,1)),flip(a)].">
      <j1 rule="para" parents="225 1278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1299">
    <literal><![CDATA[
      x * ((x \ y) * L((x \ y) \ z,u,w)) = y * L(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(490(a,1),694(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="490 694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1300">
    <literal><![CDATA[
      x * (y * R(T(x,y),z,u)) = R(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,447,a(flip),b,715,a)].">
      <j1 rule="hyper" parents="58 447 715"/>
    </justification>
  </clause>

  <clause id="1301">
    <literal><![CDATA[
      R(x,y,z) * (x * u) = x * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(238(a,1),1300(a,1,2)),flip(a)].">
      <j1 rule="para" parents="238 1300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1302">
    <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(653,a,1301,a),flip(a)].">
      <j1 rule="hyper" parents="653 1301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1303">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(598,a,1301,a)].">
      <j1 rule="hyper" parents="598 1301"/>
    </justification>
  </clause>

  <clause id="1304">
    <literal><![CDATA[
      R(x,y,z) * (x \ (R(x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(597,a,1301,a),flip(a)].">
      <j1 rule="hyper" parents="597 1301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1305">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(x,y,z) * (x \ u)) = x
    ]]></literal>
    <justification jstring="[hyper(574,a,1301,a)].">
      <j1 rule="hyper" parents="574 1301"/>
    </justification>
  </clause>

  <clause id="1306">
    <literal><![CDATA[
      x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(342,a,1301,a),flip(a)].">
      <j1 rule="hyper" parents="342 1301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1307">
    <literal><![CDATA[
      R(x,y,z) \ (x * (R(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(123,a,1301,a)].">
      <j1 rule="hyper" parents="123 1301"/>
    </justification>
  </clause>

  <clause id="1308">
    <literal><![CDATA[
      x * (R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,65,a(flip),b,1301,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 1301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1309">
    <literal><![CDATA[
      x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x)
    ]]></literal>
    <justification jstring="[para(105(a,1),1301(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 1301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1310">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * T(x,R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(285,a,1308,a)].">
      <j1 rule="hyper" parents="285 1308"/>
    </justification>
  </clause>

  <clause id="1311">
    <literal><![CDATA[
      L(R(x,y,z) \ 1,x,1 / x) = (1 / x) * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1308,a(flip),b,437,a),flip(a)].">
      <j1 rule="hyper" parents="119 1308 437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1312">
    <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(1308(a,1),980(a,1,2,1,2))].">
      <j1 rule="para" parents="1308 980"/>
    </justification>
  </clause>

  <clause id="1313">
    <literal><![CDATA[
      R(x,y,z) * (x \ (y * z)) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(101(a,1),1303(a,1,2)),flip(a)].">
      <j1 rule="para" parents="101 1303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1314">
    <literal><![CDATA[
      R(x,y,y \ z) * (x \ z) = x \ ((x * y) * (y \ z))
    ]]></literal>
    <justification jstring="[para(368(a,1),1303(a,1,2)),flip(a)].">
      <j1 rule="para" parents="368 1303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1315">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) * (x \ u) = w
    ]]></literal>
    <justification jstring="[para(1305(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1305 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1316">
    <literal><![CDATA[
      R(x,y,x) * (x \ (y * x)) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(239,a,101,a(flip),b,1306,a),flip(a)].">
      <j1 rule="hyper" parents="239 101 1306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1317">
    <literal><![CDATA[
      R(x,y,x) * T(y,x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(17(a,2),1316(a,1,2))].">
      <j1 rule="para" parents="17 1316"/>
    </justification>
  </clause>

  <clause id="1318">
    <literal><![CDATA[
      R(x,y,x) \ T(x * y,x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,1317,a)].">
      <j1 rule="hyper" parents="123 1317"/>
    </justification>
  </clause>

  <clause id="1319">
    <literal><![CDATA[
      x \ T(y * z,y) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      R(y,z,y) = x
    ]]></literal>
    <justification jstring="[para(1318(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="1318 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1320">
    <literal><![CDATA[
      R(x,y,z) = (x \ ((x * y) * z)) / (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(131,a,1313,a),flip(a)].">
      <j1 rule="hyper" parents="131 1313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1321">
    <literal><![CDATA[
      x \ ((x * (x \ y)) * ((x \ y) \ z)) = ((y * ((x \ y) \ z)) / z) * (x \ z)
    ]]></literal>
    <justification jstring="[para(698(a,1),1314(a,1,1)),flip(a)].">
      <j1 rule="para" parents="698 1314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1322">
    <literal><![CDATA[
      L((x \ y) / y,z,u) * y = (L(1 / x,z,u) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(408(a,1),728(a,1,1,1))].">
      <j1 rule="para" parents="408 728"/>
    </justification>
  </clause>

  <clause id="1323">
    <literal><![CDATA[
      x * ((x \ y) * R((x \ y) \ z,u,w)) = y * R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(119,a,754,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="119 754 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1324">
    <literal><![CDATA[
      x \ (y * R(y \ (x * z),u,w)) = (x \ y) * R((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(754(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="754 474"/>
    </justification>
  </clause>

  <clause id="1325">
    <literal><![CDATA[
      x \ (y * L(y \ (x * z),u,w)) = (x \ y) * L((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(755(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="755 474"/>
    </justification>
  </clause>

  <clause id="1326">
    <literal><![CDATA[
      (L(x / (y / z),u,w) * (y / z)) * z = L((x * z) / y,u,w) * y
    ]]></literal>
    <justification jstring="[para(525(a,1),760(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="525 760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1327">
    <literal><![CDATA[
      (R(x / (y / z),u,w) * (y / z)) * z = R((x * z) / y,u,w) * y
    ]]></literal>
    <justification jstring="[para(762(a,1),508(a,1,1)),flip(a)].">
      <j1 rule="para" parents="762 508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1328">
    <literal><![CDATA[
      (x * y) * L(T(y,x),z,u) = (L(y,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,513,a(flip),b,804,a),flip(a)].">
      <j1 rule="hyper" parents="58 513 804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1329">
    <literal><![CDATA[
      (x * y) * R(T(y,x),z,u) = (R(y,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,514,a(flip),b,805,a),flip(a)].">
      <j1 rule="hyper" parents="58 514 805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1330">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) != u / (x * y)
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(845(a,2),41(a,1))].">
      <j1 rule="para" parents="845 41"/>
    </justification>
  </clause>

  <clause id="1331">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (x * u))) / z) = x * (y * ((z * (y \ u)) / z))
    ]]></literal>
    <justification jstring="[para(92(a,1),875(a,1,2,1,2))].">
      <j1 rule="para" parents="92 875"/>
    </justification>
  </clause>

  <clause id="1332">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ u)) / z) = x * (y * ((z * (y \ (x \ u))) / z))
    ]]></literal>
    <justification jstring="[para(298(a,1),875(a,1,2,1,2))].">
      <j1 rule="para" parents="298 875"/>
    </justification>
  </clause>

  <clause id="1333">
    <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(878(a,1),286(a,1,2))].">
      <j1 rule="para" parents="878 286"/>
    </justification>
  </clause>

  <clause id="1334">
    <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(879(a,1),286(a,1,2))].">
      <j1 rule="para" parents="879 286"/>
    </justification>
  </clause>

  <clause id="1335">
    <literal><![CDATA[
      (x / y) * (y * ((z * (y \ 1)) / z)) = x * ((z * (x \ (x / y))) / z)
    ]]></literal>
    <justification jstring="[hyper(119,a,880,a(flip),b,93,a),flip(a)].">
      <j1 rule="hyper" parents="119 880 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1336">
    <literal><![CDATA[
      (1 / x) \ ((y * ((1 / x) * z)) / y) = x * ((y * (x \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(116,a,881,a(flip),b,259,a)].">
      <j1 rule="hyper" parents="116 881 259"/>
    </justification>
  </clause>

  <clause id="1337">
    <literal><![CDATA[
      ((x * (y / (1 / z))) / x) * (1 / z) = ((x * (y * z)) / x) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,885,a(flip),b,262,a),flip(a)].">
      <j1 rule="hyper" parents="117 885 262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1338">
    <literal><![CDATA[
      ((x * (y * (z \ 1))) / x) / (z \ 1) = ((x * (y / z)) / x) * z
    ]]></literal>
    <justification jstring="[hyper(117,a,886,a(flip),b,261,a)].">
      <j1 rule="hyper" parents="117 886 261"/>
    </justification>
  </clause>

  <clause id="1339">
    <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,921,a(flip),b,231,a)].">
      <j1 rule="hyper" parents="119 921 231"/>
    </justification>
  </clause>

  <clause id="1340">
    <literal><![CDATA[
      (T(x,y) * z) * T(x,z) = (x * z) * T(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,898,a(flip),b,925,a),flip(a)].">
      <j1 rule="hyper" parents="58 898 925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1341">
    <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,1340,a)].">
      <j1 rule="hyper" parents="117 64 1340"/>
    </justification>
  </clause>

  <clause id="1342">
    <literal><![CDATA[
      T(T(x,x \ 1),y) / T(x,x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,985,a(flip),b,1341,a),flip(a)].">
      <j1 rule="hyper" parents="320 985 1341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1343">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (T(z / x,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,930,a(flip),b,630,a)].">
      <j1 rule="hyper" parents="119 930 630"/>
    </justification>
  </clause>

  <clause id="1344">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(995(a,1),946(a,1))].">
      <j1 rule="para" parents="995 946"/>
    </justification>
  </clause>

  <clause id="1345">
    <literal><![CDATA[
      (x * y) / a(z,z \ y,T(x,y)) = L(x,z \ y,z) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,741,a(flip),b,947,a),flip(a)].">
      <j1 rule="hyper" parents="320 741 947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1346">
    <literal><![CDATA[
      (L(x,y \ z,y) * z) \ (x * z) = a(y,y \ z,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(188,a,1345,a)].">
      <j1 rule="hyper" parents="188 1345"/>
    </justification>
  </clause>

  <clause id="1347">
    <literal><![CDATA[
      L((x \ (y * (x * z))) / z,z,x) = T((z * y) / z,x * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,460,a(flip),b,961,a),flip(a)].">
      <j1 rule="hyper" parents="320 460 961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1348">
    <literal><![CDATA[
      L((T(x,y) * (x \ y)) / y,y,x) = (y * K(T(x,y),y)) / y
    ]]></literal>
    <justification jstring="[para(1101(a,1),962(a,1,1,1))].">
      <j1 rule="para" parents="1101 962"/>
    </justification>
  </clause>

  <clause id="1349">
    <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),972(a,1,1,1,2))].">
      <j1 rule="para" parents="72 972"/>
    </justification>
  </clause>

  <clause id="1350">
    <literal><![CDATA[
      (x * y) \ ((x \ (x * y)) * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(956(a,1),1039(a,1))].">
      <j1 rule="para" parents="956 1039"/>
    </justification>
  </clause>

  <clause id="1351">
    <literal><![CDATA[
      K(x \ (x * y),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(85(a,1),1350(a,1))].">
      <j1 rule="para" parents="85 1350"/>
    </justification>
  </clause>

  <clause id="1352">
    <literal><![CDATA[
      T((1 * x) / y,K(y / x,z)) = x / y
    ]]></literal>
    <justification jstring="[hyper(320,a,409,a(flip),b,1291,a),flip(a)].">
      <j1 rule="hyper" parents="320 409 1291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1353">
    <literal><![CDATA[
      T(x / y,K(y / x,z)) = x / y
    ]]></literal>
    <justification jstring="[para(2(a,1),1352(a,1,1,1))].">
      <j1 rule="para" parents="2 1352"/>
    </justification>
  </clause>

  <clause id="1354">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(1353(a,1),246(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1353 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1355">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,107,a(flip),b,1354,a),flip(a)].">
      <j1 rule="hyper" parents="320 107 1354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1356">
    <literal><![CDATA[
      R(x,y,a(z,u,a(w,v5,v6))) = x
    ]]></literal>
    <justification jstring="[hyper(515,a,346,a)].">
      <j1 rule="hyper" parents="515 346"/>
    </justification>
  </clause>

  <clause id="1357">
    <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(346(a,1),525(a,2,1))].">
      <j1 rule="para" parents="346 525"/>
    </justification>
  </clause>

  <clause id="1358">
    <literal><![CDATA[
      R(x,y,a(z,u,a(w,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      x = v7
    ]]></literal>
    <justification jstring="[para(1356(a,1),46(a,2))].">
      <j1 rule="para" parents="1356 46"/>
    </justification>
  </clause>

  <clause id="1359">
    <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),509(a,1,1,1))].">
      <j1 rule="para" parents="7 509"/>
    </justification>
  </clause>

  <clause id="1360">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = K(x,(y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,661,a(flip),b,665,a)].">
      <j1 rule="hyper" parents="58 661 665"/>
    </justification>
  </clause>

  <clause id="1361">
    <literal><![CDATA[
      T(x,L(y \ 1,y,z)) = T(x,(z * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(239,a,395,a(flip),b,730,a),flip(a)].">
      <j1 rule="hyper" parents="239 395 730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1362">
    <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),821(a,1,2,1))].">
      <j1 rule="para" parents="92 821"/>
    </justification>
  </clause>

  <clause id="1363">
    <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,346,a(flip),b,889,a)].">
      <j1 rule="hyper" parents="116 346 889"/>
    </justification>
  </clause>

  <clause id="1364">
    <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),911(a,1,1))].">
      <j1 rule="para" parents="90 911"/>
    </justification>
  </clause>

  <clause id="1365">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (R(1 / x,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(862,a,915,a)].">
      <j1 rule="hyper" parents="862 915"/>
    </justification>
  </clause>

  <clause id="1366">
    <literal><![CDATA[
      ((x \ ((x * y) / z)) * x) * z = x * (z * T(z \ y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,1097,a(flip),b,918,a)].">
      <j1 rule="hyper" parents="58 1097 918"/>
    </justification>
  </clause>

  <clause id="1367">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[para(5(a,1),1366(a,1,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1368">
    <literal><![CDATA[
      x * (x * T(x \ T(y,x),x)) = ((x \ y) * x) * x
    ]]></literal>
    <justification jstring="[para(225(a,1),1366(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="225 1366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1369">
    <literal><![CDATA[
      x * T(x \ T(y,x),x) = T((x \ y) * x,x)
    ]]></literal>
    <justification jstring="[hyper(240,a,1368,a),flip(a)].">
      <j1 rule="hyper" parents="240 1368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1370">
    <literal><![CDATA[
      T((x \ y) * x,x) = (x \ T(y,x)) * x
    ]]></literal>
    <justification jstring="[hyper(284,a,1369,a),flip(a)].">
      <j1 rule="hyper" parents="284 1369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1371">
    <literal><![CDATA[
      T((x \ y) * x,x) / x = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,1369,a(flip),b,105,a(flip))].">
      <j1 rule="hyper" parents="117 1369 105"/>
    </justification>
  </clause>

  <clause id="1372">
    <literal><![CDATA[
      T(x,y) \ T((y \ x) * y,y) = K(y \ T(x,y),y)
    ]]></literal>
    <justification jstring="[para(1369(a,1),432(a,1,2))].">
      <j1 rule="para" parents="1369 432"/>
    </justification>
  </clause>

  <clause id="1373">
    <literal><![CDATA[
      x * (T((x \ y) * x,x) / x) = T(y,x)
    ]]></literal>
    <justification jstring="[para(1370(a,2),71(a,1,2,1))].">
      <j1 rule="para" parents="1370 71"/>
    </justification>
  </clause>

  <clause id="1374">
    <literal><![CDATA[
      T(x * y,y) / y = y \ T(y * x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1371(a,1,1,1,1))].">
      <j1 rule="para" parents="4 1371"/>
    </justification>
  </clause>

  <clause id="1375">
    <literal><![CDATA[
      (x \ T(y,x)) * x != z
    ]]></literal>
    <literal><![CDATA[
      T((x \ y) * x,x) = z
    ]]></literal>
    <justification jstring="[para(1371(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1371 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1376">
    <literal><![CDATA[
      x \ T(x * (y / x),x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(76(a,1),1371(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 1371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1377">
    <literal><![CDATA[
      T(x * (y / x),x) = x * (T(y,x) / x)
    ]]></literal>
    <justification jstring="[para(76(a,1),1373(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="76 1373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1378">
    <literal><![CDATA[
      T(x * ((1 / x) * y),x) = x * ((1 / x) * T(y,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,992,a(flip),b,1374,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 992 1374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1379">
    <literal><![CDATA[
      x \ T(x * T((x * y) / x,z),x) = T(x * T(y,z),x) / x
    ]]></literal>
    <justification jstring="[para(454(a,1),1374(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="454 1374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1380">
    <literal><![CDATA[
      x \ T(x * L((x * y) / x,z,u),x) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[para(636(a,1),1374(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="636 1374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1381">
    <literal><![CDATA[
      T(x * y,x) \ T(y * x,x) = K(x \ T(x * y,x),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1372(a,1,2,1,1))].">
      <j1 rule="para" parents="4 1372"/>
    </justification>
  </clause>

  <clause id="1382">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = x * (T((x \ y) * z,x) / z)
    ]]></literal>
    <justification jstring="[para(993(a,1),1367(a,1,2)),flip(a)].">
      <j1 rule="para" parents="993 1367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1383">
    <literal><![CDATA[
      ((x \ (y / y)) * x) * y = x * (K(x \ 1,x) * (x \ y))
    ]]></literal>
    <justification jstring="[para(1215(a,2),1367(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1215 1367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1384">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) = ((x \ 1) * x) * y
    ]]></literal>
    <justification jstring="[para(69(a,1),1383(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="69 1383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1385">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(570,a,1384,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="570 1384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1387">
    <literal><![CDATA[
      K(x \ 1,x) * (x * y) = x * (K(x \ 1,x) * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1385(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 1385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1388">
    <literal><![CDATA[
      x * (K(x \ 1,x) * T(y,x)) = K(x \ 1,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(17(a,2),1385(a,1,2,2))].">
      <j1 rule="para" parents="17 1385"/>
    </justification>
  </clause>

  <clause id="1389">
    <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(1387(a,1),232(a,1,2))].">
      <j1 rule="para" parents="1387 232"/>
    </justification>
  </clause>

  <clause id="1390">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1218,a(flip),b,919,a),flip(a)].">
      <j1 rule="hyper" parents="58 1218 919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1391">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * y = x * ((y \ (x \ y)) * y)
    ]]></literal>
    <justification jstring="[para(105(a,1),1390(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 1390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1392">
    <literal><![CDATA[
      x * T(y * T(y \ 1,x),x) = y * ((x \ (y \ x)) * x)
    ]]></literal>
    <justification jstring="[hyper(285,a,1391,a)].">
      <j1 rule="hyper" parents="285 1391"/>
    </justification>
  </clause>

  <clause id="1393">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = (z * y) * T((z * y) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,453,a(flip),b,926,a),flip(a)].">
      <j1 rule="hyper" parents="320 453 926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1394">
    <literal><![CDATA[
      x * (y * T(L(x,z,u),y)) = L(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(284,a,968,a),flip(a)].">
      <j1 rule="hyper" parents="284 968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1395">
    <literal><![CDATA[
      L(x,y,z) * (x * u) = x * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(105(a,1),1394(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 1394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1396">
    <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(653,a,1395,a),flip(a)].">
      <j1 rule="hyper" parents="653 1395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1397">
    <literal><![CDATA[
      x \ (L(x,y,z) * u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(598,a,1395,a)].">
      <j1 rule="hyper" parents="598 1395"/>
    </justification>
  </clause>

  <clause id="1398">
    <literal><![CDATA[
      L(x,y,z) * (x \ (L(x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(597,a,1395,a),flip(a)].">
      <j1 rule="hyper" parents="597 1395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1399">
    <literal><![CDATA[
      x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(342,a,1395,a),flip(a)].">
      <j1 rule="hyper" parents="342 1395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1400">
    <literal><![CDATA[
      (x * (L(x,y,z) * u)) / (x * u) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,1395,a)].">
      <j1 rule="hyper" parents="131 1395"/>
    </justification>
  </clause>

  <clause id="1401">
    <literal><![CDATA[
      L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(123,a,1395,a)].">
      <j1 rule="hyper" parents="123 1395"/>
    </justification>
  </clause>

  <clause id="1402">
    <literal><![CDATA[
      (x * y) / (x * (L(x,z,u) \ y)) = L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,151,a(flip),b,1395,a)].">
      <j1 rule="hyper" parents="117 151 1395"/>
    </justification>
  </clause>

  <clause id="1403">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,1395,a)].">
      <j1 rule="hyper" parents="116 151 1395"/>
    </justification>
  </clause>

  <clause id="1404">
    <literal><![CDATA[
      x * (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,65,a(flip),b,1395,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 1395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1405">
    <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,1395,a(flip),b,84,a)].">
      <j1 rule="hyper" parents="116 1395 84"/>
    </justification>
  </clause>

  <clause id="1406">
    <literal><![CDATA[
      x \ (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,1404,a)].">
      <j1 rule="hyper" parents="123 1404"/>
    </justification>
  </clause>

  <clause id="1407">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,1 / x) = (1 / x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1404,a(flip),b,437,a),flip(a)].">
      <j1 rule="hyper" parents="119 1404 437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1408">
    <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(1404(a,1),307(a,1,1))].">
      <j1 rule="para" parents="1404 307"/>
    </justification>
  </clause>

  <clause id="1409">
    <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(1404(a,2),1229(a,1,2))].">
      <j1 rule="para" parents="1404 1229"/>
    </justification>
  </clause>

  <clause id="1410">
    <literal><![CDATA[
      x \ (L(x,y,z) * (u * x)) = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[para(17(a,2),1397(a,2,2))].">
      <j1 rule="para" parents="17 1397"/>
    </justification>
  </clause>

  <clause id="1411">
    <literal><![CDATA[
      x \ (L(x,y,z) \ (u * x)) = L(x,y,z) \ T(u,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,17,a,b,1398,a),flip(a)].">
      <j1 rule="hyper" parents="116 17 1398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1412">
    <literal><![CDATA[
      T((x * y) / x,L(y,z,u) * x) = L((y * x) / x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1401(a,1),1347(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1401 1347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1413">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (L(x,y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(1402(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1402 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1414">
    <literal><![CDATA[
      (x \ 1) * ((y * ((x \ 1) \ 1)) / y) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,1294,a(flip),b,973,a),flip(a)].">
      <j1 rule="hyper" parents="320 1294 973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1415">
    <literal><![CDATA[
      ((x * (y / (y / T(z,x)))) / x) \ ((y / T(z,x)) * z) = y / T(z,x)
    ]]></literal>
    <justification jstring="[para(225(a,1),975(a,1,2,2))].">
      <j1 rule="para" parents="225 975"/>
    </justification>
  </clause>

  <clause id="1416">
    <literal><![CDATA[
      x * ((x \ y) * T((x \ y) \ 1,z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(3(a,1),1086(a,2,2,1,2))].">
      <j1 rule="para" parents="3 1086"/>
    </justification>
  </clause>

  <clause id="1417">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(123,a,1416,a),flip(a)].">
      <j1 rule="hyper" parents="123 1416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1418">
    <literal><![CDATA[
      x * T(x \ y,y \ x) = y * K((y \ x) \ 1,y \ x)
    ]]></literal>
    <justification jstring="[para(358(a,1),1416(a,1,2)),flip(a)].">
      <j1 rule="para" parents="358 1416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1419">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(z \ (z / (y \ x)),z)
    ]]></literal>
    <justification jstring="[para(1017(a,2),1416(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1017 1416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1420">
    <literal><![CDATA[
      (x \ y) * K(z \ (z / ((x \ y) \ (x \ 1))),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(1042,a,1419,a),flip(a)].">
      <j1 rule="hyper" parents="1042 1419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1421">
    <literal><![CDATA[
      T(x * y,z) / y = x * K(z \ (z / (x \ (1 / y))),z)
    ]]></literal>
    <justification jstring="[hyper(1034,a,1419,a)].">
      <j1 rule="hyper" parents="1034 1419"/>
    </justification>
  </clause>

  <clause id="1422">
    <literal><![CDATA[
      K(x \ (x / (y \ z)),x) = y \ (z * T(z \ y,x))
    ]]></literal>
    <justification jstring="[hyper(536,a,1419,a),flip(a)].">
      <j1 rule="hyper" parents="536 1419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1423">
    <literal><![CDATA[
      (x * y) * K(z \ (z / ((x * y) \ x)),z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),1419(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1424">
    <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),1419(a,2,2,1,2,2))].">
      <j1 rule="para" parents="13 1419"/>
    </justification>
  </clause>

  <clause id="1425">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),x) = z \ ((y * z) * T((y * z) \ z,x))
    ]]></literal>
    <justification jstring="[para(17(a,2),1422(a,1,1,2,2))].">
      <j1 rule="para" parents="17 1422"/>
    </justification>
  </clause>

  <clause id="1426">
    <literal><![CDATA[
      K(x \ (x / (y \ (y / z))),x) = y \ ((y / z) * T(z,x))
    ]]></literal>
    <justification jstring="[para(75(a,1),1422(a,2,2,2,1))].">
      <j1 rule="para" parents="75 1422"/>
    </justification>
  </clause>

  <clause id="1427">
    <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,1417,a)].">
      <j1 rule="hyper" parents="116 92 1417"/>
    </justification>
  </clause>

  <clause id="1428">
    <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),1418(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1429">
    <literal><![CDATA[
      (x / y) * K(z \ (z / ((x / y) \ (1 / y))),z) = T(x,z) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),1421(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7 1421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1430">
    <literal><![CDATA[
      (T(x / (y / z),u) * (y / z)) * z = y * T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,453,a(flip),b,1087,a),flip(a)].">
      <j1 rule="hyper" parents="320 453 1087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1431">
    <literal><![CDATA[
      (x \ y) * (T(y / x,z) \ 1) = T(y / x,z) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),1142(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1432">
    <literal><![CDATA[
      T(x / (y \ x),z) \ ((y \ x) \ x) = ((y \ x) \ x) * (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),1431(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="72 1431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1433">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),1189(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1435">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(20(a,2),1433(a,2,2))].">
      <j1 rule="para" parents="20 1433"/>
    </justification>
  </clause>

  <clause id="1436">
    <literal><![CDATA[
      L(T(x,y),z,u) * (x \ 1) = x \ L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(20(a,2),1435(a,1,1))].">
      <j1 rule="para" parents="20 1435"/>
    </justification>
  </clause>

  <clause id="1437">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ x) = x * (y \ ((x \ y) * x))
    ]]></literal>
    <justification jstring="[para(956(a,1),1220(a,1,2)),flip(a)].">
      <j1 rule="para" parents="956 1220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1438">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ x) = x * K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(85(a,1),1437(a,2,2))].">
      <j1 rule="para" parents="85 1437"/>
    </justification>
  </clause>

  <clause id="1439">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(y \ (y * x),y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1438(a,1,1,1))].">
      <j1 rule="para" parents="4 1438"/>
    </justification>
  </clause>

  <clause id="1440">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1439(a,2,2,1))].">
      <j1 rule="para" parents="4 1439"/>
    </justification>
  </clause>

  <clause id="1441">
    <literal><![CDATA[
      (x * y) * L(x \ 1,x,y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(626,a,1440,a)].">
      <j1 rule="hyper" parents="626 1440"/>
    </justification>
  </clause>

  <clause id="1442">
    <literal><![CDATA[
      x \ (y * K(x / y,y)) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[hyper(321,a,1440,a)].">
      <j1 rule="hyper" parents="321 1440"/>
    </justification>
  </clause>

  <clause id="1444">
    <literal><![CDATA[
      ((x * y) / x) * (y * z) = y * (((x * y) / x) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),1222(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 1222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1445">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = ((y * x) / y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(598,a,1444,a)].">
      <j1 rule="hyper" parents="598 1444"/>
    </justification>
  </clause>

  <clause id="1446">
    <literal><![CDATA[
      x * (((y * x) / y) * (x \ z)) = ((y * x) / y) * z
    ]]></literal>
    <justification jstring="[hyper(342,a,1444,a),flip(a)].">
      <j1 rule="hyper" parents="342 1444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1447">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = y * (((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,1444,a)].">
      <j1 rule="hyper" parents="116 151 1444"/>
    </justification>
  </clause>

  <clause id="1448">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((((x * y) / x) \ y) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(743,a,1445,a),flip(a)].">
      <j1 rule="hyper" parents="743 1445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1449">
    <literal><![CDATA[
      ((x * y) / x) * z != y * u
    ]]></literal>
    <literal><![CDATA[
      ((x * y) / x) * (y \ z) = u
    ]]></literal>
    <justification jstring="[para(1446(a,1),38(a,1))].">
      <j1 rule="para" parents="1446 38"/>
    </justification>
  </clause>

  <clause id="1450">
    <literal><![CDATA[
      (x / (x / y)) * (y * z) = y * ((x / (x / y)) * z)
    ]]></literal>
    <justification jstring="[hyper(619,a,1223,a),flip(a)].">
      <j1 rule="hyper" parents="619 1223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1451">
    <literal><![CDATA[
      (x / (x / y)) * (y \ 1) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(416,a,1450,a),flip(a)].">
      <j1 rule="hyper" parents="416 1450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1453">
    <literal><![CDATA[
      (x / (x / y)) * z != y * ((x / (x / y)) * u)
    ]]></literal>
    <literal><![CDATA[
      y * u = z
    ]]></literal>
    <justification jstring="[para(1450(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="1450 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1454">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = x \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,1036,a(flip),b,1451,a)].">
      <j1 rule="hyper" parents="58 1036 1451"/>
    </justification>
  </clause>

  <clause id="1455">
    <literal><![CDATA[
      (L(1 / x,y,z) * x) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[hyper(854,a,1322,a),flip(a)].">
      <j1 rule="hyper" parents="854 1322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1456">
    <literal><![CDATA[
      (1 / x) \ ((y * (1 / x)) / y) = x * ((y * (x \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(3(a,1),1336(a,1,2,1,2))].">
      <j1 rule="para" parents="3 1336"/>
    </justification>
  </clause>

  <clause id="1457">
    <literal><![CDATA[
      ((x * (x * y)) / x) / y = T(x,x / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(1158,a,1337,a),flip(a)].">
      <j1 rule="hyper" parents="1158 1337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1458">
    <literal><![CDATA[
      (1 / x) * ((y * ((1 / x) \ z)) / y) = ((y * (z * x)) / y) / x
    ]]></literal>
    <justification jstring="[hyper(972,a,1337,a)].">
      <j1 rule="hyper" parents="972 1337"/>
    </justification>
  </clause>

  <clause id="1459">
    <literal><![CDATA[
      ((x * (1 / (1 / y))) / x) * (1 / y) = ((x * y) / x) / y
    ]]></literal>
    <justification jstring="[para(2(a,1),1337(a,2,1,1,2))].">
      <j1 rule="para" parents="2 1337"/>
    </justification>
  </clause>

  <clause id="1460">
    <literal><![CDATA[
      T(x,x / (1 / (x \ y))) = ((x * y) / x) / (x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),1457(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 1457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1461">
    <literal><![CDATA[
      (1 / x) * ((y * ((1 / x) \ 1)) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(972,a,1459,a)].">
      <j1 rule="hyper" parents="972 1459"/>
    </justification>
  </clause>

  <clause id="1462">
    <literal><![CDATA[
      (1 / x) * ((y * x) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[para(75(a,1),1461(a,1,2,1,2))].">
      <j1 rule="para" parents="75 1461"/>
    </justification>
  </clause>

  <clause id="1463">
    <literal><![CDATA[
      ((x * T(y,x)) / x) / T(y,x) = (1 / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(225(a,1),1462(a,1,2)),flip(a)].">
      <j1 rule="para" parents="225 1462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1465">
    <literal><![CDATA[
      x \ y != ((z * (u \ 1)) / z) / (u \ 1)
    ]]></literal>
    <literal><![CDATA[
      x * (u * ((z * (u \ 1)) / z)) = y
    ]]></literal>
    <justification jstring="[para(1462(a,1),623(a,2))].">
      <j1 rule="para" parents="1462 623"/>
    </justification>
  </clause>

  <clause id="1466">
    <literal><![CDATA[
      (1 / T(x,y)) * x = x / T(x,y)
    ]]></literal>
    <justification jstring="[para(225(a,1),1463(a,1,1)),flip(a)].">
      <j1 rule="para" parents="225 1463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1467">
    <literal><![CDATA[
      (x / T(x,y)) / x = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,1466,a)].">
      <j1 rule="hyper" parents="131 1466"/>
    </justification>
  </clause>

  <clause id="1468">
    <literal><![CDATA[
      (1 / T(x,y)) \ (x / T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(123,a,1466,a)].">
      <j1 rule="hyper" parents="123 1466"/>
    </justification>
  </clause>

  <clause id="1469">
    <literal><![CDATA[
      (1 / T(x,y)) \ (T(x,z) / T(x,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(1468(a,1),1033(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1468 1033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1470">
    <literal><![CDATA[
      T(x,1 / T(x,y)) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1468(a,1),1035(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1468 1035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1471">
    <literal><![CDATA[
      (T(x,y) / T(x,z)) / T(x,y) = 1 / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(197,a,1469,a)].">
      <j1 rule="hyper" parents="197 1469"/>
    </justification>
  </clause>

  <clause id="1472">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1298(a,1),1470(a,1,1))].">
      <j1 rule="para" parents="1298 1470"/>
    </justification>
  </clause>

  <clause id="1473">
    <literal><![CDATA[
      ((x * (y * (z \ 1))) / x) / (z \ 1) = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,864,a(flip),b,1338,a),flip(a)].">
      <j1 rule="hyper" parents="320 864 1338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1474">
    <literal><![CDATA[
      x * (y * T(y \ (x \ (z * y)),u)) = (T(z / x,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,919,a(flip),b,1343,a)].">
      <j1 rule="hyper" parents="58 919 1343"/>
    </justification>
  </clause>

  <clause id="1475">
    <literal><![CDATA[
      (T((x * y) / x,z) * x) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),1343(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1476">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[para(453(a,1),1343(a,2,1))].">
      <j1 rule="para" parents="453 1343"/>
    </justification>
  </clause>

  <clause id="1477">
    <literal><![CDATA[
      (x * T(y,z)) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(454(a,1),1475(a,1,1))].">
      <j1 rule="para" parents="454 1475"/>
    </justification>
  </clause>

  <clause id="1478">
    <literal><![CDATA[
      (x * y) / T(y,z) = (x / T(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(595,a,1477,a)].">
      <j1 rule="hyper" parents="595 1477"/>
    </justification>
  </clause>

  <clause id="1479">
    <literal><![CDATA[
      T((x / y) * T(y,z),y) = y \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(440,a,147,a(flip),b,1477,a)].">
      <j1 rule="hyper" parents="440 147 1477"/>
    </justification>
  </clause>

  <clause id="1480">
    <literal><![CDATA[
      ((x / T(y,z)) * y) * T(y,z) = x * y
    ]]></literal>
    <justification jstring="[hyper(326,a,1477,a),flip(a)].">
      <j1 rule="hyper" parents="326 1477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1481">
    <literal><![CDATA[
      ((x / y) * T(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,147,a(flip),b,1477,a),flip(a)].">
      <j1 rule="hyper" parents="320 147 1477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1482">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * y) * T(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,1477,a)].">
      <j1 rule="hyper" parents="123 1477"/>
    </justification>
  </clause>

  <clause id="1483">
    <literal><![CDATA[
      (x * T(y,z)) / y = (x / y) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,147,a(flip),b,1477,a)].">
      <j1 rule="hyper" parents="117 147 1477"/>
    </justification>
  </clause>

  <clause id="1484">
    <literal><![CDATA[
      ((x / T(y,z)) / y) * T(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(117,a,79,a(flip),b,1477,a),flip(a)].">
      <j1 rule="hyper" parents="117 79 1477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1485">
    <literal><![CDATA[
      (x * (y / z)) * T(y / z,z) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(107(a,1),1477(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1486">
    <literal><![CDATA[
      (x / T(y,z)) / y = (x / y) / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,153,a(flip),b,1478,a(flip))].">
      <j1 rule="hyper" parents="117 153 1478"/>
    </justification>
  </clause>

  <clause id="1487">
    <literal><![CDATA[
      (x * y) / T(y,z) != y * u
    ]]></literal>
    <literal><![CDATA[
      T(x / T(y,z),y) = u
    ]]></literal>
    <justification jstring="[para(1478(a,2),240(a,2)),flip(a)].">
      <j1 rule="para" parents="1478 240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1488">
    <literal><![CDATA[
      x * T(y,z) != u * y
    ]]></literal>
    <literal><![CDATA[
      (u / T(y,z)) * y = x
    ]]></literal>
    <justification jstring="[para(1480(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="1480 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1489">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[para(1170(a,2),1480(a,1,1))].">
      <j1 rule="para" parents="1170 1480"/>
    </justification>
  </clause>

  <clause id="1490">
    <literal><![CDATA[
      (x / y) * T(y,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,105,a(flip),b,1481,a),flip(a)].">
      <j1 rule="hyper" parents="117 105 1481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1491">
    <literal><![CDATA[
      T(x,y) \ ((x * y) / x) = T(y / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(440,a,xx,b,1490,a),flip(a)].">
      <j1 rule="hyper" parents="440 1490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1492">
    <literal><![CDATA[
      ((x \ y) * y) / (x \ y) = x * T(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(348,a,1490,a),flip(a)].">
      <j1 rule="hyper" parents="348 1490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1493">
    <literal><![CDATA[
      ((x * y) / x) / T(x,y) = y / x
    ]]></literal>
    <justification jstring="[hyper(131,a,1490,a)].">
      <j1 rule="hyper" parents="131 1490"/>
    </justification>
  </clause>

  <clause id="1494">
    <literal><![CDATA[
      T(x,y) = (y / x) \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(123,a,1490,a),flip(a)].">
      <j1 rule="hyper" parents="123 1490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1495">
    <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(397(a,1),1490(a,1,1)),flip(a)].">
      <j1 rule="para" parents="397 1490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1496">
    <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(423(a,1),1490(a,1,1)),flip(a)].">
      <j1 rule="para" parents="423 1490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1497">
    <literal><![CDATA[
      K(x \ (x / (x \ (x / y))),x) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(1490(a,1),1426(a,2,2))].">
      <j1 rule="para" parents="1490 1426"/>
    </justification>
  </clause>

  <clause id="1498">
    <literal><![CDATA[
      R(T(x,y * T(x,z)),y,T(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1482(a,1),1088(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1482 1088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1499">
    <literal><![CDATA[
      ((x / T(y,z)) / y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x / y = u
    ]]></literal>
    <justification jstring="[para(1483(a,1),576(a,1))].">
      <j1 rule="para" parents="1483 576"/>
    </justification>
  </clause>

  <clause id="1500">
    <literal><![CDATA[
      ((x * (1 / T(x,y))) / x) * T(x,y) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(1472(a,1),1484(a,1,1,1))].">
      <j1 rule="para" parents="1472 1484"/>
    </justification>
  </clause>

  <clause id="1501">
    <literal><![CDATA[
      R(T(x,L(x,y,x) * y),y,T(x,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(714(a,1),1498(a,1,1,2))].">
      <j1 rule="para" parents="714 1498"/>
    </justification>
  </clause>

  <clause id="1502">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(1489(a,1),1113(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1489 1113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1503">
    <literal><![CDATA[
      (x / y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * T(y,z)) / y = u
    ]]></literal>
    <justification jstring="[para(6(a,1),1499(a,1,1,1))].">
      <j1 rule="para" parents="6 1499"/>
    </justification>
  </clause>

  <clause id="1504">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x * (x * y)) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(131,a,1502,a),flip(a)].">
      <j1 rule="hyper" parents="131 1502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1505">
    <literal><![CDATA[
      (x * (x * y)) / (y * x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1170,a(flip),b,1504,a),flip(a)].">
      <j1 rule="hyper" parents="58 1170 1504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1506">
    <literal><![CDATA[
      R(((x * (x * y)) / x) / y,y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(835,a,1505,a)].">
      <j1 rule="hyper" parents="835 1505"/>
    </justification>
  </clause>

  <clause id="1507">
    <literal><![CDATA[
      R(T(x,x / (1 / y)),y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(1457(a,1),1506(a,1,1))].">
      <j1 rule="para" parents="1457 1506"/>
    </justification>
  </clause>

  <clause id="1508">
    <literal><![CDATA[
      (x * (y / z)) * (z \ y) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(107(a,1),1485(a,1,2))].">
      <j1 rule="para" parents="107 1485"/>
    </justification>
  </clause>

  <clause id="1509">
    <literal><![CDATA[
      (x * (y \ (y * z))) * ((y * z) / y) = (x * ((y * z) / y)) * z
    ]]></literal>
    <justification jstring="[para(224(a,1),1485(a,1,2)),flip(a)].">
      <j1 rule="para" parents="224 1485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1510">
    <literal><![CDATA[
      (x * (y \ z)) / (z / y) = (x / (z / y)) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(595,a,1508,a)].">
      <j1 rule="hyper" parents="595 1508"/>
    </justification>
  </clause>

  <clause id="1511">
    <literal><![CDATA[
      (x * (y / z)) / (z \ y) = (x / (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(117,a,147,a(flip),b,1508,a)].">
      <j1 rule="hyper" parents="117 147 1508"/>
    </justification>
  </clause>

  <clause id="1512">
    <literal><![CDATA[
      ((x / (y \ z)) / (z / y)) * (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x / (z / y) = u
    ]]></literal>
    <justification jstring="[para(1510(a,1),576(a,1))].">
      <j1 rule="para" parents="1510 576"/>
    </justification>
  </clause>

  <clause id="1513">
    <literal><![CDATA[
      (x / (y / z)) * (z \ y) != u
    ]]></literal>
    <literal><![CDATA[
      (x * (z \ y)) / (y / z) = u
    ]]></literal>
    <justification jstring="[para(6(a,1),1512(a,1,1,1))].">
      <j1 rule="para" parents="6 1512"/>
    </justification>
  </clause>

  <clause id="1514">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(639(a,1),1365(a,2,1))].">
      <j1 rule="para" parents="639 1365"/>
    </justification>
  </clause>

  <clause id="1515">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = (x * z) * T((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(453(a,1),1393(a,1,1))].">
      <j1 rule="para" parents="453 1393"/>
    </justification>
  </clause>

  <clause id="1516">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),x) = z \ ((y * T(y \ 1,x)) * z)
    ]]></literal>
    <justification jstring="[para(1218(a,1),1425(a,2,2))].">
      <j1 rule="para" parents="1218 1425"/>
    </justification>
  </clause>

  <clause id="1517">
    <literal><![CDATA[
      T(x * T(x \ 1,y),z) = K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,17,a,b,1516,a)].">
      <j1 rule="hyper" parents="320 17 1516"/>
    </justification>
  </clause>

  <clause id="1518">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * z = z * K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1516,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="119 1516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1519">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ 1,z) = T(x * T(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,1017,a(flip),b,1517,a)].">
      <j1 rule="hyper" parents="320 1017 1517"/>
    </justification>
  </clause>

  <clause id="1520">
    <literal><![CDATA[
      T(x,y) \ T(x * T(x \ 1,z),y) = T(T(x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,1517,a,b,1017,a(flip))].">
      <j1 rule="hyper" parents="116 1517 1017"/>
    </justification>
  </clause>

  <clause id="1521">
    <literal><![CDATA[
      K(x \ (x / T(x,y)),x) = T(K(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(358(a,1),1517(a,1,1)),flip(a)].">
      <j1 rule="para" parents="358 1517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1522">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),x) = T(K(x \ (x / y),x),z)
    ]]></literal>
    <justification jstring="[para(1017(a,2),1517(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1017 1517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1523">
    <literal><![CDATA[
      K(x \ (x / T(L(y \ 1,y,x),z)),x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(1094(a,2),1517(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1094 1517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1524">
    <literal><![CDATA[
      T(K(x \ 1,x),y) / T(x,y) = T(1 / T(x,y),x)
    ]]></literal>
    <justification jstring="[para(1521(a,1),1022(a,1,1))].">
      <j1 rule="para" parents="1521 1022"/>
    </justification>
  </clause>

  <clause id="1525">
    <literal><![CDATA[
      K(x \ (x / T(y \ x,z)),x) = T(K(x \ y,x),z)
    ]]></literal>
    <justification jstring="[para(72(a,1),1522(a,2,1,1,2))].">
      <j1 rule="para" parents="72 1522"/>
    </justification>
  </clause>

  <clause id="1526">
    <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),1525(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="106 1525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1527">
    <literal><![CDATA[
      T(x * T(x \ 1,T(x,y)),y) = (T(x,y) \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(284,a,1519,a),flip(a)].">
      <j1 rule="hyper" parents="284 1519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1528">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(x * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1241(a,1),1520(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1241 1520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1529">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ z,u)) * y = x * T(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(453(a,1),1430(a,1,1))].">
      <j1 rule="para" parents="453 1430"/>
    </justification>
  </clause>

  <clause id="1530">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(635(a,1),1455(a,1,1))].">
      <j1 rule="para" parents="635 1455"/>
    </justification>
  </clause>

  <clause id="1531">
    <literal><![CDATA[
      (x \ 1) * ((y * ((x \ 1) \ K(x \ 1,x))) / y) = ((y * x) / y) / ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(907(a,1),1473(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="907 1473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1532">
    <literal><![CDATA[
      x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[para(453(a,1),1474(a,2,1))].">
      <j1 rule="para" parents="453 1474"/>
    </justification>
  </clause>

  <clause id="1533">
    <literal><![CDATA[
      (x * y) \ ((x * T(x \ z,u)) * y) = T((x * y) \ (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(123,a,1476,a)].">
      <j1 rule="hyper" parents="123 1476"/>
    </justification>
  </clause>

  <clause id="1534">
    <literal><![CDATA[
      ((x * y) * T((x * y) \ x,z)) * y = (x * y) * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,733,a(flip),b,1476,a),flip(a)].">
      <j1 rule="hyper" parents="58 733 1476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1535">
    <literal><![CDATA[
      x * T(x \ (x \ (y * x)),z) = T(x * T(x \ y,z),x)
    ]]></literal>
    <justification jstring="[hyper(239,a,1476,a(flip),b,919,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="239 1476 919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1536">
    <literal><![CDATA[
      T(x * T(x \ y,z),x) = x * T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[para(17(a,2),1535(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 1535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1537">
    <literal><![CDATA[
      x \ T(x * T(x \ y,z),x) = T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(766,a,1536,a)].">
      <j1 rule="hyper" parents="766 1536"/>
    </justification>
  </clause>

  <clause id="1538">
    <literal><![CDATA[
      T(x \ T(x * y,x),z) = x \ T(x * T(y,z),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1537(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1539">
    <literal><![CDATA[
      x \ T(x * T(y / x,z),x) = T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[para(1376(a,1),1538(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1376 1538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1540">
    <literal><![CDATA[
      T(x * T(y / x,z),x) = x * T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,1539,a),flip(a)].">
      <j1 rule="hyper" parents="134 1539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1541">
    <literal><![CDATA[
      T(x * T(y,z),x) / x = T(T(x * y,x) / x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1379,a(flip),b,1539,a)].">
      <j1 rule="hyper" parents="58 1379 1539"/>
    </justification>
  </clause>

  <clause id="1542">
    <literal><![CDATA[
      T(x * T(1 / x,y),x) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(200(a,1),1540(a,2,2,1,1))].">
      <j1 rule="para" parents="200 1540"/>
    </justification>
  </clause>

  <clause id="1543">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(972,a,1500,a)].">
      <j1 rule="hyper" parents="972 1500"/>
    </justification>
  </clause>

  <clause id="1544">
    <literal><![CDATA[
      (x * ((y * z) / y)) * z = (x * z) * ((y * z) / y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1509(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 1509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1545">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / ((z * y) / z)) * y
    ]]></literal>
    <justification jstring="[hyper(595,a,1544,a)].">
      <j1 rule="hyper" parents="595 1544"/>
    </justification>
  </clause>

  <clause id="1546">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * y = y / ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(415,a,1544,a),flip(a)].">
      <j1 rule="hyper" parents="415 1544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1548">
    <literal><![CDATA[
      ((x / y) * y) * ((x * y) / x) = T(x,x / (x / y)) * y
    ]]></literal>
    <justification jstring="[para(1160(a,1),1544(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1160 1544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1549">
    <literal><![CDATA[
      T(x,x / (x / y)) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(326,a,1548,a),flip(a)].">
      <j1 rule="hyper" parents="326 1548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1550">
    <literal><![CDATA[
      T(x,x / (x / y)) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1126,a,1549,a)].">
      <j1 rule="hyper" parents="1126 1549"/>
    </justification>
  </clause>

  <clause id="1552">
    <literal><![CDATA[
      ((x * y) / x) / (x \ y) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(131,a,1550,a)].">
      <j1 rule="hyper" parents="131 1550"/>
    </justification>
  </clause>

  <clause id="1553">
    <literal><![CDATA[
      T(x,x / (1 / (x \ y))) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1460,a,b,1552,a)].">
      <j1 rule="hyper" parents="58 1460 1552"/>
    </justification>
  </clause>

  <clause id="1554">
    <literal><![CDATA[
      T(x,x / (x / (x * y))) = T(x,x / (1 / y))
    ]]></literal>
    <justification jstring="[para(4(a,1),1553(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4 1553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1555">
    <literal><![CDATA[
      T(x,x * R(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(239,a,911,a(flip),b,1514,a(flip))].">
      <j1 rule="hyper" parents="239 911 1514"/>
    </justification>
  </clause>

  <clause id="1556">
    <literal><![CDATA[
      T(x * R(x \ 1,y,z),x) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(239,a,1514,a(flip),b,911,a(flip))].">
      <j1 rule="hyper" parents="239 1514 911"/>
    </justification>
  </clause>

  <clause id="1557">
    <literal><![CDATA[
      T(1 / x,(1 / x) * R(x,y,z)) = 1 / x
    ]]></literal>
    <justification jstring="[para(75(a,1),1555(a,1,2,2,1))].">
      <j1 rule="para" parents="75 1555"/>
    </justification>
  </clause>

  <clause id="1558">
    <literal><![CDATA[
      T(x,(y / (x * y)) * x) = x
    ]]></literal>
    <justification jstring="[para(651(a,2),1555(a,1,2))].">
      <j1 rule="para" parents="651 1555"/>
    </justification>
  </clause>

  <clause id="1559">
    <literal><![CDATA[
      T(x \ 1,R(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(641(a,1),1555(a,1,2))].">
      <j1 rule="para" parents="641 1555"/>
    </justification>
  </clause>

  <clause id="1560">
    <literal><![CDATA[
      T(x \ 1,x \ R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1199(a,1),1555(a,1,2))].">
      <j1 rule="para" parents="1199 1555"/>
    </justification>
  </clause>

  <clause id="1561">
    <literal><![CDATA[
      T(x,y / (x * y)) * T(y / (x * y),x) = T(x * (y / (x * y)),x)
    ]]></literal>
    <justification jstring="[para(1558(a,1),1136(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1558 1136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1562">
    <literal><![CDATA[
      T(T(x \ 1,y),x \ R(x,z,u)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1560(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1560 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1563">
    <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(1557(a,1),716(a,1,1,2))].">
      <j1 rule="para" parents="1557 716"/>
    </justification>
  </clause>

  <clause id="1564">
    <literal><![CDATA[
      R(x \ 1,R(x,y,z),x \ 1) = T(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1559(a,1),803(a,1,1))].">
      <j1 rule="para" parents="1559 803"/>
    </justification>
  </clause>

  <clause id="1565">
    <literal><![CDATA[
      T(x * ((x * R(x \ 1,y,z)) / x),x) = x * ((x * R(x \ 1,y,z)) / x)
    ]]></literal>
    <justification jstring="[para(1556(a,1),1377(a,2,2,1))].">
      <j1 rule="para" parents="1556 1377"/>
    </justification>
  </clause>

  <clause id="1566">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u))
    ]]></literal>
    <justification jstring="[hyper(320,a,919,a(flip),b,1515,a),flip(a)].">
      <j1 rule="hyper" parents="320 919 1515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1567">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (z / y)) * x) * y = u
    ]]></literal>
    <justification jstring="[para(1515(a,1),569(a,1))].">
      <j1 rule="para" parents="1515 569"/>
    </justification>
  </clause>

  <clause id="1568">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(1,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),1528(a,2,2,1))].">
      <j1 rule="para" parents="5 1528"/>
    </justification>
  </clause>

  <clause id="1570">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(200(a,1),1568(a,2,2))].">
      <j1 rule="para" parents="200 1568"/>
    </justification>
  </clause>

  <clause id="1572">
    <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,919,a(flip),b,1529,a)].">
      <j1 rule="hyper" parents="117 919 1529"/>
    </justification>
  </clause>

  <clause id="1573">
    <literal><![CDATA[
      (x / y) * T((x / y) \ z,x) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,105,a(flip),b,1529,a),flip(a)].">
      <j1 rule="hyper" parents="117 105 1529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1574">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ 1,z)) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2(a,1),1529(a,2,2,1,2))].">
      <j1 rule="para" parents="2 1529"/>
    </justification>
  </clause>

  <clause id="1575">
    <literal><![CDATA[
      (x / y) * T((x / y) \ 1,z) = (x * T(x \ y,z)) / y
    ]]></literal>
    <justification jstring="[hyper(131,a,1574,a),flip(a)].">
      <j1 rule="hyper" parents="131 1574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1576">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) * y = x * T(x \ y,x / y)
    ]]></literal>
    <justification jstring="[para(358(a,1),1574(a,1,1))].">
      <j1 rule="para" parents="358 1574"/>
    </justification>
  </clause>

  <clause id="1577">
    <literal><![CDATA[
      K(x \ (x / (y / z)),x) * z = y * T(y \ z,x)
    ]]></literal>
    <justification jstring="[para(1017(a,2),1574(a,1,1))].">
      <j1 rule="para" parents="1017 1574"/>
    </justification>
  </clause>

  <clause id="1578">
    <literal><![CDATA[
      K(x \ (x / (y / z)),x) = (y * T(y \ z,x)) / z
    ]]></literal>
    <justification jstring="[hyper(131,a,1577,a),flip(a)].">
      <j1 rule="hyper" parents="131 1577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1579">
    <literal><![CDATA[
      K(x \ (x / ((y * z) / y)),x) = (y * (z * T(z \ 1,x))) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,733,a(flip),b,1577,a),flip(a)].">
      <j1 rule="hyper" parents="117 733 1577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1580">
    <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),1578(a,1,1,2))].">
      <j1 rule="para" parents="6 1578"/>
    </justification>
  </clause>

  <clause id="1581">
    <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),1578(a,1,1,2,2))].">
      <j1 rule="para" parents="15 1578"/>
    </justification>
  </clause>

  <clause id="1582">
    <literal><![CDATA[
      K(x \ (x / ((y \ x) / T(x,y))),x) = ((y \ x) * ((y \ x) \ x)) / T(x,y)
    ]]></literal>
    <justification jstring="[para(1159(a,1),1578(a,2,1,2))].">
      <j1 rule="para" parents="1159 1578"/>
    </justification>
  </clause>

  <clause id="1583">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,x / (y * x)) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,451,a(flip),b,1576,a),flip(a)].">
      <j1 rule="hyper" parents="320 451 1576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1584">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((x \ 1) \ u) = u * L(u \ ((x \ 1) \ u),y,z)
    ]]></literal>
    <justification jstring="[para(1185(a,1),1530(a,1,1))].">
      <j1 rule="para" parents="1185 1530"/>
    </justification>
  </clause>

  <clause id="1585">
    <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,1378,a,b,1532,a)].">
      <j1 rule="hyper" parents="58 1378 1532"/>
    </justification>
  </clause>

  <clause id="1586">
    <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),1532(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="92 1532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1587">
    <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(1533(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1533 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1588">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(1110(a,1),1543(a,1,2,1))].">
      <j1 rule="para" parents="1110 1543"/>
    </justification>
  </clause>

  <clause id="1589">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (z / y)) * x) * y = u
    ]]></literal>
    <justification jstring="[para(1566(a,1),569(a,1))].">
      <j1 rule="para" parents="1566 569"/>
    </justification>
  </clause>

  <clause id="1590">
    <literal><![CDATA[
      (x \ 1) * (y * T(y \ ((x \ 1) \ z),u)) = (x \ T(x * (z / y),u)) * y
    ]]></literal>
    <justification jstring="[para(932(a,1),1566(a,1,1)),flip(a)].">
      <j1 rule="para" parents="932 1566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1591">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ (x \ x),y))
    ]]></literal>
    <justification jstring="[para(1014(a,2),1566(a,1,1))].">
      <j1 rule="para" parents="1014 1566"/>
    </justification>
  </clause>

  <clause id="1592">
    <literal><![CDATA[
      K(x \ (x / ((y * x) / y)),x) = (y * K(x \ 1,x)) / y
    ]]></literal>
    <justification jstring="[para(358(a,1),1579(a,2,1,2))].">
      <j1 rule="para" parents="358 1579"/>
    </justification>
  </clause>

  <clause id="1593">
    <literal><![CDATA[
      ((x * y) / x) \ ((x * K(y \ 1,y)) / x) = T(((x * y) / x) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,1592,a(flip),b,1017,a(flip))].">
      <j1 rule="hyper" parents="116 1592 1017"/>
    </justification>
  </clause>

  <clause id="1594">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(61(a,1),1591(a,2,2,2,1,2))].">
      <j1 rule="para" parents="61 1591"/>
    </justification>
  </clause>

  <clause id="1596">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * ((y \ 1) * y)
    ]]></literal>
    <justification jstring="[para(105(a,1),1594(a,2,2))].">
      <j1 rule="para" parents="105 1594"/>
    </justification>
  </clause>

  <clause id="1597">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(358(a,1),1594(a,2,2))].">
      <j1 rule="para" parents="358 1594"/>
    </justification>
  </clause>

  <clause id="1598">
    <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,1596,a),flip(a)].">
      <j1 rule="hyper" parents="30 101 1596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1599">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * y = (x * y) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),1597(a,1,1,1))].">
      <j1 rule="para" parents="6 1597"/>
    </justification>
  </clause>

  <clause id="1600">
    <literal><![CDATA[
      (L(1 / x,x,y) * K(x \ 1,x)) * x = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(840(a,1),1597(a,1,1,1))].">
      <j1 rule="para" parents="840 1597"/>
    </justification>
  </clause>

  <clause id="1601">
    <literal><![CDATA[
      ((x / K(y \ 1,y)) * y) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(326,a,1599,a),flip(a)].">
      <j1 rule="hyper" parents="326 1599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1602">
    <literal><![CDATA[
      ((x * (y \ 1)) / K(y \ 1,y)) * y = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,520,a,b,1601,a),flip(a)].">
      <j1 rule="hyper" parents="30 520 1601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1603">
    <literal><![CDATA[
      (x * (y \ 1)) / K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ 1,y) / y = z
    ]]></literal>
    <justification jstring="[para(1598(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1598 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1604">
    <literal><![CDATA[
      L(x,T(y,y \ z),y \ z) = L(x,(y \ z) \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(29,a,448,a,b,744,a),flip(a)].">
      <j1 rule="hyper" parents="29 448 744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1605">
    <literal><![CDATA[
      x * ((x \ y) * ((z * ((x \ y) \ u)) / z)) = y * ((z * (y \ (x * u))) / z)
    ]]></literal>
    <justification jstring="[hyper(119,a,882,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="119 882 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1606">
    <literal><![CDATA[
      x \ (y * ((z * (y \ (x * u))) / z)) = (x \ y) * ((z * ((x \ y) \ u)) / z)
    ]]></literal>
    <justification jstring="[para(882(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="882 474"/>
    </justification>
  </clause>

  <clause id="1607">
    <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(496(a,1),895(a,1,2,1))].">
      <j1 rule="para" parents="496 895"/>
    </justification>
  </clause>

  <clause id="1608">
    <literal><![CDATA[
      (1 / (x \ y)) \ (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(390(a,1),1193(a,1,1)),flip(a)].">
      <j1 rule="para" parents="390 1193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1609">
    <literal><![CDATA[
      (x \ (x * y)) * ((x * y) \ x) = (1 / ((x * y) \ x)) \ y
    ]]></literal>
    <justification jstring="[para(4(a,1),1608(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 1608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1610">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) \ y = y * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1609(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 1609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1611">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * (y * ((x * y) \ x)) = y
    ]]></literal>
    <justification jstring="[hyper(134,a,1610,a)].">
      <j1 rule="hyper" parents="134 1610"/>
    </justification>
  </clause>

  <clause id="1612">
    <literal><![CDATA[
      (1 / (x / y)) * ((y / x) * (x / y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(119,a,785,a(flip),b,1210,a(flip))].">
      <j1 rule="hyper" parents="119 785 1210"/>
    </justification>
  </clause>

  <clause id="1613">
    <literal><![CDATA[
      T(1 / (x / y),(y / x) * (x / y)) = ((y / x) * (x / y)) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(440,a,xx,b,1612,a)].">
      <j1 rule="hyper" parents="440 1612"/>
    </justification>
  </clause>

  <clause id="1614">
    <literal><![CDATA[
      T(x,(x * T(x \ 1,y)) / x) = R(x,T(1 / x,y),x)
    ]]></literal>
    <justification jstring="[para(457(a,1),1239(a,1,2)),flip(a)].">
      <j1 rule="para" parents="457 1239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1615">
    <literal><![CDATA[
      R(x,T(1 / x,y),x) = T(x,T(1 / x,y))
    ]]></literal>
    <justification jstring="[para(457(a,1),1614(a,1,2)),flip(a)].">
      <j1 rule="para" parents="457 1614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1616">
    <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(1615(a,1),1317(a,1,1))].">
      <j1 rule="para" parents="1615 1317"/>
    </justification>
  </clause>

  <clause id="1617">
    <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),1412(a,2,1))].">
      <j1 rule="para" parents="6 1412"/>
    </justification>
  </clause>

  <clause id="1618">
    <literal><![CDATA[
      x * T(y,L(y,z,u) * x) = L(y,x,L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(1617(a,1),454(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1617 454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1619">
    <literal><![CDATA[
      L(T(x,y),y,L(x,z,u)) = T(x,L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(29,a,237,a,b,1618,a)].">
      <j1 rule="hyper" parents="29 237 1618"/>
    </justification>
  </clause>

  <clause id="1620">
    <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(932(a,1),1589(a,1,2))].">
      <j1 rule="para" parents="932 1589"/>
    </justification>
  </clause>

  <clause id="1621">
    <literal><![CDATA[
      R((x * y) / (x * z),u,w) * (x * z) = x * (z * R(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(646,a,1053,a)].">
      <j1 rule="hyper" parents="646 1053"/>
    </justification>
  </clause>

  <clause id="1622">
    <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,1514,a(flip),b,1053,a),flip(a)].">
      <j1 rule="hyper" parents="58 1514 1053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1623">
    <literal><![CDATA[
      x * (y * R(y \ (x \ z),x,y)) = ((z / (x * y)) * x) * y
    ]]></literal>
    <justification jstring="[hyper(847,a,1054,a),flip(a)].">
      <j1 rule="hyper" parents="847 1054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1624">
    <literal><![CDATA[
      x * (y * R(y \ (x \ y),z,u)) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1514,a(flip),b,1054,a),flip(a)].">
      <j1 rule="hyper" parents="58 1514 1054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1625">
    <literal><![CDATA[
      (((x * (y * z)) / (x * y)) * x) * y = x * (y * R(z,x,y))
    ]]></literal>
    <justification jstring="[para(62(a,1),1623(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="62 1623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1626">
    <literal><![CDATA[
      (((x * (y * z)) / (x * z)) * x) * z = x * (z * R(T(y,z),x,z))
    ]]></literal>
    <justification jstring="[para(105(a,1),1625(a,1,1,1,1,2))].">
      <j1 rule="para" parents="105 1625"/>
    </justification>
  </clause>

  <clause id="1627">
    <literal><![CDATA[
      (((x * (y * z)) / (x * z)) * x) * z = x * (R(y,x,z) * z)
    ]]></literal>
    <justification jstring="[para(238(a,1),1626(a,2,2))].">
      <j1 rule="para" parents="238 1626"/>
    </justification>
  </clause>

  <clause id="1628">
    <literal><![CDATA[
      (L((x * y) / x,z,u) * x) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(877,a,1057,a),flip(a)].">
      <j1 rule="hyper" parents="877 1057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1629">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (L(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(854,a,1057,a)].">
      <j1 rule="hyper" parents="854 1057"/>
    </justification>
  </clause>

  <clause id="1630">
    <literal><![CDATA[
      (x * L(y,z,u)) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(636(a,1),1628(a,1,1))].">
      <j1 rule="para" parents="636 1628"/>
    </justification>
  </clause>

  <clause id="1631">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = (x / L(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(595,a,1630,a)].">
      <j1 rule="hyper" parents="595 1630"/>
    </justification>
  </clause>

  <clause id="1632">
    <literal><![CDATA[
      ((x / L(y,z,u)) * y) \ (x * y) = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(571,a,1630,a)].">
      <j1 rule="hyper" parents="571 1630"/>
    </justification>
  </clause>

  <clause id="1633">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = x / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(415,a,1630,a),flip(a)].">
      <j1 rule="hyper" parents="415 1630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1634">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) * y = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,147,a(flip),b,1630,a),flip(a)].">
      <j1 rule="hyper" parents="320 147 1630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1635">
    <literal><![CDATA[
      ((1 / L(x,y,z)) * x) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(204,a,1630,a),flip(a)].">
      <j1 rule="hyper" parents="204 1630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1636">
    <literal><![CDATA[
      (x * L(y,z,u)) \ ((x * y) * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,1630,a)].">
      <j1 rule="hyper" parents="123 1630"/>
    </justification>
  </clause>

  <clause id="1637">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) \ (x * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,147,a(flip),b,1630,a)].">
      <j1 rule="hyper" parents="116 147 1630"/>
    </justification>
  </clause>

  <clause id="1638">
    <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(1630(a,1),307(a,1,1))].">
      <j1 rule="para" parents="1630 307"/>
    </justification>
  </clause>

  <clause id="1639">
    <literal><![CDATA[
      (x / L(y,z,u)) / y = (x / y) / L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,153,a(flip),b,1631,a(flip))].">
      <j1 rule="hyper" parents="117 153 1631"/>
    </justification>
  </clause>

  <clause id="1640">
    <literal><![CDATA[
      (x * y) / L(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / L(y,z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(1632(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1632 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1641">
    <literal><![CDATA[
      ((x * y) / z) * L(z,y,x) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,90,a(flip),b,1634,a),flip(a)].">
      <j1 rule="hyper" parents="117 90 1634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1642">
    <literal><![CDATA[
      R(T(x,y * L(x,z,u)),y,L(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1636(a,1),1088(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1636 1088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1643">
    <literal><![CDATA[
      ((x * (y * z)) / z) / L(z,y,x) = (x * y) / z
    ]]></literal>
    <justification jstring="[para(186(a,1),1639(a,1,1)),flip(a)].">
      <j1 rule="para" parents="186 1639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1644">
    <literal><![CDATA[
      L(x,y,z) \ ((z * (y * x)) / x) = T((z * y) / x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(440,a,xx,b,1641,a),flip(a)].">
      <j1 rule="hyper" parents="440 1641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1645">
    <literal><![CDATA[
      L(x,y,z) = ((z * y) / x) \ ((z * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(123,a,1641,a),flip(a)].">
      <j1 rule="hyper" parents="123 1641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1646">
    <literal><![CDATA[
      (x * L(y,z,u)) * T(y,x) = (y * x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,1642,a(flip),b,630,a)].">
      <j1 rule="hyper" parents="119 1642 630"/>
    </justification>
  </clause>

  <clause id="1647">
    <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(1643(a,1),421(a,1,1))].">
      <j1 rule="para" parents="1643 421"/>
    </justification>
  </clause>

  <clause id="1648">
    <literal><![CDATA[
      ((x * (y / z)) / z) \ ((x * y) / z) = L(z,y / z,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),1645(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 1645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1649">
    <literal><![CDATA[
      (L((x / y) / z,u,w) * z) * y = (z * y) * L((z * y) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,635,a(flip),b,1058,a),flip(a)].">
      <j1 rule="hyper" parents="320 635 1058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1650">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(862,a,1059,a)].">
      <j1 rule="hyper" parents="862 1059"/>
    </justification>
  </clause>

  <clause id="1651">
    <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(1186(a,1),1080(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1186 1080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1652">
    <literal><![CDATA[
      x * (y * ((x * (y \ 1)) / x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(1163,a,1089,a),flip(a)].">
      <j1 rule="hyper" parents="1163 1089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1653">
    <literal><![CDATA[
      x \ T(x,x / (x * y)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(1161,a,1089,a)].">
      <j1 rule="hyper" parents="1161 1089"/>
    </justification>
  </clause>

  <clause id="1654">
    <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),1089(a,1,1))].">
      <j1 rule="para" parents="90 1089"/>
    </justification>
  </clause>

  <clause id="1655">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(1543(a,1),1652(a,1,2))].">
      <j1 rule="para" parents="1543 1652"/>
    </justification>
  </clause>

  <clause id="1656">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) / (y \ 1) = T(y,y / (y * x))
    ]]></literal>
    <justification jstring="[hyper(117,a,1653,a(flip),b,985,a)].">
      <j1 rule="hyper" parents="117 1653 985"/>
    </justification>
  </clause>

  <clause id="1657">
    <literal><![CDATA[
      x \ y != z * ((x * (z \ 1)) / x)
    ]]></literal>
    <literal><![CDATA[
      T(x,x / (x * z)) = y
    ]]></literal>
    <justification jstring="[para(1653(a,1),42(a,1)),flip(a)].">
      <j1 rule="para" parents="1653 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1658">
    <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(1201(a,1),1656(a,1,1,2,1))].">
      <j1 rule="para" parents="1201 1656"/>
    </justification>
  </clause>

  <clause id="1659">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = (((z * (1 / x)) / z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(972,a,1090,a)].">
      <j1 rule="hyper" parents="972 1090"/>
    </justification>
  </clause>

  <clause id="1660">
    <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),1090(a,1,2))].">
      <j1 rule="para" parents="101 1090"/>
    </justification>
  </clause>

  <clause id="1661">
    <literal><![CDATA[
      (((x * y) / x) * (y \ 1)) * x = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(887,a,1151,a)].">
      <j1 rule="hyper" parents="887 1151"/>
    </justification>
  </clause>

  <clause id="1662">
    <literal><![CDATA[
      (x \ ((y * x) / y)) * y = T(y,R(x,x \ 1,y))
    ]]></literal>
    <justification jstring="[para(1294(a,1),1661(a,1,1))].">
      <j1 rule="para" parents="1294 1661"/>
    </justification>
  </clause>

  <clause id="1663">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) / x = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(131,a,1662,a)].">
      <j1 rule="hyper" parents="131 1662"/>
    </justification>
  </clause>

  <clause id="1664">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) = (T(y,x) \ y) * x
    ]]></literal>
    <justification jstring="[para(225(a,1),1662(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="225 1662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1665">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      y \ ((x * y) / x) = z
    ]]></literal>
    <justification jstring="[para(1662(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1662 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1666">
    <literal><![CDATA[
      (1 / x) \ ((y * (1 / x)) / y) = T(y,R(1 / x,x,y)) / y
    ]]></literal>
    <justification jstring="[para(75(a,1),1663(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 1663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1667">
    <literal><![CDATA[
      T(1 / x,T(x,R(y,y \ 1,x))) = L(x \ 1,x,y \ ((x * y) / x))
    ]]></literal>
    <justification jstring="[para(1663(a,1),1009(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1663 1009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1668">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) / x = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1456,a(flip),b,1666,a),flip(a)].">
      <j1 rule="hyper" parents="58 1456 1666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1669">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * y = T(y,R(1 / x,x,y))
    ]]></literal>
    <justification jstring="[hyper(133,a,1668,a)].">
      <j1 rule="hyper" parents="133 1668"/>
    </justification>
  </clause>

  <clause id="1670">
    <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(1110(a,1),1669(a,1,1,2,1))].">
      <j1 rule="para" parents="1110 1669"/>
    </justification>
  </clause>

  <clause id="1671">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) = (x \ T(x,x / (x * y))) * x
    ]]></literal>
    <justification jstring="[para(1653(a,2),1669(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1653 1669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1672">
    <literal><![CDATA[
      T(T(x,x * y) * y,R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(558(a,1),1155(a,1,1))].">
      <j1 rule="para" parents="558 1155"/>
    </justification>
  </clause>

  <clause id="1673">
    <literal><![CDATA[
      T(T(T(x,x * y) * y,z),R(x,y,y \ 1)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(1672(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1672 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1674">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,R(x / y,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(979(a,1),1673(a,1,1)),flip(a)].">
      <j1 rule="para" parents="979 1673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1675">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(523(a,1),1674(a,2,2))].">
      <j1 rule="para" parents="523 1674"/>
    </justification>
  </clause>

  <clause id="1676">
    <literal><![CDATA[
      T(x,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(7(a,1),1675(a,1,1))].">
      <j1 rule="para" parents="7 1675"/>
    </justification>
  </clause>

  <clause id="1677">
    <literal><![CDATA[
      T(x,x * (y \ 1)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),1676(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1678">
    <literal><![CDATA[
      T(x,(1 / y) \ x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[para(75(a,1),1677(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 1677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1679">
    <literal><![CDATA[
      x \ R(x * (y * (x \ 1)),z,u) = R(y,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,238,a(flip),b,1200,a),flip(a)].">
      <j1 rule="hyper" parents="320 238 1200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1680">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y) * (T(x,y) \ x),z,u) = R(x,z,u) * (T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(1110(a,1),1679(a,1,2,1,2))].">
      <j1 rule="para" parents="1110 1679"/>
    </justification>
  </clause>

  <clause id="1681">
    <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(1209(a,1),424(a,1))].">
      <j1 rule="para" parents="1209 424"/>
    </justification>
  </clause>

  <clause id="1682">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ y,z,u) = L(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[para(75(a,1),1233(a,1,2)),flip(a)].">
      <j1 rule="para" parents="75 1233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1683">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ 1,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(2(a,1),1682(a,2,1,1))].">
      <j1 rule="para" parents="2 1682"/>
    </justification>
  </clause>

  <clause id="1684">
    <literal><![CDATA[
      L((x \ 1) \ (x \ y),z,u) = (x \ 1) \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),1297(a,1,1,2,1))].">
      <j1 rule="para" parents="72 1297"/>
    </justification>
  </clause>

  <clause id="1686">
    <literal><![CDATA[
      (x / y) * (y * L(((x / y) \ x) \ z,u,w)) = x * L(x \ ((x / y) * z),u,w)
    ]]></literal>
    <justification jstring="[para(75(a,1),1299(a,1,2,1))].">
      <j1 rule="para" parents="75 1299"/>
    </justification>
  </clause>

  <clause id="1687">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ 1,z,u) = x \ (y * R(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(3(a,1),1324(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3 1324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1688">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ 1,z,u) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(3(a,1),1325(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3 1325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1689">
    <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),1325(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5 1325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1690">
    <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),1688(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13 1688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1691">
    <literal><![CDATA[
      (L(x / (y / z),u,w) * (y / z)) * z = y * L(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,635,a(flip),b,1326,a),flip(a)].">
      <j1 rule="hyper" parents="320 635 1326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1692">
    <literal><![CDATA[
      (R(1 / (x / y),z,u) * (x / y)) * y = R(y / x,z,u) * x
    ]]></literal>
    <justification jstring="[para(2(a,1),1327(a,2,1,1,1))].">
      <j1 rule="para" parents="2 1327"/>
    </justification>
  </clause>

  <clause id="1693">
    <literal><![CDATA[
      (R(1 / (x / y),z,u) * (x / y)) * y = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,639,a(flip),b,1692,a),flip(a)].">
      <j1 rule="hyper" parents="320 639 1692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1694">
    <literal><![CDATA[
      ((x / y) * R((x / y) \ 1,z,u)) * y = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(639(a,1),1693(a,1,1))].">
      <j1 rule="para" parents="639 1693"/>
    </justification>
  </clause>

  <clause id="1695">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,z,u) = (x * R(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(131,a,1694,a),flip(a)].">
      <j1 rule="hyper" parents="131 1694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1696">
    <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),1695(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15 1695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1697">
    <literal><![CDATA[
      (x / y) \ (x * ((z * (x \ (x / y))) / z)) = y * ((z * (y \ 1)) / z)
    ]]></literal>
    <justification jstring="[hyper(123,a,1335,a)].">
      <j1 rule="hyper" parents="123 1335"/>
    </justification>
  </clause>

  <clause id="1698">
    <literal><![CDATA[
      (x \ (y / (1 / x))) * x = T(y,x) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,1373,a(flip),b,1382,a),flip(a)].">
      <j1 rule="hyper" parents="117 1373 1382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1699">
    <literal><![CDATA[
      ((x * (1 / (1 / T(y,x)))) / x) \ (y / T(y,x)) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[para(1466(a,1),1415(a,1,2))].">
      <j1 rule="para" parents="1466 1415"/>
    </justification>
  </clause>

  <clause id="1700">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,z) \ 1) = T(x,z) \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(72(a,1),1432(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 1432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1702">
    <literal><![CDATA[
      (x * (y * T(y \ 1,z))) * y = (x * y) * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(733(a,1),1534(a,1,1))].">
      <j1 rule="para" parents="733 1534"/>
    </justification>
  </clause>

  <clause id="1703">
    <literal><![CDATA[
      T(x,y / (x * y)) * R(x \ 1,x,y) = T(x * (y / (x * y)),x)
    ]]></literal>
    <justification jstring="[para(645(a,1),1561(a,1,2))].">
      <j1 rule="para" parents="645 1561"/>
    </justification>
  </clause>

  <clause id="1704">
    <literal><![CDATA[
      T(x,T(1 / x,y)) * T(x \ 1,y) = T(x * T(1 / x,y),x)
    ]]></literal>
    <justification jstring="[para(246(a,1),1616(a,1,2))].">
      <j1 rule="para" parents="246 1616"/>
    </justification>
  </clause>

  <clause id="1705">
    <literal><![CDATA[
      T(x,T(1 / x,y)) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,1542,a(flip),b,1704,a),flip(a)].">
      <j1 rule="hyper" parents="320 1542 1704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1706">
    <literal><![CDATA[
      R((x * y) / (x * z),u,w) * (x * z) = x * (R(y / z,u,w) * z)
    ]]></literal>
    <justification jstring="[para(639(a,2),1621(a,2,2))].">
      <j1 rule="para" parents="639 1621"/>
    </justification>
  </clause>

  <clause id="1707">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(635(a,1),1629(a,2,1))].">
      <j1 rule="para" parents="635 1629"/>
    </justification>
  </clause>

  <clause id="1708">
    <literal><![CDATA[
      (x * L(x \ (y / z),u,w)) * z = (x * z) * L((x * z) \ y,u,w)
    ]]></literal>
    <justification jstring="[para(635(a,1),1649(a,1,1))].">
      <j1 rule="para" parents="635 1649"/>
    </justification>
  </clause>

  <clause id="1709">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(639(a,1),1650(a,2,1))].">
      <j1 rule="para" parents="639 1650"/>
    </justification>
  </clause>

  <clause id="1710">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y
    ]]></literal>
    <justification jstring="[para(864(a,1),1659(a,2,1))].">
      <j1 rule="para" parents="864 1659"/>
    </justification>
  </clause>

  <clause id="1711">
    <literal><![CDATA[
      (x \ y) \ (x \ (y * L(y \ z,u,w))) = L((x \ y) \ (x \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(123,a,1689,a)].">
      <j1 rule="hyper" parents="123 1689"/>
    </justification>
  </clause>

  <clause id="1712">
    <literal><![CDATA[
      ((x / y) * L((x / y) \ z,u,w)) * y = x * L(x \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[para(635(a,1),1691(a,1,1))].">
      <j1 rule="para" parents="635 1691"/>
    </justification>
  </clause>

  <clause id="1713">
    <literal><![CDATA[
      (x / y) \ (x * ((x / y) / x)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[para(5(a,1),1697(a,1,2,2,1))].">
      <j1 rule="para" parents="5 1697"/>
    </justification>
  </clause>

  <clause id="1714">
    <literal><![CDATA[
      K(x,(x / y) / x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(467,a,1713,a)].">
      <j1 rule="hyper" parents="467 1713"/>
    </justification>
  </clause>

  <clause id="1715">
    <literal><![CDATA[
      (x / y) \ ((x / y) * K(x,(x / y) / x)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[para(303(a,2),1713(a,1,2))].">
      <j1 rule="para" parents="303 1713"/>
    </justification>
  </clause>

  <clause id="1716">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,(y / x) / y) = z
    ]]></literal>
    <justification jstring="[para(1713(a,1),467(a,1))].">
      <j1 rule="para" parents="1713 467"/>
    </justification>
  </clause>

  <clause id="1717">
    <literal><![CDATA[
      K(x,(x / (y \ 1)) / x) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,1414,a(flip),b,1714,a),flip(a)].">
      <j1 rule="hyper" parents="320 1414 1714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1718">
    <literal><![CDATA[
      x * K(x,(x / y) / x) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(119,a,1714,a,b,1653,a)].">
      <j1 rule="hyper" parents="119 1714 1653"/>
    </justification>
  </clause>

  <clause id="1720">
    <literal><![CDATA[
      (x \ y) * ((y * ((x \ y) \ 1)) / y) = K(y,x / y)
    ]]></literal>
    <justification jstring="[para(72(a,1),1714(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 1714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1721">
    <literal><![CDATA[
      x * ((T(x,y) * (x \ 1)) / T(x,y)) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(1002(a,1),1714(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1002 1714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1722">
    <literal><![CDATA[
      x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) = K(L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[para(1076(a,1),1714(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1076 1714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1723">
    <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(1197(a,1),1714(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1197 1714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1724">
    <literal><![CDATA[
      T(x,y) * ((T(x,z) * (T(x,y) \ 1)) / T(x,z)) = K(T(x,z),1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1471(a,1),1714(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1471 1714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1725">
    <literal><![CDATA[
      K(x,(x / ((T(x,y) \ 1) \ 1)) / x) = (T(x,y) \ 1) \ ((T(x,y) \ x) / x)
    ]]></literal>
    <justification jstring="[para(1110(a,1),1717(a,2,2,1))].">
      <j1 rule="para" parents="1110 1717"/>
    </justification>
  </clause>

  <clause id="1726">
    <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(1201(a,1),1717(a,2,2,1))].">
      <j1 rule="para" parents="1201 1717"/>
    </justification>
  </clause>

  <clause id="1727">
    <literal><![CDATA[
      T(x,x / (x * (y \ x))) = x * K(x,y / x)
    ]]></literal>
    <justification jstring="[para(72(a,1),1718(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="72 1718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1728">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) = x * K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(99(a,2),1727(a,1,2))].">
      <j1 rule="para" parents="99 1727"/>
    </justification>
  </clause>

  <clause id="1729">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),1728(a,2,2,2))].">
      <j1 rule="para" parents="6 1728"/>
    </justification>
  </clause>

  <clause id="1730">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) * (x \ z) = x \ ((x * K(x,y)) * z)
    ]]></literal>
    <justification jstring="[para(1729(a,1),1101(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1729 1101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1731">
    <literal><![CDATA[
      x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(455(a,2),1721(a,1,2,1))].">
      <j1 rule="para" parents="455 1721"/>
    </justification>
  </clause>

  <clause id="1732">
    <literal><![CDATA[
      x \ ((x * K(x,y)) * z) = (x * K(x,y)) * (x \ z)
    ]]></literal>
    <justification jstring="[para(1729(a,1),1730(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1729 1730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1733">
    <literal><![CDATA[
      (x * K(x,y)) * (x \ 1) = x \ (x * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(293,a,1732,a),flip(a)].">
      <j1 rule="hyper" parents="293 1732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1734">
    <literal><![CDATA[
      (x * K(x,y)) * (x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4,a(flip),b,1733,a),flip(a)].">
      <j1 rule="hyper" parents="320 4 1733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1735">
    <literal><![CDATA[
      K(x,y) / (x \ 1) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,4,a(flip),b,1733,a)].">
      <j1 rule="hyper" parents="117 4 1733"/>
    </justification>
  </clause>

  <clause id="1737">
    <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),1706(a,2,2,1,1))].">
      <j1 rule="para" parents="6 1706"/>
    </justification>
  </clause>

  <clause id="1738">
    <literal><![CDATA[
      x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1052,a(flip),b,1707,a)].">
      <j1 rule="hyper" parents="58 1052 1707"/>
    </justification>
  </clause>

  <clause id="1739">
    <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,913,a(flip),b,1707,a),flip(a)].">
      <j1 rule="hyper" parents="58 913 1707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1740">
    <literal><![CDATA[
      x * L(x \ (x \ (y * x)),z,u) = T(x * L(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(239,a,1707,a(flip),b,1052,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="239 1707 1052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1741">
    <literal><![CDATA[
      (x * y) * L((x * y) \ y,z,u) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(2(a,1),1707(a,1,2,1,2))].">
      <j1 rule="para" parents="2 1707"/>
    </justification>
  </clause>

  <clause id="1742">
    <literal><![CDATA[
      T(x * L(x \ y,z,u),x) = x * L(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(17(a,2),1740(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 1740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1743">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,u),x) = L(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(766,a,1742,a)].">
      <j1 rule="hyper" parents="766 1742"/>
    </justification>
  </clause>

  <clause id="1744">
    <literal><![CDATA[
      T(x * L(x \ 1,y,z),x) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(200(a,1),1742(a,2,2,1,2))].">
      <j1 rule="para" parents="200 1742"/>
    </justification>
  </clause>

  <clause id="1745">
    <literal><![CDATA[
      T(x,x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,1744,a)].">
      <j1 rule="hyper" parents="49 1744"/>
    </justification>
  </clause>

  <clause id="1746">
    <literal><![CDATA[
      K(x,x * L(x \ 1,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,1745,a)].">
      <j1 rule="hyper" parents="50 1745"/>
    </justification>
  </clause>

  <clause id="1747">
    <literal><![CDATA[
      T(x \ y,(x \ y) * (y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[para(390(a,1),1745(a,1,2,2))].">
      <j1 rule="para" parents="390 1745"/>
    </justification>
  </clause>

  <clause id="1748">
    <literal><![CDATA[
      T(x \ 1,L(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(637(a,1),1745(a,1,2))].">
      <j1 rule="para" parents="637 1745"/>
    </justification>
  </clause>

  <clause id="1749">
    <literal><![CDATA[
      T(1 / x,L(x,y,z) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(1683(a,1),1745(a,1,2))].">
      <j1 rule="para" parents="1683 1745"/>
    </justification>
  </clause>

  <clause id="1750">
    <literal><![CDATA[
      T((x * (1 / y)) / x,L(y,z,u) / y) = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(1749(a,1),460(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1749 460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1751">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) * (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(1747(a,1),714(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1747 714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1752">
    <literal><![CDATA[
      R(x \ 1,L(x,y,z),x \ 1) = T(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1748(a,1),803(a,1,1))].">
      <j1 rule="para" parents="1748 803"/>
    </justification>
  </clause>

  <clause id="1753">
    <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),1743(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1754">
    <literal><![CDATA[
      x \ T(x * L(y / x,z,u),x) = L(T(y,x) / x,z,u)
    ]]></literal>
    <justification jstring="[para(1376(a,1),1753(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1376 1753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1755">
    <literal><![CDATA[
      L(T(x * y,x) / x,z,u) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,1380,a(flip),b,1754,a),flip(a)].">
      <j1 rule="hyper" parents="58 1380 1754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1756">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) = L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,841,a,b,1751,a),flip(a)].">
      <j1 rule="hyper" parents="30 841 1751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1757">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (x \ y) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(1178,a,1756,a)].">
      <j1 rule="hyper" parents="1178 1756"/>
    </justification>
  </clause>

  <clause id="1758">
    <literal><![CDATA[
      x \ (y * L(y \ x,x \ y,y \ x)) = (x \ y) * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(1756(a,2),474(a,1,2,2))].">
      <j1 rule="para" parents="1756 474"/>
    </justification>
  </clause>

  <clause id="1759">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,y \ x) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(424,a,1757,a)].">
      <j1 rule="hyper" parents="424 1757"/>
    </justification>
  </clause>

  <clause id="1760">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / (x \ (x * y))
    ]]></literal>
    <justification jstring="[para(4(a,1),1757(a,1,1,2))].">
      <j1 rule="para" parents="4 1757"/>
    </justification>
  </clause>

  <clause id="1761">
    <literal><![CDATA[
      L(((x * y) \ x) \ 1,(x * y) \ x,y) = 1 / ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1759(a,1,3))].">
      <j1 rule="para" parents="4 1759"/>
    </justification>
  </clause>

  <clause id="1762">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / y
    ]]></literal>
    <justification jstring="[para(4(a,1),1760(a,2,2))].">
      <j1 rule="para" parents="4 1760"/>
    </justification>
  </clause>

  <clause id="1763">
    <literal><![CDATA[
      L(x \ 1,x,(y * x) \ y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(424,a,1762,a)].">
      <j1 rule="hyper" parents="424 1762"/>
    </justification>
  </clause>

  <clause id="1764">
    <literal><![CDATA[
      ((x * y) \ x) / (1 / y) = ((x * y) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(197,a,1762,a)].">
      <j1 rule="hyper" parents="197 1762"/>
    </justification>
  </clause>

  <clause id="1765">
    <literal><![CDATA[
      (((x * y) \ x) * y) * (1 / y) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(134,a,1762,a)].">
      <j1 rule="hyper" parents="134 1762"/>
    </justification>
  </clause>

  <clause id="1766">
    <literal><![CDATA[
      L(x \ 1,x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[para(2(a,1),1763(a,1,3,1))].">
      <j1 rule="para" parents="2 1763"/>
    </justification>
  </clause>

  <clause id="1767">
    <literal><![CDATA[
      L(T(x \ 1,y),x,x \ 1) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(1766(a,1),20(a,2,1))].">
      <j1 rule="para" parents="1766 20"/>
    </justification>
  </clause>

  <clause id="1768">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,x \ 1) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1766(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1766 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1769">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[para(1766(a,1),397(a,1,2))].">
      <j1 rule="para" parents="1766 397"/>
    </justification>
  </clause>

  <clause id="1770">
    <literal><![CDATA[
      x * L(x \ (y \ x),y,y \ 1) = (y * (1 / y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(1766(a,1),1530(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1766 1530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1771">
    <literal><![CDATA[
      T(1 / (1 / x),x \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(1038,a,1769,a)].">
      <j1 rule="hyper" parents="1038 1769"/>
    </justification>
  </clause>

  <clause id="1772">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,258,a,b,1769,a),flip(a)].">
      <j1 rule="hyper" parents="320 258 1769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1773">
    <literal><![CDATA[
      T(T(1 / (1 / x),y),x \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1771(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1771 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1774">
    <literal><![CDATA[
      T(x,y \ 1) != T(y,z)
    ]]></literal>
    <literal><![CDATA[
      T(1 / (1 / y),z) = x
    ]]></literal>
    <justification jstring="[para(1771(a,1),138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1771 138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1775">
    <literal><![CDATA[
      T(x,x \ 1) / x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1771(a,1),1184(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1771 1184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1776">
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1272,a,1772,a)].">
      <j1 rule="hyper" parents="1272 1772"/>
    </justification>
  </clause>

  <clause id="1777">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,1772,a)].">
      <j1 rule="hyper" parents="133 1772"/>
    </justification>
  </clause>

  <clause id="1778">
    <literal><![CDATA[
      x \ (1 / (1 / x)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1454,a(flip),b,1772,a)].">
      <j1 rule="hyper" parents="58 1454 1772"/>
    </justification>
  </clause>

  <clause id="1779">
    <literal><![CDATA[
      x * K(x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1772,a(flip),b,1454,a(flip))].">
      <j1 rule="hyper" parents="119 1772 1454"/>
    </justification>
  </clause>

  <clause id="1780">
    <literal><![CDATA[
      K(x,1 / x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1267,a,1775,a)].">
      <j1 rule="hyper" parents="1267 1775"/>
    </justification>
  </clause>

  <clause id="1781">
    <literal><![CDATA[
      K(x,x \ 1) * x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,1775,a)].">
      <j1 rule="hyper" parents="133 1775"/>
    </justification>
  </clause>

  <clause id="1782">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(106(a,1),1775(a,1,1))].">
      <j1 rule="para" parents="106 1775"/>
    </justification>
  </clause>

  <clause id="1783">
    <literal><![CDATA[
      K(x,x \ 1) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(386,a,1780,a),flip(a)].">
      <j1 rule="hyper" parents="386 1780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1784">
    <literal><![CDATA[
      K((x / y) \ x,1 / y) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,674,a,b,1780,a)].">
      <j1 rule="hyper" parents="58 674 1780"/>
    </justification>
  </clause>

  <clause id="1785">
    <literal><![CDATA[
      (x \ 1) * K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(119,a,1780,a(flip),b,1266,a)].">
      <j1 rule="hyper" parents="119 1780 1266"/>
    </justification>
  </clause>

  <clause id="1786">
    <literal><![CDATA[
      x \ K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(116,a,1780,a(flip),b,260,a(flip))].">
      <j1 rule="hyper" parents="116 1780 260"/>
    </justification>
  </clause>

  <clause id="1787">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),1780(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 1780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1788">
    <literal><![CDATA[
      K(x,x \ 1) \ 1 = K(1 / x,x)
    ]]></literal>
    <justification jstring="[para(1780(a,1),434(a,1,1))].">
      <j1 rule="para" parents="1780 434"/>
    </justification>
  </clause>

  <clause id="1789">
    <literal><![CDATA[
      K(x,x \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(1780(a,1),386(a,1))].">
      <j1 rule="para" parents="1780 386"/>
    </justification>
  </clause>

  <clause id="1790">
    <literal><![CDATA[
      (1 / (1 / x)) * K(x,x \ 1) = x
    ]]></literal>
    <justification jstring="[para(1780(a,1),869(a,1,2))].">
      <j1 rule="para" parents="1780 869"/>
    </justification>
  </clause>

  <clause id="1791">
    <literal><![CDATA[
      R(x \ 1,x,y) \ (((y / (x * y)) * x) * (1 / x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,1273,a,b,1783,a)].">
      <j1 rule="hyper" parents="320 1273 1783"/>
    </justification>
  </clause>

  <clause id="1792">
    <literal><![CDATA[
      L(x,y,z) * K(x,x \ 1) = x * (L(x,y,z) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(119,a,1783,a,b,1401,a)].">
      <j1 rule="hyper" parents="119 1783 1401"/>
    </justification>
  </clause>

  <clause id="1793">
    <literal><![CDATA[
      R(x,y,1 / y) * K(y,y \ 1) = (x * y) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1783,a,b,184,a)].">
      <j1 rule="hyper" parents="119 1783 184"/>
    </justification>
  </clause>

  <clause id="1794">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ (1 / x)) = z
    ]]></literal>
    <justification jstring="[para(1783(a,2),1131(a,1,2))].">
      <j1 rule="para" parents="1783 1131"/>
    </justification>
  </clause>

  <clause id="1795">
    <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(1783(a,2),919(a,1,1))].">
      <j1 rule="para" parents="1783 919"/>
    </justification>
  </clause>

  <clause id="1796">
    <literal><![CDATA[
      x * (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(1786(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1786 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1797">
    <literal><![CDATA[
      x \ y != z * (1 / z)
    ]]></literal>
    <literal><![CDATA[
      x * K(z,z \ 1) = y
    ]]></literal>
    <justification jstring="[para(1786(a,1),340(a,2,2))].">
      <j1 rule="para" parents="1786 340"/>
    </justification>
  </clause>

  <clause id="1798">
    <literal><![CDATA[
      (x \ 1) * L(y,1 / x,K(x \ 1,x)) = K(x \ 1,x) * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(1777(a,1),90(a,1,1))].">
      <j1 rule="para" parents="1777 90"/>
    </justification>
  </clause>

  <clause id="1799">
    <literal><![CDATA[
      x * (T(x,y) \ K(x \ 1,x)) = T(x,y) \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(1778(a,1),1109(a,1,2,2))].">
      <j1 rule="para" parents="1778 1109"/>
    </justification>
  </clause>

  <clause id="1800">
    <literal><![CDATA[
      K(x \ 1,x) * x = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1293,a,1779,a)].">
      <j1 rule="hyper" parents="1293 1779"/>
    </justification>
  </clause>

  <clause id="1801">
    <literal><![CDATA[
      L(x,x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(831,a,1779,a)].">
      <j1 rule="hyper" parents="831 1779"/>
    </justification>
  </clause>

  <clause id="1802">
    <literal><![CDATA[
      L(R(x,y,z),x \ 1,x) = R(1 / (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(1801(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1801 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1803">
    <literal><![CDATA[
      1 / (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      x * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(1801(a,1),832(a,1))].">
      <j1 rule="para" parents="1801 832"/>
    </justification>
  </clause>

  <clause id="1804">
    <literal><![CDATA[
      K(x,x \ 1) * x = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,106,a(flip),b,1781,a),flip(a)].">
      <j1 rule="hyper" parents="320 106 1781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1805">
    <literal><![CDATA[
      T(x,x \ 1) * L(y,x,K(x,x \ 1)) = K(x,x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(1781(a,1),90(a,1,1))].">
      <j1 rule="para" parents="1781 90"/>
    </justification>
  </clause>

  <clause id="1806">
    <literal><![CDATA[
      T(x,x \ 1) \ (K(x,x \ 1) * y) = L(x \ y,x,K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(1781(a,1),92(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1781 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1807">
    <literal><![CDATA[
      T(x,x \ 1) * y != K(x,x \ 1) * (x * z)
    ]]></literal>
    <literal><![CDATA[
      L(z,x,K(x,x \ 1)) = y
    ]]></literal>
    <justification jstring="[para(1781(a,1),479(a,1,1))].">
      <j1 rule="para" parents="1781 479"/>
    </justification>
  </clause>

  <clause id="1808">
    <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(1781(a,1),482(a,1,2,2))].">
      <j1 rule="para" parents="1781 482"/>
    </justification>
  </clause>

  <clause id="1809">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(1283,a,1785,a)].">
      <j1 rule="hyper" parents="1283 1785"/>
    </justification>
  </clause>

  <clause id="1810">
    <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,1790,a(flip),b,184,a)].">
      <j1 rule="hyper" parents="119 1790 184"/>
    </justification>
  </clause>

  <clause id="1811">
    <literal><![CDATA[
      x * L(y,K(x,x \ 1),1 / (1 / x)) = (1 / (1 / x)) * (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(1790(a,1),90(a,1,1))].">
      <j1 rule="para" parents="1790 90"/>
    </justification>
  </clause>

  <clause id="1812">
    <literal><![CDATA[
      R(x / (1 / (1 / y)),1 / (1 / y),K(y,y \ 1)) = (x * K(y,y \ 1)) / y
    ]]></literal>
    <justification jstring="[para(1790(a,1),102(a,2,2))].">
      <j1 rule="para" parents="1790 102"/>
    </justification>
  </clause>

  <clause id="1813">
    <literal><![CDATA[
      (1 / x) / L(y,(x \ 1) / y,K(x,x \ 1)) = K(x,x \ 1) * ((x \ 1) / y)
    ]]></literal>
    <justification jstring="[para(1809(a,1),544(a,1,1))].">
      <j1 rule="para" parents="1809 544"/>
    </justification>
  </clause>

  <clause id="1814">
    <literal><![CDATA[
      K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(260(a,2),1796(a,1))].">
      <j1 rule="para" parents="260 1796"/>
    </justification>
  </clause>

  <clause id="1815">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1814,a,1776,a)].">
      <j1 rule="hyper" parents="1814 1776"/>
    </justification>
  </clause>

  <clause id="1816">
    <literal><![CDATA[
      K(1 / x,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(75(a,1),1815(a,1,2))].">
      <j1 rule="para" parents="75 1815"/>
    </justification>
  </clause>

  <clause id="1817">
    <literal><![CDATA[
      K(x,x \ 1) \ 1 = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1788,a,b,1816,a)].">
      <j1 rule="hyper" parents="58 1788 1816"/>
    </justification>
  </clause>

  <clause id="1818">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),1816(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 1816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1819">
    <literal><![CDATA[
      K(T(x \ 1,x) \ 1,T(x \ 1,x)) = K(T(x,x \ 1),T(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(1253(a,1),1816(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1253 1816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1820">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,1780,a,b,1818,a),flip(a)].">
      <j1 rule="hyper" parents="320 1780 1818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1821">
    <literal><![CDATA[
      x \ ((x \ 1) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,776,a(flip),b,1818,a)].">
      <j1 rule="hyper" parents="58 776 1818"/>
    </justification>
  </clause>

  <clause id="1822">
    <literal><![CDATA[
      x * K(x,x \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,1818,a(flip),b,776,a(flip))].">
      <j1 rule="hyper" parents="119 1818 776"/>
    </justification>
  </clause>

  <clause id="1823">
    <literal><![CDATA[
      x * K(x,x \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,1821,a(flip),b,310,a)].">
      <j1 rule="hyper" parents="119 1821 310"/>
    </justification>
  </clause>

  <clause id="1824">
    <literal><![CDATA[
      x \ ((x \ 1) \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(1822(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1822 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1825">
    <literal><![CDATA[
      T(x,x \ 1) * L(y,K(x,x \ 1),x) = x * (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(1823(a,1),90(a,1,1))].">
      <j1 rule="para" parents="1823 90"/>
    </justification>
  </clause>

  <clause id="1826">
    <literal><![CDATA[
      K(T(x \ 1,x),(x \ 1) \ 1) = K(x \ 1,1 / (x \ 1))
    ]]></literal>
    <justification jstring="[para(1252(a,2),1820(a,1,1))].">
      <j1 rule="para" parents="1252 1820"/>
    </justification>
  </clause>

  <clause id="1827">
    <literal><![CDATA[
      K(x \ 1,x) * T(1 / x,y) = (x \ 1) * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(1767(a,1),484(a,1,2))].">
      <j1 rule="para" parents="1767 484"/>
    </justification>
  </clause>

  <clause id="1828">
    <literal><![CDATA[
      K(((x * y) \ x) \ (((x * y) \ x) * y),(x * y) \ x) * y = T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(1764(a,1),1024(a,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1764 1024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1829">
    <literal><![CDATA[
      (x * y) \ x = (L(y \ 1,y,x) * y) * (1 / y)
    ]]></literal>
    <justification jstring="[para(217(a,2),1765(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="217 1765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1830">
    <literal><![CDATA[
      K(x \ 1,x) * L(1 / x,y,z) = (x \ 1) * (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(1768(a,1),484(a,1,2))].">
      <j1 rule="para" parents="1768 484"/>
    </justification>
  </clause>

  <clause id="1831">
    <literal><![CDATA[
      K(x \ 1,x) * L(1 / x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * (x * L(x \ 1,y,z)) = u
    ]]></literal>
    <justification jstring="[para(1768(a,1),822(a,1,2))].">
      <j1 rule="para" parents="1768 822"/>
    </justification>
  </clause>

  <clause id="1832">
    <literal><![CDATA[
      L(x \ 1,x,y) / (1 / x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(620,a,1829,a)].">
      <j1 rule="hyper" parents="620 1829"/>
    </justification>
  </clause>

  <clause id="1833">
    <literal><![CDATA[
      K(T(x \ 1,x),(x \ 1) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),1826(a,2,2))].">
      <j1 rule="para" parents="72 1826"/>
    </justification>
  </clause>

  <clause id="1835">
    <literal><![CDATA[
      K(T(x \ 1,x),T(x,x \ 1)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1360,a,b,1833,a)].">
      <j1 rule="hyper" parents="58 1360 1833"/>
    </justification>
  </clause>

  <clause id="1836">
    <literal><![CDATA[
      K(T((x \ 1) \ 1,x \ 1),T(x \ 1,(x \ 1) \ 1)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,1818,a(flip),b,1835,a),flip(a)].">
      <j1 rule="hyper" parents="320 1818 1835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1837">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ x = 1 / ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(500,a,1761,a)].">
      <j1 rule="hyper" parents="500 1761"/>
    </justification>
  </clause>

  <clause id="1838">
    <literal><![CDATA[
      x * L(x \ (y \ x),y,y \ 1) = K(y,y \ 1) * (y \ x)
    ]]></literal>
    <justification jstring="[para(1783(a,2),1770(a,2,1))].">
      <j1 rule="para" parents="1783 1770"/>
    </justification>
  </clause>

  <clause id="1839">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1052,a(flip),b,1741,a)].">
      <j1 rule="hyper" parents="58 1052 1741"/>
    </justification>
  </clause>

  <clause id="1840">
    <literal><![CDATA[
      T(x * L(x \ 1,T(x,y),y),y) = T(x,y) * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(239,a,1741,a(flip),b,481,a(flip))].">
      <j1 rule="hyper" parents="239 1741 481"/>
    </justification>
  </clause>

  <clause id="1841">
    <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,1827,a(flip),b,632,a)].">
      <j1 rule="hyper" parents="119 1827 632"/>
    </justification>
  </clause>

  <clause id="1842">
    <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),1839(a,1,2,2,1,2))].">
      <j1 rule="para" parents="4 1839"/>
    </justification>
  </clause>

  <clause id="1843">
    <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(1584(a,2),1839(a,1,2))].">
      <j1 rule="para" parents="1584 1839"/>
    </justification>
  </clause>

  <clause id="1844">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),x,x \ 1)) = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1766(a,1),1839(a,2,1,2))].">
      <j1 rule="para" parents="1766 1839"/>
    </justification>
  </clause>

  <clause id="1845">
    <literal><![CDATA[
      x * (K(x,x \ 1) * (x \ y)) = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1838(a,1),1844(a,1,2))].">
      <j1 rule="para" parents="1838 1844"/>
    </justification>
  </clause>

  <clause id="1846">
    <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,1845,a),flip(a)].">
      <j1 rule="hyper" parents="29 90 1845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1847">
    <literal><![CDATA[
      x * (K(x,x \ 1) * (x \ y)) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1783(a,2),1845(a,2,1))].">
      <j1 rule="para" parents="1783 1845"/>
    </justification>
  </clause>

  <clause id="1848">
    <literal><![CDATA[
      x \ (K(x,x \ 1) * y) = K(x,x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(123,a,1847,a)].">
      <j1 rule="hyper" parents="123 1847"/>
    </justification>
  </clause>

  <clause id="1849">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = x * (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1847(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 1847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1850">
    <literal><![CDATA[
      x * (K(x,x \ 1) * T(y,x)) = K(x,x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(17(a,2),1847(a,1,2,2))].">
      <j1 rule="para" parents="17 1847"/>
    </justification>
  </clause>

  <clause id="1851">
    <literal><![CDATA[
      K(x,x \ 1) * y != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * (x \ y) = z
    ]]></literal>
    <justification jstring="[para(1847(a,1),38(a,1))].">
      <j1 rule="para" parents="1847 38"/>
    </justification>
  </clause>

  <clause id="1852">
    <literal><![CDATA[
      (1 / x) * (K(x \ 1,x) * ((1 / x) \ y)) = K(1 / x,(1 / x) \ 1) * y
    ]]></literal>
    <justification jstring="[para(1815(a,1),1847(a,1,2,1))].">
      <j1 rule="para" parents="1815 1847"/>
    </justification>
  </clause>

  <clause id="1853">
    <literal><![CDATA[
      K(x,x \ 1) * y != (1 / x) * z
    ]]></literal>
    <literal><![CDATA[
      x \ L(z,1 / x,x) = y
    ]]></literal>
    <justification jstring="[para(1846(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="1846 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1854">
    <literal><![CDATA[
      x * L(x \ y,y \ x,x \ y) = y * K(y \ x,(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(1797,a,1758,a),flip(a)].">
      <j1 rule="hyper" parents="1797 1758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1855">
    <literal><![CDATA[
      T(x,x \ 1) * L(y,x,K(x,x \ 1)) = x * (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,1849,a(flip),b,1805,a),flip(a)].">
      <j1 rule="hyper" parents="320 1849 1805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1856">
    <literal><![CDATA[
      L(x,K(y,y \ 1),y) = L(x,y,K(y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(29,a,1825,a,b,1855,a)].">
      <j1 rule="hyper" parents="29 1825 1855"/>
    </justification>
  </clause>

  <clause id="1857">
    <literal><![CDATA[
      L(x,1 / y,K(1 / y,(1 / y) \ 1)) = L(x,K(y \ 1,y),1 / y)
    ]]></literal>
    <justification jstring="[para(1815(a,1),1856(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1815 1856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1858">
    <literal><![CDATA[
      x * (y * R(y \ (x \ (z * y)),u,w)) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1054,a(flip),b,1709,a)].">
      <j1 rule="hyper" parents="58 1054 1709"/>
    </justification>
  </clause>

  <clause id="1859">
    <literal><![CDATA[
      (x \ (y * x)) * R((x \ (y * x)) \ x,z,u) = T(y * R(y \ x,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(239,a,1709,a(flip),b,1323,a),flip(a)].">
      <j1 rule="hyper" parents="239 1709 1323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1860">
    <literal><![CDATA[
      x * R(x \ (x \ (y * x)),z,u) = T(x * R(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(239,a,1709,a(flip),b,1054,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="239 1709 1054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1861">
    <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,1709,a(flip),b,1323,a),flip(a)].">
      <j1 rule="hyper" parents="116 1709 1323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1862">
    <literal><![CDATA[
      x \ ((x * R(x \ y,z,u)) * w) = w * R(w \ (x \ (y * w)),z,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,1709,a(flip),b,1054,a(flip))].">
      <j1 rule="hyper" parents="116 1709 1054"/>
    </justification>
  </clause>

  <clause id="1863">
    <literal><![CDATA[
      (x * R(x \ (x * y),z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),1709(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1864">
    <literal><![CDATA[
      (x * R(y,z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),1863(a,1,1,2,1))].">
      <j1 rule="para" parents="4 1863"/>
    </justification>
  </clause>

  <clause id="1865">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = x / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(415,a,1864,a),flip(a)].">
      <j1 rule="hyper" parents="415 1864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1866">
    <literal><![CDATA[
      ((x / R(y,z,u)) * y) * R(y,z,u) = x * y
    ]]></literal>
    <justification jstring="[hyper(326,a,1864,a),flip(a)].">
      <j1 rule="hyper" parents="326 1864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1867">
    <literal><![CDATA[
      (x * R(y,z,u)) \ ((x * y) * R(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,1864,a)].">
      <j1 rule="hyper" parents="123 1864"/>
    </justification>
  </clause>

  <clause id="1868">
    <literal><![CDATA[
      (x * R(y,z,u)) / y = (x / y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,147,a(flip),b,1864,a)].">
      <j1 rule="hyper" parents="117 147 1864"/>
    </justification>
  </clause>

  <clause id="1869">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,73,a(flip),b,1864,a),flip(a)].">
      <j1 rule="hyper" parents="117 73 1864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1870">
    <literal><![CDATA[
      ((x / y) * R(y,z,u)) \ (x * R(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,147,a(flip),b,1864,a)].">
      <j1 rule="hyper" parents="116 147 1864"/>
    </justification>
  </clause>

  <clause id="1871">
    <literal><![CDATA[
      (x / R(x,y,z)) / x = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,1865,a)].">
      <j1 rule="hyper" parents="131 1865"/>
    </justification>
  </clause>

  <clause id="1872">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) * (1 / x) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(917,a,1869,a)].">
      <j1 rule="hyper" parents="917 1869"/>
    </justification>
  </clause>

  <clause id="1873">
    <literal><![CDATA[
      (R(x,y,z) / x) / R(x,y,z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(131,a,1869,a)].">
      <j1 rule="hyper" parents="131 1869"/>
    </justification>
  </clause>

  <clause id="1874">
    <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(1869(a,1),240(a,2)),flip(a)].">
      <j1 rule="para" parents="1869 240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1875">
    <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(1869(a,1),92(a,2,1))].">
      <j1 rule="para" parents="1869 92"/>
    </justification>
  </clause>

  <clause id="1876">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x != u
    ]]></literal>
    <literal><![CDATA[
      x / R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1871(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1871 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1877">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) / x = u
    ]]></literal>
    <justification jstring="[para(1873(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1873 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1878">
    <literal><![CDATA[
      (x * y) / R(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / R(y,z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(1866(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1866 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1879">
    <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(1866(a,1),800(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1866 800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1880">
    <literal><![CDATA[
      R(T(x,y * R(x,z,u)),y,R(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1867(a,1),1088(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1867 1088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1881">
    <literal><![CDATA[
      (x * R(y / x,z,u)) \ (y * R(y / x,z,u)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[hyper(929,a,1880,a)].">
      <j1 rule="hyper" parents="929 1880"/>
    </justification>
  </clause>

  <clause id="1882">
    <literal><![CDATA[
      (x * R(y,z,u)) * T(y,x) = (y * x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,1880,a(flip),b,630,a)].">
      <j1 rule="hyper" parents="119 1880 630"/>
    </justification>
  </clause>

  <clause id="1883">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) * (y * R(x,z,u)) = (y * R(x,z,u)) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1880,a(flip),b,110,a),flip(a)].">
      <j1 rule="hyper" parents="119 1880 110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1884">
    <literal><![CDATA[
      (1 / x) * R((1 / x) \ 1,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(862,a,1872,a)].">
      <j1 rule="hyper" parents="862 1872"/>
    </justification>
  </clause>

  <clause id="1885">
    <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,1882,a)].">
      <j1 rule="hyper" parents="117 64 1882"/>
    </justification>
  </clause>

  <clause id="1886">
    <literal><![CDATA[
      R(x,y,z) / ((x \ 1) \ 1) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(675,a,1885,a)].">
      <j1 rule="hyper" parents="675 1885"/>
    </justification>
  </clause>

  <clause id="1887">
    <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),1860(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 1860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1888">
    <literal><![CDATA[
      x \ T(x * R(x \ y,z,u),x) = R(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(766,a,1887,a)].">
      <j1 rule="hyper" parents="766 1887"/>
    </justification>
  </clause>

  <clause id="1889">
    <literal><![CDATA[
      T(x * R(x \ y,z,u),x) / x = R(T(y,x) / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,1887,a,b,639,a)].">
      <j1 rule="hyper" parents="117 1887 639"/>
    </justification>
  </clause>

  <clause id="1890">
    <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),1889(a,1,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1891">
    <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),1879(a,2,1))].">
      <j1 rule="para" parents="2 1879"/>
    </justification>
  </clause>

  <clause id="1892">
    <literal><![CDATA[
      (x * R(y / x,z,u)) \ (y * R(y / x,z,u)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,107,a(flip),b,1881,a),flip(a)].">
      <j1 rule="hyper" parents="320 107 1881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1893">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * x = x * (x * ((y * (x \ 1)) / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1089,a(flip),b,1710,a),flip(a)].">
      <j1 rule="hyper" parents="58 1089 1710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1894">
    <literal><![CDATA[
      (x * (((x * y) * (x \ 1)) / (x * y))) * y = (x * y) * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(5(a,1),1710(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1895">
    <literal><![CDATA[
      (1 / x) * ((1 / x) * ((y * ((1 / x) \ 1)) / y)) = (((y * x) / y) / x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(1461(a,1),1893(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1461 1893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1896">
    <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(1711(a,2),45(a,1)),flip(a)].">
      <j1 rule="para" parents="1711 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1897">
    <literal><![CDATA[
      (x * L(x \ (y * z),u,w)) / z = (x / z) * L((x / z) \ y,u,w)
    ]]></literal>
    <justification jstring="[hyper(131,a,1712,a)].">
      <j1 rule="hyper" parents="131 1712"/>
    </justification>
  </clause>

  <clause id="1898">
    <literal><![CDATA[
      ((x / y) * L((x / y) \ 1,z,u)) * y = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(2(a,1),1712(a,2,2,1,2))].">
      <j1 rule="para" parents="2 1712"/>
    </justification>
  </clause>

  <clause id="1899">
    <literal><![CDATA[
      (x / y) * L((x / y) \ 1,z,u) = (x * L(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(131,a,1898,a),flip(a)].">
      <j1 rule="hyper" parents="131 1898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1900">
    <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),1899(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15 1899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1901">
    <literal><![CDATA[
      x \ y != z * ((u * (z \ 1)) / u)
    ]]></literal>
    <literal><![CDATA[
      x * K(u,(u / z) / u) = y
    ]]></literal>
    <justification jstring="[para(1715(a,1),581(a,1)),flip(a)].">
      <j1 rule="para" parents="1715 581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1902">
    <literal><![CDATA[
      R(T(x,y),z,u) * (x * w) = x * (R(T(x,y),z,u) * w)
    ]]></literal>
    <justification jstring="[para(1107(a,1),1737(a,1,1,1))].">
      <j1 rule="para" parents="1107 1737"/>
    </justification>
  </clause>

  <clause id="1903">
    <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,1902,a)].">
      <j1 rule="hyper" parents="116 151 1902"/>
    </justification>
  </clause>

  <clause id="1904">
    <literal><![CDATA[
      K(T(x \ 1,x) \ 1,T(x \ 1,(x \ 1) \ 1)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1256(a,1),1836(a,1,1))].">
      <j1 rule="para" parents="1256 1836"/>
    </justification>
  </clause>

  <clause id="1905">
    <literal><![CDATA[
      K(T(x \ 1,x) \ 1,T(x \ 1,x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1255(a,1),1904(a,1,2))].">
      <j1 rule="para" parents="1255 1904"/>
    </justification>
  </clause>

  <clause id="1906">
    <literal><![CDATA[
      K(T(x,x \ 1),T(x \ 1,x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,1819,a(flip),b,1905,a)].">
      <j1 rule="hyper" parents="58 1819 1905"/>
    </justification>
  </clause>

  <clause id="1907">
    <literal><![CDATA[
      K(T(x,x \ 1),T(x,x \ 1) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1249(a,2),1906(a,1,2))].">
      <j1 rule="para" parents="1249 1906"/>
    </justification>
  </clause>

  <clause id="1908">
    <literal><![CDATA[
      K(T(x,x \ 1),T(x,x \ 1) \ 1) * (T(x,x \ 1) \ y) = T(x,x \ 1) \ (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(1907(a,1),1848(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1907 1848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1909">
    <literal><![CDATA[
      L(x,1 / (1 / y),K(1 / (1 / y),(1 / (1 / y)) \ 1)) = L(x,K(y,y \ 1),1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(1784(a,1),1857(a,2,2))].">
      <j1 rule="para" parents="1784 1857"/>
    </justification>
  </clause>

  <clause id="1910">
    <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(184(a,1),1858(a,1,2,2,1,2))].">
      <j1 rule="para" parents="184 1858"/>
    </justification>
  </clause>

  <clause id="1911">
    <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(1862(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1862 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1912">
    <literal><![CDATA[
      (x / y) * L((x / y) \ (z / y),u,w) = (x * L(x \ z,u,w)) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),1897(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 1897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1913">
    <literal><![CDATA[
      (x * L(x \ (y * x),z,u)) / y = (x / y) * L(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(1494(a,2),1912(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1494 1912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1914">
    <literal><![CDATA[
      (x / y) * L(T(y,x),z,u) = (L(y,z,u) * x) / y
    ]]></literal>
    <justification jstring="[para(633(a,1),1913(a,1,1)),flip(a)].">
      <j1 rule="para" parents="633 1913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1915">
    <literal><![CDATA[
      (L(x,y,z) * (u * x)) / x = u * L(T(x,u * x),y,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),1914(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 1914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1916">
    <literal><![CDATA[
      T(x * L(T(y,x * y),z,u),y) = y \ (L(y,z,u) * (x * y))
    ]]></literal>
    <justification jstring="[para(1915(a,1),107(a,1,1))].">
      <j1 rule="para" parents="1915 107"/>
    </justification>
  </clause>

  <clause id="1917">
    <literal><![CDATA[
      T(x * L(T(y,x * y),z,u),y) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,1410,a(flip),b,1916,a),flip(a)].">
      <j1 rule="hyper" parents="320 1410 1916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1918">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,9,a,b,501,a)].">
      <j1 rule="hyper" parents="320 9 501"/>
    </justification>
  </clause>

  <clause id="1919">
    <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(501(a,1),402(a,1,1)),flip(a)].">
      <j1 rule="para" parents="501 402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1920">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ a(x,y,z) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(893,a,1918,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="893 1918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1921">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(x,y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(703,a,1918,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="703 1918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1922">
    <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),1918(a,2,2))].">
      <j1 rule="para" parents="13 1918"/>
    </justification>
  </clause>

  <clause id="1923">
    <literal><![CDATA[
      L(K(x,y),z,u) * a(u,z,K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,1921,a)].">
      <j1 rule="hyper" parents="134 1921"/>
    </justification>
  </clause>

  <clause id="1924">
    <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(1921(a,1),340(a,2,2))].">
      <j1 rule="para" parents="1921 340"/>
    </justification>
  </clause>

  <clause id="1925">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * a(w,u,a(x,y,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,1920,a)].">
      <j1 rule="hyper" parents="134 1920"/>
    </justification>
  </clause>

  <clause id="1926">
    <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(1920(a,1),503(a,1,1,1))].">
      <j1 rule="para" parents="1920 503"/>
    </justification>
  </clause>

  <clause id="1927">
    <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(1922(a,2),791(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1922 791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1928">
    <literal><![CDATA[
      K(x,(y \ z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,y \ z)) = u
    ]]></literal>
    <justification jstring="[para(665(a,1),662(a,1))].">
      <j1 rule="para" parents="665 662"/>
    </justification>
  </clause>

  <clause id="1929">
    <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(919(a,1),1587(a,1))].">
      <j1 rule="para" parents="919 1587"/>
    </justification>
  </clause>

  <clause id="1930">
    <literal><![CDATA[
      (T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,(1 * x) / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(529(a,1),1670(a,2,2))].">
      <j1 rule="para" parents="529 1670"/>
    </justification>
  </clause>

  <clause id="1931">
    <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),1930(a,2,2,1))].">
      <j1 rule="para" parents="2 1930"/>
    </justification>
  </clause>

  <clause id="1932">
    <literal><![CDATA[
      (T(x,T(x,y) \ 1) / x) * x = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(1588(a,1),1931(a,1,1))].">
      <j1 rule="para" parents="1588 1931"/>
    </justification>
  </clause>

  <clause id="1933">
    <literal><![CDATA[
      T(x,x / (x * T(x,y))) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(252,a,1932,a),flip(a)].">
      <j1 rule="hyper" parents="252 1932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1935">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,1655,a,b,1933,a)].">
      <j1 rule="hyper" parents="58 1655 1933"/>
    </justification>
  </clause>

  <clause id="1936">
    <literal><![CDATA[
      x * (T(x,y) * ((T(x,y) \ x) / x)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(1588(a,2),1935(a,1,2))].">
      <j1 rule="para" parents="1588 1935"/>
    </justification>
  </clause>

  <clause id="1937">
    <literal><![CDATA[
      L(x \ L(y,1 / x,K(x \ 1,x)),x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(1095,a,1798,a(flip))].">
      <j1 rule="hyper" parents="1095 1798"/>
    </justification>
  </clause>

  <clause id="1938">
    <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),1929(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="5 1929"/>
    </justification>
  </clause>

  <clause id="1939">
    <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(1491(a,1),1153(a,1,2,1))].">
      <j1 rule="para" parents="1491 1153"/>
    </justification>
  </clause>

  <clause id="1940">
    <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,1939,a)].">
      <j1 rule="hyper" parents="134 1939"/>
    </justification>
  </clause>

  <clause id="1941">
    <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,1417,a(flip),b,1940,a),flip(a)].">
      <j1 rule="hyper" parents="58 1417 1940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1942">
    <literal><![CDATA[
      (1 / x) \ L((y * x) \ y,z,u) = L((y * x) \ y,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(916,a,1195,a),flip(a)].">
      <j1 rule="hyper" parents="916 1195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1943">
    <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(1563(a,1),1206(a,1,1))].">
      <j1 rule="para" parents="1563 1206"/>
    </justification>
  </clause>

  <clause id="1944">
    <literal><![CDATA[
      L(x \ 1,R(x,y,z),1 / x) = (x \ R(x,y,z)) / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(855,a,1943,a)].">
      <j1 rule="hyper" parents="855 1943"/>
    </justification>
  </clause>

  <clause id="1945">
    <literal><![CDATA[
      ((x * ((y \ x) \ z)) / z) * (y \ z) = y \ (x * ((y \ x) \ z))
    ]]></literal>
    <justification jstring="[para(5(a,1),1321(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1947">
    <literal><![CDATA[
      x * ((x * y) * ((z * ((x * y) \ y)) / z)) = (x * ((z * (x \ 1)) / z)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1710,a(flip),b,1331,a),flip(a)].">
      <j1 rule="hyper" parents="58 1710 1331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1948">
    <literal><![CDATA[
      T(x * T(x \ ((y * z) / y),u),y) = T(x,y) * T(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(239,a,1515,a,b,1339,a(flip))].">
      <j1 rule="hyper" parents="239 1515 1339"/>
    </justification>
  </clause>

  <clause id="1949">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(x * T(x \ y,z),y)
    ]]></literal>
    <justification jstring="[hyper(239,a,1476,a(flip),b,1339,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="239 1476 1339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1950">
    <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),1339(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 1339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1951">
    <literal><![CDATA[
      x * L(y,T(y,x) \ y,T(y,x)) = (y * x) * T(K(x,y),y)
    ]]></literal>
    <justification jstring="[para(1137(a,1),1950(a,1,2))].">
      <j1 rule="para" parents="1137 1950"/>
    </justification>
  </clause>

  <clause id="1952">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ T(z,y),u) = T(x * T(x \ z,u),y)
    ]]></literal>
    <justification jstring="[para(225(a,1),1948(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="225 1948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1953">
    <literal><![CDATA[
      T(x * ((x * R(x \ 1,y,z)) / x),x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(644(a,1),1565(a,2,2))].">
      <j1 rule="para" parents="644 1565"/>
    </justification>
  </clause>

  <clause id="1954">
    <literal><![CDATA[
      T(x * R(1 / x,y,z),x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(644(a,1),1953(a,1,1,2))].">
      <j1 rule="para" parents="644 1953"/>
    </justification>
  </clause>

  <clause id="1955">
    <literal><![CDATA[
      T(x * (y / (x * y)),x) = x * R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(219(a,1),1954(a,1,1,2))].">
      <j1 rule="para" parents="219 1954"/>
    </justification>
  </clause>

  <clause id="1956">
    <literal><![CDATA[
      T(x * (y / (x * y)),x) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(320,a,404,a(flip),b,1955,a),flip(a)].">
      <j1 rule="hyper" parents="320 404 1955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1957">
    <literal><![CDATA[
      T(x,y / (x * y)) * R(x \ 1,x,y) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1703,a,b,1956,a)].">
      <j1 rule="hyper" parents="58 1703 1956"/>
    </justification>
  </clause>

  <clause id="1958">
    <literal><![CDATA[
      T(x,x * (y / (x * y))) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,1956,a)].">
      <j1 rule="hyper" parents="49 1956"/>
    </justification>
  </clause>

  <clause id="1959">
    <literal><![CDATA[
      T(x / y,(x / y) * (y / x)) = x / y
    ]]></literal>
    <justification jstring="[para(7(a,1),1958(a,1,2,2,2))].">
      <j1 rule="para" parents="7 1958"/>
    </justification>
  </clause>

  <clause id="1960">
    <literal><![CDATA[
      T(x \ y,(y / x) * (x / y)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(1959(a,1),246(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1959 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1961">
    <literal><![CDATA[
      T(x \ y,(y / x) * (x / y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,107,a(flip),b,1960,a),flip(a)].">
      <j1 rule="hyper" parents="320 107 1960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1962">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = (y * (y \ x)) / x
    ]]></literal>
    <justification jstring="[para(1961(a,1),1580(a,2,1,2))].">
      <j1 rule="para" parents="1961 1580"/>
    </justification>
  </clause>

  <clause id="1963">
    <literal><![CDATA[
      K(x \ (x / ((y \ x) / T(x,y))),x) = x / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(338,a,1582,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="338 1582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1964">
    <literal><![CDATA[
      (x \ T(x * (y / z),z)) * z = (x \ 1) * ((z \ ((x \ 1) \ y)) * z)
    ]]></literal>
    <justification jstring="[para(105(a,1),1590(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 1590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1965">
    <literal><![CDATA[
      (x \ T(x * (y / y),z)) * y = (x \ 1) * ((x \ T(x,z)) * ((x \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(1296(a,2),1590(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1296 1590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1966">
    <literal><![CDATA[
      T((x \ (x * (y / x))) * x,x) = (x \ 1) * ((x \ ((x \ 1) \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(1375,a,1964,a)].">
      <j1 rule="hyper" parents="1375 1964"/>
    </justification>
  </clause>

  <clause id="1967">
    <literal><![CDATA[
      T(x,y) = (y \ 1) * ((y \ ((y \ 1) \ x)) * y)
    ]]></literal>
    <justification jstring="[para(76(a,1),1966(a,1,1))].">
      <j1 rule="para" parents="76 1966"/>
    </justification>
  </clause>

  <clause id="1968">
    <literal><![CDATA[
      (x \ ((x \ 1) \ y)) * x = (x \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(766,a,1967,a),flip(a)].">
      <j1 rule="hyper" parents="766 1967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1969">
    <literal><![CDATA[
      (x \ 1) * ((x \ y) * x) = T((x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1967(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4 1967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1970">
    <literal><![CDATA[
      T((x \ 1) * (x * y),x) = (x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(62(a,1),1967(a,2,2,1))].">
      <j1 rule="para" parents="62 1967"/>
    </justification>
  </clause>

  <clause id="1971">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = L(K(x \ y,x),y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,1969,a(flip),b,487,a)].">
      <j1 rule="hyper" parents="116 1969 487"/>
    </justification>
  </clause>

  <clause id="1972">
    <literal><![CDATA[
      T(((x / y) \ 1) * x,x / y) = ((x / y) \ 1) * (y * (x / y))
    ]]></literal>
    <justification jstring="[para(75(a,1),1969(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 1969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1973">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * (K(y \ x,y) * x)
    ]]></literal>
    <justification jstring="[para(85(a,1),1969(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="85 1969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1974">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * x = x * ((x \ 1) * (y * x))
    ]]></literal>
    <justification jstring="[hyper(119,a,1970,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1970 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1975">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * x = L(y * x,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,257,a(flip),b,1974,a),flip(a)].">
      <j1 rule="hyper" parents="320 257 1974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1976">
    <literal><![CDATA[
      x * ((x \ y) * ((z * ((x \ y) \ 1)) / z)) = y * ((z * (y \ x)) / z)
    ]]></literal>
    <justification jstring="[para(3(a,1),1605(a,2,2,1,2,2))].">
      <j1 rule="para" parents="3 1605"/>
    </justification>
  </clause>

  <clause id="1977">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ 1)) / z) = x \ (y * ((z * (y \ x)) / z))
    ]]></literal>
    <justification jstring="[hyper(123,a,1976,a),flip(a)].">
      <j1 rule="hyper" parents="123 1976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1978">
    <literal><![CDATA[
      x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[para(1714(a,2),1976(a,1,2))].">
      <j1 rule="para" parents="1714 1976"/>
    </justification>
  </clause>

  <clause id="1979">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = y * K(z,(z / T(x,y)) / z)
    ]]></literal>
    <justification jstring="[para(17(a,2),1978(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 1978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1980">
    <literal><![CDATA[
      T(x * ((y * (x \ 1)) / y),z) = K(y,(y / T(x,z)) / y)
    ]]></literal>
    <justification jstring="[hyper(239,a,1710,a(flip),b,1979,a(flip))].">
      <j1 rule="hyper" parents="239 1710 1979"/>
    </justification>
  </clause>

  <clause id="1981">
    <literal><![CDATA[
      T(x,y) * ((z * (T(x,y) \ 1)) / z) = T(x * ((z * (x \ 1)) / z),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,1714,a(flip),b,1980,a)].">
      <j1 rule="hyper" parents="320 1714 1980"/>
    </justification>
  </clause>

  <clause id="1982">
    <literal><![CDATA[
      K(x,(x / T(y \ x,z)) / x) = T(K(x,y / x),z)
    ]]></literal>
    <justification jstring="[para(1720(a,1),1980(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1720 1980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1983">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,(x / (y \ x)) / x)
    ]]></literal>
    <justification jstring="[para(1355(a,1),1982(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1355 1982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1984">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(72(a,1),1983(a,2,2,1))].">
      <j1 rule="para" parents="72 1983"/>
    </justification>
  </clause>

  <clause id="1986">
    <literal><![CDATA[
      T(K(x,y),K((y * x) / x,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(6(a,1),1984(a,1,1,2))].">
      <j1 rule="para" parents="6 1984"/>
    </justification>
  </clause>

  <clause id="1987">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(6(a,1),1986(a,1,2,1))].">
      <j1 rule="para" parents="6 1986"/>
    </justification>
  </clause>

  <clause id="1988">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),1987(a,2,2))].">
      <j1 rule="para" parents="6 1987"/>
    </justification>
  </clause>

  <clause id="1989">
    <literal><![CDATA[
      K(K(x,y),K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,1988,a)].">
      <j1 rule="hyper" parents="50 1988"/>
    </justification>
  </clause>

  <clause id="1990">
    <literal><![CDATA[
      T(K(x,y),K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,1988,a)].">
      <j1 rule="hyper" parents="49 1988"/>
    </justification>
  </clause>

  <clause id="1991">
    <literal><![CDATA[
      K(x,y) * K(z,x) = K(z,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1988,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 1988 17"/>
    </justification>
  </clause>

  <clause id="1992">
    <literal><![CDATA[
      T(x,K(y,z)) != K(u,y)
    ]]></literal>
    <literal><![CDATA[
      K(u,y) = x
    ]]></literal>
    <justification jstring="[para(1988(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="1988 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1993">
    <literal><![CDATA[
      K(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(1988(a,1),284(a,1,2))].">
      <j1 rule="para" parents="1988 284"/>
    </justification>
  </clause>

  <clause id="1994">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,w) = K(y,w) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(1988(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1988 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1995">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(y,w) = K(y,w) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(1988(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1988 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1996">
    <literal><![CDATA[
      T(x,K(y,z)) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = x
    ]]></literal>
    <justification jstring="[para(1990(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="1990 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1997">
    <literal><![CDATA[
      K(x,y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(1990(a,1),284(a,1,2))].">
      <j1 rule="para" parents="1990 284"/>
    </justification>
  </clause>

  <clause id="1998">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(w,x) = K(w,x) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(1990(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1990 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1999">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(w,x) = K(w,x) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(1990(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1990 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2000">
    <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(1990(a,1),579(a,2,2))].">
      <j1 rule="para" parents="1990 579"/>
    </justification>
  </clause>

  <clause id="2001">
    <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(1990(a,1),420(a,1,2,1))].">
      <j1 rule="para" parents="1990 420"/>
    </justification>
  </clause>

  <clause id="2002">
    <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),1981(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2003">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(5(a,1),1981(a,2,1,2,1))].">
      <j1 rule="para" parents="5 1981"/>
    </justification>
  </clause>

  <clause id="2004">
    <literal><![CDATA[
      T(x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)),z) = T(x,z) * ((T(x,y) * (T(x,z) \ 1)) / T(x,y))
    ]]></literal>
    <justification jstring="[para(455(a,2),1981(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="455 1981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2005">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1110(a,1),2003(a,1,2,1))].">
      <j1 rule="para" parents="1110 2003"/>
    </justification>
  </clause>

  <clause id="2006">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(K(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1783(a,2),2005(a,2,1))].">
      <j1 rule="para" parents="1783 2005"/>
    </justification>
  </clause>

  <clause id="2007">
    <literal><![CDATA[
      x * T(K(x,x \ 1),y) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(2006(a,1),1936(a,1,2))].">
      <j1 rule="para" parents="2006 1936"/>
    </justification>
  </clause>

  <clause id="2008">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      T(K(x,x \ 1),y) = z
    ]]></literal>
    <justification jstring="[para(2007(a,1),38(a,1))].">
      <j1 rule="para" parents="2007 38"/>
    </justification>
  </clause>

  <clause id="2009">
    <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(320,a,1783,a,b,2002,a),flip(a)].">
      <j1 rule="hyper" parents="320 1783 2002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2010">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = T(K(T(x,y),1 / x),y)
    ]]></literal>
    <justification jstring="[para(1721(a,1),2009(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1721 2009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2011">
    <literal><![CDATA[
      T(x,y) != K(T(z,y),T(z,y) \ 1)
    ]]></literal>
    <literal><![CDATA[
      K(T(z,y),1 / z) = x
    ]]></literal>
    <justification jstring="[para(2010(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2010 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2012">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ (x \ u))) / z) = x \ (y * ((z * (y \ u)) / z))
    ]]></literal>
    <justification jstring="[para(5(a,1),1606(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 1606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2013">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) * (x * u) = x * ((x * R(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1514(a,1),1622(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1514 1622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2014">
    <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(1199(a,1),2013(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1199 2013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2015">
    <literal><![CDATA[
      R(x,y,z) * (T(x,u) \ 1) = T(x,u) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),1680(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2016">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ T(x,z)) / T(x,z)) = K(T(x,z),1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1139(a,1),1724(a,1,2,1))].">
      <j1 rule="para" parents="1139 1724"/>
    </justification>
  </clause>

  <clause id="2017">
    <literal><![CDATA[
      (x * (y * L(y \ 1,z,u))) * y = (x * y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(913(a,1),1739(a,1,1))].">
      <j1 rule="para" parents="913 1739"/>
    </justification>
  </clause>

  <clause id="2018">
    <literal><![CDATA[
      (x * (y * L(y \ 1,z,u))) / y = (x / y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(117,a,147,a(flip),b,2017,a)].">
      <j1 rule="hyper" parents="117 147 2017"/>
    </justification>
  </clause>

  <clause id="2019">
    <literal><![CDATA[
      (x * y) * (y * L(y \ 1,y,1 / y)) = (x * (y * (1 / y))) * y
    ]]></literal>
    <justification jstring="[para(389(a,1),2017(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="389 2017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2020">
    <literal><![CDATA[
      (x * (y * (1 / y))) * y = (x * y) * (y * (1 / y))
    ]]></literal>
    <justification jstring="[para(389(a,1),2019(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="389 2019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2021">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = (x * y) * (y * (1 / y))
    ]]></literal>
    <justification jstring="[para(1783(a,2),2020(a,1,1,2))].">
      <j1 rule="para" parents="1783 2020"/>
    </justification>
  </clause>

  <clause id="2022">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = (x * y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(1783(a,2),2021(a,2,2))].">
      <j1 rule="para" parents="1783 2021"/>
    </justification>
  </clause>

  <clause id="2023">
    <literal><![CDATA[
      T((x / y) * K(y,y \ 1),y) = y \ (x * K(y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(440,a,147,a(flip),b,2022,a)].">
      <j1 rule="hyper" parents="440 147 2022"/>
    </justification>
  </clause>

  <clause id="2024">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ ((x * y) * K(y,y \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,2022,a)].">
      <j1 rule="hyper" parents="123 2022"/>
    </justification>
  </clause>

  <clause id="2025">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / y = (x / y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,147,a(flip),b,2022,a)].">
      <j1 rule="hyper" parents="117 147 2022"/>
    </justification>
  </clause>

  <clause id="2026">
    <literal><![CDATA[
      R(T(x,y * K(x,x \ 1)),y,K(x,x \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2024(a,1),1088(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2024 1088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2027">
    <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(2025(a,1),421(a,1,1))].">
      <j1 rule="para" parents="2025 421"/>
    </justification>
  </clause>

  <clause id="2028">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x * u) = x * ((x * L(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1741(a,1),1842(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1741 1842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2029">
    <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,2028,a)].">
      <j1 rule="hyper" parents="116 151 2028"/>
    </justification>
  </clause>

  <clause id="2030">
    <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(604,a,2029,a)].">
      <j1 rule="hyper" parents="604 2029"/>
    </justification>
  </clause>

  <clause id="2031">
    <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(437(a,1),1852(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="437 1852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2032">
    <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),1859(a,1,1))].">
      <j1 rule="para" parents="17 1859"/>
    </justification>
  </clause>

  <clause id="2033">
    <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),2032(a,1,2,1,1))].">
      <j1 rule="para" parents="17 2032"/>
    </justification>
  </clause>

  <clause id="2034">
    <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),2033(a,2,1,2,1))].">
      <j1 rule="para" parents="4 2033"/>
    </justification>
  </clause>

  <clause id="2035">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = x / x
    ]]></literal>
    <justification jstring="[hyper(338,a,1962,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="338 1962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2036">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,69,a(flip),b,2035,a),flip(a)].">
      <j1 rule="hyper" parents="320 69 2035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2038">
    <literal><![CDATA[
      T(1 / (x / y),(y / x) * (x / y)) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[para(2036(a,1),1027(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2036 1027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2039">
    <literal><![CDATA[
      ((x / y) * (y / x)) \ (x / y) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1613,a(flip),b,2038,a)].">
      <j1 rule="hyper" parents="58 1613 2038"/>
    </justification>
  </clause>

  <clause id="2040">
    <literal><![CDATA[
      K(1 / (x / y),(y / x) * (x / y)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,2038,a)].">
      <j1 rule="hyper" parents="50 2038"/>
    </justification>
  </clause>

  <clause id="2041">
    <literal><![CDATA[
      ((x / y) * (y / x)) * (1 / (y / x)) = x / y
    ]]></literal>
    <justification jstring="[hyper(119,a,2038,a(flip),b,1613,a(flip))].">
      <j1 rule="hyper" parents="119 2038 1613"/>
    </justification>
  </clause>

  <clause id="2042">
    <literal><![CDATA[
      K(1 / x,(y / (x * y)) * ((x * y) / y)) = 1
    ]]></literal>
    <justification jstring="[para(6(a,1),2040(a,1,1,2))].">
      <j1 rule="para" parents="6 2040"/>
    </justification>
  </clause>

  <clause id="2043">
    <literal><![CDATA[
      ((x * y) / y) * (y / (x * y)) = x / (1 / (y / (x * y)))
    ]]></literal>
    <justification jstring="[hyper(117,a,6,a(flip),b,2041,a),flip(a)].">
      <j1 rule="hyper" parents="117 6 2041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2044">
    <literal><![CDATA[
      K(1 / x,(y / (x * y)) * x) = 1
    ]]></literal>
    <justification jstring="[para(6(a,1),2042(a,1,2,2))].">
      <j1 rule="para" parents="6 2042"/>
    </justification>
  </clause>

  <clause id="2045">
    <literal><![CDATA[
      T(1 / x,(y / (x * y)) * x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(51,a,2044,a)].">
      <j1 rule="hyper" parents="51 2044"/>
    </justification>
  </clause>

  <clause id="2046">
    <literal><![CDATA[
      L(x \ 1,x,y / (x * y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(1681,a,2045,a)].">
      <j1 rule="hyper" parents="1681 2045"/>
    </justification>
  </clause>

  <clause id="2047">
    <literal><![CDATA[
      ((x / (y * x)) * y) * (1 / y) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2045,a(flip),b,1209,a)].">
      <j1 rule="hyper" parents="119 2045 1209"/>
    </justification>
  </clause>

  <clause id="2048">
    <literal><![CDATA[
      L(x \ 1,x,R(1 / x,x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[para(219(a,2),2046(a,1,3))].">
      <j1 rule="para" parents="219 2046"/>
    </justification>
  </clause>

  <clause id="2049">
    <literal><![CDATA[
      R(1 / x,x,y) / (1 / x) = R(1 / x,x,y) * x
    ]]></literal>
    <justification jstring="[para(2048(a,1),397(a,1,2))].">
      <j1 rule="para" parents="2048 397"/>
    </justification>
  </clause>

  <clause id="2050">
    <literal><![CDATA[
      R(x \ 1,x,y) \ (y / (x * y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2047(a,1),1791(a,1,2))].">
      <j1 rule="para" parents="2047 1791"/>
    </justification>
  </clause>

  <clause id="2051">
    <literal><![CDATA[
      x / (y * x) = R(y \ 1,y,x) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,2050,a),flip(a)].">
      <j1 rule="hyper" parents="134 2050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2052">
    <literal><![CDATA[
      T(1 / (1 / x),R(1 / x,x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(1874,a,2049,a)].">
      <j1 rule="hyper" parents="1874 2049"/>
    </justification>
  </clause>

  <clause id="2053">
    <literal><![CDATA[
      T(1 / (1 / x),y / (x * y)) = x
    ]]></literal>
    <justification jstring="[para(219(a,1),2052(a,1,2))].">
      <j1 rule="para" parents="219 2052"/>
    </justification>
  </clause>

  <clause id="2054">
    <literal><![CDATA[
      T(x,y / (x * y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2053(a,1),1773(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2053 1773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2055">
    <literal><![CDATA[
      T(x,y / (x * y)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,106,a(flip),b,2054,a),flip(a)].">
      <j1 rule="hyper" parents="320 106 2054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2056">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,y \ 1) * x
    ]]></literal>
    <justification jstring="[para(2054(a,1),1583(a,2,1))].">
      <j1 rule="para" parents="2054 1583"/>
    </justification>
  </clause>

  <clause id="2057">
    <literal><![CDATA[
      T(x / y,y / x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(7(a,1),2055(a,1,2,2))].">
      <j1 rule="para" parents="7 2055"/>
    </justification>
  </clause>

  <clause id="2058">
    <literal><![CDATA[
      x \ T(x,y / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2055(a,2),1824(a,1,2))].">
      <j1 rule="para" parents="2055 1824"/>
    </justification>
  </clause>

  <clause id="2059">
    <literal><![CDATA[
      T(x / (y * x),y) = ((x / (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(6(a,1),2057(a,1,2))].">
      <j1 rule="para" parents="6 2057"/>
    </justification>
  </clause>

  <clause id="2060">
    <literal><![CDATA[
      ((((x * y) / x) \ 1) \ 1) * x = x * T(y,x / (x * y))
    ]]></literal>
    <justification jstring="[para(2057(a,1),454(a,1,1))].">
      <j1 rule="para" parents="2057 454"/>
    </justification>
  </clause>

  <clause id="2061">
    <literal><![CDATA[
      R(x \ 1,x,y) = ((y / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,645,a(flip),b,2059,a)].">
      <j1 rule="hyper" parents="58 645 2059"/>
    </justification>
  </clause>

  <clause id="2062">
    <literal><![CDATA[
      (R(1 / x,x,y) \ 1) \ 1 = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(219(a,2),2061(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="219 2061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2063">
    <literal><![CDATA[
      x / (1 / (y / (x * y))) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(6(a,1),2043(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 2043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2064">
    <literal><![CDATA[
      K(x \ (x * (y / (x * y))),x) = R(x \ 1,x,y) / (y / (x * y))
    ]]></literal>
    <justification jstring="[para(2063(a,1),1025(a,1,1,2))].">
      <j1 rule="para" parents="2063 1025"/>
    </justification>
  </clause>

  <clause id="2065">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = T(x,y / (y * x))
    ]]></literal>
    <justification jstring="[hyper(944,a,2060,a)].">
      <j1 rule="hyper" parents="944 2060"/>
    </justification>
  </clause>

  <clause id="2066">
    <literal><![CDATA[
      R(x \ 1,x,y) / (y / (x * y)) = K(y / (x * y),x)
    ]]></literal>
    <justification jstring="[hyper(1351,a,2064,a),flip(a)].">
      <j1 rule="hyper" parents="1351 2064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2068">
    <literal><![CDATA[
      K(x / (y * x),y) * (x / (y * x)) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,2066,a)].">
      <j1 rule="hyper" parents="133 2066"/>
    </justification>
  </clause>

  <clause id="2070">
    <literal><![CDATA[
      (x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)) = (x \ T(x * 1,y)) * z
    ]]></literal>
    <justification jstring="[para(69(a,1),1965(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="69 1965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2071">
    <literal><![CDATA[
      (x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)) = (x \ T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(3(a,1),2070(a,2,1,2,1))].">
      <j1 rule="para" parents="3 2070"/>
    </justification>
  </clause>

  <clause id="2073">
    <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,2071,a),flip(a)].">
      <j1 rule="hyper" parents="115 5 2071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2074">
    <literal><![CDATA[
      R((x * (y * z)) / (x * y),u,w) = (x * (y * R(z,u,w))) / (x * y)
    ]]></literal>
    <justification jstring="[para(447(a,1),861(a,1,1)),flip(a)].">
      <j1 rule="para" parents="447 861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2075">
    <literal><![CDATA[
      (T(x,y) * (1 / x)) / T(x,y) = L(1 / x,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1247,a(flip),b,1008,a)].">
      <j1 rule="hyper" parents="58 1247 1008"/>
    </justification>
  </clause>

  <clause id="2077">
    <literal><![CDATA[
      T(L(1 / x,T(x,y),1 / x),x) = (T(x,y) * (x \ 1)) / T(x,y)
    ]]></literal>
    <justification jstring="[para(2075(a,1),679(a,1,1))].">
      <j1 rule="para" parents="2075 679"/>
    </justification>
  </clause>

  <clause id="2078">
    <literal><![CDATA[
      (T(x,y) * (x \ 1)) / T(x,y) = L(x \ 1,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(855,a,2077,a),flip(a)].">
      <j1 rule="hyper" parents="855 2077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2079">
    <literal><![CDATA[
      x * L(x \ 1,T(x,y),1 / x) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(2078(a,1),1721(a,1,2))].">
      <j1 rule="para" parents="2078 1721"/>
    </justification>
  </clause>

  <clause id="2080">
    <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(1389(a,1),288(a,1))].">
      <j1 rule="para" parents="1389 288"/>
    </justification>
  </clause>

  <clause id="2081">
    <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),1427(a,1,2,1,2,1))].">
      <j1 rule="para" parents="4 1427"/>
    </justification>
  </clause>

  <clause id="2082">
    <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,362,a,b,2081,a),flip(a)].">
      <j1 rule="hyper" parents="33 362 2081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2083">
    <literal><![CDATA[
      (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = y * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,449,a(flip),b,1495,a),flip(a)].">
      <j1 rule="hyper" parents="320 449 1495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2084">
    <literal><![CDATA[
      T(x,x * (y * T(y \ 1,x))) = x
    ]]></literal>
    <justification jstring="[para(2083(a,1),276(a,1,2))].">
      <j1 rule="para" parents="2083 276"/>
    </justification>
  </clause>

  <clause id="2085">
    <literal><![CDATA[
      x \ ((L(y \ 1,y,x) * x) / L(y \ 1,y,x)) = (x * (y * T(y \ 1,x))) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(2083(a,1),1294(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2083 1294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2086">
    <literal><![CDATA[
      ((L(x \ 1,x,y) * y) / L(x \ 1,x,y)) / y = (1 / y) * (y * (x * T(x \ 1,y)))
    ]]></literal>
    <justification jstring="[para(2083(a,1),1462(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2083 1462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2087">
    <literal><![CDATA[
      T(x,x * K(y,x)) = x
    ]]></literal>
    <justification jstring="[para(1015(a,2),2084(a,1,2,2))].">
      <j1 rule="para" parents="1015 2084"/>
    </justification>
  </clause>

  <clause id="2088">
    <literal><![CDATA[
      T(x,x * (y \ (z * T(z \ y,x)))) = x
    ]]></literal>
    <justification jstring="[para(1417(a,1),2084(a,1,2,2))].">
      <j1 rule="para" parents="1417 2084"/>
    </justification>
  </clause>

  <clause id="2089">
    <literal><![CDATA[
      T(x * K(y,x),x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(49,a,2087,a)].">
      <j1 rule="hyper" parents="49 2087"/>
    </justification>
  </clause>

  <clause id="2090">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ ((y \ x) * ((y \ x) \ x)))) = x
    ]]></literal>
    <justification jstring="[para(1159(a,1),2088(a,1,2,2,2,2))].">
      <j1 rule="para" parents="1159 2088"/>
    </justification>
  </clause>

  <clause id="2091">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ x)) = x
    ]]></literal>
    <justification jstring="[para(5(a,1),2090(a,1,2,2,2))].">
      <j1 rule="para" parents="5 2090"/>
    </justification>
  </clause>

  <clause id="2092">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,z) \ x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2091(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2091 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2093">
    <literal><![CDATA[
      (x * (T(x,y) \ x)) \ (x * x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1104,a(flip),b,2092,a)].">
      <j1 rule="hyper" parents="58 1104 2092"/>
    </justification>
  </clause>

  <clause id="2094">
    <literal><![CDATA[
      (x * x) / T(x,y) = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(197,a,2093,a)].">
      <j1 rule="hyper" parents="197 2093"/>
    </justification>
  </clause>

  <clause id="2095">
    <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(1664(a,1),2093(a,1,1,2,1))].">
      <j1 rule="para" parents="1664 2093"/>
    </justification>
  </clause>

  <clause id="2096">
    <literal><![CDATA[
      T(x / T(x,y),x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(1487,a,2094,a)].">
      <j1 rule="hyper" parents="1487 2094"/>
    </justification>
  </clause>

  <clause id="2097">
    <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(2094(a,2),717(a,1,2))].">
      <j1 rule="para" parents="2094 717"/>
    </justification>
  </clause>

  <clause id="2098">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(2096(a,1),453(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2096 453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2099">
    <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(1054(a,2),1911(a,1))].">
      <j1 rule="para" parents="1054 1911"/>
    </justification>
  </clause>

  <clause id="2100">
    <literal><![CDATA[
      (x * (((T(y,x) \ y) * x) \ x)) \ (x * x) = (T(y,x) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,1664,a(flip),b,2095,a),flip(a)].">
      <j1 rule="hyper" parents="320 1664 2095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2101">
    <literal><![CDATA[
      L(x,y,T(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z \ u) \ u) = w
    ]]></literal>
    <justification jstring="[para(664(a,1),829(a,1))].">
      <j1 rule="para" parents="664 829"/>
    </justification>
  </clause>

  <clause id="2102">
    <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),910(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="105 910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2103">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ 1,z,u) = T(x * R(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(239,a,1514,a(flip),b,2102,a),flip(a)].">
      <j1 rule="hyper" parents="239 1514 2102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2104">
    <literal><![CDATA[
      T(x * R(x \ 1,T(x,y),z),y) = (z / (T(x,y) * z)) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(652,a,2103,a),flip(a)].">
      <j1 rule="hyper" parents="652 2103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2105">
    <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(985(a,1),2104(a,2,1,2))].">
      <j1 rule="para" parents="985 2104"/>
    </justification>
  </clause>

  <clause id="2106">
    <literal><![CDATA[
      ((x \ 1) / (x \ T(x,y))) * T(x,y) = T(x * T(x \ 1,T(x,y)),y)
    ]]></literal>
    <justification jstring="[para(1257(a,1),2105(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1257 2105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2107">
    <literal><![CDATA[
      (x \ 1) / (x \ T(x,y)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(30,a,1527,a(flip),b,2106,a),flip(a)].">
      <j1 rule="hyper" parents="30 1527 2106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2108">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,y)) = (x \ T(x,y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(2107(a,1),107(a,1,1))].">
      <j1 rule="para" parents="2107 107"/>
    </justification>
  </clause>

  <clause id="2109">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,1570,a(flip),b,2108,a),flip(a)].">
      <j1 rule="hyper" parents="58 1570 2108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2111">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ (T(x,y) \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(2109(a,1),2073(a,1,2,2))].">
      <j1 rule="para" parents="2109 2073"/>
    </justification>
  </clause>

  <clause id="2112">
    <literal><![CDATA[
      (x \ 1) \ (T(x,y) \ 1) = (x \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,2111,a),flip(a)].">
      <j1 rule="hyper" parents="123 2111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2113">
    <literal><![CDATA[
      ((x * ((y \ z) / z)) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),1091(a,1,1,1,2,2))].">
      <j1 rule="para" parents="5 1091"/>
    </justification>
  </clause>

  <clause id="2114">
    <literal><![CDATA[
      (((x * ((y \ z) / z)) / x) * z) / (y \ z) = ((x * (1 / y)) / x) * y
    ]]></literal>
    <justification jstring="[hyper(537,a,2113,a)].">
      <j1 rule="hyper" parents="537 2113"/>
    </justification>
  </clause>

  <clause id="2115">
    <literal><![CDATA[
      (((x * ((y \ z) / z)) / x) * z) / (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      ((x * (1 / y)) / x) * y = u
    ]]></literal>
    <justification jstring="[para(2113(a,2),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2113 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2116">
    <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(320,a,1868,a,b,2114,a),flip(a)].">
      <j1 rule="hyper" parents="320 1868 2114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2117">
    <literal><![CDATA[
      T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),1312(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2118">
    <literal><![CDATA[
      ((x * y) / x) / ((y \ 1) \ 1) = (y \ 1) * ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(360(a,1),1531(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="360 1531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2119">
    <literal><![CDATA[
      (T(x,y) \ 1) * ((y * T(x,y)) / y) = x / ((T(x,y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(225(a,1),2118(a,1,1)),flip(a)].">
      <j1 rule="para" parents="225 2118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2120">
    <literal><![CDATA[
      x / ((T(x,y) \ 1) \ 1) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(225(a,1),2119(a,1,2)),flip(a)].">
      <j1 rule="para" parents="225 2119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2121">
    <literal><![CDATA[
      (T(x,y) \ 1) \ ((T(x,y) \ x) / x) = K(x,((T(x,y) \ 1) * x) / x)
    ]]></literal>
    <justification jstring="[para(2120(a,1),1725(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2120 1725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2122">
    <literal><![CDATA[
      (T(x,y) \ 1) \ ((T(x,y) \ x) / x) = K(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(6(a,1),2121(a,2,2))].">
      <j1 rule="para" parents="6 2121"/>
    </justification>
  </clause>

  <clause id="2123">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x,T(x,y) \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(134,a,2122,a)].">
      <j1 rule="hyper" parents="134 2122"/>
    </justification>
  </clause>

  <clause id="2125">
    <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(239,a,1708,a,b,1607,a(flip))].">
      <j1 rule="hyper" parents="239 1708 1607"/>
    </justification>
  </clause>

  <clause id="2126">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ y,z,u) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(239,a,1707,a(flip),b,1607,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="239 1707 1607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2127">
    <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),2126(a,2,1,2,1))].">
      <j1 rule="para" parents="4 2126"/>
    </justification>
  </clause>

  <clause id="2128">
    <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(225(a,1),2125(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="225 2125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2129">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[para(200(a,1),2128(a,1,2,1,2))].">
      <j1 rule="para" parents="200 2128"/>
    </justification>
  </clause>

  <clause id="2130">
    <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(2128(a,2),766(a,1))].">
      <j1 rule="para" parents="2128 766"/>
    </justification>
  </clause>

  <clause id="2131">
    <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,2129,a)].">
      <j1 rule="hyper" parents="123 2129"/>
    </justification>
  </clause>

  <clause id="2132">
    <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,395,a(flip),b,2129,a),flip(a)].">
      <j1 rule="hyper" parents="58 395 2129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2133">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,x,1 / x) = T(x * T(1 / x,1),y)
    ]]></literal>
    <justification jstring="[para(748(a,1),2129(a,2,1,2))].">
      <j1 rule="para" parents="748 2129"/>
    </justification>
  </clause>

  <clause id="2134">
    <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(390(a,1),2131(a,1,2,1,2))].">
      <j1 rule="para" parents="390 2131"/>
    </justification>
  </clause>

  <clause id="2135">
    <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(1000(a,1),2132(a,2,2,1))].">
      <j1 rule="para" parents="1000 2132"/>
    </justification>
  </clause>

  <clause id="2136">
    <literal><![CDATA[
      T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * T(1 / x,1),y)
    ]]></literal>
    <justification jstring="[para(1118(a,1),2133(a,1,2))].">
      <j1 rule="para" parents="1118 2133"/>
    </justification>
  </clause>

  <clause id="2137">
    <literal><![CDATA[
      T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(198(a,1),2136(a,2,1,2))].">
      <j1 rule="para" parents="198 2136"/>
    </justification>
  </clause>

  <clause id="2138">
    <literal><![CDATA[
      (1 / x) * (T(x,y) \ x) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(29,a,2005,a,b,2137,a),flip(a)].">
      <j1 rule="hyper" parents="29 2005 2137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2139">
    <literal><![CDATA[
      (T(x,y) \ x) \ ((T(x,y) \ x) / x) = T(1 / x,T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(440,a,xx,b,2138,a),flip(a)].">
      <j1 rule="hyper" parents="440 2138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2140">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) = (1 / x) * ((T(x,y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(2138(a,1),1120(a,1,1))].">
      <j1 rule="para" parents="2138 1120"/>
    </justification>
  </clause>

  <clause id="2141">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(1119,a,2140,a),flip(a)].">
      <j1 rule="hyper" parents="1119 2140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2142">
    <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(2139(a,1),1014(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2139 1014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2143">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = T(K(T(x,y),1 / x),y)
    ]]></literal>
    <justification jstring="[para(2079(a,1),2135(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2079 2135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2144">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = K(T(x,y),T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,2010,a,b,2143,a),flip(a)].">
      <j1 rule="hyper" parents="320 2010 2143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2145">
    <literal><![CDATA[
      (T(x,y) / x) \ (1 / x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,1783,a(flip),b,2144,a),flip(a)].">
      <j1 rule="hyper" parents="29 1783 2144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2146">
    <literal><![CDATA[
      (T(x,y) / x) * (1 / T(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(134,a,2145,a)].">
      <j1 rule="hyper" parents="134 2145"/>
    </justification>
  </clause>

  <clause id="2147">
    <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(265(a,1),2145(a,1,2))].">
      <j1 rule="para" parents="265 2145"/>
    </justification>
  </clause>

  <clause id="2148">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = 1 / T(T(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1342(a,1),2147(a,1,1))].">
      <j1 rule="para" parents="1342 2147"/>
    </justification>
  </clause>

  <clause id="2149">
    <literal><![CDATA[
      1 / T(T(x,x \ 1),y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2109,a(flip),b,2148,a),flip(a)].">
      <j1 rule="hyper" parents="58 2109 2148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2150">
    <literal><![CDATA[
      T(T(x,x \ 1),y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(188,a,2149,a),flip(a)].">
      <j1 rule="hyper" parents="188 2149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2151">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ 1 = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(357(a,1),2149(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="357 2149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2152">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,663,a(flip),b,2150,a)].">
      <j1 rule="hyper" parents="58 663 2150"/>
    </justification>
  </clause>

  <clause id="2153">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) \ 1 = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(642(a,1),2150(a,1,1)),flip(a)].">
      <j1 rule="para" parents="642 2150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2154">
    <literal><![CDATA[
      1 / (1 / T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(197,a,2151,a)].">
      <j1 rule="hyper" parents="197 2151"/>
    </justification>
  </clause>

  <clause id="2155">
    <literal><![CDATA[
      x * ((T(y,x) \ 1) \ 1) = ((y \ 1) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,2152,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2152 17"/>
    </justification>
  </clause>

  <clause id="2156">
    <literal><![CDATA[
      T(((x / y) \ 1) \ 1,y) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(107(a,1),2152(a,2,1,1))].">
      <j1 rule="para" parents="107 2152"/>
    </justification>
  </clause>

  <clause id="2157">
    <literal><![CDATA[
      T(x,y) * K(T(x,y) \ 1,T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(1803,a,2154,a)].">
      <j1 rule="hyper" parents="1803 2154"/>
    </justification>
  </clause>

  <clause id="2158">
    <literal><![CDATA[
      T(1 / (1 / (x / y)),y) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[para(107(a,1),2154(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 2154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2159">
    <literal><![CDATA[
      ((x * T(1 / (1 / y),x)) / x) \ (y / T(y,x)) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[para(2154(a,1),1699(a,1,1,1,2))].">
      <j1 rule="para" parents="2154 1699"/>
    </justification>
  </clause>

  <clause id="2160">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(737,a,2155,a)].">
      <j1 rule="hyper" parents="737 2155"/>
    </justification>
  </clause>

  <clause id="2161">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) * y = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,1),2155(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="107 2155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2162">
    <literal><![CDATA[
      ((R(x / y,y,z) \ 1) \ 1) * (y * z) = (y * z) * ((((y * z) \ (x * z)) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(528(a,1),2155(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="528 2155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2163">
    <literal><![CDATA[
      (T(x,y) \ 1) \ (T(x,y) \ x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(1121,a,2160,a)].">
      <j1 rule="hyper" parents="1121 2160"/>
    </justification>
  </clause>

  <clause id="2164">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = x * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,1822,a,b,2160,a),flip(a)].">
      <j1 rule="hyper" parents="320 1822 2160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2165">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,106,a,b,2160,a),flip(a)].">
      <j1 rule="hyper" parents="320 106 2160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2166">
    <literal><![CDATA[
      T(K(x,x \ 1),y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2008,a,2164,a)].">
      <j1 rule="hyper" parents="2008 2164"/>
    </justification>
  </clause>

  <clause id="2167">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(2011,a,2166,a),flip(a)].">
      <j1 rule="hyper" parents="2011 2166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2168">
    <literal><![CDATA[
      T(x,K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,2166,a)].">
      <j1 rule="hyper" parents="49 2166"/>
    </justification>
  </clause>

  <clause id="2169">
    <literal><![CDATA[
      K(x,x \ 1) * y = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,2166,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 2166 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2170">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,2166,a(flip),b,2006,a)].">
      <j1 rule="hyper" parents="116 2166 2006"/>
    </justification>
  </clause>

  <clause id="2171">
    <literal><![CDATA[
      x * K(y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,y \ 1) * x = z
    ]]></literal>
    <justification jstring="[para(2166(a,1),284(a,1,2))].">
      <j1 rule="para" parents="2166 284"/>
    </justification>
  </clause>

  <clause id="2172">
    <literal><![CDATA[
      x \ y != z * K(u,u \ 1)
    ]]></literal>
    <literal><![CDATA[
      x * (K(u,u \ 1) * z) = y
    ]]></literal>
    <justification jstring="[para(2166(a,1),579(a,2,2))].">
      <j1 rule="para" parents="2166 579"/>
    </justification>
  </clause>

  <clause id="2174">
    <literal><![CDATA[
      T(x,K(y,y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(2168(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2168 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2175">
    <literal><![CDATA[
      T(x,K(1 / y,y)) = x
    ]]></literal>
    <justification jstring="[para(75(a,1),2168(a,1,2,2))].">
      <j1 rule="para" parents="75 2168"/>
    </justification>
  </clause>

  <clause id="2176">
    <literal><![CDATA[
      K(x,x \ 1) * y != z * K(x,x \ 1)
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(2168(a,1),241(a,1,2))].">
      <j1 rule="para" parents="2168 241"/>
    </justification>
  </clause>

  <clause id="2177">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2168(a,1),284(a,1,2))].">
      <j1 rule="para" parents="2168 284"/>
    </justification>
  </clause>

  <clause id="2178">
    <literal><![CDATA[
      T(x,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(1787(a,1),2168(a,1,2))].">
      <j1 rule="para" parents="1787 2168"/>
    </justification>
  </clause>

  <clause id="2179">
    <literal><![CDATA[
      T(K(x \ 1,x),y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(49,a,2178,a)].">
      <j1 rule="hyper" parents="49 2178"/>
    </justification>
  </clause>

  <clause id="2180">
    <literal><![CDATA[
      K(x \ 1,x) * y = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2178,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2178 17"/>
    </justification>
  </clause>

  <clause id="2181">
    <literal><![CDATA[
      (x * K(y \ 1,y)) / x = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2178(a,1),187(a,1,2))].">
      <j1 rule="para" parents="2178 187"/>
    </justification>
  </clause>

  <clause id="2182">
    <literal><![CDATA[
      T(x,(y \ 1) * y) = x
    ]]></literal>
    <justification jstring="[para(258(a,1),2178(a,1,2))].">
      <j1 rule="para" parents="258 2178"/>
    </justification>
  </clause>

  <clause id="2183">
    <literal><![CDATA[
      K(x \ 1,x) * y != z * K(x \ 1,x)
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(2178(a,1),241(a,1,2))].">
      <j1 rule="para" parents="2178 241"/>
    </justification>
  </clause>

  <clause id="2184">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(2178(a,1),284(a,1,2))].">
      <j1 rule="para" parents="2178 284"/>
    </justification>
  </clause>

  <clause id="2185">
    <literal><![CDATA[
      R(x,y,z) * K(u \ 1,u) = K(u \ 1,u) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2178(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2178 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2186">
    <literal><![CDATA[
      K(x \ 1,x) \ ((y * (x \ 1)) * x) = R(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2178(a,1),1060(a,2,1))].">
      <j1 rule="para" parents="2178 1060"/>
    </justification>
  </clause>

  <clause id="2187">
    <literal><![CDATA[
      ((x \ 1) * x) * y = y * ((x \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2182,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2182 17"/>
    </justification>
  </clause>

  <clause id="2188">
    <literal><![CDATA[
      K(x \ (x / T(x,y)),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1521,a,b,2179,a)].">
      <j1 rule="hyper" parents="58 1521 2179"/>
    </justification>
  </clause>

  <clause id="2189">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,y) * x = z
    ]]></literal>
    <justification jstring="[para(2179(a,1),284(a,1,2))].">
      <j1 rule="para" parents="2179 284"/>
    </justification>
  </clause>

  <clause id="2190">
    <literal><![CDATA[
      K(x \ 1,x) / T(x,y) = T(1 / T(x,y),x)
    ]]></literal>
    <justification jstring="[para(2179(a,1),1524(a,1,1))].">
      <j1 rule="para" parents="2179 1524"/>
    </justification>
  </clause>

  <clause id="2191">
    <literal><![CDATA[
      K(x,x \ 1) * L(x,y,z) = x * (L(x,y,z) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(320,a,1792,a(flip),b,2169,a),flip(a)].">
      <j1 rule="hyper" parents="320 1792 2169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2192">
    <literal><![CDATA[
      K(x,x \ 1) * (1 / (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,1790,a(flip),b,2169,a),flip(a)].">
      <j1 rule="hyper" parents="320 1790 2169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2193">
    <literal><![CDATA[
      (K(x,x \ 1) * y) / z = (y * K(x,x \ 1)) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,2169,a,b,7,a)].">
      <j1 rule="hyper" parents="117 2169 7"/>
    </justification>
  </clause>

  <clause id="2194">
    <literal><![CDATA[
      K(x,x \ 1) \ x = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,1790,a(flip),b,2169,a)].">
      <j1 rule="hyper" parents="116 1790 2169"/>
    </justification>
  </clause>

  <clause id="2195">
    <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(2169(a,2),505(a,1,2))].">
      <j1 rule="para" parents="2169 505"/>
    </justification>
  </clause>

  <clause id="2196">
    <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(2169(a,2),630(a,1,1))].">
      <j1 rule="para" parents="2169 630"/>
    </justification>
  </clause>

  <clause id="2197">
    <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(2169(a,1),769(a,1,2))].">
      <j1 rule="para" parents="2169 769"/>
    </justification>
  </clause>

  <clause id="2198">
    <literal><![CDATA[
      K(x,1 / x) * (1 / (1 / x)) = x
    ]]></literal>
    <justification jstring="[para(1780(a,2),2192(a,1,1))].">
      <j1 rule="para" parents="1780 2192"/>
    </justification>
  </clause>

  <clause id="2199">
    <literal><![CDATA[
      L(x,1 / x,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(627,a,2198,a)].">
      <j1 rule="hyper" parents="627 2198"/>
    </justification>
  </clause>

  <clause id="2200">
    <literal><![CDATA[
      L(T(x,y),1 / x,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(2199(a,1),20(a,2,1))].">
      <j1 rule="para" parents="2199 20"/>
    </justification>
  </clause>

  <clause id="2201">
    <literal><![CDATA[
      L(1 / x,y,z) * K(x \ 1,x) = (x \ 1) * (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(1831,a,2180,a),flip(a)].">
      <j1 rule="hyper" parents="1831 2180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2202">
    <literal><![CDATA[
      K(x \ 1,x) * (y / x) = y * T(y \ (y / x),x)
    ]]></literal>
    <justification jstring="[hyper(320,a,1014,a(flip),b,2180,a),flip(a)].">
      <j1 rule="hyper" parents="320 1014 2180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2203">
    <literal><![CDATA[
      x * (K(y \ 1,y) * z) = x * (z * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,2180,a,b,4,a)].">
      <j1 rule="hyper" parents="119 2180 4"/>
    </justification>
  </clause>

  <clause id="2204">
    <literal><![CDATA[
      R(K(x \ 1,x),y,z) * (y * z) = (y * K(x \ 1,x)) * z
    ]]></literal>
    <justification jstring="[para(2180(a,1),101(a,2,1))].">
      <j1 rule="para" parents="2180 101"/>
    </justification>
  </clause>

  <clause id="2205">
    <literal><![CDATA[
      L(x \ (K(y \ 1,y) \ z),x,K(y \ 1,y)) = (x * K(y \ 1,y)) \ z
    ]]></literal>
    <justification jstring="[para(2180(a,1),298(a,2,1))].">
      <j1 rule="para" parents="2180 298"/>
    </justification>
  </clause>

  <clause id="2206">
    <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(2180(a,2),505(a,1,2))].">
      <j1 rule="para" parents="2180 505"/>
    </justification>
  </clause>

  <clause id="2207">
    <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(2180(a,2),630(a,1,1))].">
      <j1 rule="para" parents="2180 630"/>
    </justification>
  </clause>

  <clause id="2208">
    <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(2180(a,1),769(a,1,2))].">
      <j1 rule="para" parents="2180 769"/>
    </justification>
  </clause>

  <clause id="2209">
    <literal><![CDATA[
      T(K(x \ 1,x),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(2181(a,1),292(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2181 292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2210">
    <literal><![CDATA[
      ((x * y) / x) \ K(y \ 1,y) = T(((x * y) / x) \ 1,y)
    ]]></literal>
    <justification jstring="[para(2181(a,1),1593(a,1,2))].">
      <j1 rule="para" parents="2181 1593"/>
    </justification>
  </clause>

  <clause id="2211">
    <literal><![CDATA[
      a(x \ 1,x,x \ 1) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(789,a,2187,a)].">
      <j1 rule="hyper" parents="789 2187"/>
    </justification>
  </clause>

  <clause id="2213">
    <literal><![CDATA[
      x * K(x \ (x / T(x,y)),x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2188,a,b,1778,a)].">
      <j1 rule="hyper" parents="119 2188 1778"/>
    </justification>
  </clause>

  <clause id="2214">
    <literal><![CDATA[
      K(x,1 / x) * T(1 / (1 / x),y) = x * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2200,a(flip),b,1051,a)].">
      <j1 rule="hyper" parents="119 2200 1051"/>
    </justification>
  </clause>

  <clause id="2215">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = ((y \ (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(788,a,2156,a)].">
      <j1 rule="hyper" parents="788 2156"/>
    </justification>
  </clause>

  <clause id="2216">
    <literal><![CDATA[
      (x * (((x \ y) \ 1) \ 1)) / x = ((y / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(271,a,2156,a)].">
      <j1 rule="hyper" parents="271 2156"/>
    </justification>
  </clause>

  <clause id="2217">
    <literal><![CDATA[
      T(T(x / y,y / x),y) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2057(a,2),2156(a,1,1))].">
      <j1 rule="para" parents="2057 2156"/>
    </justification>
  </clause>

  <clause id="2218">
    <literal><![CDATA[
      (x * (1 / (1 / (x \ y)))) / x = 1 / (1 / (y / x))
    ]]></literal>
    <justification jstring="[hyper(271,a,2158,a)].">
      <j1 rule="hyper" parents="271 2158"/>
    </justification>
  </clause>

  <clause id="2219">
    <literal><![CDATA[
      (T(x,y) \ 1) * ((x \ 1) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(134,a,2163,a)].">
      <j1 rule="hyper" parents="134 2163"/>
    </justification>
  </clause>

  <clause id="2222">
    <literal><![CDATA[
      T(x,y) \ (1 / (1 / x)) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(116,a,2213,a(flip),b,1138,a)].">
      <j1 rule="hyper" parents="116 2213 1138"/>
    </justification>
  </clause>

  <clause id="2223">
    <literal><![CDATA[
      T(x \ y,x / y) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(678,a,2217,a)].">
      <j1 rule="hyper" parents="678 2217"/>
    </justification>
  </clause>

  <clause id="2224">
    <literal><![CDATA[
      T((x * y) \ y,x) = (((x * y) \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(6(a,1),2223(a,1,2))].">
      <j1 rule="para" parents="6 2223"/>
    </justification>
  </clause>

  <clause id="2225">
    <literal><![CDATA[
      T(x \ (y \ x),y) = ((x \ (y \ x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(72(a,1),2223(a,1,2))].">
      <j1 rule="para" parents="72 2223"/>
    </justification>
  </clause>

  <clause id="2226">
    <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(732(a,2),2184(a,1))].">
      <j1 rule="para" parents="732 2184"/>
    </justification>
  </clause>

  <clause id="2227">
    <literal><![CDATA[
      x * T(x \ (x / y),y) != z
    ]]></literal>
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2202(a,1),2184(a,1))].">
      <j1 rule="para" parents="2202 2184"/>
    </justification>
  </clause>

  <clause id="2228">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),2215(a,2,1,1))].">
      <j1 rule="para" parents="4 2215"/>
    </justification>
  </clause>

  <clause id="2229">
    <literal><![CDATA[
      T(x,y / (y * x)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2065,a(flip),b,2228,a)].">
      <j1 rule="hyper" parents="58 2065 2228"/>
    </justification>
  </clause>

  <clause id="2231">
    <literal><![CDATA[
      T(x,y / (y * x)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,106,a,b,2229,a),flip(a)].">
      <j1 rule="hyper" parents="320 106 2229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2232">
    <literal><![CDATA[
      T(1 / (1 / x),y / (y * x)) = x
    ]]></literal>
    <justification jstring="[hyper(1774,a,2231,a(flip))].">
      <j1 rule="hyper" parents="1774 2231"/>
    </justification>
  </clause>

  <clause id="2233">
    <literal><![CDATA[
      T(1 / (1 / x),(y / x) / y) = x
    ]]></literal>
    <justification jstring="[para(7(a,1),2232(a,1,2,2))].">
      <j1 rule="para" parents="7 2232"/>
    </justification>
  </clause>

  <clause id="2234">
    <literal><![CDATA[
      (1 / (1 / x)) \ (((y / x) / y) * x) = (y / x) / y
    ]]></literal>
    <justification jstring="[para(2233(a,1),226(a,1,2,2))].">
      <j1 rule="para" parents="2233 226"/>
    </justification>
  </clause>

  <clause id="2235">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) / x = (((x * y) / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),2216(a,1,1,2,1,1))].">
      <j1 rule="para" parents="4 2216"/>
    </justification>
  </clause>

  <clause id="2236">
    <literal><![CDATA[
      (x * (1 / (1 / y))) / x = 1 / (1 / ((x * y) / x))
    ]]></literal>
    <justification jstring="[para(4(a,1),2218(a,1,1,2,2,2))].">
      <j1 rule="para" parents="4 2218"/>
    </justification>
  </clause>

  <clause id="2237">
    <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(2018(a,2),2234(a,1,2))].">
      <j1 rule="para" parents="2018 2234"/>
    </justification>
  </clause>

  <clause id="2238">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ L(x,y,z)) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1851,a,2191,a)].">
      <j1 rule="hyper" parents="1851 2191"/>
    </justification>
  </clause>

  <clause id="2239">
    <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(2210(a,2),1229(a,1,1,2))].">
      <j1 rule="para" parents="2210 1229"/>
    </justification>
  </clause>

  <clause id="2241">
    <literal><![CDATA[
      K(x,x \ 1) * T(1 / (1 / x),y) = x * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(1780(a,1),2214(a,1,1))].">
      <j1 rule="para" parents="1780 2214"/>
    </justification>
  </clause>

  <clause id="2242">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K(x,x \ 1) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(2177,a,2238,a)].">
      <j1 rule="hyper" parents="2177 2238"/>
    </justification>
  </clause>

  <clause id="2243">
    <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(320,a,1275,a(flip),b,2238,a),flip(a)].">
      <j1 rule="hyper" parents="320 1275 2238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2244">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ x,y) = x * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(2194(a,2),2241(a,1,2,1))].">
      <j1 rule="para" parents="2194 2241"/>
    </justification>
  </clause>

  <clause id="2245">
    <literal><![CDATA[
      (1 / (1 / x)) \ (x / T(x,y)) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(225(a,1),2159(a,1,1))].">
      <j1 rule="para" parents="225 2159"/>
    </justification>
  </clause>

  <clause id="2247">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * (K(x,x \ 1) \ 1) = T(x * (K(x,x \ 1) \ 1),y)
    ]]></literal>
    <justification jstring="[para(2244(a,1),1031(a,1,1))].">
      <j1 rule="para" parents="2244 1031"/>
    </justification>
  </clause>

  <clause id="2248">
    <literal><![CDATA[
      ((x \ 1) * (x * L(x \ 1,x,y))) * x = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2201(a,1),1600(a,1,1))].">
      <j1 rule="para" parents="2201 1600"/>
    </justification>
  </clause>

  <clause id="2249">
    <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(320,a,361,a(flip),b,2205,a),flip(a)].">
      <j1 rule="hyper" parents="320 361 2205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2250">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * (K(x,x \ 1) \ 1),y)
    ]]></literal>
    <justification jstring="[para(1817(a,1),2247(a,1,2))].">
      <j1 rule="para" parents="1817 2247"/>
    </justification>
  </clause>

  <clause id="2251">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * K(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(1817(a,1),2250(a,2,1,2))].">
      <j1 rule="para" parents="1817 2250"/>
    </justification>
  </clause>

  <clause id="2252">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1779(a,1),2251(a,2,1))].">
      <j1 rule="para" parents="1779 2251"/>
    </justification>
  </clause>

  <clause id="2253">
    <literal><![CDATA[
      (x / y) * (y * L(y \ z,u,w)) = x * L(x \ ((x / y) * z),u,w)
    ]]></literal>
    <justification jstring="[para(75(a,1),1686(a,1,2,2,1,1))].">
      <j1 rule="para" parents="75 1686"/>
    </justification>
  </clause>

  <clause id="2254">
    <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),2253(a,2,2,1,2))].">
      <j1 rule="para" parents="5 2253"/>
    </justification>
  </clause>

  <clause id="2255">
    <literal><![CDATA[
      K(x,(y * x) \ y) * x = T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1828(a,1,1,1))].">
      <j1 rule="para" parents="4 1828"/>
    </justification>
  </clause>

  <clause id="2256">
    <literal><![CDATA[
      T(K(x,(y * x) \ y),x) = x \ T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(440,a,xx,b,2255,a)].">
      <j1 rule="hyper" parents="440 2255"/>
    </justification>
  </clause>

  <clause id="2258">
    <literal><![CDATA[
      L(T(K(x,(y * x) \ y),x),x,y) = K(((y * x) \ y) \ 1,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(2256(a,2),2082(a,1,1))].">
      <j1 rule="para" parents="2256 2082"/>
    </justification>
  </clause>

  <clause id="2259">
    <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(641(a,1),1861(a,2,2,1))].">
      <j1 rule="para" parents="641 1861"/>
    </justification>
  </clause>

  <clause id="2260">
    <literal><![CDATA[
      (((x * y) / x) / y) * (1 / y) = (1 / y) * (((x * y) / x) / y)
    ]]></literal>
    <justification jstring="[para(1461(a,1),1895(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1461 1895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2261">
    <literal><![CDATA[
      ((1 / x) * (((y * x) / y) / x)) / (1 / x) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,2260,a)].">
      <j1 rule="hyper" parents="131 2260"/>
    </justification>
  </clause>

  <clause id="2262">
    <literal><![CDATA[
      R(((x * y) / x) / y,y,x) = ((1 / y) * ((x * y) / (y * x))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(2261(a,1),884(a,1,1))].">
      <j1 rule="para" parents="2261 884"/>
    </justification>
  </clause>

  <clause id="2263">
    <literal><![CDATA[
      ((1 / x) * ((y * x) / (x * y))) / (1 / x) = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(621,a,2262,a),flip(a)].">
      <j1 rule="hyper" parents="621 2262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2264">
    <literal><![CDATA[
      T((x * y) / (y * x),y * x) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(2263(a,1),679(a,1,1))].">
      <j1 rule="para" parents="2263 679"/>
    </justification>
  </clause>

  <clause id="2265">
    <literal><![CDATA[
      ((1 / x) * ((x * y) \ (y * x))) / (1 / x) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(421,a,2264,a),flip(a)].">
      <j1 rule="hyper" parents="421 2264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2266">
    <literal><![CDATA[
      K(x,y) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,11,a,b,2265,a)].">
      <j1 rule="hyper" parents="320 11 2265"/>
    </justification>
  </clause>

  <clause id="2267">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) / (1 / x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(11(a,2),2266(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 2266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2268">
    <literal><![CDATA[
      T(1 / x,K(y,x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(266,a,2267,a)].">
      <j1 rule="hyper" parents="266 2267"/>
    </justification>
  </clause>

  <clause id="2269">
    <literal><![CDATA[
      K(x,y) * (1 / y) = (1 / y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,2267,a)].">
      <j1 rule="hyper" parents="133 2267"/>
    </justification>
  </clause>

  <clause id="2270">
    <literal><![CDATA[
      K(1 / x,K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,2268,a)].">
      <j1 rule="hyper" parents="50 2268"/>
    </justification>
  </clause>

  <clause id="2271">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = T(1 / x,x)
    ]]></literal>
    <justification jstring="[para(2268(a,1),246(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2268 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2272">
    <literal><![CDATA[
      K(x,K(y,x \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(72(a,1),2270(a,1,1))].">
      <j1 rule="para" parents="72 2270"/>
    </justification>
  </clause>

  <clause id="2273">
    <literal><![CDATA[
      K(x,y \ 1) * y = y * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(538,a,2272,a)].">
      <j1 rule="hyper" parents="538 2272"/>
    </justification>
  </clause>

  <clause id="2274">
    <literal><![CDATA[
      T(x,K(y,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,2272,a)].">
      <j1 rule="hyper" parents="51 2272"/>
    </justification>
  </clause>

  <clause id="2275">
    <literal><![CDATA[
      L(x,y,z) * K(u,x \ 1) = K(u,x \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2274(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2274 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2276">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,107,a(flip),b,2271,a),flip(a)].">
      <j1 rule="hyper" parents="320 107 2271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2277">
    <literal><![CDATA[
      T((x * y) \ x,K(z,y)) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(2276(a,1),400(a,2,1))].">
      <j1 rule="para" parents="2276 400"/>
    </justification>
  </clause>

  <clause id="2278">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = L((y \ x) \ 1,y \ x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),2277(a,1,1,1))].">
      <j1 rule="para" parents="5 2277"/>
    </justification>
  </clause>

  <clause id="2279">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,390,a(flip),b,2278,a),flip(a)].">
      <j1 rule="hyper" parents="320 390 2278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2280">
    <literal><![CDATA[
      K(x,y \ z) * (z \ y) = (z \ y) * K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,2279,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2279 17"/>
    </justification>
  </clause>

  <clause id="2281">
    <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(2275(a,2),39(a,1))].">
      <j1 rule="para" parents="2275 39"/>
    </justification>
  </clause>

  <clause id="2282">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * (x * z) = x * ((x * ((y * (x \ 1)) / y)) * z)
    ]]></literal>
    <justification jstring="[para(1710(a,1),1947(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1710 1947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2283">
    <literal><![CDATA[
      L(x \ R(x,y \ 1,y),x,K(y \ 1,y)) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2186(a,1),2249(a,1,1,2))].">
      <j1 rule="para" parents="2186 2249"/>
    </justification>
  </clause>

  <clause id="2284">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (((z * (u / x)) / z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(887,a,974,a),flip(a)].">
      <j1 rule="hyper" parents="887 974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2285">
    <literal><![CDATA[
      (((x * ((y / z) / u)) / x) * u) * z = (u * z) * ((x * ((u * z) \ y)) / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),2284(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 2284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2286">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (x * ((z * (x \ u)) / z)) * y
    ]]></literal>
    <justification jstring="[para(864(a,1),2284(a,2,1))].">
      <j1 rule="para" parents="864 2284"/>
    </justification>
  </clause>

  <clause id="2287">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(326,a,2285,a),flip(a)].">
      <j1 rule="hyper" parents="326 2285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2288">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) != u
    ]]></literal>
    <literal><![CDATA[
      (x * ((z / y) / x)) * y = u
    ]]></literal>
    <justification jstring="[para(2285(a,1),326(a,1))].">
      <j1 rule="para" parents="2285 326"/>
    </justification>
  </clause>

  <clause id="2289">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(1163,a,2287,a),flip(a)].">
      <j1 rule="hyper" parents="1163 2287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2290">
    <literal><![CDATA[
      x * (y * ((x * (y \ (x \ z))) / x)) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1332,a(flip),b,2287,a)].">
      <j1 rule="hyper" parents="58 1332 2287"/>
    </justification>
  </clause>

  <clause id="2291">
    <literal><![CDATA[
      T(x,x / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x * ((x / y) / x),y) = y \ z
    ]]></literal>
    <justification jstring="[para(2289(a,1),277(a,1))].">
      <j1 rule="para" parents="2289 277"/>
    </justification>
  </clause>

  <clause id="2292">
    <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(365(a,2),2290(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="365 2290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2293">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((z * ((x * (z \ 1)) / x)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(1710(a,1),2290(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1710 2290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2294">
    <literal><![CDATA[
      T(x,x / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = z
    ]]></literal>
    <justification jstring="[para(1156(a,1),2288(a,1))].">
      <j1 rule="para" parents="1156 2288"/>
    </justification>
  </clause>

  <clause id="2295">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (((x / y) * y) \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[hyper(326,a,2286,a),flip(a)].">
      <j1 rule="hyper" parents="326 2286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2296">
    <literal><![CDATA[
      (x \ (y * x)) * ((z * ((x \ (y * x)) \ x)) / z) = T(y * ((z * (y \ x)) / z),x)
    ]]></literal>
    <justification jstring="[hyper(239,a,2286,a(flip),b,1605,a),flip(a)].">
      <j1 rule="hyper" parents="239 2286 1605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2297">
    <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),2296(a,1,1))].">
      <j1 rule="para" parents="17 2296"/>
    </justification>
  </clause>

  <clause id="2298">
    <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),2297(a,1,2,1,2,1))].">
      <j1 rule="para" parents="17 2297"/>
    </justification>
  </clause>

  <clause id="2299">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,x,y) \ (x * ((y * x) \ y))) = K(x \ 1,x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(1413,a,1071,a)].">
      <j1 rule="hyper" parents="1413 1071"/>
    </justification>
  </clause>

  <clause id="2300">
    <literal><![CDATA[
      ((x * y) \ x) * K(y \ 1,y * ((x * y) \ x)) = (y \ 1) * (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(731,a,1071,a)].">
      <j1 rule="hyper" parents="731 1071"/>
    </justification>
  </clause>

  <clause id="2301">
    <literal><![CDATA[
      (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * ((1 / x) * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,449,a(flip),b,1496,a),flip(a)].">
      <j1 rule="hyper" parents="320 449 1496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2302">
    <literal><![CDATA[
      (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(1000(a,1),2301(a,2,2))].">
      <j1 rule="para" parents="1000 2301"/>
    </justification>
  </clause>

  <clause id="2303">
    <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(2302(a,1),1447(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2302 1447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2304">
    <literal><![CDATA[
      (x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * (y * T(y \ 1,u))) * z
    ]]></literal>
    <justification jstring="[para(733(a,1),1586(a,1,1)),flip(a)].">
      <j1 rule="para" parents="733 1586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2305">
    <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),2304(a,1,2))].">
      <j1 rule="para" parents="105 2304"/>
    </justification>
  </clause>

  <clause id="2306">
    <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(1387(a,1),2031(a,2,2))].">
      <j1 rule="para" parents="1387 2031"/>
    </justification>
  </clause>

  <clause id="2307">
    <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(1492(a,1),2097(a,1,1))].">
      <j1 rule="para" parents="1492 2097"/>
    </justification>
  </clause>

  <clause id="2308">
    <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(1137(a,1),2307(a,1,1))].">
      <j1 rule="para" parents="1137 2307"/>
    </justification>
  </clause>

  <clause id="2309">
    <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(2094(a,1),2308(a,1,2))].">
      <j1 rule="para" parents="2094 2308"/>
    </justification>
  </clause>

  <clause id="2310">
    <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,2309,a)].">
      <j1 rule="hyper" parents="58 20 2309"/>
    </justification>
  </clause>

  <clause id="2311">
    <literal><![CDATA[
      L(x,T(x,y) \ x,T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(2091(a,1),2310(a,1,1))].">
      <j1 rule="para" parents="2091 2310"/>
    </justification>
  </clause>

  <clause id="2312">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1137,a,b,2311,a)].">
      <j1 rule="hyper" parents="58 1137 2311"/>
    </justification>
  </clause>

  <clause id="2313">
    <literal><![CDATA[
      x * L(y,T(y,x) \ y,y) = (y * x) * T(K(x,y),y)
    ]]></literal>
    <justification jstring="[para(2311(a,1),1951(a,1,2))].">
      <j1 rule="para" parents="2311 1951"/>
    </justification>
  </clause>

  <clause id="2314">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2098,a(flip),b,2312,a),flip(a)].">
      <j1 rule="hyper" parents="58 2098 2312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2315">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = (x \ 1) * T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(729(a,1),2299(a,1,2)),flip(a)].">
      <j1 rule="para" parents="729 2299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2316">
    <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(320,a,259,a(flip),b,2306,a),flip(a)].">
      <j1 rule="hyper" parents="320 259 2306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2317">
    <literal><![CDATA[
      L(K(x \ 1,x) * y,x,1 / x) = K(x \ 1,x) * L(y,x,1 / x)
    ]]></literal>
    <justification jstring="[para(1815(a,1),2316(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1815 2316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2318">
    <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),2317(a,1,1)),flip(a)].">
      <j1 rule="para" parents="105 2317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2319">
    <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(258(a,2),1056(a,1,2,1,1))].">
      <j1 rule="para" parents="258 1056"/>
    </justification>
  </clause>

  <clause id="2320">
    <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),1572(a,1,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 1572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2321">
    <literal><![CDATA[
      (x * T(x \ y,x)) * (1 / x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(68(a,1),1585(a,1,1)),flip(a)].">
      <j1 rule="para" parents="68 1585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2322">
    <literal><![CDATA[
      ((x \ y) * x) * (1 / x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(569,a,2321,a)].">
      <j1 rule="hyper" parents="569 2321"/>
    </justification>
  </clause>

  <clause id="2324">
    <literal><![CDATA[
      T((x * y) * (1 / x),x) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2322(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2325">
    <literal><![CDATA[
      T(x * (1 / y),y) != z * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      (y \ x) * y = z
    ]]></literal>
    <justification jstring="[para(2322(a,1),39(a,1))].">
      <j1 rule="para" parents="2322 39"/>
    </justification>
  </clause>

  <clause id="2326">
    <literal><![CDATA[
      T((x * y) * (1 / x),x) != z * (1 / x)
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(2324(a,2),39(a,1))].">
      <j1 rule="para" parents="2324 39"/>
    </justification>
  </clause>

  <clause id="2327">
    <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(1783(a,2),1795(a,1,2,1,1))].">
      <j1 rule="para" parents="1783 1795"/>
    </justification>
  </clause>

  <clause id="2328">
    <literal><![CDATA[
      (x \ 1) * ((x \ L(x,y,z)) * ((x \ 1) \ u)) = (x \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[para(1185(a,1),1843(a,2,1))].">
      <j1 rule="para" parents="1185 1843"/>
    </justification>
  </clause>

  <clause id="2329">
    <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),2328(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 2328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2330">
    <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,2329,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 2329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2331">
    <literal><![CDATA[
      (x \ R(x,y,z)) * ((x \ 1) * u) = (x \ 1) * ((x \ R(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1199(a,1),2014(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1199 2014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2332">
    <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,2331,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 2331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2333">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) * (x \ 1) = x \ (x * (y * T(y \ 1,x)))
    ]]></literal>
    <justification jstring="[para(2083(a,1),2085(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2083 2085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2334">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) * (x \ 1) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4,a(flip),b,2333,a),flip(a)].">
      <j1 rule="hyper" parents="320 4 2333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2336">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = (y * (x \ T(x,y))) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(983(a,1),2334(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="983 2334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2337">
    <literal><![CDATA[
      ((x * y) \ x) * T(((x * y) \ x) \ 1,x) = (x * K(y,x)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1015(a,2),2334(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1015 2334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2338">
    <literal><![CDATA[
      (x * (y \ T(y,x))) * (x \ 1) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(989,a,2336,a),flip(a)].">
      <j1 rule="hyper" parents="989 2336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2339">
    <literal><![CDATA[
      (x * K(y,x)) * (x \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(1039,a,2337,a),flip(a)].">
      <j1 rule="hyper" parents="1039 2337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2340">
    <literal><![CDATA[
      (1 / x) * K(y,1 / x) = K(y,1 / x) / x
    ]]></literal>
    <justification jstring="[hyper(353,a,2339,a),flip(a)].">
      <j1 rule="hyper" parents="353 2339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2341">
    <literal><![CDATA[
      (1 / x) * (x * (y * T(y \ 1,x))) = (x * (y * T(y \ 1,x))) / x
    ]]></literal>
    <justification jstring="[para(2083(a,1),2086(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2083 2086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2342">
    <literal><![CDATA[
      L(x * T(x \ 1,y),y,1 / y) = (y * (x * T(x \ 1,y))) / y
    ]]></literal>
    <justification jstring="[hyper(486,a,2341,a)].">
      <j1 rule="hyper" parents="486 2341"/>
    </justification>
  </clause>

  <clause id="2343">
    <literal><![CDATA[
      (x * (((x * y) \ x) * T(((x * y) \ x) \ 1,x))) / x = L(K(y,x),x,1 / x)
    ]]></literal>
    <justification jstring="[para(1015(a,2),2342(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1015 2342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2344">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = (y * K(x,y)) / y
    ]]></literal>
    <justification jstring="[para(1015(a,2),2343(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1015 2343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2345">
    <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(246(a,1),2142(a,1,2))].">
      <j1 rule="para" parents="246 2142"/>
    </justification>
  </clause>

  <clause id="2346">
    <literal><![CDATA[
      ((T(x,y) \ x) / x) * K(x \ 1,x) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(284,a,2345,a),flip(a)].">
      <j1 rule="hyper" parents="284 2345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2347">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) \ L(1 / x,y,z)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(1815(a,1),2243(a,1,1))].">
      <j1 rule="para" parents="1815 2243"/>
    </justification>
  </clause>

  <clause id="2348">
    <literal><![CDATA[
      K(x \ 1,x) * (x * L(x \ 1,y,z)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(1062(a,1),2347(a,1,2))].">
      <j1 rule="para" parents="1062 2347"/>
    </justification>
  </clause>

  <clause id="2349">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(2226,a,2348,a)].">
      <j1 rule="hyper" parents="2226 2348"/>
    </justification>
  </clause>

  <clause id="2350">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,1832,a(flip),b,2349,a),flip(a)].">
      <j1 rule="hyper" parents="320 1832 2349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2351">
    <literal><![CDATA[
      (x \ 1) * (x * L(x \ 1,x,y)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,2248,a,b,2350,a(flip))].">
      <j1 rule="hyper" parents="30 2248 2350"/>
    </justification>
  </clause>

  <clause id="2352">
    <literal><![CDATA[
      (x * y) \ x = (y \ 1) * (y * L(y \ 1,y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,217,a(flip),b,2351,a)].">
      <j1 rule="hyper" parents="320 217 2351"/>
    </justification>
  </clause>

  <clause id="2353">
    <literal><![CDATA[
      (x \ 1) * (x * ((y * x) \ y)) = (y * x) \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,732,a(flip),b,2352,a)].">
      <j1 rule="hyper" parents="320 732 2352"/>
    </justification>
  </clause>

  <clause id="2354">
    <literal><![CDATA[
      (x \ 1) \ ((y * x) \ y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,2352,a,b,732,a(flip))].">
      <j1 rule="hyper" parents="116 2352 732"/>
    </justification>
  </clause>

  <clause id="2355">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,2353,a(flip),b,2300,a),flip(a)].">
      <j1 rule="hyper" parents="115 2353 2300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2356">
    <literal><![CDATA[
      T(x,(y * x) \ y) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,2355,a(flip),b,2315,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 2355 2315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2357">
    <literal><![CDATA[
      T(x,(y * x) \ y) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,106,a,b,2356,a),flip(a)].">
      <j1 rule="hyper" parents="320 106 2356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2358">
    <literal><![CDATA[
      K(x,(y * x) \ y) = ((x \ 1) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,2356,a(flip),b,2255,a),flip(a)].">
      <j1 rule="hyper" parents="117 2356 2255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2359">
    <literal><![CDATA[
      T(x \ y,y \ x) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(5(a,1),2356(a,1,2,1))].">
      <j1 rule="para" parents="5 2356"/>
    </justification>
  </clause>

  <clause id="2360">
    <literal><![CDATA[
      T(1 / (1 / x),(y * x) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(1774,a,2357,a(flip))].">
      <j1 rule="hyper" parents="1774 2357"/>
    </justification>
  </clause>

  <clause id="2361">
    <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),2357(a,1,2,1))].">
      <j1 rule="para" parents="84 2357"/>
    </justification>
  </clause>

  <clause id="2362">
    <literal><![CDATA[
      T(1 / (1 / (x \ y)),y \ x) = x \ y
    ]]></literal>
    <justification jstring="[para(5(a,1),2360(a,1,2,1))].">
      <j1 rule="para" parents="5 2360"/>
    </justification>
  </clause>

  <clause id="2363">
    <literal><![CDATA[
      K(x,(y * x) \ y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,1782,a(flip),b,2358,a),flip(a)].">
      <j1 rule="hyper" parents="320 1782 2358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2364">
    <literal><![CDATA[
      K(x,(y * x) \ y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / x) = z
    ]]></literal>
    <justification jstring="[para(2358(a,2),1271(a,1))].">
      <j1 rule="para" parents="2358 1271"/>
    </justification>
  </clause>

  <clause id="2365">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ 1) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(5(a,1),2363(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 2363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2366">
    <literal><![CDATA[
      K(x,y \ (y / x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),2363(a,1,2,1))].">
      <j1 rule="para" parents="7 2363"/>
    </justification>
  </clause>

  <clause id="2367">
    <literal><![CDATA[
      K(x \ y,T(y,x) \ ((y * x) / y)) = K(x \ y,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1143(a,2),2363(a,1,2,1))].">
      <j1 rule="para" parents="1143 2363"/>
    </justification>
  </clause>

  <clause id="2368">
    <literal><![CDATA[
      K(x,(y * x) \ y) \ 1 = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2363(a,2),1817(a,1,1))].">
      <j1 rule="para" parents="2363 1817"/>
    </justification>
  </clause>

  <clause id="2369">
    <literal><![CDATA[
      T(K(x,(y * x) \ y),z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2363(a,2),2166(a,1,1))].">
      <j1 rule="para" parents="2363 2166"/>
    </justification>
  </clause>

  <clause id="2370">
    <literal><![CDATA[
      K((x / y) \ x,z \ (z / y)) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,674,a,b,2366,a)].">
      <j1 rule="hyper" parents="58 674 2366"/>
    </justification>
  </clause>

  <clause id="2371">
    <literal><![CDATA[
      T(x \ y,x / y) = T(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,2223,a,b,2359,a)].">
      <j1 rule="hyper" parents="320 2223 2359"/>
    </justification>
  </clause>

  <clause id="2372">
    <literal><![CDATA[
      1 / T(x \ y,y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(197,a,2359,a(flip))].">
      <j1 rule="hyper" parents="197 2359"/>
    </justification>
  </clause>

  <clause id="2373">
    <literal><![CDATA[
      T(K(x \ (x / (y \ 1)),x),T(y,x) \ y) = ((y \ T(y,x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(1020(a,2),2359(a,1,1))].">
      <j1 rule="para" parents="1020 2359"/>
    </justification>
  </clause>

  <clause id="2374">
    <literal><![CDATA[
      x * K((x \ y) \ 1,x \ y) = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2359(a,1),1418(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2359 1418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2375">
    <literal><![CDATA[
      K(x \ (x / T(y \ x,x \ y)),x) = T(K(x \ y,x),(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(2359(a,2),1526(a,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2359 1526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2376">
    <literal><![CDATA[
      (1 / (1 / (x \ y))) * (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,2362,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 2362 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2377">
    <literal><![CDATA[
      T(1 / (1 / K(x \ (x / (y \ 1)),x)),T(y,x) \ y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(1020(a,2),2362(a,1,1,2,2))].">
      <j1 rule="para" parents="1020 2362"/>
    </justification>
  </clause>

  <clause id="2378">
    <literal><![CDATA[
      L(K(x,x \ 1),x,y) = K(((y * x) \ y) \ 1,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(2369(a,1),2258(a,1,1))].">
      <j1 rule="para" parents="2369 2258"/>
    </justification>
  </clause>

  <clause id="2379">
    <literal><![CDATA[
      T(T(x / y,x \ y),y) = T(y \ x,y / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,246,a,b,2371,a)].">
      <j1 rule="hyper" parents="320 246 2371"/>
    </justification>
  </clause>

  <clause id="2380">
    <literal><![CDATA[
      1 / T((x * y) \ x,y) = ((x * y) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),2372(a,1,2,2))].">
      <j1 rule="para" parents="4 2372"/>
    </justification>
  </clause>

  <clause id="2381">
    <literal><![CDATA[
      1 / T(x \ (x / y),y) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),2372(a,1,2,2))].">
      <j1 rule="para" parents="75 2372"/>
    </justification>
  </clause>

  <clause id="2382">
    <literal><![CDATA[
      L(x * ((y * x) \ y),x \ 1,y * x) = ((y * x) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(2354(a,1),298(a,1,1))].">
      <j1 rule="para" parents="2354 298"/>
    </justification>
  </clause>

  <clause id="2383">
    <literal><![CDATA[
      (x \ y) * (1 / (x \ y)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(1789,a,2365,a)].">
      <j1 rule="hyper" parents="1789 2365"/>
    </justification>
  </clause>

  <clause id="2384">
    <literal><![CDATA[
      K((x * y) \ x,((x * y) \ x) \ 1) = K((x * y) \ x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),2365(a,2,2))].">
      <j1 rule="para" parents="4 2365"/>
    </justification>
  </clause>

  <clause id="2385">
    <literal><![CDATA[
      T(x,K(y \ z,z \ y)) = x
    ]]></literal>
    <justification jstring="[para(2365(a,1),2168(a,1,2))].">
      <j1 rule="para" parents="2365 2168"/>
    </justification>
  </clause>

  <clause id="2386">
    <literal><![CDATA[
      K(x \ y,y \ x) * z = z * K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(2326,a,2385,a),flip(a)].">
      <j1 rule="hyper" parents="2326 2385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2387">
    <literal><![CDATA[
      T(x / y,y / x) = T(x / y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(35,a,246,a,b,2379,a)].">
      <j1 rule="hyper" parents="35 246 2379"/>
    </justification>
  </clause>

  <clause id="2388">
    <literal><![CDATA[
      T(x / y,x \ y) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2057,a(flip),b,2387,a),flip(a)].">
      <j1 rule="hyper" parents="58 2057 2387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2389">
    <literal><![CDATA[
      T(x / (x * y),y) = ((x / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),2388(a,1,2))].">
      <j1 rule="para" parents="4 2388"/>
    </justification>
  </clause>

  <clause id="2390">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(30,a,1751,a,b,2376,a)].">
      <j1 rule="hyper" parents="30 1751 2376"/>
    </justification>
  </clause>

  <clause id="2391">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(30,a,841,a,b,2376,a)].">
      <j1 rule="hyper" parents="30 841 2376"/>
    </justification>
  </clause>

  <clause id="2392">
    <literal><![CDATA[
      x * K(x \ y,(x \ y) \ 1) = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(2390(a,1),1854(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2390 1854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2393">
    <literal><![CDATA[
      T(K(x,y),K(x,y) \ 1) = T(K(x,y),K(y,x))
    ]]></literal>
    <justification jstring="[para(11(a,2),2361(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11 2361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2394">
    <literal><![CDATA[
      T(K(x,y),K(y,x)) = (K(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(428,a,2393,a),flip(a)].">
      <j1 rule="hyper" parents="428 2393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2395">
    <literal><![CDATA[
      (K(x,y) \ 1) \ 1 = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1990,a(flip),b,2394,a),flip(a)].">
      <j1 rule="hyper" parents="58 1990 2394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2398">
    <literal><![CDATA[
      1 / (1 / K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2395(a,1),190(a,1,2,2))].">
      <j1 rule="para" parents="2395 190"/>
    </justification>
  </clause>

  <clause id="2399">
    <literal><![CDATA[
      K(x,y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      1 / K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2398(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2398 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2400">
    <literal><![CDATA[
      x * K(x \ y,y \ x) = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(2365(a,1),2392(a,1,2))].">
      <j1 rule="para" parents="2365 2392"/>
    </justification>
  </clause>

  <clause id="2401">
    <literal><![CDATA[
      (x / y) * K(y,y \ 1) = x * (1 / (1 / (x \ (x / y))))
    ]]></literal>
    <justification jstring="[para(2370(a,1),2400(a,1,2))].">
      <j1 rule="para" parents="2370 2400"/>
    </justification>
  </clause>

  <clause id="2402">
    <literal><![CDATA[
      K((x * y) \ x,((x * y) \ x) \ 1) = L(K(y,y \ 1),y,x) \ 1
    ]]></literal>
    <justification jstring="[para(2378(a,2),433(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2378 433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2404">
    <literal><![CDATA[
      K(x \ y,T(x / y,T(y,x))) = K(x \ y,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1491(a,1),2367(a,1,2))].">
      <j1 rule="para" parents="1491 2367"/>
    </justification>
  </clause>

  <clause id="2405">
    <literal><![CDATA[
      K(x \ y,T(x / y,T(y,x))) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,2365,a(flip),b,2404,a),flip(a)].">
      <j1 rule="hyper" parents="320 2365 2404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2406">
    <literal><![CDATA[
      L(x * ((y * x) \ y),x \ 1,y * x) = R(y,x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(261(a,1),2382(a,2,1))].">
      <j1 rule="para" parents="261 2382"/>
    </justification>
  </clause>

  <clause id="2407">
    <literal><![CDATA[
      K((x * y) \ x,y) = L(K(y,y \ 1),y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2384,a(flip),b,2402,a)].">
      <j1 rule="hyper" parents="58 2384 2402"/>
    </justification>
  </clause>

  <clause id="2408">
    <literal><![CDATA[
      T(K(x \ y,x),(y \ x) \ 1) = T(K(x \ y,x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1525,a(flip),b,2375,a),flip(a)].">
      <j1 rule="hyper" parents="58 1525 2375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2409">
    <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),2408(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2410">
    <literal><![CDATA[
      T(K(x \ (x / (y \ 1)),x),T(y,x) \ y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(2398(a,1),2377(a,1,1))].">
      <j1 rule="para" parents="2398 2377"/>
    </justification>
  </clause>

  <clause id="2411">
    <literal><![CDATA[
      ((x \ T(x,y)) \ 1) \ 1 = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2373,a(flip),b,2410,a)].">
      <j1 rule="hyper" parents="58 2373 2410"/>
    </justification>
  </clause>

  <clause id="2412">
    <literal><![CDATA[
      1 / (x \ T(x,y)) = (x \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(197,a,2411,a)].">
      <j1 rule="hyper" parents="197 2411"/>
    </justification>
  </clause>

  <clause id="2413">
    <literal><![CDATA[
      T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),y \ (y * x))
    ]]></literal>
    <justification jstring="[para(4(a,1),2409(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2414">
    <literal><![CDATA[
      T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2413(a,2,2))].">
      <j1 rule="para" parents="4 2413"/>
    </justification>
  </clause>

  <clause id="2416">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (x \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[para(7(a,1),2295(a,2,2,1,2,1))].">
      <j1 rule="para" parents="7 2295"/>
    </justification>
  </clause>

  <clause id="2417">
    <literal><![CDATA[
      (x * ((y * (x \ (z * u))) / y)) / u = (x / u) * ((y * ((x / u) \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(131,a,2416,a)].">
      <j1 rule="hyper" parents="131 2416"/>
    </justification>
  </clause>

  <clause id="2418">
    <literal><![CDATA[
      (x / y) * ((z * ((x / y) \ 1)) / z) = (x * ((z * (x \ y)) / z)) / y
    ]]></literal>
    <justification jstring="[para(2(a,1),2417(a,1,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2 2417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2419">
    <literal><![CDATA[
      (x * (T(y,x) / y)) \ (x * z) = x * ((x * (T(y,x) / y)) \ z)
    ]]></literal>
    <justification jstring="[para(2302(a,1),2303(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2302 2303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2420">
    <literal><![CDATA[
      L(x * K(y \ 1,y),y,1 / y) = L(x,y,1 / y) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(419,a,2318,a),flip(a)].">
      <j1 rule="hyper" parents="419 2318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2421">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,1590,a(flip),b,2319,a),flip(a)].">
      <j1 rule="hyper" parents="320 1590 2319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2422">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,z) = x * (T((x \ y) * x,z) / x)
    ]]></literal>
    <justification jstring="[para(993(a,1),2327(a,2,2))].">
      <j1 rule="para" parents="993 2327"/>
    </justification>
  </clause>

  <clause id="2423">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,1373,a(flip),b,2422,a),flip(a)].">
      <j1 rule="hyper" parents="320 1373 2422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2424">
    <literal><![CDATA[
      T(x * K(y,y \ 1),y) = T(x,y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(738,a,2423,a),flip(a)].">
      <j1 rule="hyper" parents="738 2423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2425">
    <literal><![CDATA[
      T((1 / K(x,x \ 1)) * y,x) = (1 / K(x,x \ 1)) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2423,a(flip),b,939,a),flip(a)].">
      <j1 rule="hyper" parents="119 2423 939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2426">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,x) = K(x,x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2423(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 2423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2427">
    <literal><![CDATA[
      T((x / y) * K(y,y \ 1),y) = (y \ x) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,1),2424(a,2,1))].">
      <j1 rule="para" parents="107 2424"/>
    </justification>
  </clause>

  <clause id="2428">
    <literal><![CDATA[
      x * T(K(x,x \ 1) * y,x) = K(x,x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(2426(a,2),1850(a,1,2))].">
      <j1 rule="para" parents="2426 1850"/>
    </justification>
  </clause>

  <clause id="2429">
    <literal><![CDATA[
      x \ (y * K(x,x \ 1)) = (x \ y) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2027,a,2427,a)].">
      <j1 rule="hyper" parents="2027 2427"/>
    </justification>
  </clause>

  <clause id="2430">
    <literal><![CDATA[
      x * ((x \ y) * K(x,x \ 1)) = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,2427,a(flip),b,2023,a(flip))].">
      <j1 rule="hyper" parents="119 2427 2023"/>
    </justification>
  </clause>

  <clause id="2431">
    <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(2427(a,2),39(a,1))].">
      <j1 rule="para" parents="2427 39"/>
    </justification>
  </clause>

  <clause id="2432">
    <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),2429(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="75 2429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2433">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = x * (y * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(4(a,1),2430(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 2430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2434">
    <literal><![CDATA[
      R(x,y,K(x,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(515,a,2433,a)].">
      <j1 rule="hyper" parents="515 2433"/>
    </justification>
  </clause>

  <clause id="2435">
    <literal><![CDATA[
      (1 / x) * (y * K(1 / x,(1 / x) \ 1)) = ((1 / x) * y) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(1815(a,1),2433(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1815 2433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2436">
    <literal><![CDATA[
      R(T(x,y),z,K(x,x \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2434(a,1),22(a,2,1))].">
      <j1 rule="para" parents="2434 22"/>
    </justification>
  </clause>

  <clause id="2437">
    <literal><![CDATA[
      T(x,y * K(x,x \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2026,a(flip),b,2436,a),flip(a)].">
      <j1 rule="hyper" parents="58 2026 2436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2439">
    <literal><![CDATA[
      T(x \ 1,y * K(x \ 1,x)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1787(a,1),2437(a,1,2,2))].">
      <j1 rule="para" parents="1787 2437"/>
    </justification>
  </clause>

  <clause id="2440">
    <literal><![CDATA[
      T(x,R(x \ 1,x,y)) = T(x,y / (x * y))
    ]]></literal>
    <justification jstring="[para(2051(a,2),2437(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2051 2437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2441">
    <literal><![CDATA[
      (x * R(x \ 1,x,y)) \ (T(x,y / (x * y)) * R(x \ 1,x,y)) = K(T(x,R(x \ 1,x,y)),R(x \ 1,x,y))
    ]]></literal>
    <justification jstring="[para(2440(a,1),230(a,1,2,1))].">
      <j1 rule="para" parents="2440 230"/>
    </justification>
  </clause>

  <clause id="2442">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = K(x,x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(284,a,2428,a)].">
      <j1 rule="hyper" parents="284 2428"/>
    </justification>
  </clause>

  <clause id="2443">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = z
    ]]></literal>
    <justification jstring="[para(2428(a,1),284(a,1))].">
      <j1 rule="para" parents="2428 284"/>
    </justification>
  </clause>

  <clause id="2444">
    <literal><![CDATA[
      L(x,y,K(x,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,2442,a)].">
      <j1 rule="hyper" parents="479 2442"/>
    </justification>
  </clause>

  <clause id="2445">
    <literal><![CDATA[
      L(1 / x,y,K(x \ 1,x)) = 1 / x
    ]]></literal>
    <justification jstring="[para(1815(a,1),2444(a,1,3))].">
      <j1 rule="para" parents="1815 2444"/>
    </justification>
  </clause>

  <clause id="2446">
    <literal><![CDATA[
      L(T(1 / x,y),z,K(x \ 1,x)) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(2445(a,1),20(a,2,1))].">
      <j1 rule="para" parents="2445 20"/>
    </justification>
  </clause>

  <clause id="2447">
    <literal><![CDATA[
      (1 / K(x,x \ 1)) * T(y,x) = T(K(x \ 1,x) * y,x)
    ]]></literal>
    <justification jstring="[para(468(a,1),2425(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="468 2425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2448">
    <literal><![CDATA[
      T(K(x \ 1,x) * y,x) = K(x \ 1,x) * T(y,x)
    ]]></literal>
    <justification jstring="[para(468(a,1),2447(a,1,1)),flip(a)].">
      <j1 rule="para" parents="468 2447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2449">
    <literal><![CDATA[
      x * T(K(x \ 1,x) * y,x) = K(x \ 1,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(2448(a,2),1388(a,1,2))].">
      <j1 rule="para" parents="2448 1388"/>
    </justification>
  </clause>

  <clause id="2450">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * x = K(x \ 1,x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(284,a,2449,a)].">
      <j1 rule="hyper" parents="284 2449"/>
    </justification>
  </clause>

  <clause id="2451">
    <literal><![CDATA[
      L(x,y,K(x \ 1,x)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,2450,a)].">
      <j1 rule="hyper" parents="479 2450"/>
    </justification>
  </clause>

  <clause id="2452">
    <literal><![CDATA[
      L(T(x,y),z,K(x \ 1,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2451(a,1),20(a,2,1))].">
      <j1 rule="para" parents="2451 20"/>
    </justification>
  </clause>

  <clause id="2453">
    <literal><![CDATA[
      T(x,K(x \ 1,x) * y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2080,a,2452,a)].">
      <j1 rule="hyper" parents="2080 2452"/>
    </justification>
  </clause>

  <clause id="2454">
    <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(437(a,1),2432(a,1,1)),flip(a)].">
      <j1 rule="para" parents="437 2432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2455">
    <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(2138(a,1),2435(a,2,1))].">
      <j1 rule="para" parents="2138 2435"/>
    </justification>
  </clause>

  <clause id="2456">
    <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(1816(a,1),2454(a,1,2,2))].">
      <j1 rule="para" parents="1816 2454"/>
    </justification>
  </clause>

  <clause id="2457">
    <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(2420(a,2),2456(a,1,2))].">
      <j1 rule="para" parents="2420 2456"/>
    </justification>
  </clause>

  <clause id="2458">
    <literal><![CDATA[
      (x * y) * K(1 / x,(1 / x) \ 1) = x * (y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(555,a,2457,a),flip(a)].">
      <j1 rule="hyper" parents="555 2457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2459">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x) = x * (y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(1815(a,1),2458(a,1,2))].">
      <j1 rule="para" parents="1815 2458"/>
    </justification>
  </clause>

  <clause id="2460">
    <literal><![CDATA[
      R(x,y,K(x \ 1,x)) = x
    ]]></literal>
    <justification jstring="[hyper(515,a,2459,a)].">
      <j1 rule="hyper" parents="515 2459"/>
    </justification>
  </clause>

  <clause id="2461">
    <literal><![CDATA[
      x * ((T(x,y) \ 1) * K(x \ 1,x)) = (T(x,y) \ x) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(1110(a,1),2459(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1110 2459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2462">
    <literal><![CDATA[
      R(T(x,y),z,K(x \ 1,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2460(a,1),22(a,2,1))].">
      <j1 rule="para" parents="2460 22"/>
    </justification>
  </clause>

  <clause id="2463">
    <literal><![CDATA[
      x * (y * K(x \ 1,x)) != z
    ]]></literal>
    <literal><![CDATA[
      (x * y) * K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(2460(a,1),283(a,1,1))].">
      <j1 rule="para" parents="2460 283"/>
    </justification>
  </clause>

  <clause id="2464">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x \ 1,x) = T(x,y) \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2462(a,1),426(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2462 426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2465">
    <literal><![CDATA[
      (T(x,y) \ x) * K(x \ 1,x) = x * (T(x,y) \ K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(2464(a,1),2461(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2464 2461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2466">
    <literal><![CDATA[
      (T(x,y) \ x) * K(x \ 1,x) = T(x,y) \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(320,a,1799,a(flip),b,2465,a),flip(a)].">
      <j1 rule="hyper" parents="320 1799 2465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2467">
    <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(320,a,512,a(flip),b,724,a),flip(a)].">
      <j1 rule="hyper" parents="320 512 724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2468">
    <literal><![CDATA[
      x * (K(x,y) * T(K(x,y) \ y,z)) = (T(y,z) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(922,a,2467,a)].">
      <j1 rule="hyper" parents="922 2467"/>
    </justification>
  </clause>

  <clause id="2469">
    <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),2468(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 2468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2470">
    <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,1750,a(flip),b,1078,a)].">
      <j1 rule="hyper" parents="58 1750 1078"/>
    </justification>
  </clause>

  <clause id="2472">
    <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(2470(a,1),864(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2470 864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2473">
    <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(320,a,635,a(flip),b,2472,a),flip(a)].">
      <j1 rule="hyper" parents="320 635 2472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2474">
    <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,1722,a(flip),b,2473,a),flip(a)].">
      <j1 rule="hyper" parents="58 1722 2473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2475">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * ((y * u) * T((y * u) \ y,z))
    ]]></literal>
    <justification jstring="[hyper(922,a,1424,a),flip(a)].">
      <j1 rule="hyper" parents="922 1424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2476">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * (y * (u * T(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(733(a,1),2475(a,2,2))].">
      <j1 rule="para" parents="733 2475"/>
    </justification>
  </clause>

  <clause id="2477">
    <literal><![CDATA[
      L(x * T(x \ 1,y),z,u) = K(y \ (y / L(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(479,a,2476,a)].">
      <j1 rule="hyper" parents="479 2476"/>
    </justification>
  </clause>

  <clause id="2478">
    <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(320,a,1017,a(flip),b,2477,a)].">
      <j1 rule="hyper" parents="320 1017 2477"/>
    </justification>
  </clause>

  <clause id="2479">
    <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),2477(a,2,1,2))].">
      <j1 rule="para" parents="69 2477"/>
    </justification>
  </clause>

  <clause id="2480">
    <literal><![CDATA[
      L(x \ T(x,y),z,u) = K(y \ (y / L(x \ 1,z,u)),y)
    ]]></literal>
    <justification jstring="[para(983(a,1),2477(a,1,1))].">
      <j1 rule="para" parents="983 2477"/>
    </justification>
  </clause>

  <clause id="2481">
    <literal><![CDATA[
      L(T(x,y) / x,z,u) = K(y \ (y / L(1 / x,z,u)),y)
    ]]></literal>
    <justification jstring="[para(999(a,1),2477(a,1,1))].">
      <j1 rule="para" parents="999 2477"/>
    </justification>
  </clause>

  <clause id="2482">
    <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),2480(a,2,1,2))].">
      <j1 rule="para" parents="6 2480"/>
    </justification>
  </clause>

  <clause id="2483">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * z) * T((y * z) \ z,x)) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(1476(a,1),1581(a,2,1))].">
      <j1 rule="para" parents="1476 1581"/>
    </justification>
  </clause>

  <clause id="2484">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * T(y \ 1,x)) * z) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(1218(a,1),2483(a,2,1,1))].">
      <j1 rule="para" parents="1218 2483"/>
    </justification>
  </clause>

  <clause id="2485">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(y \ (y / R(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,15,a,b,2484,a)].">
      <j1 rule="hyper" parents="320 15 2484"/>
    </justification>
  </clause>

  <clause id="2486">
    <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(2484(a,2),518(a,1))].">
      <j1 rule="para" parents="2484 518"/>
    </justification>
  </clause>

  <clause id="2487">
    <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(320,a,1017,a(flip),b,2485,a)].">
      <j1 rule="hyper" parents="320 1017 2485"/>
    </justification>
  </clause>

  <clause id="2488">
    <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(1203(a,1),2485(a,2,1,2))].">
      <j1 rule="para" parents="1203 2485"/>
    </justification>
  </clause>

  <clause id="2489">
    <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(1017(a,1),2486(a,1))].">
      <j1 rule="para" parents="1017 2486"/>
    </justification>
  </clause>

  <clause id="2490">
    <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(284,a,2487,a),flip(a)].">
      <j1 rule="hyper" parents="284 2487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2491">
    <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),1651(a,1,1))].">
      <j1 rule="para" parents="60 1651"/>
    </justification>
  </clause>

  <clause id="2492">
    <literal><![CDATA[
      (((x * y) \ x) \ K(y,x)) / (((x * y) \ x) \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,1015,a,b,1041,a),flip(a)].">
      <j1 rule="hyper" parents="320 1015 1041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2493">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = T(K(y,x),((x * y) \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(2492(a,1),107(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2492 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2494">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = T(K(y,x),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2414,a(flip),b,2493,a),flip(a)].">
      <j1 rule="hyper" parents="320 2414 2493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2495">
    <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(258(a,2),1079(a,1,2,1,1))].">
      <j1 rule="para" parents="258 1079"/>
    </justification>
  </clause>

  <clause id="2496">
    <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(258(a,2),1082(a,1,2,1,1))].">
      <j1 rule="para" parents="258 1082"/>
    </justification>
  </clause>

  <clause id="2497">
    <literal><![CDATA[
      K(T(x,R(x \ 1,y,z)),R(x \ 1,y,z)) = x \ T(x,R(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(17(a,2),1236(a,1,1))].">
      <j1 rule="para" parents="17 1236"/>
    </justification>
  </clause>

  <clause id="2498">
    <literal><![CDATA[
      K(T(x,R(x \ 1,x,y)),R(x \ 1,x,y)) = x \ T(x,y / (x * y))
    ]]></literal>
    <justification jstring="[para(2440(a,1),2497(a,2,2))].">
      <j1 rule="para" parents="2440 2497"/>
    </justification>
  </clause>

  <clause id="2499">
    <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(2478(a,1),1409(a,1,1))].">
      <j1 rule="para" parents="2478 1409"/>
    </justification>
  </clause>

  <clause id="2500">
    <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(358(a,1),2499(a,1,1,1))].">
      <j1 rule="para" parents="358 2499"/>
    </justification>
  </clause>

  <clause id="2501">
    <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(1404(a,1),2500(a,1,2))].">
      <j1 rule="para" parents="1404 2500"/>
    </justification>
  </clause>

  <clause id="2502">
    <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,2501,a)].">
      <j1 rule="hyper" parents="58 20 2501"/>
    </justification>
  </clause>

  <clause id="2503">
    <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(1406(a,1),2502(a,2,1))].">
      <j1 rule="para" parents="1406 2502"/>
    </justification>
  </clause>

  <clause id="2504">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(2179(a,1),2503(a,1,1))].">
      <j1 rule="para" parents="2179 2503"/>
    </justification>
  </clause>

  <clause id="2505">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x) \ 1,z) = x * (y * K(z \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,2504,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 2504 13"/>
    </justification>
  </clause>

  <clause id="2507">
    <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),2259(a,1,1))].">
      <j1 rule="para" parents="85 2259"/>
    </justification>
  </clause>

  <clause id="2508">
    <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),2507(a,1,2,1,1))].">
      <j1 rule="para" parents="85 2507"/>
    </justification>
  </clause>

  <clause id="2509">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ x) * K(1 / x,(1 / x) \ 1)) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,2346,a(flip),b,2455,a),flip(a)].">
      <j1 rule="hyper" parents="320 2346 2455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2510">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ x) * K(x \ 1,x)) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(1815(a,1),2509(a,1,2,2))].">
      <j1 rule="para" parents="1815 2509"/>
    </justification>
  </clause>

  <clause id="2511">
    <literal><![CDATA[
      (1 / x) * (T(x,y) \ (1 / (1 / x))) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(2466(a,1),2510(a,1,2))].">
      <j1 rule="para" parents="2466 2510"/>
    </justification>
  </clause>

  <clause id="2512">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(2222(a,1),2511(a,1,2))].">
      <j1 rule="para" parents="2222 2511"/>
    </justification>
  </clause>

  <clause id="2513">
    <literal><![CDATA[
      (x \ 1) \ (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,2141,a(flip),b,2512,a(flip))].">
      <j1 rule="hyper" parents="116 2141 2512"/>
    </justification>
  </clause>

  <clause id="2514">
    <literal><![CDATA[
      (x \ T(x,y)) \ 1 = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,2112,a(flip),b,2513,a)].">
      <j1 rule="hyper" parents="58 2112 2513"/>
    </justification>
  </clause>

  <clause id="2515">
    <literal><![CDATA[
      1 / (x \ T(x,y)) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,2412,a,b,2514,a)].">
      <j1 rule="hyper" parents="58 2412 2514"/>
    </justification>
  </clause>

  <clause id="2516">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = ((x / y) \ (y \ x)) \ 1
    ]]></literal>
    <justification jstring="[para(107(a,1),2514(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 2514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2517">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) \ x = (x \ (x * K(x,y))) \ 1
    ]]></literal>
    <justification jstring="[para(1729(a,1),2514(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1729 2514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2518">
    <literal><![CDATA[
      ((x / y) \ (y \ x)) \ 1 = (y \ x) \ (x / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),2516(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 2516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2519">
    <literal><![CDATA[
      (x \ (x * y)) \ ((x * y) / x) = (((x * y) / x) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),2518(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 2518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2520">
    <literal><![CDATA[
      (((x * y) / x) \ y) \ 1 = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2519(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2521">
    <literal><![CDATA[
      1 / (x \ ((y * x) / y)) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(197,a,2520,a)].">
      <j1 rule="hyper" parents="197 2520"/>
    </justification>
  </clause>

  <clause id="2522">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) \ x = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),2517(a,2,1))].">
      <j1 rule="para" parents="4 2517"/>
    </justification>
  </clause>

  <clause id="2524">
    <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(320,a,1858,a(flip),b,2495,a),flip(a)].">
      <j1 rule="hyper" parents="320 1858 2495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2525">
    <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(320,a,1738,a(flip),b,2496,a),flip(a)].">
      <j1 rule="hyper" parents="320 1738 2496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2526">
    <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(1083(a,1),2524(a,2,1))].">
      <j1 rule="para" parents="1083 2524"/>
    </justification>
  </clause>

  <clause id="2527">
    <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(1061(a,1),2525(a,2,1))].">
      <j1 rule="para" parents="1061 2525"/>
    </justification>
  </clause>

  <clause id="2528">
    <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(320,a,514,a(flip),b,846,a),flip(a)].">
      <j1 rule="hyper" parents="320 514 846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2529">
    <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(1362,a,2528,a)].">
      <j1 rule="hyper" parents="1362 2528"/>
    </justification>
  </clause>

  <clause id="2530">
    <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(1243(a,1),2529(a,2,1,1))].">
      <j1 rule="para" parents="1243 2529"/>
    </justification>
  </clause>

  <clause id="2531">
    <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),1910(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="17 1910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2532">
    <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(238(a,1),2531(a,2,2))].">
      <j1 rule="para" parents="238 2531"/>
    </justification>
  </clause>

  <clause id="2533">
    <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),1919(a,2,1,2))].">
      <j1 rule="para" parents="3 1919"/>
    </justification>
  </clause>

  <clause id="2534">
    <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(2197,a,2196,a),flip(a)].">
      <j1 rule="hyper" parents="2197 2196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2535">
    <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(2208,a,2207,a),flip(a)].">
      <j1 rule="hyper" parents="2208 2207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2536">
    <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),1181(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 1181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2537">
    <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),2536(a,2,2,2,1))].">
      <j1 rule="para" parents="75 2536"/>
    </justification>
  </clause>

  <clause id="2538">
    <literal><![CDATA[
      x * T(x \ T(x,y),(1 / x) \ 1) = (1 / x) \ (x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),2537(a,1,2,1,2,1))].">
      <j1 rule="para" parents="75 2537"/>
    </justification>
  </clause>

  <clause id="2539">
    <literal><![CDATA[
      (1 / x) \ (x \ T(x,y)) = x * T(x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[para(75(a,1),2538(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 2538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2540">
    <literal><![CDATA[
      (1 / x) \ (x \ T(x,y)) = (x \ T(x,y)) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,105,a(flip),b,2539,a),flip(a)].">
      <j1 rule="hyper" parents="320 105 2539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2541">
    <literal><![CDATA[
      (x \ T(x,R(y,x,(y * x) \ x))) * x = (1 / x) \ (x \ (x * K(x,y)))
    ]]></literal>
    <justification jstring="[para(1729(a,1),2540(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1729 2540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2542">
    <literal><![CDATA[
      (x \ T(x,R(y,x,(y * x) \ x))) * x = (1 / x) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),2541(a,2,2))].">
      <j1 rule="para" parents="4 2541"/>
    </justification>
  </clause>

  <clause id="2544">
    <literal><![CDATA[
      (x \ (x * K(x,y))) * x = (1 / x) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(1729(a,1),2542(a,1,1,2))].">
      <j1 rule="para" parents="1729 2542"/>
    </justification>
  </clause>

  <clause id="2545">
    <literal><![CDATA[
      (1 / x) \ K(x,y) = K(x,y) * x
    ]]></literal>
    <justification jstring="[para(4(a,1),2544(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2547">
    <literal><![CDATA[
      K(T(x,x \ 1),T(x,x \ 1) \ 1) * (T(x,x \ 1) \ y) = L(x \ y,x,K(x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,1806,a(flip),b,1908,a),flip(a)].">
      <j1 rule="hyper" parents="320 1806 1908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2548">
    <literal><![CDATA[
      K(x,x \ 1) * (T(x,x \ 1) \ y) = L(x \ y,x,K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(1907(a,1),2547(a,1,1))].">
      <j1 rule="para" parents="1907 2547"/>
    </justification>
  </clause>

  <clause id="2549">
    <literal><![CDATA[
      L(x \ y,x,K(x,x \ 1)) = K(x,x \ 1) * (((x \ 1) \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(106(a,1),2548(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="106 2548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2550">
    <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(1745(a,1),2482(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1745 2482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2551">
    <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),2550(a,2,1))].">
      <j1 rule="para" parents="61 2550"/>
    </justification>
  </clause>

  <clause id="2552">
    <literal><![CDATA[
      K((x * L(x \ 1,y,z)) \ x,x * L(x \ 1,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,179,a(flip),b,2551,a),flip(a)].">
      <j1 rule="hyper" parents="320 179 2551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2555">
    <literal><![CDATA[
      ((x * L(x \ 1,y,z)) \ x) * (x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(167,a,85,a,b,2552,a(flip))].">
      <j1 rule="hyper" parents="167 85 2552"/>
    </justification>
  </clause>

  <clause id="2556">
    <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(2555(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="2555 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2557">
    <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(1886(a,1),1726(a,1,2,1))].">
      <j1 rule="para" parents="1886 1726"/>
    </justification>
  </clause>

  <clause id="2558">
    <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),2557(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 2557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2560">
    <literal><![CDATA[
      x \ y != (z \ 1) * K(R(z,u,w),z \ 1)
    ]]></literal>
    <literal><![CDATA[
      x * ((z \ R(z,u,w)) / R(z,u,w)) = y
    ]]></literal>
    <justification jstring="[para(2558(a,1),340(a,2,2))].">
      <j1 rule="para" parents="2558 340"/>
    </justification>
  </clause>

  <clause id="2561">
    <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),1723(a,2,2))].">
      <j1 rule="para" parents="6 1723"/>
    </justification>
  </clause>

  <clause id="2562">
    <literal><![CDATA[
      (((x \ y) * (y \ x)) / (x \ y)) * ((y \ x) \ 1) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,973,a(flip),b,2561,a)].">
      <j1 rule="hyper" parents="58 973 2561"/>
    </justification>
  </clause>

  <clause id="2564">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) * ((y \ x) \ 1) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(842(a,1),2562(a,1,1))].">
      <j1 rule="para" parents="842 2562"/>
    </justification>
  </clause>

  <clause id="2565">
    <literal><![CDATA[
      (x \ y) * K(y \ x,x \ y) = L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,2339,a,b,2564,a)].">
      <j1 rule="hyper" parents="30 2339 2564"/>
    </justification>
  </clause>

  <clause id="2566">
    <literal><![CDATA[
      (x \ y) * K(y \ x,x \ y) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,2391,a(flip),b,2565,a),flip(a)].">
      <j1 rule="hyper" parents="320 2391 2565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2567">
    <literal><![CDATA[
      K((x \ y) \ 1,x \ y) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(29,a,1779,a,b,2566,a)].">
      <j1 rule="hyper" parents="29 1779 2566"/>
    </justification>
  </clause>

  <clause id="2568">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,(x * y) \ x) = K(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,673,a(flip),b,2567,a),flip(a)].">
      <j1 rule="hyper" parents="320 673 2567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2569">
    <literal><![CDATA[
      K(1 / (x \ y),x \ y) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1816,a,b,2567,a)].">
      <j1 rule="hyper" parents="58 1816 2567"/>
    </justification>
  </clause>

  <clause id="2570">
    <literal><![CDATA[
      x * K(y \ x,x \ y) = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2567(a,1),2374(a,1,2))].">
      <j1 rule="para" parents="2567 2374"/>
    </justification>
  </clause>

  <clause id="2571">
    <literal><![CDATA[
      K(1 / ((x * y) \ x),(x * y) \ x) = K(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,673,a(flip),b,2569,a),flip(a)].">
      <j1 rule="hyper" parents="320 673 2569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2572">
    <literal><![CDATA[
      L(K(x,x \ 1),x,y) = K(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2378,a,b,2568,a)].">
      <j1 rule="hyper" parents="58 2378 2568"/>
    </justification>
  </clause>

  <clause id="2573">
    <literal><![CDATA[
      (x * y) * K(y,(x * y) \ x) = x * T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(2568(a,1),1428(a,1,2))].">
      <j1 rule="para" parents="2568 1428"/>
    </justification>
  </clause>

  <clause id="2574">
    <literal><![CDATA[
      L(K(x,x \ 1),x,y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,2363,a(flip),b,2572,a),flip(a)].">
      <j1 rule="hyper" parents="320 2363 2572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2575">
    <literal><![CDATA[
      K(x,(y * x) \ y) \ 1 = K((y * x) \ y,x)
    ]]></literal>
    <justification jstring="[para(2572(a,1),2407(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2572 2407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2577">
    <literal><![CDATA[
      L(K(x \ 1,x),1 / x,y) = K(1 / x,(1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(1815(a,1),2574(a,1,1))].">
      <j1 rule="para" parents="1815 2574"/>
    </justification>
  </clause>

  <clause id="2578">
    <literal><![CDATA[
      K((x * y) \ x,y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2368,a(flip),b,2575,a),flip(a)].">
      <j1 rule="hyper" parents="58 2368 2575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2580">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) = K((x * y) \ y,T(x,y))
    ]]></literal>
    <justification jstring="[para(105(a,1),2578(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="105 2578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2581">
    <literal><![CDATA[
      K((x * y) \ y,y \ (x * y)) = K(T(x,y) \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(17(a,1),2580(a,2,2)),flip(a)].">
      <j1 rule="para" parents="17 2580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2582">
    <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(1490(a,1),2580(a,2,1,1))].">
      <j1 rule="para" parents="1490 2580"/>
    </justification>
  </clause>

  <clause id="2583">
    <literal><![CDATA[
      L(K(x \ 1,x),1 / x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,1815,a(flip),b,2577,a),flip(a)].">
      <j1 rule="hyper" parents="320 1815 2577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2584">
    <literal><![CDATA[
      (x * (y \ 1)) / K(y \ 1,y) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(2583(a,1),778(a,1,2))].">
      <j1 rule="para" parents="2583 778"/>
    </justification>
  </clause>

  <clause id="2585">
    <literal><![CDATA[
      (x / (y \ 1)) * (1 / y) = x / K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2583(a,1),779(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2583 779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2586">
    <literal><![CDATA[
      R(x,y \ 1,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(1603,a,2584,a)].">
      <j1 rule="hyper" parents="1603 2584"/>
    </justification>
  </clause>

  <clause id="2587">
    <literal><![CDATA[
      (x / (1 / y)) * (y \ 1) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2584,a),flip(a)].">
      <j1 rule="hyper" parents="325 2584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2588">
    <literal><![CDATA[
      (x * (1 / y)) * K(y \ 1,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,2584,a)].">
      <j1 rule="hyper" parents="133 2584"/>
    </justification>
  </clause>

  <clause id="2589">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2584(a,1),1602(a,1,1))].">
      <j1 rule="para" parents="2584 1602"/>
    </justification>
  </clause>

  <clause id="2591">
    <literal><![CDATA[
      R(x,1 / y,y) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1072,a,2586,a),flip(a)].">
      <j1 rule="hyper" parents="1072 2586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2592">
    <literal><![CDATA[
      R(T(x / (1 / y),z),y \ 1,y) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(996,a,2586,a),flip(a)].">
      <j1 rule="hyper" parents="996 2586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2593">
    <literal><![CDATA[
      R(x / (1 / y),y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(325,a,2586,a),flip(a)].">
      <j1 rule="hyper" parents="325 2586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2594">
    <literal><![CDATA[
      x / y != z * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      R(z,y \ 1,y) = x
    ]]></literal>
    <justification jstring="[para(2586(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="2586 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2595">
    <literal><![CDATA[
      x \ R(y,x \ 1,x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(2586(a,1),107(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2586 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2596">
    <literal><![CDATA[
      (x * (1 / y)) * y != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2586(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2586 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2597">
    <literal><![CDATA[
      R(x,(y \ 1) \ 1,y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),2591(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 2591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2598">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) * x = R(K(y,x),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2269(a,1),2589(a,1,1))].">
      <j1 rule="para" parents="2269 2589"/>
    </justification>
  </clause>

  <clause id="2599">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * R(y / (1 / x),x \ 1,x)) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(2593(a,1),1892(a,1,1,2))].">
      <j1 rule="para" parents="2593 1892"/>
    </justification>
  </clause>

  <clause id="2601">
    <literal><![CDATA[
      (x * (y \ 1)) / (1 / y) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1513,a,2587,a)].">
      <j1 rule="hyper" parents="1513 2587"/>
    </justification>
  </clause>

  <clause id="2602">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y \ 1,y) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(1512,a,2587,a),flip(a)].">
      <j1 rule="hyper" parents="1512 2587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2603">
    <literal><![CDATA[
      K(x \ 1,x) * (y * (1 / x)) = y * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2189,a,2588,a)].">
      <j1 rule="hyper" parents="2189 2588"/>
    </justification>
  </clause>

  <clause id="2604">
    <literal><![CDATA[
      R(x,1 / y,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(834,a,2588,a)].">
      <j1 rule="hyper" parents="834 2588"/>
    </justification>
  </clause>

  <clause id="2605">
    <literal><![CDATA[
      R(x,1 / (1 / y),K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1784(a,1),2604(a,1,3))].">
      <j1 rule="para" parents="1784 2604"/>
    </justification>
  </clause>

  <clause id="2606">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / y = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1812,a(flip),b,2605,a)].">
      <j1 rule="hyper" parents="58 1812 2605"/>
    </justification>
  </clause>

  <clause id="2607">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * K(y,y \ 1) = x * y
    ]]></literal>
    <justification jstring="[para(2605(a,1),1810(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2605 1810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2608">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * (1 / y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,2601,a)].">
      <j1 rule="hyper" parents="133 2601"/>
    </justification>
  </clause>

  <clause id="2609">
    <literal><![CDATA[
      R(x * K(y \ 1,y),y \ 1,y) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[para(2601(a,1),2593(a,1,1))].">
      <j1 rule="para" parents="2601 2593"/>
    </justification>
  </clause>

  <clause id="2610">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (x \ 1)) = y / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(2189,a,2602,a)].">
      <j1 rule="hyper" parents="2189 2602"/>
    </justification>
  </clause>

  <clause id="2612">
    <literal><![CDATA[
      (x / y) * K(y,y \ 1) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,2025,a(flip),b,2606,a)].">
      <j1 rule="hyper" parents="58 2025 2606"/>
    </justification>
  </clause>

  <clause id="2613">
    <literal><![CDATA[
      x * K(y,y \ 1) != z * y
    ]]></literal>
    <literal><![CDATA[
      z * (1 / (1 / y)) = x
    ]]></literal>
    <justification jstring="[para(2607(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="2607 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2614">
    <literal><![CDATA[
      K(x,x \ 1) * (y / x) = y / (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(2171,a,2612,a)].">
      <j1 rule="hyper" parents="2171 2612"/>
    </justification>
  </clause>

  <clause id="2615">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (x / y)))) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,2401,a(flip),b,2612,a)].">
      <j1 rule="hyper" parents="58 2401 2612"/>
    </justification>
  </clause>

  <clause id="2616">
    <literal><![CDATA[
      1 / (1 / (x \ (x / y))) = x \ (x / (1 / (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(116,a,2612,a(flip),b,2401,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 2612 2401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2617">
    <literal><![CDATA[
      K(x,1 / x) * (y / x) = y / (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(1780(a,2),2614(a,1,1))].">
      <j1 rule="para" parents="1780 2614"/>
    </justification>
  </clause>

  <clause id="2618">
    <literal><![CDATA[
      T(x * y,x \ (1 / y)) = R(((x / (1 / y)) \ 1) \ 1,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2388(a,1),2592(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2388 2592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2619">
    <literal><![CDATA[
      x / (1 / (1 / (y \ x))) = x * (1 / (1 / (x \ y)))
    ]]></literal>
    <justification jstring="[para(72(a,1),2615(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="72 2615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2620">
    <literal><![CDATA[
      (x / (1 / (1 / y))) / x = 1 / (1 / ((x / y) / x))
    ]]></literal>
    <justification jstring="[para(2615(a,1),2218(a,1,1))].">
      <j1 rule="para" parents="2615 2218"/>
    </justification>
  </clause>

  <clause id="2621">
    <literal><![CDATA[
      (x \ (x / (1 / (1 / y)))) \ 1 = 1 / (x \ (x / y))
    ]]></literal>
    <justification jstring="[hyper(188,a,2616,a)].">
      <j1 rule="hyper" parents="188 2616"/>
    </justification>
  </clause>

  <clause id="2622">
    <literal><![CDATA[
      1 / (1 / (x \ (x / (y \ 1)))) = x \ (x / (1 / y))
    ]]></literal>
    <justification jstring="[para(72(a,1),2616(a,2,2,2,2))].">
      <j1 rule="para" parents="72 2616"/>
    </justification>
  </clause>

  <clause id="2623">
    <literal><![CDATA[
      (x * (1 / (1 / (x \ y)))) \ x = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(188,a,2619,a)].">
      <j1 rule="hyper" parents="188 2619"/>
    </justification>
  </clause>

  <clause id="2624">
    <literal><![CDATA[
      x / (1 / (1 / ((x * y) \ x))) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(4(a,1),2619(a,2,2,2,2))].">
      <j1 rule="para" parents="4 2619"/>
    </justification>
  </clause>

  <clause id="2625">
    <literal><![CDATA[
      1 / (1 / ((x / (y \ 1)) / x)) = (x / (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(72(a,1),2620(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 2620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2626">
    <literal><![CDATA[
      1 / (x \ (x / (y \ 1))) = (x \ (x / (1 / y))) \ 1
    ]]></literal>
    <justification jstring="[para(72(a,1),2621(a,1,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="72 2621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2627">
    <literal><![CDATA[
      1 / (x \ (x / ((y \ 1) \ 1))) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[para(190(a,1),2621(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="190 2621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2628">
    <literal><![CDATA[
      (x * (1 / (1 / T(y,x)))) \ x = 1 / (1 / ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(17(a,2),2623(a,1,1,2,2,2))].">
      <j1 rule="para" parents="17 2623"/>
    </justification>
  </clause>

  <clause id="2629">
    <literal><![CDATA[
      1 / ((x / (y \ 1)) / x) = ((x / (1 / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(188,a,2625,a),flip(a)].">
      <j1 rule="hyper" parents="188 2625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2630">
    <literal><![CDATA[
      T(x \ (x / (1 / y)),1 / y) = x \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(31,a,2381,a,b,2626,a)].">
      <j1 rule="hyper" parents="31 2381 2626"/>
    </justification>
  </clause>

  <clause id="2631">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ 1 = x \ (x / ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(188,a,2627,a)].">
      <j1 rule="hyper" parents="188 2627"/>
    </justification>
  </clause>

  <clause id="2632">
    <literal><![CDATA[
      T(x \ (x / y),y) = x \ (x / ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(31,a,2381,a,b,2627,a)].">
      <j1 rule="hyper" parents="31 2381 2627"/>
    </justification>
  </clause>

  <clause id="2633">
    <literal><![CDATA[
      x * (((x \ (x / y)) \ 1) \ 1) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2627(a,1),195(a,1,2,1))].">
      <j1 rule="para" parents="2627 195"/>
    </justification>
  </clause>

  <clause id="2634">
    <literal><![CDATA[
      x * T(x \ (x / y),y) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,2632,a,b,xx)].">
      <j1 rule="hyper" parents="119 2632"/>
    </justification>
  </clause>

  <clause id="2635">
    <literal><![CDATA[
      x * (y \ (y / ((x \ 1) \ 1))) = (y \ (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,2632,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2632 17"/>
    </justification>
  </clause>

  <clause id="2636">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2227,a,2634,a)].">
      <j1 rule="hyper" parents="2227 2634"/>
    </justification>
  </clause>

  <clause id="2637">
    <literal><![CDATA[
      (x * y) / ((y \ 1) \ 1) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),2636(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 2636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2638">
    <literal><![CDATA[
      (x / ((y \ 1) \ 1)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2636(a,1),1597(a,1,1))].">
      <j1 rule="para" parents="2636 1597"/>
    </justification>
  </clause>

  <clause id="2639">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * ((y \ 1) \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(133,a,2637,a)].">
      <j1 rule="hyper" parents="133 2637"/>
    </justification>
  </clause>

  <clause id="2640">
    <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(2150(a,2),2637(a,1,2))].">
      <j1 rule="para" parents="2150 2637"/>
    </justification>
  </clause>

  <clause id="2641">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),2638(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 2638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2642">
    <literal><![CDATA[
      (x / T(y,y \ 1)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(106(a,2),2638(a,1,1,2))].">
      <j1 rule="para" parents="106 2638"/>
    </justification>
  </clause>

  <clause id="2643">
    <literal><![CDATA[
      (x * T(y,y \ 1)) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[para(660(a,1),2638(a,1,1)),flip(a)].">
      <j1 rule="para" parents="660 2638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2644">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * ((x \ 1) \ 1) = y * x
    ]]></literal>
    <justification jstring="[para(2180(a,2),2639(a,1,1))].">
      <j1 rule="para" parents="2180 2639"/>
    </justification>
  </clause>

  <clause id="2645">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ 1) = (x * (1 / y)) * y
    ]]></literal>
    <justification jstring="[para(2588(a,1),2639(a,1,1))].">
      <j1 rule="para" parents="2588 2639"/>
    </justification>
  </clause>

  <clause id="2646">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ 1) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,520,a,b,2641,a),flip(a)].">
      <j1 rule="hyper" parents="30 520 2641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2647">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T(x,x \ 1)) = y * x
    ]]></literal>
    <justification jstring="[hyper(2189,a,2643,a)].">
      <j1 rule="hyper" parents="2189 2643"/>
    </justification>
  </clause>

  <clause id="2648">
    <literal><![CDATA[
      K(x \ 1,x) \ (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,2643,a(flip),b,2180,a)].">
      <j1 rule="hyper" parents="116 2643 2180"/>
    </justification>
  </clause>

  <clause id="2649">
    <literal><![CDATA[
      x * K(y \ 1,y) != z * y
    ]]></literal>
    <literal><![CDATA[
      z * T(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[para(2643(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="2643 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2650">
    <literal><![CDATA[
      x * ((y \ 1) \ 1) != z * y
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,y) * z = x
    ]]></literal>
    <justification jstring="[para(2644(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="2644 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2651">
    <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(2648(a,1),2526(a,1,2,1))].">
      <j1 rule="para" parents="2648 2526"/>
    </justification>
  </clause>

  <clause id="2652">
    <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(2648(a,1),2527(a,1,2,1))].">
      <j1 rule="para" parents="2648 2527"/>
    </justification>
  </clause>

  <clause id="2653">
    <literal><![CDATA[
      R(x,y \ 1,(y \ 1) \ 1) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(521,a,2646,a)].">
      <j1 rule="hyper" parents="521 2646"/>
    </justification>
  </clause>

  <clause id="2654">
    <literal><![CDATA[
      T(x * ((y \ 1) \ 1),y \ 1) = R((y \ 1) \ x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,783,a(flip),b,2646,a)].">
      <j1 rule="hyper" parents="58 783 2646"/>
    </justification>
  </clause>

  <clause id="2655">
    <literal><![CDATA[
      x \ R(x,y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ 1,(y \ 1) \ 1) = z
    ]]></literal>
    <justification jstring="[para(2646(a,1),790(a,1,2))].">
      <j1 rule="para" parents="2646 790"/>
    </justification>
  </clause>

  <clause id="2656">
    <literal><![CDATA[
      x / (((y \ x) \ 1) \ 1) = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),2633(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 2633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2657">
    <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(1219(a,1),2609(a,2,1))].">
      <j1 rule="para" parents="1219 2609"/>
    </justification>
  </clause>

  <clause id="2658">
    <literal><![CDATA[
      K(1 / ((x * y) \ x),(x * y) \ x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,1 / y) = z
    ]]></literal>
    <justification jstring="[para(2571(a,2),2364(a,1))].">
      <j1 rule="para" parents="2571 2364"/>
    </justification>
  </clause>

  <clause id="2659">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(2363(a,1),2573(a,1,2))].">
      <j1 rule="para" parents="2363 2573"/>
    </justification>
  </clause>

  <clause id="2660">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2356(a,1),2659(a,2,2))].">
      <j1 rule="para" parents="2356 2659"/>
    </justification>
  </clause>

  <clause id="2661">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(2357(a,1),2659(a,2,2))].">
      <j1 rule="para" parents="2357 2659"/>
    </justification>
  </clause>

  <clause id="2663">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2171,a,2660,a)].">
      <j1 rule="hyper" parents="2171 2660"/>
    </justification>
  </clause>

  <clause id="2664">
    <literal><![CDATA[
      (x * y) * K(T(x,y),T(x,y) \ 1) = y * ((T(x,y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(569,a,2660,a)].">
      <j1 rule="hyper" parents="569 2660"/>
    </justification>
  </clause>

  <clause id="2665">
    <literal><![CDATA[
      (x / y) * ((y \ 1) \ 1) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(326,a,2660,a),flip(a)].">
      <j1 rule="hyper" parents="326 2660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2666">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2022,a,b,2660,a)].">
      <j1 rule="hyper" parents="58 2022 2660"/>
    </justification>
  </clause>

  <clause id="2668">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2171,a,2661,a)].">
      <j1 rule="hyper" parents="2171 2661"/>
    </justification>
  </clause>

  <clause id="2669">
    <literal><![CDATA[
      (x / y) * T(y,y \ 1) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(326,a,2661,a),flip(a)].">
      <j1 rule="hyper" parents="326 2661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2670">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (x * T(y,y \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,2661,a(flip),b,2022,a)].">
      <j1 rule="hyper" parents="116 2661 2022"/>
    </justification>
  </clause>

  <clause id="2671">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2443,a,2663,a)].">
      <j1 rule="hyper" parents="2443 2663"/>
    </justification>
  </clause>

  <clause id="2672">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x,x \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,2219,a(flip),b,2666,a),flip(a)].">
      <j1 rule="hyper" parents="117 2219 2666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2673">
    <literal><![CDATA[
      (x / T(y,y \ 1)) * K(y,y \ 1) = x / y
    ]]></literal>
    <justification jstring="[hyper(117,a,369,a(flip),b,2666,a),flip(a)].">
      <j1 rule="hyper" parents="117 369 2666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2674">
    <literal><![CDATA[
      (x * (y \ 1)) * K(y,y \ 1) = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(30,a,2645,a(flip),b,2666,a),flip(a)].">
      <j1 rule="hyper" parents="30 2645 2666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2675">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(30,a,2644,a(flip),b,2666,a),flip(a)].">
      <j1 rule="hyper" parents="30 2644 2666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2676">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * K(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(30,a,2639,a(flip),b,2666,a),flip(a)].">
      <j1 rule="hyper" parents="30 2639 2666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2677">
    <literal><![CDATA[
      K(x \ 1,x) * (y * K(x,x \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(2650,a,2666,a(flip))].">
      <j1 rule="hyper" parents="2650 2666"/>
    </justification>
  </clause>

  <clause id="2678">
    <literal><![CDATA[
      K(x,x \ 1) * (K(x \ 1,x) * y) = y
    ]]></literal>
    <justification jstring="[hyper(2171,a,2675,a)].">
      <j1 rule="hyper" parents="2171 2675"/>
    </justification>
  </clause>

  <clause id="2679">
    <literal><![CDATA[
      K(x \ 1,x) * (K(x,x \ 1) * y) = y
    ]]></literal>
    <justification jstring="[hyper(30,a,2169,a(flip),b,2675,a),flip(a)].">
      <j1 rule="hyper" parents="30 2169 2675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2680">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (x * y)) = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,2051,a(flip),b,2675,a),flip(a)].">
      <j1 rule="hyper" parents="30 2051 2675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2681">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * K(x,x \ 1) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(484(a,1),2675(a,1,1))].">
      <j1 rule="para" parents="484 2675"/>
    </justification>
  </clause>

  <clause id="2682">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) * z = y
    ]]></literal>
    <justification jstring="[para(2675(a,1),2176(a,2)),flip(b)].">
      <j1 rule="para" parents="2675 2176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2683">
    <literal><![CDATA[
      (x / (1 / y)) * K(y,y \ 1) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(2610(a,1),2675(a,1,1))].">
      <j1 rule="para" parents="2610 2675"/>
    </justification>
  </clause>

  <clause id="2684">
    <literal><![CDATA[
      (x * y) * K(y \ 1,y) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(2613,a,2676,a),flip(a)].">
      <j1 rule="hyper" parents="2613 2676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2685">
    <literal><![CDATA[
      K(x,x \ 1) * (y * K(x \ 1,x)) = y
    ]]></literal>
    <justification jstring="[hyper(2171,a,2676,a)].">
      <j1 rule="hyper" parents="2171 2676"/>
    </justification>
  </clause>

  <clause id="2686">
    <literal><![CDATA[
      x / K(y \ 1,y) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(326,a,2676,a),flip(a)].">
      <j1 rule="hyper" parents="326 2676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2687">
    <literal><![CDATA[
      (x / (1 / (1 / y))) * K(y \ 1,y) = x / y
    ]]></literal>
    <justification jstring="[hyper(30,a,2612,a,b,2676,a),flip(a)].">
      <j1 rule="hyper" parents="30 2612 2676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2688">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[hyper(30,a,2169,a(flip),b,2676,a),flip(a)].">
      <j1 rule="hyper" parents="30 2169 2676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2689">
    <literal><![CDATA[
      K(x,x \ 1) \ y = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,2676,a(flip),b,2169,a)].">
      <j1 rule="hyper" parents="116 2676 2169"/>
    </justification>
  </clause>

  <clause id="2690">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      z * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(2676(a,1),2176(a,2)),flip(b)].">
      <j1 rule="para" parents="2676 2176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2691">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      z * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(2677(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="2677 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2692">
    <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(2677(a,1),92(a,2,1))].">
      <j1 rule="para" parents="2677 92"/>
    </justification>
  </clause>

  <clause id="2693">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z * K(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[para(2677(a,1),2183(a,1)),flip(a)].">
      <j1 rule="para" parents="2677 2183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2694">
    <literal><![CDATA[
      K(x \ 1,x) \ y = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(342,a,2678,a),flip(a)].">
      <j1 rule="hyper" parents="342 2678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2695">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) * y) = L(x \ y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1055(a,1),2678(a,1,2))].">
      <j1 rule="para" parents="1055 2678"/>
    </justification>
  </clause>

  <clause id="2696">
    <literal><![CDATA[
      K(x,x \ 1) * (y / (1 / x)) = y / (x \ 1)
    ]]></literal>
    <justification jstring="[para(2610(a,1),2678(a,1,2))].">
      <j1 rule="para" parents="2610 2678"/>
    </justification>
  </clause>

  <clause id="2697">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * z = y
    ]]></literal>
    <justification jstring="[para(2679(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="2679 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2698">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,y \ 1) * z = x
    ]]></literal>
    <justification jstring="[para(2679(a,1),2183(a,1)),flip(a)].">
      <j1 rule="para" parents="2679 2183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2699">
    <literal><![CDATA[
      (x / (y \ 1)) * (1 / y) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2585,a,b,2686,a)].">
      <j1 rule="hyper" parents="58 2585 2686"/>
    </justification>
  </clause>

  <clause id="2700">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(2686(a,1),251(a,1,1))].">
      <j1 rule="para" parents="2686 251"/>
    </justification>
  </clause>

  <clause id="2701">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * K(y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(2686(a,1),328(a,1))].">
      <j1 rule="para" parents="2686 328"/>
    </justification>
  </clause>

  <clause id="2702">
    <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(2686(a,1),621(a,1,1,1))].">
      <j1 rule="para" parents="2686 621"/>
    </justification>
  </clause>

  <clause id="2703">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[para(2694(a,1),2421(a,1,2,1))].">
      <j1 rule="para" parents="2694 2421"/>
    </justification>
  </clause>

  <clause id="2704">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2443,a,2668,a)].">
      <j1 rule="hyper" parents="2443 2668"/>
    </justification>
  </clause>

  <clause id="2705">
    <literal><![CDATA[
      L(x,K(x,x \ 1),y) = x
    ]]></literal>
    <justification jstring="[hyper(1808,a,2670,a)].">
      <j1 rule="hyper" parents="1808 2670"/>
    </justification>
  </clause>

  <clause id="2706">
    <literal><![CDATA[
      L(1 / x,K(x \ 1,x),y) = 1 / x
    ]]></literal>
    <justification jstring="[para(1815(a,1),2705(a,1,2))].">
      <j1 rule="para" parents="1815 2705"/>
    </justification>
  </clause>

  <clause id="2707">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(30,a,1793,a,b,2674,a),flip(a)].">
      <j1 rule="hyper" parents="30 1793 2674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2708">
    <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(2674(a,1),510(a,1,1))].">
      <j1 rule="para" parents="2674 510"/>
    </justification>
  </clause>

  <clause id="2709">
    <literal><![CDATA[
      R(x,y,1 / y) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(131,a,2707,a)].">
      <j1 rule="hyper" parents="131 2707"/>
    </justification>
  </clause>

  <clause id="2710">
    <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,2707,a)].">
      <j1 rule="hyper" parents="117 22 2707"/>
    </justification>
  </clause>

  <clause id="2711">
    <literal><![CDATA[
      R(x \ y,x,1 / x) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,783,a(flip),b,2707,a),flip(a)].">
      <j1 rule="hyper" parents="58 783 2707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2712">
    <literal><![CDATA[
      R(1 / L(x,y,z),x,1 / x) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1633(a,1),2707(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1633 2707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2713">
    <literal><![CDATA[
      (R(x,y,y \ 1) / (1 / y)) * K(y,y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(320,a,441,a(flip),b,2683,a),flip(a)].">
      <j1 rule="hyper" parents="320 441 2683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2714">
    <literal><![CDATA[
      (x / (1 / (1 / y))) / (1 / y) = (x / y) / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,2687,a(flip),b,2587,a),flip(a)].">
      <j1 rule="hyper" parents="117 2687 2587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2715">
    <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(2154(a,1),2696(a,1,2,2))].">
      <j1 rule="para" parents="2154 2696"/>
    </justification>
  </clause>

  <clause id="2716">
    <literal><![CDATA[
      K(x / (y * x),y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,2068,a,b,2680,a)].">
      <j1 rule="hyper" parents="30 2068 2680"/>
    </justification>
  </clause>

  <clause id="2717">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) = K(y / x,x / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),2716(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 2716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2719">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) = K(y,x / (y * x))
    ]]></literal>
    <justification jstring="[para(6(a,1),2717(a,2,1))].">
      <j1 rule="para" parents="6 2717"/>
    </justification>
  </clause>

  <clause id="2720">
    <literal><![CDATA[
      K(x,T(x,y) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(29,a,2123,a,b,2672,a)].">
      <j1 rule="hyper" parents="29 2123 2672"/>
    </justification>
  </clause>

  <clause id="2721">
    <literal><![CDATA[
      T(K(x,x \ 1),y) = K(x,T(x,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,2166,a,b,2720,a)].">
      <j1 rule="hyper" parents="320 2166 2720"/>
    </justification>
  </clause>

  <clause id="2723">
    <literal><![CDATA[
      K(x,T(x,y) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2721(a,1),177(a,1)),flip(b)].">
      <j1 rule="para" parents="2721 177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2724">
    <literal><![CDATA[
      T(K(T(x,y),1 / x),z) = K(T(x,y),T(T(x,y),u) \ 1)
    ]]></literal>
    <justification jstring="[para(2167(a,1),2721(a,1,1))].">
      <j1 rule="para" parents="2167 2721"/>
    </justification>
  </clause>

  <clause id="2725">
    <literal><![CDATA[
      R(x,y,y \ 1) / (1 / y) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(2613,a,2713,a),flip(a)].">
      <j1 rule="hyper" parents="2613 2713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2726">
    <literal><![CDATA[
      x / (1 / y) != z * (1 / (1 / y))
    ]]></literal>
    <literal><![CDATA[
      R(z,y,y \ 1) = x
    ]]></literal>
    <justification jstring="[para(2725(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="2725 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2727">
    <literal><![CDATA[
      (x * T(1 / (1 / y),x)) \ x = 1 / (1 / ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(2154(a,1),2628(a,1,1,2))].">
      <j1 rule="para" parents="2154 2628"/>
    </justification>
  </clause>

  <clause id="2728">
    <literal><![CDATA[
      T(K(T(x,y),1 / x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = u
    ]]></literal>
    <justification jstring="[para(2724(a,2),2723(a,1))].">
      <j1 rule="para" parents="2724 2723"/>
    </justification>
  </clause>

  <clause id="2729">
    <literal><![CDATA[
      1 / (1 / ((x * y) \ y)) = ((1 / (1 / x)) * y) \ y
    ]]></literal>
    <justification jstring="[para(105(a,1),2727(a,1,1)),flip(a)].">
      <j1 rule="para" parents="105 2727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2730">
    <literal><![CDATA[
      (((1 / (1 / x)) * y) \ y) \ 1 = 1 / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(188,a,2729,a)].">
      <j1 rule="hyper" parents="188 2729"/>
    </justification>
  </clause>

  <clause id="2731">
    <literal><![CDATA[
      1 / (((x \ 1) * y) \ y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(72(a,1),2730(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 2730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2732">
    <literal><![CDATA[
      ((((1 / x) * y) \ y) \ 1) \ 1 = ((x \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(188,a,2731,a)].">
      <j1 rule="hyper" parents="188 2731"/>
    </justification>
  </clause>

  <clause id="2733">
    <literal><![CDATA[
      (((x * y) \ y) \ 1) \ 1 = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[para(72(a,1),2732(a,1,1,1,1,1))].">
      <j1 rule="para" parents="72 2732"/>
    </justification>
  </clause>

  <clause id="2734">
    <literal><![CDATA[
      T((x * y) \ y,x) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,2224,a,b,2733,a)].">
      <j1 rule="hyper" parents="58 2224 2733"/>
    </justification>
  </clause>

  <clause id="2735">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ y = T((x * y) \ y,x)
    ]]></literal>
    <justification jstring="[para(106(a,2),2734(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="106 2734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2736">
    <literal><![CDATA[
      R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(T(x,y) \ x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2219(a,1),2654(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2219 2654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2737">
    <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,644,a,b,2712,a)].">
      <j1 rule="hyper" parents="58 644 2712"/>
    </justification>
  </clause>

  <clause id="2738">
    <literal><![CDATA[
      (x * y) * K(T(x,y),1 / x) = y * ((T(x,y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2167(a,1),2664(a,1,2))].">
      <j1 rule="para" parents="2167 2664"/>
    </justification>
  </clause>

  <clause id="2739">
    <literal><![CDATA[
      (x * y) * K(T(x,y),1 / x) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,2155,a(flip),b,2738,a),flip(a)].">
      <j1 rule="hyper" parents="320 2155 2738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2740">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * (y * x)) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(2593(a,1),2599(a,1,2,2))].">
      <j1 rule="para" parents="2593 2599"/>
    </justification>
  </clause>

  <clause id="2741">
    <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(2669(a,1),2652(a,1,2,1))].">
      <j1 rule="para" parents="2669 2652"/>
    </justification>
  </clause>

  <clause id="2742">
    <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(1815(a,1),2715(a,1,1))].">
      <j1 rule="para" parents="1815 2715"/>
    </justification>
  </clause>

  <clause id="2743">
    <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(1144(a,1),2582(a,2,1))].">
      <j1 rule="para" parents="1144 2582"/>
    </justification>
  </clause>

  <clause id="2744">
    <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(320,a,2405,a(flip),b,2743,a),flip(a)].">
      <j1 rule="hyper" parents="320 2405 2743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2745">
    <literal><![CDATA[
      T(x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)),z) = T(x,z) * ((T(x,z) \ T(x,y)) / T(x,y))
    ]]></literal>
    <justification jstring="[para(1139(a,1),2004(a,2,2,1))].">
      <j1 rule="para" parents="1139 2004"/>
    </justification>
  </clause>

  <clause id="2746">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ T(x,z)) / T(x,z)) = T(K(T(x,z),1 / x),y)
    ]]></literal>
    <justification jstring="[para(1731(a,1),2745(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1731 2745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2747">
    <literal><![CDATA[
      K(T(x,y),1 / T(x,z)) = T(K(T(x,y),1 / x),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,2016,a(flip),b,2746,a)].">
      <j1 rule="hyper" parents="58 2016 2746"/>
    </justification>
  </clause>

  <clause id="2748">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(T(x,y),1 / T(x,z))
    ]]></literal>
    <justification jstring="[hyper(2728,a,2747,a(flip))].">
      <j1 rule="hyper" parents="2728 2747"/>
    </justification>
  </clause>

  <clause id="2749">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(T(x,y),x \ 1)
    ]]></literal>
    <justification jstring="[para(265(a,1),2748(a,2,2))].">
      <j1 rule="para" parents="265 2748"/>
    </justification>
  </clause>

  <clause id="2750">
    <literal><![CDATA[
      K(T(x,y),1 / x) = K(T(x,y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2167,a(flip),b,2749,a)].">
      <j1 rule="hyper" parents="58 2167 2749"/>
    </justification>
  </clause>

  <clause id="2751">
    <literal><![CDATA[
      (x * y) * K(T(x,y),x \ 1) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(2750(a,1),2739(a,1,2))].">
      <j1 rule="para" parents="2750 2739"/>
    </justification>
  </clause>

  <clause id="2752">
    <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(262(a,1),2116(a,2,1))].">
      <j1 rule="para" parents="262 2116"/>
    </justification>
  </clause>

  <clause id="2753">
    <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(1891(a,1),2752(a,2,1))].">
      <j1 rule="para" parents="1891 2752"/>
    </justification>
  </clause>

  <clause id="2754">
    <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(2115,a,2753,a)].">
      <j1 rule="hyper" parents="2115 2753"/>
    </justification>
  </clause>

  <clause id="2755">
    <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),2239(a,1,1))].">
      <j1 rule="para" parents="5 2239"/>
    </justification>
  </clause>

  <clause id="2756">
    <literal><![CDATA[
      K(x \ (((y * x) / y) \ x),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(2209,a,2755,a),flip(a)].">
      <j1 rule="hyper" parents="2209 2755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2759">
    <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(2674(a,1),2708(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2674 2708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2760">
    <literal><![CDATA[
      R(R(x,y,z \ 1),y * (z \ 1),K(z,z \ 1)) = R(x,y,1 / z)
    ]]></literal>
    <justification jstring="[hyper(320,a,15,a,b,2759,a),flip(a)].">
      <j1 rule="hyper" parents="320 15 2759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2761">
    <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(2759(a,2),518(a,1))].">
      <j1 rule="para" parents="2759 518"/>
    </justification>
  </clause>

  <clause id="2762">
    <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),2760(a,1,2,2))].">
      <j1 rule="para" parents="106 2760"/>
    </justification>
  </clause>

  <clause id="2764">
    <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(1787(a,1),2762(a,1,3))].">
      <j1 rule="para" parents="1787 2762"/>
    </justification>
  </clause>

  <clause id="2765">
    <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),2764(a,2,3))].">
      <j1 rule="para" parents="72 2764"/>
    </justification>
  </clause>

  <clause id="2767">
    <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(2439(a,1),1841(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2439 1841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2768">
    <literal><![CDATA[
      x * ((y \ 1) * (y * T(y \ 1,x))) = (1 / y) * (x * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(2706(a,1),2767(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2706 2767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2770">
    <literal><![CDATA[
      (x * R(x \ 1,x,y)) \ (x * (y / (x * y))) = K(T(x,R(x \ 1,x,y)),R(x \ 1,x,y))
    ]]></literal>
    <justification jstring="[para(1957(a,1),2441(a,1,2))].">
      <j1 rule="para" parents="1957 2441"/>
    </justification>
  </clause>

  <clause id="2771">
    <literal><![CDATA[
      K(T(x,R(x \ 1,x,y)),R(x \ 1,x,y)) = K(x,y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(786,a,2770,a),flip(a)].">
      <j1 rule="hyper" parents="786 2770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2772">
    <literal><![CDATA[
      x \ T(x,y / (x * y)) = K(x,y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,2498,a(flip),b,2771,a)].">
      <j1 rule="hyper" parents="58 2498 2771"/>
    </justification>
  </clause>

  <clause id="2773">
    <literal><![CDATA[
      K(x,y / (x * y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2058,a,2772,a),flip(a)].">
      <j1 rule="hyper" parents="2058 2772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2774">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2719,a,b,2773,a)].">
      <j1 rule="hyper" parents="58 2719 2773"/>
    </justification>
  </clause>

  <clause id="2775">
    <literal><![CDATA[
      K(x / y,(x / y) \ 1) = K(x / y,y / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),2773(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 2773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2777">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(2774(a,1),2056(a,1,1))].">
      <j1 rule="para" parents="2774 2056"/>
    </justification>
  </clause>

  <clause id="2778">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(2177,a,2777,a)].">
      <j1 rule="hyper" parents="2177 2777"/>
    </justification>
  </clause>

  <clause id="2779">
    <literal><![CDATA[
      T(x,x \ 1) \ (K(x,x \ 1) * y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(598,a,2777,a)].">
      <j1 rule="hyper" parents="598 2777"/>
    </justification>
  </clause>

  <clause id="2780">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,314,a(flip),b,2777,a),flip(a)].">
      <j1 rule="hyper" parents="320 314 2777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2781">
    <literal><![CDATA[
      x * (((x \ 1) \ 1) \ y) = K(x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,309,a(flip),b,2777,a),flip(a)].">
      <j1 rule="hyper" parents="116 309 2777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2782">
    <literal><![CDATA[
      x * (K(x,x \ 1) * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1849,a(flip),b,2777,a)].">
      <j1 rule="hyper" parents="58 1849 2777"/>
    </justification>
  </clause>

  <clause id="2783">
    <literal><![CDATA[
      L(x,y,K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(1807,a,2777,a(flip))].">
      <j1 rule="hyper" parents="1807 2777"/>
    </justification>
  </clause>

  <clause id="2785">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,2549,a(flip),b,2783,a)].">
      <j1 rule="hyper" parents="58 2549 2783"/>
    </justification>
  </clause>

  <clause id="2786">
    <literal><![CDATA[
      L(x,K(y,y \ 1),1 / (1 / y)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,1909,a(flip),b,2783,a)].">
      <j1 rule="hyper" parents="58 1909 2783"/>
    </justification>
  </clause>

  <clause id="2787">
    <literal><![CDATA[
      L(x,K(y \ 1,y),1 / y) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,1857,a(flip),b,2783,a)].">
      <j1 rule="hyper" parents="58 1857 2783"/>
    </justification>
  </clause>

  <clause id="2788">
    <literal><![CDATA[
      L(x,1 / y,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(1815(a,1),2783(a,1,3))].">
      <j1 rule="para" parents="1815 2783"/>
    </justification>
  </clause>

  <clause id="2790">
    <literal><![CDATA[
      (1 / x) * (K(x \ 1,x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,2787,a(flip),b,777,a),flip(a)].">
      <j1 rule="hyper" parents="119 2787 777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2791">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(2788(a,1),1798(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2788 1798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2792">
    <literal><![CDATA[
      L(x \ y,x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(2788(a,1),1937(a,1,1,2))].">
      <j1 rule="para" parents="2788 1937"/>
    </justification>
  </clause>

  <clause id="2794">
    <literal><![CDATA[
      (1 / (1 / x)) * (K(x,x \ 1) * y) = x * y
    ]]></literal>
    <justification jstring="[para(2786(a,1),1811(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2786 1811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2795">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,(x \ 1) \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(320,a,183,a(flip),b,2792,a),flip(a)].">
      <j1 rule="hyper" parents="320 183 2792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2796">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,2695,a,b,2792,a)].">
      <j1 rule="hyper" parents="58 2695 2792"/>
    </justification>
  </clause>

  <clause id="2797">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),2792(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2798">
    <literal><![CDATA[
      L(T(x,y),y,y \ 1) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[para(17(a,2),2792(a,1,1))].">
      <j1 rule="para" parents="17 2792"/>
    </justification>
  </clause>

  <clause id="2799">
    <literal><![CDATA[
      L(T(x \ y,z),x,x \ 1) = T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(2792(a,1),20(a,2,1))].">
      <j1 rule="para" parents="2792 20"/>
    </justification>
  </clause>

  <clause id="2800">
    <literal><![CDATA[
      L(L(x \ y,z,u),x,x \ 1) = L((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(2792(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2792 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2801">
    <literal><![CDATA[
      x * ((1 / x) * (y * x)) = L(y,x,x \ 1) * x
    ]]></literal>
    <justification jstring="[para(2792(a,1),633(a,1,2))].">
      <j1 rule="para" parents="2792 633"/>
    </justification>
  </clause>

  <clause id="2802">
    <literal><![CDATA[
      L(x,y,y \ 1) / (y * x) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(131,a,2797,a)].">
      <j1 rule="hyper" parents="131 2797"/>
    </justification>
  </clause>

  <clause id="2803">
    <literal><![CDATA[
      (1 / x) \ L(y,x,x \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(123,a,2797,a)].">
      <j1 rule="hyper" parents="123 2797"/>
    </justification>
  </clause>

  <clause id="2804">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x = a(1 / y,y,x)
    ]]></literal>
    <justification jstring="[para(2797(a,1),218(a,1,1))].">
      <j1 rule="para" parents="2797 218"/>
    </justification>
  </clause>

  <clause id="2805">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = L(K(x,y),y * x,1 / y)
    ]]></literal>
    <justification jstring="[para(2797(a,1),304(a,1,1))].">
      <j1 rule="para" parents="2797 304"/>
    </justification>
  </clause>

  <clause id="2806">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = ((y \ 1) * (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(2797(a,1),2732(a,1,1,1,1))].">
      <j1 rule="para" parents="2797 2732"/>
    </justification>
  </clause>

  <clause id="2807">
    <literal><![CDATA[
      (1 / x) * (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2802(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2802 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2808">
    <literal><![CDATA[
      (1 / (1 / x)) \ L(y,1 / x,x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),2803(a,1,2,3))].">
      <j1 rule="para" parents="75 2803"/>
    </justification>
  </clause>

  <clause id="2809">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,314,a(flip),b,2778,a),flip(a)].">
      <j1 rule="hyper" parents="320 314 2778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2810">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (x \ y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(659,a,2779,a)].">
      <j1 rule="hyper" parents="659 2779"/>
    </justification>
  </clause>

  <clause id="2812">
    <literal><![CDATA[
      K(x \ 1,x) * (((x \ 1) \ 1) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(2682,a,2780,a)].">
      <j1 rule="hyper" parents="2682 2780"/>
    </justification>
  </clause>

  <clause id="2813">
    <literal><![CDATA[
      x * (((x \ 1) \ 1) \ y) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,2689,a(flip),b,2781,a),flip(a)].">
      <j1 rule="hyper" parents="320 2689 2781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2814">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ ((K(x,x \ 1) * y) * x) = K(K(x,x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(2782(a,1),11(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2782 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2815">
    <literal><![CDATA[
      T(x,x \ 1) * (K(x \ 1,x) * y) = x * y
    ]]></literal>
    <justification jstring="[para(2678(a,1),2782(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2678 2782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2816">
    <literal><![CDATA[
      (x \ y) * K(x \ 1,x) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(2690,a,2785,a)].">
      <j1 rule="hyper" parents="2690 2785"/>
    </justification>
  </clause>

  <clause id="2817">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(2682,a,2785,a)].">
      <j1 rule="hyper" parents="2682 2785"/>
    </justification>
  </clause>

  <clause id="2818">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * K(x,x \ 1) = x \ y
    ]]></literal>
    <justification jstring="[hyper(2177,a,2785,a)].">
      <j1 rule="hyper" parents="2177 2785"/>
    </justification>
  </clause>

  <clause id="2820">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(2785(a,1),2671(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2785 2671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2821">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,2790,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 2790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2822">
    <literal><![CDATA[
      (1 / x) * (y * K(x \ 1,x)) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,2203,a(flip),b,2790,a)].">
      <j1 rule="hyper" parents="58 2203 2790"/>
    </justification>
  </clause>

  <clause id="2823">
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = (x \ 1) * (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(2610(a,1),2790(a,1,2))].">
      <j1 rule="para" parents="2610 2790"/>
    </justification>
  </clause>

  <clause id="2824">
    <literal><![CDATA[
      (x \ 1) * (K(x,x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(2679(a,1),2790(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2679 2790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2825">
    <literal><![CDATA[
      ((x \ 1) * y) * K(x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(2691,a,2791,a)].">
      <j1 rule="hyper" parents="2691 2791"/>
    </justification>
  </clause>

  <clause id="2826">
    <literal><![CDATA[
      ((1 / x) * y) * K(x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(2184,a,2791,a)].">
      <j1 rule="hyper" parents="2184 2791"/>
    </justification>
  </clause>

  <clause id="2827">
    <literal><![CDATA[
      (x \ 1) * ((1 / x) \ y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(342,a,2791,a),flip(a)].">
      <j1 rule="hyper" parents="342 2791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2828">
    <literal><![CDATA[
      K(x \ 1,x) * y != (x \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * z = y
    ]]></literal>
    <justification jstring="[para(2791(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="2791 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2829">
    <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(2791(a,1),92(a,2,1))].">
      <j1 rule="para" parents="2791 92"/>
    </justification>
  </clause>

  <clause id="2830">
    <literal><![CDATA[
      ((x \ 1) * y) / L(T(1 / x,y),y,K(x \ 1,x)) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(2791(a,1),545(a,1,1))].">
      <j1 rule="para" parents="2791 545"/>
    </justification>
  </clause>

  <clause id="2831">
    <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(2791(a,1),477(a,1,1))].">
      <j1 rule="para" parents="2791 477"/>
    </justification>
  </clause>

  <clause id="2832">
    <literal><![CDATA[
      T(x,(1 / x) * y) = T(x,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(2791(a,1),2453(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2791 2453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2833">
    <literal><![CDATA[
      ((x \ 1) * y) * ((x \ 1) \ 1) = ((1 / x) * y) * x
    ]]></literal>
    <justification jstring="[para(2791(a,1),2644(a,1,1))].">
      <j1 rule="para" parents="2791 2644"/>
    </justification>
  </clause>

  <clause id="2834">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / (1 / x)) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(1453,a,2794,a),flip(a)].">
      <j1 rule="hyper" parents="1453 2794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2835">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,2794,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 2794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2836">
    <literal><![CDATA[
      (1 / (1 / x)) * (y / (1 / (1 / x))) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(2614(a,1),2794(a,1,2))].">
      <j1 rule="para" parents="2614 2794"/>
    </justification>
  </clause>

  <clause id="2837">
    <literal><![CDATA[
      x * (K(x \ 1,x) * y) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(2678(a,1),2794(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2678 2794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2838">
    <literal><![CDATA[
      x \ L(y,1 / x,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(1853,a,2796,a)].">
      <j1 rule="hyper" parents="1853 2796"/>
    </justification>
  </clause>

  <clause id="2839">
    <literal><![CDATA[
      L(x,1 / y,y) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(838,a,2838,a)].">
      <j1 rule="hyper" parents="838 2838"/>
    </justification>
  </clause>

  <clause id="2840">
    <literal><![CDATA[
      (x \ 1) \ L(y,x,x \ 1) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(72(a,1),2838(a,1,2,2))].">
      <j1 rule="para" parents="72 2838"/>
    </justification>
  </clause>

  <clause id="2841">
    <literal><![CDATA[
      L(x,(y \ 1) \ 1,y \ 1) = L(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),2839(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 2839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2842">
    <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(312(a,2),2839(a,1,2)),flip(a)].">
      <j1 rule="para" parents="312 2839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2843">
    <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(2839(a,1),2101(a,1))].">
      <j1 rule="para" parents="2839 2101"/>
    </justification>
  </clause>

  <clause id="2844">
    <literal><![CDATA[
      x * (y * K(x,x \ 1)) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,2433,a(flip),b,2809,a)].">
      <j1 rule="hyper" parents="58 2433 2809"/>
    </justification>
  </clause>

  <clause id="2845">
    <literal><![CDATA[
      K(T(x,y),x \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(29,a,2751,a,b,2809,a)].">
      <j1 rule="hyper" parents="29 2751 2809"/>
    </justification>
  </clause>

  <clause id="2848">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2749,a,b,2845,a)].">
      <j1 rule="hyper" parents="58 2749 2845"/>
    </justification>
  </clause>

  <clause id="2852">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,2848,a(flip),b,1783,a(flip))].">
      <j1 rule="hyper" parents="116 2848 1783"/>
    </justification>
  </clause>

  <clause id="2855">
    <literal><![CDATA[
      x * (T(x,y) \ (1 / x)) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1794,a,2852,a)].">
      <j1 rule="hyper" parents="1794 2852"/>
    </justification>
  </clause>

  <clause id="2856">
    <literal><![CDATA[
      (T(x,y) \ x) / x = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2170,a(flip),b,2852,a)].">
      <j1 rule="hyper" parents="58 2170 2852"/>
    </justification>
  </clause>

  <clause id="2857">
    <literal><![CDATA[
      (1 / T(x,y)) * x = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(133,a,2856,a)].">
      <j1 rule="hyper" parents="133 2856"/>
    </justification>
  </clause>

  <clause id="2858">
    <literal><![CDATA[
      x / T(x,y) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(32,a,1467,a,b,2856,a)].">
      <j1 rule="hyper" parents="32 1467 2856"/>
    </justification>
  </clause>

  <clause id="2859">
    <literal><![CDATA[
      T(1 / T(x,y),x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(2856(a,1),1115(a,1,1))].">
      <j1 rule="para" parents="2856 1115"/>
    </justification>
  </clause>

  <clause id="2860">
    <literal><![CDATA[
      (T(x,y) \ x) \ x = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(188,a,2858,a)].">
      <j1 rule="hyper" parents="188 2858"/>
    </justification>
  </clause>

  <clause id="2861">
    <literal><![CDATA[
      (T(x,y) \ x) * T(x,y) = x
    ]]></literal>
    <justification jstring="[hyper(133,a,2858,a)].">
      <j1 rule="hyper" parents="133 2858"/>
    </justification>
  </clause>

  <clause id="2862">
    <literal><![CDATA[
      K(x \ (x / ((y \ x) / T(x,y))),x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,1963,a,b,2858,a)].">
      <j1 rule="hyper" parents="58 1963 2858"/>
    </justification>
  </clause>

  <clause id="2863">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,2314,a,b,2861,a)].">
      <j1 rule="hyper" parents="58 2314 2861"/>
    </justification>
  </clause>

  <clause id="2865">
    <literal><![CDATA[
      (x * y) * T(K(y,x),x) = y * x
    ]]></literal>
    <justification jstring="[para(2863(a,1),2313(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2863 2313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2866">
    <literal><![CDATA[
      K(x \ 1,x) / T(x,y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2190,a,b,2859,a)].">
      <j1 rule="hyper" parents="58 2190 2859"/>
    </justification>
  </clause>

  <clause id="2867">
    <literal><![CDATA[
      T(K(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(306,a,2865,a),flip(a)].">
      <j1 rule="hyper" parents="306 2865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2868">
    <literal><![CDATA[
      (x * K(y,x)) / x = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(271,a,2867,a)].">
      <j1 rule="hyper" parents="271 2867"/>
    </justification>
  </clause>

  <clause id="2869">
    <literal><![CDATA[
      T(x,K(y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,2867,a)].">
      <j1 rule="hyper" parents="49 2867"/>
    </justification>
  </clause>

  <clause id="2870">
    <literal><![CDATA[
      K(x,y) * y = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,2867,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 2867 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2871">
    <literal><![CDATA[
      T(L(K(x,y),z,u),y) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2867(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2867 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2872">
    <literal><![CDATA[
      (x * K(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2867(a,1),331(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="2867 331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2873">
    <literal><![CDATA[
      T(x,K(y,R(x,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(143,a,2869,a)].">
      <j1 rule="hyper" parents="143 2869"/>
    </justification>
  </clause>

  <clause id="2874">
    <literal><![CDATA[
      T(x,K(y,T(x,z))) = x
    ]]></literal>
    <justification jstring="[hyper(138,a,2869,a)].">
      <j1 rule="hyper" parents="138 2869"/>
    </justification>
  </clause>

  <clause id="2875">
    <literal><![CDATA[
      T(T(x,y),K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2869(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2869 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2876">
    <literal><![CDATA[
      T(x,y) * K(z,x) = K(z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(2869(a,1),236(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2869 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2877">
    <literal><![CDATA[
      L(x,y,z) * K(u,x) = K(u,x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2869(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2869 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2878">
    <literal><![CDATA[
      R(x,y,z) * K(u,x) = K(u,x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2869(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2869 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2879">
    <literal><![CDATA[
      K(x,y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2869(a,1),418(a,1,2,1))].">
      <j1 rule="para" parents="2869 418"/>
    </justification>
  </clause>

  <clause id="2880">
    <literal><![CDATA[
      L(x \ y,x,K(z,y)) = (K(z,y) * x) \ (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(2869(a,1),450(a,1,1,2))].">
      <j1 rule="para" parents="2869 450"/>
    </justification>
  </clause>

  <clause id="2881">
    <literal><![CDATA[
      T(T(x,y),z) * K(u,x) = K(u,x) * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(2869(a,1),452(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2869 452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2882">
    <literal><![CDATA[
      T(x,y * T(y \ 1,x)) = x
    ]]></literal>
    <justification jstring="[para(1017(a,1),2869(a,1,2))].">
      <j1 rule="para" parents="1017 2869"/>
    </justification>
  </clause>

  <clause id="2883">
    <literal><![CDATA[
      T(x,y \ T(y,x)) = x
    ]]></literal>
    <justification jstring="[para(1020(a,1),2869(a,1,2))].">
      <j1 rule="para" parents="1020 2869"/>
    </justification>
  </clause>

  <clause id="2884">
    <literal><![CDATA[
      T(x,x \ ((y * x) / y)) = x
    ]]></literal>
    <justification jstring="[para(1497(a,1),2869(a,1,2))].">
      <j1 rule="para" parents="1497 2869"/>
    </justification>
  </clause>

  <clause id="2885">
    <literal><![CDATA[
      x * ((K(x,y) \ y) * K(x,y)) = (y * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(2869(a,1),2469(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2869 2469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2886">
    <literal><![CDATA[
      K(x,T(y,z)) * y = y * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,2874,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2874 17"/>
    </justification>
  </clause>

  <clause id="2887">
    <literal><![CDATA[
      T(x / y,K(z,y \ x)) = x / y
    ]]></literal>
    <justification jstring="[para(107(a,1),2874(a,1,2,2))].">
      <j1 rule="para" parents="107 2874"/>
    </justification>
  </clause>

  <clause id="2888">
    <literal><![CDATA[
      T(x \ T(x,y),y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,2883,a)].">
      <j1 rule="hyper" parents="49 2883"/>
    </justification>
  </clause>

  <clause id="2889">
    <literal><![CDATA[
      T(T(x,y),K(z,R(x,u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2873(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2873 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2890">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2344,a,b,2868,a)].">
      <j1 rule="hyper" parents="58 2344 2868"/>
    </justification>
  </clause>

  <clause id="2891">
    <literal><![CDATA[
      L((T(x,y) * (x \ y)) / y,y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1348,a,b,2868,a)].">
      <j1 rule="hyper" parents="58 1348 2868"/>
    </justification>
  </clause>

  <clause id="2892">
    <literal><![CDATA[
      T(K(x,y),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2868(a,1),292(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2868 292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2893">
    <literal><![CDATA[
      R(K(x,y),y,(y * K(x,y)) \ z) \ z = y * ((y * K(x,y)) \ z)
    ]]></literal>
    <justification jstring="[para(2868(a,1),504(a,1,1,1))].">
      <j1 rule="para" parents="2868 504"/>
    </justification>
  </clause>

  <clause id="2894">
    <literal><![CDATA[
      R(x,K(y,z),z) * (z * K(y,z)) = (x * K(y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,2870,a(flip),b,184,a)].">
      <j1 rule="hyper" parents="119 2870 184"/>
    </justification>
  </clause>

  <clause id="2895">
    <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(2870(a,1),515(a,2,2))].">
      <j1 rule="para" parents="2870 515"/>
    </justification>
  </clause>

  <clause id="2896">
    <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(2870(a,1),518(a,1,2))].">
      <j1 rule="para" parents="2870 518"/>
    </justification>
  </clause>

  <clause id="2897">
    <literal><![CDATA[
      T(K(x,y),T(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,2875,a)].">
      <j1 rule="hyper" parents="49 2875"/>
    </justification>
  </clause>

  <clause id="2898">
    <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(2875(a,1),418(a,1,2,1))].">
      <j1 rule="para" parents="2875 418"/>
    </justification>
  </clause>

  <clause id="2899">
    <literal><![CDATA[
      T(x * T(x \ 1,y),y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,2882,a)].">
      <j1 rule="hyper" parents="49 2882"/>
    </justification>
  </clause>

  <clause id="2900">
    <literal><![CDATA[
      ((x * y) / x) / y = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(2884(a,1),265(a,1,2))].">
      <j1 rule="para" parents="2884 265"/>
    </justification>
  </clause>

  <clause id="2901">
    <literal><![CDATA[
      K(K(x,y),T(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,2897,a)].">
      <j1 rule="hyper" parents="50 2897"/>
    </justification>
  </clause>

  <clause id="2902">
    <literal><![CDATA[
      T(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(2897(a,1),284(a,1,2))].">
      <j1 rule="para" parents="2897 284"/>
    </justification>
  </clause>

  <clause id="2903">
    <literal><![CDATA[
      K(x \ T(x,y),T(y,z)) = 1
    ]]></literal>
    <justification jstring="[para(1020(a,1),2901(a,1,1))].">
      <j1 rule="para" parents="1020 2901"/>
    </justification>
  </clause>

  <clause id="2904">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(51,a,2903,a)].">
      <j1 rule="hyper" parents="51 2903"/>
    </justification>
  </clause>

  <clause id="2905">
    <literal><![CDATA[
      (1 / x) * (x * K(y,x)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(387,a,2890,a)].">
      <j1 rule="hyper" parents="387 2890"/>
    </justification>
  </clause>

  <clause id="2906">
    <literal><![CDATA[
      K(x,y) / (y * K(x,y)) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(117,a,2890,a(flip),b,259,a)].">
      <j1 rule="hyper" parents="117 2890 259"/>
    </justification>
  </clause>

  <clause id="2907">
    <literal><![CDATA[
      (1 / x) \ K(y,x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,2890,a(flip),b,259,a)].">
      <j1 rule="hyper" parents="116 2890 259"/>
    </justification>
  </clause>

  <clause id="2908">
    <literal><![CDATA[
      x * (y \ T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      (y \ T(y,x)) * x = z
    ]]></literal>
    <justification jstring="[para(2888(a,1),284(a,1,2))].">
      <j1 rule="para" parents="2888 284"/>
    </justification>
  </clause>

  <clause id="2909">
    <literal><![CDATA[
      (x \ 1) * K(y,x \ 1) = x \ K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,2905,a(flip),b,183,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 2905 183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2910">
    <literal><![CDATA[
      (T(x,y) \ 1) * T(x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,2866,a)].">
      <j1 rule="hyper" parents="133 2866"/>
    </justification>
  </clause>

  <clause id="2911">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(32,a,359,a,b,2866,a)].">
      <j1 rule="hyper" parents="32 359 2866"/>
    </justification>
  </clause>

  <clause id="2912">
    <literal><![CDATA[
      T(x,L(K(y,x),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,2871,a)].">
      <j1 rule="hyper" parents="49 2871"/>
    </justification>
  </clause>

  <clause id="2913">
    <literal><![CDATA[
      x * (((y * x) / y) / x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(119,a,2900,a,b,xx)].">
      <j1 rule="hyper" parents="119 2900"/>
    </justification>
  </clause>

  <clause id="2914">
    <literal><![CDATA[
      (x \ 1) * (x * ((y * (x \ 1)) / y)) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(1465,a,2900,a(flip))].">
      <j1 rule="hyper" parents="1465 2900"/>
    </justification>
  </clause>

  <clause id="2915">
    <literal><![CDATA[
      (1 / T(x,y)) * K(x \ 1,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(2910(a,1),770(a,1,2))].">
      <j1 rule="para" parents="2910 770"/>
    </justification>
  </clause>

  <clause id="2917">
    <literal><![CDATA[
      K((x * y) \ y,y \ (x * y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2581,a,b,2911,a)].">
      <j1 rule="hyper" parents="58 2581 2911"/>
    </justification>
  </clause>

  <clause id="2918">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2744,a(flip),b,2911,a),flip(a)].">
      <j1 rule="hyper" parents="58 2744 2911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2919">
    <literal><![CDATA[
      T(x,y) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(2911(a,1),2157(a,1,2))].">
      <j1 rule="para" parents="2911 2157"/>
    </justification>
  </clause>

  <clause id="2920">
    <literal><![CDATA[
      (x * T(y,z)) / T(T(y,y \ 1),z) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2911(a,1),2640(a,2,2))].">
      <j1 rule="para" parents="2911 2640"/>
    </justification>
  </clause>

  <clause id="2921">
    <literal><![CDATA[
      K(x \ 1,x) * (y / T(1 / (1 / x),z)) = y / ((1 / T(x,z)) \ 1)
    ]]></literal>
    <justification jstring="[para(2911(a,1),2742(a,1,1))].">
      <j1 rule="para" parents="2911 2742"/>
    </justification>
  </clause>

  <clause id="2922">
    <literal><![CDATA[
      x \ (K(x \ 1,x) * y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,2678,a(flip),b,2810,a),flip(a)].">
      <j1 rule="hyper" parents="116 2678 2810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2923">
    <literal><![CDATA[
      x * K(y \ 1,y) != y * z
    ]]></literal>
    <literal><![CDATA[
      ((y \ 1) \ 1) * z = x
    ]]></literal>
    <justification jstring="[para(2812(a,1),2183(a,1)),flip(a)].">
      <j1 rule="para" parents="2812 2183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2924">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (x * y) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,2459,a(flip),b,2813,a),flip(a)].">
      <j1 rule="hyper" parents="29 2459 2813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2925">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (x * y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(655,a,2815,a)].">
      <j1 rule="hyper" parents="655 2815"/>
    </justification>
  </clause>

  <clause id="2926">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = T(x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,2815,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 2815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2927">
    <literal><![CDATA[
      x * T(x \ (y \ x),y) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(1217,a,2817,a)].">
      <j1 rule="hyper" parents="1217 2817"/>
    </justification>
  </clause>

  <clause id="2928">
    <literal><![CDATA[
      ((1 / x) \ y) * K(x,x \ 1) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(2691,a,2821,a)].">
      <j1 rule="hyper" parents="2691 2821"/>
    </justification>
  </clause>

  <clause id="2929">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(2184,a,2821,a)].">
      <j1 rule="hyper" parents="2184 2821"/>
    </justification>
  </clause>

  <clause id="2930">
    <literal><![CDATA[
      T((x \ 1) * y,K(z \ 1,z)) = (1 / x) * (y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,2178,a,b,2822,a)].">
      <j1 rule="hyper" parents="320 2178 2822"/>
    </justification>
  </clause>

  <clause id="2932">
    <literal><![CDATA[
      (x \ 1) \ ((1 / x) * y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(123,a,2824,a)].">
      <j1 rule="hyper" parents="123 2824"/>
    </justification>
  </clause>

  <clause id="2933">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,x \ 1,x) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,2824,a(flip),b,438,a),flip(a)].">
      <j1 rule="hyper" parents="119 2824 438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2934">
    <literal><![CDATA[
      (1 / x) \ (y * (1 / x)) = T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(239,a,2603,a(flip),b,2827,a),flip(a)].">
      <j1 rule="hyper" parents="239 2603 2827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2935">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(2827(a,1),584(a,1))].">
      <j1 rule="para" parents="2827 584"/>
    </justification>
  </clause>

  <clause id="2936">
    <literal><![CDATA[
      T(x,1 / y) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(288,a,2934,a)].">
      <j1 rule="hyper" parents="288 2934"/>
    </justification>
  </clause>

  <clause id="2937">
    <literal><![CDATA[
      T(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,1 / y) = z
    ]]></literal>
    <justification jstring="[para(2934(a,1),288(a,1))].">
      <j1 rule="para" parents="2934 288"/>
    </justification>
  </clause>

  <clause id="2939">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),2936(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 2936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2940">
    <literal><![CDATA[
      T(x,1 / (1 / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),2936(a,2,2))].">
      <j1 rule="para" parents="75 2936"/>
    </justification>
  </clause>

  <clause id="2941">
    <literal><![CDATA[
      T(T(x,y),K(z,z \ 1)) = T(x,(y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,2168,a,b,2939,a)].">
      <j1 rule="hyper" parents="320 2168 2939"/>
    </justification>
  </clause>

  <clause id="2942">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(y,x) = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,2939,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2939 17"/>
    </justification>
  </clause>

  <clause id="2943">
    <literal><![CDATA[
      T(x,T(y,y \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(106(a,2),2939(a,1,2))].">
      <j1 rule="para" parents="106 2939"/>
    </justification>
  </clause>

  <clause id="2945">
    <literal><![CDATA[
      T(x,R(1 / y,y,z)) = T(x,R(y \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(2062(a,1),2939(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2062 2939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2946">
    <literal><![CDATA[
      T(x,x \ 1) * T(y,x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,2943,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2943 17"/>
    </justification>
  </clause>

  <clause id="2947">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(2690,a,2834,a)].">
      <j1 rule="hyper" parents="2690 2834"/>
    </justification>
  </clause>

  <clause id="2948">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ (1 / (1 / x))) * y) = x * K(y \ (1 / (1 / x)),y)
    ]]></literal>
    <justification jstring="[para(302(a,1),2834(a,1,2))].">
      <j1 rule="para" parents="302 2834"/>
    </justification>
  </clause>

  <clause id="2949">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / (1 / x)) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(2682,a,2835,a)].">
      <j1 rule="hyper" parents="2682 2835"/>
    </justification>
  </clause>

  <clause id="2950">
    <literal><![CDATA[
      (x \ y) * K(x,x \ 1) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(2177,a,2835,a)].">
      <j1 rule="hyper" parents="2177 2835"/>
    </justification>
  </clause>

  <clause id="2951">
    <literal><![CDATA[
      K(x,1 / x) * (x \ y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(1780(a,2),2835(a,1,1))].">
      <j1 rule="para" parents="1780 2835"/>
    </justification>
  </clause>

  <clause id="2952">
    <literal><![CDATA[
      ((1 / (1 / x)) \ y) * x = (x \ y) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2835(a,1),2671(a,1,1))].">
      <j1 rule="para" parents="2835 2671"/>
    </justification>
  </clause>

  <clause id="2953">
    <literal><![CDATA[
      T(x,y) * (K(x \ 1,x) * z) = (1 / (1 / T(x,y))) * z
    ]]></literal>
    <justification jstring="[para(2911(a,1),2837(a,1,2,1))].">
      <j1 rule="para" parents="2911 2837"/>
    </justification>
  </clause>

  <clause id="2954">
    <literal><![CDATA[
      L(((x \ 1) \ 1) \ y,x,x \ 1) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(499,a,2841,a),flip(a)].">
      <j1 rule="hyper" parents="499 2841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2955">
    <literal><![CDATA[
      T(K(x,y),L(y,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(240,a,2877,a)].">
      <j1 rule="hyper" parents="240 2877"/>
    </justification>
  </clause>

  <clause id="2956">
    <literal><![CDATA[
      x * ((y \ (x \ y)) * y) = y * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(2899(a,1),1392(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2899 1392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2957">
    <literal><![CDATA[
      x * ((x \ R(x,y,z)) / R(x,y,z)) = K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2560,a,2909,a(flip))].">
      <j1 rule="hyper" parents="2560 2909"/>
    </justification>
  </clause>

  <clause id="2958">
    <literal><![CDATA[
      x * ((1 / T(x,y)) * K(x \ 1,x)) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,2915,a,b,1117,a)].">
      <j1 rule="hyper" parents="119 2915 1117"/>
    </justification>
  </clause>

  <clause id="2960">
    <literal><![CDATA[
      (x * y) * ((((x * y) \ y) \ 1) \ 1) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2917(a,1),2570(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2917 2570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2962">
    <literal><![CDATA[
      K(x / y,y / x) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2717,a(flip),b,2918,a)].">
      <j1 rule="hyper" parents="58 2717 2918"/>
    </justification>
  </clause>

  <clause id="2963">
    <literal><![CDATA[
      K(1 / (x \ y),x \ y) = K(x / y,y / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,2569,a,b,2962,a)].">
      <j1 rule="hyper" parents="320 2569 2962"/>
    </justification>
  </clause>

  <clause id="2964">
    <literal><![CDATA[
      K(x / y,(x / y) \ 1) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2775,a,b,2962,a)].">
      <j1 rule="hyper" parents="58 2775 2962"/>
    </justification>
  </clause>

  <clause id="2965">
    <literal><![CDATA[
      x * (T(x,y) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,2252,a,b,2919,a)].">
      <j1 rule="hyper" parents="30 2252 2919"/>
    </justification>
  </clause>

  <clause id="2967">
    <literal><![CDATA[
      T(x,y) / x = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,2965,a),flip(a)].">
      <j1 rule="hyper" parents="123 2965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2968">
    <literal><![CDATA[
      K(x,T(x,y) / x) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,2965,a(flip),b,303,a),flip(a)].">
      <j1 rule="hyper" parents="115 2965 303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2969">
    <literal><![CDATA[
      (x \ T(x,y)) * x = T(x,y)
    ]]></literal>
    <justification jstring="[para(2965(a,1),76(a,1,1,2))].">
      <j1 rule="para" parents="2965 76"/>
    </justification>
  </clause>

  <clause id="2970">
    <literal><![CDATA[
      T(1 / x,T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,2968,a(flip),b,1174,a),flip(a)].">
      <j1 rule="hyper" parents="116 2968 1174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2971">
    <literal><![CDATA[
      x \ T(x,R(y,y \ 1,x)) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(1665,a,2967,a),flip(a)].">
      <j1 rule="hyper" parents="1665 2967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2972">
    <literal><![CDATA[
      (1 / x) * T(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1344,a,2967,a)].">
      <j1 rule="hyper" parents="1344 2967"/>
    </justification>
  </clause>

  <clause id="2973">
    <literal><![CDATA[
      (x \ 1) \ T(x \ 1,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1007,a,2967,a),flip(a)].">
      <j1 rule="hyper" parents="1007 2967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2974">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1003,a,2967,a)].">
      <j1 rule="hyper" parents="1003 2967"/>
    </justification>
  </clause>

  <clause id="2975">
    <literal><![CDATA[
      T(x,x \ T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(31,a,265,a,b,2967,a)].">
      <j1 rule="hyper" parents="31 265 2967"/>
    </justification>
  </clause>

  <clause id="2976">
    <literal><![CDATA[
      (x \ T(x,y)) * x != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2967(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2967 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2977">
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = (T(x,y) * z) / (x * z)
    ]]></literal>
    <justification jstring="[para(2967(a,1),102(a,1,1))].">
      <j1 rule="para" parents="2967 102"/>
    </justification>
  </clause>

  <clause id="2978">
    <literal><![CDATA[
      R((x / y) \ T(x / y,z),x / y,y) = (T(x / y,z) * y) / x
    ]]></literal>
    <justification jstring="[para(2967(a,1),525(a,1,1))].">
      <j1 rule="para" parents="2967 525"/>
    </justification>
  </clause>

  <clause id="2979">
    <literal><![CDATA[
      (x \ T(x,y)) * (1 / T(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[para(2967(a,1),2146(a,1,1))].">
      <j1 rule="para" parents="2967 2146"/>
    </justification>
  </clause>

  <clause id="2980">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * z) = x * ((x * (T(y,x) / y)) \ z)
    ]]></literal>
    <justification jstring="[para(2967(a,1),2419(a,1,1,2))].">
      <j1 rule="para" parents="2967 2419"/>
    </justification>
  </clause>

  <clause id="2981">
    <literal><![CDATA[
      T(x,K(y \ (y / (x \ 1)),y)) = x
    ]]></literal>
    <justification jstring="[para(1020(a,2),2975(a,1,2))].">
      <j1 rule="para" parents="1020 2975"/>
    </justification>
  </clause>

  <clause id="2982">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1671,a,b,2969,a)].">
      <j1 rule="hyper" parents="58 1671 2969"/>
    </justification>
  </clause>

  <clause id="2983">
    <literal><![CDATA[
      T(x,y) \ ((x \ T(x,y)) * (x * z)) = L(z,x,x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(2969(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2969 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2984">
    <literal><![CDATA[
      T(x,y) * L(z,x,x \ T(x,y)) = (x \ T(x,y)) * (x * z)
    ]]></literal>
    <justification jstring="[para(2969(a,1),90(a,1,1))].">
      <j1 rule="para" parents="2969 90"/>
    </justification>
  </clause>

  <clause id="2985">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = u
    ]]></literal>
    <justification jstring="[para(2969(a,1),518(a,1,1,1))].">
      <j1 rule="para" parents="2969 518"/>
    </justification>
  </clause>

  <clause id="2986">
    <literal><![CDATA[
      L(x,x \ T(x,y),x) = T(x,y) / (x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(2969(a,1),952(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2969 952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2987">
    <literal><![CDATA[
      T(1 / (1 / x),T(1 / x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,75,a(flip),b,2970,a),flip(a)].">
      <j1 rule="hyper" parents="320 75 2970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2988">
    <literal><![CDATA[
      L(x \ 1,x,y \ ((x * y) / x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,1667,a(flip),b,2970,a)].">
      <j1 rule="hyper" parents="58 1667 2970"/>
    </justification>
  </clause>

  <clause id="2989">
    <literal><![CDATA[
      T(x,y) * (x \ 1) = (1 / x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,2970,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2970 17"/>
    </justification>
  </clause>

  <clause id="2990">
    <literal><![CDATA[
      T(x \ 1,T(x,y)) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2970(a,1),246(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2970 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2991">
    <literal><![CDATA[
      T(x / (y * x),T(y,z)) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(2970(a,1),410(a,2,1))].">
      <j1 rule="para" parents="2970 410"/>
    </justification>
  </clause>

  <clause id="2992">
    <literal><![CDATA[
      x * T(x \ 1,T(x,y)) = K(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(2970(a,1),1023(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2970 1023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2993">
    <literal><![CDATA[
      (((x * y) / x) \ y) \ y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1183,a,2981,a)].">
      <j1 rule="hyper" parents="1183 2981"/>
    </justification>
  </clause>

  <clause id="2994">
    <literal><![CDATA[
      (((x * y) / x) \ y) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[hyper(119,a,2981,a(flip),b,1182,a(flip))].">
      <j1 rule="hyper" parents="119 2981 1182"/>
    </justification>
  </clause>

  <clause id="2995">
    <literal><![CDATA[
      T(x,T(1 / x,y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2987(a,1),1773(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2987 1773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2997">
    <literal><![CDATA[
      T(x,x \ 1) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(2995(a,1),1705(a,1,1))].">
      <j1 rule="para" parents="2995 1705"/>
    </justification>
  </clause>

  <clause id="2998">
    <literal><![CDATA[
      (1 / x) * T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2989(a,1),988(a,1))].">
      <j1 rule="para" parents="2989 988"/>
    </justification>
  </clause>

  <clause id="3000">
    <literal><![CDATA[
      x / ((y * x) / y) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(197,a,2993,a)].">
      <j1 rule="hyper" parents="197 2993"/>
    </justification>
  </clause>

  <clause id="3001">
    <literal><![CDATA[
      (((x * y) / x) \ y) / y = 1 / ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,3000,a(flip),b,1546,a)].">
      <j1 rule="hyper" parents="117 3000 1546"/>
    </justification>
  </clause>

  <clause id="3002">
    <literal><![CDATA[
      T(x,x / (y * x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[para(219(a,1),2982(a,1,2))].">
      <j1 rule="para" parents="219 2982"/>
    </justification>
  </clause>

  <clause id="3004">
    <literal><![CDATA[
      L(x \ 1,x,T(y,x) \ y) = x \ 1
    ]]></literal>
    <justification jstring="[para(225(a,1),2988(a,1,3,2))].">
      <j1 rule="para" parents="225 2988"/>
    </justification>
  </clause>

  <clause id="3005">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ ((x \ 1) \ y) = x \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(2821(a,1),2922(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2821 2922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3006">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) \ 1) \ y = z
    ]]></literal>
    <justification jstring="[para(2926(a,2),656(a,1))].">
      <j1 rule="para" parents="2926 656"/>
    </justification>
  </clause>

  <clause id="3007">
    <literal><![CDATA[
      x * (((x \ (y \ x)) \ 1) \ 1) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(2225(a,1),2927(a,1,2))].">
      <j1 rule="para" parents="2225 2927"/>
    </justification>
  </clause>

  <clause id="3008">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) \ y = z
    ]]></literal>
    <justification jstring="[para(2928(a,1),2700(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2928 2700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3009">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) * K(x \ 1,x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,2907,a(flip),b,2929,a),flip(a)].">
      <j1 rule="hyper" parents="320 2907 2929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3010">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2941(a,1),2174(a,1)),flip(b)].">
      <j1 rule="para" parents="2941 2174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3011">
    <literal><![CDATA[
      T(x,T(y,y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(106(a,2),3010(a,1,2))].">
      <j1 rule="para" parents="106 3010"/>
    </justification>
  </clause>

  <clause id="3012">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * y = T(y,R(x \ 1,x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1669,a,b,2945,a)].">
      <j1 rule="hyper" parents="58 1669 2945"/>
    </justification>
  </clause>

  <clause id="3013">
    <literal><![CDATA[
      ((x \ y) * z) * K(y \ x,x \ y) = (1 / (1 / (x \ y))) * z
    ]]></literal>
    <justification jstring="[para(2567(a,1),2947(a,1,2))].">
      <j1 rule="para" parents="2567 2947"/>
    </justification>
  </clause>

  <clause id="3014">
    <literal><![CDATA[
      ((1 / (1 / x)) * y) * (1 / x) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(2947(a,1),2608(a,1,1))].">
      <j1 rule="para" parents="2947 2608"/>
    </justification>
  </clause>

  <clause id="3015">
    <literal><![CDATA[
      K(x \ 1,x) * (K(1 / x,y) * (1 / x)) = x \ K(1 / x,y)
    ]]></literal>
    <justification jstring="[para(2545(a,1),2949(a,1,2))].">
      <j1 rule="para" parents="2545 2949"/>
    </justification>
  </clause>

  <clause id="3016">
    <literal><![CDATA[
      ((1 / (1 / x)) \ y) / (1 / x) = (x \ y) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,2950,a(flip),b,2699,a)].">
      <j1 rule="hyper" parents="117 2950 2699"/>
    </justification>
  </clause>

  <clause id="3017">
    <literal><![CDATA[
      (x \ y) * K(x,1 / x) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(1780(a,2),2950(a,1,2))].">
      <j1 rule="para" parents="1780 2950"/>
    </justification>
  </clause>

  <clause id="3018">
    <literal><![CDATA[
      K((x * y) / x,x / (x * y)) = K(y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(2658,a,2963,a),flip(a)].">
      <j1 rule="hyper" parents="2658 2963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3019">
    <literal><![CDATA[
      x * K(x / y,(x / y) \ 1) = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2964(a,2),2570(a,1,2))].">
      <j1 rule="para" parents="2964 2570"/>
    </justification>
  </clause>

  <clause id="3020">
    <literal><![CDATA[
      L(x * T(x \ 1,y),x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2973(a,1),747(a,1,1))].">
      <j1 rule="para" parents="2973 747"/>
    </justification>
  </clause>

  <clause id="3021">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ 1 = T(x \ 1,y) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(2973(a,1),2514(a,1,1))].">
      <j1 rule="para" parents="2973 2514"/>
    </justification>
  </clause>

  <clause id="3023">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = x * T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2990(a,1),2992(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2990 2992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3024">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,358,a(flip),b,3023,a),flip(a)].">
      <j1 rule="hyper" parents="320 358 3023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3027">
    <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(2801(a,1),2994(a,1,1,1,1))].">
      <j1 rule="para" parents="2801 2994"/>
    </justification>
  </clause>

  <clause id="3028">
    <literal><![CDATA[
      L(x * K(y \ 1,y),y,y \ 1) = (y \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(2924(a,1),2954(a,1,1))].">
      <j1 rule="para" parents="2924 2954"/>
    </justification>
  </clause>

  <clause id="3029">
    <literal><![CDATA[
      x \ ((y * x) / y) != y \ z
    ]]></literal>
    <literal><![CDATA[
      T(y,R(x,x \ 1,y)) = z
    ]]></literal>
    <justification jstring="[para(2971(a,1),42(a,1))].">
      <j1 rule="para" parents="2971 42"/>
    </justification>
  </clause>

  <clause id="3030">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ x = 1 / (y \ ((x * y) / x))
    ]]></literal>
    <justification jstring="[para(2971(a,1),2515(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2971 2515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3031">
    <literal><![CDATA[
      T(x,y \ ((x * y) / x)) = x
    ]]></literal>
    <justification jstring="[para(2971(a,1),2975(a,1,2))].">
      <j1 rule="para" parents="2971 2975"/>
    </justification>
  </clause>

  <clause id="3032">
    <literal><![CDATA[
      T(x,T(y,x) \ y) = x
    ]]></literal>
    <justification jstring="[para(225(a,1),3031(a,1,2,2))].">
      <j1 rule="para" parents="225 3031"/>
    </justification>
  </clause>

  <clause id="3033">
    <literal><![CDATA[
      (T(x,y) \ x) * y = y * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,3032,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 3032 17"/>
    </justification>
  </clause>

  <clause id="3034">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1664,a,b,3033,a)].">
      <j1 rule="hyper" parents="58 1664 3033"/>
    </justification>
  </clause>

  <clause id="3035">
    <literal><![CDATA[
      (x * ((x * (T(y,x) \ y)) \ x)) \ (x * x) = (T(y,x) \ y) * x
    ]]></literal>
    <justification jstring="[para(3033(a,1),2100(a,1,1,2,1))].">
      <j1 rule="para" parents="3033 2100"/>
    </justification>
  </clause>

  <clause id="3037">
    <literal><![CDATA[
      L(x,x \ T(x,y),x) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,72,a(flip),b,2986,a),flip(a)].">
      <j1 rule="hyper" parents="320 72 2986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3038">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,x) = z
    ]]></literal>
    <justification jstring="[para(2820(a,2),464(a,1))].">
      <j1 rule="para" parents="2820 464"/>
    </justification>
  </clause>

  <clause id="3039">
    <literal><![CDATA[
      T((x \ 1) * (y / (x \ 1)),K(z \ 1,z)) = (1 / x) * (y / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(320,a,2178,a,b,2823,a)].">
      <j1 rule="hyper" parents="320 2178 2823"/>
    </justification>
  </clause>

  <clause id="3040">
    <literal><![CDATA[
      (1 / x) * K(y,x \ 1) = K(y,x \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,2339,a(flip),b,2833,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="117 2339 2833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3041">
    <literal><![CDATA[
      T(x \ 1,T(x,y) \ x) = x \ 1
    ]]></literal>
    <justification jstring="[para(2862(a,1),2276(a,1,2))].">
      <j1 rule="para" parents="2862 2276"/>
    </justification>
  </clause>

  <clause id="3042">
    <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(2862(a,1),2598(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2862 2598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3043">
    <literal><![CDATA[
      T(T(x,y) \ x,x \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(49,a,3041,a)].">
      <j1 rule="hyper" parents="49 3041"/>
    </justification>
  </clause>

  <clause id="3044">
    <literal><![CDATA[
      R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,2736,a,b,3043,a)].">
      <j1 rule="hyper" parents="58 2736 3043"/>
    </justification>
  </clause>

  <clause id="3045">
    <literal><![CDATA[
      (K(x,y) \ y) * K(x,y) = y
    ]]></literal>
    <justification jstring="[hyper(29,a,84,a(flip),b,2885,a),flip(a)].">
      <j1 rule="hyper" parents="29 84 2885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3046">
    <literal><![CDATA[
      x / K(y,x) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(131,a,3045,a)].">
      <j1 rule="hyper" parents="131 3045"/>
    </justification>
  </clause>

  <clause id="3047">
    <literal><![CDATA[
      (K(x,y) \ y) \ y = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,3045,a)].">
      <j1 rule="hyper" parents="123 3045"/>
    </justification>
  </clause>

  <clause id="3048">
    <literal><![CDATA[
      K(x,y) != z \ y
    ]]></literal>
    <literal><![CDATA[
      K(x,y) \ y = z
    ]]></literal>
    <justification jstring="[para(3047(a,1),43(a,1))].">
      <j1 rule="para" parents="3047 43"/>
    </justification>
  </clause>

  <clause id="3049">
    <literal><![CDATA[
      (x * (1 / T(x,y))) * K(x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(2463,a,2958,a)].">
      <j1 rule="hyper" parents="2463 2958"/>
    </justification>
  </clause>

  <clause id="3050">
    <literal><![CDATA[
      K(x,x \ 1) * T(x \ 1,y) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,2782,a,b,2997,a(flip))].">
      <j1 rule="hyper" parents="29 2782 2997"/>
    </justification>
  </clause>

  <clause id="3052">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) / y = (((x \ y) / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(117,a,3007,a(flip),b,2161,a)].">
      <j1 rule="hyper" parents="117 3007 2161"/>
    </justification>
  </clause>

  <clause id="3053">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) \ x = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),3007(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 3007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3054">
    <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(184(a,1),3007(a,1,2,1,1,2))].">
      <j1 rule="para" parents="184 3007"/>
    </justification>
  </clause>

  <clause id="3055">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 / (1 / x))) * y) * (1 / x)
    ]]></literal>
    <justification jstring="[para(302(a,1),3014(a,1,1)),flip(a)].">
      <j1 rule="para" parents="302 3014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3056">
    <literal><![CDATA[
      T(x / (1 / (1 / y)),1 / (1 / y)) / (1 / y) = (y \ x) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,2),3016(a,1,1))].">
      <j1 rule="para" parents="107 3016"/>
    </justification>
  </clause>

  <clause id="3057">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1) = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(1094(a,2),3021(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1094 3021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3058">
    <literal><![CDATA[
      T((x \ y) \ 1,z) \ ((x \ y) \ 1) = (x \ (y * T(y \ x,z))) \ 1
    ]]></literal>
    <justification jstring="[para(1417(a,1),3021(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1417 3021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3059">
    <literal><![CDATA[
      (x \ 1) * (x * (1 / T(x,y))) = (1 / x) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(3049(a,1),2822(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3049 2822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3060">
    <literal><![CDATA[
      ((((1 / x) \ y) / y) \ 1) \ 1 = ((x \ 1) \ y) / y
    ]]></literal>
    <justification jstring="[para(75(a,1),3052(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 3052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3061">
    <literal><![CDATA[
      x / (x * (((x \ y) \ 1) \ 1)) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(197,a,3053,a)].">
      <j1 rule="hyper" parents="197 3053"/>
    </justification>
  </clause>

  <clause id="3062">
    <literal><![CDATA[
      x / (x * ((y \ 1) \ 1)) = ((x / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),3061(a,1,2,2,1,1))].">
      <j1 rule="para" parents="4 3061"/>
    </justification>
  </clause>

  <clause id="3063">
    <literal><![CDATA[
      x / ((((y / x) \ 1) \ 1) * x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2161(a,2),3061(a,1,2))].">
      <j1 rule="para" parents="2161 3061"/>
    </justification>
  </clause>

  <clause id="3064">
    <literal><![CDATA[
      T(x / (x * y),y) = x / (x * ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,2389,a,b,3062,a)].">
      <j1 rule="hyper" parents="320 2389 3062"/>
    </justification>
  </clause>

  <clause id="3065">
    <literal><![CDATA[
      x / (x * T(y,y \ 1)) = T(x / (x * y),y)
    ]]></literal>
    <justification jstring="[para(106(a,2),3064(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="106 3064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3066">
    <literal><![CDATA[
      T(x / (x * y),y) \ x = x * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(188,a,3065,a)].">
      <j1 rule="hyper" parents="188 3065"/>
    </justification>
  </clause>

  <clause id="3067">
    <literal><![CDATA[
      x / (((y \ 1) \ 1) * x) = ((x / (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(6(a,1),3063(a,1,2,1,1,1))].">
      <j1 rule="para" parents="6 3063"/>
    </justification>
  </clause>

  <clause id="3068">
    <literal><![CDATA[
      R(x \ 1,x,y) = y / (((x \ 1) \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2061,a,b,3067,a)].">
      <j1 rule="hyper" parents="320 2061 3067"/>
    </justification>
  </clause>

  <clause id="3069">
    <literal><![CDATA[
      R(x \ 1,(x \ 1) \ 1,y) = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,215,a,b,3068,a)].">
      <j1 rule="hyper" parents="320 215 3068"/>
    </justification>
  </clause>

  <clause id="3070">
    <literal><![CDATA[
      R(x \ 1,x,y) \ y = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(188,a,3068,a(flip))].">
      <j1 rule="hyper" parents="188 3068"/>
    </justification>
  </clause>

  <clause id="3071">
    <literal><![CDATA[
      x / (T(y,y \ 1) * x) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(106(a,2),3068(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="106 3068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3072">
    <literal><![CDATA[
      R(x,1 / x,y) \ y = (((1 / x) \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),3070(a,1,1,1))].">
      <j1 rule="para" parents="75 3070"/>
    </justification>
  </clause>

  <clause id="3073">
    <literal><![CDATA[
      R(x,1 / x,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),3072(a,2,1,1))].">
      <j1 rule="para" parents="75 3072"/>
    </justification>
  </clause>

  <clause id="3074">
    <literal><![CDATA[
      R(x,1 / x,y) = R(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(599,a,3073,a),flip(a)].">
      <j1 rule="hyper" parents="599 3073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3075">
    <literal><![CDATA[
      L(R(x,x \ 1,y),x \ 1,x) = R(1 / (1 / x),1 / x,y)
    ]]></literal>
    <justification jstring="[para(3074(a,1),1802(a,1,1))].">
      <j1 rule="para" parents="3074 1802"/>
    </justification>
  </clause>

  <clause id="3076">
    <literal><![CDATA[
      ((x \ 1) \ 1) * K(y,x) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(2923,a,3009,a)].">
      <j1 rule="hyper" parents="2923 3009"/>
    </justification>
  </clause>

  <clause id="3077">
    <literal><![CDATA[
      x * (K(y,x) * K(x,x \ 1)) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2844,a,b,3076,a)].">
      <j1 rule="hyper" parents="58 2844 3076"/>
    </justification>
  </clause>

  <clause id="3078">
    <literal><![CDATA[
      K(x \ 1,x) * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * (x * K(y,x)) = z
    ]]></literal>
    <justification jstring="[para(2905(a,1),2935(a,1,2))].">
      <j1 rule="para" parents="2905 2935"/>
    </justification>
  </clause>

  <clause id="3079">
    <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,2282,a(flip),b,3012,a)].">
      <j1 rule="hyper" parents="58 2282 3012"/>
    </justification>
  </clause>

  <clause id="3080">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ x = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,2521,a(flip),b,3030,a),flip(a)].">
      <j1 rule="hyper" parents="320 2521 3030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3081">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ 1 = x \ (((x * y) / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,3080,a(flip),b,1110,a),flip(a)].">
      <j1 rule="hyper" parents="116 3080 1110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3082">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(225(a,1),3080(a,2,1))].">
      <j1 rule="para" parents="225 3080"/>
    </justification>
  </clause>

  <clause id="3083">
    <literal><![CDATA[
      R(T(x,y) \ x,x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[para(2513(a,1),3044(a,1,1))].">
      <j1 rule="para" parents="2513 3044"/>
    </justification>
  </clause>

  <clause id="3084">
    <literal><![CDATA[
      T(x,x \ (((x * y) / x) \ y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3081(a,1),2165(a,1,2))].">
      <j1 rule="para" parents="3081 2165"/>
    </justification>
  </clause>

  <clause id="3085">
    <literal><![CDATA[
      T(x,x \ (y \ T(y,x))) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(225(a,1),3084(a,1,2,2,1))].">
      <j1 rule="para" parents="225 3084"/>
    </justification>
  </clause>

  <clause id="3086">
    <literal><![CDATA[
      T(x,x \ ((((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)))) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1016(a,1),3085(a,1,2,2,2))].">
      <j1 rule="para" parents="1016 3085"/>
    </justification>
  </clause>

  <clause id="3087">
    <literal><![CDATA[
      (x * (T(y,x) \ y)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(3034(a,1),3082(a,1,1))].">
      <j1 rule="para" parents="3034 3082"/>
    </justification>
  </clause>

  <clause id="3088">
    <literal><![CDATA[
      x / (y \ T(y,x)) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(197,a,3087,a)].">
      <j1 rule="hyper" parents="197 3087"/>
    </justification>
  </clause>

  <clause id="3089">
    <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(1016(a,1),3088(a,1,2,2))].">
      <j1 rule="para" parents="1016 3088"/>
    </justification>
  </clause>

  <clause id="3090">
    <literal><![CDATA[
      (x * T(y,z)) / T((y \ 1) \ 1,z) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(106(a,1),2920(a,1,2,1))].">
      <j1 rule="para" parents="106 2920"/>
    </justification>
  </clause>

  <clause id="3092">
    <literal><![CDATA[
      T(x,y) * (K(x \ 1,x) * z) = T(1 / (1 / x),y) * z
    ]]></literal>
    <justification jstring="[para(2154(a,1),2953(a,2,1))].">
      <j1 rule="para" parents="2154 2953"/>
    </justification>
  </clause>

  <clause id="3093">
    <literal><![CDATA[
      L((1 / T(x,y)) * x,x \ 1,x) = ((1 / x) * (T(x,y) \ x)) * x
    ]]></literal>
    <justification jstring="[para(3059(a,1),1975(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3059 1975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3094">
    <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(3090(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3090 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3095">
    <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,3092,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 3092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3096">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (T(x,y) \ z) = x * (T(1 / (1 / x),y) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,3095,a(flip),b,2925,a)].">
      <j1 rule="hyper" parents="119 3095 2925"/>
    </justification>
  </clause>

  <clause id="3097">
    <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(2957(a,1),1658(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2957 1658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3098">
    <literal><![CDATA[
      L(x * y,x \ T(x,z),x) = x * L(y,x,x \ T(x,z))
    ]]></literal>
    <justification jstring="[para(2983(a,1),1129(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2983 1129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3099">
    <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),3098(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 3098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3100">
    <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,2125,a,b,2984,a)].">
      <j1 rule="hyper" parents="58 2125 2984"/>
    </justification>
  </clause>

  <clause id="3101">
    <literal><![CDATA[
      R(1 / (1 / x),1 / x,y) = R(1 / (1 / x),x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1802,a(flip),b,3075,a),flip(a)].">
      <j1 rule="hyper" parents="58 1802 3075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3102">
    <literal><![CDATA[
      R(1 / (1 / x),x \ 1,(1 / x) \ y) = ((1 / x) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(936,a,3101,a),flip(a)].">
      <j1 rule="hyper" parents="936 3101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3103">
    <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(3102(a,2),87(a,1,2,2))].">
      <j1 rule="para" parents="3102 87"/>
    </justification>
  </clause>

  <clause id="3104">
    <literal><![CDATA[
      T((x \ 1) * y,K(z \ 1,z)) = y * ((x \ 1) * (x * T(x \ 1,y)))
    ]]></literal>
    <justification jstring="[hyper(320,a,2768,a,b,2930,a),flip(a)].">
      <j1 rule="hyper" parents="320 2768 2930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3105">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * z) = x * ((x * (y \ T(y,x))) \ z)
    ]]></literal>
    <justification jstring="[para(2967(a,1),2980(a,2,2,1,2))].">
      <j1 rule="para" parents="2967 2980"/>
    </justification>
  </clause>

  <clause id="3106">
    <literal><![CDATA[
      ((x \ (x / y)) * z) * K(y,y \ 1) = (1 / (1 / (x \ (x / y)))) * z
    ]]></literal>
    <justification jstring="[para(2370(a,1),3013(a,1,2))].">
      <j1 rule="para" parents="2370 3013"/>
    </justification>
  </clause>

  <clause id="3107">
    <literal><![CDATA[
      (x * ((x * (T(y,x) \ y)) \ x)) \ (x * x) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3033,a(flip),b,3035,a),flip(a)].">
      <j1 rule="hyper" parents="320 3033 3035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3108">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * x) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[para(3087(a,1),3107(a,1,1,2))].">
      <j1 rule="para" parents="3087 3107"/>
    </justification>
  </clause>

  <clause id="3109">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ x = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(29,a,3105,a(flip),b,3108,a(flip))].">
      <j1 rule="hyper" parents="29 3105 3108"/>
    </justification>
  </clause>

  <clause id="3110">
    <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(2893(a,2),982(a,1,1,2))].">
      <j1 rule="para" parents="2893 982"/>
    </justification>
  </clause>

  <clause id="3111">
    <literal><![CDATA[
      R((x / y) \ T(x / y,z),x / y,y) = (y * T(y \ x,z)) / x
    ]]></literal>
    <justification jstring="[para(453(a,1),2978(a,2,1))].">
      <j1 rule="para" parents="453 2978"/>
    </justification>
  </clause>

  <clause id="3112">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,(x \ 1) \ 1) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(3038,a,302,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3038 302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3113">
    <literal><![CDATA[
      ((1 / x) * (T(x,y) \ x)) * x = L(T(x,y) \ x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2857(a,1),3093(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2857 3093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3114">
    <literal><![CDATA[
      K(x \ 1,x) * (y / T(1 / (1 / x),z)) = y / T(x,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),2921(a,2,2))].">
      <j1 rule="para" parents="75 2921"/>
    </justification>
  </clause>

  <clause id="3116">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (y / T(x,z)) = x * (y / T(1 / (1 / x),z))
    ]]></literal>
    <justification jstring="[hyper(119,a,3114,a(flip),b,2925,a)].">
      <j1 rule="hyper" parents="119 3114 2925"/>
    </justification>
  </clause>

  <clause id="3118">
    <literal><![CDATA[
      L(x \ 1,x,K(y,x) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[para(3057(a,1),3004(a,1,3))].">
      <j1 rule="para" parents="3057 3004"/>
    </justification>
  </clause>

  <clause id="3119">
    <literal><![CDATA[
      T(x,K(y,x) \ 1) = x
    ]]></literal>
    <justification jstring="[para(3057(a,1),3032(a,1,2))].">
      <j1 rule="para" parents="3057 3032"/>
    </justification>
  </clause>

  <clause id="3120">
    <literal><![CDATA[
      (K(x,y) \ 1) * y = y * (K(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,3119,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 3119 17"/>
    </justification>
  </clause>

  <clause id="3121">
    <literal><![CDATA[
      (x * (K(y,x) \ 1)) \ (K(y,x) \ 1) = L(x \ 1,x,K(y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(3120(a,1),217(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3120 217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3122">
    <literal><![CDATA[
      (x * (K(y,x) \ 1)) \ (K(y,x) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,3118,a(flip),b,3121,a),flip(a)].">
      <j1 rule="hyper" parents="320 3118 3121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3124">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (1 / (1 / (x \ (x / (y \ 1))))) * z
    ]]></literal>
    <justification jstring="[para(1787(a,1),3106(a,1,2))].">
      <j1 rule="para" parents="1787 3106"/>
    </justification>
  </clause>

  <clause id="3125">
    <literal><![CDATA[
      ((x \ 1) * y) / T(1 / x,y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(2446(a,1),2830(a,1,2))].">
      <j1 rule="para" parents="2446 2830"/>
    </justification>
  </clause>

  <clause id="3126">
    <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(3125(a,1),1518(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3125 1518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3128">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ (y * T(x,x \ 1)) = K(K(x,x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(2704(a,1),2814(a,1,2))].">
      <j1 rule="para" parents="2704 2814"/>
    </justification>
  </clause>

  <clause id="3129">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,x) = K(y,T(x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(307,a,3128,a),flip(a)].">
      <j1 rule="hyper" parents="307 3128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3130">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,x) = K(y,(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,1360,a(flip),b,3129,a),flip(a)].">
      <j1 rule="hyper" parents="320 1360 3129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3131">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,(x \ 1) \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[para(2678(a,1),3130(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2678 3130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3132">
    <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(320,a,441,a,b,3055,a)].">
      <j1 rule="hyper" parents="320 441 3055"/>
    </justification>
  </clause>

  <clause id="3133">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (x \ (x / (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(2622(a,1),3124(a,2,1))].">
      <j1 rule="para" parents="2622 3124"/>
    </justification>
  </clause>

  <clause id="3134">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y
    ]]></literal>
    <justification jstring="[para(3133(a,1),2657(a,1,1))].">
      <j1 rule="para" parents="3133 2657"/>
    </justification>
  </clause>

  <clause id="3135">
    <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(320,a,3113,a(flip),b,3042,a),flip(a)].">
      <j1 rule="hyper" parents="320 3113 3042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3136">
    <literal><![CDATA[
      R(T(x,y) \ x,x \ 1,x) = L(T(x,y) \ x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2862(a,1),3135(a,1,1))].">
      <j1 rule="para" parents="2862 3135"/>
    </justification>
  </clause>

  <clause id="3137">
    <literal><![CDATA[
      L(T(x,y) \ x,x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,3083,a(flip),b,3136,a),flip(a)].">
      <j1 rule="hyper" parents="58 3083 3136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3138">
    <literal><![CDATA[
      L(T(x,y) \ x,T(x,y),y) = L((x * y) \ (y * x),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3137(a,1),924(a,1,1))].">
      <j1 rule="para" parents="3137 924"/>
    </justification>
  </clause>

  <clause id="3139">
    <literal><![CDATA[
      L((x * y) \ (y * x),x \ 1,x) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,496,a(flip),b,3138,a),flip(a)].">
      <j1 rule="hyper" parents="58 496 3138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3140">
    <literal><![CDATA[
      K(x,y) = L((y * x) \ (x * y),y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,11,a,b,3139,a)].">
      <j1 rule="hyper" parents="320 11 3139"/>
    </justification>
  </clause>

  <clause id="3141">
    <literal><![CDATA[
      L(K(x,y),y \ 1,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,2),3140(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11 3140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3142">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3141,a(flip),b,257,a),flip(a)].">
      <j1 rule="hyper" parents="116 3141 257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3143">
    <literal><![CDATA[
      T(x * y,R(x \ 1,x,x * y)) = x * ((x * y) * (y / (x * y)))
    ]]></literal>
    <justification jstring="[para(1894(a,1),3079(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1894 3079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3144">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[para(983(a,1),3134(a,2,1,2))].">
      <j1 rule="para" parents="983 3134"/>
    </justification>
  </clause>

  <clause id="3145">
    <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(320,a,1735,a(flip),b,3097,a),flip(a)].">
      <j1 rule="hyper" parents="320 1735 3097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3146">
    <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,3002,a,b,3145,a)].">
      <j1 rule="hyper" parents="58 3002 3145"/>
    </justification>
  </clause>

  <clause id="3147">
    <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,3146,a)].">
      <j1 rule="hyper" parents="58 22 3146"/>
    </justification>
  </clause>

  <clause id="3148">
    <literal><![CDATA[
      R(x,y,z) * K(R(x,y,z),x \ 1) = R((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(2055(a,1),3147(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2055 3147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3149">
    <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,824,a,b,3148,a)].">
      <j1 rule="hyper" parents="116 824 3148"/>
    </justification>
  </clause>

  <clause id="3151">
    <literal><![CDATA[
      a(R(x,y,z),1 / x,x) = K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,1274,a(flip),b,3149,a)].">
      <j1 rule="hyper" parents="58 1274 3149"/>
    </justification>
  </clause>

  <clause id="3152">
    <literal><![CDATA[
      x * ((x \ R(x,y,z)) / R(x,y,z)) = a(R(x,y,z),1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,2957,a,b,3151,a)].">
      <j1 rule="hyper" parents="320 2957 3151"/>
    </justification>
  </clause>

  <clause id="3153">
    <literal><![CDATA[
      x * L(x \ 1,R(x,y,z),1 / x) = a(R(x,y,z),1 / x,x)
    ]]></literal>
    <justification jstring="[para(1944(a,2),3152(a,1,2))].">
      <j1 rule="para" parents="1944 3152"/>
    </justification>
  </clause>

  <clause id="3154">
    <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(3099(a,1),3100(a,1,1))].">
      <j1 rule="para" parents="3099 3100"/>
    </justification>
  </clause>

  <clause id="3155">
    <literal><![CDATA[
      L(x \ (x * y),z \ T(z,x),z) = (z \ T(z,x)) * (z * (T(z,x) \ y))
    ]]></literal>
    <justification jstring="[hyper(855,a,3154,a)].">
      <j1 rule="hyper" parents="855 3154"/>
    </justification>
  </clause>

  <clause id="3156">
    <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),3155(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 3155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3157">
    <literal><![CDATA[
      (x \ T(x,y)) \ x = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3037,a(flip),b,3156,a)].">
      <j1 rule="hyper" parents="116 3037 3156"/>
    </justification>
  </clause>

  <clause id="3158">
    <literal><![CDATA[
      L(1 / x,x \ T(x,y),x) = (x \ T(x,y)) * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(2855(a,1),3156(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2855 3156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3159">
    <literal><![CDATA[
      x * (T(x,R(y,x,(y * x) \ x)) \ x) = (x \ (x * K(x,y))) \ x
    ]]></literal>
    <justification jstring="[para(1729(a,1),3157(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1729 3157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3160">
    <literal><![CDATA[
      x * (T(x,R(y,y \ 1,x)) \ x) = (y \ ((x * y) / x)) \ x
    ]]></literal>
    <justification jstring="[para(2971(a,1),3157(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2971 3157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3161">
    <literal><![CDATA[
      L(1 / x,x \ T(x,y),x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(320,a,2979,a(flip),b,3158,a),flip(a)].">
      <j1 rule="hyper" parents="320 2979 3158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3163">
    <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(3161(a,1),631(a,2,1))].">
      <j1 rule="para" parents="3161 631"/>
    </justification>
  </clause>

  <clause id="3164">
    <literal><![CDATA[
      (x \ ((y * x) / y)) \ y = y * (((y * x) / y) \ x)
    ]]></literal>
    <justification jstring="[para(3080(a,1),3160(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3080 3160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3165">
    <literal><![CDATA[
      x * (((x * T(y,x)) / x) \ T(y,x)) = (T(y,x) \ y) \ x
    ]]></literal>
    <justification jstring="[para(225(a,1),3164(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="225 3164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3166">
    <literal><![CDATA[
      (T(x,y) \ x) \ y = y * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(225(a,1),3165(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="225 3165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3167">
    <literal><![CDATA[
      x * (T(x,R(y,x,(y * x) \ x)) \ x) = K(x,y) \ x
    ]]></literal>
    <justification jstring="[para(4(a,1),3159(a,2,1))].">
      <j1 rule="para" parents="4 3159"/>
    </justification>
  </clause>

  <clause id="3169">
    <literal><![CDATA[
      x * (K(x,y) \ 1) = K(x,y) \ x
    ]]></literal>
    <justification jstring="[para(2522(a,1),3167(a,1,2))].">
      <j1 rule="para" parents="2522 3167"/>
    </justification>
  </clause>

  <clause id="3170">
    <literal><![CDATA[
      x \ (K(x,y) \ x) = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,3169,a)].">
      <j1 rule="hyper" parents="123 3169"/>
    </justification>
  </clause>

  <clause id="3171">
    <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),3163(a,1,2,2,2))].">
      <j1 rule="para" parents="5 3163"/>
    </justification>
  </clause>

  <clause id="3173">
    <literal><![CDATA[
      (1 / x) * (x * (x \ T(x,y))) = x * ((x \ T(x,y)) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(2970(a,1),3171(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2970 3171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3174">
    <literal><![CDATA[
      (1 / x) * (x * (x \ T(x,y))) = x * ((x \ 1) * (x \ T(x,y)))
    ]]></literal>
    <justification jstring="[para(1246(a,1),3173(a,2,2))].">
      <j1 rule="para" parents="1246 3173"/>
    </justification>
  </clause>

  <clause id="3176">
    <literal><![CDATA[
      (1 / x) * (x * (x \ T(x,y))) = L(x \ T(x,y),x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,257,a(flip),b,3174,a),flip(a)].">
      <j1 rule="hyper" parents="320 257 3174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3177">
    <literal><![CDATA[
      L(x \ T(x,y),x \ 1,x) = (1 / x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(342,a,3176,a),flip(a)].">
      <j1 rule="hyper" parents="342 3176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3179">
    <literal><![CDATA[
      L(x \ T(x,y),x \ 1,x) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2972,a(flip),b,3177,a),flip(a)].">
      <j1 rule="hyper" parents="320 2972 3177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3180">
    <literal><![CDATA[
      L(x \ (x * K(x,y)),x \ 1,x) = x \ T(x,R(y,x,(y * x) \ x))
    ]]></literal>
    <justification jstring="[para(1729(a,1),3179(a,1,1,2))].">
      <j1 rule="para" parents="1729 3179"/>
    </justification>
  </clause>

  <clause id="3181">
    <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),3180(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 3180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3183">
    <literal><![CDATA[
      L(K(x,y),x \ 1,x) = x \ (x * K(x,y))
    ]]></literal>
    <justification jstring="[para(1729(a,1),3181(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1729 3181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3184">
    <literal><![CDATA[
      L(K(x,y),x \ 1,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4,a(flip),b,3183,a),flip(a)].">
      <j1 rule="hyper" parents="320 4 3183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3186">
    <literal><![CDATA[
      (x \ 1) * K(x,y) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,3184,a(flip),b,257,a),flip(a)].">
      <j1 rule="hyper" parents="116 3184 257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3187">
    <literal><![CDATA[
      K(x,y) * (x \ 1) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1283,a,3186,a)].">
      <j1 rule="hyper" parents="1283 3186"/>
    </justification>
  </clause>

  <clause id="3188">
    <literal><![CDATA[
      K(x,y) \ (x \ K(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,3186,a(flip),b,1282,a)].">
      <j1 rule="hyper" parents="116 3186 1282"/>
    </justification>
  </clause>

  <clause id="3189">
    <literal><![CDATA[
      x \ K(x,y) != z * K(x,y)
    ]]></literal>
    <literal><![CDATA[
      x \ 1 = z
    ]]></literal>
    <justification jstring="[para(3186(a,1),39(a,1))].">
      <j1 rule="para" parents="3186 39"/>
    </justification>
  </clause>

  <clause id="3190">
    <literal><![CDATA[
      K(x,y) \ (x \ K(x,y)) != z * u
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) / u = z
    ]]></literal>
    <justification jstring="[para(3187(a,1),575(a,1,2))].">
      <j1 rule="para" parents="3187 575"/>
    </justification>
  </clause>

  <clause id="3191">
    <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(3187(a,1),479(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3187 479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3192">
    <literal><![CDATA[
      x \ y != K(z,u) * (z \ 1)
    ]]></literal>
    <literal><![CDATA[
      x * (z \ K(z,u)) = y
    ]]></literal>
    <justification jstring="[para(3188(a,1),340(a,2,2))].">
      <j1 rule="para" parents="3188 340"/>
    </justification>
  </clause>

  <clause id="3193">
    <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(2791(a,1),2831(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2791 2831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3194">
    <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(3193(a,2),482(a,1))].">
      <j1 rule="para" parents="3193 482"/>
    </justification>
  </clause>

  <clause id="3195">
    <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),3027(a,1,1,1))].">
      <j1 rule="para" parents="6 3027"/>
    </justification>
  </clause>

  <clause id="3197">
    <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(3195(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="3195 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3198">
    <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(2974(a,1),3126(a,2,1))].">
      <j1 rule="para" parents="2974 3126"/>
    </justification>
  </clause>

  <clause id="3199">
    <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),1364(a,1,2,1,1))].">
      <j1 rule="para" parents="90 1364"/>
    </justification>
  </clause>

  <clause id="3200">
    <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(1362,a,3199,a),flip(a)].">
      <j1 rule="hyper" parents="1362 3199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3201">
    <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(911(a,1),3200(a,2,2))].">
      <j1 rule="para" parents="911 3200"/>
    </justification>
  </clause>

  <clause id="3202">
    <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(479,a,3201,a),flip(a)].">
      <j1 rule="hyper" parents="479 3201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3203">
    <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,1188,a(flip),b,3202,a),flip(a)].">
      <j1 rule="hyper" parents="58 1188 3202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3204">
    <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(3202(a,1),2737(a,1,1))].">
      <j1 rule="para" parents="3202 2737"/>
    </justification>
  </clause>

  <clause id="3205">
    <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(2711(a,1),3204(a,1,1,1,2))].">
      <j1 rule="para" parents="2711 3204"/>
    </justification>
  </clause>

  <clause id="3206">
    <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),3205(a,1,1,1,2,1))].">
      <j1 rule="para" parents="2 3205"/>
    </justification>
  </clause>

  <clause id="3207">
    <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(1752(a,1),3203(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1752 3203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3208">
    <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(320,a,2479,a(flip),b,3207,a),flip(a)].">
      <j1 rule="hyper" parents="320 2479 3207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3209">
    <literal><![CDATA[
      (x \ 1) / (x \ L(x,y,z)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(30,a,258,a(flip),b,3208,a),flip(a)].">
      <j1 rule="hyper" parents="30 258 3208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3210">
    <literal><![CDATA[
      x / ((1 / x) \ L(1 / x,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),3209(a,1,1))].">
      <j1 rule="para" parents="75 3209"/>
    </justification>
  </clause>

  <clause id="3211">
    <literal><![CDATA[
      x / (x * L(x \ 1,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1062(a,1),3210(a,1,2))].">
      <j1 rule="para" parents="1062 3210"/>
    </justification>
  </clause>

  <clause id="3212">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) * (x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(133,a,3211,a)].">
      <j1 rule="hyper" parents="133 3211"/>
    </justification>
  </clause>

  <clause id="3213">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ x = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(2556,a,3212,a)].">
      <j1 rule="hyper" parents="2556 3212"/>
    </justification>
  </clause>

  <clause id="3214">
    <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(424,a,3213,a)].">
      <j1 rule="hyper" parents="424 3213"/>
    </justification>
  </clause>

  <clause id="3215">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 = (L(x,y,z) / x) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(1683(a,1),3213(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1683 3213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3216">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ 1 = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,3214,a(flip),b,2030,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 3214 2030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3217">
    <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(320,a,2290,a(flip),b,2292,a),flip(a)].">
      <j1 rule="hyper" parents="320 2290 2292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3218">
    <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),3132(a,1,1,3))].">
      <j1 rule="para" parents="75 3132"/>
    </justification>
  </clause>

  <clause id="3219">
    <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(2591(a,1),3218(a,1,1))].">
      <j1 rule="para" parents="2591 3218"/>
    </justification>
  </clause>

  <clause id="3220">
    <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),1927(a,1,2,2,2))].">
      <j1 rule="para" parents="13 1927"/>
    </justification>
  </clause>

  <clause id="3221">
    <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),3220(a,2,2))].">
      <j1 rule="para" parents="13 3220"/>
    </justification>
  </clause>

  <clause id="3222">
    <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(1249(a,1),2488(a,1,1,2,1))].">
      <j1 rule="para" parents="1249 2488"/>
    </justification>
  </clause>

  <clause id="3223">
    <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(1562(a,1),3222(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1562 3222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3225">
    <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(2946(a,1),3223(a,2,1))].">
      <j1 rule="para" parents="2946 3223"/>
    </justification>
  </clause>

  <clause id="3226">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = R(1,y,z)
    ]]></literal>
    <justification jstring="[para(223(a,1),3225(a,2,1))].">
      <j1 rule="para" parents="223 3225"/>
    </justification>
  </clause>

  <clause id="3227">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,376,a(flip),b,3226,a),flip(a)].">
      <j1 rule="hyper" parents="320 376 3226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3230">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ (x \ 1)) * (x \ R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(167,a,85,a,b,3227,a(flip))].">
      <j1 rule="hyper" parents="167 85 3227"/>
    </justification>
  </clause>

  <clause id="3231">
    <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(3230(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3230 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3232">
    <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),1654(a,1,2,1,2,1))].">
      <j1 rule="para" parents="90 1654"/>
    </justification>
  </clause>

  <clause id="3233">
    <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(1333,a,3232,a),flip(a)].">
      <j1 rule="hyper" parents="1333 3232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3234">
    <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(1089(a,1),3233(a,2,2))].">
      <j1 rule="para" parents="1089 3233"/>
    </justification>
  </clause>

  <clause id="3235">
    <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(479,a,3234,a),flip(a)].">
      <j1 rule="hyper" parents="479 3234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3236">
    <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),3235(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 3235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3237">
    <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(320,a,1783,a,b,3236,a),flip(a)].">
      <j1 rule="hyper" parents="320 1783 3236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3238">
    <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(1722(a,1),3237(a,1,1))].">
      <j1 rule="para" parents="1722 3237"/>
    </justification>
  </clause>

  <clause id="3239">
    <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),1660(a,1,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="101 1660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3240">
    <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(320,a,864,a(flip),b,3239,a),flip(a)].">
      <j1 rule="hyper" parents="320 864 3239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3241">
    <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(320,a,2286,a(flip),b,3240,a),flip(a)].">
      <j1 rule="hyper" parents="320 2286 3240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3242">
    <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,2284,a(flip),b,3240,a)].">
      <j1 rule="hyper" parents="117 2284 3240"/>
    </justification>
  </clause>

  <clause id="3243">
    <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(864(a,1),3241(a,1,1))].">
      <j1 rule="para" parents="864 3241"/>
    </justification>
  </clause>

  <clause id="3244">
    <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(1090(a,1),3242(a,1,1,1))].">
      <j1 rule="para" parents="1090 3242"/>
    </justification>
  </clause>

  <clause id="3245">
    <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(518,a,3244,a),flip(a)].">
      <j1 rule="hyper" parents="518 3244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3246">
    <literal><![CDATA[
      R(((x * (1 / x)) / x) * x,y,z) = T(x,1 / R(x,y,z)) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,2754,a(flip),b,3245,a),flip(a)].">
      <j1 rule="hyper" parents="58 2754 3245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3247">
    <literal><![CDATA[
      R((K(x,1 / x) / x) * x,y,z) = T(x,1 / R(x,y,z)) / x
    ]]></literal>
    <justification jstring="[para(260(a,2),3246(a,1,1,1,1))].">
      <j1 rule="para" parents="260 3246"/>
    </justification>
  </clause>

  <clause id="3248">
    <literal><![CDATA[
      T(x,1 / R(x,y,z)) / x = R(K(x,1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),3247(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 3247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3250">
    <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(1710(a,1),3243(a,2,1))].">
      <j1 rule="para" parents="1710 3243"/>
    </justification>
  </clause>

  <clause id="3251">
    <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,3250,a),flip(a)].">
      <j1 rule="hyper" parents="30 101 3250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3252">
    <literal><![CDATA[
      R(x * ((y * (x \ 1)) / y),z,u) = K(y,(y / R(x,z,u)) / y)
    ]]></literal>
    <justification jstring="[hyper(1716,a,3251,a),flip(a)].">
      <j1 rule="hyper" parents="1716 3251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3253">
    <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),3251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 3251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3254">
    <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(320,a,1783,a,b,3253,a),flip(a)].">
      <j1 rule="hyper" parents="320 1783 3253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3255">
    <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(1201(a,1),3254(a,1,1,2,1))].">
      <j1 rule="para" parents="1201 3254"/>
    </justification>
  </clause>

  <clause id="3256">
    <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(2957(a,1),3255(a,1,1))].">
      <j1 rule="para" parents="2957 3255"/>
    </justification>
  </clause>

  <clause id="3257">
    <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),1690(a,2,2,1,1))].">
      <j1 rule="para" parents="13 1690"/>
    </justification>
  </clause>

  <clause id="3258">
    <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(1052(a,1),3257(a,1,2))].">
      <j1 rule="para" parents="1052 3257"/>
    </justification>
  </clause>

  <clause id="3259">
    <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),3258(a,1,2,2,2,1,2))].">
      <j1 rule="para" parents="4 3258"/>
    </justification>
  </clause>

  <clause id="3260">
    <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(913(a,1),3259(a,1,2,2))].">
      <j1 rule="para" parents="913 3259"/>
    </justification>
  </clause>

  <clause id="3261">
    <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(577,a,3260,a)].">
      <j1 rule="hyper" parents="577 3260"/>
    </justification>
  </clause>

  <clause id="3262">
    <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(482,a,3260,a),flip(a)].">
      <j1 rule="hyper" parents="482 3260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3263">
    <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,217,a(flip),b,3261,a),flip(a)].">
      <j1 rule="hyper" parents="119 217 3261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3264">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ 1,x,1 / x) = L(x * T(1 / x,1),y,z)
    ]]></literal>
    <justification jstring="[para(748(a,1),3262(a,2,1,2))].">
      <j1 rule="para" parents="748 3262"/>
    </justification>
  </clause>

  <clause id="3265">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * (L(x,y,z) \ x)) = L(x * T(1 / x,1),y,z)
    ]]></literal>
    <justification jstring="[para(1407(a,1),3264(a,1,2))].">
      <j1 rule="para" parents="1407 3264"/>
    </justification>
  </clause>

  <clause id="3266">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * (L(x,y,z) \ x)) = L(x * (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(198(a,1),3265(a,2,1,2))].">
      <j1 rule="para" parents="198 3265"/>
    </justification>
  </clause>

  <clause id="3267">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * (L(x,y,z) \ x)) = L(K(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1783(a,2),3266(a,2,1))].">
      <j1 rule="para" parents="1783 3266"/>
    </justification>
  </clause>

  <clause id="3268">
    <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(1077(a,1),3263(a,2,2,1))].">
      <j1 rule="para" parents="1077 3263"/>
    </justification>
  </clause>

  <clause id="3269">
    <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(2474(a,1),3268(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2474 3268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3270">
    <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(320,a,3238,a(flip),b,3269,a),flip(a)].">
      <j1 rule="hyper" parents="320 3238 3269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3271">
    <literal><![CDATA[
      (L(x,y,z) / x) \ (1 / x) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,1783,a(flip),b,3270,a),flip(a)].">
      <j1 rule="hyper" parents="29 1783 3270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3272">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3215,a,b,3271,a)].">
      <j1 rule="hyper" parents="58 3215 3271"/>
    </justification>
  </clause>

  <clause id="3273">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) = 1 / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(197,a,3272,a),flip(a)].">
      <j1 rule="hyper" parents="197 3272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3274">
    <literal><![CDATA[
      1 / L(x \ 1,y,z) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(72(a,1),3272(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 3272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3275">
    <literal><![CDATA[
      1 / (1 / L(x \ 1,y,z)) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),3273(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 3273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3276">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      1 / L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3273(a,2),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3273 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3277">
    <literal><![CDATA[
      T(1 / (1 / L(x,y,z)),1 / x) = L((1 / x) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(3273(a,1),247(a,1,1))].">
      <j1 rule="para" parents="3273 247"/>
    </justification>
  </clause>

  <clause id="3278">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) \ 1 = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(188,a,3274,a)].">
      <j1 rule="hyper" parents="188 3274"/>
    </justification>
  </clause>

  <clause id="3279">
    <literal><![CDATA[
      L(1 / x,x,y) \ 1 = 1 / ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,394,a(flip),b,3274,a),flip(a)].">
      <j1 rule="hyper" parents="58 394 3274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3280">
    <literal><![CDATA[
      L(1 / x,x,y) = 1 / (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(197,a,3279,a),flip(a)].">
      <j1 rule="hyper" parents="197 3279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3281">
    <literal><![CDATA[
      L(x,x \ 1,y) = 1 / (1 / ((y * (x \ 1)) \ y))
    ]]></literal>
    <justification jstring="[para(72(a,1),3280(a,1,1))].">
      <j1 rule="para" parents="72 3280"/>
    </justification>
  </clause>

  <clause id="3282">
    <literal><![CDATA[
      1 / (1 / L(L(x \ 1,y,z),u,w)) = L(L(1 / x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(3275(a,1),3273(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3275 3273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3283">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) = (L(x,y,z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(72(a,1),3278(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 3278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3284">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * L((x \ 1) \ 1,y,z) = 1
    ]]></literal>
    <justification jstring="[hyper(119,a,3283,a,b,xx)].">
      <j1 rule="hyper" parents="119 3283"/>
    </justification>
  </clause>

  <clause id="3285">
    <literal><![CDATA[
      L(((x \ y) \ 1) \ 1,x,1 / x) = (((1 / x) * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(488(a,1),3283(a,2,1,1))].">
      <j1 rule="para" parents="488 3283"/>
    </justification>
  </clause>

  <clause id="3286">
    <literal><![CDATA[
      L((((x \ y) \ z) \ 1) \ 1,x \ y,x) = ((y \ (x * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(490(a,1),3283(a,2,1,1))].">
      <j1 rule="para" parents="490 3283"/>
    </justification>
  </clause>

  <clause id="3287">
    <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(167,a,438,a,b,3284,a(flip))].">
      <j1 rule="hyper" parents="167 438 3284"/>
    </justification>
  </clause>

  <clause id="3288">
    <literal><![CDATA[
      x / L(y,y \ 1,x) = x * (1 / (1 / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(3281(a,2),2624(a,1,2))].">
      <j1 rule="para" parents="3281 2624"/>
    </justification>
  </clause>

  <clause id="3289">
    <literal><![CDATA[
      x / L(y,y \ 1,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(72(a,1),3288(a,2,2,2))].">
      <j1 rule="para" parents="72 3288"/>
    </justification>
  </clause>

  <clause id="3291">
    <literal><![CDATA[
      K(x \ (x / L(y,y \ 1,x)),z) = K(1 / y,z)
    ]]></literal>
    <justification jstring="[para(3289(a,2),673(a,1,1,2))].">
      <j1 rule="para" parents="3289 673"/>
    </justification>
  </clause>

  <clause id="3292">
    <literal><![CDATA[
      L(x * T(x \ 1,y),x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2477,a,b,3291,a)].">
      <j1 rule="hyper" parents="58 2477 3291"/>
    </justification>
  </clause>

  <clause id="3293">
    <literal><![CDATA[
      K(1 / x,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(3020,a,3292,a),flip(a)].">
      <j1 rule="hyper" parents="3020 3292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3294">
    <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,3292,a)].">
      <j1 rule="hyper" parents="58 93 3292"/>
    </justification>
  </clause>

  <clause id="3295">
    <literal><![CDATA[
      L((1 / x) * T((1 / x) \ 1,y),x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(75(a,1),3292(a,1,2))].">
      <j1 rule="para" parents="75 3292"/>
    </justification>
  </clause>

  <clause id="3296">
    <literal><![CDATA[
      K(1 / (1 / x),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,674,a(flip),b,3293,a),flip(a)].">
      <j1 rule="hyper" parents="320 674 3293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3297">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = (T(y,1 / x) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1045,a(flip),b,3293,a),flip(a)].">
      <j1 rule="hyper" parents="58 1045 3293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3298">
    <literal><![CDATA[
      K((x \ 1) \ 1,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),3293(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 3293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3300">
    <literal><![CDATA[
      K(T(1 / x,y),z) = K(T(x \ 1,y),z)
    ]]></literal>
    <justification jstring="[para(2153(a,1),3298(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2153 3298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3301">
    <literal><![CDATA[
      K(((1 / x) * y) \ y,z) = K(((x \ 1) * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(2732(a,1),3298(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2732 3298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3302">
    <literal><![CDATA[
      T(1 / (1 / L(x,y,z)),1 / x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),3277(a,2,1))].">
      <j1 rule="para" parents="75 3277"/>
    </justification>
  </clause>

  <clause id="3303">
    <literal><![CDATA[
      T(T(1 / (1 / L(x,y,z)),u),1 / x) = T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(3302(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3302 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3304">
    <literal><![CDATA[
      (1 / x) \ ((((1 / x) * y) \ 1) \ 1) = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,3285,a(flip),b,259,a)].">
      <j1 rule="hyper" parents="116 3285 259"/>
    </justification>
  </clause>

  <clause id="3305">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(999(a,1),3295(a,1,1))].">
      <j1 rule="para" parents="999 3295"/>
    </justification>
  </clause>

  <clause id="3306">
    <literal><![CDATA[
      K(1 / (1 / x),y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,860,a(flip),b,3305,a),flip(a)].">
      <j1 rule="hyper" parents="58 860 3305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3307">
    <literal><![CDATA[
      T(K(1 / (1 / x),y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3306(a,2),224(a,1,1))].">
      <j1 rule="para" parents="3306 224"/>
    </justification>
  </clause>

  <clause id="3308">
    <literal><![CDATA[
      T(K(x,y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3296(a,1),3307(a,1,1))].">
      <j1 rule="para" parents="3296 3307"/>
    </justification>
  </clause>

  <clause id="3309">
    <literal><![CDATA[
      T(K(x,y),x) = K((x \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3298,a,b,3308,a),flip(a)].">
      <j1 rule="hyper" parents="320 3298 3308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3310">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2494,a,b,3308,a)].">
      <j1 rule="hyper" parents="58 2494 3308"/>
    </justification>
  </clause>

  <clause id="3311">
    <literal><![CDATA[
      T(x,K(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,3308,a)].">
      <j1 rule="hyper" parents="49 3308"/>
    </justification>
  </clause>

  <clause id="3312">
    <literal><![CDATA[
      R(K(x,y),z,u) * x = x * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3308(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3308 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3313">
    <literal><![CDATA[
      T(T(x,y),K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3311(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3311 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3314">
    <literal><![CDATA[
      K(x,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3311(a,1),284(a,1,2))].">
      <j1 rule="para" parents="3311 284"/>
    </justification>
  </clause>

  <clause id="3315">
    <literal><![CDATA[
      T(x,y) * K(x,z) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3311(a,1),236(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3311 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3316">
    <literal><![CDATA[
      T(T(T(x,y),z),K(x,u)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(3311(a,1),109(a,2,1,1))].">
      <j1 rule="para" parents="3311 109"/>
    </justification>
  </clause>

  <clause id="3317">
    <literal><![CDATA[
      L(x,y,z) * K(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3311(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3311 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3318">
    <literal><![CDATA[
      R(x,y,z) * K(x,u) = K(x,u) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3311(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3311 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3319">
    <literal><![CDATA[
      T((x \ y) \ y,K(x,z)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(3311(a,1),316(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3311 316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3320">
    <literal><![CDATA[
      T((x * y) / x,K(y,z)) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(3311(a,1),460(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3311 460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3321">
    <literal><![CDATA[
      T(K(x,y),T(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,3313,a)].">
      <j1 rule="hyper" parents="49 3313"/>
    </justification>
  </clause>

  <clause id="3322">
    <literal><![CDATA[
      T(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(3321(a,1),284(a,1,2))].">
      <j1 rule="para" parents="3321 284"/>
    </justification>
  </clause>

  <clause id="3323">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),x) = z
    ]]></literal>
    <justification jstring="[para(3321(a,1),3011(a,1))].">
      <j1 rule="para" parents="3321 3011"/>
    </justification>
  </clause>

  <clause id="3324">
    <literal><![CDATA[
      x * K((x \ 1) \ 1,y) = K(x,y) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,3309,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 3309 17"/>
    </justification>
  </clause>

  <clause id="3325">
    <literal><![CDATA[
      T(K(x,y),T(T(x,z),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,3316,a)].">
      <j1 rule="hyper" parents="49 3316"/>
    </justification>
  </clause>

  <clause id="3326">
    <literal><![CDATA[
      T(K(x,y),(z * x) / z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,3320,a)].">
      <j1 rule="hyper" parents="49 3320"/>
    </justification>
  </clause>

  <clause id="3327">
    <literal><![CDATA[
      T(K(x \ y,z),y / x) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),3326(a,1,2,1))].">
      <j1 rule="para" parents="5 3326"/>
    </justification>
  </clause>

  <clause id="3328">
    <literal><![CDATA[
      K(1 / x,y) * (1 / x) = (1 / x) * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),3324(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="75 3324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3329">
    <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(820,a,3312,a),flip(a)].">
      <j1 rule="hyper" parents="820 3312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3330">
    <literal><![CDATA[
      T(x,R(K(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(240,a,3312,a)].">
      <j1 rule="hyper" parents="240 3312"/>
    </justification>
  </clause>

  <clause id="3331">
    <literal><![CDATA[
      K(x,R(K(x,y),z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,3312,a,b,84,a),flip(a)].">
      <j1 rule="hyper" parents="115 3312 84"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3332">
    <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(3330(a,1),237(a,1,2,1))].">
      <j1 rule="para" parents="3330 237"/>
    </justification>
  </clause>

  <clause id="3333">
    <literal><![CDATA[
      T(K(x,y),L(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(240,a,3317,a)].">
      <j1 rule="hyper" parents="240 3317"/>
    </justification>
  </clause>

  <clause id="3334">
    <literal><![CDATA[
      T(K(x,y),R(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(240,a,3318,a)].">
      <j1 rule="hyper" parents="240 3318"/>
    </justification>
  </clause>

  <clause id="3335">
    <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(3334(a,1),284(a,1,2))].">
      <j1 rule="para" parents="3334 284"/>
    </justification>
  </clause>

  <clause id="3336">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * K(x \ 1,y)) = x \ K(1 / x,y)
    ]]></literal>
    <justification jstring="[para(3328(a,1),3015(a,1,2))].">
      <j1 rule="para" parents="3328 3015"/>
    </justification>
  </clause>

  <clause id="3337">
    <literal><![CDATA[
      T(x,x \ K(y,x)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3310(a,1),3086(a,1,2,2))].">
      <j1 rule="para" parents="3310 3086"/>
    </justification>
  </clause>

  <clause id="3338">
    <literal><![CDATA[
      x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(3310(a,1),3089(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3310 3089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3339">
    <literal><![CDATA[
      K(x,y) / T(y,y \ 1) = y \ K(x,y)
    ]]></literal>
    <justification jstring="[para(3337(a,1),265(a,1,2))].">
      <j1 rule="para" parents="3337 265"/>
    </justification>
  </clause>

  <clause id="3340">
    <literal><![CDATA[
      K(x,y) * K(y \ 1,y) = (y \ K(x,y)) * y
    ]]></literal>
    <justification jstring="[para(3339(a,1),2642(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3339 2642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3341">
    <literal><![CDATA[
      (x \ K(y,x)) * K(x,x \ 1) = K(y,x) / x
    ]]></literal>
    <justification jstring="[para(3339(a,1),2673(a,1,1))].">
      <j1 rule="para" parents="3339 2673"/>
    </justification>
  </clause>

  <clause id="3342">
    <literal><![CDATA[
      K(x,y) * K(y,y \ 1) = y * (K(x,y) / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,3341,a(flip),b,2429,a),flip(a)].">
      <j1 rule="hyper" parents="119 3341 2429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3343">
    <literal><![CDATA[
      x * (x * (K(y,x) / x)) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(3342(a,1),3077(a,1,2))].">
      <j1 rule="para" parents="3342 3077"/>
    </justification>
  </clause>

  <clause id="3344">
    <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,3343,a(flip),b,1106,a),flip(a)].">
      <j1 rule="hyper" parents="116 3343 1106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3345">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = (T(y,x \ 1) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[para(2936(a,1),3297(a,2,1,1))].">
      <j1 rule="para" parents="2936 3297"/>
    </justification>
  </clause>

  <clause id="3346">
    <literal><![CDATA[
      (1 / x) \ ((((1 / x) * y) \ 1) \ 1) = y * K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,2570,a,b,3304,a),flip(a)].">
      <j1 rule="hyper" parents="320 2570 3304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3347">
    <literal><![CDATA[
      (x \ 1) * K(x \ 1,y) = x \ K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(2935,a,3336,a)].">
      <j1 rule="hyper" parents="2935 3336"/>
    </justification>
  </clause>

  <clause id="3348">
    <literal><![CDATA[
      (x \ K(1 / x,y)) * ((x \ 1) \ 1) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(3347(a,1),1734(a,1,1))].">
      <j1 rule="para" parents="3347 1734"/>
    </justification>
  </clause>

  <clause id="3349">
    <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),3348(a,1,1,2))].">
      <j1 rule="para" parents="87 3348"/>
    </justification>
  </clause>

  <clause id="3350">
    <literal><![CDATA[
      L(T((x \ y) \ z,z \ (x \ y)),x \ y,x) = ((y \ (x * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2359(a,2),3286(a,1,1))].">
      <j1 rule="para" parents="2359 3286"/>
    </justification>
  </clause>

  <clause id="3351">
    <literal><![CDATA[
      L((x \ 1) \ 1,L(x,y,z) \ 1,L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(142,a,3287,a)].">
      <j1 rule="hyper" parents="142 3287"/>
    </justification>
  </clause>

  <clause id="3352">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * ((x \ 1) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,3351,a(flip),b,257,a),flip(a)].">
      <j1 rule="hyper" parents="116 3351 257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3354">
    <literal><![CDATA[
      T(x,L(x,y,z) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(239,a,1404,a,b,3352,a)].">
      <j1 rule="hyper" parents="239 1404 3352"/>
    </justification>
  </clause>

  <clause id="3355">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(x \ 1,x) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(3352(a,1),2641(a,1,1))].">
      <j1 rule="para" parents="3352 2641"/>
    </justification>
  </clause>

  <clause id="3356">
    <literal><![CDATA[
      T(x,L(x,y,z) \ 1) = K(x,x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,1804,a,b,3354,a),flip(a)].">
      <j1 rule="hyper" parents="320 1804 3354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3357">
    <literal><![CDATA[
      T(x,L(x,y,z) \ 1) != u * x
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = u
    ]]></literal>
    <justification jstring="[para(3356(a,2),39(a,1))].">
      <j1 rule="para" parents="3356 39"/>
    </justification>
  </clause>

  <clause id="3358">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ ((L(x,y,z) \ 1) * x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,3355,a)].">
      <j1 rule="hyper" parents="123 3355"/>
    </justification>
  </clause>

  <clause id="3359">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1408,a,3358,a)].">
      <j1 rule="hyper" parents="1408 3358"/>
    </justification>
  </clause>

  <clause id="3360">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2504,a,b,3359,a)].">
      <j1 rule="hyper" parents="58 2504 3359"/>
    </justification>
  </clause>

  <clause id="3361">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) = x * (y * K(z \ 1,z))
    ]]></literal>
    <justification jstring="[para(3359(a,1),2505(a,1,2))].">
      <j1 rule="para" parents="3359 2505"/>
    </justification>
  </clause>

  <clause id="3364">
    <literal><![CDATA[
      a(x,y,K(z \ 1,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,3360,a,b,1923,a),flip(a)].">
      <j1 rule="hyper" parents="115 3360 1923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3365">
    <literal><![CDATA[
      (x \ 1) * K(y \ 1,y) = x \ K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,3360,a(flip),b,257,a),flip(a)].">
      <j1 rule="hyper" parents="116 3360 257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3366">
    <literal><![CDATA[
      x \ (y * K(z \ 1,z)) = (x \ y) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(3360(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="3360 474"/>
    </justification>
  </clause>

  <clause id="3369">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(1784(a,1),3364(a,1,3))].">
      <j1 rule="para" parents="1784 3364"/>
    </justification>
  </clause>

  <clause id="3370">
    <literal><![CDATA[
      a(x,y,K(1 / z,z)) = 1
    ]]></literal>
    <justification jstring="[para(1816(a,2),3364(a,1,3))].">
      <j1 rule="para" parents="1816 3364"/>
    </justification>
  </clause>

  <clause id="3371">
    <literal><![CDATA[
      (x * y) * K(z,z \ 1) = x * (y * K(z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(969,a,3369,a)].">
      <j1 rule="hyper" parents="969 3369"/>
    </justification>
  </clause>

  <clause id="3372">
    <literal><![CDATA[
      L(K(x,x \ 1),y,z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(47,a,3369,a)].">
      <j1 rule="hyper" parents="47 3369"/>
    </justification>
  </clause>

  <clause id="3374">
    <literal><![CDATA[
      (x * y) * K(1 / z,z) = x * (y * K(1 / z,z))
    ]]></literal>
    <justification jstring="[hyper(969,a,3370,a)].">
      <j1 rule="hyper" parents="969 3370"/>
    </justification>
  </clause>

  <clause id="3375">
    <literal><![CDATA[
      L(K(1 / x,x),y,z) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(47,a,3370,a)].">
      <j1 rule="hyper" parents="47 3370"/>
    </justification>
  </clause>

  <clause id="3377">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * (L(x,y,z) \ x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3267,a,b,3372,a)].">
      <j1 rule="hyper" parents="58 3267 3372"/>
    </justification>
  </clause>

  <clause id="3378">
    <literal><![CDATA[
      (x \ 1) * K(y,y \ 1) = x \ K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,3372,a(flip),b,257,a),flip(a)].">
      <j1 rule="hyper" parents="116 3372 257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3379">
    <literal><![CDATA[
      x \ (y * K(z,z \ 1)) = (x \ y) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(3372(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="3372 474"/>
    </justification>
  </clause>

  <clause id="3380">
    <literal><![CDATA[
      (x \ K(y,y \ 1)) * y = (x \ 1) * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3378(a,1),2666(a,1,1))].">
      <j1 rule="para" parents="3378 2666"/>
    </justification>
  </clause>

  <clause id="3381">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(2189,a,3361,a)].">
      <j1 rule="hyper" parents="2189 3361"/>
    </justification>
  </clause>

  <clause id="3382">
    <literal><![CDATA[
      R(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(515,a,3361,a)].">
      <j1 rule="hyper" parents="515 3361"/>
    </justification>
  </clause>

  <clause id="3383">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) = x * (K(z \ 1,z) * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2203,a,b,3361,a),flip(a)].">
      <j1 rule="hyper" parents="320 2203 3361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3388">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / z = x / (z * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(2702,a,3382,a),flip(a)].">
      <j1 rule="hyper" parents="2702 3382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3389">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,2765,a(flip),b,3382,a),flip(a)].">
      <j1 rule="hyper" parents="58 2765 3382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3390">
    <literal><![CDATA[
      R(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[para(75(a,1),3382(a,1,3,1))].">
      <j1 rule="para" parents="75 3382"/>
    </justification>
  </clause>

  <clause id="3392">
    <literal><![CDATA[
      R(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1784(a,1),3382(a,1,3))].">
      <j1 rule="para" parents="1784 3382"/>
    </justification>
  </clause>

  <clause id="3393">
    <literal><![CDATA[
      R(x,y,K(1 / z,z)) = x
    ]]></literal>
    <justification jstring="[para(1816(a,2),3382(a,1,3))].">
      <j1 rule="para" parents="1816 3382"/>
    </justification>
  </clause>

  <clause id="3394">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = (x \ z) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(3382(a,1),2206(a,1,1))].">
      <j1 rule="para" parents="3382 2206"/>
    </justification>
  </clause>

  <clause id="3395">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / z != u
    ]]></literal>
    <literal><![CDATA[
      x / (z * K(y \ 1,y)) = u
    ]]></literal>
    <justification jstring="[para(3382(a,1),2702(a,1))].">
      <j1 rule="para" parents="3382 2702"/>
    </justification>
  </clause>

  <clause id="3396">
    <literal><![CDATA[
      R(x,y,K(z,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3390(a,1),46(a,2))].">
      <j1 rule="para" parents="3390 46"/>
    </justification>
  </clause>

  <clause id="3397">
    <literal><![CDATA[
      (x * y) * K(z,1 / z) = x * (y * K(z,1 / z))
    ]]></literal>
    <justification jstring="[para(3390(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3390 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3398">
    <literal><![CDATA[
      R(x,y,1 / z) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(2761,a,3392,a)].">
      <j1 rule="hyper" parents="2761 3392"/>
    </justification>
  </clause>

  <clause id="3401">
    <literal><![CDATA[
      R(x,y,K(z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3392(a,1),46(a,2))].">
      <j1 rule="para" parents="3392 46"/>
    </justification>
  </clause>

  <clause id="3402">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * z) = (x \ z) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3392(a,1),2195(a,1,1))].">
      <j1 rule="para" parents="3392 2195"/>
    </justification>
  </clause>

  <clause id="3403">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * K(1 / u,u)) = L(z,y,x) * K(1 / u,u)
    ]]></literal>
    <justification jstring="[para(3393(a,1),543(a,1,1))].">
      <j1 rule="para" parents="3393 543"/>
    </justification>
  </clause>

  <clause id="3405">
    <literal><![CDATA[
      R(x,y,z) * (y * ((z \ 1) \ 1)) = (x * y) * ((z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3389(a,1),101(a,1,1))].">
      <j1 rule="para" parents="3389 101"/>
    </justification>
  </clause>

  <clause id="3409">
    <literal><![CDATA[
      x \ (y * K(z \ 1,z)) = K(z \ 1,z) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2180,a,b,3366,a),flip(a)].">
      <j1 rule="hyper" parents="320 2180 3366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3410">
    <literal><![CDATA[
      (x \ (1 / y)) * K(y \ 1,y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(774(a,1),3366(a,1,2)),flip(a)].">
      <j1 rule="para" parents="774 3366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3411">
    <literal><![CDATA[
      (x \ ((y \ 1) \ 1)) * K(y \ 1,y) = x \ y
    ]]></literal>
    <justification jstring="[para(1250(a,1),3366(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1250 3366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3413">
    <literal><![CDATA[
      (x \ (y / (z \ 1))) * K(z \ 1,z) = x \ (y / (1 / z))
    ]]></literal>
    <justification jstring="[para(2602(a,1),3366(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2602 3366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3414">
    <literal><![CDATA[
      (x \ y) * K(y,y \ 1) = x \ ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2693,a,3411,a)].">
      <j1 rule="hyper" parents="2693 3411"/>
    </justification>
  </clause>

  <clause id="3415">
    <literal><![CDATA[
      T(x,y) \ ((x \ 1) \ 1) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(30,a,3049,a,b,3411,a),flip(a)].">
      <j1 rule="hyper" parents="30 3049 3411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3416">
    <literal><![CDATA[
      x \ (y * K(z,z \ 1)) = K(z,z \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2169,a,b,3379,a),flip(a)].">
      <j1 rule="hyper" parents="320 2169 3379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3418">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,2203,a,b,3381,a),flip(a)].">
      <j1 rule="hyper" parents="320 2203 3381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3419">
    <literal><![CDATA[
      (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(u * K(z \ 1,z),y,x)
    ]]></literal>
    <justification jstring="[para(3381(a,2),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3381 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3420">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (K(x \ 1,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(2698,a,3383,a)].">
      <j1 rule="hyper" parents="2698 3383"/>
    </justification>
  </clause>

  <clause id="3421">
    <literal><![CDATA[
      x \ (y * (K(z \ 1,z) * u)) = (x \ (y * u)) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(3383(a,1),3366(a,1,2))].">
      <j1 rule="para" parents="3383 3366"/>
    </justification>
  </clause>

  <clause id="3422">
    <literal><![CDATA[
      1 / (x * K(y \ 1,y)) = K(y,y \ 1) / x
    ]]></literal>
    <justification jstring="[para(2(a,1),3388(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2 3388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3423">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / (z * ((y \ 1) \ 1)) = x / (z * y)
    ]]></literal>
    <justification jstring="[para(2641(a,1),3388(a,2,2))].">
      <j1 rule="para" parents="2641 3388"/>
    </justification>
  </clause>

  <clause id="3424">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = K(y \ 1,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,2180,a,b,3394,a),flip(a)].">
      <j1 rule="hyper" parents="320 2180 3394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3426">
    <literal><![CDATA[
      x * (K(y,y \ 1) * (x \ z)) = K(y,y \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(2172,a,3402,a)].">
      <j1 rule="hyper" parents="2172 3402"/>
    </justification>
  </clause>

  <clause id="3428">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ x) = y \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(1779(a,1),3409(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1779 3409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3429">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ (z * (1 / x))) = y \ (z * (x \ 1))
    ]]></literal>
    <justification jstring="[para(2588(a,1),3409(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2588 3409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3431">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ ((x \ 1) * z)) = y \ ((1 / x) * z)
    ]]></literal>
    <justification jstring="[para(2825(a,1),3416(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2825 3416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3432">
    <literal><![CDATA[
      (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(K(z \ 1,z) * u,y,x)
    ]]></literal>
    <justification jstring="[para(3418(a,2),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3418 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3435">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * (x \ 1))) = y * (z * (1 / x))
    ]]></literal>
    <justification jstring="[para(2603(a,1),3420(a,1,2,2))].">
      <j1 rule="para" parents="2603 3420"/>
    </justification>
  </clause>

  <clause id="3436">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z / (1 / x))) = y * (z / (x \ 1))
    ]]></literal>
    <justification jstring="[para(2610(a,1),3420(a,1,2,2))].">
      <j1 rule="para" parents="2610 3420"/>
    </justification>
  </clause>

  <clause id="3437">
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) = y * (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2679(a,1),3420(a,1,2,2))].">
      <j1 rule="para" parents="2679 3420"/>
    </justification>
  </clause>

  <clause id="3438">
    <literal><![CDATA[
      K(x,x \ 1) * (y * ((1 / x) \ z)) = y * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2821(a,1),3420(a,1,2,2))].">
      <j1 rule="para" parents="2821 3420"/>
    </justification>
  </clause>

  <clause id="3443">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * x)) = y * (z * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(2663(a,1),3437(a,2,2))].">
      <j1 rule="para" parents="2663 3437"/>
    </justification>
  </clause>

  <clause id="3444">
    <literal><![CDATA[
      x \ (y * (K(z,z \ 1) * u)) = (x \ (y * u)) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(3437(a,1),3402(a,1,2))].">
      <j1 rule="para" parents="3437 3402"/>
    </justification>
  </clause>

  <clause id="3446">
    <literal><![CDATA[
      (1 / (1 / x)) / (y * x) = x / (y * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(1790(a,1),3423(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1790 3423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3447">
    <literal><![CDATA[
      (1 / x) * (y * ((1 / x) \ z)) = (x \ 1) * (y * ((x \ 1) \ z))
    ]]></literal>
    <justification jstring="[hyper(119,a,3438,a(flip),b,2932,a),flip(a)].">
      <j1 rule="hyper" parents="119 3438 2932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3448">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ (z * ((1 / x) \ u))) = y \ (z * ((x \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(116,a,3438,a(flip),b,3426,a),flip(a)].">
      <j1 rule="hyper" parents="116 3438 3426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3450">
    <literal><![CDATA[
      (x * y) * ((z \ 1) \ 1) != u * (y * ((z \ 1) \ 1))
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3405(a,1),39(a,1))].">
      <j1 rule="para" parents="3405 39"/>
    </justification>
  </clause>

  <clause id="3451">
    <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),3421(a,2,1))].">
      <j1 rule="para" parents="13 3421"/>
    </justification>
  </clause>

  <clause id="3452">
    <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(691,a,3444,a),flip(a)].">
      <j1 rule="hyper" parents="691 3444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3453">
    <literal><![CDATA[
      x * (((x * y) \ (x * T(x \ (x * y),x))) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(3058(a,1),3338(a,1,2))].">
      <j1 rule="para" parents="3058 3338"/>
    </justification>
  </clause>

  <clause id="3454">
    <literal><![CDATA[
      x * (((x * y) \ (x * T(y,x))) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),3453(a,1,2,1,2,2,1))].">
      <j1 rule="para" parents="4 3453"/>
    </justification>
  </clause>

  <clause id="3455">
    <literal><![CDATA[
      x * (((x * y) \ (y * x)) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(105(a,1),3454(a,1,2,1,2))].">
      <j1 rule="para" parents="105 3454"/>
    </justification>
  </clause>

  <clause id="3456">
    <literal><![CDATA[
      x * (K(y,x) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(11(a,2),3455(a,1,2,1))].">
      <j1 rule="para" parents="11 3455"/>
    </justification>
  </clause>

  <clause id="3457">
    <literal><![CDATA[
      x * (K(y,x) \ 1) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(320,a,3046,a(flip),b,3456,a),flip(a)].">
      <j1 rule="hyper" parents="320 3046 3456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3458">
    <literal><![CDATA[
      (K(x,y) \ 1) \ (K(x,y) \ y) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,3457,a(flip),b,3120,a)].">
      <j1 rule="hyper" parents="116 3457 3120"/>
    </justification>
  </clause>

  <clause id="3459">
    <literal><![CDATA[
      K(x,y) \ y != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) \ 1 = z
    ]]></literal>
    <justification jstring="[para(3457(a,1),38(a,1))].">
      <j1 rule="para" parents="3457 38"/>
    </justification>
  </clause>

  <clause id="3460">
    <literal><![CDATA[
      (K(x,y) \ y) \ (K(x,y) \ 1) = y \ 1
    ]]></literal>
    <justification jstring="[para(3457(a,1),3122(a,1,1))].">
      <j1 rule="para" parents="3457 3122"/>
    </justification>
  </clause>

  <clause id="3461">
    <literal><![CDATA[
      (K(x,y) \ 1) * T(y,z) = K(x,y) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(3458(a,1),984(a,1,2,1))].">
      <j1 rule="para" parents="3458 984"/>
    </justification>
  </clause>

  <clause id="3462">
    <literal><![CDATA[
      (K(x,y) \ y) * (y \ 1) = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(134,a,3460,a)].">
      <j1 rule="hyper" parents="134 3460"/>
    </justification>
  </clause>

  <clause id="3463">
    <literal><![CDATA[
      R(K(x,y) \ y,y \ 1,y) = (K(x,y) \ 1) * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3462(a,1),2646(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3462 2646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3464">
    <literal><![CDATA[
      K(x,y) \ T(y,y \ z) = (K(x,y) \ 1) * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,313,a(flip),b,3461,a),flip(a)].">
      <j1 rule="hyper" parents="58 313 3461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3465">
    <literal><![CDATA[
      (K(x,y) \ 1) * ((y \ z) \ z) = K(x,y) \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,310,a(flip),b,3464,a),flip(a)].">
      <j1 rule="hyper" parents="58 310 3464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3466">
    <literal><![CDATA[
      R(K(x,y) \ y,y \ 1,y) = K(x,y) \ ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3465,a(flip),b,3463,a),flip(a)].">
      <j1 rule="hyper" parents="320 3465 3463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3467">
    <literal><![CDATA[
      x * (K(x,y) * (K(x,y) \ ((y \ 1) \ 1))) = (T(y,y \ 1) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(3466(a,1),2530(a,1,2,2))].">
      <j1 rule="para" parents="3466 2530"/>
    </justification>
  </clause>

  <clause id="3468">
    <literal><![CDATA[
      x * (x * (T(x,y) \ (K(z,x) / x))) = T(x,y) \ ((x \ 1) \ K(z,x))
    ]]></literal>
    <justification jstring="[para(1108(a,1),3344(a,1,2))].">
      <j1 rule="para" parents="1108 3344"/>
    </justification>
  </clause>

  <clause id="3469">
    <literal><![CDATA[
      T(x \ (y * z),z \ (y \ x)) = ((x \ (y * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,753,a(flip),b,3350,a)].">
      <j1 rule="hyper" parents="58 753 3350"/>
    </justification>
  </clause>

  <clause id="3470">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * K(1 / u,u))) = L(z,y,x) * K(1 / u,u)
    ]]></literal>
    <justification jstring="[para(3374(a,1),3403(a,1,2))].">
      <j1 rule="para" parents="3374 3403"/>
    </justification>
  </clause>

  <clause id="3471">
    <literal><![CDATA[
      L(K(x \ 1,x) * y,z,u) = L(y,z,u) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3432,a(flip),b,3451,a)].">
      <j1 rule="hyper" parents="58 3432 3451"/>
    </justification>
  </clause>

  <clause id="3472">
    <literal><![CDATA[
      L(x * K(y \ 1,y),z,u) = L(x,z,u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3419,a(flip),b,3451,a)].">
      <j1 rule="hyper" parents="58 3419 3451"/>
    </justification>
  </clause>

  <clause id="3473">
    <literal><![CDATA[
      L(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,2180,a,b,3471,a),flip(a)].">
      <j1 rule="hyper" parents="320 2180 3471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3474">
    <literal><![CDATA[
      L(x,y,z) * K(x \ 1,x) = L(1 / (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(1800(a,1),3471(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1800 3471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3476">
    <literal><![CDATA[
      K(x \ 1,x) * L((x \ 1) \ 1,y,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(907(a,1),3473(a,1,1)),flip(a)].">
      <j1 rule="para" parents="907 3473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3477">
    <literal><![CDATA[
      K(x \ 1,x) * L(1 / x,y,z) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1777(a,1),3473(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1777 3473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3479">
    <literal><![CDATA[
      K(x \ 1,x) * L(y * K(x,x \ 1),z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[para(2677(a,1),3473(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2677 3473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3480">
    <literal><![CDATA[
      K(x,x \ 1) * L(x,y,z) = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(2697,a,3476,a)].">
      <j1 rule="hyper" parents="2697 3476"/>
    </justification>
  </clause>

  <clause id="3481">
    <literal><![CDATA[
      L(x,y,z) * K(x,x \ 1) = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(2691,a,3476,a)].">
      <j1 rule="hyper" parents="2691 3476"/>
    </justification>
  </clause>

  <clause id="3482">
    <literal><![CDATA[
      K(x \ 1,x) * ((y * (x \ 1)) \ y) = L(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,395,a(flip),b,3476,a)].">
      <j1 rule="hyper" parents="58 395 3476"/>
    </justification>
  </clause>

  <clause id="3483">
    <literal><![CDATA[
      L(x \ 1,y,z) * K(x,x \ 1) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2691,a,3477,a)].">
      <j1 rule="hyper" parents="2691 3477"/>
    </justification>
  </clause>

  <clause id="3485">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,3477,a(flip),b,1830,a(flip))].">
      <j1 rule="hyper" parents="116 3477 1830"/>
    </justification>
  </clause>

  <clause id="3486">
    <literal><![CDATA[
      K(x,x \ 1) * L(x,y,z) = L(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,823,a,b,3480,a),flip(a)].">
      <j1 rule="hyper" parents="320 823 3480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3487">
    <literal><![CDATA[
      x \ L((x \ 1) \ 1,y,z) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3480,a(flip),b,2191,a(flip))].">
      <j1 rule="hyper" parents="116 3480 2191"/>
    </justification>
  </clause>

  <clause id="3488">
    <literal><![CDATA[
      L(x,y,z) * K(x,1 / x) = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1780(a,2),3481(a,1,2))].">
      <j1 rule="para" parents="1780 3481"/>
    </justification>
  </clause>

  <clause id="3489">
    <literal><![CDATA[
      x \ L(T(x,x \ 1),y,z) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3486,a(flip),b,2191,a(flip))].">
      <j1 rule="hyper" parents="116 3486 2191"/>
    </justification>
  </clause>

  <clause id="3490">
    <literal><![CDATA[
      T(L(x,y,z) * (1 / x),x) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1276,a,b,3487,a)].">
      <j1 rule="hyper" parents="58 1276 3487"/>
    </justification>
  </clause>

  <clause id="3491">
    <literal><![CDATA[
      (x \ L(x,y,z)) * x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2325,a,3490,a)].">
      <j1 rule="hyper" parents="2325 3490"/>
    </justification>
  </clause>

  <clause id="3492">
    <literal><![CDATA[
      T(x,x \ L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(355,a,3491,a)].">
      <j1 rule="hyper" parents="355 3491"/>
    </justification>
  </clause>

  <clause id="3493">
    <literal><![CDATA[
      L(x,y,z) / x = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,3491,a)].">
      <j1 rule="hyper" parents="131 3491"/>
    </justification>
  </clause>

  <clause id="3494">
    <literal><![CDATA[
      K(x \ L(x,y,z),x) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,3491,a(flip),b,302,a),flip(a)].">
      <j1 rule="hyper" parents="115 3491 302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3495">
    <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(3491(a,1),424(a,1,1))].">
      <j1 rule="para" parents="3491 424"/>
    </justification>
  </clause>

  <clause id="3496">
    <literal><![CDATA[
      T(x,y) * (x \ L(x,z,u)) = (x \ L(x,z,u)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3492(a,1),236(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3492 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3497">
    <literal><![CDATA[
      L(x * K(y,y \ 1),z,u) = K(y,y \ 1) * L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(2697,a,3479,a),flip(a)].">
      <j1 rule="hyper" parents="2697 3479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3498">
    <literal><![CDATA[
      L(x * K(y,y \ 1),z,u) = L(x,z,u) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2691,a,3479,a),flip(a)].">
      <j1 rule="hyper" parents="2691 3479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3499">
    <literal><![CDATA[
      (x \ L(x * (y / x),z,u)) * x = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,2741,a(flip),b,3479,a)].">
      <j1 rule="hyper" parents="58 2741 3479"/>
    </justification>
  </clause>

  <clause id="3501">
    <literal><![CDATA[
      (x \ L(x * y,z,u)) * x = L(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(6(a,1),3499(a,1,1,2,1,2))].">
      <j1 rule="para" parents="6 3499"/>
    </justification>
  </clause>

  <clause id="3502">
    <literal><![CDATA[
      L(x * (y / x),z,u) = x * (L(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(3499(a,1),71(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3499 71"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3503">
    <literal><![CDATA[
      L((x \ y) * x,z,u) = (x \ L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(71(a,1),3499(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="71 3499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3504">
    <literal><![CDATA[
      (x \ 1) \ L((x \ 1) * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(30,a,1231,a,b,3501,a),flip(a)].">
      <j1 rule="hyper" parents="30 1231 3501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3505">
    <literal><![CDATA[
      L(x * ((y \ (z \ u)) / x),y,z) = x * (((z * y) \ u) / x)
    ]]></literal>
    <justification jstring="[para(298(a,1),3502(a,2,2,1))].">
      <j1 rule="para" parents="298 3502"/>
    </justification>
  </clause>

  <clause id="3506">
    <literal><![CDATA[
      L(x * (y / x),y \ 1,y) = x * ((1 / (1 / y)) / x)
    ]]></literal>
    <justification jstring="[para(1801(a,1),3502(a,2,2,1))].">
      <j1 rule="para" parents="1801 3502"/>
    </justification>
  </clause>

  <clause id="3507">
    <literal><![CDATA[
      L((x \ y) * x,z,u) != w * x
    ]]></literal>
    <literal><![CDATA[
      x \ L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(3503(a,2),39(a,1))].">
      <j1 rule="para" parents="3503 39"/>
    </justification>
  </clause>

  <clause id="3508">
    <literal><![CDATA[
      L((x \ (y \ (z \ u))) * x,y,z) = (x \ ((z * y) \ u)) * x
    ]]></literal>
    <justification jstring="[para(298(a,1),3503(a,2,1,2))].">
      <j1 rule="para" parents="298 3503"/>
    </justification>
  </clause>

  <clause id="3509">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ z)) * x,y \ 1,y) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(489(a,1),3503(a,2,1,2))].">
      <j1 rule="para" parents="489 3503"/>
    </justification>
  </clause>

  <clause id="3510">
    <literal><![CDATA[
      L((x \ ((y \ z) \ u)) * x,y \ z,y) = (x \ (z \ (y * u))) * x
    ]]></literal>
    <justification jstring="[para(490(a,1),3503(a,2,1,2))].">
      <j1 rule="para" parents="490 3503"/>
    </justification>
  </clause>

  <clause id="3511">
    <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,3496,a(flip),b,1105,a)].">
      <j1 rule="hyper" parents="116 3496 1105"/>
    </justification>
  </clause>

  <clause id="3512">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,z,u) = K(x,x \ 1) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(2169(a,2),3497(a,1,1))].">
      <j1 rule="para" parents="2169 3497"/>
    </justification>
  </clause>

  <clause id="3513">
    <literal><![CDATA[
      x \ L(y * K(z,z \ 1),u,w) = (x \ L(y,u,w)) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(3497(a,2),3402(a,1,2))].">
      <j1 rule="para" parents="3497 3402"/>
    </justification>
  </clause>

  <clause id="3514">
    <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(2365(a,1),3498(a,2,2))].">
      <j1 rule="para" parents="2365 3498"/>
    </justification>
  </clause>

  <clause id="3515">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ u) / z)) = x * (y * (z * ((y \ (x \ u)) / z)))
    ]]></literal>
    <justification jstring="[hyper(119,a,3505,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 3505 13"/>
    </justification>
  </clause>

  <clause id="3516">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ u)) * z) = x * (y * ((z \ (y \ (x \ u))) * z))
    ]]></literal>
    <justification jstring="[hyper(119,a,3508,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 3508 13"/>
    </justification>
  </clause>

  <clause id="3517">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(116,a,3509,a(flip),b,257,a),flip(a)].">
      <j1 rule="hyper" parents="116 3509 257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3518">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * K(1 / u,u)))) = L(z,y,x) * K(1 / u,u)
    ]]></literal>
    <justification jstring="[para(3374(a,1),3470(a,1,2,2))].">
      <j1 rule="para" parents="3374 3470"/>
    </justification>
  </clause>

  <clause id="3519">
    <literal><![CDATA[
      L(x \ 1,x,x \ L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(3495,a,1187,a)].">
      <j1 rule="hyper" parents="3495 1187"/>
    </justification>
  </clause>

  <clause id="3520">
    <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(3519(a,1),3261(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3519 3261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3521">
    <literal><![CDATA[
      L(x * K(1 / y,y),z,u) = L(x,z,u) * K(1 / y,y)
    ]]></literal>
    <justification jstring="[hyper(482,a,3518,a)].">
      <j1 rule="hyper" parents="482 3518"/>
    </justification>
  </clause>

  <clause id="3522">
    <literal><![CDATA[
      K(x,y) = (T(y,y \ 1) * x) \ (x * ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(598,a,3467,a),flip(a)].">
      <j1 rule="hyper" parents="598 3467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3523">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,665,a(flip),b,3522,a)].">
      <j1 rule="hyper" parents="320 665 3522"/>
    </justification>
  </clause>

  <clause id="3525">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = z
    ]]></literal>
    <justification jstring="[para(3522(a,2),666(a,1))].">
      <j1 rule="para" parents="3522 666"/>
    </justification>
  </clause>

  <clause id="3526">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3130,a,b,3523,a)].">
      <j1 rule="hyper" parents="58 3130 3523"/>
    </justification>
  </clause>

  <clause id="3527">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3112,a(flip),b,3523,a),flip(a)].">
      <j1 rule="hyper" parents="58 3112 3523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3528">
    <literal><![CDATA[
      K(x,1 / y) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),3523(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 3523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3529">
    <literal><![CDATA[
      K(x,1 / (1 / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(196(a,1),3523(a,1,2)),flip(a)].">
      <j1 rule="para" parents="196 3523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3530">
    <literal><![CDATA[
      K(x,T(y,1 / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1259(a,2),3523(a,1,2))].">
      <j1 rule="para" parents="1259 3523"/>
    </justification>
  </clause>

  <clause id="3531">
    <literal><![CDATA[
      K(x,T(y / z,z / y)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(2057(a,2),3523(a,1,2))].">
      <j1 rule="para" parents="2057 3523"/>
    </justification>
  </clause>

  <clause id="3532">
    <literal><![CDATA[
      K(x,T(y / z,y \ z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(2388(a,2),3523(a,1,2))].">
      <j1 rule="para" parents="2388 3523"/>
    </justification>
  </clause>

  <clause id="3533">
    <literal><![CDATA[
      K(x,((1 / y) \ z) / z) = K(x,((y \ 1) \ z) / z)
    ]]></literal>
    <justification jstring="[para(3060(a,1),3523(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3060 3523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3537">
    <literal><![CDATA[
      (1 / x) * K(y,1 / x) = K(y,x \ 1) / x
    ]]></literal>
    <justification jstring="[para(3528(a,1),2340(a,2,1))].">
      <j1 rule="para" parents="3528 2340"/>
    </justification>
  </clause>

  <clause id="3538">
    <literal><![CDATA[
      (x \ 1) * K(y,x \ 1) = x \ K(y,1 / x)
    ]]></literal>
    <justification jstring="[para(3528(a,2),2909(a,2,2))].">
      <j1 rule="para" parents="3528 2909"/>
    </justification>
  </clause>

  <clause id="3540">
    <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(3282(a,1),3529(a,1,2))].">
      <j1 rule="para" parents="3282 3529"/>
    </justification>
  </clause>

  <clause id="3541">
    <literal><![CDATA[
      K((1 / x) * y,x) = K((x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(2796(a,1),3526(a,1,1))].">
      <j1 rule="para" parents="2796 3526"/>
    </justification>
  </clause>

  <clause id="3542">
    <literal><![CDATA[
      K(x \ ((1 / x) \ y),x) = K(x \ ((x \ 1) \ y),x)
    ]]></literal>
    <justification jstring="[para(3005(a,1),3527(a,1,1))].">
      <j1 rule="para" parents="3005 3527"/>
    </justification>
  </clause>

  <clause id="3543">
    <literal><![CDATA[
      K((1 / (1 / x)) * y,1 / x) = K(x * y,1 / x)
    ]]></literal>
    <justification jstring="[para(75(a,1),3541(a,2,1,1))].">
      <j1 rule="para" parents="75 3541"/>
    </justification>
  </clause>

  <clause id="3544">
    <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,3103,a,b,3533,a)].">
      <j1 rule="hyper" parents="58 3103 3533"/>
    </justification>
  </clause>

  <clause id="3545">
    <literal><![CDATA[
      ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((x \ 1) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,888,a,b,3542,a)].">
      <j1 rule="hyper" parents="58 888 3542"/>
    </justification>
  </clause>

  <clause id="3546">
    <literal><![CDATA[
      L(x * K(y \ z,z \ y),u,w) = L(x,u,w) * K(y \ z,z \ y)
    ]]></literal>
    <justification jstring="[para(2365(a,1),3514(a,1,1,2))].">
      <j1 rule="para" parents="2365 3514"/>
    </justification>
  </clause>

  <clause id="3547">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ x) / z)) = x * (y * (z * ((y \ 1) / z)))
    ]]></literal>
    <justification jstring="[para(61(a,1),3515(a,2,2,2,2,1,2))].">
      <j1 rule="para" parents="61 3515"/>
    </justification>
  </clause>

  <clause id="3548">
    <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),3520(a,2,2,1))].">
      <j1 rule="para" parents="5 3520"/>
    </justification>
  </clause>

  <clause id="3550">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,x \ L(x,u,w)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(179(a,1),3548(a,2,2))].">
      <j1 rule="para" parents="179 3548"/>
    </justification>
  </clause>

  <clause id="3551">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * x) * (L(x,u,w) \ 1) = (x \ L(x,y,z)) * (x * (L(x,u,w) \ 1))
    ]]></literal>
    <justification jstring="[hyper(119,a,3550,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 3550 13"/>
    </justification>
  </clause>

  <clause id="3553">
    <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="[para(3491(a,1),3551(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3491 3551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3554">
    <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(1404(a,1),3553(a,1,2))].">
      <j1 rule="para" parents="1404 3553"/>
    </justification>
  </clause>

  <clause id="3555">
    <literal><![CDATA[
      1 / (L(x,y,z) \ x) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,5,a(flip),b,3554,a)].">
      <j1 rule="hyper" parents="117 5 3554"/>
    </justification>
  </clause>

  <clause id="3556">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,3554,a)].">
      <j1 rule="hyper" parents="116 5 3554"/>
    </justification>
  </clause>

  <clause id="3557">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) = (x \ 1) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(3556(a,1),2330(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3556 2330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3558">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ 1 = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(3485(a,1),3556(a,1,1))].">
      <j1 rule="para" parents="3485 3556"/>
    </justification>
  </clause>

  <clause id="3559">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ 1) = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3216,a(flip),b,3558,a),flip(a)].">
      <j1 rule="hyper" parents="58 3216 3558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3560">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) \ ((x \ 1) \ 1) = (x \ L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(1185(a,1),3558(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1185 3558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3561">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) \ ((x \ 1) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(320,a,3556,a(flip),b,3560,a),flip(a)].">
      <j1 rule="hyper" parents="320 3556 3560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3562">
    <literal><![CDATA[
      x \ T((y \ 1) * (x / (y \ 1)),K(z \ 1,z)) = K(1 / y,x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(3104(a,2),3294(a,1,2))].">
      <j1 rule="para" parents="3104 3294"/>
    </justification>
  </clause>

  <clause id="3563">
    <literal><![CDATA[
      x \ ((1 / y) * (x / (1 / y))) = K(1 / y,x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(3039(a,1),3562(a,1,2))].">
      <j1 rule="para" parents="3039 3562"/>
    </justification>
  </clause>

  <clause id="3564">
    <literal><![CDATA[
      (x \ K(1 / x,y / (x \ 1))) * ((x \ 1) \ 1) = K(x \ 1,y / (1 / x))
    ]]></literal>
    <justification jstring="[para(3563(a,1),3349(a,1,1,2))].">
      <j1 rule="para" parents="3563 3349"/>
    </justification>
  </clause>

  <clause id="3565">
    <literal><![CDATA[
      K(x \ 1,y / (1 / x)) = K(x \ 1,y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,3348,a(flip),b,3564,a),flip(a)].">
      <j1 rule="hyper" parents="58 3348 3564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3566">
    <literal><![CDATA[
      K(x \ 1,(y * (1 / x)) / (x \ 1)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),3565(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 3565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3567">
    <literal><![CDATA[
      K(x \ 1,(y / (x \ 1)) * (1 / x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1511(a,1),3566(a,1,2))].">
      <j1 rule="para" parents="1511 3566"/>
    </justification>
  </clause>

  <clause id="3568">
    <literal><![CDATA[
      K(x \ 1,y * K(x,x \ 1)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(2699(a,1),3567(a,1,2))].">
      <j1 rule="para" parents="2699 3567"/>
    </justification>
  </clause>

  <clause id="3569">
    <literal><![CDATA[
      K(x \ 1,((x \ 1) \ 1) * y) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(2809(a,1),3568(a,1,2))].">
      <j1 rule="para" parents="2809 3568"/>
    </justification>
  </clause>

  <clause id="3570">
    <literal><![CDATA[
      ((x * (K(y,y \ 1) * (z * u))) \ ((x * z) * u)) * K(y,y \ 1) = a(x,z,K(y,y \ 1) * u)
    ]]></literal>
    <justification jstring="[para(3437(a,2),3452(a,1,1,1,2))].">
      <j1 rule="para" parents="3437 3452"/>
    </justification>
  </clause>

  <clause id="3571">
    <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),1696(a,2,2,1,1))].">
      <j1 rule="para" parents="15 1696"/>
    </justification>
  </clause>

  <clause id="3572">
    <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(1709(a,1),3571(a,1,1))].">
      <j1 rule="para" parents="1709 3571"/>
    </justification>
  </clause>

  <clause id="3573">
    <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(1514(a,1),3572(a,1,1,1))].">
      <j1 rule="para" parents="1514 3572"/>
    </justification>
  </clause>

  <clause id="3574">
    <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(518,a,3573,a),flip(a)].">
      <j1 rule="hyper" parents="518 3573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3575">
    <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,1205,a(flip),b,3574,a),flip(a)].">
      <j1 rule="hyper" parents="58 1205 3574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3576">
    <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(650(a,1),3574(a,2,1,2))].">
      <j1 rule="para" parents="650 3574"/>
    </justification>
  </clause>

  <clause id="3577">
    <literal><![CDATA[
      R(x * T(1 * (x \ 1),x),y,z) = a(1 / R(x,y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1211,a,3576,a),flip(a)].">
      <j1 rule="hyper" parents="1211 3576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3578">
    <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),3577(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2 3577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3579">
    <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(1564(a,1),3575(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1564 3575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3580">
    <literal><![CDATA[
      (x \ 1) / (x \ R(x,y,z)) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(30,a,2490,a(flip),b,3579,a),flip(a)].">
      <j1 rule="hyper" parents="30 2490 3579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3581">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(3231,a,3580,a)].">
      <j1 rule="hyper" parents="3231 3580"/>
    </justification>
  </clause>

  <clause id="3582">
    <literal><![CDATA[
      (x \ 1) \ (R(x,y,z) \ 1) = (x \ R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,3581,a(flip),b,2332,a)].">
      <j1 rule="hyper" parents="116 3581 2332"/>
    </justification>
  </clause>

  <clause id="3583">
    <literal><![CDATA[
      ((1 / x) \ R(1 / x,y,z)) \ x = R(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),3581(a,1,2))].">
      <j1 rule="para" parents="75 3581"/>
    </justification>
  </clause>

  <clause id="3584">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) \ x = R(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1207(a,1),3583(a,1,1))].">
      <j1 rule="para" parents="1207 3583"/>
    </justification>
  </clause>

  <clause id="3585">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) \ 1 = (R(x,y,z) / x) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(1884(a,1),3584(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1884 3584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3586">
    <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),1900(a,2,2,1,1))].">
      <j1 rule="para" parents="15 1900"/>
    </justification>
  </clause>

  <clause id="3587">
    <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(1707(a,1),3586(a,1,1))].">
      <j1 rule="para" parents="1707 3586"/>
    </justification>
  </clause>

  <clause id="3588">
    <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(1741(a,1),3587(a,1,1,1))].">
      <j1 rule="para" parents="1741 3587"/>
    </justification>
  </clause>

  <clause id="3589">
    <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(518,a,3588,a),flip(a)].">
      <j1 rule="hyper" parents="518 3588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3590">
    <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(748(a,1),3589(a,2,1,2))].">
      <j1 rule="para" parents="748 3589"/>
    </justification>
  </clause>

  <clause id="3591">
    <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(1875(a,1),3589(a,1,2))].">
      <j1 rule="para" parents="1875 3589"/>
    </justification>
  </clause>

  <clause id="3592">
    <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(1311(a,1),3590(a,1,2))].">
      <j1 rule="para" parents="1311 3590"/>
    </justification>
  </clause>

  <clause id="3593">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(x * (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(198(a,1),3592(a,2,1,2))].">
      <j1 rule="para" parents="198 3592"/>
    </justification>
  </clause>

  <clause id="3594">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(K(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1783(a,2),3593(a,2,1))].">
      <j1 rule="para" parents="1783 3593"/>
    </justification>
  </clause>

  <clause id="3595">
    <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),3591(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3 3591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3596">
    <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(3153(a,1),3595(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3153 3595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3597">
    <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(3151(a,1),3596(a,2,1))].">
      <j1 rule="para" parents="3151 3596"/>
    </justification>
  </clause>

  <clause id="3598">
    <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(320,a,3256,a(flip),b,3597,a),flip(a)].">
      <j1 rule="hyper" parents="320 3256 3597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3599">
    <literal><![CDATA[
      (R(x,y,z) / x) \ (1 / x) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,1783,a(flip),b,3598,a),flip(a)].">
      <j1 rule="hyper" parents="29 1783 3598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3600">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) \ 1 = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3585,a,b,3599,a)].">
      <j1 rule="hyper" parents="58 3585 3599"/>
    </justification>
  </clause>

  <clause id="3601">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) = 1 / (1 / R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(197,a,3600,a),flip(a)].">
      <j1 rule="hyper" parents="197 3600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3602">
    <literal><![CDATA[
      (R(1 / (1 / x),y,z) \ 1) \ 1 = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(188,a,3600,a(flip))].">
      <j1 rule="hyper" parents="188 3600"/>
    </justification>
  </clause>

  <clause id="3603">
    <literal><![CDATA[
      R(T(1 / (1 / x),y),z,u) \ 1 = 1 / R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2154(a,1),3600(a,1,1,1))].">
      <j1 rule="para" parents="2154 3600"/>
    </justification>
  </clause>

  <clause id="3604">
    <literal><![CDATA[
      1 / (1 / R(x \ 1,y,z)) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),3601(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 3601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3605">
    <literal><![CDATA[
      (R(1 / x,y,z) \ 1) \ 1 = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),3602(a,1,1,1,1,2))].">
      <j1 rule="para" parents="72 3602"/>
    </justification>
  </clause>

  <clause id="3606">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) = (R(x,y,z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(190(a,1),3602(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="190 3602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3607">
    <literal><![CDATA[
      T(x,R(1 / y,z,u)) = T(x,R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(3604(a,1),2940(a,1,2))].">
      <j1 rule="para" parents="3604 2940"/>
    </justification>
  </clause>

  <clause id="3608">
    <literal><![CDATA[
      T(x,R(x,y,z) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(701,a,3606,a)].">
      <j1 rule="hyper" parents="701 3606"/>
    </justification>
  </clause>

  <clause id="3609">
    <literal><![CDATA[
      R(((x / y) \ 1) \ 1,y,y \ 1) = ((x * (y \ 1)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(523(a,1),3606(a,2,1,1))].">
      <j1 rule="para" parents="523 3606"/>
    </justification>
  </clause>

  <clause id="3610">
    <literal><![CDATA[
      R(((x / y) \ 1) \ 1,y,z) * (y * z) = (y * z) * ((((y * z) \ (x * z)) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3606(a,2),2162(a,1,1))].">
      <j1 rule="para" parents="3606 2162"/>
    </justification>
  </clause>

  <clause id="3611">
    <literal><![CDATA[
      R(((x / (1 / y)) \ 1) \ 1,y \ 1,y) = ((x * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2593(a,1),3606(a,2,1,1))].">
      <j1 rule="para" parents="2593 3606"/>
    </justification>
  </clause>

  <clause id="3612">
    <literal><![CDATA[
      T(x,R((y \ 1) \ 1,z,u)) = T(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(3606(a,2),2939(a,1,2))].">
      <j1 rule="para" parents="3606 2939"/>
    </justification>
  </clause>

  <clause id="3613">
    <literal><![CDATA[
      T(x,1 / R(x,y,z)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(2937,a,3608,a)].">
      <j1 rule="hyper" parents="2937 3608"/>
    </justification>
  </clause>

  <clause id="3614">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * ((x \ 1) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(3608(a,1),1310(a,1,2))].">
      <j1 rule="para" parents="3608 1310"/>
    </justification>
  </clause>

  <clause id="3615">
    <literal><![CDATA[
      R(K(x,1 / x),y,z) = ((x \ 1) \ 1) / x
    ]]></literal>
    <justification jstring="[para(3613(a,1),3248(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3613 3248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3616">
    <literal><![CDATA[
      R(K(x,1 / x),y,z) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,1261,a(flip),b,3615,a),flip(a)].">
      <j1 rule="hyper" parents="320 1261 3615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3618">
    <literal><![CDATA[
      K(x,1 / x) * (1 / y) = K(x,1 / x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,3616,a(flip),b,2589,a),flip(a)].">
      <j1 rule="hyper" parents="117 3616 2589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3619">
    <literal><![CDATA[
      R(K(x \ 1,x),y,z) = K(x \ 1,1 / (x \ 1))
    ]]></literal>
    <justification jstring="[para(72(a,1),3616(a,1,1,2))].">
      <j1 rule="para" parents="72 3616"/>
    </justification>
  </clause>

  <clause id="3620">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = K(x,1 / x) * (y * z)
    ]]></literal>
    <justification jstring="[para(3616(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3616 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3621">
    <literal><![CDATA[
      K(x,1 / x) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = u
    ]]></literal>
    <justification jstring="[para(3616(a,1),283(a,1,1))].">
      <j1 rule="para" parents="3616 283"/>
    </justification>
  </clause>

  <clause id="3622">
    <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(3422(a,1),3607(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3422 3607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3623">
    <literal><![CDATA[
      R(K(x \ 1,x),y,z) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),3619(a,2,2))].">
      <j1 rule="para" parents="72 3619"/>
    </justification>
  </clause>

  <clause id="3625">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / y) = K(x \ 1,x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,3623,a(flip),b,2589,a),flip(a)].">
      <j1 rule="hyper" parents="117 3623 2589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3626">
    <literal><![CDATA[
      R(x,y,z) != K(u \ 1,u)
    ]]></literal>
    <literal><![CDATA[
      K(u \ 1,u) = x
    ]]></literal>
    <justification jstring="[para(3623(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="3623 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3627">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * z = K(x \ 1,x) * (y * z)
    ]]></literal>
    <justification jstring="[para(3623(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3623 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3628">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(3623(a,1),2204(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3623 2204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3629">
    <literal><![CDATA[
      (1 / x) * K(y \ 1,y) = K(y \ 1,y) / x
    ]]></literal>
    <justification jstring="[hyper(2184,a,3625,a)].">
      <j1 rule="hyper" parents="2184 3625"/>
    </justification>
  </clause>

  <clause id="3630">
    <literal><![CDATA[
      (R(x,y,z) \ 1) \ (R(x,y,z) \ x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,3614,a)].">
      <j1 rule="hyper" parents="123 3614"/>
    </justification>
  </clause>

  <clause id="3632">
    <literal><![CDATA[
      L(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,3620,a)].">
      <j1 rule="hyper" parents="479 3620"/>
    </justification>
  </clause>

  <clause id="3633">
    <literal><![CDATA[
      K(x,1 / x) * ((x \ y) * z) = ((1 / (1 / x)) \ y) * z
    ]]></literal>
    <justification jstring="[para(2951(a,1),3620(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2951 3620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3634">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[para(72(a,1),3632(a,1,3,2))].">
      <j1 rule="para" parents="72 3632"/>
    </justification>
  </clause>

  <clause id="3635">
    <literal><![CDATA[
      L(x,y,1) = x
    ]]></literal>
    <justification jstring="[para(201(a,1),3632(a,1,3))].">
      <j1 rule="para" parents="201 3632"/>
    </justification>
  </clause>

  <clause id="3636">
    <literal><![CDATA[
      L(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1780(a,1),3632(a,1,3))].">
      <j1 rule="para" parents="1780 3632"/>
    </justification>
  </clause>

  <clause id="3637">
    <literal><![CDATA[
      L(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(3635(a,1),45(a,2))].">
      <j1 rule="para" parents="3635 45"/>
    </justification>
  </clause>

  <clause id="3638">
    <literal><![CDATA[
      L(x,y,1 / z) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(3194,a,3634,a),flip(a)].">
      <j1 rule="hyper" parents="3194 3634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3639">
    <literal><![CDATA[
      ((x \ 1) * y) \ (K(x \ 1,x) * z) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,2829,a(flip),b,3634,a)].">
      <j1 rule="hyper" parents="58 2829 3634"/>
    </justification>
  </clause>

  <clause id="3640">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ z = x \ (K(y \ 1,y) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,2692,a(flip),b,3634,a),flip(a)].">
      <j1 rule="hyper" parents="58 2692 3634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3641">
    <literal><![CDATA[
      x \ R(x,y \ 1,y) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2283,a(flip),b,3634,a),flip(a)].">
      <j1 rule="hyper" parents="58 2283 3634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3642">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ (K(x \ 1,x) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,92,a(flip),b,3634,a)].">
      <j1 rule="hyper" parents="58 92 3634"/>
    </justification>
  </clause>

  <clause id="3643">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(3634(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="3634 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3644">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3634(a,1),45(a,2))].">
      <j1 rule="para" parents="3634 45"/>
    </justification>
  </clause>

  <clause id="3645">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / z = K(x \ 1,x) * (y / z)
    ]]></literal>
    <justification jstring="[para(3634(a,1),544(a,1,2))].">
      <j1 rule="para" parents="3634 544"/>
    </justification>
  </clause>

  <clause id="3646">
    <literal><![CDATA[
      L(x,y,K(z \ u,u \ z)) = x
    ]]></literal>
    <justification jstring="[para(2567(a,1),3634(a,1,3))].">
      <j1 rule="para" parents="2567 3634"/>
    </justification>
  </clause>

  <clause id="3648">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z = K(x,x \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1330,a,3636,a),flip(a)].">
      <j1 rule="hyper" parents="1330 3636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3653">
    <literal><![CDATA[
      R(T(x,y * K(z,z \ 1)),y,K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2534,a,b,3636,a)].">
      <j1 rule="hyper" parents="58 2534 3636"/>
    </justification>
  </clause>

  <clause id="3654">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ (K(x,x \ 1) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,92,a(flip),b,3636,a)].">
      <j1 rule="hyper" parents="58 92 3636"/>
    </justification>
  </clause>

  <clause id="3655">
    <literal><![CDATA[
      K(x,x \ 1) * (1 / y) = K(x,x \ 1) / y
    ]]></literal>
    <justification jstring="[para(3636(a,1),423(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3636 423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3656">
    <literal><![CDATA[
      (K(x,x \ 1) * y) / z = K(x,x \ 1) * (y / z)
    ]]></literal>
    <justification jstring="[para(3636(a,1),544(a,1,2))].">
      <j1 rule="para" parents="3636 544"/>
    </justification>
  </clause>

  <clause id="3657">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) / y) = (1 / x) / y
    ]]></literal>
    <justification jstring="[para(3636(a,1),1813(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3636 1813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3658">
    <literal><![CDATA[
      (K(x \ y,y \ x) * z) * u = K(x \ y,y \ x) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(1330,a,3646,a),flip(a)].">
      <j1 rule="hyper" parents="1330 3646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3659">
    <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,2805,a,b,3638,a)].">
      <j1 rule="hyper" parents="58 2805 3638"/>
    </justification>
  </clause>

  <clause id="3660">
    <literal><![CDATA[
      ((1 / x) * y) * L(z,y,x \ 1) = (1 / x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,3638,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 3638 13"/>
    </justification>
  </clause>

  <clause id="3661">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),3638(a,1,3)),flip(a)].">
      <j1 rule="para" parents="72 3638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3662">
    <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(2535(a,2),3643(a,1)),flip(b)].">
      <j1 rule="para" parents="2535 3643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3663">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ 1),u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(2150(a,2),3661(a,1,3))].">
      <j1 rule="para" parents="2150 3661"/>
    </justification>
  </clause>

  <clause id="3664">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ L(y,x \ 1,x) = (((x \ 1) \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(3661(a,1),2840(a,1,2))].">
      <j1 rule="para" parents="3661 2840"/>
    </justification>
  </clause>

  <clause id="3665">
    <literal><![CDATA[
      L(x,y,R(1 / z,u,w)) = L(x,y,R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(3605(a,1),3661(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3605 3661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3666">
    <literal><![CDATA[
      a(x,y \ 1,(y \ 1) \ 1) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2655,a,3641,a)].">
      <j1 rule="hyper" parents="2655 3641"/>
    </justification>
  </clause>

  <clause id="3668">
    <literal><![CDATA[
      K(x,x \ 1) / y != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(3655(a,1),2177(a,1))].">
      <j1 rule="para" parents="3655 2177"/>
    </justification>
  </clause>

  <clause id="3670">
    <literal><![CDATA[
      K(x,x \ 1) * ((K(x \ 1,x) * y) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(2697,a,3627,a(flip))].">
      <j1 rule="hyper" parents="2697 3627"/>
    </justification>
  </clause>

  <clause id="3671">
    <literal><![CDATA[
      ((K(x \ 1,x) * (y * z)) * u) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(3627(a,1),15(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3627 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3672">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) * u = K(z \ 1,z) * ((x * y) * u)
    ]]></literal>
    <justification jstring="[para(3381(a,1),3627(a,1,1))].">
      <j1 rule="para" parents="3381 3627"/>
    </justification>
  </clause>

  <clause id="3673">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T((x \ 1) \ 1,z)) = y * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(3094,a,3628,a),flip(a)].">
      <j1 rule="hyper" parents="3094 3628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3674">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = x * (K(y \ 1,y) * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3418,a(flip),b,3628,a),flip(a)].">
      <j1 rule="hyper" parents="320 3418 3628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3676">
    <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(3628(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3628 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3677">
    <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(3628(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3628 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3678">
    <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(3628(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3628 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3679">
    <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(3628(a,1),307(a,1,2))].">
      <j1 rule="para" parents="3628 307"/>
    </justification>
  </clause>

  <clause id="3681">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * ((x \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(3630(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3630 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3682">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ z = K(y \ 1,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3424,a(flip),b,3640,a),flip(a)].">
      <j1 rule="hyper" parents="320 3424 3640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3684">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ 1 = x \ K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(293,a,3640,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="293 3640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3685">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (1 / y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(1777(a,1),3640(a,2,2))].">
      <j1 rule="para" parents="1777 3640"/>
    </justification>
  </clause>

  <clause id="3686">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) \ 1 = L(x,y,z) \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3481(a,1),3684(a,1,1))].">
      <j1 rule="para" parents="3481 3684"/>
    </justification>
  </clause>

  <clause id="3687">
    <literal><![CDATA[
      L(1 / x,y,z) \ (1 / x) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(3483(a,1),3685(a,1,1))].">
      <j1 rule="para" parents="3483 3685"/>
    </justification>
  </clause>

  <clause id="3688">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = y \ (z * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(2677(a,1),3642(a,1,2))].">
      <j1 rule="para" parents="2677 3642"/>
    </justification>
  </clause>

  <clause id="3689">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = y \ (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2679(a,1),3642(a,1,2))].">
      <j1 rule="para" parents="2679 3642"/>
    </justification>
  </clause>

  <clause id="3690">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ (K(z \ 1,z) * u) = (x * y) \ u
    ]]></literal>
    <justification jstring="[para(3381(a,1),3642(a,1,1))].">
      <j1 rule="para" parents="3381 3642"/>
    </justification>
  </clause>

  <clause id="3691">
    <literal><![CDATA[
      R(K(x,x \ 1),y,z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(3450,a,3648,a)].">
      <j1 rule="hyper" parents="3450 3648"/>
    </justification>
  </clause>

  <clause id="3693">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = K(y,y \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[para(2169(a,1),3648(a,1,1))].">
      <j1 rule="para" parents="2169 3648"/>
    </justification>
  </clause>

  <clause id="3694">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3594,a,b,3691,a)].">
      <j1 rule="hyper" parents="58 3594 3691"/>
    </justification>
  </clause>

  <clause id="3696">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = y \ (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(2685(a,1),3654(a,1,2))].">
      <j1 rule="para" parents="2685 3654"/>
    </justification>
  </clause>

  <clause id="3697">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / z = K(y,y \ 1) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,2193,a(flip),b,3656,a)].">
      <j1 rule="hyper" parents="58 2193 3656"/>
    </justification>
  </clause>

  <clause id="3698">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ 1 = y \ K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(416,a,3670,a),flip(a)].">
      <j1 rule="hyper" parents="416 3670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3699">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ (1 / (1 / x))) * z) = (y \ x) * z
    ]]></literal>
    <justification jstring="[para(3428(a,1),3670(a,1,2,1))].">
      <j1 rule="para" parents="3428 3670"/>
    </justification>
  </clause>

  <clause id="3700">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ 1 = x \ K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(2180(a,1),3698(a,1,1))].">
      <j1 rule="para" parents="2180 3698"/>
    </justification>
  </clause>

  <clause id="3701">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 = L(x,y,z) \ K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3474(a,1),3700(a,1,1))].">
      <j1 rule="para" parents="3474 3700"/>
    </justification>
  </clause>

  <clause id="3702">
    <literal><![CDATA[
      R(x,K(y \ 1,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(3450,a,3674,a)].">
      <j1 rule="hyper" parents="3450 3674"/>
    </justification>
  </clause>

  <clause id="3704">
    <literal><![CDATA[
      R(x,K(y,y \ 1),z) = x
    ]]></literal>
    <justification jstring="[para(1784(a,1),3702(a,1,2))].">
      <j1 rule="para" parents="1784 3702"/>
    </justification>
  </clause>

  <clause id="3705">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = x * (K(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3704(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3704 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3706">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = K(x \ 1,x) * (y \ z)
    ]]></literal>
    <justification jstring="[para(2169(a,2),3682(a,1,1))].">
      <j1 rule="para" parents="2169 3682"/>
    </justification>
  </clause>

  <clause id="3707">
    <literal><![CDATA[
      K(x \ 1,x) * ((y * x) \ z) = (y * ((x \ 1) \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(2660(a,1),3682(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2660 3682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3708">
    <literal><![CDATA[
      K(x \ 1,x) * ((x * y) \ z) = (((x \ 1) \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(2809(a,1),3682(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2809 3682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3709">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = K(x,x \ 1) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3416,a(flip),b,3688,a),flip(a)].">
      <j1 rule="hyper" parents="320 3416 3688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3710">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = (y \ z) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3379,a(flip),b,3688,a),flip(a)].">
      <j1 rule="hyper" parents="320 3379 3688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3711">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ u = (x * y) \ (K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(3381(a,1),3689(a,1,1))].">
      <j1 rule="para" parents="3381 3689"/>
    </justification>
  </clause>

  <clause id="3714">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ x) * z) = (y \ ((x \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(3414(a,1),3693(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3414 3693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3715">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = (y \ z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,3366,a(flip),b,3696,a),flip(a)].">
      <j1 rule="hyper" parents="320 3366 3696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3716">
    <literal><![CDATA[
      x / (y * K(z \ 1,z)) = K(z,z \ 1) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(3395,a,3697,a)].">
      <j1 rule="hyper" parents="3395 3697"/>
    </justification>
  </clause>

  <clause id="3719">
    <literal><![CDATA[
      (x * (y * K(z,z \ 1))) * u = (x * y) * (K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(3371(a,1),3705(a,1,1))].">
      <j1 rule="para" parents="3371 3705"/>
    </justification>
  </clause>

  <clause id="3720">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) \ y) \ z) = ((1 / x) \ y) \ z
    ]]></literal>
    <justification jstring="[para(2821(a,1),3709(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2821 3709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3721">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ u = K(z,z \ 1) * ((x * y) \ u)
    ]]></literal>
    <justification jstring="[para(3381(a,1),3709(a,1,1))].">
      <j1 rule="para" parents="3381 3709"/>
    </justification>
  </clause>

  <clause id="3722">
    <literal><![CDATA[
      (((1 / x) * y) \ z) * K(x,x \ 1) = ((x \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(2791(a,1),3710(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2791 3710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3723">
    <literal><![CDATA[
      (((x \ 1) * y) \ z) * K(x \ 1,x) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[para(2796(a,1),3715(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2796 3715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3724">
    <literal><![CDATA[
      (x * (K(y,y \ 1) * z)) \ u = ((x * z) \ u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(3437(a,1),3715(a,1,1))].">
      <j1 rule="para" parents="3437 3715"/>
    </justification>
  </clause>

  <clause id="3725">
    <literal><![CDATA[
      x / (K(y \ 1,y) * z) = K(y,y \ 1) * (x / z)
    ]]></literal>
    <justification jstring="[para(2180(a,2),3716(a,1,2))].">
      <j1 rule="para" parents="2180 3716"/>
    </justification>
  </clause>

  <clause id="3726">
    <literal><![CDATA[
      x / (y * (z * K(u \ 1,u))) = K(u,u \ 1) * (x / (y * z))
    ]]></literal>
    <justification jstring="[para(3361(a,1),3716(a,1,2))].">
      <j1 rule="para" parents="3361 3716"/>
    </justification>
  </clause>

  <clause id="3727">
    <literal><![CDATA[
      T(x,y * K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3401,a,3653,a)].">
      <j1 rule="hyper" parents="3401 3653"/>
    </justification>
  </clause>

  <clause id="3729">
    <literal><![CDATA[
      T(x,R(1 / y,z,u) * K(w,w \ 1)) = T(x,R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,3607,a(flip),b,3727,a),flip(a)].">
      <j1 rule="hyper" parents="320 3607 3727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3731">
    <literal><![CDATA[
      T(x,y * K(z \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1787(a,1),3727(a,1,2,2))].">
      <j1 rule="para" parents="1787 3727"/>
    </justification>
  </clause>

  <clause id="3732">
    <literal><![CDATA[
      T(x,K(y,y \ 1) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2169(a,2),3727(a,1,2))].">
      <j1 rule="para" parents="2169 3727"/>
    </justification>
  </clause>

  <clause id="3733">
    <literal><![CDATA[
      T(x,L(y,z,u) * (1 / y)) = T(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(2242(a,1),3727(a,1,2))].">
      <j1 rule="para" parents="2242 3727"/>
    </justification>
  </clause>

  <clause id="3734">
    <literal><![CDATA[
      T(x,K(y \ 1,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2675(a,1),3727(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2675 3727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3735">
    <literal><![CDATA[
      T(x,y * (1 / z)) = T(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(2674(a,1),3727(a,1,2))].">
      <j1 rule="para" parents="2674 3727"/>
    </justification>
  </clause>

  <clause id="3736">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(2683(a,1),3727(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2683 3727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3737">
    <literal><![CDATA[
      T(x,T(y,y \ 1) * z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(2778(a,1),3727(a,1,2))].">
      <j1 rule="para" parents="2778 3727"/>
    </justification>
  </clause>

  <clause id="3738">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) \ z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2818(a,1),3727(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2818 3727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3739">
    <literal><![CDATA[
      T(x,(1 / y) * z) = T(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2825(a,1),3727(a,1,2))].">
      <j1 rule="para" parents="2825 3727"/>
    </justification>
  </clause>

  <clause id="3740">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2928(a,1),3727(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2928 3727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3741">
    <literal><![CDATA[
      T(x,y * (((y \ z) \ 1) \ 1)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(3019(a,1),3727(a,1,2))].">
      <j1 rule="para" parents="3019 3727"/>
    </justification>
  </clause>

  <clause id="3742">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ 1)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(3414(a,1),3727(a,1,2))].">
      <j1 rule="para" parents="3414 3727"/>
    </justification>
  </clause>

  <clause id="3743">
    <literal><![CDATA[
      T(x,y * (z * K(u,u \ 1))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(3371(a,1),3727(a,1,2))].">
      <j1 rule="para" parents="3371 3727"/>
    </justification>
  </clause>

  <clause id="3745">
    <literal><![CDATA[
      T(x,(y \ 1) \ K(z,y)) = T(x,y * K(z,y))
    ]]></literal>
    <justification jstring="[para(3009(a,1),3731(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3009 3731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3746">
    <literal><![CDATA[
      T(x,y \ (1 / z)) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(3410(a,1),3731(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3410 3731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3747">
    <literal><![CDATA[
      T(x,(K(y,y \ 1) * z) \ u) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(3715(a,2),3731(a,1,2))].">
      <j1 rule="para" parents="3715 3731"/>
    </justification>
  </clause>

  <clause id="3748">
    <literal><![CDATA[
      T(x,L(K(y,y \ 1) * z,u,w)) = T(x,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(3512(a,2),3732(a,1,2))].">
      <j1 rule="para" parents="3512 3732"/>
    </justification>
  </clause>

  <clause id="3749">
    <literal><![CDATA[
      T(x,y \ (z * (1 / u))) = T(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3429(a,1),3734(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3429 3734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3750">
    <literal><![CDATA[
      T((x \ 1) * y,x \ y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,683,a(flip),b,3738,a),flip(a)].">
      <j1 rule="hyper" parents="58 683 3738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3751">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ u) = T(x,(z / (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(2061(a,2),3738(a,1,2,1))].">
      <j1 rule="para" parents="2061 3738"/>
    </justification>
  </clause>

  <clause id="3752">
    <literal><![CDATA[
      T(x,(1 / y) * K(z,y \ 1)) = T(x,y \ K(z,y \ 1))
    ]]></literal>
    <justification jstring="[para(2909(a,1),3739(a,2,2))].">
      <j1 rule="para" parents="2909 3739"/>
    </justification>
  </clause>

  <clause id="3753">
    <literal><![CDATA[
      T(x,y \ (L(1 / z,u,w) \ 1)) = T(x,y \ (L(z \ 1,u,w) \ 1))
    ]]></literal>
    <justification jstring="[para(3278(a,1),3742(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3278 3742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3754">
    <literal><![CDATA[
      (1 / x) / T(y,y \ (x \ 1)) = y \ (1 / x)
    ]]></literal>
    <justification jstring="[para(3746(a,1),265(a,1,2))].">
      <j1 rule="para" parents="3746 265"/>
    </justification>
  </clause>

  <clause id="3755">
    <literal><![CDATA[
      K((x \ 1) * y,x \ y) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,3750,a)].">
      <j1 rule="hyper" parents="50 3750"/>
    </justification>
  </clause>

  <clause id="3756">
    <literal><![CDATA[
      T(x,y * ((1 / z) * u)) = T(x,y * ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(2825(a,1),3743(a,1,2,2))].">
      <j1 rule="para" parents="2825 3743"/>
    </justification>
  </clause>

  <clause id="3757">
    <literal><![CDATA[
      T(x,(((y \ 1) \ 1) \ z) \ u) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(2785(a,1),3747(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2785 3747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3758">
    <literal><![CDATA[
      T(x,L(y * (z * (1 / u)),w,v5)) = T(x,L(y * (z * (u \ 1)),w,v5))
    ]]></literal>
    <justification jstring="[para(3435(a,1),3748(a,1,2,1))].">
      <j1 rule="para" parents="3435 3748"/>
    </justification>
  </clause>

  <clause id="3759">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),1 / x,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(735(a,1),3603(a,1,1)),flip(a)].">
      <j1 rule="para" parents="735 3603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3761">
    <literal><![CDATA[
      (x \ T(x,(x \ 1) * y)) * y = y * K(((1 / x) * y) \ y,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(3639(a,1),3198(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3639 3198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3762">
    <literal><![CDATA[
      L(x,y,z) \ K(x \ 1,x) = ((L(x,y,z) \ 1) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(3283(a,1),3686(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3283 3686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3763">
    <literal><![CDATA[
      L(1 / x,y,z) \ (1 / x) = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3559,a(flip),b,3687,a),flip(a)].">
      <j1 rule="hyper" parents="320 3559 3687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3765">
    <literal><![CDATA[
      x * K(y \ (1 / (1 / x)),y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,2948,a(flip),b,3699,a)].">
      <j1 rule="hyper" parents="58 2948 3699"/>
    </justification>
  </clause>

  <clause id="3766">
    <literal><![CDATA[
      L(x,y,z) \ K(x,x \ 1) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3276,a,3701,a),flip(a)].">
      <j1 rule="hyper" parents="3276 3701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3767">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ x) * z) = (y \ T(x,x \ 1)) * z
    ]]></literal>
    <justification jstring="[para(106(a,2),3714(a,2,1,2))].">
      <j1 rule="para" parents="106 3714"/>
    </justification>
  </clause>

  <clause id="3768">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ 1)) * z,y \ 1,y) = y * ((1 / y) * ((x \ y) * z))
    ]]></literal>
    <justification jstring="[para(3714(a,1),2933(a,1,1))].">
      <j1 rule="para" parents="3714 2933"/>
    </justification>
  </clause>

  <clause id="3769">
    <literal><![CDATA[
      T(x,K(y,z \ 1) / z) = T(x,z \ K(y,z \ 1))
    ]]></literal>
    <justification jstring="[para(3040(a,1),3752(a,1,2))].">
      <j1 rule="para" parents="3040 3752"/>
    </justification>
  </clause>

  <clause id="3770">
    <literal><![CDATA[
      L(x,y,z) \ u != ((L(x,y,z) \ 1) \ 1) \ 1
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = u
    ]]></literal>
    <justification jstring="[para(3762(a,1),42(a,1)),flip(a)].">
      <j1 rule="para" parents="3762 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3771">
    <literal><![CDATA[
      (x \ 1) * ((y \ T(x,x \ 1)) * z) = (1 / x) * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,3767,a(flip),b,2932,a)].">
      <j1 rule="hyper" parents="119 3767 2932"/>
    </justification>
  </clause>

  <clause id="3772">
    <literal><![CDATA[
      T(x * y,x \ (1 / y)) = ((x * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2618,a,b,3611,a)].">
      <j1 rule="hyper" parents="58 2618 3611"/>
    </justification>
  </clause>

  <clause id="3773">
    <literal><![CDATA[
      T(x * y,x \ (y \ 1)) = ((x * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,3746,a(flip),b,3772,a)].">
      <j1 rule="hyper" parents="58 3746 3772"/>
    </justification>
  </clause>

  <clause id="3774">
    <literal><![CDATA[
      (x * K(y \ z,z \ y)) * u = K(y \ z,z \ y) * (x * u)
    ]]></literal>
    <justification jstring="[para(2386(a,1),3658(a,1,1))].">
      <j1 rule="para" parents="2386 3658"/>
    </justification>
  </clause>

  <clause id="3775">
    <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(2602(a,1),3662(a,1,1,2))].">
      <j1 rule="para" parents="2602 3662"/>
    </justification>
  </clause>

  <clause id="3776">
    <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,3672,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="117 3672 101"/>
    </justification>
  </clause>

  <clause id="3777">
    <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,3719,a(flip),b,80,a)].">
      <j1 rule="hyper" parents="116 3719 80"/>
    </justification>
  </clause>

  <clause id="3778">
    <literal><![CDATA[
      K(x,x \ 1) * ((y * (z / (x \ 1))) \ u) = (y * (z / (1 / x))) \ u
    ]]></literal>
    <justification jstring="[para(2602(a,1),3721(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2602 3721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3779">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) * K(u \ 1,u)) * K(u,u \ 1) = a(x,y,K(u,u \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3724(a,1),3570(a,1,1))].">
      <j1 rule="para" parents="3724 3570"/>
    </justification>
  </clause>

  <clause id="3780">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (z * (u * K(x \ 1,x)))) = y / (z * u)
    ]]></literal>
    <justification jstring="[hyper(119,a,3726,a,b,2694,a)].">
      <j1 rule="hyper" parents="119 3726 2694"/>
    </justification>
  </clause>

  <clause id="3781">
    <literal><![CDATA[
      (x * K(y \ z,z \ y)) * (x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ z,z \ y) = u
    ]]></literal>
    <justification jstring="[para(3774(a,2),206(a,1)),flip(b)].">
      <j1 rule="para" parents="3774 206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3782">
    <literal><![CDATA[
      x / (K(y,y \ 1) * z) = K(y \ 1,y) * (x / z)
    ]]></literal>
    <justification jstring="[para(2685(a,1),3780(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2685 3780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3783">
    <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(3753(a,1),265(a,1,2))].">
      <j1 rule="para" parents="3753 265"/>
    </justification>
  </clause>

  <clause id="3784">
    <literal><![CDATA[
      (K(x \ 1,x) * ((y * z) * u)) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(3627(a,1),3671(a,1,1))].">
      <j1 rule="para" parents="3627 3671"/>
    </justification>
  </clause>

  <clause id="3785">
    <literal><![CDATA[
      K(x \ 1,x) * (((y * z) * u) / (z * u)) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,3645,a(flip),b,3784,a)].">
      <j1 rule="hyper" parents="58 3645 3784"/>
    </justification>
  </clause>

  <clause id="3786">
    <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),3785(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15 3785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3787">
    <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(320,a,2651,a(flip),b,3786,a),flip(a)].">
      <j1 rule="hyper" parents="320 2651 3786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3788">
    <literal><![CDATA[
      K(x,x \ 1) * R(K(x \ 1,x) * y,z,u) = R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(2697,a,3786,a(flip))].">
      <j1 rule="hyper" parents="2697 3786"/>
    </justification>
  </clause>

  <clause id="3789">
    <literal><![CDATA[
      R(x * K(y \ 1,y),z,u) = K(y \ 1,y) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(2180(a,1),3786(a,1,1))].">
      <j1 rule="para" parents="2180 3786"/>
    </justification>
  </clause>

  <clause id="3790">
    <literal><![CDATA[
      K(x,x \ 1) * R(x \ 1,y,z) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1777(a,1),3788(a,1,2,1))].">
      <j1 rule="para" parents="1777 3788"/>
    </justification>
  </clause>

  <clause id="3791">
    <literal><![CDATA[
      R(K(x,x \ 1) * y,z,u) = K(x,x \ 1) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(2679(a,1),3788(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2679 3788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3792">
    <literal><![CDATA[
      K(x \ 1,x) * (R(x \ 1,y,z) \ u) = R(1 / x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(3790(a,1),3706(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3790 3706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3793">
    <literal><![CDATA[
      R(x * K(y \ 1,y),z,u) = R(x,z,u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2185,a,b,3789,a),flip(a)].">
      <j1 rule="hyper" parents="320 2185 3789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3794">
    <literal><![CDATA[
      R(K(x,x \ 1) * y,z,u) = R(y,z,u) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,2169,a(flip),b,3791,a),flip(a)].">
      <j1 rule="hyper" parents="320 2169 3791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3795">
    <literal><![CDATA[
      T(x,R(K(y,y \ 1) * (1 / z),u,w)) = T(x,R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(3794(a,2),3729(a,1,2))].">
      <j1 rule="para" parents="3794 3729"/>
    </justification>
  </clause>

  <clause id="3796">
    <literal><![CDATA[
      T(x,R(K(y,y \ 1) / z,u,w)) = T(x,R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(3655(a,1),3795(a,1,2,1))].">
      <j1 rule="para" parents="3655 3795"/>
    </justification>
  </clause>

  <clause id="3797">
    <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(3700(a,1),3622(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3700 3622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3798">
    <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,3796,a(flip),b,3797,a),flip(a)].">
      <j1 rule="hyper" parents="58 3796 3797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3800">
    <literal><![CDATA[
      (x \ T(x,(x \ 1) * y)) * y = y * K(((x \ 1) * y) \ y,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(3301(a,1),3761(a,2,2))].">
      <j1 rule="para" parents="3301 3761"/>
    </justification>
  </clause>

  <clause id="3801">
    <literal><![CDATA[
      (x \ R(x * y,z,u)) * x = R(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(2647(a,1),3787(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2647 3787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3802">
    <literal><![CDATA[
      (x \ 1) \ R((x \ 1) * y,z,u) = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(30,a,1212,a,b,3801,a),flip(a)].">
      <j1 rule="hyper" parents="30 1212 3801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3803">
    <literal><![CDATA[
      R((x \ y) * x,z,u) = (x \ R(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(5(a,1),3801(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 3801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3804">
    <literal><![CDATA[
      x * (R(y * x,z,u) / x) = R(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(3801(a,1),71(a,1,2,1))].">
      <j1 rule="para" parents="3801 71"/>
    </justification>
  </clause>

  <clause id="3805">
    <literal><![CDATA[
      R((x \ (y / z)) * x,z,z \ 1) = (x \ (y * (z \ 1))) * x
    ]]></literal>
    <justification jstring="[para(523(a,1),3803(a,2,1,2))].">
      <j1 rule="para" parents="523 3803"/>
    </justification>
  </clause>

  <clause id="3806">
    <literal><![CDATA[
      R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(2593(a,1),3803(a,2,1,2))].">
      <j1 rule="para" parents="2593 3803"/>
    </justification>
  </clause>

  <clause id="3807">
    <literal><![CDATA[
      R(x * (y / x),z,u) = x * (R(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),3804(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 3804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3808">
    <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(3807(a,2),3217(a,1,1))].">
      <j1 rule="para" parents="3807 3217"/>
    </justification>
  </clause>

  <clause id="3809">
    <literal><![CDATA[
      (x \ 1) \ R(x \ 1,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(3(a,1),3802(a,1,2,1))].">
      <j1 rule="para" parents="3 3802"/>
    </justification>
  </clause>

  <clause id="3810">
    <literal><![CDATA[
      (x \ 1) * (x * R(x \ 1,y,z)) = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,3809,a)].">
      <j1 rule="hyper" parents="134 3809"/>
    </justification>
  </clause>

  <clause id="3811">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = ((x \ (y / z)) * x) * z
    ]]></literal>
    <justification jstring="[hyper(117,a,3805,a(flip),b,261,a)].">
      <j1 rule="hyper" parents="117 3805 261"/>
    </justification>
  </clause>

  <clause id="3812">
    <literal><![CDATA[
      (x \ (x * y)) * x = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,3144,a(flip),b,3806,a),flip(a)].">
      <j1 rule="hyper" parents="58 3144 3806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3813">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,3806,a(flip),b,2589,a),flip(a)].">
      <j1 rule="hyper" parents="117 3806 2589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3814">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 * x)) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(3806(a,1),3219(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3806 3219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3815">
    <literal><![CDATA[
      (x * (y \ T(y,x))) * y = y * x
    ]]></literal>
    <justification jstring="[para(4(a,1),3812(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 3812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3816">
    <literal><![CDATA[
      x * (y \ T(y,x)) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(131,a,3815,a),flip(a)].">
      <j1 rule="hyper" parents="131 3815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3817">
    <literal><![CDATA[
      (x \ y) * (x \ T(x,x \ y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(117,a,5,a(flip),b,3815,a),flip(a)].">
      <j1 rule="hyper" parents="117 5 3815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3818">
    <literal><![CDATA[
      (x \ T(x,y)) * y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(2908,a,3816,a)].">
      <j1 rule="hyper" parents="2908 3816"/>
    </justification>
  </clause>

  <clause id="3819">
    <literal><![CDATA[
      x \ ((y * x) / y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,3816,a)].">
      <j1 rule="hyper" parents="123 3816"/>
    </justification>
  </clause>

  <clause id="3820">
    <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,818,a(flip),b,3816,a)].">
      <j1 rule="hyper" parents="116 818 3816"/>
    </justification>
  </clause>

  <clause id="3821">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,225,a(flip),b,3816,a)].">
      <j1 rule="hyper" parents="116 225 3816"/>
    </justification>
  </clause>

  <clause id="3822">
    <literal><![CDATA[
      (x / y) \ T(x / y,y) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(116,a,153,a(flip),b,3816,a),flip(a)].">
      <j1 rule="hyper" parents="116 153 3816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3823">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = y \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(29,a,2914,a,b,3816,a)].">
      <j1 rule="hyper" parents="29 2914 3816"/>
    </justification>
  </clause>

  <clause id="3824">
    <literal><![CDATA[
      ((x * y) / x) / y = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,2913,a,b,3816,a)].">
      <j1 rule="hyper" parents="29 2913 3816"/>
    </justification>
  </clause>

  <clause id="3825">
    <literal><![CDATA[
      (T(x,y) \ x) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[hyper(119,a,3816,a(flip),b,3166,a)].">
      <j1 rule="hyper" parents="119 3816 3166"/>
    </justification>
  </clause>

  <clause id="3826">
    <literal><![CDATA[
      (x * y) \ ((x * y) / x) = L(x \ 1,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(3816(a,1),987(a,1,2))].">
      <j1 rule="para" parents="3816 987"/>
    </justification>
  </clause>

  <clause id="3827">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3816(a,1),2338(a,1,1))].">
      <j1 rule="para" parents="3816 2338"/>
    </justification>
  </clause>

  <clause id="3828">
    <literal><![CDATA[
      ((x * y) / x) \ y = T(x,y) \ x
    ]]></literal>
    <justification jstring="[para(3816(a,1),3109(a,1,1))].">
      <j1 rule="para" parents="3816 3109"/>
    </justification>
  </clause>

  <clause id="3829">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(3818(a,1),184(a,1,2,1))].">
      <j1 rule="para" parents="3818 184"/>
    </justification>
  </clause>

  <clause id="3830">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3029,a,3819,a)].">
      <j1 rule="hyper" parents="3029 3819"/>
    </justification>
  </clause>

  <clause id="3831">
    <literal><![CDATA[
      L(x \ T(x,y),y,x) = K(x,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(3819(a,1),491(a,1,1))].">
      <j1 rule="para" parents="3819 491"/>
    </justification>
  </clause>

  <clause id="3832">
    <literal><![CDATA[
      T(x,R(y \ 1,y,x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(3069(a,1),3830(a,1,2))].">
      <j1 rule="para" parents="3069 3830"/>
    </justification>
  </clause>

  <clause id="3833">
    <literal><![CDATA[
      T(x,T(y,x)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(3830(a,1),3082(a,1,1))].">
      <j1 rule="para" parents="3830 3082"/>
    </justification>
  </clause>

  <clause id="3834">
    <literal><![CDATA[
      R(T(x,y) \ x,y,z) = (T(y,T(x,y)) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(3821(a,2),2977(a,1,1))].">
      <j1 rule="para" parents="3821 2977"/>
    </justification>
  </clause>

  <clause id="3835">
    <literal><![CDATA[
      x \ y != (z \ T(z,u)) * u
    ]]></literal>
    <literal><![CDATA[
      x * ((z * u) / z) = y
    ]]></literal>
    <justification jstring="[para(3824(a,1),580(a,2,1))].">
      <j1 rule="para" parents="3824 580"/>
    </justification>
  </clause>

  <clause id="3836">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = y * (((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[para(3824(a,1),504(a,1,1,1))].">
      <j1 rule="para" parents="3824 504"/>
    </justification>
  </clause>

  <clause id="3837">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(3197,a,3825,a)].">
      <j1 rule="hyper" parents="3197 3825"/>
    </justification>
  </clause>

  <clause id="3838">
    <literal><![CDATA[
      T(x,x \ y) \ x = (y / x) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),3828(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 3828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3839">
    <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(3828(a,1),1180(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3828 1180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3840">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(3828(a,1),1448(a,1,2,2,1))].">
      <j1 rule="para" parents="3828 1448"/>
    </justification>
  </clause>

  <clause id="3841">
    <literal><![CDATA[
      (x \ T(x,y)) \ y = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[para(3833(a,1),2860(a,1,1))].">
      <j1 rule="para" parents="3833 2860"/>
    </justification>
  </clause>

  <clause id="3842">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ y = T(y,T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(2973(a,1),3841(a,1,1))].">
      <j1 rule="para" parents="2973 3841"/>
    </justification>
  </clause>

  <clause id="3843">
    <literal><![CDATA[
      x * ((x * y) * (y / (x * y))) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3143,a(flip),b,3832,a)].">
      <j1 rule="hyper" parents="58 3143 3832"/>
    </justification>
  </clause>

  <clause id="3845">
    <literal><![CDATA[
      (x \ y) \ (y / x) = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,3817,a(flip),b,654,a(flip))].">
      <j1 rule="hyper" parents="116 3817 654"/>
    </justification>
  </clause>

  <clause id="3846">
    <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(3827(a,1),482(a,1,1))].">
      <j1 rule="para" parents="3827 482"/>
    </justification>
  </clause>

  <clause id="3847">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[para(225(a,1),3831(a,2,2)),flip(a)].">
      <j1 rule="para" parents="225 3831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3848">
    <literal><![CDATA[
      (x / y) \ (y \ x) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[para(107(a,1),3822(a,1,2))].">
      <j1 rule="para" parents="107 3822"/>
    </justification>
  </clause>

  <clause id="3849">
    <literal><![CDATA[
      T(x,x \ y) \ x = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,3838,a,b,3848,a)].">
      <j1 rule="hyper" parents="58 3838 3848"/>
    </justification>
  </clause>

  <clause id="3850">
    <literal><![CDATA[
      x / (x / y) = y * (T(y,y \ x) \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,3838,a,b,3848,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 3838 3848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3851">
    <literal><![CDATA[
      (x * y) / ((x * y) / x) = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),3850(a,2,2,1,2))].">
      <j1 rule="para" parents="4 3850"/>
    </justification>
  </clause>

  <clause id="3852">
    <literal><![CDATA[
      K(x,(x / y) / x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1716,a,3823,a)].">
      <j1 rule="hyper" parents="1716 3823"/>
    </justification>
  </clause>

  <clause id="3853">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,1213,a,b,3823,a)].">
      <j1 rule="hyper" parents="58 1213 3823"/>
    </justification>
  </clause>

  <clause id="3854">
    <literal><![CDATA[
      L(x * ((y * (x \ 1)) / y),z,u) = y \ T(y,L(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3235,a(flip),b,3823,a)].">
      <j1 rule="hyper" parents="58 3235 3823"/>
    </justification>
  </clause>

  <clause id="3855">
    <literal><![CDATA[
      x \ (y * ((z * (y \ x)) / z)) = z \ T(z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,1977,a(flip),b,3823,a)].">
      <j1 rule="hyper" parents="58 1977 3823"/>
    </justification>
  </clause>

  <clause id="3856">
    <literal><![CDATA[
      x * K(x,(x / y) / x) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1901,a,3823,a(flip))].">
      <j1 rule="hyper" parents="1901 3823"/>
    </justification>
  </clause>

  <clause id="3857">
    <literal><![CDATA[
      T(x,x / (x * y)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1657,a,3823,a(flip))].">
      <j1 rule="hyper" parents="1657 3823"/>
    </justification>
  </clause>

  <clause id="3858">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) = x * K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1720,a(flip),b,3823,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1720 3823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3859">
    <literal><![CDATA[
      x \ T(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,(x / y) / x) = z
    ]]></literal>
    <justification jstring="[para(3823(a,1),1716(a,1))].">
      <j1 rule="para" parents="3823 1716"/>
    </justification>
  </clause>

  <clause id="3860">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,(x / T(y,z)) / x)
    ]]></literal>
    <justification jstring="[para(3823(a,1),1980(a,1,1))].">
      <j1 rule="para" parents="3823 1980"/>
    </justification>
  </clause>

  <clause id="3861">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((x \ T(x,z \ 1)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(3823(a,1),2293(a,2,2,1))].">
      <j1 rule="para" parents="3823 2293"/>
    </justification>
  </clause>

  <clause id="3862">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = K(x,(x / R(y,z,u)) / x)
    ]]></literal>
    <justification jstring="[para(3823(a,1),3252(a,1,1))].">
      <j1 rule="para" parents="3823 3252"/>
    </justification>
  </clause>

  <clause id="3863">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2294,a,3857,a)].">
      <j1 rule="hyper" parents="2294 3857"/>
    </justification>
  </clause>

  <clause id="3864">
    <literal><![CDATA[
      T(x * ((x / y) / x),y) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2291,a,3857,a)].">
      <j1 rule="hyper" parents="2291 3857"/>
    </justification>
  </clause>

  <clause id="3867">
    <literal><![CDATA[
      T(x,x / (y * x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3002,a,b,3857,a)].">
      <j1 rule="hyper" parents="58 3002 3857"/>
    </justification>
  </clause>

  <clause id="3868">
    <literal><![CDATA[
      T(x,y \ 1) / y = x * ((x / y) / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,3857,a(flip),b,2289,a)].">
      <j1 rule="hyper" parents="117 3857 2289"/>
    </justification>
  </clause>

  <clause id="3869">
    <literal><![CDATA[
      (x * ((x / y) / x)) \ T(x,y \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,3857,a(flip),b,2289,a)].">
      <j1 rule="hyper" parents="116 3857 2289"/>
    </justification>
  </clause>

  <clause id="3870">
    <literal><![CDATA[
      x * (y * ((x \ y) / y)) = T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1176,a,3867,a)].">
      <j1 rule="hyper" parents="1176 3867"/>
    </justification>
  </clause>

  <clause id="3871">
    <literal><![CDATA[
      x \ T(y,x \ 1) = y * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(116,a,3867,a(flip),b,1175,a)].">
      <j1 rule="hyper" parents="116 3867 1175"/>
    </justification>
  </clause>

  <clause id="3872">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) = x * K(x,(y \ x) / x)
    ]]></literal>
    <justification jstring="[para(265(a,1),3856(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="265 3856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3873">
    <literal><![CDATA[
      T(x,y) / (y \ 1) = x * ((x / (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,2939,a(flip),b,3863,a)].">
      <j1 rule="hyper" parents="117 2939 3863"/>
    </justification>
  </clause>

  <clause id="3874">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(72(a,1),3868(a,2,2,1))].">
      <j1 rule="para" parents="72 3868"/>
    </justification>
  </clause>

  <clause id="3875">
    <literal><![CDATA[
      T(x,y) / (1 / y) = x * ((x / (1 / y)) / x)
    ]]></literal>
    <justification jstring="[para(75(a,1),3868(a,1,1,2))].">
      <j1 rule="para" parents="75 3868"/>
    </justification>
  </clause>

  <clause id="3876">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = (T(x,y \ 1) / y) \ x
    ]]></literal>
    <justification jstring="[para(3868(a,2),217(a,2,1))].">
      <j1 rule="para" parents="3868 217"/>
    </justification>
  </clause>

  <clause id="3877">
    <literal><![CDATA[
      (x \ 1) \ T(y,x) = y * (((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(116,a,2939,a(flip),b,3870,a)].">
      <j1 rule="hyper" parents="116 2939 3870"/>
    </justification>
  </clause>

  <clause id="3878">
    <literal><![CDATA[
      x * R(1 / y,y,y \ x) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,590,a,b,3871,a)].">
      <j1 rule="hyper" parents="320 590 3871"/>
    </justification>
  </clause>

  <clause id="3879">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(75(a,1),3871(a,2,2,1))].">
      <j1 rule="para" parents="75 3871"/>
    </justification>
  </clause>

  <clause id="3880">
    <literal><![CDATA[
      R(x,(y \ x) / x,x) = ((y \ T(x,y \ 1)) * x) / (y \ x)
    ]]></literal>
    <justification jstring="[para(3871(a,2),103(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3871 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3881">
    <literal><![CDATA[
      x / (y \ ((y * x) / y)) = y * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1169,a(flip),b,3851,a)].">
      <j1 rule="hyper" parents="58 1169 3851"/>
    </justification>
  </clause>

  <clause id="3882">
    <literal><![CDATA[
      x \ (T(x,y) / (1 / y)) = (x / (1 / y)) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,3875,a,b,xx)].">
      <j1 rule="hyper" parents="116 3875"/>
    </justification>
  </clause>

  <clause id="3883">
    <literal><![CDATA[
      (((x / y) \ 1) \ y) * ((x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1013,a(flip),b,3879,a)].">
      <j1 rule="hyper" parents="58 1013 3879"/>
    </justification>
  </clause>

  <clause id="3884">
    <literal><![CDATA[
      (x * (T(x,y) \ x)) \ y = x \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(188,a,3881,a)].">
      <j1 rule="hyper" parents="188 3881"/>
    </justification>
  </clause>

  <clause id="3885">
    <literal><![CDATA[
      x * R(1 / (1 / y),1 / y,(1 / y) \ x) = (1 / y) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),3878(a,2,2,2))].">
      <j1 rule="para" parents="75 3878"/>
    </justification>
  </clause>

  <clause id="3886">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = (x * y) * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(29,a,940,a,b,3843,a)].">
      <j1 rule="hyper" parents="29 940 3843"/>
    </justification>
  </clause>

  <clause id="3887">
    <literal><![CDATA[
      x \ y != (x * ((z \ x) / x)) / (z \ x)
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ 1) = y
    ]]></literal>
    <justification jstring="[para(3853(a,2),42(a,1)),flip(a)].">
      <j1 rule="para" parents="3853 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3888">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = x \ T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3852,a(flip),b,3860,a),flip(a)].">
      <j1 rule="hyper" parents="320 3852 3860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3889">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ x) / x) = z
    ]]></literal>
    <justification jstring="[para(3872(a,2),38(a,1))].">
      <j1 rule="para" parents="3872 38"/>
    </justification>
  </clause>

  <clause id="3890">
    <literal><![CDATA[
      x \ (y * (x / y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(((y / x) \ 1) \ x,(y / x) \ 1) = z
    ]]></literal>
    <justification jstring="[para(3883(a,1),465(a,1,2))].">
      <j1 rule="para" parents="3883 465"/>
    </justification>
  </clause>

  <clause id="3891">
    <literal><![CDATA[
      ((x \ 1) * y) * (y / ((x \ 1) * y)) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,2820,a(flip),b,3886,a),flip(a)].">
      <j1 rule="hyper" parents="58 2820 3886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3892">
    <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(2991(a,1),3888(a,2,2,2,1))].">
      <j1 rule="para" parents="2991 3888"/>
    </justification>
  </clause>

  <clause id="3893">
    <literal><![CDATA[
      ((x \ 1) * y) * R(x,x \ 1,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(215(a,2),3891(a,1,2))].">
      <j1 rule="para" parents="215 3891"/>
    </justification>
  </clause>

  <clause id="3894">
    <literal><![CDATA[
      ((((x \ 1) * y) * x) / ((x \ 1) * y)) * (x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,3893,a(flip),b,848,a),flip(a)].">
      <j1 rule="hyper" parents="117 3893 848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3895">
    <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(3834(a,1),923(a,1,1))].">
      <j1 rule="para" parents="3834 923"/>
    </justification>
  </clause>

  <clause id="3896">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = x \ T(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3852,a(flip),b,3862,a),flip(a)].">
      <j1 rule="hyper" parents="320 3852 3862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3897">
    <literal><![CDATA[
      x * (T((x \ y) * z,x) / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(58,a,1382,a(flip),b,3813,a)].">
      <j1 rule="hyper" parents="58 1382 3813"/>
    </justification>
  </clause>

  <clause id="3898">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = x \ T(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(3823(a,1),3854(a,1,1))].">
      <j1 rule="para" parents="3823 3854"/>
    </justification>
  </clause>

  <clause id="3899">
    <literal><![CDATA[
      x * R(1 / (1 / y),y \ 1,(1 / y) \ x) = (1 / y) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3101(a,1),3885(a,1,2))].">
      <j1 rule="para" parents="3101 3885"/>
    </justification>
  </clause>

  <clause id="3900">
    <literal><![CDATA[
      K(x,((y \ 1) \ x) / x) = ((1 / y) \ x) \ ((1 / y) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(3899(a,1),3544(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3899 3544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3901">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3545,a(flip),b,3900,a)].">
      <j1 rule="hyper" parents="320 3545 3900"/>
    </justification>
  </clause>

  <clause id="3902">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(58,a,3827,a(flip),b,3894,a)].">
      <j1 rule="hyper" parents="58 3827 3894"/>
    </justification>
  </clause>

  <clause id="3903">
    <literal><![CDATA[
      L(K(x \ y,x),y,x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(58,a,1971,a(flip),b,3902,a)].">
      <j1 rule="hyper" parents="58 1971 3902"/>
    </justification>
  </clause>

  <clause id="3904">
    <literal><![CDATA[
      ((x \ (x * y)) * x) / (x * y) = L(K(y,x),x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),3903(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 3903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3905">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = (x * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(4(a,1),3904(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 3904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3906">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,3659,a(flip),b,3837,a)].">
      <j1 rule="hyper" parents="58 3659 3837"/>
    </justification>
  </clause>

  <clause id="3907">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(y \ 1) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[para(2832(a,1),3906(a,2,1))].">
      <j1 rule="para" parents="2832 3906"/>
    </justification>
  </clause>

  <clause id="3908">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) \ x = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3905,a(flip),b,3907,a),flip(a)].">
      <j1 rule="hyper" parents="58 3905 3907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3909">
    <literal><![CDATA[
      x \ y != (z * y) / (y * z)
    ]]></literal>
    <literal><![CDATA[
      T(y,(y \ 1) * (z * y)) = x
    ]]></literal>
    <justification jstring="[para(3908(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="3908 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3910">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = (x \ T(x,(x \ 1) * y)) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,302,a(flip),b,3800,a)].">
      <j1 rule="hyper" parents="320 302 3800"/>
    </justification>
  </clause>

  <clause id="3911">
    <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),3895(a,2,1))].">
      <j1 rule="para" parents="11 3895"/>
    </justification>
  </clause>

  <clause id="3912">
    <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(320,a,3896,a,b,3892,a),flip(a)].">
      <j1 rule="hyper" parents="320 3896 3892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3913">
    <literal><![CDATA[
      T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = R(x \ T(x,z),z,y)
    ]]></literal>
    <justification jstring="[para(2939(a,1),3912(a,2,1,2))].">
      <j1 rule="para" parents="2939 3912"/>
    </justification>
  </clause>

  <clause id="3914">
    <literal><![CDATA[
      T(x,y / (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y / (z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(3382(a,1),3775(a,1))].">
      <j1 rule="para" parents="3382 3775"/>
    </justification>
  </clause>

  <clause id="3916">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(2(a,1),3814(a,2,1,1,2))].">
      <j1 rule="para" parents="2 3814"/>
    </justification>
  </clause>

  <clause id="3917">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / x
    ]]></literal>
    <justification jstring="[para(75(a,1),3916(a,2,2))].">
      <j1 rule="para" parents="75 3916"/>
    </justification>
  </clause>

  <clause id="3918">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[para(3765(a,1),3917(a,1,1))].">
      <j1 rule="para" parents="3765 3917"/>
    </justification>
  </clause>

  <clause id="3919">
    <literal><![CDATA[
      ((x \ y) * x) / y != ((x \ y) * x) * z
    ]]></literal>
    <literal><![CDATA[
      y \ 1 = z
    ]]></literal>
    <justification jstring="[para(3918(a,1),38(a,1))].">
      <j1 rule="para" parents="3918 38"/>
    </justification>
  </clause>

  <clause id="3920">
    <literal><![CDATA[
      (x * y) * ((((x * y) \ (z * y)) \ 1) \ 1) = ((((z / x) \ 1) \ 1) * x) * y
    ]]></literal>
    <justification jstring="[hyper(283,a,3610,a),flip(a)].">
      <j1 rule="hyper" parents="283 3610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3921">
    <literal><![CDATA[
      (x * y) * ((((x * y) \ (z * y)) \ 1) \ 1) = (x * (((x \ z) \ 1) \ 1)) * y
    ]]></literal>
    <justification jstring="[para(2161(a,1),3920(a,2,1))].">
      <j1 rule="para" parents="2161 3920"/>
    </justification>
  </clause>

  <clause id="3922">
    <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,3054,a(flip),b,3921,a)].">
      <j1 rule="hyper" parents="58 3054 3921"/>
    </justification>
  </clause>

  <clause id="3923">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,T(x,y) \ x,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(3828(a,1),3840(a,2,2))].">
      <j1 rule="para" parents="3828 3840"/>
    </justification>
  </clause>

  <clause id="3924">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) \ ((x * y) * z) = ((x * y) * ((((x * y) \ y) \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(3606(a,2),3922(a,1,1))].">
      <j1 rule="para" parents="3606 3922"/>
    </justification>
  </clause>

  <clause id="3925">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) \ ((x * y) * z) = (y * K(x \ 1,x)) * z
    ]]></literal>
    <justification jstring="[para(2960(a,1),3924(a,2,1))].">
      <j1 rule="para" parents="2960 3924"/>
    </justification>
  </clause>

  <clause id="3926">
    <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(3609(a,1),3925(a,1,1))].">
      <j1 rule="para" parents="3609 3925"/>
    </justification>
  </clause>

  <clause id="3927">
    <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(3628(a,1),3677(a,1,2))].">
      <j1 rule="para" parents="3628 3677"/>
    </justification>
  </clause>

  <clause id="3928">
    <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,3711,a(flip),b,3678,a)].">
      <j1 rule="hyper" parents="58 3711 3678"/>
    </justification>
  </clause>

  <clause id="3929">
    <literal><![CDATA[
      K(x * K(y \ 1,y),z) = (z * x) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(3679,a,3690,a)].">
      <j1 rule="hyper" parents="3679 3690"/>
    </justification>
  </clause>

  <clause id="3930">
    <literal><![CDATA[
      K(x * K(y \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,11,a,b,3929,a),flip(a)].">
      <j1 rule="hyper" parents="320 11 3929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3931">
    <literal><![CDATA[
      K(x * K(y,y \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1784(a,1),3930(a,1,1,2))].">
      <j1 rule="para" parents="1784 3930"/>
    </justification>
  </clause>

  <clause id="3932">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(2180(a,2),3930(a,1,1))].">
      <j1 rule="para" parents="2180 3930"/>
    </justification>
  </clause>

  <clause id="3933">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2588(a,1),3930(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2588 3930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3934">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x / (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2602(a,1),3930(a,1,1))].">
      <j1 rule="para" parents="2602 3930"/>
    </justification>
  </clause>

  <clause id="3935">
    <literal><![CDATA[
      K(x * ((y \ 1) \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(2641(a,1),3930(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2641 3930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3936">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(2688(a,1),3930(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2688 3930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3937">
    <literal><![CDATA[
      K(x * (1 / (1 / y)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(2684(a,1),3930(a,1,1))].">
      <j1 rule="para" parents="2684 3930"/>
    </justification>
  </clause>

  <clause id="3938">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2816(a,1),3930(a,1,1))].">
      <j1 rule="para" parents="2816 3930"/>
    </justification>
  </clause>

  <clause id="3939">
    <literal><![CDATA[
      K((1 / x) * y,z) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(2826(a,1),3930(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2826 3930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3940">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(2929(a,1),3930(a,1,1))].">
      <j1 rule="para" parents="2929 3930"/>
    </justification>
  </clause>

  <clause id="3942">
    <literal><![CDATA[
      K(x \ K(y \ 1,y),z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(3365(a,1),3930(a,1,1))].">
      <j1 rule="para" parents="3365 3930"/>
    </justification>
  </clause>

  <clause id="3943">
    <literal><![CDATA[
      K(x \ (1 / y),z) = K(x \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(3410(a,1),3930(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3410 3930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3944">
    <literal><![CDATA[
      K(x \ ((y \ 1) \ 1),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(3411(a,1),3930(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3411 3930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3945">
    <literal><![CDATA[
      K((K(x,x \ 1) * y) \ z,u) = K(y \ z,u)
    ]]></literal>
    <justification jstring="[para(3715(a,2),3930(a,1,1))].">
      <j1 rule="para" parents="3715 3930"/>
    </justification>
  </clause>

  <clause id="3946">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,u) = K(((x \ 1) * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(3723(a,1),3930(a,1,1))].">
      <j1 rule="para" parents="3723 3930"/>
    </justification>
  </clause>

  <clause id="3947">
    <literal><![CDATA[
      K((x * (K(y,y \ 1) * z)) \ u,w) = K((x * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(3724(a,2),3930(a,1,1))].">
      <j1 rule="para" parents="3724 3930"/>
    </justification>
  </clause>

  <clause id="3948">
    <literal><![CDATA[
      K(x \ (y * K(z,z \ 1)),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(3379(a,2),3931(a,1,1))].">
      <j1 rule="para" parents="3379 3931"/>
    </justification>
  </clause>

  <clause id="3950">
    <literal><![CDATA[
      K(x \ (y * (1 / z)),u) = K(x \ (y * (z \ 1)),u)
    ]]></literal>
    <justification jstring="[para(3429(a,1),3932(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3429 3932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3951">
    <literal><![CDATA[
      K((x * ((y \ 1) \ 1)) \ z,u) = K((x * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(3707(a,1),3932(a,1,1))].">
      <j1 rule="para" parents="3707 3932"/>
    </justification>
  </clause>

  <clause id="3953">
    <literal><![CDATA[
      K(T(K(x,x \ 1) * y,x),z) = K(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(2426(a,2),3936(a,1,1))].">
      <j1 rule="para" parents="2426 3936"/>
    </justification>
  </clause>

  <clause id="3954">
    <literal><![CDATA[
      K(x * T((y * z) \ z,y),u) = K(x * ((y * z) \ z),u)
    ]]></literal>
    <justification jstring="[para(2224(a,2),3935(a,1,1,2))].">
      <j1 rule="para" parents="2224 3935"/>
    </justification>
  </clause>

  <clause id="3955">
    <literal><![CDATA[
      K(x * R(1 / y,z,u),w) = K(x * R(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(3605(a,1),3935(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3605 3935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3958">
    <literal><![CDATA[
      K(L(1 / x,y,z) \ u,w) = K(L(x \ 1,y,z) \ u,w)
    ]]></literal>
    <justification jstring="[para(3278(a,1),3938(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3278 3938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3959">
    <literal><![CDATA[
      K(x \ ((y \ 1) * y),z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(258(a,1),3942(a,1,1,2))].">
      <j1 rule="para" parents="258 3942"/>
    </justification>
  </clause>

  <clause id="3960">
    <literal><![CDATA[
      K(x \ R(1 / y,z,u),w) = K(x \ R(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(3605(a,1),3944(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3605 3944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3961">
    <literal><![CDATA[
      K((((x \ 1) \ 1) \ y) \ z,u) = K((x \ y) \ z,u)
    ]]></literal>
    <justification jstring="[para(2785(a,1),3945(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2785 3945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3962">
    <literal><![CDATA[
      K(((1 / x) / y) \ z,u) = K(((x \ 1) / y) \ z,u)
    ]]></literal>
    <justification jstring="[para(3657(a,1),3945(a,1,1,1))].">
      <j1 rule="para" parents="3657 3945"/>
    </justification>
  </clause>

  <clause id="3963">
    <literal><![CDATA[
      K((((1 / x) \ y) \ z) \ u,w) = K((((x \ 1) \ y) \ z) \ u,w)
    ]]></literal>
    <justification jstring="[para(3720(a,1),3945(a,1,1,1))].">
      <j1 rule="para" parents="3720 3945"/>
    </justification>
  </clause>

  <clause id="3965">
    <literal><![CDATA[
      K(x \ (y * (((y \ z) \ 1) \ 1)),u) = K(x \ z,u)
    ]]></literal>
    <justification jstring="[para(3019(a,1),3948(a,1,1,2))].">
      <j1 rule="para" parents="3019 3948"/>
    </justification>
  </clause>

  <clause id="3966">
    <literal><![CDATA[
      K(T((1 / x) * y,x),z) = K(T((x \ 1) * y,x),z)
    ]]></literal>
    <justification jstring="[para(2796(a,1),3953(a,1,1,1))].">
      <j1 rule="para" parents="2796 3953"/>
    </justification>
  </clause>

  <clause id="3967">
    <literal><![CDATA[
      K(((x \ 1) * (x * y)) \ z,u) = K(L(y,x,x \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[para(2797(a,1),3946(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2797 3946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3968">
    <literal><![CDATA[
      K((x * ((1 / y) / z)) \ u,w) = K((x * ((y \ 1) / z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(3657(a,1),3947(a,1,1,1,2))].">
      <j1 rule="para" parents="3657 3947"/>
    </justification>
  </clause>

  <clause id="3969">
    <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(3628(a,1),3776(a,1,2))].">
      <j1 rule="para" parents="3628 3776"/>
    </justification>
  </clause>

  <clause id="3970">
    <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(828,a,3927,a)].">
      <j1 rule="hyper" parents="828 3927"/>
    </justification>
  </clause>

  <clause id="3971">
    <literal><![CDATA[
      L(x,y,z * K(u \ 1,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3644,a,3970,a),flip(a)].">
      <j1 rule="hyper" parents="3644 3970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3973">
    <literal><![CDATA[
      L(x,y,z * K(u,u \ 1)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1784(a,1),3971(a,1,3,2))].">
      <j1 rule="para" parents="1784 3971"/>
    </justification>
  </clause>

  <clause id="3974">
    <literal><![CDATA[
      L(x,y,((z \ 1) \ 1) * u) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(2809(a,1),3973(a,1,3))].">
      <j1 rule="para" parents="2809 3973"/>
    </justification>
  </clause>

  <clause id="3975">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = (u * y) \ (u * (y * x))
    ]]></literal>
    <justification jstring="[para(3420(a,1),3928(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3420 3928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3976">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13,a,b,3975,a),flip(a)].">
      <j1 rule="hyper" parents="320 13 3975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3978">
    <literal><![CDATA[
      L(x,1 / y,z) = L(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(774(a,1),3976(a,1,2)),flip(a)].">
      <j1 rule="para" parents="774 3976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3979">
    <literal><![CDATA[
      L(x,(y \ 1) \ 1,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1250(a,1),3976(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1250 3976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3980">
    <literal><![CDATA[
      L(x,1 / (1 / y),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1779(a,1),3976(a,1,2))].">
      <j1 rule="para" parents="1779 3976"/>
    </justification>
  </clause>

  <clause id="3981">
    <literal><![CDATA[
      L(x,K(y \ 1,y) * z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(2180(a,2),3976(a,1,2))].">
      <j1 rule="para" parents="2180 3976"/>
    </justification>
  </clause>

  <clause id="3982">
    <literal><![CDATA[
      L(x,y * (1 / z),u) = L(x,y * (z \ 1),u)
    ]]></literal>
    <justification jstring="[para(2588(a,1),3976(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2588 3976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3983">
    <literal><![CDATA[
      L(x,y / ((z \ 1) \ 1),u) = L(x,y / z,u)
    ]]></literal>
    <justification jstring="[para(2636(a,1),3976(a,1,2))].">
      <j1 rule="para" parents="2636 3976"/>
    </justification>
  </clause>

  <clause id="3986">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * L(z,y,x) = x * ((1 / (1 / y)) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,3980,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 3980 13"/>
    </justification>
  </clause>

  <clause id="3987">
    <literal><![CDATA[
      L(x,y / T(1 / z,u),w) = L(x,y / T(z \ 1,u),w)
    ]]></literal>
    <justification jstring="[para(2153(a,1),3983(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2153 3983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3988">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * z != x * ((1 / (1 / y)) * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,y,x) = z
    ]]></literal>
    <justification jstring="[para(3986(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="3986 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3989">
    <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,3725,a(flip),b,3969,a)].">
      <j1 rule="hyper" parents="58 3725 3969"/>
    </justification>
  </clause>

  <clause id="3990">
    <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(3784(a,1),3989(a,1,2))].">
      <j1 rule="para" parents="3784 3989"/>
    </justification>
  </clause>

  <clause id="3991">
    <literal><![CDATA[
      R(x,y * K(z \ 1,z),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,3788,a(flip),b,3990,a),flip(a)].">
      <j1 rule="hyper" parents="58 3788 3990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3993">
    <literal><![CDATA[
      R(x,1 / y,z) = R(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(774(a,1),3991(a,1,2)),flip(a)].">
      <j1 rule="para" parents="774 3991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3994">
    <literal><![CDATA[
      R(x,(y \ 1) \ 1,z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1250(a,1),3991(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1250 3991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3996">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(3993(a,1),3759(a,1,2))].">
      <j1 rule="para" parents="3993 3759"/>
    </justification>
  </clause>

  <clause id="3997">
    <literal><![CDATA[
      R(x,y,z) * (((y \ 1) \ 1) * z) = (x * ((y \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(3994(a,1),101(a,1,1))].">
      <j1 rule="para" parents="3994 101"/>
    </justification>
  </clause>

  <clause id="3998">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * z != u * (((y \ 1) \ 1) * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3997(a,1),39(a,1))].">
      <j1 rule="para" parents="3997 39"/>
    </justification>
  </clause>

  <clause id="3999">
    <literal><![CDATA[
      1 / R(T(x,(x \ 1) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(2832(a,1),3996(a,1,2,1))].">
      <j1 rule="para" parents="2832 3996"/>
    </justification>
  </clause>

  <clause id="4000">
    <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(3628(a,1),3676(a,1,2,1))].">
      <j1 rule="para" parents="3628 3676"/>
    </justification>
  </clause>

  <clause id="4001">
    <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(3705(a,1),3777(a,1,1,2))].">
      <j1 rule="para" parents="3705 3777"/>
    </justification>
  </clause>

  <clause id="4002">
    <literal><![CDATA[
      (a(x,y,z) * K(u \ 1,u)) * K(u,u \ 1) = a(x,y,K(u,u \ 1) * z)
    ]]></literal>
    <justification jstring="[para(9(a,2),3779(a,1,1,1))].">
      <j1 rule="para" parents="9 3779"/>
    </justification>
  </clause>

  <clause id="4003">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(2701,a,4002,a),flip(a)].">
      <j1 rule="hyper" parents="2701 4002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4004">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(4002(a,1),2701(a,1))].">
      <j1 rule="para" parents="4002 2701"/>
    </justification>
  </clause>

  <clause id="4006">
    <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,3452,a,b,4003,a)].">
      <j1 rule="hyper" parents="58 3452 4003"/>
    </justification>
  </clause>

  <clause id="4008">
    <literal><![CDATA[
      a(x,y,1 / z) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(1809(a,1),4003(a,1,3))].">
      <j1 rule="para" parents="1809 4003"/>
    </justification>
  </clause>

  <clause id="4009">
    <literal><![CDATA[
      a(x,y,K(z \ 1,z) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(1787(a,1),4003(a,1,3,1))].">
      <j1 rule="para" parents="1787 4003"/>
    </justification>
  </clause>

  <clause id="4010">
    <literal><![CDATA[
      a(x,y,L(z,z \ 1,u)) = a(x,y,(u * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(3482(a,1),4009(a,1,3))].">
      <j1 rule="para" parents="3482 4009"/>
    </justification>
  </clause>

  <clause id="4012">
    <literal><![CDATA[
      ((x * (y * (z * K(u,u \ 1)))) \ ((x * y) * z)) * K(u,u \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(2169(a,1),4006(a,1,1,1,2,2))].">
      <j1 rule="para" parents="2169 4006"/>
    </justification>
  </clause>

  <clause id="4013">
    <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(3627(a,1),4000(a,1,2))].">
      <j1 rule="para" parents="3627 4000"/>
    </justification>
  </clause>

  <clause id="4014">
    <literal><![CDATA[
      a(x,y * K(z,z \ 1),u) = a(x,y,K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(691,a,4001,a),flip(a)].">
      <j1 rule="hyper" parents="691 4001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4015">
    <literal><![CDATA[
      a(x,y * K(z,z \ 1),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,4003,a(flip),b,4014,a),flip(a)].">
      <j1 rule="hyper" parents="320 4003 4014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4016">
    <literal><![CDATA[
      a(x,y * K(z,z \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(4014(a,2),4004(a,1))].">
      <j1 rule="para" parents="4014 4004"/>
    </justification>
  </clause>

  <clause id="4018">
    <literal><![CDATA[
      a(x,1 / y,z) = a(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(1785(a,1),4015(a,1,2))].">
      <j1 rule="para" parents="1785 4015"/>
    </justification>
  </clause>

  <clause id="4019">
    <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(830,a,4013,a)].">
      <j1 rule="hyper" parents="830 4013"/>
    </justification>
  </clause>

  <clause id="4020">
    <literal><![CDATA[
      a(x * K(y \ 1,y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(3644,a,4019,a),flip(a)].">
      <j1 rule="hyper" parents="3644 4019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4022">
    <literal><![CDATA[
      a(1 / x,y,z) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(774(a,1),4020(a,1,1)),flip(a)].">
      <j1 rule="para" parents="774 4020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4023">
    <literal><![CDATA[
      a((x \ 1) \ 1,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(1250(a,1),4020(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1250 4020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4024">
    <literal><![CDATA[
      a((1 / x) \ y,z,u) = a((x \ 1) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(2929(a,1),4020(a,1,1))].">
      <j1 rule="para" parents="2929 4020"/>
    </justification>
  </clause>

  <clause id="4025">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x = a(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2804,a,b,4022,a)].">
      <j1 rule="hyper" parents="58 2804 4022"/>
    </justification>
  </clause>

  <clause id="4026">
    <literal><![CDATA[
      L(x,y,y \ 1) * a(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,4022,a(flip),b,2804,a)].">
      <j1 rule="hyper" parents="119 4022 2804"/>
    </justification>
  </clause>

  <clause id="4027">
    <literal><![CDATA[
      L(x,y,y \ 1) \ 1 = x \ a(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4025,a(flip),b,1404,a),flip(a)].">
      <j1 rule="hyper" parents="116 4025 1404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4028">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x != z
    ]]></literal>
    <literal><![CDATA[
      a(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(4026(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4026 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4029">
    <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(4026(a,1),90(a,1,1))].">
      <j1 rule="para" parents="4026 90"/>
    </justification>
  </clause>

  <clause id="4030">
    <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,1399,a,b,4029,a)].">
      <j1 rule="hyper" parents="29 1399 4029"/>
    </justification>
  </clause>

  <clause id="4031">
    <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),4030(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 4030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4032">
    <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(2320(a,1),3839(a,1,1))].">
      <j1 rule="para" parents="2320 3839"/>
    </justification>
  </clause>

  <clause id="4033">
    <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),4032(a,1,1,1,2))].">
      <j1 rule="para" parents="105 4032"/>
    </justification>
  </clause>

  <clause id="4034">
    <literal><![CDATA[
      ((x * ((y \ T(z,x)) * y)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(3828(a,1),4033(a,1,2))].">
      <j1 rule="para" parents="3828 4033"/>
    </justification>
  </clause>

  <clause id="4035">
    <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),3926(a,1,2,1))].">
      <j1 rule="para" parents="7 3926"/>
    </justification>
  </clause>

  <clause id="4036">
    <literal><![CDATA[
      (x * K((y / x) \ 1,y / x)) * (x \ 1) = K((y * (x \ 1)) \ 1,y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(1251,a,4035,a),flip(a)].">
      <j1 rule="hyper" parents="1251 4035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4038">
    <literal><![CDATA[
      (x * ((y / (z * (u \ y))) / x)) * (z * (u \ y)) = ((x * ((u / z) / x)) * z) * (u \ y)
    ]]></literal>
    <justification jstring="[hyper(283,a,3808,a),flip(a)].">
      <j1 rule="hyper" parents="283 3808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4039">
    <literal><![CDATA[
      ((x * ((x / y) / x)) * y) * (x \ z) = x * ((x \ T(x,y \ 1)) * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,3861,a(flip),b,4038,a),flip(a)].">
      <j1 rule="hyper" parents="58 3861 4038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4040">
    <literal><![CDATA[
      x * ((x \ T(x,y \ 1)) * (x \ z)) = T(x,y \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[para(3863(a,1),4039(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3863 4039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4041">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) * (x \ z) = x * ((x \ T(x,y)) * (x \ z))
    ]]></literal>
    <justification jstring="[para(2939(a,1),4040(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2939 4040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4042">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * (x \ z)) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(2939(a,1),4041(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2939 4041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4043">
    <literal><![CDATA[
      T(x,y) * (x \ (x * z)) = x * ((x \ T(x,y)) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),4042(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 4042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4044">
    <literal><![CDATA[
      (T(x,y) * z) / ((x \ T(x,y)) * z) = x
    ]]></literal>
    <justification jstring="[hyper(616,a,4043,a)].">
      <j1 rule="hyper" parents="616 4043"/>
    </justification>
  </clause>

  <clause id="4045">
    <literal><![CDATA[
      x \ (T(x,y) * z) = (x \ T(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(614,a,4043,a)].">
      <j1 rule="hyper" parents="614 4043"/>
    </justification>
  </clause>

  <clause id="4046">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(584,a,4043,a),flip(a)].">
      <j1 rule="hyper" parents="584 4043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4047">
    <literal><![CDATA[
      (x \ T(x,y)) * z = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(1125,a,4044,a),flip(a)].">
      <j1 rule="hyper" parents="1125 4044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4048">
    <literal><![CDATA[
      R(x,x \ T(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(759,a,4044,a)].">
      <j1 rule="hyper" parents="759 4044"/>
    </justification>
  </clause>

  <clause id="4049">
    <literal><![CDATA[
      R(x,T(y,x) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(3821(a,2),4048(a,1,2))].">
      <j1 rule="para" parents="3821 4048"/>
    </justification>
  </clause>

  <clause id="4050">
    <literal><![CDATA[
      R(x,K(y,x) \ 1,z) = x
    ]]></literal>
    <justification jstring="[para(3057(a,1),4049(a,1,2))].">
      <j1 rule="para" parents="3057 4049"/>
    </justification>
  </clause>

  <clause id="4051">
    <literal><![CDATA[
      T(x,y) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(3835,a,4045,a),flip(a)].">
      <j1 rule="hyper" parents="3835 4045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4052">
    <literal><![CDATA[
      L(x,y \ T(y,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(751,a,4045,a),flip(a)].">
      <j1 rule="hyper" parents="751 4045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4054">
    <literal><![CDATA[
      (x \ T(x,y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(4045(a,1),1127(a,1))].">
      <j1 rule="para" parents="4045 1127"/>
    </justification>
  </clause>

  <clause id="4057">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,4052,a(flip),b,3156,a)].">
      <j1 rule="hyper" parents="116 4052 3156"/>
    </justification>
  </clause>

  <clause id="4059">
    <literal><![CDATA[
      L(x,T(y,T(z,y)) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(3833(a,2),4052(a,1,2))].">
      <j1 rule="para" parents="3833 4052"/>
    </justification>
  </clause>

  <clause id="4060">
    <literal><![CDATA[
      L(x,T(y,z) \ y,(y * z) / y) = x
    ]]></literal>
    <justification jstring="[para(224(a,1),4059(a,1,2,1,2))].">
      <j1 rule="para" parents="224 4059"/>
    </justification>
  </clause>

  <clause id="4061">
    <literal><![CDATA[
      T(x,y) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1126,a,4051,a)].">
      <j1 rule="hyper" parents="1126 4051"/>
    </justification>
  </clause>

  <clause id="4062">
    <literal><![CDATA[
      (x * (x * y)) / x = T(x,x * y) * y
    ]]></literal>
    <justification jstring="[hyper(1112,a,4051,a),flip(a)].">
      <j1 rule="hyper" parents="1112 4051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4063">
    <literal><![CDATA[
      T(x,x / (x / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,1549,a,b,4051,a)].">
      <j1 rule="hyper" parents="30 1549 4051"/>
    </justification>
  </clause>

  <clause id="4064">
    <literal><![CDATA[
      T(x,x \ y) * (x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(5(a,1),4051(a,2,2,1))].">
      <j1 rule="para" parents="5 4051"/>
    </justification>
  </clause>

  <clause id="4065">
    <literal><![CDATA[
      ((T(x,y) * y) / x) \ ((x * (x * y)) / x) = L(x,(x * y) / x,x)
    ]]></literal>
    <justification jstring="[para(4051(a,2),1648(a,1,1,1))].">
      <j1 rule="para" parents="4051 1648"/>
    </justification>
  </clause>

  <clause id="4066">
    <literal><![CDATA[
      T(x,y) = ((x * y) / x) / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1552,a,b,4063,a),flip(a)].">
      <j1 rule="hyper" parents="58 1552 4063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4067">
    <literal><![CDATA[
      T(x,x / (1 / y)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1554,a(flip),b,4063,a)].">
      <j1 rule="hyper" parents="58 1554 4063"/>
    </justification>
  </clause>

  <clause id="4068">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,1170,a(flip),b,4063,a)].">
      <j1 rule="hyper" parents="58 1170 4063"/>
    </justification>
  </clause>

  <clause id="4069">
    <literal><![CDATA[
      T(x,y) / ((x * y) / x) = x / y
    ]]></literal>
    <justification jstring="[hyper(117,a,4063,a(flip),b,1160,a)].">
      <j1 rule="hyper" parents="117 4063 1160"/>
    </justification>
  </clause>

  <clause id="4070">
    <literal><![CDATA[
      (x / y) \ T(x,y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,4063,a(flip),b,1160,a)].">
      <j1 rule="hyper" parents="116 4063 1160"/>
    </justification>
  </clause>

  <clause id="4071">
    <literal><![CDATA[
      T(x * y,(x * y) / x) = T(x * y,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),4063(a,1,2,2))].">
      <j1 rule="para" parents="6 4063"/>
    </justification>
  </clause>

  <clause id="4072">
    <literal><![CDATA[
      T(x,x / y) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(72(a,1),4063(a,1,2,2))].">
      <j1 rule="para" parents="72 4063"/>
    </justification>
  </clause>

  <clause id="4073">
    <literal><![CDATA[
      T(x,(y \ x) \ x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(190(a,1),4063(a,1,2)),flip(a)].">
      <j1 rule="para" parents="190 4063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4074">
    <literal><![CDATA[
      T(x,T(y,x)) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(4063(a,1),1502(a,1,1))].">
      <j1 rule="para" parents="4063 1502"/>
    </justification>
  </clause>

  <clause id="4075">
    <literal><![CDATA[
      T(x,T(y,y \ x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(106(a,2),4073(a,1,2))].">
      <j1 rule="para" parents="106 4073"/>
    </justification>
  </clause>

  <clause id="4076">
    <literal><![CDATA[
      T(x * y,T(x,y)) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),4075(a,1,2,2))].">
      <j1 rule="para" parents="4 4075"/>
    </justification>
  </clause>

  <clause id="4077">
    <literal><![CDATA[
      T(x / y,T(y,x)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(239,a,1490,a,b,4061,a)].">
      <j1 rule="hyper" parents="239 1490 4061"/>
    </justification>
  </clause>

  <clause id="4078">
    <literal><![CDATA[
      T(x,T(y,x * y)) = y \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(239,a,817,a(flip),b,4061,a)].">
      <j1 rule="hyper" parents="239 817 4061"/>
    </justification>
  </clause>

  <clause id="4079">
    <literal><![CDATA[
      T(x,y) \ ((x * y) / x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(123,a,4061,a)].">
      <j1 rule="hyper" parents="123 4061"/>
    </justification>
  </clause>

  <clause id="4080">
    <literal><![CDATA[
      ((x * y) / x) \ (T(x,y) * ((x \ y) * z)) = L(z,x \ y,T(x,y))
    ]]></literal>
    <justification jstring="[para(4061(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4061 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4081">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,T(x,y)) = ((x * y) / x) \ (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4061(a,1),92(a,2,1))].">
      <j1 rule="para" parents="4061 92"/>
    </justification>
  </clause>

  <clause id="4082">
    <literal><![CDATA[
      L(((x * y) / x) / y,y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4061(a,1),2891(a,1,1,1))].">
      <j1 rule="para" parents="4061 2891"/>
    </justification>
  </clause>

  <clause id="4083">
    <literal><![CDATA[
      T(x \ y,T(x,y)) = T(x \ y,x)
    ]]></literal>
    <justification jstring="[para(4077(a,1),246(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4077 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4084">
    <literal><![CDATA[
      x \ (y * T(y \ x,T(y,x))) = K(y \ x,T(y,x))
    ]]></literal>
    <justification jstring="[para(4077(a,1),1941(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4077 1941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4085">
    <literal><![CDATA[
      T(x,y) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x * y) / x = z
    ]]></literal>
    <justification jstring="[para(4066(a,2),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4066 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4086">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(4067(a,1),1507(a,1,1))].">
      <j1 rule="para" parents="4067 1507"/>
    </justification>
  </clause>

  <clause id="4087">
    <literal><![CDATA[
      T(x / T(y,x),y) = T(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(239,a,4068,a,b,1128,a)].">
      <j1 rule="hyper" parents="239 4068 1128"/>
    </justification>
  </clause>

  <clause id="4088">
    <literal><![CDATA[
      ((x * y) * y) / (x * y) = x \ T(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(31,a,181,a(flip),b,4069,a),flip(a)].">
      <j1 rule="hyper" parents="31 181 4069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4089">
    <literal><![CDATA[
      T(x,T(y,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,17,a,b,4078,a),flip(a)].">
      <j1 rule="hyper" parents="320 17 4078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4090">
    <literal><![CDATA[
      T(x,x \ y) \ (y / x) = x \ (x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),4079(a,1,2,1))].">
      <j1 rule="para" parents="5 4079"/>
    </justification>
  </clause>

  <clause id="4091">
    <literal><![CDATA[
      T(x,y) * T(x \ y,x) = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4083,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4083 17"/>
    </justification>
  </clause>

  <clause id="4092">
    <literal><![CDATA[
      x \ (y * T(y \ x,T(y,x))) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4083(a,2),432(a,1,2,2))].">
      <j1 rule="para" parents="4083 432"/>
    </justification>
  </clause>

  <clause id="4093">
    <literal><![CDATA[
      T(x / T(y,x),z) * y = y * T(T(y,x) \ x,z)
    ]]></literal>
    <justification jstring="[para(4087(a,1),236(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4087 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4094">
    <literal><![CDATA[
      x \ ((T(y,x) \ y) * z) = ((y * x) / y) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,4060,a(flip),b,3923,a),flip(a)].">
      <j1 rule="hyper" parents="116 4060 3923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4096">
    <literal><![CDATA[
      (x \ T(x,y)) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(29,a,1100,a(flip),b,4046,a),flip(a)].">
      <j1 rule="hyper" parents="29 1100 4046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4099">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,152,a(flip),b,4047,a)].">
      <j1 rule="hyper" parents="117 152 4047"/>
    </justification>
  </clause>

  <clause id="4100">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(116,a,152,a(flip),b,4047,a)].">
      <j1 rule="hyper" parents="116 152 4047"/>
    </justification>
  </clause>

  <clause id="4101">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(4057(a,2),584(a,1))].">
      <j1 rule="para" parents="4057 584"/>
    </justification>
  </clause>

  <clause id="4102">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(4057(a,2),1135(a,1))].">
      <j1 rule="para" parents="4057 1135"/>
    </justification>
  </clause>

  <clause id="4105">
    <literal><![CDATA[
      (T(x,x * y) * y) * x = x * (x * y)
    ]]></literal>
    <justification jstring="[hyper(133,a,4062,a)].">
      <j1 rule="hyper" parents="133 4062"/>
    </justification>
  </clause>

  <clause id="4106">
    <literal><![CDATA[
      T(T(x,x * y) * y,x) = x * y
    ]]></literal>
    <justification jstring="[para(4062(a,1),224(a,1,1))].">
      <j1 rule="para" parents="4062 224"/>
    </justification>
  </clause>

  <clause id="4107">
    <literal><![CDATA[
      ((x \ y) \ y) * (x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(667,a,4064,a)].">
      <j1 rule="hyper" parents="667 4064"/>
    </justification>
  </clause>

  <clause id="4108">
    <literal><![CDATA[
      T(x,x \ (y \ x)) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3871,a,b,4064,a)].">
      <j1 rule="hyper" parents="116 3871 4064"/>
    </justification>
  </clause>

  <clause id="4109">
    <literal><![CDATA[
      (x \ T(x,x \ y)) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4047,a,b,4064,a)].">
      <j1 rule="hyper" parents="58 4047 4064"/>
    </justification>
  </clause>

  <clause id="4110">
    <literal><![CDATA[
      (x * (y / x)) \ (T(x,x \ y) * ((x \ y) * z)) = L(z,x \ y,T(x,x \ y))
    ]]></literal>
    <justification jstring="[para(4064(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4064 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4111">
    <literal><![CDATA[
      x * (x * T(T(x,x \ (y * x)) \ ((y * x) / x),z)) = (x * T(x \ y,z)) * x
    ]]></literal>
    <justification jstring="[para(4090(a,2),1532(a,1,2,2,1))].">
      <j1 rule="para" parents="4090 1532"/>
    </justification>
  </clause>

  <clause id="4112">
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2985,a,4099,a)].">
      <j1 rule="hyper" parents="2985 4099"/>
    </justification>
  </clause>

  <clause id="4113">
    <literal><![CDATA[
      R(K(x,y),x,z) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4099(a,1),3911(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4099 3911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4115">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = (y / x) \ T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3111,a(flip),b,4112,a)].">
      <j1 rule="hyper" parents="58 3111 4112"/>
    </justification>
  </clause>

  <clause id="4116">
    <literal><![CDATA[
      L(x \ T(x,y),y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(3824(a,1),4082(a,1,1))].">
      <j1 rule="para" parents="3824 4082"/>
    </justification>
  </clause>

  <clause id="4117">
    <literal><![CDATA[
      K(T(x,T(y,x)),T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3847,a,b,4116,a),flip(a)].">
      <j1 rule="hyper" parents="58 3847 4116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4118">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,4068,a(flip),b,4086,a),flip(a)].">
      <j1 rule="hyper" parents="320 4068 4086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4119">
    <literal><![CDATA[
      L(R(x,y,x),y,x) * y = y * T(x,T(y,x))
    ]]></literal>
    <justification jstring="[para(4118(a,1),965(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4118 965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4120">
    <literal><![CDATA[
      T(x \ T(x * y,y),x) = R(y,x,y)
    ]]></literal>
    <justification jstring="[para(4088(a,1),781(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4088 781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4121">
    <literal><![CDATA[
      (x \ T(x * y,y)) * x = x * R(y,x,y)
    ]]></literal>
    <justification jstring="[para(4088(a,1),798(a,1,1))].">
      <j1 rule="para" parents="4088 798"/>
    </justification>
  </clause>

  <clause id="4122">
    <literal><![CDATA[
      x * R(y,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ T(x * y,y)) * x = z
    ]]></literal>
    <justification jstring="[para(4120(a,1),284(a,1,2))].">
      <j1 rule="para" parents="4120 284"/>
    </justification>
  </clause>

  <clause id="4123">
    <literal><![CDATA[
      (x * R(y,x,y)) \ T(x * y,y) = K(x,x \ T(x * y,y))
    ]]></literal>
    <justification jstring="[para(4121(a,1),86(a,1,1))].">
      <j1 rule="para" parents="4121 86"/>
    </justification>
  </clause>

  <clause id="4124">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(134,a,4094,a)].">
      <j1 rule="hyper" parents="134 4094"/>
    </justification>
  </clause>

  <clause id="4125">
    <literal><![CDATA[
      (T(x,y) \ x) * (x * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(119,a,75,a(flip),b,4094,a),flip(a)].">
      <j1 rule="hyper" parents="119 75 4094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4126">
    <literal><![CDATA[
      K(x,y) = T(T(y,x) \ y,y * x)
    ]]></literal>
    <justification jstring="[hyper(239,a,4125,a,b,84,a),flip(a)].">
      <j1 rule="hyper" parents="239 4125 84"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4127">
    <literal><![CDATA[
      (x * y) / (y * x) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(131,a,4125,a)].">
      <j1 rule="hyper" parents="131 4125"/>
    </justification>
  </clause>

  <clause id="4128">
    <literal><![CDATA[
      T(x,y * z) != K(z,y)
    ]]></literal>
    <literal><![CDATA[
      T(y,z) \ y = x
    ]]></literal>
    <justification jstring="[para(4126(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="4126 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4129">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3909,a,4127,a(flip))].">
      <j1 rule="hyper" parents="3909 4127"/>
    </justification>
  </clause>

  <clause id="4130">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = (y * (x / y)) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),4127(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 4127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4131">
    <literal><![CDATA[
      T(x,y / x) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y / (x * (y / x)) = z
    ]]></literal>
    <justification jstring="[para(4127(a,1),576(a,1))].">
      <j1 rule="para" parents="4127 576"/>
    </justification>
  </clause>

  <clause id="4132">
    <literal><![CDATA[
      T(x,T((x \ 1) * y,x)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(1969(a,1),4129(a,1,2))].">
      <j1 rule="para" parents="1969 4129"/>
    </justification>
  </clause>

  <clause id="4133">
    <literal><![CDATA[
      (((1 / x) * (y * x)) \ (y * x)) \ 1 = 1 / R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(4129(a,1),3999(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4129 3999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4134">
    <literal><![CDATA[
      T((x * y) / x,T(x,y)) = L(R(y,x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,454,a,b,4119,a)].">
      <j1 rule="hyper" parents="30 454 4119"/>
    </justification>
  </clause>

  <clause id="4135">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,3836,a,b,4124,a)].">
      <j1 rule="hyper" parents="58 3836 4124"/>
    </justification>
  </clause>

  <clause id="4136">
    <literal><![CDATA[
      (x * (y / x)) / y = (x \ y) \ (y / x)
    ]]></literal>
    <justification jstring="[para(107(a,1),4130(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 4130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4137">
    <literal><![CDATA[
      (x * (y / x)) / y = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3845,a(flip),b,4136,a),flip(a)].">
      <j1 rule="hyper" parents="320 3845 4136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4138">
    <literal><![CDATA[
      (x \ (y \ x)) \ (y \ x) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3887,a,4137,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3887 4137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4139">
    <literal><![CDATA[
      T(x,x \ (y \ x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(356,a,4138,a)].">
      <j1 rule="hyper" parents="356 4138"/>
    </justification>
  </clause>

  <clause id="4140">
    <literal><![CDATA[
      (x \ y) / T(y,x \ 1) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(197,a,4138,a)].">
      <j1 rule="hyper" parents="197 4138"/>
    </justification>
  </clause>

  <clause id="4141">
    <literal><![CDATA[
      (x \ (y \ x)) * T(x,y \ 1) = y \ x
    ]]></literal>
    <justification jstring="[hyper(134,a,4138,a)].">
      <j1 rule="hyper" parents="134 4138"/>
    </justification>
  </clause>

  <clause id="4142">
    <literal><![CDATA[
      T(x * y,(x * y) \ y) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),4139(a,1,2,2))].">
      <j1 rule="para" parents="4 4139"/>
    </justification>
  </clause>

  <clause id="4143">
    <literal><![CDATA[
      T(x,(x / y) \ 1) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(75(a,1),4139(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 4139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4144">
    <literal><![CDATA[
      x \ ((y \ x) / ((y \ x) / x)) = T(x,y \ 1) \ x
    ]]></literal>
    <justification jstring="[para(4139(a,1),3849(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4139 3849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4145">
    <literal><![CDATA[
      (x / y) \ T(x,x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4143(a,1),3879(a,1,2))].">
      <j1 rule="para" parents="4143 3879"/>
    </justification>
  </clause>

  <clause id="4146">
    <literal><![CDATA[
      ((x \ 1) \ y) / T(y,x) = y \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(2939(a,1),4140(a,1,2))].">
      <j1 rule="para" parents="2939 4140"/>
    </justification>
  </clause>

  <clause id="4147">
    <literal><![CDATA[
      ((x * y) \ (y \ (x * y))) * T(x * y,y \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,17,a,b,4141,a),flip(a)].">
      <j1 rule="hyper" parents="320 17 4141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4148">
    <literal><![CDATA[
      (x \ ((1 / y) \ x)) * T(x,y) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[para(75(a,1),4141(a,1,2,2))].">
      <j1 rule="para" parents="75 4141"/>
    </justification>
  </clause>

  <clause id="4149">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,x \ (y * x)) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),4145(a,2,2))].">
      <j1 rule="para" parents="6 4145"/>
    </justification>
  </clause>

  <clause id="4150">
    <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(4088(a,1),4134(a,1,1))].">
      <j1 rule="para" parents="4088 4134"/>
    </justification>
  </clause>

  <clause id="4151">
    <literal><![CDATA[
      T(x * y,x \ 1) = ((x * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(428,a,4142,a),flip(a)].">
      <j1 rule="hyper" parents="428 4142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4152">
    <literal><![CDATA[
      x / T(y * x,y \ 1) = (y * x) \ x
    ]]></literal>
    <justification jstring="[para(4142(a,1),265(a,1,2))].">
      <j1 rule="para" parents="4142 265"/>
    </justification>
  </clause>

  <clause id="4153">
    <literal><![CDATA[
      T((x \ 1) * y,x) = (((x \ 1) * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(3010,a,4151,a)].">
      <j1 rule="hyper" parents="3010 4151"/>
    </justification>
  </clause>

  <clause id="4154">
    <literal><![CDATA[
      x * ((x * y) * (y / (x * y))) = ((x * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,3843,a,b,4151,a)].">
      <j1 rule="hyper" parents="58 3843 4151"/>
    </justification>
  </clause>

  <clause id="4155">
    <literal><![CDATA[
      (x \ 1) * (((x * y) \ y) \ y) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,4151,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4151 17"/>
    </justification>
  </clause>

  <clause id="4156">
    <literal><![CDATA[
      T((1 / x) * y,x) = (((1 / x) * y) \ y) \ y
    ]]></literal>
    <justification jstring="[para(75(a,1),4151(a,1,2))].">
      <j1 rule="para" parents="75 4151"/>
    </justification>
  </clause>

  <clause id="4157">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,T(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(17(a,2),4149(a,1,2,2))].">
      <j1 rule="para" parents="17 4149"/>
    </justification>
  </clause>

  <clause id="4158">
    <literal><![CDATA[
      (x \ T(x,y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(5(a,1),4101(a,1,2))].">
      <j1 rule="para" parents="5 4101"/>
    </justification>
  </clause>

  <clause id="4159">
    <literal><![CDATA[
      K(x \ y,T(x,y)) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4092,a(flip),b,4084,a),flip(a)].">
      <j1 rule="hyper" parents="58 4092 4084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4160">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(y,T(x,x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,673,a(flip),b,4159,a),flip(a)].">
      <j1 rule="hyper" parents="58 673 4159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4161">
    <literal><![CDATA[
      K(x,T(y,y * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1351,a,4160,a),flip(a)].">
      <j1 rule="hyper" parents="1351 4160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4163">
    <literal><![CDATA[
      R(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3847,a,b,4113,a),flip(a)].">
      <j1 rule="hyper" parents="320 3847 4113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4164">
    <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(4113(a,1),384(a,1)),flip(b)].">
      <j1 rule="para" parents="4113 384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4166">
    <literal><![CDATA[
      (K(x,y) * x) * z = K(x,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(4163(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4163 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4167">
    <literal><![CDATA[
      L(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,4166,a)].">
      <j1 rule="hyper" parents="479 4166"/>
    </justification>
  </clause>

  <clause id="4173">
    <literal><![CDATA[
      L(x,y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(4167(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="4167 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4174">
    <literal><![CDATA[
      L(x,y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(4167(a,1),45(a,2))].">
      <j1 rule="para" parents="4167 45"/>
    </justification>
  </clause>

  <clause id="4176">
    <literal><![CDATA[
      ((x \ y) / y) \ T((x \ y) / y,z) = x * T(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(1295,a,4115,a),flip(a)].">
      <j1 rule="hyper" parents="1295 4115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4178">
    <literal><![CDATA[
      K(T(x,T(y,x)),T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4116(a,1),4164(a,1))].">
      <j1 rule="para" parents="4116 4164"/>
    </justification>
  </clause>

  <clause id="4179">
    <literal><![CDATA[
      R(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(4113(a,2),4164(a,1))].">
      <j1 rule="para" parents="4113 4164"/>
    </justification>
  </clause>

  <clause id="4180">
    <literal><![CDATA[
      T(x,y \ 1) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[para(4139(a,1),4108(a,1,1))].">
      <j1 rule="para" parents="4139 4108"/>
    </justification>
  </clause>

  <clause id="4181">
    <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(2803(a,1),4180(a,2,2))].">
      <j1 rule="para" parents="2803 4180"/>
    </justification>
  </clause>

  <clause id="4182">
    <literal><![CDATA[
      ((x * y) \ T(x,y)) * T(x * y,y \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(17(a,2),4147(a,1,1,2))].">
      <j1 rule="para" parents="17 4147"/>
    </justification>
  </clause>

  <clause id="4183">
    <literal><![CDATA[
      x \ ((y \ x) / ((y \ x) / x)) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3822,a(flip),b,4176,a)].">
      <j1 rule="hyper" parents="58 3822 4176"/>
    </justification>
  </clause>

  <clause id="4184">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = (y * T(y \ 1,x)) \ x
    ]]></literal>
    <justification jstring="[para(4176(a,1),3841(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4176 3841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4185">
    <literal><![CDATA[
      T(x,y \ 1) \ x = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4144,a(flip),b,4183,a)].">
      <j1 rule="hyper" parents="58 4144 4183"/>
    </justification>
  </clause>

  <clause id="4186">
    <literal><![CDATA[
      K(x \ (x / y),x) = T(x,y \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(320,a,1017,a,b,4185,a)].">
      <j1 rule="hyper" parents="320 1017 4185"/>
    </justification>
  </clause>

  <clause id="4187">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,983,a(flip),b,4185,a),flip(a)].">
      <j1 rule="hyper" parents="320 983 4185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4188">
    <literal><![CDATA[
      K(x \ (x / y),x) \ x = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3048,a,4186,a)].">
      <j1 rule="hyper" parents="3048 4186"/>
    </justification>
  </clause>

  <clause id="4189">
    <literal><![CDATA[
      K(x \ (x / y),x) != z \ x
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(4186(a,2),43(a,1))].">
      <j1 rule="para" parents="4186 43"/>
    </justification>
  </clause>

  <clause id="4190">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(2939(a,1),4187(a,1,1))].">
      <j1 rule="para" parents="2939 4187"/>
    </justification>
  </clause>

  <clause id="4191">
    <literal><![CDATA[
      T(x,y / x) \ x = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(320,a,3822,a(flip),b,4190,a),flip(a)].">
      <j1 rule="hyper" parents="320 3822 4190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4192">
    <literal><![CDATA[
      (x * y) / x = y * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4190,a,b,3819,a),flip(a)].">
      <j1 rule="hyper" parents="119 4190 3819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4193">
    <literal><![CDATA[
      T(x,T(y,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,3833,a,b,4190,a)].">
      <j1 rule="hyper" parents="34 3833 4190"/>
    </justification>
  </clause>

  <clause id="4194">
    <literal><![CDATA[
      x * ((T(y,x) \ y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(4190(a,2),4046(a,1,2,1))].">
      <j1 rule="para" parents="4190 4046"/>
    </justification>
  </clause>

  <clause id="4195">
    <literal><![CDATA[
      T(x,y) * (x \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[para(4190(a,2),4047(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4190 4047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4196">
    <literal><![CDATA[
      K(x,y) = T(x \ T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(4190(a,1),4126(a,2,1))].">
      <j1 rule="para" parents="4190 4126"/>
    </justification>
  </clause>

  <clause id="4197">
    <literal><![CDATA[
      (T(x,y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) * (y \ z) = u
    ]]></literal>
    <justification jstring="[para(4190(a,2),4054(a,1,1))].">
      <j1 rule="para" parents="4190 4054"/>
    </justification>
  </clause>

  <clause id="4198">
    <literal><![CDATA[
      x * (T(x,y) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(1171,a,4193,a)].">
      <j1 rule="hyper" parents="1171 4193"/>
    </justification>
  </clause>

  <clause id="4199">
    <literal><![CDATA[
      T(x \ y,x) = ((x \ y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(601,a,4193,a),flip(a)].">
      <j1 rule="hyper" parents="601 4193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4200">
    <literal><![CDATA[
      T(x,y) \ (x * y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(429,a,4193,a)].">
      <j1 rule="hyper" parents="429 4193"/>
    </justification>
  </clause>

  <clause id="4201">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4118,a,b,4193,a)].">
      <j1 rule="hyper" parents="58 4118 4193"/>
    </justification>
  </clause>

  <clause id="4202">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4068,a,b,4193,a)].">
      <j1 rule="hyper" parents="58 4068 4193"/>
    </justification>
  </clause>

  <clause id="4203">
    <literal><![CDATA[
      T(x,(x \ 1) * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4132,a(flip),b,4193,a),flip(a)].">
      <j1 rule="hyper" parents="58 4132 4193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4204">
    <literal><![CDATA[
      T(x / T(y,x),y) = y \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(440,a,4193,a(flip),b,4068,a)].">
      <j1 rule="hyper" parents="440 4193 4068"/>
    </justification>
  </clause>

  <clause id="4205">
    <literal><![CDATA[
      T(x,y) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(119,a,4193,a(flip),b,235,a)].">
      <j1 rule="hyper" parents="119 4193 235"/>
    </justification>
  </clause>

  <clause id="4206">
    <literal><![CDATA[
      T(x,y) / y = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,4193,a(flip),b,4068,a)].">
      <j1 rule="hyper" parents="117 4193 4068"/>
    </justification>
  </clause>

  <clause id="4207">
    <literal><![CDATA[
      T(x,y) / (T(y,x) \ x) = y
    ]]></literal>
    <justification jstring="[hyper(117,a,4193,a(flip),b,1128,a)].">
      <j1 rule="hyper" parents="117 4193 1128"/>
    </justification>
  </clause>

  <clause id="4208">
    <literal><![CDATA[
      T(x,y) \ y = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4193,a(flip),b,1128,a),flip(a)].">
      <j1 rule="hyper" parents="116 4193 1128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4209">
    <literal><![CDATA[
      T(T(x,y),T(z,x)) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(4193(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4193 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4210">
    <literal><![CDATA[
      T(x,T(T(y,x),z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(18(a,1),4193(a,1,2))].">
      <j1 rule="para" parents="18 4193"/>
    </justification>
  </clause>

  <clause id="4211">
    <literal><![CDATA[
      T(L(x,y,z),T(u,x)) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(4193(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4193 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4212">
    <literal><![CDATA[
      T(x,L(T(y,x),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(20(a,2),4193(a,1,2))].">
      <j1 rule="para" parents="20 4193"/>
    </justification>
  </clause>

  <clause id="4213">
    <literal><![CDATA[
      T(x,y / x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),4193(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 4193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4215">
    <literal><![CDATA[
      T(x,y) * T(T(y,x),z) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4193(a,1),236(a,1,2,1))].">
      <j1 rule="para" parents="4193 236"/>
    </justification>
  </clause>

  <clause id="4216">
    <literal><![CDATA[
      T(x,y) * L(T(y,x),z,u) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4193(a,1),237(a,1,2,1))].">
      <j1 rule="para" parents="4193 237"/>
    </justification>
  </clause>

  <clause id="4217">
    <literal><![CDATA[
      T(x,y) * R(T(y,x),z,u) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4193(a,1),238(a,1,2,1))].">
      <j1 rule="para" parents="4193 238"/>
    </justification>
  </clause>

  <clause id="4218">
    <literal><![CDATA[
      T(x,T(y,y * x)) = T(x,L(y,x,y))
    ]]></literal>
    <justification jstring="[para(711(a,1),4193(a,1,2))].">
      <j1 rule="para" parents="711 4193"/>
    </justification>
  </clause>

  <clause id="4219">
    <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(4193(a,1),418(a,1,2,1))].">
      <j1 rule="para" parents="4193 418"/>
    </justification>
  </clause>

  <clause id="4220">
    <literal><![CDATA[
      T(x,y) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(4193(a,1),4074(a,1,1))].">
      <j1 rule="para" parents="4193 4074"/>
    </justification>
  </clause>

  <clause id="4221">
    <literal><![CDATA[
      K(T(x,y),T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4193(a,1),4117(a,1,1))].">
      <j1 rule="para" parents="4193 4117"/>
    </justification>
  </clause>

  <clause id="4222">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,y) = x * y
    ]]></literal>
    <justification jstring="[para(4193(a,1),4157(a,1,2))].">
      <j1 rule="para" parents="4193 4157"/>
    </justification>
  </clause>

  <clause id="4224">
    <literal><![CDATA[
      T(x,y) * (x \ T(y,x)) = y
    ]]></literal>
    <justification jstring="[para(4198(a,1),67(a,1,2,2))].">
      <j1 rule="para" parents="4198 67"/>
    </justification>
  </clause>

  <clause id="4226">
    <literal><![CDATA[
      (x * y) / T(y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(197,a,4200,a)].">
      <j1 rule="hyper" parents="197 4200"/>
    </justification>
  </clause>

  <clause id="4228">
    <literal><![CDATA[
      T(x,y) = (x \ (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(17(a,1),4200(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17 4200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4229">
    <literal><![CDATA[
      T(x,y) / T(y,x) = x / T(T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(117,a,4193,a(flip),b,4202,a)].">
      <j1 rule="hyper" parents="117 4193 4202"/>
    </justification>
  </clause>

  <clause id="4230">
    <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(4202(a,1),604(a,1,2))].">
      <j1 rule="para" parents="4202 604"/>
    </justification>
  </clause>

  <clause id="4231">
    <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,4205,a(flip),b,184,a)].">
      <j1 rule="hyper" parents="119 4205 184"/>
    </justification>
  </clause>

  <clause id="4232">
    <literal><![CDATA[
      (T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4205(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4205 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4233">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * (T(y,x) * z)) = L(z,T(y,x),T(x,y))
    ]]></literal>
    <justification jstring="[para(4205(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4205 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4234">
    <literal><![CDATA[
      (x * (y * z)) * a(x,T(y,z),T(z,y)) = (x * T(y,z)) * T(z,y)
    ]]></literal>
    <justification jstring="[para(4205(a,1),80(a,1,1,2))].">
      <j1 rule="para" parents="4205 80"/>
    </justification>
  </clause>

  <clause id="4235">
    <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(4205(a,1),518(a,1,1,1))].">
      <j1 rule="para" parents="4205 518"/>
    </justification>
  </clause>

  <clause id="4236">
    <literal><![CDATA[
      (T(x,y) / y) * z = (x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[hyper(52,a,4206,a)].">
      <j1 rule="hyper" parents="52 4206"/>
    </justification>
  </clause>

  <clause id="4237">
    <literal><![CDATA[
      (T(x,y) / y) \ x = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(188,a,4206,a(flip))].">
      <j1 rule="hyper" parents="188 4206"/>
    </justification>
  </clause>

  <clause id="4238">
    <literal><![CDATA[
      T(x * (y / x),x) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,4206,a(flip),b,1376,a),flip(a)].">
      <j1 rule="hyper" parents="119 4206 1376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4239">
    <literal><![CDATA[
      (x / T(y,x)) * y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4206(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4206 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4240">
    <literal><![CDATA[
      T(x,T(y,z)) / (T(T(y,x),z) \ x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(18(a,1),4207(a,1,2,1))].">
      <j1 rule="para" parents="18 4207"/>
    </justification>
  </clause>

  <clause id="4241">
    <literal><![CDATA[
      (T(x,y) \ y) * z = (x \ T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(4207(a,1),194(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4207 194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4242">
    <literal><![CDATA[
      (x \ T(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      (T(x,y) \ y) * z = u
    ]]></literal>
    <justification jstring="[para(4207(a,1),619(a,1,1,1))].">
      <j1 rule="para" parents="4207 619"/>
    </justification>
  </clause>

  <clause id="4243">
    <literal><![CDATA[
      (T(x,y) \ y) \ z = (x \ T(y,x)) \ z
    ]]></literal>
    <justification jstring="[hyper(56,a,4208,a)].">
      <j1 rule="hyper" parents="56 4208"/>
    </justification>
  </clause>

  <clause id="4244">
    <literal><![CDATA[
      T(x,y) \ ((T(y,x) \ x) * y) = K(y \ T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4208(a,2),85(a,1,2,1))].">
      <j1 rule="para" parents="4208 85"/>
    </justification>
  </clause>

  <clause id="4245">
    <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(4208(a,1),81(a,1,1,2,1))].">
      <j1 rule="para" parents="4208 81"/>
    </justification>
  </clause>

  <clause id="4246">
    <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(4208(a,1),2034(a,1,2,1))].">
      <j1 rule="para" parents="4208 2034"/>
    </justification>
  </clause>

  <clause id="4247">
    <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(4208(a,1),2127(a,1,2,1))].">
      <j1 rule="para" parents="4208 2127"/>
    </justification>
  </clause>

  <clause id="4248">
    <literal><![CDATA[
      T(x,y / x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,106,a(flip),b,4213,a),flip(a)].">
      <j1 rule="hyper" parents="320 106 4213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4249">
    <literal><![CDATA[
      (x / y) * T(y,y \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4213,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4213 17"/>
    </justification>
  </clause>

  <clause id="4250">
    <literal><![CDATA[
      x / T(y,x / y) = y \ x
    ]]></literal>
    <justification jstring="[para(4213(a,2),265(a,1,2))].">
      <j1 rule="para" parents="4213 265"/>
    </justification>
  </clause>

  <clause id="4252">
    <literal><![CDATA[
      (x * (y / x)) * x = y * T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4213(a,1),902(a,2,2))].">
      <j1 rule="para" parents="4213 902"/>
    </justification>
  </clause>

  <clause id="4253">
    <literal><![CDATA[
      (x * y) \ (y * T(x,x \ y)) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[para(4213(a,1),908(a,1,2,2))].">
      <j1 rule="para" parents="4213 908"/>
    </justification>
  </clause>

  <clause id="4254">
    <literal><![CDATA[
      x \ (T(x,y / x) / (1 / (x \ y))) = (x / (1 / (x \ y))) / x
    ]]></literal>
    <justification jstring="[para(4213(a,2),3882(a,1,2,1))].">
      <j1 rule="para" parents="4213 3882"/>
    </justification>
  </clause>

  <clause id="4255">
    <literal><![CDATA[
      T(x,T(y,x / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4213(a,2),4075(a,1,2))].">
      <j1 rule="para" parents="4213 4075"/>
    </justification>
  </clause>

  <clause id="4258">
    <literal><![CDATA[
      T(x,y) * z != y
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4224(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="4224 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4259">
    <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),4226(a,1,2))].">
      <j1 rule="para" parents="22 4226"/>
    </justification>
  </clause>

  <clause id="4260">
    <literal><![CDATA[
      (T(x,y) * (y * x)) / T(x,y) = T(y,x) * T(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(4226(a,1),1490(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4226 1490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4261">
    <literal><![CDATA[
      (x / T(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      (T(x,y) / y) * z = u
    ]]></literal>
    <justification jstring="[para(4237(a,1),348(a,1,1,2))].">
      <j1 rule="para" parents="4237 348"/>
    </justification>
  </clause>

  <clause id="4262">
    <literal><![CDATA[
      T(T(x,y),z / x) = T((x \ z) \ z,y)
    ]]></literal>
    <justification jstring="[para(4248(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4248 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4263">
    <literal><![CDATA[
      (x * (y / x)) * x = y * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(4248(a,1),902(a,2,2))].">
      <j1 rule="para" parents="4248 902"/>
    </justification>
  </clause>

  <clause id="4264">
    <literal><![CDATA[
      x / T(y \ x,y) = (y \ x) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),4250(a,1,2,2))].">
      <j1 rule="para" parents="72 4250"/>
    </justification>
  </clause>

  <clause id="4265">
    <literal><![CDATA[
      T(x,x * (y / x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(810,a,4201,a),flip(a)].">
      <j1 rule="hyper" parents="810 4201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4266">
    <literal><![CDATA[
      T(x,y * x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(806,a,4201,a)].">
      <j1 rule="hyper" parents="806 4201"/>
    </justification>
  </clause>

  <clause id="4267">
    <literal><![CDATA[
      T(R(x,y,x),x * y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(629,a,4201,a)].">
      <j1 rule="hyper" parents="629 4201"/>
    </justification>
  </clause>

  <clause id="4268">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),4201(a,1,1,2))].">
      <j1 rule="para" parents="5 4201"/>
    </justification>
  </clause>

  <clause id="4269">
    <literal><![CDATA[
      T(x,y * z) != T(y,z)
    ]]></literal>
    <literal><![CDATA[
      R(y,z,y) = x
    ]]></literal>
    <justification jstring="[para(4201(a,1),140(a,2))].">
      <j1 rule="para" parents="4201 140"/>
    </justification>
  </clause>

  <clause id="4270">
    <literal><![CDATA[
      T(x,(x \ y) * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(71(a,1),4265(a,1,2)),flip(a)].">
      <j1 rule="para" parents="71 4265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4271">
    <literal><![CDATA[
      T(x,x * T(y / x,z)) = T(x,x * T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(457(a,1),4265(a,1,2,2))].">
      <j1 rule="para" parents="457 4265"/>
    </justification>
  </clause>

  <clause id="4272">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * (y / x),x)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4265(a,1),4224(a,1,1))].">
      <j1 rule="para" parents="4265 4224"/>
    </justification>
  </clause>

  <clause id="4273">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(320,a,711,a,b,4266,a)].">
      <j1 rule="hyper" parents="320 711 4266"/>
    </justification>
  </clause>

  <clause id="4274">
    <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,4266,a)].">
      <j1 rule="hyper" parents="58 22 4266"/>
    </justification>
  </clause>

  <clause id="4275">
    <literal><![CDATA[
      T(T(x,x * y),z) = T(T(x,z),y * x)
    ]]></literal>
    <justification jstring="[para(4266(a,1),18(a,1,1))].">
      <j1 rule="para" parents="4266 18"/>
    </justification>
  </clause>

  <clause id="4276">
    <literal><![CDATA[
      T(T(x,y * x),z) = T(T(x,z),x * y)
    ]]></literal>
    <justification jstring="[para(4266(a,2),18(a,1,1))].">
      <j1 rule="para" parents="4266 18"/>
    </justification>
  </clause>

  <clause id="4277">
    <literal><![CDATA[
      T(x,y * z) != T(y,z * y)
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(4266(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="4266 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4278">
    <literal><![CDATA[
      x * T(y,x * y) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[para(4266(a,2),714(a,1,2))].">
      <j1 rule="para" parents="4266 714"/>
    </justification>
  </clause>

  <clause id="4279">
    <literal><![CDATA[
      x * L(T(y,x * y),z,u) = L(L(y,x,y),z,u) * x
    ]]></literal>
    <justification jstring="[para(4266(a,2),719(a,1,2,1))].">
      <j1 rule="para" parents="4266 719"/>
    </justification>
  </clause>

  <clause id="4280">
    <literal><![CDATA[
      T(x,T(y,y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4266(a,1),4089(a,1,2))].">
      <j1 rule="para" parents="4266 4089"/>
    </justification>
  </clause>

  <clause id="4281">
    <literal><![CDATA[
      (T(x,y * x) * y) * x = x * (x * y)
    ]]></literal>
    <justification jstring="[para(4266(a,2),4105(a,1,1,1))].">
      <j1 rule="para" parents="4266 4105"/>
    </justification>
  </clause>

  <clause id="4282">
    <literal><![CDATA[
      K(x,T(y,x * y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4266(a,2),4161(a,1,2))].">
      <j1 rule="para" parents="4266 4161"/>
    </justification>
  </clause>

  <clause id="4283">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) = x * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,4270,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4270 17"/>
    </justification>
  </clause>

  <clause id="4284">
    <literal><![CDATA[
      (((x \ y) * x) / T(x,y)) * x = T((x \ y) * x,x)
    ]]></literal>
    <justification jstring="[para(4270(a,1),4202(a,1,1,2))].">
      <j1 rule="para" parents="4270 4202"/>
    </justification>
  </clause>

  <clause id="4285">
    <literal><![CDATA[
      T(x,x * y) * L(T(y,x),z,u) = L(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[para(4280(a,1),237(a,1,2,1))].">
      <j1 rule="para" parents="4280 237"/>
    </justification>
  </clause>

  <clause id="4286">
    <literal><![CDATA[
      T(x,x * y) * R(T(y,x),z,u) = R(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[para(4280(a,1),238(a,1,2,1))].">
      <j1 rule="para" parents="4280 238"/>
    </justification>
  </clause>

  <clause id="4287">
    <literal><![CDATA[
      K(x,T(x \ y,y)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),4282(a,1,2,2))].">
      <j1 rule="para" parents="5 4282"/>
    </justification>
  </clause>

  <clause id="4288">
    <literal><![CDATA[
      R(x,y,T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(900,a,4267,a)].">
      <j1 rule="hyper" parents="900 4267"/>
    </justification>
  </clause>

  <clause id="4289">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(1167,a,4288,a)].">
      <j1 rule="hyper" parents="1167 4288"/>
    </justification>
  </clause>

  <clause id="4290">
    <literal><![CDATA[
      x * R(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4288,a(flip),b,1166,a)].">
      <j1 rule="hyper" parents="119 4288 1166"/>
    </justification>
  </clause>

  <clause id="4291">
    <literal><![CDATA[
      L(R(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[para(4288(a,1),1168(a,1,1))].">
      <j1 rule="para" parents="4288 1168"/>
    </justification>
  </clause>

  <clause id="4292">
    <literal><![CDATA[
      R(x,T(y,x),T(x,y)) = R(x,T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4193(a,1),4288(a,1,3))].">
      <j1 rule="para" parents="4193 4288"/>
    </justification>
  </clause>

  <clause id="4293">
    <literal><![CDATA[
      T((x * y) / x,x * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(461,a,4273,a)].">
      <j1 rule="hyper" parents="461 4273"/>
    </justification>
  </clause>

  <clause id="4294">
    <literal><![CDATA[
      R(x,x \ y,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),4289(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 4289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4295">
    <literal><![CDATA[
      R(x / y,y,x / y) = y \ T(x,x / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),4289(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 4289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4296">
    <literal><![CDATA[
      (x * y) \ (x * T(z * y,z)) = L(R(z,y,z),y,x)
    ]]></literal>
    <justification jstring="[para(4289(a,1),92(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4289 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4297">
    <literal><![CDATA[
      (x \ T(x * y,y)) * x = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(4122,a,4290,a)].">
      <j1 rule="hyper" parents="4122 4290"/>
    </justification>
  </clause>

  <clause id="4298">
    <literal><![CDATA[
      T(x * y,x) != y * z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(4290(a,1),38(a,1))].">
      <j1 rule="para" parents="4290 38"/>
    </justification>
  </clause>

  <clause id="4299">
    <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(4290(a,1),482(a,1,2,2))].">
      <j1 rule="para" parents="4290 482"/>
    </justification>
  </clause>

  <clause id="4300">
    <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(4290(a,1),1052(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4290 1052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4301">
    <literal><![CDATA[
      T(x * y,x) * T(x,y) = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4290(a,1),1882(a,1,1))].">
      <j1 rule="para" parents="4290 1882"/>
    </justification>
  </clause>

  <clause id="4302">
    <literal><![CDATA[
      ((x \ y) * x) / (x \ y) = y / (y / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,3850,a,b,4192,a),flip(a)].">
      <j1 rule="hyper" parents="320 3850 4192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4303">
    <literal><![CDATA[
      T(x * (T(x,y) \ x),y) = x
    ]]></literal>
    <justification jstring="[para(4192(a,1),224(a,1,1))].">
      <j1 rule="para" parents="4192 224"/>
    </justification>
  </clause>

  <clause id="4304">
    <literal><![CDATA[
      ((x * y) / x) \ x = y \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(4192(a,2),3884(a,1,1))].">
      <j1 rule="para" parents="4192 3884"/>
    </justification>
  </clause>

  <clause id="4305">
    <literal><![CDATA[
      T(x / (x / y),y \ x) = y
    ]]></literal>
    <justification jstring="[para(3850(a,2),4303(a,1,1))].">
      <j1 rule="para" parents="3850 4303"/>
    </justification>
  </clause>

  <clause id="4307">
    <literal><![CDATA[
      T(x / (x / (x / y)),y) = x / y
    ]]></literal>
    <justification jstring="[para(75(a,1),4305(a,1,2))].">
      <j1 rule="para" parents="75 4305"/>
    </justification>
  </clause>

  <clause id="4309">
    <literal><![CDATA[
      x \ T(x,T(y,(y \ 1) * x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3888,a(flip),b,4196,a)].">
      <j1 rule="hyper" parents="320 3888 4196"/>
    </justification>
  </clause>

  <clause id="4310">
    <literal><![CDATA[
      T(x,y * z) != K(z,y)
    ]]></literal>
    <literal><![CDATA[
      z \ T(z,y) = x
    ]]></literal>
    <justification jstring="[para(4196(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="4196 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4311">
    <literal><![CDATA[
      T(T(x \ y,z),x) = T(((x \ y) \ y) \ y,z)
    ]]></literal>
    <justification jstring="[para(4199(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4199 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4313">
    <literal><![CDATA[
      L((((x \ y) \ z) \ z) \ z,x \ y,x) = T(y \ (x * z),x \ y)
    ]]></literal>
    <justification jstring="[para(4199(a,1),753(a,1,1))].">
      <j1 rule="para" parents="4199 753"/>
    </justification>
  </clause>

  <clause id="4314">
    <literal><![CDATA[
      T(x \ (y \ x),x) = T(x,y \ 1) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(4138(a,1),4199(a,2,1))].">
      <j1 rule="para" parents="4138 4199"/>
    </justification>
  </clause>

  <clause id="4316">
    <literal><![CDATA[
      T(x,(1 / x) * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3739,a,b,4203,a)].">
      <j1 rule="hyper" parents="58 3739 4203"/>
    </justification>
  </clause>

  <clause id="4317">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = (x \ T(x,x \ y)) * y
    ]]></literal>
    <justification jstring="[para(4203(a,1),3910(a,2,1,2))].">
      <j1 rule="para" parents="4203 3910"/>
    </justification>
  </clause>

  <clause id="4318">
    <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),4209(a,1,2))].">
      <j1 rule="para" parents="20 4209"/>
    </justification>
  </clause>

  <clause id="4319">
    <literal><![CDATA[
      T(x,T(y,T(z,T(y,x)))) = T(x,T(T(y,x),z))
    ]]></literal>
    <justification jstring="[para(4193(a,1),4210(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4193 4210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4320">
    <literal><![CDATA[
      (x * (x * y)) \ ((x * y) * x) = K(y * x,T(x,y))
    ]]></literal>
    <justification jstring="[para(4220(a,1),905(a,1,1))].">
      <j1 rule="para" parents="4220 905"/>
    </justification>
  </clause>

  <clause id="4321">
    <literal><![CDATA[
      ((T(x,y) * y) / x) \ ((x * (x * y)) / x) = L(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[para(4220(a,1),1645(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4220 1645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4322">
    <literal><![CDATA[
      T(x,x \ y) / y = x / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(351,a,4222,a)].">
      <j1 rule="hyper" parents="351 4222"/>
    </justification>
  </clause>

  <clause id="4323">
    <literal><![CDATA[
      T(x,y) / (x * y) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(197,a,4222,a)].">
      <j1 rule="hyper" parents="197 4222"/>
    </justification>
  </clause>

  <clause id="4324">
    <literal><![CDATA[
      (x * (y / x)) / x = y / (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(271,a,4307,a)].">
      <j1 rule="hyper" parents="271 4307"/>
    </justification>
  </clause>

  <clause id="4325">
    <literal><![CDATA[
      x / T(y,(1 / y) * x) = y \ x
    ]]></literal>
    <justification jstring="[para(4316(a,2),265(a,1,2))].">
      <j1 rule="para" parents="4316 265"/>
    </justification>
  </clause>

  <clause id="4326">
    <literal><![CDATA[
      T(x,y) / (x * y) = R(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,219,a,b,4323,a),flip(a)].">
      <j1 rule="hyper" parents="320 219 4323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4327">
    <literal><![CDATA[
      x / T(y \ 1,y * x) = (y \ 1) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),4325(a,1,2,2,1))].">
      <j1 rule="para" parents="72 4325"/>
    </justification>
  </clause>

  <clause id="4328">
    <literal><![CDATA[
      T(x,L(y,x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4280,a(flip),b,4218,a),flip(a)].">
      <j1 rule="hyper" parents="58 4280 4218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4329">
    <literal><![CDATA[
      T((x * y) / x,L(x,y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(461,a,4328,a(flip))].">
      <j1 rule="hyper" parents="461 4328"/>
    </justification>
  </clause>

  <clause id="4330">
    <literal><![CDATA[
      L(x,y,x) * T(y,x) = y * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,4328,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4328 17"/>
    </justification>
  </clause>

  <clause id="4331">
    <literal><![CDATA[
      L(x,y,x) \ ((x * (y * x)) / x) = y
    ]]></literal>
    <justification jstring="[hyper(1647,a,4329,a)].">
      <j1 rule="hyper" parents="1647 4329"/>
    </justification>
  </clause>

  <clause id="4332">
    <literal><![CDATA[
      (x * (y * x)) / x = L(x,y,x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,4329,a(flip),b,1644,a),flip(a)].">
      <j1 rule="hyper" parents="119 4329 1644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4333">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4068(a,1),4239(a,1))].">
      <j1 rule="para" parents="4068 4239"/>
    </justification>
  </clause>

  <clause id="4334">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,106,a(flip),b,4268,a),flip(a)].">
      <j1 rule="hyper" parents="320 106 4268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4335">
    <literal><![CDATA[
      T(L(x,y,x) * y,x) = y * x
    ]]></literal>
    <justification jstring="[para(4278(a,1),816(a,1,1))].">
      <j1 rule="para" parents="4278 816"/>
    </justification>
  </clause>

  <clause id="4336">
    <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(4093(a,1),4278(a,1,2,2))].">
      <j1 rule="para" parents="4093 4278"/>
    </justification>
  </clause>

  <clause id="4337">
    <literal><![CDATA[
      T(x,L(x,y,x) * y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[para(4335(a,1),4193(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4335 4193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4338">
    <literal><![CDATA[
      R(1 / x,x,T(y,x)) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(670,a,4326,a)].">
      <j1 rule="hyper" parents="670 4326"/>
    </justification>
  </clause>

  <clause id="4339">
    <literal><![CDATA[
      (x * ((x \ y) * x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4332(a,2),953(a,1))].">
      <j1 rule="para" parents="4332 953"/>
    </justification>
  </clause>

  <clause id="4340">
    <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(4093(a,1),4332(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4093 4332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4341">
    <literal><![CDATA[
      R(x,x \ y,x) * y = y * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4334,a(flip),b,110,a),flip(a)].">
      <j1 rule="hyper" parents="119 4334 110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4342">
    <literal><![CDATA[
      T(x,L(x,y,x) * y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4266,a(flip),b,4337,a),flip(a)].">
      <j1 rule="hyper" parents="320 4266 4337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4343">
    <literal><![CDATA[
      T(x,(x \ y) * T(x,y)) = T(x,(x \ y) * x)
    ]]></literal>
    <justification jstring="[para(720(a,1),4337(a,1,2))].">
      <j1 rule="para" parents="720 4337"/>
    </justification>
  </clause>

  <clause id="4344">
    <literal><![CDATA[
      R(T(x,x * y),y,T(x,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4342(a,1),1501(a,1,1))].">
      <j1 rule="para" parents="4342 1501"/>
    </justification>
  </clause>

  <clause id="4345">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) = K(x \ y,x) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),4188(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 4188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4346">
    <literal><![CDATA[
      x / (y * (x / y)) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(4131,a,4191,a)].">
      <j1 rule="hyper" parents="4131 4191"/>
    </justification>
  </clause>

  <clause id="4347">
    <literal><![CDATA[
      x \ (y / (y / x)) != z
    ]]></literal>
    <literal><![CDATA[
      y / (x * (y / x)) = z
    ]]></literal>
    <justification jstring="[para(4191(a,1),4131(a,1))].">
      <j1 rule="para" parents="4191 4131"/>
    </justification>
  </clause>

  <clause id="4348">
    <literal><![CDATA[
      (T(x,y / z) \ x) * y = z * T(z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,1173,a,b,4194,a),flip(a)].">
      <j1 rule="hyper" parents="29 1173 4194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4349">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4124,a,b,4195,a)].">
      <j1 rule="hyper" parents="320 4124 4195"/>
    </justification>
  </clause>

  <clause id="4350">
    <literal><![CDATA[
      T(T(x,y) / y,z) = T(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(239,a,4236,a,b,105,a)].">
      <j1 rule="hyper" parents="239 4236 105"/>
    </justification>
  </clause>

  <clause id="4351">
    <literal><![CDATA[
      T(T(x,y) \ y,z) = T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(239,a,4241,a,b,105,a)].">
      <j1 rule="hyper" parents="239 4241 105"/>
    </justification>
  </clause>

  <clause id="4352">
    <literal><![CDATA[
      x \ ((T(y,z) \ z) \ u) = x \ ((y \ T(z,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(116,a,4243,a,b,5,a)].">
      <j1 rule="hyper" parents="116 4243 5"/>
    </justification>
  </clause>

  <clause id="4353">
    <literal><![CDATA[
      (x / (x / y)) * (y \ x) = (x / y) * (x / (x / y))
    ]]></literal>
    <justification jstring="[para(642(a,1),4249(a,1,2))].">
      <j1 rule="para" parents="642 4249"/>
    </justification>
  </clause>

  <clause id="4354">
    <literal><![CDATA[
      T(x * (y / x),x) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(440,a,313,a(flip),b,4252,a)].">
      <j1 rule="hyper" parents="440 313 4252"/>
    </justification>
  </clause>

  <clause id="4355">
    <literal><![CDATA[
      (x \ y) * T(y,y \ (x \ y)) = (x \ T(y,x \ 1)) * y
    ]]></literal>
    <justification jstring="[para(3871(a,2),4252(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3871 4252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4356">
    <literal><![CDATA[
      T(T(x,y),z / x) = T(T(x,y),x \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,316,a,b,4262,a),flip(a)].">
      <j1 rule="hyper" parents="320 316 4262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4357">
    <literal><![CDATA[
      T(T(x,y),z * x) = T(T(x,y),x * z)
    ]]></literal>
    <justification jstring="[hyper(435,a,4275,a),flip(a)].">
      <j1 rule="hyper" parents="435 4275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4358">
    <literal><![CDATA[
      T(T(x,y),x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,y),z * x) = u
    ]]></literal>
    <justification jstring="[para(4276(a,1),435(a,1))].">
      <j1 rule="para" parents="4276 435"/>
    </justification>
  </clause>

  <clause id="4359">
    <literal><![CDATA[
      (x / (x / y)) * (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      (y \ x) * y = z
    ]]></literal>
    <justification jstring="[para(4302(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4302 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4360">
    <literal><![CDATA[
      T(x / (x / y),x) = L(y,y \ x,y)
    ]]></literal>
    <justification jstring="[para(4302(a,1),722(a,1,1))].">
      <j1 rule="para" parents="4302 722"/>
    </justification>
  </clause>

  <clause id="4361">
    <literal><![CDATA[
      x * T(x / (x / y),x) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4360,a,b,91,a)].">
      <j1 rule="hyper" parents="119 4360 91"/>
    </justification>
  </clause>

  <clause id="4362">
    <literal><![CDATA[
      T(T(x / (x / y),x),z) = L(T(y,z),y \ x,y)
    ]]></literal>
    <justification jstring="[para(4360(a,2),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4360 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4363">
    <literal><![CDATA[
      L(x \ y,(x \ y) \ y,x \ y) = T(y / x,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),4360(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 4360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4364">
    <literal><![CDATA[
      (T(x,x \ y) / y) \ x = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(188,a,4322,a(flip))].">
      <j1 rule="hyper" parents="188 4322"/>
    </justification>
  </clause>

  <clause id="4365">
    <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(4322(a,2),687(a,1,2,1))].">
      <j1 rule="para" parents="4322 687"/>
    </justification>
  </clause>

  <clause id="4366">
    <literal><![CDATA[
      T(x,y \ 1) / (y \ x) = x / ((x \ (y \ x)) * x)
    ]]></literal>
    <justification jstring="[para(4139(a,1),4322(a,1,1))].">
      <j1 rule="para" parents="4139 4322"/>
    </justification>
  </clause>

  <clause id="4367">
    <literal><![CDATA[
      R(1 / (1 / (1 / x)),x,y) = (x * (y / (x * y))) / x
    ]]></literal>
    <justification jstring="[para(4324(a,1),850(a,1,1))].">
      <j1 rule="para" parents="4324 850"/>
    </justification>
  </clause>

  <clause id="4368">
    <literal><![CDATA[
      T(x \ 1,x * y) = ((x \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(188,a,4327,a),flip(a)].">
      <j1 rule="hyper" parents="188 4327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4369">
    <literal><![CDATA[
      R(1 / x,x,y / x) = R(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),4338(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 4338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4370">
    <literal><![CDATA[
      K(x \ y,x) \ x = x * K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3858,a(flip),b,4345,a),flip(a)].">
      <j1 rule="hyper" parents="58 3858 4345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4371">
    <literal><![CDATA[
      T(T(x,y),z * x) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,x * z),y) = u
    ]]></literal>
    <justification jstring="[para(4357(a,2),435(a,1))].">
      <j1 rule="para" parents="4357 435"/>
    </justification>
  </clause>

  <clause id="4372">
    <literal><![CDATA[
      (T(x,y \ 1) / (y \ x)) \ x = (x \ (y \ x)) * x
    ]]></literal>
    <justification jstring="[para(4139(a,1),4364(a,1,1,1))].">
      <j1 rule="para" parents="4139 4364"/>
    </justification>
  </clause>

  <clause id="4373">
    <literal><![CDATA[
      T((x / y) \ 1,x) = (((x / y) \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[para(7(a,1),4368(a,1,2))].">
      <j1 rule="para" parents="7 4368"/>
    </justification>
  </clause>

  <clause id="4374">
    <literal><![CDATA[
      K(x \ y,x) \ 1 = K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(3459,a,4370,a)].">
      <j1 rule="hyper" parents="3459 4370"/>
    </justification>
  </clause>

  <clause id="4375">
    <literal><![CDATA[
      K(x,(x * y) / x) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),4374(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 4374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4376">
    <literal><![CDATA[
      K(T(x,y),y) \ 1 = K(y,x)
    ]]></literal>
    <justification jstring="[para(225(a,1),4375(a,1,2)),flip(a)].">
      <j1 rule="para" parents="225 4375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4378">
    <literal><![CDATA[
      R(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[para(4376(a,1),4050(a,1,2))].">
      <j1 rule="para" parents="4376 4050"/>
    </justification>
  </clause>

  <clause id="4379">
    <literal><![CDATA[
      R(T(x,y),K(x,z),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4378(a,1),22(a,2,1))].">
      <j1 rule="para" parents="4378 22"/>
    </justification>
  </clause>

  <clause id="4380">
    <literal><![CDATA[
      (L(x,y,z) * K(x,u)) * w = L(x,y,z) * (K(x,u) * w)
    ]]></literal>
    <justification jstring="[para(4378(a,1),513(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4378 513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4381">
    <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(4379(a,1),514(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4379 514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4382">
    <literal><![CDATA[
      R(x / y,y,x / y) = y \ T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(4072(a,1),4295(a,2,2))].">
      <j1 rule="para" parents="4072 4295"/>
    </justification>
  </clause>

  <clause id="4383">
    <literal><![CDATA[
      R(x,x \ y,x) * y = (x * (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,4263,a,b,4341,a),flip(a)].">
      <j1 rule="hyper" parents="320 4263 4341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4384">
    <literal><![CDATA[
      R(x,y / x,x) = R(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,508,a,b,4383,a)].">
      <j1 rule="hyper" parents="30 508 4383"/>
    </justification>
  </clause>

  <clause id="4385">
    <literal><![CDATA[
      R(x,y / x,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4294,a(flip),b,4384,a),flip(a)].">
      <j1 rule="hyper" parents="320 4294 4384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4386">
    <literal><![CDATA[
      R(x,x \ (y \ x),x) = ((y \ T(x,y \ 1)) * x) / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3880,a(flip),b,4384,a),flip(a)].">
      <j1 rule="hyper" parents="58 3880 4384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4387">
    <literal><![CDATA[
      R(x,(x * y) / x,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),4384(a,2,2))].">
      <j1 rule="para" parents="4 4384"/>
    </justification>
  </clause>

  <clause id="4388">
    <literal><![CDATA[
      R(x,T(y,x),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(225(a,1),4387(a,1,2)),flip(a)].">
      <j1 rule="para" parents="225 4387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4389">
    <literal><![CDATA[
      R(x,T(y,x),T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4292,a,b,4388,a)].">
      <j1 rule="hyper" parents="58 4292 4388"/>
    </justification>
  </clause>

  <clause id="4390">
    <literal><![CDATA[
      R(R(x,y,z),T(u,x),T(x,u)) = R(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(4389(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4389 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4391">
    <literal><![CDATA[
      (x \ (y * x)) \ T(y * x,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(6(a,1),4385(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 4385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4392">
    <literal><![CDATA[
      (x * y) / T(T(x,y),y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,4205,a(flip),b,4215,a)].">
      <j1 rule="hyper" parents="117 4205 4215"/>
    </justification>
  </clause>

  <clause id="4393">
    <literal><![CDATA[
      T(x,y) \ (y * x) = T(T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4205,a(flip),b,4215,a)].">
      <j1 rule="hyper" parents="116 4205 4215"/>
    </justification>
  </clause>

  <clause id="4394">
    <literal><![CDATA[
      T(x,y) * T(T(y,z),x) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,150,a,b,4215,a)].">
      <j1 rule="hyper" parents="58 150 4215"/>
    </justification>
  </clause>

  <clause id="4395">
    <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),4393(a,1,1))].">
      <j1 rule="para" parents="20 4393"/>
    </justification>
  </clause>

  <clause id="4396">
    <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(4193(a,1),4240(a,1,2,1))].">
      <j1 rule="para" parents="4193 4240"/>
    </justification>
  </clause>

  <clause id="4397">
    <literal><![CDATA[
      T(x,T(y,T(z,T(y,x)))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,4210,a(flip),b,4319,a),flip(a)].">
      <j1 rule="hyper" parents="320 4210 4319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4398">
    <literal><![CDATA[
      T(x,(x \ y) * T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4270,a(flip),b,4343,a),flip(a)].">
      <j1 rule="hyper" parents="320 4270 4343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4399">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,y)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4398(a,1),1498(a,1,1))].">
      <j1 rule="para" parents="4398 1498"/>
    </justification>
  </clause>

  <clause id="4400">
    <literal><![CDATA[
      x * K(y \ (y / (x \ z)),y) = (T(y,x / z) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,1419,a(flip),b,4348,a)].">
      <j1 rule="hyper" parents="320 1419 4348"/>
    </justification>
  </clause>

  <clause id="4401">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = T(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1447,a,b,4349,a)].">
      <j1 rule="hyper" parents="58 1447 4349"/>
    </justification>
  </clause>

  <clause id="4402">
    <literal><![CDATA[
      T(x,y) * z != x * (((y * x) / y) \ u)
    ]]></literal>
    <literal><![CDATA[
      x \ u = z
    ]]></literal>
    <justification jstring="[para(4349(a,2),38(a,1)),flip(a)].">
      <j1 rule="para" parents="4349 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4403">
    <literal><![CDATA[
      ((x / y) \ T((x / y) * y,y)) * (x / y) = y \ (x * ((y \ x) \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4297,a,b,4354,a)].">
      <j1 rule="hyper" parents="58 4297 4354"/>
    </justification>
  </clause>

  <clause id="4404">
    <literal><![CDATA[
      x \ (y * ((x \ y) \ y)) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,4238,a(flip),b,4354,a),flip(a)].">
      <j1 rule="hyper" parents="58 4238 4354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4405">
    <literal><![CDATA[
      (x / (x / y)) * x = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(284,a,4361,a)].">
      <j1 rule="hyper" parents="284 4361"/>
    </justification>
  </clause>

  <clause id="4406">
    <literal><![CDATA[
      R(1 / x,x,y / x) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(320,a,408,a(flip),b,4369,a),flip(a)].">
      <j1 rule="hyper" parents="320 408 4369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4407">
    <literal><![CDATA[
      (x / y) / (y * (x / y)) = (y \ x) / x
    ]]></literal>
    <justification jstring="[hyper(734,a,4406,a)].">
      <j1 rule="hyper" parents="734 4406"/>
    </justification>
  </clause>

  <clause id="4408">
    <literal><![CDATA[
      ((x \ y) / y) * (x * (y / x)) = y / x
    ]]></literal>
    <justification jstring="[hyper(133,a,4407,a)].">
      <j1 rule="hyper" parents="133 4407"/>
    </justification>
  </clause>

  <clause id="4409">
    <literal><![CDATA[
      T(x,y) * (T(y,z) * x) = x * (T(y,z) * T(x,y))
    ]]></literal>
    <justification jstring="[para(4394(a,1),1113(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4394 1113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4410">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = T(x,T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,3842,a(flip),b,4184,a),flip(a)].">
      <j1 rule="hyper" parents="320 3842 4184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4411">
    <literal><![CDATA[
      T(x,T(y \ 1,x)) = T(x,(y \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(4333,a,4410,a),flip(a)].">
      <j1 rule="hyper" parents="4333 4410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4412">
    <literal><![CDATA[
      T(x,(y \ z) / z) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4333,a,4411,a),flip(a)].">
      <j1 rule="hyper" parents="4333 4411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4413">
    <literal><![CDATA[
      T(x,(y \ z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(4411(a,1),4333(a,1))].">
      <j1 rule="para" parents="4411 4333"/>
    </justification>
  </clause>

  <clause id="4414">
    <literal><![CDATA[
      T(x,y / (z * y)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),4412(a,1,2,1))].">
      <j1 rule="para" parents="4 4412"/>
    </justification>
  </clause>

  <clause id="4415">
    <literal><![CDATA[
      T(x,(y / z) \ 1) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),4412(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 4412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4416">
    <literal><![CDATA[
      T(x / (y * x),y \ 1) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(344,a,4414,a),flip(a)].">
      <j1 rule="hyper" parents="344 4414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4420">
    <literal><![CDATA[
      T(x \ T(x,(y * z) / z),T(y,u)) = R(x \ T(x,y),y,z)
    ]]></literal>
    <justification jstring="[para(4415(a,1),3913(a,1,1,2))].">
      <j1 rule="para" parents="4415 3913"/>
    </justification>
  </clause>

  <clause id="4421">
    <literal><![CDATA[
      T(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(z / y) \ 1) = u
    ]]></literal>
    <justification jstring="[para(75(a,1),4413(a,1,2,1))].">
      <j1 rule="para" parents="75 4413"/>
    </justification>
  </clause>

  <clause id="4422">
    <literal><![CDATA[
      L(T(x,y),T(y,x),x) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(1085,a,4216,a),flip(a)].">
      <j1 rule="hyper" parents="1085 4216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4423">
    <literal><![CDATA[
      L(x,T(y,x),x) * y = y * T(x,y * x)
    ]]></literal>
    <justification jstring="[para(4422(a,1),237(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4422 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4424">
    <literal><![CDATA[
      L(x,T(y,x),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,4278,a(flip),b,4423,a),flip(a)].">
      <j1 rule="hyper" parents="30 4278 4423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4425">
    <literal><![CDATA[
      L(x,(x * y) / x,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(224(a,1),4424(a,1,2)),flip(a)].">
      <j1 rule="para" parents="224 4424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4426">
    <literal><![CDATA[
      L(x,T(y,x),x) * T(y,x) = y * L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4424(a,2),4330(a,1,1))].">
      <j1 rule="para" parents="4424 4330"/>
    </justification>
  </clause>

  <clause id="4427">
    <literal><![CDATA[
      T(x,y) * T(y,x * y) = x * L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,721,a(flip),b,4426,a)].">
      <j1 rule="hyper" parents="58 721 4426"/>
    </justification>
  </clause>

  <clause id="4428">
    <literal><![CDATA[
      T(x,y) * T(y,y * x) = x * L(y,x,y)
    ]]></literal>
    <justification jstring="[para(4266(a,1),4427(a,1,2))].">
      <j1 rule="para" parents="4266 4427"/>
    </justification>
  </clause>

  <clause id="4429">
    <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(4217(a,1),229(a,1,1,2))].">
      <j1 rule="para" parents="4217 229"/>
    </justification>
  </clause>

  <clause id="4430">
    <literal><![CDATA[
      R(x,y,x) * T(x * y,x) = T(x * y,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4201(a,1),4217(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4201 4217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4431">
    <literal><![CDATA[
      T(x,x * T(T(x,y) \ y,z)) = T(x,x * T(T(y,x) / x,z))
    ]]></literal>
    <justification jstring="[para(4208(a,2),4271(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4208 4271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4432">
    <literal><![CDATA[
      T(x,y) * (T(y,x) / x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(1376(a,1),4272(a,1,2))].">
      <j1 rule="para" parents="1376 4272"/>
    </justification>
  </clause>

  <clause id="4433">
    <literal><![CDATA[
      T(x,y) * z != x * (y / x)
    ]]></literal>
    <literal><![CDATA[
      T(y,x) / x = z
    ]]></literal>
    <justification jstring="[para(4432(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="4432 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4434">
    <literal><![CDATA[
      T(x,y) * (y / T(x,y)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4206(a,1),4432(a,1,2))].">
      <j1 rule="para" parents="4206 4432"/>
    </justification>
  </clause>

  <clause id="4435">
    <literal><![CDATA[
      T(x,y) * z != x * (y / x)
    ]]></literal>
    <literal><![CDATA[
      y / T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4434(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="4434 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4436">
    <literal><![CDATA[
      ((x \ y) * x) / T(x,y) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,1370,a(flip),b,4284,a),flip(a)].">
      <j1 rule="hyper" parents="30 1370 4284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4437">
    <literal><![CDATA[
      (x \ T(y,x)) * T(x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,4436,a)].">
      <j1 rule="hyper" parents="133 4436"/>
    </justification>
  </clause>

  <clause id="4438">
    <literal><![CDATA[
      (T(x,y) \ y) * T(x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(4242,a,4437,a)].">
      <j1 rule="hyper" parents="4242 4437"/>
    </justification>
  </clause>

  <clause id="4439">
    <literal><![CDATA[
      x \ T(x,T(y,y \ x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(4203(a,1),4309(a,1,2,2,1))].">
      <j1 rule="para" parents="4203 4309"/>
    </justification>
  </clause>

  <clause id="4440">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) = x * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,4439,a),flip(a)].">
      <j1 rule="hyper" parents="134 4439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4441">
    <literal><![CDATA[
      K(x,(y \ x) / x) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3889,a,4440,a)].">
      <j1 rule="hyper" parents="3889 4440"/>
    </justification>
  </clause>

  <clause id="4442">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3901,a,b,4441,a)].">
      <j1 rule="hyper" parents="58 3901 4441"/>
    </justification>
  </clause>

  <clause id="4443">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,3523,a(flip),b,4442,a),flip(a)].">
      <j1 rule="hyper" parents="320 3523 4442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4444">
    <literal><![CDATA[
      K(x \ ((1 / x) \ y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3542,a,b,4443,a)].">
      <j1 rule="hyper" parents="58 3542 4443"/>
    </justification>
  </clause>

  <clause id="4445">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),4444(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 4444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4446">
    <literal><![CDATA[
      K((1 / x) * (y * x),x) = K(T(y,x),x)
    ]]></literal>
    <justification jstring="[para(17(a,2),4445(a,2,1))].">
      <j1 rule="para" parents="17 4445"/>
    </justification>
  </clause>

  <clause id="4447">
    <literal><![CDATA[
      K((x \ 1) \ y,x \ 1) = K(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),4445(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 4445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4448">
    <literal><![CDATA[
      K(T((1 / x) * y,x),x) = K(T(x \ y,x),x)
    ]]></literal>
    <justification jstring="[para(796(a,1),4446(a,1,1))].">
      <j1 rule="para" parents="796 4446"/>
    </justification>
  </clause>

  <clause id="4449">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = y * K(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,4447,a(flip),b,85,a),flip(a)].">
      <j1 rule="hyper" parents="119 4447 85"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4450">
    <literal><![CDATA[
      K(T((x \ 1) * y,x),x) = K(T(x \ y,x),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3966,a(flip),b,4448,a)].">
      <j1 rule="hyper" parents="58 3966 4448"/>
    </justification>
  </clause>

  <clause id="4451">
    <literal><![CDATA[
      K(T(x \ y,x),x) \ 1 = K(x,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(4450(a,1),4376(a,1,1))].">
      <j1 rule="para" parents="4450 4376"/>
    </justification>
  </clause>

  <clause id="4452">
    <literal><![CDATA[
      K(x,(x \ 1) * y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4376,a(flip),b,4451,a),flip(a)].">
      <j1 rule="hyper" parents="58 4376 4451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4453">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3569,a(flip),b,4452,a),flip(a)].">
      <j1 rule="hyper" parents="58 3569 4452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4454">
    <literal><![CDATA[
      K(x * y,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y * x,y) = z
    ]]></literal>
    <justification jstring="[para(4320(a,1),307(a,1))].">
      <j1 rule="para" parents="4320 307"/>
    </justification>
  </clause>

  <clause id="4455">
    <literal><![CDATA[
      (x / y) * (x / (x / y)) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(4359,a,4353,a),flip(a)].">
      <j1 rule="hyper" parents="4359 4353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4456">
    <literal><![CDATA[
      ((x \ y) * x) * x = y * (y / (y / x))
    ]]></literal>
    <justification jstring="[para(4455(a,1),909(a,1,1))].">
      <j1 rule="para" parents="4455 909"/>
    </justification>
  </clause>

  <clause id="4457">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) = y * (y / (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(4438(a,1),4456(a,1,1))].">
      <j1 rule="para" parents="4438 4456"/>
    </justification>
  </clause>

  <clause id="4458">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = x / ((x \ ((y \ 1) \ x)) * x)
    ]]></literal>
    <justification jstring="[para(2939(a,1),4366(a,1,1))].">
      <j1 rule="para" parents="2939 4366"/>
    </justification>
  </clause>

  <clause id="4459">
    <literal><![CDATA[
      (T(x,y) / ((y \ 1) \ x)) \ x = (x \ ((y \ 1) \ x)) * x
    ]]></literal>
    <justification jstring="[para(2939(a,1),4372(a,1,1,1))].">
      <j1 rule="para" parents="2939 4372"/>
    </justification>
  </clause>

  <clause id="4460">
    <literal><![CDATA[
      x * (x / (x / T(y,x))) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4283,a(flip),b,4457,a),flip(a)].">
      <j1 rule="hyper" parents="58 4283 4457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4461">
    <literal><![CDATA[
      x / (x / T(y,x)) = T(x / (x / y),x)
    ]]></literal>
    <justification jstring="[hyper(239,a,4405,a,b,4460,a),flip(a)].">
      <j1 rule="hyper" parents="239 4405 4460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4462">
    <literal><![CDATA[
      T(x / (x / y),x) \ x = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(188,a,4461,a)].">
      <j1 rule="hyper" parents="188 4461"/>
    </justification>
  </clause>

  <clause id="4463">
    <literal><![CDATA[
      x / T(y \ x,x) = T(x / y,x) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),4462(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 4462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4464">
    <literal><![CDATA[
      L(x,x \ y,x) \ y = y / T(x,y)
    ]]></literal>
    <justification jstring="[para(4360(a,1),4462(a,1,1))].">
      <j1 rule="para" parents="4360 4462"/>
    </justification>
  </clause>

  <clause id="4465">
    <literal><![CDATA[
      L(x,x \ y,x) \ y = T(y,x) / x
    ]]></literal>
    <justification jstring="[hyper(320,a,4206,a,b,4464,a),flip(a)].">
      <j1 rule="hyper" parents="320 4206 4464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4466">
    <literal><![CDATA[
      (x * R(x * K(y,x),z,u)) / R(x * K(y,x),z,u) = T(x,R(x * K(y,x),z,u))
    ]]></literal>
    <justification jstring="[para(2089(a,1),4259(a,1,2,1))].">
      <j1 rule="para" parents="2089 4259"/>
    </justification>
  </clause>

  <clause id="4467">
    <literal><![CDATA[
      T(L(L(x,y,x),z,u) * y,x) = L(x,z,u) * T(y,x)
    ]]></literal>
    <justification jstring="[para(4279(a,1),1917(a,1,1))].">
      <j1 rule="para" parents="4279 1917"/>
    </justification>
  </clause>

  <clause id="4468">
    <literal><![CDATA[
      R(x,y,x) * T(x * y,x) = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4301,a(flip),b,4430,a),flip(a)].">
      <j1 rule="hyper" parents="320 4301 4430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4469">
    <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(4468(a,1),4296(a,1,2))].">
      <j1 rule="para" parents="4468 4296"/>
    </justification>
  </clause>

  <clause id="4470">
    <literal><![CDATA[
      (x \ T(y,x \ 1)) * y = (x \ y) * T(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(4139(a,1),4355(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4139 4355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4471">
    <literal><![CDATA[
      L(x,K(y,z),L(y,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,4380,a)].">
      <j1 rule="hyper" parents="479 4380"/>
    </justification>
  </clause>

  <clause id="4472">
    <literal><![CDATA[
      (K(x,y) * L(x,z,u)) * w = L(x,z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(3317(a,1),4380(a,1,1))].">
      <j1 rule="para" parents="3317 4380"/>
    </justification>
  </clause>

  <clause id="4473">
    <literal><![CDATA[
      L(x,K(y,z),L(y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(4471(a,1),45(a,2))].">
      <j1 rule="para" parents="4471 45"/>
    </justification>
  </clause>

  <clause id="4474">
    <literal><![CDATA[
      L(x,K(y,z),y) = x
    ]]></literal>
    <justification jstring="[para(372(a,1),4471(a,1,3))].">
      <j1 rule="para" parents="372 4471"/>
    </justification>
  </clause>

  <clause id="4479">
    <literal><![CDATA[
      (T(x,(y / z) / (1 / z)) \ x) * (y / z) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(58,a,1429,a(flip),b,4400,a),flip(a)].">
      <j1 rule="hyper" parents="58 1429 4400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4480">
    <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(4390(a,1),4231(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4390 4231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4481">
    <literal><![CDATA[
      R(x,x \ (y \ x),x) = ((y \ x) * T(x,y \ 1)) / (y \ x)
    ]]></literal>
    <justification jstring="[para(4470(a,1),4386(a,2,1))].">
      <j1 rule="para" parents="4470 4386"/>
    </justification>
  </clause>

  <clause id="4482">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) = R(x \ T(x,y),y,u)
    ]]></literal>
    <justification jstring="[para(6(a,1),4420(a,1,1,2,2))].">
      <j1 rule="para" parents="6 4420"/>
    </justification>
  </clause>

  <clause id="4483">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2904,a(flip),b,4482,a),flip(a)].">
      <j1 rule="hyper" parents="58 2904 4482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4484">
    <literal><![CDATA[
      (x \ T(x,y)) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(4483(a,1),3829(a,1,1))].">
      <j1 rule="para" parents="4483 3829"/>
    </justification>
  </clause>

  <clause id="4485">
    <literal><![CDATA[
      L(x,y \ 1,(z * y) / z) = y * ((y \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(3846,a,4484,a)].">
      <j1 rule="hyper" parents="3846 4484"/>
    </justification>
  </clause>

  <clause id="4486">
    <literal><![CDATA[
      (x \ T(x,x \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(77(a,1),4484(a,1,2))].">
      <j1 rule="para" parents="77 4484"/>
    </justification>
  </clause>

  <clause id="4488">
    <literal><![CDATA[
      (x \ ((x \ y) \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,658,a(flip),b,4486,a)].">
      <j1 rule="hyper" parents="58 658 4486"/>
    </justification>
  </clause>

  <clause id="4489">
    <literal><![CDATA[
      x / ((y \ x) * y) = y \ ((y \ x) \ x)
    ]]></literal>
    <justification jstring="[hyper(197,a,4488,a)].">
      <j1 rule="hyper" parents="197 4488"/>
    </justification>
  </clause>

  <clause id="4490">
    <literal><![CDATA[
      (x * (y / x)) / y = y / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4137,a,b,4489,a)].">
      <j1 rule="hyper" parents="320 4137 4489"/>
    </justification>
  </clause>

  <clause id="4491">
    <literal><![CDATA[
      L(x,y \ 1,(z * y) / z) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,257,a(flip),b,4485,a),flip(a)].">
      <j1 rule="hyper" parents="320 257 4485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4492">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * z) = L(z,T(x,y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(225(a,1),4485(a,1,3)),flip(a)].">
      <j1 rule="para" parents="225 4485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4493">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,T(y,z)) = L(x,T(y,z) \ 1,y)
    ]]></literal>
    <justification jstring="[para(225(a,1),4491(a,1,3)),flip(a)].">
      <j1 rule="para" parents="225 4491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4494">
    <literal><![CDATA[
      L(x,1 / T(y,y \ z),(y \ z) \ z) = L(x,T(y,y \ z) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2843,a,4493,a)].">
      <j1 rule="hyper" parents="2843 4493"/>
    </justification>
  </clause>

  <clause id="4495">
    <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(4260(a,2),4219(a,1))].">
      <j1 rule="para" parents="4260 4219"/>
    </justification>
  </clause>

  <clause id="4496">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4109,a(flip),b,4317,a),flip(a)].">
      <j1 rule="hyper" parents="320 4109 4317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4497">
    <literal><![CDATA[
      T(x,T(x * T(y / x,z),x)) = T(x,x * T(T(x,y) \ y,z))
    ]]></literal>
    <justification jstring="[para(1540(a,2),4431(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1540 4431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4498">
    <literal><![CDATA[
      T(x,x * T(T(x,y) \ y,z)) = T(x,x * T(y / x,z))
    ]]></literal>
    <justification jstring="[hyper(4333,a,4497,a),flip(a)].">
      <j1 rule="hyper" parents="4333 4497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4499">
    <literal><![CDATA[
      T(x,x * T(T(x,y) \ y,z)) = T(x,x * T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,4271,a(flip),b,4498,a),flip(a)].">
      <j1 rule="hyper" parents="320 4271 4498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4500">
    <literal><![CDATA[
      L(x,(x * y) / x,x) = L(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,4321,a(flip),b,4065,a),flip(a)].">
      <j1 rule="hyper" parents="58 4321 4065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4501">
    <literal><![CDATA[
      L(x,y,T(x,y)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4425,a(flip),b,4500,a),flip(a)].">
      <j1 rule="hyper" parents="58 4425 4500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4502">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[para(4483(a,1),4135(a,1,1))].">
      <j1 rule="para" parents="4483 4135"/>
    </justification>
  </clause>

  <clause id="4503">
    <literal><![CDATA[
      (T(x,y) \ x) * z = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(4158,a,4502,a),flip(a)].">
      <j1 rule="hyper" parents="4158 4502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4504">
    <literal><![CDATA[
      (T(x,y) \ x) * (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(4101,a,4502,a),flip(a)].">
      <j1 rule="hyper" parents="4101 4502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4505">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = T(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4195,a,b,4502,a),flip(a)].">
      <j1 rule="hyper" parents="320 4195 4502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4507">
    <literal><![CDATA[
      T(x,y) * (x \ z) = y * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(4197,a,4503,a)].">
      <j1 rule="hyper" parents="4197 4503"/>
    </justification>
  </clause>

  <clause id="4508">
    <literal><![CDATA[
      x * (T(x,(y / z) / (1 / z)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(58,a,4479,a(flip),b,4503,a),flip(a)].">
      <j1 rule="hyper" parents="58 4479 4503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4509">
    <literal><![CDATA[
      x * T(x \ y,z) = z * (T(z,y / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4348,a(flip),b,4503,a)].">
      <j1 rule="hyper" parents="58 4348 4503"/>
    </justification>
  </clause>

  <clause id="4510">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(4197,a,4504,a)].">
      <j1 rule="hyper" parents="4197 4504"/>
    </justification>
  </clause>

  <clause id="4511">
    <literal><![CDATA[
      ((x * y) / x) \ (T(x,y) * z) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(116,a,4504,a(flip),b,4124,a),flip(a)].">
      <j1 rule="hyper" parents="116 4504 4124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4512">
    <literal><![CDATA[
      T(x,y) * (T(y,x) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(4504(a,1),4194(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4504 4194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4513">
    <literal><![CDATA[
      T(x,y) \ (T(y,x) \ z) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,1109,a(flip),b,4507,a)].">
      <j1 rule="hyper" parents="116 1109 4507"/>
    </justification>
  </clause>

  <clause id="4514">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y * z) = w
    ]]></literal>
    <justification jstring="[para(4507(a,2),614(a,1))].">
      <j1 rule="para" parents="4507 614"/>
    </justification>
  </clause>

  <clause id="4515">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (y * z) / w = u
    ]]></literal>
    <justification jstring="[para(4507(a,2),616(a,1))].">
      <j1 rule="para" parents="4507 616"/>
    </justification>
  </clause>

  <clause id="4516">
    <literal><![CDATA[
      x * (T(x,y) \ x) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) / y = z
    ]]></literal>
    <justification jstring="[para(4507(a,1),4085(a,1))].">
      <j1 rule="para" parents="4507 4085"/>
    </justification>
  </clause>

  <clause id="4517">
    <literal><![CDATA[
      ((x * y) / x) * (x * z) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4510,a(flip),b,4401,a)].">
      <j1 rule="hyper" parents="119 4510 4401"/>
    </justification>
  </clause>

  <clause id="4518">
    <literal><![CDATA[
      T(x,y) * ((x \ T(y,x)) * z) = y * L(z,x \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(474(a,1),4510(a,1,2))].">
      <j1 rule="para" parents="474 4510"/>
    </justification>
  </clause>

  <clause id="4519">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y))
    ]]></literal>
    <justification jstring="[para(4512(a,1),4233(a,1,2))].">
      <j1 rule="para" parents="4512 4233"/>
    </justification>
  </clause>

  <clause id="4520">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,(y * x) / y) \ z) = ((y * x) / y) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(717(a,1),4513(a,1,1))].">
      <j1 rule="para" parents="717 4513"/>
    </justification>
  </clause>

  <clause id="4521">
    <literal><![CDATA[
      x \ T(x * y,z) = z * (T(z,y / (x \ 1)) \ y)
    ]]></literal>
    <justification jstring="[hyper(1029,a,4509,a)].">
      <j1 rule="hyper" parents="1029 4509"/>
    </justification>
  </clause>

  <clause id="4522">
    <literal><![CDATA[
      x \ (y * ((y \ x) * z)) = L(z,y \ x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4080,a(flip),b,4511,a),flip(a)].">
      <j1 rule="hyper" parents="58 4080 4511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4523">
    <literal><![CDATA[
      (x \ y) * (T(x,x \ y) * z) = (y / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),4517(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 4517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4524">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,z \ 1) = y * (T(x,y) * a(x,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(705(a,1),4517(a,1,2))].">
      <j1 rule="para" parents="705 4517"/>
    </justification>
  </clause>

  <clause id="4525">
    <literal><![CDATA[
      a((x * y) / x,x,z) = (y * (T(x,y) * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(4517(a,1),83(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4517 83"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4526">
    <literal><![CDATA[
      L(x,T(y,z),T(z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(482,a,4519,a),flip(a)].">
      <j1 rule="hyper" parents="482 4519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4527">
    <literal><![CDATA[
      L(x,T(y,z),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4519(a,1),482(a,1))].">
      <j1 rule="para" parents="4519 482"/>
    </justification>
  </clause>

  <clause id="4528">
    <literal><![CDATA[
      L(x,y \ z,T(y,z / y)) = L(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(107(a,1),4526(a,1,2))].">
      <j1 rule="para" parents="107 4526"/>
    </justification>
  </clause>

  <clause id="4529">
    <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(4143(a,1),4527(a,1,2))].">
      <j1 rule="para" parents="4143 4527"/>
    </justification>
  </clause>

  <clause id="4530">
    <literal><![CDATA[
      L(x,y \ z,T(y,y \ z)) = L(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(4213(a,1),4528(a,1,3))].">
      <j1 rule="para" parents="4213 4528"/>
    </justification>
  </clause>

  <clause id="4531">
    <literal><![CDATA[
      x * (T(x,(y / z) / (z \ 1)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[para(3736(a,1),4508(a,1,2,1))].">
      <j1 rule="para" parents="3736 4508"/>
    </justification>
  </clause>

  <clause id="4532">
    <literal><![CDATA[
      x \ T(x * (y / x),z) = T(y,z) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,4521,a,b,4531,a)].">
      <j1 rule="hyper" parents="58 4521 4531"/>
    </justification>
  </clause>

  <clause id="4533">
    <literal><![CDATA[
      T(x * (y / x),z) = x * (T(y,z) / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,4531,a(flip),b,4521,a),flip(a)].">
      <j1 rule="hyper" parents="119 4531 4521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4534">
    <literal><![CDATA[
      (x \ T(x * (y / x),z)) * x = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,4532,a(flip))].">
      <j1 rule="hyper" parents="133 4532"/>
    </justification>
  </clause>

  <clause id="4535">
    <literal><![CDATA[
      T(x * y,z) / y = y \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),4532(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6 4532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4536">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,z) = T(y,z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(72(a,1),4532(a,1,2,1,2))].">
      <j1 rule="para" parents="72 4532"/>
    </justification>
  </clause>

  <clause id="4537">
    <literal><![CDATA[
      T((x \ y) * x,z) / x = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(71(a,1),4532(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="71 4532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4538">
    <literal><![CDATA[
      x * (y * (T(z,x) / y)) = (y * (z / y)) * x
    ]]></literal>
    <justification jstring="[para(4532(a,1),227(a,1,2,2))].">
      <j1 rule="para" parents="4532 227"/>
    </justification>
  </clause>

  <clause id="4541">
    <literal><![CDATA[
      x \ T(T(x,y) * y,z) = T(x * y,z) / x
    ]]></literal>
    <justification jstring="[para(4051(a,2),4532(a,1,2,1))].">
      <j1 rule="para" parents="4051 4532"/>
    </justification>
  </clause>

  <clause id="4542">
    <literal><![CDATA[
      x * (T(y * x,z) / x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),4533(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6 4533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4543">
    <literal><![CDATA[
      T(x * (y / x),z) != x * u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) / x = u
    ]]></literal>
    <justification jstring="[para(4533(a,2),38(a,1))].">
      <j1 rule="para" parents="4533 38"/>
    </justification>
  </clause>

  <clause id="4544">
    <literal><![CDATA[
      T(x * (y / x),y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(104(a,1),4533(a,2,2,1))].">
      <j1 rule="para" parents="104 4533"/>
    </justification>
  </clause>

  <clause id="4545">
    <literal><![CDATA[
      T(x * ((y / z) / x),z) = x * ((z \ y) / x)
    ]]></literal>
    <justification jstring="[para(107(a,1),4533(a,2,2,1))].">
      <j1 rule="para" parents="107 4533"/>
    </justification>
  </clause>

  <clause id="4548">
    <literal><![CDATA[
      T(x * (y / x),K(z,y)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(2869(a,1),4533(a,2,2,1))].">
      <j1 rule="para" parents="2869 4533"/>
    </justification>
  </clause>

  <clause id="4549">
    <literal><![CDATA[
      T(x * (y / x),K(y,z)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(3311(a,1),4533(a,2,2,1))].">
      <j1 rule="para" parents="3311 4533"/>
    </justification>
  </clause>

  <clause id="4550">
    <literal><![CDATA[
      T(x * (y / x),z / y) = x * (T(y,y \ z) / x)
    ]]></literal>
    <justification jstring="[para(4213(a,1),4533(a,2,2,1))].">
      <j1 rule="para" parents="4213 4533"/>
    </justification>
  </clause>

  <clause id="4551">
    <literal><![CDATA[
      T(x,y * (x / y)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,4544,a)].">
      <j1 rule="hyper" parents="49 4544"/>
    </justification>
  </clause>

  <clause id="4552">
    <literal><![CDATA[
      T(x * (y / x),y) / y = y / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(4544(a,2),4490(a,1,1))].">
      <j1 rule="para" parents="4544 4490"/>
    </justification>
  </clause>

  <clause id="4553">
    <literal><![CDATA[
      T((x \ y) * x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(71(a,1),4551(a,1,2))].">
      <j1 rule="para" parents="71 4551"/>
    </justification>
  </clause>

  <clause id="4554">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,2703,a,b,4534,a)].">
      <j1 rule="hyper" parents="58 2703 4534"/>
    </justification>
  </clause>

  <clause id="4555">
    <literal><![CDATA[
      (x \ T(x * y,z)) * x = T(y * x,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),4534(a,1,1,2,1,2))].">
      <j1 rule="para" parents="6 4534"/>
    </justification>
  </clause>

  <clause id="4556">
    <literal><![CDATA[
      T((x \ y) * x,z) = (x \ T(y,z)) * x
    ]]></literal>
    <justification jstring="[para(71(a,1),4534(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="71 4534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4557">
    <literal><![CDATA[
      x \ T(x * y,1 / x) = ((1 / x) \ y) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1032,a,4535,a),flip(a)].">
      <j1 rule="hyper" parents="1032 4535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4558">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(998,a,4535,a)].">
      <j1 rule="hyper" parents="998 4535"/>
    </justification>
  </clause>

  <clause id="4559">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(320,a,932,a,b,4535,a)].">
      <j1 rule="hyper" parents="320 932 4535"/>
    </justification>
  </clause>

  <clause id="4561">
    <literal><![CDATA[
      T(x \ T(x * y,z),x) = x \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(4535(a,1),107(a,1,1))].">
      <j1 rule="para" parents="4535 107"/>
    </justification>
  </clause>

  <clause id="4562">
    <literal><![CDATA[
      T(K(x,y) * (y * x),z) / (y * x) = (y * x) \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(84(a,1),4535(a,2,2,1))].">
      <j1 rule="para" parents="84 4535"/>
    </justification>
  </clause>

  <clause id="4563">
    <literal><![CDATA[
      x * (T(y * x,z) / x) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ T(x * y,z) = w
    ]]></literal>
    <justification jstring="[para(4535(a,2),417(a,1,2))].">
      <j1 rule="para" parents="4535 417"/>
    </justification>
  </clause>

  <clause id="4564">
    <literal><![CDATA[
      x * (y \ T(y * (x \ z),x)) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[para(4535(a,1),3897(a,1,2))].">
      <j1 rule="para" parents="4535 3897"/>
    </justification>
  </clause>

  <clause id="4566">
    <literal><![CDATA[
      x \ T((x \ y) * x,z) = T(x \ T(y,z),x)
    ]]></literal>
    <justification jstring="[para(4537(a,1),107(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4537 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4568">
    <literal><![CDATA[
      x \ T(x * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y * x,z) / x = u
    ]]></literal>
    <justification jstring="[para(4542(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4542 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4569">
    <literal><![CDATA[
      T(x,T(y * x,z)) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[para(4542(a,1),4265(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4542 4265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4570">
    <literal><![CDATA[
      T(x * ((1 / (1 / y)) / x),K(z,y)) = x * ((1 / (1 / y)) / x)
    ]]></literal>
    <justification jstring="[para(3529(a,1),4548(a,1,2))].">
      <j1 rule="para" parents="3529 4548"/>
    </justification>
  </clause>

  <clause id="4571">
    <literal><![CDATA[
      T(K(x,y),z * (x / z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,4549,a)].">
      <j1 rule="hyper" parents="49 4549"/>
    </justification>
  </clause>

  <clause id="4572">
    <literal><![CDATA[
      T(K(x * y,z),y * x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),4571(a,1,2,2))].">
      <j1 rule="para" parents="6 4571"/>
    </justification>
  </clause>

  <clause id="4576">
    <literal><![CDATA[
      x * ((y \ T(z,x)) * y) = ((y \ z) * y) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,4556,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4556 17"/>
    </justification>
  </clause>

  <clause id="4577">
    <literal><![CDATA[
      T((x \ y) * x,z) != u * x
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(4556(a,2),39(a,1))].">
      <j1 rule="para" parents="4556 39"/>
    </justification>
  </clause>

  <clause id="4578">
    <literal><![CDATA[
      T((x \ (y / z)) * x,z) = (x \ (z \ y)) * x
    ]]></literal>
    <justification jstring="[para(107(a,1),4556(a,2,1,2))].">
      <j1 rule="para" parents="107 4556"/>
    </justification>
  </clause>

  <clause id="4579">
    <literal><![CDATA[
      T((x \ y) * x,z) \ T(y,z) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(4556(a,2),86(a,1,1))].">
      <j1 rule="para" parents="4556 86"/>
    </justification>
  </clause>

  <clause id="4580">
    <literal><![CDATA[
      ((x * T((y \ z) * y,x)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(4556(a,2),4034(a,1,1,1,2))].">
      <j1 rule="para" parents="4556 4034"/>
    </justification>
  </clause>

  <clause id="4581">
    <literal><![CDATA[
      K(x * y,z) * (y * x) = (y * x) * K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4572,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 4572 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4582">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = z * (x * ((z \ y) / x))
    ]]></literal>
    <justification jstring="[para(107(a,1),4538(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="107 4538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4583">
    <literal><![CDATA[
      (x * (((y * z) / y) / x)) * y = y * (x * (z / x))
    ]]></literal>
    <justification jstring="[para(224(a,1),4538(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="224 4538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4584">
    <literal><![CDATA[
      x / ((((y \ 1) * x) \ x) * ((y \ 1) * x)) = T((y \ x) * y,x) / x
    ]]></literal>
    <justification jstring="[para(3891(a,1),4552(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3891 4552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4586">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = (1 / y) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3771,a(flip),b,4576,a),flip(a)].">
      <j1 rule="hyper" parents="58 3771 4576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4587">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[para(107(a,1),4576(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="107 4576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4588">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) / x = (y \ (z / x)) * y
    ]]></literal>
    <justification jstring="[hyper(271,a,4578,a)].">
      <j1 rule="hyper" parents="271 4578"/>
    </justification>
  </clause>

  <clause id="4589">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(320,a,1149,a(flip),b,4536,a),flip(a)].">
      <j1 rule="hyper" parents="320 1149 4536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4590">
    <literal><![CDATA[
      T(x * (y / x),z / y) = T(x * (y / x),y \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4533,a,b,4550,a),flip(a)].">
      <j1 rule="hyper" parents="320 4533 4550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4591">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,z) = K(x,x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(2697,a,4554,a),flip(a)].">
      <j1 rule="hyper" parents="2697 4554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4594">
    <literal><![CDATA[
      T(x * K(y \ 1,y),z) = K(y \ 1,y) * T(x,z)
    ]]></literal>
    <justification jstring="[para(2685(a,1),4554(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2685 4554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4596">
    <literal><![CDATA[
      ((1 / x) / y) * T(((1 / x) / y) \ z,u) = (x \ T(x * (z * y),u)) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,4558,a(flip),b,1529,a),flip(a)].">
      <j1 rule="hyper" parents="117 4558 1529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4597">
    <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(1611(a,1),4559(a,2,1,1))].">
      <j1 rule="para" parents="1611 4559"/>
    </justification>
  </clause>

  <clause id="4598">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = ((u * ((y / x) / u)) * x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4038,a(flip),b,4582,a),flip(a)].">
      <j1 rule="hyper" parents="58 4038 4582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4599">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = ((y \ x) * y) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,3918,a(flip),b,4586,a),flip(a)].">
      <j1 rule="hyper" parents="58 3918 4586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4600">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = y * ((x \ (y \ z)) * x)
    ]]></literal>
    <justification jstring="[hyper(1098,a,4587,a)].">
      <j1 rule="hyper" parents="1098 4587"/>
    </justification>
  </clause>

  <clause id="4601">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3811,a,b,4587,a)].">
      <j1 rule="hyper" parents="58 3811 4587"/>
    </justification>
  </clause>

  <clause id="4602">
    <literal><![CDATA[
      ((x \ R(1 / y,y,z)) * x) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(219(a,2),4587(a,1,1,1,2))].">
      <j1 rule="para" parents="219 4587"/>
    </justification>
  </clause>

  <clause id="4603">
    <literal><![CDATA[
      (x * ((y \ z) * y)) / x = (y \ ((x * z) / x)) * y
    ]]></literal>
    <justification jstring="[para(4(a,1),4588(a,1,1,2,1,2))].">
      <j1 rule="para" parents="4 4588"/>
    </justification>
  </clause>

  <clause id="4604">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x \ (z \ y)) * x) = u
    ]]></literal>
    <justification jstring="[para(4588(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4588 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4605">
    <literal><![CDATA[
      (x \ ((y * (x * z)) / y)) * x = (y * (z * x)) / y
    ]]></literal>
    <justification jstring="[para(62(a,1),4588(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="62 4588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4606">
    <literal><![CDATA[
      T(x * (y / x),(y / z) \ 1) = T(x * (y / x),y \ z)
    ]]></literal>
    <justification jstring="[hyper(4421,a,4590,a)].">
      <j1 rule="hyper" parents="4421 4590"/>
    </justification>
  </clause>

  <clause id="4608">
    <literal><![CDATA[
      T(x * K(y,y \ 1),z) = K(y,y \ 1) * T(x,z)
    ]]></literal>
    <justification jstring="[para(2169(a,1),4591(a,1,1))].">
      <j1 rule="para" parents="2169 4591"/>
    </justification>
  </clause>

  <clause id="4609">
    <literal><![CDATA[
      x \ T(y * K(z \ 1,z),u) = (x \ T(y,u)) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(4594(a,2),3394(a,1,2))].">
      <j1 rule="para" parents="4594 3394"/>
    </justification>
  </clause>

  <clause id="4610">
    <literal><![CDATA[
      T(x,T(y * K(z \ 1,z),u)) = T(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(4594(a,2),3734(a,1,2))].">
      <j1 rule="para" parents="4594 3734"/>
    </justification>
  </clause>

  <clause id="4611">
    <literal><![CDATA[
      T(x,T((1 / y) * z,u)) = T(x,T((y \ 1) * z,u))
    ]]></literal>
    <justification jstring="[para(2826(a,1),4610(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2826 4610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4612">
    <literal><![CDATA[
      (x \ ((x * y) / x)) * x = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4339,a,4603,a),flip(a)].">
      <j1 rule="hyper" parents="4339 4603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4614">
    <literal><![CDATA[
      ((x \ (y / (z \ 1))) * x) * (z \ 1) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(1620,a,4564,a)].">
      <j1 rule="hyper" parents="1620 4564"/>
    </justification>
  </clause>

  <clause id="4615">
    <literal><![CDATA[
      a((x * y) / x,x,z) = a(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,229,a(flip),b,4525,a),flip(a)].">
      <j1 rule="hyper" parents="320 229 4525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4616">
    <literal><![CDATA[
      a(x \ y,T(x,x \ y),z) = a(y / x,x,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),4615(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 4615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4617">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      y * ((x \ (y \ z)) * x) = u
    ]]></literal>
    <justification jstring="[para(1097(a,2),4604(a,1))].">
      <j1 rule="para" parents="1097 4604"/>
    </justification>
  </clause>

  <clause id="4618">
    <literal><![CDATA[
      T(x * ((1 / (1 / y)) / x),K(z,y)) = L(x * (y / x),y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3506,a,b,4570,a),flip(a)].">
      <j1 rule="hyper" parents="320 3506 4570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4619">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = ((y \ (z * x)) * y) / x
    ]]></literal>
    <justification jstring="[hyper(4604,a,4614,a)].">
      <j1 rule="hyper" parents="4604 4614"/>
    </justification>
  </clause>

  <clause id="4620">
    <literal><![CDATA[
      ((x \ (y * z)) * x) / z = z \ ((x \ (z * y)) * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3517,a(flip),b,4619,a),flip(a)].">
      <j1 rule="hyper" parents="58 3517 4619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4621">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * x = (y \ (z * x)) * y
    ]]></literal>
    <justification jstring="[hyper(133,a,4620,a)].">
      <j1 rule="hyper" parents="133 4620"/>
    </justification>
  </clause>

  <clause id="4622">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * x != u
    ]]></literal>
    <literal><![CDATA[
      (y \ (z * x)) * y = u
    ]]></literal>
    <justification jstring="[para(4620(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4620 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4623">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4512(a,1),4232(a,1,1))].">
      <j1 rule="para" parents="4512 4232"/>
    </justification>
  </clause>

  <clause id="4624">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(691,a,4623,a),flip(a)].">
      <j1 rule="hyper" parents="691 4623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4625">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4623(a,1),691(a,1))].">
      <j1 rule="para" parents="4623 691"/>
    </justification>
  </clause>

  <clause id="4626">
    <literal><![CDATA[
      a(T(x,y),T(T(y,x),x),z) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4193(a,1),4624(a,1,1))].">
      <j1 rule="para" parents="4193 4624"/>
    </justification>
  </clause>

  <clause id="4627">
    <literal><![CDATA[
      (R(x,y,z) * T(u,x)) * T(x,u) = (R(x,y,z) * u) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,514,a(flip),b,4480,a),flip(a)].">
      <j1 rule="hyper" parents="320 514 4480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4628">
    <literal><![CDATA[
      T(x * y,x) * T(x,y) = (R(x,y,x) * y) * x
    ]]></literal>
    <justification jstring="[para(1317(a,1),4627(a,1,1))].">
      <j1 rule="para" parents="1317 4627"/>
    </justification>
  </clause>

  <clause id="4629">
    <literal><![CDATA[
      (R(x,y,x) * y) * x = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4301,a(flip),b,4628,a),flip(a)].">
      <j1 rule="hyper" parents="58 4301 4628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4630">
    <literal><![CDATA[
      (R(x,y,x) * y) \ (R(x,y,x) * T(x * y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(116,a,4430,a,b,4628,a(flip))].">
      <j1 rule="hyper" parents="116 4430 4628"/>
    </justification>
  </clause>

  <clause id="4631">
    <literal><![CDATA[
      (R(x,y,x) * y) \ ((x * y) * R(x,y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(4629(a,1),341(a,1,2))].">
      <j1 rule="para" parents="4629 341"/>
    </justification>
  </clause>

  <clause id="4632">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(4299,a,4630,a)].">
      <j1 rule="hyper" parents="4299 4630"/>
    </justification>
  </clause>

  <clause id="4633">
    <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(4618(a,2),550(a,1))].">
      <j1 rule="para" parents="4618 550"/>
    </justification>
  </clause>

  <clause id="4634">
    <literal><![CDATA[
      T(x \ T(x * y,y),T(x * y,y)) = y
    ]]></literal>
    <justification jstring="[hyper(320,a,4291,a(flip),b,4150,a),flip(a)].">
      <j1 rule="hyper" parents="320 4291 4150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4636">
    <literal><![CDATA[
      K(x,x \ T(x * y,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4634(a,1),4287(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4634 4287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4637">
    <literal><![CDATA[
      K(x,y) = (x * R(y,x,y)) \ T(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4123,a,b,4636,a),flip(a)].">
      <j1 rule="hyper" parents="58 4123 4636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4638">
    <literal><![CDATA[
      K(x,y) = T(y * x,y) \ T(x * y,y)
    ]]></literal>
    <justification jstring="[para(4290(a,1),4637(a,2,1))].">
      <j1 rule="para" parents="4290 4637"/>
    </justification>
  </clause>

  <clause id="4639">
    <literal><![CDATA[
      K(x \ T(x * y,x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,1381,a(flip),b,4638,a)].">
      <j1 rule="hyper" parents="320 1381 4638"/>
    </justification>
  </clause>

  <clause id="4640">
    <literal><![CDATA[
      K(x \ T(y,x),x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),4639(a,1,1,2,1))].">
      <j1 rule="para" parents="5 4639"/>
    </justification>
  </clause>

  <clause id="4641">
    <literal><![CDATA[
      T(x,y) * K(y \ x,y) = (T(y,x) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,4640,a(flip),b,4244,a)].">
      <j1 rule="hyper" parents="119 4640 4244"/>
    </justification>
  </clause>

  <clause id="4642">
    <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(4395(a,2),435(a,1))].">
      <j1 rule="para" parents="4395 435"/>
    </justification>
  </clause>

  <clause id="4643">
    <literal><![CDATA[
      T(x,T(y,z)) / (T(T(y,x),z) \ x) = T(y,T(z,T(y,x)))
    ]]></literal>
    <justification jstring="[para(4397(a,1),4396(a,1,1))].">
      <j1 rule="para" parents="4397 4396"/>
    </justification>
  </clause>

  <clause id="4644">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4240,a(flip),b,4643,a),flip(a)].">
      <j1 rule="hyper" parents="58 4240 4643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4646">
    <literal><![CDATA[
      T(x,T(y,z)) * T(y,x) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,4644,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4644 17"/>
    </justification>
  </clause>

  <clause id="4648">
    <literal><![CDATA[
      T(x / (x / y),T(z,y)) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[para(244(a,1),4644(a,1,2,2))].">
      <j1 rule="para" parents="244 4644"/>
    </justification>
  </clause>

  <clause id="4651">
    <literal><![CDATA[
      T(x,y) \ (x * T(y,T(x,z))) = T(T(y,x),T(x,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,4646,a(flip),b,4215,a)].">
      <j1 rule="hyper" parents="116 4646 4215"/>
    </justification>
  </clause>

  <clause id="4652">
    <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(4648(a,1),4362(a,1,1))].">
      <j1 rule="para" parents="4648 4362"/>
    </justification>
  </clause>

  <clause id="4653">
    <literal><![CDATA[
      ((x / y) \ T(x,y)) * (x / y) = y \ (x * ((y \ x) \ x))
    ]]></literal>
    <justification jstring="[para(7(a,1),4403(a,1,1,2,1))].">
      <j1 rule="para" parents="7 4403"/>
    </justification>
  </clause>

  <clause id="4654">
    <literal><![CDATA[
      x \ (y * ((x \ y) \ y)) = ((y * x) / y) * (y / x)
    ]]></literal>
    <justification jstring="[para(4070(a,1),4653(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4070 4653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4655">
    <literal><![CDATA[
      ((x * y) / x) * (x / y) = y * (x / T(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4404,a(flip),b,4654,a),flip(a)].">
      <j1 rule="hyper" parents="58 4404 4654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4656">
    <literal><![CDATA[
      (x \ y) * (y / T(x \ y,y)) = ((y * (x \ y)) / y) * x
    ]]></literal>
    <justification jstring="[para(72(a,1),4655(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 4655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4657">
    <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),4656(a,1,2,2,1))].">
      <j1 rule="para" parents="106 4656"/>
    </justification>
  </clause>

  <clause id="4658">
    <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,2842,a,b,4494,a),flip(a)].">
      <j1 rule="hyper" parents="58 2842 4494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4659">
    <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(4524(a,2),38(a,1))].">
      <j1 rule="para" parents="4524 38"/>
    </justification>
  </clause>

  <clause id="4660">
    <literal><![CDATA[
      T((x \ y) * x,y) / y = y / (x * (y / x))
    ]]></literal>
    <justification jstring="[para(4496(a,1),4584(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4496 4584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4661">
    <literal><![CDATA[
      ((x \ y) * x) / y = y / (x * (y / x))
    ]]></literal>
    <justification jstring="[para(4553(a,1),4660(a,1,1))].">
      <j1 rule="para" parents="4553 4660"/>
    </justification>
  </clause>

  <clause id="4662">
    <literal><![CDATA[
      ((x \ y) * x) / y = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(320,a,4346,a(flip),b,4661,a),flip(a)].">
      <j1 rule="hyper" parents="320 4346 4661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4663">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,4599,a,b,4662,a)].">
      <j1 rule="hyper" parents="58 4599 4662"/>
    </justification>
  </clause>

  <clause id="4664">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ 1)) * x,y \ 1,y) = y * (x \ (y / (y / x)))
    ]]></literal>
    <justification jstring="[para(4663(a,1),3768(a,2,2))].">
      <j1 rule="para" parents="4663 3768"/>
    </justification>
  </clause>

  <clause id="4665">
    <literal><![CDATA[
      (x \ (1 \ (y * 1))) * x = y * (x \ (y / (y / x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,3510,a(flip),b,4664,a)].">
      <j1 rule="hyper" parents="58 3510 4664"/>
    </justification>
  </clause>

  <clause id="4666">
    <literal><![CDATA[
      x * (y \ (x / (x / y))) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(162(a,1),4665(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="162 4665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4667">
    <literal><![CDATA[
      x \ (y / (y / x)) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,302,a,b,4666,a),flip(a)].">
      <j1 rule="hyper" parents="29 302 4666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4668">
    <literal><![CDATA[
      x / (y * (x / y)) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(4347,a,4667,a)].">
      <j1 rule="hyper" parents="4347 4667"/>
    </justification>
  </clause>

  <clause id="4669">
    <literal><![CDATA[
      x / (x / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,4667,a),flip(a)].">
      <j1 rule="hyper" parents="134 4667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4670">
    <literal><![CDATA[
      T(x,y) / (T(x,y) / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4640,a(flip),b,4667,a),flip(a)].">
      <j1 rule="hyper" parents="119 4640 4667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4671">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4663,a,b,4667,a)].">
      <j1 rule="hyper" parents="58 4663 4667"/>
    </justification>
  </clause>

  <clause id="4672">
    <literal><![CDATA[
      ((x \ y) * x) / y = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4662,a,b,4667,a)].">
      <j1 rule="hyper" parents="58 4662 4667"/>
    </justification>
  </clause>

  <clause id="4676">
    <literal><![CDATA[
      K(x \ y,x) * (x * (y / x)) = y
    ]]></literal>
    <justification jstring="[hyper(133,a,4668,a)].">
      <j1 rule="hyper" parents="133 4668"/>
    </justification>
  </clause>

  <clause id="4678">
    <literal><![CDATA[
      x \ K((x \ 1) \ y,x \ 1) = y / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,2909,a(flip),b,4669,a)].">
      <j1 rule="hyper" parents="320 2909 4669"/>
    </justification>
  </clause>

  <clause id="4679">
    <literal><![CDATA[
      (x * y) * K((x * y) \ y,x * y) = y / R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(219(a,2),4669(a,1,2)),flip(a)].">
      <j1 rule="para" parents="219 4669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4680">
    <literal><![CDATA[
      T(x * K(x \ y,x),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(4669(a,1),4360(a,1,1))].">
      <j1 rule="para" parents="4669 4360"/>
    </justification>
  </clause>

  <clause id="4681">
    <literal><![CDATA[
      K(x \ y,x) * y = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,4672,a)].">
      <j1 rule="hyper" parents="133 4672"/>
    </justification>
  </clause>

  <clause id="4682">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3918,a,b,4672,a)].">
      <j1 rule="hyper" parents="58 3918 4672"/>
    </justification>
  </clause>

  <clause id="4683">
    <literal><![CDATA[
      T(x,K(y \ x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(466,a,4681,a)].">
      <j1 rule="hyper" parents="466 4681"/>
    </justification>
  </clause>

  <clause id="4684">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(4681(a,1),1973(a,2,2))].">
      <j1 rule="para" parents="4681 1973"/>
    </justification>
  </clause>

  <clause id="4685">
    <literal><![CDATA[
      T(x * y,K(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(4(a,1),4683(a,1,2,1))].">
      <j1 rule="para" parents="4 4683"/>
    </justification>
  </clause>

  <clause id="4686">
    <literal><![CDATA[
      T(x,K(y,x / y)) = x
    ]]></literal>
    <justification jstring="[para(75(a,1),4683(a,1,2,1))].">
      <j1 rule="para" parents="75 4683"/>
    </justification>
  </clause>

  <clause id="4687">
    <literal><![CDATA[
      T(K(x,y),y * x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,4685,a)].">
      <j1 rule="hyper" parents="49 4685"/>
    </justification>
  </clause>

  <clause id="4688">
    <literal><![CDATA[
      K(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4310,a,4687,a),flip(a)].">
      <j1 rule="hyper" parents="4310 4687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4689">
    <literal><![CDATA[
      K(x,y) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(4128,a,4687,a),flip(a)].">
      <j1 rule="hyper" parents="4128 4687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4691">
    <literal><![CDATA[
      T(K(x,y),x) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3323,a,4688,a)].">
      <j1 rule="hyper" parents="3323 4688"/>
    </justification>
  </clause>

  <clause id="4692">
    <literal><![CDATA[
      T(T(x,y),x \ 1) = (x \ 1) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(440,a,4688,a,b,985,a)].">
      <j1 rule="hyper" parents="440 4688 985"/>
    </justification>
  </clause>

  <clause id="4693">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4115,a,b,4688,a)].">
      <j1 rule="hyper" parents="320 4115 4688"/>
    </justification>
  </clause>

  <clause id="4694">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4099,a,b,4688,a)].">
      <j1 rule="hyper" parents="320 4099 4688"/>
    </justification>
  </clause>

  <clause id="4695">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3898,a,b,4688,a)].">
      <j1 rule="hyper" parents="320 3898 4688"/>
    </justification>
  </clause>

  <clause id="4696">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3888,a,b,4688,a)].">
      <j1 rule="hyper" parents="320 3888 4688"/>
    </justification>
  </clause>

  <clause id="4698">
    <literal><![CDATA[
      K(x,y) = ((x * y) / x) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3827,a,b,4688,a),flip(a)].">
      <j1 rule="hyper" parents="320 3827 4688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4699">
    <literal><![CDATA[
      K(x,y) = ((x * y) / x) / y
    ]]></literal>
    <justification jstring="[hyper(320,a,3824,a,b,4688,a),flip(a)].">
      <j1 rule="hyper" parents="320 3824 4688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4700">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3823,a,b,4688,a)].">
      <j1 rule="hyper" parents="320 3823 4688"/>
    </justification>
  </clause>

  <clause id="4701">
    <literal><![CDATA[
      K(x,y) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,3819,a,b,4688,a),flip(a)].">
      <j1 rule="hyper" parents="320 3819 4688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4702">
    <literal><![CDATA[
      K(x,y) = (1 / x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2972,a,b,4688,a),flip(a)].">
      <j1 rule="hyper" parents="320 2972 4688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4703">
    <literal><![CDATA[
      K(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(320,a,2967,a,b,4688,a),flip(a)].">
      <j1 rule="hyper" parents="320 2967 4688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4704">
    <literal><![CDATA[
      K(x,y) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,985,a,b,4688,a),flip(a)].">
      <j1 rule="hyper" parents="320 985 4688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4705">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2973,a(flip),b,4688,a)].">
      <j1 rule="hyper" parents="320 2973 4688"/>
    </justification>
  </clause>

  <clause id="4706">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,740,a(flip),b,4688,a)].">
      <j1 rule="hyper" parents="320 740 4688"/>
    </justification>
  </clause>

  <clause id="4708">
    <literal><![CDATA[
      T(x,y) * K(y,x) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,4688,a,b,4190,a)].">
      <j1 rule="hyper" parents="119 4688 4190"/>
    </justification>
  </clause>

  <clause id="4709">
    <literal><![CDATA[
      x * K(y,(x \ z) \ 1) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4688,a,b,3855,a)].">
      <j1 rule="hyper" parents="119 4688 3855"/>
    </justification>
  </clause>

  <clause id="4710">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,4688,a,b,3821,a)].">
      <j1 rule="hyper" parents="119 4688 3821"/>
    </justification>
  </clause>

  <clause id="4711">
    <literal><![CDATA[
      (x * y) / x = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4688,a,b,3819,a),flip(a)].">
      <j1 rule="hyper" parents="119 4688 3819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4712">
    <literal><![CDATA[
      x / (x / y) = y * K(x / y,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4688,a,b,3822,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 4688 3822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4714">
    <literal><![CDATA[
      T(x,y) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4688,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="119 4688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4715">
    <literal><![CDATA[
      K(x,y) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(117,a,4688,a,b,2972,a)].">
      <j1 rule="hyper" parents="117 4688 2972"/>
    </justification>
  </clause>

  <clause id="4716">
    <literal><![CDATA[
      T(x,y) = K(x,y) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,4688,a,b,985,a),flip(a)].">
      <j1 rule="hyper" parents="117 4688 985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4717">
    <literal><![CDATA[
      ((x * y) / x) \ K(x,y) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,4688,a,b,3827,a)].">
      <j1 rule="hyper" parents="116 4688 3827"/>
    </justification>
  </clause>

  <clause id="4718">
    <literal><![CDATA[
      x \ K(y,x \ 1) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(116,a,4688,a,b,3823,a)].">
      <j1 rule="hyper" parents="116 4688 3823"/>
    </justification>
  </clause>

  <clause id="4719">
    <literal><![CDATA[
      T(x,y) \ K(x,y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,4688,a,b,985,a)].">
      <j1 rule="hyper" parents="116 4688 985"/>
    </justification>
  </clause>

  <clause id="4721">
    <literal><![CDATA[
      x \ T(x,y \ 1) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3528,a,b,4688,a),flip(a)].">
      <j1 rule="hyper" parents="58 3528 4688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4722">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,y) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,3293,a(flip),b,4688,a(flip))].">
      <j1 rule="hyper" parents="119 3293 4688"/>
    </justification>
  </clause>

  <clause id="4723">
    <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),4688(a,2,2)),flip(a)].">
      <j1 rule="para" parents="20 4688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4724">
    <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),4688(a,2,2)),flip(a)].">
      <j1 rule="para" parents="22 4688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4725">
    <literal><![CDATA[
      x * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4688(a,2),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4688 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4726">
    <literal><![CDATA[
      L(K(x \ y,z),x \ y,x) = y \ (x * T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(4688(a,2),490(a,1,1))].">
      <j1 rule="para" parents="4688 490"/>
    </justification>
  </clause>

  <clause id="4727">
    <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(4688(a,2),586(a,1,1))].">
      <j1 rule="para" parents="4688 586"/>
    </justification>
  </clause>

  <clause id="4728">
    <literal><![CDATA[
      K(x,x * (y \ 1)) = x \ T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(1677(a,1),4688(a,2,2))].">
      <j1 rule="para" parents="1677 4688"/>
    </justification>
  </clause>

  <clause id="4729">
    <literal><![CDATA[
      T(x,y) = K(x,y) * x
    ]]></literal>
    <justification jstring="[para(4688(a,2),2969(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4688 2969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4730">
    <literal><![CDATA[
      K(x,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4688(a,2),2976(a,1,1))].">
      <j1 rule="para" parents="4688 2976"/>
    </justification>
  </clause>

  <clause id="4731">
    <literal><![CDATA[
      (x \ (y * z)) \ (((x \ (y * z)) \ 1) \ 1) = K(x \ (y * z),z \ (y \ x))
    ]]></literal>
    <justification jstring="[para(3469(a,1),4688(a,2,2)),flip(a)].">
      <j1 rule="para" parents="3469 4688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4732">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3727(a,1),4688(a,2,2))].">
      <j1 rule="para" parents="3727 4688"/>
    </justification>
  </clause>

  <clause id="4733">
    <literal><![CDATA[
      (x * K(y,x)) * y = y * x
    ]]></literal>
    <justification jstring="[para(4688(a,2),3815(a,1,1,2))].">
      <j1 rule="para" parents="4688 3815"/>
    </justification>
  </clause>

  <clause id="4734">
    <literal><![CDATA[
      (x * y) / x = K(x,y) * y
    ]]></literal>
    <justification jstring="[para(4688(a,2),3818(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4688 3818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4735">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(4688(a,2),3817(a,1,2))].">
      <j1 rule="para" parents="4688 3817"/>
    </justification>
  </clause>

  <clause id="4736">
    <literal><![CDATA[
      x \ (T(x,y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(4688(a,2),4045(a,2,1))].">
      <j1 rule="para" parents="4688 4045"/>
    </justification>
  </clause>

  <clause id="4737">
    <literal><![CDATA[
      x * (K(x,y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(4688(a,2),4046(a,1,2,1))].">
      <j1 rule="para" parents="4688 4046"/>
    </justification>
  </clause>

  <clause id="4738">
    <literal><![CDATA[
      T(x,y) * (x \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(4688(a,2),4047(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4688 4047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4739">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(x,y) \ z
    ]]></literal>
    <justification jstring="[para(4688(a,2),4057(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4688 4057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4740">
    <literal><![CDATA[
      K(x,y) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(4688(a,2),4096(a,1,1))].">
      <j1 rule="para" parents="4688 4096"/>
    </justification>
  </clause>

  <clause id="4741">
    <literal><![CDATA[
      K(x,y) \ (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[para(4688(a,2),4100(a,1,1))].">
      <j1 rule="para" parents="4688 4100"/>
    </justification>
  </clause>

  <clause id="4742">
    <literal><![CDATA[
      K(x,x \ y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4688(a,2),4109(a,1,1))].">
      <j1 rule="para" parents="4688 4109"/>
    </justification>
  </clause>

  <clause id="4743">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(4688(a,2),4054(a,1,1))].">
      <j1 rule="para" parents="4688 4054"/>
    </justification>
  </clause>

  <clause id="4744">
    <literal><![CDATA[
      K(x,y) \ (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(4688(a,2),4102(a,1,1))].">
      <j1 rule="para" parents="4688 4102"/>
    </justification>
  </clause>

  <clause id="4745">
    <literal><![CDATA[
      K(x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(4688(a,2),4158(a,1,1))].">
      <j1 rule="para" parents="4688 4158"/>
    </justification>
  </clause>

  <clause id="4746">
    <literal><![CDATA[
      K(x,(y \ z) / z) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(4412(a,1),4688(a,2,2))].">
      <j1 rule="para" parents="4412 4688"/>
    </justification>
  </clause>

  <clause id="4747">
    <literal><![CDATA[
      T(x,y) * (x \ z) = K(y,x) \ z
    ]]></literal>
    <justification jstring="[para(4688(a,2),4505(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4688 4505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4748">
    <literal><![CDATA[
      T(x,x \ (x / y)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4189,a,4689,a),flip(a)].">
      <j1 rule="hyper" parents="4189 4689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4749">
    <literal><![CDATA[
      T(x,y) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(3048,a,4689,a),flip(a)].">
      <j1 rule="hyper" parents="3048 4689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4750">
    <literal><![CDATA[
      K(x \ (x / y),x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4186,a,b,4689,a)].">
      <j1 rule="hyper" parents="320 4186 4689"/>
    </justification>
  </clause>

  <clause id="4751">
    <literal><![CDATA[
      K(x,y) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(320,a,3828,a,b,4689,a),flip(a)].">
      <j1 rule="hyper" parents="320 3828 4689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4752">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ 1 = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3021,a,b,4689,a)].">
      <j1 rule="hyper" parents="320 3021 4689"/>
    </justification>
  </clause>

  <clause id="4753">
    <literal><![CDATA[
      K(x,y) = y / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,2858,a,b,4689,a),flip(a)].">
      <j1 rule="hyper" parents="320 2858 4689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4754">
    <literal><![CDATA[
      K(x,y) = (1 / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,2857,a,b,4689,a),flip(a)].">
      <j1 rule="hyper" parents="320 2857 4689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4755">
    <literal><![CDATA[
      K(x,y) = y * (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,1110,a,b,4689,a),flip(a)].">
      <j1 rule="hyper" parents="320 1110 4689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4756">
    <literal><![CDATA[
      T(T(x,y),z) \ T(x,z) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,154,a,b,4689,a)].">
      <j1 rule="hyper" parents="320 154 4689"/>
    </justification>
  </clause>

  <clause id="4757">
    <literal><![CDATA[
      K(T(x,y),y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3833,a(flip),b,4689,a),flip(a)].">
      <j1 rule="hyper" parents="320 3833 4689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4758">
    <literal><![CDATA[
      ((x \ y) \ y) \ x = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,311,a(flip),b,4689,a)].">
      <j1 rule="hyper" parents="320 311 4689"/>
    </justification>
  </clause>

  <clause id="4759">
    <literal><![CDATA[
      ((x * y) / x) * K(y,x) = y
    ]]></literal>
    <justification jstring="[hyper(119,a,4689,a,b,3828,a)].">
      <j1 rule="hyper" parents="119 4689 3828"/>
    </justification>
  </clause>

  <clause id="4760">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,4689,a,b,2513,a)].">
      <j1 rule="hyper" parents="119 4689 2513"/>
    </justification>
  </clause>

  <clause id="4761">
    <literal><![CDATA[
      ((x \ y) \ y) * K(x \ y,x) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,4689,a,b,311,a(flip))].">
      <j1 rule="hyper" parents="119 4689 311"/>
    </justification>
  </clause>

  <clause id="4762">
    <literal><![CDATA[
      K(x,y) / y = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,4689,a,b,2857,a)].">
      <j1 rule="hyper" parents="117 4689 2857"/>
    </justification>
  </clause>

  <clause id="4763">
    <literal><![CDATA[
      T(x,y) \ 1 = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4689,a,b,1110,a),flip(a)].">
      <j1 rule="hyper" parents="116 4689 1110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4764">
    <literal><![CDATA[
      T(x,y) = x / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(197,a,4689,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="197 4689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4765">
    <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),4689(a,2,1)),flip(a)].">
      <j1 rule="para" parents="20 4689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4766">
    <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),4689(a,2,1)),flip(a)].">
      <j1 rule="para" parents="22 4689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4768">
    <literal><![CDATA[
      x / K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4689(a,2),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4689 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4769">
    <literal><![CDATA[
      K((1 / x) \ y,y) = T(y,y * x) \ y
    ]]></literal>
    <justification jstring="[para(1678(a,1),4689(a,2,1))].">
      <j1 rule="para" parents="1678 4689"/>
    </justification>
  </clause>

  <clause id="4770">
    <literal><![CDATA[
      K(x,y) * T(y,x) = y
    ]]></literal>
    <justification jstring="[para(4689(a,2),2861(a,1,1))].">
      <j1 rule="para" parents="4689 2861"/>
    </justification>
  </clause>

  <clause id="4771">
    <literal><![CDATA[
      K(x,y) * ((y * x) / y) = x
    ]]></literal>
    <justification jstring="[para(4689(a,2),3825(a,1,1))].">
      <j1 rule="para" parents="4689 3825"/>
    </justification>
  </clause>

  <clause id="4772">
    <literal><![CDATA[
      K(x,y) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[para(4689(a,2),4125(a,1,1))].">
      <j1 rule="para" parents="4689 4125"/>
    </justification>
  </clause>

  <clause id="4773">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(4689(a,2),4124(a,2,1))].">
      <j1 rule="para" parents="4689 4124"/>
    </justification>
  </clause>

  <clause id="4775">
    <literal><![CDATA[
      T(x * K(y,x),y) = x
    ]]></literal>
    <justification jstring="[para(4689(a,2),4303(a,1,1,2))].">
      <j1 rule="para" parents="4689 4303"/>
    </justification>
  </clause>

  <clause id="4776">
    <literal><![CDATA[
      K(x / y,z) * x = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(4689(a,2),4348(a,1,1))].">
      <j1 rule="para" parents="4689 4348"/>
    </justification>
  </clause>

  <clause id="4777">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(4689(a,2),4503(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4689 4503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4778">
    <literal><![CDATA[
      K(x,y) * (T(y,x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(4689(a,2),4504(a,1,1))].">
      <j1 rule="para" parents="4689 4504"/>
    </justification>
  </clause>

  <clause id="4779">
    <literal><![CDATA[
      T(x,y) * (x \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[para(4689(a,2),4507(a,2,2))].">
      <j1 rule="para" parents="4689 4507"/>
    </justification>
  </clause>

  <clause id="4780">
    <literal><![CDATA[
      x * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) / y = z
    ]]></literal>
    <justification jstring="[para(4689(a,2),4516(a,1,2))].">
      <j1 rule="para" parents="4689 4516"/>
    </justification>
  </clause>

  <clause id="4782">
    <literal><![CDATA[
      K(x \ (x / L(1 / y,z,u)),x) = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(4703(a,2),2481(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4703 2481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4784">
    <literal><![CDATA[
      T(x,y) != x
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = 1
    ]]></literal>
    <justification jstring="[para(4708(a,1),121(a,1)),flip(a),flip(b)].">
      <j1 rule="para" parents="4708 121"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4785">
    <literal><![CDATA[
      (x \ y) * K(x,y / x) = y / x
    ]]></literal>
    <justification jstring="[para(107(a,1),4708(a,1,1))].">
      <j1 rule="para" parents="107 4708"/>
    </justification>
  </clause>

  <clause id="4786">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4708(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4708 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4787">
    <literal><![CDATA[
      T(x \ T(y,x),z) * K(z,T(x,y) \ y) = T(x,y) \ y
    ]]></literal>
    <justification jstring="[para(4351(a,1),4708(a,1,1))].">
      <j1 rule="para" parents="4351 4708"/>
    </justification>
  </clause>

  <clause id="4788">
    <literal><![CDATA[
      x * (y * K(x,y)) = T(x,y) * y
    ]]></literal>
    <justification jstring="[para(4708(a,1),4512(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4708 4512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4789">
    <literal><![CDATA[
      ((x * y) / x) \ x = y \ (x * K(y,x))
    ]]></literal>
    <justification jstring="[para(4708(a,1),4511(a,1,2))].">
      <j1 rule="para" parents="4708 4511"/>
    </justification>
  </clause>

  <clause id="4790">
    <literal><![CDATA[
      (x * y) * L(K(y,z),y,x) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4714,a,b,296,a),flip(a)].">
      <j1 rule="hyper" parents="119 4714 296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4791">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4644,a,b,4714,a)].">
      <j1 rule="hyper" parents="58 4644 4714"/>
    </justification>
  </clause>

  <clause id="4793">
    <literal><![CDATA[
      T(x,T(y,x / y)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4255,a,b,4714,a)].">
      <j1 rule="hyper" parents="58 4255 4714"/>
    </justification>
  </clause>

  <clause id="4796">
    <literal><![CDATA[
      T(x,y) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4714(a,2),38(a,1))].">
      <j1 rule="para" parents="4714 38"/>
    </justification>
  </clause>

  <clause id="4797">
    <literal><![CDATA[
      x \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4714(a,2),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4714 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4798">
    <literal><![CDATA[
      x / (y * K(y,y \ x)) = y \ x
    ]]></literal>
    <justification jstring="[para(4714(a,1),265(a,1,2))].">
      <j1 rule="para" parents="4714 265"/>
    </justification>
  </clause>

  <clause id="4800">
    <literal><![CDATA[
      K(x,L(x,y,z) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(3357,a,4729,a),flip(a)].">
      <j1 rule="hyper" parents="3357 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4801">
    <literal><![CDATA[
      K(T(x,y),z) * T(x,y) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(435,a,4729,a),flip(a)].">
      <j1 rule="hyper" parents="435 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4803">
    <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,4729,a),flip(a)].">
      <j1 rule="hyper" parents="58 20 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4806">
    <literal><![CDATA[
      x * (K(y,x) * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(119,a,4729,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4729 17"/>
    </justification>
  </clause>

  <clause id="4809">
    <literal><![CDATA[
      L(x \ y,x,K(y,z)) = (K(y,z) * x) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(4729(a,2),92(a,2,2))].">
      <j1 rule="para" parents="4729 92"/>
    </justification>
  </clause>

  <clause id="4812">
    <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(4729(a,2),482(a,1,2,2))].">
      <j1 rule="para" parents="4729 482"/>
    </justification>
  </clause>

  <clause id="4813">
    <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(4729(a,2),515(a,2,2))].">
      <j1 rule="para" parents="4729 515"/>
    </justification>
  </clause>

  <clause id="4814">
    <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(4729(a,2),604(a,1,2))].">
      <j1 rule="para" parents="4729 604"/>
    </justification>
  </clause>

  <clause id="4815">
    <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(4729(a,2),690(a,1,1))].">
      <j1 rule="para" parents="4729 690"/>
    </justification>
  </clause>

  <clause id="4816">
    <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(4729(a,2),948(a,1,2,1))].">
      <j1 rule="para" parents="4729 948"/>
    </justification>
  </clause>

  <clause id="4817">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4729(a,2),3314(a,1))].">
      <j1 rule="para" parents="4729 3314"/>
    </justification>
  </clause>

  <clause id="4818">
    <literal><![CDATA[
      K(x,y / x) * (x \ y) = y / x
    ]]></literal>
    <justification jstring="[hyper(780,a,4749,a)].">
      <j1 rule="hyper" parents="780 4749"/>
    </justification>
  </clause>

  <clause id="4819">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4345,a,b,4749,a)].">
      <j1 rule="hyper" parents="320 4345 4749"/>
    </justification>
  </clause>

  <clause id="4821">
    <literal><![CDATA[
      x / T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4749(a,2),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4749 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4822">
    <literal><![CDATA[
      L(T(x,y),K(y,x),z) = (z * K(y,x)) \ (z * x)
    ]]></literal>
    <justification jstring="[para(4749(a,2),92(a,1,1))].">
      <j1 rule="para" parents="4749 92"/>
    </justification>
  </clause>

  <clause id="4823">
    <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(4749(a,2),2508(a,1,2,1))].">
      <j1 rule="para" parents="4749 2508"/>
    </justification>
  </clause>

  <clause id="4824">
    <literal><![CDATA[
      K(x,y) \ y != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4753(a,2),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4753 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4825">
    <literal><![CDATA[
      (1 / (1 / x)) \ K(y,x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(4753(a,2),2245(a,1,2))].">
      <j1 rule="para" parents="4753 2245"/>
    </justification>
  </clause>

  <clause id="4827">
    <literal><![CDATA[
      (1 / (1 / x)) / K(y,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(3529(a,1),4764(a,2,2)),flip(a)].">
      <j1 rule="para" parents="3529 4764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4828">
    <literal><![CDATA[
      K(x,y * K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,4775,a(flip),b,4764,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="118 4775 4764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4829">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) = T(x,z)
    ]]></literal>
    <justification jstring="[para(4775(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4775 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4830">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      z * K(y,z) = x
    ]]></literal>
    <justification jstring="[para(4775(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="4775 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4831">
    <literal><![CDATA[
      (x * y) / x != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4775(a,1),331(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="4775 331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4832">
    <literal><![CDATA[
      T(x * K(y,x),z) * y = y * T(x,z)
    ]]></literal>
    <justification jstring="[para(4775(a,1),236(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4775 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4833">
    <literal><![CDATA[
      T(x * K(y,x),z) = (y * T(x,z)) / y
    ]]></literal>
    <justification jstring="[para(4775(a,1),269(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4775 269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4834">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * y = y * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(4775(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4775 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4835">
    <literal><![CDATA[
      R(x * K(y,x),z,u) * y = y * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(4775(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4775 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4836">
    <literal><![CDATA[
      T((x * (y * K(z,y))) / x,z) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(4775(a,1),460(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4775 460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4837">
    <literal><![CDATA[
      T(1 / (1 / (x * K(y,x))),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(4775(a,1),2154(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4775 2154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4838">
    <literal><![CDATA[
      T(K(x,y) * y,x) = y
    ]]></literal>
    <justification jstring="[para(2870(a,2),4775(a,1,1))].">
      <j1 rule="para" parents="2870 4775"/>
    </justification>
  </clause>

  <clause id="4839">
    <literal><![CDATA[
      T(x \ K(y,x \ 1),y) = x \ 1
    ]]></literal>
    <justification jstring="[para(2909(a,1),4775(a,1,1))].">
      <j1 rule="para" parents="2909 4775"/>
    </justification>
  </clause>

  <clause id="4840">
    <literal><![CDATA[
      (x * K(y,x)) * ((y \ 1) \ 1) = ((y \ 1) \ 1) * x
    ]]></literal>
    <justification jstring="[para(4775(a,1),2942(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4775 2942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4841">
    <literal><![CDATA[
      T(K(x,y \ 1) / y,x) = 1 / y
    ]]></literal>
    <justification jstring="[para(3537(a,1),4775(a,1,1))].">
      <j1 rule="para" parents="3537 4775"/>
    </justification>
  </clause>

  <clause id="4842">
    <literal><![CDATA[
      T(x,y * K(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4775(a,1),4193(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4775 4193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4843">
    <literal><![CDATA[
      T(x,L(y * K(x,y),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(4775(a,1),4212(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4775 4212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4844">
    <literal><![CDATA[
      L(x * K(y,x),y,x * K(y,x)) = L(x * K(y,x),y,x)
    ]]></literal>
    <justification jstring="[para(4775(a,1),4501(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4775 4501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4845">
    <literal><![CDATA[
      ((x \ (y * K(z,y))) * x) * z = z * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(4775(a,1),4576(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4775 4576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4847">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * z = x
    ]]></literal>
    <justification jstring="[para(4838(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="4838 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4848">
    <literal><![CDATA[
      K(x,y) = (1 / y) * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,1462,a,b,4699,a),flip(a)].">
      <j1 rule="hyper" parents="320 1462 4699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4849">
    <literal><![CDATA[
      R(K(x,y / z),y / z,z) = (((x * (y / z)) / x) * z) / y
    ]]></literal>
    <justification jstring="[para(4699(a,2),525(a,1,1))].">
      <j1 rule="para" parents="4699 525"/>
    </justification>
  </clause>

  <clause id="4850">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(y,(x * z) / x)
    ]]></literal>
    <justification jstring="[para(971(a,1),4699(a,2,1)),flip(a)].">
      <j1 rule="para" parents="971 4699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4851">
    <literal><![CDATA[
      (x \ T(x * y,y)) / y = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(4088(a,1),4699(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4088 4699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4853">
    <literal><![CDATA[
      (x \ 1) \ K(y,x) = (y * ((x \ 1) \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(116,a,4701,a,b,1414,a)].">
      <j1 rule="hyper" parents="116 4701 1414"/>
    </justification>
  </clause>

  <clause id="4854">
    <literal><![CDATA[
      x \ K(y,1 / x) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(116,a,4701,a,b,1456,a(flip))].">
      <j1 rule="hyper" parents="116 4701 1456"/>
    </justification>
  </clause>

  <clause id="4855">
    <literal><![CDATA[
      (x \ y) \ (y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),4701(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 4701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4856">
    <literal><![CDATA[
      x * ((y * z) / y) = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[para(4701(a,2),151(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4701 151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4857">
    <literal><![CDATA[
      ((x * y) / x) \ z = (y * K(x,y)) \ z
    ]]></literal>
    <justification jstring="[para(4701(a,2),155(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4701 155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4858">
    <literal><![CDATA[
      x * (y * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * ((z * y) / z) = u
    ]]></literal>
    <justification jstring="[para(4701(a,2),342(a,1,2,2))].">
      <j1 rule="para" parents="4701 342"/>
    </justification>
  </clause>

  <clause id="4859">
    <literal><![CDATA[
      R(x,y,z) \ R((u * x) / u,y,z) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(849(a,2),4701(a,2,2)),flip(a)].">
      <j1 rule="para" parents="849 4701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4860">
    <literal><![CDATA[
      T(x,y) \ ((z * x) / z) = x * (T(x,y) \ K(z,x))
    ]]></literal>
    <justification jstring="[para(4701(a,2),1109(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4701 1109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4861">
    <literal><![CDATA[
      K(x,y) * K(x \ 1,x) = (x \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4702(a,2),2826(a,1,1))].">
      <j1 rule="para" parents="4702 2826"/>
    </justification>
  </clause>

  <clause id="4862">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4702(a,2),2998(a,1))].">
      <j1 rule="para" parents="4702 2998"/>
    </justification>
  </clause>

  <clause id="4863">
    <literal><![CDATA[
      K(1 / x,y) / x = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,4704,a,b,193,a(flip))].">
      <j1 rule="hyper" parents="117 4704 193"/>
    </justification>
  </clause>

  <clause id="4864">
    <literal><![CDATA[
      ((x * y) / x) \ 1 = y \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4704,a,b,4349,a),flip(a)].">
      <j1 rule="hyper" parents="116 4704 4349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4865">
    <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(4704(a,2),482(a,1,2,2))].">
      <j1 rule="para" parents="4704 482"/>
    </justification>
  </clause>

  <clause id="4866">
    <literal><![CDATA[
      T(x,y * x) * (x \ 1) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(4266(a,2),4704(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4266 4704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4867">
    <literal><![CDATA[
      K(x,T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,4708,a,b,4710,a),flip(a)].">
      <j1 rule="hyper" parents="29 4708 4710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4869">
    <literal><![CDATA[
      K(x,x \ (y * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(17(a,1),4867(a,1,2))].">
      <j1 rule="para" parents="17 4867"/>
    </justification>
  </clause>

  <clause id="4870">
    <literal><![CDATA[
      K(x,L(T(y,x),z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(20(a,2),4867(a,1,2))].">
      <j1 rule="para" parents="20 4867"/>
    </justification>
  </clause>

  <clause id="4871">
    <literal><![CDATA[
      K(x,y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),4867(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 4867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4872">
    <literal><![CDATA[
      K(x,L(y / x,z,u)) = K(x,L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(247(a,1),4867(a,1,2)),flip(a)].">
      <j1 rule="para" parents="247 4867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4873">
    <literal><![CDATA[
      K(x,R(y / x,z,u)) = K(x,R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(248(a,1),4867(a,1,2)),flip(a)].">
      <j1 rule="para" parents="248 4867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4874">
    <literal><![CDATA[
      K(x,(x * y) * (x \ 1)) = K(x,R(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[para(784(a,1),4867(a,1,2)),flip(a)].">
      <j1 rule="para" parents="784 4867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4875">
    <literal><![CDATA[
      K(x,y) \ T(y,x) = T(T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4867(a,1),4749(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4867 4749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4876">
    <literal><![CDATA[
      (x * y) * K(T(y,x),x * y) = T(y,x * y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4495,a,4711,a),flip(a)].">
      <j1 rule="hyper" parents="4495 4711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4877">
    <literal><![CDATA[
      K(x,y \ 1) / y = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[hyper(320,a,3537,a(flip),b,4711,a)].">
      <j1 rule="hyper" parents="320 3537 4711"/>
    </justification>
  </clause>

  <clause id="4878">
    <literal><![CDATA[
      (x * y) \ ((x * y) / x) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,4711,a,b,1441,a)].">
      <j1 rule="hyper" parents="116 4711 1441"/>
    </justification>
  </clause>

  <clause id="4879">
    <literal><![CDATA[
      x / ((y * z) / y) = x / (z * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(55,a,4711,a)].">
      <j1 rule="hyper" parents="55 4711"/>
    </justification>
  </clause>

  <clause id="4880">
    <literal><![CDATA[
      (x / ((y * z) / y)) * (z * K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,4711,a(flip),b,75,a)].">
      <j1 rule="hyper" parents="119 4711 75"/>
    </justification>
  </clause>

  <clause id="4881">
    <literal><![CDATA[
      x \ ((y * x) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4711(a,2),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4711 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4882">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(4711(a,1),331(a,1))].">
      <j1 rule="para" parents="4711 331"/>
    </justification>
  </clause>

  <clause id="4883">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(4711(a,1),333(a,1))].">
      <j1 rule="para" parents="4711 333"/>
    </justification>
  </clause>

  <clause id="4884">
    <literal><![CDATA[
      T(x * K(y,x),y) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(4711(a,1),345(a,1,1))].">
      <j1 rule="para" parents="4711 345"/>
    </justification>
  </clause>

  <clause id="4885">
    <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),4711(a,1,1))].">
      <j1 rule="para" parents="101 4711"/>
    </justification>
  </clause>

  <clause id="4886">
    <literal><![CDATA[
      R(x * K(y,x),y,z) = ((y * x) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(4711(a,1),102(a,1,1))].">
      <j1 rule="para" parents="4711 102"/>
    </justification>
  </clause>

  <clause id="4887">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y / x = z
    ]]></literal>
    <justification jstring="[para(4711(a,1),338(a,1))].">
      <j1 rule="para" parents="4711 338"/>
    </justification>
  </clause>

  <clause id="4888">
    <literal><![CDATA[
      R(x / y,y,K(z,x)) \ ((z * x) / z) = y * K(z,x)
    ]]></literal>
    <justification jstring="[para(4711(a,2),506(a,1,2))].">
      <j1 rule="para" parents="4711 506"/>
    </justification>
  </clause>

  <clause id="4889">
    <literal><![CDATA[
      R(x * K(y,x),y,y \ 1) = (y * x) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(4711(a,1),523(a,1,1))].">
      <j1 rule="para" parents="4711 523"/>
    </justification>
  </clause>

  <clause id="4890">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(4711(a,1),681(a,1,1,1))].">
      <j1 rule="para" parents="4711 681"/>
    </justification>
  </clause>

  <clause id="4891">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4711(a,1),781(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4711 781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4892">
    <literal><![CDATA[
      L(x * K(y,x),z,u) = (y * L(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(4711(a,1),843(a,1,1))].">
      <j1 rule="para" parents="4711 843"/>
    </justification>
  </clause>

  <clause id="4893">
    <literal><![CDATA[
      R(x * K(y,x),z,u) = (y * R(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(4711(a,1),849(a,1,1))].">
      <j1 rule="para" parents="4711 849"/>
    </justification>
  </clause>

  <clause id="4894">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = a(x / y,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(4711(a,2),83(a,1,2))].">
      <j1 rule="para" parents="4711 83"/>
    </justification>
  </clause>

  <clause id="4895">
    <literal><![CDATA[
      T(T(x * K(y,x),z),x * y) = L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(4711(a,1),954(a,1,1,1))].">
      <j1 rule="para" parents="4711 954"/>
    </justification>
  </clause>

  <clause id="4896">
    <literal><![CDATA[
      L(x * K(y * z,x),z,y) = (y * (z * x)) / (y * z)
    ]]></literal>
    <justification jstring="[para(4711(a,1),845(a,1,1))].">
      <j1 rule="para" parents="4711 845"/>
    </justification>
  </clause>

  <clause id="4897">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / (y * K(z,y))) * y
    ]]></literal>
    <justification jstring="[para(4711(a,1),1545(a,2,1,2))].">
      <j1 rule="para" parents="4711 1545"/>
    </justification>
  </clause>

  <clause id="4898">
    <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(1630(a,1),4711(a,1,1))].">
      <j1 rule="para" parents="1630 4711"/>
    </justification>
  </clause>

  <clause id="4899">
    <literal><![CDATA[
      (x * K(y,x)) \ ((y * (x * y)) / y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(4711(a,1),1645(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4711 1645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4900">
    <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(1864(a,1),4711(a,1,1))].">
      <j1 rule="para" parents="1864 4711"/>
    </justification>
  </clause>

  <clause id="4901">
    <literal><![CDATA[
      T(x * y,y * K(x,y)) = T(x * y,y)
    ]]></literal>
    <justification jstring="[para(4711(a,1),4071(a,1,2))].">
      <j1 rule="para" parents="4711 4071"/>
    </justification>
  </clause>

  <clause id="4902">
    <literal><![CDATA[
      T(x * K(y,x),y * x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4711(a,1),4293(a,1,1))].">
      <j1 rule="para" parents="4711 4293"/>
    </justification>
  </clause>

  <clause id="4903">
    <literal><![CDATA[
      (x \ (y * K(x,y))) * x = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4711(a,1),4612(a,1,1,2))].">
      <j1 rule="para" parents="4711 4612"/>
    </justification>
  </clause>

  <clause id="4905">
    <literal><![CDATA[
      T(x,y) * (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4716(a,2),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4716 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4906">
    <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(30,a,1883,a,b,4733,a),flip(a)].">
      <j1 rule="hyper" parents="30 1883 4733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4907">
    <literal><![CDATA[
      (x \ K(y,x \ 1)) * y = y * (x \ 1)
    ]]></literal>
    <justification jstring="[para(2909(a,1),4733(a,1,1))].">
      <j1 rule="para" parents="2909 4733"/>
    </justification>
  </clause>

  <clause id="4908">
    <literal><![CDATA[
      x / ((y * K(x,y)) * ((x \ 1) \ 1)) = (1 / (1 / x)) / (x * y)
    ]]></literal>
    <justification jstring="[para(4733(a,1),3446(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4733 3446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4909">
    <literal><![CDATA[
      K(x,y) = x / ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3000,a,b,4751,a),flip(a)].">
      <j1 rule="hyper" parents="320 3000 4751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4910">
    <literal><![CDATA[
      K(x \ K(x,y),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(4751(a,2),2756(a,1,1,2))].">
      <j1 rule="para" parents="4751 2756"/>
    </justification>
  </clause>

  <clause id="4911">
    <literal><![CDATA[
      K(x,y) / x = 1 / ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(4751(a,2),3001(a,1,1))].">
      <j1 rule="para" parents="4751 3001"/>
    </justification>
  </clause>

  <clause id="4912">
    <literal><![CDATA[
      K(x,x \ 1) / ((y * x) \ y) = 1 / T((y * x) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,2363,a(flip),b,4754,a(flip))].">
      <j1 rule="hyper" parents="117 2363 4754"/>
    </justification>
  </clause>

  <clause id="4913">
    <literal><![CDATA[
      K(x,y) != 1
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = y
    ]]></literal>
    <justification jstring="[para(4754(a,2),125(a,1))].">
      <j1 rule="para" parents="4754 125"/>
    </justification>
  </clause>

  <clause id="4914">
    <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(4754(a,2),518(a,1,2))].">
      <j1 rule="para" parents="4754 518"/>
    </justification>
  </clause>

  <clause id="4915">
    <literal><![CDATA[
      (x * y) \ (x * K(z,y)) = L(T(y,z) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(4755(a,2),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4755 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4916">
    <literal><![CDATA[
      x * (T(y,z) \ 1) = x * (y \ K(z,y))
    ]]></literal>
    <justification jstring="[para(4755(a,2),152(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4755 152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4917">
    <literal><![CDATA[
      L(T(x \ y,z) \ 1,x \ y,x) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[para(4755(a,2),91(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4755 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4918">
    <literal><![CDATA[
      K(T(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4688,a,b,4757,a),flip(a)].">
      <j1 rule="hyper" parents="320 4688 4757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4922">
    <literal><![CDATA[
      (T(x,y) * y) / T(x,y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4918,a(flip),b,4701,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 4918 4701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4923">
    <literal><![CDATA[
      K(x \ (y * x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(17(a,1),4918(a,1,1))].">
      <j1 rule="para" parents="17 4918"/>
    </justification>
  </clause>

  <clause id="4924">
    <literal><![CDATA[
      K(x / y,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(107(a,1),4918(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 4918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4925">
    <literal><![CDATA[
      K((x \ y) \ y,x \ y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(106(a,1),4918(a,1,1))].">
      <j1 rule="para" parents="106 4918"/>
    </justification>
  </clause>

  <clause id="4926">
    <literal><![CDATA[
      K(R(x,y,x),y * x) = K(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(802(a,1),4918(a,1,1)),flip(a)].">
      <j1 rule="para" parents="802 4918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4927">
    <literal><![CDATA[
      K(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4918(a,1),4178(a,1))].">
      <j1 rule="para" parents="4918 4178"/>
    </justification>
  </clause>

  <clause id="4928">
    <literal><![CDATA[
      K(x / (x / y),y \ x) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(4305(a,1),4918(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4305 4918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4929">
    <literal><![CDATA[
      K(x,y) \ 1 = K(y,x)
    ]]></literal>
    <justification jstring="[para(4918(a,1),4376(a,1,1))].">
      <j1 rule="para" parents="4918 4376"/>
    </justification>
  </clause>

  <clause id="4930">
    <literal><![CDATA[
      K(x * K(y,x),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4775(a,1),4918(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4775 4918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4931">
    <literal><![CDATA[
      1 / K(x,y) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(2399,a,4929,a)].">
      <j1 rule="hyper" parents="2399 4929"/>
    </justification>
  </clause>

  <clause id="4933">
    <literal><![CDATA[
      K(x,y) * K(y,x) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,4929,a)].">
      <j1 rule="hyper" parents="134 4929"/>
    </justification>
  </clause>

  <clause id="4934">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) = K(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4929,a(flip),b,4719,a)].">
      <j1 rule="hyper" parents="119 4929 4719"/>
    </justification>
  </clause>

  <clause id="4935">
    <literal><![CDATA[
      K(x,y) \ x = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,4929,a(flip),b,3170,a),flip(a)].">
      <j1 rule="hyper" parents="119 4929 3170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4936">
    <literal><![CDATA[
      K(x,y) != z \ 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4929(a,1),43(a,1))].">
      <j1 rule="para" parents="4929 43"/>
    </justification>
  </clause>

  <clause id="4937">
    <literal><![CDATA[
      x * K(y,z) != 1
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = x
    ]]></literal>
    <justification jstring="[para(4929(a,1),129(a,1,2))].">
      <j1 rule="para" parents="4929 129"/>
    </justification>
  </clause>

  <clause id="4938">
    <literal><![CDATA[
      1 / K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4929(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4929 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4939">
    <literal><![CDATA[
      L(x \ K(y,z),x,K(z,y)) = (K(z,y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(4929(a,1),298(a,1,1,2))].">
      <j1 rule="para" parents="4929 298"/>
    </justification>
  </clause>

  <clause id="4940">
    <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(4929(a,1),2103(a,2,1,2,1))].">
      <j1 rule="para" parents="4929 2103"/>
    </justification>
  </clause>

  <clause id="4942">
    <literal><![CDATA[
      T(x * K(y,z),x \ K(z,y)) = ((x * K(y,z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4929(a,1),3773(a,1,2,2))].">
      <j1 rule="para" parents="4929 3773"/>
    </justification>
  </clause>

  <clause id="4943">
    <literal><![CDATA[
      1 / K(x \ 1,y) = K(y,1 / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,3528,a,b,4931,a),flip(a)].">
      <j1 rule="hyper" parents="320 3528 4931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4944">
    <literal><![CDATA[
      K(x,y) * z != 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4931(a,1),125(a,1,1))].">
      <j1 rule="para" parents="4931 125"/>
    </justification>
  </clause>

  <clause id="4945">
    <literal><![CDATA[
      K(x,y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4931(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4931 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4946">
    <literal><![CDATA[
      K(x,y) \ 1 != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(4931(a,1),582(a,1,1))].">
      <j1 rule="para" parents="4931 582"/>
    </justification>
  </clause>

  <clause id="4947">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) = L(z,K(y,x),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(168,a,186,a,b,4933,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="168 186 4933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4949">
    <literal><![CDATA[
      ((x * y) / x) \ y != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4759(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4759 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4951">
    <literal><![CDATA[
      T(x,y) = (K(y,x) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(188,a,4762,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="188 4762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4952">
    <literal><![CDATA[
      ((x \ y) \ y) \ 1 = x \ K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(656,a,4763,a)].">
      <j1 rule="hyper" parents="656 4763"/>
    </justification>
  </clause>

  <clause id="4953">
    <literal><![CDATA[
      T(x,y) = 1 / (x \ K(y,x))
    ]]></literal>
    <justification jstring="[hyper(197,a,4763,a),flip(a)].">
      <j1 rule="hyper" parents="197 4763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4954">
    <literal><![CDATA[
      1 / (x \ K(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4763(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4763 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4955">
    <literal><![CDATA[
      T(x,y) * L(x \ K(y,x),z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[para(4763(a,1),2129(a,1,2,1))].">
      <j1 rule="para" parents="4763 2129"/>
    </justification>
  </clause>

  <clause id="4956">
    <literal><![CDATA[
      T(T(x,x \ 1),y) = (x \ K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(4763(a,1),2150(a,2,1))].">
      <j1 rule="para" parents="4763 2150"/>
    </justification>
  </clause>

  <clause id="4957">
    <literal><![CDATA[
      K(x,y) * K(y \ 1,y) = (T(y,x) \ 1) * y
    ]]></literal>
    <justification jstring="[para(4763(a,2),3340(a,2,1))].">
      <j1 rule="para" parents="4763 3340"/>
    </justification>
  </clause>

  <clause id="4958">
    <literal><![CDATA[
      K(x \ y,x) * (y / x) = x \ y
    ]]></literal>
    <justification jstring="[para(5(a,1),4771(a,1,2,1))].">
      <j1 rule="para" parents="5 4771"/>
    </justification>
  </clause>

  <clause id="4960">
    <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),4771(a,1,2,1))].">
      <j1 rule="para" parents="80 4771"/>
    </justification>
  </clause>

  <clause id="4962">
    <literal><![CDATA[
      K(x,y / x) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),4772(a,1,2))].">
      <j1 rule="para" parents="7 4772"/>
    </justification>
  </clause>

  <clause id="4963">
    <literal><![CDATA[
      x * (y * z) != z * y
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = x
    ]]></literal>
    <justification jstring="[para(4772(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="4772 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4964">
    <literal><![CDATA[
      K(L(x,y,z),z * y) * (z * (y * x)) = L(x,y,z) * (z * y)
    ]]></literal>
    <justification jstring="[para(90(a,1),4772(a,1,2))].">
      <j1 rule="para" parents="90 4772"/>
    </justification>
  </clause>

  <clause id="4965">
    <literal><![CDATA[
      L(x \ (y * z),x,K(z,y)) = (K(z,y) * x) \ (z * y)
    ]]></literal>
    <justification jstring="[para(4772(a,1),92(a,2,2))].">
      <j1 rule="para" parents="4772 92"/>
    </justification>
  </clause>

  <clause id="4966">
    <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(4772(a,1),479(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4772 479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4967">
    <literal><![CDATA[
      (x * y) \ (K(x,y) * (y * (x * z))) = L(L(z,x,y),y * x,K(x,y))
    ]]></literal>
    <justification jstring="[para(4772(a,1),477(a,1,1))].">
      <j1 rule="para" parents="4772 477"/>
    </justification>
  </clause>

  <clause id="4968">
    <literal><![CDATA[
      T(x * y,z) / (y * x) = (y * x) \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(4772(a,1),4562(a,1,1,1))].">
      <j1 rule="para" parents="4772 4562"/>
    </justification>
  </clause>

  <clause id="4969">
    <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(4842(a,1),4467(a,2,2))].">
      <j1 rule="para" parents="4842 4467"/>
    </justification>
  </clause>

  <clause id="4972">
    <literal><![CDATA[
      x \ (y * (x / y)) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,87,a,b,4871,a)].">
      <j1 rule="hyper" parents="58 87 4871"/>
    </justification>
  </clause>

  <clause id="4973">
    <literal><![CDATA[
      K(x,x \ (y \ x)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,4441,a(flip),b,4871,a),flip(a)].">
      <j1 rule="hyper" parents="58 4441 4871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4974">
    <literal><![CDATA[
      x * K(y,y \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4871,a(flip),b,87,a)].">
      <j1 rule="hyper" parents="119 4871 87"/>
    </justification>
  </clause>

  <clause id="4975">
    <literal><![CDATA[
      T(x,K(y,y \ x)) = x
    ]]></literal>
    <justification jstring="[para(4871(a,1),4686(a,1,2))].">
      <j1 rule="para" parents="4871 4686"/>
    </justification>
  </clause>

  <clause id="4977">
    <literal><![CDATA[
      (x \ y) / (y / x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),4909(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 4909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4978">
    <literal><![CDATA[
      x / (y / (y / x)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4302(a,1),4909(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4302 4909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4979">
    <literal><![CDATA[
      x * K(x / y,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,4924,a,b,85,a)].">
      <j1 rule="hyper" parents="119 4924 85"/>
    </justification>
  </clause>

  <clause id="4984">
    <literal><![CDATA[
      L(x * K(y,x),K(x,y),z) = (z * K(x,y)) \ (z * x)
    ]]></literal>
    <justification jstring="[para(4935(a,1),92(a,1,1))].">
      <j1 rule="para" parents="4935 92"/>
    </justification>
  </clause>

  <clause id="4985">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(3293(a,1),4725(a,1,2))].">
      <j1 rule="para" parents="3293 4725"/>
    </justification>
  </clause>

  <clause id="4986">
    <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),4786(a,1,1))].">
      <j1 rule="para" parents="18 4786"/>
    </justification>
  </clause>

  <clause id="4987">
    <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),4786(a,1,1))].">
      <j1 rule="para" parents="20 4786"/>
    </justification>
  </clause>

  <clause id="4989">
    <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(317(a,1),4786(a,1,1))].">
      <j1 rule="para" parents="317 4786"/>
    </justification>
  </clause>

  <clause id="4990">
    <literal><![CDATA[
      x * T(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(4185(a,1),4786(a,1))].">
      <j1 rule="para" parents="4185 4786"/>
    </justification>
  </clause>

  <clause id="4991">
    <literal><![CDATA[
      K(x \ (x / y),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(4186(a,2),4786(a,1))].">
      <j1 rule="para" parents="4186 4786"/>
    </justification>
  </clause>

  <clause id="4992">
    <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),4797(a,1,2))].">
      <j1 rule="para" parents="20 4797"/>
    </justification>
  </clause>

  <clause id="4994">
    <literal><![CDATA[
      x \ L(T(x,y),y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(710(a,2),4797(a,1,2))].">
      <j1 rule="para" parents="710 4797"/>
    </justification>
  </clause>

  <clause id="4996">
    <literal><![CDATA[
      T(K(x,y),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4691(a,2),4797(a,1))].">
      <j1 rule="para" parents="4691 4797"/>
    </justification>
  </clause>

  <clause id="4997">
    <literal><![CDATA[
      K(x,x \ (y * x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(17(a,1),4927(a,1,2))].">
      <j1 rule="para" parents="17 4927"/>
    </justification>
  </clause>

  <clause id="4998">
    <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),4927(a,1,2))].">
      <j1 rule="para" parents="20 4927"/>
    </justification>
  </clause>

  <clause id="4999">
    <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(1088(a,1),4927(a,1,2))].">
      <j1 rule="para" parents="1088 4927"/>
    </justification>
  </clause>

  <clause id="5001">
    <literal><![CDATA[
      K((x \ 1) \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3309(a,1),4996(a,1))].">
      <j1 rule="para" parents="3309 4996"/>
    </justification>
  </clause>

  <clause id="5002">
    <literal><![CDATA[
      K(x,y) * (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(4694(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4694 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5003">
    <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),4694(a,1,2))].">
      <j1 rule="para" parents="101 4694"/>
    </justification>
  </clause>

  <clause id="5004">
    <literal><![CDATA[
      (T(x,y) * R(x \ 1,x,z)) / ((z / (x * z)) * x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(651(a,2),4694(a,1,2))].">
      <j1 rule="para" parents="651 4694"/>
    </justification>
  </clause>

  <clause id="5005">
    <literal><![CDATA[
      (x * T(x \ y,y)) * (y \ 1) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[para(1492(a,1),4698(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1492 4698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5006">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2489,a,4705,a)].">
      <j1 rule="hyper" parents="2489 4705"/>
    </justification>
  </clause>

  <clause id="5007">
    <literal><![CDATA[
      x * (y * T(y \ (x \ 1),z)) = K((x * y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(935,a,4705,a)].">
      <j1 rule="hyper" parents="935 4705"/>
    </justification>
  </clause>

  <clause id="5008">
    <literal><![CDATA[
      T(1 / x,y) * x = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(459,a,4705,a)].">
      <j1 rule="hyper" parents="459 4705"/>
    </justification>
  </clause>

  <clause id="5010">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K((x / y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1575,a(flip),b,4705,a)].">
      <j1 rule="hyper" parents="58 1575 4705"/>
    </justification>
  </clause>

  <clause id="5011">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1417,a(flip),b,4705,a)].">
      <j1 rule="hyper" parents="58 1417 4705"/>
    </justification>
  </clause>

  <clause id="5012">
    <literal><![CDATA[
      (x \ (x / y)) * x = (x / y) * K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,4705,a(flip),b,958,a),flip(a)].">
      <j1 rule="hyper" parents="119 4705 958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5013">
    <literal><![CDATA[
      ((x * y) \ x) * (x * y) = x * K(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4705,a(flip),b,943,a),flip(a)].">
      <j1 rule="hyper" parents="119 4705 943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5014">
    <literal><![CDATA[
      L(x \ 1,x,y) * (y * x) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,4705,a(flip),b,632,a),flip(a)].">
      <j1 rule="hyper" parents="119 4705 632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5015">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K((y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4705,a(flip),b,1417,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 4705 1417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5016">
    <literal><![CDATA[
      x \ K((x * y) \ 1,z) = y * T(y \ (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(116,a,4705,a(flip),b,919,a(flip))].">
      <j1 rule="hyper" parents="116 4705 919"/>
    </justification>
  </clause>

  <clause id="5017">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = K(x \ 1,z) * y
    ]]></literal>
    <justification jstring="[para(4705(a,1),1218(a,2,1))].">
      <j1 rule="para" parents="4705 1218"/>
    </justification>
  </clause>

  <clause id="5018">
    <literal><![CDATA[
      K(x \ 1,y) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(4705(a,1),1227(a,1,1))].">
      <j1 rule="para" parents="4705 1227"/>
    </justification>
  </clause>

  <clause id="5019">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = K(x \ 1,z) * y
    ]]></literal>
    <justification jstring="[para(4705(a,1),1390(a,2,1))].">
      <j1 rule="para" parents="4705 1390"/>
    </justification>
  </clause>

  <clause id="5020">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),x) = T(K(y \ 1,x),z)
    ]]></literal>
    <justification jstring="[para(4705(a,1),1517(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4705 1517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5021">
    <literal><![CDATA[
      K((x / y) \ 1,z) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(4705(a,1),1574(a,1,1))].">
      <j1 rule="para" parents="4705 1574"/>
    </justification>
  </clause>

  <clause id="5023">
    <literal><![CDATA[
      K((x * y) \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = z
    ]]></literal>
    <justification jstring="[para(4705(a,1),1567(a,1))].">
      <j1 rule="para" parents="4705 1567"/>
    </justification>
  </clause>

  <clause id="5024">
    <literal><![CDATA[
      (x * (y * T(y \ 1,z))) * y = (x * y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(4705(a,1),1702(a,2,2))].">
      <j1 rule="para" parents="4705 1702"/>
    </justification>
  </clause>

  <clause id="5025">
    <literal><![CDATA[
      (x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * K(y \ 1,u)) * z
    ]]></literal>
    <justification jstring="[para(4705(a,1),2304(a,2,1,2))].">
      <j1 rule="para" parents="4705 2304"/>
    </justification>
  </clause>

  <clause id="5026">
    <literal><![CDATA[
      (x * y) * ((z \ L(y \ z,y,x)) * z) = (x * K(y \ 1,z)) * z
    ]]></literal>
    <justification jstring="[para(4705(a,1),2305(a,2,1,2))].">
      <j1 rule="para" parents="4705 2305"/>
    </justification>
  </clause>

  <clause id="5027">
    <literal><![CDATA[
      K(x \ (x / L(y,z,u)),x) = L(K(y \ 1,x),z,u)
    ]]></literal>
    <justification jstring="[para(4705(a,1),2477(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4705 2477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5029">
    <literal><![CDATA[
      x * ((y \ (x \ y)) * y) = y * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(4705(a,1),2956(a,2,2))].">
      <j1 rule="para" parents="4705 2956"/>
    </justification>
  </clause>

  <clause id="5030">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K(1 / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1575,a(flip),b,4706,a)].">
      <j1 rule="hyper" parents="58 1575 4706"/>
    </justification>
  </clause>

  <clause id="5031">
    <literal><![CDATA[
      L(K(1 / x,x),y,z) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(4706(a,1),3206(a,1,1,1))].">
      <j1 rule="para" parents="4706 3206"/>
    </justification>
  </clause>

  <clause id="5032">
    <literal><![CDATA[
      (x * (y / x)) \ x = y \ (y / (y / x))
    ]]></literal>
    <justification jstring="[para(4712(a,2),1442(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4712 1442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5033">
    <literal><![CDATA[
      K(x,(x / y) / x) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(3859,a,4721,a)].">
      <j1 rule="hyper" parents="3859 4721"/>
    </justification>
  </clause>

  <clause id="5035">
    <literal><![CDATA[
      x \ (y * ((z * (y \ x)) / z)) = K(z,1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,3855,a,b,4721,a)].">
      <j1 rule="hyper" parents="58 3855 4721"/>
    </justification>
  </clause>

  <clause id="5036">
    <literal><![CDATA[
      K(x,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(4721(a,1),4797(a,1))].">
      <j1 rule="para" parents="4721 4797"/>
    </justification>
  </clause>

  <clause id="5037">
    <literal><![CDATA[
      K(x,x \ y) / (y / x) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[para(4735(a,1),2906(a,1,2))].">
      <j1 rule="para" parents="4735 2906"/>
    </justification>
  </clause>

  <clause id="5038">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ 1,x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(3298(a,2),4735(a,1,2))].">
      <j1 rule="para" parents="3298 4735"/>
    </justification>
  </clause>

  <clause id="5039">
    <literal><![CDATA[
      T(x,y) * T(z,K(x,y)) = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(579,a,4736,a),flip(a)].">
      <j1 rule="hyper" parents="579 4736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5040">
    <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,4220,a,b,4736,a)].">
      <j1 rule="hyper" parents="119 4220 4736"/>
    </justification>
  </clause>

  <clause id="5041">
    <literal><![CDATA[
      T(x,y) \ (K(x,y) * z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,4736,a(flip),b,1101,a(flip))].">
      <j1 rule="hyper" parents="116 4736 1101"/>
    </justification>
  </clause>

  <clause id="5042">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[para(5(a,1),4736(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 4736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5043">
    <literal><![CDATA[
      x \ y != K(x,z) * u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) * u = y
    ]]></literal>
    <justification jstring="[para(4736(a,1),42(a,1)),flip(a)].">
      <j1 rule="para" parents="4736 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5044">
    <literal><![CDATA[
      K(x,y) * T(z,T(x,y)) = x \ (z * T(x,y))
    ]]></literal>
    <justification jstring="[para(105(a,1),4736(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 4736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5045">
    <literal><![CDATA[
      x * (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(4736(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4736 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5047">
    <literal><![CDATA[
      x \ ((x * y) / x) = K(x,y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(4061(a,1),4736(a,1,2))].">
      <j1 rule="para" parents="4061 4736"/>
    </justification>
  </clause>

  <clause id="5048">
    <literal><![CDATA[
      K(x,y) \ (x \ z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(597,a,4737,a),flip(a)].">
      <j1 rule="hyper" parents="597 4737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5049">
    <literal><![CDATA[
      ((x * y) / x) \ z = K(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(29,a,4349,a,b,4737,a)].">
      <j1 rule="hyper" parents="29 4349 4737"/>
    </justification>
  </clause>

  <clause id="5050">
    <literal><![CDATA[
      K(x,y) * (z * x) = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,1113,a,b,4737,a),flip(a)].">
      <j1 rule="hyper" parents="29 1113 4737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5051">
    <literal><![CDATA[
      K(x,y) * T(y,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,4428,a(flip),b,4737,a),flip(a)].">
      <j1 rule="hyper" parents="29 4428 4737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5052">
    <literal><![CDATA[
      K(x,y) * T(y,x * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,4427,a(flip),b,4737,a),flip(a)].">
      <j1 rule="hyper" parents="29 4427 4737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5053">
    <literal><![CDATA[
      K(x,y) * (T(y,z) * x) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,4409,a(flip),b,4737,a),flip(a)].">
      <j1 rule="hyper" parents="29 4409 4737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5054">
    <literal><![CDATA[
      K(x * y,x) * T(x,y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,4301,a(flip),b,4737,a),flip(a)].">
      <j1 rule="hyper" parents="29 4301 4737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5055">
    <literal><![CDATA[
      (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(4737(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4737 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5057">
    <literal><![CDATA[
      x \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(4737(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4737 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5058">
    <literal><![CDATA[
      T(x,y) * (K(x,y) * z) = T(T(x,y),y) * z
    ]]></literal>
    <justification jstring="[para(4918(a,1),4737(a,1,2,1))].">
      <j1 rule="para" parents="4918 4737"/>
    </justification>
  </clause>

  <clause id="5059">
    <literal><![CDATA[
      (x * y) / (T(x,z) * y) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(4515,a,4738,a)].">
      <j1 rule="hyper" parents="4515 4738"/>
    </justification>
  </clause>

  <clause id="5060">
    <literal><![CDATA[
      K(x,y) \ (y * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(4514,a,4738,a)].">
      <j1 rule="hyper" parents="4514 4738"/>
    </justification>
  </clause>

  <clause id="5061">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = K(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(945,a,4738,a)].">
      <j1 rule="hyper" parents="945 4738"/>
    </justification>
  </clause>

  <clause id="5063">
    <literal><![CDATA[
      T(x,y) * (x \ R(x,z,u)) = R(x,z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3318,a,b,4738,a),flip(a)].">
      <j1 rule="hyper" parents="320 3318 4738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5064">
    <literal><![CDATA[
      x * (K(x,y) * (x \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,4737,a,b,4738,a)].">
      <j1 rule="hyper" parents="58 4737 4738"/>
    </justification>
  </clause>

  <clause id="5065">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,4401,a,b,4738,a)].">
      <j1 rule="hyper" parents="58 4401 4738"/>
    </justification>
  </clause>

  <clause id="5066">
    <literal><![CDATA[
      (x \ L(x,y,z)) * T(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3496,a(flip),b,4738,a)].">
      <j1 rule="hyper" parents="58 3496 4738"/>
    </justification>
  </clause>

  <clause id="5068">
    <literal><![CDATA[
      x \ (K(y,x) * z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,4738,a(flip),b,4507,a(flip))].">
      <j1 rule="hyper" parents="116 4738 4507"/>
    </justification>
  </clause>

  <clause id="5069">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * (K(y,z) * u)) = L(y \ u,T(y,z),x)
    ]]></literal>
    <justification jstring="[para(4738(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4738 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5070">
    <literal><![CDATA[
      K(x * y,z) * (x * (y * u)) = T(x * y,z) * L(u,y,x)
    ]]></literal>
    <justification jstring="[para(13(a,2),4738(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13 4738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5071">
    <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),4738(a,1,2)),flip(a)].">
      <j1 rule="para" parents="110 4738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5072">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ z = u
    ]]></literal>
    <justification jstring="[para(4738(a,1),1134(a,1))].">
      <j1 rule="para" parents="4738 1134"/>
    </justification>
  </clause>

  <clause id="5073">
    <literal><![CDATA[
      K(x,y) * T(x,z) = T(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[para(4688(a,2),4738(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4688 4738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5074">
    <literal><![CDATA[
      K(x,y / z) \ y = z * T(z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4509,a,b,4739,a),flip(a)].">
      <j1 rule="hyper" parents="58 4509 4739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5075">
    <literal><![CDATA[
      K(x,y / (z \ 1)) * (z \ T(z * y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(119,a,4521,a,b,4739,a(flip))].">
      <j1 rule="hyper" parents="119 4521 4739"/>
    </justification>
  </clause>

  <clause id="5076">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) = x * T(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(17(a,2),4739(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17 4739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5079">
    <literal><![CDATA[
      K(x,x \ y) * (x * z) = ((x \ y) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(320,a,314,a(flip),b,4740,a),flip(a)].">
      <j1 rule="hyper" parents="320 314 4740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5080">
    <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),4740(a,2,1))].">
      <j1 rule="para" parents="22 4740"/>
    </justification>
  </clause>

  <clause id="5081">
    <literal><![CDATA[
      T(x,y) * (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(4740(a,1),342(a,1))].">
      <j1 rule="para" parents="4740 342"/>
    </justification>
  </clause>

  <clause id="5082">
    <literal><![CDATA[
      K(x,y) * (L(z,u,w) * x) = T(x,y) * L(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(237(a,1),4740(a,1,2))].">
      <j1 rule="para" parents="237 4740"/>
    </justification>
  </clause>

  <clause id="5083">
    <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(4740(a,1),518(a,1,1,1))].">
      <j1 rule="para" parents="4740 518"/>
    </justification>
  </clause>

  <clause id="5084">
    <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(4740(a,1),477(a,1,1))].">
      <j1 rule="para" parents="4740 477"/>
    </justification>
  </clause>

  <clause id="5085">
    <literal><![CDATA[
      (T(x,y) * (z * u)) \ (K(x,y) * ((x * z) * u)) = L(a(x,z,u),x * (z * u),K(x,y))
    ]]></literal>
    <justification jstring="[para(4740(a,1),493(a,1,1))].">
      <j1 rule="para" parents="4740 493"/>
    </justification>
  </clause>

  <clause id="5086">
    <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(4740(a,1),493(a,1,2))].">
      <j1 rule="para" parents="4740 493"/>
    </justification>
  </clause>

  <clause id="5088">
    <literal><![CDATA[
      K(x,y) * (T(x,y) * z) = T(T(x,y),y) * z
    ]]></literal>
    <justification jstring="[para(4918(a,1),4740(a,1,1))].">
      <j1 rule="para" parents="4918 4740"/>
    </justification>
  </clause>

  <clause id="5089">
    <literal><![CDATA[
      T(x * (y / x),z) / T(y,z) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(117,a,4533,a,b,4742,a)].">
      <j1 rule="hyper" parents="117 4533 4742"/>
    </justification>
  </clause>

  <clause id="5090">
    <literal><![CDATA[
      K(x,(x \ 1) * y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4452(a,2),4742(a,1,1))].">
      <j1 rule="para" parents="4452 4742"/>
    </justification>
  </clause>

  <clause id="5091">
    <literal><![CDATA[
      K(x,y) \ (T(y,x) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(1134,a,4747,a),flip(a)].">
      <j1 rule="hyper" parents="1134 4747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5092">
    <literal><![CDATA[
      K(x,y) \ z = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,4738,a(flip),b,4747,a),flip(a)].">
      <j1 rule="hyper" parents="58 4738 4747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5093">
    <literal><![CDATA[
      K(x,y) * (y \ z) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(1133,a,4747,a(flip))].">
      <j1 rule="hyper" parents="1133 4747"/>
    </justification>
  </clause>

  <clause id="5094">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(440,a,4747,a(flip),b,4738,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="440 4747 4738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5095">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) = z
    ]]></literal>
    <justification jstring="[hyper(119,a,4738,a(flip),b,4747,a(flip))].">
      <j1 rule="hyper" parents="119 4738 4747"/>
    </justification>
  </clause>

  <clause id="5096">
    <literal><![CDATA[
      (K(x,y) \ z) / z = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,4747,a(flip),b,4738,a(flip))].">
      <j1 rule="hyper" parents="117 4747 4738"/>
    </justification>
  </clause>

  <clause id="5097">
    <literal><![CDATA[
      K(x,y) \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(4747(a,1),584(a,1))].">
      <j1 rule="para" parents="4747 584"/>
    </justification>
  </clause>

  <clause id="5099">
    <literal><![CDATA[
      K(x,y) * (y \ K(y,x)) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(3192,a,5092,a)].">
      <j1 rule="hyper" parents="3192 5092"/>
    </justification>
  </clause>

  <clause id="5100">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(3190,a,5092,a)].">
      <j1 rule="hyper" parents="3190 5092"/>
    </justification>
  </clause>

  <clause id="5101">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * K(y,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(2000,a,5092,a)].">
      <j1 rule="hyper" parents="2000 5092"/>
    </justification>
  </clause>

  <clause id="5102">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z,z \ 1) = a(K(y,x),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(707,a,5092,a),flip(a)].">
      <j1 rule="hyper" parents="707 5092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5103">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(579,a,5092,a)].">
      <j1 rule="hyper" parents="579 5092"/>
    </justification>
  </clause>

  <clause id="5104">
    <literal><![CDATA[
      x / (K(y,z) * x) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(575,a,5092,a)].">
      <j1 rule="hyper" parents="575 5092"/>
    </justification>
  </clause>

  <clause id="5105">
    <literal><![CDATA[
      K(x,y) \ T(T(x,z),u) = T(T(x,z),u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,2881,a,b,5092,a),flip(a)].">
      <j1 rule="hyper" parents="320 2881 5092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5106">
    <literal><![CDATA[
      K(x,y) * (R(x,z,u) * K(y,x)) = R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,2878,a,b,5092,a)].">
      <j1 rule="hyper" parents="119 2878 5092"/>
    </justification>
  </clause>

  <clause id="5107">
    <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,3641,a(flip),b,5092,a),flip(a)].">
      <j1 rule="hyper" parents="58 3641 5092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5108">
    <literal><![CDATA[
      x * (K(y,z) * u) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = x
    ]]></literal>
    <justification jstring="[para(5092(a,1),129(a,1,2))].">
      <j1 rule="para" parents="5092 129"/>
    </justification>
  </clause>

  <clause id="5109">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * u = z
    ]]></literal>
    <justification jstring="[para(5092(a,1),134(a,1))].">
      <j1 rule="para" parents="5092 134"/>
    </justification>
  </clause>

  <clause id="5110">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      u = z
    ]]></literal>
    <justification jstring="[para(5092(a,1),255(a,1,2))].">
      <j1 rule="para" parents="5092 255"/>
    </justification>
  </clause>

  <clause id="5111">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(5092(a,1),256(a,1,2))].">
      <j1 rule="para" parents="5092 256"/>
    </justification>
  </clause>

  <clause id="5112">
    <literal><![CDATA[
      x / (K(y,z) * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(5092(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5092 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5113">
    <literal><![CDATA[
      (K(x,y) \ z) * L(u,z,K(y,x)) = K(y,x) * (z * u)
    ]]></literal>
    <justification jstring="[para(5092(a,2),90(a,1,1))].">
      <j1 rule="para" parents="5092 90"/>
    </justification>
  </clause>

  <clause id="5114">
    <literal><![CDATA[
      L(K(x,y) * z,K(y,x),u) = (u * K(y,x)) \ (u * z)
    ]]></literal>
    <justification jstring="[para(5092(a,1),92(a,1,1))].">
      <j1 rule="para" parents="5092 92"/>
    </justification>
  </clause>

  <clause id="5115">
    <literal><![CDATA[
      L(x \ (K(y,z) * u),x,K(z,y)) = (K(z,y) * x) \ u
    ]]></literal>
    <justification jstring="[para(5092(a,1),298(a,1,1,2))].">
      <j1 rule="para" parents="5092 298"/>
    </justification>
  </clause>

  <clause id="5116">
    <literal><![CDATA[
      L(K(x,y) * (z \ u),K(y,x),z) = (z * K(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(5092(a,1),298(a,1,1))].">
      <j1 rule="para" parents="5092 298"/>
    </justification>
  </clause>

  <clause id="5117">
    <literal><![CDATA[
      x \ y != K(z,u) * (K(u,z) * w)
    ]]></literal>
    <literal><![CDATA[
      x * w = y
    ]]></literal>
    <justification jstring="[para(5092(a,1),340(a,2,2))].">
      <j1 rule="para" parents="5092 340"/>
    </justification>
  </clause>

  <clause id="5118">
    <literal><![CDATA[
      T((x \ K(y,z)) \ 1,K(z,y) * x) = (x \ K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(5092(a,1),587(a,1,2))].">
      <j1 rule="para" parents="5092 587"/>
    </justification>
  </clause>

  <clause id="5119">
    <literal><![CDATA[
      R(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5092(a,1),368(a,1,1,3))].">
      <j1 rule="para" parents="5092 368"/>
    </justification>
  </clause>

  <clause id="5120">
    <literal><![CDATA[
      L(T(K(x,y) * (z \ u),w),K(y,x),z) = T((z * K(y,x)) \ u,w)
    ]]></literal>
    <justification jstring="[para(5092(a,1),564(a,1,1,1))].">
      <j1 rule="para" parents="5092 564"/>
    </justification>
  </clause>

  <clause id="5121">
    <literal><![CDATA[
      (K(x,y) * T(K(y,x) * z,u)) * K(y,x) = T(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(5092(a,1),4555(a,1,1))].">
      <j1 rule="para" parents="5092 4555"/>
    </justification>
  </clause>

  <clause id="5122">
    <literal><![CDATA[
      (K(x,y) \ 1) * z = K(x,y) \ z
    ]]></literal>
    <justification jstring="[para(4929(a,2),5092(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4929 5092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5123">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(119,a,5095,a(flip),b,4736,a),flip(a)].">
      <j1 rule="hyper" parents="119 5095 4736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5124">
    <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,5095,a(flip),b,184,a)].">
      <j1 rule="hyper" parents="119 5095 184"/>
    </justification>
  </clause>

  <clause id="5125">
    <literal><![CDATA[
      K(x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5095(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5095 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5126">
    <literal><![CDATA[
      L((K(x,y) * z) \ u,K(x,y) * z,K(y,x)) = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(5095(a,1),92(a,2,1))].">
      <j1 rule="para" parents="5095 92"/>
    </justification>
  </clause>

  <clause id="5127">
    <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(5095(a,1),477(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5095 477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5128">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ 1 = z
    ]]></literal>
    <justification jstring="[para(5096(a,1),171(a,1)),flip(b)].">
      <j1 rule="para" parents="5096 171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5129">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(5096(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5096 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5130">
    <literal><![CDATA[
      K(x,y) != z / u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5104(a,1),40(a,1))].">
      <j1 rule="para" parents="5104 40"/>
    </justification>
  </clause>

  <clause id="5131">
    <literal><![CDATA[
      (x / y) / T(x,y \ 1) = x \ (x / y)
    ]]></literal>
    <justification jstring="[para(4748(a,1),265(a,1,2))].">
      <j1 rule="para" parents="4748 265"/>
    </justification>
  </clause>

  <clause id="5133">
    <literal><![CDATA[
      (x \ y) * K(((x \ y) \ (x \ 1)) \ 1,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(4750(a,1),1420(a,1,2))].">
      <j1 rule="para" parents="4750 1420"/>
    </justification>
  </clause>

  <clause id="5134">
    <literal><![CDATA[
      (x / y) * K(((x / y) \ (1 / y)) \ 1,z) = T(x,z) / y
    ]]></literal>
    <justification jstring="[para(4750(a,1),1429(a,1,2))].">
      <j1 rule="para" parents="4750 1429"/>
    </justification>
  </clause>

  <clause id="5136">
    <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(4760(a,1),482(a,1,2,2))].">
      <j1 rule="para" parents="4760 482"/>
    </justification>
  </clause>

  <clause id="5137">
    <literal><![CDATA[
      T(x,y) \ (x * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(1172,a,4777,a)].">
      <j1 rule="hyper" parents="1172 4777"/>
    </justification>
  </clause>

  <clause id="5138">
    <literal><![CDATA[
      K(x,y) * (1 / y) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2855,a(flip),b,4777,a),flip(a)].">
      <j1 rule="hyper" parents="58 2855 4777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5139">
    <literal><![CDATA[
      K((x / y) / (y \ 1),z) = (T(x,z) / y) / (x / y)
    ]]></literal>
    <justification jstring="[hyper(117,a,4531,a(flip),b,4777,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="117 4531 4777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5140">
    <literal><![CDATA[
      x \ (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(4777(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4777 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5141">
    <literal><![CDATA[
      L(T(x \ y,z) \ u,x \ y,x) = y \ (x * (K(z,x \ y) * u))
    ]]></literal>
    <justification jstring="[para(4777(a,1),91(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4777 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5142">
    <literal><![CDATA[
      K(x,y) * (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(4777(a,1),1135(a,1))].">
      <j1 rule="para" parents="4777 1135"/>
    </justification>
  </clause>

  <clause id="5143">
    <literal><![CDATA[
      K(x,y) * (y \ z) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (T(y,x) \ z) = w
    ]]></literal>
    <justification jstring="[para(4777(a,1),1124(a,1))].">
      <j1 rule="para" parents="4777 1124"/>
    </justification>
  </clause>

  <clause id="5144">
    <literal><![CDATA[
      K(x,y) * T(T(y,x),z) = y * K(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4688(a,2),4777(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4688 4777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5145">
    <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,4778,a)].">
      <j1 rule="hyper" parents="117 101 4778"/>
    </justification>
  </clause>

  <clause id="5147">
    <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(4778(a,1),477(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4778 477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5148">
    <literal><![CDATA[
      K(x,y) * (K(z,T(y,x)) * u) = y * (T(T(y,x),z) \ u)
    ]]></literal>
    <justification jstring="[para(4777(a,1),4778(a,1,2))].">
      <j1 rule="para" parents="4777 4778"/>
    </justification>
  </clause>

  <clause id="5149">
    <literal><![CDATA[
      x \ (y * K(x,y)) = K(x,y) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,4779,a(flip),b,4737,a)].">
      <j1 rule="hyper" parents="116 4779 4737"/>
    </justification>
  </clause>

  <clause id="5150">
    <literal><![CDATA[
      ((x * y) * (z * K(y,z))) / (T(y,z) * z) = R(x,y,z * K(y,z))
    ]]></literal>
    <justification jstring="[para(4788(a,1),15(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4788 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5151">
    <literal><![CDATA[
      T(x,y * K(x,y)) / (T(x,y) * y) = x / ((y * K(x,y)) * x)
    ]]></literal>
    <justification jstring="[para(4788(a,1),4323(a,1,2))].">
      <j1 rule="para" parents="4788 4323"/>
    </justification>
  </clause>

  <clause id="5152">
    <literal><![CDATA[
      K(x,T(y,T(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4796,a,4791,a)].">
      <j1 rule="hyper" parents="4796 4791"/>
    </justification>
  </clause>

  <clause id="5153">
    <literal><![CDATA[
      T(x,y * K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4791(a,1),4397(a,1,2))].">
      <j1 rule="para" parents="4791 4397"/>
    </justification>
  </clause>

  <clause id="5154">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(4791(a,2),4725(a,1))].">
      <j1 rule="para" parents="4791 4725"/>
    </justification>
  </clause>

  <clause id="5155">
    <literal><![CDATA[
      K(x / y,T(z,y \ x)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),5152(a,1,2,2))].">
      <j1 rule="para" parents="107 5152"/>
    </justification>
  </clause>

  <clause id="5156">
    <literal><![CDATA[
      K(x,T(y,x / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4796,a,4793,a)].">
      <j1 rule="hyper" parents="4796 4793"/>
    </justification>
  </clause>

  <clause id="5157">
    <literal><![CDATA[
      K(x * y,T(y,x)) = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),5156(a,1,2,2))].">
      <j1 rule="para" parents="6 5156"/>
    </justification>
  </clause>

  <clause id="5158">
    <literal><![CDATA[
      K(x,(y \ x) \ x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4248(a,1),5156(a,1,2))].">
      <j1 rule="para" parents="4248 5156"/>
    </justification>
  </clause>

  <clause id="5159">
    <literal><![CDATA[
      K(x,x / y) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(75(a,1),5158(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 5158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5162">
    <literal><![CDATA[
      T(x,x \ y) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4819(a,1),3874(a,1,1))].">
      <j1 rule="para" parents="4819 3874"/>
    </justification>
  </clause>

  <clause id="5163">
    <literal><![CDATA[
      K(x,T(y,z)) * T(y,z) = T(y * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(4847,a,4829,a)].">
      <j1 rule="hyper" parents="4847 4829"/>
    </justification>
  </clause>

  <clause id="5164">
    <literal><![CDATA[
      T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(4830,a,4829,a)].">
      <j1 rule="hyper" parents="4830 4829"/>
    </justification>
  </clause>

  <clause id="5165">
    <literal><![CDATA[
      T(x * K(x * y,x),y * x) = x
    ]]></literal>
    <justification jstring="[hyper(4277,a,4829,a),flip(a)].">
      <j1 rule="hyper" parents="4277 4829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5166">
    <literal><![CDATA[
      T(x * K(x * y,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(4269,a,4829,a),flip(a)].">
      <j1 rule="hyper" parents="4269 4829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5167">
    <literal><![CDATA[
      T(x,y) != T(z,u)
    ]]></literal>
    <literal><![CDATA[
      T(z * K(y,z),u) = x
    ]]></literal>
    <justification jstring="[para(4829(a,1),44(a,2)),flip(b)].">
      <j1 rule="para" parents="4829 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5168">
    <literal><![CDATA[
      T(1 / x,(y * x) / y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(239,a,4848,a(flip),b,4698,a(flip))].">
      <j1 rule="hyper" parents="239 4848 4698"/>
    </justification>
  </clause>

  <clause id="5169">
    <literal><![CDATA[
      T(x,x \ K(x,y)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4864(a,1),2228(a,1,2))].">
      <j1 rule="para" parents="4864 2228"/>
    </justification>
  </clause>

  <clause id="5170">
    <literal><![CDATA[
      (x * y) \ K(x * y,y) = (L(y,x,y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(4332(a,1),4864(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4332 4864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5171">
    <literal><![CDATA[
      (x * K(y,x)) \ 1 = x \ K(x,y)
    ]]></literal>
    <justification jstring="[para(4711(a,1),4864(a,1,1))].">
      <j1 rule="para" parents="4711 4864"/>
    </justification>
  </clause>

  <clause id="5172">
    <literal><![CDATA[
      K(x,y) * K(x \ 1,x) = (x \ K(x,y)) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,4910,a(flip),b,85,a)].">
      <j1 rule="hyper" parents="119 4910 85"/>
    </justification>
  </clause>

  <clause id="5173">
    <literal><![CDATA[
      1 / (x * K(y,x)) = K(x,y) / x
    ]]></literal>
    <justification jstring="[para(4711(a,1),4911(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4711 4911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5175">
    <literal><![CDATA[
      K(x,y \ 1) * (y \ x) = x * ((y \ x) / x)
    ]]></literal>
    <justification jstring="[para(4441(a,1),4962(a,1,1))].">
      <j1 rule="para" parents="4441 4962"/>
    </justification>
  </clause>

  <clause id="5176">
    <literal><![CDATA[
      K(((x / y) \ 1) \ y,(x / y) \ 1) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(3890,a,4972,a)].">
      <j1 rule="hyper" parents="3890 4972"/>
    </justification>
  </clause>

  <clause id="5177">
    <literal><![CDATA[
      x * (K(x \ 1,x) * K(y,y \ (1 / (1 / x)))) = y * ((1 / (1 / x)) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2837,a,b,4974,a)].">
      <j1 rule="hyper" parents="58 2837 4974"/>
    </justification>
  </clause>

  <clause id="5178">
    <literal><![CDATA[
      T(x,y) * K(x * y,(x * y) \ T(x,y)) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(4323(a,1),4974(a,2,2))].">
      <j1 rule="para" parents="4323 4974"/>
    </justification>
  </clause>

  <clause id="5180">
    <literal><![CDATA[
      K(x * y,x / (x * y)) = K(x * y,1 / y)
    ]]></literal>
    <justification jstring="[para(6(a,1),5033(a,1,2,1))].">
      <j1 rule="para" parents="6 5033"/>
    </justification>
  </clause>

  <clause id="5181">
    <literal><![CDATA[
      K(x,1 / (y \ x)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(72(a,1),5033(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 5033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5186">
    <literal><![CDATA[
      x \ y != K(x,z) * u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) \ y = u
    ]]></literal>
    <justification jstring="[para(5042(a,1),38(a,1))].">
      <j1 rule="para" parents="5042 38"/>
    </justification>
  </clause>

  <clause id="5187">
    <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(5042(a,1),92(a,2,1))].">
      <j1 rule="para" parents="5042 92"/>
    </justification>
  </clause>

  <clause id="5188">
    <literal><![CDATA[
      L(x \ (T(y,z) \ u),x,K(y,z)) = (K(y,z) * x) \ (y \ u)
    ]]></literal>
    <justification jstring="[para(5042(a,1),92(a,2,2))].">
      <j1 rule="para" parents="5042 92"/>
    </justification>
  </clause>

  <clause id="5189">
    <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),5059(a,1,2,1))].">
      <j1 rule="para" parents="22 5059"/>
    </justification>
  </clause>

  <clause id="5191">
    <literal><![CDATA[
      K(x,T(y,z)) * K(z,y) = T(T(y,z),x) \ y
    ]]></literal>
    <justification jstring="[hyper(119,a,4689,a,b,5091,a)].">
      <j1 rule="hyper" parents="119 4689 5091"/>
    </justification>
  </clause>

  <clause id="5192">
    <literal><![CDATA[
      T(x,y) \ T(x,z) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4688,a,b,5091,a),flip(a)].">
      <j1 rule="hyper" parents="119 4688 5091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5193">
    <literal><![CDATA[
      K(x,y \ z) * T(y,y \ z) = T(y \ z,x) \ z
    ]]></literal>
    <justification jstring="[hyper(119,a,106,a,b,5091,a)].">
      <j1 rule="hyper" parents="119 106 5091"/>
    </justification>
  </clause>

  <clause id="5194">
    <literal><![CDATA[
      T(x,y) \ (z * x) = K(y,x) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,17,a,b,5091,a),flip(a)].">
      <j1 rule="hyper" parents="119 17 5091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5195">
    <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,5091,a),flip(a)].">
      <j1 rule="hyper" parents="119 13 5091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5196">
    <literal><![CDATA[
      T(x,y) \ (T(x,z) * u) = K(y,x) * (K(x,z) * u)
    ]]></literal>
    <justification jstring="[hyper(119,a,4736,a(flip),b,5091,a),flip(a)].">
      <j1 rule="hyper" parents="119 4736 5091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5197">
    <literal><![CDATA[
      x \ (K(y,x) * z) = K(y,x) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5068,a,b,5093,a)].">
      <j1 rule="hyper" parents="320 5068 5093"/>
    </justification>
  </clause>

  <clause id="5198">
    <literal><![CDATA[
      ((x \ y) \ y) \ z = K(x \ y,x) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,311,a(flip),b,5093,a)].">
      <j1 rule="hyper" parents="320 311 5093"/>
    </justification>
  </clause>

  <clause id="5199">
    <literal><![CDATA[
      x * (K(y,x) * (x \ z)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,5093,a,b,5068,a)].">
      <j1 rule="hyper" parents="119 5093 5068"/>
    </justification>
  </clause>

  <clause id="5201">
    <literal><![CDATA[
      K(x,y) * (T(y,x) \ z) = T(T(y,x),x) \ z
    ]]></literal>
    <justification jstring="[para(4867(a,1),5093(a,1,1))].">
      <j1 rule="para" parents="4867 5093"/>
    </justification>
  </clause>

  <clause id="5202">
    <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(5094(a,1),1624(a,1,2,2,1))].">
      <j1 rule="para" parents="5094 1624"/>
    </justification>
  </clause>

  <clause id="5203">
    <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(5094(a,1),1839(a,1,2,2,1))].">
      <j1 rule="para" parents="5094 1839"/>
    </justification>
  </clause>

  <clause id="5204">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5099(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5099 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5207">
    <literal><![CDATA[
      L(x,K(y,z) \ 1,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(29,a,438,a(flip),b,5122,a),flip(a)].">
      <j1 rule="hyper" parents="29 438 5122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5208">
    <literal><![CDATA[
      L(x,K(y,z),K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(4929(a,1),5207(a,1,2))].">
      <j1 rule="para" parents="4929 5207"/>
    </justification>
  </clause>

  <clause id="5210">
    <literal><![CDATA[
      L(x,K(y,z),K(z,y)) / (K(u,w) * x) = K(w,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,5208,a,b,5095,a)].">
      <j1 rule="hyper" parents="117 5208 5095"/>
    </justification>
  </clause>

  <clause id="5211">
    <literal><![CDATA[
      K(x,y) * (x / y) = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(4435,a,5123,a),flip(a)].">
      <j1 rule="hyper" parents="4435 5123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5212">
    <literal><![CDATA[
      K(x,y) * (x / y) = T(x,y) / y
    ]]></literal>
    <justification jstring="[hyper(4433,a,5123,a),flip(a)].">
      <j1 rule="hyper" parents="4433 5123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5213">
    <literal><![CDATA[
      K(x,y) * (((x * y) / x) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(4402,a,5123,a),flip(a)].">
      <j1 rule="hyper" parents="4402 5123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5214">
    <literal><![CDATA[
      x \ T(x * y,x) = K(x * y,x) * y
    ]]></literal>
    <justification jstring="[hyper(4258,a,5123,a)].">
      <j1 rule="hyper" parents="4258 5123"/>
    </justification>
  </clause>

  <clause id="5216">
    <literal><![CDATA[
      (x * y) / (K(z,x) * y) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,5123,a)].">
      <j1 rule="hyper" parents="131 5123"/>
    </justification>
  </clause>

  <clause id="5217">
    <literal><![CDATA[
      T(x,y) / (K(z,x) * K(x,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,4714,a,b,5123,a)].">
      <j1 rule="hyper" parents="117 4714 5123"/>
    </justification>
  </clause>

  <clause id="5218">
    <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,5123,a)].">
      <j1 rule="hyper" parents="117 101 5123"/>
    </justification>
  </clause>

  <clause id="5219">
    <literal><![CDATA[
      K(x,y) * (y * z) = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5123,a(flip),b,5060,a)].">
      <j1 rule="hyper" parents="119 5123 5060"/>
    </justification>
  </clause>

  <clause id="5220">
    <literal><![CDATA[
      x * (y * (K(x,y) * z)) = T(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(5123(a,1),4512(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5123 4512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5221">
    <literal><![CDATA[
      K(x,y) * T(x,T(y,z)) = T(T(x,y),T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,4651,a(flip),b,5137,a),flip(a)].">
      <j1 rule="hyper" parents="58 4651 5137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5222">
    <literal><![CDATA[
      x * (K(x * y,x) * y) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5137,a(flip),b,4208,a(flip))].">
      <j1 rule="hyper" parents="119 5137 4208"/>
    </justification>
  </clause>

  <clause id="5223">
    <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),5137(a,1,1))].">
      <j1 rule="para" parents="20 5137"/>
    </justification>
  </clause>

  <clause id="5224">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(5137(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5137 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5225">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * (T(y,x) \ z) = u
    ]]></literal>
    <justification jstring="[para(5137(a,1),1131(a,1))].">
      <j1 rule="para" parents="5137 1131"/>
    </justification>
  </clause>

  <clause id="5226">
    <literal><![CDATA[
      T(x,y) * (1 / y) = x * (1 / T(y,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,5138,a(flip),b,4736,a),flip(a)].">
      <j1 rule="hyper" parents="119 5138 4736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5228">
    <literal><![CDATA[
      K(x * y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(4454,a,5157,a),flip(a)].">
      <j1 rule="hyper" parents="4454 5157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5229">
    <literal><![CDATA[
      (x \ K(x,y)) * T((x \ 1) \ 1,z) = T(x,z) * (x \ K(x,y))
    ]]></literal>
    <justification jstring="[para(5169(a,1),236(a,1,2,1))].">
      <j1 rule="para" parents="5169 236"/>
    </justification>
  </clause>

  <clause id="5230">
    <literal><![CDATA[
      1 / (x \ K(x,y)) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(197,a,5171,a)].">
      <j1 rule="hyper" parents="197 5171"/>
    </justification>
  </clause>

  <clause id="5231">
    <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(5171(a,1),3110(a,2,2,2))].">
      <j1 rule="para" parents="5171 3110"/>
    </justification>
  </clause>

  <clause id="5232">
    <literal><![CDATA[
      (K(x,y) / x) \ 1 = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(188,a,5173,a)].">
      <j1 rule="hyper" parents="188 5173"/>
    </justification>
  </clause>

  <clause id="5233">
    <literal><![CDATA[
      1 / ((x \ 1) * K(y,x \ 1)) = K(1 / x,y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(3293(a,2),5173(a,2,1))].">
      <j1 rule="para" parents="3293 5173"/>
    </justification>
  </clause>

  <clause id="5234">
    <literal><![CDATA[
      K(1 / x,y) / (1 / x) = 1 / (K(y,x \ 1) / x)
    ]]></literal>
    <justification jstring="[para(3537(a,1),5173(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3537 5173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5235">
    <literal><![CDATA[
      K(((x * K(y,x)) \ 1) * z,u) = K((K(x,y) / x) * z,u)
    ]]></literal>
    <justification jstring="[para(5173(a,1),3939(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5173 3939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5236">
    <literal><![CDATA[
      (x / T(y,x)) * L(z,x / y,K(x,y)) = K(x,y) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(5211(a,1),90(a,1,1))].">
      <j1 rule="para" parents="5211 90"/>
    </justification>
  </clause>

  <clause id="5237">
    <literal><![CDATA[
      R(K(x,y),x / y,z) \ ((x / T(y,x)) * z) = (x / y) * z
    ]]></literal>
    <justification jstring="[para(5211(a,1),184(a,1,2,1))].">
      <j1 rule="para" parents="5211 184"/>
    </justification>
  </clause>

  <clause id="5238">
    <literal><![CDATA[
      1 / x != y * K(z,y)
    ]]></literal>
    <literal><![CDATA[
      y \ K(y,z) = x
    ]]></literal>
    <justification jstring="[para(5230(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="5230 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5239">
    <literal><![CDATA[
      L(x,y,z) \ K(x,L(x,u,w) \ 1) = (1 / x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4800,a,b,3377,a)].">
      <j1 rule="hyper" parents="116 4800 3377"/>
    </justification>
  </clause>

  <clause id="5240">
    <literal><![CDATA[
      L(x,y,z) \ K(x,L(x,u,w) \ 1) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4800(a,2),3766(a,1,2))].">
      <j1 rule="para" parents="4800 3766"/>
    </justification>
  </clause>

  <clause id="5242">
    <literal><![CDATA[
      (x \ 1) * ((y * ((x \ 1) \ 1)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(1414(a,2),4881(a,1))].">
      <j1 rule="para" parents="1414 4881"/>
    </justification>
  </clause>

  <clause id="5243">
    <literal><![CDATA[
      T(K(x * (1 / y),y \ 1) / y,x) = R(1 / y,x,1 / y)
    ]]></literal>
    <justification jstring="[para(3537(a,1),4891(a,1,1))].">
      <j1 rule="para" parents="3537 4891"/>
    </justification>
  </clause>

  <clause id="5244">
    <literal><![CDATA[
      K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(75(a,1),5001(a,1,1,1))].">
      <j1 rule="para" parents="75 5001"/>
    </justification>
  </clause>

  <clause id="5245">
    <literal><![CDATA[
      K(L(x \ 1,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(1 / x,y,z),u) = w
    ]]></literal>
    <justification jstring="[para(3278(a,1),5001(a,1,1))].">
      <j1 rule="para" parents="3278 5001"/>
    </justification>
  </clause>

  <clause id="5246">
    <literal><![CDATA[
      T(x,x * y) * K(y,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2879,a,5051,a)].">
      <j1 rule="hyper" parents="2879 5051"/>
    </justification>
  </clause>

  <clause id="5247">
    <literal><![CDATA[
      K(x,y) = T(y,y * x) \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5051,a(flip),b,2876,a),flip(a)].">
      <j1 rule="hyper" parents="116 5051 2876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5248">
    <literal><![CDATA[
      T(x,y) * K(x * y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2879,a,5054,a)].">
      <j1 rule="hyper" parents="2879 5054"/>
    </justification>
  </clause>

  <clause id="5249">
    <literal><![CDATA[
      T(x,x * y) \ T(x,y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5054,a(flip),b,4777,a),flip(a)].">
      <j1 rule="hyper" parents="116 5054 4777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5250">
    <literal><![CDATA[
      T(x,y) \ R(x,y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5054,a(flip),b,2876,a)].">
      <j1 rule="hyper" parents="116 5054 2876"/>
    </justification>
  </clause>

  <clause id="5251">
    <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),5125(a,1))].">
      <j1 rule="para" parents="17 5125"/>
    </justification>
  </clause>

  <clause id="5252">
    <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(248(a,1),5154(a,1,2))].">
      <j1 rule="para" parents="248 5154"/>
    </justification>
  </clause>

  <clause id="5253">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = T(R(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(5166(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5166 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5254">
    <literal><![CDATA[
      K(x,x * y) * K(y,x) = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5246,a(flip),b,4737,a),flip(a)].">
      <j1 rule="hyper" parents="116 5246 4737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5255">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5248,a(flip),b,4737,a),flip(a)].">
      <j1 rule="hyper" parents="116 5248 4737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5256">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = L(K(y * z,y),T(y,z),x)
    ]]></literal>
    <justification jstring="[para(5248(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5248 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5257">
    <literal><![CDATA[
      x \ R(y,z,y) != K(y * z,y)
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = x
    ]]></literal>
    <justification jstring="[para(5250(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="5250 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5258">
    <literal><![CDATA[
      K(x \ y,x) != 1
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * x = y
    ]]></literal>
    <justification jstring="[para(4671(a,1),125(a,1)),flip(b)].">
      <j1 rule="para" parents="4671 125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5259">
    <literal><![CDATA[
      K(x \ (x * y),x) = (y * x) * ((x * y) \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),4682(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 4682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5260">
    <literal><![CDATA[
      (x * (y * T(y \ z,u))) / (x * z) = K((x * z) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(918(a,1),4693(a,1,1))].">
      <j1 rule="para" parents="918 4693"/>
    </justification>
  </clause>

  <clause id="5262">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / z = K(y,(x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2418,a(flip),b,4700,a)].">
      <j1 rule="hyper" parents="58 2418 4700"/>
    </justification>
  </clause>

  <clause id="5264">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(4700(a,1),1089(a,2,2))].">
      <j1 rule="para" parents="4700 1089"/>
    </justification>
  </clause>

  <clause id="5265">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = K(z,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(4700(a,1),1710(a,2,1))].">
      <j1 rule="para" parents="4700 1710"/>
    </justification>
  </clause>

  <clause id="5266">
    <literal><![CDATA[
      K(x,(y * x) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      y * (x * ((y \ 1) / x)) = z
    ]]></literal>
    <justification jstring="[para(4700(a,1),963(a,1))].">
      <j1 rule="para" parents="4700 963"/>
    </justification>
  </clause>

  <clause id="5267">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) * (z * u) = ((y * z) * ((x * ((y * z) \ z)) / x)) * u
    ]]></literal>
    <justification jstring="[para(4700(a,1),3243(a,1,1))].">
      <j1 rule="para" parents="4700 3243"/>
    </justification>
  </clause>

  <clause id="5268">
    <literal><![CDATA[
      L(x,y,z) \ K(x,L(x,y,z) \ 1) = (L(x,y,z) \ x) / x
    ]]></literal>
    <justification jstring="[para(1404(a,1),4718(a,2,1))].">
      <j1 rule="para" parents="1404 4718"/>
    </justification>
  </clause>

  <clause id="5269">
    <literal><![CDATA[
      K(x,x * (y \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4688,a,b,4728,a),flip(a)].">
      <j1 rule="hyper" parents="320 4688 4728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5270">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4688,a,b,4732,a),flip(a)].">
      <j1 rule="hyper" parents="320 4688 4732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5271">
    <literal><![CDATA[
      K(x,y * K(z,1 / z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1780(a,2),5270(a,1,2,2))].">
      <j1 rule="para" parents="1780 5270"/>
    </justification>
  </clause>

  <clause id="5272">
    <literal><![CDATA[
      K(x,y * K(z \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1787(a,1),5270(a,1,2,2))].">
      <j1 rule="para" parents="1787 5270"/>
    </justification>
  </clause>

  <clause id="5273">
    <literal><![CDATA[
      K(x,K(y,y \ 1) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2169(a,2),5270(a,1,2))].">
      <j1 rule="para" parents="2169 5270"/>
    </justification>
  </clause>

  <clause id="5274">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(2660(a,1),5270(a,1,2))].">
      <j1 rule="para" parents="2660 5270"/>
    </justification>
  </clause>

  <clause id="5275">
    <literal><![CDATA[
      K(x,y * T(z,z \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(2661(a,1),5270(a,1,2))].">
      <j1 rule="para" parents="2661 5270"/>
    </justification>
  </clause>

  <clause id="5276">
    <literal><![CDATA[
      K(x,K(y \ 1,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2675(a,1),5270(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2675 5270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5277">
    <literal><![CDATA[
      K(x,y * (1 / z)) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(2674(a,1),5270(a,1,2))].">
      <j1 rule="para" parents="2674 5270"/>
    </justification>
  </clause>

  <clause id="5278">
    <literal><![CDATA[
      K(x,y / (1 / z)) = K(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(2683(a,1),5270(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2683 5270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5279">
    <literal><![CDATA[
      K(x,(y / (z \ 1)) * (1 / z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2699(a,2),5270(a,1,2))].">
      <j1 rule="para" parents="2699 5270"/>
    </justification>
  </clause>

  <clause id="5280">
    <literal><![CDATA[
      K(x,(y \ 1) * (y * z)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(2681(a,1),5270(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2681 5270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5281">
    <literal><![CDATA[
      K(x,T(y,y \ 1) * z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(2778(a,1),5270(a,1,2))].">
      <j1 rule="para" parents="2778 5270"/>
    </justification>
  </clause>

  <clause id="5283">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2818(a,1),5270(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2818 5270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5284">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2825(a,1),5270(a,1,2))].">
      <j1 rule="para" parents="2825 5270"/>
    </justification>
  </clause>

  <clause id="5285">
    <literal><![CDATA[
      K(x,(1 / y) \ z) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2928(a,1),5270(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2928 5270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5286">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ 1) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(3402(a,2),5270(a,1,2))].">
      <j1 rule="para" parents="3402 5270"/>
    </justification>
  </clause>

  <clause id="5287">
    <literal><![CDATA[
      K(x,(K(y \ 1,y) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(3710(a,2),5270(a,1,2))].">
      <j1 rule="para" parents="3710 5270"/>
    </justification>
  </clause>

  <clause id="5288">
    <literal><![CDATA[
      K(x,((1 / y) * z) \ u) = K(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[para(3722(a,1),5270(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3722 5270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5289">
    <literal><![CDATA[
      K(x,y * (z * K(u,1 / u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3397(a,1),5271(a,1,2))].">
      <j1 rule="para" parents="3397 5271"/>
    </justification>
  </clause>

  <clause id="5290">
    <literal><![CDATA[
      K(x,y * (z * K(u \ 1,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3361(a,1),5272(a,1,2))].">
      <j1 rule="para" parents="3361 5272"/>
    </justification>
  </clause>

  <clause id="5291">
    <literal><![CDATA[
      K(x,y \ (z / (1 / u))) = K(x,y \ (z / (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3413(a,1),5272(a,1,2))].">
      <j1 rule="para" parents="3413 5272"/>
    </justification>
  </clause>

  <clause id="5292">
    <literal><![CDATA[
      K(x,K(y,1 / y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1780(a,2),5273(a,1,2,1))].">
      <j1 rule="para" parents="1780 5273"/>
    </justification>
  </clause>

  <clause id="5293">
    <literal><![CDATA[
      K(x,y \ ((1 / z) * u)) = K(x,y \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(3431(a,1),5273(a,1,2))].">
      <j1 rule="para" parents="3431 5273"/>
    </justification>
  </clause>

  <clause id="5294">
    <literal><![CDATA[
      K(x,y * (z * (1 / u))) = K(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3435(a,1),5273(a,1,2))].">
      <j1 rule="para" parents="3435 5273"/>
    </justification>
  </clause>

  <clause id="5295">
    <literal><![CDATA[
      K(x,y * (z / (1 / u))) = K(x,y * (z / (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3436(a,1),5273(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3436 5273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5296">
    <literal><![CDATA[
      K(x,y * ((1 / z) \ u)) = K(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(3438(a,1),5273(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3438 5273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5297">
    <literal><![CDATA[
      K(x,y * (z * ((u \ 1) \ 1))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(3443(a,1),5273(a,1,2))].">
      <j1 rule="para" parents="3443 5273"/>
    </justification>
  </clause>

  <clause id="5298">
    <literal><![CDATA[
      K(x,y \ (z * ((1 / u) \ w))) = K(x,y \ (z * ((u \ 1) \ w)))
    ]]></literal>
    <justification jstring="[para(3448(a,1),5273(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3448 5273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5299">
    <literal><![CDATA[
      K(x,y / (K(z \ 1,z) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(3725(a,2),5273(a,1,2))].">
      <j1 rule="para" parents="3725 5273"/>
    </justification>
  </clause>

  <clause id="5300">
    <literal><![CDATA[
      K(x,(y * (z / (1 / u))) \ w) = K(x,(y * (z / (u \ 1))) \ w)
    ]]></literal>
    <justification jstring="[para(3778(a,1),5273(a,1,2))].">
      <j1 rule="para" parents="3778 5273"/>
    </justification>
  </clause>

  <clause id="5301">
    <literal><![CDATA[
      K(x,T(y * K(z,z \ 1),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(4608(a,2),5273(a,1,2))].">
      <j1 rule="para" parents="4608 5273"/>
    </justification>
  </clause>

  <clause id="5302">
    <literal><![CDATA[
      K(x,y \ (z * (1 / u))) = K(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3429(a,1),5276(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3429 5276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5303">
    <literal><![CDATA[
      K(x,(K(y \ 1,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[para(3645(a,2),5276(a,1,2))].">
      <j1 rule="para" parents="3645 5276"/>
    </justification>
  </clause>

  <clause id="5304">
    <literal><![CDATA[
      K(x,y / (K(z,z \ 1) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(3782(a,2),5276(a,1,2))].">
      <j1 rule="para" parents="3782 5276"/>
    </justification>
  </clause>

  <clause id="5305">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ w) = K(x,R(y \ 1,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(3792(a,1),5276(a,1,2))].">
      <j1 rule="para" parents="3792 5276"/>
    </justification>
  </clause>

  <clause id="5306">
    <literal><![CDATA[
      K(x,K(y,1 / y) / z) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(3618(a,1),5292(a,1,2))].">
      <j1 rule="para" parents="3618 5292"/>
    </justification>
  </clause>

  <clause id="5307">
    <literal><![CDATA[
      K(x,(y \ z) / z) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,4688,a,b,4746,a),flip(a)].">
      <j1 rule="hyper" parents="320 4688 4746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5308">
    <literal><![CDATA[
      K(x,(y \ z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(4746(a,2),4797(a,1))].">
      <j1 rule="para" parents="4746 4797"/>
    </justification>
  </clause>

  <clause id="5311">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),5307(a,1,2,1))].">
      <j1 rule="para" parents="4 5307"/>
    </justification>
  </clause>

  <clause id="5312">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),5307(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 5307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5313">
    <literal><![CDATA[
      K(x,y \ 1) * (((y \ z) / z) \ u) = T((y \ z) / z,x) \ u
    ]]></literal>
    <justification jstring="[para(5307(a,1),5093(a,1,1))].">
      <j1 rule="para" parents="5307 5093"/>
    </justification>
  </clause>

  <clause id="5314">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3528,a,b,5311,a),flip(a)].">
      <j1 rule="hyper" parents="320 3528 5311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5315">
    <literal><![CDATA[
      K(x * y,x \ 1) * ((x * y) \ y) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(5311(a,1),4818(a,1,1))].">
      <j1 rule="para" parents="5311 4818"/>
    </justification>
  </clause>

  <clause id="5316">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(z / y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,4929,a,b,5312,a),flip(a)].">
      <j1 rule="hyper" parents="320 4929 5312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5317">
    <literal><![CDATA[
      K(x,1 / (y / z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3528,a,b,5312,a)].">
      <j1 rule="hyper" parents="58 3528 5312"/>
    </justification>
  </clause>

  <clause id="5318">
    <literal><![CDATA[
      K(x,y / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(5314(a,2),5036(a,1))].">
      <j1 rule="para" parents="5314 5036"/>
    </justification>
  </clause>

  <clause id="5319">
    <literal><![CDATA[
      K((x * y) / x,1 / ((x * y) / x)) = K(y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3018,a(flip),b,5317,a),flip(a)].">
      <j1 rule="hyper" parents="320 3018 5317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5320">
    <literal><![CDATA[
      K(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ 1) = u
    ]]></literal>
    <justification jstring="[para(5317(a,1),5036(a,1))].">
      <j1 rule="para" parents="5317 5036"/>
    </justification>
  </clause>

  <clause id="5321">
    <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(4752(a,1),3574(a,2,1,2,1))].">
      <j1 rule="para" parents="4752 3574"/>
    </justification>
  </clause>

  <clause id="5322">
    <literal><![CDATA[
      K((1 / x) \ y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4689,a,b,4769,a),flip(a)].">
      <j1 rule="hyper" parents="320 4689 4769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5323">
    <literal><![CDATA[
      K((x \ 1) \ y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3940,a(flip),b,5322,a)].">
      <j1 rule="hyper" parents="58 3940 5322"/>
    </justification>
  </clause>

  <clause id="5324">
    <literal><![CDATA[
      K(x * (y \ 1),x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),5322(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 5322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5325">
    <literal><![CDATA[
      K((x \ 1) \ y,y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5228,a,b,5323,a),flip(a)].">
      <j1 rule="hyper" parents="320 5228 5323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5326">
    <literal><![CDATA[
      K((x \ 1) * y,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5228,a,b,5324,a)].">
      <j1 rule="hyper" parents="58 5228 5324"/>
    </justification>
  </clause>

  <clause id="5327">
    <literal><![CDATA[
      K(((x * y) / x) \ z,z) = K(z * (y \ K(y,x)),z)
    ]]></literal>
    <justification jstring="[para(4864(a,1),5324(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4864 5324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5328">
    <literal><![CDATA[
      T(x * K(y \ x,x),y \ 1) = R(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(5324(a,1),5166(a,1,1,2))].">
      <j1 rule="para" parents="5324 5166"/>
    </justification>
  </clause>

  <clause id="5329">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x * y,y) = T((x \ 1) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5325,a(flip),b,4688,a(flip))].">
      <j1 rule="hyper" parents="119 5325 4688"/>
    </justification>
  </clause>

  <clause id="5330">
    <literal><![CDATA[
      K((1 / x) * y,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),5325(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 5325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5331">
    <literal><![CDATA[
      (x * y) / (((z * x) / z) * y) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(616,a,4773,a)].">
      <j1 rule="hyper" parents="616 4773"/>
    </justification>
  </clause>

  <clause id="5332">
    <literal><![CDATA[
      K(x,y) * (((y * x) / y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(584,a,4773,a),flip(a)].">
      <j1 rule="hyper" parents="584 4773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5333">
    <literal><![CDATA[
      (x \ y) * ((y / x) \ z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),4773(a,1,2,1,1))].">
      <j1 rule="para" parents="5 4773"/>
    </justification>
  </clause>

  <clause id="5334">
    <literal><![CDATA[
      x * ((y / (y / x)) \ z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[para(4302(a,1),4773(a,1,2,1))].">
      <j1 rule="para" parents="4302 4773"/>
    </justification>
  </clause>

  <clause id="5335">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) = K(z,x / y)
    ]]></literal>
    <justification jstring="[para(4776(a,1),5104(a,1,2))].">
      <j1 rule="para" parents="4776 5104"/>
    </justification>
  </clause>

  <clause id="5336">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x / y) = u
    ]]></literal>
    <justification jstring="[para(4776(a,1),5112(a,1,2))].">
      <j1 rule="para" parents="4776 5112"/>
    </justification>
  </clause>

  <clause id="5337">
    <literal><![CDATA[
      (x * K(y,x)) \ y = x \ (y * K(x,y))
    ]]></literal>
    <justification jstring="[para(4711(a,1),4789(a,1,1))].">
      <j1 rule="para" parents="4711 4789"/>
    </justification>
  </clause>

  <clause id="5338">
    <literal><![CDATA[
      K(x,y) / (1 / T(y,x)) = 1 / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(197,a,4825,a)].">
      <j1 rule="hyper" parents="197 4825"/>
    </justification>
  </clause>

  <clause id="5339">
    <literal><![CDATA[
      T(x * K(y * R(x,z,u),x),y) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(30,a,1883,a,b,4832,a),flip(a)].">
      <j1 rule="hyper" parents="30 1883 4832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5340">
    <literal><![CDATA[
      T(x * K(y \ x,x),y \ 1) = R(x,x \ (y \ x),x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4481,a,b,4833,a),flip(a)].">
      <j1 rule="hyper" parents="320 4481 4833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5341">
    <literal><![CDATA[
      T(x,y) \ T(x * K(z,x),y) = K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,4833,a,b,4711,a(flip))].">
      <j1 rule="hyper" parents="116 4833 4711"/>
    </justification>
  </clause>

  <clause id="5342">
    <literal><![CDATA[
      T(x * K(y,x),z) \ T(x,z) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(4833(a,2),4751(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4833 4751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5343">
    <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(4833(a,2),4831(a,1))].">
      <j1 rule="para" parents="4833 4831"/>
    </justification>
  </clause>

  <clause id="5344">
    <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(4833(a,2),4881(a,1,2))].">
      <j1 rule="para" parents="4833 4881"/>
    </justification>
  </clause>

  <clause id="5345">
    <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(4851(a,1),764(a,1,1))].">
      <j1 rule="para" parents="4851 764"/>
    </justification>
  </clause>

  <clause id="5346">
    <literal><![CDATA[
      K(x,y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(4905,a,4866,a)].">
      <j1 rule="hyper" parents="4905 4866"/>
    </justification>
  </clause>

  <clause id="5347">
    <literal><![CDATA[
      K(x,x * (y / x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),5346(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 5346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5348">
    <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),5346(a,2,2))].">
      <j1 rule="para" parents="80 5346"/>
    </justification>
  </clause>

  <clause id="5349">
    <literal><![CDATA[
      K(x,T(y * x,z)) = K(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[para(4542(a,1),5347(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4542 5347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5350">
    <literal><![CDATA[
      K(x,(1 / x) * (y * x)) = K(x,L(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[para(2798(a,1),4870(a,1,2))].">
      <j1 rule="para" parents="2798 4870"/>
    </justification>
  </clause>

  <clause id="5351">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * T(y,x) = T(y,x) * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(4922(a,1),636(a,1,1,1))].">
      <j1 rule="para" parents="4922 636"/>
    </justification>
  </clause>

  <clause id="5352">
    <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(4922(a,1),1458(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4922 1458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5356">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(3770,a,4952,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3770 4952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5357">
    <literal><![CDATA[
      x * ((y * (x / y)) \ y) = x / (x / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5032,a,b,xx)].">
      <j1 rule="hyper" parents="119 5032"/>
    </justification>
  </clause>

  <clause id="5358">
    <literal><![CDATA[
      x \ (y \ ((y * z) / y)) = x \ (K(y,z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(116,a,5047,a,b,5,a)].">
      <j1 rule="hyper" parents="116 5047 5"/>
    </justification>
  </clause>

  <clause id="5359">
    <literal><![CDATA[
      L(x \ (y \ z),x,K(y,z)) = (K(y,z) * x) \ (y \ ((y * z) / y))
    ]]></literal>
    <justification jstring="[para(5047(a,2),92(a,2,2))].">
      <j1 rule="para" parents="5047 92"/>
    </justification>
  </clause>

  <clause id="5360">
    <literal><![CDATA[
      (x * K(y,x)) \ z = K(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4857,a(flip),b,5049,a)].">
      <j1 rule="hyper" parents="58 4857 5049"/>
    </justification>
  </clause>

  <clause id="5361">
    <literal><![CDATA[
      K(x \ y,x) * ((x \ y) \ z) = (y / x) \ z
    ]]></literal>
    <justification jstring="[para(5(a,1),5049(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 5049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5363">
    <literal><![CDATA[
      (x / (x / y)) \ z = K(y,y \ x) * (y \ z)
    ]]></literal>
    <justification jstring="[para(4302(a,1),5049(a,1,1))].">
      <j1 rule="para" parents="4302 5049"/>
    </justification>
  </clause>

  <clause id="5366">
    <literal><![CDATA[
      ((x * y) / x) * z = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5095,a(flip),b,5065,a)].">
      <j1 rule="hyper" parents="119 5095 5065"/>
    </justification>
  </clause>

  <clause id="5367">
    <literal><![CDATA[
      K(x,y) * T(x,z) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3315,a(flip),b,5073,a)].">
      <j1 rule="hyper" parents="320 3315 5073"/>
    </justification>
  </clause>

  <clause id="5368">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) / T(x,y) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,3315,a(flip),b,5073,a)].">
      <j1 rule="hyper" parents="117 3315 5073"/>
    </justification>
  </clause>

  <clause id="5369">
    <literal><![CDATA[
      K(x,y) * T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(5073(a,2),3322(a,1))].">
      <j1 rule="para" parents="5073 3322"/>
    </justification>
  </clause>

  <clause id="5370">
    <literal><![CDATA[
      K(x,(y \ z) / (y \ 1)) * (y \ T(z,x)) = y \ z
    ]]></literal>
    <justification jstring="[hyper(1043,a,5074,a)].">
      <j1 rule="hyper" parents="1043 5074"/>
    </justification>
  </clause>

  <clause id="5371">
    <literal><![CDATA[
      T(x,x \ (y * x)) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),5162(a,2,2))].">
      <j1 rule="para" parents="6 5162"/>
    </justification>
  </clause>

  <clause id="5372">
    <literal><![CDATA[
      T(x,y) \ T(x,z) = K(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,1991,a,b,5192,a),flip(a)].">
      <j1 rule="hyper" parents="320 1991 5192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5373">
    <literal><![CDATA[
      x * (K(y,x) * T(z,x)) = K(y,x) * (z * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5194,a(flip),b,5068,a)].">
      <j1 rule="hyper" parents="119 5194 5068"/>
    </justification>
  </clause>

  <clause id="5374">
    <literal><![CDATA[
      x * (K(y,x) * (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5197(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5197 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5375">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(584,a,5213,a),flip(a)].">
      <j1 rule="hyper" parents="584 5213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5376">
    <literal><![CDATA[
      K(x,x \ y) * ((y / x) \ z) = (x \ y) \ z
    ]]></literal>
    <justification jstring="[para(5(a,1),5213(a,1,2,1,1))].">
      <j1 rule="para" parents="5 5213"/>
    </justification>
  </clause>

  <clause id="5377">
    <literal><![CDATA[
      K(x \ y,x) * ((y / (y / x)) \ z) = x \ z
    ]]></literal>
    <justification jstring="[para(4302(a,1),5213(a,1,2,1))].">
      <j1 rule="para" parents="4302 5213"/>
    </justification>
  </clause>

  <clause id="5378">
    <literal><![CDATA[
      K(x,y) * (K((x * y) / x,z) * u) = y \ (T((x * y) / x,z) * u)
    ]]></literal>
    <justification jstring="[para(4736(a,1),5213(a,1,2))].">
      <j1 rule="para" parents="4736 5213"/>
    </justification>
  </clause>

  <clause id="5379">
    <literal><![CDATA[
      x \ T(x * y,x) != y * z
    ]]></literal>
    <literal><![CDATA[
      T(K(x * y,x),y) = z
    ]]></literal>
    <justification jstring="[para(5214(a,2),240(a,2)),flip(a)].">
      <j1 rule="para" parents="5214 240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5380">
    <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(4775(a,1),5217(a,1,1))].">
      <j1 rule="para" parents="4775 5217"/>
    </justification>
  </clause>

  <clause id="5381">
    <literal><![CDATA[
      R(K(x,y),y * z,u) * ((y * z) * u) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[para(5219(a,1),101(a,2,1))].">
      <j1 rule="para" parents="5219 101"/>
    </justification>
  </clause>

  <clause id="5383">
    <literal><![CDATA[
      x * (K(y \ x,x) * (y \ 1)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[para(5324(a,1),5222(a,1,2,1))].">
      <j1 rule="para" parents="5324 5222"/>
    </justification>
  </clause>

  <clause id="5384">
    <literal><![CDATA[
      K(x,(y \ 1) \ x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5269,a(flip),b,5274,a)].">
      <j1 rule="hyper" parents="58 5269 5274"/>
    </justification>
  </clause>

  <clause id="5385">
    <literal><![CDATA[
      K(x \ (y \ 1),z * T(u,u \ 1)) = K(x \ (1 / y),z * u)
    ]]></literal>
    <justification jstring="[hyper(320,a,3943,a,b,5275,a),flip(a)].">
      <j1 rule="hyper" parents="320 3943 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5388">
    <literal><![CDATA[
      K(x,(1 / x) * y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(5284(a,2),5090(a,1,1))].">
      <j1 rule="para" parents="5284 5090"/>
    </justification>
  </clause>

  <clause id="5389">
    <literal><![CDATA[
      K((x / y) \ 1,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(4936,a,5316,a)].">
      <j1 rule="hyper" parents="4936 5316"/>
    </justification>
  </clause>

  <clause id="5390">
    <literal><![CDATA[
      K(x,(y / z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(5316(a,2),4945(a,1))].">
      <j1 rule="para" parents="5316 4945"/>
    </justification>
  </clause>

  <clause id="5391">
    <literal><![CDATA[
      K(1 / (x / y),z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(5244,a,5389,a)].">
      <j1 rule="hyper" parents="5244 5389"/>
    </justification>
  </clause>

  <clause id="5392">
    <literal><![CDATA[
      R(K(x / y,z),x / y,u) = K((y / x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4163,a,b,5389,a)].">
      <j1 rule="hyper" parents="320 4163 5389"/>
    </justification>
  </clause>

  <clause id="5393">
    <literal><![CDATA[
      K((x / y) \ 1,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4924,a(flip),b,5389,a),flip(a)].">
      <j1 rule="hyper" parents="320 4924 5389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5394">
    <literal><![CDATA[
      K(x / (y * x),z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),5389(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6 5389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5396">
    <literal><![CDATA[
      K((x \ y) / y,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),5389(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 5389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5397">
    <literal><![CDATA[
      K((x / ((1 / x) \ y)) \ 1,x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4444,a(flip),b,5393,a),flip(a)].">
      <j1 rule="hyper" parents="320 4444 5393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5398">
    <literal><![CDATA[
      (x / y) \ K(x \ y,x) = T((x / y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5393,a(flip),b,4705,a)].">
      <j1 rule="hyper" parents="116 5393 4705"/>
    </justification>
  </clause>

  <clause id="5399">
    <literal><![CDATA[
      K((x * y) \ y,x * y) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(6(a,1),5393(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6 5393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5400">
    <literal><![CDATA[
      K(x \ (y \ x),x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),5393(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 5393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5401">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(5394(a,1),4979(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5394 4979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5402">
    <literal><![CDATA[
      K(x / (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / y,z) = u
    ]]></literal>
    <justification jstring="[para(5394(a,2),5244(a,1))].">
      <j1 rule="para" parents="5394 5244"/>
    </justification>
  </clause>

  <clause id="5404">
    <literal><![CDATA[
      K(x,y) * (y * z) = ((x * y) / x) * z
    ]]></literal>
    <justification jstring="[hyper(31,a,5104,a,b,5331,a)].">
      <j1 rule="hyper" parents="31 5104 5331"/>
    </justification>
  </clause>

  <clause id="5405">
    <literal><![CDATA[
      K(x \ y,x) * ((y / x) * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),5332(a,1,2,1,1))].">
      <j1 rule="para" parents="5 5332"/>
    </justification>
  </clause>

  <clause id="5407">
    <literal><![CDATA[
      x / (((y \ (x * z)) * y) / z) = K(y,x / (y / z))
    ]]></literal>
    <justification jstring="[para(1573(a,1),5335(a,1,2))].">
      <j1 rule="para" parents="1573 5335"/>
    </justification>
  </clause>

  <clause id="5408">
    <literal><![CDATA[
      K(x,y) / (K(x,y) / y) = 1 / (1 / y)
    ]]></literal>
    <justification jstring="[para(4762(a,2),5338(a,1,2))].">
      <j1 rule="para" parents="4762 5338"/>
    </justification>
  </clause>

  <clause id="5409">
    <literal><![CDATA[
      (x * K(y,x)) \ z = K(y,x) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5092,a,b,5360,a),flip(a)].">
      <j1 rule="hyper" parents="320 5092 5360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5410">
    <literal><![CDATA[
      ((x * y) / x) * (y \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(1449,a,5366,a)].">
      <j1 rule="hyper" parents="1449 5366"/>
    </justification>
  </clause>

  <clause id="5411">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),5366(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 5366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5412">
    <literal><![CDATA[
      (x * (K(y * z,x) * y)) * z = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5366(a,1),848(a,1,1))].">
      <j1 rule="para" parents="5366 848"/>
    </justification>
  </clause>

  <clause id="5413">
    <literal><![CDATA[
      (x / (x / y)) * z = y * (K(y \ x,y) * z)
    ]]></literal>
    <justification jstring="[para(4302(a,1),5366(a,1,1))].">
      <j1 rule="para" parents="4302 5366"/>
    </justification>
  </clause>

  <clause id="5414">
    <literal><![CDATA[
      (x * K(y,x)) * z = x * (K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(4711(a,1),5366(a,1,1))].">
      <j1 rule="para" parents="4711 5366"/>
    </justification>
  </clause>

  <clause id="5415">
    <literal><![CDATA[
      (x / y) * (K(y,y \ x) * z) = ((y * (x / y)) / y) * z
    ]]></literal>
    <justification jstring="[para(4871(a,1),5366(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4871 5366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5416">
    <literal><![CDATA[
      K(x,y) * (K(y,z) * T(y,x)) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(5109,a,5367,a)].">
      <j1 rule="hyper" parents="5109 5367"/>
    </justification>
  </clause>

  <clause id="5417">
    <literal><![CDATA[
      (x / (K(y,z) * T(y,u))) \ x = K(y,u) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(364,a,5367,a)].">
      <j1 rule="hyper" parents="364 5367"/>
    </justification>
  </clause>

  <clause id="5418">
    <literal><![CDATA[
      K(x / (x / y),y \ x) * K(z,x / (x / y)) = T(x / (x / y),z) \ y
    ]]></literal>
    <justification jstring="[para(4305(a,1),5372(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4305 5372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5419">
    <literal><![CDATA[
      (x \ y) \ ((y / x) * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),5375(a,1,2,1,1))].">
      <j1 rule="para" parents="5 5375"/>
    </justification>
  </clause>

  <clause id="5420">
    <literal><![CDATA[
      x \ ((y / (y / x)) * z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(4302(a,1),5375(a,1,2,1))].">
      <j1 rule="para" parents="4302 5375"/>
    </justification>
  </clause>

  <clause id="5421">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),5404(a,2,1,1))].">
      <j1 rule="para" parents="5 5404"/>
    </justification>
  </clause>

  <clause id="5422">
    <literal><![CDATA[
      (x * K(y,x)) * z = K(y,x) * (x * z)
    ]]></literal>
    <justification jstring="[para(4711(a,1),5404(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4711 5404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5423">
    <literal><![CDATA[
      (K(x,y) * y) * z = K(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(4734(a,1),5404(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4734 5404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5424">
    <literal><![CDATA[
      (x * K(y,x)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(5409(a,2),5125(a,1))].">
      <j1 rule="para" parents="5409 5125"/>
    </justification>
  </clause>

  <clause id="5425">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ y)) / z) = K(z,x) * y
    ]]></literal>
    <justification jstring="[hyper(1349,a,5410,a)].">
      <j1 rule="hyper" parents="1349 5410"/>
    </justification>
  </clause>

  <clause id="5426">
    <literal><![CDATA[
      R(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(3450,a,5414,a)].">
      <j1 rule="hyper" parents="3450 5414"/>
    </justification>
  </clause>

  <clause id="5427">
    <literal><![CDATA[
      L(x,K(y,z),z) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,5414,a)].">
      <j1 rule="hyper" parents="479 5414"/>
    </justification>
  </clause>

  <clause id="5428">
    <literal><![CDATA[
      (T(x,y) * K(z,x)) * u = T(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(5426(a,1),512(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5426 512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5429">
    <literal><![CDATA[
      (R(x,y,z) * K(u,x)) * w = R(x,y,z) * (K(u,x) * w)
    ]]></literal>
    <justification jstring="[para(5426(a,1),514(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5426 514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5430">
    <literal><![CDATA[
      L(x,K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5427(a,1),45(a,2))].">
      <j1 rule="para" parents="5427 45"/>
    </justification>
  </clause>

  <clause id="5431">
    <literal><![CDATA[
      (x * K(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,x) * z) = u
    ]]></literal>
    <justification jstring="[para(5427(a,1),286(a,1,2))].">
      <j1 rule="para" parents="5427 286"/>
    </justification>
  </clause>

  <clause id="5433">
    <literal><![CDATA[
      (x * K(y,x)) * K(x,z) = K(y,x) * T(x,z)
    ]]></literal>
    <justification jstring="[para(4714(a,2),5422(a,2,2))].">
      <j1 rule="para" parents="4714 5422"/>
    </justification>
  </clause>

  <clause id="5434">
    <literal><![CDATA[
      R(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3450,a,5423,a)].">
      <j1 rule="hyper" parents="3450 5423"/>
    </justification>
  </clause>

  <clause id="5435">
    <literal><![CDATA[
      L(x,y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,5423,a)].">
      <j1 rule="hyper" parents="479 5423"/>
    </justification>
  </clause>

  <clause id="5436">
    <literal><![CDATA[
      a(K(x,y),y,z) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,5423,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="115 5423 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5437">
    <literal><![CDATA[
      L(x,y,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5435(a,1),45(a,2))].">
      <j1 rule="para" parents="5435 45"/>
    </justification>
  </clause>

  <clause id="5438">
    <literal><![CDATA[
      R(K(x,y / (z * y)),y / (z * y),u) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,5311,a(flip),b,5434,a),flip(a)].">
      <j1 rule="hyper" parents="320 5311 5434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5439">
    <literal><![CDATA[
      K(x / y,z) \ y != u
    ]]></literal>
    <literal><![CDATA[
      T(x / y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(75(a,1),4744(a,1,2))].">
      <j1 rule="para" parents="75 4744"/>
    </justification>
  </clause>

  <clause id="5440">
    <literal><![CDATA[
      L(x \ 1,T(x,y),y) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3826,a(flip),b,4878,a)].">
      <j1 rule="hyper" parents="58 3826 4878"/>
    </justification>
  </clause>

  <clause id="5441">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),y) = T(x,y) * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(5440(a,1),1840(a,1,1,2))].">
      <j1 rule="para" parents="5440 1840"/>
    </justification>
  </clause>

  <clause id="5442">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ y) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(1417(a,1),4990(a,1))].">
      <j1 rule="para" parents="1417 4990"/>
    </justification>
  </clause>

  <clause id="5443">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(5248(a,1),5057(a,1,2))].">
      <j1 rule="para" parents="5248 5057"/>
    </justification>
  </clause>

  <clause id="5444">
    <literal><![CDATA[
      K(x,x * y) * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      x \ L(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(5247(a,2),5072(a,1,2))].">
      <j1 rule="para" parents="5247 5072"/>
    </justification>
  </clause>

  <clause id="5445">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(5250(a,1),5072(a,1,2))].">
      <j1 rule="para" parents="5250 5072"/>
    </justification>
  </clause>

  <clause id="5446">
    <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),5081(a,1,2))].">
      <j1 rule="para" parents="17 5081"/>
    </justification>
  </clause>

  <clause id="5447">
    <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(5068(a,1),5081(a,1,2))].">
      <j1 rule="para" parents="5068 5081"/>
    </justification>
  </clause>

  <clause id="5448">
    <literal><![CDATA[
      K(x,y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(4688(a,2),5142(a,1,2))].">
      <j1 rule="para" parents="4688 5142"/>
    </justification>
  </clause>

  <clause id="5449">
    <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(2280(a,1),5224(a,1,2))].">
      <j1 rule="para" parents="2280 5224"/>
    </justification>
  </clause>

  <clause id="5450">
    <literal><![CDATA[
      T(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(5095(a,1),5224(a,1,2))].">
      <j1 rule="para" parents="5095 5224"/>
    </justification>
  </clause>

  <clause id="5451">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5192,a(flip),b,5249,a)].">
      <j1 rule="hyper" parents="58 5192 5249"/>
    </justification>
  </clause>

  <clause id="5452">
    <literal><![CDATA[
      K(x,y) * K(y,y * x) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(1993,a,5254,a)].">
      <j1 rule="hyper" parents="1993 5254"/>
    </justification>
  </clause>

  <clause id="5453">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5255(a,1),1993(a,1))].">
      <j1 rule="para" parents="5255 1993"/>
    </justification>
  </clause>

  <clause id="5454">
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(5228(a,2),5255(a,1,2))].">
      <j1 rule="para" parents="5228 5255"/>
    </justification>
  </clause>

  <clause id="5455">
    <literal><![CDATA[
      K(x,x * y) * (x \ R(x,y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5255(a,1),5101(a,1,2))].">
      <j1 rule="para" parents="5255 5101"/>
    </justification>
  </clause>

  <clause id="5456">
    <literal><![CDATA[
      R(K(x,y / z),y / z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ 1) = w
    ]]></literal>
    <justification jstring="[para(5434(a,2),5320(a,1))].">
      <j1 rule="para" parents="5434 5320"/>
    </justification>
  </clause>

  <clause id="5457">
    <literal><![CDATA[
      K(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / y) = z
    ]]></literal>
    <justification jstring="[para(70(a,1),5390(a,1,2,1))].">
      <j1 rule="para" parents="70 5390"/>
    </justification>
  </clause>

  <clause id="5458">
    <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),5390(a,1,2,1))].">
      <j1 rule="para" parents="102 5390"/>
    </justification>
  </clause>

  <clause id="5460">
    <literal><![CDATA[
      K(x,y / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / z) = u
    ]]></literal>
    <justification jstring="[para(5311(a,2),5457(a,1))].">
      <j1 rule="para" parents="5311 5457"/>
    </justification>
  </clause>

  <clause id="5461">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = K(y,x) * K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),5451(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 5451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5462">
    <literal><![CDATA[
      K(x * y,y) * K(y,x) = y \ R(y,x,y)
    ]]></literal>
    <justification jstring="[para(5228(a,2),5451(a,1,1))].">
      <j1 rule="para" parents="5228 5451"/>
    </justification>
  </clause>

  <clause id="5463">
    <literal><![CDATA[
      K(x,y) * K(y,x * y) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[para(5346(a,2),5452(a,1,2))].">
      <j1 rule="para" parents="5346 5452"/>
    </justification>
  </clause>

  <clause id="5464">
    <literal><![CDATA[
      x \ y != K(x,z) * K(z * x,x)
    ]]></literal>
    <literal><![CDATA[
      R(x,z,x) = y
    ]]></literal>
    <justification jstring="[para(5454(a,2),42(a,1)),flip(a)].">
      <j1 rule="para" parents="5454 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5465">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = z
    ]]></literal>
    <justification jstring="[para(5462(a,1),1997(a,1))].">
      <j1 rule="para" parents="5462 1997"/>
    </justification>
  </clause>

  <clause id="5466">
    <literal><![CDATA[
      T(T(x * K(x \ y,x),y),z) = L(T(x,z),x \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4670(a,1),4652(a,1,1,1))].">
      <j1 rule="para" parents="4670 4652"/>
    </justification>
  </clause>

  <clause id="5467">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = T(K(x,y \ 1),z)
    ]]></literal>
    <justification jstring="[para(4688(a,2),4696(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4688 4696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5469">
    <literal><![CDATA[
      x * K(y,T(z,x) \ 1) = K(y,z \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,5467,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="119 5467 17"/>
    </justification>
  </clause>

  <clause id="5471">
    <literal><![CDATA[
      K(x,T(1 / y,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(75(a,1),5467(a,2,1,2))].">
      <j1 rule="para" parents="75 5467"/>
    </justification>
  </clause>

  <clause id="5472">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(3523(a,1),5467(a,2,1))].">
      <j1 rule="para" parents="3523 5467"/>
    </justification>
  </clause>

  <clause id="5473">
    <literal><![CDATA[
      x * T(K(x,y \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(5467(a,1),4725(a,1,2))].">
      <j1 rule="para" parents="5467 4725"/>
    </justification>
  </clause>

  <clause id="5474">
    <literal><![CDATA[
      K(x,1 / T(1 / y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(5457,a,5471,a)].">
      <j1 rule="hyper" parents="5457 5471"/>
    </justification>
  </clause>

  <clause id="5475">
    <literal><![CDATA[
      K(x,1 / T(y,z)) = T(K(x,1 / y),z)
    ]]></literal>
    <justification jstring="[para(2151(a,1),5471(a,1,2))].">
      <j1 rule="para" parents="2151 5471"/>
    </justification>
  </clause>

  <clause id="5476">
    <literal><![CDATA[
      K(x,R(T(K(x,y),z),u,w)) = 1
    ]]></literal>
    <justification jstring="[para(5471(a,1),3331(a,1,2,1))].">
      <j1 rule="para" parents="5471 3331"/>
    </justification>
  </clause>

  <clause id="5477">
    <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(320,a,149,a,b,4834,a),flip(a)].">
      <j1 rule="hyper" parents="320 149 4834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5478">
    <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,4733,a,b,4834,a)].">
      <j1 rule="hyper" parents="30 4733 4834"/>
    </justification>
  </clause>

  <clause id="5479">
    <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,4733,a,b,4835,a)].">
      <j1 rule="hyper" parents="30 4733 4835"/>
    </justification>
  </clause>

  <clause id="5480">
    <literal><![CDATA[
      T(1 / (K(x,y) / x),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(5173(a,1),4837(a,1,1,2))].">
      <j1 rule="para" parents="5173 4837"/>
    </justification>
  </clause>

  <clause id="5481">
    <literal><![CDATA[
      (1 / (K(x,y) / x)) * y = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(119,a,5480,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 5480 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5482">
    <literal><![CDATA[
      (((x * y) / x) \ 1) \ 1 = (y \ 1) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2235,a(flip),b,4853,a)].">
      <j1 rule="hyper" parents="320 2235 4853"/>
    </justification>
  </clause>

  <clause id="5483">
    <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,4892,a,b,4734,a(flip))].">
      <j1 rule="hyper" parents="117 4892 4734"/>
    </justification>
  </clause>

  <clause id="5484">
    <literal><![CDATA[
      L(x,y,z) / L(x * K(u,x),y,z) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(4892(a,2),4909(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4892 4909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5485">
    <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,4893,a,b,4711,a(flip))].">
      <j1 rule="hyper" parents="116 4893 4711"/>
    </justification>
  </clause>

  <clause id="5486">
    <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(4893(a,2),4304(a,1,1))].">
      <j1 rule="para" parents="4893 4304"/>
    </justification>
  </clause>

  <clause id="5487">
    <literal><![CDATA[
      R(x * K(y,x),z,u) \ R(x,z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(4893(a,2),4751(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4893 4751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5488">
    <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(4893(a,2),4949(a,1,1))].">
      <j1 rule="para" parents="4893 4949"/>
    </justification>
  </clause>

  <clause id="5489">
    <literal><![CDATA[
      K(x \ 1,x) * K(y,x) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(2189,a,4957,a)].">
      <j1 rule="hyper" parents="2189 4957"/>
    </justification>
  </clause>

  <clause id="5490">
    <literal><![CDATA[
      K((x / y) \ 1,z) \ (x * T(x \ y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(188,a,5010,a)].">
      <j1 rule="hyper" parents="188 5010"/>
    </justification>
  </clause>

  <clause id="5491">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) / z = K(((x * y) / z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(919(a,1),5010(a,1,1))].">
      <j1 rule="para" parents="919 5010"/>
    </justification>
  </clause>

  <clause id="5492">
    <literal><![CDATA[
      x \ (((y \ (x / z)) * y) * z) = K((x \ (y * z)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(1097(a,1),5011(a,1,2))].">
      <j1 rule="para" parents="1097 5011"/>
    </justification>
  </clause>

  <clause id="5493">
    <literal><![CDATA[
      x \ (y * (z * T(z \ (y \ x),u))) = K((x \ (y * z)) \ 1,u)
    ]]></literal>
    <justification jstring="[para(919(a,1),5011(a,1,2))].">
      <j1 rule="para" parents="919 5011"/>
    </justification>
  </clause>

  <clause id="5494">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((x \ (y / z)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(1573(a,1),5011(a,1,2))].">
      <j1 rule="para" parents="1573 5011"/>
    </justification>
  </clause>

  <clause id="5495">
    <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(1952(a,1),5011(a,1,2))].">
      <j1 rule="para" parents="1952 5011"/>
    </justification>
  </clause>

  <clause id="5496">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * x = (x / (y \ 1)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(3298(a,1),5012(a,2,2))].">
      <j1 rule="para" parents="3298 5012"/>
    </justification>
  </clause>

  <clause id="5497">
    <literal><![CDATA[
      x * K((x \ (y * z)) \ 1,y) = z * ((y \ (z \ x)) * y)
    ]]></literal>
    <justification jstring="[hyper(4617,a,5015,a),flip(a)].">
      <j1 rule="hyper" parents="4617 5015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5498">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K((y \ (x \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(1029,a,5015,a)].">
      <j1 rule="hyper" parents="1029 5015"/>
    </justification>
  </clause>

  <clause id="5499">
    <literal><![CDATA[
      x * K((x \ (y * z)) \ 1,u) = y * (z * T(z \ (y \ x),u))
    ]]></literal>
    <justification jstring="[hyper(935,a,5015,a),flip(a)].">
      <j1 rule="hyper" parents="935 5015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5500">
    <literal><![CDATA[
      (x * y) * K(((x * y) \ y) \ 1,z) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(738,a,5015,a),flip(a)].">
      <j1 rule="hyper" parents="738 5015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5501">
    <literal><![CDATA[
      T(K(x / y,z),x) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(239,a,4776,a,b,5015,a(flip))].">
      <j1 rule="hyper" parents="239 4776 5015"/>
    </justification>
  </clause>

  <clause id="5502">
    <literal><![CDATA[
      x * (y * K((y \ (x \ 1)) \ 1,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5015,a(flip),b,932,a(flip))].">
      <j1 rule="hyper" parents="119 5015 932"/>
    </justification>
  </clause>

  <clause id="5503">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) / y = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,5015,a(flip),b,453,a)].">
      <j1 rule="hyper" parents="117 5015 453"/>
    </justification>
  </clause>

  <clause id="5505">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = T(K(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(4991,a,5020,a)].">
      <j1 rule="hyper" parents="4991 5020"/>
    </justification>
  </clause>

  <clause id="5507">
    <literal><![CDATA[
      T(K(x \ 1,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z) \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(5020(a,1),4991(a,1))].">
      <j1 rule="para" parents="5020 4991"/>
    </justification>
  </clause>

  <clause id="5508">
    <literal><![CDATA[
      K(T(1 / x,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(75(a,1),5505(a,2,1,1))].">
      <j1 rule="para" parents="75 5505"/>
    </justification>
  </clause>

  <clause id="5509">
    <literal><![CDATA[
      K(T(x \ 1,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(3298(a,1),5505(a,2,1))].">
      <j1 rule="para" parents="3298 5505"/>
    </justification>
  </clause>

  <clause id="5510">
    <literal><![CDATA[
      K(1 / T(x,y),z) = T(K(1 / x,z),y)
    ]]></literal>
    <justification jstring="[para(2151(a,1),5508(a,1,1))].">
      <j1 rule="para" parents="2151 5508"/>
    </justification>
  </clause>

  <clause id="5511">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = 1 / T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(5509(a,1),4931(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5509 4931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5512">
    <literal><![CDATA[
      T(x,y) != K(1 / T(z,y),u)
    ]]></literal>
    <literal><![CDATA[
      K(1 / z,u) = x
    ]]></literal>
    <justification jstring="[para(5510(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="5510 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5513">
    <literal><![CDATA[
      T(x * y,z) / y = K(((1 / y) / x) \ 1,z) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,993,a(flip),b,5021,a)].">
      <j1 rule="hyper" parents="320 993 5021"/>
    </justification>
  </clause>

  <clause id="5514">
    <literal><![CDATA[
      K(((x \ 1) / (x \ y)) \ 1,z) * (x \ y) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,984,a(flip),b,5021,a),flip(a)].">
      <j1 rule="hyper" parents="320 984 5021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5516">
    <literal><![CDATA[
      K((x / (x * y)) \ 1,z) * (x * y) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),5021(a,2,2,1))].">
      <j1 rule="para" parents="4 5021"/>
    </justification>
  </clause>

  <clause id="5517">
    <literal><![CDATA[
      K(1 / ((1 / x) / y),z) = (T(y * x,z) / x) / y
    ]]></literal>
    <justification jstring="[para(993(a,1),5030(a,1,1)),flip(a)].">
      <j1 rule="para" parents="993 5030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5518">
    <literal><![CDATA[
      ((x \ y) \ ((x \ 1) \ (x \ y))) * (x \ y) = (x \ 1) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5038,a(flip),b,5029,a),flip(a)].">
      <j1 rule="hyper" parents="116 5038 5029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5519">
    <literal><![CDATA[
      K(x,y) * (T(y,z) * x) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5050,a,b,5053,a),flip(a)].">
      <j1 rule="hyper" parents="320 5050 5053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5520">
    <literal><![CDATA[
      T(T(x,y),z) * K(y,x) = x * K(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(2898,a,5144,a)].">
      <j1 rule="hyper" parents="2898 5144"/>
    </justification>
  </clause>

  <clause id="5521">
    <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(5144(a,1),2898(a,1))].">
      <j1 rule="para" parents="5144 2898"/>
    </justification>
  </clause>

  <clause id="5522">
    <literal><![CDATA[
      (x \ K(x,y)) * T(x,x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2649,a,5172,a)].">
      <j1 rule="hyper" parents="2649 5172"/>
    </justification>
  </clause>

  <clause id="5523">
    <literal><![CDATA[
      (x \ K(x,y)) * x = (x \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4861,a(flip),b,5172,a),flip(a)].">
      <j1 rule="hyper" parents="58 4861 5172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5524">
    <literal><![CDATA[
      (x \ T(y,x \ 1)) / (x \ y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,3871,a,b,5175,a)].">
      <j1 rule="hyper" parents="117 3871 5175"/>
    </justification>
  </clause>

  <clause id="5525">
    <literal><![CDATA[
      (x * y) * (x / (x * y)) = x * K(x * y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5180,a(flip),b,87,a),flip(a)].">
      <j1 rule="hyper" parents="119 5180 87"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5526">
    <literal><![CDATA[
      T(T(x,y),y) \ x = K(y,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(4867(a,1),5191(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4867 5191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5527">
    <literal><![CDATA[
      K(T(x,T(y,z)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,4801,a,b,5221,a)].">
      <j1 rule="hyper" parents="30 4801 5221"/>
    </justification>
  </clause>

  <clause id="5528">
    <literal><![CDATA[
      K(x / T(y,z),y) = K(T(y,z) \ x,y)
    ]]></literal>
    <justification jstring="[para(107(a,1),5527(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 5527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5529">
    <literal><![CDATA[
      K(x,y) = (x * y) * ((y * x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(1351,a,5259,a)].">
      <j1 rule="hyper" parents="1351 5259"/>
    </justification>
  </clause>

  <clause id="5530">
    <literal><![CDATA[
      (x * y) \ K(x,y) = (y * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,673,a(flip),b,5259,a(flip))].">
      <j1 rule="hyper" parents="116 673 5259"/>
    </justification>
  </clause>

  <clause id="5531">
    <literal><![CDATA[
      ((x \ y) * x) \ 1 = y \ K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5529,a,b,148,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 5529 148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5533">
    <literal><![CDATA[
      K(x,y) != 1
    ]]></literal>
    <literal><![CDATA[
      x * y = y * x
    ]]></literal>
    <justification jstring="[para(5529(a,2),130(a,1))].">
      <j1 rule="para" parents="5529 130"/>
    </justification>
  </clause>

  <clause id="5534">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ 1) * u)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(2780(a,1),5286(a,1,2,2))].">
      <j1 rule="para" parents="2780 5286"/>
    </justification>
  </clause>

  <clause id="5535">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) \ u) = K(x,L(z,y,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(484(a,1),5287(a,1,2,1))].">
      <j1 rule="para" parents="484 5287"/>
    </justification>
  </clause>

  <clause id="5536">
    <literal><![CDATA[
      K(x,((((y \ 1) \ 1) * z) \ u) \ w) = K(x,((y * z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(3708(a,1),5287(a,1,2,1))].">
      <j1 rule="para" parents="3708 5287"/>
    </justification>
  </clause>

  <clause id="5537">
    <literal><![CDATA[
      K(x,y * (z / ((u \ 1) \ 1))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(2636(a,1),5290(a,1,2,2))].">
      <j1 rule="para" parents="2636 5290"/>
    </justification>
  </clause>

  <clause id="5538">
    <literal><![CDATA[
      K(x,y * (((z \ 1) \ 1) \ u)) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(2816(a,1),5290(a,1,2,2))].">
      <j1 rule="para" parents="2816 5290"/>
    </justification>
  </clause>

  <clause id="5539">
    <literal><![CDATA[
      K(x,y / (z * (1 / u))) = K(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(2603(a,1),5299(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2603 5299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5540">
    <literal><![CDATA[
      K(x,y / (((z \ 1) \ 1) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(2812(a,1),5299(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2812 5299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5541">
    <literal><![CDATA[
      K(x,T((1 / y) * z,u)) = K(x,T((y \ 1) * z,u))
    ]]></literal>
    <justification jstring="[para(2825(a,1),5301(a,1,2,1))].">
      <j1 rule="para" parents="2825 5301"/>
    </justification>
  </clause>

  <clause id="5542">
    <literal><![CDATA[
      K(x,((1 / y) * z) / u) = K(x,((y \ 1) * z) / u)
    ]]></literal>
    <justification jstring="[para(2791(a,1),5303(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2791 5303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5544">
    <literal><![CDATA[
      K(x,y / T(1 / z,u)) = K(x,y / T(z \ 1,u))
    ]]></literal>
    <justification jstring="[para(3050(a,1),5304(a,1,2,2))].">
      <j1 rule="para" parents="3050 5304"/>
    </justification>
  </clause>

  <clause id="5545">
    <literal><![CDATA[
      K(x \ y,x) * (z * (y / x)) = (x \ y) * T(z,y / x)
    ]]></literal>
    <justification jstring="[para(17(a,2),5333(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17 5333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5548">
    <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(5341(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5341 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5549">
    <literal><![CDATA[
      T(x,y) \ T(x * K(x * z,x),y) = K(z * x,T(x,y))
    ]]></literal>
    <justification jstring="[para(5228(a,1),5341(a,1,2,1,2))].">
      <j1 rule="para" parents="5228 5341"/>
    </justification>
  </clause>

  <clause id="5550">
    <literal><![CDATA[
      T(x,y) \ T(z * T(z \ x,x),y) = K((x \ z) \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(5015(a,2),5341(a,1,2,1))].">
      <j1 rule="para" parents="5015 5341"/>
    </justification>
  </clause>

  <clause id="5551">
    <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(5164(a,1),5342(a,1,1,1))].">
      <j1 rule="para" parents="5164 5342"/>
    </justification>
  </clause>

  <clause id="5552">
    <literal><![CDATA[
      K(x \ 1,x) / L(x,y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(117,a,5356,a(flip),b,258,a(flip))].">
      <j1 rule="hyper" parents="117 5356 258"/>
    </justification>
  </clause>

  <clause id="5553">
    <literal><![CDATA[
      K(x \ y,x) \ ((y / x) \ z) = (x \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(123,a,5361,a)].">
      <j1 rule="hyper" parents="123 5361"/>
    </justification>
  </clause>

  <clause id="5555">
    <literal><![CDATA[
      T(x,x \ y) \ ((x \ y) \ z) = x \ ((y / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,5361,a(flip),b,4777,a),flip(a)].">
      <j1 rule="hyper" parents="116 5361 4777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5556">
    <literal><![CDATA[
      K(x \ y,x) * T(z,x \ y) = (y / x) \ (z * (x \ y))
    ]]></literal>
    <justification jstring="[para(17(a,2),5361(a,1,2))].">
      <j1 rule="para" parents="17 5361"/>
    </justification>
  </clause>

  <clause id="5558">
    <literal><![CDATA[
      T(x,T(y,x)) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(17(a,2),5371(a,1,1,2))].">
      <j1 rule="para" parents="17 5371"/>
    </justification>
  </clause>

  <clause id="5559">
    <literal><![CDATA[
      T(x,y) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(4193(a,1),5558(a,1,1))].">
      <j1 rule="para" parents="4193 5558"/>
    </justification>
  </clause>

  <clause id="5560">
    <literal><![CDATA[
      ((x \ y) * x) \ x = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(349,a,5559,a),flip(a)].">
      <j1 rule="hyper" parents="349 5559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5561">
    <literal><![CDATA[
      (x * y) \ T(x,y) = (y * x) \ x
    ]]></literal>
    <justification jstring="[hyper(188,a,5559,a)].">
      <j1 rule="hyper" parents="188 5559"/>
    </justification>
  </clause>

  <clause id="5562">
    <literal><![CDATA[
      T(x,y) = (x * y) * ((y * x) \ x)
    ]]></literal>
    <justification jstring="[hyper(133,a,5559,a),flip(a)].">
      <j1 rule="hyper" parents="133 5559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5563">
    <literal><![CDATA[
      T(x * y,z) * ((y * x) \ x) = K(x * y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5561,a(flip),b,5041,a)].">
      <j1 rule="hyper" parents="119 5561 5041"/>
    </justification>
  </clause>

  <clause id="5564">
    <literal><![CDATA[
      ((x * y) \ y) * T(y * x,x \ 1) = T(y,x)
    ]]></literal>
    <justification jstring="[para(5561(a,1),4182(a,1,1))].">
      <j1 rule="para" parents="5561 4182"/>
    </justification>
  </clause>

  <clause id="5565">
    <literal><![CDATA[
      (x / (x / y)) \ ((x / y) \ z) = y \ ((y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,5376,a(flip),b,5334,a),flip(a)].">
      <j1 rule="hyper" parents="116 5376 5334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5572">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * z = u
    ]]></literal>
    <justification jstring="[para(5419(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5419 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5573">
    <literal><![CDATA[
      (x * K(y,x)) \ L(x,y,x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5051,a(flip),b,5433,a)].">
      <j1 rule="hyper" parents="116 5051 5433"/>
    </justification>
  </clause>

  <clause id="5574">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * z = z * K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,1),5469(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="107 5469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5575">
    <literal><![CDATA[
      ((x * K(y,x)) \ 1) \ 1 = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(4711(a,1),5482(a,1,1,1))].">
      <j1 rule="para" parents="4711 5482"/>
    </justification>
  </clause>

  <clause id="5576">
    <literal><![CDATA[
      (x \ K(x,y)) \ 1 = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(4864(a,1),5482(a,1,1))].">
      <j1 rule="para" parents="4864 5482"/>
    </justification>
  </clause>

  <clause id="5577">
    <literal><![CDATA[
      (x \ 1) * (x * K(y,x)) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(3078,a,5489,a)].">
      <j1 rule="hyper" parents="3078 5489"/>
    </justification>
  </clause>

  <clause id="5578">
    <literal><![CDATA[
      1 / T(K(x,y),z) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5472,a(flip),b,5511,a),flip(a)].">
      <j1 rule="hyper" parents="58 5472 5511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5579">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(188,a,5578,a)].">
      <j1 rule="hyper" parents="188 5578"/>
    </justification>
  </clause>

  <clause id="5580">
    <literal><![CDATA[
      T(K(x,y),z) * T(K(y,x),z) = 1
    ]]></literal>
    <justification jstring="[hyper(133,a,5578,a)].">
      <j1 rule="hyper" parents="133 5578"/>
    </justification>
  </clause>

  <clause id="5581">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(5578(a,1),4754(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5578 4754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5582">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,5579,a(flip),b,4763,a(flip))].">
      <j1 rule="hyper" parents="119 5579 4763"/>
    </justification>
  </clause>

  <clause id="5583">
    <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(836,a,5580,a)].">
      <j1 rule="hyper" parents="836 5580"/>
    </justification>
  </clause>

  <clause id="5584">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4934,a(flip),b,5581,a)].">
      <j1 rule="hyper" parents="58 4934 5581"/>
    </justification>
  </clause>

  <clause id="5585">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(5128,a,5584,a)].">
      <j1 rule="hyper" parents="5128 5584"/>
    </justification>
  </clause>

  <clause id="5586">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,5584,a,b,4688,a(flip))].">
      <j1 rule="hyper" parents="119 5584 4688"/>
    </justification>
  </clause>

  <clause id="5587">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5584,a(flip),b,4688,a(flip))].">
      <j1 rule="hyper" parents="119 5584 4688"/>
    </justification>
  </clause>

  <clause id="5588">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[para(5584(a,1),4729(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5584 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5589">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5584(a,1),4945(a,1,1))].">
      <j1 rule="para" parents="5584 4945"/>
    </justification>
  </clause>

  <clause id="5590">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) = T(K(z,y),x) * u
    ]]></literal>
    <justification jstring="[para(5584(a,1),4740(a,1,1))].">
      <j1 rule="para" parents="5584 4740"/>
    </justification>
  </clause>

  <clause id="5591">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y),x) = u
    ]]></literal>
    <justification jstring="[para(5585(a,1),4945(a,1))].">
      <j1 rule="para" parents="5585 4945"/>
    </justification>
  </clause>

  <clause id="5592">
    <literal><![CDATA[
      T(K(x,y) \ z,K(y,x)) = z / K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4887,a,5586,a),flip(a)].">
      <j1 rule="hyper" parents="4887 5586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5593">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(4883,a,5586,a),flip(a)].">
      <j1 rule="hyper" parents="4883 5586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5594">
    <literal><![CDATA[
      T(x,K(y,z)) * K(z,y) = K(z,y) * x
    ]]></literal>
    <justification jstring="[para(5586(a,1),4733(a,1,1))].">
      <j1 rule="para" parents="5586 4733"/>
    </justification>
  </clause>

  <clause id="5595">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5586(a,1),4884(a,1,1))].">
      <j1 rule="para" parents="5586 4884"/>
    </justification>
  </clause>

  <clause id="5596">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(5586(a,1),4882(a,1))].">
      <j1 rule="para" parents="5586 4882"/>
    </justification>
  </clause>

  <clause id="5597">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y) * x) = L(x,K(z,y),x)
    ]]></literal>
    <justification jstring="[para(5586(a,1),4902(a,1,1))].">
      <j1 rule="para" parents="5586 4902"/>
    </justification>
  </clause>

  <clause id="5598">
    <literal><![CDATA[
      T(K(x,y) * z,T(z,K(y,x))) = T(K(x,y) * z,z)
    ]]></literal>
    <justification jstring="[para(5586(a,1),4901(a,1,2))].">
      <j1 rule="para" parents="5586 4901"/>
    </justification>
  </clause>

  <clause id="5599">
    <literal><![CDATA[
      T(K(x,y),K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1996,a,5593,a),flip(a)].">
      <j1 rule="hyper" parents="1996 5593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5600">
    <literal><![CDATA[
      T(K(x,y),K(z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1992,a,5593,a),flip(a)].">
      <j1 rule="hyper" parents="1992 5593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5601">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(u,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(5593(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="5593 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5602">
    <literal><![CDATA[
      K(x,y) * K(x,z) = K(x,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5599,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 5599 17"/>
    </justification>
  </clause>

  <clause id="5603">
    <literal><![CDATA[
      K(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5599(a,1),284(a,1,2))].">
      <j1 rule="para" parents="5599 284"/>
    </justification>
  </clause>

  <clause id="5604">
    <literal><![CDATA[
      K(x,y) \ K(z,x) = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5600,a(flip),b,5094,a),flip(a)].">
      <j1 rule="hyper" parents="119 5600 5094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5605">
    <literal><![CDATA[
      K(x,y) * K(z,y) = K(z,y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5600,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 5600 17"/>
    </justification>
  </clause>

  <clause id="5606">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(5587(a,1),5110(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5587 5110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5607">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z / K(y,x)
    ]]></literal>
    <justification jstring="[para(5092(a,1),5592(a,1,1))].">
      <j1 rule="para" parents="5092 5592"/>
    </justification>
  </clause>

  <clause id="5608">
    <literal><![CDATA[
      (x * T(x \ y,z)) / K((x / y) \ 1,z) = T(y,K(z,(x / y) \ 1))
    ]]></literal>
    <justification jstring="[para(5490(a,1),5592(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5490 5592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5609">
    <literal><![CDATA[
      K(x,1 / x) * y = y * K(x,1 / x)
    ]]></literal>
    <justification jstring="[para(2175(a,1),5594(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2175 5594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5610">
    <literal><![CDATA[
      K(x \ y,z) * (y \ x) = (y \ x) * K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2279(a,1),5594(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2279 5594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5611">
    <literal><![CDATA[
      T(x,y) * (x \ K(x,z)) = K(x,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4743,a,5602,a)].">
      <j1 rule="hyper" parents="4743 5602"/>
    </justification>
  </clause>

  <clause id="5612">
    <literal><![CDATA[
      K(x,y) * K(x,z) != K(x,z) * u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5602(a,1),38(a,1))].">
      <j1 rule="para" parents="5602 38"/>
    </justification>
  </clause>

  <clause id="5613">
    <literal><![CDATA[
      x * (T(x,y) \ K(z,x)) = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(4745,a,5604,a)].">
      <j1 rule="hyper" parents="4745 5604"/>
    </justification>
  </clause>

  <clause id="5614">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = (y * z) * K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(3621,a,5609,a)].">
      <j1 rule="hyper" parents="3621 5609"/>
    </justification>
  </clause>

  <clause id="5615">
    <literal><![CDATA[
      K(x,1 / x) * (y * z) = y * (z * K(x,1 / x))
    ]]></literal>
    <justification jstring="[hyper(320,a,3397,a(flip),b,5609,a),flip(a)].">
      <j1 rule="hyper" parents="320 3397 5609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5616">
    <literal><![CDATA[
      K(x,y * (K(z,1 / z) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(5609(a,2),5289(a,1,2,2))].">
      <j1 rule="para" parents="5609 5289"/>
    </justification>
  </clause>

  <clause id="5617">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(4929(a,1),5589(a,1))].">
      <j1 rule="para" parents="4929 5589"/>
    </justification>
  </clause>

  <clause id="5618">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(4934(a,2),5617(a,1))].">
      <j1 rule="para" parents="4934 5617"/>
    </justification>
  </clause>

  <clause id="5619">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * (y * x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) * y = u
    ]]></literal>
    <justification jstring="[para(5519(a,1),5110(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5519 5110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5620">
    <literal><![CDATA[
      K(1 / x,x) / L(x,y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1816(a,2),5552(a,1,1))].">
      <j1 rule="para" parents="1816 5552"/>
    </justification>
  </clause>

  <clause id="5621">
    <literal><![CDATA[
      (x \ 1) * ((y * x) / y) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,4856,a,b,5577,a)].">
      <j1 rule="hyper" parents="58 4856 5577"/>
    </justification>
  </clause>

  <clause id="5622">
    <literal><![CDATA[
      T(x,y) \ K(z,x) = T(x,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,4777,a,b,5613,a)].">
      <j1 rule="hyper" parents="29 4777 5613"/>
    </justification>
  </clause>

  <clause id="5623">
    <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(5613(a,1),3974(a,2,3))].">
      <j1 rule="para" parents="5613 3974"/>
    </justification>
  </clause>

  <clause id="5624">
    <literal><![CDATA[
      T(x,y) \ K(z,x) != T(x,z) \ u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = u
    ]]></literal>
    <justification jstring="[para(5622(a,1),42(a,1))].">
      <j1 rule="para" parents="5622 42"/>
    </justification>
  </clause>

  <clause id="5625">
    <literal><![CDATA[
      K(x,y * (((1 / (1 / z)) \ u) * w)) = K(x,y * ((z \ u) * w))
    ]]></literal>
    <justification jstring="[para(3633(a,1),5616(a,1,2,2))].">
      <j1 rule="para" parents="3633 5616"/>
    </justification>
  </clause>

  <clause id="5627">
    <literal><![CDATA[
      ((x * K(y,x)) \ ((y * (x * y)) / y)) \ ((y * (x * y)) / y) = x
    ]]></literal>
    <justification jstring="[para(4899(a,2),4331(a,1,1))].">
      <j1 rule="para" parents="4899 4331"/>
    </justification>
  </clause>

  <clause id="5628">
    <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(5210(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5210 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5629">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,22,a,b,5253,a),flip(a)].">
      <j1 rule="hyper" parents="320 22 5253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5630">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x / (z * y)) = u
    ]]></literal>
    <justification jstring="[para(4600(a,1),5336(a,1,2))].">
      <j1 rule="para" parents="4600 5336"/>
    </justification>
  </clause>

  <clause id="5631">
    <literal><![CDATA[
      K(x,L(y,x,x \ 1)) * (y * x) = x * ((y * x) / x)
    ]]></literal>
    <justification jstring="[para(5350(a,1),5388(a,1,1))].">
      <j1 rule="para" parents="5350 5388"/>
    </justification>
  </clause>

  <clause id="5632">
    <literal><![CDATA[
      K((x / y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(5392(a,1),384(a,1)),flip(b)].">
      <j1 rule="para" parents="5392 384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5633">
    <literal><![CDATA[
      K(1 / (x / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(3293(a,2),5632(a,1))].">
      <j1 rule="para" parents="3293 5632"/>
    </justification>
  </clause>

  <clause id="5634">
    <literal><![CDATA[
      ((x * y) / x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * (K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(4711(a,2),5431(a,1,1))].">
      <j1 rule="para" parents="4711 5431"/>
    </justification>
  </clause>

  <clause id="5635">
    <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),5446(a,1,2))].">
      <j1 rule="para" parents="20 5446"/>
    </justification>
  </clause>

  <clause id="5636">
    <literal><![CDATA[
      K(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) \ T(x,y) = u
    ]]></literal>
    <justification jstring="[para(1991(a,2),5448(a,1))].">
      <j1 rule="para" parents="1991 5448"/>
    </justification>
  </clause>

  <clause id="5637">
    <literal><![CDATA[
      x \ K(x * y,x \ 1) = y / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(4447(a,1),4678(a,1,2))].">
      <j1 rule="para" parents="4447 4678"/>
    </justification>
  </clause>

  <clause id="5638">
    <literal><![CDATA[
      (x \ K(x * y,x \ 1)) \ y = y / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(188,a,5637,a(flip))].">
      <j1 rule="hyper" parents="188 5637"/>
    </justification>
  </clause>

  <clause id="5639">
    <literal><![CDATA[
      L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(4688(a,2),4695(a,1,1))].">
      <j1 rule="para" parents="4688 4695"/>
    </justification>
  </clause>

  <clause id="5641">
    <literal><![CDATA[
      K(x,L(1 / y,z,u) \ 1) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(75(a,1),5639(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 5639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5642">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3523(a,1),5639(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3523 5639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5643">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ 1) = L(K(x,K(z,y)),u,w)
    ]]></literal>
    <justification jstring="[para(4929(a,1),5639(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4929 5639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5644">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z),u,w) \ 1) = L(T(K(x,y),z),u,w)
    ]]></literal>
    <justification jstring="[para(5472(a,1),5639(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5472 5639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5645">
    <literal><![CDATA[
      L(K(x,y \ z),y \ z,y) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(390(a,1),5642(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="390 5642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5646">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ 1,u) * w = L(K(u,x),y,z) \ w
    ]]></literal>
    <justification jstring="[para(5642(a,1),5092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5642 5092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5647">
    <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(5642(a,1),5639(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5642 5639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5648">
    <literal><![CDATA[
      x * ((x \ y) * K(z,x \ y)) = y * K(z,(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,5645,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="119 5645 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5649">
    <literal><![CDATA[
      K(L(1 / x,y,z) \ 1,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(4991,a,4782,a)].">
      <j1 rule="hyper" parents="4991 4782"/>
    </justification>
  </clause>

  <clause id="5650">
    <literal><![CDATA[
      K(1 / L(1 / x,y,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(5244,a,5649,a)].">
      <j1 rule="hyper" parents="5244 5649"/>
    </justification>
  </clause>

  <clause id="5651">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3958,a(flip),b,5649,a)].">
      <j1 rule="hyper" parents="58 3958 5649"/>
    </justification>
  </clause>

  <clause id="5652">
    <literal><![CDATA[
      L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),5649(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 5649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5653">
    <literal><![CDATA[
      L(K(1 / x,y),z,u) = K(1 / L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(3272(a,1),5649(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3272 5649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5654">
    <literal><![CDATA[
      K(L(K(x,y),z,u) \ 1,w) = L(K(K(y,x),w),z,u)
    ]]></literal>
    <justification jstring="[para(4931(a,1),5649(a,1,1,1,1))].">
      <j1 rule="para" parents="4931 5649"/>
    </justification>
  </clause>

  <clause id="5655">
    <literal><![CDATA[
      K(x,1 / L(1 / y,z,u)) = 1 / L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5649(a,1),4943(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5649 4943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5656">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = L(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(5651(a,1),4929(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5651 4929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5658">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,(x \ 1) * L((x \ 1) \ 1,u,w)) = L(1,y,z)
    ]]></literal>
    <justification jstring="[para(1746(a,1),5652(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1746 5652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5659">
    <literal><![CDATA[
      K(L(T(1 / x,y),z,u) \ 1,w) = L(T(K(x,w),y),z,u)
    ]]></literal>
    <justification jstring="[para(5508(a,1),5652(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5508 5652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5660">
    <literal><![CDATA[
      K(L(T(x \ 1,y),z,u) \ 1,w) = L(T(K(x,w),y),z,u)
    ]]></literal>
    <justification jstring="[para(5509(a,1),5652(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5509 5652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5661">
    <literal><![CDATA[
      ((x \ y) * x) * K(z,(x \ y) * x) = (x \ (y * K(z,y))) * x
    ]]></literal>
    <justification jstring="[hyper(30,a,4733,a,b,4845,a)].">
      <j1 rule="hyper" parents="30 4733 4845"/>
    </justification>
  </clause>

  <clause id="5662">
    <literal><![CDATA[
      T(x,y) \ ((z * x) / z) = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5613,a(flip),b,4860,a),flip(a)].">
      <j1 rule="hyper" parents="320 5613 4860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5663">
    <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(5662(a,1),91(a,1,2,2,1))].">
      <j1 rule="para" parents="5662 91"/>
    </justification>
  </clause>

  <clause id="5664">
    <literal><![CDATA[
      (x * y) / (y * K(z,y)) = (x / (y * K(z,y))) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,4879,a(flip),b,4897,a)].">
      <j1 rule="hyper" parents="58 4879 4897"/>
    </justification>
  </clause>

  <clause id="5665">
    <literal><![CDATA[
      ((x * y) \ T(y * x,z)) * (x * y) = T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,4968,a)].">
      <j1 rule="hyper" parents="133 4968"/>
    </justification>
  </clause>

  <clause id="5666">
    <literal><![CDATA[
      a(1 / R(x,y,z),x,x \ 1) = K(R(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3578,a,b,5006,a)].">
      <j1 rule="hyper" parents="58 3578 5006"/>
    </justification>
  </clause>

  <clause id="5667">
    <literal><![CDATA[
      R(K(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(4705(a,1),5006(a,1,1))].">
      <j1 rule="para" parents="4705 5006"/>
    </justification>
  </clause>

  <clause id="5668">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(3626,a,5667,a)].">
      <j1 rule="hyper" parents="3626 5667"/>
    </justification>
  </clause>

  <clause id="5669">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5434,a(flip),b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="58 5434 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5670">
    <literal><![CDATA[
      K(R(1 / x,y,z) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),5667(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5671">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) * (y * z) = (K(x \ 1,u) * y) * z
    ]]></literal>
    <justification jstring="[para(5667(a,1),101(a,1,1))].">
      <j1 rule="para" parents="5667 101"/>
    </justification>
  </clause>

  <clause id="5672">
    <literal><![CDATA[
      R(K((x / y) \ 1,z),y,u) = K(((x * u) / (y * u)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(102(a,1),5667(a,2,1,1))].">
      <j1 rule="para" parents="102 5667"/>
    </justification>
  </clause>

  <clause id="5673">
    <literal><![CDATA[
      K(R(x \ 1,y,z) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3298(a,1),5667(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3298 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5674">
    <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(763(a,1),5669(a,1,1,1))].">
      <j1 rule="para" parents="763 5669"/>
    </justification>
  </clause>

  <clause id="5675">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) * w = R(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(5673(a,1),5092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5673 5092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5676">
    <literal><![CDATA[
      (x * T(x \ y,z)) * (y \ 1) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(1938,a,5007,a)].">
      <j1 rule="hyper" parents="1938 5007"/>
    </justification>
  </clause>

  <clause id="5677">
    <literal><![CDATA[
      (1 / x) * (y * T(y \ x,z)) = K(((1 / x) * y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),5007(a,1,2,2,1,2))].">
      <j1 rule="para" parents="75 5007"/>
    </justification>
  </clause>

  <clause id="5678">
    <literal><![CDATA[
      x * ((y \ (x \ 1)) * y) = K((x * y) \ 1,y)
    ]]></literal>
    <justification jstring="[para(105(a,1),5007(a,1,2))].">
      <j1 rule="para" parents="105 5007"/>
    </justification>
  </clause>

  <clause id="5679">
    <literal><![CDATA[
      x * (y \ T(y * (x \ 1),z)) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(932(a,1),5007(a,1,2))].">
      <j1 rule="para" parents="932 5007"/>
    </justification>
  </clause>

  <clause id="5680">
    <literal><![CDATA[
      ((1 / x) * y) * T(((1 / x) * y) \ y,z) = K(x,z) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),5017(a,2,1,1))].">
      <j1 rule="para" parents="75 5017"/>
    </justification>
  </clause>

  <clause id="5681">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),T(x,z))
    ]]></literal>
    <justification jstring="[para(3024(a,1),5018(a,1,1))].">
      <j1 rule="para" parents="3024 5018"/>
    </justification>
  </clause>

  <clause id="5682">
    <literal><![CDATA[
      K(x \ 1,y) * (x \ K(x,z)) = K(x,z) * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(3188(a,1),5018(a,2,2,1))].">
      <j1 rule="para" parents="3188 5018"/>
    </justification>
  </clause>

  <clause id="5683">
    <literal><![CDATA[
      x * (y \ T(y * (x \ (y \ 1)),z)) = K(x \ 1,z) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(932(a,1),5019(a,1,2))].">
      <j1 rule="para" parents="932 5019"/>
    </justification>
  </clause>

  <clause id="5684">
    <literal><![CDATA[
      x * (K(x \ 1,y) * (x \ z)) = K(x \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(5018(a,2),5019(a,1,2))].">
      <j1 rule="para" parents="5018 5019"/>
    </justification>
  </clause>

  <clause id="5685">
    <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(5027(a,1),4991(a,1))].">
      <j1 rule="para" parents="5027 4991"/>
    </justification>
  </clause>

  <clause id="5686">
    <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(407(a,1),5035(a,1,2,2,1,2))].">
      <j1 rule="para" parents="407 5035"/>
    </justification>
  </clause>

  <clause id="5687">
    <literal><![CDATA[
      K(((x \ 1) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5389,a,b,5139,a)].">
      <j1 rule="hyper" parents="58 5389 5139"/>
    </justification>
  </clause>

  <clause id="5688">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / z = K(y,z / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5312,a(flip),b,5262,a),flip(a)].">
      <j1 rule="hyper" parents="320 5312 5262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5689">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * z = y * ((x * (y \ z)) / x)
    ]]></literal>
    <justification jstring="[hyper(133,a,5262,a)].">
      <j1 rule="hyper" parents="133 5262"/>
    </justification>
  </clause>

  <clause id="5690">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,((x * y) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(960(a,1),5262(a,1,1))].">
      <j1 rule="para" parents="960 5262"/>
    </justification>
  </clause>

  <clause id="5691">
    <literal><![CDATA[
      T(x * ((y * (x \ z)) / y),z) / z = K(y,(T(x,z) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(2298(a,1),5262(a,1,1))].">
      <j1 rule="para" parents="2298 5262"/>
    </justification>
  </clause>

  <clause id="5692">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,z / (x * y))
    ]]></literal>
    <justification jstring="[para(960(a,1),5688(a,1,1))].">
      <j1 rule="para" parents="960 5688"/>
    </justification>
  </clause>

  <clause id="5693">
    <literal><![CDATA[
      K(x,y \ ((z \ 1) * (z * u))) = K(x,y \ L(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(2797(a,1),5293(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2797 5293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5694">
    <literal><![CDATA[
      K(x,y * (((1 / z) * (u * z)) \ (u * (u * z)))) = K(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(2740(a,2),5296(a,1,2,2))].">
      <j1 rule="para" parents="2740 5296"/>
    </justification>
  </clause>

  <clause id="5695">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * ((1 / u) \ K(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(4864(a,2),5296(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4864 5296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5696">
    <literal><![CDATA[
      (((x * y) / x) \ z) * K(y,1 / y) = (1 / (1 / ((x * y) / x))) \ z
    ]]></literal>
    <justification jstring="[para(5319(a,1),3017(a,1,2))].">
      <j1 rule="para" parents="5319 3017"/>
    </justification>
  </clause>

  <clause id="5697">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(4601(a,1),5407(a,1,2))].">
      <j1 rule="para" parents="4601 5407"/>
    </justification>
  </clause>

  <clause id="5698">
    <literal><![CDATA[
      L(x,K(y,z),T(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,5428,a)].">
      <j1 rule="hyper" parents="479 5428"/>
    </justification>
  </clause>

  <clause id="5699">
    <literal><![CDATA[
      L(x,K(y,z),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(5698(a,1),45(a,2))].">
      <j1 rule="para" parents="5698 45"/>
    </justification>
  </clause>

  <clause id="5700">
    <literal><![CDATA[
      x \ (((x * y) \ z) \ z) = y * K((y \ (x \ 1)) \ 1,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,310,a(flip),b,5498,a)].">
      <j1 rule="hyper" parents="58 310 5498"/>
    </justification>
  </clause>

  <clause id="5701">
    <literal><![CDATA[
      K(x,y) * (z * K((z \ K(y,x)) \ 1,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(4929(a,1),5502(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="4929 5502"/>
    </justification>
  </clause>

  <clause id="5702">
    <literal><![CDATA[
      K(((1 / x) / (y / x)) \ 1,z) * (y / x) = T(y,z) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),5513(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7 5513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5703">
    <literal><![CDATA[
      (x * y) * (x / (x * y)) = x * K(x * y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3528(a,1),5525(a,2,2))].">
      <j1 rule="para" parents="3528 5525"/>
    </justification>
  </clause>

  <clause id="5704">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = x * K(x * (1 / y),y)
    ]]></literal>
    <justification jstring="[para(3529(a,1),5525(a,2,2))].">
      <j1 rule="para" parents="3529 5525"/>
    </justification>
  </clause>

  <clause id="5705">
    <literal><![CDATA[
      K(x,y \ (T(1 / z,u) * w)) = K(x,y \ (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[para(2153(a,1),5534(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2153 5534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5706">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,T(K(z \ y,z),u))
    ]]></literal>
    <justification jstring="[para(4671(a,1),5541(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4671 5541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5707">
    <literal><![CDATA[
      T(x,y / T(1 / z,u)) = T(x,y / T(z \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,5544,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 5544 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5709">
    <literal><![CDATA[
      K(x,y \ K(y,z)) * z = z * K(x,(z \ (z * y)) \ 1)
    ]]></literal>
    <justification jstring="[para(4864(a,1),5574(a,1,1,2))].">
      <j1 rule="para" parents="4864 5574"/>
    </justification>
  </clause>

  <clause id="5710">
    <literal><![CDATA[
      x * K(y,(x \ z) \ 1) = K(y,x / z) * x
    ]]></literal>
    <justification jstring="[para(5312(a,1),5574(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5312 5574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5711">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(240,a,5710,a)].">
      <j1 rule="hyper" parents="240 5710"/>
    </justification>
  </clause>

  <clause id="5712">
    <literal><![CDATA[
      T(x,y) != K(z,(y \ u) \ 1)
    ]]></literal>
    <literal><![CDATA[
      K(z,y / u) = x
    ]]></literal>
    <justification jstring="[para(5711(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="5711 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5713">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = y * (z * K(x,1 / x))
    ]]></literal>
    <justification jstring="[hyper(320,a,3397,a(flip),b,5614,a),flip(a)].">
      <j1 rule="hyper" parents="320 3397 5614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5714">
    <literal><![CDATA[
      (x * K(y,1 / y)) / z = K(y,1 / y) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(117,a,147,a(flip),b,5614,a)].">
      <j1 rule="hyper" parents="117 147 5614"/>
    </justification>
  </clause>

  <clause id="5715">
    <literal><![CDATA[
      K(x,1 / x) * (y * L(x,z,u)) = y * L((x \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(3488(a,1),5615(a,2,2))].">
      <j1 rule="para" parents="3488 5615"/>
    </justification>
  </clause>

  <clause id="5716">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5642,a(flip),b,5656,a),flip(a)].">
      <j1 rule="hyper" parents="58 5642 5656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5717">
    <literal><![CDATA[
      1 / L(K(x,y),z,u) = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(197,a,5716,a)].">
      <j1 rule="hyper" parents="197 5716"/>
    </justification>
  </clause>

  <clause id="5718">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(5716(a,1),5643(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5716 5643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5719">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(5717(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5717 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5720">
    <literal><![CDATA[
      x * L(K(x,K(y,z)),u,w) = T(x,L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,5718,a,b,4688,a(flip))].">
      <j1 rule="hyper" parents="119 5718 4688"/>
    </justification>
  </clause>

  <clause id="5721">
    <literal><![CDATA[
      ((x * K(y,z)) / (z * K(y,z))) * z = R(x,K(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(2896,a,5664,a),flip(a)].">
      <j1 rule="hyper" parents="2896 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5724">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K((1 / x) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(75(a,1),5684(a,1,2,1,1))].">
      <j1 rule="para" parents="75 5684"/>
    </justification>
  </clause>

  <clause id="5725">
    <literal><![CDATA[
      K(x,y \ 1) * (y \ z) = z * ((x * (z \ (y \ z))) / x)
    ]]></literal>
    <justification jstring="[para(72(a,1),5689(a,1,1,2,1))].">
      <j1 rule="para" parents="72 5689"/>
    </justification>
  </clause>

  <clause id="5726">
    <literal><![CDATA[
      R(K(x,(y / z) / (u * x)),y / z,z) = ((u * (x * ((u \ (y / z)) / x))) * z) / y
    ]]></literal>
    <justification jstring="[para(5692(a,1),525(a,1,1))].">
      <j1 rule="para" parents="5692 525"/>
    </justification>
  </clause>

  <clause id="5727">
    <literal><![CDATA[
      (x / y) * (z * K(y,1 / y)) = (x / (1 / (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(2617(a,1),5713(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2617 5713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5728">
    <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,525,a,b,5714,a)].">
      <j1 rule="hyper" parents="58 525 5714"/>
    </justification>
  </clause>

  <clause id="5729">
    <literal><![CDATA[
      L(x \ (y * z),x,K(z,y)) = (K(y,z) \ x) \ (z * y)
    ]]></literal>
    <justification jstring="[para(5092(a,2),4965(a,2,1))].">
      <j1 rule="para" parents="5092 4965"/>
    </justification>
  </clause>

  <clause id="5730">
    <literal><![CDATA[
      L(x * K(y,x),K(x * K(y,x),y),z) = (z * K(x,y)) \ (z * x)
    ]]></literal>
    <justification jstring="[para(4930(a,2),4984(a,1,2))].">
      <j1 rule="para" parents="4930 4984"/>
    </justification>
  </clause>

  <clause id="5731">
    <literal><![CDATA[
      (K(x,y) \ z) \ (K(x,y) \ (z * u)) = L(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(116,a,5092,a,b,5113,a)].">
      <j1 rule="hyper" parents="116 5092 5113"/>
    </justification>
  </clause>

  <clause id="5732">
    <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(5095(a,1),5114(a,2,2))].">
      <j1 rule="para" parents="5095 5114"/>
    </justification>
  </clause>

  <clause id="5733">
    <literal><![CDATA[
      L(K(x \ y,x) * z,K(x,x \ y),y) = (x * (y / x)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(4974(a,1),5114(a,2,1))].">
      <j1 rule="para" parents="4974 5114"/>
    </justification>
  </clause>

  <clause id="5734">
    <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(5115(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="5115 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5735">
    <literal><![CDATA[
      (T(x,y) * K(z,x)) \ u = K(x,z) * (T(x,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(5699,a,5116,a),flip(a)].">
      <j1 rule="hyper" parents="5699 5116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5736">
    <literal><![CDATA[
      (L(x,y,z) * K(x,u)) \ w = K(u,x) * (L(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(4473,a,5116,a),flip(a)].">
      <j1 rule="hyper" parents="4473 5116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5737">
    <literal><![CDATA[
      (K(x,y) * T(y,z)) \ u = K(y,x) * (T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(2876(a,1),5735(a,1,1))].">
      <j1 rule="para" parents="2876 5735"/>
    </justification>
  </clause>

  <clause id="5738">
    <literal><![CDATA[
      K(x,y) * (T(x,x * y) \ z) = L(x,y,x) \ z
    ]]></literal>
    <justification jstring="[para(5246(a,1),5735(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5246 5735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5739">
    <literal><![CDATA[
      K(x,x * y) * (T(x,y) \ z) = R(x,y,x) \ z
    ]]></literal>
    <justification jstring="[para(5248(a,1),5735(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5248 5735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5740">
    <literal><![CDATA[
      K(x,x * y) * K(y,x) = R(x,y,x) \ x
    ]]></literal>
    <justification jstring="[para(4689(a,2),5739(a,1,2))].">
      <j1 rule="para" parents="4689 5739"/>
    </justification>
  </clause>

  <clause id="5741">
    <literal><![CDATA[
      R(x,y,x) \ x = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5444,a,5740,a),flip(a)].">
      <j1 rule="hyper" parents="5444 5740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5742">
    <literal><![CDATA[
      x \ (x \ L(x,y,x)) = R(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,5741,a(flip),b,1308,a)].">
      <j1 rule="hyper" parents="116 5741 1308"/>
    </justification>
  </clause>

  <clause id="5743">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = T(x,z) * (R(x,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(5742(a,1),3511(a,2,2))].">
      <j1 rule="para" parents="5742 3511"/>
    </justification>
  </clause>

  <clause id="5744">
    <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),5143(a,1,2))].">
      <j1 rule="para" parents="75 5143"/>
    </justification>
  </clause>

  <clause id="5745">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4700(a,1),5242(a,1))].">
      <j1 rule="para" parents="4700 5242"/>
    </justification>
  </clause>

  <clause id="5746">
    <literal><![CDATA[
      K(x,T(y,y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(106(a,2),5745(a,1,2))].">
      <j1 rule="para" parents="106 5745"/>
    </justification>
  </clause>

  <clause id="5747">
    <literal><![CDATA[
      K(x,T(y / z,z / y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(2057(a,2),5745(a,1,2))].">
      <j1 rule="para" parents="2057 5745"/>
    </justification>
  </clause>

  <clause id="5748">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(1 / y,z)) = u
    ]]></literal>
    <justification jstring="[para(2153(a,1),5745(a,1,2))].">
      <j1 rule="para" parents="2153 5745"/>
    </justification>
  </clause>

  <clause id="5749">
    <literal><![CDATA[
      K(x,T(y \ z,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(2359(a,2),5745(a,1,2))].">
      <j1 rule="para" parents="2359 5745"/>
    </justification>
  </clause>

  <clause id="5750">
    <literal><![CDATA[
      K(x,T(y / z,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(2388(a,2),5745(a,1,2))].">
      <j1 rule="para" parents="2388 5745"/>
    </justification>
  </clause>

  <clause id="5751">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(3354(a,2),5745(a,1,2))].">
      <j1 rule="para" parents="3354 5745"/>
    </justification>
  </clause>

  <clause id="5752">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,(z \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(3938(a,2),5745(a,1))].">
      <j1 rule="para" parents="3938 5745"/>
    </justification>
  </clause>

  <clause id="5754">
    <literal><![CDATA[
      K((x * y) \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(L(1 / y,y,x),z) = u
    ]]></literal>
    <justification jstring="[para(217(a,1),5245(a,1,1))].">
      <j1 rule="para" parents="217 5245"/>
    </justification>
  </clause>

  <clause id="5755">
    <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(219(a,1),5339(a,2,3))].">
      <j1 rule="para" parents="219 5339"/>
    </justification>
  </clause>

  <clause id="5756">
    <literal><![CDATA[
      R(x,x \ (y \ x),x) = R(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5328,a(flip),b,5340,a),flip(a)].">
      <j1 rule="hyper" parents="58 5328 5340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5757">
    <literal><![CDATA[
      R(K(x,y / (z * y)),R(1 / z,z,y),u) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(219(a,2),5438(a,1,2))].">
      <j1 rule="para" parents="219 5438"/>
    </justification>
  </clause>

  <clause id="5758">
    <literal><![CDATA[
      K(x \ y,L(y \ x,z,u)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(29,a,3546,a(flip),b,5478,a),flip(a)].">
      <j1 rule="hyper" parents="29 3546 5478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5759">
    <literal><![CDATA[
      K(1 / x,L(x,y,z)) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,3521,a(flip),b,5478,a),flip(a)].">
      <j1 rule="hyper" parents="29 3521 5478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5760">
    <literal><![CDATA[
      K(x \ 1,L(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,3472,a(flip),b,5478,a),flip(a)].">
      <j1 rule="hyper" parents="29 3472 5478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5761">
    <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(5478(a,1),2872(a,1,1))].">
      <j1 rule="para" parents="5478 2872"/>
    </justification>
  </clause>

  <clause id="5762">
    <literal><![CDATA[
      K(1 / L(x,y,z),L(x,u,w)) = L(K(1 / x,x),y,z)
    ]]></literal>
    <justification jstring="[para(5759(a,1),5653(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5759 5653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5763">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) = K(x \ 1,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,3359,a,b,5760,a)].">
      <j1 rule="hyper" parents="320 3359 5760"/>
    </justification>
  </clause>

  <clause id="5764">
    <literal><![CDATA[
      L(K(x \ 1,L(x,y,z)),u,w) = K(L(x,u,w) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5760(a,2),2504(a,1,1))].">
      <j1 rule="para" parents="5760 2504"/>
    </justification>
  </clause>

  <clause id="5765">
    <literal><![CDATA[
      K(x \ (y \ 1),(y \ 1) \ x) = K(x \ (y \ 1),y * x)
    ]]></literal>
    <justification jstring="[para(489(a,1),5758(a,1,2)),flip(a)].">
      <j1 rule="para" parents="489 5758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5766">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,3793,a(flip),b,5479,a),flip(a)].">
      <j1 rule="hyper" parents="29 3793 5479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5767">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(x \ 1,x) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5766(a,1),1204(a,1,2))].">
      <j1 rule="para" parents="5766 1204"/>
    </justification>
  </clause>

  <clause id="5768">
    <literal><![CDATA[
      (x \ y) * (((x \ y) \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * (x * z) = u
    ]]></literal>
    <justification jstring="[para(5079(a,1),5572(a,1,2))].">
      <j1 rule="para" parents="5079 5572"/>
    </justification>
  </clause>

  <clause id="5769">
    <literal><![CDATA[
      K(x,L(y,x,x \ 1)) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),5631(a,2,2))].">
      <j1 rule="para" parents="6 5631"/>
    </justification>
  </clause>

  <clause id="5770">
    <literal><![CDATA[
      K(x,L(y,x,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4963,a,5769,a),flip(a)].">
      <j1 rule="hyper" parents="4963 5769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5771">
    <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,5666,a(flip),b,216,a)].">
      <j1 rule="hyper" parents="119 5666 216"/>
    </justification>
  </clause>

  <clause id="5772">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5766,a(flip),b,5668,a),flip(a)].">
      <j1 rule="hyper" parents="320 5766 5668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5773">
    <literal><![CDATA[
      R(x,y,z) * K(x \ 1,R(x,y,z)) = 1 / (1 / R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,5668,a(flip),b,4667,a)].">
      <j1 rule="hyper" parents="119 5668 4667"/>
    </justification>
  </clause>

  <clause id="5775">
    <literal><![CDATA[
      (x \ (1 / R(y,z,u))) * K(y \ 1,y) = x \ (R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(5772(a,1),3410(a,1,2))].">
      <j1 rule="para" parents="5772 3410"/>
    </justification>
  </clause>

  <clause id="5776">
    <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(3298(a,1),5685(a,1,1))].">
      <j1 rule="para" parents="3298 5685"/>
    </justification>
  </clause>

  <clause id="5777">
    <literal><![CDATA[
      R(x * y,K(z,y),y) = R(x,y,K(z,y)) * y
    ]]></literal>
    <justification jstring="[para(15(a,2),5721(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15 5721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5778">
    <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(5777(a,2),39(a,1))].">
      <j1 rule="para" parents="5777 39"/>
    </justification>
  </clause>

  <clause id="5779">
    <literal><![CDATA[
      L(x \ y,x,K(z,u)) = (K(u,z) \ x) \ (K(u,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(1896,a,5731,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="1896 5731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5780">
    <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),5731(a,1,2,2))].">
      <j1 rule="para" parents="90 5731"/>
    </justification>
  </clause>

  <clause id="5781">
    <literal><![CDATA[
      K(1 / L(x,y,z),L(x,u,w)) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,3375,a(flip),b,5762,a),flip(a)].">
      <j1 rule="hyper" parents="320 3375 5762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5783">
    <literal><![CDATA[
      L(x,y,z) * K(1 / x,x) = 1 / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[para(5781(a,1),4712(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5781 4712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5784">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,u,w)) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(5685,a,5764,a)].">
      <j1 rule="hyper" parents="5685 5764"/>
    </justification>
  </clause>

  <clause id="5786">
    <literal><![CDATA[
      L(x \ T(y,z),x,K(y,z)) = (K(z,y) \ x) \ T(T(y,z),z)
    ]]></literal>
    <justification jstring="[para(4875(a,1),5779(a,2,2))].">
      <j1 rule="para" parents="4875 5779"/>
    </justification>
  </clause>

  <clause id="5787">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,u,w)) = K(x \ 1,L(x,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(320,a,5763,a(flip),b,5784,a),flip(a)].">
      <j1 rule="hyper" parents="320 5763 5784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5790">
    <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(298(a,1),5787(a,1,1,1))].">
      <j1 rule="para" parents="298 5787"/>
    </justification>
  </clause>

  <clause id="5791">
    <literal><![CDATA[
      K(x,x \ 1) / ((y * x) \ y) = ((y * x) \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,2380,a(flip),b,4912,a),flip(a)].">
      <j1 rule="hyper" parents="320 2380 4912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5792">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * K(y,y \ 1) = ((x * y) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(3668,a,5791,a)].">
      <j1 rule="hyper" parents="3668 5791"/>
    </justification>
  </clause>

  <clause id="5793">
    <literal><![CDATA[
      T(x * K(y,x),x \ K(x,y)) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5575,a(flip),b,4942,a),flip(a)].">
      <j1 rule="hyper" parents="320 5575 4942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5794">
    <literal><![CDATA[
      T(K(x,y) * K(x,z),K(x,y) \ K(z,x)) = ((K(x,z) * K(x,y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(5602(a,1),4942(a,2,1,1))].">
      <j1 rule="para" parents="5602 4942"/>
    </justification>
  </clause>

  <clause id="5795">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * y = (x * y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(4705(a,1),5024(a,1,1,2))].">
      <j1 rule="para" parents="4705 5024"/>
    </justification>
  </clause>

  <clause id="5798">
    <literal><![CDATA[
      (x * K(y \ 1,z)) \ ((x * y) * K(y \ 1,z)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,5795,a)].">
      <j1 rule="hyper" parents="123 5795"/>
    </justification>
  </clause>

  <clause id="5799">
    <literal><![CDATA[
      (x * K(y \ 1,z)) / y = (x / y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,147,a(flip),b,5795,a)].">
      <j1 rule="hyper" parents="117 147 5795"/>
    </justification>
  </clause>

  <clause id="5800">
    <literal><![CDATA[
      R(T(x,y * K(x \ 1,z)),y,K(x \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5798(a,1),1088(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5798 1088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5801">
    <literal><![CDATA[
      (T(x,y \ 1) / y) * K(y \ 1,x) = x / y
    ]]></literal>
    <justification jstring="[para(4708(a,1),5799(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4708 5799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5802">
    <literal><![CDATA[
      (T(x,y \ 1) / y) \ (x / y) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,5801,a)].">
      <j1 rule="hyper" parents="123 5801"/>
    </justification>
  </clause>

  <clause id="5803">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3345,a,b,5802,a)].">
      <j1 rule="hyper" parents="58 3345 5802"/>
    </justification>
  </clause>

  <clause id="5804">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(6(a,1),5803(a,1,2,2))].">
      <j1 rule="para" parents="6 5803"/>
    </justification>
  </clause>

  <clause id="5805">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(5244,a,5804,a)].">
      <j1 rule="hyper" parents="5244 5804"/>
    </justification>
  </clause>

  <clause id="5806">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5285,a(flip),b,5804,a)].">
      <j1 rule="hyper" parents="58 5285 5804"/>
    </justification>
  </clause>

  <clause id="5807">
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5805,a(flip),b,4972,a),flip(a)].">
      <j1 rule="hyper" parents="119 5805 4972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5808">
    <literal><![CDATA[
      K(x \ 1,y * x) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4453,a(flip),b,5806,a),flip(a)].">
      <j1 rule="hyper" parents="58 4453 5806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5809">
    <literal><![CDATA[
      (x \ 1) * (y / (x \ 1)) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5806,a(flip),b,4972,a),flip(a)].">
      <j1 rule="hyper" parents="119 5806 4972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5810">
    <literal><![CDATA[
      T(x \ 1,y * x) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,5808,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 5808 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5811">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(5808(a,2),5401(a,2,2))].">
      <j1 rule="para" parents="5808 5401"/>
    </justification>
  </clause>

  <clause id="5812">
    <literal><![CDATA[
      T(x \ 1,y * x) = ((x \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,4368,a(flip),b,5810,a),flip(a)].">
      <j1 rule="hyper" parents="320 4368 5810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5813">
    <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(5810(a,1),2129(a,1,2,1,1))].">
      <j1 rule="para" parents="5810 2129"/>
    </justification>
  </clause>

  <clause id="5814">
    <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(5810(a,2),2129(a,1,1))].">
      <j1 rule="para" parents="5810 2129"/>
    </justification>
  </clause>

  <clause id="5815">
    <literal><![CDATA[
      T((x \ y) \ 1,y) = (((x \ y) \ 1) \ x) \ x
    ]]></literal>
    <justification jstring="[para(5(a,1),5812(a,1,2))].">
      <j1 rule="para" parents="5 5812"/>
    </justification>
  </clause>

  <clause id="5816">
    <literal><![CDATA[
      K(T(1 / x,y * x),z) = K(((x \ 1) \ y) \ y,z)
    ]]></literal>
    <justification jstring="[para(5812(a,1),3300(a,2,1))].">
      <j1 rule="para" parents="5812 3300"/>
    </justification>
  </clause>

  <clause id="5817">
    <literal><![CDATA[
      x * K((1 / y) \ 1,x * (1 / y)) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2836,a(flip),b,5807,a),flip(a)].">
      <j1 rule="hyper" parents="58 2836 5807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5818">
    <literal><![CDATA[
      (x \ 1) * ((y / x) / (x \ 1)) = (y / x) * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),5809(a,2,2,2))].">
      <j1 rule="para" parents="7 5809"/>
    </justification>
  </clause>

  <clause id="5819">
    <literal><![CDATA[
      x * K(y,x * (1 / y)) = y * (x / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),5817(a,1,2,1))].">
      <j1 rule="para" parents="75 5817"/>
    </justification>
  </clause>

  <clause id="5820">
    <literal><![CDATA[
      K(x,y * (1 / x)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(29,a,4974,a,b,5819,a),flip(a)].">
      <j1 rule="hyper" parents="29 4974 5819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5821">
    <literal><![CDATA[
      (x / y) * z != x * K(y,x * (1 / y))
    ]]></literal>
    <literal><![CDATA[
      T(y,x / y) = z
    ]]></literal>
    <justification jstring="[para(5819(a,2),240(a,2))].">
      <j1 rule="para" parents="5819 240"/>
    </justification>
  </clause>

  <clause id="5823">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y,x) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(5279(a,1),5819(a,1,2))].">
      <j1 rule="para" parents="5279 5819"/>
    </justification>
  </clause>

  <clause id="5824">
    <literal><![CDATA[
      K(x,y * (x \ 1)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5277,a(flip),b,5820,a)].">
      <j1 rule="hyper" parents="58 5277 5820"/>
    </justification>
  </clause>

  <clause id="5825">
    <literal><![CDATA[
      K(x * (1 / y),y) = 1 / K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(5820(a,1),4931(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5820 4931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5826">
    <literal><![CDATA[
      K(x,R(y,x,x \ 1)) = K(x,x \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,4874,a(flip),b,5824,a)].">
      <j1 rule="hyper" parents="58 4874 5824"/>
    </justification>
  </clause>

  <clause id="5827">
    <literal><![CDATA[
      K(x * (1 / y),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4931,a(flip),b,5825,a),flip(a)].">
      <j1 rule="hyper" parents="320 4931 5825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5828">
    <literal><![CDATA[
      K(x * (1 / y),y) = K(x / y,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4924,a,b,5827,a),flip(a)].">
      <j1 rule="hyper" parents="320 4924 5827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5829">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4445,a,b,5827,a)].">
      <j1 rule="hyper" parents="320 4445 5827"/>
    </justification>
  </clause>

  <clause id="5830">
    <literal><![CDATA[
      K(x * (y \ 1),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3933,a(flip),b,5827,a)].">
      <j1 rule="hyper" parents="58 3933 5827"/>
    </justification>
  </clause>

  <clause id="5831">
    <literal><![CDATA[
      K((x \ 1) \ y,x \ 1) = K(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),5827(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 5827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5832">
    <literal><![CDATA[
      K(x \ y,x) * (y * (1 / x)) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(5827(a,1),4729(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5827 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5833">
    <literal><![CDATA[
      K(x / (1 / y),1 / y) = K(x * y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3937,a(flip),b,5828,a),flip(a)].">
      <j1 rule="hyper" parents="58 3937 5828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5834">
    <literal><![CDATA[
      x * K(x * (y \ 1),y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,5830,a,b,85,a)].">
      <j1 rule="hyper" parents="119 5830 85"/>
    </justification>
  </clause>

  <clause id="5835">
    <literal><![CDATA[
      K((1 / (1 / x)) * y,1 / x) = K(y * x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,3937,a(flip),b,5829,a),flip(a)].">
      <j1 rule="hyper" parents="320 3937 5829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5836">
    <literal><![CDATA[
      ((1 / x) \ y) * (1 / x) = y * K(y * x,1 / x)
    ]]></literal>
    <justification jstring="[para(75(a,1),5834(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="75 5834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5837">
    <literal><![CDATA[
      K(x,R(y,x,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),5826(a,2,2))].">
      <j1 rule="para" parents="4 5826"/>
    </justification>
  </clause>

  <clause id="5838">
    <literal><![CDATA[
      K(x,y) = x \ T(x,R(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(4862,a,5837,a),flip(a)].">
      <j1 rule="hyper" parents="4862 5837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5839">
    <literal><![CDATA[
      R(x,y,y \ 1) * K(y,x) = (y * x) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,5838,a,b,3820,a)].">
      <j1 rule="hyper" parents="119 5838 3820"/>
    </justification>
  </clause>

  <clause id="5840">
    <literal><![CDATA[
      K(x * y,y \ 1) = K(y * x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,4447,a(flip),b,5831,a),flip(a)].">
      <j1 rule="hyper" parents="58 4447 5831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5841">
    <literal><![CDATA[
      K(x,y) * ((y * x) * (y \ 1)) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(5839(a,1),5106(a,1,2))].">
      <j1 rule="para" parents="5839 5106"/>
    </justification>
  </clause>

  <clause id="5842">
    <literal><![CDATA[
      K(x * y,1 / y) = K(y * x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3543,a(flip),b,5835,a),flip(a)].">
      <j1 rule="hyper" parents="58 3543 5835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5843">
    <literal><![CDATA[
      K((x \ y) * x,1 / x) = K(y,1 / x)
    ]]></literal>
    <justification jstring="[para(5(a,1),5842(a,2,1))].">
      <j1 rule="para" parents="5 5842"/>
    </justification>
  </clause>

  <clause id="5844">
    <literal><![CDATA[
      K(x,x * y) * (R(y,z,u) * x) = R(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4286,a(flip),b,5071,a),flip(a)].">
      <j1 rule="hyper" parents="320 4286 5071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5845">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * x) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4217,a(flip),b,5071,a),flip(a)].">
      <j1 rule="hyper" parents="320 4217 5071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5846">
    <literal><![CDATA[
      K(x,x * y) * (L(y,z,u) * x) = L(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4285,a(flip),b,5082,a),flip(a)].">
      <j1 rule="hyper" parents="320 4285 5082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5847">
    <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),5133(a,2,2))].">
      <j1 rule="para" parents="22 5133"/>
    </justification>
  </clause>

  <clause id="5848">
    <literal><![CDATA[
      K(x,y) * (K(x,y) * z) = y * (T(T(y,x),x) \ z)
    ]]></literal>
    <justification jstring="[para(4867(a,1),5148(a,1,2,1))].">
      <j1 rule="para" parents="4867 5148"/>
    </justification>
  </clause>

  <clause id="5849">
    <literal><![CDATA[
      K(1 / x,y) / (x \ 1) = 1 / (x \ K(y,1 / x))
    ]]></literal>
    <justification jstring="[para(3538(a,1),5233(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3538 5233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5850">
    <literal><![CDATA[
      K((K(x,y) / x) * z,u) = K((x \ K(x,y)) * z,u)
    ]]></literal>
    <justification jstring="[para(5171(a,1),5235(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5171 5235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5851">
    <literal><![CDATA[
      ((x * y) * ((z * ((x * y) \ x)) / z)) * y = (x * y) * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2286,a(flip),b,5264,a)].">
      <j1 rule="hyper" parents="58 2286 5264"/>
    </justification>
  </clause>

  <clause id="5852">
    <literal><![CDATA[
      (x * (y \ 1)) * ((z * ((x * (y \ 1)) \ x)) / z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[para(3523(a,1),5264(a,2,2))].">
      <j1 rule="para" parents="3523 5264"/>
    </justification>
  </clause>

  <clause id="5853">
    <literal><![CDATA[
      x * (y * ((z * (y \ (x \ y))) / z)) = K(z,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(1334,a,5265,a)].">
      <j1 rule="hyper" parents="1334 5265"/>
    </justification>
  </clause>

  <clause id="5854">
    <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(5415(a,2),5294(a,1,2,2))].">
      <j1 rule="para" parents="5415 5294"/>
    </justification>
  </clause>

  <clause id="5855">
    <literal><![CDATA[
      (K(x,y) * R(y,z,u)) * w = R(y,z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(2878(a,1),5429(a,1,1))].">
      <j1 rule="para" parents="2878 5429"/>
    </justification>
  </clause>

  <clause id="5856">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) = x \ (((y \ (x / z)) * y) * z)
    ]]></literal>
    <justification jstring="[para(3811(a,1),5494(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3811 5494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5857">
    <literal><![CDATA[
      K(x * y,T(y,z)) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(5344,a,5549,a),flip(a)].">
      <j1 rule="hyper" parents="5344 5549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5858">
    <literal><![CDATA[
      L(K(x,y),z,u) \ w = L(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(5651(a,1),5646(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5651 5646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5859">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(1924,a,5858,a)].">
      <j1 rule="hyper" parents="1924 5858"/>
    </justification>
  </clause>

  <clause id="5860">
    <literal><![CDATA[
      L(K(x,y),z,u) * (L(K(y,x),z,u) * w) = w
    ]]></literal>
    <justification jstring="[hyper(341,a,5858,a),flip(a)].">
      <j1 rule="hyper" parents="341 5858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5861">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z,u) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1998,a(flip),b,5859,a)].">
      <j1 rule="hyper" parents="58 1998 5859"/>
    </justification>
  </clause>

  <clause id="5862">
    <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(5859(a,1),4937(a,1)),flip(b)].">
      <j1 rule="para" parents="5859 4937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5863">
    <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(5860(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5860 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5864">
    <literal><![CDATA[
      K(x,y) \ L(K(x,y),z,u) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(5129,a,5861,a)].">
      <j1 rule="hyper" parents="5129 5861"/>
    </justification>
  </clause>

  <clause id="5865">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = L(K(x,y),u,z)
    ]]></literal>
    <justification jstring="[hyper(5109,a,5861,a)].">
      <j1 rule="hyper" parents="5109 5861"/>
    </justification>
  </clause>

  <clause id="5866">
    <literal><![CDATA[
      (K(x,y) / z) * (z * K(y,x)) = a(K(x,y) / z,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(696,a,5861,a)].">
      <j1 rule="hyper" parents="696 5861"/>
    </justification>
  </clause>

  <clause id="5867">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,L(x,z,u) \ 1) = a(u,z,K(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(5639(a,1),5861(a,1,2))].">
      <j1 rule="para" parents="5639 5861"/>
    </justification>
  </clause>

  <clause id="5868">
    <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(5865(a,1),5110(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5865 5110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5869">
    <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(1994(a,2),5868(a,1))].">
      <j1 rule="para" parents="1994 5868"/>
    </justification>
  </clause>

  <clause id="5870">
    <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(5660(a,1),5092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5660 5092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5871">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5005,a(flip),b,5676,a),flip(a)].">
      <j1 rule="hyper" parents="58 5005 5676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5872">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) * (x \ 1) = K((y * (x \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(5015(a,1),5676(a,1,1))].">
      <j1 rule="para" parents="5015 5676"/>
    </justification>
  </clause>

  <clause id="5873">
    <literal><![CDATA[
      K(((1 / x) * (y \ 1)) \ 1,z) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[para(932(a,1),5677(a,1,2)),flip(a)].">
      <j1 rule="para" parents="932 5677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5874">
    <literal><![CDATA[
      K(x \ y,y) / (y \ T(y * (x \ 1),y)) = x
    ]]></literal>
    <justification jstring="[hyper(117,a,5871,a(flip),b,5679,a)].">
      <j1 rule="hyper" parents="117 5871 5679"/>
    </justification>
  </clause>

  <clause id="5875">
    <literal><![CDATA[
      x \ T(x * (y \ 1),x) = y \ K(y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5871,a(flip),b,5679,a),flip(a)].">
      <j1 rule="hyper" parents="116 5871 5679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5876">
    <literal><![CDATA[
      x * (y \ K(y \ x,x)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[para(5874(a,1),195(a,1,2,1))].">
      <j1 rule="para" parents="5874 195"/>
    </justification>
  </clause>

  <clause id="5877">
    <literal><![CDATA[
      (x \ K(x \ y,y)) * y = T((x \ 1) * y,y)
    ]]></literal>
    <justification jstring="[para(5875(a,1),4555(a,1,1))].">
      <j1 rule="para" parents="5875 4555"/>
    </justification>
  </clause>

  <clause id="5878">
    <literal><![CDATA[
      ((x * (K(y \ x,x) * (y \ 1))) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(5876(a,1),1473(a,2,2,1))].">
      <j1 rule="para" parents="5876 1473"/>
    </justification>
  </clause>

  <clause id="5879">
    <literal><![CDATA[
      x * T(x \ (y \ x),T(y,z)) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(3006,a,5681,a),flip(a)].">
      <j1 rule="hyper" parents="3006 5681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5880">
    <literal><![CDATA[
      K(((1 / x) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3962,a,b,5687,a)].">
      <j1 rule="hyper" parents="58 3962 5687"/>
    </justification>
  </clause>

  <clause id="5881">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z / (x * y)) = u
    ]]></literal>
    <justification jstring="[para(5690(a,2),5390(a,1))].">
      <j1 rule="para" parents="5690 5390"/>
    </justification>
  </clause>

  <clause id="5882">
    <literal><![CDATA[
      K(x,y \ K(y,z)) * z = z * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),5709(a,2,2,2,1))].">
      <j1 rule="para" parents="4 5709"/>
    </justification>
  </clause>

  <clause id="5883">
    <literal><![CDATA[
      K(x,(y / (1 / (1 / z))) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(5727(a,1),5289(a,1,2))].">
      <j1 rule="para" parents="5727 5289"/>
    </justification>
  </clause>

  <clause id="5884">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,2826,a,b,5767,a)].">
      <j1 rule="hyper" parents="30 2826 5767"/>
    </justification>
  </clause>

  <clause id="5886">
    <literal><![CDATA[
      R(x,y,z) / x = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1877,a,5884,a)].">
      <j1 rule="hyper" parents="1877 5884"/>
    </justification>
  </clause>

  <clause id="5888">
    <literal><![CDATA[
      x \ R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) / x = u
    ]]></literal>
    <justification jstring="[para(5884(a,1),1877(a,1))].">
      <j1 rule="para" parents="5884 1877"/>
    </justification>
  </clause>

  <clause id="5890">
    <literal><![CDATA[
      (x \ R(x,y,z)) * x = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,5886,a)].">
      <j1 rule="hyper" parents="133 5886"/>
    </justification>
  </clause>

  <clause id="5891">
    <literal><![CDATA[
      T(x,x \ R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(31,a,265,a,b,5886,a)].">
      <j1 rule="hyper" parents="31 265 5886"/>
    </justification>
  </clause>

  <clause id="5892">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,y * z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(5886(a,1),532(a,1,1))].">
      <j1 rule="para" parents="5886 532"/>
    </justification>
  </clause>

  <clause id="5893">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = R(x,y,z) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5891(a,1),4724(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5891 4724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5894">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) / ((y \ 1) \ 1) = (1 / ((x * y) \ x)) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,5792,a(flip),b,2665,a)].">
      <j1 rule="hyper" parents="117 5792 2665"/>
    </justification>
  </clause>

  <clause id="5895">
    <literal><![CDATA[
      (x \ 1) \ ((y \ (y / x)) * y) = (y / x) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,5012,a,b,5818,a)].">
      <j1 rule="hyper" parents="116 5012 5818"/>
    </justification>
  </clause>

  <clause id="5896">
    <literal><![CDATA[
      (x / (y \ x)) / ((y \ x) \ 1) = ((y \ x) \ 1) \ ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(72(a,1),5895(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 5895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5897">
    <literal><![CDATA[
      x * (K(y,x \ 1) * (x \ z)) = K(y,x \ 1) * z
    ]]></literal>
    <justification jstring="[para(5725(a,2),5853(a,1,2))].">
      <j1 rule="para" parents="5725 5853"/>
    </justification>
  </clause>

  <clause id="5899">
    <literal><![CDATA[
      K(x,y \ 1) * (y * z) = y * (K(x,y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),5897(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 5897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5902">
    <literal><![CDATA[
      1 \ (x * (K(y,x \ 1) * z)) = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,60,a,b,5899,a)].">
      <j1 rule="hyper" parents="320 60 5899"/>
    </justification>
  </clause>

  <clause id="5903">
    <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(5855(a,1),515(a,1))].">
      <j1 rule="para" parents="5855 515"/>
    </justification>
  </clause>

  <clause id="5904">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,61,a(flip),b,5893,a),flip(a)].">
      <j1 rule="hyper" parents="320 61 5893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5906">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x * y) = y / R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(5399(a,1),4679(a,1,2))].">
      <j1 rule="para" parents="5399 4679"/>
    </justification>
  </clause>

  <clause id="5907">
    <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(1492(a,1),4849(a,2,1,1))].">
      <j1 rule="para" parents="1492 4849"/>
    </justification>
  </clause>

  <clause id="5908">
    <literal><![CDATA[
      T(x \ y,z) \ T((x \ y) * (y \ x),z) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,2134,a,b,4917,a)].">
      <j1 rule="hyper" parents="58 2134 4917"/>
    </justification>
  </clause>

  <clause id="5909">
    <literal><![CDATA[
      ((x \ y) * T(x,x \ y)) \ ((y / x) * z) = L(x \ z,T(x,x \ y),x \ y)
    ]]></literal>
    <justification jstring="[para(5411(a,1),5069(a,1,2))].">
      <j1 rule="para" parents="5411 5069"/>
    </justification>
  </clause>

  <clause id="5910">
    <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(5080(a,1),5112(a,1,2))].">
      <j1 rule="para" parents="5080 5112"/>
    </justification>
  </clause>

  <clause id="5911">
    <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,5861,a(flip),b,5195,a)].">
      <j1 rule="hyper" parents="119 5861 5195"/>
    </justification>
  </clause>

  <clause id="5912">
    <literal><![CDATA[
      T(K(x * (y \ 1),y \ 1) / y,x) = R(1 / y,x,1 / y)
    ]]></literal>
    <justification jstring="[para(3933(a,1),5243(a,1,1,1))].">
      <j1 rule="para" parents="3933 5243"/>
    </justification>
  </clause>

  <clause id="5913">
    <literal><![CDATA[
      (L(x,y,z) \ x) / x = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5240,a(flip),b,5268,a),flip(a)].">
      <j1 rule="hyper" parents="58 5240 5268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5915">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(133,a,5913,a)].">
      <j1 rule="hyper" parents="133 5913"/>
    </justification>
  </clause>

  <clause id="5916">
    <literal><![CDATA[
      x / L(x,y,z) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,1633,a(flip),b,5915,a)].">
      <j1 rule="hyper" parents="58 1633 5915"/>
    </justification>
  </clause>

  <clause id="5917">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[para(5915(a,1),1635(a,1,1))].">
      <j1 rule="para" parents="5915 1635"/>
    </justification>
  </clause>

  <clause id="5918">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(188,a,5916,a)].">
      <j1 rule="hyper" parents="188 5916"/>
    </justification>
  </clause>

  <clause id="5919">
    <literal><![CDATA[
      T(L(x,y,z),L(x,y,z) \ x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(31,a,265,a,b,5916,a)].">
      <j1 rule="hyper" parents="31 265 5916"/>
    </justification>
  </clause>

  <clause id="5920">
    <literal><![CDATA[
      L(x / L(x,y,z),L(x,y,z),z * y) = (z * (y * x)) \ ((z * y) * x)
    ]]></literal>
    <justification jstring="[para(5916(a,2),501(a,1,1))].">
      <j1 rule="para" parents="5916 501"/>
    </justification>
  </clause>

  <clause id="5921">
    <literal><![CDATA[
      x / L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(5917(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5917 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5922">
    <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(5917(a,1),92(a,2,2))].">
      <j1 rule="para" parents="5917 92"/>
    </justification>
  </clause>

  <clause id="5923">
    <literal><![CDATA[
      a(x,y,K(z,u)) * L(K(z,u),y,x) = K(z,u)
    ]]></literal>
    <justification jstring="[para(1921(a,1),5917(a,1,1))].">
      <j1 rule="para" parents="1921 5917"/>
    </justification>
  </clause>

  <clause id="5924">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = T(a(x,y,z),L(z,y,x))
    ]]></literal>
    <justification jstring="[para(5917(a,1),3221(a,1,2,2))].">
      <j1 rule="para" parents="5917 3221"/>
    </justification>
  </clause>

  <clause id="5925">
    <literal><![CDATA[
      a(x \ 1,x,y) * L(y,x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(4025(a,1),5917(a,1,1))].">
      <j1 rule="para" parents="4025 5917"/>
    </justification>
  </clause>

  <clause id="5926">
    <literal><![CDATA[
      a(x \ 1,x,y) \ y = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(4025(a,1),5918(a,1,1))].">
      <j1 rule="para" parents="4025 5918"/>
    </justification>
  </clause>

  <clause id="5927">
    <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(5923(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="5923 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5928">
    <literal><![CDATA[
      T(a(x,y,z),L(z,y,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(691,a,5924,a),flip(a)].">
      <j1 rule="hyper" parents="691 5924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5929">
    <literal><![CDATA[
      L(T(x,y),x \ T(z,x),x) = T(L(x,x \ z,x),y)
    ]]></literal>
    <justification jstring="[para(4680(a,1),5466(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4680 5466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5930">
    <literal><![CDATA[
      L(T(x,y),x \ T(z,x),x) = L(T(x,y),x \ z,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,20,a,b,5929,a),flip(a)].">
      <j1 rule="hyper" parents="320 20 5929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5931">
    <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(5930(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5930 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5932">
    <literal><![CDATA[
      K(x,y / (x / (z \ 1))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x * z)) = u
    ]]></literal>
    <justification jstring="[para(5697(a,1),5630(a,1))].">
      <j1 rule="para" parents="5697 5630"/>
    </justification>
  </clause>

  <clause id="5933">
    <literal><![CDATA[
      R(K(x \ y,x),y,z) = K(((x * z) / (y * z)) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5393(a,1),5672(a,1,1))].">
      <j1 rule="para" parents="5393 5672"/>
    </justification>
  </clause>

  <clause id="5934">
    <literal><![CDATA[
      R(K(x \ (y / z),x),y / z,z) = K(((x * z) / y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),5933(a,2,1,1,2))].">
      <j1 rule="para" parents="7 5933"/>
    </justification>
  </clause>

  <clause id="5935">
    <literal><![CDATA[
      K(x / y,z) \ y != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (T(x / y,z) \ x) = w
    ]]></literal>
    <justification jstring="[para(5092(a,2),5744(a,1))].">
      <j1 rule="para" parents="5092 5744"/>
    </justification>
  </clause>

  <clause id="5936">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(3523(a,1),5752(a,1))].">
      <j1 rule="para" parents="3523 5752"/>
    </justification>
  </clause>

  <clause id="5937">
    <literal><![CDATA[
      K((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((1 / x) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(75(a,1),5936(a,1,1,1,1))].">
      <j1 rule="para" parents="75 5936"/>
    </justification>
  </clause>

  <clause id="5938">
    <literal><![CDATA[
      K(x * (y \ 1),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,x) = z
    ]]></literal>
    <justification jstring="[para(5323(a,1),5936(a,1))].">
      <j1 rule="para" parents="5323 5936"/>
    </justification>
  </clause>

  <clause id="5939">
    <literal><![CDATA[
      R(x,y,z) \ K(R(x,y,z),x \ 1) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(5238,a,5773,a(flip))].">
      <j1 rule="hyper" parents="5238 5773"/>
    </justification>
  </clause>

  <clause id="5940">
    <literal><![CDATA[
      R(x,y,z) * (1 / R(x,y,z)) = K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,5939,a)].">
      <j1 rule="hyper" parents="134 5939"/>
    </justification>
  </clause>

  <clause id="5941">
    <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(4106(a,1),5786(a,1,1,2))].">
      <j1 rule="para" parents="4106 5786"/>
    </justification>
  </clause>

  <clause id="5942">
    <literal><![CDATA[
      T(K(x * (y \ 1),y \ 1) / y,x) = R(1 / y,x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3398,a(flip),b,5912,a),flip(a)].">
      <j1 rule="hyper" parents="320 3398 5912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5943">
    <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(5934(a,2),5632(a,1))].">
      <j1 rule="para" parents="5934 5632"/>
    </justification>
  </clause>

  <clause id="5944">
    <literal><![CDATA[
      (x * y) * K(R(y,x,y),x * y) = ((y * x) / R(y,x,y)) * y
    ]]></literal>
    <justification jstring="[hyper(1878,a,4885,a),flip(a)].">
      <j1 rule="hyper" parents="1878 4885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5945">
    <literal><![CDATA[
      (1 / (1 / x)) / (x * y) = x / (((x \ 1) \ 1) * y)
    ]]></literal>
    <justification jstring="[para(4840(a,1),4908(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4840 4908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5946">
    <literal><![CDATA[
      (1 / (1 / x)) / (x * (T(x,y) \ 1)) = x / (T(x,y) \ ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(1700(a,1),5945(a,2,2))].">
      <j1 rule="para" parents="1700 5945"/>
    </justification>
  </clause>

  <clause id="5947">
    <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(4955(a,1),5450(a,1))].">
      <j1 rule="para" parents="4955 5450"/>
    </justification>
  </clause>

  <clause id="5948">
    <literal><![CDATA[
      ((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(512(a,1),5003(a,1,1))].">
      <j1 rule="para" parents="512 5003"/>
    </justification>
  </clause>

  <clause id="5949">
    <literal><![CDATA[
      (K(x,y) * T(K(x,y) \ z,u)) * K(y,x) = T(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(5092(a,2),5121(a,1,1,2,1))].">
      <j1 rule="para" parents="5092 5121"/>
    </justification>
  </clause>

  <clause id="5950">
    <literal><![CDATA[
      T((K(x,y) * z) * K(y,x),u) = (K(x,y) * T(z,u)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(5095(a,1),5121(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5095 5121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5951">
    <literal><![CDATA[
      ((x * y) * z) / ((T(x,u) * y) * z) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(512(a,1),5145(a,1,2))].">
      <j1 rule="para" parents="512 5145"/>
    </justification>
  </clause>

  <clause id="5952">
    <literal><![CDATA[
      T(x,y) / (T(x,y) * y) = x / ((y * K(x,y)) * x)
    ]]></literal>
    <justification jstring="[para(4842(a,1),5151(a,1,1))].">
      <j1 rule="para" parents="4842 5151"/>
    </justification>
  </clause>

  <clause id="5953">
    <literal><![CDATA[
      T(x,y) / (T(x,y) * y) = x / (x * y)
    ]]></literal>
    <justification jstring="[para(4733(a,1),5952(a,2,2))].">
      <j1 rule="para" parents="4733 5952"/>
    </justification>
  </clause>

  <clause id="5954">
    <literal><![CDATA[
      (x / (x * y)) \ T(x,y) = T(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(188,a,5953,a)].">
      <j1 rule="hyper" parents="188 5953"/>
    </justification>
  </clause>

  <clause id="5955">
    <literal><![CDATA[
      (x \ K(x,y)) * T((x \ 1) \ 1,z) = K(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5611,a(flip),b,5229,a),flip(a)].">
      <j1 rule="hyper" parents="320 5611 5229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5956">
    <literal><![CDATA[
      K(x \ 1,x) * (K(x,y) * K(x,z)) = (x \ K(x,y)) * T(x,z)
    ]]></literal>
    <justification jstring="[para(5955(a,1),3673(a,1,2))].">
      <j1 rule="para" parents="5955 3673"/>
    </justification>
  </clause>

  <clause id="5957">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = (x * (K(z,u) * y)) / (x * y)
    ]]></literal>
    <justification jstring="[para(5061(a,1),5260(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5061 5260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5958">
    <literal><![CDATA[
      ((x \ T(x * (y / z),u)) * z) / y = K((((x \ 1) * z) / y) \ 1,u)
    ]]></literal>
    <justification jstring="[para(1590(a,1),5491(a,1,1))].">
      <j1 rule="para" parents="1590 5491"/>
    </justification>
  </clause>

  <clause id="5959">
    <literal><![CDATA[
      x * K((x \ (y * z)) \ 1,z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(105(a,1),5499(a,2,2))].">
      <j1 rule="para" parents="105 5499"/>
    </justification>
  </clause>

  <clause id="5960">
    <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),5499(a,2,2,2,1))].">
      <j1 rule="para" parents="62 5499"/>
    </justification>
  </clause>

  <clause id="5961">
    <literal><![CDATA[
      T(x \ y,x) / ((x \ 1) \ (x \ y)) = (x \ y) / ((x \ 1) \ (y / x))
    ]]></literal>
    <justification jstring="[para(5518(a,1),4458(a,2,2))].">
      <j1 rule="para" parents="5518 4458"/>
    </justification>
  </clause>

  <clause id="5962">
    <literal><![CDATA[
      K(x,y * ((z \ L(u,1 / z,z)) * w)) = K(x,y * (((1 / z) * u) * w))
    ]]></literal>
    <justification jstring="[para(2808(a,1),5625(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2808 5625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5963">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = T(K(x,y) * z,z) / z
    ]]></literal>
    <justification jstring="[para(5425(a,1),5691(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5425 5691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5964">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = z \ T(z * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4535,a(flip),b,5963,a),flip(a)].">
      <j1 rule="hyper" parents="320 4535 5963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5965">
    <literal><![CDATA[
      K(x,y / T(z \ y,y)) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(5390,a,5964,a)].">
      <j1 rule="hyper" parents="5390 5964"/>
    </justification>
  </clause>

  <clause id="5966">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(4463(a,1),5965(a,1,2))].">
      <j1 rule="para" parents="4463 5965"/>
    </justification>
  </clause>

  <clause id="5967">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * T(K(y,x) \ z,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5015(a,2),5701(a,1,2))].">
      <j1 rule="para" parents="5015 5701"/>
    </justification>
  </clause>

  <clause id="5968">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,x)),u) = K(x,y) * (T(z,u) * K(y,x))
    ]]></literal>
    <justification jstring="[para(5500(a,1),5701(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5500 5701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5969">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = x * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(5827(a,1),5704(a,2,2))].">
      <j1 rule="para" parents="5827 5704"/>
    </justification>
  </clause>

  <clause id="5970">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,302,a(flip),b,5969,a),flip(a)].">
      <j1 rule="hyper" parents="320 302 5969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5971">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(75(a,1),5724(a,2,1,1))].">
      <j1 rule="para" parents="75 5724"/>
    </justification>
  </clause>

  <clause id="5972">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * ((x \ 1) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,3447,a(flip),b,5971,a)].">
      <j1 rule="hyper" parents="58 3447 5971"/>
    </justification>
  </clause>

  <clause id="5973">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) = (1 / x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),5971(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 5971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5975">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * z) = (x \ 1) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),5972(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 5972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5976">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * T(z,x \ 1)) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[para(17(a,2),5972(a,1,2,2))].">
      <j1 rule="para" parents="17 5972"/>
    </justification>
  </clause>

  <clause id="5977">
    <literal><![CDATA[
      (K(x,y) * z) \ (K(x,y) * ((1 / x) * z)) = T(1 / x,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(440,a,5973,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="440 5973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5978">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(5973(a,1),342(a,1))].">
      <j1 rule="para" parents="5973 342"/>
    </justification>
  </clause>

  <clause id="5979">
    <literal><![CDATA[
      x * (K(x,y) * ((x \ 1) * z)) = L(K(x,y) * z,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5975,a,b,438,a)].">
      <j1 rule="hyper" parents="119 5975 438"/>
    </justification>
  </clause>

  <clause id="5980">
    <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),5975(a,2,2))].">
      <j1 rule="para" parents="105 5975"/>
    </justification>
  </clause>

  <clause id="5981">
    <literal><![CDATA[
      ((x \ 1) * y) / ((x \ 1) * (K(x,z) * y)) = K(z,x)
    ]]></literal>
    <justification jstring="[para(5975(a,1),5104(a,1,2))].">
      <j1 rule="para" parents="5975 5104"/>
    </justification>
  </clause>

  <clause id="5982">
    <literal><![CDATA[
      ((x \ 1) * (K(y,x) * z)) / ((x \ 1) * z) = K(y,x)
    ]]></literal>
    <justification jstring="[para(5095(a,1),5981(a,1,2,2))].">
      <j1 rule="para" parents="5095 5981"/>
    </justification>
  </clause>

  <clause id="5983">
    <literal><![CDATA[
      L(K(x,y) * z,x \ 1,x) = T(x,y) * ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(5045,a,5979,a),flip(a)].">
      <j1 rule="hyper" parents="5045 5979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5984">
    <literal><![CDATA[
      T(x,y) * ((x \ 1) * (K(y,x) * z)) = L(z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(5095(a,1),5983(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5095 5983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5985">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = R(x,y,x) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,2117,a(flip),b,5743,a),flip(a)].">
      <j1 rule="hyper" parents="320 2117 5743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5986">
    <literal><![CDATA[
      x \ (K(x,y) * L(x,z,x)) = R(x,z,x) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(5066(a,1),5985(a,1,2))].">
      <j1 rule="para" parents="5066 5985"/>
    </justification>
  </clause>

  <clause id="5987">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = (x \ 1) \ (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(3008,a,5775,a)].">
      <j1 rule="hyper" parents="3008 5775"/>
    </justification>
  </clause>

  <clause id="5988">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = (x \ R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,3582,a(flip),b,5987,a),flip(a)].">
      <j1 rule="hyper" parents="320 3582 5987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5989">
    <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(4290(a,1),5844(a,1,2))].">
      <j1 rule="para" parents="4290 5844"/>
    </justification>
  </clause>

  <clause id="5990">
    <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(4290(a,1),5846(a,1,2))].">
      <j1 rule="para" parents="4290 5846"/>
    </justification>
  </clause>

  <clause id="5991">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) = K((x \ (y * z)) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5492,a(flip),b,5856,a),flip(a)].">
      <j1 rule="hyper" parents="320 5492 5856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5992">
    <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(5651(a,1),5867(a,1,1))].">
      <j1 rule="para" parents="5651 5867"/>
    </justification>
  </clause>

  <clause id="5993">
    <literal><![CDATA[
      K((x * ((1 / y) \ 1)) \ 1,z) / y = (1 / y) * K(((1 / y) \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(353,a,5872,a)].">
      <j1 rule="hyper" parents="353 5872"/>
    </justification>
  </clause>

  <clause id="5994">
    <literal><![CDATA[
      ((1 / x) * T((1 / x) \ y,z)) * (y \ 1) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5676,a,b,5873,a)].">
      <j1 rule="hyper" parents="58 5676 5873"/>
    </justification>
  </clause>

  <clause id="5995">
    <literal><![CDATA[
      K(((x \ 1) * (y \ 1)) \ 1,z) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,3946,a(flip),b,5873,a)].">
      <j1 rule="hyper" parents="58 3946 5873"/>
    </justification>
  </clause>

  <clause id="5996">
    <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(5892(a,2),2156(a,1,1,1,1))].">
      <j1 rule="para" parents="5892 2156"/>
    </justification>
  </clause>

  <clause id="5997">
    <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(5092(a,1),5892(a,1,1))].">
      <j1 rule="para" parents="5092 5892"/>
    </justification>
  </clause>

  <clause id="5998">
    <literal><![CDATA[
      ((x \ y) \ 1) \ ((y \ x) * y) = x / ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),5896(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 5896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6000">
    <literal><![CDATA[
      x / ((x \ L(x,y,z)) \ 1) = ((x \ L(x,y,z)) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(5917(a,1),5998(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5917 5998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6001">
    <literal><![CDATA[
      ((x * y) / R(x,y,x)) * x = (y * x) * K(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(4926(a,1),5944(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4926 5944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6002">
    <literal><![CDATA[
      ((x * y) / R(x,y,x)) * x = T(x,y * x) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4876,a(flip),b,6001,a),flip(a)].">
      <j1 rule="hyper" parents="320 4876 6001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6003">
    <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),6002(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 6002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6004">
    <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(5949(a,1),39(a,1))].">
      <j1 rule="para" parents="5949 39"/>
    </justification>
  </clause>

  <clause id="6005">
    <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(5950(a,2),39(a,1))].">
      <j1 rule="para" parents="5950 39"/>
    </justification>
  </clause>

  <clause id="6006">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ K(x,x \ 1) = ((x \ K(x,y)) * T(x,z)) \ 1
    ]]></literal>
    <justification jstring="[para(5956(a,1),3698(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5956 3698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6007">
    <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(5956(a,1),3981(a,1,2))].">
      <j1 rule="para" parents="5956 3981"/>
    </justification>
  </clause>

  <clause id="6008">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * (K(u,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(5130,a,5957,a)].">
      <j1 rule="hyper" parents="5130 5957"/>
    </justification>
  </clause>

  <clause id="6009">
    <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(5628,a,5967,a)].">
      <j1 rule="hyper" parents="5628 5967"/>
    </justification>
  </clause>

  <clause id="6010">
    <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,4947,a,b,6009,a)].">
      <j1 rule="hyper" parents="58 4947 6009"/>
    </justification>
  </clause>

  <clause id="6011">
    <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(5968(a,2),38(a,1))].">
      <j1 rule="para" parents="5968 38"/>
    </justification>
  </clause>

  <clause id="6012">
    <literal><![CDATA[
      K((((x \ y) \ 1) * (x \ 1)) \ 1,z) = (1 / (x \ y)) * (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),5995(a,2,2,2,1))].">
      <j1 rule="para" parents="5 5995"/>
    </justification>
  </clause>

  <clause id="6013">
    <literal><![CDATA[
      1 / ((1 / x) * (y \ T(y * x,z))) = K(z,((x \ 1) * (y \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[para(5995(a,1),4931(a,1,2))].">
      <j1 rule="para" parents="5995 4931"/>
    </justification>
  </clause>

  <clause id="6014">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) = (y * z) / (y * (K(u,x) * z))
    ]]></literal>
    <justification jstring="[hyper(131,a,6008,a),flip(a)].">
      <j1 rule="hyper" parents="131 6008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6015">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * (K(y,x) * w)) = R(y,z,u) * w
    ]]></literal>
    <justification jstring="[para(1305(a,1),6008(a,1,1,2))].">
      <j1 rule="para" parents="1305 6008"/>
    </justification>
  </clause>

  <clause id="6016">
    <literal><![CDATA[
      R(x,y,z) * (K(u,x) * w) = K(u,x) * (R(x,y,z) * w)
    ]]></literal>
    <justification jstring="[para(5095(a,1),6015(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5095 6015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6017">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * (y \ w)) = R(y,z,u) * (T(y,x) \ w)
    ]]></literal>
    <justification jstring="[para(5042(a,1),6015(a,1,2,2))].">
      <j1 rule="para" parents="5042 6015"/>
    </justification>
  </clause>

  <clause id="6018">
    <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(6010(a,1),38(a,1))].">
      <j1 rule="para" parents="6010 38"/>
    </justification>
  </clause>

  <clause id="6019">
    <literal><![CDATA[
      (x * y) * L((z \ (y \ z)) * z,y,x) = (x * K(y \ 1,z)) * z
    ]]></literal>
    <justification jstring="[para(3503(a,2),5026(a,1,2))].">
      <j1 rule="para" parents="3503 5026"/>
    </justification>
  </clause>

  <clause id="6020">
    <literal><![CDATA[
      K(1 / x,x) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(3375(a,1),5031(a,1,1))].">
      <j1 rule="para" parents="3375 5031"/>
    </justification>
  </clause>

  <clause id="6021">
    <literal><![CDATA[
      (x / L(x,y,z)) * (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,5620,a(flip),b,6020,a),flip(a)].">
      <j1 rule="hyper" parents="58 5620 6020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6023">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(5916(a,1),6021(a,1,1))].">
      <j1 rule="para" parents="5916 6021"/>
    </justification>
  </clause>

  <clause id="6024">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) / x = L(1 / x,y,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(353,a,6023,a)].">
      <j1 rule="hyper" parents="353 6023"/>
    </justification>
  </clause>

  <clause id="6025">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (L(x,y,z) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,6023,a)].">
      <j1 rule="hyper" parents="123 6023"/>
    </justification>
  </clause>

  <clause id="6026">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) / x = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3763,a(flip),b,6024,a),flip(a)].">
      <j1 rule="hyper" parents="320 3763 6024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6027">
    <literal><![CDATA[
      T(x,x \ (L(x \ 1,y,z) \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(31,a,3783,a,b,6026,a)].">
      <j1 rule="hyper" parents="31 3783 6026"/>
    </justification>
  </clause>

  <clause id="6028">
    <literal><![CDATA[
      T(x,x \ (((y * x) \ y) \ 1)) = x
    ]]></literal>
    <justification jstring="[para(217(a,1),6027(a,1,2,2,1))].">
      <j1 rule="para" parents="217 6027"/>
    </justification>
  </clause>

  <clause id="6029">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) / y = y \ (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(6028(a,1),3754(a,1,2))].">
      <j1 rule="para" parents="6028 3754"/>
    </justification>
  </clause>

  <clause id="6030">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) / ((y \ 1) \ 1) = y \ (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5894,a,b,6029,a)].">
      <j1 rule="hyper" parents="58 5894 6029"/>
    </justification>
  </clause>

  <clause id="6031">
    <literal><![CDATA[
      L(T(x \ 1,y) \ z,x \ 1,x) = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5902,a(flip),b,5141,a),flip(a)].">
      <j1 rule="hyper" parents="320 5902 5141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6032">
    <literal><![CDATA[
      (1 / x) * (L(x,y,z) \ x) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5240,a(flip),b,5239,a),flip(a)].">
      <j1 rule="hyper" parents="58 5240 5239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6033">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,(x \ 1) * L((x \ 1) \ 1,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,179,a(flip),b,5658,a),flip(a)].">
      <j1 rule="hyper" parents="320 179 5658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6035">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x \ L(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[para(1185(a,1),6033(a,1,2))].">
      <j1 rule="para" parents="1185 6033"/>
    </justification>
  </clause>

  <clause id="6036">
    <literal><![CDATA[
      T(x \ L(x,y,z),L(x,u,w) \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(4913,a,6035,a)].">
      <j1 rule="hyper" parents="4913 6035"/>
    </justification>
  </clause>

  <clause id="6037">
    <literal><![CDATA[
      T(L(x,y,z) * (x \ 1),L(x,u,w) \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1186(a,2),6036(a,1,1))].">
      <j1 rule="para" parents="1186 6036"/>
    </justification>
  </clause>

  <clause id="6038">
    <literal><![CDATA[
      (L(x,y,z) * (x \ 1)) \ (x \ 1) = (x \ 1) / (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(6037(a,1),4152(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6037 4152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6039">
    <literal><![CDATA[
      (L(x,y,z) * (x \ 1)) \ (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,3209,a(flip),b,6038,a),flip(a)].">
      <j1 rule="hyper" parents="320 3209 6038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6040">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1186(a,1),6039(a,1,1))].">
      <j1 rule="para" parents="1186 6039"/>
    </justification>
  </clause>

  <clause id="6041">
    <literal><![CDATA[
      (x \ 1) * (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,3557,a(flip),b,6040,a)].">
      <j1 rule="hyper" parents="58 3557 6040"/>
    </justification>
  </clause>

  <clause id="6042">
    <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(6040(a,1),1689(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6040 1689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6043">
    <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(6040(a,1),3504(a,2,2,1))].">
      <j1 rule="para" parents="6040 3504"/>
    </justification>
  </clause>

  <clause id="6044">
    <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(6040(a,1),5015(a,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6040 5015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6045">
    <literal><![CDATA[
      T(L(x,y,z) \ x,x \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(239,a,6023,a,b,6041,a)].">
      <j1 rule="hyper" parents="239 6023 6041"/>
    </justification>
  </clause>

  <clause id="6046">
    <literal><![CDATA[
      (x / R(y,y \ x,y)) * y = T(y,x) * T(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4270(a,1),6003(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4270 6003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6047">
    <literal><![CDATA[
      (x / R(y,y \ x,y)) * y = (y \ x) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4091,a(flip),b,6046,a),flip(a)].">
      <j1 rule="hyper" parents="320 4091 6046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6048">
    <literal><![CDATA[
      x / R(y,y \ x,y) = y \ (x * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(30,a,4903,a,b,6047,a),flip(a)].">
      <j1 rule="hyper" parents="30 4903 6047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6049">
    <literal><![CDATA[
      x / R(y,y \ x,y) = (y * K(x,y)) \ x
    ]]></literal>
    <justification jstring="[hyper(320,a,5337,a,b,6048,a),flip(a)].">
      <j1 rule="hyper" parents="320 5337 6048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6050">
    <literal><![CDATA[
      x / R(y,y \ x,y) = K(y,x) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5149,a(flip),b,6048,a),flip(a)].">
      <j1 rule="hyper" parents="320 5149 6048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6051">
    <literal><![CDATA[
      x / ((y \ x) \ T(x,y)) = (y * K(x,y)) \ x
    ]]></literal>
    <justification jstring="[para(4294(a,1),6049(a,1,2))].">
      <j1 rule="para" parents="4294 6049"/>
    </justification>
  </clause>

  <clause id="6052">
    <literal><![CDATA[
      ((x * K(y,x)) \ y) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(188,a,6051,a)].">
      <j1 rule="hyper" parents="188 6051"/>
    </justification>
  </clause>

  <clause id="6053">
    <literal><![CDATA[
      (x \ (y * K(x,y))) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5337(a,1),6052(a,1,1))].">
      <j1 rule="para" parents="5337 6052"/>
    </justification>
  </clause>

  <clause id="6054">
    <literal><![CDATA[
      (x \ ((x * y) / x)) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4711(a,2),6053(a,1,1,2))].">
      <j1 rule="para" parents="4711 6053"/>
    </justification>
  </clause>

  <clause id="6055">
    <literal><![CDATA[
      x * (y * ((z \ (y \ z)) * z)) = (x * K(y \ 1,z)) * z
    ]]></literal>
    <justification jstring="[hyper(286,a,6019,a)].">
      <j1 rule="hyper" parents="286 6019"/>
    </justification>
  </clause>

  <clause id="6056">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * z = x * (z * K(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(5029(a,1),6055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5029 6055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6057">
    <literal><![CDATA[
      R(x,K(y \ 1,z),z) = x
    ]]></literal>
    <justification jstring="[hyper(2895,a,6056,a)].">
      <j1 rule="hyper" parents="2895 6056"/>
    </justification>
  </clause>

  <clause id="6058">
    <literal><![CDATA[
      R(x,K(y,z),z) = x
    ]]></literal>
    <justification jstring="[para(75(a,1),6057(a,1,2,1))].">
      <j1 rule="para" parents="75 6057"/>
    </justification>
  </clause>

  <clause id="6059">
    <literal><![CDATA[
      R(x,y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(5778,a,6058,a)].">
      <j1 rule="hyper" parents="5778 6058"/>
    </justification>
  </clause>

  <clause id="6060">
    <literal><![CDATA[
      (x * K(y,z)) * z = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[para(6058(a,1),2894(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6058 2894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6061">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(6059(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6059 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6062">
    <literal><![CDATA[
      (x * (y * K(z,y))) / y = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,6060,a)].">
      <j1 rule="hyper" parents="131 6060"/>
    </justification>
  </clause>

  <clause id="6063">
    <literal><![CDATA[
      (x / ((y * z) / y)) * K(y,z) = x / z
    ]]></literal>
    <justification jstring="[hyper(117,a,4880,a(flip),b,6060,a),flip(a)].">
      <j1 rule="hyper" parents="117 4880 6060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6064">
    <literal><![CDATA[
      L(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(479,a,6061,a)].">
      <j1 rule="hyper" parents="479 6061"/>
    </justification>
  </clause>

  <clause id="6065">
    <literal><![CDATA[
      (x / y) * (y * K(z,y)) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(326,a,6061,a),flip(a)].">
      <j1 rule="hyper" parents="326 6061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6066">
    <literal><![CDATA[
      (x * K(y,z)) * z = (x * z) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,6060,a,b,6061,a)].">
      <j1 rule="hyper" parents="320 6060 6061"/>
    </justification>
  </clause>

  <clause id="6067">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * ((z * y) / z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4856,a,b,6061,a),flip(a)].">
      <j1 rule="hyper" parents="320 4856 6061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6068">
    <literal><![CDATA[
      (x / (y * K(z,y))) * y = x / K(z,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,6061,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 6061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6069">
    <literal><![CDATA[
      a(x,y,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,6061,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="115 6061 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6071">
    <literal><![CDATA[
      (x * (y \ z)) * K(y,y \ z) = x * (z / y)
    ]]></literal>
    <justification jstring="[para(4735(a,1),6061(a,2,2))].">
      <j1 rule="para" parents="4735 6061"/>
    </justification>
  </clause>

  <clause id="6072">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5862,a,6069,a)].">
      <j1 rule="hyper" parents="5862 6069"/>
    </justification>
  </clause>

  <clause id="6073">
    <literal><![CDATA[
      a(x,1,y) = a(z,u,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,375,a,b,6069,a)].">
      <j1 rule="hyper" parents="320 375 6069"/>
    </justification>
  </clause>

  <clause id="6074">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,6069,a(flip),b,5861,a),flip(a)].">
      <j1 rule="hyper" parents="116 6069 5861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6075">
    <literal><![CDATA[
      a(x,T(y,z),K(z,y)) = 1
    ]]></literal>
    <justification jstring="[para(4117(a,1),6069(a,1,3))].">
      <j1 rule="para" parents="4117 6069"/>
    </justification>
  </clause>

  <clause id="6076">
    <literal><![CDATA[
      L(K(x,y),y,z) = L(K(x,y),y,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,6064,a,b,6064,a)].">
      <j1 rule="hyper" parents="320 6064 6064"/>
    </justification>
  </clause>

  <clause id="6078">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5645,a(flip),b,6064,a)].">
      <j1 rule="hyper" parents="58 5645 6064"/>
    </justification>
  </clause>

  <clause id="6080">
    <literal><![CDATA[
      K(L(x \ 1,x,y) \ 1,z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(5776,a,6072,a)].">
      <j1 rule="hyper" parents="5776 6072"/>
    </justification>
  </clause>

  <clause id="6081">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(4727,a,6072,a)].">
      <j1 rule="hyper" parents="4727 6072"/>
    </justification>
  </clause>

  <clause id="6082">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(u \ (u * x),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,673,a,b,6072,a),flip(a)].">
      <j1 rule="hyper" parents="320 673 6072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6084">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,6072,a(flip),b,4726,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 6072 4726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6085">
    <literal><![CDATA[
      (x * y) * K(y,z) = x * (y * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,6072,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 6072 13"/>
    </justification>
  </clause>

  <clause id="6086">
    <literal><![CDATA[
      (x * y) * K(y,z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(6072(a,1),4790(a,1,2))].">
      <j1 rule="para" parents="6072 4790"/>
    </justification>
  </clause>

  <clause id="6087">
    <literal><![CDATA[
      L(K(x,y),T(y,x),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(47,a,6075,a)].">
      <j1 rule="hyper" parents="47 6075"/>
    </justification>
  </clause>

  <clause id="6088">
    <literal><![CDATA[
      L(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6074(a,2),4945(a,1))].">
      <j1 rule="para" parents="6074 4945"/>
    </justification>
  </clause>

  <clause id="6089">
    <literal><![CDATA[
      L(K(x,y),T(y,x),z) \ u = T(y,x) * (y \ u)
    ]]></literal>
    <justification jstring="[para(6087(a,2),4747(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6087 4747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6091">
    <literal><![CDATA[
      L(K(x,y \ z),y \ z,u) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,5645,a(flip),b,6076,a),flip(a)].">
      <j1 rule="hyper" parents="320 5645 6076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6092">
    <literal><![CDATA[
      L(K(x,y),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6076(a,1),3637(a,1))].">
      <j1 rule="para" parents="6076 3637"/>
    </justification>
  </clause>

  <clause id="6093">
    <literal><![CDATA[
      K(x,1 / (y \ z)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(5457,a,6078,a)].">
      <j1 rule="hyper" parents="5457 6078"/>
    </justification>
  </clause>

  <clause id="6094">
    <literal><![CDATA[
      K((x \ y) \ 1,(y \ x) \ 1) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2567,a(flip),b,6078,a),flip(a)].">
      <j1 rule="hyper" parents="320 2567 6078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6095">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(118,a,6078,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 6078 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6096">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5711,a,b,6078,a)].">
      <j1 rule="hyper" parents="58 5711 6078"/>
    </justification>
  </clause>

  <clause id="6097">
    <literal><![CDATA[
      K(x,(y * z) \ y) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),6078(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 6078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6099">
    <literal><![CDATA[
      K(x,((y * z) * u) \ (y * (z * u))) = K(x,a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,2),6078(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 6078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6101">
    <literal><![CDATA[
      K(x,(y \ (y / z)) \ 1) = K(x,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),6078(a,2,2))].">
      <j1 rule="para" parents="75 6078"/>
    </justification>
  </clause>

  <clause id="6102">
    <literal><![CDATA[
      K(x,L(y \ z,y,u) \ 1) = K(x,(u * z) \ (u * y))
    ]]></literal>
    <justification jstring="[para(92(a,2),6078(a,1,2,1))].">
      <j1 rule="para" parents="92 6078"/>
    </justification>
  </clause>

  <clause id="6103">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ y) = K(x,a(y,z,z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(704(a,1),6078(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="704 6078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6104">
    <literal><![CDATA[
      K(x,(T(y,z) * (y \ u)) \ 1) = K(x,(T(y,z) * u) \ y)
    ]]></literal>
    <justification jstring="[para(1101(a,1),6078(a,1,2,1))].">
      <j1 rule="para" parents="1101 6078"/>
    </justification>
  </clause>

  <clause id="6107">
    <literal><![CDATA[
      (((x \ y) \ 1) \ z) * ((x \ y) \ 1) = z * K((x \ y) * z,y \ x)
    ]]></literal>
    <justification jstring="[para(6078(a,1),4449(a,2,2))].">
      <j1 rule="para" parents="6078 4449"/>
    </justification>
  </clause>

  <clause id="6108">
    <literal><![CDATA[
      K((x \ y) \ 1,z) = K(z,y \ x) \ 1
    ]]></literal>
    <justification jstring="[para(6078(a,1),4929(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6078 4929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6109">
    <literal><![CDATA[
      K(x,(T(y,z) * (y \ u)) \ 1) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[para(4747(a,2),6078(a,1,2,1))].">
      <j1 rule="para" parents="4747 6078"/>
    </justification>
  </clause>

  <clause id="6110">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[para(5092(a,1),6078(a,1,2,1))].">
      <j1 rule="para" parents="5092 6078"/>
    </justification>
  </clause>

  <clause id="6111">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) \ 1) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(5092(a,1),6078(a,2,2))].">
      <j1 rule="para" parents="5092 6078"/>
    </justification>
  </clause>

  <clause id="6112">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,(z * u) \ T(z,y))
    ]]></literal>
    <justification jstring="[para(5137(a,1),6078(a,1,2,1))].">
      <j1 rule="para" parents="5137 6078"/>
    </justification>
  </clause>

  <clause id="6113">
    <literal><![CDATA[
      K(x,y \ z) * K(x * ((z \ y) \ 1),x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(6078(a,1),5255(a,1,1))].">
      <j1 rule="para" parents="6078 5255"/>
    </justification>
  </clause>

  <clause id="6114">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) \ 1) = L(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(6078(a,1),5639(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6078 5639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6115">
    <literal><![CDATA[
      x * K(y,z \ x) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[para(6078(a,1),4709(a,1,2))].">
      <j1 rule="para" parents="6078 4709"/>
    </justification>
  </clause>

  <clause id="6116">
    <literal><![CDATA[
      T(x,y) != K(z,u \ y)
    ]]></literal>
    <literal><![CDATA[
      K(z,y / u) = x
    ]]></literal>
    <justification jstring="[para(6078(a,1),5712(a,2))].">
      <j1 rule="para" parents="6078 5712"/>
    </justification>
  </clause>

  <clause id="6117">
    <literal><![CDATA[
      x \ (y * K(x \ y,z)) = T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(613,a,6086,a)].">
      <j1 rule="hyper" parents="613 6086"/>
    </justification>
  </clause>

  <clause id="6118">
    <literal><![CDATA[
      (x * K(y,z)) / T(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(595,a,6086,a)].">
      <j1 rule="hyper" parents="595 6086"/>
    </justification>
  </clause>

  <clause id="6119">
    <literal><![CDATA[
      (x / y) \ (x * K(y,z)) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(571,a,6086,a)].">
      <j1 rule="hyper" parents="571 6086"/>
    </justification>
  </clause>

  <clause id="6120">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) = T(z * x,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(440,a,xx,b,6086,a),flip(a)].">
      <j1 rule="hyper" parents="440 6086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6121">
    <literal><![CDATA[
      (x / y) * T(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(326,a,6086,a),flip(a)].">
      <j1 rule="hyper" parents="326 6086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6123">
    <literal><![CDATA[
      K(x,y) * (z * T(y,x)) = T(z * y,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(239,a,6086,a,b,5095,a),flip(a)].">
      <j1 rule="hyper" parents="239 6086 5095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6124">
    <literal><![CDATA[
      (x * y) \ (x * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,6086,a)].">
      <j1 rule="hyper" parents="123 6086"/>
    </justification>
  </clause>

  <clause id="6125">
    <literal><![CDATA[
      x * T(x \ y,z) != y * u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(6086(a,1),322(a,1)),flip(b)].">
      <j1 rule="para" parents="6086 322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6126">
    <literal><![CDATA[
      R(x,T(y,x),K(x,z)) \ (y * T(x,z)) = T(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(6086(a,1),540(a,1,2))].">
      <j1 rule="para" parents="6086 540"/>
    </justification>
  </clause>

  <clause id="6127">
    <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(6086(a,1),541(a,1,2))].">
      <j1 rule="para" parents="6086 541"/>
    </justification>
  </clause>

  <clause id="6128">
    <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(6086(a,1),510(a,1,1))].">
      <j1 rule="para" parents="6086 510"/>
    </justification>
  </clause>

  <clause id="6130">
    <literal><![CDATA[
      K(x,y) * T(y * x,z) = (x * y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(4772(a,1),6086(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4772 6086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6131">
    <literal><![CDATA[
      (x * y) * (z * K(y,z)) = (x * T(y,z)) * z
    ]]></literal>
    <justification jstring="[para(6086(a,1),6060(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6086 6060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6135">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(4726(a,1),6088(a,1))].">
      <j1 rule="para" parents="4726 6088"/>
    </justification>
  </clause>

  <clause id="6136">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(5645(a,1),6092(a,1))].">
      <j1 rule="para" parents="5645 6092"/>
    </justification>
  </clause>

  <clause id="6137">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ (y * z)) = K(x,1 / L(u,z,y))
    ]]></literal>
    <justification jstring="[para(13(a,2),6093(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13 6093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6138">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(75(a,1),6093(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 6093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6139">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = z * K(z * (x \ y),y \ x)
    ]]></literal>
    <justification jstring="[para(6093(a,1),5836(a,2,2))].">
      <j1 rule="para" parents="6093 5836"/>
    </justification>
  </clause>

  <clause id="6141">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = K(z \ y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(320,a,4749,a(flip),b,6095,a),flip(a)].">
      <j1 rule="hyper" parents="320 4749 6095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6142">
    <literal><![CDATA[
      (1 / (x \ y)) * T(z,y \ x) = z * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(119,a,6095,a(flip),b,2934,a)].">
      <j1 rule="hyper" parents="119 6095 2934"/>
    </justification>
  </clause>

  <clause id="6143">
    <literal><![CDATA[
      ((x \ y) \ 1) * T(z,y \ x) = z * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,6095,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 6095 17"/>
    </justification>
  </clause>

  <clause id="6144">
    <literal><![CDATA[
      T(x,(y * z) \ y) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),6095(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 6095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6145">
    <literal><![CDATA[
      T(x,((y * z) \ y) \ 1) = T(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6095(a,2,2))].">
      <j1 rule="para" parents="4 6095"/>
    </justification>
  </clause>

  <clause id="6147">
    <literal><![CDATA[
      T(x,y \ (y / z)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),6095(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 6095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6148">
    <literal><![CDATA[
      T(x \ y,y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ 1) \ 1 = z
    ]]></literal>
    <justification jstring="[para(6095(a,1),428(a,1))].">
      <j1 rule="para" parents="6095 428"/>
    </justification>
  </clause>

  <clause id="6149">
    <literal><![CDATA[
      T(x,y \ z) / ((z \ y) \ x) = x / ((x \ ((z \ y) \ x)) * x)
    ]]></literal>
    <justification jstring="[para(6095(a,1),4366(a,1,1))].">
      <j1 rule="para" parents="6095 4366"/>
    </justification>
  </clause>

  <clause id="6150">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(72(a,1),6096(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6151">
    <literal><![CDATA[
      T(x,K(y,x / z)) = T(x,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(6096(a,1),4193(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6096 4193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6152">
    <literal><![CDATA[
      T(K(x / (y / z),y / z),y) = K(x * (1 / (y / z)),z \ y)
    ]]></literal>
    <justification jstring="[para(5828(a,1),6096(a,1,1))].">
      <j1 rule="para" parents="5828 6096"/>
    </justification>
  </clause>

  <clause id="6154">
    <literal><![CDATA[
      (((x * y) \ x) * z) * K(z,y \ 1) = z * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,6097,a(flip),b,11,a(flip))].">
      <j1 rule="hyper" parents="119 6097 11"/>
    </justification>
  </clause>

  <clause id="6159">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(32,a,1486,a(flip),b,6118,a),flip(a)].">
      <j1 rule="hyper" parents="32 1486 6118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6160">
    <literal><![CDATA[
      (x / y) * ((y \ z) \ z) = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[para(6118(a,1),369(a,1,1))].">
      <j1 rule="para" parents="6118 369"/>
    </justification>
  </clause>

  <clause id="6161">
    <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(6119(a,1),1012(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6119 1012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6162">
    <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(6119(a,1),5524(a,1,2))].">
      <j1 rule="para" parents="6119 5524"/>
    </justification>
  </clause>

  <clause id="6163">
    <literal><![CDATA[
      T(x,y * (1 / x)) = T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(5821,a,6121,a),flip(a)].">
      <j1 rule="hyper" parents="5821 6121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6164">
    <literal><![CDATA[
      (x * T(y,z)) / y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(1503,a,6121,a)].">
      <j1 rule="hyper" parents="1503 6121"/>
    </justification>
  </clause>

  <clause id="6165">
    <literal><![CDATA[
      (x * K(y,z)) / (x / y) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(117,a,6121,a(flip),b,456,a)].">
      <j1 rule="hyper" parents="117 6121 456"/>
    </justification>
  </clause>

  <clause id="6166">
    <literal><![CDATA[
      x * K(y \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(6121(a,1),348(a,1))].">
      <j1 rule="para" parents="6121 348"/>
    </justification>
  </clause>

  <clause id="6167">
    <literal><![CDATA[
      (x * K(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(6121(a,1),1481(a,1,1))].">
      <j1 rule="para" parents="6121 1481"/>
    </justification>
  </clause>

  <clause id="6168">
    <literal><![CDATA[
      T(x * K(y,z),y) = y \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[para(6121(a,1),1479(a,1,1))].">
      <j1 rule="para" parents="6121 1479"/>
    </justification>
  </clause>

  <clause id="6169">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x / y = u
    ]]></literal>
    <justification jstring="[para(6121(a,1),1499(a,1))].">
      <j1 rule="para" parents="6121 1499"/>
    </justification>
  </clause>

  <clause id="6170">
    <literal><![CDATA[
      (x * y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6124(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6124 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6173">
    <literal><![CDATA[
      (x * (y / x)) \ (K(x,x \ y) * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(4742(a,1),6124(a,1,1))].">
      <j1 rule="para" parents="4742 6124"/>
    </justification>
  </clause>

  <clause id="6174">
    <literal><![CDATA[
      T(x,y \ (y / z)) = T(x,1 / z)
    ]]></literal>
    <justification jstring="[hyper(118,a,6138,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 6138 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6175">
    <literal><![CDATA[
      K(x,y \ (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(6138(a,2),5036(a,1))].">
      <j1 rule="para" parents="6138 5036"/>
    </justification>
  </clause>

  <clause id="6176">
    <literal><![CDATA[
      T(x * y,y \ 1) = ((x * y) \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(428,a,6144,a),flip(a)].">
      <j1 rule="hyper" parents="428 6144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6177">
    <literal><![CDATA[
      T(x,L(y \ 1,y,z)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,1361,a,b,6144,a)].">
      <j1 rule="hyper" parents="58 1361 6144"/>
    </justification>
  </clause>

  <clause id="6178">
    <literal><![CDATA[
      ((x * y) \ x) * T(z,y \ 1) = z * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,6144,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 6144 17"/>
    </justification>
  </clause>

  <clause id="6179">
    <literal><![CDATA[
      x / T(x * y,y \ 1) = (x * y) \ x
    ]]></literal>
    <justification jstring="[para(6144(a,1),265(a,1,2))].">
      <j1 rule="para" parents="6144 265"/>
    </justification>
  </clause>

  <clause id="6181">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * T(z,y) = z * (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(119,a,6145,a(flip),b,2934,a)].">
      <j1 rule="hyper" parents="119 6145 2934"/>
    </justification>
  </clause>

  <clause id="6183">
    <literal><![CDATA[
      T(x,L(y \ 1,y,z) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(217(a,2),6145(a,1,2,1))].">
      <j1 rule="para" parents="217 6145"/>
    </justification>
  </clause>

  <clause id="6184">
    <literal><![CDATA[
      T(x,y \ (y / z)) = T(x,(z \ u) / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,4412,a,b,6147,a),flip(a)].">
      <j1 rule="hyper" parents="320 4412 6147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6187">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(1928,a,6150,a)].">
      <j1 rule="hyper" parents="1928 6150"/>
    </justification>
  </clause>

  <clause id="6188">
    <literal><![CDATA[
      K(x,T(y,z / y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(4248(a,2),6150(a,1,2))].">
      <j1 rule="para" parents="4248 6150"/>
    </justification>
  </clause>

  <clause id="6189">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4228(a,2),6150(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4228 6150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6190">
    <literal><![CDATA[
      (T(x,y) / y) * K(y,x) = x / y
    ]]></literal>
    <justification jstring="[hyper(4261,a,6159,a)].">
      <j1 rule="hyper" parents="4261 6159"/>
    </justification>
  </clause>

  <clause id="6191">
    <literal><![CDATA[
      T(x / T(y,z),K(y,z)) = K(z,y) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(239,a,6159,a,b,5095,a)].">
      <j1 rule="hyper" parents="239 6159 5095"/>
    </justification>
  </clause>

  <clause id="6192">
    <literal><![CDATA[
      (x / (y \ z)) * K(z / y,y) = x / (z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),6159(a,1,1,2))].">
      <j1 rule="para" parents="107 6159"/>
    </justification>
  </clause>

  <clause id="6193">
    <literal><![CDATA[
      (1 / x) * K(x,y) = K(x,y) / x
    ]]></literal>
    <justification jstring="[para(4715(a,1),6159(a,1,1))].">
      <j1 rule="para" parents="4715 6159"/>
    </justification>
  </clause>

  <clause id="6194">
    <literal><![CDATA[
      (x * K(y,x)) * K(y,x) = (T(y,x) * x) / y
    ]]></literal>
    <justification jstring="[para(4922(a,1),6159(a,1,1))].">
      <j1 rule="para" parents="4922 6159"/>
    </justification>
  </clause>

  <clause id="6195">
    <literal><![CDATA[
      (x * K(y,z)) / y = (x / y) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6118(a,1),6159(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6118 6159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6196">
    <literal><![CDATA[
      T(x,(y / (1 / x)) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),6163(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 6163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6197">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * T(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(188,a,6164,a)].">
      <j1 rule="hyper" parents="188 6164"/>
    </justification>
  </clause>

  <clause id="6198">
    <literal><![CDATA[
      (x * K(y,z)) * y != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6164(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6164 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6199">
    <literal><![CDATA[
      R(x,K(y,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(4813,a,6167,a)].">
      <j1 rule="hyper" parents="4813 6167"/>
    </justification>
  </clause>

  <clause id="6201">
    <literal><![CDATA[
      (x * K(y,z)) * y = (x * y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,6086,a,b,6167,a),flip(a)].">
      <j1 rule="hyper" parents="320 6086 6167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6202">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * y = T(y,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2876,a,b,6167,a),flip(a)].">
      <j1 rule="hyper" parents="320 2876 6167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6204">
    <literal><![CDATA[
      (x * K(y,z)) \ ((x * y) * K(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,6086,a,b,6167,a)].">
      <j1 rule="hyper" parents="116 6086 6167"/>
    </justification>
  </clause>

  <clause id="6205">
    <literal><![CDATA[
      ((x / y) * K(y,z)) \ (x * K(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,6121,a(flip),b,6167,a)].">
      <j1 rule="hyper" parents="116 6121 6167"/>
    </justification>
  </clause>

  <clause id="6206">
    <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,449,a(flip),b,6167,a)].">
      <j1 rule="hyper" parents="116 449 6167"/>
    </justification>
  </clause>

  <clause id="6207">
    <literal><![CDATA[
      (x * y) * K(T(x,y),z) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(30,a,1340,a,b,6167,a),flip(a)].">
      <j1 rule="hyper" parents="30 1340 6167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6208">
    <literal><![CDATA[
      (x * (y * T(z,u))) \ ((x * (y * K(z,u))) * z) = a(x,y * K(z,u),z)
    ]]></literal>
    <justification jstring="[para(6167(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6167 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6209">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) = (y * T(x,z)) \ (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(6167(a,1),217(a,2,1))].">
      <j1 rule="para" parents="6167 217"/>
    </justification>
  </clause>

  <clause id="6210">
    <literal><![CDATA[
      x \ (y * T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y * K(x,z),x) = u
    ]]></literal>
    <justification jstring="[para(6167(a,1),288(a,1,2))].">
      <j1 rule="para" parents="6167 288"/>
    </justification>
  </clause>

  <clause id="6211">
    <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(6167(a,1),482(a,1,2,2))].">
      <j1 rule="para" parents="6167 482"/>
    </justification>
  </clause>

  <clause id="6212">
    <literal><![CDATA[
      (T(x,y) \ 1) * y = (x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(4760(a,1),6167(a,1,1))].">
      <j1 rule="para" parents="4760 6167"/>
    </justification>
  </clause>

  <clause id="6213">
    <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(6167(a,1),5454(a,1,2,1))].">
      <j1 rule="para" parents="6167 5454"/>
    </justification>
  </clause>

  <clause id="6214">
    <literal><![CDATA[
      (x * (y * K(z,y))) * z = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(6061(a,1),6167(a,1,1))].">
      <j1 rule="para" parents="6061 6167"/>
    </justification>
  </clause>

  <clause id="6215">
    <literal><![CDATA[
      T(K(x,y),y * z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),6187(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 6187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6216">
    <literal><![CDATA[
      K(x,y) * (1 / x) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(1290,a,6193,a)].">
      <j1 rule="hyper" parents="1290 6193"/>
    </justification>
  </clause>

  <clause id="6217">
    <literal><![CDATA[
      (K(x,y) / x) * L(z,K(x,y),x \ 1) = (1 / x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(6193(a,1),3660(a,1,1))].">
      <j1 rule="para" parents="6193 3660"/>
    </justification>
  </clause>

  <clause id="6218">
    <literal><![CDATA[
      L(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(4812,a,6197,a)].">
      <j1 rule="hyper" parents="4812 6197"/>
    </justification>
  </clause>

  <clause id="6219">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * y) = y * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5730,a(flip),b,6218,a)].">
      <j1 rule="hyper" parents="58 5730 6218"/>
    </justification>
  </clause>

  <clause id="6220">
    <literal><![CDATA[
      (x * K(y,z)) * L(y,u,w) = x * (K(y,z) * L(y,u,w))
    ]]></literal>
    <justification jstring="[para(6218(a,1),446(a,1,2,1))].">
      <j1 rule="para" parents="6218 446"/>
    </justification>
  </clause>

  <clause id="6222">
    <literal><![CDATA[
      L(x * y,K(y * x,z),u) = (y \ (y * x)) * y
    ]]></literal>
    <justification jstring="[para(6218(a,1),3501(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6218 3501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6223">
    <literal><![CDATA[
      L(x,x \ T(x,y),z) = x
    ]]></literal>
    <justification jstring="[para(4688(a,1),6218(a,1,2))].">
      <j1 rule="para" parents="4688 6218"/>
    </justification>
  </clause>

  <clause id="6226">
    <literal><![CDATA[
      T(K(x,y),z * y) = T(K(x,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,6189,a,b,6215,a)].">
      <j1 rule="hyper" parents="320 6189 6215"/>
    </justification>
  </clause>

  <clause id="6227">
    <literal><![CDATA[
      (x * y) * K(z,T(x,y)) = K(z,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,6215,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 6215 17"/>
    </justification>
  </clause>

  <clause id="6228">
    <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(6215(a,1),5606(a,1,2))].">
      <j1 rule="para" parents="6215 5606"/>
    </justification>
  </clause>

  <clause id="6229">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(217(a,1),6080(a,1,1,1))].">
      <j1 rule="para" parents="217 6080"/>
    </justification>
  </clause>

  <clause id="6230">
    <literal><![CDATA[
      K((x \ y) \ 1,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(390(a,1),6080(a,1,1,1))].">
      <j1 rule="para" parents="390 6080"/>
    </justification>
  </clause>

  <clause id="6235">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,z) = ((x * y) \ x) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,6229,a(flip),b,4705,a),flip(a)].">
      <j1 rule="hyper" parents="116 6229 4705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6236">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * K(y,z) = T(1 / ((x * y) \ x),z)
    ]]></literal>
    <justification jstring="[para(6229(a,1),4722(a,1,2))].">
      <j1 rule="para" parents="6229 4722"/>
    </justification>
  </clause>

  <clause id="6237">
    <literal><![CDATA[
      K(1 / (x \ y),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(5244,a,6230,a)].">
      <j1 rule="hyper" parents="5244 6230"/>
    </justification>
  </clause>

  <clause id="6239">
    <literal><![CDATA[
      T(K(x / y,z),x) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5501,a,b,6230,a)].">
      <j1 rule="hyper" parents="58 5501 6230"/>
    </justification>
  </clause>

  <clause id="6240">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((y / z) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5494,a,b,6230,a)].">
      <j1 rule="hyper" parents="58 5494 6230"/>
    </justification>
  </clause>

  <clause id="6241">
    <literal><![CDATA[
      K((x \ (y * z)) \ 1,y) = K((y / (z \ 1)) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5991,a(flip),b,6230,a)].">
      <j1 rule="hyper" parents="58 5991 6230"/>
    </justification>
  </clause>

  <clause id="6242">
    <literal><![CDATA[
      (x \ y) \ K(y \ x,z) = T((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,6230,a(flip),b,4705,a)].">
      <j1 rule="hyper" parents="116 6230 4705"/>
    </justification>
  </clause>

  <clause id="6243">
    <literal><![CDATA[
      K((x * y) \ x,z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6230(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 6230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6244">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K((x * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(17(a,2),6230(a,1,1,1))].">
      <j1 rule="para" parents="17 6230"/>
    </justification>
  </clause>

  <clause id="6248">
    <literal><![CDATA[
      K((K(x,y) * z) \ 1,u) = K(z \ K(y,x),u)
    ]]></literal>
    <justification jstring="[para(5092(a,1),6230(a,1,1,1))].">
      <j1 rule="para" parents="5092 6230"/>
    </justification>
  </clause>

  <clause id="6250">
    <literal><![CDATA[
      (x * K(y \ x,z)) / y = T(x / y,z)
    ]]></literal>
    <justification jstring="[para(6230(a,1),5503(a,1,1,2))].">
      <j1 rule="para" parents="6230 5503"/>
    </justification>
  </clause>

  <clause id="6251">
    <literal><![CDATA[
      (((x \ y) * z) \ z) * ((x \ y) * z) = z * K(y \ x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[para(6230(a,1),5401(a,2,2))].">
      <j1 rule="para" parents="6230 5401"/>
    </justification>
  </clause>

  <clause id="6252">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(6230(a,1),5498(a,2,2))].">
      <j1 rule="para" parents="6230 5498"/>
    </justification>
  </clause>

  <clause id="6253">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = z * K(y \ x,z * (x \ y))
    ]]></literal>
    <justification jstring="[para(6230(a,1),5807(a,2,2))].">
      <j1 rule="para" parents="6230 5807"/>
    </justification>
  </clause>

  <clause id="6254">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(6230(a,1),5133(a,1,2))].">
      <j1 rule="para" parents="6230 5133"/>
    </justification>
  </clause>

  <clause id="6255">
    <literal><![CDATA[
      x * K((y * z) \ x,y) = z * ((y \ (z \ x)) * y)
    ]]></literal>
    <justification jstring="[para(6230(a,1),5497(a,1,2))].">
      <j1 rule="para" parents="6230 5497"/>
    </justification>
  </clause>

  <clause id="6256">
    <literal><![CDATA[
      x * K((y * z) \ x,z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(6230(a,1),5959(a,1,2))].">
      <j1 rule="para" parents="6230 5959"/>
    </justification>
  </clause>

  <clause id="6257">
    <literal><![CDATA[
      K(1 / L(x \ y,z,u),w) = L(K(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[para(6237(a,1),5653(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6237 5653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6258">
    <literal><![CDATA[
      K(x / y,x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(2892,a,6239,a)].">
      <j1 rule="hyper" parents="2892 6239"/>
    </justification>
  </clause>

  <clause id="6259">
    <literal><![CDATA[
      K(x,K(y,x / z)) * K(x / z,y) = K(z \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5588,a,b,6239,a)].">
      <j1 rule="hyper" parents="58 5588 6239"/>
    </justification>
  </clause>

  <clause id="6260">
    <literal><![CDATA[
      K(L(x,y,z) / u,x) = K(u \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2955,a(flip),b,6239,a)].">
      <j1 rule="hyper" parents="58 2955 6239"/>
    </justification>
  </clause>

  <clause id="6261">
    <literal><![CDATA[
      K(x / y,z) * x = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,6239,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 6239 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6262">
    <literal><![CDATA[
      T(x,y) != K(z \ y,u)
    ]]></literal>
    <literal><![CDATA[
      K(y / z,u) = x
    ]]></literal>
    <justification jstring="[para(6239(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="6239 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6263">
    <literal><![CDATA[
      K((x \ y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(72(a,1),6239(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 6239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6264">
    <literal><![CDATA[
      K((x \ y) \ y,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),6258(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 6258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6265">
    <literal><![CDATA[
      K(L(1 / x,x,y),z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(5754,a,6243,a)].">
      <j1 rule="hyper" parents="5754 6243"/>
    </justification>
  </clause>

  <clause id="6268">
    <literal><![CDATA[
      K(T(x,x \ y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(106(a,2),6263(a,1,1))].">
      <j1 rule="para" parents="106 6263"/>
    </justification>
  </clause>

  <clause id="6269">
    <literal><![CDATA[
      K((x \ y) \ y,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(6263(a,2),2892(a,1))].">
      <j1 rule="para" parents="6263 2892"/>
    </justification>
  </clause>

  <clause id="6270">
    <literal><![CDATA[
      K(x \ (x * y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6082(a,1),3637(a,1))].">
      <j1 rule="para" parents="6082 3637"/>
    </justification>
  </clause>

  <clause id="6271">
    <literal><![CDATA[
      L(x \ 1,x,y) \ y = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(430,a,6177,a)].">
      <j1 rule="hyper" parents="430 6177"/>
    </justification>
  </clause>

  <clause id="6273">
    <literal><![CDATA[
      K(L(1 / x,x,y),z) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3293,a,b,6265,a),flip(a)].">
      <j1 rule="hyper" parents="320 3293 6265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6274">
    <literal><![CDATA[
      K((x / y) \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(7(a,1),6270(a,1,1,2))].">
      <j1 rule="para" parents="7 6270"/>
    </justification>
  </clause>

  <clause id="6275">
    <literal><![CDATA[
      K(1 / ((x * y) \ x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6237(a,2),6270(a,1))].">
      <j1 rule="para" parents="6237 6270"/>
    </justification>
  </clause>

  <clause id="6276">
    <literal><![CDATA[
      K(L(x,x \ 1,y),z) = K(1 / (x \ 1),z)
    ]]></literal>
    <justification jstring="[para(72(a,1),6273(a,1,1,1))].">
      <j1 rule="para" parents="72 6273"/>
    </justification>
  </clause>

  <clause id="6277">
    <literal><![CDATA[
      L(T(x,K(y,x)),K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(768,a,6062,a)].">
      <j1 rule="hyper" parents="768 6062"/>
    </justification>
  </clause>

  <clause id="6278">
    <literal><![CDATA[
      L(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[para(2869(a,1),6277(a,1,1))].">
      <j1 rule="para" parents="2869 6277"/>
    </justification>
  </clause>

  <clause id="6279">
    <literal><![CDATA[
      L(T(x,y),K(z,x),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6278(a,1),20(a,2,1))].">
      <j1 rule="para" parents="6278 20"/>
    </justification>
  </clause>

  <clause id="6280">
    <literal><![CDATA[
      L((x \ y) \ y,K(z,x),u) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(6278(a,1),317(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6278 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6281">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,u) = x * (K(y,z) * T(z,u))
    ]]></literal>
    <justification jstring="[para(6278(a,1),449(a,1,2,1))].">
      <j1 rule="para" parents="6278 449"/>
    </justification>
  </clause>

  <clause id="6282">
    <literal><![CDATA[
      (x * K(y,z)) * L(z,u,w) = x * (K(y,z) * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(6278(a,1),446(a,1,2,1))].">
      <j1 rule="para" parents="6278 446"/>
    </justification>
  </clause>

  <clause id="6283">
    <literal><![CDATA[
      (x * K(y,z)) * R(z,u,w) = x * (K(y,z) * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(6278(a,1),447(a,1,2,1))].">
      <j1 rule="para" parents="6278 447"/>
    </justification>
  </clause>

  <clause id="6286">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * z) = T(z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4822,a(flip),b,6279,a)].">
      <j1 rule="hyper" parents="58 4822 6279"/>
    </justification>
  </clause>

  <clause id="6287">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,y) = x * z
    ]]></literal>
    <justification jstring="[hyper(119,a,6279,a(flip),b,4822,a(flip))].">
      <j1 rule="hyper" parents="119 6279 4822"/>
    </justification>
  </clause>

  <clause id="6288">
    <literal><![CDATA[
      x / T(y \ x,z) = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(366,a,6286,a)].">
      <j1 rule="hyper" parents="366 6286"/>
    </justification>
  </clause>

  <clause id="6290">
    <literal><![CDATA[
      (x * y) / T(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(197,a,6286,a)].">
      <j1 rule="hyper" parents="197 6286"/>
    </justification>
  </clause>

  <clause id="6292">
    <literal><![CDATA[
      (x * K(y,x \ z)) \ z = T(x \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6286(a,1,2))].">
      <j1 rule="para" parents="5 6286"/>
    </justification>
  </clause>

  <clause id="6293">
    <literal><![CDATA[
      (x / y) * K(z,y) = x / T(y,z)
    ]]></literal>
    <justification jstring="[para(6286(a,1),324(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6286 324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6295">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * y) * z) = T(z,y)
    ]]></literal>
    <justification jstring="[para(6086(a,1),6286(a,1,1))].">
      <j1 rule="para" parents="6086 6286"/>
    </justification>
  </clause>

  <clause id="6296">
    <literal><![CDATA[
      (x / T(y,z)) * y = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(1488,a,6287,a)].">
      <j1 rule="hyper" parents="1488 6287"/>
    </justification>
  </clause>

  <clause id="6297">
    <literal><![CDATA[
      (x / T(y,z)) / K(z,y) = x / y
    ]]></literal>
    <justification jstring="[hyper(594,a,6287,a),flip(a)].">
      <j1 rule="hyper" parents="594 6287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6298">
    <literal><![CDATA[
      (x \ y) * K(y,x) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,4437,a,b,6287,a),flip(a)].">
      <j1 rule="hyper" parents="30 4437 6287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6300">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) = x
    ]]></literal>
    <justification jstring="[hyper(30,a,6167,a(flip),b,6287,a),flip(a)].">
      <j1 rule="hyper" parents="30 6167 6287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6301">
    <literal><![CDATA[
      (x \ K(x,y)) * K(y,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(30,a,5523,a(flip),b,6287,a),flip(a)].">
      <j1 rule="hyper" parents="30 5523 6287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6302">
    <literal><![CDATA[
      (x * T(y,z)) * K(z,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(30,a,1477,a(flip),b,6287,a),flip(a)].">
      <j1 rule="hyper" parents="30 1477 6287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6303">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(z,y) = u
    ]]></literal>
    <justification jstring="[para(6287(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6287 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6304">
    <literal><![CDATA[
      (x * T(y,z)) * T(z,y) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(6086(a,1),6287(a,1,1))].">
      <j1 rule="para" parents="6086 6287"/>
    </justification>
  </clause>

  <clause id="6305">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(440,a,xx,b,6300,a)].">
      <j1 rule="hyper" parents="440 6300"/>
    </justification>
  </clause>

  <clause id="6306">
    <literal><![CDATA[
      x / K(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(326,a,6300,a),flip(a)].">
      <j1 rule="hyper" parents="326 6300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6308">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(239,a,6300,a,b,5095,a)].">
      <j1 rule="hyper" parents="239 6300 5095"/>
    </justification>
  </clause>

  <clause id="6309">
    <literal><![CDATA[
      (x * K(y,z)) \ x = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,6300,a)].">
      <j1 rule="hyper" parents="123 6300"/>
    </justification>
  </clause>

  <clause id="6310">
    <literal><![CDATA[
      (x / y) * K(x,y) = T(x,y) / y
    ]]></literal>
    <justification jstring="[hyper(30,a,6190,a,b,6300,a),flip(a)].">
      <j1 rule="hyper" parents="30 6190 6300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6311">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(30,a,5594,a,b,6300,a),flip(a)].">
      <j1 rule="hyper" parents="30 5594 6300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6312">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * K(y,x) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,1991,a,b,6300,a),flip(a)].">
      <j1 rule="hyper" parents="30 1991 6300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6313">
    <literal><![CDATA[
      (x * K(y,z)) / z = x / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,6300,a(flip),b,6121,a),flip(a)].">
      <j1 rule="hyper" parents="117 6300 6121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6314">
    <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(6300(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6300 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6315">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      u * K(z,y) = x
    ]]></literal>
    <justification jstring="[para(6300(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="6300 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6316">
    <literal><![CDATA[
      (x * K(y,z)) \ x != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(6300(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6300 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6317">
    <literal><![CDATA[
      x / K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(z,y) = u
    ]]></literal>
    <justification jstring="[para(6300(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6300 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6318">
    <literal><![CDATA[
      x * L(y,K(z,u),x * K(u,z)) = (x * K(u,z)) * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(6300(a,1),90(a,1,1))].">
      <j1 rule="para" parents="6300 90"/>
    </justification>
  </clause>

  <clause id="6319">
    <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(6300(a,1),482(a,1,1))].">
      <j1 rule="para" parents="6300 482"/>
    </justification>
  </clause>

  <clause id="6320">
    <literal><![CDATA[
      (x * y) / K(z,y) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,6086,a(flip),b,6306,a),flip(a)].">
      <j1 rule="hyper" parents="320 6086 6306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6321">
    <literal><![CDATA[
      T(x,K(y,z)) / K(y,z) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,5594,a(flip),b,6306,a),flip(a)].">
      <j1 rule="hyper" parents="320 5594 6306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6322">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5607,a,b,6306,a)].">
      <j1 rule="hyper" parents="58 5607 6306"/>
    </justification>
  </clause>

  <clause id="6323">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(6306(a,1),251(a,1,1))].">
      <j1 rule="para" parents="6306 251"/>
    </justification>
  </clause>

  <clause id="6325">
    <literal><![CDATA[
      R((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(6306(a,1),301(a,1,1))].">
      <j1 rule="para" parents="6306 301"/>
    </justification>
  </clause>

  <clause id="6326">
    <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(6306(a,1),621(a,1,1,1))].">
      <j1 rule="para" parents="6306 621"/>
    </justification>
  </clause>

  <clause id="6327">
    <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(6306(a,1),621(a,1,1))].">
      <j1 rule="para" parents="6306 621"/>
    </justification>
  </clause>

  <clause id="6328">
    <literal><![CDATA[
      ((K(x,y) / z) * (z * K(y,x))) \ (K(x,y) / z) = 1 / (z / K(x,y))
    ]]></literal>
    <justification jstring="[para(6306(a,1),2039(a,1,1,2))].">
      <j1 rule="para" parents="6306 2039"/>
    </justification>
  </clause>

  <clause id="6330">
    <literal><![CDATA[
      K(x,1 / (K(y,z) / u)) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(6306(a,1),5317(a,2,2))].">
      <j1 rule="para" parents="6306 5317"/>
    </justification>
  </clause>

  <clause id="6331">
    <literal><![CDATA[
      (x * K(L(y \ 1,z,u) \ 1,w)) \ x = L(K(w,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,5642,a(flip),b,6309,a),flip(a)].">
      <j1 rule="hyper" parents="320 5642 6309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6332">
    <literal><![CDATA[
      ((x * K(y,z)) \ x) \ u = K(y,z) * u
    ]]></literal>
    <justification jstring="[para(6309(a,2),5092(a,1,1))].">
      <j1 rule="para" parents="6309 5092"/>
    </justification>
  </clause>

  <clause id="6333">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ K(x,y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(5255(a,1),6309(a,1,1))].">
      <j1 rule="para" parents="5255 6309"/>
    </justification>
  </clause>

  <clause id="6334">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ K(x * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(5451(a,1),6309(a,1,1))].">
      <j1 rule="para" parents="5451 6309"/>
    </justification>
  </clause>

  <clause id="6335">
    <literal><![CDATA[
      (x / y) \ (x / T(y,z)) = K(z,y)
    ]]></literal>
    <justification jstring="[para(6159(a,1),6309(a,1,1))].">
      <j1 rule="para" parents="6159 6309"/>
    </justification>
  </clause>

  <clause id="6336">
    <literal><![CDATA[
      R(x * K(y,z),K(u,w),u) = (x * z) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6199,a,b,6290,a)].">
      <j1 rule="hyper" parents="320 6199 6290"/>
    </justification>
  </clause>

  <clause id="6337">
    <literal><![CDATA[
      T(x / T(y,z),y) = y \ (x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(440,a,6290,a(flip),b,1478,a(flip))].">
      <j1 rule="hyper" parents="440 6290 1478"/>
    </justification>
  </clause>

  <clause id="6338">
    <literal><![CDATA[
      (x / y) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6290(a,1),576(a,1))].">
      <j1 rule="para" parents="6290 576"/>
    </justification>
  </clause>

  <clause id="6340">
    <literal><![CDATA[
      x * (K(y,x) * K(z,y)) = (y * x) / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(5634,a,6293,a)].">
      <j1 rule="hyper" parents="5634 6293"/>
    </justification>
  </clause>

  <clause id="6342">
    <literal><![CDATA[
      T(x / y,K(x,y)) = x / y
    ]]></literal>
    <justification jstring="[hyper(239,a,6293,a,b,5211,a)].">
      <j1 rule="hyper" parents="239 6293 5211"/>
    </justification>
  </clause>

  <clause id="6343">
    <literal><![CDATA[
      K(x \ y,x) * K(z,y / x) = x \ (y / T(y / x,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,6293,a(flip),b,5413,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 6293 5413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6344">
    <literal><![CDATA[
      x \ (y / T(x \ y,z)) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,6293,a(flip),b,183,a(flip))].">
      <j1 rule="hyper" parents="116 6293 183"/>
    </justification>
  </clause>

  <clause id="6345">
    <literal><![CDATA[
      T(x / y,K(y,x)) = x / y
    ]]></literal>
    <justification jstring="[hyper(5601,a,6342,a)].">
      <j1 rule="hyper" parents="5601 6342"/>
    </justification>
  </clause>

  <clause id="6346">
    <literal><![CDATA[
      K(x,y) * (y / x) = (y / x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6342(a,1),5594(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6342 5594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6347">
    <literal><![CDATA[
      T((x * y) / T(z,y),z) = z \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(440,a,6086,a(flip),b,6296,a)].">
      <j1 rule="hyper" parents="440 6086 6296"/>
    </justification>
  </clause>

  <clause id="6348">
    <literal><![CDATA[
      x / T(x * y,y \ 1) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,5014,a,b,6296,a),flip(a)].">
      <j1 rule="hyper" parents="30 5014 6296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6349">
    <literal><![CDATA[
      (x / ((y \ z) \ z)) * y = x * K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(106(a,1),6296(a,1,1,2))].">
      <j1 rule="para" parents="106 6296"/>
    </justification>
  </clause>

  <clause id="6350">
    <literal><![CDATA[
      x \ (y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / T(x,z),x) = u
    ]]></literal>
    <justification jstring="[para(6296(a,1),288(a,1,2))].">
      <j1 rule="para" parents="6296 288"/>
    </justification>
  </clause>

  <clause id="6351">
    <literal><![CDATA[
      x \ y != (z * K(u,w)) / w
    ]]></literal>
    <literal><![CDATA[
      x * (z / T(w,u)) = y
    ]]></literal>
    <justification jstring="[para(6296(a,1),622(a,2,1))].">
      <j1 rule="para" parents="6296 622"/>
    </justification>
  </clause>

  <clause id="6352">
    <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(6296(a,1),521(a,1,1))].">
      <j1 rule="para" parents="6296 521"/>
    </justification>
  </clause>

  <clause id="6353">
    <literal><![CDATA[
      (x / T(y,z)) * T(y,u) = (x * K(z,y)) * K(y,u)
    ]]></literal>
    <justification jstring="[para(6296(a,1),6086(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6296 6086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6355">
    <literal><![CDATA[
      x \ T(x * y,x) = y * K(x * y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),6298(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 6298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6356">
    <literal><![CDATA[
      (x \ T(y,x)) \ ((x \ y) * (K(y,x) * z)) = L(z,K(y,x),x \ y)
    ]]></literal>
    <justification jstring="[para(6298(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6298 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6357">
    <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(6301(a,1),102(a,2,2))].">
      <j1 rule="para" parents="6301 102"/>
    </justification>
  </clause>

  <clause id="6358">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,6302,a)].">
      <j1 rule="hyper" parents="116 5 6302"/>
    </justification>
  </clause>

  <clause id="6359">
    <literal><![CDATA[
      x * K(y,z) != u * z
    ]]></literal>
    <literal><![CDATA[
      u * T(z,y) = x
    ]]></literal>
    <justification jstring="[para(6302(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="6302 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6361">
    <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(6302(a,1),510(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6302 510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6362">
    <literal><![CDATA[
      x * (K(y,x) * K(y * x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[hyper(5634,a,6310,a)].">
      <j1 rule="hyper" parents="5634 6310"/>
    </justification>
  </clause>

  <clause id="6363">
    <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(6313(a,1),4360(a,1,1,2))].">
      <j1 rule="para" parents="6313 4360"/>
    </justification>
  </clause>

  <clause id="6364">
    <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(6313(a,1),4362(a,1,1,1,2))].">
      <j1 rule="para" parents="6313 4362"/>
    </justification>
  </clause>

  <clause id="6365">
    <literal><![CDATA[
      (x \ K(y,x)) \ (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3142(a,1),6316(a,1,1))].">
      <j1 rule="para" parents="3142 6316"/>
    </justification>
  </clause>

  <clause id="6366">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5607(a,2),6317(a,1))].">
      <j1 rule="para" parents="5607 6317"/>
    </justification>
  </clause>

  <clause id="6367">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x / K(z,y) = u
    ]]></literal>
    <justification jstring="[para(7(a,1),6323(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7 6323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6368">
    <literal><![CDATA[
      x / ((y * z) / y) = (x / z) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6315,a,6063,a),flip(a)].">
      <j1 rule="hyper" parents="6315 6063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6369">
    <literal><![CDATA[
      (x / (y / z)) * K(z,z \ y) = x / (z \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6063(a,1,1,2,1))].">
      <j1 rule="para" parents="5 6063"/>
    </justification>
  </clause>

  <clause id="6370">
    <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(6063(a,1),959(a,2,1,2))].">
      <j1 rule="para" parents="6063 959"/>
    </justification>
  </clause>

  <clause id="6372">
    <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(6063(a,1),4557(a,1,2,1))].">
      <j1 rule="para" parents="6063 4557"/>
    </justification>
  </clause>

  <clause id="6373">
    <literal><![CDATA[
      (x / (y \ z)) * (z / y) = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[para(4735(a,1),6065(a,1,2))].">
      <j1 rule="para" parents="4735 6065"/>
    </justification>
  </clause>

  <clause id="6375">
    <literal><![CDATA[
      T(K(x \ 1,y) * y,K(x \ 1,y)) = x * ((y \ (x \ y)) * y)
    ]]></literal>
    <justification jstring="[hyper(239,a,6066,a(flip),b,6055,a)].">
      <j1 rule="hyper" parents="239 6066 6055"/>
    </justification>
  </clause>

  <clause id="6376">
    <literal><![CDATA[
      (x * ((y * z) / y)) * K(z,y) = x * z
    ]]></literal>
    <justification jstring="[hyper(6315,a,6067,a)].">
      <j1 rule="hyper" parents="6315 6067"/>
    </justification>
  </clause>

  <clause id="6377">
    <literal><![CDATA[
      (x * ((y * z) / y)) * y = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[para(6067(a,1),6167(a,1,1))].">
      <j1 rule="para" parents="6067 6167"/>
    </justification>
  </clause>

  <clause id="6378">
    <literal><![CDATA[
      (x / (y * K(z,y))) * y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,6306,a(flip),b,6068,a),flip(a)].">
      <j1 rule="hyper" parents="320 6306 6068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6380">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) = z \ (y * (x * T(x \ (y \ z),u)))
    ]]></literal>
    <justification jstring="[para(6081(a,1),490(a,1,1))].">
      <j1 rule="para" parents="6081 490"/>
    </justification>
  </clause>

  <clause id="6381">
    <literal><![CDATA[
      x \ (y \ T(y * x,z)) = K((y \ 1) \ x,z)
    ]]></literal>
    <justification jstring="[para(932(a,1),6081(a,1,2))].">
      <j1 rule="para" parents="932 6081"/>
    </justification>
  </clause>

  <clause id="6382">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) = K((y \ z) \ x,z)
    ]]></literal>
    <justification jstring="[para(957(a,1),6081(a,1,2))].">
      <j1 rule="para" parents="957 6081"/>
    </justification>
  </clause>

  <clause id="6384">
    <literal><![CDATA[
      K(x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(6081(a,1),5442(a,1))].">
      <j1 rule="para" parents="6081 5442"/>
    </justification>
  </clause>

  <clause id="6386">
    <literal><![CDATA[
      x * (y * K((x \ z) \ y,z)) = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,6084,a(flip),b,957,a(flip))].">
      <j1 rule="hyper" parents="119 6084 957"/>
    </justification>
  </clause>

  <clause id="6387">
    <literal><![CDATA[
      (x * K(y \ x,z)) * (y \ 1) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(6084(a,1),1031(a,1,1))].">
      <j1 rule="para" parents="6084 1031"/>
    </justification>
  </clause>

  <clause id="6388">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6084(a,1),1042(a,1))].">
      <j1 rule="para" parents="6084 1042"/>
    </justification>
  </clause>

  <clause id="6389">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(y * K(x \ y,z),y)
    ]]></literal>
    <justification jstring="[para(6084(a,1),1949(a,2,1))].">
      <j1 rule="para" parents="6084 1949"/>
    </justification>
  </clause>

  <clause id="6390">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x \ y) = u
    ]]></literal>
    <justification jstring="[para(6084(a,2),6316(a,1,1))].">
      <j1 rule="para" parents="6084 6316"/>
    </justification>
  </clause>

  <clause id="6391">
    <literal><![CDATA[
      R(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(515,a,6085,a)].">
      <j1 rule="hyper" parents="515 6085"/>
    </justification>
  </clause>

  <clause id="6396">
    <literal><![CDATA[
      K((x \ y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(6108(a,2),4945(a,1))].">
      <j1 rule="para" parents="6108 4945"/>
    </justification>
  </clause>

  <clause id="6398">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(6141(a,2),4824(a,1))].">
      <j1 rule="para" parents="6141 4824"/>
    </justification>
  </clause>

  <clause id="6399">
    <literal><![CDATA[
      T(x,K(y,(z / x) \ 1)) = T(x,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(5312(a,2),6151(a,1,2))].">
      <j1 rule="para" parents="5312 6151"/>
    </justification>
  </clause>

  <clause id="6400">
    <literal><![CDATA[
      (x \ 1) * (((y * x) \ y) \ y) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,6176,a(flip),b,556,a)].">
      <j1 rule="hyper" parents="119 6176 556"/>
    </justification>
  </clause>

  <clause id="6401">
    <literal><![CDATA[
      T(x * (1 / y),y) = ((x * (1 / y)) \ x) \ x
    ]]></literal>
    <justification jstring="[para(75(a,1),6176(a,1,2))].">
      <j1 rule="para" parents="75 6176"/>
    </justification>
  </clause>

  <clause id="6402">
    <literal><![CDATA[
      x / T(x * (1 / y),y) = (x * (1 / y)) \ x
    ]]></literal>
    <justification jstring="[para(75(a,1),6179(a,1,2,2))].">
      <j1 rule="para" parents="75 6179"/>
    </justification>
  </clause>

  <clause id="6403">
    <literal><![CDATA[
      T(x,y \ (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(6184(a,2),4413(a,1))].">
      <j1 rule="para" parents="6184 4413"/>
    </justification>
  </clause>

  <clause id="6405">
    <literal><![CDATA[
      R(T(x,y * K(x,z)),y,K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6204(a,1),1088(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6204 1088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6406">
    <literal><![CDATA[
      (x * K(y,z)) / y != u
    ]]></literal>
    <literal><![CDATA[
      (x / y) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6205(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6205 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6408">
    <literal><![CDATA[
      (x * y) \ (T(x,z) * y) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(123,a,6207,a)].">
      <j1 rule="hyper" parents="123 6207"/>
    </justification>
  </clause>

  <clause id="6412">
    <literal><![CDATA[
      x / (y * K(z,y)) = (x / y) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6219(a,1),324(a,1,2))].">
      <j1 rule="para" parents="6219 324"/>
    </justification>
  </clause>

  <clause id="6413">
    <literal><![CDATA[
      T(K(x,y),z * y) * K(y,x) = K(K(x,y),y * z)
    ]]></literal>
    <justification jstring="[para(6226(a,2),4934(a,1,1))].">
      <j1 rule="para" parents="6226 4934"/>
    </justification>
  </clause>

  <clause id="6414">
    <literal><![CDATA[
      K(((x \ 1) * y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5509,a(flip),b,6244,a),flip(a)].">
      <j1 rule="hyper" parents="58 5509 6244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6415">
    <literal><![CDATA[
      K(x \ y,z) \ K(K(x \ y,z),y) = ((K(y / x,z) * y) / y) \ 1
    ]]></literal>
    <justification jstring="[para(6261(a,2),4864(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6261 4864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6417">
    <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),6295(a,1,2))].">
      <j1 rule="para" parents="90 6295"/>
    </justification>
  </clause>

  <clause id="6419">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) = R(x,T(y,z),T(z,y))
    ]]></literal>
    <justification jstring="[hyper(117,a,6304,a(flip),b,4231,a)].">
      <j1 rule="hyper" parents="117 6304 4231"/>
    </justification>
  </clause>

  <clause id="6420">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(x,T(y,z),T(z,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,6304,a(flip),b,4234,a)].">
      <j1 rule="hyper" parents="116 6304 4234"/>
    </justification>
  </clause>

  <clause id="6421">
    <literal><![CDATA[
      T(x,K(y,z)) != K(y,z) \ u
    ]]></literal>
    <literal><![CDATA[
      u * K(z,y) = x
    ]]></literal>
    <justification jstring="[para(6305(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="6305 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6422">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(6305(a,2),5125(a,1))].">
      <j1 rule="para" parents="6305 5125"/>
    </justification>
  </clause>

  <clause id="6423">
    <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(6308(a,1),109(a,2,1,1))].">
      <j1 rule="para" parents="6308 109"/>
    </justification>
  </clause>

  <clause id="6424">
    <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(6308(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6308 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6425">
    <literal><![CDATA[
      (K(x,y) \ z) * K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5092(a,2),6311(a,1,1))].">
      <j1 rule="para" parents="5092 6311"/>
    </justification>
  </clause>

  <clause id="6426">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) = (x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4778(a,1),6311(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4778 6311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6427">
    <literal><![CDATA[
      (K(x,y) * z) \ z = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(6321(a,1),4237(a,1,1))].">
      <j1 rule="para" parents="6321 4237"/>
    </justification>
  </clause>

  <clause id="6428">
    <literal><![CDATA[
      T(K(x * y,x),y) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(5379,a,6355,a)].">
      <j1 rule="hyper" parents="5379 6355"/>
    </justification>
  </clause>

  <clause id="6429">
    <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(6355(a,2),4915(a,1,1))].">
      <j1 rule="para" parents="6355 4915"/>
    </justification>
  </clause>

  <clause id="6430">
    <literal><![CDATA[
      K(x,K(y,y * x)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,6428,a(flip),b,5587,a),flip(a)].">
      <j1 rule="hyper" parents="115 6428 5587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6431">
    <literal><![CDATA[
      T(x,K(y,y * x)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,6430,a)].">
      <j1 rule="hyper" parents="51 6430"/>
    </justification>
  </clause>

  <clause id="6432">
    <literal><![CDATA[
      T(x \ y,K(x,y)) = x \ y
    ]]></literal>
    <justification jstring="[para(5(a,1),6431(a,1,2,2))].">
      <j1 rule="para" parents="5 6431"/>
    </justification>
  </clause>

  <clause id="6433">
    <literal><![CDATA[
      K(x,y) * (x \ y) = (x \ y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,6432,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 6432 17"/>
    </justification>
  </clause>

  <clause id="6435">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y = K(z,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(932(a,1),6358(a,1,1))].">
      <j1 rule="para" parents="932 6358"/>
    </justification>
  </clause>

  <clause id="6436">
    <literal><![CDATA[
      (((x \ (y / z)) * x) * z) \ y = K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[para(1097(a,1),6358(a,1,1))].">
      <j1 rule="para" parents="1097 6358"/>
    </justification>
  </clause>

  <clause id="6437">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(919(a,1),6358(a,1,1))].">
      <j1 rule="para" parents="919 6358"/>
    </justification>
  </clause>

  <clause id="6438">
    <literal><![CDATA[
      ((x * T(x \ y,z)) * u) \ (y * u) = K(z,(x * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(1476(a,1),6358(a,1,1))].">
      <j1 rule="para" parents="1476 6358"/>
    </justification>
  </clause>

  <clause id="6439">
    <literal><![CDATA[
      T(x * T(x \ y,z),u) \ T(y,u) = K(z,T(x,u) \ T(y,u))
    ]]></literal>
    <justification jstring="[para(1952(a,1),6358(a,1,1))].">
      <j1 rule="para" parents="1952 6358"/>
    </justification>
  </clause>

  <clause id="6440">
    <literal><![CDATA[
      x / ((x * y) / x) = K(y,x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6346,a,b,6368,a),flip(a)].">
      <j1 rule="hyper" parents="320 6346 6368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6441">
    <literal><![CDATA[
      (x / (y \ z)) * K(y \ z,y) = x / (z / y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6368(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 6368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6442">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),6368(a,2,1))].">
      <j1 rule="para" parents="6 6368"/>
    </justification>
  </clause>

  <clause id="6443">
    <literal><![CDATA[
      x / (y / (y / z)) = (x / z) * K(z,y / z)
    ]]></literal>
    <justification jstring="[para(7(a,1),6368(a,1,2,1))].">
      <j1 rule="para" parents="7 6368"/>
    </justification>
  </clause>

  <clause id="6444">
    <literal><![CDATA[
      x / (y / (y / z)) = (x / z) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(4302(a,1),6368(a,1,2))].">
      <j1 rule="para" parents="4302 6368"/>
    </justification>
  </clause>

  <clause id="6445">
    <literal><![CDATA[
      K(x,((y / z) * K(z,u)) \ 1) = K(x,((u * z) / u) / y)
    ]]></literal>
    <justification jstring="[para(6368(a,1),5312(a,1,2,1))].">
      <j1 rule="para" parents="6368 5312"/>
    </justification>
  </clause>

  <clause id="6446">
    <literal><![CDATA[
      (x * (y / z)) * K(z \ y,z) = x * (z \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6376(a,1,1,2,1))].">
      <j1 rule="para" parents="5 6376"/>
    </justification>
  </clause>

  <clause id="6447">
    <literal><![CDATA[
      (x * (y / (y / z))) * K(z,z \ y) = x * z
    ]]></literal>
    <justification jstring="[para(4302(a,1),6376(a,1,1,2))].">
      <j1 rule="para" parents="4302 6376"/>
    </justification>
  </clause>

  <clause id="6448">
    <literal><![CDATA[
      (x / (y / z)) * (z \ y) = x * K(z \ y,z)
    ]]></literal>
    <justification jstring="[para(4735(a,1),6378(a,1,1,2))].">
      <j1 rule="para" parents="4735 6378"/>
    </justification>
  </clause>

  <clause id="6453">
    <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),6136(a,1,2,1))].">
      <j1 rule="para" parents="92 6136"/>
    </justification>
  </clause>

  <clause id="6454">
    <literal><![CDATA[
      K(x,1 / (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(3528(a,2),6136(a,1))].">
      <j1 rule="para" parents="3528 6136"/>
    </justification>
  </clause>

  <clause id="6455">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(5092(a,1),6136(a,1,2,1))].">
      <j1 rule="para" parents="5092 6136"/>
    </justification>
  </clause>

  <clause id="6456">
    <literal><![CDATA[
      T(K(x,y / z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(5711(a,2),6136(a,1))].">
      <j1 rule="para" parents="5711 6136"/>
    </justification>
  </clause>

  <clause id="6457">
    <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(635(a,1),6170(a,1,1))].">
      <j1 rule="para" parents="635 6170"/>
    </justification>
  </clause>

  <clause id="6458">
    <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(6296(a,1),6170(a,1,1))].">
      <j1 rule="para" parents="6296 6170"/>
    </justification>
  </clause>

  <clause id="6460">
    <literal><![CDATA[
      K(x,(y * z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(6(a,1),6175(a,1,2,2))].">
      <j1 rule="para" parents="6 6175"/>
    </justification>
  </clause>

  <clause id="6461">
    <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(442(a,1),6175(a,1,2,2))].">
      <j1 rule="para" parents="442 6175"/>
    </justification>
  </clause>

  <clause id="6462">
    <literal><![CDATA[
      (x * ((y * z) / y)) * y != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6067(a,1),6198(a,1,1))].">
      <j1 rule="para" parents="6067 6198"/>
    </justification>
  </clause>

  <clause id="6463">
    <literal><![CDATA[
      T(x,x \ T(x * y,y \ 1)) = T(x,L(y \ 1,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(6271(a,1),4139(a,1,2,2))].">
      <j1 rule="para" parents="6271 4139"/>
    </justification>
  </clause>

  <clause id="6464">
    <literal><![CDATA[
      K(1 / (x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5(a,1),6275(a,1,1,2,1))].">
      <j1 rule="para" parents="5 6275"/>
    </justification>
  </clause>

  <clause id="6466">
    <literal><![CDATA[
      K(L(x,x \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),6276(a,2,1))].">
      <j1 rule="para" parents="72 6276"/>
    </justification>
  </clause>

  <clause id="6468">
    <literal><![CDATA[
      K(x,L(y,y \ 1,z)) = 1 / K(y,x)
    ]]></literal>
    <justification jstring="[para(6466(a,1),4931(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6466 4931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6469">
    <literal><![CDATA[
      K(x,L(y,y \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4931,a(flip),b,6468,a),flip(a)].">
      <j1 rule="hyper" parents="320 4931 6468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6470">
    <literal><![CDATA[
      K(x,L(y,y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6468(a,2),4938(a,1))].">
      <j1 rule="para" parents="6468 4938"/>
    </justification>
  </clause>

  <clause id="6471">
    <literal><![CDATA[
      K(x,L(1 / y,y,z)) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),6469(a,1,2,2))].">
      <j1 rule="para" parents="75 6469"/>
    </justification>
  </clause>

  <clause id="6472">
    <literal><![CDATA[
      x * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      (z * x) / T(T(z,x),y) = u
    ]]></literal>
    <justification jstring="[para(187(a,1),6338(a,1,1))].">
      <j1 rule="para" parents="187 6338"/>
    </justification>
  </clause>

  <clause id="6473">
    <literal><![CDATA[
      x / T(x * (y / x),y \ x) = L((y / x) \ 1,y / x,x)
    ]]></literal>
    <justification jstring="[para(4606(a,1),6348(a,1,2))].">
      <j1 rule="para" parents="4606 6348"/>
    </justification>
  </clause>

  <clause id="6474">
    <literal><![CDATA[
      K((K(x,y) * z) \ 1,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z \ K(y,x),u) = w
    ]]></literal>
    <justification jstring="[para(5092(a,1),6396(a,1,1,1))].">
      <j1 rule="para" parents="5092 6396"/>
    </justification>
  </clause>

  <clause id="6475">
    <literal><![CDATA[
      T(K(x / y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5501(a,2),6396(a,1))].">
      <j1 rule="para" parents="5501 6396"/>
    </justification>
  </clause>

  <clause id="6476">
    <literal><![CDATA[
      x \ (y * (z * T(z \ (y \ x),u))) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * z) \ x,u) = w
    ]]></literal>
    <justification jstring="[para(5493(a,2),6396(a,1))].">
      <j1 rule="para" parents="5493 6396"/>
    </justification>
  </clause>

  <clause id="6477">
    <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),6398(a,1,2,1))].">
      <j1 rule="para" parents="17 6398"/>
    </justification>
  </clause>

  <clause id="6478">
    <literal><![CDATA[
      T(x,(y * z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(6(a,1),6403(a,1,2,2))].">
      <j1 rule="para" parents="6 6403"/>
    </justification>
  </clause>

  <clause id="6479">
    <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(3334(a,1),6456(a,1))].">
      <j1 rule="para" parents="3334 6456"/>
    </justification>
  </clause>

  <clause id="6480">
    <literal><![CDATA[
      K(x / y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,x) = z
    ]]></literal>
    <justification jstring="[para(2867(a,1),6475(a,1))].">
      <j1 rule="para" parents="2867 6475"/>
    </justification>
  </clause>

  <clause id="6481">
    <literal><![CDATA[
      (x * (y \ z)) / K(y \ z,y) = x * (z / y)
    ]]></literal>
    <justification jstring="[hyper(6367,a,6071,a)].">
      <j1 rule="hyper" parents="6367 6071"/>
    </justification>
  </clause>

  <clause id="6483">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2287,a(flip),b,6115,a)].">
      <j1 rule="hyper" parents="320 2287 6115"/>
    </justification>
  </clause>

  <clause id="6484">
    <literal><![CDATA[
      T(x * y,K(y,z)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5076,a(flip),b,6120,a),flip(a)].">
      <j1 rule="hyper" parents="58 5076 6120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6485">
    <literal><![CDATA[
      (x * y) * K(y,T(x,z)) = T(y * x,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,6086,a,b,6484,a)].">
      <j1 rule="hyper" parents="320 6086 6484"/>
    </justification>
  </clause>

  <clause id="6486">
    <literal><![CDATA[
      x * T(y / x,T(x,z)) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),6484(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 6484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6487">
    <literal><![CDATA[
      T(x / y,T(y,z)) = y \ T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(123,a,6486,a),flip(a)].">
      <j1 rule="hyper" parents="123 6486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6488">
    <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(6487(a,2),4568(a,1))].">
      <j1 rule="para" parents="6487 4568"/>
    </justification>
  </clause>

  <clause id="6489">
    <literal><![CDATA[
      ((x * T(y,z)) * z) / (T(y,z) * z) = R(x,y,z * K(y,z))
    ]]></literal>
    <justification jstring="[para(6131(a,1),5150(a,1,1))].">
      <j1 rule="para" parents="6131 5150"/>
    </justification>
  </clause>

  <clause id="6492">
    <literal><![CDATA[
      x * (K(y,x) * K(y,x)) = (T(y,x) * x) / y
    ]]></literal>
    <justification jstring="[hyper(5431,a,6194,a)].">
      <j1 rule="hyper" parents="5431 6194"/>
    </justification>
  </clause>

  <clause id="6493">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * T(y,x) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(6359,a,6202,a(flip))].">
      <j1 rule="hyper" parents="6359 6202"/>
    </justification>
  </clause>

  <clause id="6494">
    <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,6214,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="117 6214 101"/>
    </justification>
  </clause>

  <clause id="6495">
    <literal><![CDATA[
      ((x \ y) * z) * K(x,T(x \ y,z)) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(320,a,5421,a(flip),b,6227,a),flip(a)].">
      <j1 rule="hyper" parents="320 5421 6227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6498">
    <literal><![CDATA[
      K(T(K(x,y) * z,u) \ 1,w) = T(K(z \ K(y,x),w),u)
    ]]></literal>
    <justification jstring="[para(6248(a,1),5505(a,2,1))].">
      <j1 rule="para" parents="6248 5505"/>
    </justification>
  </clause>

  <clause id="6499">
    <literal><![CDATA[
      T(x,y) / (z \ x) = z * K(((z \ x) \ 1) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4536,a(flip),b,6252,a)].">
      <j1 rule="hyper" parents="58 4536 6252"/>
    </justification>
  </clause>

  <clause id="6500">
    <literal><![CDATA[
      K((x \ 1) \ y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,6355,a(flip),b,6252,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="29 6355 6252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6501">
    <literal><![CDATA[
      (x * K((y \ 1) \ x,z)) * y = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(6252(a,1),4555(a,1,1))].">
      <j1 rule="para" parents="6252 4555"/>
    </justification>
  </clause>

  <clause id="6502">
    <literal><![CDATA[
      T(x * K((y \ 1) \ x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(6252(a,1),4561(a,1,1))].">
      <j1 rule="para" parents="6252 4561"/>
    </justification>
  </clause>

  <clause id="6503">
    <literal><![CDATA[
      K((x \ 1) * y,x \ 1) = K(x \ y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(5936,a,6500,a),flip(a)].">
      <j1 rule="hyper" parents="5936 6500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6504">
    <literal><![CDATA[
      T(x,y) / ((y \ x) \ x) = T(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(30,a,4641,a(flip),b,6349,a),flip(a)].">
      <j1 rule="hyper" parents="30 4641 6349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6505">
    <literal><![CDATA[
      (T(x,y) \ y) * ((x \ y) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,6504,a)].">
      <j1 rule="hyper" parents="133 6504"/>
    </justification>
  </clause>

  <clause id="6507">
    <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(320,a,3329,a,b,6377,a),flip(a)].">
      <j1 rule="hyper" parents="320 3329 6377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6511">
    <literal><![CDATA[
      (x * K(y,z / (z / u))) * K(u,u \ z) = (x / T(z / (z / u),y)) * u
    ]]></literal>
    <justification jstring="[para(6296(a,1),6447(a,1,1))].">
      <j1 rule="para" parents="6296 6447"/>
    </justification>
  </clause>

  <clause id="6512">
    <literal><![CDATA[
      T(x * y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6485(a,1),6170(a,1))].">
      <j1 rule="para" parents="6485 6170"/>
    </justification>
  </clause>

  <clause id="6513">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K((x \ y) \ z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(6136,a,6503,a)].">
      <j1 rule="hyper" parents="6136 6503"/>
    </justification>
  </clause>

  <clause id="6514">
    <literal><![CDATA[
      K(x * (y \ 1),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5228,a,b,6503,a)].">
      <j1 rule="hyper" parents="58 5228 6503"/>
    </justification>
  </clause>

  <clause id="6515">
    <literal><![CDATA[
      T(K(x \ y,x \ 1) / x,y) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[para(6514(a,1),5942(a,1,1,1))].">
      <j1 rule="para" parents="6514 5942"/>
    </justification>
  </clause>

  <clause id="6516">
    <literal><![CDATA[
      T(L(K(x,y),T(y,x),z),u) * (T(y,x) * (y \ u)) = u * K(L(K(x,y),T(y,x),z),u)
    ]]></literal>
    <justification jstring="[para(6089(a,1),4779(a,1,2))].">
      <j1 rule="para" parents="6089 4779"/>
    </justification>
  </clause>

  <clause id="6517">
    <literal><![CDATA[
      L(T(K(x,y \ z),u),y \ z,w) = T(K(x,(z \ y) \ 1),u)
    ]]></literal>
    <justification jstring="[para(6091(a,1),20(a,2,1))].">
      <j1 rule="para" parents="6091 20"/>
    </justification>
  </clause>

  <clause id="6518">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ z) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(957(a,1),6135(a,1,2))].">
      <j1 rule="para" parents="957 6135"/>
    </justification>
  </clause>

  <clause id="6519">
    <literal><![CDATA[
      L(x * y,K(y * x,z),u) = x * y
    ]]></literal>
    <justification jstring="[para(4(a,1),6222(a,2,1))].">
      <j1 rule="para" parents="4 6222"/>
    </justification>
  </clause>

  <clause id="6520">
    <literal><![CDATA[
      (x * K(y * z,u)) * (z * y) = x * (K(y * z,u) * (z * y))
    ]]></literal>
    <justification jstring="[hyper(119,a,6519,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 6519 13"/>
    </justification>
  </clause>

  <clause id="6521">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(4740(a,1),6366(a,1,1))].">
      <j1 rule="para" parents="4740 6366"/>
    </justification>
  </clause>

  <clause id="6522">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      (K(z,y) * x) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(5095(a,1),6366(a,1,1))].">
      <j1 rule="para" parents="5095 6366"/>
    </justification>
  </clause>

  <clause id="6524">
    <literal><![CDATA[
      R(x,T(y,z),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(6419(a,1),518(a,1))].">
      <j1 rule="para" parents="6419 518"/>
    </justification>
  </clause>

  <clause id="6525">
    <literal><![CDATA[
      K(x,(y * z) \ T(y,u)) = K(x,z \ K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6110,a(flip),b,6112,a),flip(a)].">
      <j1 rule="hyper" parents="58 6110 6112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6526">
    <literal><![CDATA[
      T(x,(y * z) \ T(y,u)) = T(x,z \ K(y,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,6525,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 6525 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6527">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) = (u \ 1) / (u \ K(u,y \ K(x,z)))
    ]]></literal>
    <justification jstring="[para(6525(a,1),5100(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6525 5100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6528">
    <literal><![CDATA[
      K(x,(y * z) \ z) = K(x,y \ K(z,y))
    ]]></literal>
    <justification jstring="[para(5561(a,1),6525(a,1,2))].">
      <j1 rule="para" parents="5561 6525"/>
    </justification>
  </clause>

  <clause id="6529">
    <literal><![CDATA[
      T(x,(y \ z) \ K(y,u)) = T(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),6526(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 6526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6530">
    <literal><![CDATA[
      L(K(x,y \ z),z,z \ 1) = K(x,((1 / z) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(2792(a,1),6114(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2792 6114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6531">
    <literal><![CDATA[
      K(x * y,z) * (y * x) = K(y,x) * T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4581,a,b,6130,a)].">
      <j1 rule="hyper" parents="320 4581 6130"/>
    </justification>
  </clause>

  <clause id="6532">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,z) = ((y * x) \ y) \ K(x,z)
    ]]></literal>
    <justification jstring="[para(217(a,2),6235(a,1,1,1))].">
      <j1 rule="para" parents="217 6235"/>
    </justification>
  </clause>

  <clause id="6536">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) = K((z / y) \ x,z)
    ]]></literal>
    <justification jstring="[para(4620(a,1),6240(a,1,2))].">
      <j1 rule="para" parents="4620 6240"/>
    </justification>
  </clause>

  <clause id="6537">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) = K((x * y) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(6396,a,6241,a),flip(a)].">
      <j1 rule="hyper" parents="6396 6241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6538">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,(x \ 1) \ (x \ y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(6315,a,6254,a)].">
      <j1 rule="hyper" parents="6315 6254"/>
    </justification>
  </clause>

  <clause id="6539">
    <literal><![CDATA[
      K((x * y) \ z,y) = K((y * x) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,6255,a,b,6256,a),flip(a)].">
      <j1 rule="hyper" parents="29 6255 6256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6540">
    <literal><![CDATA[
      1 / K((x * y) \ z,x) = K(x,(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(6539(a,1),4931(a,1,2))].">
      <j1 rule="para" parents="6539 4931"/>
    </justification>
  </clause>

  <clause id="6541">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(4938,a,6540,a),flip(a)].">
      <j1 rule="hyper" parents="4938 6540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6542">
    <literal><![CDATA[
      R(x,K(y,z),T(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(515,a,6281,a)].">
      <j1 rule="hyper" parents="515 6281"/>
    </justification>
  </clause>

  <clause id="6543">
    <literal><![CDATA[
      R(x,K(y,z),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(6542(a,1),46(a,2))].">
      <j1 rule="para" parents="6542 46"/>
    </justification>
  </clause>

  <clause id="6544">
    <literal><![CDATA[
      x * (y \ R(y,x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[para(5255(a,1),6362(a,1,2))].">
      <j1 rule="para" parents="5255 6362"/>
    </justification>
  </clause>

  <clause id="6545">
    <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(6544(a,1),215(a,2,2))].">
      <j1 rule="para" parents="6544 215"/>
    </justification>
  </clause>

  <clause id="6546">
    <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(6387(a,2),766(a,1))].">
      <j1 rule="para" parents="6387 766"/>
    </justification>
  </clause>

  <clause id="6547">
    <literal><![CDATA[
      K(K(x,y),y * z) = K(z * y,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(5618,a,6413,a),flip(a)].">
      <j1 rule="hyper" parents="5618 6413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6548">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(y * x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5617,a,6547,a),flip(a)].">
      <j1 rule="hyper" parents="5617 6547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6549">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = (1 / z) * K((((1 / z) \ x) \ 1) \ (z \ 1),y)
    ]]></literal>
    <justification jstring="[para(3943(a,1),6499(a,2,2))].">
      <j1 rule="para" parents="3943 6499"/>
    </justification>
  </clause>

  <clause id="6550">
    <literal><![CDATA[
      T(x * K(x * y,y \ 1),y) = y \ T(x * y,y \ 1)
    ]]></literal>
    <justification jstring="[para(5831(a,1),6502(a,1,1,2))].">
      <j1 rule="para" parents="5831 6502"/>
    </justification>
  </clause>

  <clause id="6551">
    <literal><![CDATA[
      K((x / y) \ z,x) = K((y \ x) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6382,a(flip),b,6536,a),flip(a)].">
      <j1 rule="hyper" parents="58 6382 6536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6552">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ ((T(y,x) / z) \ y)) = z \ ((T(y,x) / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(354,a,6538,a),flip(a)].">
      <j1 rule="hyper" parents="354 6538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6553">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6114,a(flip),b,6102,a)].">
      <j1 rule="hyper" parents="58 6114 6102"/>
    </justification>
  </clause>

  <clause id="6554">
    <literal><![CDATA[
      K(x,(y * z) \ (y * x)) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(6088,a,6553,a),flip(a)].">
      <j1 rule="hyper" parents="6088 6553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6555">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),u,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(5(a,1),6553(a,2,2,1))].">
      <j1 rule="para" parents="5 6553"/>
    </justification>
  </clause>

  <clause id="6556">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),6553(a,2,2,2))].">
      <j1 rule="para" parents="5 6553"/>
    </justification>
  </clause>

  <clause id="6557">
    <literal><![CDATA[
      K(x,(y * (z / u)) \ (y * z)) = L(K(x,u),z,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),6553(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 6553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6558">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,L(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(92(a,2),6553(a,2,2))].">
      <j1 rule="para" parents="92 6553"/>
    </justification>
  </clause>

  <clause id="6559">
    <literal><![CDATA[
      K(x,(y * z) \ (y * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ x) = u
    ]]></literal>
    <justification jstring="[para(6553(a,1),6088(a,1))].">
      <j1 rule="para" parents="6553 6088"/>
    </justification>
  </clause>

  <clause id="6560">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[para(5(a,1),6554(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 6554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6561">
    <literal><![CDATA[
      K(x \ y,(x * z) \ y) = K(x \ y,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(5(a,1),6554(a,1,2,2))].">
      <j1 rule="para" parents="5 6554"/>
    </justification>
  </clause>

  <clause id="6562">
    <literal><![CDATA[
      K(x,L(y \ x,y,z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(92(a,2),6554(a,1,2))].">
      <j1 rule="para" parents="92 6554"/>
    </justification>
  </clause>

  <clause id="6563">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ x) = K(x,u \ (K(z,y) * x))
    ]]></literal>
    <justification jstring="[para(5095(a,1),6554(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5095 6554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6564">
    <literal><![CDATA[
      T(x,L(y \ x,y,z)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(118,a,6562,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 6562 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6565">
    <literal><![CDATA[
      T(x,(y \ z) \ x) = T(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[para(490(a,1),6564(a,1,2)),flip(a)].">
      <j1 rule="para" parents="490 6564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6566">
    <literal><![CDATA[
      K(x,((y * K(z,y)) \ u) \ x) = K(x,u \ (y * (K(z,y) * x)))
    ]]></literal>
    <justification jstring="[para(5414(a,1),6560(a,2,2,2))].">
      <j1 rule="para" parents="5414 6560"/>
    </justification>
  </clause>

  <clause id="6567">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,z) \ x) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[para(5815(a,2),6560(a,1,2,1))].">
      <j1 rule="para" parents="5815 6560"/>
    </justification>
  </clause>

  <clause id="6568">
    <literal><![CDATA[
      K(x,L(y \ z,y,K(z,u))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(4174,a,6558,a),flip(a)].">
      <j1 rule="hyper" parents="4174 6558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6569">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6553,a(flip),b,6558,a),flip(a)].">
      <j1 rule="hyper" parents="58 6553 6558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6570">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ T(y,z)) = K(x,u \ y)
    ]]></literal>
    <justification jstring="[para(4809(a,1),6568(a,1,2))].">
      <j1 rule="para" parents="4809 6568"/>
    </justification>
  </clause>

  <clause id="6571">
    <literal><![CDATA[
      K(x,T(y,z) \ z) = K(x,y \ T(z,y))
    ]]></literal>
    <justification jstring="[para(4770(a,1),6570(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4770 6570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6572">
    <literal><![CDATA[
      T(x,T(y,z) \ z) = T(x,y \ T(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,6571,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 6571 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6573">
    <literal><![CDATA[
      (x * y) * K(z,u \ (x * y)) = x * (y * K(z,(x \ u) \ y))
    ]]></literal>
    <justification jstring="[hyper(119,a,6555,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 6555 13"/>
    </justification>
  </clause>

  <clause id="6574">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = T(K(x,z \ (y * u)),w)
    ]]></literal>
    <justification jstring="[para(6555(a,1),20(a,2,1))].">
      <j1 rule="para" parents="6555 20"/>
    </justification>
  </clause>

  <clause id="6575">
    <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(6555(a,1),5430(a,1))].">
      <j1 rule="para" parents="6555 5430"/>
    </justification>
  </clause>

  <clause id="6576">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ y) \ x) = u
    ]]></literal>
    <justification jstring="[para(6555(a,1),6088(a,1))].">
      <j1 rule="para" parents="6555 6088"/>
    </justification>
  </clause>

  <clause id="6577">
    <literal><![CDATA[
      K(x,(y * ((y \ z) / u)) \ z) = L(K(x,u),y \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6557(a,1,2,2))].">
      <j1 rule="para" parents="5 6557"/>
    </justification>
  </clause>

  <clause id="6578">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(94(a,2),6557(a,1,2))].">
      <j1 rule="para" parents="94 6557"/>
    </justification>
  </clause>

  <clause id="6579">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,5716,a,b,6578,a),flip(a)].">
      <j1 rule="hyper" parents="320 5716 6578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6580">
    <literal><![CDATA[
      L(K(x,y),z * y,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(6(a,1),6578(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 6578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6581">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z * y,K(y,x))
    ]]></literal>
    <justification jstring="[para(6580(a,1),5859(a,1,1))].">
      <j1 rule="para" parents="6580 5859"/>
    </justification>
  </clause>

  <clause id="6582">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(u,z * x,K(x,y))
    ]]></literal>
    <justification jstring="[para(6580(a,1),5861(a,1,2))].">
      <j1 rule="para" parents="6580 5861"/>
    </justification>
  </clause>

  <clause id="6583">
    <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(6580(a,1),5869(a,1,1))].">
      <j1 rule="para" parents="6580 5869"/>
    </justification>
  </clause>

  <clause id="6584">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(4936,a,6579,a)].">
      <j1 rule="hyper" parents="4936 6579"/>
    </justification>
  </clause>

  <clause id="6585">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(6579(a,2),5719(a,1))].">
      <j1 rule="para" parents="6579 5719"/>
    </justification>
  </clause>

  <clause id="6586">
    <literal><![CDATA[
      L(K(x,y),z * x,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(6(a,1),6584(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6 6584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6587">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K(L(x \ y,x,u),z)
    ]]></literal>
    <justification jstring="[para(72(a,1),6584(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6588">
    <literal><![CDATA[
      L(K(x,y),z * T(x,u),w) = K(L(x,z * K(x,u),w),y)
    ]]></literal>
    <justification jstring="[para(6164(a,1),6584(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6164 6584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6589">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(6092,a,6586,a),flip(a)].">
      <j1 rule="hyper" parents="6092 6586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6590">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * y)) = K(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,304,a,b,6586,a)].">
      <j1 rule="hyper" parents="58 304 6586"/>
    </justification>
  </clause>

  <clause id="6591">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = a(u,z * y,K(x,y))
    ]]></literal>
    <justification jstring="[para(6586(a,1),5861(a,1,2))].">
      <j1 rule="para" parents="6586 5861"/>
    </justification>
  </clause>

  <clause id="6592">
    <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(6586(a,1),5868(a,1,2))].">
      <j1 rule="para" parents="6586 5868"/>
    </justification>
  </clause>

  <clause id="6593">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5346,a(flip),b,6589,a),flip(a)].">
      <j1 rule="hyper" parents="320 5346 6589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6594">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K((u * x) \ (u * y),z)
    ]]></literal>
    <justification jstring="[para(92(a,1),6587(a,2,1))].">
      <j1 rule="para" parents="92 6587"/>
    </justification>
  </clause>

  <clause id="6595">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(298(a,1),6587(a,2,1))].">
      <j1 rule="para" parents="298 6587"/>
    </justification>
  </clause>

  <clause id="6596">
    <literal><![CDATA[
      L(K(x \ T(y,z),u),T(y,z),z) = K((z * x) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(450(a,1),6587(a,2,1))].">
      <j1 rule="para" parents="450 6587"/>
    </justification>
  </clause>

  <clause id="6597">
    <literal><![CDATA[
      L(K((x \ y) \ z,u),z,x) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(490(a,1),6587(a,2,1))].">
      <j1 rule="para" parents="490 6587"/>
    </justification>
  </clause>

  <clause id="6598">
    <literal><![CDATA[
      L(K(L(x,y,z) \ x,u),x,z * y) = K(a(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(1918(a,2),6587(a,2,1))].">
      <j1 rule="para" parents="1918 6587"/>
    </justification>
  </clause>

  <clause id="6599">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = K((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(2792(a,1),6587(a,2,1))].">
      <j1 rule="para" parents="2792 6587"/>
    </justification>
  </clause>

  <clause id="6600">
    <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(5126(a,1),6587(a,2,1))].">
      <j1 rule="para" parents="5126 6587"/>
    </justification>
  </clause>

  <clause id="6601">
    <literal><![CDATA[
      T(x,L(y \ z,y,u)) = T(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(118,a,6569,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 6569 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6602">
    <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(6400(a,1),6569(a,2,2,1))].">
      <j1 rule="para" parents="6400 6569"/>
    </justification>
  </clause>

  <clause id="6603">
    <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),6585(a,1,2))].">
      <j1 rule="para" parents="94 6585"/>
    </justification>
  </clause>

  <clause id="6604">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(34,a,6309,a,b,6590,a)].">
      <j1 rule="hyper" parents="34 6309 6590"/>
    </justification>
  </clause>

  <clause id="6605">
    <literal><![CDATA[
      (x * (y * z)) / K(L(y,z,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = u
    ]]></literal>
    <justification jstring="[para(6590(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6590 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6606">
    <literal><![CDATA[
      L(K(x \ y,z),y,y \ 1) = K(((y \ 1) * x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3959,a(flip),b,6594,a),flip(a)].">
      <j1 rule="hyper" parents="320 3959 6594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6607">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K((z * (x \ 1)) \ (z * y),x)
    ]]></literal>
    <justification jstring="[para(6500(a,1),6594(a,1,1))].">
      <j1 rule="para" parents="6500 6594"/>
    </justification>
  </clause>

  <clause id="6608">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(y \ (x * z),z)
    ]]></literal>
    <justification jstring="[hyper(6092,a,6597,a)].">
      <j1 rule="hyper" parents="6092 6597"/>
    </justification>
  </clause>

  <clause id="6609">
    <literal><![CDATA[
      K((x \ y) \ z,u \ (x * z)) = K(y \ (x * z),(x \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6555,a(flip),b,6597,a)].">
      <j1 rule="hyper" parents="58 6555 6597"/>
    </justification>
  </clause>

  <clause id="6610">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,z) = u
    ]]></literal>
    <justification jstring="[para(6597(a,1),6092(a,1))].">
      <j1 rule="para" parents="6597 6092"/>
    </justification>
  </clause>

  <clause id="6611">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3939,a(flip),b,6599,a),flip(a)].">
      <j1 rule="hyper" parents="320 3939 6599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6613">
    <literal><![CDATA[
      L(x,y,z \ 1) != K((z \ 1) * y,u)
    ]]></literal>
    <literal><![CDATA[
      K(z \ y,u) = x
    ]]></literal>
    <justification jstring="[para(6611(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="6611 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6614">
    <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,6591,a(flip),b,5420,a),flip(a)].">
      <j1 rule="hyper" parents="119 6591 5420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6615">
    <literal><![CDATA[
      K(x,L(L(y \ 1,y,z),z * y,u)) = K(x,1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[para(425(a,2),6137(a,1,2))].">
      <j1 rule="para" parents="425 6137"/>
    </justification>
  </clause>

  <clause id="6616">
    <literal><![CDATA[
      x / (K(y,z) * T(z,u)) = (x / T(z,u)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6543,a,6325,a),flip(a)].">
      <j1 rule="hyper" parents="6543 6325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6617">
    <literal><![CDATA[
      (x / T(y \ 1,z)) * K(y \ 1,y) = x / T(1 / y,z)
    ]]></literal>
    <justification jstring="[para(3050(a,1),6616(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3050 6616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6618">
    <literal><![CDATA[
      (x / T(y,y * z)) * K(y,z) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(5051(a,1),6616(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5051 6616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6619">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,y * z) = x / R(y,z,y)
    ]]></literal>
    <justification jstring="[para(5054(a,1),6616(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5054 6616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6620">
    <literal><![CDATA[
      (x / T(y,z)) * T(y,y * z) = (x / R(y,z,y)) * y
    ]]></literal>
    <justification jstring="[para(6619(a,1),6167(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6619 6167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6621">
    <literal><![CDATA[
      a(x,T(y,z),T(z,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(691,a,6420,a),flip(a)].">
      <j1 rule="hyper" parents="691 6420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6622">
    <literal><![CDATA[
      a(x,T(y,z),T(z,y)) != 1
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = x * (y * z)
    ]]></literal>
    <justification jstring="[para(6621(a,2),969(a,1))].">
      <j1 rule="para" parents="6621 969"/>
    </justification>
  </clause>

  <clause id="6623">
    <literal><![CDATA[
      L(K(x,y \ z),z,z \ 1) = K(x,((z \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,5288,a(flip),b,6530,a),flip(a)].">
      <j1 rule="hyper" parents="320 5288 6530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6624">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,x * L(x \ 1,z,u)) = ((y * x) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(1746(a,1),6532(a,2,2))].">
      <j1 rule="para" parents="1746 6532"/>
    </justification>
  </clause>

  <clause id="6625">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(u * K(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(5092(a,1),6556(a,1,1,2))].">
      <j1 rule="para" parents="5092 6556"/>
    </justification>
  </clause>

  <clause id="6626">
    <literal><![CDATA[
      K((x * y) \ 1,x) = K(y \ (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3141,a(flip),b,6595,a),flip(a)].">
      <j1 rule="hyper" parents="58 3141 6595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6627">
    <literal><![CDATA[
      x * ((x \ y) * K(z \ (x \ y),u)) = y * K((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,6595,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="119 6595 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6628">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K((y * (x \ 1)) \ z,x)
    ]]></literal>
    <justification jstring="[para(6500(a,1),6595(a,1,1))].">
      <j1 rule="para" parents="6500 6595"/>
    </justification>
  </clause>

  <clause id="6629">
    <literal><![CDATA[
      L(K((x \ y) \ (z \ u),y),z \ u,z) = K((z * (y / x)) \ u,y)
    ]]></literal>
    <justification jstring="[para(6551(a,1),6595(a,1,1))].">
      <j1 rule="para" parents="6551 6595"/>
    </justification>
  </clause>

  <clause id="6630">
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = K(y \ (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(5023,a,6626,a)].">
      <j1 rule="hyper" parents="5023 6626"/>
    </justification>
  </clause>

  <clause id="6631">
    <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(6598(a,1),1923(a,1,1))].">
      <j1 rule="para" parents="6598 1923"/>
    </justification>
  </clause>

  <clause id="6632">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,z * y) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,6353,a(flip),b,6620,a)].">
      <j1 rule="hyper" parents="58 6353 6620"/>
    </justification>
  </clause>

  <clause id="6633">
    <literal><![CDATA[
      (1 / x) \ K(y,((x \ 1) * z) \ 1) = x * K(y,z \ x)
    ]]></literal>
    <justification jstring="[hyper(116,a,6623,a(flip),b,2797,a)].">
      <j1 rule="hyper" parents="116 6623 2797"/>
    </justification>
  </clause>

  <clause id="6634">
    <literal><![CDATA[
      K(x,((y \ 1) * (y / z)) \ 1) = L(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),6623(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 6623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6635">
    <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(2406(a,2),6103(a,1,2))].">
      <j1 rule="para" parents="2406 6103"/>
    </justification>
  </clause>

  <clause id="6636">
    <literal><![CDATA[
      K(x,(T(y,z) * u) \ y) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6109,a(flip),b,6104,a),flip(a)].">
      <j1 rule="hyper" parents="58 6109 6104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6637">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) \ K(z,y)) = K(x,u \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6636(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 6636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6638">
    <literal><![CDATA[
      R(x,K(y,z),L(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(515,a,6282,a)].">
      <j1 rule="hyper" parents="515 6282"/>
    </justification>
  </clause>

  <clause id="6639">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) \ x = L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(5651(a,1),6331(a,1,1,2))].">
      <j1 rule="para" parents="5651 6331"/>
    </justification>
  </clause>

  <clause id="6640">
    <literal><![CDATA[
      x / L(K(y,z),u,w) = x * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(197,a,6639,a)].">
      <j1 rule="hyper" parents="197 6639"/>
    </justification>
  </clause>

  <clause id="6641">
    <literal><![CDATA[
      (x * (y * K(z,u))) * L(K(u,z),y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(137,a,6639,a),flip(a)].">
      <j1 rule="hyper" parents="137 6639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6642">
    <literal><![CDATA[
      x / L(K(y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * L(K(z,y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(6639(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6639 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6643">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) = L(K(u,z),y,x)
    ]]></literal>
    <justification jstring="[para(90(a,1),6639(a,1,1))].">
      <j1 rule="para" parents="90 6639"/>
    </justification>
  </clause>

  <clause id="6644">
    <literal><![CDATA[
      (x * ((x \ y) * K(z,u))) \ y = L(K(u,z),x \ y,x)
    ]]></literal>
    <justification jstring="[para(448(a,1),6639(a,1,1))].">
      <j1 rule="para" parents="448 6639"/>
    </justification>
  </clause>

  <clause id="6645">
    <literal><![CDATA[
      (x * (y * K(z,u))) * w != x * y
    ]]></literal>
    <literal><![CDATA[
      L(K(u,z),y,x) = w
    ]]></literal>
    <justification jstring="[para(6641(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="6641 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6646">
    <literal><![CDATA[
      (x * (y \ T(y * z,y))) \ (x * z) = L(K(y,y * z),z,x)
    ]]></literal>
    <justification jstring="[para(6355(a,2),6643(a,1,1,2))].">
      <j1 rule="para" parents="6355 6643"/>
    </justification>
  </clause>

  <clause id="6647">
    <literal><![CDATA[
      x \ T(x * K(y \ x,z),x) = K(T(y,x) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,6389,a(flip),b,6084,a(flip))].">
      <j1 rule="hyper" parents="116 6389 6084"/>
    </justification>
  </clause>

  <clause id="6648">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = x \ T(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(75(a,1),6647(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 6647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6649">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = K(y,T(x / z,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5966,a,b,6648,a),flip(a)].">
      <j1 rule="hyper" parents="320 5966 6648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6650">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * z)) = L(T(z,y),y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,20,a,b,6417,a),flip(a)].">
      <j1 rule="hyper" parents="320 20 6417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6651">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (y \ z)) \ u)
    ]]></literal>
    <justification jstring="[para(957(a,1),6437(a,1,1,2))].">
      <j1 rule="para" parents="957 6437"/>
    </justification>
  </clause>

  <clause id="6652">
    <literal><![CDATA[
      (x * (y * (z * T(z \ (y \ (x \ u)),w)))) \ u = K(w,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(919(a,1),6437(a,1,1,2))].">
      <j1 rule="para" parents="919 6437"/>
    </justification>
  </clause>

  <clause id="6653">
    <literal><![CDATA[
      (x * (((y \ ((x \ z) * u)) * y) / u)) \ z = K(y,(x * (y / u)) \ z)
    ]]></literal>
    <justification jstring="[para(1573(a,1),6437(a,1,1,2))].">
      <j1 rule="para" parents="1573 6437"/>
    </justification>
  </clause>

  <clause id="6654">
    <literal><![CDATA[
      T(K(x \ K(x,y),z),y) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(4838(a,1),6498(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4838 6498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6655">
    <literal><![CDATA[
      K(x \ K(x,y),z) * y = y * K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,6654,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 6654 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6656">
    <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),6603(a,1,2,1,2))].">
      <j1 rule="para" parents="72 6603"/>
    </justification>
  </clause>

  <clause id="6657">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = u
    ]]></literal>
    <justification jstring="[para(6306(a,1),6605(a,1))].">
      <j1 rule="para" parents="6306 6605"/>
    </justification>
  </clause>

  <clause id="6658">
    <literal><![CDATA[
      (x / T(y \ 1,z)) \ K(y,y \ 1) = (x / T(1 / y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(6617(a,1),3700(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6617 3700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6659">
    <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(4775(a,1),6650(a,2,1))].">
      <j1 rule="para" parents="4775 6650"/>
    </justification>
  </clause>

  <clause id="6660">
    <literal><![CDATA[
      K(x,L(y \ L(y,z,u),y,u * z)) = K(x,a(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(502(a,2),6099(a,1,2))].">
      <j1 rule="para" parents="502 6099"/>
    </justification>
  </clause>

  <clause id="6661">
    <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(6209(a,2),4865(a,1))].">
      <j1 rule="para" parents="6209 4865"/>
    </justification>
  </clause>

  <clause id="6662">
    <literal><![CDATA[
      T(x,x \ T(x * y,y \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6183,a(flip),b,6463,a),flip(a)].">
      <j1 rule="hyper" parents="320 6183 6463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6664">
    <literal><![CDATA[
      T(x / y,(x / y) \ T(x,y \ 1)) = T(x / y,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),6662(a,1,2,2,1))].">
      <j1 rule="para" parents="7 6662"/>
    </justification>
  </clause>

  <clause id="6665">
    <literal><![CDATA[
      T(x / y,(x / y) \ T(x,y \ 1)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(320,a,107,a(flip),b,6664,a),flip(a)].">
      <j1 rule="hyper" parents="320 107 6664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6666">
    <literal><![CDATA[
      T(x,y \ 1) / (y \ x) = (x / y) \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(6665(a,1),265(a,1,2))].">
      <j1 rule="para" parents="6665 265"/>
    </justification>
  </clause>

  <clause id="6667">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) / ((y \ 1) \ x) = (x / (y \ 1)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(2939(a,1),6666(a,2,2))].">
      <j1 rule="para" parents="2939 6666"/>
    </justification>
  </clause>

  <clause id="6668">
    <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),6473(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 6473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6669">
    <literal><![CDATA[
      R(x,y,z * K(y,z)) = R(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(518,a,6489,a),flip(a)].">
      <j1 rule="hyper" parents="518 6489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6670">
    <literal><![CDATA[
      K((x / y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,x) = u
    ]]></literal>
    <justification jstring="[para(6536(a,1),6518(a,1))].">
      <j1 rule="para" parents="6536 6518"/>
    </justification>
  </clause>

  <clause id="6671">
    <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,3540,a,b,6615,a)].">
      <j1 rule="hyper" parents="58 3540 6615"/>
    </justification>
  </clause>

  <clause id="6672">
    <literal><![CDATA[
      K(x * (y \ T(y * z,y)),L(K(y,y * z),z,x)) / ((x * z) / (x * (y \ T(y * z,y)))) = 1 / ((x * (y \ T(y * z,y))) \ (x * z))
    ]]></literal>
    <justification jstring="[para(6646(a,1),5037(a,1,1,2))].">
      <j1 rule="para" parents="6646 5037"/>
    </justification>
  </clause>

  <clause id="6673">
    <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,6660,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 6660 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6674">
    <literal><![CDATA[
      K(x * (1 / (y / z)),z \ y) = K(x / (y / z),z \ y)
    ]]></literal>
    <justification jstring="[hyper(6456,a,6152,a),flip(a)].">
      <j1 rule="hyper" parents="6456 6152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6675">
    <literal><![CDATA[
      x / (K(y / (z / u),u \ z) * x) = K(u \ z,y * (1 / (z / u)))
    ]]></literal>
    <justification jstring="[para(6674(a,1),5104(a,1,2,1))].">
      <j1 rule="para" parents="6674 5104"/>
    </justification>
  </clause>

  <clause id="6676">
    <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(4708(a,1),6326(a,1,1,1))].">
      <j1 rule="para" parents="4708 6326"/>
    </justification>
  </clause>

  <clause id="6677">
    <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(6423(a,1),44(a,1))].">
      <j1 rule="para" parents="6423 44"/>
    </justification>
  </clause>

  <clause id="6678">
    <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(6423(a,1),5595(a,1))].">
      <j1 rule="para" parents="6423 5595"/>
    </justification>
  </clause>

  <clause id="6679">
    <literal><![CDATA[
      (((x / y) * T(y,z)) * u) \ (x * u) = K(z,((x / y) * u) \ (x * u))
    ]]></literal>
    <justification jstring="[para(75(a,1),6438(a,1,1,1,2,1))].">
      <j1 rule="para" parents="75 6438"/>
    </justification>
  </clause>

  <clause id="6680">
    <literal><![CDATA[
      K(x,T(y \ z,u) \ T(z,u)) = T(K(y,x) * z,u) \ T(z,u)
    ]]></literal>
    <justification jstring="[para(5061(a,1),6439(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5061 6439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6681">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * y) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(6114(a,1),6453(a,1))].">
      <j1 rule="para" parents="6114 6453"/>
    </justification>
  </clause>

  <clause id="6682">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * y) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(6558(a,1),6681(a,1))].">
      <j1 rule="para" parents="6558 6681"/>
    </justification>
  </clause>

  <clause id="6683">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K((x \ y) \ z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,6078,a(flip),b,6513,a),flip(a)].">
      <j1 rule="hyper" parents="320 6078 6513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6684">
    <literal><![CDATA[
      (x * K(y * z,u)) * (z * y) = x * (K(z,y) * T(y * z,u))
    ]]></literal>
    <justification jstring="[para(6531(a,1),6520(a,2,2))].">
      <j1 rule="para" parents="6531 6520"/>
    </justification>
  </clause>

  <clause id="6685">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ K(x,z),u) = w
    ]]></literal>
    <justification jstring="[para(6527(a,2),5204(a,1))].">
      <j1 rule="para" parents="6527 5204"/>
    </justification>
  </clause>

  <clause id="6686">
    <literal><![CDATA[
      K(x,(K(y,z) * (y \ u)) \ x) = K(x,u \ (y * (K(z,y) * x)))
    ]]></literal>
    <justification jstring="[para(5360(a,1),6566(a,1,2,1))].">
      <j1 rule="para" parents="5360 6566"/>
    </justification>
  </clause>

  <clause id="6687">
    <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(6573(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="6573 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6688">
    <literal><![CDATA[
      K((x \ 1) \ y,z \ (x * y)) = K(x * y,(x \ z) \ y)
    ]]></literal>
    <justification jstring="[para(60(a,1),6609(a,2,1))].">
      <j1 rule="para" parents="60 6609"/>
    </justification>
  </clause>

  <clause id="6689">
    <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(1302(a,1),6609(a,2,1))].">
      <j1 rule="para" parents="1302 6609"/>
    </justification>
  </clause>

  <clause id="6690">
    <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(6627(a,2),6316(a,1,1))].">
      <j1 rule="para" parents="6627 6316"/>
    </justification>
  </clause>

  <clause id="6691">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = (x / (y \ 1)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(2939(a,1),6667(a,1,1))].">
      <j1 rule="para" parents="2939 6667"/>
    </justification>
  </clause>

  <clause id="6692">
    <literal><![CDATA[
      ((x / y) / (y \ 1)) \ T(x / y,y) = (y \ x) / ((y \ 1) \ (x / y))
    ]]></literal>
    <justification jstring="[para(107(a,1),6691(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 6691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6693">
    <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,6680,a,b,xx)].">
      <j1 rule="hyper" parents="119 6680"/>
    </justification>
  </clause>

  <clause id="6694">
    <literal><![CDATA[
      (K(x,y) * K(x * y,z)) * (y * x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5095,a(flip),b,6684,a),flip(a)].">
      <j1 rule="hyper" parents="320 5095 6684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6695">
    <literal><![CDATA[
      (x * y) \ T(y * x,z) = K(y,x) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,5665,a,b,6694,a)].">
      <j1 rule="hyper" parents="30 5665 6694"/>
    </justification>
  </clause>

  <clause id="6696">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / (y * T(z,y)) = R(x,y * K(z,y),z)
    ]]></literal>
    <justification jstring="[para(6167(a,1),6494(a,1,2))].">
      <j1 rule="para" parents="6167 6494"/>
    </justification>
  </clause>

  <clause id="6697">
    <literal><![CDATA[
      R(x,y * K(z,y),z) = R(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(518,a,6696,a),flip(a)].">
      <j1 rule="hyper" parents="518 6696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6698">
    <literal><![CDATA[
      R(x,y \ z,T(y,y \ z)) = R(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(4735(a,1),6697(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4735 6697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6699">
    <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(5882(a,2),6625(a,2,2,1))].">
      <j1 rule="para" parents="5882 6625"/>
    </justification>
  </clause>

  <clause id="6700">
    <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(6655(a,2),6625(a,2,2,1))].">
      <j1 rule="para" parents="6655 6625"/>
    </justification>
  </clause>

  <clause id="6701">
    <literal><![CDATA[
      K((x * (y / z)) \ u,y) = K((x * (z \ y)) \ u,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6595,a(flip),b,6629,a),flip(a)].">
      <j1 rule="hyper" parents="58 6595 6629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6702">
    <literal><![CDATA[
      K((x * (y / x)) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6701(a,2,1,1))].">
      <j1 rule="para" parents="5 6701"/>
    </justification>
  </clause>

  <clause id="6703">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),6702(a,1,1,1,2))].">
      <j1 rule="para" parents="72 6702"/>
    </justification>
  </clause>

  <clause id="6704">
    <literal><![CDATA[
      T(x,((y \ x) * y) \ z) = (u * K(x \ z,x)) \ (u * x)
    ]]></literal>
    <justification jstring="[para(6703(a,1),6286(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6703 6286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6705">
    <literal><![CDATA[
      T(x,((y \ x) * y) \ z) = T(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,6286,a(flip),b,6704,a),flip(a)].">
      <j1 rule="hyper" parents="320 6286 6704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6706">
    <literal><![CDATA[
      T(x,x \ T(y,y \ x)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5560(a,1),6705(a,1,2))].">
      <j1 rule="para" parents="5560 6705"/>
    </justification>
  </clause>

  <clause id="6707">
    <literal><![CDATA[
      T(x,x \ y) / T(y,y \ x) = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(6706(a,1),265(a,1,2))].">
      <j1 rule="para" parents="6706 265"/>
    </justification>
  </clause>

  <clause id="6708">
    <literal><![CDATA[
      T(x,x \ y) / ((y \ x) \ x) = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(675,a,6707,a)].">
      <j1 rule="hyper" parents="675 6707"/>
    </justification>
  </clause>

  <clause id="6709">
    <literal><![CDATA[
      x \ T(y,y \ x) = y / ((y \ ((x \ y) \ y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6149,a(flip),b,6708,a),flip(a)].">
      <j1 rule="hyper" parents="58 6149 6708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6710">
    <literal><![CDATA[
      (x * (1 / T(y,z))) * T(y,z) = R(x,1 / T(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(4914,a,6320,a),flip(a)].">
      <j1 rule="hyper" parents="4914 6320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6711">
    <literal><![CDATA[
      R(x,1 / T(y,z),y) / y = (x * (1 / T(y,z))) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,6710,a(flip),b,6167,a)].">
      <j1 rule="hyper" parents="117 6710 6167"/>
    </justification>
  </clause>

  <clause id="6712">
    <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(6710(a,1),2596(a,1))].">
      <j1 rule="para" parents="6710 2596"/>
    </justification>
  </clause>

  <clause id="6713">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = (x * (1 / T(y,z))) * K(y,z)
    ]]></literal>
    <justification jstring="[para(3993(a,1),6711(a,1,1))].">
      <j1 rule="para" parents="3993 6711"/>
    </justification>
  </clause>

  <clause id="6714">
    <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(3993(a,1),6712(a,1))].">
      <j1 rule="para" parents="3993 6712"/>
    </justification>
  </clause>

  <clause id="6715">
    <literal><![CDATA[
      (x * y) \ (y * (K(x,y) * (x * z))) = L(L(z,x,y),y * x,K(x,y))
    ]]></literal>
    <justification jstring="[para(5219(a,1),4967(a,1,2))].">
      <j1 rule="para" parents="5219 4967"/>
    </justification>
  </clause>

  <clause id="6716">
    <literal><![CDATA[
      R(K(x,y),x * z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(5083,a,5948,a)].">
      <j1 rule="hyper" parents="5083 5948"/>
    </justification>
  </clause>

  <clause id="6717">
    <literal><![CDATA[
      K(R(x,y,z),x \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3691,a(flip),b,6716,a),flip(a)].">
      <j1 rule="hyper" parents="58 3691 6716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6718">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),6716(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 6716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6719">
    <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(6716(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6716 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6720">
    <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(5064(a,1),6716(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5064 6716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6721">
    <literal><![CDATA[
      R(x,y,z) * (1 / R(x,y,z)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5940,a,b,6717,a)].">
      <j1 rule="hyper" parents="58 5940 6717"/>
    </justification>
  </clause>

  <clause id="6722">
    <literal><![CDATA[
      R(x,y,z) \ K(x,x \ 1) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,6717,a(flip),b,5940,a)].">
      <j1 rule="hyper" parents="116 6717 5940"/>
    </justification>
  </clause>

  <clause id="6723">
    <literal><![CDATA[
      K(R(x,x \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,379,a(flip),b,6718,a),flip(a)].">
      <j1 rule="hyper" parents="320 379 6718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6724">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) * (y * z) = (K(x,u) * y) * z
    ]]></literal>
    <justification jstring="[para(6718(a,2),101(a,1,1))].">
      <j1 rule="para" parents="6718 101"/>
    </justification>
  </clause>

  <clause id="6725">
    <literal><![CDATA[
      K((x * y) / ((z \ x) * y),u) = R(K(z,u),x,y)
    ]]></literal>
    <justification jstring="[para(98(a,1),6718(a,1,1))].">
      <j1 rule="para" parents="98 6718"/>
    </justification>
  </clause>

  <clause id="6726">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = (w * R(K(y,x),z,u)) \ w
    ]]></literal>
    <justification jstring="[para(6718(a,1),6309(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6718 6309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6727">
    <literal><![CDATA[
      K(R(x,x \ 1,y),L(z,x,x \ 1)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5770,a(flip),b,6723,a),flip(a)].">
      <j1 rule="hyper" parents="320 5770 6723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6730">
    <literal><![CDATA[
      (1 / x) * (R(x,y,z) \ x) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,3694,a,b,6721,a)].">
      <j1 rule="hyper" parents="29 3694 6721"/>
    </justification>
  </clause>

  <clause id="6731">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * ((x \ 1) \ 1) = (1 / R(x,y,z)) * x
    ]]></literal>
    <justification jstring="[para(6722(a,1),3380(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6722 3380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6732">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(123,a,6730,a)].">
      <j1 rule="hyper" parents="123 6730"/>
    </justification>
  </clause>

  <clause id="6733">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,5988,a(flip),b,6732,a)].">
      <j1 rule="hyper" parents="58 5988 6732"/>
    </justification>
  </clause>

  <clause id="6734">
    <literal><![CDATA[
      (x \ 1) * (R(x,y,z) \ x) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,6732,a(flip),b,5987,a(flip))].">
      <j1 rule="hyper" parents="119 6732 5987"/>
    </justification>
  </clause>

  <clause id="6735">
    <literal><![CDATA[
      K(x,(R(y,z,u) \ y) \ x) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(6733(a,1),5384(a,1,2,1))].">
      <j1 rule="para" parents="6733 5384"/>
    </justification>
  </clause>

  <clause id="6736">
    <literal><![CDATA[
      R(K(x / y,z),x,u) = K((x * u) / (y * u),z)
    ]]></literal>
    <justification jstring="[para(75(a,1),6725(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 6725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6737">
    <literal><![CDATA[
      R(K(x / (y / z),u),x,z) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(7(a,1),6736(a,2,1,2))].">
      <j1 rule="para" parents="7 6736"/>
    </justification>
  </clause>

  <clause id="6738">
    <literal><![CDATA[
      K((x * y) / z,x) = K(x / (z / y),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5434,a(flip),b,6737,a),flip(a)].">
      <j1 rule="hyper" parents="58 5434 6737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6739">
    <literal><![CDATA[
      K((x * y) / z,x) = K((z / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,6258,a(flip),b,6738,a),flip(a)].">
      <j1 rule="hyper" parents="320 6258 6738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6740">
    <literal><![CDATA[
      K((x * y) / z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K((z / y) \ x,x) = u
    ]]></literal>
    <justification jstring="[para(6738(a,2),6480(a,1))].">
      <j1 rule="para" parents="6738 6480"/>
    </justification>
  </clause>

  <clause id="6741">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) * u = K(x,y) * (T(x,z) * u)
    ]]></literal>
    <justification jstring="[para(4048(a,1),6724(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4048 6724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6742">
    <literal><![CDATA[
      L(x,T(y,z),K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,6741,a)].">
      <j1 rule="hyper" parents="479 6741"/>
    </justification>
  </clause>

  <clause id="6743">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ 1 = T(x,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4939,a(flip),b,6742,a)].">
      <j1 rule="hyper" parents="58 4939 6742"/>
    </justification>
  </clause>

  <clause id="6744">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ 1 = T(x,y) \ K(z,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5622,a,b,6743,a),flip(a)].">
      <j1 rule="hyper" parents="320 5622 6743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6745">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(3681,a,6731,a),flip(a)].">
      <j1 rule="hyper" parents="3681 6731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6746">
    <literal><![CDATA[
      x / R(x,y,z) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(1876,a,6745,a)].">
      <j1 rule="hyper" parents="1876 6745"/>
    </justification>
  </clause>

  <clause id="6747">
    <literal><![CDATA[
      T(1 / R(x,y,z),x) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(239,a,6745,a,b,1308,a)].">
      <j1 rule="hyper" parents="239 6745 1308"/>
    </justification>
  </clause>

  <clause id="6748">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ x = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(188,a,6746,a)].">
      <j1 rule="hyper" parents="188 6746"/>
    </justification>
  </clause>

  <clause id="6749">
    <literal><![CDATA[
      (R(x,y,z) \ x) * R(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(133,a,6746,a)].">
      <j1 rule="hyper" parents="133 6746"/>
    </justification>
  </clause>

  <clause id="6750">
    <literal><![CDATA[
      (x / R(x,y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      (R(x,y,z) \ x) * u = w
    ]]></literal>
    <justification jstring="[para(6748(a,1),348(a,1,1,2))].">
      <j1 rule="para" parents="6748 348"/>
    </justification>
  </clause>

  <clause id="6751">
    <literal><![CDATA[
      T(x,y) / R(x,z,u) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(6749(a,1),4537(a,1,1,1))].">
      <j1 rule="para" parents="6749 4537"/>
    </justification>
  </clause>

  <clause id="6752">
    <literal><![CDATA[
      (R(x,y,z) \ T(x,u)) \ T(x,u) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(188,a,6751,a)].">
      <j1 rule="hyper" parents="188 6751"/>
    </justification>
  </clause>

  <clause id="6753">
    <literal><![CDATA[
      K(x,(y / R(y,z,u)) \ x) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(6746(a,2),6735(a,1,2,1))].">
      <j1 rule="para" parents="6746 6735"/>
    </justification>
  </clause>

  <clause id="6754">
    <literal><![CDATA[
      T(x,y) * K(x * y,(y * x) \ x) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(5561(a,1),5178(a,1,2,2))].">
      <j1 rule="para" parents="5561 5178"/>
    </justification>
  </clause>

  <clause id="6755">
    <literal><![CDATA[
      K((T(x,y) \ T(z,y)) \ 1,x) = K((x \ z) \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,5550,a(flip),b,5495,a),flip(a)].">
      <j1 rule="hyper" parents="58 5550 5495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6756">
    <literal><![CDATA[
      K((T(x,y) \ T(z,y)) \ 1,x) = K(z \ x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,6230,a(flip),b,6755,a),flip(a)].">
      <j1 rule="hyper" parents="320 6230 6755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6757">
    <literal><![CDATA[
      K(T(x,y) \ T(z,y),z) = K(x \ z,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(6396,a,6756,a)].">
      <j1 rule="hyper" parents="6396 6756"/>
    </justification>
  </clause>

  <clause id="6758">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) = 1 / K(y \ x,T(x,z))
    ]]></literal>
    <justification jstring="[para(6757(a,1),4931(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6757 4931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6759">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) = K(T(x,z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4931,a(flip),b,6758,a),flip(a)].">
      <j1 rule="hyper" parents="320 4931 6758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6760">
    <literal><![CDATA[
      (x * T(x \ y,z)) / K((x / y) \ 1,z) = T(y,K(z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,6399,a(flip),b,5608,a),flip(a)].">
      <j1 rule="hyper" parents="320 6399 5608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6761">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) / K((y / x) \ 1,z) = T(x,K(z,y \ x))
    ]]></literal>
    <justification jstring="[para(5015(a,1),6760(a,1,1))].">
      <j1 rule="para" parents="5015 6760"/>
    </justification>
  </clause>

  <clause id="6762">
    <literal><![CDATA[
      (1 / (1 / ((x * y) / x))) \ K(x,y) = (y \ 1) * K(y,1 / y)
    ]]></literal>
    <justification jstring="[para(4717(a,1),5696(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4717 5696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6763">
    <literal><![CDATA[
      (1 / (1 / ((x * y) / x))) \ K(x,y) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(320,a,4785,a(flip),b,6762,a),flip(a)].">
      <j1 rule="hyper" parents="320 4785 6762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6765">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,(y \ 1) \ 1) = (x * K(z,y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(5852(a,1),5851(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5852 5851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6766">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = (x * (z \ 1)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(3523(a,1),6765(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3523 6765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6767">
    <literal><![CDATA[
      R(x / T(y,z),y,y \ 1) = (x * (y \ 1)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6352,a,6766,a)].">
      <j1 rule="hyper" parents="6352 6766"/>
    </justification>
  </clause>

  <clause id="6768">
    <literal><![CDATA[
      ((x * T(y,z)) * (y \ 1)) * K(z,y) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(6(a,1),6767(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 6767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6769">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) \ v5 = L(T(K(y,x),z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(5644(a,1),5870(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5644 5870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6770">
    <literal><![CDATA[
      L(T(K(x,y),z),z,z \ 1) * u = ((1 / z) * (K(y,x) * z)) \ u
    ]]></literal>
    <justification jstring="[para(2798(a,1),6769(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2798 6769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6771">
    <literal><![CDATA[
      ((1 / x) * (K(y,z) * x)) \ u = ((1 / x) * (K(z,y) * x)) * u
    ]]></literal>
    <justification jstring="[para(2798(a,1),6770(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2798 6770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6772">
    <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(5029(a,2),5922(a,2,1))].">
      <j1 rule="para" parents="5029 5922"/>
    </justification>
  </clause>

  <clause id="6773">
    <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(320,a,24,a(flip),b,5931,a),flip(a)].">
      <j1 rule="hyper" parents="320 24 5931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6774">
    <literal><![CDATA[
      x / (T(x,y) \ ((x \ 1) \ 1)) = (1 / (1 / x)) / K(y,x)
    ]]></literal>
    <justification jstring="[para(4755(a,2),5946(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4755 5946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6775">
    <literal><![CDATA[
      x / (T(x,y) \ ((x \ 1) \ 1)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4827,a(flip),b,6774,a),flip(a)].">
      <j1 rule="hyper" parents="320 4827 6774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6776">
    <literal><![CDATA[
      x / (x * (1 / T(x,y))) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(3415(a,1),6775(a,1,2))].">
      <j1 rule="para" parents="3415 6775"/>
    </justification>
  </clause>

  <clause id="6777">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ x = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(188,a,6776,a)].">
      <j1 rule="hyper" parents="188 6776"/>
    </justification>
  </clause>

  <clause id="6778">
    <literal><![CDATA[
      ((x \ y) / (x \ 1)) \ T(x \ y,x) = (x \ y) / ((x \ 1) \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6691,a(flip),b,5961,a)].">
      <j1 rule="hyper" parents="58 6691 5961"/>
    </justification>
  </clause>

  <clause id="6779">
    <literal><![CDATA[
      L(T(1 / x,y),y,K(x,z)) = T(1 / x,K(x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(769,a,5977,a)].">
      <j1 rule="hyper" parents="769 5977"/>
    </justification>
  </clause>

  <clause id="6780">
    <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(6779(a,1),5659(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6779 5659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6781">
    <literal><![CDATA[
      L(T(K(x,y),z),z,K(x,u)) = T(K(x,y),K(x,u) * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5508,a(flip),b,6780,a),flip(a)].">
      <j1 rule="hyper" parents="320 5508 6780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6782">
    <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(6781(a,1),694(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6781 694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6783">
    <literal><![CDATA[
      ((K(x,y) / z) * (z * K(y,x))) \ (K(x,y) / z) = 1 / (z * K(y,x))
    ]]></literal>
    <justification jstring="[para(6306(a,1),6328(a,2,2))].">
      <j1 rule="para" parents="6306 6328"/>
    </justification>
  </clause>

  <clause id="6784">
    <literal><![CDATA[
      K(x \ y,z) \ K(K(x \ y,z),y) = K(y / x,z) \ 1
    ]]></literal>
    <justification jstring="[para(6(a,1),6415(a,2,1))].">
      <j1 rule="para" parents="6 6415"/>
    </justification>
  </clause>

  <clause id="6785">
    <literal><![CDATA[
      K(x \ y,z) \ K(K(x \ y,z),y) = K(z,y / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4929,a(flip),b,6784,a),flip(a)].">
      <j1 rule="hyper" parents="320 4929 6784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6787">
    <literal><![CDATA[
      K(x \ y,z) \ K(y,K(z,x \ y)) = K(z,y / x)
    ]]></literal>
    <justification jstring="[para(5584(a,1),6785(a,1,2))].">
      <j1 rule="para" parents="5584 6785"/>
    </justification>
  </clause>

  <clause id="6788">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(4620(a,1),6653(a,1,1,2))].">
      <j1 rule="para" parents="4620 6653"/>
    </justification>
  </clause>

  <clause id="6789">
    <literal><![CDATA[
      K(x \ y,z * (1 / (y / x))) = K(x \ y,z / (y / x))
    ]]></literal>
    <justification jstring="[hyper(5112,a,6675,a),flip(a)].">
      <j1 rule="hyper" parents="5112 6675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6790">
    <literal><![CDATA[
      K(x,((y / z) * u) \ (y * u)) = ((y * K(z,x)) * u) \ (y * u)
    ]]></literal>
    <justification jstring="[para(6121(a,1),6679(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6121 6679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6791">
    <literal><![CDATA[
      ((x * K(y,z)) * u) * K(z,((x / y) * u) \ (x * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(119,a,6790,a,b,xx)].">
      <j1 rule="hyper" parents="119 6790"/>
    </justification>
  </clause>

  <clause id="6792">
    <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(6220(a,1),6790(a,2,1))].">
      <j1 rule="para" parents="6220 6790"/>
    </justification>
  </clause>

  <clause id="6793">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) = (x * z) \ ((x * K(y,u)) * z)
    ]]></literal>
    <justification jstring="[para(6791(a,1),6309(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6791 6309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6794">
    <literal><![CDATA[
      ((x * K(y,z)) * K(y,u)) * K(z,y) = x * K(y,u)
    ]]></literal>
    <justification jstring="[para(6205(a,1),6791(a,1,2,2))].">
      <j1 rule="para" parents="6205 6791"/>
    </justification>
  </clause>

  <clause id="6795">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = (x * K(u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6300(a,1),6794(a,1,1,1))].">
      <j1 rule="para" parents="6300 6794"/>
    </justification>
  </clause>

  <clause id="6796">
    <literal><![CDATA[
      ((x * K(y,z)) * K(z,u)) / z = (x * K(z,u)) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,6795,a(flip),b,6296,a)].">
      <j1 rule="hyper" parents="117 6795 6296"/>
    </justification>
  </clause>

  <clause id="6797">
    <literal><![CDATA[
      ((x * K(y,z)) * K(u,y)) * K(z,y) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(u,y) = w
    ]]></literal>
    <justification jstring="[para(6795(a,2),6323(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6795 6323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6798">
    <literal><![CDATA[
      ((x * K(y,z)) / z) * K(z,u) = (x * K(z,u)) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6406,a,6796,a)].">
      <j1 rule="hyper" parents="6406 6796"/>
    </justification>
  </clause>

  <clause id="6799">
    <literal><![CDATA[
      (x * K(y,z)) / T(y,u) = (x / T(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6313(a,1),6798(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6313 6798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6800">
    <literal><![CDATA[
      ((x / T(y,z)) * K(y,u)) \ (x * K(y,u)) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(188,a,6799,a)].">
      <j1 rule="hyper" parents="188 6799"/>
    </justification>
  </clause>

  <clause id="6801">
    <literal><![CDATA[
      (1 / T(x,y)) * K(x,z) = K(x,z) / T(x,y)
    ]]></literal>
    <justification jstring="[para(2(a,1),6799(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2 6799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6802">
    <literal><![CDATA[
      ((x \ y) * K(x,z)) \ (y * K(x,z)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(265(a,1),6800(a,1,1,1))].">
      <j1 rule="para" parents="265 6800"/>
    </justification>
  </clause>

  <clause id="6803">
    <literal><![CDATA[
      (x \ y) / ((x \ 1) \ (y / x)) = ((y / x) / (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),6692(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 6692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6804">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(y,z)) = (y * z) \ (z * (T(y,z) * x))
    ]]></literal>
    <justification jstring="[para(4740(a,1),6715(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4740 6715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6805">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(y,z)) = L(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,231,a(flip),b,6804,a),flip(a)].">
      <j1 rule="hyper" parents="320 231 6804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6806">
    <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(6804(a,2),827(a,1))].">
      <j1 rule="para" parents="6804 827"/>
    </justification>
  </clause>

  <clause id="6807">
    <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(5134(a,1),6761(a,1,1))].">
      <j1 rule="para" parents="5134 6761"/>
    </justification>
  </clause>

  <clause id="6808">
    <literal><![CDATA[
      ((x \ y) / (x \ 1)) \ T(x \ y,x) = ((y / x) / (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6803,a(flip),b,6778,a),flip(a)].">
      <j1 rule="hyper" parents="320 6803 6778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6809">
    <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,6783,a)].">
      <j1 rule="hyper" parents="134 6783"/>
    </justification>
  </clause>

  <clause id="6810">
    <literal><![CDATA[
      K(x,(y * (x / z)) \ u) = K(x,(y * (z \ x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6651,a(flip),b,6788,a),flip(a)].">
      <j1 rule="hyper" parents="58 6651 6788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6811">
    <literal><![CDATA[
      K(x,(y * (x / y)) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),6810(a,2,2,1))].">
      <j1 rule="para" parents="5 6810"/>
    </justification>
  </clause>

  <clause id="6812">
    <literal><![CDATA[
      K(x,(y * ((z \ x) \ x)) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(72(a,1),6810(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6813">
    <literal><![CDATA[
      K(x,((y / T(z,z \ x)) * z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(369(a,1),6812(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="369 6812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6814">
    <literal><![CDATA[
      K(x,(y * K(z \ x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(6296(a,1),6813(a,1,2,1))].">
      <j1 rule="para" parents="6296 6813"/>
    </justification>
  </clause>

  <clause id="6815">
    <literal><![CDATA[
      K(x,((y \ x) \ x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(4761(a,1),6814(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4761 6814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6816">
    <literal><![CDATA[
      a(K(x,y) / z,z,K(x,y)) * (1 / (z * K(y,x))) = K(x,y) / z
    ]]></literal>
    <justification jstring="[para(5866(a,1),6809(a,1,1))].">
      <j1 rule="para" parents="5866 6809"/>
    </justification>
  </clause>

  <clause id="6817">
    <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(4518(a,1),4245(a,1,1))].">
      <j1 rule="para" parents="4518 4245"/>
    </justification>
  </clause>

  <clause id="6818">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(4469(a,1),4631(a,1))].">
      <j1 rule="para" parents="4469 4631"/>
    </justification>
  </clause>

  <clause id="6819">
    <literal><![CDATA[
      T(x * K(y * L(x,z,u),x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(4898(a,1),781(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4898 781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6820">
    <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(5343,a,6819,a)].">
      <j1 rule="hyper" parents="5343 6819"/>
    </justification>
  </clause>

  <clause id="6821">
    <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(4900(a,1),976(a,1,1,1))].">
      <j1 rule="para" parents="4900 976"/>
    </justification>
  </clause>

  <clause id="6822">
    <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(932(a,1),5025(a,1,2))].">
      <j1 rule="para" parents="932 5025"/>
    </justification>
  </clause>

  <clause id="6823">
    <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(5478(a,1),5477(a,1,1,1))].">
      <j1 rule="para" parents="5478 5477"/>
    </justification>
  </clause>

  <clause id="6824">
    <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(5583(a,1),39(a,1))].">
      <j1 rule="para" parents="5583 39"/>
    </justification>
  </clause>

  <clause id="6825">
    <literal><![CDATA[
      K(x,y * (((1 / z) * u) * w)) = K(x,y * (((z \ 1) * u) * w))
    ]]></literal>
    <justification jstring="[para(2838(a,1),5962(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2838 5962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6826">
    <literal><![CDATA[
      K(x,y * ((((K(z,u) / z) \ 1) * u) * w)) = K(x,y * ((u * (1 / (1 / z))) * w))
    ]]></literal>
    <justification jstring="[para(5481(a,1),6825(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5481 6825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6827">
    <literal><![CDATA[
      K(x,y \ z) * K((z \ y) \ x,x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5324(a,1),6113(a,1,2))].">
      <j1 rule="para" parents="5324 6113"/>
    </justification>
  </clause>

  <clause id="6828">
    <literal><![CDATA[
      K(x,y \ z) * K(y \ (z * x),x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(6608(a,1),6827(a,1,2))].">
      <j1 rule="para" parents="6608 6827"/>
    </justification>
  </clause>

  <clause id="6829">
    <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(6380(a,2),6476(a,1))].">
      <j1 rule="para" parents="6380 6476"/>
    </justification>
  </clause>

  <clause id="6830">
    <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(6500(a,1),6829(a,1,1))].">
      <j1 rule="para" parents="6500 6829"/>
    </justification>
  </clause>

  <clause id="6831">
    <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(1232(a,1),6457(a,1,1))].">
      <j1 rule="para" parents="1232 6457"/>
    </justification>
  </clause>

  <clause id="6832">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = x / (y \ T(x,y \ 1))
    ]]></literal>
    <justification jstring="[para(3864(a,1),6668(a,2,2))].">
      <j1 rule="para" parents="3864 6668"/>
    </justification>
  </clause>

  <clause id="6833">
    <literal><![CDATA[
      x / (y \ T(x,y \ 1)) = (T(x,y \ 1) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,3876,a(flip),b,6832,a),flip(a)].">
      <j1 rule="hyper" parents="58 3876 6832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6834">
    <literal><![CDATA[
      (T(x,(y \ 1) \ 1) / (y \ 1)) \ x = x / ((y \ 1) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(2939(a,1),6833(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2939 6833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6835">
    <literal><![CDATA[
      x / ((y \ 1) \ T(x,y)) = (T(x,y) / (y \ 1)) \ x
    ]]></literal>
    <justification jstring="[para(2939(a,1),6834(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2939 6834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6836">
    <literal><![CDATA[
      ((T(x,y) / (y \ 1)) \ x) \ x = (y \ 1) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(188,a,6835,a)].">
      <j1 rule="hyper" parents="188 6835"/>
    </justification>
  </clause>

  <clause id="6837">
    <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(6644(a,1),6690(a,1))].">
      <j1 rule="para" parents="6644 6690"/>
    </justification>
  </clause>

  <clause id="6838">
    <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),6837(a,1,1,2))].">
      <j1 rule="para" parents="75 6837"/>
    </justification>
  </clause>

  <clause id="6839">
    <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(5092(a,1),6837(a,1,1,2))].">
      <j1 rule="para" parents="5092 6837"/>
    </justification>
  </clause>

  <clause id="6840">
    <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(258(a,2),4596(a,2,1,2,1,2))].">
      <j1 rule="para" parents="258 4596"/>
    </justification>
  </clause>

  <clause id="6841">
    <literal><![CDATA[
      K(x \ (y * z),(x \ (y * z)) \ 1) = K(x \ (y * z),z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(1824,a,4731,a)].">
      <j1 rule="hyper" parents="1824 4731"/>
    </justification>
  </clause>

  <clause id="6842">
    <literal><![CDATA[
      K(x \ (y * z),(y * z) \ x) = K(x \ (y * z),z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(6136,a,6841,a)].">
      <j1 rule="hyper" parents="6136 6841"/>
    </justification>
  </clause>

  <clause id="6843">
    <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,4823,a(flip),b,4777,a),flip(a)].">
      <j1 rule="hyper" parents="116 4823 4777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6844">
    <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(4740(a,1),5084(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4740 5084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6845">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(z,u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,13,a,b,6844,a),flip(a)].">
      <j1 rule="hyper" parents="320 13 6844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6846">
    <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(6844(a,2),482(a,1))].">
      <j1 rule="para" parents="6844 482"/>
    </justification>
  </clause>

  <clause id="6847">
    <literal><![CDATA[
      L(L(x,y * z,K(y,u)),z,y) = L(x,z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(970,a,6845,a)].">
      <j1 rule="hyper" parents="970 6845"/>
    </justification>
  </clause>

  <clause id="6848">
    <literal><![CDATA[
      x * (K(x \ 1,x) * K(y,y \ (1 / (x \ 1)))) = y * ((1 / (1 / x)) / y)
    ]]></literal>
    <justification jstring="[para(5291(a,1),5177(a,1,2,2))].">
      <j1 rule="para" parents="5291 5177"/>
    </justification>
  </clause>

  <clause id="6849">
    <literal><![CDATA[
      K(x,x \ y) * K(z,y / (y / x)) = T(y / (y / x),z) \ x
    ]]></literal>
    <justification jstring="[para(4928(a,1),5418(a,1,1))].">
      <j1 rule="para" parents="4928 5418"/>
    </justification>
  </clause>

  <clause id="6850">
    <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(3096(a,1),5623(a,1,3))].">
      <j1 rule="para" parents="3096 5623"/>
    </justification>
  </clause>

  <clause id="6851">
    <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(5848(a,1),5694(a,1,2,2,2))].">
      <j1 rule="para" parents="5848 5694"/>
    </justification>
  </clause>

  <clause id="6852">
    <literal><![CDATA[
      T(K(x,y) * K(x,z),K(z,x) * K(y,x)) = ((K(x,z) * K(x,y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(5604(a,1),5794(a,1,2))].">
      <j1 rule="para" parents="5604 5794"/>
    </justification>
  </clause>

  <clause id="6853">
    <literal><![CDATA[
      (1 / x) * K(((1 / x) \ y) \ 1,z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(75(a,1),5993(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 5993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6855">
    <literal><![CDATA[
      (1 / x) * K(y \ (1 / x),z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(6230(a,1),6853(a,1,2))].">
      <j1 rule="para" parents="6230 6853"/>
    </justification>
  </clause>

  <clause id="6856">
    <literal><![CDATA[
      K((x * y) \ 1,x * y) = K(x \ (1 / y),x * y)
    ]]></literal>
    <justification jstring="[hyper(29,a,3629,a,b,6855,a)].">
      <j1 rule="hyper" parents="29 3629 6855"/>
    </justification>
  </clause>

  <clause id="6857">
    <literal><![CDATA[
      (1 / x) * K(y \ (x \ 1),z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(3943(a,1),6855(a,1,2))].">
      <j1 rule="para" parents="3943 6855"/>
    </justification>
  </clause>

  <clause id="6858">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,x * (y \ 1)) = K(x \ y,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(72(a,1),6856(a,2,1,2))].">
      <j1 rule="para" parents="72 6856"/>
    </justification>
  </clause>

  <clause id="6859">
    <literal><![CDATA[
      (x * K((y / x) \ 1,y / x)) * (x \ 1) = K(y \ x,y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,4036,a,b,6858,a)].">
      <j1 rule="hyper" parents="58 4036 6858"/>
    </justification>
  </clause>

  <clause id="6860">
    <literal><![CDATA[
      (x * K(y \ x,x \ y)) * (x \ 1) = K(y \ x,y * (x \ 1))
    ]]></literal>
    <justification jstring="[para(2918(a,1),6859(a,1,1,2))].">
      <j1 rule="para" parents="2918 6859"/>
    </justification>
  </clause>

  <clause id="6861">
    <literal><![CDATA[
      K(x \ y,x * (y \ 1)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(3781,a,6860,a),flip(a)].">
      <j1 rule="hyper" parents="3781 6860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6862">
    <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),6861(a,1,2,2))].">
      <j1 rule="para" parents="106 6861"/>
    </justification>
  </clause>

  <clause id="6863">
    <literal><![CDATA[
      K(x \ (y \ 1),(y \ 1) \ x) = K(x \ (1 / y),x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5385,a(flip),b,6862,a),flip(a)].">
      <j1 rule="hyper" parents="58 5385 6862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6864">
    <literal><![CDATA[
      K(x \ (1 / y),x * y) = K(x \ (y \ 1),y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5765,a(flip),b,6863,a),flip(a)].">
      <j1 rule="hyper" parents="58 5765 6863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6865">
    <literal><![CDATA[
      K((x * y) \ 1,x * y) = K(x \ (y \ 1),y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6856,a,b,6864,a)].">
      <j1 rule="hyper" parents="58 6856 6864"/>
    </justification>
  </clause>

  <clause id="6866">
    <literal><![CDATA[
      (T(x * y,z) / y) * (x \ 1) = (1 / y) * (x \ T(x * y,z))
    ]]></literal>
    <justification jstring="[para(993(a,1),5994(a,1,1))].">
      <j1 rule="para" parents="993 5994"/>
    </justification>
  </clause>

  <clause id="6867">
    <literal><![CDATA[
      (1 / x) * ((x \ y) \ T((x \ y) * x,x)) = (x \ T(y,x)) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1371(a,1),6866(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1371 6866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6869">
    <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(6086(a,1),6128(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6086 6128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6870">
    <literal><![CDATA[
      R(R(x,y,z),y * z,K(z,u)) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,15,a,b,6869,a),flip(a)].">
      <j1 rule="hyper" parents="320 15 6869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6871">
    <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(6869(a,2),518(a,1))].">
      <j1 rule="para" parents="6869 518"/>
    </justification>
  </clause>

  <clause id="6872">
    <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,6870,a)].">
      <j1 rule="hyper" parents="58 26 6870"/>
    </justification>
  </clause>

  <clause id="6873">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = (1 / z) * K((((z \ 1) \ x) \ 1) \ (z \ 1),y)
    ]]></literal>
    <justification jstring="[para(3963(a,1),6549(a,2,2))].">
      <j1 rule="para" parents="3963 6549"/>
    </justification>
  </clause>

  <clause id="6874">
    <literal><![CDATA[
      (x * (y * ((z \ (y \ (x \ u))) * z))) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(105(a,1),6652(a,1,1,2,2))].">
      <j1 rule="para" parents="105 6652"/>
    </justification>
  </clause>

  <clause id="6875">
    <literal><![CDATA[
      ((x * y) * ((z \ ((x * y) \ u)) * z)) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(3516(a,2),6874(a,1,1))].">
      <j1 rule="para" parents="3516 6874"/>
    </justification>
  </clause>

  <clause id="6876">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * (z * K(y,z)))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(4843(a,1),6659(a,1,1,2))].">
      <j1 rule="para" parents="4843 6659"/>
    </justification>
  </clause>

  <clause id="6877">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (T(y,z) * z)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(4788(a,1),6876(a,1,2,2))].">
      <j1 rule="para" parents="4788 6876"/>
    </justification>
  </clause>

  <clause id="6878">
    <literal><![CDATA[
      x * (K(x \ 1,x) * K(y,y \ x)) = y * ((1 / (1 / x)) / y)
    ]]></literal>
    <justification jstring="[para(72(a,1),6848(a,1,2,2,2,2))].">
      <j1 rule="para" parents="72 6848"/>
    </justification>
  </clause>

  <clause id="6880">
    <literal><![CDATA[
      T(x * ((1 / (1 / y)) / x),K(z,y)) = y * (K(y \ 1,y) * K(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,4570,a,b,6878,a)].">
      <j1 rule="hyper" parents="320 4570 6878"/>
    </justification>
  </clause>

  <clause id="6881">
    <literal><![CDATA[
      (x \ T(y,x)) * ((x \ y) \ 1) = (1 / x) * ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(4589(a,1),6867(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4589 6867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6882">
    <literal><![CDATA[
      K(x,y) = (y \ T(x,y)) * ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,4848,a,b,6881,a)].">
      <j1 rule="hyper" parents="320 4848 6881"/>
    </justification>
  </clause>

  <clause id="6883">
    <literal><![CDATA[
      (x \ T(x * y,x)) * (y \ 1) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),6882(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 6882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6884">
    <literal><![CDATA[
      (x \ T(x * K(y,z),x)) * (K(z,y) * 1) = K(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(5092(a,1),6883(a,1,2))].">
      <j1 rule="para" parents="5092 6883"/>
    </justification>
  </clause>

  <clause id="6885">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * (K(z,x) * 1) = K(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(5966(a,2),6884(a,1,1))].">
      <j1 rule="para" parents="5966 6884"/>
    </justification>
  </clause>

  <clause id="6886">
    <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),6885(a,1,2))].">
      <j1 rule="para" parents="3 6885"/>
    </justification>
  </clause>

  <clause id="6887">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = K(((((z \ 1) \ x) \ 1) * z) \ 1,y) / z
    ]]></literal>
    <justification jstring="[hyper(320,a,6857,a(flip),b,6873,a),flip(a)].">
      <j1 rule="hyper" parents="320 6857 6873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6888">
    <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(6254(a,1),4110(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6254 4110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6889">
    <literal><![CDATA[
      R((x \ (1 / y)) * x,y,z) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(3803(a,2),4602(a,1,1))].">
      <j1 rule="para" parents="3803 4602"/>
    </justification>
  </clause>

  <clause id="6890">
    <literal><![CDATA[
      K(x \ 1,x) * K(y,y \ x) = (x \ 1) * (y * (x / y))
    ]]></literal>
    <justification jstring="[hyper(4633,a,6880,a),flip(a)].">
      <j1 rule="hyper" parents="4633 6880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6891">
    <literal><![CDATA[
      (1 / x) * (y * (x / y)) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(2828,a,6890,a)].">
      <j1 rule="hyper" parents="2828 6890"/>
    </justification>
  </clause>

  <clause id="6892">
    <literal><![CDATA[
      x \ K(y,y \ (x \ 1)) = y * ((x \ 1) / y)
    ]]></literal>
    <justification jstring="[hyper(116,a,6891,a(flip),b,183,a(flip))].">
      <j1 rule="hyper" parents="116 6891 183"/>
    </justification>
  </clause>

  <clause id="6893">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) * (z * u) = (K(x,y \ 1) * z) * u
    ]]></literal>
    <justification jstring="[para(5265(a,1),5267(a,2,1))].">
      <j1 rule="para" parents="5265 5267"/>
    </justification>
  </clause>

  <clause id="6894">
    <literal><![CDATA[
      R(K(x,y \ 1),z,u) = K(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(30,a,101,a,b,6893,a)].">
      <j1 rule="hyper" parents="30 101 6893"/>
    </justification>
  </clause>

  <clause id="6895">
    <literal><![CDATA[
      K(x,R(y,x,z) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(30,a,4166,a(flip),b,6893,a),flip(a)].">
      <j1 rule="hyper" parents="30 4166 6893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6896">
    <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),6895(a,1,2,1))].">
      <j1 rule="para" parents="26 6895"/>
    </justification>
  </clause>

  <clause id="6898">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3523(a,1),6894(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3523 6894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6899">
    <literal><![CDATA[
      K(x,R(y / z,u,w) \ 1) = R(K(x,z / y),u,w)
    ]]></literal>
    <justification jstring="[para(5312(a,1),6894(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5312 6894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6900">
    <literal><![CDATA[
      K(x,R(y \ z,u,w) \ 1) = R(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(6078(a,1),6894(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6078 6894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6901">
    <literal><![CDATA[
      T(x,R(y \ 1,z,u) \ 1) = x * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,6898,a(flip),b,4688,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 6898 4688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6902">
    <literal><![CDATA[
      R(K(x,y),z,u) \ w = R(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(6898(a,1),5675(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6898 5675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6903">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 = R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(3189,a,6902,a)].">
      <j1 rule="hyper" parents="3189 6902"/>
    </justification>
  </clause>

  <clause id="6904">
    <literal><![CDATA[
      (x * y) / ((K(z,u) * x) * y) = R(K(u,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(617,a,6902,a)].">
      <j1 rule="hyper" parents="617 6902"/>
    </justification>
  </clause>

  <clause id="6905">
    <literal><![CDATA[
      x / (R(K(y,z),u,w) * x) = R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(575,a,6902,a)].">
      <j1 rule="hyper" parents="575 6902"/>
    </justification>
  </clause>

  <clause id="6906">
    <literal><![CDATA[
      R(K(x,y),z,u) \ (z * u) = (K(y,x) * z) * u
    ]]></literal>
    <justification jstring="[hyper(320,a,101,a(flip),b,6902,a),flip(a)].">
      <j1 rule="hyper" parents="320 101 6902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6907">
    <literal><![CDATA[
      R(K(x,y),y / x,z) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,5237,a(flip),b,6902,a),flip(a)].">
      <j1 rule="hyper" parents="58 5237 6902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6908">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      R(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(6902(a,2),127(a,1)),flip(b)].">
      <j1 rule="para" parents="6902 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6909">
    <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(6902(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6902 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6910">
    <literal><![CDATA[
      R(K(x,y),z,(K(y,x) * z) \ 1) = z * ((K(y,x) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(891,a,6903,a),flip(a)].">
      <j1 rule="hyper" parents="891 6903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6911">
    <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(6903(a,1),5638(a,1,1,2,2))].">
      <j1 rule="para" parents="6903 5638"/>
    </justification>
  </clause>

  <clause id="6912">
    <literal><![CDATA[
      ((x \ 1) * y) / ((x \ K(x,z)) * y) = R(K(z,x),x \ 1,y)
    ]]></literal>
    <justification jstring="[para(3187(a,1),6904(a,1,2,1))].">
      <j1 rule="para" parents="3187 6904"/>
    </justification>
  </clause>

  <clause id="6913">
    <literal><![CDATA[
      R(K(x,y / z),y,u) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[hyper(5458,a,6899,a),flip(a)].">
      <j1 rule="hyper" parents="5458 6899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6914">
    <literal><![CDATA[
      R(K(x,y / z),y,y \ 1) = K(x,(z * (y \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[para(523(a,1),6899(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="523 6899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6915">
    <literal><![CDATA[
      R(K(x,y / z),y,z \ 1) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(504(a,1),6899(a,1,2)),flip(a)].">
      <j1 rule="para" parents="504 6899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6916">
    <literal><![CDATA[
      R(K(x,y / z),y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * u) / (z * u)) = w
    ]]></literal>
    <justification jstring="[para(6899(a,1),5458(a,1))].">
      <j1 rule="para" parents="6899 5458"/>
    </justification>
  </clause>

  <clause id="6917">
    <literal><![CDATA[
      R(K(x,(y / z) / u),y / z,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(7(a,1),6913(a,2,2,1))].">
      <j1 rule="para" parents="7 6913"/>
    </justification>
  </clause>

  <clause id="6918">
    <literal><![CDATA[
      R(K(x,y / (z / u)),y,u) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(7(a,1),6913(a,2,2,2))].">
      <j1 rule="para" parents="7 6913"/>
    </justification>
  </clause>

  <clause id="6919">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),6913(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6920">
    <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(6746(a,1),6913(a,1,1,2))].">
      <j1 rule="para" parents="6746 6913"/>
    </justification>
  </clause>

  <clause id="6921">
    <literal><![CDATA[
      R(K(x,(y / z) \ x),x,z) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[para(5159(a,1),6918(a,1,1))].">
      <j1 rule="para" parents="5159 6918"/>
    </justification>
  </clause>

  <clause id="6922">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(98(a,2),6919(a,1,2))].">
      <j1 rule="para" parents="98 6919"/>
    </justification>
  </clause>

  <clause id="6923">
    <literal><![CDATA[
      R(K(x,y),T(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4044(a,1),6919(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4044 6919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6924">
    <literal><![CDATA[
      (K(x,y) * T(y,z)) * u = K(x,y) * (T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(6923(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6923 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6925">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),y,u) = z
    ]]></literal>
    <justification jstring="[para(6923(a,1),6524(a,1))].">
      <j1 rule="para" parents="6923 6524"/>
    </justification>
  </clause>

  <clause id="6926">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) \ x = R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,6726,a(flip),b,6922,a)].">
      <j1 rule="hyper" parents="58 6726 6922"/>
    </justification>
  </clause>

  <clause id="6927">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) * R(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,6922,a(flip),b,6726,a(flip))].">
      <j1 rule="hyper" parents="119 6922 6726"/>
    </justification>
  </clause>

  <clause id="6928">
    <literal><![CDATA[
      R(K(x,y),y * z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),6922(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 6922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6929">
    <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(184(a,1),6922(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="184 6922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6930">
    <literal><![CDATA[
      R(K(x,y),K(z,y) * u,w) = K(x,R(y,T(y,z) \ u,w))
    ]]></literal>
    <justification jstring="[para(5068(a,1),6922(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5068 6922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6931">
    <literal><![CDATA[
      K(x * y,R(x,y,z)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(4179,a,6928,a),flip(a)].">
      <j1 rule="hyper" parents="4179 6928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6932">
    <literal><![CDATA[
      K(R(x,y * z,u) \ 1,y) = K(x \ 1,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,5667,a(flip),b,6928,a)].">
      <j1 rule="hyper" parents="58 5667 6928"/>
    </justification>
  </clause>

  <clause id="6933">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = T(K(x,R(y,u,w)),z)
    ]]></literal>
    <justification jstring="[para(6928(a,1),22(a,2,1))].">
      <j1 rule="para" parents="6928 22"/>
    </justification>
  </clause>

  <clause id="6934">
    <literal><![CDATA[
      K(x,R(y,z,u)) * ((y * z) * u) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[para(6928(a,1),5381(a,1,1))].">
      <j1 rule="para" parents="6928 5381"/>
    </justification>
  </clause>

  <clause id="6935">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(4179,a,6921,a),flip(a)].">
      <j1 rule="hyper" parents="4179 6921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6936">
    <literal><![CDATA[
      R(K(x,(y / z) \ x),x,z) = K(x,(y / (x * z)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,5312,a,b,6921,a),flip(a)].">
      <j1 rule="hyper" parents="320 5312 6921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6937">
    <literal><![CDATA[
      K(x,(x * y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(6921(a,1),4179(a,1))].">
      <j1 rule="para" parents="6921 4179"/>
    </justification>
  </clause>

  <clause id="6939">
    <literal><![CDATA[
      K(x,(L(y,z,u) / y) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(1631(a,1),6935(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1631 6935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6940">
    <literal><![CDATA[
      L(x,T(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,6924,a)].">
      <j1 rule="hyper" parents="479 6924"/>
    </justification>
  </clause>

  <clause id="6941">
    <literal><![CDATA[
      (K(x,y) * T(y,z)) \ u = T(y,z) \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(5734,a,6940,a),flip(a)].">
      <j1 rule="hyper" parents="5734 6940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6942">
    <literal><![CDATA[
      L(x,T(y,z),K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(6940(a,1),45(a,2))].">
      <j1 rule="para" parents="6940 45"/>
    </justification>
  </clause>

  <clause id="6943">
    <literal><![CDATA[
      T(x,y) \ (K(x,z) * u) = K(x,z) * (T(x,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5737,a(flip),b,6941,a),flip(a)].">
      <j1 rule="hyper" parents="58 5737 6941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6944">
    <literal><![CDATA[
      T(x,x * y) * (L(x,y,x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,5738,a(flip),b,6943,a)].">
      <j1 rule="hyper" parents="119 5738 6943"/>
    </justification>
  </clause>

  <clause id="6947">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) = K(x,(((y * z) * u) / ((x * z) * u)) \ 1)
    ]]></literal>
    <justification jstring="[para(534(a,1),6896(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="534 6896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6948">
    <literal><![CDATA[
      K(x,((y \ z) * (z \ 1)) \ 1) = R(K(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),6914(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6949">
    <literal><![CDATA[
      R(K(x,y \ x),x,z) = K(x,((y * z) / (x * z)) \ 1)
    ]]></literal>
    <justification jstring="[para(6(a,1),6936(a,1,1,2,1))].">
      <j1 rule="para" parents="6 6936"/>
    </justification>
  </clause>

  <clause id="6950">
    <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),6949(a,2,2,1,2))].">
      <j1 rule="para" parents="7 6949"/>
    </justification>
  </clause>

  <clause id="6951">
    <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),6916(a,1,1,2))].">
      <j1 rule="para" parents="72 6916"/>
    </justification>
  </clause>

  <clause id="6952">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(3493(a,1),6939(a,1,2,1))].">
      <j1 rule="para" parents="3493 6939"/>
    </justification>
  </clause>

  <clause id="6953">
    <literal><![CDATA[
      K(x,L(y,z,u) \ (y * x)) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6560,a(flip),b,6952,a)].">
      <j1 rule="hyper" parents="58 6560 6952"/>
    </justification>
  </clause>

  <clause id="6954">
    <literal><![CDATA[
      K(x,(x / L(y,z,u)) * y) = K(x,y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(1403(a,1),6953(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1403 6953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6955">
    <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,6905,a,b,6910,a)].">
      <j1 rule="hyper" parents="58 6905 6910"/>
    </justification>
  </clause>

  <clause id="6956">
    <literal><![CDATA[
      ((x * (K(y,x) * z)) * u) / ((x * z) * u) = K(y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,6934,a)].">
      <j1 rule="hyper" parents="131 6934"/>
    </justification>
  </clause>

  <clause id="6957">
    <literal><![CDATA[
      K(x,R(y,z,u)) * ((y * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      (y * (K(x,y) * z)) * u = w
    ]]></literal>
    <justification jstring="[para(6956(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6956 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6958">
    <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(6931(a,1),6929(a,1,1))].">
      <j1 rule="para" parents="6931 6929"/>
    </justification>
  </clause>

  <clause id="6959">
    <literal><![CDATA[
      K((x / y) \ 1,z \ (y / x)) = K(y / x,((z * x) / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5392,a(flip),b,6950,a)].">
      <j1 rule="hyper" parents="58 5392 6950"/>
    </justification>
  </clause>

  <clause id="6960">
    <literal><![CDATA[
      K((x / y) \ 1,z \ (y / x)) = K(y / x,y / (z * x))
    ]]></literal>
    <justification jstring="[hyper(320,a,5312,a(flip),b,6959,a),flip(a)].">
      <j1 rule="hyper" parents="320 5312 6959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6962">
    <literal><![CDATA[
      K(x / y,x / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / y,z \ (x / y)) = u
    ]]></literal>
    <justification jstring="[para(6960(a,1),5632(a,1))].">
      <j1 rule="para" parents="6960 5632"/>
    </justification>
  </clause>

  <clause id="6963">
    <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,6716,a(flip),b,6958,a),flip(a)].">
      <j1 rule="hyper" parents="58 6716 6958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6964">
    <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(6963(a,1),5104(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6963 5104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6965">
    <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(6964(a,2),5112(a,1))].">
      <j1 rule="para" parents="6964 5112"/>
    </justification>
  </clause>

  <clause id="6966">
    <literal><![CDATA[
      ((1 / R(x,y,z)) * x) * (x \ 1) = T(1 / R(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(4985,a,5771,a),flip(a)].">
      <j1 rule="hyper" parents="4985 5771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6967">
    <literal><![CDATA[
      (x / R(x,y,z)) * (x \ 1) = T(1 / R(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(1865(a,1),6966(a,1,1))].">
      <j1 rule="para" parents="1865 6966"/>
    </justification>
  </clause>

  <clause id="6968">
    <literal><![CDATA[
      (x / R(x,y,z)) * (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,6747,a(flip),b,6967,a),flip(a)].">
      <j1 rule="hyper" parents="320 6747 6967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6969">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(6750,a,6968,a)].">
      <j1 rule="hyper" parents="6750 6968"/>
    </justification>
  </clause>

  <clause id="6970">
    <literal><![CDATA[
      T(R(x,y,z) \ x,x \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(239,a,6969,a,b,6734,a)].">
      <j1 rule="hyper" parents="239 6969 6734"/>
    </justification>
  </clause>

  <clause id="6971">
    <literal><![CDATA[
      K(R(x,y,z) \ x,x \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,6970,a)].">
      <j1 rule="hyper" parents="50 6970"/>
    </justification>
  </clause>

  <clause id="6972">
    <literal><![CDATA[
      T(1 / x,R(x,y,z) \ x) = 1 / x
    ]]></literal>
    <justification jstring="[para(6971(a,1),4841(a,1,1,1))].">
      <j1 rule="para" parents="6971 4841"/>
    </justification>
  </clause>

  <clause id="6973">
    <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(6972(a,1),2103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6972 2103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6974">
    <literal><![CDATA[
      L(x \ y,T(x,x \ z),x \ z) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[para(223(a,1),5909(a,1,1)),flip(a)].">
      <j1 rule="para" parents="223 5909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6975">
    <literal><![CDATA[
      L(x \ y,(x \ z) \ z,x \ z) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1604,a(flip),b,6974,a)].">
      <j1 rule="hyper" parents="58 1604 6974"/>
    </justification>
  </clause>

  <clause id="6976">
    <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(6337(a,2),6363(a,2,2))].">
      <j1 rule="para" parents="6337 6363"/>
    </justification>
  </clause>

  <clause id="6977">
    <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),6821(a,2,1,1))].">
      <j1 rule="para" parents="4 6821"/>
    </justification>
  </clause>

  <clause id="6978">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = (((z \ (1 / x)) * z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(283,a,6889,a),flip(a)].">
      <j1 rule="hyper" parents="283 6889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6979">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = K(x \ (z \ 1),z) * y
    ]]></literal>
    <justification jstring="[para(6630(a,1),6978(a,2,1))].">
      <j1 rule="para" parents="6630 6978"/>
    </justification>
  </clause>

  <clause id="6980">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) = y / (K(z \ (x \ 1),x) * y)
    ]]></literal>
    <justification jstring="[para(6979(a,1),5697(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6979 5697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6981">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,5104,a(flip),b,6980,a),flip(a)].">
      <j1 rule="hyper" parents="320 5104 6980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6982">
    <literal><![CDATA[
      K(x,y / (x * (z * y))) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(5932,a,6981,a)].">
      <j1 rule="hyper" parents="5932 6981"/>
    </justification>
  </clause>

  <clause id="6984">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(320,a,5312,a(flip),b,6947,a),flip(a)].">
      <j1 rule="hyper" parents="320 5312 6947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6985">
    <literal><![CDATA[
      R(K(x,x / y),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6899,a(flip),b,6984,a)].">
      <j1 rule="hyper" parents="58 6899 6984"/>
    </justification>
  </clause>

  <clause id="6986">
    <literal><![CDATA[
      R(K(x,y \ x),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(5159(a,1),6985(a,1,1))].">
      <j1 rule="para" parents="5159 6985"/>
    </justification>
  </clause>

  <clause id="6987">
    <literal><![CDATA[
      K(x,((x * y) * z) / ((u * y) * z)) = K(R(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6716,a(flip),b,6986,a),flip(a)].">
      <j1 rule="hyper" parents="58 6716 6986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6988">
    <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),6987(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 6987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6989">
    <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(5412(a,1),6987(a,1,2,1))].">
      <j1 rule="para" parents="5412 6987"/>
    </justification>
  </clause>

  <clause id="6990">
    <literal><![CDATA[
      K(x,(y * z) / ((u * (x \ y)) * z)) = R(K(x,u \ x),y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6718,a(flip),b,6988,a),flip(a)].">
      <j1 rule="hyper" parents="58 6718 6988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6991">
    <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(320,a,4424,a(flip),b,6976,a),flip(a)].">
      <j1 rule="hyper" parents="320 4424 6976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6992">
    <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),4111(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="17 4111"/>
    </justification>
  </clause>

  <clause id="6993">
    <literal><![CDATA[
      x * (x * T(T(x,y) \ ((y * x) / x),z)) = (x * T(x \ y,z)) * x
    ]]></literal>
    <justification jstring="[para(4193(a,1),6992(a,1,2,2,1,1))].">
      <j1 rule="para" parents="4193 6992"/>
    </justification>
  </clause>

  <clause id="6994">
    <literal><![CDATA[
      x * (x * T(T(x,y) \ y,z)) = (x * T(x \ y,z)) * x
    ]]></literal>
    <justification jstring="[para(6(a,1),6993(a,1,2,2,1,2))].">
      <j1 rule="para" parents="6 6993"/>
    </justification>
  </clause>

  <clause id="6995">
    <literal><![CDATA[
      (x \ (y * (T(z,x) \ z))) * x = ((x \ y) * x) * (T(z,x) \ z)
    ]]></literal>
    <justification jstring="[para(225(a,1),4580(a,1,1)),flip(a)].">
      <j1 rule="para" parents="225 4580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6997">
    <literal><![CDATA[
      ((x \ y) * x) * (T(z,x) \ z) = (x \ (y * K(x,z))) * x
    ]]></literal>
    <justification jstring="[para(4689(a,2),6995(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4689 6995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6998">
    <literal><![CDATA[
      (x \ (y * K(x,z))) * x = ((x \ y) * x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(4689(a,2),6997(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4689 6997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7000">
    <literal><![CDATA[
      x \ (y * K(x,z)) = (x \ y) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,6201,a,b,6998,a),flip(a)].">
      <j1 rule="hyper" parents="30 6201 6998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7001">
    <literal><![CDATA[
      x * ((x \ y) * K(x,z)) = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,7000,a)].">
      <j1 rule="hyper" parents="134 7000"/>
    </justification>
  </clause>

  <clause id="7002">
    <literal><![CDATA[
      T(x,y) \ (z * K(x,y)) = T(x \ z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(239,a,7000,a(flip),b,5042,a),flip(a)].">
      <j1 rule="hyper" parents="239 7000 5042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7004">
    <literal><![CDATA[
      (x * y) * K(x,z) = x * (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),7001(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 7001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7005">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(6687,a,7004,a),flip(a)].">
      <j1 rule="hyper" parents="6687 7004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7006">
    <literal><![CDATA[
      R(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(3998,a,7004,a)].">
      <j1 rule="hyper" parents="3998 7004"/>
    </justification>
  </clause>

  <clause id="7007">
    <literal><![CDATA[
      L(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3988,a,7004,a)].">
      <j1 rule="hyper" parents="3988 7004"/>
    </justification>
  </clause>

  <clause id="7008">
    <literal><![CDATA[
      T(x,y) * T(z,K(x,y)) = (x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5039,a,b,7004,a)].">
      <j1 rule="hyper" parents="320 5039 7004"/>
    </justification>
  </clause>

  <clause id="7009">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6426,a,b,7004,a)].">
      <j1 rule="hyper" parents="58 6426 7004"/>
    </justification>
  </clause>

  <clause id="7010">
    <literal><![CDATA[
      a(x,y,K(x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,7004,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="115 7004 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7011">
    <literal><![CDATA[
      (x * (y * K(x,z))) * x = (x * y) * T(x,z)
    ]]></literal>
    <justification jstring="[para(7004(a,1),6167(a,1,1))].">
      <j1 rule="para" parents="7004 6167"/>
    </justification>
  </clause>

  <clause id="7012">
    <literal><![CDATA[
      (x * (y * K(x,z))) / x = ((x * y) / x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(7004(a,1),6195(a,1,1))].">
      <j1 rule="para" parents="7004 6195"/>
    </justification>
  </clause>

  <clause id="7013">
    <literal><![CDATA[
      R(T(x,y),z,K(x,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7006(a,1),22(a,2,1))].">
      <j1 rule="para" parents="7006 22"/>
    </justification>
  </clause>

  <clause id="7014">
    <literal><![CDATA[
      (T(x,y) * z) * K(x,u) = T(x,y) * (z * K(x,u))
    ]]></literal>
    <justification jstring="[para(7006(a,1),512(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7006 512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7015">
    <literal><![CDATA[
      (L(x,y,z) * u) * K(x,w) = L(x,y,z) * (u * K(x,w))
    ]]></literal>
    <justification jstring="[para(7006(a,1),513(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7006 513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7016">
    <literal><![CDATA[
      (R(x,y,z) * u) * K(x,w) = R(x,y,z) * (u * K(x,w))
    ]]></literal>
    <justification jstring="[para(7006(a,1),514(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7006 514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7017">
    <literal><![CDATA[
      x \ (y * T(x,z)) = T(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(7006(a,1),6126(a,1,1))].">
      <j1 rule="para" parents="7006 6126"/>
    </justification>
  </clause>

  <clause id="7018">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,u) = K(x,y) * (z * K(x,u))
    ]]></literal>
    <justification jstring="[para(7006(a,1),6724(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7006 6724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7019">
    <literal><![CDATA[
      R(x,y,T(x,z)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(7006(a,1),6872(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7006 6872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7020">
    <literal><![CDATA[
      R(K(x,y),z,K(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7006(a,1),6922(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7006 6922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7021">
    <literal><![CDATA[
      L(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5862,a,7010,a)].">
      <j1 rule="hyper" parents="5862 7010"/>
    </justification>
  </clause>

  <clause id="7022">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(6837,a,7007,a)].">
      <j1 rule="hyper" parents="6837 7007"/>
    </justification>
  </clause>

  <clause id="7023">
    <literal><![CDATA[
      L(K(x,y),z,x) = u \ (u * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,4,a,b,7007,a),flip(a)].">
      <j1 rule="hyper" parents="320 4 7007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7024">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6586,a(flip),b,7007,a)].">
      <j1 rule="hyper" parents="58 6586 7007"/>
    </justification>
  </clause>

  <clause id="7025">
    <literal><![CDATA[
      K(x,L(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6580,a(flip),b,7007,a)].">
      <j1 rule="hyper" parents="58 6580 7007"/>
    </justification>
  </clause>

  <clause id="7026">
    <literal><![CDATA[
      (1 / x) \ K(x \ 1,y) = x * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,7007,a(flip),b,2797,a)].">
      <j1 rule="hyper" parents="116 7007 2797"/>
    </justification>
  </clause>

  <clause id="7027">
    <literal><![CDATA[
      a(x,y,K(z,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,7007,a(flip),b,5865,a),flip(a)].">
      <j1 rule="hyper" parents="115 7007 5865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7028">
    <literal><![CDATA[
      (x * y) * K(z,x) = x * (y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(969,a,7027,a)].">
      <j1 rule="hyper" parents="969 7027"/>
    </justification>
  </clause>

  <clause id="7029">
    <literal><![CDATA[
      K((x * y) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(6829,a,7021,a)].">
      <j1 rule="hyper" parents="6829 7021"/>
    </justification>
  </clause>

  <clause id="7030">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(y \ (x * z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6597,a(flip),b,7021,a),flip(a)].">
      <j1 rule="hyper" parents="58 6597 7021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7031">
    <literal><![CDATA[
      K(L(x,y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6586,a(flip),b,7021,a)].">
      <j1 rule="hyper" parents="58 6586 7021"/>
    </justification>
  </clause>

  <clause id="7032">
    <literal><![CDATA[
      K(x,L(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6580,a(flip),b,7021,a)].">
      <j1 rule="hyper" parents="58 6580 7021"/>
    </justification>
  </clause>

  <clause id="7034">
    <literal><![CDATA[
      x \ (y * K(z,x)) = (x \ y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(7021(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="7021 474"/>
    </justification>
  </clause>

  <clause id="7036">
    <literal><![CDATA[
      L(x,y,x) * K(x,z) = L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7024,a(flip),b,4723,a)].">
      <j1 rule="hyper" parents="119 7024 4723"/>
    </justification>
  </clause>

  <clause id="7037">
    <literal><![CDATA[
      K(T(x / (x / y),x),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(4360(a,2),7024(a,1,1))].">
      <j1 rule="para" parents="4360 7024"/>
    </justification>
  </clause>

  <clause id="7038">
    <literal><![CDATA[
      K(R(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4632(a,1),7024(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4632 7024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7039">
    <literal><![CDATA[
      T(x,L(y,z,y)) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(7024(a,1),4764(a,2,2))].">
      <j1 rule="para" parents="7024 4764"/>
    </justification>
  </clause>

  <clause id="7040">
    <literal><![CDATA[
      K(x,y) * L(x,z,x) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(7024(a,1),4803(a,1,1))].">
      <j1 rule="para" parents="7024 4803"/>
    </justification>
  </clause>

  <clause id="7041">
    <literal><![CDATA[
      T(x,L(y,z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7025,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 7025 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7042">
    <literal><![CDATA[
      K(x,L(L(y,z,x),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(25(a,1),7025(a,1,2))].">
      <j1 rule="para" parents="25 7025"/>
    </justification>
  </clause>

  <clause id="7043">
    <literal><![CDATA[
      K(x,T((x \ y) \ z,u)) = K(x,T(y \ (x * z),u))
    ]]></literal>
    <justification jstring="[para(753(a,1),7025(a,1,2)),flip(a)].">
      <j1 rule="para" parents="753 7025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7044">
    <literal><![CDATA[
      K(x,(y * (x / y)) \ (x * z)) = K(x,K(y \ x,y) * z)
    ]]></literal>
    <justification jstring="[para(5733(a,1),7025(a,1,2))].">
      <j1 rule="para" parents="5733 7025"/>
    </justification>
  </clause>

  <clause id="7045">
    <literal><![CDATA[
      K(L(x,y,z),L(u,w,x)) = L(K(x,u),y * x,z)
    ]]></literal>
    <justification jstring="[para(7025(a,1),6586(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7025 6586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7046">
    <literal><![CDATA[
      K(L(L(x,y,z),u,w),z) = K(L(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(25(a,1),7031(a,1,1))].">
      <j1 rule="para" parents="25 7031"/>
    </justification>
  </clause>

  <clause id="7047">
    <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(7031(a,1),5485(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7031 5485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7048">
    <literal><![CDATA[
      K((x * (y / x)) \ (y * z),y) = K(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[para(5733(a,1),7031(a,1,1))].">
      <j1 rule="para" parents="5733 7031"/>
    </justification>
  </clause>

  <clause id="7049">
    <literal><![CDATA[
      T(x,L(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7032,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 7032 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7050">
    <literal><![CDATA[
      K(x,T(y / z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4363(a,1),7032(a,1,2))].">
      <j1 rule="para" parents="4363 7032"/>
    </justification>
  </clause>

  <clause id="7051">
    <literal><![CDATA[
      K(x,R(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4632(a,1),7032(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4632 7032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7052">
    <literal><![CDATA[
      R(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6718,a(flip),b,7038,a)].">
      <j1 rule="hyper" parents="58 6718 7038"/>
    </justification>
  </clause>

  <clause id="7053">
    <literal><![CDATA[
      R(x,y,x) * K(x,z) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7038,a(flip),b,4724,a)].">
      <j1 rule="hyper" parents="119 7038 4724"/>
    </justification>
  </clause>

  <clause id="7054">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4294(a,1),7038(a,1,1))].">
      <j1 rule="para" parents="4294 7038"/>
    </justification>
  </clause>

  <clause id="7055">
    <literal><![CDATA[
      K(T(x,x * y),z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(4344(a,1),7038(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4344 7038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7056">
    <literal><![CDATA[
      K(T(x,x \ y),z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(4399(a,1),7038(a,1,1))].">
      <j1 rule="para" parents="4399 7038"/>
    </justification>
  </clause>

  <clause id="7057">
    <literal><![CDATA[
      K(x,R(y,z,y)) = 1 / K(y,x)
    ]]></literal>
    <justification jstring="[para(7038(a,1),4931(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7038 4931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7058">
    <literal><![CDATA[
      K(x,y) * (R(x,z,x) * u) = R(T(x,y),z,x) * u
    ]]></literal>
    <justification jstring="[para(7038(a,1),5080(a,1,1))].">
      <j1 rule="para" parents="7038 5080"/>
    </justification>
  </clause>

  <clause id="7059">
    <literal><![CDATA[
      (K(x,y) * z) * x = K(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(7038(a,1),6724(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7038 6724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7060">
    <literal><![CDATA[
      T(x,(x * y) \ z) = T(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(298(a,1),7041(a,1,2))].">
      <j1 rule="para" parents="298 7041"/>
    </justification>
  </clause>

  <clause id="7061">
    <literal><![CDATA[
      T(x / L(y,z,y),y) = L(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(421,a,7049,a),flip(a)].">
      <j1 rule="hyper" parents="421 7049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7064">
    <literal><![CDATA[
      L(x,y,x) * T(z,x) = z * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7049,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7049 17"/>
    </justification>
  </clause>

  <clause id="7065">
    <literal><![CDATA[
      T(x,T(y / z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4363(a,1),7049(a,1,2))].">
      <j1 rule="para" parents="4363 7049"/>
    </justification>
  </clause>

  <clause id="7066">
    <literal><![CDATA[
      T(x,R(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4632(a,1),7049(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4632 7049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7067">
    <literal><![CDATA[
      R(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6922,a(flip),b,7051,a)].">
      <j1 rule="hyper" parents="58 6922 7051"/>
    </justification>
  </clause>

  <clause id="7068">
    <literal><![CDATA[
      R(x * K(y,x),z,x) = R(x,z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7051,a(flip),b,5485,a),flip(a)].">
      <j1 rule="hyper" parents="119 7051 5485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7069">
    <literal><![CDATA[
      K(x,T(y,y * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4344(a,1),7051(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4344 7051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7070">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4399(a,1),7051(a,1,2))].">
      <j1 rule="para" parents="4399 7051"/>
    </justification>
  </clause>

  <clause id="7071">
    <literal><![CDATA[
      K(x,R(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6928,a(flip),b,7052,a)].">
      <j1 rule="hyper" parents="58 6928 7052"/>
    </justification>
  </clause>

  <clause id="7072">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y / (z / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6918,a(flip),b,7052,a)].">
      <j1 rule="hyper" parents="58 6918 7052"/>
    </justification>
  </clause>

  <clause id="7073">
    <literal><![CDATA[
      K(x,(y / x) / z) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6917,a(flip),b,7052,a),flip(a)].">
      <j1 rule="hyper" parents="58 6917 7052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7074">
    <literal><![CDATA[
      R(x,y,z) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = x
    ]]></literal>
    <justification jstring="[para(7052(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="7052 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7076">
    <literal><![CDATA[
      (x * (K(y,x) * z)) * y = K(y,x) * ((x * z) * y)
    ]]></literal>
    <justification jstring="[para(7052(a,1),5381(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7052 5381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7077">
    <literal><![CDATA[
      T(x / y,R(y,z,y)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(458,a,7066,a)].">
      <j1 rule="hyper" parents="458 7066"/>
    </justification>
  </clause>

  <clause id="7078">
    <literal><![CDATA[
      T(x / R(y,z,y),y) = R(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(421,a,7066,a),flip(a)].">
      <j1 rule="hyper" parents="421 7066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7079">
    <literal><![CDATA[
      R(x,y,x) * T(z,x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7066,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7066 17"/>
    </justification>
  </clause>

  <clause id="7080">
    <literal><![CDATA[
      T(x,(y \ z) \ T(z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4294(a,1),7066(a,1,2))].">
      <j1 rule="para" parents="4294 7066"/>
    </justification>
  </clause>

  <clause id="7081">
    <literal><![CDATA[
      T(x,T(y,y \ z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4399(a,1),7066(a,1,2))].">
      <j1 rule="para" parents="4399 7066"/>
    </justification>
  </clause>

  <clause id="7082">
    <literal><![CDATA[
      (K(x,y) * z) * y = K(x,y) * (z * y)
    ]]></literal>
    <justification jstring="[para(7067(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7067 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7083">
    <literal><![CDATA[
      T(x,R(y,z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7071,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 7071 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7085">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,y / (z / x))
    ]]></literal>
    <justification jstring="[para(525(a,1),7083(a,1,2))].">
      <j1 rule="para" parents="525 7083"/>
    </justification>
  </clause>

  <clause id="7091">
    <literal><![CDATA[
      R(x / y,z,x / y) = R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),7019(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 7019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7095">
    <literal><![CDATA[
      T(x,y * K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6405,a(flip),b,7013,a),flip(a)].">
      <j1 rule="hyper" parents="58 6405 7013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7096">
    <literal><![CDATA[
      R(T(x,y),z,T(x,u)) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(7013(a,1),6872(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7013 6872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7099">
    <literal><![CDATA[
      K(x,y * K(x,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,7095,a(flip),b,4714,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 7095 4714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7102">
    <literal><![CDATA[
      T(x,y * L(K(x,z),u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5641(a,1),7095(a,1,2,2))].">
      <j1 rule="para" parents="5641 7095"/>
    </justification>
  </clause>

  <clause id="7105">
    <literal><![CDATA[
      T(x,y * K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6300(a,1),7095(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6300 7095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7106">
    <literal><![CDATA[
      T(x,y / (z / x)) = T(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[para(6369(a,1),7095(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6369 7095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7108">
    <literal><![CDATA[
      T(x,y * (z * x)) = T(x,y * (x * z))
    ]]></literal>
    <justification jstring="[para(6604(a,1),7095(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6604 7095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7109">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,u) = K(x,y) * (z * K(y,u))
    ]]></literal>
    <justification jstring="[para(7020(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7020 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7110">
    <literal><![CDATA[
      T(x,L(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(7039(a,2),4768(a,1))].">
      <j1 rule="para" parents="7039 4768"/>
    </justification>
  </clause>

  <clause id="7111">
    <literal><![CDATA[
      K(x,R(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7057(a,2),4938(a,1))].">
      <j1 rule="para" parents="7057 4938"/>
    </justification>
  </clause>

  <clause id="7112">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = (z / x) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7077,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7077 17"/>
    </justification>
  </clause>

  <clause id="7113">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(190(a,1),7037(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="190 7037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7114">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),7050(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 7050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7115">
    <literal><![CDATA[
      K(x,L(y \ z,y,u) \ (u * z)) = K(x,T(u * y,u * z))
    ]]></literal>
    <justification jstring="[para(471(a,1),7050(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="471 7050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7116">
    <literal><![CDATA[
      K(x,R(T(y / z,y * u),z,u)) = K(x,(z * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(526(a,1),7050(a,1,2))].">
      <j1 rule="para" parents="526 7050"/>
    </justification>
  </clause>

  <clause id="7117">
    <literal><![CDATA[
      K(T(x,y * x),z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(4266(a,2),7055(a,1,1))].">
      <j1 rule="para" parents="4266 7055"/>
    </justification>
  </clause>

  <clause id="7118">
    <literal><![CDATA[
      K(T(x,y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6268,a(flip),b,7056,a),flip(a)].">
      <j1 rule="hyper" parents="58 6268 7056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7119">
    <literal><![CDATA[
      K(T(x,y),y / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6096,a(flip),b,7118,a),flip(a)].">
      <j1 rule="hyper" parents="320 6096 7118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7120">
    <literal><![CDATA[
      K(T(x,K(y,z)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,1988,a(flip),b,7118,a),flip(a)].">
      <j1 rule="hyper" parents="320 1988 7118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7121">
    <literal><![CDATA[
      (K(x,y) * z) * K(T(y,z),x) = z
    ]]></literal>
    <justification jstring="[hyper(119,a,7118,a,b,6427,a)].">
      <j1 rule="hyper" parents="119 7118 6427"/>
    </justification>
  </clause>

  <clause id="7122">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,7118,a,b,5094,a)].">
      <j1 rule="hyper" parents="119 7118 5094"/>
    </justification>
  </clause>

  <clause id="7123">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,7118,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7118 17"/>
    </justification>
  </clause>

  <clause id="7124">
    <literal><![CDATA[
      T(K(x,y),z) * T(x,z) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(7118(a,1),4729(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7118 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7125">
    <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,7120,a(flip),b,5247,a(flip))].">
      <j1 rule="hyper" parents="119 7120 5247"/>
    </justification>
  </clause>

  <clause id="7126">
    <literal><![CDATA[
      T(x,(y \ z) \ z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),7065(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 7065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7127">
    <literal><![CDATA[
      T(x,y \ T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(x,z) / y) = u
    ]]></literal>
    <justification jstring="[para(7065(a,1),5154(a,1))].">
      <j1 rule="para" parents="7065 5154"/>
    </justification>
  </clause>

  <clause id="7128">
    <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(1399(a,1),7069(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1399 7069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7129">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ y))
    ]]></literal>
    <justification jstring="[para(1677(a,1),7069(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1677 7069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7130">
    <literal><![CDATA[
      K(x,T(y,z * y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4266(a,2),7069(a,1,2))].">
      <j1 rule="para" parents="4266 7069"/>
    </justification>
  </clause>

  <clause id="7131">
    <literal><![CDATA[
      K(x,T(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6187,a(flip),b,7070,a),flip(a)].">
      <j1 rule="hyper" parents="58 6187 7070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7132">
    <literal><![CDATA[
      K(x,T(y * z,y \ 1)) = K(x,T(y * z,z))
    ]]></literal>
    <justification jstring="[para(4142(a,1),7070(a,1,2))].">
      <j1 rule="para" parents="4142 7070"/>
    </justification>
  </clause>

  <clause id="7133">
    <literal><![CDATA[
      K(T(x,y),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7118,a,b,7131,a)].">
      <j1 rule="hyper" parents="320 7118 7131"/>
    </justification>
  </clause>

  <clause id="7134">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = K(x,T(R(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(320,a,6933,a,b,7131,a)].">
      <j1 rule="hyper" parents="320 6933 7131"/>
    </justification>
  </clause>

  <clause id="7135">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[hyper(320,a,6574,a,b,7131,a)].">
      <j1 rule="hyper" parents="320 6574 7131"/>
    </justification>
  </clause>

  <clause id="7136">
    <literal><![CDATA[
      L(T(K(x,y \ z),u),y \ z,w) = K(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,6517,a,b,7131,a)].">
      <j1 rule="hyper" parents="320 6517 7131"/>
    </justification>
  </clause>

  <clause id="7137">
    <literal><![CDATA[
      (K(x,y) * z) \ z = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,6427,a,b,7131,a)].">
      <j1 rule="hyper" parents="320 6427 7131"/>
    </justification>
  </clause>

  <clause id="7138">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,6263,a,b,7131,a)].">
      <j1 rule="hyper" parents="320 6263 7131"/>
    </justification>
  </clause>

  <clause id="7139">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,5588,a,b,7131,a)].">
      <j1 rule="hyper" parents="320 5588 7131"/>
    </justification>
  </clause>

  <clause id="7140">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,5587,a,b,7131,a)].">
      <j1 rule="hyper" parents="320 5587 7131"/>
    </justification>
  </clause>

  <clause id="7141">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K(x \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,5505,a,b,7131,a)].">
      <j1 rule="hyper" parents="320 5505 7131"/>
    </justification>
  </clause>

  <clause id="7142">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,5467,a,b,7131,a),flip(a)].">
      <j1 rule="hyper" parents="320 5467 7131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7143">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,5094,a,b,7131,a)].">
      <j1 rule="hyper" parents="320 5094 7131"/>
    </justification>
  </clause>

  <clause id="7144">
    <literal><![CDATA[
      K(x / y,T(z,x)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,6239,a(flip),b,7131,a),flip(a)].">
      <j1 rule="hyper" parents="320 6239 7131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7145">
    <literal><![CDATA[
      K(x,T(y,K(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5599,a(flip),b,7131,a),flip(a)].">
      <j1 rule="hyper" parents="320 5599 7131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7146">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3334,a(flip),b,7131,a),flip(a)].">
      <j1 rule="hyper" parents="320 3334 7131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7147">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3333,a(flip),b,7131,a),flip(a)].">
      <j1 rule="hyper" parents="320 3333 7131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7148">
    <literal><![CDATA[
      K(x,T(y,T(T(x,z),u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3325,a(flip),b,7131,a),flip(a)].">
      <j1 rule="hyper" parents="320 3325 7131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7149">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,T(x,z)) = z
    ]]></literal>
    <justification jstring="[hyper(119,a,7131,a,b,6427,a)].">
      <j1 rule="hyper" parents="119 7131 6427"/>
    </justification>
  </clause>

  <clause id="7150">
    <literal><![CDATA[
      x * K(y,T(z,x)) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,7131,a,b,5094,a)].">
      <j1 rule="hyper" parents="119 7131 5094"/>
    </justification>
  </clause>

  <clause id="7151">
    <literal><![CDATA[
      x * K(y,T(z,u)) = x * T(K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(119,a,7131,a,b,4,a)].">
      <j1 rule="hyper" parents="119 7131 4"/>
    </justification>
  </clause>

  <clause id="7152">
    <literal><![CDATA[
      x * K(y,T(z,x)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,7131,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7131 17"/>
    </justification>
  </clause>

  <clause id="7153">
    <literal><![CDATA[
      x * T(K(x,y),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7131,a(flip),b,4688,a(flip))].">
      <j1 rule="hyper" parents="119 7131 4688"/>
    </justification>
  </clause>

  <clause id="7154">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = T(K(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(18(a,1),7131(a,1,2))].">
      <j1 rule="para" parents="18 7131"/>
    </justification>
  </clause>

  <clause id="7155">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,w) = T(L(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(7131(a,2),20(a,1,1))].">
      <j1 rule="para" parents="7131 20"/>
    </justification>
  </clause>

  <clause id="7156">
    <literal><![CDATA[
      T(x,y) != K(z,T(u,y))
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = x
    ]]></literal>
    <justification jstring="[para(7131(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="7131 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7157">
    <literal><![CDATA[
      x * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(7131(a,2),284(a,1,2))].">
      <j1 rule="para" parents="7131 284"/>
    </justification>
  </clause>

  <clause id="7158">
    <literal><![CDATA[
      x * (y * K(z,T(u,x * y))) = L(K(z,u),y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(7131(a,2),631(a,1,2,2))].">
      <j1 rule="para" parents="7131 631"/>
    </justification>
  </clause>

  <clause id="7159">
    <literal><![CDATA[
      x * T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7131(a,1),4725(a,1,2))].">
      <j1 rule="para" parents="7131 4725"/>
    </justification>
  </clause>

  <clause id="7160">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * x) = T(x,y) * K(z,T(u,x))
    ]]></literal>
    <justification jstring="[para(7131(a,2),5050(a,2,2))].">
      <j1 rule="para" parents="7131 5050"/>
    </justification>
  </clause>

  <clause id="7161">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(7131(a,2),5582(a,1,2))].">
      <j1 rule="para" parents="7131 5582"/>
    </justification>
  </clause>

  <clause id="7162">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) * K(u,z) = K(u,z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7131(a,2),5594(a,1,1))].">
      <j1 rule="para" parents="7131 5594"/>
    </justification>
  </clause>

  <clause id="7163">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) = K(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[para(7131(a,2),5590(a,2,1))].">
      <j1 rule="para" parents="7131 5590"/>
    </justification>
  </clause>

  <clause id="7164">
    <literal><![CDATA[
      T(K(x,y),y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(7131(a,1),5746(a,1))].">
      <j1 rule="para" parents="7131 5746"/>
    </justification>
  </clause>

  <clause id="7165">
    <literal><![CDATA[
      x * (K(x,T(y,z)) * (z * K(x,y))) = T(x,y) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7131(a,2),5040(a,1,2,1))].">
      <j1 rule="para" parents="7131 5040"/>
    </justification>
  </clause>

  <clause id="7166">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,K(z \ y,T(z,u)))
    ]]></literal>
    <justification jstring="[para(7131(a,2),5706(a,2,2))].">
      <j1 rule="para" parents="7131 5706"/>
    </justification>
  </clause>

  <clause id="7167">
    <literal><![CDATA[
      K(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(7131(a,2),6456(a,1))].">
      <j1 rule="para" parents="7131 6456"/>
    </justification>
  </clause>

  <clause id="7168">
    <literal><![CDATA[
      K(x / y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(7131(a,2),6475(a,1))].">
      <j1 rule="para" parents="7131 6475"/>
    </justification>
  </clause>

  <clause id="7169">
    <literal><![CDATA[
      K(x,T(L(y,z / y,u),w)) = T(L(K(x,y),z,u),w)
    ]]></literal>
    <justification jstring="[para(6578(a,1),7131(a,2,1))].">
      <j1 rule="para" parents="6578 7131"/>
    </justification>
  </clause>

  <clause id="7170">
    <literal><![CDATA[
      K(x,T(y,z)) \ 1 = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(5128,a,7133,a)].">
      <j1 rule="hyper" parents="5128 7133"/>
    </justification>
  </clause>

  <clause id="7171">
    <literal><![CDATA[
      K(T(T(x,y),z),u) = K(x,T(T(u,z),y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7133,a(flip),b,7133,a),flip(a)].">
      <j1 rule="hyper" parents="320 7133 7133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7172">
    <literal><![CDATA[
      x * K(T(y,z),u) = x * K(y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7133,a,b,4,a)].">
      <j1 rule="hyper" parents="119 7133 4"/>
    </justification>
  </clause>

  <clause id="7173">
    <literal><![CDATA[
      x * K(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,7133,a,b,4688,a(flip))].">
      <j1 rule="hyper" parents="119 7133 4688"/>
    </justification>
  </clause>

  <clause id="7174">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6759,a,b,7133,a)].">
      <j1 rule="hyper" parents="58 6759 7133"/>
    </justification>
  </clause>

  <clause id="7175">
    <literal><![CDATA[
      (x * y) \ (T(x,z) * y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6408,a,b,7133,a)].">
      <j1 rule="hyper" parents="58 6408 7133"/>
    </justification>
  </clause>

  <clause id="7176">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ x = K(z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6309,a,b,7133,a)].">
      <j1 rule="hyper" parents="58 6309 7133"/>
    </justification>
  </clause>

  <clause id="7177">
    <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,5551,a,b,7133,a)].">
      <j1 rule="hyper" parents="58 5551 7133"/>
    </justification>
  </clause>

  <clause id="7178">
    <literal><![CDATA[
      K(x,T(y,x * z)) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7055,a(flip),b,7133,a),flip(a)].">
      <j1 rule="hyper" parents="58 7055 7133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7179">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6268,a(flip),b,7133,a),flip(a)].">
      <j1 rule="hyper" parents="58 6268 7133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7180">
    <literal><![CDATA[
      K(((x \ 1) \ y) \ y,z) = K(1 / x,T(z,y * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5816,a(flip),b,7133,a)].">
      <j1 rule="hyper" parents="58 5816 7133"/>
    </justification>
  </clause>

  <clause id="7181">
    <literal><![CDATA[
      (x / y) * K(z,T(y,u)) = x / T(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,7133,a(flip),b,6335,a)].">
      <j1 rule="hyper" parents="119 7133 6335"/>
    </justification>
  </clause>

  <clause id="7182">
    <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,7133,a(flip),b,5247,a(flip))].">
      <j1 rule="hyper" parents="119 7133 5247"/>
    </justification>
  </clause>

  <clause id="7183">
    <literal><![CDATA[
      T(x,T(y,z)) \ 1 = x \ K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,7133,a(flip),b,4755,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 7133 4755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7184">
    <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),7133(a,1,1))].">
      <j1 rule="para" parents="20 7133"/>
    </justification>
  </clause>

  <clause id="7185">
    <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),7133(a,1,1))].">
      <j1 rule="para" parents="22 7133"/>
    </justification>
  </clause>

  <clause id="7186">
    <literal><![CDATA[
      K(x / y,T(z,y)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),7133(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 7133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7187">
    <literal><![CDATA[
      K(T(x,y),z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(107(a,1),7133(a,2,2))].">
      <j1 rule="para" parents="107 7133"/>
    </justification>
  </clause>

  <clause id="7188">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(224(a,1),7133(a,1,1)),flip(a)].">
      <j1 rule="para" parents="224 7133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7189">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z),u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(212(a,1),7133(a,1,1)),flip(a)].">
      <j1 rule="para" parents="212 7133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7190">
    <literal><![CDATA[
      K(T(x,y),L(y,z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(176(a,1),7133(a,2,2))].">
      <j1 rule="para" parents="176 7133"/>
    </justification>
  </clause>

  <clause id="7191">
    <literal><![CDATA[
      K(T(x,(1 / y) \ z),z * y) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(1050(a,1),7133(a,2,2))].">
      <j1 rule="para" parents="1050 7133"/>
    </justification>
  </clause>

  <clause id="7192">
    <literal><![CDATA[
      K(x \ T(x * y,z),T(u,x)) = K(x \ T(y * x,z),u)
    ]]></literal>
    <justification jstring="[para(4561(a,1),7133(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4561 7133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7193">
    <literal><![CDATA[
      K(x,T(y,z)) * T(x,z) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(7133(a,1),4729(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7133 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7194">
    <literal><![CDATA[
      x / K(y,T(x,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7133(a,1),4764(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7133 4764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7195">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4975(a,1),7133(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4975 7133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7196">
    <literal><![CDATA[
      1 / K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7133(a,1),4938(a,1,2))].">
      <j1 rule="para" parents="7133 4938"/>
    </justification>
  </clause>

  <clause id="7197">
    <literal><![CDATA[
      K(x,T(y,z)) \ u = K(y,T(x,z)) * u
    ]]></literal>
    <justification jstring="[para(7133(a,1),5092(a,1,1))].">
      <j1 rule="para" parents="7133 5092"/>
    </justification>
  </clause>

  <clause id="7198">
    <literal><![CDATA[
      (x * y) / (K(z,T(x,u)) * y) = T(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(7133(a,1),5216(a,1,2,1))].">
      <j1 rule="para" parents="7133 5216"/>
    </justification>
  </clause>

  <clause id="7199">
    <literal><![CDATA[
      K(x,T(y,z)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7133(a,1),5125(a,1,1))].">
      <j1 rule="para" parents="7133 5125"/>
    </justification>
  </clause>

  <clause id="7200">
    <literal><![CDATA[
      K(x,T(y,z)) * T(x,z) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(7133(a,1),4801(a,1,1))].">
      <j1 rule="para" parents="7133 4801"/>
    </justification>
  </clause>

  <clause id="7201">
    <literal><![CDATA[
      K(x,T(y,z)) \ (y * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,T(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7133(a,1),5097(a,1,1))].">
      <j1 rule="para" parents="7133 5097"/>
    </justification>
  </clause>

  <clause id="7202">
    <literal><![CDATA[
      a(x,y,K(z,T(y,u))) = 1
    ]]></literal>
    <justification jstring="[para(7133(a,1),6069(a,1,3))].">
      <j1 rule="para" parents="7133 6069"/>
    </justification>
  </clause>

  <clause id="7203">
    <literal><![CDATA[
      x / K(y,T(z,u)) = x * K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(7133(a,1),6306(a,1,2))].">
      <j1 rule="para" parents="7133 6306"/>
    </justification>
  </clause>

  <clause id="7204">
    <literal><![CDATA[
      x * K(y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w * K(z,T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(7133(a,1),6315(a,1,2))].">
      <j1 rule="para" parents="7133 6315"/>
    </justification>
  </clause>

  <clause id="7205">
    <literal><![CDATA[
      x / K(y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(z,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(7133(a,1),6317(a,1,2))].">
      <j1 rule="para" parents="7133 6317"/>
    </justification>
  </clause>

  <clause id="7206">
    <literal><![CDATA[
      (x * K(T(y,z),u)) * K(u,w) = (x * K(u,w)) * K(y,T(u,z))
    ]]></literal>
    <justification jstring="[para(7133(a,1),6795(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7133 6795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7207">
    <literal><![CDATA[
      L(K(x,T(y,z)),y,u) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(47,a,7202,a)].">
      <j1 rule="hyper" parents="47 7202"/>
    </justification>
  </clause>

  <clause id="7208">
    <literal><![CDATA[
      K(x,K(T(y,K(x,z)),u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7118(a,2),7145(a,1,2))].">
      <j1 rule="para" parents="7118 7145"/>
    </justification>
  </clause>

  <clause id="7209">
    <literal><![CDATA[
      K(x,y / R(x,z,u)) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7146(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 7146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7210">
    <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(7147(a,1),5548(a,1,2))].">
      <j1 rule="para" parents="7147 5548"/>
    </justification>
  </clause>

  <clause id="7211">
    <literal><![CDATA[
      K(x,y * K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4688,a,b,7099,a),flip(a)].">
      <j1 rule="hyper" parents="320 4688 7099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7212">
    <literal><![CDATA[
      T(x,K(y,x * K(y,z))) = x
    ]]></literal>
    <justification jstring="[para(7099(a,2),2883(a,1,2))].">
      <j1 rule="para" parents="7099 2883"/>
    </justification>
  </clause>

  <clause id="7213">
    <literal><![CDATA[
      K(x,y * K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7099(a,2),4797(a,1))].">
      <j1 rule="para" parents="7099 4797"/>
    </justification>
  </clause>

  <clause id="7214">
    <literal><![CDATA[
      K(x,y * L(K(x,z),u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5641(a,1),7211(a,1,2,2))].">
      <j1 rule="para" parents="5641 7211"/>
    </justification>
  </clause>

  <clause id="7215">
    <literal><![CDATA[
      K(x,y * T(x,z)) = K(x,y * x)
    ]]></literal>
    <justification jstring="[para(6086(a,1),7211(a,1,2))].">
      <j1 rule="para" parents="6086 7211"/>
    </justification>
  </clause>

  <clause id="7216">
    <literal><![CDATA[
      K(x,y * K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6300(a,1),7211(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6300 7211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7217">
    <literal><![CDATA[
      K(x,y / K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6306(a,2),7211(a,1,2))].">
      <j1 rule="para" parents="6306 7211"/>
    </justification>
  </clause>

  <clause id="7218">
    <literal><![CDATA[
      K(x,y / T(z,x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(6293(a,1),7211(a,1,2))].">
      <j1 rule="para" parents="6293 7211"/>
    </justification>
  </clause>

  <clause id="7219">
    <literal><![CDATA[
      K(x,y / (z / x)) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[para(6369(a,1),7211(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6369 7211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7220">
    <literal><![CDATA[
      K(x \ y,z / (y / x)) = K(x \ y,z / (x \ y))
    ]]></literal>
    <justification jstring="[para(6441(a,1),7211(a,1,2))].">
      <j1 rule="para" parents="6441 7211"/>
    </justification>
  </clause>

  <clause id="7221">
    <literal><![CDATA[
      K(x,T(K(y,x) * z,u)) = K(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(6693(a,1),7211(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6693 7211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7222">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * T(x,z),x)
    ]]></literal>
    <justification jstring="[para(7211(a,1),6213(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7211 6213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7223">
    <literal><![CDATA[
      K(x,K(y,x * K(y,z))) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,7212,a)].">
      <j1 rule="hyper" parents="50 7212"/>
    </justification>
  </clause>

  <clause id="7224">
    <literal><![CDATA[
      K(x,(y * z) * (z \ K(u,x))) = K(x,R(y,z,z \ K(u,x)))
    ]]></literal>
    <justification jstring="[para(368(a,1),7216(a,1,2))].">
      <j1 rule="para" parents="368 7216"/>
    </justification>
  </clause>

  <clause id="7225">
    <literal><![CDATA[
      K(x * K(y,z),z) = 1 / K(z,x)
    ]]></literal>
    <justification jstring="[para(7216(a,1),4931(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7216 4931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7226">
    <literal><![CDATA[
      R(K(x,y),y * K(z,x),u) = K(x,y * K(z,x))
    ]]></literal>
    <justification jstring="[para(7216(a,1),5434(a,1,1))].">
      <j1 rule="para" parents="7216 5434"/>
    </justification>
  </clause>

  <clause id="7228">
    <literal><![CDATA[
      K(x,y \ K(z,x)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5308,a,7217,a),flip(a)].">
      <j1 rule="hyper" parents="5308 7217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7229">
    <literal><![CDATA[
      T(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(4363(a,1),7110(a,1,2))].">
      <j1 rule="para" parents="4363 7110"/>
    </justification>
  </clause>

  <clause id="7230">
    <literal><![CDATA[
      K(x,T(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(4399(a,1),7111(a,1,2))].">
      <j1 rule="para" parents="4399 7111"/>
    </justification>
  </clause>

  <clause id="7231">
    <literal><![CDATA[
      K(T(R(x,x \ y,y \ z),z),u) = K(((x \ y) * (y \ z)) \ z,u)
    ]]></literal>
    <justification jstring="[para(699(a,1),7113(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="699 7113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7232">
    <literal><![CDATA[
      K(T(x * K(y,z),x),u) = K(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(6332(a,1),7113(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6332 7113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7233">
    <literal><![CDATA[
      K((x * (y \ z)) \ (x * z),u) = L(K(T(y,z),u),z,x)
    ]]></literal>
    <justification jstring="[para(7113(a,1),6594(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7113 6594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7234">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = L(K(x,T(z,u)),u,y)
    ]]></literal>
    <justification jstring="[para(7114(a,1),6553(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7114 6553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7235">
    <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(7114(a,1),6681(a,1,1))].">
      <j1 rule="para" parents="7114 6681"/>
    </justification>
  </clause>

  <clause id="7236">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(212(a,1),7119(a,1,1))].">
      <j1 rule="para" parents="212 7119"/>
    </justification>
  </clause>

  <clause id="7237">
    <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(213(a,1),7119(a,1,1))].">
      <j1 rule="para" parents="213 7119"/>
    </justification>
  </clause>

  <clause id="7238">
    <literal><![CDATA[
      T(x,K(x,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(7121(a,1),7105(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7121 7105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7239">
    <literal><![CDATA[
      K(x,K(x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7121(a,1),7216(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7121 7216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7240">
    <literal><![CDATA[
      T(x,K(x,y) * L(K(z,x),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,2912,a(flip),b,7238,a),flip(a)].">
      <j1 rule="hyper" parents="320 2912 7238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7241">
    <literal><![CDATA[
      K(x,K(x,y) * z) = x \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,7238,a(flip),b,4714,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 7238 4714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7242">
    <literal><![CDATA[
      T(T(x,y),K(x,z) * u) = T(T(x,u),y)
    ]]></literal>
    <justification jstring="[para(7238(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7238 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7243">
    <literal><![CDATA[
      T(x,K(y,x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(5095(a,1),7238(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5095 7238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7245">
    <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(7238(a,1),5164(a,1,1))].">
      <j1 rule="para" parents="7238 5164"/>
    </justification>
  </clause>

  <clause id="7246">
    <literal><![CDATA[
      T(x,y * (K(z,x) * u)) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(6008(a,1),7238(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6008 7238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7247">
    <literal><![CDATA[
      K(x,T(y,K(x,z) * u)) = K(T(x,u),y)
    ]]></literal>
    <justification jstring="[para(7238(a,1),7133(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7238 7133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7248">
    <literal><![CDATA[
      K(x,T(x,y) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[para(4740(a,1),7239(a,1,2))].">
      <j1 rule="para" parents="4740 7239"/>
    </justification>
  </clause>

  <clause id="7249">
    <literal><![CDATA[
      K(x,K(y,x) \ z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5092(a,2),7239(a,1,2))].">
      <j1 rule="para" parents="5092 7239"/>
    </justification>
  </clause>

  <clause id="7250">
    <literal><![CDATA[
      K(x,K(y,x) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5095(a,1),7239(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5095 7239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7251">
    <literal><![CDATA[
      K(x,T(x,y) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(5042(a,1),7239(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5042 7239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7252">
    <literal><![CDATA[
      K(x,y * (K(z,x) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(6008(a,1),7239(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6008 7239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7253">
    <literal><![CDATA[
      K(x,R(K(x,y),z,u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(6898(a,1),7239(a,1,2,1))].">
      <j1 rule="para" parents="6898 7239"/>
    </justification>
  </clause>

  <clause id="7254">
    <literal><![CDATA[
      T(x,K(y,x) * z) = L(T(x,z),u,K(w \ 1,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,3634,a,b,7243,a),flip(a)].">
      <j1 rule="hyper" parents="320 3634 7243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7256">
    <literal><![CDATA[
      K(x,R(K(y,x),z,u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(5670(a,1),7250(a,1,2,1))].">
      <j1 rule="para" parents="5670 7250"/>
    </justification>
  </clause>

  <clause id="7257">
    <literal><![CDATA[
      K(x,(K(y,x) * z) * u) = K(x,z * u)
    ]]></literal>
    <justification jstring="[para(6724(a,1),7250(a,1,2))].">
      <j1 rule="para" parents="6724 7250"/>
    </justification>
  </clause>

  <clause id="7258">
    <literal><![CDATA[
      x / K(y,T(z,x)) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(6367,a,7123,a)].">
      <j1 rule="hyper" parents="6367 7123"/>
    </justification>
  </clause>

  <clause id="7259">
    <literal><![CDATA[
      K(T(x,L(y,z,u)),y \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2281,a,7123,a)].">
      <j1 rule="hyper" parents="2281 7123"/>
    </justification>
  </clause>

  <clause id="7260">
    <literal><![CDATA[
      K(x / y,z) * y = y * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),7123(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 7123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7261">
    <literal><![CDATA[
      K((x * y) / x,z) * x = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(224(a,1),7123(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="224 7123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7262">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (x * u) = L(K(z,T(y,u)),u,x)
    ]]></literal>
    <justification jstring="[para(7123(a,1),6643(a,1,1,2))].">
      <j1 rule="para" parents="7123 6643"/>
    </justification>
  </clause>

  <clause id="7263">
    <literal><![CDATA[
      T(x / ((y \ z) \ z),T(y,z)) = ((y \ z) \ z) \ x
    ]]></literal>
    <justification jstring="[hyper(421,a,7126,a),flip(a)].">
      <j1 rule="hyper" parents="421 7126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7264">
    <literal><![CDATA[
      K(x,y) * (z * K(y,T(x,z))) = z
    ]]></literal>
    <justification jstring="[para(7143(a,1),68(a,1,2,2))].">
      <j1 rule="para" parents="7143 68"/>
    </justification>
  </clause>

  <clause id="7266">
    <literal><![CDATA[
      L(x,y / z,K(z \ y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(7144(a,1),4173(a,1,3))].">
      <j1 rule="para" parents="7144 4173"/>
    </justification>
  </clause>

  <clause id="7270">
    <literal><![CDATA[
      T(x,T(y,T(T(x,z),u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7148,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 7148 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7271">
    <literal><![CDATA[
      (x \ y) * K(z,T(x,x \ y)) = T(x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,5048,a(flip),b,7150,a),flip(a)].">
      <j1 rule="hyper" parents="320 5048 7150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7272">
    <literal><![CDATA[
      K(x / y,z) \ y = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),7150(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 7150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7273">
    <literal><![CDATA[
      (x * y) / T(T(x,y),z) = K(z,x) * y
    ]]></literal>
    <justification jstring="[hyper(6472,a,7152,a)].">
      <j1 rule="hyper" parents="6472 7152"/>
    </justification>
  </clause>

  <clause id="7274">
    <literal><![CDATA[
      x * (y * K(z,T(u,y))) = x * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7152,a,b,4,a)].">
      <j1 rule="hyper" parents="119 7152 4"/>
    </justification>
  </clause>

  <clause id="7275">
    <literal><![CDATA[
      K(x \ y,T(z,y \ x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,5610,a(flip),b,7152,a),flip(a)].">
      <j1 rule="hyper" parents="29 5610 7152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7276">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,z)) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(29,a,5574,a(flip),b,7152,a),flip(a)].">
      <j1 rule="hyper" parents="29 5574 7152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7277">
    <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),7152(a,1,2,2))].">
      <j1 rule="para" parents="20 7152"/>
    </justification>
  </clause>

  <clause id="7278">
    <literal><![CDATA[
      K(x,y) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7152(a,1),38(a,1))].">
      <j1 rule="para" parents="7152 38"/>
    </justification>
  </clause>

  <clause id="7279">
    <literal><![CDATA[
      K(x,y / z) * z = z * K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7152(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 7152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7280">
    <literal><![CDATA[
      x * K(y,K(z,T(u,x))) = K(y,K(z,u)) * x
    ]]></literal>
    <justification jstring="[para(7131(a,2),7152(a,1,2,2))].">
      <j1 rule="para" parents="7131 7152"/>
    </justification>
  </clause>

  <clause id="7281">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(5473,a,7153,a),flip(a)].">
      <j1 rule="hyper" parents="5473 7153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7282">
    <literal><![CDATA[
      T(x,T(y,z)) != x * u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(7153(a,1),38(a,1))].">
      <j1 rule="para" parents="7153 38"/>
    </justification>
  </clause>

  <clause id="7283">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(7170(a,1),4945(a,1))].">
      <j1 rule="para" parents="7170 4945"/>
    </justification>
  </clause>

  <clause id="7284">
    <literal><![CDATA[
      T(T(x,y),z) * K(y,x) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(5521,a,7173,a)].">
      <j1 rule="hyper" parents="5521 7173"/>
    </justification>
  </clause>

  <clause id="7285">
    <literal><![CDATA[
      T(x,T(y,z)) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(7173(a,1),38(a,1))].">
      <j1 rule="para" parents="7173 38"/>
    </justification>
  </clause>

  <clause id="7286">
    <literal><![CDATA[
      K(x,T(y,x * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7133,a(flip),b,7178,a),flip(a)].">
      <j1 rule="hyper" parents="320 7133 7178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7287">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7131,a,b,7179,a),flip(a)].">
      <j1 rule="hyper" parents="320 7131 7179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7288">
    <literal><![CDATA[
      K(x / (y \ z),z \ y) = K((y \ z) \ x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(5749,a,7186,a)].">
      <j1 rule="hyper" parents="5749 7186"/>
    </justification>
  </clause>

  <clause id="7289">
    <literal><![CDATA[
      K(x \ (y \ x),z) = K(y \ 1,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5396,a(flip),b,7186,a),flip(a)].">
      <j1 rule="hyper" parents="58 5396 7186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7290">
    <literal><![CDATA[
      K(x \ y,z) * (y / x) = T(y / x,T(z,x))
    ]]></literal>
    <justification jstring="[para(7186(a,1),4729(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7186 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7291">
    <literal><![CDATA[
      K(x \ y,z) * (y / x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7186(a,1),4730(a,1,1))].">
      <j1 rule="para" parents="7186 4730"/>
    </justification>
  </clause>

  <clause id="7292">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(7186(a,2),6270(a,1))].">
      <j1 rule="para" parents="7186 6270"/>
    </justification>
  </clause>

  <clause id="7293">
    <literal><![CDATA[
      K(T(x,y),z \ 1) = K(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(5308,a,7187,a)].">
      <j1 rule="hyper" parents="5308 7187"/>
    </justification>
  </clause>

  <clause id="7294">
    <literal><![CDATA[
      (x / (y / z)) * K(u,z \ y) = x / T(y / z,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7187,a(flip),b,6335,a)].">
      <j1 rule="hyper" parents="119 7187 6335"/>
    </justification>
  </clause>

  <clause id="7296">
    <literal><![CDATA[
      K(x,y / R(T(x,z),u,w)) = K(x,R(T(x,z),u,w) \ y)
    ]]></literal>
    <justification jstring="[para(212(a,1),7187(a,1,1))].">
      <j1 rule="para" parents="212 7187"/>
    </justification>
  </clause>

  <clause id="7297">
    <literal><![CDATA[
      a(x,T(y,z),K(u,y)) = 1
    ]]></literal>
    <justification jstring="[para(7188(a,1),6069(a,1,3))].">
      <j1 rule="para" parents="7188 6069"/>
    </justification>
  </clause>

  <clause id="7298">
    <literal><![CDATA[
      R(x,K(y,z),L(T(z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(7188(a,1),6638(a,1,2))].">
      <j1 rule="para" parents="7188 6638"/>
    </justification>
  </clause>

  <clause id="7299">
    <literal><![CDATA[
      (x * T(y,z)) * K(u,y) = x * (T(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(969,a,7297,a)].">
      <j1 rule="hyper" parents="969 7297"/>
    </justification>
  </clause>

  <clause id="7300">
    <literal><![CDATA[
      L(K(x,y),T(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(47,a,7297,a)].">
      <j1 rule="hyper" parents="47 7297"/>
    </justification>
  </clause>

  <clause id="7301">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5256,a,b,7300,a)].">
      <j1 rule="hyper" parents="58 5256 7300"/>
    </justification>
  </clause>

  <clause id="7303">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) = K(x,z * K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(6308(a,1),7195(a,1,2))].">
      <j1 rule="para" parents="6308 7195"/>
    </justification>
  </clause>

  <clause id="7304">
    <literal><![CDATA[
      K(x,y * T(x,z)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5346,a(flip),b,7215,a),flip(a)].">
      <j1 rule="hyper" parents="320 5346 7215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7305">
    <literal><![CDATA[
      K(x,y / T(z / T(u,z),x)) = K(x,y / (T(z,u) / u))
    ]]></literal>
    <justification jstring="[para(4350(a,1),7218(a,1,2,2))].">
      <j1 rule="para" parents="4350 7218"/>
    </justification>
  </clause>

  <clause id="7306">
    <literal><![CDATA[
      K(x * K(y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4931,a(flip),b,7225,a),flip(a)].">
      <j1 rule="hyper" parents="320 4931 7225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7307">
    <literal><![CDATA[
      K(x * K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7225(a,2),4938(a,1))].">
      <j1 rule="para" parents="7225 4938"/>
    </justification>
  </clause>

  <clause id="7308">
    <literal><![CDATA[
      K(x * T(y,z),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(1423(a,1),7306(a,1,1))].">
      <j1 rule="para" parents="1423 7306"/>
    </justification>
  </clause>

  <clause id="7309">
    <literal><![CDATA[
      K(x \ T(y,z),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(1420(a,1),7306(a,1,1))].">
      <j1 rule="para" parents="1420 7306"/>
    </justification>
  </clause>

  <clause id="7310">
    <literal><![CDATA[
      R(K(x,y),x * K(z,y),u) = K(x * K(z,y),y)
    ]]></literal>
    <justification jstring="[para(7306(a,1),4163(a,1,1))].">
      <j1 rule="para" parents="7306 4163"/>
    </justification>
  </clause>

  <clause id="7311">
    <literal><![CDATA[
      K(x * L(K(y,z),u,w),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4782(a,1),7306(a,1,1,2))].">
      <j1 rule="para" parents="4782 7306"/>
    </justification>
  </clause>

  <clause id="7313">
    <literal><![CDATA[
      K(x * K(y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6300(a,1),7306(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6300 7306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7314">
    <literal><![CDATA[
      K(x * T(y,z),y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(6302(a,1),7306(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6302 7306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7315">
    <literal><![CDATA[
      K(x * K(y,T(z,u)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7133(a,1),7306(a,1,1,2))].">
      <j1 rule="para" parents="7133 7306"/>
    </justification>
  </clause>

  <clause id="7316">
    <literal><![CDATA[
      K(K(x,y) * z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(7121(a,1),7306(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7121 7306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7317">
    <literal><![CDATA[
      K(K(x,y) \ z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(7122(a,1),7306(a,1,1))].">
      <j1 rule="para" parents="7122 7306"/>
    </justification>
  </clause>

  <clause id="7318">
    <literal><![CDATA[
      K(K(x,y) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(7123(a,1),7306(a,1,1))].">
      <j1 rule="para" parents="7123 7306"/>
    </justification>
  </clause>

  <clause id="7319">
    <literal><![CDATA[
      K(x * K(y,z),T(z,u)) = K(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(7188(a,1),7306(a,1,1,2))].">
      <j1 rule="para" parents="7188 7306"/>
    </justification>
  </clause>

  <clause id="7320">
    <literal><![CDATA[
      K(x * L(K(y,z),u,w),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5641(a,1),7313(a,1,1,2))].">
      <j1 rule="para" parents="5641 7313"/>
    </justification>
  </clause>

  <clause id="7322">
    <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(7313(a,1),5487(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7313 5487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7325">
    <literal><![CDATA[
      K(T(x,y) * z,x) = K(x * z,x)
    ]]></literal>
    <justification jstring="[para(4740(a,1),7316(a,1,1))].">
      <j1 rule="para" parents="4740 7316"/>
    </justification>
  </clause>

  <clause id="7326">
    <literal><![CDATA[
      K(T(x,y) \ z,x) = K(x \ z,x)
    ]]></literal>
    <justification jstring="[para(5042(a,1),7316(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5042 7316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7327">
    <literal><![CDATA[
      K(x * (K(y,z) * u),z) = K(x * u,z)
    ]]></literal>
    <justification jstring="[para(6008(a,1),7316(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6008 7316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7328">
    <literal><![CDATA[
      L(K(x,y),K(y,z) * x,u) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[para(7316(a,1),6072(a,1,1))].">
      <j1 rule="para" parents="7316 6072"/>
    </justification>
  </clause>

  <clause id="7329">
    <literal><![CDATA[
      K(R(K(x,y),z,u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(6898(a,1),7316(a,1,1,1))].">
      <j1 rule="para" parents="6898 7316"/>
    </justification>
  </clause>

  <clause id="7330">
    <literal><![CDATA[
      K(K(x,y) * z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) = u
    ]]></literal>
    <justification jstring="[para(7317(a,1),6270(a,1))].">
      <j1 rule="para" parents="7317 6270"/>
    </justification>
  </clause>

  <clause id="7334">
    <literal><![CDATA[
      K(x,K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7241(a,2),4797(a,1))].">
      <j1 rule="para" parents="7241 4797"/>
    </justification>
  </clause>

  <clause id="7336">
    <literal><![CDATA[
      T(x * K(y,x),T(z,T(x,u))) = T(x * K(y,x),z)
    ]]></literal>
    <justification jstring="[para(4775(a,1),7270(a,1,2,2,1))].">
      <j1 rule="para" parents="4775 7270"/>
    </justification>
  </clause>

  <clause id="7337">
    <literal><![CDATA[
      T(x,T(y,x * z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7286,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 7286 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7338">
    <literal><![CDATA[
      K(x,T(y / (x * z),z)) = K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7286(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 7286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7339">
    <literal><![CDATA[
      T(x,T(y,x \ z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7287,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 7287 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7340">
    <literal><![CDATA[
      T(x,T(y,x \ z)) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7287,a(flip),b,4688,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 7287 4688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7341">
    <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),7287(a,1,2))].">
      <j1 rule="para" parents="22 7287"/>
    </justification>
  </clause>

  <clause id="7342">
    <literal><![CDATA[
      K(x * y,T(z,y \ 1)) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(6144(a,1),7287(a,1,2))].">
      <j1 rule="para" parents="6144 7287"/>
    </justification>
  </clause>

  <clause id="7343">
    <literal><![CDATA[
      R(K(x,T(y,z)),x * u,w) = K(R(x,u,w),T(y,x \ z))
    ]]></literal>
    <justification jstring="[para(7287(a,1),6716(a,1,1))].">
      <j1 rule="para" parents="7287 6716"/>
    </justification>
  </clause>

  <clause id="7344">
    <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(7298(a,1),542(a,1,1))].">
      <j1 rule="para" parents="7298 542"/>
    </justification>
  </clause>

  <clause id="7345">
    <literal><![CDATA[
      T(x,y * T(x,z)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7304,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 7304 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7346">
    <literal><![CDATA[
      K((1 / ((x * y) \ x)) * z,y) = K(z * (1 / ((x * y) \ x)),y)
    ]]></literal>
    <justification jstring="[para(6181(a,1),7308(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6181 7308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7347">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[para(17(a,1),7309(a,1,1,2))].">
      <j1 rule="para" parents="17 7309"/>
    </justification>
  </clause>

  <clause id="7348">
    <literal><![CDATA[
      K(x * T(y,z),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5228,a(flip),b,7314,a),flip(a)].">
      <j1 rule="hyper" parents="320 5228 7314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7349">
    <literal><![CDATA[
      K(T(x,y) * z,x) = K(z * T(x,y),x)
    ]]></literal>
    <justification jstring="[para(84(a,1),7315(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 7315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7350">
    <literal><![CDATA[
      K(T(x,T(y,z)) * u,y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(5500(a,1),7315(a,1,1))].">
      <j1 rule="para" parents="5500 7315"/>
    </justification>
  </clause>

  <clause id="7351">
    <literal><![CDATA[
      x * K(T(y,z) \ x,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,7326,a,b,85,a)].">
      <j1 rule="hyper" parents="119 7326 85"/>
    </justification>
  </clause>

  <clause id="7352">
    <literal><![CDATA[
      K(x / T(y,z),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5528,a,b,7326,a)].">
      <j1 rule="hyper" parents="58 5528 7326"/>
    </justification>
  </clause>

  <clause id="7354">
    <literal><![CDATA[
      T(x / y,T(z,y)) = T(x / y,T(z,x))
    ]]></literal>
    <justification jstring="[para(7(a,1),7337(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 7337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7355">
    <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(7339(a,1),4723(a,1,2,1))].">
      <j1 rule="para" parents="7339 4723"/>
    </justification>
  </clause>

  <clause id="7356">
    <literal><![CDATA[
      T(x * y,T(z,y \ 1)) = T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(6144(a,1),7339(a,1,2))].">
      <j1 rule="para" parents="6144 7339"/>
    </justification>
  </clause>

  <clause id="7358">
    <literal><![CDATA[
      T(x,x * (y / T(x,z))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),7345(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 7345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7361">
    <literal><![CDATA[
      K(x * (y / T(x,z)),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),7348(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 7348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7363">
    <literal><![CDATA[
      (x / T(y,z)) * K(y \ x,y) = T(x / T(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7352,a(flip),b,4688,a(flip))].">
      <j1 rule="hyper" parents="119 7352 4688"/>
    </justification>
  </clause>

  <clause id="7364">
    <literal><![CDATA[
      L(K(x,y),z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7023(a,2),287(a,1)),flip(b)].">
      <j1 rule="para" parents="7023 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7366">
    <literal><![CDATA[
      K(x,(x * y) \ (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(6553(a,1),7364(a,1))].">
      <j1 rule="para" parents="6553 7364"/>
    </justification>
  </clause>

  <clause id="7367">
    <literal><![CDATA[
      K(L(x,y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(6586(a,1),7364(a,1))].">
      <j1 rule="para" parents="6586 7364"/>
    </justification>
  </clause>

  <clause id="7368">
    <literal><![CDATA[
      K(x,(x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(6556(a,1),7364(a,1))].">
      <j1 rule="para" parents="6556 7364"/>
    </justification>
  </clause>

  <clause id="7369">
    <literal><![CDATA[
      K(T(x / (x / y),x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(4360(a,2),7367(a,1,1))].">
      <j1 rule="para" parents="4360 7367"/>
    </justification>
  </clause>

  <clause id="7370">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(R(x,u,x),y) = z
    ]]></literal>
    <justification jstring="[para(4632(a,1),7367(a,1,1))].">
      <j1 rule="para" parents="4632 7367"/>
    </justification>
  </clause>

  <clause id="7371">
    <literal><![CDATA[
      T(x,y * (z * K(x,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(90(a,1),7102(a,1,2))].">
      <j1 rule="para" parents="90 7102"/>
    </justification>
  </clause>

  <clause id="7372">
    <literal><![CDATA[
      T(x,y * K(L(x,z,u),w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6586(a,1),7102(a,1,2,2))].">
      <j1 rule="para" parents="6586 7102"/>
    </justification>
  </clause>

  <clause id="7373">
    <literal><![CDATA[
      T(K(x,y),(z * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6144(a,2),7164(a,1))].">
      <j1 rule="para" parents="6144 7164"/>
    </justification>
  </clause>

  <clause id="7374">
    <literal><![CDATA[
      K((x \ y) \ z,T(z,u)) = K(y \ (x * z),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6597,a(flip),b,7207,a),flip(a)].">
      <j1 rule="hyper" parents="58 6597 7207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7375">
    <literal><![CDATA[
      K(x,y / T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(6293(a,1),7213(a,1,2))].">
      <j1 rule="para" parents="6293 7213"/>
    </justification>
  </clause>

  <clause id="7376">
    <literal><![CDATA[
      K(x,y / (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (z / x)) = u
    ]]></literal>
    <justification jstring="[para(6369(a,1),7213(a,1,2))].">
      <j1 rule="para" parents="6369 7213"/>
    </justification>
  </clause>

  <clause id="7377">
    <literal><![CDATA[
      K(x,y * (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * x)) = u
    ]]></literal>
    <justification jstring="[para(6604(a,1),7213(a,1,2))].">
      <j1 rule="para" parents="6604 7213"/>
    </justification>
  </clause>

  <clause id="7378">
    <literal><![CDATA[
      K(x,y * (z * K(x,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(90(a,1),7214(a,1,2))].">
      <j1 rule="para" parents="90 7214"/>
    </justification>
  </clause>

  <clause id="7379">
    <literal><![CDATA[
      K(x,y * (z * K(u,x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(6641(a,1),7214(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6641 7214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7380">
    <literal><![CDATA[
      T(x,a(y,z,K(x,u))) = x
    ]]></literal>
    <justification jstring="[para(5861(a,1),7240(a,1,2))].">
      <j1 rule="para" parents="5861 7240"/>
    </justification>
  </clause>

  <clause id="7381">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,w)) = a(z,u,K(y,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7380(a,1),7152(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7380 7152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7382">
    <literal><![CDATA[
      K(x,(K(x,y) * z) * u) = K(x,z * u)
    ]]></literal>
    <justification jstring="[para(101(a,1),7253(a,1,2))].">
      <j1 rule="para" parents="101 7253"/>
    </justification>
  </clause>

  <clause id="7383">
    <literal><![CDATA[
      K(x,K(R(x,y,z),u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(6716(a,1),7253(a,1,2,1))].">
      <j1 rule="para" parents="6716 7253"/>
    </justification>
  </clause>

  <clause id="7384">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u)) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(6928(a,1),7256(a,1,2,1))].">
      <j1 rule="para" parents="6928 7256"/>
    </justification>
  </clause>

  <clause id="7385">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(7131(a,1),7283(a,1))].">
      <j1 rule="para" parents="7131 7283"/>
    </justification>
  </clause>

  <clause id="7386">
    <literal><![CDATA[
      K(x \ T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(1420(a,1),7307(a,1,1))].">
      <j1 rule="para" parents="1420 7307"/>
    </justification>
  </clause>

  <clause id="7387">
    <literal><![CDATA[
      K(K(x,y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) = u
    ]]></literal>
    <justification jstring="[para(7122(a,1),7307(a,1,1))].">
      <j1 rule="para" parents="7122 7307"/>
    </justification>
  </clause>

  <clause id="7388">
    <literal><![CDATA[
      K(x * (y * K(z,u)),u) = K(x * y,u)
    ]]></literal>
    <justification jstring="[para(90(a,1),7311(a,1,1))].">
      <j1 rule="para" parents="90 7311"/>
    </justification>
  </clause>

  <clause id="7389">
    <literal><![CDATA[
      K(x * K(y,L(z,u,w)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(6580(a,1),7311(a,1,1,2))].">
      <j1 rule="para" parents="6580 7311"/>
    </justification>
  </clause>

  <clause id="7390">
    <literal><![CDATA[
      K(x * (y * K(z,u)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(6641(a,1),7311(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6641 7311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7391">
    <literal><![CDATA[
      K(x * K(L(y,z,u),w),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6586(a,1),7320(a,1,1,2))].">
      <j1 rule="para" parents="6586 7320"/>
    </justification>
  </clause>

  <clause id="7392">
    <literal><![CDATA[
      K((K(x,y) * z) * u,x) = K(z * u,x)
    ]]></literal>
    <justification jstring="[para(101(a,1),7329(a,1,1))].">
      <j1 rule="para" parents="101 7329"/>
    </justification>
  </clause>

  <clause id="7393">
    <literal><![CDATA[
      K(K(R(x,y,z),u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(6716(a,1),7329(a,1,1,1))].">
      <j1 rule="para" parents="6716 7329"/>
    </justification>
  </clause>

  <clause id="7394">
    <literal><![CDATA[
      K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y * x,x) = z
    ]]></literal>
    <justification jstring="[para(4772(a,1),7330(a,1,1))].">
      <j1 rule="para" parents="4772 7330"/>
    </justification>
  </clause>

  <clause id="7395">
    <literal><![CDATA[
      K(T(x,y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(5093(a,1),7330(a,1,1))].">
      <j1 rule="para" parents="5093 7330"/>
    </justification>
  </clause>

  <clause id="7396">
    <literal><![CDATA[
      K(x,T(y,x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(5093(a,1),7334(a,1,2))].">
      <j1 rule="para" parents="5093 7334"/>
    </justification>
  </clause>

  <clause id="7397">
    <literal><![CDATA[
      K(x,(x \ y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / x) \ z) = u
    ]]></literal>
    <justification jstring="[para(5376(a,1),7334(a,1,2))].">
      <j1 rule="para" parents="5376 7334"/>
    </justification>
  </clause>

  <clause id="7398">
    <literal><![CDATA[
      T(x,L(x,y,z) * (z * y)) = T(x,z * (y * x))
    ]]></literal>
    <justification jstring="[para(483(a,1),7372(a,1,2))].">
      <j1 rule="para" parents="483 7372"/>
    </justification>
  </clause>

  <clause id="7399">
    <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(7372(a,1),4765(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7372 4765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7400">
    <literal><![CDATA[
      K(x,R(x,y,z) * u) = K(x,u * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(4772(a,1),7383(a,1,2))].">
      <j1 rule="para" parents="4772 7383"/>
    </justification>
  </clause>

  <clause id="7401">
    <literal><![CDATA[
      K(x,T(R(x,y,z),u) \ w) = K(x,R(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(5042(a,1),7383(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5042 7383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7402">
    <literal><![CDATA[
      K(x,(y / R(x,z,u)) \ w) = K(x,(R(x,z,u) \ y) \ w)
    ]]></literal>
    <justification jstring="[para(5376(a,1),7383(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5376 7383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7403">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) * w) = K(x,R(x,z,u) * w)
    ]]></literal>
    <justification jstring="[para(5080(a,1),7383(a,1,2))].">
      <j1 rule="para" parents="5080 7383"/>
    </justification>
  </clause>

  <clause id="7404">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) \ z,x \ y) = u
    ]]></literal>
    <justification jstring="[para(5553(a,1),7387(a,1,1))].">
      <j1 rule="para" parents="5553 7387"/>
    </justification>
  </clause>

  <clause id="7405">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) = K(u * L(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(84(a,1),7389(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 7389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7406">
    <literal><![CDATA[
      K((L(x,y,z) \ u) * L(x,y,z),x) = K(u,x)
    ]]></literal>
    <justification jstring="[para(302(a,1),7389(a,1,1))].">
      <j1 rule="para" parents="302 7389"/>
    </justification>
  </clause>

  <clause id="7407">
    <literal><![CDATA[
      K(K(L(x,y,z),u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(7121(a,1),7389(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7121 7389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7408">
    <literal><![CDATA[
      K(R(x,y,z) * u,x) = K(u * R(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(4772(a,1),7393(a,1,1))].">
      <j1 rule="para" parents="4772 7393"/>
    </justification>
  </clause>

  <clause id="7409">
    <literal><![CDATA[
      K(T(x,R(y,z,u)) * w,y) = K(x * w,y)
    ]]></literal>
    <justification jstring="[para(4778(a,1),7393(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4778 7393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7410">
    <literal><![CDATA[
      K((x \ 1) \ y,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,y) = z
    ]]></literal>
    <justification jstring="[para(5323(a,2),7394(a,1))].">
      <j1 rule="para" parents="5323 7394"/>
    </justification>
  </clause>

  <clause id="7411">
    <literal><![CDATA[
      K(x,(x \ y) \ (x \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),7005(a,2,2,2))].">
      <j1 rule="para" parents="5 7005"/>
    </justification>
  </clause>

  <clause id="7412">
    <literal><![CDATA[
      T(x * K(y,z),y) = T(x,y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6210,a,7017,a)].">
      <j1 rule="hyper" parents="6210 7017"/>
    </justification>
  </clause>

  <clause id="7413">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(239,a,7017,a(flip),b,5044,a)].">
      <j1 rule="hyper" parents="239 7017 5044"/>
    </justification>
  </clause>

  <clause id="7414">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,y)) = T(z * K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(6678,a,7413,a),flip(a)].">
      <j1 rule="hyper" parents="6678 7413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7415">
    <literal><![CDATA[
      T(T(x,K(y,z)),y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(435,a,7413,a)].">
      <j1 rule="hyper" parents="435 7413"/>
    </justification>
  </clause>

  <clause id="7416">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = x * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7153,a,b,7413,a),flip(a)].">
      <j1 rule="hyper" parents="320 7153 7413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7417">
    <literal><![CDATA[
      T(T(T(x,y),z),K(y,u)) = T(T(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(7413(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7413 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7418">
    <literal><![CDATA[
      T(x / y,T(y,z)) = T(y \ x,K(y,z))
    ]]></literal>
    <justification jstring="[para(107(a,1),7413(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 7413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7419">
    <literal><![CDATA[
      T((x * y) / x,T(x,z)) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(224(a,1),7413(a,1,1)),flip(a)].">
      <j1 rule="para" parents="224 7413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7420">
    <literal><![CDATA[
      T(x / y,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7415(a,1),678(a,1))].">
      <j1 rule="para" parents="7415 678"/>
    </justification>
  </clause>

  <clause id="7421">
    <literal><![CDATA[
      L(x,T(y,K(x,z)),x) = L(x,T(y,T(x,z)),x)
    ]]></literal>
    <justification jstring="[para(7415(a,1),4424(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7415 4424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7422">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(5593(a,1),7415(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5593 7415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7423">
    <literal><![CDATA[
      T(K(x,y),T(z,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5600(a,1),7415(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5600 7415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7424">
    <literal><![CDATA[
      T(x * K(y,z),T(z,y)) = T(K(y,z) * x,z)
    ]]></literal>
    <justification jstring="[para(6308(a,1),7415(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6308 7415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7425">
    <literal><![CDATA[
      T(K(x,y \ z),T(y,z)) = T(K(x,y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7081,a(flip),b,7423,a)].">
      <j1 rule="hyper" parents="58 7081 7423"/>
    </justification>
  </clause>

  <clause id="7426">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6541,a,b,7022,a)].">
      <j1 rule="hyper" parents="58 6541 7022"/>
    </justification>
  </clause>

  <clause id="7427">
    <literal><![CDATA[
      (((x \ (y / z)) * x) * z) \ y = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6436,a,b,7022,a)].">
      <j1 rule="hyper" parents="58 6436 7022"/>
    </justification>
  </clause>

  <clause id="7428">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(7022(a,1),6483(a,2,2))].">
      <j1 rule="para" parents="7022 6483"/>
    </justification>
  </clause>

  <clause id="7429">
    <literal><![CDATA[
      R(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(3998,a,7028,a)].">
      <j1 rule="hyper" parents="3998 7028"/>
    </justification>
  </clause>

  <clause id="7430">
    <literal><![CDATA[
      (x * (y * K(z,x))) / x = (x * y) / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,7028,a(flip),b,6296,a)].">
      <j1 rule="hyper" parents="117 7028 6296"/>
    </justification>
  </clause>

  <clause id="7432">
    <literal><![CDATA[
      R(x,y,K(z,T(x,u))) = x
    ]]></literal>
    <justification jstring="[hyper(140,a,7429,a(flip))].">
      <j1 rule="hyper" parents="140 7429"/>
    </justification>
  </clause>

  <clause id="7434">
    <literal><![CDATA[
      R(R(x,y,z),u,K(w,x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(7429(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7429 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7436">
    <literal><![CDATA[
      (L(x,y,z) * u) * K(w,x) = L(x,y,z) * (u * K(w,x))
    ]]></literal>
    <justification jstring="[para(7429(a,1),513(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7429 513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7437">
    <literal><![CDATA[
      R(x,y,T(K(z,x),u)) = x
    ]]></literal>
    <justification jstring="[para(1523(a,1),7429(a,1,3))].">
      <j1 rule="para" parents="1523 7429"/>
    </justification>
  </clause>

  <clause id="7438">
    <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(7432(a,1),513(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7432 513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7439">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,T(x,w)) = K(x,y) * (z * K(u,T(x,w)))
    ]]></literal>
    <justification jstring="[para(7432(a,1),6724(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7432 6724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7440">
    <literal><![CDATA[
      x \ (y * T(K(z,x),u)) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(7437(a,1),505(a,1,1))].">
      <j1 rule="para" parents="7437 505"/>
    </justification>
  </clause>

  <clause id="7441">
    <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(7434(a,1),852(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7434 852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7442">
    <literal><![CDATA[
      K((x * y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6539,a,b,7029,a)].">
      <j1 rule="hyper" parents="58 6539 7029"/>
    </justification>
  </clause>

  <clause id="7443">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6537,a,b,7029,a)].">
      <j1 rule="hyper" parents="58 6537 7029"/>
    </justification>
  </clause>

  <clause id="7444">
    <literal><![CDATA[
      K((x \ y) \ (x \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),7029(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 7029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7445">
    <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(1398(a,1),7029(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1398 7029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7446">
    <literal><![CDATA[
      x * K(y \ (z \ x),z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(7029(a,1),6255(a,1,2))].">
      <j1 rule="para" parents="7029 6255"/>
    </justification>
  </clause>

  <clause id="7447">
    <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(7030(a,1),5483(a,1,1,1,2))].">
      <j1 rule="para" parents="7030 5483"/>
    </justification>
  </clause>

  <clause id="7448">
    <literal><![CDATA[
      T(x / T(y,z),y) = (y \ x) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6350,a,7034,a)].">
      <j1 rule="hyper" parents="6350 7034"/>
    </justification>
  </clause>

  <clause id="7449">
    <literal><![CDATA[
      K(x,y) * (L(y,z,y) \ u) = L(T(y,x),z,y) \ u
    ]]></literal>
    <justification jstring="[para(7036(a,1),5736(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7036 5736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7450">
    <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(6901(a,1),7036(a,2,1))].">
      <j1 rule="para" parents="6901 7036"/>
    </justification>
  </clause>

  <clause id="7451">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,x) = x \ L(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,7040,a(flip),b,4738,a)].">
      <j1 rule="hyper" parents="116 7040 4738"/>
    </justification>
  </clause>

  <clause id="7452">
    <literal><![CDATA[
      R(x,y,x) \ T(x,z) = x \ L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(7040(a,1),5986(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7040 5986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7453">
    <literal><![CDATA[
      K(x,y) * R(x,z,x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(3335,a,7053,a)].">
      <j1 rule="hyper" parents="3335 7053"/>
    </justification>
  </clause>

  <clause id="7454">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,7053,a(flip),b,5063,a)].">
      <j1 rule="hyper" parents="116 7053 5063"/>
    </justification>
  </clause>

  <clause id="7455">
    <literal><![CDATA[
      L(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(3988,a,7059,a)].">
      <j1 rule="hyper" parents="3988 7059"/>
    </justification>
  </clause>

  <clause id="7456">
    <literal><![CDATA[
      (K(x,y) * z) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5050,a(flip),b,7059,a),flip(a)].">
      <j1 rule="hyper" parents="320 5050 7059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7458">
    <literal><![CDATA[
      T(K(x \ y,x) * z,x \ y) = (y / x) \ (z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(239,a,7059,a,b,5333,a)].">
      <j1 rule="hyper" parents="239 7059 5333"/>
    </justification>
  </clause>

  <clause id="7459">
    <literal><![CDATA[
      (K(x,y) * (z * x)) \ (K(x,y) * z) = L(x \ 1,x,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7059(a,1),217(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7059 217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7460">
    <literal><![CDATA[
      L(T(x,y),z,K(x,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7455(a,1),20(a,2,1))].">
      <j1 rule="para" parents="7455 20"/>
    </justification>
  </clause>

  <clause id="7461">
    <literal><![CDATA[
      (K(x,y) * z) * R(x,u,w) = K(x,y) * (z * R(x,u,w))
    ]]></literal>
    <justification jstring="[para(7455(a,1),447(a,1,2,1))].">
      <j1 rule="para" parents="7455 447"/>
    </justification>
  </clause>

  <clause id="7464">
    <literal><![CDATA[
      L(K(x,y),z,K(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7455(a,1),6578(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7455 6578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7465">
    <literal><![CDATA[
      L(K(x,y),z,K(x,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7455(a,1),6584(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7455 6584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7466">
    <literal><![CDATA[
      L(x,y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(7455(a,1),6847(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7455 6847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7470">
    <literal><![CDATA[
      T(L(x / y,z,y \ x),y) = L(y \ x,z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,247,a,b,7466,a)].">
      <j1 rule="hyper" parents="320 247 7466"/>
    </justification>
  </clause>

  <clause id="7471">
    <literal><![CDATA[
      L(x / y,z,x / y) = L(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),7466(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 7466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7474">
    <literal><![CDATA[
      K(x,L(y,z,T(y,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7466(a,2),7032(a,1,2))].">
      <j1 rule="para" parents="7466 7032"/>
    </justification>
  </clause>

  <clause id="7475">
    <literal><![CDATA[
      L(L(T(x,y),z,u),w,K(x,v5)) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(7460(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7460 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7478">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(7460(a,1),6847(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7460 6847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7480">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,y) = K(z \ (K(y,x) * u),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6600,a(flip),b,7464,a),flip(a)].">
      <j1 rule="hyper" parents="58 6600 7464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7481">
    <literal><![CDATA[
      K(x,L(y,z,K(y,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6580,a(flip),b,7464,a)].">
      <j1 rule="hyper" parents="58 6580 7464"/>
    </justification>
  </clause>

  <clause id="7482">
    <literal><![CDATA[
      K(x,L(y,z,K(x,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6580,a(flip),b,7465,a)].">
      <j1 rule="hyper" parents="58 6580 7465"/>
    </justification>
  </clause>

  <clause id="7483">
    <literal><![CDATA[
      L(K(x,y),z,T(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6585,a,7474,a)].">
      <j1 rule="hyper" parents="6585 7474"/>
    </justification>
  </clause>

  <clause id="7484">
    <literal><![CDATA[
      K(x,L(L(y,z,K(x,u)),w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(25(a,1),7482(a,1,2))].">
      <j1 rule="para" parents="25 7482"/>
    </justification>
  </clause>

  <clause id="7485">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ (K(x,y) * u))
    ]]></literal>
    <justification jstring="[para(5126(a,1),7482(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5126 7482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7486">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,x) = K(z \ (T(x,y) \ u),x)
    ]]></literal>
    <justification jstring="[hyper(6829,a,7483,a)].">
      <j1 rule="hyper" parents="6829 7483"/>
    </justification>
  </clause>

  <clause id="7487">
    <literal><![CDATA[
      T(x,(x \ y) \ (x \ z)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),7060(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 7060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7488">
    <literal><![CDATA[
      (x / L(y,z,y)) * y = y * (L(y,z,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7061,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 7061 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7489">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = (z / x) * L(x,y,x)
    ]]></literal>
    <justification jstring="[para(107(a,1),7064(a,1,2))].">
      <j1 rule="para" parents="107 7064"/>
    </justification>
  </clause>

  <clause id="7491">
    <literal><![CDATA[
      K(x * (y / R(z,u,z)),z) = K(x * (R(z,u,z) \ y),z)
    ]]></literal>
    <justification jstring="[para(7078(a,1),7308(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7078 7308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7493">
    <literal><![CDATA[
      L(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(3988,a,7082,a)].">
      <j1 rule="hyper" parents="3988 7082"/>
    </justification>
  </clause>

  <clause id="7495">
    <literal><![CDATA[
      T(K(x,y) * z,y) = K(x,y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(239,a,7082,a,b,5373,a)].">
      <j1 rule="hyper" parents="239 7082 5373"/>
    </justification>
  </clause>

  <clause id="7496">
    <literal><![CDATA[
      T(K(x,y) * z,y) = T(y,x) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(239,a,7082,a,b,4777,a)].">
      <j1 rule="hyper" parents="239 7082 4777"/>
    </justification>
  </clause>

  <clause id="7497">
    <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(7082(a,1),5052(a,1,2,2))].">
      <j1 rule="para" parents="7082 5052"/>
    </justification>
  </clause>

  <clause id="7499">
    <literal><![CDATA[
      L(R(x,y,z),u,K(w,x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(7493(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7493 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7500">
    <literal><![CDATA[
      (K(x,y) * z) * T(y,u) = K(x,y) * (z * T(y,u))
    ]]></literal>
    <justification jstring="[para(7493(a,1),449(a,1,2,1))].">
      <j1 rule="para" parents="7493 449"/>
    </justification>
  </clause>

  <clause id="7501">
    <literal><![CDATA[
      L(K(x,y),z,K(u,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7493(a,1),6578(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7493 6578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7502">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6586,a(flip),b,7501,a)].">
      <j1 rule="hyper" parents="58 6586 7501"/>
    </justification>
  </clause>

  <clause id="7503">
    <literal><![CDATA[
      T(x,L(y,z,K(u,x))) = (K(y,x) / x) \ 1
    ]]></literal>
    <justification jstring="[para(7502(a,1),4951(a,2,1,1))].">
      <j1 rule="para" parents="7502 4951"/>
    </justification>
  </clause>

  <clause id="7504">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,z)) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,4334,a(flip),b,7096,a),flip(a)].">
      <j1 rule="hyper" parents="320 4334 7096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7506">
    <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(7096(a,1),1318(a,1,1))].">
      <j1 rule="para" parents="7096 1318"/>
    </justification>
  </clause>

  <clause id="7507">
    <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(4775(a,1),7096(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4775 7096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7508">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7085,a,b,7106,a)].">
      <j1 rule="hyper" parents="58 7085 7106"/>
    </justification>
  </clause>

  <clause id="7509">
    <literal><![CDATA[
      K(x,T(y,(z \ u) \ y)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6095(a,1),7129(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6095 7129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7510">
    <literal><![CDATA[
      K(x \ 1,T(y,L(x,z,u))) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(173(a,1),7141(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="173 7141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7511">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = T(T(K(x,y),u),z)
    ]]></literal>
    <justification jstring="[para(7131(a,1),7154(a,2,1))].">
      <j1 rule="para" parents="7131 7154"/>
    </justification>
  </clause>

  <clause id="7512">
    <literal><![CDATA[
      K(x * y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(6228,a,7161,a)].">
      <j1 rule="hyper" parents="6228 7161"/>
    </justification>
  </clause>

  <clause id="7513">
    <literal><![CDATA[
      K(x,K(y,z)) * T(z,y) = T(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(7161(a,1),6493(a,1,1))].">
      <j1 rule="para" parents="7161 6493"/>
    </justification>
  </clause>

  <clause id="7514">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6548,a,b,7512,a)].">
      <j1 rule="hyper" parents="58 6548 7512"/>
    </justification>
  </clause>

  <clause id="7515">
    <literal><![CDATA[
      K(x \ y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),7512(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 7512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7516">
    <literal><![CDATA[
      K(x * y,K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7515(a,1),6270(a,1))].">
      <j1 rule="para" parents="7515 6270"/>
    </justification>
  </clause>

  <clause id="7517">
    <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,5551,a,b,7171,a)].">
      <j1 rule="hyper" parents="58 5551 7171"/>
    </justification>
  </clause>

  <clause id="7518">
    <literal><![CDATA[
      K(T(T(x,y),z),u) = K(x,T(T(u,y),z))
    ]]></literal>
    <justification jstring="[para(18(a,1),7171(a,1,1))].">
      <j1 rule="para" parents="18 7171"/>
    </justification>
  </clause>

  <clause id="7519">
    <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(7183(a,1),2015(a,1,2))].">
      <j1 rule="para" parents="7183 2015"/>
    </justification>
  </clause>

  <clause id="7520">
    <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),7190(a,1,1))].">
      <j1 rule="para" parents="22 7190"/>
    </justification>
  </clause>

  <clause id="7521">
    <literal><![CDATA[
      K(x,y) * T(x,T(z,y)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(5369,a,7193,a)].">
      <j1 rule="hyper" parents="5369 7193"/>
    </justification>
  </clause>

  <clause id="7522">
    <literal><![CDATA[
      K(x,y) \ T(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,7193,a(flip),b,5367,a)].">
      <j1 rule="hyper" parents="116 7193 5367"/>
    </justification>
  </clause>

  <clause id="7523">
    <literal><![CDATA[
      K(x,K(y,z)) * T(x,y) = T(T(x,y),K(y,z))
    ]]></literal>
    <justification jstring="[para(3308(a,1),7193(a,1,1,2))].">
      <j1 rule="para" parents="3308 7193"/>
    </justification>
  </clause>

  <clause id="7524">
    <literal><![CDATA[
      K(x,y) * T(T(y,z),x) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(7200(a,1),5416(a,1,2))].">
      <j1 rule="para" parents="7200 5416"/>
    </justification>
  </clause>

  <clause id="7525">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7072,a,b,7219,a)].">
      <j1 rule="hyper" parents="58 7072 7219"/>
    </justification>
  </clause>

  <clause id="7526">
    <literal><![CDATA[
      K(x,T(K(x,y) * z,u)) = K(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(5095(a,1),7221(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5095 7221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7527">
    <literal><![CDATA[
      T(T(x,y),K(x,z) * u) = T(T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,18,a,b,7242,a),flip(a)].">
      <j1 rule="hyper" parents="320 18 7242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7528">
    <literal><![CDATA[
      T(x,y * (K(x,z) * u)) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(5095(a,1),7246(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5095 7246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7529">
    <literal><![CDATA[
      K(x,T(y,K(x,z) * u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7133,a(flip),b,7247,a),flip(a)].">
      <j1 rule="hyper" parents="320 7133 7247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7530">
    <literal><![CDATA[
      K(x,y * (K(x,z) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(5095(a,1),7252(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5095 7252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7531">
    <literal><![CDATA[
      K(x,(y * x) * z) = K(x,(x * y) * z)
    ]]></literal>
    <justification jstring="[para(4772(a,1),7257(a,1,2,1))].">
      <j1 rule="para" parents="4772 7257"/>
    </justification>
  </clause>

  <clause id="7532">
    <literal><![CDATA[
      K(x,(T(y,x) * z) * u) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[para(4740(a,1),7257(a,1,2,1))].">
      <j1 rule="para" parents="4740 7257"/>
    </justification>
  </clause>

  <clause id="7533">
    <literal><![CDATA[
      K(x,(y \ T(z,x)) * u) = K(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[para(5514(a,1),7257(a,1,2,1))].">
      <j1 rule="para" parents="5514 7257"/>
    </justification>
  </clause>

  <clause id="7534">
    <literal><![CDATA[
      K(x,(T(y,x) / z) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(5702(a,1),7257(a,1,2,1))].">
      <j1 rule="para" parents="5702 7257"/>
    </justification>
  </clause>

  <clause id="7535">
    <literal><![CDATA[
      K(x,y * K(z,R(x,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7261(a,1),7384(a,1,2))].">
      <j1 rule="para" parents="7261 7384"/>
    </justification>
  </clause>

  <clause id="7536">
    <literal><![CDATA[
      K(x,y / (z / R(x,u,w))) = K(x,y / (R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(6192(a,1),7535(a,1,2))].">
      <j1 rule="para" parents="6192 7535"/>
    </justification>
  </clause>

  <clause id="7537">
    <literal><![CDATA[
      x \ (T(y / x,z) \ y) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(5935,a,7272,a)].">
      <j1 rule="hyper" parents="5935 7272"/>
    </justification>
  </clause>

  <clause id="7538">
    <literal><![CDATA[
      T(x / y,z) \ x = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(5439,a,7272,a)].">
      <j1 rule="hyper" parents="5439 7272"/>
    </justification>
  </clause>

  <clause id="7539">
    <literal><![CDATA[
      (x * L(y,z,y)) / T(T(x,y),u) = K(u,x) * L(y,z,y)
    ]]></literal>
    <justification jstring="[para(7049(a,1),7273(a,1,2,1))].">
      <j1 rule="para" parents="7049 7273"/>
    </justification>
  </clause>

  <clause id="7540">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * y = y * K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5312(a,2),7279(a,1,1))].">
      <j1 rule="para" parents="5312 7279"/>
    </justification>
  </clause>

  <clause id="7541">
    <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(6402(a,1),7279(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6402 7279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7542">
    <literal><![CDATA[
      T(T(x,y),z) * K(z,x) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(18(a,1),7284(a,1,1))].">
      <j1 rule="para" parents="18 7284"/>
    </justification>
  </clause>

  <clause id="7543">
    <literal><![CDATA[
      K(R(x,y,(x * y) \ z) \ 1,T(u,z)) = K(z \ (y * ((x * y) \ z)),u)
    ]]></literal>
    <justification jstring="[para(367(a,1),7289(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="367 7289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7544">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7133,a(flip),b,7293,a)].">
      <j1 rule="hyper" parents="58 7133 7293"/>
    </justification>
  </clause>

  <clause id="7545">
    <literal><![CDATA[
      K(x * T(y,z),T(z,u)) = K(x * y,T(z,u))
    ]]></literal>
    <justification jstring="[para(1423(a,1),7319(a,1,1))].">
      <j1 rule="para" parents="1423 7319"/>
    </justification>
  </clause>

  <clause id="7546">
    <literal><![CDATA[
      K(x * T(y,z),T(y,u)) = K(x * y,T(y,u))
    ]]></literal>
    <justification jstring="[para(6302(a,1),7319(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6302 7319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7547">
    <literal><![CDATA[
      K(x * (K(y,z) * u),y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(5095(a,1),7327(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5095 7327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7548">
    <literal><![CDATA[
      K(x * (T(y,z) * u),y) = K(x * (y * u),y)
    ]]></literal>
    <justification jstring="[para(4778(a,1),7327(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4778 7327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7549">
    <literal><![CDATA[
      K(x * (y / (z * y)),z \ 1) = K(x * ((z * y) \ y),z \ 1)
    ]]></literal>
    <justification jstring="[para(5315(a,1),7327(a,1,1,2))].">
      <j1 rule="para" parents="5315 7327"/>
    </justification>
  </clause>

  <clause id="7550">
    <literal><![CDATA[
      K(x * (y \ T(z,u)),u) = K(x * (y \ z),u)
    ]]></literal>
    <justification jstring="[para(5514(a,1),7327(a,1,1,2))].">
      <j1 rule="para" parents="5514 7327"/>
    </justification>
  </clause>

  <clause id="7551">
    <literal><![CDATA[
      T(x,T(y,x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7340(a,2),4725(a,1))].">
      <j1 rule="para" parents="7340 4725"/>
    </justification>
  </clause>

  <clause id="7552">
    <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(7350(a,1),5339(a,1,1,2))].">
      <j1 rule="para" parents="7350 5339"/>
    </justification>
  </clause>

  <clause id="7553">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ z,x) = (x \ z) * x
    ]]></literal>
    <justification jstring="[hyper(6166,a,7351,a)].">
      <j1 rule="hyper" parents="6166 7351"/>
    </justification>
  </clause>

  <clause id="7554">
    <literal><![CDATA[
      K(x,y * (z * L(K(x,u),w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(5641(a,1),7378(a,1,2,2,2))].">
      <j1 rule="para" parents="5641 7378"/>
    </justification>
  </clause>

  <clause id="7555">
    <literal><![CDATA[
      K(x,y * (z * L(K(u,x),w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(4782(a,1),7379(a,1,2,2,2))].">
      <j1 rule="para" parents="4782 7379"/>
    </justification>
  </clause>

  <clause id="7556">
    <literal><![CDATA[
      K(x,T(y * (z * K(u,x)),w)) = T(K(x,y * z),w)
    ]]></literal>
    <justification jstring="[para(7379(a,1),7131(a,2,1))].">
      <j1 rule="para" parents="7379 7131"/>
    </justification>
  </clause>

  <clause id="7557">
    <literal><![CDATA[
      K(x * (y / T(z,u)),u) = K(x * (y / z),u)
    ]]></literal>
    <justification jstring="[para(6159(a,1),7388(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6159 7388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7558">
    <literal><![CDATA[
      K(x * (y / R(z,u,z)),z) = K(x * (y / T(z,u)),z)
    ]]></literal>
    <justification jstring="[para(6619(a,1),7390(a,1,1,2))].">
      <j1 rule="para" parents="6619 7390"/>
    </justification>
  </clause>

  <clause id="7559">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,y) = T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6004,a,7412,a)].">
      <j1 rule="hyper" parents="6004 7412"/>
    </justification>
  </clause>

  <clause id="7560">
    <literal><![CDATA[
      (T(x,y) / y) * T(y,z) = T(x * K(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6121,a,b,7412,a)].">
      <j1 rule="hyper" parents="320 6121 7412"/>
    </justification>
  </clause>

  <clause id="7562">
    <literal><![CDATA[
      x \ T(x * K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(7412(a,2),5057(a,1,2))].">
      <j1 rule="para" parents="7412 5057"/>
    </justification>
  </clause>

  <clause id="7563">
    <literal><![CDATA[
      K(x,T(x * K(y,z),y)) = K(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(7412(a,2),7248(a,1,2))].">
      <j1 rule="para" parents="7412 7248"/>
    </justification>
  </clause>

  <clause id="7564">
    <literal><![CDATA[
      T(T(x,1 / y),K(1 / y,z)) = x * K(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[para(5475(a,2),7416(a,2,2))].">
      <j1 rule="para" parents="5475 7416"/>
    </justification>
  </clause>

  <clause id="7565">
    <literal><![CDATA[
      T(x \ y,K(x,z)) = x \ T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6487,a(flip),b,7418,a),flip(a)].">
      <j1 rule="hyper" parents="58 6487 7418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7566">
    <literal><![CDATA[
      T(x * y,K(y,z)) / y = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6488,a,7419,a)].">
      <j1 rule="hyper" parents="6488 7419"/>
    </justification>
  </clause>

  <clause id="7567">
    <literal><![CDATA[
      T(x * y,K(x,z)) = x * T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7419,a(flip),b,6487,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 7419 6487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7568">
    <literal><![CDATA[
      x * (y * ((x \ 1) / y)) = K(y,x \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(5266,a,7426,a)].">
      <j1 rule="hyper" parents="5266 7426"/>
    </justification>
  </clause>

  <clause id="7569">
    <literal><![CDATA[
      K(x,L(x \ y,x,z)) = K(x,z \ (x \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,6569,a,b,7426,a)].">
      <j1 rule="hyper" parents="58 6569 7426"/>
    </justification>
  </clause>

  <clause id="7570">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(T(z,x),x,y))
    ]]></literal>
    <justification jstring="[para(232(a,1),7426(a,1,2)),flip(a)].">
      <j1 rule="para" parents="232 7426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7571">
    <literal><![CDATA[
      L(K(x,y \ (x \ z)),u * x,w) = K(L(x,u,w),(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(7426(a,1),6586(a,1,1))].">
      <j1 rule="para" parents="7426 6586"/>
    </justification>
  </clause>

  <clause id="7572">
    <literal><![CDATA[
      K(x,y \ (x \ (y * z))) != u
    ]]></literal>
    <literal><![CDATA[
      L(K(x,x \ z),z,y) = u
    ]]></literal>
    <justification jstring="[para(7426(a,1),6656(a,1))].">
      <j1 rule="para" parents="7426 6656"/>
    </justification>
  </clause>

  <clause id="7573">
    <literal><![CDATA[
      K((x * y) \ (z * y),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7347,a(flip),b,7442,a),flip(a)].">
      <j1 rule="hyper" parents="320 7347 7442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7574">
    <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(7442(a,1),5483(a,1,1,1,2))].">
      <j1 rule="para" parents="7442 5483"/>
    </justification>
  </clause>

  <clause id="7575">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7347,a(flip),b,7444,a)].">
      <j1 rule="hyper" parents="58 7347 7444"/>
    </justification>
  </clause>

  <clause id="7576">
    <literal><![CDATA[
      T(x / T(y,z),y) * y = (y \ x) * (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(7448(a,2),6060(a,1,1))].">
      <j1 rule="para" parents="7448 6060"/>
    </justification>
  </clause>

  <clause id="7577">
    <literal><![CDATA[
      K(x,y) * R(T(y,x),z,y) = R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(5109,a,7453,a)].">
      <j1 rule="hyper" parents="5109 7453"/>
    </justification>
  </clause>

  <clause id="7578">
    <literal><![CDATA[
      K(x,y) * (x \ R(x,z,x)) = x \ R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,7453,a(flip),b,5064,a),flip(a)].">
      <j1 rule="hyper" parents="116 7453 5064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7579">
    <literal><![CDATA[
      T(K(x,y) * z,x) = K(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(239,a,7456,a,b,4737,a)].">
      <j1 rule="hyper" parents="239 7456 4737"/>
    </justification>
  </clause>

  <clause id="7580">
    <literal><![CDATA[
      (T(x,y) * (x \ z)) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[para(4738(a,2),7456(a,1,1))].">
      <j1 rule="para" parents="4738 7456"/>
    </justification>
  </clause>

  <clause id="7582">
    <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(7478(a,1),4527(a,1))].">
      <j1 rule="para" parents="7478 4527"/>
    </justification>
  </clause>

  <clause id="7583">
    <literal><![CDATA[
      K(x,L(T(y,z),u,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7478(a,1),7032(a,1,2))].">
      <j1 rule="para" parents="7478 7032"/>
    </justification>
  </clause>

  <clause id="7584">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6585,a,7583,a)].">
      <j1 rule="hyper" parents="6585 7583"/>
    </justification>
  </clause>

  <clause id="7585">
    <literal><![CDATA[
      K((x * y) \ z,T(x,u)) = K(y \ (x \ z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(6829,a,7584,a)].">
      <j1 rule="hyper" parents="6829 7584"/>
    </justification>
  </clause>

  <clause id="7586">
    <literal><![CDATA[
      K((x \ 1) * y,T(x \ 1,z)) = K(x \ y,T(x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(6613,a,7584,a),flip(a)].">
      <j1 rule="hyper" parents="6613 7584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7587">
    <literal><![CDATA[
      K((x \ y) \ z,T(x,u)) = K(y \ (x * z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6597,a(flip),b,7584,a),flip(a)].">
      <j1 rule="hyper" parents="58 6597 7584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7588">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,x) = T(z,x)
    ]]></literal>
    <justification jstring="[hyper(6018,a,7495,a)].">
      <j1 rule="hyper" parents="6018 7495"/>
    </justification>
  </clause>

  <clause id="7589">
    <literal><![CDATA[
      T(K(x,y \ z) * y,y \ z) = T(y \ z,x) \ z
    ]]></literal>
    <justification jstring="[hyper(320,a,5193,a(flip),b,7495,a),flip(a)].">
      <j1 rule="hyper" parents="320 5193 7495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7591">
    <literal><![CDATA[
      K(x,y) * T(K(x * y,x),y) = T(x \ R(x,y,x),y)
    ]]></literal>
    <justification jstring="[para(5255(a,1),7495(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5255 7495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7592">
    <literal><![CDATA[
      T(K(x,y) * (z / y),y) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[para(7(a,1),7496(a,2,2))].">
      <j1 rule="para" parents="7 7496"/>
    </justification>
  </clause>

  <clause id="7593">
    <literal><![CDATA[
      T(K(x,y) * (z * (1 / y)),y) = T(y,x) \ R(z,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2589(a,1),7496(a,2,2))].">
      <j1 rule="para" parents="2589 7496"/>
    </justification>
  </clause>

  <clause id="7594">
    <literal><![CDATA[
      K(x,T(y,T(z,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7513(a,1),7239(a,1,2))].">
      <j1 rule="para" parents="7513 7239"/>
    </justification>
  </clause>

  <clause id="7595">
    <literal><![CDATA[
      K(T(x,T(y,z)),z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(7513(a,1),7316(a,1,1))].">
      <j1 rule="para" parents="7513 7316"/>
    </justification>
  </clause>

  <clause id="7596">
    <literal><![CDATA[
      K(x,T(y,T(z,R(x,u,w)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7513(a,1),7383(a,1,2))].">
      <j1 rule="para" parents="7513 7383"/>
    </justification>
  </clause>

  <clause id="7597">
    <literal><![CDATA[
      K(x,T(y,x / z)) = K(x,T(y,z \ x))
    ]]></literal>
    <justification jstring="[para(7065(a,1),7594(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7065 7594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7598">
    <literal><![CDATA[
      K(x,y) * T(x,K(z,T(u,y))) = T(T(x,y),K(z,u))
    ]]></literal>
    <justification jstring="[para(7131(a,2),7521(a,1,2,2))].">
      <j1 rule="para" parents="7131 7521"/>
    </justification>
  </clause>

  <clause id="7599">
    <literal><![CDATA[
      K(x,y / z) * T(z \ y,x) = T(y / z,T(z,x))
    ]]></literal>
    <justification jstring="[para(107(a,1),7524(a,1,2,1))].">
      <j1 rule="para" parents="107 7524"/>
    </justification>
  </clause>

  <clause id="7600">
    <literal><![CDATA[
      T(T(x,y),T(x,z) \ u) = T(T(x,y),x \ u)
    ]]></literal>
    <justification jstring="[para(5042(a,1),7527(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5042 7527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7601">
    <literal><![CDATA[
      K(x,T(y,K(z,x) * u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(5095(a,1),7529(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5095 7529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7602">
    <literal><![CDATA[
      K(x,y * (z * (K(u,x) * w))) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(6008(a,1),7530(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6008 7530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7603">
    <literal><![CDATA[
      x / T(y \ x,z) = T(x / y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(33,a,6344,a,b,7537,a)].">
      <j1 rule="hyper" parents="33 6344 7537"/>
    </justification>
  </clause>

  <clause id="7604">
    <literal><![CDATA[
      x / (y * K(z,y \ x)) = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(197,a,7538,a)].">
      <j1 rule="hyper" parents="197 7538"/>
    </justification>
  </clause>

  <clause id="7605">
    <literal><![CDATA[
      (T(x / y,z) \ x) \ x = T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(7538(a,2),6292(a,1,1))].">
      <j1 rule="para" parents="7538 6292"/>
    </justification>
  </clause>

  <clause id="7606">
    <literal><![CDATA[
      T(T(x,y) * K(z,x),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7412,a,b,7542,a)].">
      <j1 rule="hyper" parents="58 7412 7542"/>
    </justification>
  </clause>

  <clause id="7607">
    <literal><![CDATA[
      x \ (T(y,z) * T(x,y)) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7017,a,b,7542,a)].">
      <j1 rule="hyper" parents="58 7017 7542"/>
    </justification>
  </clause>

  <clause id="7608">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7544,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 7544 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7609">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7142,a(flip),b,7544,a)].">
      <j1 rule="hyper" parents="58 7142 7544"/>
    </justification>
  </clause>

  <clause id="7610">
    <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(7547(a,1),5484(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7547 5484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7611">
    <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(7547(a,1),5485(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7547 5485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7612">
    <literal><![CDATA[
      T(x * K(y,z),z) = T(x,z) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(738,a,7559,a),flip(a)].">
      <j1 rule="hyper" parents="738 7559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7613">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = (y * T(y \ u,x)) \ u
    ]]></literal>
    <justification jstring="[para(7559(a,1),6437(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7559 6437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7614">
    <literal><![CDATA[
      x \ T(L(y,x \ 1,x),K(x,z)) = T((x \ 1) * y,K(x,z))
    ]]></literal>
    <justification jstring="[para(438(a,1),7565(a,1,1)),flip(a)].">
      <j1 rule="para" parents="438 7565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7615">
    <literal><![CDATA[
      T(x * y,K(y,z)) = T(x,K(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(133,a,7566,a),flip(a)].">
      <j1 rule="hyper" parents="133 7566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7616">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7444,a(flip),b,7575,a),flip(a)].">
      <j1 rule="hyper" parents="58 7444 7575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7617">
    <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(7577(a,1),5140(a,1,2))].">
      <j1 rule="para" parents="7577 5140"/>
    </justification>
  </clause>

  <clause id="7618">
    <literal><![CDATA[
      T(K(x,y) * T(y,z),x) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,7524,a(flip),b,7579,a),flip(a)].">
      <j1 rule="hyper" parents="320 7524 7579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7619">
    <literal><![CDATA[
      T(K(x,y) * z,x) / z = K(x,y) * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,7579,a,b,6167,a)].">
      <j1 rule="hyper" parents="117 7579 6167"/>
    </justification>
  </clause>

  <clause id="7620">
    <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),7579(a,2,2))].">
      <j1 rule="para" parents="20 7579"/>
    </justification>
  </clause>

  <clause id="7622">
    <literal><![CDATA[
      (x \ K(y,z)) * T((x \ K(y,z)) \ u,y) = x \ T(x * u,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,7588,a(flip),b,1086,a),flip(a)].">
      <j1 rule="hyper" parents="116 7588 1086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7623">
    <literal><![CDATA[
      K(x,y) * (z * T(z \ (K(x,y) \ u),x)) = T(u / z,x) * z
    ]]></literal>
    <justification jstring="[para(7588(a,1),1566(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7588 1566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7624">
    <literal><![CDATA[
      (x / y) * K(x,T(z,y \ x)) = K(x,z) * (x / y)
    ]]></literal>
    <justification jstring="[para(7597(a,1),7152(a,1,2))].">
      <j1 rule="para" parents="7597 7152"/>
    </justification>
  </clause>

  <clause id="7625">
    <literal><![CDATA[
      K(x,T(y,K(z,x) * u)) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,7131,a(flip),b,7601,a),flip(a)].">
      <j1 rule="hyper" parents="320 7131 7601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7626">
    <literal><![CDATA[
      K(x,T(y,z * K(u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7261(a,1),7601(a,1,2,2))].">
      <j1 rule="para" parents="7261 7601"/>
    </justification>
  </clause>

  <clause id="7627">
    <literal><![CDATA[
      x / T((y \ x) \ x,z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),7603(a,2,1,1))].">
      <j1 rule="para" parents="72 7603"/>
    </justification>
  </clause>

  <clause id="7628">
    <literal><![CDATA[
      T(x / (x / y),z) \ x = x / T(y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),7603(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 7603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7629">
    <literal><![CDATA[
      (x * y) / (x * K(z,y)) = T((x * y) / x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),7604(a,1,2,2,2))].">
      <j1 rule="para" parents="4 7604"/>
    </justification>
  </clause>

  <clause id="7630">
    <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(7604(a,1),4356(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7604 4356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7631">
    <literal><![CDATA[
      x / ((x * y) * K(z,y \ 1)) = T(x / (x * y),z)
    ]]></literal>
    <justification jstring="[para(6097(a,1),7604(a,1,2,2))].">
      <j1 rule="para" parents="6097 7604"/>
    </justification>
  </clause>

  <clause id="7632">
    <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(6402(a,1),7604(a,2,1))].">
      <j1 rule="para" parents="6402 7604"/>
    </justification>
  </clause>

  <clause id="7633">
    <literal><![CDATA[
      T((x \ y) \ y,z) = (T(x,z) \ y) \ y
    ]]></literal>
    <justification jstring="[para(72(a,1),7605(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 7605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7634">
    <literal><![CDATA[
      ((x \ T(y,x)) \ y) \ y = T(T(x,y) \ y,x)
    ]]></literal>
    <justification jstring="[para(4204(a,1),7605(a,1,1,1))].">
      <j1 rule="para" parents="4204 7605"/>
    </justification>
  </clause>

  <clause id="7635">
    <literal><![CDATA[
      K(x,T(T(y / z,u),y)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(7605(a,1),7114(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7605 7114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7636">
    <literal><![CDATA[
      T(x * K(y,x),T(z,y)) = T(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(5167,a,7606,a)].">
      <j1 rule="hyper" parents="5167 7606"/>
    </justification>
  </clause>

  <clause id="7637">
    <literal><![CDATA[
      x \ (K(y,z) * (x * y)) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(5050(a,2),7607(a,1,2))].">
      <j1 rule="para" parents="5050 7607"/>
    </justification>
  </clause>

  <clause id="7638">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7281,a(flip),b,7608,a)].">
      <j1 rule="hyper" parents="58 7281 7608"/>
    </justification>
  </clause>

  <clause id="7639">
    <literal><![CDATA[
      T(x,T((y / z) \ 1,y)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(75(a,1),7608(a,2,2,2))].">
      <j1 rule="para" parents="75 7608"/>
    </justification>
  </clause>

  <clause id="7640">
    <literal><![CDATA[
      K(x,y \ K(z,y)) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[para(4763(a,1),7609(a,1,2))].">
      <j1 rule="para" parents="4763 7609"/>
    </justification>
  </clause>

  <clause id="7641">
    <literal><![CDATA[
      T(K(x,y) * T(y,z),x) = y * K(T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7173,a,b,7618,a),flip(a)].">
      <j1 rule="hyper" parents="320 7173 7618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7642">
    <literal><![CDATA[
      T(K(x,y),K(z,x) * u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7131,a(flip),b,7625,a)].">
      <j1 rule="hyper" parents="58 7131 7625"/>
    </justification>
  </clause>

  <clause id="7643">
    <literal><![CDATA[
      K(x,T(y,z * L(K(u,x),w,v5))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4782(a,1),7626(a,1,2,2,2))].">
      <j1 rule="para" parents="4782 7626"/>
    </justification>
  </clause>

  <clause id="7644">
    <literal><![CDATA[
      K(x,T(y,z * K(x,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6300(a,1),7626(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6300 7626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7645">
    <literal><![CDATA[
      x / T(T(y,y \ x),z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(106(a,2),7627(a,1,2,1))].">
      <j1 rule="para" parents="106 7627"/>
    </justification>
  </clause>

  <clause id="7646">
    <literal><![CDATA[
      T(x,y) / T(R(x,z,u),w) = T(R(x,z,u),w) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(6752(a,1),7627(a,1,2,1))].">
      <j1 rule="para" parents="6752 7627"/>
    </justification>
  </clause>

  <clause id="7647">
    <literal><![CDATA[
      x / (x / T(y,z)) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(197,a,7628,a)].">
      <j1 rule="hyper" parents="197 7628"/>
    </justification>
  </clause>

  <clause id="7648">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ K(z,x) = K(z,x) / T(x,y)
    ]]></literal>
    <justification jstring="[para(5408(a,1),7628(a,1,1,1))].">
      <j1 rule="para" parents="5408 7628"/>
    </justification>
  </clause>

  <clause id="7649">
    <literal><![CDATA[
      T(T(x,y),x \ z) = (T(x,y) \ z) \ z
    ]]></literal>
    <justification jstring="[hyper(602,a,7633,a)].">
      <j1 rule="hyper" parents="602 7633"/>
    </justification>
  </clause>

  <clause id="7653">
    <literal><![CDATA[
      K(x,y) * (z * x) = z * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(134,a,7637,a),flip(a)].">
      <j1 rule="hyper" parents="134 7637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7654">
    <literal><![CDATA[
      T(x,(y * z) \ z) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(6477,a,7638,a)].">
      <j1 rule="hyper" parents="6477 7638"/>
    </justification>
  </clause>

  <clause id="7655">
    <literal><![CDATA[
      K(T(x,(y / z) \ 1),y) = K(T(x,y \ z),y)
    ]]></literal>
    <justification jstring="[para(7639(a,1),7595(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7639 7595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7656">
    <literal><![CDATA[
      K(x,(y * z) \ z) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6528,a,b,7640,a)].">
      <j1 rule="hyper" parents="58 6528 7640"/>
    </justification>
  </clause>

  <clause id="7657">
    <literal><![CDATA[
      T(K(x,y),R(K(z,x),u,w) * v5) = T(K(x,y),v5)
    ]]></literal>
    <justification jstring="[para(5670(a,1),7642(a,1,2,1))].">
      <j1 rule="para" parents="5670 7642"/>
    </justification>
  </clause>

  <clause id="7658">
    <literal><![CDATA[
      T(K(x,y),z * K(u,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7261(a,1),7642(a,1,2))].">
      <j1 rule="para" parents="7261 7642"/>
    </justification>
  </clause>

  <clause id="7659">
    <literal><![CDATA[
      K(x,T(y,z * (u * x))) = K(x,T(y,z * (x * u)))
    ]]></literal>
    <justification jstring="[para(6604(a,1),7644(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6604 7644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7660">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,x)) * w)) = K(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(6791(a,1),7644(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6791 7644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7664">
    <literal><![CDATA[
      T(x,T(T(y,z),y \ u)) = T(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(7649(a,2),7126(a,1,2))].">
      <j1 rule="para" parents="7649 7126"/>
    </justification>
  </clause>

  <clause id="7665">
    <literal><![CDATA[
      T(K(x,y),z * x) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(239,a,7653,a,b,6086,a)].">
      <j1 rule="hyper" parents="239 7653 6086"/>
    </justification>
  </clause>

  <clause id="7666">
    <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(7653(a,1),92(a,2,1))].">
      <j1 rule="para" parents="7653 92"/>
    </justification>
  </clause>

  <clause id="7667">
    <literal><![CDATA[
      T(K(x,y),z * x) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7131,a(flip),b,7665,a),flip(a)].">
      <j1 rule="hyper" parents="320 7131 7665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7668">
    <literal><![CDATA[
      K(x,T(y,z * x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7131,a,b,7665,a)].">
      <j1 rule="hyper" parents="58 7131 7665"/>
    </justification>
  </clause>

  <clause id="7669">
    <literal><![CDATA[
      K(L(x,y,x),T(z,u)) = K(x,T(z,u * x))
    ]]></literal>
    <justification jstring="[hyper(320,a,7024,a,b,7668,a)].">
      <j1 rule="hyper" parents="320 7024 7668"/>
    </justification>
  </clause>

  <clause id="7670">
    <literal><![CDATA[
      K(x,T(y,z / x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),7668(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 7668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7671">
    <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),7668(a,1,2,2))].">
      <j1 rule="para" parents="80 7668"/>
    </justification>
  </clause>

  <clause id="7672">
    <literal><![CDATA[
      T(x,T(y,z / x)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7670,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 7670 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7673">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ x))
    ]]></literal>
    <justification jstring="[para(4412(a,1),7670(a,1,2))].">
      <j1 rule="para" parents="4412 7670"/>
    </justification>
  </clause>

  <clause id="7674">
    <literal><![CDATA[
      T(x \ y,T(z,y)) = T(x \ y,T(z,x))
    ]]></literal>
    <justification jstring="[para(72(a,1),7672(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 7672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7675">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7544,a,b,7656,a)].">
      <j1 rule="hyper" parents="320 7544 7656"/>
    </justification>
  </clause>

  <clause id="7676">
    <literal><![CDATA[
      T(K(x,y),z * L(K(u,x),w,v5)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(4782(a,1),7658(a,1,2,2))].">
      <j1 rule="para" parents="4782 7658"/>
    </justification>
  </clause>

  <clause id="7677">
    <literal><![CDATA[
      K(x,T(y \ x,T(z,y))) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(7674(a,1),7594(a,1,2))].">
      <j1 rule="para" parents="7674 7594"/>
    </justification>
  </clause>

  <clause id="7678">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7416(a,2),7159(a,1))].">
      <j1 rule="para" parents="7416 7159"/>
    </justification>
  </clause>

  <clause id="7679">
    <literal><![CDATA[
      K(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(4931(a,1),7196(a,1))].">
      <j1 rule="para" parents="4931 7196"/>
    </justification>
  </clause>

  <clause id="7680">
    <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(6758(a,2),7196(a,1))].">
      <j1 rule="para" parents="6758 7196"/>
    </justification>
  </clause>

  <clause id="7681">
    <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),7679(a,1,1))].">
      <j1 rule="para" parents="20 7679"/>
    </justification>
  </clause>

  <clause id="7682">
    <literal><![CDATA[
      (x * y) \ (T(x,z) * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6408(a,2),7679(a,1))].">
      <j1 rule="para" parents="6408 7679"/>
    </justification>
  </clause>

  <clause id="7683">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7118(a,1),7679(a,1))].">
      <j1 rule="para" parents="7118 7679"/>
    </justification>
  </clause>

  <clause id="7684">
    <literal><![CDATA[
      K((x \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7113(a,2),7679(a,1))].">
      <j1 rule="para" parents="7113 7679"/>
    </justification>
  </clause>

  <clause id="7685">
    <literal><![CDATA[
      K(x,T(y,x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7178(a,2),7679(a,1))].">
      <j1 rule="para" parents="7178 7679"/>
    </justification>
  </clause>

  <clause id="7686">
    <literal><![CDATA[
      K(x,y \ (z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ 1,y)) = u
    ]]></literal>
    <justification jstring="[para(7293(a,1),7679(a,1))].">
      <j1 rule="para" parents="7293 7679"/>
    </justification>
  </clause>

  <clause id="7687">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5505(a,2),7683(a,1))].">
      <j1 rule="para" parents="5505 7683"/>
    </justification>
  </clause>

  <clause id="7688">
    <literal><![CDATA[
      K(1 / T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5510(a,2),7683(a,1))].">
      <j1 rule="para" parents="5510 7683"/>
    </justification>
  </clause>

  <clause id="7689">
    <literal><![CDATA[
      K(x,T(y,x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7179(a,2),7683(a,1))].">
      <j1 rule="para" parents="7179 7683"/>
    </justification>
  </clause>

  <clause id="7690">
    <literal><![CDATA[
      T(K(x,y),z * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7667(a,2),7683(a,1))].">
      <j1 rule="para" parents="7667 7683"/>
    </justification>
  </clause>

  <clause id="7691">
    <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(6288(a,1),7229(a,1,2,1))].">
      <j1 rule="para" parents="6288 7229"/>
    </justification>
  </clause>

  <clause id="7693">
    <literal><![CDATA[
      K(x / y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5(a,1),7292(a,1,1,1))].">
      <j1 rule="para" parents="5 7292"/>
    </justification>
  </clause>

  <clause id="7694">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(17(a,1),7386(a,1,1,2))].">
      <j1 rule="para" parents="17 7386"/>
    </justification>
  </clause>

  <clause id="7695">
    <literal><![CDATA[
      T(x,L(y,z,K(u,x))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4951,a,b,7503,a),flip(a)].">
      <j1 rule="hyper" parents="320 4951 7503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7696">
    <literal><![CDATA[
      T(x,(K(y,x) * z) \ (K(y,x) * u)) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6601,a(flip),b,7695,a)].">
      <j1 rule="hyper" parents="58 6601 7695"/>
    </justification>
  </clause>

  <clause id="7697">
    <literal><![CDATA[
      T(x * y,T(z,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(6144(a,1),7551(a,1,2))].">
      <j1 rule="para" parents="6144 7551"/>
    </justification>
  </clause>

  <clause id="7698">
    <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),7596(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 7596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7699">
    <literal><![CDATA[
      K(x,T(y,z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7669(a,1),7367(a,1))].">
      <j1 rule="para" parents="7669 7367"/>
    </justification>
  </clause>

  <clause id="7700">
    <literal><![CDATA[
      T(K(x,y),x * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7131(a,1),7685(a,1))].">
      <j1 rule="para" parents="7131 7685"/>
    </justification>
  </clause>

  <clause id="7701">
    <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(4535(a,1),7693(a,1,1))].">
      <j1 rule="para" parents="4535 7693"/>
    </justification>
  </clause>

  <clause id="7702">
    <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(4886(a,2),7693(a,1,1))].">
      <j1 rule="para" parents="4886 7693"/>
    </justification>
  </clause>

  <clause id="7703">
    <literal><![CDATA[
      T(x \ (y / z),K(x,z)) = T(x,z) \ (y / T(z,x))
    ]]></literal>
    <justification jstring="[para(6293(a,1),7002(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6293 7002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7704">
    <literal><![CDATA[
      T(x / y,z) * T(y,K(x / y,z)) = x * K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,147,a(flip),b,7008,a),flip(a)].">
      <j1 rule="hyper" parents="320 147 7008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7705">
    <literal><![CDATA[
      (x * (y * T(x,z))) \ ((x * y) * T(x,z)) = a(x,y * K(x,z),x)
    ]]></literal>
    <justification jstring="[para(7011(a,1),6208(a,1,2))].">
      <j1 rule="para" parents="7011 6208"/>
    </justification>
  </clause>

  <clause id="7706">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * (u * K(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(7026(a,1),5695(a,2,2,2))].">
      <j1 rule="para" parents="7026 5695"/>
    </justification>
  </clause>

  <clause id="7707">
    <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(320,a,6373,a,b,7068,a)].">
      <j1 rule="hyper" parents="320 6373 7068"/>
    </justification>
  </clause>

  <clause id="7708">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(6345(a,2),7091(a,1,1))].">
      <j1 rule="para" parents="6345 7091"/>
    </justification>
  </clause>

  <clause id="7709">
    <literal><![CDATA[
      K(x,y) * ((z / y) * R(y,u,y)) = R(y,u,y) * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[para(7112(a,1),6017(a,1,2))].">
      <j1 rule="para" parents="7112 6017"/>
    </justification>
  </clause>

  <clause id="7710">
    <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(7155(a,2),793(a,1))].">
      <j1 rule="para" parents="7155 793"/>
    </justification>
  </clause>

  <clause id="7711">
    <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(717(a,1),7185(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="717 7185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7712">
    <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(1880(a,1),7185(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1880 7185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7713">
    <literal><![CDATA[
      K(R(T(x,K(y,z)),u,w),z) = K(R(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(2869(a,1),7185(a,2,2))].">
      <j1 rule="para" parents="2869 7185"/>
    </justification>
  </clause>

  <clause id="7714">
    <literal><![CDATA[
      (x \ y) * K(z,T(x,y)) = T(x,z) \ y
    ]]></literal>
    <justification jstring="[para(7070(a,1),7271(a,1,2))].">
      <j1 rule="para" parents="7070 7271"/>
    </justification>
  </clause>

  <clause id="7715">
    <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(214(a,1),7714(a,1,2,2))].">
      <j1 rule="para" parents="214 7714"/>
    </justification>
  </clause>

  <clause id="7716">
    <literal><![CDATA[
      (T(x,y) \ z) \ (x \ z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7714(a,1),7176(a,1,1))].">
      <j1 rule="para" parents="7714 7176"/>
    </justification>
  </clause>

  <clause id="7717">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(7276(a,2),6136(a,1))].">
      <j1 rule="para" parents="7276 6136"/>
    </justification>
  </clause>

  <clause id="7718">
    <literal><![CDATA[
      K(x \ y,z \ (x \ y)) * (y / x) = T(y / x,T((x * z) \ y,x))
    ]]></literal>
    <justification jstring="[para(6561(a,1),7290(a,1,1))].">
      <j1 rule="para" parents="6561 7290"/>
    </justification>
  </clause>

  <clause id="7719">
    <literal><![CDATA[
      K(x,T(y / (x * z),z)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7022,a(flip),b,7338,a),flip(a)].">
      <j1 rule="hyper" parents="320 7022 7338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7720">
    <literal><![CDATA[
      K(x * L(y,z,u),T(y,x)) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(5751,a,7342,a),flip(a)].">
      <j1 rule="hyper" parents="5751 7342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7721">
    <literal><![CDATA[
      T(x * y,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x * y,y) = z
    ]]></literal>
    <justification jstring="[para(7356(a,1),3011(a,1))].">
      <j1 rule="para" parents="7356 3011"/>
    </justification>
  </clause>

  <clause id="7722">
    <literal><![CDATA[
      T(T(x * K(y,z),u),T(z,y)) = T(T(K(y,z) * x,z),u)
    ]]></literal>
    <justification jstring="[para(7424(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7424 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7723">
    <literal><![CDATA[
      K(((x \ 1) \ y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(6670,a,7443,a)].">
      <j1 rule="hyper" parents="6670 7443"/>
    </justification>
  </clause>

  <clause id="7724">
    <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(7451(a,1),5072(a,1,2))].">
      <j1 rule="para" parents="7451 5072"/>
    </justification>
  </clause>

  <clause id="7725">
    <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(7452(a,1),7448(a,2,1))].">
      <j1 rule="para" parents="7452 7448"/>
    </justification>
  </clause>

  <clause id="7726">
    <literal><![CDATA[
      K(x,T(y,z \ (u * y))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(6565(a,1),7509(a,1,2))].">
      <j1 rule="para" parents="6565 7509"/>
    </justification>
  </clause>

  <clause id="7727">
    <literal><![CDATA[
      K(x,K(y,z)) * T(x,y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7413,a(flip),b,7523,a),flip(a)].">
      <j1 rule="hyper" parents="320 7413 7523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7728">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(30,a,7513,a,b,7727,a)].">
      <j1 rule="hyper" parents="30 7513 7727"/>
    </justification>
  </clause>

  <clause id="7729">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(30,a,6493,a,b,7727,a)].">
      <j1 rule="hyper" parents="30 6493 7727"/>
    </justification>
  </clause>

  <clause id="7730">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5591,a,7728,a)].">
      <j1 rule="hyper" parents="5591 7728"/>
    </justification>
  </clause>

  <clause id="7731">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,7514,a,b,7728,a)].">
      <j1 rule="hyper" parents="320 7514 7728"/>
    </justification>
  </clause>

  <clause id="7732">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,7728,a,b,4688,a(flip))].">
      <j1 rule="hyper" parents="119 7728 4688"/>
    </justification>
  </clause>

  <clause id="7733">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,K(x,z)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7728,a,b,11,a(flip))].">
      <j1 rule="hyper" parents="119 7728 11"/>
    </justification>
  </clause>

  <clause id="7734">
    <literal><![CDATA[
      K(x,K(y,z)) \ K(y,x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(7728(a,1),4749(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7728 4749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7735">
    <literal><![CDATA[
      K(x,K(y,z)) \ K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(y,x),z) = u
    ]]></literal>
    <justification jstring="[para(7728(a,1),4824(a,1,1))].">
      <j1 rule="para" parents="7728 4824"/>
    </justification>
  </clause>

  <clause id="7736">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(7728(a,1),5585(a,1,1))].">
      <j1 rule="para" parents="7728 5585"/>
    </justification>
  </clause>

  <clause id="7737">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(7728(a,1),5591(a,1))].">
      <j1 rule="para" parents="7728 5591"/>
    </justification>
  </clause>

  <clause id="7738">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7728(a,1),5587(a,1,2))].">
      <j1 rule="para" parents="7728 5587"/>
    </justification>
  </clause>

  <clause id="7739">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7728(a,1),5588(a,1,1))].">
      <j1 rule="para" parents="7728 5588"/>
    </justification>
  </clause>

  <clause id="7740">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7728(a,1),7139(a,1,1))].">
      <j1 rule="para" parents="7728 7139"/>
    </justification>
  </clause>

  <clause id="7741">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7728(a,1),7140(a,1,2))].">
      <j1 rule="para" parents="7728 7140"/>
    </justification>
  </clause>

  <clause id="7742">
    <literal><![CDATA[
      K(K(R(x \ 1,y,z) \ 1,u),w) = R(K(x,K(u,w)),y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5673,a(flip),b,7730,a),flip(a)].">
      <j1 rule="hyper" parents="320 5673 7730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7743">
    <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,6894,a,b,7730,a)].">
      <j1 rule="hyper" parents="58 6894 7730"/>
    </justification>
  </clause>

  <clause id="7744">
    <literal><![CDATA[
      (x / y) * K(z,K(u,y)) = x / T(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,7730,a(flip),b,6335,a)].">
      <j1 rule="hyper" parents="119 7730 6335"/>
    </justification>
  </clause>

  <clause id="7745">
    <literal><![CDATA[
      (x * K(y,z)) * K(y,K(z,u)) = x * T(K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(119,a,7730,a(flip),b,6124,a)].">
      <j1 rule="hyper" parents="119 7730 6124"/>
    </justification>
  </clause>

  <clause id="7746">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(7730(a,1),4725(a,1,2))].">
      <j1 rule="para" parents="7730 4725"/>
    </justification>
  </clause>

  <clause id="7747">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ u) = T(z,K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(7730(a,1),5093(a,1,1))].">
      <j1 rule="para" parents="7730 5093"/>
    </justification>
  </clause>

  <clause id="7748">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) \ u = w
    ]]></literal>
    <justification jstring="[para(7730(a,1),5142(a,1,1))].">
      <j1 rule="para" parents="7730 5142"/>
    </justification>
  </clause>

  <clause id="7749">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(7730(a,1),5617(a,1))].">
      <j1 rule="para" parents="7730 5617"/>
    </justification>
  </clause>

  <clause id="7750">
    <literal><![CDATA[
      K(L(K(x,y),z,u) \ 1,w) = L(K(y,K(x,w)),z,u)
    ]]></literal>
    <justification jstring="[para(7730(a,1),5654(a,2,1))].">
      <j1 rule="para" parents="7730 5654"/>
    </justification>
  </clause>

  <clause id="7751">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(7316(a,1),7730(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7316 7730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7752">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7728,a,b,7731,a)].">
      <j1 rule="hyper" parents="58 7728 7731"/>
    </justification>
  </clause>

  <clause id="7753">
    <literal><![CDATA[
      K(x,T(y,T(z,K(u,x)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7732(a,1),7644(a,1,2,2))].">
      <j1 rule="para" parents="7732 7644"/>
    </justification>
  </clause>

  <clause id="7754">
    <literal><![CDATA[
      K(x,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(5589,a,7736,a)].">
      <j1 rule="hyper" parents="5589 7736"/>
    </justification>
  </clause>

  <clause id="7755">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(4945,a,7736,a)].">
      <j1 rule="hyper" parents="4945 7736"/>
    </justification>
  </clause>

  <clause id="7756">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7736(a,1),5589(a,1))].">
      <j1 rule="para" parents="7736 5589"/>
    </justification>
  </clause>

  <clause id="7757">
    <literal><![CDATA[
      K(x,K(x * y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(7516,a,7754,a),flip(a)].">
      <j1 rule="hyper" parents="7516 7754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7758">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7730,a,b,7754,a)].">
      <j1 rule="hyper" parents="320 7730 7754"/>
    </justification>
  </clause>

  <clause id="7759">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7728,a,b,7754,a),flip(a)].">
      <j1 rule="hyper" parents="320 7728 7754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7760">
    <literal><![CDATA[
      x * K(y,K(x,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7754,a,b,4688,a(flip))].">
      <j1 rule="hyper" parents="119 7754 4688"/>
    </justification>
  </clause>

  <clause id="7761">
    <literal><![CDATA[
      K(x,K(y,z)) * y = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(7754(a,1),4729(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7754 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7762">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * u) = T(y,K(x,z)) * u
    ]]></literal>
    <justification jstring="[para(7754(a,1),4740(a,1,1))].">
      <j1 rule="para" parents="7754 4740"/>
    </justification>
  </clause>

  <clause id="7763">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(y,K(x,y * z))
    ]]></literal>
    <justification jstring="[para(5346(a,2),7754(a,1,2))].">
      <j1 rule="para" parents="5346 7754"/>
    </justification>
  </clause>

  <clause id="7764">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,K(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7754(a,1),5002(a,1,1))].">
      <j1 rule="para" parents="7754 5002"/>
    </justification>
  </clause>

  <clause id="7765">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7754(a,1),5587(a,1,2))].">
      <j1 rule="para" parents="7754 5587"/>
    </justification>
  </clause>

  <clause id="7766">
    <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(7754(a,1),5170(a,1,2))].">
      <j1 rule="para" parents="7754 5170"/>
    </justification>
  </clause>

  <clause id="7767">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[para(7239(a,1),7754(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7239 7754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7768">
    <literal><![CDATA[
      K(x,K(y,L(z,u,K(x,w)))) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(7482(a,1),7754(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7482 7754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7769">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7754(a,1),7732(a,1,2))].">
      <j1 rule="para" parents="7754 7732"/>
    </justification>
  </clause>

  <clause id="7770">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7728,a,b,7755,a),flip(a)].">
      <j1 rule="hyper" parents="320 7728 7755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7771">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7728,a,b,7758,a),flip(a)].">
      <j1 rule="hyper" parents="320 7728 7758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7772">
    <literal><![CDATA[
      K(x,K(y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7755,a(flip),b,7758,a)].">
      <j1 rule="hyper" parents="58 7755 7758"/>
    </justification>
  </clause>

  <clause id="7773">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * K(y,x)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(7758(a,1),4772(a,1,1))].">
      <j1 rule="para" parents="7758 4772"/>
    </justification>
  </clause>

  <clause id="7774">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(7758(a,1),5617(a,1))].">
      <j1 rule="para" parents="7758 5617"/>
    </justification>
  </clause>

  <clause id="7775">
    <literal><![CDATA[
      K(x,K(R(y \ 1,z,u) \ 1,w)) = K(R(K(y,x),z,u),w)
    ]]></literal>
    <justification jstring="[para(5673(a,1),7758(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5673 7758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7776">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7758(a,2),7732(a,1,2))].">
      <j1 rule="para" parents="7758 7732"/>
    </justification>
  </clause>

  <clause id="7777">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7161,a,b,7759,a)].">
      <j1 rule="hyper" parents="320 7161 7759"/>
    </justification>
  </clause>

  <clause id="7778">
    <literal><![CDATA[
      K(x,K(y,x \ z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7515,a(flip),b,7759,a),flip(a)].">
      <j1 rule="hyper" parents="320 7515 7759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7779">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7514,a(flip),b,7759,a),flip(a)].">
      <j1 rule="hyper" parents="320 7514 7759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7780">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(119,a,7759,a,b,7736,a)].">
      <j1 rule="hyper" parents="119 7759 7736"/>
    </justification>
  </clause>

  <clause id="7781">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,(x \ 1) \ y))
    ]]></literal>
    <justification jstring="[hyper(119,a,7759,a,b,6381,a),flip(a)].">
      <j1 rule="hyper" parents="119 7759 6381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7782">
    <literal><![CDATA[
      x * T(x \ y,K(z,u)) = y * K(z,K(u,x \ y))
    ]]></literal>
    <justification jstring="[hyper(119,a,7759,a,b,6081,a),flip(a)].">
      <j1 rule="hyper" parents="119 7759 6081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7783">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(7759(a,2),4729(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7759 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7784">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) * u = w
    ]]></literal>
    <justification jstring="[para(7759(a,2),5002(a,1,1))].">
      <j1 rule="para" parents="7759 5002"/>
    </justification>
  </clause>

  <clause id="7785">
    <literal><![CDATA[
      K(x,y) * K(x,K(z,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7759(a,1),5587(a,1,2))].">
      <j1 rule="para" parents="7759 5587"/>
    </justification>
  </clause>

  <clause id="7786">
    <literal><![CDATA[
      x * L(K(y,K(z,x)),u,w) = T(x,L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(7759(a,2),5720(a,1,2,1))].">
      <j1 rule="para" parents="7759 5720"/>
    </justification>
  </clause>

  <clause id="7787">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / (u / z)) \ 1)) * (u / z) = T(u,K(x,y)) / z
    ]]></literal>
    <justification jstring="[para(7759(a,2),5702(a,1,1))].">
      <j1 rule="para" parents="7759 5702"/>
    </justification>
  </clause>

  <clause id="7788">
    <literal><![CDATA[
      (x * K(y,K(z,u))) / K(y,z) = x / T(K(y,z),u)
    ]]></literal>
    <justification jstring="[para(7759(a,2),6313(a,1,1,2))].">
      <j1 rule="para" parents="7759 6313"/>
    </justification>
  </clause>

  <clause id="7789">
    <literal><![CDATA[
      (x * K(y,K(z,u \ x))) / u = T(x / u,K(y,z))
    ]]></literal>
    <justification jstring="[para(7759(a,2),6250(a,1,1,2))].">
      <j1 rule="para" parents="7759 6250"/>
    </justification>
  </clause>

  <clause id="7790">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,T(y,u)))
    ]]></literal>
    <justification jstring="[para(7133(a,1),7759(a,1,2))].">
      <j1 rule="para" parents="7133 7759"/>
    </justification>
  </clause>

  <clause id="7791">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7759(a,1),7139(a,1,1))].">
      <j1 rule="para" parents="7759 7139"/>
    </justification>
  </clause>

  <clause id="7792">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(7759(a,2),7139(a,1,1))].">
      <j1 rule="para" parents="7759 7139"/>
    </justification>
  </clause>

  <clause id="7793">
    <literal><![CDATA[
      K(x,y) * K(x,K(z,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7759(a,1),7140(a,1,2))].">
      <j1 rule="para" parents="7759 7140"/>
    </justification>
  </clause>

  <clause id="7794">
    <literal><![CDATA[
      K(x,K(y,z)) / y = 1 / T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(117,a,7770,a(flip),b,4754,a(flip))].">
      <j1 rule="hyper" parents="117 7770 4754"/>
    </justification>
  </clause>

  <clause id="7795">
    <literal><![CDATA[
      K(x,K(y,z)) * (y \ u) = T(y,K(x,z)) \ u
    ]]></literal>
    <justification jstring="[para(7770(a,1),5093(a,1,1))].">
      <j1 rule="para" parents="7770 5093"/>
    </justification>
  </clause>

  <clause id="7796">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7770(a,1),5617(a,1))].">
      <j1 rule="para" parents="7770 5617"/>
    </justification>
  </clause>

  <clause id="7797">
    <literal><![CDATA[
      K(x,y) \ K(K(x,y),z) = T(K(x,y),z) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,7771,a,b,4755,a(flip))].">
      <j1 rule="hyper" parents="116 7771 4755"/>
    </justification>
  </clause>

  <clause id="7798">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,K(y,z)) * u) = u
    ]]></literal>
    <justification jstring="[hyper(118,a,7771,a(flip),b,5104,a),flip(a)].">
      <j1 rule="hyper" parents="118 7771 5104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7799">
    <literal><![CDATA[
      K(x,K(y,z)) \ u = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(7771(a,1),5092(a,1,1))].">
      <j1 rule="para" parents="7771 5092"/>
    </justification>
  </clause>

  <clause id="7800">
    <literal><![CDATA[
      x * (T(x,K(y,z)) \ u) = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(7771(a,1),4777(a,2,1))].">
      <j1 rule="para" parents="7771 4777"/>
    </justification>
  </clause>

  <clause id="7801">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ u) = T(x,K(y,z)) \ u
    ]]></literal>
    <justification jstring="[para(7771(a,1),5093(a,1,1))].">
      <j1 rule="para" parents="7771 5093"/>
    </justification>
  </clause>

  <clause id="7802">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) * w = u
    ]]></literal>
    <justification jstring="[para(7771(a,1),5109(a,1,1))].">
      <j1 rule="para" parents="7771 5109"/>
    </justification>
  </clause>

  <clause id="7803">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,K(y,z)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(7771(a,1),5111(a,1,1))].">
      <j1 rule="para" parents="7771 5111"/>
    </justification>
  </clause>

  <clause id="7804">
    <literal><![CDATA[
      K(x,K(y,z)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7771(a,1),5125(a,1,1))].">
      <j1 rule="para" parents="7771 5125"/>
    </justification>
  </clause>

  <clause id="7805">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(7771(a,1),5129(a,1,1))].">
      <j1 rule="para" parents="7771 5129"/>
    </justification>
  </clause>

  <clause id="7806">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7771(a,1),5617(a,1))].">
      <j1 rule="para" parents="7771 5617"/>
    </justification>
  </clause>

  <clause id="7807">
    <literal><![CDATA[
      T(x,K(y,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,7772,a,b,5368,a)].">
      <j1 rule="hyper" parents="118 7772 5368"/>
    </justification>
  </clause>

  <clause id="7808">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,L(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(7772(a,1),5718(a,1,1))].">
      <j1 rule="para" parents="7772 5718"/>
    </justification>
  </clause>

  <clause id="7809">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / (u / z)) \ 1)) = K(x,(T(u,y) / z) / (u / z))
    ]]></literal>
    <justification jstring="[para(5880(a,1),7772(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5880 7772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7810">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,T(K(z,y),u))
    ]]></literal>
    <justification jstring="[para(7118(a,1),7772(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7118 7772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7811">
    <literal><![CDATA[
      K(x,y) * K(z,K(x,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7772(a,1),7140(a,1,2))].">
      <j1 rule="para" parents="7772 7140"/>
    </justification>
  </clause>

  <clause id="7812">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7678,a,7807,a),flip(a)].">
      <j1 rule="hyper" parents="7678 7807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7813">
    <literal><![CDATA[
      T(T(x * K(y,z),u),K(y,z)) = T(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(6677,a,7807,a)].">
      <j1 rule="hyper" parents="6677 7807"/>
    </justification>
  </clause>

  <clause id="7814">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6522,a,7807,a)].">
      <j1 rule="hyper" parents="6522 7807"/>
    </justification>
  </clause>

  <clause id="7815">
    <literal><![CDATA[
      T(x * y,K(z,y)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6512,a,7807,a),flip(a)].">
      <j1 rule="hyper" parents="6512 7807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7816">
    <literal><![CDATA[
      T(x * K(y,z),K(y,z)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(6422,a,7807,a),flip(a)].">
      <j1 rule="hyper" parents="6422 7807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7817">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6366,a,7807,a),flip(a)].">
      <j1 rule="hyper" parents="6366 7807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7818">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(5601,a,7807,a)].">
      <j1 rule="hyper" parents="5601 7807"/>
    </justification>
  </clause>

  <clause id="7819">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(5251,a,7807,a)].">
      <j1 rule="hyper" parents="5251 7807"/>
    </justification>
  </clause>

  <clause id="7820">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) = T(T(x,u),K(z,y))
    ]]></literal>
    <justification jstring="[hyper(435,a,7807,a)].">
      <j1 rule="hyper" parents="435 7807"/>
    </justification>
  </clause>

  <clause id="7821">
    <literal><![CDATA[
      T(x \ y,K(z,x)) = x \ T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7565,a(flip),b,7807,a),flip(a)].">
      <j1 rule="hyper" parents="320 7565 7807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7822">
    <literal><![CDATA[
      K(x,y) * T(z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7807,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7807 17"/>
    </justification>
  </clause>

  <clause id="7823">
    <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(7807(a,1),435(a,1,1))].">
      <j1 rule="para" parents="7807 435"/>
    </justification>
  </clause>

  <clause id="7824">
    <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(7807(a,1),435(a,1))].">
      <j1 rule="para" parents="7807 435"/>
    </justification>
  </clause>

  <clause id="7825">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(7807(a,1),5595(a,1,1))].">
      <j1 rule="para" parents="7807 5595"/>
    </justification>
  </clause>

  <clause id="7826">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(u,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(7807(a,1),5601(a,1))].">
      <j1 rule="para" parents="7807 5601"/>
    </justification>
  </clause>

  <clause id="7827">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[para(7807(a,1),5594(a,1,1))].">
      <j1 rule="para" parents="7807 5594"/>
    </justification>
  </clause>

  <clause id="7828">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7807(a,1),6366(a,1))].">
      <j1 rule="para" parents="7807 6366"/>
    </justification>
  </clause>

  <clause id="7829">
    <literal><![CDATA[
      T(x,L(K(y,z),T(z,u),w)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(7300(a,2),7807(a,1,2))].">
      <j1 rule="para" parents="7300 7807"/>
    </justification>
  </clause>

  <clause id="7830">
    <literal><![CDATA[
      T(T(x,K(y,z)),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7807(a,1),7415(a,1,1))].">
      <j1 rule="para" parents="7807 7415"/>
    </justification>
  </clause>

  <clause id="7831">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7807(a,1),7422(a,1,1))].">
      <j1 rule="para" parents="7807 7422"/>
    </justification>
  </clause>

  <clause id="7832">
    <literal><![CDATA[
      T(x * y,K(x,z)) = x * T(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(7807(a,1),7567(a,2,2))].">
      <j1 rule="para" parents="7807 7567"/>
    </justification>
  </clause>

  <clause id="7833">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7807(a,1),7678(a,1))].">
      <j1 rule="para" parents="7807 7678"/>
    </justification>
  </clause>

  <clause id="7834">
    <literal><![CDATA[
      T(K(x,y) \ z,K(x,y)) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(6421,a,7818,a),flip(a)].">
      <j1 rule="hyper" parents="6421 7818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7835">
    <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(799,a,7818,a)].">
      <j1 rule="hyper" parents="799 7818"/>
    </justification>
  </clause>

  <clause id="7836">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(681,a,7818,a),flip(a)].">
      <j1 rule="hyper" parents="681 7818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7837">
    <literal><![CDATA[
      T(x * (y * K(x,z)),K(x,z)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(35,a,7009,a,b,7818,a),flip(a)].">
      <j1 rule="hyper" parents="35 7009 7818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7838">
    <literal><![CDATA[
      T(K(x,y),z) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7818,a(flip),b,4393,a)].">
      <j1 rule="hyper" parents="119 7818 4393"/>
    </justification>
  </clause>

  <clause id="7839">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) != u
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(7818(a,1),331(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="7818 331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7840">
    <literal><![CDATA[
      (x * K(y,z)) / x = T(K(y,z),x)
    ]]></literal>
    <justification jstring="[para(7818(a,1),4392(a,1,2))].">
      <j1 rule="para" parents="7818 4392"/>
    </justification>
  </clause>

  <clause id="7841">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7818(a,1),5595(a,1,1))].">
      <j1 rule="para" parents="7818 5595"/>
    </justification>
  </clause>

  <clause id="7842">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7772,a,b,7752,a),flip(a)].">
      <j1 rule="hyper" parents="320 7772 7752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7843">
    <literal><![CDATA[
      K(x,K(y,z / y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),7752(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 7752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7844">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5346(a,1),7752(a,1,2))].">
      <j1 rule="para" parents="5346 7752"/>
    </justification>
  </clause>

  <clause id="7845">
    <literal><![CDATA[
      K(x,K(x * y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7754,a,b,7757,a),flip(a)].">
      <j1 rule="hyper" parents="320 7754 7757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7846">
    <literal><![CDATA[
      T(x,y * T(z,K(x,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(7760(a,1),7371(a,1,2,2))].">
      <j1 rule="para" parents="7760 7371"/>
    </justification>
  </clause>

  <clause id="7847">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * K(z,u)) = T(y * K(z,u),K(x,z))
    ]]></literal>
    <justification jstring="[para(7313(a,1),7761(a,1,1,2))].">
      <j1 rule="para" parents="7313 7761"/>
    </justification>
  </clause>

  <clause id="7848">
    <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,5134,a(flip),b,7769,a),flip(a)].">
      <j1 rule="hyper" parents="58 5134 7769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7849">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u) = R(x,K(y,z),T(u,K(y,z)))
    ]]></literal>
    <justification jstring="[para(7776(a,1),6669(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7776 6669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7850">
    <literal><![CDATA[
      K(x,K(y,x \ z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7759,a,b,7778,a),flip(a)].">
      <j1 rule="hyper" parents="320 7759 7778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7851">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7759,a,b,7779,a),flip(a)].">
      <j1 rule="hyper" parents="320 7759 7779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7852">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7754,a,b,7779,a),flip(a)].">
      <j1 rule="hyper" parents="320 7754 7779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7853">
    <literal><![CDATA[
      T(T(K(x,y),z),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(167,a,5526,a,b,7780,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 5526 7780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7854">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7156,a,7853,a),flip(a)].">
      <j1 rule="hyper" parents="7156 7853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7855">
    <literal><![CDATA[
      T(K(x \ y,z),y) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(6262,a,7853,a),flip(a)].">
      <j1 rule="hyper" parents="6262 7853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7856">
    <literal><![CDATA[
      T(K(x,y \ z),z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(6116,a,7853,a),flip(a)].">
      <j1 rule="hyper" parents="6116 7853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7857">
    <literal><![CDATA[
      T(K(1 / T(x,y),z),y) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(5512,a,7853,a),flip(a)].">
      <j1 rule="hyper" parents="5512 7853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7858">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7511,a,b,7853,a)].">
      <j1 rule="hyper" parents="58 7511 7853"/>
    </justification>
  </clause>

  <clause id="7859">
    <literal><![CDATA[
      T(x,y) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      T(K(z,u),y) = x
    ]]></literal>
    <justification jstring="[para(7853(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="7853 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7860">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) * z = z * L(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7853(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7853 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7861">
    <literal><![CDATA[
      R(T(K(x,y),z),u,w) * z = z * R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7853(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7853 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7862">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) \ (z * L(K(x,y),u,w)) = z
    ]]></literal>
    <justification jstring="[para(7853(a,1),274(a,1,2,2,1))].">
      <j1 rule="para" parents="7853 274"/>
    </justification>
  </clause>

  <clause id="7863">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(7385,a,7854,a)].">
      <j1 rule="hyper" parents="7385 7854"/>
    </justification>
  </clause>

  <clause id="7864">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(6475,a,7854,a)].">
      <j1 rule="hyper" parents="6475 7854"/>
    </justification>
  </clause>

  <clause id="7865">
    <literal><![CDATA[
      K(x,T(y \ z,z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(6116,a,7854,a),flip(a)].">
      <j1 rule="hyper" parents="6116 7854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7866">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,y)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(5712,a,7854,a),flip(a)].">
      <j1 rule="hyper" parents="5712 7854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7867">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(z,y)) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(5507,a,7854,a)].">
      <j1 rule="hyper" parents="5507 7854"/>
    </justification>
  </clause>

  <clause id="7868">
    <literal><![CDATA[
      (x * K(y,z)) / x = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(271,a,7854,a)].">
      <j1 rule="hyper" parents="271 7854"/>
    </justification>
  </clause>

  <clause id="7870">
    <literal><![CDATA[
      K(x \ K(x,y),z) = K(x \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6654,a(flip),b,7854,a),flip(a)].">
      <j1 rule="hyper" parents="58 6654 7854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7871">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),z)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,7154,a(flip),b,7854,a),flip(a)].">
      <j1 rule="hyper" parents="35 7154 7854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7872">
    <literal><![CDATA[
      K(x,T(y,z)) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7854,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 7854 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7873">
    <literal><![CDATA[
      T(x,y) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      K(z,T(u,y)) = x
    ]]></literal>
    <justification jstring="[para(7854(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="7854 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7874">
    <literal><![CDATA[
      T(K(x,y \ z),y) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7854(a,1,1,2))].">
      <j1 rule="para" parents="107 7854"/>
    </justification>
  </clause>

  <clause id="7875">
    <literal><![CDATA[
      K(x,T(y,z)) \ (z * K(x,y)) = z
    ]]></literal>
    <justification jstring="[para(7854(a,1),226(a,1,2,2))].">
      <j1 rule="para" parents="7854 226"/>
    </justification>
  </clause>

  <clause id="7876">
    <literal><![CDATA[
      x * K(y,z) != u * x
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7854(a,1),241(a,1,2))].">
      <j1 rule="para" parents="7854 241"/>
    </justification>
  </clause>

  <clause id="7877">
    <literal><![CDATA[
      R(K(x,T(y,z)),u,w) * z = z * R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7854(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7854 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7878">
    <literal><![CDATA[
      (K(x,T(y,z * u)) * z) * u = (z * u) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(7854(a,1),638(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7854 638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7879">
    <literal><![CDATA[
      (K(x,T(y,z)) * u) * (u \ z) = z * R(K(x,y),u,u \ z)
    ]]></literal>
    <justification jstring="[para(7854(a,1),726(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7854 726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7880">
    <literal><![CDATA[
      T(K(x \ y,z),x) = K(y / x,z)
    ]]></literal>
    <justification jstring="[para(7186(a,1),7854(a,1,1))].">
      <j1 rule="para" parents="7186 7854"/>
    </justification>
  </clause>

  <clause id="7881">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7854(a,1),7124(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7854 7124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7882">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(7693,a,7858,a)].">
      <j1 rule="hyper" parents="7693 7858"/>
    </justification>
  </clause>

  <clause id="7883">
    <literal><![CDATA[
      K((x * y) / x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(7292,a,7858,a),flip(a)].">
      <j1 rule="hyper" parents="7292 7858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7884">
    <literal><![CDATA[
      T(x,T(T(y,z),z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7858,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 7858 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7885">
    <literal><![CDATA[
      K(R(T(x,y),z,u),T(w,y)) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,7185,a,b,7858,a)].">
      <j1 rule="hyper" parents="58 7185 7858"/>
    </justification>
  </clause>

  <clause id="7886">
    <literal><![CDATA[
      K(L(T(x,y),z,u),T(w,y)) = K(L(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,7184,a,b,7858,a)].">
      <j1 rule="hyper" parents="58 7184 7858"/>
    </justification>
  </clause>

  <clause id="7887">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(x,T(T(z,u),u * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7669,a(flip),b,7858,a),flip(a)].">
      <j1 rule="hyper" parents="58 7669 7858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7888">
    <literal><![CDATA[
      K(x,T(y \ z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7858(a,1,2,1))].">
      <j1 rule="para" parents="107 7858"/>
    </justification>
  </clause>

  <clause id="7889">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(224(a,1),7858(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="224 7858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7890">
    <literal><![CDATA[
      K(x,T(T(T(y,z),z),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(109(a,2),7858(a,1,2))].">
      <j1 rule="para" parents="109 7858"/>
    </justification>
  </clause>

  <clause id="7891">
    <literal><![CDATA[
      K(x,y * K(z,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4775(a,1),7858(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4775 7858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7892">
    <literal><![CDATA[
      K((x * y) / x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7858(a,1),7292(a,1))].">
      <j1 rule="para" parents="7858 7292"/>
    </justification>
  </clause>

  <clause id="7893">
    <literal><![CDATA[
      K(x / (x / y),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(7369,a,7863,a),flip(a)].">
      <j1 rule="hyper" parents="7369 7863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7894">
    <literal><![CDATA[
      x * K(T(x,y),T(z,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,7863,a,b,4688,a(flip))].">
      <j1 rule="hyper" parents="119 7863 4688"/>
    </justification>
  </clause>

  <clause id="7896">
    <literal><![CDATA[
      K(x,T(y,z)) \ z = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7863,a(flip),b,7143,a),flip(a)].">
      <j1 rule="hyper" parents="119 7863 7143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7897">
    <literal><![CDATA[
      K(T(T(x,y),z),T(u,y)) = K(T(x,z),u)
    ]]></literal>
    <justification jstring="[para(18(a,1),7863(a,1,1))].">
      <j1 rule="para" parents="18 7863"/>
    </justification>
  </clause>

  <clause id="7898">
    <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),7863(a,1,2))].">
      <j1 rule="para" parents="20 7863"/>
    </justification>
  </clause>

  <clause id="7899">
    <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),7863(a,1,2))].">
      <j1 rule="para" parents="22 7863"/>
    </justification>
  </clause>

  <clause id="7900">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7863(a,1,2))].">
      <j1 rule="para" parents="107 7863"/>
    </justification>
  </clause>

  <clause id="7901">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(224(a,1),7863(a,1,2)),flip(a)].">
      <j1 rule="para" parents="224 7863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7902">
    <literal><![CDATA[
      K(T(x,y),R(T(z,y * u),y,u)) = K(x,(y * u) \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(1088(a,1),7863(a,1,2))].">
      <j1 rule="para" parents="1088 7863"/>
    </justification>
  </clause>

  <clause id="7903">
    <literal><![CDATA[
      K(T(x,y \ z),y) = K(x,z / (z / y))
    ]]></literal>
    <justification jstring="[para(4305(a,1),7863(a,1,2))].">
      <j1 rule="para" parents="4305 7863"/>
    </justification>
  </clause>

  <clause id="7904">
    <literal><![CDATA[
      L(x,K(y,z),T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(7863(a,1),4474(a,1,2))].">
      <j1 rule="para" parents="7863 4474"/>
    </justification>
  </clause>

  <clause id="7905">
    <literal><![CDATA[
      K(x * K(y,x),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(4775(a,1),7863(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4775 7863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7906">
    <literal><![CDATA[
      K(x,y * K(z,y)) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(4775(a,1),7863(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4775 7863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7907">
    <literal><![CDATA[
      T(x * K(T(y,z),x),z) = K(y,x) * T(x,z)
    ]]></literal>
    <justification jstring="[para(7863(a,1),5163(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7863 5163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7908">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) \ x = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7863(a,1),5191(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7863 5191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7909">
    <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(7863(a,1),6015(a,1,1))].">
      <j1 rule="para" parents="7863 6015"/>
    </justification>
  </clause>

  <clause id="7910">
    <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(7863(a,1),6928(a,1,1))].">
      <j1 rule="para" parents="7863 6928"/>
    </justification>
  </clause>

  <clause id="7911">
    <literal><![CDATA[
      K(T(x,y),z) * y = y * K(x,z)
    ]]></literal>
    <justification jstring="[para(7863(a,1),7152(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7863 7152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7912">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(y,x)) = z
    ]]></literal>
    <justification jstring="[para(7863(a,1),7264(a,1,2,2))].">
      <j1 rule="para" parents="7863 7264"/>
    </justification>
  </clause>

  <clause id="7913">
    <literal><![CDATA[
      K(x / (x / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7863(a,1),7369(a,1))].">
      <j1 rule="para" parents="7863 7369"/>
    </justification>
  </clause>

  <clause id="7914">
    <literal><![CDATA[
      L(x,K(y / z,u),z \ y) = x
    ]]></literal>
    <justification jstring="[para(107(a,1),7904(a,1,3))].">
      <j1 rule="para" parents="107 7904"/>
    </justification>
  </clause>

  <clause id="7915">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * x) = z * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7884,a(flip),b,7637,a),flip(a)].">
      <j1 rule="hyper" parents="119 7884 7637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7916">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = K(x,y) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,7884,a(flip),b,7522,a),flip(a)].">
      <j1 rule="hyper" parents="119 7884 7522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7917">
    <literal><![CDATA[
      T(x,T(y \ z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7884(a,1,2,1))].">
      <j1 rule="para" parents="107 7884"/>
    </justification>
  </clause>

  <clause id="7918">
    <literal><![CDATA[
      T(x,(y * z) / y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(224(a,1),7884(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="224 7884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7919">
    <literal><![CDATA[
      T(x,T(T(y \ z,u),y)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(246(a,1),7884(a,1,2,1))].">
      <j1 rule="para" parents="246 7884"/>
    </justification>
  </clause>

  <clause id="7920">
    <literal><![CDATA[
      T(x,y * K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4775(a,1),7884(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4775 7884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7921">
    <literal><![CDATA[
      L(x,K(y \ 1,z),u \ (y \ u)) = x
    ]]></literal>
    <justification jstring="[para(5396(a,1),7914(a,1,2))].">
      <j1 rule="para" parents="5396 7914"/>
    </justification>
  </clause>

  <clause id="7922">
    <literal><![CDATA[
      T(x,K(y,z)) * (x \ z) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(4743,a,7783,a)].">
      <j1 rule="hyper" parents="4743 7783"/>
    </justification>
  </clause>

  <clause id="7923">
    <literal><![CDATA[
      T(T(x,y / z),K(y,y / z)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7065,a(flip),b,7812,a),flip(a)].">
      <j1 rule="hyper" parents="320 7065 7812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7924">
    <literal><![CDATA[
      T(x,K(y,z)) * z = z * T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,7812,a(flip),b,108,a),flip(a)].">
      <j1 rule="hyper" parents="119 7812 108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7925">
    <literal><![CDATA[
      T(x,T(y,z)) * K(y,z) = K(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7812(a,1),5594(a,1,1))].">
      <j1 rule="para" parents="7812 5594"/>
    </justification>
  </clause>

  <clause id="7926">
    <literal><![CDATA[
      T(T(x,y) * z,K(z,y)) = T(x,T(y,z)) * z
    ]]></literal>
    <justification jstring="[para(7812(a,1),7615(a,2,1))].">
      <j1 rule="para" parents="7812 7615"/>
    </justification>
  </clause>

  <clause id="7927">
    <literal><![CDATA[
      T(T(x,y) \ z,K(x,y)) = T(z / T(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(678,a,7831,a)].">
      <j1 rule="hyper" parents="678 7831"/>
    </justification>
  </clause>

  <clause id="7928">
    <literal><![CDATA[
      T(x,T(y,z)) != T(u,y)
    ]]></literal>
    <literal><![CDATA[
      T(u,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(7831(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="7831 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7929">
    <literal><![CDATA[
      K(x \ y,z) * y = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(6239(a,1),7838(a,1,1))].">
      <j1 rule="para" parents="6239 7838"/>
    </justification>
  </clause>

  <clause id="7930">
    <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(7840(a,1),4859(a,1,2,1))].">
      <j1 rule="para" parents="7840 4859"/>
    </justification>
  </clause>

  <clause id="7931">
    <literal><![CDATA[
      T(x,K(y,z * y)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,7842,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 7842 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7932">
    <literal><![CDATA[
      T(x,K(y,z / y)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7843,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 7843 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7933">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z \ y))
    ]]></literal>
    <justification jstring="[para(4441(a,1),7843(a,1,2))].">
      <j1 rule="para" parents="4441 7843"/>
    </justification>
  </clause>

  <clause id="7934">
    <literal><![CDATA[
      K(x,K(y,y \ z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4871(a,1),7843(a,1,2))].">
      <j1 rule="para" parents="4871 7843"/>
    </justification>
  </clause>

  <clause id="7935">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,7759,a,b,7844,a),flip(a)].">
      <j1 rule="hyper" parents="320 7759 7844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7936">
    <literal><![CDATA[
      K(x,K(y / z,z)) = K(x,K(y / z,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),7844(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 7844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7937">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y * z,y) = K(y * z,T(y,x))
    ]]></literal>
    <justification jstring="[para(7844(a,1),7139(a,1,1))].">
      <j1 rule="para" parents="7844 7139"/>
    </justification>
  </clause>

  <clause id="7938">
    <literal><![CDATA[
      K(x,K(y,x * z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7772,a,b,7845,a)].">
      <j1 rule="hyper" parents="58 7772 7845"/>
    </justification>
  </clause>

  <clause id="7939">
    <literal><![CDATA[
      K(x,K(x \ y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),7845(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 7845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7940">
    <literal><![CDATA[
      T(x,K(y,x \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7850,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 7850 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7941">
    <literal><![CDATA[
      K(x,K(y,x * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),7850(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 7850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7942">
    <literal><![CDATA[
      T(x,K(y,z * x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7851,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 7851 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7943">
    <literal><![CDATA[
      K(x,K(y * x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7772,a,b,7852,a)].">
      <j1 rule="hyper" parents="58 7772 7852"/>
    </justification>
  </clause>

  <clause id="7944">
    <literal><![CDATA[
      K(x / y,x / z) = K(y \ x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(6456,a,7855,a),flip(a)].">
      <j1 rule="hyper" parents="6456 7855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7945">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) = K((y * z) / x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6215,a(flip),b,7855,a)].">
      <j1 rule="hyper" parents="58 6215 7855"/>
    </justification>
  </clause>

  <clause id="7946">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[hyper(7700,a,7856,a)].">
      <j1 rule="hyper" parents="7700 7856"/>
    </justification>
  </clause>

  <clause id="7947">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) = K(x,(z * x) / y)
    ]]></literal>
    <justification jstring="[hyper(7690,a,7856,a)].">
      <j1 rule="hyper" parents="7690 7856"/>
    </justification>
  </clause>

  <clause id="7949">
    <literal><![CDATA[
      x * T(x \ y,T(z,y)) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,7864,a(flip),b,6081,a),flip(a)].">
      <j1 rule="hyper" parents="119 7864 6081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7951">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),T(y,u)) = K((K(y,z) * u) / x,y)
    ]]></literal>
    <justification jstring="[para(7238(a,1),7864(a,1,2))].">
      <j1 rule="para" parents="7238 7864"/>
    </justification>
  </clause>

  <clause id="7952">
    <literal><![CDATA[
      K(x,y \ z) * (z * K(z / y,x)) = z
    ]]></literal>
    <justification jstring="[para(7864(a,1),7264(a,1,2,2))].">
      <j1 rule="para" parents="7864 7264"/>
    </justification>
  </clause>

  <clause id="7954">
    <literal><![CDATA[
      T(x,T(y \ z,z)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7865,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 7865 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7955">
    <literal><![CDATA[
      K(x,y / (y / z)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),7865(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 7865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7956">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7868(a,1),292(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7868 292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7957">
    <literal><![CDATA[
      K(x,T(y,z)) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7868(a,1),126(a,1,1))].">
      <j1 rule="para" parents="7868 126"/>
    </justification>
  </clause>

  <clause id="7958">
    <literal><![CDATA[
      R(T(K(x,T(y,z)),z * u),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(7868(a,1),928(a,1,1,1))].">
      <j1 rule="para" parents="7868 928"/>
    </justification>
  </clause>

  <clause id="7959">
    <literal><![CDATA[
      (x * (y * K(z,u))) / (x * y) = L(K(z,T(u,x * y)),y,x)
    ]]></literal>
    <justification jstring="[para(7868(a,1),845(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7868 845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7960">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,y \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(30,a,5882,a,b,7872,a),flip(a)].">
      <j1 rule="hyper" parents="30 5882 7872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7961">
    <literal><![CDATA[
      T(x,T(y,z)) * z = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,7872,a(flip),b,4736,a),flip(a)].">
      <j1 rule="hyper" parents="119 7872 4736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7962">
    <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),7872(a,1,1,2))].">
      <j1 rule="para" parents="20 7872"/>
    </justification>
  </clause>

  <clause id="7963">
    <literal><![CDATA[
      K(x,y \ z) * y = y * K(x,z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7872(a,1,1,2))].">
      <j1 rule="para" parents="107 7872"/>
    </justification>
  </clause>

  <clause id="7964">
    <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(7872(a,1),102(a,2,2))].">
      <j1 rule="para" parents="7872 102"/>
    </justification>
  </clause>

  <clause id="7965">
    <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(7872(a,1),5124(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="7872 5124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7966">
    <literal><![CDATA[
      T(K(x,y),z) * (z / y) = (z / y) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6188(a,1),7872(a,1,1))].">
      <j1 rule="para" parents="6188 7872"/>
    </justification>
  </clause>

  <clause id="7967">
    <literal><![CDATA[
      K(x * K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7872(a,1),7330(a,1,1))].">
      <j1 rule="para" parents="7872 7330"/>
    </justification>
  </clause>

  <clause id="7968">
    <literal><![CDATA[
      K(x,(y * K(x,z)) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(7872(a,1),7382(a,1,2,1))].">
      <j1 rule="para" parents="7872 7382"/>
    </justification>
  </clause>

  <clause id="7969">
    <literal><![CDATA[
      K(x,T(y * K(x,z),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(7872(a,1),7526(a,1,2,1))].">
      <j1 rule="para" parents="7872 7526"/>
    </justification>
  </clause>

  <clause id="7971">
    <literal><![CDATA[
      x / (x * K(y,z)) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(117,a,7875,a(flip),b,7197,a(flip))].">
      <j1 rule="hyper" parents="117 7875 7197"/>
    </justification>
  </clause>

  <clause id="7972">
    <literal><![CDATA[
      (x \ y) * K(y / x,z) = T(x \ y,T(z,x))
    ]]></literal>
    <justification jstring="[para(7880(a,1),7153(a,1,2))].">
      <j1 rule="para" parents="7880 7153"/>
    </justification>
  </clause>

  <clause id="7973">
    <literal><![CDATA[
      K(x / ((y * z) \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(((y * z) \ y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(7880(a,1),7373(a,1))].">
      <j1 rule="para" parents="7880 7373"/>
    </justification>
  </clause>

  <clause id="7974">
    <literal><![CDATA[
      K((x \ y) \ 1,T(z,y)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(6384,a,7882,a)].">
      <j1 rule="hyper" parents="6384 7882"/>
    </justification>
  </clause>

  <clause id="7975">
    <literal><![CDATA[
      x * T(x \ y,T(z,x)) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,7882,a(flip),b,6081,a),flip(a)].">
      <j1 rule="hyper" parents="119 7882 6081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7976">
    <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),7882(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 7882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7977">
    <literal><![CDATA[
      K(x \ y,T(z,x)) / (x \ y) = (1 / (x \ y)) * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(7882(a,1),6193(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7882 6193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7978">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,T(y,x)) = K(u / (x * K(y,z)),y)
    ]]></literal>
    <justification jstring="[para(7095(a,1),7882(a,1,2))].">
      <j1 rule="para" parents="7095 7882"/>
    </justification>
  </clause>

  <clause id="7979">
    <literal><![CDATA[
      K(x \ T(x * y,y),z) = K(y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(4088(a,1),7883(a,1,1))].">
      <j1 rule="para" parents="4088 7883"/>
    </justification>
  </clause>

  <clause id="7980">
    <literal><![CDATA[
      x \ (T((y * x) / y,z) * u) = K(y,x) * (K(x,T(z,y)) * u)
    ]]></literal>
    <justification jstring="[para(7883(a,1),5378(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7883 5378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7981">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7883(a,1),7292(a,1))].">
      <j1 rule="para" parents="7883 7292"/>
    </justification>
  </clause>

  <clause id="7982">
    <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),7888(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 7888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7983">
    <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),7888(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13 7888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7984">
    <literal><![CDATA[
      K(x,T((y * z) \ (y * u),z)) = K(x,L(u / z,z,y))
    ]]></literal>
    <justification jstring="[para(856(a,1),7889(a,1,2)),flip(a)].">
      <j1 rule="para" parents="856 7889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7985">
    <literal><![CDATA[
      K(x,L((y \ z) / u,u,y)) = K(x,T((y * u) \ z,u))
    ]]></literal>
    <justification jstring="[para(857(a,2),7889(a,1,2))].">
      <j1 rule="para" parents="857 7889"/>
    </justification>
  </clause>

  <clause id="7986">
    <literal><![CDATA[
      K(x,T(L(y,z,u),w / y)) = K(x,L(w / (w / y),z,u))
    ]]></literal>
    <justification jstring="[para(853(a,1),7889(a,1,2)),flip(a)].">
      <j1 rule="para" parents="853 7889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7987">
    <literal><![CDATA[
      K((x * y) / ((x / z) * y),u) = R(K(z,T(u,x)),x,y)
    ]]></literal>
    <justification jstring="[para(7893(a,1),6736(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7893 6736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7988">
    <literal><![CDATA[
      K(T(x / (x / y),z),u) = K(T(y,z),T(u,x))
    ]]></literal>
    <justification jstring="[para(7647(a,1),7893(a,1,1))].">
      <j1 rule="para" parents="7647 7893"/>
    </justification>
  </clause>

  <clause id="7989">
    <literal><![CDATA[
      T(x,(y * z) / y) = x * K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(224(a,1),7894(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="224 7894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7990">
    <literal><![CDATA[
      T(x,y \ K(z,y \ 1)) = x * K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(4839(a,1),7894(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4839 7894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7991">
    <literal><![CDATA[
      K(T(x,y),(y * K(z,x)) \ u) = K(x,u / (y * K(z,x)))
    ]]></literal>
    <justification jstring="[para(7105(a,1),7900(a,1,1))].">
      <j1 rule="para" parents="7105 7900"/>
    </justification>
  </clause>

  <clause id="7992">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4850,a,b,7901,a)].">
      <j1 rule="hyper" parents="58 4850 7901"/>
    </justification>
  </clause>

  <clause id="7993">
    <literal><![CDATA[
      K(x,T(y,L(z,u,x))) = K(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(7031(a,1),7905(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7031 7905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7994">
    <literal><![CDATA[
      K(x,T(y,K(L(x,z,u),w) * v5)) = K(x * K(v5,x),y)
    ]]></literal>
    <justification jstring="[para(7407(a,1),7905(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7407 7905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7995">
    <literal><![CDATA[
      T(x,T(y,z * K(u,z))) = T(x,y * K(T(y,u),z))
    ]]></literal>
    <justification jstring="[para(7906(a,1),5153(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7906 5153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7996">
    <literal><![CDATA[
      x / (K(T(y,z),x) * K(x * K(z,x),z)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(7906(a,1),5380(a,1,2,1))].">
      <j1 rule="para" parents="7906 5380"/>
    </justification>
  </clause>

  <clause id="7997">
    <literal><![CDATA[
      K(x,y * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7906(a,2),7679(a,1))].">
      <j1 rule="para" parents="7906 7679"/>
    </justification>
  </clause>

  <clause id="7998">
    <literal><![CDATA[
      K(K(x,y) * z,u) * z = z * K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(7232(a,1),7911(a,1,1))].">
      <j1 rule="para" parents="7232 7911"/>
    </justification>
  </clause>

  <clause id="7999">
    <literal><![CDATA[
      T(x,T(y * z,u) / y) = T(x,y \ T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4561(a,1),7917(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4561 7917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8000">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = T(x,T(R(z,u,w),y))
    ]]></literal>
    <justification jstring="[para(849(a,2),7918(a,1,2))].">
      <j1 rule="para" parents="849 7918"/>
    </justification>
  </clause>

  <clause id="8001">
    <literal><![CDATA[
      T(x,T(T(y \ (z \ y),T(z,u)),y)) = T(x,(((z \ 1) \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[para(5879(a,1),7918(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5879 7918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8002">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,T(x,y)) \ z) = ((y * x) / y) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(7918(a,1),4520(a,1,2,1))].">
      <j1 rule="para" parents="7918 4520"/>
    </justification>
  </clause>

  <clause id="8003">
    <literal><![CDATA[
      T(x,(y \ 1) \ K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,3745,a,b,7920,a)].">
      <j1 rule="hyper" parents="58 3745 7920"/>
    </justification>
  </clause>

  <clause id="8004">
    <literal><![CDATA[
      T(x,K(y,1 / z) / z) = T(x,T(1 / z,y))
    ]]></literal>
    <justification jstring="[para(2340(a,1),7920(a,1,2))].">
      <j1 rule="para" parents="2340 7920"/>
    </justification>
  </clause>

  <clause id="8005">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(5346(a,1),7931(a,1,2))].">
      <j1 rule="para" parents="5346 7931"/>
    </justification>
  </clause>

  <clause id="8006">
    <literal><![CDATA[
      T(x,K(y,y \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4871(a,1),7932(a,1,2))].">
      <j1 rule="para" parents="4871 7932"/>
    </justification>
  </clause>

  <clause id="8007">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(y,K(x,x * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7842,a,b,7935,a)].">
      <j1 rule="hyper" parents="320 7842 7935"/>
    </justification>
  </clause>

  <clause id="8008">
    <literal><![CDATA[
      T(x,K(y,x * z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,7938,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 7938 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8009">
    <literal><![CDATA[
      T(x,K(y,z / x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),7942(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 7942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8010">
    <literal><![CDATA[
      T(x / y,T(z \ x,y)) = T(x / y,x / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7354,a,b,7954,a)].">
      <j1 rule="hyper" parents="58 7354 7954"/>
    </justification>
  </clause>

  <clause id="8012">
    <literal><![CDATA[
      K(x,x \ y) * K(z,T(x,y)) = T(y / (y / x),z) \ x
    ]]></literal>
    <justification jstring="[para(7955(a,1),6849(a,1,2))].">
      <j1 rule="para" parents="7955 6849"/>
    </justification>
  </clause>

  <clause id="8013">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * K(z,z \ u) = (x / T(u / (u / z),y)) * z
    ]]></literal>
    <justification jstring="[para(7955(a,1),6511(a,1,1,2))].">
      <j1 rule="para" parents="7955 6511"/>
    </justification>
  </clause>

  <clause id="8014">
    <literal><![CDATA[
      K(x,y / (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(7955(a,2),7283(a,1))].">
      <j1 rule="para" parents="7955 7283"/>
    </justification>
  </clause>

  <clause id="8015">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,T(z * y,z))
    ]]></literal>
    <justification jstring="[para(8005(a,1),7830(a,1,1))].">
      <j1 rule="para" parents="8005 7830"/>
    </justification>
  </clause>

  <clause id="8016">
    <literal><![CDATA[
      T(x * K(y \ z,y),K(y,z)) = K(y \ z,y) * x
    ]]></literal>
    <justification jstring="[hyper(6422,a,8006,a),flip(a)].">
      <j1 rule="hyper" parents="6422 8006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8017">
    <literal><![CDATA[
      T(T(x,K(y,z)),x * y) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[para(8008(a,1),7830(a,1,1))].">
      <j1 rule="para" parents="8008 7830"/>
    </justification>
  </clause>

  <clause id="8018">
    <literal><![CDATA[
      T(x,K(y,z / x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7807,a,b,8009,a),flip(a)].">
      <j1 rule="hyper" parents="320 7807 8009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8019">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(7758(a,2),7749(a,1))].">
      <j1 rule="para" parents="7758 7749"/>
    </justification>
  </clause>

  <clause id="8020">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7770(a,2),7749(a,1))].">
      <j1 rule="para" parents="7770 7749"/>
    </justification>
  </clause>

  <clause id="8021">
    <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(7118(a,1),7806(a,1,2))].">
      <j1 rule="para" parents="7118 7806"/>
    </justification>
  </clause>

  <clause id="8022">
    <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(7133(a,1),7806(a,1,2))].">
      <j1 rule="para" parents="7133 7806"/>
    </justification>
  </clause>

  <clause id="8023">
    <literal><![CDATA[
      K(x,K(y,z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7752(a,2),7806(a,1))].">
      <j1 rule="para" parents="7752 7806"/>
    </justification>
  </clause>

  <clause id="8024">
    <literal><![CDATA[
      L(x,K(y \ 1,z),u \ (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(7921(a,1),45(a,2))].">
      <j1 rule="para" parents="7921 45"/>
    </justification>
  </clause>

  <clause id="8025">
    <literal><![CDATA[
      T(K(x,y \ z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),7956(a,1,1,2))].">
      <j1 rule="para" parents="107 7956"/>
    </justification>
  </clause>

  <clause id="8026">
    <literal><![CDATA[
      K(x \ y,T(z,y / x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(3327(a,1),7956(a,1))].">
      <j1 rule="para" parents="3327 7956"/>
    </justification>
  </clause>

  <clause id="8027">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(5505(a,2),7956(a,1))].">
      <j1 rule="para" parents="5505 7956"/>
    </justification>
  </clause>

  <clause id="8028">
    <literal><![CDATA[
      K(x \ y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(6239(a,1),7956(a,1))].">
      <j1 rule="para" parents="6239 7956"/>
    </justification>
  </clause>

  <clause id="8029">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7118(a,2),7956(a,1))].">
      <j1 rule="para" parents="7118 7956"/>
    </justification>
  </clause>

  <clause id="8030">
    <literal><![CDATA[
      T(K(x \ y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7144(a,1),7956(a,1,1))].">
      <j1 rule="para" parents="7144 7956"/>
    </justification>
  </clause>

  <clause id="8031">
    <literal><![CDATA[
      T(K(x \ y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7186(a,1),7956(a,1,1))].">
      <j1 rule="para" parents="7186 7956"/>
    </justification>
  </clause>

  <clause id="8032">
    <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(7854(a,1),7956(a,1,1,2))].">
      <j1 rule="para" parents="7854 7956"/>
    </justification>
  </clause>

  <clause id="8033">
    <literal><![CDATA[
      K(x,T(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),7981(a,1,2,1))].">
      <j1 rule="para" parents="107 7981"/>
    </justification>
  </clause>

  <clause id="8034">
    <literal><![CDATA[
      K(x \ y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7186(a,1),7981(a,1))].">
      <j1 rule="para" parents="7186 7981"/>
    </justification>
  </clause>

  <clause id="8035">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7195(a,1),7981(a,1))].">
      <j1 rule="para" parents="7195 7981"/>
    </justification>
  </clause>

  <clause id="8036">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z),u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(7189(a,1),7981(a,1))].">
      <j1 rule="para" parents="7189 7981"/>
    </justification>
  </clause>

  <clause id="8037">
    <literal><![CDATA[
      K(x \ y,T(z,y \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(7275(a,1),7981(a,1))].">
      <j1 rule="para" parents="7275 7981"/>
    </justification>
  </clause>

  <clause id="8038">
    <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(7184(a,2),7981(a,1))].">
      <j1 rule="para" parents="7184 7981"/>
    </justification>
  </clause>

  <clause id="8039">
    <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),8029(a,1,2))].">
      <j1 rule="para" parents="18 8029"/>
    </justification>
  </clause>

  <clause id="8040">
    <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),8029(a,1,2))].">
      <j1 rule="para" parents="22 8029"/>
    </justification>
  </clause>

  <clause id="8041">
    <literal><![CDATA[
      K(T(x,y),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),8029(a,1,2))].">
      <j1 rule="para" parents="107 8029"/>
    </justification>
  </clause>

  <clause id="8042">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(1997,a,7729,a)].">
      <j1 rule="hyper" parents="1997 7729"/>
    </justification>
  </clause>

  <clause id="8043">
    <literal><![CDATA[
      K(x,K(y,z)) != 1
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7729(a,1),4944(a,1)),flip(b)].">
      <j1 rule="para" parents="7729 4944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8044">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7729(a,1),5110(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7729 5110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8045">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) \ K(y,x) = T(K(y,x),T(z,y \ u))
    ]]></literal>
    <justification jstring="[para(7287(a,1),7734(a,1,1,2))].">
      <j1 rule="para" parents="7287 7734"/>
    </justification>
  </clause>

  <clause id="8046">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) = K(x,y) * K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7249(a,1),7738(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7249 7738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8047">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = K(x,K(y,z)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7145(a,1),7739(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7145 7739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8048">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7740(a,1),5603(a,1))].">
      <j1 rule="para" parents="7740 5603"/>
    </justification>
  </clause>

  <clause id="8049">
    <literal><![CDATA[
      K(x,T(y,z)) != K(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7740(a,1),5612(a,1))].">
      <j1 rule="para" parents="7740 5612"/>
    </justification>
  </clause>

  <clause id="8050">
    <literal><![CDATA[
      K(x,T(y,z)) \ K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = u
    ]]></literal>
    <justification jstring="[para(7740(a,1),6316(a,1,1))].">
      <j1 rule="para" parents="7740 6316"/>
    </justification>
  </clause>

  <clause id="8051">
    <literal><![CDATA[
      K(x,K(y,R(T(x,z),u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,7189,a(flip),b,7741,a),flip(a)].">
      <j1 rule="hyper" parents="115 7189 7741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8052">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(x,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7755,a(flip),b,7751,a),flip(a)].">
      <j1 rule="hyper" parents="320 7755 7751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8053">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7730,a(flip),b,7751,a),flip(a)].">
      <j1 rule="hyper" parents="320 7730 7751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8054">
    <literal><![CDATA[
      T(K(x,y),T(z,K(u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7131,a(flip),b,7753,a)].">
      <j1 rule="hyper" parents="58 7131 7753"/>
    </justification>
  </clause>

  <clause id="8055">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,T(x,u))) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(7133(a,1),7765(a,1,2,2))].">
      <j1 rule="para" parents="7133 7765"/>
    </justification>
  </clause>

  <clause id="8056">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7754,a,b,7767,a),flip(a)].">
      <j1 rule="hyper" parents="320 7754 7767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8057">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(1997,a,7777,a)].">
      <j1 rule="hyper" parents="1997 7777"/>
    </justification>
  </clause>

  <clause id="8058">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(y,T(x,u)))
    ]]></literal>
    <justification jstring="[hyper(7756,a,7790,a)].">
      <j1 rule="hyper" parents="7756 7790"/>
    </justification>
  </clause>

  <clause id="8059">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7792,a(flip),b,5372,a)].">
      <j1 rule="hyper" parents="119 7792 5372"/>
    </justification>
  </clause>

  <clause id="8060">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7793(a,1),5603(a,1))].">
      <j1 rule="para" parents="7793 5603"/>
    </justification>
  </clause>

  <clause id="8061">
    <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(5650(a,1),7810(a,2,2,1))].">
      <j1 rule="para" parents="5650 7810"/>
    </justification>
  </clause>

  <clause id="8062">
    <literal><![CDATA[
      T(x * K(y,y \ z),K(y,z)) = K(y,y \ z) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,8006,a(flip),b,7816,a)].">
      <j1 rule="hyper" parents="58 8006 7816"/>
    </justification>
  </clause>

  <clause id="8063">
    <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(7816(a,1),5597(a,1,1))].">
      <j1 rule="para" parents="7816 5597"/>
    </justification>
  </clause>

  <clause id="8064">
    <literal><![CDATA[
      T(x * T(y,z),K(y,z)) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(6086(a,1),7816(a,1,1))].">
      <j1 rule="para" parents="6086 7816"/>
    </justification>
  </clause>

  <clause id="8065">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,x) = K(y,x) * T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(7817(a,1),236(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7817 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8066">
    <literal><![CDATA[
      L((x \ y) * K(z,u),K(u,z),x) = T((x * K(u,z)) \ y,K(u,z))
    ]]></literal>
    <justification jstring="[para(7817(a,1),5120(a,1,1))].">
      <j1 rule="para" parents="7817 5120"/>
    </justification>
  </clause>

  <clause id="8067">
    <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,7819,a(flip),b,4741,a)].">
      <j1 rule="hyper" parents="119 7819 4741"/>
    </justification>
  </clause>

  <clause id="8068">
    <literal><![CDATA[
      T(x \ K(x,y),K(z,x)) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[para(5599(a,1),7821(a,2,2))].">
      <j1 rule="para" parents="5599 7821"/>
    </justification>
  </clause>

  <clause id="8069">
    <literal><![CDATA[
      T(x \ y,K(z,x)) = x \ T(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(7807(a,1),7821(a,2,2))].">
      <j1 rule="para" parents="7807 7821"/>
    </justification>
  </clause>

  <clause id="8070">
    <literal><![CDATA[
      T(x * K(y,z),u) / x = x \ T(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(7827(a,1),4541(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7827 4541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8071">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z * x) = K(y,z * x) * x
    ]]></literal>
    <justification jstring="[para(7942(a,1),7827(a,1,1))].">
      <j1 rule="para" parents="7942 7827"/>
    </justification>
  </clause>

  <clause id="8072">
    <literal><![CDATA[
      T(x * y,K(z,x)) = x * T(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(7841,a,7832,a)].">
      <j1 rule="hyper" parents="7841 7832"/>
    </justification>
  </clause>

  <clause id="8073">
    <literal><![CDATA[
      K(1 / T(T(x,y),y),z) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(5512,a,7857,a),flip(a)].">
      <j1 rule="hyper" parents="5512 7857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8074">
    <literal><![CDATA[
      K(x,T(1 / (y \ z),y)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(5748,a,7866,a)].">
      <j1 rule="hyper" parents="5748 7866"/>
    </justification>
  </clause>

  <clause id="8075">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ y) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7675,a(flip),b,7866,a)].">
      <j1 rule="hyper" parents="58 7675 7866"/>
    </justification>
  </clause>

  <clause id="8076">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,z / (z * y))
    ]]></literal>
    <justification jstring="[para(4(a,1),7866(a,1,2,1,1))].">
      <j1 rule="para" parents="4 7866"/>
    </justification>
  </clause>

  <clause id="8078">
    <literal><![CDATA[
      K((x / (x / y)) \ 1,z) = K(y \ 1,T(z,y \ x))
    ]]></literal>
    <justification jstring="[para(4305(a,1),7867(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4305 7867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8079">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K(x \ K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7141,a,b,7870,a)].">
      <j1 rule="hyper" parents="320 7141 7870"/>
    </justification>
  </clause>

  <clause id="8080">
    <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(7871(a,1),7956(a,1,1))].">
      <j1 rule="para" parents="7871 7956"/>
    </justification>
  </clause>

  <clause id="8081">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) / T(z,y) = 1 / (K(z,x) * T(z,y))
    ]]></literal>
    <justification jstring="[para(7881(a,1),4762(a,2,2))].">
      <j1 rule="para" parents="7881 4762"/>
    </justification>
  </clause>

  <clause id="8082">
    <literal><![CDATA[
      K(T(x / (x / y),z),u) = K(T(y,z),T(u,y \ x))
    ]]></literal>
    <justification jstring="[para(4305(a,1),7897(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4305 7897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8083">
    <literal><![CDATA[
      (x * T(y,z)) / T(x,y) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(117,a,7915,a(flip),b,5050,a(flip))].">
      <j1 rule="hyper" parents="117 7915 5050"/>
    </justification>
  </clause>

  <clause id="8084">
    <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(7915(a,1),493(a,1,2))].">
      <j1 rule="para" parents="7915 493"/>
    </justification>
  </clause>

  <clause id="8085">
    <literal><![CDATA[
      T(K(x,y),z) * ((x \ z) * x) = (x \ z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7179(a,1),7915(a,1,1))].">
      <j1 rule="para" parents="7179 7915"/>
    </justification>
  </clause>

  <clause id="8086">
    <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(7916(a,2),233(a,1,1,1))].">
      <j1 rule="para" parents="7916 233"/>
    </justification>
  </clause>

  <clause id="8087">
    <literal><![CDATA[
      T(x * y,K(z,y)) = T(x,K(z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,7815,a,b,7924,a)].">
      <j1 rule="hyper" parents="320 7815 7924"/>
    </justification>
  </clause>

  <clause id="8088">
    <literal><![CDATA[
      K(x \ y,z) \ (y * K(y / x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = y
    ]]></literal>
    <justification jstring="[para(7929(a,1),287(a,1,2))].">
      <j1 rule="para" parents="7929 287"/>
    </justification>
  </clause>

  <clause id="8089">
    <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(7929(a,2),6355(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7929 6355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8090">
    <literal><![CDATA[
      K(x,K(y \ z,y)) = K(x,K(z / y,z))
    ]]></literal>
    <justification jstring="[para(4924(a,1),7936(a,1,2))].">
      <j1 rule="para" parents="4924 7936"/>
    </justification>
  </clause>

  <clause id="8091">
    <literal><![CDATA[
      K(x / y,z \ (x / y)) = K(y \ x,(z * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(6962,a,7944,a)].">
      <j1 rule="hyper" parents="6962 7944"/>
    </justification>
  </clause>

  <clause id="8092">
    <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(440,a,2324,a,b,7952,a)].">
      <j1 rule="hyper" parents="440 2324 7952"/>
    </justification>
  </clause>

  <clause id="8093">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,x \ K(x,z)) = K(x \ 1,K(y,z))
    ]]></literal>
    <justification jstring="[para(7960(a,1),7777(a,1,2))].">
      <j1 rule="para" parents="7960 7777"/>
    </justification>
  </clause>

  <clause id="8094">
    <literal><![CDATA[
      (x * (K(y,z) * K(x,u))) * K(z,y) = T(x,T(u,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(6315,a,7961,a)].">
      <j1 rule="hyper" parents="6315 7961"/>
    </justification>
  </clause>

  <clause id="8095">
    <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(7961(a,1),6323(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7961 6323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8096">
    <literal><![CDATA[
      K(x,(y / T(z,x)) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(6293(a,1),7968(a,1,2,1))].">
      <j1 rule="para" parents="6293 7968"/>
    </justification>
  </clause>

  <clause id="8097">
    <literal><![CDATA[
      K(x,T(T(K(y,x) * z,u),w)) = K(x,T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(6693(a,1),7969(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6693 7969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8098">
    <literal><![CDATA[
      K((x \ y) \ 1,T(z,y)) = K((y / x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5389,a,b,7974,a),flip(a)].">
      <j1 rule="hyper" parents="320 5389 7974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8099">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = x * K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(849(a,2),7989(a,1,2))].">
      <j1 rule="para" parents="849 7989"/>
    </justification>
  </clause>

  <clause id="8100">
    <literal><![CDATA[
      K(K(x,y) * z,K(y,u)) = K(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(5095(a,1),8053(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5095 8053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8101">
    <literal><![CDATA[
      R(x,K(y,z) * u,K(u,K(y,w))) = x
    ]]></literal>
    <justification jstring="[para(8053(a,1),6391(a,1,3))].">
      <j1 rule="para" parents="8053 6391"/>
    </justification>
  </clause>

  <clause id="8102">
    <literal><![CDATA[
      R(x,K(y,z),T(u,K(y,w))) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(6871,a,8101,a)].">
      <j1 rule="hyper" parents="6871 8101"/>
    </justification>
  </clause>

  <clause id="8103">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * K(u,K(y,z)) = x * (u * K(y,z))
    ]]></literal>
    <justification jstring="[para(8101(a,1),517(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8101 517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8104">
    <literal><![CDATA[
      K(x,K(y,(z / x) \ u)) = K(x,K(y,(x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(5376(a,1),8056(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5376 8056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8105">
    <literal><![CDATA[
      K(x,K(y \ z,T(y,u))) = K(y,K(z,T(x,u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,7939,a(flip),b,8058,a),flip(a)].">
      <j1 rule="hyper" parents="320 7939 8058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8106">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7412,a,b,8059,a)].">
      <j1 rule="hyper" parents="58 7412 8059"/>
    </justification>
  </clause>

  <clause id="8107">
    <literal><![CDATA[
      T(x \ K(x,y),T(x,z)) = T(x \ K(x,y),x)
    ]]></literal>
    <justification jstring="[para(8068(a,1),7422(a,1,1))].">
      <j1 rule="para" parents="8068 7422"/>
    </justification>
  </clause>

  <clause id="8108">
    <literal><![CDATA[
      x * T(x \ y,K(z,x)) = T(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,8069,a,b,xx)].">
      <j1 rule="hyper" parents="119 8069"/>
    </justification>
  </clause>

  <clause id="8109">
    <literal><![CDATA[
      T(x,K(y,z)) / z = T(x / z,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(4543,a,8072,a)].">
      <j1 rule="hyper" parents="4543 8072"/>
    </justification>
  </clause>

  <clause id="8110">
    <literal><![CDATA[
      K(1 / T(x,y / x),z) = K(1 / (y / (y / x)),z)
    ]]></literal>
    <justification jstring="[para(244(a,1),8073(a,1,1,2,1))].">
      <j1 rule="para" parents="244 8073"/>
    </justification>
  </clause>

  <clause id="8111">
    <literal><![CDATA[
      K(1 / T(T(x,x * y),y),z) = K(1 / L(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(711(a,1),8073(a,1,1,2,1))].">
      <j1 rule="para" parents="711 8073"/>
    </justification>
  </clause>

  <clause id="8112">
    <literal><![CDATA[
      T(x,1 / T(T(y,z),z)) = x / K(1 / y,x)
    ]]></literal>
    <justification jstring="[para(8073(a,1),4764(a,2,2))].">
      <j1 rule="para" parents="8073 4764"/>
    </justification>
  </clause>

  <clause id="8113">
    <literal><![CDATA[
      K(x,T(1 / y,z)) = K(x,z / (z * y))
    ]]></literal>
    <justification jstring="[para(4(a,1),8074(a,1,2,1,2))].">
      <j1 rule="para" parents="4 8074"/>
    </justification>
  </clause>

  <clause id="8114">
    <literal><![CDATA[
      K(x,y \ T(z,z \ y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(5560(a,1),8075(a,1,2))].">
      <j1 rule="para" parents="5560 8075"/>
    </justification>
  </clause>

  <clause id="8115">
    <literal><![CDATA[
      K(x,y / (y * z)) = K(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7544,a(flip),b,8076,a),flip(a)].">
      <j1 rule="hyper" parents="58 7544 8076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8116">
    <literal><![CDATA[
      K(((x * y) / x) \ 1,z) = K(T(y,x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(4864(a,2),8079(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4864 8079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8117">
    <literal><![CDATA[
      K(x,K(y / z,y)) = K(x,K(z,z \ y))
    ]]></literal>
    <justification jstring="[hyper(7806,a,8090,a),flip(a)].">
      <j1 rule="hyper" parents="7806 8090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8118">
    <literal><![CDATA[
      T(x * K(y,x),K(y,z)) = x * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(5167,a,8106,a)].">
      <j1 rule="hyper" parents="5167 8106"/>
    </justification>
  </clause>

  <clause id="8119">
    <literal><![CDATA[
      T(x * K(y,T(x,z * (u * x))),y) = T(x,K(y,z * (x * u)))
    ]]></literal>
    <justification jstring="[para(7108(a,2),8106(a,1,1,2,2))].">
      <j1 rule="para" parents="7108 8106"/>
    </justification>
  </clause>

  <clause id="8120">
    <literal><![CDATA[
      T(T(x,y) / z,K(y,z)) = T(x,T(y,z)) / z
    ]]></literal>
    <justification jstring="[para(7413(a,1),8109(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7413 8109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8122">
    <literal><![CDATA[
      K(x,y \ T(z,z \ y)) = K(x,T(y \ z,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7865,a,b,8114,a),flip(a)].">
      <j1 rule="hyper" parents="320 7865 8114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8123">
    <literal><![CDATA[
      K(x,(y / z) / y) = K(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[para(642(a,1),8114(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="642 8114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8124">
    <literal><![CDATA[
      T(x,y / (y * z)) = T(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(118,a,8115,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 8115 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8125">
    <literal><![CDATA[
      K(x,K(y / z,y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7934,a(flip),b,8117,a),flip(a)].">
      <j1 rule="hyper" parents="320 7934 8117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8126">
    <literal><![CDATA[
      K(x,K(y / z,y)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7759,a(flip),b,8125,a),flip(a)].">
      <j1 rule="hyper" parents="320 7759 8125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8127">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),8125(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 8125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8128">
    <literal><![CDATA[
      K(x,K(y,y / z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(7806,a,8126,a)].">
      <j1 rule="hyper" parents="7806 8126"/>
    </justification>
  </clause>

  <clause id="8129">
    <literal><![CDATA[
      K(x,K(y,x / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7774,a,8126,a)].">
      <j1 rule="hyper" parents="7774 8126"/>
    </justification>
  </clause>

  <clause id="8130">
    <literal><![CDATA[
      K(x,K(x / y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(7749,a,8126,a)].">
      <j1 rule="hyper" parents="7749 8126"/>
    </justification>
  </clause>

  <clause id="8131">
    <literal><![CDATA[
      K(x,K(y,z \ y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(7806,a,8127,a)].">
      <j1 rule="hyper" parents="7806 8127"/>
    </justification>
  </clause>

  <clause id="8132">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,7728,a,b,8127,a),flip(a)].">
      <j1 rule="hyper" parents="320 7728 8127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8133">
    <literal><![CDATA[
      (x / y) * K(x,K(z,y)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(8128(a,1),7732(a,1,2))].">
      <j1 rule="para" parents="8128 7732"/>
    </justification>
  </clause>

  <clause id="8134">
    <literal><![CDATA[
      T(x,K(y,x / z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8129,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 8129 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8135">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),8129(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 8129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8136">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x / z,y) = K(z \ x,y)
    ]]></literal>
    <justification jstring="[para(8129(a,1),6259(a,1,1))].">
      <j1 rule="para" parents="8129 6259"/>
    </justification>
  </clause>

  <clause id="8137">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(72(a,1),8130(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 8130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8138">
    <literal><![CDATA[
      K(x,K(y,z \ y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7772,a,b,8131,a),flip(a)].">
      <j1 rule="hyper" parents="320 7772 8131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8139">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7933,a,b,8131,a)].">
      <j1 rule="hyper" parents="58 7933 8131"/>
    </justification>
  </clause>

  <clause id="8140">
    <literal><![CDATA[
      K(x,K(y \ x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7749,a,8132,a)].">
      <j1 rule="hyper" parents="7749 8132"/>
    </justification>
  </clause>

  <clause id="8141">
    <literal><![CDATA[
      K(x,K(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8132(a,2),7749(a,1))].">
      <j1 rule="para" parents="8132 7749"/>
    </justification>
  </clause>

  <clause id="8142">
    <literal><![CDATA[
      K(1 / ((1 / x) / y),K(z,(y * x) / u)) = (T(y * x,K(z,u)) / x) / y
    ]]></literal>
    <justification jstring="[para(8134(a,1),5517(a,2,1,1))].">
      <j1 rule="para" parents="8134 5517"/>
    </justification>
  </clause>

  <clause id="8143">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7759,a(flip),b,8135,a),flip(a)].">
      <j1 rule="hyper" parents="320 7759 8135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8144">
    <literal><![CDATA[
      K(x \ y,z) \ K(y,K(x,z)) = K(z,y / x)
    ]]></literal>
    <justification jstring="[para(8137(a,1),6787(a,1,2))].">
      <j1 rule="para" parents="8137 6787"/>
    </justification>
  </clause>

  <clause id="8145">
    <literal><![CDATA[
      T(x,K(y,z \ y)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8138,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 8138 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8146">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7933,a,b,8138,a)].">
      <j1 rule="hyper" parents="58 7933 8138"/>
    </justification>
  </clause>

  <clause id="8147">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7806,a,8139,a)].">
      <j1 rule="hyper" parents="7806 8139"/>
    </justification>
  </clause>

  <clause id="8148">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(7774,a,8139,a)].">
      <j1 rule="hyper" parents="7774 8139"/>
    </justification>
  </clause>

  <clause id="8149">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7754,a,b,8139,a),flip(a)].">
      <j1 rule="hyper" parents="320 7754 8139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8150">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,8139,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 8139 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8151">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(3523(a,1),8139(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3523 8139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8152">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) = K(x,K(u,y))
    ]]></literal>
    <justification jstring="[para(5311(a,2),8139(a,1,2))].">
      <j1 rule="para" parents="5311 8139"/>
    </justification>
  </clause>

  <clause id="8153">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(6078(a,1),8139(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6078 8139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8154">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8139(a,2),7806(a,1))].">
      <j1 rule="para" parents="8139 7806"/>
    </justification>
  </clause>

  <clause id="8155">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ y) = T(x \ y,K(y,z))
    ]]></literal>
    <justification jstring="[para(8143(a,1),7783(a,1,1))].">
      <j1 rule="para" parents="8143 7783"/>
    </justification>
  </clause>

  <clause id="8156">
    <literal><![CDATA[
      T(x,K(y \ z,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(7841,a,8145,a)].">
      <j1 rule="hyper" parents="7841 8145"/>
    </justification>
  </clause>

  <clause id="8157">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(7796,a,8146,a)].">
      <j1 rule="hyper" parents="7796 8146"/>
    </justification>
  </clause>

  <clause id="8158">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(7774,a,8146,a)].">
      <j1 rule="hyper" parents="7774 8146"/>
    </justification>
  </clause>

  <clause id="8159">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8146,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 8146 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8160">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(75(a,1),8146(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 8146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8161">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(5311(a,2),8146(a,1,2))].">
      <j1 rule="para" parents="5311 8146"/>
    </justification>
  </clause>

  <clause id="8162">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[para(5312(a,1),8146(a,1,2))].">
      <j1 rule="para" parents="5312 8146"/>
    </justification>
  </clause>

  <clause id="8163">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6078(a,1),8146(a,1,2))].">
      <j1 rule="para" parents="6078 8146"/>
    </justification>
  </clause>

  <clause id="8164">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[para(8146(a,1),7738(a,1,2))].">
      <j1 rule="para" parents="8146 7738"/>
    </justification>
  </clause>

  <clause id="8165">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7754,a,b,8147,a),flip(a)].">
      <j1 rule="hyper" parents="320 7754 8147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8166">
    <literal><![CDATA[
      (x * K(y \ 1,z)) \ K(x,K(y,z)) = (K(y \ 1,z) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,8147,a(flip),b,5529,a(flip))].">
      <j1 rule="hyper" parents="116 8147 5529"/>
    </justification>
  </clause>

  <clause id="8167">
    <literal><![CDATA[
      K(x,y * ((z \ (y \ 1)) * z)) = K(x,K(y * z,z))
    ]]></literal>
    <justification jstring="[para(5678(a,2),8147(a,1,2))].">
      <j1 rule="para" parents="5678 8147"/>
    </justification>
  </clause>

  <clause id="8168">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8147(a,2),7806(a,1))].">
      <j1 rule="para" parents="8147 7806"/>
    </justification>
  </clause>

  <clause id="8169">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7754,a,b,8148,a),flip(a)].">
      <j1 rule="hyper" parents="320 7754 8148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8170">
    <literal><![CDATA[
      T(1 / x,K(y,z)) = K(y,K(x,z)) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,8148,a(flip),b,5008,a),flip(a)].">
      <j1 rule="hyper" parents="117 8148 5008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8171">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8148(a,2),7806(a,1))].">
      <j1 rule="para" parents="8148 7806"/>
    </justification>
  </clause>

  <clause id="8172">
    <literal><![CDATA[
      K(1 / x,K(y,z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(75(a,1),8149(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 8149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8173">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(3528(a,2),8149(a,1,2))].">
      <j1 rule="para" parents="3528 8149"/>
    </justification>
  </clause>

  <clause id="8174">
    <literal><![CDATA[
      T(x,K(y \ z,u)) = T(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(6078(a,1),8150(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6078 8150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8175">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8150(a,2),7841(a,1))].">
      <j1 rule="para" parents="8150 7841"/>
    </justification>
  </clause>

  <clause id="8176">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8151(a,2),7806(a,1))].">
      <j1 rule="para" parents="8151 7806"/>
    </justification>
  </clause>

  <clause id="8177">
    <literal><![CDATA[
      T(x,K(y,y / z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),8156(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 8156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8178">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,(T(u,x) / z) / (u / z))
    ]]></literal>
    <justification jstring="[para(5687(a,1),8157(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5687 8157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8179">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = T(x,T(y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(7678,a,8159,a),flip(a)].">
      <j1 rule="hyper" parents="7678 8159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8180">
    <literal><![CDATA[
      K(x,y \ 1) * T(z,K(x,y)) = z * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,8159,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 8159 17"/>
    </justification>
  </clause>

  <clause id="8181">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6078(a,1),8159(a,1,2))].">
      <j1 rule="para" parents="6078 8159"/>
    </justification>
  </clause>

  <clause id="8182">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(8159(a,1),7678(a,1))].">
      <j1 rule="para" parents="8159 7678"/>
    </justification>
  </clause>

  <clause id="8183">
    <literal><![CDATA[
      (T(x * y,K(z,u)) / y) / x = K(z,K(u,(1 / y) / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5517,a(flip),b,8172,a)].">
      <j1 rule="hyper" parents="58 5517 8172"/>
    </justification>
  </clause>

  <clause id="8184">
    <literal><![CDATA[
      K(1 / x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8172(a,2),7806(a,1))].">
      <j1 rule="para" parents="8172 7806"/>
    </justification>
  </clause>

  <clause id="8185">
    <literal><![CDATA[
      K(x,K(y,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8173(a,2),7796(a,1))].">
      <j1 rule="para" parents="8173 7796"/>
    </justification>
  </clause>

  <clause id="8186">
    <literal><![CDATA[
      K(x,(y / z) / y) = K(x,y / (y * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8115,a,b,8123,a),flip(a)].">
      <j1 rule="hyper" parents="320 8115 8123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8187">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(8152(a,2),7806(a,1))].">
      <j1 rule="para" parents="8152 7806"/>
    </justification>
  </clause>

  <clause id="8188">
    <literal><![CDATA[
      K(x,K(y \ (z * u),u \ (z \ 1))) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(6688(a,1),8153(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6688 8153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8189">
    <literal><![CDATA[
      K(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(8153(a,1),7806(a,1))].">
      <j1 rule="para" parents="8153 7806"/>
    </justification>
  </clause>

  <clause id="8190">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(8161(a,2),7806(a,1))].">
      <j1 rule="para" parents="8161 7806"/>
    </justification>
  </clause>

  <clause id="8191">
    <literal><![CDATA[
      1 / T(x,K(y,z)) = T(1 / x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7794,a(flip),b,8170,a)].">
      <j1 rule="hyper" parents="320 7794 8170"/>
    </justification>
  </clause>

  <clause id="8192">
    <literal><![CDATA[
      T(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(8174(a,1),7841(a,1))].">
      <j1 rule="para" parents="8174 7841"/>
    </justification>
  </clause>

  <clause id="8193">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7678,a,8179,a),flip(a)].">
      <j1 rule="hyper" parents="7678 8179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8194">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8179(a,1),7678(a,1))].">
      <j1 rule="para" parents="8179 7678"/>
    </justification>
  </clause>

  <clause id="8195">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,4714,a(flip),b,8193,a),flip(a)].">
      <j1 rule="hyper" parents="320 4714 8193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8196">
    <literal><![CDATA[
      T(x * y,T(z,y)) = T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7356,a(flip),b,8193,a),flip(a)].">
      <j1 rule="hyper" parents="58 7356 8193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8197">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8193(a,2),4796(a,1))].">
      <j1 rule="para" parents="8193 4796"/>
    </justification>
  </clause>

  <clause id="8199">
    <literal><![CDATA[
      T(1 / (x * K(y,z)),K(z,y)) = 1 / (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(6308(a,1),8191(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6308 8191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8200">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(4796,a,8195,a)].">
      <j1 rule="hyper" parents="4796 8195"/>
    </justification>
  </clause>

  <clause id="8203">
    <literal><![CDATA[
      K(x,T(y,z \ x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7673,a(flip),b,8200,a)].">
      <j1 rule="hyper" parents="58 7673 8200"/>
    </justification>
  </clause>

  <clause id="8204">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7342,a(flip),b,8200,a),flip(a)].">
      <j1 rule="hyper" parents="58 7342 8200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8205">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,T(y * z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7132,a(flip),b,8200,a)].">
      <j1 rule="hyper" parents="58 7132 8200"/>
    </justification>
  </clause>

  <clause id="8206">
    <literal><![CDATA[
      K(x,T(y,z \ y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7129,a(flip),b,8200,a)].">
      <j1 rule="hyper" parents="58 7129 8200"/>
    </justification>
  </clause>

  <clause id="8207">
    <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),8200(a,1,2))].">
      <j1 rule="para" parents="20 8200"/>
    </justification>
  </clause>

  <clause id="8208">
    <literal><![CDATA[
      K(x,T(y,1 / z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(75(a,1),8200(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 8200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8209">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),z)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),8200(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 8200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8210">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u / z))
    ]]></literal>
    <justification jstring="[para(4415(a,1),8200(a,1,2))].">
      <j1 rule="para" parents="4415 8200"/>
    </justification>
  </clause>

  <clause id="8211">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6095(a,1),8200(a,1,2))].">
      <j1 rule="para" parents="6095 8200"/>
    </justification>
  </clause>

  <clause id="8212">
    <literal><![CDATA[
      (x \ 1) * K(y,T(z,x)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(8200(a,1),7152(a,1,2))].">
      <j1 rule="para" parents="8200 7152"/>
    </justification>
  </clause>

  <clause id="8213">
    <literal><![CDATA[
      (x \ 1) * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(8200(a,1),7157(a,1,2))].">
      <j1 rule="para" parents="8200 7157"/>
    </justification>
  </clause>

  <clause id="8214">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ 1) = (z \ 1) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8200(a,1),7872(a,1,1))].">
      <j1 rule="para" parents="8200 7872"/>
    </justification>
  </clause>

  <clause id="8215">
    <literal><![CDATA[
      (x \ y) * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x \ y) = u
    ]]></literal>
    <justification jstring="[para(8203(a,1),7157(a,1,2))].">
      <j1 rule="para" parents="8203 7157"/>
    </justification>
  </clause>

  <clause id="8216">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ x) = (z \ x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8203(a,1),7872(a,1,1))].">
      <j1 rule="para" parents="8203 7872"/>
    </justification>
  </clause>

  <clause id="8217">
    <literal><![CDATA[
      K((x \ y) \ z,T(y,x)) = K(z / (x \ y),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7882,a(flip),b,8206,a),flip(a)].">
      <j1 rule="hyper" parents="58 7882 8206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8218">
    <literal><![CDATA[
      (x \ y) * K(z,T(y,x)) = K(z,y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(8206(a,1),7152(a,1,2))].">
      <j1 rule="para" parents="8206 7152"/>
    </justification>
  </clause>

  <clause id="8219">
    <literal><![CDATA[
      K(x,T(y,z)) * (1 / z) = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8208(a,1),7872(a,1,1))].">
      <j1 rule="para" parents="8208 7872"/>
    </justification>
  </clause>

  <clause id="8220">
    <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(213(a,1),8196(a,1,2)),flip(a)].">
      <j1 rule="para" parents="213 8196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8221">
    <literal><![CDATA[
      K(x * R(y,z,u),T(y,x)) = K(x * R(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(172(a,1),8204(a,1,2)),flip(a)].">
      <j1 rule="para" parents="172 8204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8222">
    <literal><![CDATA[
      K(L(x,y,z) * u,T(x,u)) = K(L(x,y,z) * u,x)
    ]]></literal>
    <justification jstring="[para(173(a,1),8204(a,2,2))].">
      <j1 rule="para" parents="173 8204"/>
    </justification>
  </clause>

  <clause id="8223">
    <literal><![CDATA[
      K(x / y,T(z,x \ y)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5155,a(flip),b,8211,a),flip(a)].">
      <j1 rule="hyper" parents="320 5155 8211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8224">
    <literal><![CDATA[
      K(x,T(y,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8211(a,1),7230(a,1))].">
      <j1 rule="para" parents="8211 7230"/>
    </justification>
  </clause>

  <clause id="8225">
    <literal><![CDATA[
      K(x,T(y,z \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8211(a,1),7689(a,1))].">
      <j1 rule="para" parents="8211 7689"/>
    </justification>
  </clause>

  <clause id="8226">
    <literal><![CDATA[
      T(x,L(K(y,z),T(z,u),w)) = T(z,K(y,x)) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,7922,a,b,7829,a),flip(a)].">
      <j1 rule="hyper" parents="320 7922 7829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8227">
    <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(849(a,2),7892(a,1,1))].">
      <j1 rule="para" parents="849 7892"/>
    </justification>
  </clause>

  <clause id="8228">
    <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(857(a,2),7892(a,1,1))].">
      <j1 rule="para" parents="857 7892"/>
    </justification>
  </clause>

  <clause id="8229">
    <literal><![CDATA[
      K(x * K(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(4711(a,1),7892(a,1,1))].">
      <j1 rule="para" parents="4711 7892"/>
    </justification>
  </clause>

  <clause id="8230">
    <literal><![CDATA[
      K(T(x * K(y,x),z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),T(u,y)) = w
    ]]></literal>
    <justification jstring="[para(4833(a,2),7892(a,1,1))].">
      <j1 rule="para" parents="4833 7892"/>
    </justification>
  </clause>

  <clause id="8231">
    <literal><![CDATA[
      K(x,T(y,L(z,u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7905,a(flip),b,7993,a),flip(a)].">
      <j1 rule="hyper" parents="320 7905 7993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8232">
    <literal><![CDATA[
      K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ (x * u)))
    ]]></literal>
    <justification jstring="[para(490(a,1),8231(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="490 8231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8233">
    <literal><![CDATA[
      K(T(x,y \ z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(7903(a,2),8014(a,1))].">
      <j1 rule="para" parents="7903 8014"/>
    </justification>
  </clause>

  <clause id="8234">
    <literal><![CDATA[
      K(x \ (y \ z),T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ z) / x,y) = u
    ]]></literal>
    <justification jstring="[para(7070(a,1),8028(a,1))].">
      <j1 rule="para" parents="7070 8028"/>
    </justification>
  </clause>

  <clause id="8235">
    <literal><![CDATA[
      K(((x \ y) \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7138(a,2),8028(a,1))].">
      <j1 rule="para" parents="7138 8028"/>
    </justification>
  </clause>

  <clause id="8236">
    <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(2955(a,1),8031(a,1))].">
      <j1 rule="para" parents="2955 8031"/>
    </justification>
  </clause>

  <clause id="8237">
    <literal><![CDATA[
      K(T(x \ y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7118(a,2),8031(a,1))].">
      <j1 rule="para" parents="7118 8031"/>
    </justification>
  </clause>

  <clause id="8238">
    <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(1403(a,1),8033(a,1,2,1))].">
      <j1 rule="para" parents="1403 8033"/>
    </justification>
  </clause>

  <clause id="8239">
    <literal><![CDATA[
      K((x / y) \ z,y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z / (x / y),y \ x) = u
    ]]></literal>
    <justification jstring="[para(275(a,1),8034(a,1,2))].">
      <j1 rule="para" parents="275 8034"/>
    </justification>
  </clause>

  <clause id="8240">
    <literal><![CDATA[
      K(x,K(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(5312(a,1),8154(a,1,2))].">
      <j1 rule="para" parents="5312 8154"/>
    </justification>
  </clause>

  <clause id="8241">
    <literal><![CDATA[
      T(x,K(y,z / (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(5311(a,2),8175(a,1,2))].">
      <j1 rule="para" parents="5311 8175"/>
    </justification>
  </clause>

  <clause id="8242">
    <literal><![CDATA[
      T(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(2939(a,1),8194(a,1,2))].">
      <j1 rule="para" parents="2939 8194"/>
    </justification>
  </clause>

  <clause id="8243">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7129(a,2),8224(a,1))].">
      <j1 rule="para" parents="7129 8224"/>
    </justification>
  </clause>

  <clause id="8244">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(7509(a,1),8224(a,1))].">
      <j1 rule="para" parents="7509 8224"/>
    </justification>
  </clause>

  <clause id="8245">
    <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(8205(a,1),8225(a,1))].">
      <j1 rule="para" parents="8205 8225"/>
    </justification>
  </clause>

  <clause id="8246">
    <literal><![CDATA[
      K(x,T(y,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(2936(a,2),8243(a,1,2))].">
      <j1 rule="para" parents="2936 8243"/>
    </justification>
  </clause>

  <clause id="8247">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(4415(a,1),8243(a,1,2))].">
      <j1 rule="para" parents="4415 8243"/>
    </justification>
  </clause>

  <clause id="8248">
    <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(7638(a,1),8243(a,1,2))].">
      <j1 rule="para" parents="7638 8243"/>
    </justification>
  </clause>

  <clause id="8249">
    <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(3873(a,2),7532(a,1,2,1))].">
      <j1 rule="para" parents="3873 7532"/>
    </justification>
  </clause>

  <clause id="8250">
    <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),7534(a,1,2,1,1))].">
      <j1 rule="para" parents="18 7534"/>
    </justification>
  </clause>

  <clause id="8251">
    <literal><![CDATA[
      K(x / y,((x / (x / y)) / z) * u) = K(x / y,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(244(a,1),7534(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="244 7534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8253">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T(y \ x,u)) = K(z * ((x \ y) \ 1),T(y \ x,u))
    ]]></literal>
    <justification jstring="[para(6143(a,1),7545(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6143 7545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8254">
    <literal><![CDATA[
      T(T(x,y) \ T(x * z,u),x) = T(x,y) \ T(z * x,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,4555,a(flip),b,7553,a),flip(a)].">
      <j1 rule="hyper" parents="116 4555 7553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8255">
    <literal><![CDATA[
      K(x * (((y \ 1) \ z) / z),y) = K(x * (z \ ((y \ 1) \ z)),y)
    ]]></literal>
    <justification jstring="[para(4146(a,1),7557(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4146 7557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8256">
    <literal><![CDATA[
      T((1 / ((x * y) \ x)) * K(y,z),y) = ((1 / ((x * y) \ x)) / y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(682(a,1),7560(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="682 7560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8257">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ x) / z)) = x * K(z,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(7568(a,1),3547(a,2,2))].">
      <j1 rule="para" parents="7568 3547"/>
    </justification>
  </clause>

  <clause id="8258">
    <literal><![CDATA[
      T(T(x,y) * (x \ z),x) = T(x,y) * (x \ T(z,x))
    ]]></literal>
    <justification jstring="[hyper(239,a,7580,a,b,1105,a)].">
      <j1 rule="hyper" parents="239 7580 1105"/>
    </justification>
  </clause>

  <clause id="8260">
    <literal><![CDATA[
      K(x,y) * K(z \ 1,x) = z * T(z \ K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(991,a,7619,a),flip(a)].">
      <j1 rule="hyper" parents="991 7619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8261">
    <literal><![CDATA[
      (x * (y * K(z,y))) / (x * K(z,y * K(z,y))) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(320,a,4836,a(flip),b,7629,a),flip(a)].">
      <j1 rule="hyper" parents="320 4836 7629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8262">
    <literal><![CDATA[
      K(x,T(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(7635(a,1),7981(a,1))].">
      <j1 rule="para" parents="7635 7981"/>
    </justification>
  </clause>

  <clause id="8263">
    <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(7189(a,1),8262(a,1))].">
      <j1 rule="para" parents="7189 8262"/>
    </justification>
  </clause>

  <clause id="8264">
    <literal><![CDATA[
      T(x,T(y,z)) * K(z,x) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7884,a(flip),b,7636,a),flip(a)].">
      <j1 rule="hyper" parents="58 7884 7636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8265">
    <literal><![CDATA[
      K(x * K(T(x,y),z),T(u,y)) = K(K(y,x) * T(x,z),u)
    ]]></literal>
    <justification jstring="[para(7641(a,1),7863(a,1,1))].">
      <j1 rule="para" parents="7641 7863"/>
    </justification>
  </clause>

  <clause id="8266">
    <literal><![CDATA[
      T(x,T(T(y,z),y * u)) = T(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(4(a,1),7664(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 7664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8267">
    <literal><![CDATA[
      K(x,T(y \ x,z / y)) = K(x,T(y \ x,y \ z))
    ]]></literal>
    <justification jstring="[para(107(a,1),7677(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 7677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8268">
    <literal><![CDATA[
      K(R(K(x,y) * z,u,w),y) = K(R(z * K(x,y),u,w),y)
    ]]></literal>
    <justification jstring="[para(6322(a,1),7713(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6322 7713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8269">
    <literal><![CDATA[
      K((x \ 1) \ (y \ z),y) = K((x \ y) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3961,a(flip),b,7723,a),flip(a)].">
      <j1 rule="hyper" parents="58 3961 7723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8270">
    <literal><![CDATA[
      K(x,T(y \ z,u \ z)) = K(x,T(y \ z,u \ y))
    ]]></literal>
    <justification jstring="[para(5(a,1),7726(a,1,2,2,2))].">
      <j1 rule="para" parents="5 7726"/>
    </justification>
  </clause>

  <clause id="8271">
    <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(8056(a,1),7747(a,1,1))].">
      <j1 rule="para" parents="8056 7747"/>
    </justification>
  </clause>

  <clause id="8272">
    <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,4777,a(flip),b,7762,a)].">
      <j1 rule="hyper" parents="116 4777 7762"/>
    </justification>
  </clause>

  <clause id="8273">
    <literal><![CDATA[
      K(x,K(y,z)) * (z / K(x,y)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(6306(a,2),7773(a,1,2))].">
      <j1 rule="para" parents="6306 7773"/>
    </justification>
  </clause>

  <clause id="8274">
    <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,5375,a(flip),b,7795,a)].">
      <j1 rule="hyper" parents="116 5375 7795"/>
    </justification>
  </clause>

  <clause id="8275">
    <literal><![CDATA[
      K(1 / x,y) \ K(K(1 / x,y),z) = K(1 / T(x,z),y) \ 1
    ]]></literal>
    <justification jstring="[para(5510(a,2),7797(a,2,1))].">
      <j1 rule="para" parents="5510 7797"/>
    </justification>
  </clause>

  <clause id="8276">
    <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(7857(a,1),7797(a,2,1))].">
      <j1 rule="para" parents="7857 7797"/>
    </justification>
  </clause>

  <clause id="8277">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(7837(a,1),7825(a,1,1))].">
      <j1 rule="para" parents="7837 7825"/>
    </justification>
  </clause>

  <clause id="8278">
    <literal><![CDATA[
      K(R(x / (x / y),z,u),w) = K(R(y,z,u),T(w,y \ x))
    ]]></literal>
    <justification jstring="[para(4305(a,1),7885(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4305 7885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8279">
    <literal><![CDATA[
      K(K(R(x,y,z),u) * w,T(x,v5)) = K(w,T(x,v5))
    ]]></literal>
    <justification jstring="[para(7885(a,1),7393(a,1,1,1))].">
      <j1 rule="para" parents="7885 7393"/>
    </justification>
  </clause>

  <clause id="8280">
    <literal><![CDATA[
      L(K(T(x,y),T(z,y)),u,w) = K(L(x,u / T(x,y),w),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6584,a(flip),b,7886,a)].">
      <j1 rule="hyper" parents="58 6584 7886"/>
    </justification>
  </clause>

  <clause id="8281">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(L(x,T(x,y) \ 1,u),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6466,a(flip),b,7886,a)].">
      <j1 rule="hyper" parents="58 6466 7886"/>
    </justification>
  </clause>

  <clause id="8282">
    <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(1619(a,1),7886(a,1,1))].">
      <j1 rule="para" parents="1619 7886"/>
    </justification>
  </clause>

  <clause id="8283">
    <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(6585,a,7898,a)].">
      <j1 rule="hyper" parents="6585 7898"/>
    </justification>
  </clause>

  <clause id="8284">
    <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(1619(a,1),7898(a,1,2))].">
      <j1 rule="para" parents="1619 7898"/>
    </justification>
  </clause>

  <clause id="8285">
    <literal><![CDATA[
      K(K(x,y) * T(y,z),T(u,z)) = K(y * K(T(x,z),y),u)
    ]]></literal>
    <justification jstring="[para(7907(a,1),7863(a,1,1))].">
      <j1 rule="para" parents="7907 7863"/>
    </justification>
  </clause>

  <clause id="8286">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ x = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7916(a,1),7908(a,1,1))].">
      <j1 rule="para" parents="7916 7908"/>
    </justification>
  </clause>

  <clause id="8287">
    <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(7538(a,1),7919(a,1,2,1,1))].">
      <j1 rule="para" parents="7538 7919"/>
    </justification>
  </clause>

  <clause id="8288">
    <literal><![CDATA[
      T(T(x,y / z),K(z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8177,a(flip),b,7923,a)].">
      <j1 rule="hyper" parents="58 8177 7923"/>
    </justification>
  </clause>

  <clause id="8289">
    <literal><![CDATA[
      T(T(x,y \ z),K(y,z)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(7826,a,8288,a)].">
      <j1 rule="hyper" parents="7826 8288"/>
    </justification>
  </clause>

  <clause id="8290">
    <literal><![CDATA[
      T(T(x,K(y,z)),z / y) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(435,a,8288,a)].">
      <j1 rule="hyper" parents="435 8288"/>
    </justification>
  </clause>

  <clause id="8291">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7820,a,b,8288,a)].">
      <j1 rule="hyper" parents="58 7820 8288"/>
    </justification>
  </clause>

  <clause id="8292">
    <literal><![CDATA[
      T(T(x,y \ z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(8288(a,1),7825(a,1,1))].">
      <j1 rule="para" parents="8288 7825"/>
    </justification>
  </clause>

  <clause id="8293">
    <literal><![CDATA[
      T(T(x,K(y,z)),z \ y) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7820,a,b,8289,a)].">
      <j1 rule="hyper" parents="58 7820 8289"/>
    </justification>
  </clause>

  <clause id="8295">
    <literal><![CDATA[
      T(x * K(y / z,x),z \ y) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5167,a,8291,a)].">
      <j1 rule="hyper" parents="5167 8291"/>
    </justification>
  </clause>

  <clause id="8296">
    <literal><![CDATA[
      T(x / (y / z),z \ y) = T((y / z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(678,a,8291,a),flip(a)].">
      <j1 rule="hyper" parents="678 8291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8297">
    <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(5283(a,1),8293(a,1,1,2))].">
      <j1 rule="para" parents="5283 8293"/>
    </justification>
  </clause>

  <clause id="8298">
    <literal><![CDATA[
      T(T(x,K(y,T(z,u))),z \ T(y,u)) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[para(7133(a,1),8293(a,1,1,2))].">
      <j1 rule="para" parents="7133 8293"/>
    </justification>
  </clause>

  <clause id="8299">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = K(z \ y,z) * T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(7917(a,1),7925(a,1,1))].">
      <j1 rule="para" parents="7917 7925"/>
    </justification>
  </clause>

  <clause id="8300">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) = K((x / z) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6739,a(flip),b,7945,a),flip(a)].">
      <j1 rule="hyper" parents="320 6739 7945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8301">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((x / z) \ y,y) = u
    ]]></literal>
    <justification jstring="[para(7945(a,2),6740(a,1))].">
      <j1 rule="para" parents="7945 6740"/>
    </justification>
  </clause>

  <clause id="8302">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,6935,a(flip),b,7946,a),flip(a)].">
      <j1 rule="hyper" parents="320 6935 7946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8303">
    <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(4206(a,1),7949(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4206 7949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8304">
    <literal><![CDATA[
      T(K(x,y),z) * (z / y) = z / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,6293,a(flip),b,7966,a),flip(a)].">
      <j1 rule="hyper" parents="320 6293 7966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8305">
    <literal><![CDATA[
      K(x,y) * (K(z,y) / y) = K(z,y) / T(y,x)
    ]]></literal>
    <justification jstring="[para(5600(a,1),8304(a,1,1))].">
      <j1 rule="para" parents="5600 8304"/>
    </justification>
  </clause>

  <clause id="8306">
    <literal><![CDATA[
      K(x,y \ z) * (z / (z / y)) = z / T(z / y,x)
    ]]></literal>
    <justification jstring="[para(6096(a,1),8304(a,1,1))].">
      <j1 rule="para" parents="6096 8304"/>
    </justification>
  </clause>

  <clause id="8307">
    <literal><![CDATA[
      K(T(x,y),z) * (y / z) = y / T(z,x)
    ]]></literal>
    <justification jstring="[para(7118(a,2),8304(a,1,1))].">
      <j1 rule="para" parents="7118 8304"/>
    </justification>
  </clause>

  <clause id="8308">
    <literal><![CDATA[
      K(x,y) * (z / T(y,z)) = z / T(T(y,z),x)
    ]]></literal>
    <justification jstring="[para(7854(a,1),8304(a,1,1))].">
      <j1 rule="para" parents="7854 8304"/>
    </justification>
  </clause>

  <clause id="8309">
    <literal><![CDATA[
      T(x / T(y,z),y) = T(y,T(z,x)) \ x
    ]]></literal>
    <justification jstring="[para(8307(a,1),7592(a,1,1))].">
      <j1 rule="para" parents="8307 7592"/>
    </justification>
  </clause>

  <clause id="8310">
    <literal><![CDATA[
      T(x \ y,T(z,x)) != (x \ y) * u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7972(a,1),38(a,1))].">
      <j1 rule="para" parents="7972 38"/>
    </justification>
  </clause>

  <clause id="8311">
    <literal><![CDATA[
      K(T(x * y,y) / x,z) = K(y,T(T(z,x),x * y))
    ]]></literal>
    <justification jstring="[hyper(8034,a,7979,a)].">
      <j1 rule="hyper" parents="8034 7979"/>
    </justification>
  </clause>

  <clause id="8312">
    <literal><![CDATA[
      T(x,K(y,z / y) / (z \ y)) = T(x,T(1 / (z \ y),y))
    ]]></literal>
    <justification jstring="[para(5181(a,1),8004(a,1,2,1))].">
      <j1 rule="para" parents="5181 8004"/>
    </justification>
  </clause>

  <clause id="8313">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * x) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(4358,a,8017,a)].">
      <j1 rule="hyper" parents="4358 8017"/>
    </justification>
  </clause>

  <clause id="8314">
    <literal><![CDATA[
      K(x * T(y,z),T(u,K(y,z))) = K(K(y,z) * (x * y),u)
    ]]></literal>
    <justification jstring="[para(8064(a,1),7133(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8064 7133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8315">
    <literal><![CDATA[
      K((x / (x / y)) \ 1,z) = K(y \ 1,T(z,x))
    ]]></literal>
    <justification jstring="[para(75(a,1),8098(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 8098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8316">
    <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(8102(a,2),5119(a,1,1))].">
      <j1 rule="para" parents="8102 5119"/>
    </justification>
  </clause>

  <clause id="8317">
    <literal><![CDATA[
      T(x,y) * T(x \ K(x,z),x) = (x \ K(x,z)) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8107,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 8107 17"/>
    </justification>
  </clause>

  <clause id="8318">
    <literal><![CDATA[
      T(x,1 / T(T(y,z),z)) = T(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4764,a,b,8112,a),flip(a)].">
      <j1 rule="hyper" parents="320 4764 8112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8319">
    <literal><![CDATA[
      T(x,1 / T(y \ z,y)) = T(x,1 / (z / y))
    ]]></literal>
    <justification jstring="[para(107(a,1),8318(a,1,2,2,1))].">
      <j1 rule="para" parents="107 8318"/>
    </justification>
  </clause>

  <clause id="8320">
    <literal><![CDATA[
      K(L(x / (y \ 1),y \ 1,y) \ 1,z) = K(T(y * x,y \ 1) \ 1,z)
    ]]></literal>
    <justification jstring="[para(859(a,1),8116(a,1,1,1))].">
      <j1 rule="para" parents="859 8116"/>
    </justification>
  </clause>

  <clause id="8321">
    <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(8118(a,2),38(a,1))].">
      <j1 rule="para" parents="8118 38"/>
    </justification>
  </clause>

  <clause id="8322">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8118(a,1),4890(a,1,1))].">
      <j1 rule="para" parents="8118 4890"/>
    </justification>
  </clause>

  <clause id="8323">
    <literal><![CDATA[
      K(x,y \ T(z,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(8122(a,2),8262(a,1))].">
      <j1 rule="para" parents="8122 8262"/>
    </justification>
  </clause>

  <clause id="8324">
    <literal><![CDATA[
      x / T(y,K(x,z)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7744,a(flip),b,8133,a)].">
      <j1 rule="hyper" parents="58 7744 8133"/>
    </justification>
  </clause>

  <clause id="8325">
    <literal><![CDATA[
      x / T(y,K(z,x)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(7807(a,1),8324(a,1,2))].">
      <j1 rule="para" parents="7807 8324"/>
    </justification>
  </clause>

  <clause id="8326">
    <literal><![CDATA[
      x / T(y,K(z,x)) = T(x / y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,7807,a,b,8325,a),flip(a)].">
      <j1 rule="hyper" parents="320 7807 8325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8327">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y / x,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(7759(a,1),8136(a,1,1))].">
      <j1 rule="para" parents="7759 8136"/>
    </justification>
  </clause>

  <clause id="8328">
    <literal><![CDATA[
      K(x,y \ z) * K(z,K(y,x)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(5125,a,8144,a)].">
      <j1 rule="hyper" parents="5125 8144"/>
    </justification>
  </clause>

  <clause id="8329">
    <literal><![CDATA[
      T(x \ y,K(y,z)) = T(x,K(y,z)) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,7801,a(flip),b,8155,a),flip(a)].">
      <j1 rule="hyper" parents="58 7801 8155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8330">
    <literal><![CDATA[
      T(K(x,y),z \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7738,a(flip),b,8164,a),flip(a)].">
      <j1 rule="hyper" parents="58 7738 8164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8331">
    <literal><![CDATA[
      K(T(x,y \ 1) \ 1,z) = T(K(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(5507,a,8330,a)].">
      <j1 rule="hyper" parents="5507 8330"/>
    </justification>
  </clause>

  <clause id="8332">
    <literal><![CDATA[
      T(K(x,y),z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(8330(a,1),3010(a,1))].">
      <j1 rule="para" parents="8330 3010"/>
    </justification>
  </clause>

  <clause id="8335">
    <literal><![CDATA[
      K(x,y) * T(y,T(z,x)) = T(y * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(2902,a,8264,a)].">
      <j1 rule="hyper" parents="2902 8264"/>
    </justification>
  </clause>

  <clause id="8336">
    <literal><![CDATA[
      K((x \ y) \ (z * y),y) = K((x \ 1) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7347,a(flip),b,8269,a),flip(a)].">
      <j1 rule="hyper" parents="58 7347 8269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8337">
    <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(5904(a,1),8273(a,1,1,2))].">
      <j1 rule="para" parents="5904 8273"/>
    </justification>
  </clause>

  <clause id="8338">
    <literal><![CDATA[
      (K(x,y) * T(x,K(z,u))) \ x = K(z,K(u,x)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7730(a,1),8286(a,2,1))].">
      <j1 rule="para" parents="7730 8286"/>
    </justification>
  </clause>

  <clause id="8339">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(8295(a,1),4890(a,1,1))].">
      <j1 rule="para" parents="8295 4890"/>
    </justification>
  </clause>

  <clause id="8340">
    <literal><![CDATA[
      x * (T(x,y) \ (K(z,x) / x)) = K(z,x) / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(5225,a,8305,a)].">
      <j1 rule="hyper" parents="5225 8305"/>
    </justification>
  </clause>

  <clause id="8341">
    <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(8308(a,2),2595(a,2,1,2))].">
      <j1 rule="para" parents="8308 2595"/>
    </justification>
  </clause>

  <clause id="8342">
    <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(8308(a,2),6402(a,1,2,1,2))].">
      <j1 rule="para" parents="8308 6402"/>
    </justification>
  </clause>

  <clause id="8343">
    <literal><![CDATA[
      K(x,y) * T(z,T(z * x,y)) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8313,a(flip),b,108,a)].">
      <j1 rule="hyper" parents="119 8313 108"/>
    </justification>
  </clause>

  <clause id="8344">
    <literal><![CDATA[
      T(x,1 / (((y \ z) \ z) \ z)) = T(x,1 / (z / y))
    ]]></literal>
    <justification jstring="[para(4199(a,1),8319(a,1,2,2))].">
      <j1 rule="para" parents="4199 8319"/>
    </justification>
  </clause>

  <clause id="8345">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ y,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,7798,a,b,8327,a)].">
      <j1 rule="hyper" parents="29 7798 8327"/>
    </justification>
  </clause>

  <clause id="8346">
    <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(4871(a,1),8327(a,1,2))].">
      <j1 rule="para" parents="4871 8327"/>
    </justification>
  </clause>

  <clause id="8347">
    <literal><![CDATA[
      K(x,y \ z) * K(x,K(z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(7759(a,1),8328(a,1,2))].">
      <j1 rule="para" parents="7759 8328"/>
    </justification>
  </clause>

  <clause id="8348">
    <literal><![CDATA[
      K(T(x,y \ 1) \ 1,z) = K(T(x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5505,a,b,8331,a),flip(a)].">
      <j1 rule="hyper" parents="320 5505 8331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8349">
    <literal><![CDATA[
      K(x,y) \ T(x,T(z,y)) = T(x * K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(5129,a,8335,a)].">
      <j1 rule="hyper" parents="5129 8335"/>
    </justification>
  </clause>

  <clause id="8350">
    <literal><![CDATA[
      K(x,y) * T(x * K(y,x),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(5109,a,8335,a)].">
      <j1 rule="hyper" parents="5109 8335"/>
    </justification>
  </clause>

  <clause id="8351">
    <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(8335(a,1),5110(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8335 5110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8352">
    <literal><![CDATA[
      T(x,(y \ x) \ (z * x)) = 1 / (x \ K((y \ 1) \ z,x))
    ]]></literal>
    <justification jstring="[para(8336(a,1),4953(a,2,2,2))].">
      <j1 rule="para" parents="8336 4953"/>
    </justification>
  </clause>

  <clause id="8353">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ z,y) = K(z / x,y)
    ]]></literal>
    <justification jstring="[para(7772(a,1),8345(a,1,1))].">
      <j1 rule="para" parents="7772 8345"/>
    </justification>
  </clause>

  <clause id="8354">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z \ y) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(5603,a,8347,a)].">
      <j1 rule="hyper" parents="5603 8347"/>
    </justification>
  </clause>

  <clause id="8355">
    <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(7005(a,1),8347(a,1,2,2))].">
      <j1 rule="para" parents="7005 8347"/>
    </justification>
  </clause>

  <clause id="8356">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z \ x) = K(y,x / z)
    ]]></literal>
    <justification jstring="[para(7754(a,1),8354(a,1,1))].">
      <j1 rule="para" parents="7754 8354"/>
    </justification>
  </clause>

  <clause id="8357">
    <literal><![CDATA[
      K(K(x,y),z) * K(y,z \ x) = K(y,x / z)
    ]]></literal>
    <justification jstring="[para(7758(a,2),8354(a,1,1))].">
      <j1 rule="para" parents="7758 8354"/>
    </justification>
  </clause>

  <clause id="8358">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(7772(a,1),8354(a,1,1))].">
      <j1 rule="para" parents="7772 8354"/>
    </justification>
  </clause>

  <clause id="8359">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y / x) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(5109,a,8357,a)].">
      <j1 rule="hyper" parents="5109 8357"/>
    </justification>
  </clause>

  <clause id="8360">
    <literal><![CDATA[
      K(x,y / z) * K(z \ y,x) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6315,a,8358,a)].">
      <j1 rule="hyper" parents="6315 8358"/>
    </justification>
  </clause>

  <clause id="8361">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(29,a,7798,a,b,8358,a)].">
      <j1 rule="hyper" parents="29 7798 8358"/>
    </justification>
  </clause>

  <clause id="8362">
    <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(7005(a,1),8358(a,1,1,2))].">
      <j1 rule="para" parents="7005 8358"/>
    </justification>
  </clause>

  <clause id="8363">
    <literal><![CDATA[
      K(x / y,z) * K(z,K(y,x)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(5109,a,8360,a)].">
      <j1 rule="hyper" parents="5109 8360"/>
    </justification>
  </clause>

  <clause id="8364">
    <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(1400(a,1),8361(a,1,2,2))].">
      <j1 rule="para" parents="1400 8361"/>
    </justification>
  </clause>

  <clause id="8365">
    <literal><![CDATA[
      L(K(x,y),z * x,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(7045(a,1),6470(a,1))].">
      <j1 rule="para" parents="7045 6470"/>
    </justification>
  </clause>

  <clause id="8366">
    <literal><![CDATA[
      K(T(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) * u = w
    ]]></literal>
    <justification jstring="[para(5092(a,1),7199(a,1))].">
      <j1 rule="para" parents="5092 7199"/>
    </justification>
  </clause>

  <clause id="8367">
    <literal><![CDATA[
      x * K(T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(y,T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(6306(a,1),7205(a,1))].">
      <j1 rule="para" parents="6306 7205"/>
    </justification>
  </clause>

  <clause id="8368">
    <literal><![CDATA[
      K(x,R(y,K(z,x),u)) = K(x,y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6928,a(flip),b,7226,a)].">
      <j1 rule="hyper" parents="58 6928 7226"/>
    </justification>
  </clause>

  <clause id="8369">
    <literal><![CDATA[
      K(x,y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7226(a,1),384(a,1)),flip(b)].">
      <j1 rule="para" parents="7226 384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8370">
    <literal><![CDATA[
      K(x,y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(84(a,1),8369(a,1,2))].">
      <j1 rule="para" parents="84 8369"/>
    </justification>
  </clause>

  <clause id="8371">
    <literal><![CDATA[
      K(x,y \ T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(1420(a,1),8369(a,1,2))].">
      <j1 rule="para" parents="1420 8369"/>
    </justification>
  </clause>

  <clause id="8372">
    <literal><![CDATA[
      K(x,T(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(5500(a,1),8369(a,1,2))].">
      <j1 rule="para" parents="5500 8369"/>
    </justification>
  </clause>

  <clause id="8373">
    <literal><![CDATA[
      K(x,y / (z / x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(6192(a,1),8369(a,1,2))].">
      <j1 rule="para" parents="6192 8369"/>
    </justification>
  </clause>

  <clause id="8374">
    <literal><![CDATA[
      K(x,K(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7122(a,1),8369(a,1,2))].">
      <j1 rule="para" parents="7122 8369"/>
    </justification>
  </clause>

  <clause id="8375">
    <literal><![CDATA[
      K(L(x,y,z),y * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = u
    ]]></literal>
    <justification jstring="[para(6589(a,2),8370(a,1))].">
      <j1 rule="para" parents="6589 8370"/>
    </justification>
  </clause>

  <clause id="8377">
    <literal><![CDATA[
      K(x,R(y,K(z,x),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7216,a(flip),b,8368,a),flip(a)].">
      <j1 rule="hyper" parents="320 7216 8368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8379">
    <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),8377(a,1,2))].">
      <j1 rule="para" parents="26 8377"/>
    </justification>
  </clause>

  <clause id="8380">
    <literal><![CDATA[
      K(x,y \ (x \ (z * x))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(17(a,1),8371(a,1,2,2))].">
      <j1 rule="para" parents="17 8371"/>
    </justification>
  </clause>

  <clause id="8381">
    <literal><![CDATA[
      K(x,y \ R(T(z,x),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ R(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(22(a,2),8371(a,1,2,2))].">
      <j1 rule="para" parents="22 8371"/>
    </justification>
  </clause>

  <clause id="8383">
    <literal><![CDATA[
      T(x,K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(7254(a,2),373(a,1)),flip(b)].">
      <j1 rule="para" parents="7254 373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8384">
    <literal><![CDATA[
      T(x,(x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(y / x) * z) = u
    ]]></literal>
    <justification jstring="[para(5405(a,1),8383(a,1,2))].">
      <j1 rule="para" parents="5405 8383"/>
    </justification>
  </clause>

  <clause id="8386">
    <literal><![CDATA[
      K(R(x,K(y,z),u),z) = K(x * K(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6716,a(flip),b,7310,a)].">
      <j1 rule="hyper" parents="58 6716 7310"/>
    </justification>
  </clause>

  <clause id="8387">
    <literal><![CDATA[
      K(R(x,K(y,z),u),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7306,a(flip),b,8386,a),flip(a)].">
      <j1 rule="hyper" parents="320 7306 8386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8389">
    <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),8387(a,1,1))].">
      <j1 rule="para" parents="26 8387"/>
    </justification>
  </clause>

  <clause id="8390">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6586,a(flip),b,7328,a)].">
      <j1 rule="hyper" parents="58 6586 7328"/>
    </justification>
  </clause>

  <clause id="8391">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7316,a(flip),b,8390,a),flip(a)].">
      <j1 rule="hyper" parents="320 7316 8390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8392">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(8390(a,2),7330(a,1))].">
      <j1 rule="para" parents="8390 7330"/>
    </justification>
  </clause>

  <clause id="8394">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(K(y,z) \ (x \ u),y)
    ]]></literal>
    <justification jstring="[para(298(a,1),8391(a,1,1))].">
      <j1 rule="para" parents="298 8391"/>
    </justification>
  </clause>

  <clause id="8395">
    <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(7475(a,1),6846(a,1))].">
      <j1 rule="para" parents="7475 6846"/>
    </justification>
  </clause>

  <clause id="8396">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,x)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(6641(a,1),7554(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6641 7554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8397">
    <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(4148(a,1),7569(a,2,2,2,2))].">
      <j1 rule="para" parents="4148 7569"/>
    </justification>
  </clause>

  <clause id="8398">
    <literal><![CDATA[
      K(x,T(y,z * (u * K(w,x)))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(90(a,1),7643(a,1,2,2))].">
      <j1 rule="para" parents="90 7643"/>
    </justification>
  </clause>

  <clause id="8399">
    <literal><![CDATA[
      T(K(x,y),z * (u * K(w,x))) = T(K(x,y),z * u)
    ]]></literal>
    <justification jstring="[para(90(a,1),7676(a,1,2))].">
      <j1 rule="para" parents="90 7676"/>
    </justification>
  </clause>

  <clause id="8400">
    <literal><![CDATA[
      K((x * y) \ (z * y),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(7442(a,2),7694(a,1))].">
      <j1 rule="para" parents="7442 7694"/>
    </justification>
  </clause>

  <clause id="8401">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((z \ x) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(7444(a,1),7694(a,1))].">
      <j1 rule="para" parents="7444 7694"/>
    </justification>
  </clause>

  <clause id="8403">
    <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),7717(a,1,2,1,1))].">
      <j1 rule="para" parents="6 7717"/>
    </justification>
  </clause>

  <clause id="8404">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(7741(a,1),7746(a,1))].">
      <j1 rule="para" parents="7741 7746"/>
    </justification>
  </clause>

  <clause id="8405">
    <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(7790(a,2),7746(a,1,2))].">
      <j1 rule="para" parents="7790 7746"/>
    </justification>
  </clause>

  <clause id="8406">
    <literal><![CDATA[
      K((x \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(7138(a,2),8404(a,1))].">
      <j1 rule="para" parents="7138 8404"/>
    </justification>
  </clause>

  <clause id="8407">
    <literal><![CDATA[
      K(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,z \ y),z) = u
    ]]></literal>
    <justification jstring="[para(7888(a,1),8404(a,1))].">
      <j1 rule="para" parents="7888 8404"/>
    </justification>
  </clause>

  <clause id="8408">
    <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(8105(a,2),8022(a,1))].">
      <j1 rule="para" parents="8105 8022"/>
    </justification>
  </clause>

  <clause id="8409">
    <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(7514(a,1),8044(a,1,2))].">
      <j1 rule="para" parents="7514 8044"/>
    </justification>
  </clause>

  <clause id="8410">
    <literal><![CDATA[
      K(L(x,T(x,y) \ 1,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(8029,a,8281,a),flip(a)].">
      <j1 rule="hyper" parents="8029 8281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8412">
    <literal><![CDATA[
      K(L(x,x \ K(y,x),z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(4763(a,1),8410(a,1,1,2))].">
      <j1 rule="para" parents="4763 8410"/>
    </justification>
  </clause>

  <clause id="8413">
    <literal><![CDATA[
      T(T(x,K(y,z)),z \ y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(7820(a,2),8292(a,1))].">
      <j1 rule="para" parents="7820 8292"/>
    </justification>
  </clause>

  <clause id="8414">
    <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(7045(a,2),8365(a,1))].">
      <j1 rule="para" parents="7045 8365"/>
    </justification>
  </clause>

  <clause id="8415">
    <literal><![CDATA[
      T(K(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7118(a,1),8366(a,1,1))].">
      <j1 rule="para" parents="7118 8366"/>
    </justification>
  </clause>

  <clause id="8416">
    <literal><![CDATA[
      x * T(K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(7118(a,1),8367(a,1,2))].">
      <j1 rule="para" parents="7118 8367"/>
    </justification>
  </clause>

  <clause id="8417">
    <literal><![CDATA[
      K(x,(y * x) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(7072(a,2),8373(a,1))].">
      <j1 rule="para" parents="7072 8373"/>
    </justification>
  </clause>

  <clause id="8418">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(8380,a,7411,a)].">
      <j1 rule="hyper" parents="8380 7411"/>
    </justification>
  </clause>

  <clause id="8419">
    <literal><![CDATA[
      K(x,(x * y) \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(7022(a,2),8380(a,1))].">
      <j1 rule="para" parents="7022 8380"/>
    </justification>
  </clause>

  <clause id="8420">
    <literal><![CDATA[
      K(x,(y / x) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(7397,a,8418,a)].">
      <j1 rule="hyper" parents="7397 8418"/>
    </justification>
  </clause>

  <clause id="8421">
    <literal><![CDATA[
      T(x,(x \ y) \ z) = T(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(118,a,8418,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 8418 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8422">
    <literal><![CDATA[
      K(x,y \ ((x \ z) * x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7411,a(flip),b,8418,a),flip(a)].">
      <j1 rule="hyper" parents="58 7411 8418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8423">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7005,a(flip),b,8418,a),flip(a)].">
      <j1 rule="hyper" parents="58 7005 8418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8424">
    <literal><![CDATA[
      K(x,y \ (((x \ y) * z) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),8418(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 8418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8425">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (x \ y)) \ u)
    ]]></literal>
    <justification jstring="[para(8418(a,1),6556(a,1,1))].">
      <j1 rule="para" parents="8418 6556"/>
    </justification>
  </clause>

  <clause id="8426">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z \ (u * y))) = K(x,T(y,(y \ z) \ u))
    ]]></literal>
    <justification jstring="[para(8418(a,1),7741(a,1,2,2))].">
      <j1 rule="para" parents="8418 7741"/>
    </justification>
  </clause>

  <clause id="8427">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / x) \ z) = u
    ]]></literal>
    <justification jstring="[para(8418(a,1),7397(a,1))].">
      <j1 rule="para" parents="8418 7397"/>
    </justification>
  </clause>

  <clause id="8428">
    <literal><![CDATA[
      T(x,(y / x) \ z) = T(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(118,a,8420,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 8420 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8429">
    <literal><![CDATA[
      T(x,y \ ((x \ z) * x)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7487,a(flip),b,8421,a),flip(a)].">
      <j1 rule="hyper" parents="58 7487 8421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8430">
    <literal><![CDATA[
      K(x,T(y,(y \ z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(8421(a,2),7726(a,1,2))].">
      <j1 rule="para" parents="8421 7726"/>
    </justification>
  </clause>

  <clause id="8431">
    <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(8428(a,1),4765(a,1,1,1))].">
      <j1 rule="para" parents="8428 4765"/>
    </justification>
  </clause>

  <clause id="8432">
    <literal><![CDATA[
      T(x,y \ ((x \ z) * x)) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(8429(a,2),4817(a,1))].">
      <j1 rule="para" parents="8429 4817"/>
    </justification>
  </clause>

  <clause id="8433">
    <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(8429(a,1),4765(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8429 4765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8434">
    <literal><![CDATA[
      K(x \ y,T(x,y \ z)) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(7689,a,8430,a),flip(a)].">
      <j1 rule="hyper" parents="7689 8430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8435">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z \ u)) = K(x,T(y,(y \ z) \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7741,a,b,8430,a)].">
      <j1 rule="hyper" parents="320 7741 8430"/>
    </justification>
  </clause>

  <clause id="8436">
    <literal><![CDATA[
      K(x,T(y,(y * z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(4(a,1),8430(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 8430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8437">
    <literal><![CDATA[
      K(x \ y,T(x,y * z)) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),8434(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8438">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(x \ (y / z),T(x,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),8434(a,1,2,2))].">
      <j1 rule="para" parents="75 8434"/>
    </justification>
  </clause>

  <clause id="8439">
    <literal><![CDATA[
      K(x * y,T(x,y \ z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(7689,a,8436,a),flip(a)].">
      <j1 rule="hyper" parents="7689 8436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8440">
    <literal><![CDATA[
      K(x * y,T(x,y \ z)) = K(y * x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,5857,a,b,8439,a),flip(a)].">
      <j1 rule="hyper" parents="320 5857 8439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8441">
    <literal><![CDATA[
      K(x * y,T(y,x \ z)) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5857,a,b,8440,a)].">
      <j1 rule="hyper" parents="58 5857 8440"/>
    </justification>
  </clause>

  <clause id="8442">
    <literal><![CDATA[
      K(x * y,T(y,x * z)) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),8441(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8443">
    <literal><![CDATA[
      K((x * y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ (y \ z),y) = u
    ]]></literal>
    <justification jstring="[para(7616(a,1),8400(a,1))].">
      <j1 rule="para" parents="7616 8400"/>
    </justification>
  </clause>

  <clause id="8444">
    <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(7133(a,1),8413(a,1,1,2))].">
      <j1 rule="para" parents="7133 8413"/>
    </justification>
  </clause>

  <clause id="8445">
    <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(5590(a,2),8415(a,1))].">
      <j1 rule="para" parents="5590 8415"/>
    </justification>
  </clause>

  <clause id="8446">
    <literal><![CDATA[
      T(K(x,y) * K(z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(z,T(u,x)) = w
    ]]></literal>
    <justification jstring="[para(7579(a,2),8416(a,1))].">
      <j1 rule="para" parents="7579 8416"/>
    </justification>
  </clause>

  <clause id="8447">
    <literal><![CDATA[
      L(K(x \ y,x),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z \ (x \ (z * y)),x) = u
    ]]></literal>
    <justification jstring="[para(6594(a,2),8443(a,1))].">
      <j1 rule="para" parents="6594 8443"/>
    </justification>
  </clause>

  <clause id="8448">
    <literal><![CDATA[
      L(K(x,y),z,T(x,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3988,a,7014,a)].">
      <j1 rule="hyper" parents="3988 7014"/>
    </justification>
  </clause>

  <clause id="8449">
    <literal><![CDATA[
      K(x,(T(x,y) * z) \ u) = K(x,z \ (T(x,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(6837,a,8448,a)].">
      <j1 rule="hyper" parents="6837 8448"/>
    </justification>
  </clause>

  <clause id="8450">
    <literal><![CDATA[
      K(x,L(y,z,T(x,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6580,a(flip),b,8448,a)].">
      <j1 rule="hyper" parents="58 6580 8448"/>
    </justification>
  </clause>

  <clause id="8451">
    <literal><![CDATA[
      K(x,T(L(y,z,T(x,u)),w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(20(a,1),8450(a,1,2))].">
      <j1 rule="para" parents="20 8450"/>
    </justification>
  </clause>

  <clause id="8452">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,z / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(8262,a,7043,a),flip(a)].">
      <j1 rule="hyper" parents="8262 7043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8453">
    <literal><![CDATA[
      K(x,y / (x \ z)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8302,a(flip),b,8452,a),flip(a)].">
      <j1 rule="hyper" parents="58 8302 8452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8454">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7946,a(flip),b,8452,a)].">
      <j1 rule="hyper" parents="58 7946 8452"/>
    </justification>
  </clause>

  <clause id="8455">
    <literal><![CDATA[
      K(x,y / (z / x)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(7376,a,8453,a)].">
      <j1 rule="hyper" parents="7376 8453"/>
    </justification>
  </clause>

  <clause id="8456">
    <literal><![CDATA[
      T(x,y / (x \ z)) = T(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(118,a,8453,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 8453 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8457">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7525,a,b,8453,a)].">
      <j1 rule="hyper" parents="58 7525 8453"/>
    </justification>
  </clause>

  <clause id="8458">
    <literal><![CDATA[
      K(x,((x * y) / z) \ x) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(4(a,1),8453(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8459">
    <literal><![CDATA[
      R(K(x,(y / (z / u)) \ x),z / u,u) = K(x,z / ((x \ y) * u))
    ]]></literal>
    <justification jstring="[para(8453(a,1),6917(a,1,1))].">
      <j1 rule="para" parents="8453 6917"/>
    </justification>
  </clause>

  <clause id="8460">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,(x * y) / z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7525,a,b,8454,a)].">
      <j1 rule="hyper" parents="320 7525 8454"/>
    </justification>
  </clause>

  <clause id="8461">
    <literal><![CDATA[
      T(x,(x * y) / z) = T(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8454,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 8454 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8462">
    <literal><![CDATA[
      K(x,(x \ y) / (x \ z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(5(a,1),8454(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 8454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8463">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7508,a,b,8456,a)].">
      <j1 rule="hyper" parents="58 7508 8456"/>
    </justification>
  </clause>

  <clause id="8464">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),y) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(8407,a,8457,a)].">
      <j1 rule="hyper" parents="8407 8457"/>
    </justification>
  </clause>

  <clause id="8465">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7947,a,b,8457,a)].">
      <j1 rule="hyper" parents="58 7947 8457"/>
    </justification>
  </clause>

  <clause id="8466">
    <literal><![CDATA[
      K(x,(y \ (x * z)) / z) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(72(a,1),8458(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 8458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8467">
    <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(6050(a,1),8458(a,1,2,1))].">
      <j1 rule="para" parents="6050 8458"/>
    </justification>
  </clause>

  <clause id="8468">
    <literal><![CDATA[
      K(x,(y * x) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(8460(a,2),6937(a,1))].">
      <j1 rule="para" parents="8460 6937"/>
    </justification>
  </clause>

  <clause id="8469">
    <literal><![CDATA[
      K(x,(x \ y) / (z / x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(7376,a,8462,a)].">
      <j1 rule="hyper" parents="7376 8462"/>
    </justification>
  </clause>

  <clause id="8470">
    <literal><![CDATA[
      K(x,(x \ y) / z) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[para(4(a,1),8462(a,1,2,2))].">
      <j1 rule="para" parents="4 8462"/>
    </justification>
  </clause>

  <clause id="8471">
    <literal><![CDATA[
      K(x,(y \ R(x,z,z \ 1)) / a(x,z,z \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(705(a,1),8466(a,1,2,1,2))].">
      <j1 rule="para" parents="705 8466"/>
    </justification>
  </clause>

  <clause id="8472">
    <literal><![CDATA[
      K(x,(x \ y) / z) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(6(a,1),8469(a,1,2,2))].">
      <j1 rule="para" parents="6 8469"/>
    </justification>
  </clause>

  <clause id="8473">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8470,a(flip),b,8472,a),flip(a)].">
      <j1 rule="hyper" parents="58 8470 8472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8474">
    <literal><![CDATA[
      K(x,(x * y) / (z * x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(4(a,1),8472(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 8472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8475">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,6982,a(flip),b,8473,a),flip(a)].">
      <j1 rule="hyper" parents="320 6982 8473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8477">
    <literal><![CDATA[
      K(x,R(y / x,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[para(102(a,2),8473(a,2,2)),flip(a)].">
      <j1 rule="para" parents="102 8473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8478">
    <literal><![CDATA[
      K(x,T((y / z) \ x,y)) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(7873,a,8464,a)].">
      <j1 rule="hyper" parents="7873 8464"/>
    </justification>
  </clause>

  <clause id="8479">
    <literal><![CDATA[
      K(x,(y / z) \ (x \ 1)) = K(x,z / (y * x))
    ]]></literal>
    <justification jstring="[para(7(a,1),8475(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 8475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8480">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,((y \ z) / z) \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(4408(a,1),8475(a,1,2,2,1))].">
      <j1 rule="para" parents="4408 8475"/>
    </justification>
  </clause>

  <clause id="8481">
    <literal><![CDATA[
      K(x,y \ ((z \ y) * x)) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(72(a,1),8478(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="72 8478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8482">
    <literal><![CDATA[
      K(x,(y / x) \ (z \ y)) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(8427,a,8481,a)].">
      <j1 rule="hyper" parents="8427 8481"/>
    </justification>
  </clause>

  <clause id="8483">
    <literal><![CDATA[
      K(x,T(y \ x,x * z)) = K(x,z \ (y \ (x * z)))
    ]]></literal>
    <justification jstring="[hyper(8419,a,8481,a),flip(a)].">
      <j1 rule="hyper" parents="8419 8481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8484">
    <literal><![CDATA[
      K(x \ y,T(z \ (x \ y),y)) = K(x \ y,x \ (z \ y))
    ]]></literal>
    <justification jstring="[para(72(a,1),8482(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 8482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8485">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / z) \ x) = u
    ]]></literal>
    <justification jstring="[para(7947(a,2),8468(a,1))].">
      <j1 rule="para" parents="7947 8468"/>
    </justification>
  </clause>

  <clause id="8486">
    <literal><![CDATA[
      K(x,R(x \ y,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4873,a(flip),b,8477,a)].">
      <j1 rule="hyper" parents="58 4873 8477"/>
    </justification>
  </clause>

  <clause id="8487">
    <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(7109(a,1),1088(a,1,1,2))].">
      <j1 rule="para" parents="7109 1088"/>
    </justification>
  </clause>

  <clause id="8488">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,u)),K(y,u)) = K(y,u) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7109(a,1),7816(a,1,1))].">
      <j1 rule="para" parents="7109 7816"/>
    </justification>
  </clause>

  <clause id="8489">
    <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),7134(a,2,2))].">
      <j1 rule="para" parents="22 7134"/>
    </justification>
  </clause>

  <clause id="8490">
    <literal><![CDATA[
      K(x \ y,z) * K(u,y / x) = K(u,y / x) * K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2887(a,1),7162(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2887 7162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8491">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(7728(a,1),7163(a,1,1))].">
      <j1 rule="para" parents="7728 7163"/>
    </justification>
  </clause>

  <clause id="8492">
    <literal><![CDATA[
      K(1 / x,T(y,z * x)) = T(K(x \ 1,y),z)
    ]]></literal>
    <justification jstring="[hyper(8406,a,7180,a),flip(a)].">
      <j1 rule="hyper" parents="8406 7180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8493">
    <literal><![CDATA[
      K(1 / x,T(y,z * x)) = T(K(1 / x,y),z)
    ]]></literal>
    <justification jstring="[para(3293(a,2),8492(a,2,1))].">
      <j1 rule="para" parents="3293 8492"/>
    </justification>
  </clause>

  <clause id="8494">
    <literal><![CDATA[
      K(1 / x,T(y,z * x)) = K(1 / T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5510,a,b,8493,a),flip(a)].">
      <j1 rule="hyper" parents="320 5510 8493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8495">
    <literal><![CDATA[
      K(1 / x,T(y,z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8493(a,2),7683(a,1))].">
      <j1 rule="para" parents="8493 7683"/>
    </justification>
  </clause>

  <clause id="8496">
    <literal><![CDATA[
      K(1 / T(x,y / x),z) = K(1 / x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),8494(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 8494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8497">
    <literal><![CDATA[
      x * K(y \ z,x / (z / y)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7220,a,b,87,a)].">
      <j1 rule="hyper" parents="119 7220 87"/>
    </justification>
  </clause>

  <clause id="8499">
    <literal><![CDATA[
      ((x \ y) \ y) \ (z * T(x,x \ y)) = T(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(660(a,1),7263(a,1,1)),flip(a)].">
      <j1 rule="para" parents="660 7263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8500">
    <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(7277(a,2),536(a,1))].">
      <j1 rule="para" parents="7277 536"/>
    </justification>
  </clause>

  <clause id="8501">
    <literal><![CDATA[
      x * K(y,(1 / x) * (z * x)) = K(y,L(z,x,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(2798(a,1),7277(a,1,2,2))].">
      <j1 rule="para" parents="2798 7277"/>
    </justification>
  </clause>

  <clause id="8502">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K(z / (x \ y),y \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,6683,a,b,7288,a)].">
      <j1 rule="hyper" parents="320 6683 7288"/>
    </justification>
  </clause>

  <clause id="8503">
    <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),7341(a,2,2))].">
      <j1 rule="para" parents="22 7341"/>
    </justification>
  </clause>

  <clause id="8504">
    <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(7452(a,1),7363(a,1,2,1))].">
      <j1 rule="para" parents="7452 7363"/>
    </justification>
  </clause>

  <clause id="8505">
    <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),7401(a,1,2,1))].">
      <j1 rule="para" parents="22 7401"/>
    </justification>
  </clause>

  <clause id="8506">
    <literal><![CDATA[
      (((x \ y) * x) * z) \ (y * z) = K(x,z \ (x \ (y * z)))
    ]]></literal>
    <justification jstring="[para(6(a,1),7427(a,1,1,1,1,2))].">
      <j1 rule="para" parents="6 7427"/>
    </justification>
  </clause>

  <clause id="8507">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z = K(y,x \ (y \ z))
    ]]></literal>
    <justification jstring="[para(4587(a,1),7427(a,1,1))].">
      <j1 rule="para" parents="4587 7427"/>
    </justification>
  </clause>

  <clause id="8508">
    <literal><![CDATA[
      (x * y) * K(z,x \ (z \ (x * y))) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,4583,a(flip),b,7428,a),flip(a)].">
      <j1 rule="hyper" parents="58 4583 7428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8509">
    <literal><![CDATA[
      x * K(y,z \ (y \ x)) = z * (y * ((z \ x) / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,4582,a(flip),b,7428,a),flip(a)].">
      <j1 rule="hyper" parents="58 4582 7428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8510">
    <literal><![CDATA[
      x \ (y * K(z,T(x,u))) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(7131(a,2),7440(a,1,2,2))].">
      <j1 rule="para" parents="7131 7440"/>
    </justification>
  </clause>

  <clause id="8511">
    <literal><![CDATA[
      (x * K(y \ (z \ x),z)) * u = (y * ((z \ (y \ x)) * z)) * u
    ]]></literal>
    <justification jstring="[hyper(52,a,7446,a)].">
      <j1 rule="hyper" parents="52 7446"/>
    </justification>
  </clause>

  <clause id="8512">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(7446(a,1),6316(a,1,1))].">
      <j1 rule="para" parents="7446 6316"/>
    </justification>
  </clause>

  <clause id="8513">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = x * (L(x,z,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(119,a,7449,a(flip),b,5137,a)].">
      <j1 rule="hyper" parents="119 7449 5137"/>
    </justification>
  </clause>

  <clause id="8514">
    <literal><![CDATA[
      K(x,T(y * (z * K(u,x)),w)) = K(x,T(y * z,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,7131,a,b,7556,a),flip(a)].">
      <j1 rule="hyper" parents="320 7131 7556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8515">
    <literal><![CDATA[
      K(x \ (y \ z),T(y,z)) = K(z / (y * x),y)
    ]]></literal>
    <justification jstring="[hyper(8028,a,7585,a),flip(a)].">
      <j1 rule="hyper" parents="8028 7585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8516">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) = K(z / (y \ x),y)
    ]]></literal>
    <justification jstring="[hyper(8028,a,7587,a),flip(a)].">
      <j1 rule="hyper" parents="8028 7587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8517">
    <literal><![CDATA[
      K((x * y) / z,x) = K(y / (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7945,a(flip),b,8516,a)].">
      <j1 rule="hyper" parents="58 7945 8516"/>
    </justification>
  </clause>

  <clause id="8518">
    <literal><![CDATA[
      K(x / (y \ z),y) * ((y * x) / z) = T((y * x) / z,y)
    ]]></literal>
    <justification jstring="[para(8517(a,1),4729(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8517 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8519">
    <literal><![CDATA[
      T(x * K(y,z / x),x \ z) = T(x \ z,y) \ z
    ]]></literal>
    <justification jstring="[para(7963(a,1),7589(a,1,1))].">
      <j1 rule="para" parents="7963 7589"/>
    </justification>
  </clause>

  <clause id="8520">
    <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(3755(a,1),7598(a,1,1))].">
      <j1 rule="para" parents="3755 7598"/>
    </justification>
  </clause>

  <clause id="8521">
    <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(5865(a,1),7602(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5865 7602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8522">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(320,a,6358,a(flip),b,7613,a),flip(a)].">
      <j1 rule="hyper" parents="320 6358 7613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8523">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ u) = w
    ]]></literal>
    <justification jstring="[para(7613(a,2),6390(a,1))].">
      <j1 rule="para" parents="7613 6390"/>
    </justification>
  </clause>

  <clause id="8524">
    <literal><![CDATA[
      T(x,(y * K(z,x)) \ u) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,8522,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 8522 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8525">
    <literal><![CDATA[
      K(x,(y \ T(z,x)) \ u) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(1420(a,1),8522(a,1,2,1))].">
      <j1 rule="para" parents="1420 8522"/>
    </justification>
  </clause>

  <clause id="8527">
    <literal><![CDATA[
      K(x,(y * K(x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(6300(a,1),8522(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6300 8522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8528">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[para(6446(a,1),8522(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6446 8522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8529">
    <literal><![CDATA[
      K(x,(K(x,y) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7121(a,1),8522(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7121 8522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8530">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7123(a,1),8522(a,1,2,1))].">
      <j1 rule="para" parents="7123 8522"/>
    </justification>
  </clause>

  <clause id="8531">
    <literal><![CDATA[
      K(T(x,y),(z * K(u,x)) \ w) = K(T(x,y),z \ w)
    ]]></literal>
    <justification jstring="[para(7188(a,1),8522(a,1,2,1,2))].">
      <j1 rule="para" parents="7188 8522"/>
    </justification>
  </clause>

  <clause id="8532">
    <literal><![CDATA[
      T(x,(K(y,x) * z) \ u) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7123(a,1),8524(a,1,2,1))].">
      <j1 rule="para" parents="7123 8524"/>
    </justification>
  </clause>

  <clause id="8533">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) = K(x,(y * (x * z)) \ u)
    ]]></literal>
    <justification jstring="[para(6604(a,1),8527(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6604 8527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8535">
    <literal><![CDATA[
      K(x,y \ K(x,z)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(6460,a,8529,a),flip(a)].">
      <j1 rule="hyper" parents="6460 8529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8536">
    <literal><![CDATA[
      K(x,y \ T(x,z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6570,a(flip),b,8529,a),flip(a)].">
      <j1 rule="hyper" parents="58 6570 8529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8537">
    <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),8529(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 8529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8538">
    <literal><![CDATA[
      K(x,(y * (K(z,x) * u)) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(6008(a,1),8529(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6008 8529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8539">
    <literal><![CDATA[
      T(x,y \ K(x,z)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(118,a,8535,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 8535 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8540">
    <literal><![CDATA[
      T(x,y \ T(x,z)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(118,a,8536,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 8536 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8541">
    <literal><![CDATA[
      K(x,T(y \ x,z)) = K(x,T(y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7174,a(flip),b,8536,a)].">
      <j1 rule="hyper" parents="58 7174 8536"/>
    </justification>
  </clause>

  <clause id="8542">
    <literal><![CDATA[
      K(T(x,y),z \ T(T(x,u),y)) = K(T(x,y),z \ T(x,y))
    ]]></literal>
    <justification jstring="[para(18(a,1),8536(a,1,2,2))].">
      <j1 rule="para" parents="18 8536"/>
    </justification>
  </clause>

  <clause id="8543">
    <literal><![CDATA[
      K(x / y,z \ (x / y)) = K(x / y,z \ (y \ x))
    ]]></literal>
    <justification jstring="[para(107(a,1),8536(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 8536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8544">
    <literal><![CDATA[
      (x \ K(x,y)) * (T(x,x \ 1) * z) = (K(x,y) / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(8539(a,1),4523(a,1,2,1))].">
      <j1 rule="para" parents="8539 4523"/>
    </justification>
  </clause>

  <clause id="8545">
    <literal><![CDATA[
      T(x,T(x,y) / z) = T(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(7127,a,8540,a)].">
      <j1 rule="hyper" parents="7127 8540"/>
    </justification>
  </clause>

  <clause id="8546">
    <literal><![CDATA[
      K(x,y \ (K(x,z) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7485,a(flip),b,8530,a)].">
      <j1 rule="hyper" parents="58 7485 8530"/>
    </justification>
  </clause>

  <clause id="8547">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x)) \ x) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(8035,a,8541,a),flip(a)].">
      <j1 rule="hyper" parents="8035 8541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8549">
    <literal><![CDATA[
      K(x,T(((y \ z) \ 1) \ x,z)) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[hyper(320,a,6567,a(flip),b,8541,a),flip(a)].">
      <j1 rule="hyper" parents="320 6567 8541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8551">
    <literal><![CDATA[
      K(x,y \ (T(x,z) \ u)) = K(x,y \ (x \ u))
    ]]></literal>
    <justification jstring="[para(5042(a,1),8546(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5042 8546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8552">
    <literal><![CDATA[
      K(x,y \ (z \ T(u,x))) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(5370(a,1),8546(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5370 8546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8553">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,x) * w))) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(6008(a,1),8546(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6008 8546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8554">
    <literal><![CDATA[
      K(x,T(y \ (K(x,z) * u),w)) = T(K(x,y \ u),w)
    ]]></literal>
    <justification jstring="[para(8546(a,1),7131(a,2,1))].">
      <j1 rule="para" parents="8546 7131"/>
    </justification>
  </clause>

  <clause id="8555">
    <literal><![CDATA[
      K(x,y \ (z * K(x,u))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(7872(a,1),8546(a,1,2,2))].">
      <j1 rule="para" parents="7872 8546"/>
    </justification>
  </clause>

  <clause id="8556">
    <literal><![CDATA[
      K(x,y \ (z * (u / x))) = K(x,y \ (z * (x \ u)))
    ]]></literal>
    <justification jstring="[para(6071(a,1),8555(a,1,2,2))].">
      <j1 rule="para" parents="6071 8555"/>
    </justification>
  </clause>

  <clause id="8557">
    <literal><![CDATA[
      K(x,y \ (z * (u * x))) = K(x,y \ (z * (x * u)))
    ]]></literal>
    <justification jstring="[para(6604(a,1),8555(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6604 8555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8558">
    <literal><![CDATA[
      K(x,(K(y \ x,y) * z) \ x) = K(x,(z * K(y \ x,y)) \ x)
    ]]></literal>
    <justification jstring="[para(6308(a,1),8547(a,1,2,1))].">
      <j1 rule="para" parents="6308 8547"/>
    </justification>
  </clause>

  <clause id="8559">
    <literal><![CDATA[
      K(x,y \ ((T(z,x) / u) \ z)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(75(a,1),8552(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 8552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8560">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ z) = z \ ((T(y,x) / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6552,a(flip),b,8559,a),flip(a)].">
      <j1 rule="hyper" parents="58 6552 8559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8561">
    <literal><![CDATA[
      K(x,(T(y,x) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(5500(a,1),8523(a,1,2,1))].">
      <j1 rule="para" parents="5500 8523"/>
    </justification>
  </clause>

  <clause id="8562">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ u) = w
    ]]></literal>
    <justification jstring="[para(7123(a,1),8523(a,1,2,1))].">
      <j1 rule="para" parents="7123 8523"/>
    </justification>
  </clause>

  <clause id="8563">
    <literal><![CDATA[
      K(x,y \ (K(x,z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ u) = w
    ]]></literal>
    <justification jstring="[para(7485(a,1),8562(a,1))].">
      <j1 rule="para" parents="7485 8562"/>
    </justification>
  </clause>

  <clause id="8564">
    <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(5841(a,1),8563(a,1,2,2))].">
      <j1 rule="para" parents="5841 8563"/>
    </justification>
  </clause>

  <clause id="8565">
    <literal><![CDATA[
      (x / y) * K(x,T(z,y)) = K(x,z) * (x / y)
    ]]></literal>
    <justification jstring="[para(8203(a,1),7624(a,1,2))].">
      <j1 rule="para" parents="8203 7624"/>
    </justification>
  </clause>

  <clause id="8566">
    <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(7648(a,1),6850(a,1,3,2))].">
      <j1 rule="para" parents="7648 6850"/>
    </justification>
  </clause>

  <clause id="8567">
    <literal><![CDATA[
      K(x,T(y,(z * x) * u)) = K(x,T(y,(x * z) * u))
    ]]></literal>
    <justification jstring="[para(84(a,1),7660(a,1,2,2,1))].">
      <j1 rule="para" parents="84 7660"/>
    </justification>
  </clause>

  <clause id="8568">
    <literal><![CDATA[
      T(x,y \ (K(z,x) * u)) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,8532,a(flip),b,7696,a)].">
      <j1 rule="hyper" parents="58 8532 7696"/>
    </justification>
  </clause>

  <clause id="8570">
    <literal><![CDATA[
      T(x,y \ ((z / x) \ u)) = T(x,y \ ((x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(5361(a,1),8568(a,1,2,2))].">
      <j1 rule="para" parents="5361 8568"/>
    </justification>
  </clause>

  <clause id="8571">
    <literal><![CDATA[
      T(x,y) * K(y * L(x,z,u),x) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(7720(a,1),6820(a,1,2))].">
      <j1 rule="para" parents="7720 6820"/>
    </justification>
  </clause>

  <clause id="8572">
    <literal><![CDATA[
      (x * K(y,z)) * T(K(z,y),u) = x * K(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(6300(a,1),7745(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6300 7745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8573">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(L(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(5716(a,1),7750(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5716 7750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8574">
    <literal><![CDATA[
      x * K(L(K(y,z),u,w),x) = T(x,L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(8573(a,1),7786(a,1,2))].">
      <j1 rule="para" parents="8573 7786"/>
    </justification>
  </clause>

  <clause id="8575">
    <literal><![CDATA[
      T(x,K(y,z \ x)) / z = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(4714(a,2),7789(a,1,1))].">
      <j1 rule="para" parents="4714 7789"/>
    </justification>
  </clause>

  <clause id="8576">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,8102,a(flip),b,7849,a),flip(a)].">
      <j1 rule="hyper" parents="320 8102 7849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8578">
    <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,6641,a(flip),b,7860,a),flip(a)].">
      <j1 rule="hyper" parents="117 6641 7860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8579">
    <literal><![CDATA[
      ((1 / x) * (K(y,z) * x)) * x = x * L(K(y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2798(a,1),7860(a,1,1))].">
      <j1 rule="para" parents="2798 7860"/>
    </justification>
  </clause>

  <clause id="8580">
    <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),7861(a,1,1))].">
      <j1 rule="para" parents="22 7861"/>
    </justification>
  </clause>

  <clause id="8581">
    <literal><![CDATA[
      T(T(x,L(K(y,z),u,w)),L(K(y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(4642,a,7862,a)].">
      <j1 rule="hyper" parents="4642 7862"/>
    </justification>
  </clause>

  <clause id="8582">
    <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(678,a,8581,a)].">
      <j1 rule="hyper" parents="678 8581"/>
    </justification>
  </clause>

  <clause id="8583">
    <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(7095(a,1),7877(a,1,1,1,2))].">
      <j1 rule="para" parents="7095 7877"/>
    </justification>
  </clause>

  <clause id="8584">
    <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(7962(a,2),537(a,1))].">
      <j1 rule="para" parents="7962 537"/>
    </justification>
  </clause>

  <clause id="8585">
    <literal><![CDATA[
      T(x,K(y,z \ 1) / z) = x * K(T(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3769,a,b,7990,a)].">
      <j1 rule="hyper" parents="58 3769 7990"/>
    </justification>
  </clause>

  <clause id="8586">
    <literal><![CDATA[
      K(T(x,y * K(z,y)),u) = u / T(u,x * K(T(x,z),y))
    ]]></literal>
    <justification jstring="[para(7995(a,1),4753(a,2,2))].">
      <j1 rule="para" parents="7995 4753"/>
    </justification>
  </clause>

  <clause id="8587">
    <literal><![CDATA[
      K(x * K(y,z),(x / u) \ 1) = K(K(y,z) * x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(30,a,7540,a,b,7998,a)].">
      <j1 rule="hyper" parents="30 7540 7998"/>
    </justification>
  </clause>

  <clause id="8588">
    <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),8000(a,2,2))].">
      <j1 rule="para" parents="22 8000"/>
    </justification>
  </clause>

  <clause id="8589">
    <literal><![CDATA[
      K(x \ y,x) * (z * (y / x)) = T(z * (x \ y),K(x,y))
    ]]></literal>
    <justification jstring="[para(6446(a,1),8016(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6446 8016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8590">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,7738,a(flip),b,8046,a),flip(a)].">
      <j1 rule="hyper" parents="320 7738 8046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8591">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7739,a(flip),b,8047,a),flip(a)].">
      <j1 rule="hyper" parents="320 7739 8047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8592">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),K(u,y) \ z)
    ]]></literal>
    <justification jstring="[para(5592(a,1),8591(a,1,2))].">
      <j1 rule="para" parents="5592 8591"/>
    </justification>
  </clause>

  <clause id="8593">
    <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(4266(a,1),8055(a,1,2,2,2))].">
      <j1 rule="para" parents="4266 8055"/>
    </justification>
  </clause>

  <clause id="8594">
    <literal><![CDATA[
      K(x \ 1,T(y,x \ z)) = K(x \ 1,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8315,a(flip),b,8078,a),flip(a)].">
      <j1 rule="hyper" parents="58 8315 8078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8595">
    <literal><![CDATA[
      K(T(x,y),T(z,x \ u)) = K(T(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,7988,a(flip),b,8082,a),flip(a)].">
      <j1 rule="hyper" parents="58 7988 8082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8596">
    <literal><![CDATA[
      K(T(x,y),T(z,x * u)) = K(T(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),8595(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8597">
    <literal><![CDATA[
      K(x,T(T(T(x,y) * z,u),w)) = K(x,T(T(x * z,u),w))
    ]]></literal>
    <justification jstring="[para(4778(a,1),8097(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4778 8097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8598">
    <literal><![CDATA[
      K(1 / (x / (x / y)),z) = K(1 / y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,8496,a(flip),b,8110,a),flip(a)].">
      <j1 rule="hyper" parents="58 8496 8110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8599">
    <literal><![CDATA[
      K(1 / (x \ y),T(z,y)) = K(1 / (y / x),z)
    ]]></literal>
    <justification jstring="[para(72(a,1),8598(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 8598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8600">
    <literal><![CDATA[
      K(1 / (x / y),T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / (y \ x),z) = u
    ]]></literal>
    <justification jstring="[para(8599(a,1),7981(a,1))].">
      <j1 rule="para" parents="8599 7981"/>
    </justification>
  </clause>

  <clause id="8601">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y \ z,z))
    ]]></literal>
    <justification jstring="[para(5330(a,1),8167(a,2,2))].">
      <j1 rule="para" parents="5330 8167"/>
    </justification>
  </clause>

  <clause id="8602">
    <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),8207(a,2,2))].">
      <j1 rule="para" parents="20 8207"/>
    </justification>
  </clause>

  <clause id="8603">
    <literal><![CDATA[
      T(x,y) * K(y * R(x,z,u),x) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(8221(a,1),4906(a,1,2))].">
      <j1 rule="para" parents="8221 4906"/>
    </justification>
  </clause>

  <clause id="8604">
    <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(8221(a,2),7765(a,2,1))].">
      <j1 rule="para" parents="8221 7765"/>
    </justification>
  </clause>

  <clause id="8605">
    <literal><![CDATA[
      K(T(L(x,y,z) * u,u),x) = K(L(x,y,z) * u,x)
    ]]></literal>
    <justification jstring="[hyper(7283,a,8222,a)].">
      <j1 rule="hyper" parents="7283 8222"/>
    </justification>
  </clause>

  <clause id="8606">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * z,x)) = T(T(x,y) * z,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),8258(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 8258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8608">
    <literal><![CDATA[
      K(x,T(x \ y,z \ y)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8203,a(flip),b,8270,a),flip(a)].">
      <j1 rule="hyper" parents="320 8203 8270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8609">
    <literal><![CDATA[
      K(x,T(x \ y,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(8270(a,2),8225(a,1))].">
      <j1 rule="para" parents="8270 8225"/>
    </justification>
  </clause>

  <clause id="8610">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(T(u * x,x) / u,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7887,a,b,8311,a)].">
      <j1 rule="hyper" parents="320 7887 8311"/>
    </justification>
  </clause>

  <clause id="8611">
    <literal><![CDATA[
      K(T(x * y,y) / x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(8392,a,8610,a),flip(a)].">
      <j1 rule="hyper" parents="8392 8610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8613">
    <literal><![CDATA[
      K(T(x,y) / (x / y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),8611(a,1,1,1,1))].">
      <j1 rule="para" parents="7 8611"/>
    </justification>
  </clause>

  <clause id="8614">
    <literal><![CDATA[
      T(x,y) \ ((x \ 1) \ K(z,x)) = x * (K(z,x) / T(x,y))
    ]]></literal>
    <justification jstring="[para(8340(a,1),3468(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8340 3468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8615">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7317,a(flip),b,8394,a),flip(a)].">
      <j1 rule="hyper" parents="320 7317 8394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8617">
    <literal><![CDATA[
      K(T(x \ T(y,x),z) \ u,z) = K((T(x,y) \ y) \ u,z)
    ]]></literal>
    <justification jstring="[para(4787(a,1),8615(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4787 8615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8618">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(6300(a,1),8615(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6300 8615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8619">
    <literal><![CDATA[
      K((x * T(y,z)) \ u,z) = K((x * y) \ u,z)
    ]]></literal>
    <justification jstring="[para(6302(a,1),8615(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6302 8615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8620">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) = K((x * (z \ y)) \ u,z)
    ]]></literal>
    <justification jstring="[para(6071(a,1),8615(a,1,1,1))].">
      <j1 rule="para" parents="6071 8615"/>
    </justification>
  </clause>

  <clause id="8621">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) = K((x * (z * y)) \ u,z)
    ]]></literal>
    <justification jstring="[para(6604(a,1),8615(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6604 8615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8622">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,y) = K(z \ u,y)
    ]]></literal>
    <justification jstring="[para(7149(a,1),8615(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7149 8615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8623">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,T(y,w)) = K(x \ u,T(y,w))
    ]]></literal>
    <justification jstring="[para(7863(a,1),8615(a,1,1,1,2))].">
      <j1 rule="para" parents="7863 8615"/>
    </justification>
  </clause>

  <clause id="8624">
    <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(6168(a,2),8618(a,1,1))].">
      <j1 rule="para" parents="6168 8618"/>
    </justification>
  </clause>

  <clause id="8625">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7480,a(flip),b,8622,a)].">
      <j1 rule="hyper" parents="58 7480 8622"/>
    </justification>
  </clause>

  <clause id="8627">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(5095(a,1),8625(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5095 8625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8628">
    <literal><![CDATA[
      K(x \ (y / z),z \ y) = K(x \ (z \ y),z \ y)
    ]]></literal>
    <justification jstring="[para(4958(a,1),8625(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4958 8625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8629">
    <literal><![CDATA[
      K(x \ (T(y,z) \ u),y) = K(x \ (y \ u),y)
    ]]></literal>
    <justification jstring="[para(5042(a,1),8625(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5042 8625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8631">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),T(y,w)) = K(x \ u,T(y,w))
    ]]></literal>
    <justification jstring="[para(7863(a,1),8625(a,1,1,2,1))].">
      <j1 rule="para" parents="7863 8625"/>
    </justification>
  </clause>

  <clause id="8632">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(7872(a,1),8625(a,1,1,2))].">
      <j1 rule="para" parents="7872 8625"/>
    </justification>
  </clause>

  <clause id="8633">
    <literal><![CDATA[
      K(x \ (y / (z * y)),z \ 1) = K(x \ ((z * y) \ y),z \ 1)
    ]]></literal>
    <justification jstring="[para(5315(a,1),8627(a,1,1,2))].">
      <j1 rule="para" parents="5315 8627"/>
    </justification>
  </clause>

  <clause id="8634">
    <literal><![CDATA[
      K(x \ (y * T(z,u)),u) = K(x \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(5516(a,1),8627(a,1,1,2))].">
      <j1 rule="para" parents="5516 8627"/>
    </justification>
  </clause>

  <clause id="8635">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(x \ (y * (u * z)),u)
    ]]></literal>
    <justification jstring="[para(6604(a,1),8632(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6604 8632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8636">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,x) = K(z \ (x \ u),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7486,a,b,8629,a)].">
      <j1 rule="hyper" parents="58 7486 8629"/>
    </justification>
  </clause>

  <clause id="8637">
    <literal><![CDATA[
      K((x * (y * z)) \ ((x * z) * y),z) = K(a(x,z,T(y,z)),z)
    ]]></literal>
    <justification jstring="[para(228(a,1),8634(a,1,1)),flip(a)].">
      <j1 rule="para" parents="228 8634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8639">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(w,K(z \ (x \ u),x))
    ]]></literal>
    <justification jstring="[para(8636(a,1),7759(a,2,2))].">
      <j1 rule="para" parents="8636 7759"/>
    </justification>
  </clause>

  <clause id="8640">
    <literal><![CDATA[
      K(T(x,y * (z * K(u,w))),w) = (v5 * K(w,T(x,y * z))) \ v5
    ]]></literal>
    <justification jstring="[para(8398(a,1),6309(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8398 6309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8641">
    <literal><![CDATA[
      K(x,(T(x,y) * z) \ u) = K(x,z \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,8551,a(flip),b,8449,a),flip(a)].">
      <j1 rule="hyper" parents="320 8551 8449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8643">
    <literal><![CDATA[
      K(x,y \ (z \ (x * y))) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(7685,a,8483,a),flip(a)].">
      <j1 rule="hyper" parents="7685 8483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8644">
    <literal><![CDATA[
      R(K(x,T(y,z)),y * u,w) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(7131(a,2),8489(a,1,1))].">
      <j1 rule="para" parents="7131 8489"/>
    </justification>
  </clause>

  <clause id="8645">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,x \ y) * u) = K(x,T(x \ y,z)) * u
    ]]></literal>
    <justification jstring="[para(7939(a,1),8491(a,1,1))].">
      <j1 rule="para" parents="7939 8491"/>
    </justification>
  </clause>

  <clause id="8646">
    <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),8503(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4 8503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8647">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6875,a(flip),b,8507,a)].">
      <j1 rule="hyper" parents="58 6875 8507"/>
    </justification>
  </clause>

  <clause id="8648">
    <literal><![CDATA[
      (x * (y * ((z \ (y \ (x \ u))) * z))) \ u = K(z,(x * y) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(3516(a,1),8507(a,1,1))].">
      <j1 rule="para" parents="3516 8507"/>
    </justification>
  </clause>

  <clause id="8649">
    <literal><![CDATA[
      x * (y * ((x \ z) / y)) != z * u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(8509(a,1),38(a,1))].">
      <j1 rule="para" parents="8509 38"/>
    </justification>
  </clause>

  <clause id="8650">
    <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(1315,a,8510,a),flip(a)].">
      <j1 rule="hyper" parents="1315 8510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8651">
    <literal><![CDATA[
      K(x,T(y * (z / T(u,x)),w)) = K(x,T(y * (z / u),w))
    ]]></literal>
    <justification jstring="[para(6159(a,1),8514(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6159 8514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8652">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * (x \ z)) \ u)) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(8528(a,1),5100(a,1,2,2))].">
      <j1 rule="para" parents="8528 5100"/>
    </justification>
  </clause>

  <clause id="8653">
    <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(8533(a,1),6586(a,1,1))].">
      <j1 rule="para" parents="8533 6586"/>
    </justification>
  </clause>

  <clause id="8654">
    <literal><![CDATA[
      K(x,(y * (K(x,z) * u)) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(5095(a,1),8538(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5095 8538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8655">
    <literal><![CDATA[
      K(x / y,z \ (y \ x)) = K(y \ x,(z * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8091,a(flip),b,8543,a),flip(a)].">
      <j1 rule="hyper" parents="58 8091 8543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8656">
    <literal><![CDATA[
      K(x,y \ (z * (K(x,u) * w))) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(5095(a,1),8553(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5095 8553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8657">
    <literal><![CDATA[
      K(x,T(y \ (K(x,z) * u),w)) = K(x,T(y \ u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,7131,a,b,8554,a),flip(a)].">
      <j1 rule="hyper" parents="320 7131 8554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8658">
    <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,7656,a(flip),b,8556,a),flip(a)].">
      <j1 rule="hyper" parents="58 7656 8556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8659">
    <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(8570(a,1),4765(a,1,1,1))].">
      <j1 rule="para" parents="8570 4765"/>
    </justification>
  </clause>

  <clause id="8660">
    <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(5462(a,1),8572(a,1,1))].">
      <j1 rule="para" parents="5462 8572"/>
    </justification>
  </clause>

  <clause id="8661">
    <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(239,a,8580,a(flip),b,4064,a(flip))].">
      <j1 rule="hyper" parents="239 8580 4064"/>
    </justification>
  </clause>

  <clause id="8662">
    <literal><![CDATA[
      K(x,K(y,z \ 1) / z) = K(T(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(4796,a,8585,a)].">
      <j1 rule="hyper" parents="4796 8585"/>
    </justification>
  </clause>

  <clause id="8663">
    <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(5397(a,1),8662(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5397 8662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8664">
    <literal><![CDATA[
      T(x,R(T(y,y \ z),u,w)) = T(x,R(z / (z / y),u,w))
    ]]></literal>
    <justification jstring="[para(4302(a,1),8588(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4302 8588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8665">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,8590,a(flip),b,8592,a),flip(a)].">
      <j1 rule="hyper" parents="320 8590 8592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8667">
    <literal><![CDATA[
      T(K(x,y),z * K(y,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(6306(a,1),8665(a,1,2))].">
      <j1 rule="para" parents="6306 8665"/>
    </justification>
  </clause>

  <clause id="8668">
    <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(8667(a,1),8576(a,1,2))].">
      <j1 rule="para" parents="8667 8576"/>
    </justification>
  </clause>

  <clause id="8669">
    <literal><![CDATA[
      T(T(x,y) * L(x \ z,u,w),x) = T(x,y) * L(x \ T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(1743(a,1),8606(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1743 8606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8670">
    <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(1888(a,1),8606(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1888 8606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8671">
    <literal><![CDATA[
      K(((x \ 1) * (y * x)) \ z,x) = K(L(y,x,x \ 1) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,3967,a(flip),b,8621,a),flip(a)].">
      <j1 rule="hyper" parents="320 3967 8621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8672">
    <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(8628(a,1),5487(a,1,1,1,2))].">
      <j1 rule="para" parents="8628 5487"/>
    </justification>
  </clause>

  <clause id="8673">
    <literal><![CDATA[
      K(x \ (y * z),T(z,u)) = K(x \ (z * y),T(z,u))
    ]]></literal>
    <justification jstring="[para(4772(a,1),8631(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4772 8631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8674">
    <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(477(a,1),8635(a,2,1))].">
      <j1 rule="para" parents="477 8635"/>
    </justification>
  </clause>

  <clause id="8675">
    <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),8644(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 8644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8676">
    <literal><![CDATA[
      K(x,(x * y) \ ((x * z) * y)) = K(x,R(T(z,y),x,y))
    ]]></literal>
    <justification jstring="[hyper(4999,a,8646,a)].">
      <j1 rule="hyper" parents="4999 8646"/>
    </justification>
  </clause>

  <clause id="8677">
    <literal><![CDATA[
      K(x,(y * (x * z)) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8533,a(flip),b,8647,a)].">
      <j1 rule="hyper" parents="58 8533 8647"/>
    </justification>
  </clause>

  <clause id="8678">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(7(a,1),8647(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 8647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8679">
    <literal><![CDATA[
      K(x,((1 / y) * y) \ (x \ z)) = K(x,L(x,y,y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2797(a,1),8647(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2797 8647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8680">
    <literal><![CDATA[
      (x * K(y,(z * u) \ (y \ w))) \ x = K((z * (u * y)) \ w,y)
    ]]></literal>
    <justification jstring="[para(8647(a,1),6309(a,1,1,2))].">
      <j1 rule="para" parents="8647 6309"/>
    </justification>
  </clause>

  <clause id="8681">
    <literal><![CDATA[
      K(x,L(L(y,z,K(x,u)),K(x,u) * z,w)) = K(x,(w * (K(x,u) * z)) \ (w * (z * y)))
    ]]></literal>
    <justification jstring="[para(477(a,1),8656(a,1,2))].">
      <j1 rule="para" parents="477 8656"/>
    </justification>
  </clause>

  <clause id="8682">
    <literal><![CDATA[
      K(x,T(y \ T(x,z),u)) = K(x,T(y \ x,u))
    ]]></literal>
    <justification jstring="[para(4729(a,2),8657(a,1,2,1,2))].">
      <j1 rule="para" parents="4729 8657"/>
    </justification>
  </clause>

  <clause id="8683">
    <literal><![CDATA[
      K(x,T(y \ T(T(x,z),u),w)) = K(x,T(y \ T(x,u),w))
    ]]></literal>
    <justification jstring="[para(7200(a,1),8657(a,1,2,1,2))].">
      <j1 rule="para" parents="7200 8657"/>
    </justification>
  </clause>

  <clause id="8684">
    <literal><![CDATA[
      K(x \ (y * z),T(z,y)) = K((x / y) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,8300,a(flip),b,8673,a),flip(a)].">
      <j1 rule="hyper" parents="320 8300 8673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8685">
    <literal><![CDATA[
      K((x \ y) \ z,T(z,x)) = K((y / x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7374,a,b,8684,a)].">
      <j1 rule="hyper" parents="58 7374 8684"/>
    </justification>
  </clause>

  <clause id="8686">
    <literal><![CDATA[
      K(((x * y) / x) \ z,z) = K(y \ z,T(z,x))
    ]]></literal>
    <justification jstring="[para(4(a,1),8685(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 8685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8687">
    <literal><![CDATA[
      K(x * (y \ K(y,z)),x) = K(y \ x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5327,a(flip),b,8686,a)].">
      <j1 rule="hyper" parents="58 5327 8686"/>
    </justification>
  </clause>

  <clause id="8688">
    <literal><![CDATA[
      K((x \ K(x,y)) * z,z) = K(x \ z,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(7394,a,8687,a)].">
      <j1 rule="hyper" parents="7394 8687"/>
    </justification>
  </clause>

  <clause id="8689">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,379,a(flip),b,8675,a),flip(a)].">
      <j1 rule="hyper" parents="320 379 8675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8690">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7131,a(flip),b,8689,a),flip(a)].">
      <j1 rule="hyper" parents="320 7131 8689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8691">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),8677(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5 8677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8692">
    <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(8677(a,1),6586(a,1,1))].">
      <j1 rule="para" parents="8677 6586"/>
    </justification>
  </clause>

  <clause id="8693">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(8380,a,8678,a)].">
      <j1 rule="hyper" parents="8380 8678"/>
    </justification>
  </clause>

  <clause id="8694">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(8380,a,8691,a)].">
      <j1 rule="hyper" parents="8380 8691"/>
    </justification>
  </clause>

  <clause id="8695">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * z) \ (u * x))) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(8693(a,1),5100(a,1,2,2))].">
      <j1 rule="para" parents="8693 5100"/>
    </justification>
  </clause>

  <clause id="8696">
    <literal><![CDATA[
      L(K(x,(y * z) \ ((u \ w) * x)),u \ w,u) = K(x,(u * (y * (z / x))) \ w)
    ]]></literal>
    <justification jstring="[para(8693(a,1),6556(a,1,1))].">
      <j1 rule="para" parents="8693 6556"/>
    </justification>
  </clause>

  <clause id="8697">
    <literal><![CDATA[
      K(x,((y * K(x \ z,y)) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(4733(a,1),8694(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4733 8694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8698">
    <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(7182(a,1),39(a,1))].">
      <j1 rule="para" parents="7182 39"/>
    </justification>
  </clause>

  <clause id="8699">
    <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(1396(a,1),7234(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1396 7234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8700">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,4870,a(flip),b,7570,a),flip(a)].">
      <j1 rule="hyper" parents="320 4870 7570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8701">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z,x,y)) = u
    ]]></literal>
    <justification jstring="[para(7570(a,2),4998(a,1))].">
      <j1 rule="para" parents="7570 4998"/>
    </justification>
  </clause>

  <clause id="8702">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = T(x \ R(x,y,x),y)
    ]]></literal>
    <justification jstring="[para(6428(a,1),7591(a,1,2))].">
      <j1 rule="para" parents="6428 7591"/>
    </justification>
  </clause>

  <clause id="8703">
    <literal><![CDATA[
      T(x \ R(x,y,x),y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5445,a,8702,a),flip(a)].">
      <j1 rule="hyper" parents="5445 8702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8704">
    <literal><![CDATA[
      (x * (y \ R(y,x,y))) / x = y \ R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(271,a,8703,a)].">
      <j1 rule="hyper" parents="271 8703"/>
    </justification>
  </clause>

  <clause id="8705">
    <literal><![CDATA[
      (T(x * y,x) / x) / y = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(6544(a,1),8704(a,1,1))].">
      <j1 rule="para" parents="6544 8704"/>
    </justification>
  </clause>

  <clause id="8706">
    <literal><![CDATA[
      K(x,T(y,z) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ x,z)) = u
    ]]></literal>
    <justification jstring="[para(8536(a,1),7680(a,1))].">
      <j1 rule="para" parents="8536 7680"/>
    </justification>
  </clause>

  <clause id="8708">
    <literal><![CDATA[
      T(x * y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8193(a,1),7697(a,1))].">
      <j1 rule="para" parents="8193 7697"/>
    </justification>
  </clause>

  <clause id="8709">
    <literal><![CDATA[
      K(x,T(y,K(L(x,z,u),w) * v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,7905,a(flip),b,7994,a),flip(a)].">
      <j1 rule="hyper" parents="320 7905 7994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8710">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u) * (u * z))) = K(x,T(y,u * (z * x)))
    ]]></literal>
    <justification jstring="[para(4964(a,1),8709(a,1,2,2))].">
      <j1 rule="para" parents="4964 8709"/>
    </justification>
  </clause>

  <clause id="8711">
    <literal><![CDATA[
      K(1 / T(T(x,y),y * x),z) = K(1 / L(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(4275(a,1),8111(a,1,1,2))].">
      <j1 rule="para" parents="4275 8111"/>
    </justification>
  </clause>

  <clause id="8712">
    <literal><![CDATA[
      (x \ 1) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) * (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(7858(a,1),8213(a,1,2))].">
      <j1 rule="para" parents="7858 8213"/>
    </justification>
  </clause>

  <clause id="8713">
    <literal><![CDATA[
      (x \ y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) * (x \ y) = u
    ]]></literal>
    <justification jstring="[para(7858(a,1),8215(a,1,2))].">
      <j1 rule="para" parents="7858 8215"/>
    </justification>
  </clause>

  <clause id="8714">
    <literal><![CDATA[
      x * K(L(K(y,z),T(z,u),w),x) = T(z,K(y,x)) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8574,a,b,8226,a)].">
      <j1 rule="hyper" parents="58 8574 8226"/>
    </justification>
  </clause>

  <clause id="8715">
    <literal><![CDATA[
      K(x / (y * z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) / z,y) = u
    ]]></literal>
    <justification jstring="[para(8515(a,1),8234(a,1))].">
      <j1 rule="para" parents="8515 8234"/>
    </justification>
  </clause>

  <clause id="8717">
    <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,8571,a(flip),b,4737,a),flip(a)].">
      <j1 rule="hyper" parents="116 8571 4737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8718">
    <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(8571(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8571 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8719">
    <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(8571(a,1),5057(a,1,2))].">
      <j1 rule="para" parents="8571 5057"/>
    </justification>
  </clause>

  <clause id="8720">
    <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,8603,a(flip),b,4737,a),flip(a)].">
      <j1 rule="hyper" parents="116 8603 4737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8721">
    <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(8603(a,1),5428(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8603 5428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8722">
    <literal><![CDATA[
      K(x,T(x \ y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(8211(a,1),8609(a,1))].">
      <j1 rule="para" parents="8211 8609"/>
    </justification>
  </clause>

  <clause id="8723">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * y))) = K(x,R(T(z,y),x,y))
    ]]></literal>
    <justification jstring="[hyper(7368,a,8676,a)].">
      <j1 rule="hyper" parents="7368 8676"/>
    </justification>
  </clause>

  <clause id="8724">
    <literal><![CDATA[
      K(1 / T(x,y),T(z,y * x)) = K(1 / L(x,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(7688,a,8711,a)].">
      <j1 rule="hyper" parents="7688 8711"/>
    </justification>
  </clause>

  <clause id="8725">
    <literal><![CDATA[
      K(1 / x,T(T(y,z * x),z)) = K(1 / L(x,z,x),y)
    ]]></literal>
    <justification jstring="[hyper(7688,a,8724,a)].">
      <j1 rule="hyper" parents="7688 8724"/>
    </justification>
  </clause>

  <clause id="8726">
    <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),8725(a,1,2))].">
      <j1 rule="para" parents="18 8725"/>
    </justification>
  </clause>

  <clause id="8727">
    <literal><![CDATA[
      K(1 / L(x,y,x),z) = K(1 / x,T(T(z,y),y))
    ]]></literal>
    <justification jstring="[hyper(8495,a,8726,a),flip(a)].">
      <j1 rule="hyper" parents="8495 8726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8728">
    <literal><![CDATA[
      K(1 / L(x,y,x),z) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7858,a(flip),b,8727,a),flip(a)].">
      <j1 rule="hyper" parents="320 7858 8727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8730">
    <literal><![CDATA[
      L(K(x,y),z,L(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3988,a,7015,a)].">
      <j1 rule="hyper" parents="3988 7015"/>
    </justification>
  </clause>

  <clause id="8731">
    <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(7015(a,1),6316(a,1,1))].">
      <j1 rule="para" parents="7015 6316"/>
    </justification>
  </clause>

  <clause id="8732">
    <literal><![CDATA[
      K(L(x,y,L(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(8365,a,8730,a)].">
      <j1 rule="hyper" parents="8365 8730"/>
    </justification>
  </clause>

  <clause id="8733">
    <literal><![CDATA[
      x * K(L(x,y,L(x,z,u)),w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(119,a,8732,a,b,4688,a(flip))].">
      <j1 rule="hyper" parents="119 8732 4688"/>
    </justification>
  </clause>

  <clause id="8734">
    <literal><![CDATA[
      K(x,(R(x,y,z) \ u) \ w) = K(x,u \ (R(x,y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(6687,a,7016,a),flip(a)].">
      <j1 rule="hyper" parents="6687 7016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8735">
    <literal><![CDATA[
      K(x,x \ (x * y)) = K(x,K(z \ x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6811,a(flip),b,7044,a)].">
      <j1 rule="hyper" parents="58 6811 7044"/>
    </justification>
  </clause>

  <clause id="8737">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),8735(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 8735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8738">
    <literal><![CDATA[
      K(x,y * K(z \ x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7303,a(flip),b,8737,a)].">
      <j1 rule="hyper" parents="58 7303 8737"/>
    </justification>
  </clause>

  <clause id="8740">
    <literal><![CDATA[
      K(x * y,K(x,y) * z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(4923(a,1),8737(a,1,2,1))].">
      <j1 rule="para" parents="4923 8737"/>
    </justification>
  </clause>

  <clause id="8741">
    <literal><![CDATA[
      K(x,K(y,y \ x) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5095(a,1),8737(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5095 8737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8742">
    <literal><![CDATA[
      K(x,(x / y) * z) = K(x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(5405(a,1),8737(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5405 8737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8744">
    <literal><![CDATA[
      K(x,y \ T(z,((y \ 1) \ (y \ z)) \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(6538(a,1),8738(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6538 8738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8745">
    <literal><![CDATA[
      T(x,K(y,y \ x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(118,a,8741,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 8741 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8746">
    <literal><![CDATA[
      T(x * y,K(y,x) * z) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(4869(a,1),8745(a,1,2,1))].">
      <j1 rule="para" parents="4869 8745"/>
    </justification>
  </clause>

  <clause id="8747">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,8746,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 8746 17"/>
    </justification>
  </clause>

  <clause id="8748">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) * (K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(8746(a,1),284(a,1,2))].">
      <j1 rule="para" parents="8746 284"/>
    </justification>
  </clause>

  <clause id="8749">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(K(z \ x,z) * y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6702,a(flip),b,7048,a)].">
      <j1 rule="hyper" parents="58 6702 7048"/>
    </justification>
  </clause>

  <clause id="8750">
    <literal><![CDATA[
      K(K(x \ y,x) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6270,a,8749,a),flip(a)].">
      <j1 rule="hyper" parents="6270 8749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8752">
    <literal><![CDATA[
      K(K(x \ y,x) * z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(8749(a,1),1351(a,1))].">
      <j1 rule="para" parents="8749 1351"/>
    </justification>
  </clause>

  <clause id="8754">
    <literal><![CDATA[
      (K(x \ y,x) * z) * K(z,y) = T(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8750,a(flip),b,4688,a(flip))].">
      <j1 rule="hyper" parents="119 8750 4688"/>
    </justification>
  </clause>

  <clause id="8755">
    <literal><![CDATA[
      K(K(x,y) * z,y * x) = K(z,y * x)
    ]]></literal>
    <justification jstring="[para(4(a,1),8750(a,1,1,1,1))].">
      <j1 rule="para" parents="4 8750"/>
    </justification>
  </clause>

  <clause id="8756">
    <literal><![CDATA[
      K(T(x,y) * z,y * x) = K(x * z,y * x)
    ]]></literal>
    <justification jstring="[para(4740(a,1),8755(a,1,1))].">
      <j1 rule="para" parents="4740 8755"/>
    </justification>
  </clause>

  <clause id="8757">
    <literal><![CDATA[
      K(((x \ y) \ y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(5198(a,2),8752(a,1,1))].">
      <j1 rule="para" parents="5198 8752"/>
    </justification>
  </clause>

  <clause id="8758">
    <literal><![CDATA[
      K((x \ y) * z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) * z,y) = u
    ]]></literal>
    <justification jstring="[para(5405(a,1),8752(a,1,1))].">
      <j1 rule="para" parents="5405 8752"/>
    </justification>
  </clause>

  <clause id="8759">
    <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,6614,a(flip),b,7294,a),flip(a)].">
      <j1 rule="hyper" parents="58 6614 7294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8760">
    <literal><![CDATA[
      K(x,y / R(T(x,z),u,w)) = K(x,R(x,u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,8505,a(flip),b,7296,a),flip(a)].">
      <j1 rule="hyper" parents="320 8505 7296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8762">
    <literal><![CDATA[
      K(x,y / (T(z,u) / u)) = K(x,y / (z / T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(7375,a,7305,a),flip(a)].">
      <j1 rule="hyper" parents="7375 7305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8763">
    <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,6716,a(flip),b,7343,a),flip(a)].">
      <j1 rule="hyper" parents="58 6716 7343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8764">
    <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,8763,a,b,5101,a),flip(a)].">
      <j1 rule="hyper" parents="115 8763 5101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8765">
    <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),8763(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8766">
    <literal><![CDATA[
      L(K(x,y),z,L(y,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3988,a,7436,a)].">
      <j1 rule="hyper" parents="3988 7436"/>
    </justification>
  </clause>

  <clause id="8767">
    <literal><![CDATA[
      K(L(x,y,L(z,u,w)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(8365,a,8766,a)].">
      <j1 rule="hyper" parents="8365 8766"/>
    </justification>
  </clause>

  <clause id="8768">
    <literal><![CDATA[
      K(x,L(y,z,L(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6580,a(flip),b,8766,a)].">
      <j1 rule="hyper" parents="58 6580 8766"/>
    </justification>
  </clause>

  <clause id="8769">
    <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(4313(a,1),8767(a,1,1))].">
      <j1 rule="para" parents="4313 8767"/>
    </justification>
  </clause>

  <clause id="8770">
    <literal><![CDATA[
      R(K(x,y),z,R(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3998,a,7461,a)].">
      <j1 rule="hyper" parents="3998 7461"/>
    </justification>
  </clause>

  <clause id="8771">
    <literal><![CDATA[
      K(x,y) * ((y * x) * R(x,z,u)) = (x * y) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(4772(a,1),7461(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4772 7461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8772">
    <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(7461(a,1),5055(a,1,1,2))].">
      <j1 rule="para" parents="7461 5055"/>
    </justification>
  </clause>

  <clause id="8773">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (w / R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,6918,a(flip),b,8770,a)].">
      <j1 rule="hyper" parents="58 6918 8770"/>
    </justification>
  </clause>

  <clause id="8774">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,6716,a(flip),b,8770,a)].">
      <j1 rule="hyper" parents="58 6716 8770"/>
    </justification>
  </clause>

  <clause id="8775">
    <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(8774(a,1),4729(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8774 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8776">
    <literal><![CDATA[
      T(L(x / y,z,x / y),y) = L(y \ x,z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[para(7471(a,2),7470(a,1,1))].">
      <j1 rule="para" parents="7471 7470"/>
    </justification>
  </clause>

  <clause id="8777">
    <literal><![CDATA[
      K(x * (R(y,z,y) \ u),y) = K(x * (u / T(y,z)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7558,a(flip),b,7491,a),flip(a)].">
      <j1 rule="hyper" parents="58 7558 7491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8778">
    <literal><![CDATA[
      K(x * (R(x,y,x) \ z),x) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,7361,a(flip),b,8777,a),flip(a)].">
      <j1 rule="hyper" parents="320 7361 8777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8779">
    <literal><![CDATA[
      K(R(x,y,x) * z,x) = K(x * z,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),8778(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 8778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8780">
    <literal><![CDATA[
      K(x * R(y,z,y),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7408,a(flip),b,8779,a)].">
      <j1 rule="hyper" parents="58 7408 8779"/>
    </justification>
  </clause>

  <clause id="8781">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = 1 / (x \ K(x * y,x))
    ]]></literal>
    <justification jstring="[para(8780(a,1),4953(a,2,2,2))].">
      <j1 rule="para" parents="8780 4953"/>
    </justification>
  </clause>

  <clause id="8782">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4953,a,b,8781,a),flip(a)].">
      <j1 rule="hyper" parents="320 4953 8781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8783">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = x * K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4714,a(flip),b,8782,a),flip(a)].">
      <j1 rule="hyper" parents="320 4714 8782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8784">
    <literal><![CDATA[
      K(x,y * R(x,z,x)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(4796,a,8783,a)].">
      <j1 rule="hyper" parents="4796 8783"/>
    </justification>
  </clause>

  <clause id="8785">
    <literal><![CDATA[
      K(x,R(x,y,x) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7400,a,b,8784,a)].">
      <j1 rule="hyper" parents="58 7400 8784"/>
    </justification>
  </clause>

  <clause id="8786">
    <literal><![CDATA[
      K(R(x,y,x),R(x,z,x) * u) = K(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(7370,a,8785,a)].">
      <j1 rule="hyper" parents="7370 8785"/>
    </justification>
  </clause>

  <clause id="8787">
    <literal><![CDATA[
      T(T(x,1 / y),K(1 / y,z)) = T(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,4714,a,b,7564,a),flip(a)].">
      <j1 rule="hyper" parents="320 4714 7564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8788">
    <literal><![CDATA[
      T(T(x,1 / y),K(z,1 / y)) = T(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7841,a,8787,a)].">
      <j1 rule="hyper" parents="7841 8787"/>
    </justification>
  </clause>

  <clause id="8789">
    <literal><![CDATA[
      T(x,1 / T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(1 / y,z)) = u
    ]]></literal>
    <justification jstring="[para(8787(a,1),7678(a,1))].">
      <j1 rule="para" parents="8787 7678"/>
    </justification>
  </clause>

  <clause id="8790">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(u,z / y)) = T(x,1 / T(y / z,u))
    ]]></literal>
    <justification jstring="[para(5317(a,1),8788(a,1,2))].">
      <j1 rule="para" parents="5317 8788"/>
    </justification>
  </clause>

  <clause id="8791">
    <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),7646(a,2,1))].">
      <j1 rule="para" parents="22 7646"/>
    </justification>
  </clause>

  <clause id="8792">
    <literal><![CDATA[
      T(x / y,z) * T(y,K(z,x / y)) = x * K(x / y,z)
    ]]></literal>
    <justification jstring="[para(7807(a,1),7704(a,1,2))].">
      <j1 rule="para" parents="7807 7704"/>
    </justification>
  </clause>

  <clause id="8793">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(R(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(5673(a,1),7742(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5673 7742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8794">
    <literal><![CDATA[
      R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w) \ 1))
    ]]></literal>
    <justification jstring="[para(7730(a,1),7743(a,1,1))].">
      <j1 rule="para" parents="7730 7743"/>
    </justification>
  </clause>

  <clause id="8795">
    <literal><![CDATA[
      K(R(K(x,y),z,u),w) = K(y,R(K(x,w),z,u))
    ]]></literal>
    <justification jstring="[para(5673(a,1),7775(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5673 7775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8796">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(y,R(K(x,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,8793,a,b,8795,a)].">
      <j1 rule="hyper" parents="58 8793 8795"/>
    </justification>
  </clause>

  <clause id="8797">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,R(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(7754(a,1),8796(a,1,1))].">
      <j1 rule="para" parents="7754 8796"/>
    </justification>
  </clause>

  <clause id="8798">
    <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),7781(a,1,2,1))].">
      <j1 rule="para" parents="7 7781"/>
    </justification>
  </clause>

  <clause id="8799">
    <literal><![CDATA[
      T(x * K(y,z),K(u,y)) = T(x,K(u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(7764,a,7847,a),flip(a)].">
      <j1 rule="hyper" parents="7764 7847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8800">
    <literal><![CDATA[
      T(K(x,y) * z,K(u,y)) = K(x,y) * T(z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(6005,a,8799,a),flip(a)].">
      <j1 rule="hyper" parents="6005 8799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8801">
    <literal><![CDATA[
      T(K(x,y) * z,K(u,y)) = K(x,y) * T(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(7807(a,1),8800(a,2,2))].">
      <j1 rule="para" parents="7807 8800"/>
    </justification>
  </clause>

  <clause id="8802">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,u)) = K(x,y) * T(z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(7841,a,8801,a)].">
      <j1 rule="hyper" parents="7841 8801"/>
    </justification>
  </clause>

  <clause id="8803">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,K(x,u)) = T(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(6018,a,8802,a)].">
      <j1 rule="hyper" parents="6018 8802"/>
    </justification>
  </clause>

  <clause id="8804">
    <literal><![CDATA[
      T(x * K(y,z),K(y,u)) = T(x,K(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6011,a,8802,a),flip(a)].">
      <j1 rule="hyper" parents="6011 8802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8805">
    <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),8803(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 8803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8806">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) = T(x,K(z,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(8803(a,1),5949(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8803 5949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8807">
    <literal><![CDATA[
      T(x * K(y,z * x),K(y,z)) = K(y,z * x) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,8071,a(flip),b,8804,a),flip(a)].">
      <j1 rule="hyper" parents="320 8071 8804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8808">
    <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(7761(a,1),8805(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7761 8805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8809">
    <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(5651(a,1),8806(a,2,2))].">
      <j1 rule="para" parents="5651 8806"/>
    </justification>
  </clause>

  <clause id="8810">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) \ T(x,K(z,u)) = K(z,y)
    ]]></literal>
    <justification jstring="[para(8806(a,2),6309(a,1,1))].">
      <j1 rule="para" parents="8806 6309"/>
    </justification>
  </clause>

  <clause id="8811">
    <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(8807(a,1),4229(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8807 4229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8812">
    <literal><![CDATA[
      R(K(x,y),T(y,z) * u,w) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,7899,a(flip),b,7910,a),flip(a)].">
      <j1 rule="hyper" parents="320 7899 7910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8813">
    <literal><![CDATA[
      R(K(x,y),T(y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(7910(a,2),8040(a,1))].">
      <j1 rule="para" parents="7910 8040"/>
    </justification>
  </clause>

  <clause id="8815">
    <literal><![CDATA[
      K(x,R(y,T(y,z) \ u,w)) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),8812(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 8812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8816">
    <literal><![CDATA[
      R(K(x,y),K(z,y) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,6930,a,b,8815,a)].">
      <j1 rule="hyper" parents="58 6930 8815"/>
    </justification>
  </clause>

  <clause id="8818">
    <literal><![CDATA[
      R(K(x,y),K(y,z) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(5095(a,1),8816(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5095 8816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8819">
    <literal><![CDATA[
      R(K(x,y),y \ K(y,z),u) = R(K(x,y),y \ 1,u)
    ]]></literal>
    <justification jstring="[para(5099(a,1),8816(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5099 8816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8820">
    <literal><![CDATA[
      R(K(x,y),z * K(u,y),w) = R(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[para(7261(a,1),8816(a,1,2))].">
      <j1 rule="para" parents="7261 8816"/>
    </justification>
  </clause>

  <clause id="8821">
    <literal><![CDATA[
      R(K(x,y),z * (K(u,y) * w),v5) = R(K(x,y),z * w,v5)
    ]]></literal>
    <justification jstring="[para(6008(a,1),8818(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6008 8818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8822">
    <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(8819(a,2),1627(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8819 1627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8823">
    <literal><![CDATA[
      R(K(x,y),y * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(104(a,1),8813(a,1,2,1))].">
      <j1 rule="para" parents="104 8813"/>
    </justification>
  </clause>

  <clause id="8824">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K((K(z,u) * y) / x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8631,a(flip),b,7951,a)].">
      <j1 rule="hyper" parents="58 8631 7951"/>
    </justification>
  </clause>

  <clause id="8825">
    <literal><![CDATA[
      K((K(x,y) * z) / u,x) = K(z / u,x)
    ]]></literal>
    <justification jstring="[hyper(8028,a,8824,a),flip(a)].">
      <j1 rule="hyper" parents="8028 8824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8827">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = (w * K(z / u,x)) \ w
    ]]></literal>
    <justification jstring="[para(8825(a,1),6309(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8825 6309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8828">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,6309,a(flip),b,8827,a),flip(a)].">
      <j1 rule="hyper" parents="320 6309 8827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8829">
    <literal><![CDATA[
      K(x,(T(y,x) * z) / u) = K(x,(y * z) / u)
    ]]></literal>
    <justification jstring="[para(4778(a,1),8828(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4778 8828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8830">
    <literal><![CDATA[
      K(x,(T(y / (z \ u),x) * K(z \ u,z)) / w) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[para(6441(a,1),8829(a,2,2,1))].">
      <j1 rule="para" parents="6441 8829"/>
    </justification>
  </clause>

  <clause id="8831">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / (x * K(z,u)),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8623,a(flip),b,7978,a)].">
      <j1 rule="hyper" parents="58 8623 7978"/>
    </justification>
  </clause>

  <clause id="8832">
    <literal><![CDATA[
      K(x / (y * K(z,u)),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(8034,a,8831,a),flip(a)].">
      <j1 rule="hyper" parents="8034 8831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8834">
    <literal><![CDATA[
      K(x / ((y * K(z,u)) * w),u) = K(x / (y * w),u)
    ]]></literal>
    <justification jstring="[para(6791(a,1),8832(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6791 8832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8835">
    <literal><![CDATA[
      K(x / ((K(y,z) * u) * w),y) = K(x / (u * w),y)
    ]]></literal>
    <justification jstring="[para(7121(a,1),8834(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7121 8834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8836">
    <literal><![CDATA[
      K(x / ((K(y,z) * u) * w),z) = K(x / (u * w),z)
    ]]></literal>
    <justification jstring="[para(7123(a,1),8834(a,1,1,2,1))].">
      <j1 rule="para" parents="7123 8834"/>
    </justification>
  </clause>

  <clause id="8837">
    <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(510(a,1),8836(a,1,1))].">
      <j1 rule="para" parents="510 8836"/>
    </justification>
  </clause>

  <clause id="8838">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / (y * K(u,x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8531,a(flip),b,7991,a)].">
      <j1 rule="hyper" parents="58 8531 7991"/>
    </justification>
  </clause>

  <clause id="8839">
    <literal><![CDATA[
      K(x,y / (z * K(u,x))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(8041,a,8838,a),flip(a)].">
      <j1 rule="hyper" parents="8041 8838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8841">
    <literal><![CDATA[
      K(x,y / (T(z,x) / u)) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[para(1429(a,1),8839(a,1,2,2))].">
      <j1 rule="para" parents="1429 8839"/>
    </justification>
  </clause>

  <clause id="8842">
    <literal><![CDATA[
      K(x,y / K(z,z \ K(u,x))) = K(x,y / (z * (K(u,x) / z)))
    ]]></literal>
    <justification jstring="[para(4742(a,1),8839(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4742 8839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8843">
    <literal><![CDATA[
      K(x,y / (T(z,x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(5500(a,1),8839(a,1,2,2))].">
      <j1 rule="para" parents="5500 8839"/>
    </justification>
  </clause>

  <clause id="8844">
    <literal><![CDATA[
      K(x,y / (z * K(x,u))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(6300(a,1),8839(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6300 8839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8845">
    <literal><![CDATA[
      K(x,y / (K(x,z) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(7121(a,1),8839(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7121 8839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8846">
    <literal><![CDATA[
      K(x,y / ((z * K(u,x)) * w)) = K(x,y / (z * w))
    ]]></literal>
    <justification jstring="[para(6791(a,1),8844(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6791 8844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8847">
    <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),8845(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15 8845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8848">
    <literal><![CDATA[
      K(x,y / (T(z \ T(u,z),x) / w)) = K(x,y / ((T(z,u) \ u) / w))
    ]]></literal>
    <justification jstring="[para(4351(a,1),8841(a,1,2,2,1))].">
      <j1 rule="para" parents="4351 8841"/>
    </justification>
  </clause>

  <clause id="8849">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(84(a,1),8846(a,1,2,2,1))].">
      <j1 rule="para" parents="84 8846"/>
    </justification>
  </clause>

  <clause id="8850">
    <literal><![CDATA[
      K(x,y / (((x \ z) * x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(302(a,1),8846(a,1,2,2,1))].">
      <j1 rule="para" parents="302 8846"/>
    </justification>
  </clause>

  <clause id="8851">
    <literal><![CDATA[
      K(x,y / ((K(x,z) * u) * w)) = K(x,y / (u * w))
    ]]></literal>
    <justification jstring="[para(7121(a,1),8846(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7121 8846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8852">
    <literal><![CDATA[
      K(x,y / ((K(z,x) * u) * w)) = K(x,y / (u * w))
    ]]></literal>
    <justification jstring="[para(7123(a,1),8846(a,1,2,2,1))].">
      <j1 rule="para" parents="7123 8846"/>
    </justification>
  </clause>

  <clause id="8853">
    <literal><![CDATA[
      K(x,y / ((z * (K(u,x) * w)) * v5)) = K(x,y / ((z * w) * v5))
    ]]></literal>
    <justification jstring="[para(6008(a,1),8851(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6008 8851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8854">
    <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(510(a,1),8852(a,1,2))].">
      <j1 rule="para" parents="510 8852"/>
    </justification>
  </clause>

  <clause id="8855">
    <literal><![CDATA[
      K(x,R(y,K(x,z),u)) = K(x,y * K(x,z))
    ]]></literal>
    <justification jstring="[para(6(a,1),8847(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 8847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8856">
    <literal><![CDATA[
      K(x,R(y,K(x,z),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7211,a(flip),b,8855,a),flip(a)].">
      <j1 rule="hyper" parents="320 7211 8855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8859">
    <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),8856(a,1,2))].">
      <j1 rule="para" parents="26 8856"/>
    </justification>
  </clause>

  <clause id="8860">
    <literal><![CDATA[
      ((x * (y * K(z,y))) / x) / ((x * y) / x) = K(T(z,x),y)
    ]]></literal>
    <justification jstring="[para(4711(a,1),7992(a,1,1,1,2))].">
      <j1 rule="para" parents="4711 7992"/>
    </justification>
  </clause>

  <clause id="8861">
    <literal><![CDATA[
      T(K(x,y),T(z,x \ u)) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(7735,a,8045,a),flip(a)].">
      <j1 rule="hyper" parents="7735 8045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8862">
    <literal><![CDATA[
      T(K(x,y),T(z,x * u)) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),8861(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8863">
    <literal><![CDATA[
      1 / (K(x,y) * T(x,z)) = K(y,x) / T(x,z)
    ]]></literal>
    <justification jstring="[para(7863(a,1),8081(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7863 8081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8864">
    <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(8863(a,1),3982(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8863 3982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8865">
    <literal><![CDATA[
      (K(x,y) / T(y,z)) \ 1 = K(y,z) * T(y,x)
    ]]></literal>
    <justification jstring="[para(8863(a,1),5417(a,1,1))].">
      <j1 rule="para" parents="8863 5417"/>
    </justification>
  </clause>

  <clause id="8867">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,x \ K(x,z)) = K(y,K(z,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,7759,a,b,8093,a),flip(a)].">
      <j1 rule="hyper" parents="320 7759 8093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8868">
    <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(320,a,8083,a,b,8094,a)].">
      <j1 rule="hyper" parents="320 8083 8094"/>
    </justification>
  </clause>

  <clause id="8869">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = x * K(T(x,z \ y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(4302(a,1),8099(a,1,2,1))].">
      <j1 rule="para" parents="4302 8099"/>
    </justification>
  </clause>

  <clause id="8870">
    <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(7018(a,1),8103(a,2,2))].">
      <j1 rule="para" parents="7018 8103"/>
    </justification>
  </clause>

  <clause id="8871">
    <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(6176(a,1),8250(a,2,2,1,1))].">
      <j1 rule="para" parents="6176 8250"/>
    </justification>
  </clause>

  <clause id="8872">
    <literal><![CDATA[
      K(R(x / (x / y),z,u),w) = K(R(y,z,u),T(w,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,8763,a(flip),b,8278,a),flip(a)].">
      <j1 rule="hyper" parents="320 8763 8278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8873">
    <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),8872(a,1,1)),flip(a)].">
      <j1 rule="para" parents="102 8872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8874">
    <literal><![CDATA[
      K(L(x,y / T(x,z),u),w) = L(K(x,w),y,u)
    ]]></literal>
    <justification jstring="[para(7863(a,1),8280(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7863 8280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8875">
    <literal><![CDATA[
      L(K(x,y),z * T(x,u),w) = K(L(x,z,w),y)
    ]]></literal>
    <justification jstring="[para(6(a,1),8874(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6 8874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8876">
    <literal><![CDATA[
      L(K(x,y),x * z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(187(a,1),8874(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="187 8874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8877">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(265(a,1),8874(a,1,1,2))].">
      <j1 rule="para" parents="265 8874"/>
    </justification>
  </clause>

  <clause id="8879">
    <literal><![CDATA[
      K(L(x,y,z),x * y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(6092,a,8876,a),flip(a)].">
      <j1 rule="hyper" parents="6092 8876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8880">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6580,a(flip),b,8876,a),flip(a)].">
      <j1 rule="hyper" parents="58 6580 8876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8881">
    <literal><![CDATA[
      K(L(x,y,z),(z \ u) \ (x * y)) = K(x,u \ (z * (x * y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,6555,a(flip),b,8876,a),flip(a)].">
      <j1 rule="hyper" parents="58 6555 8876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8882">
    <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(7863(a,1),8876(a,1,1))].">
      <j1 rule="para" parents="7863 8876"/>
    </justification>
  </clause>

  <clause id="8883">
    <literal><![CDATA[
      L(K(x,y),K(z,x),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8412,a(flip),b,8877,a),flip(a)].">
      <j1 rule="hyper" parents="58 8412 8877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8884">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,8883,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 8883 13"/>
    </justification>
  </clause>

  <clause id="8885">
    <literal><![CDATA[
      L(L(K(x,y),z,u),K(w,x),v5) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(8883(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8883 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8886">
    <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(8883(a,1),447(a,1,2,1))].">
      <j1 rule="para" parents="8883 447"/>
    </justification>
  </clause>

  <clause id="8887">
    <literal><![CDATA[
      L(K(x,y),L(K(z,x),u,w),v5) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4782(a,1),8883(a,1,2))].">
      <j1 rule="para" parents="4782 8883"/>
    </justification>
  </clause>

  <clause id="8888">
    <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,8887,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 8887 13"/>
    </justification>
  </clause>

  <clause id="8889">
    <literal><![CDATA[
      K(L(x,y * K(x,z),u),w) = K(L(x,y,u),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,6588,a(flip),b,8875,a)].">
      <j1 rule="hyper" parents="58 6588 8875"/>
    </justification>
  </clause>

  <clause id="8891">
    <literal><![CDATA[
      K(x,L(y,z * K(y,u),w)) = T(v5 * K(L(y,z,w),x),K(x,v6)) \ T(v5,K(x,v6))
    ]]></literal>
    <justification jstring="[para(8889(a,1),8810(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8889 8810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8892">
    <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(8885(a,2),6640(a,1,2))].">
      <j1 rule="para" parents="8885 6640"/>
    </justification>
  </clause>

  <clause id="8893">
    <literal><![CDATA[
      (x * (K(y,z) * K(z,u))) * K(u,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6315,a,8884,a)].">
      <j1 rule="hyper" parents="6315 8884"/>
    </justification>
  </clause>

  <clause id="8894">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(515,a,8884,a)].">
      <j1 rule="hyper" parents="515 8884"/>
    </justification>
  </clause>

  <clause id="8895">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = x * (K(u,y) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6795,a,b,8884,a)].">
      <j1 rule="hyper" parents="58 6795 8884"/>
    </justification>
  </clause>

  <clause id="8896">
    <literal><![CDATA[
      x * (K(y,z) * K(z,z * y)) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,6632,a(flip),b,8884,a),flip(a)].">
      <j1 rule="hyper" parents="58 6632 8884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8897">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[para(1991(a,2),8884(a,2,2))].">
      <j1 rule="para" parents="1991 8884"/>
    </justification>
  </clause>

  <clause id="8898">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(8894(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="8894 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8899">
    <literal><![CDATA[
      R(x,T(K(y,z),u),K(z,w)) = x
    ]]></literal>
    <justification jstring="[para(1523(a,1),8894(a,1,2))].">
      <j1 rule="para" parents="1523 8894"/>
    </justification>
  </clause>

  <clause id="8900">
    <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(8894(a,1),2532(a,1,1,1))].">
      <j1 rule="para" parents="8894 2532"/>
    </justification>
  </clause>

  <clause id="8901">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(8894(a,1),6127(a,1,1))].">
      <j1 rule="para" parents="8894 6127"/>
    </justification>
  </clause>

  <clause id="8902">
    <literal><![CDATA[
      R(x,T(K(y,z),u),T(K(z,w),v5)) = x
    ]]></literal>
    <justification jstring="[para(5471(a,1),8899(a,1,3))].">
      <j1 rule="para" parents="5471 8899"/>
    </justification>
  </clause>

  <clause id="8903">
    <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(8902(a,1),931(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8902 931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8904">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) = K(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,1991,a,b,8901,a),flip(a)].">
      <j1 rule="hyper" parents="320 1991 8901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8905">
    <literal><![CDATA[
      K(x,y) * K(y,y \ x) = a(y,x / y,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4253,a(flip),b,8901,a),flip(a)].">
      <j1 rule="hyper" parents="58 4253 8901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8906">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(8901(a,2),1997(a,1))].">
      <j1 rule="para" parents="8901 1997"/>
    </justification>
  </clause>

  <clause id="8908">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5461,a,b,8905,a)].">
      <j1 rule="hyper" parents="58 5461 8905"/>
    </justification>
  </clause>

  <clause id="8909">
    <literal><![CDATA[
      a(x,y / x,x) \ K(y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(8905(a,1),6309(a,1,1))].">
      <j1 rule="para" parents="8905 6309"/>
    </justification>
  </clause>

  <clause id="8910">
    <literal><![CDATA[
      a(x,y / x,x) * K(x,y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(8905(a,1),6312(a,1,1))].">
      <j1 rule="para" parents="8905 6312"/>
    </justification>
  </clause>

  <clause id="8911">
    <literal><![CDATA[
      a(x,(x * y) / x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),8908(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8912">
    <literal><![CDATA[
      x \ R(x,T(y,x),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(225(a,1),8911(a,1,2)),flip(a)].">
      <j1 rule="para" parents="225 8911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8913">
    <literal><![CDATA[
      x \ R(x,y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(4388(a,1),8912(a,1,2))].">
      <j1 rule="para" parents="4388 8912"/>
    </justification>
  </clause>

  <clause id="8914">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,x) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(7617,a,8913,a)].">
      <j1 rule="hyper" parents="7617 8913"/>
    </justification>
  </clause>

  <clause id="8915">
    <literal><![CDATA[
      R(x,y,x) / x = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5888,a,8913,a)].">
      <j1 rule="hyper" parents="5888 8913"/>
    </justification>
  </clause>

  <clause id="8916">
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5465,a,8913,a)].">
      <j1 rule="hyper" parents="5465 8913"/>
    </justification>
  </clause>

  <clause id="8917">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5453,a,8913,a)].">
      <j1 rule="hyper" parents="5453 8913"/>
    </justification>
  </clause>

  <clause id="8918">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5443,a,8913,a)].">
      <j1 rule="hyper" parents="5443 8913"/>
    </justification>
  </clause>

  <clause id="8919">
    <literal><![CDATA[
      x * a(x,y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,8913,a)].">
      <j1 rule="hyper" parents="134 8913"/>
    </justification>
  </clause>

  <clause id="8920">
    <literal><![CDATA[
      K(x,y \ z) * K(y \ (z * x),x) = a(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6828,a,b,8913,a)].">
      <j1 rule="hyper" parents="58 6828 8913"/>
    </justification>
  </clause>

  <clause id="8921">
    <literal><![CDATA[
      T(x,y) * a(x,z,x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,8913,a(flip),b,7454,a)].">
      <j1 rule="hyper" parents="119 8913 7454"/>
    </justification>
  </clause>

  <clause id="8922">
    <literal><![CDATA[
      T(x,y) \ R(x,z,x) = K(y,x) * a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,8913,a(flip),b,5091,a),flip(a)].">
      <j1 rule="hyper" parents="119 8913 5091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8923">
    <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(8913(a,1),5142(a,1,2))].">
      <j1 rule="para" parents="8913 5142"/>
    </justification>
  </clause>

  <clause id="8924">
    <literal><![CDATA[
      K(x,x * y) * a(x,y,x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8913(a,1),5455(a,1,2))].">
      <j1 rule="para" parents="8913 5455"/>
    </justification>
  </clause>

  <clause id="8925">
    <literal><![CDATA[
      a(x,x \ (y \ x),x) = x \ R(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(5756(a,1),8913(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5756 8913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8926">
    <literal><![CDATA[
      a(x,y,x) * x = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(8913(a,1),5890(a,1,1))].">
      <j1 rule="para" parents="8913 5890"/>
    </justification>
  </clause>

  <clause id="8927">
    <literal><![CDATA[
      a(x,y,x) \ K(x,y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(8913(a,1),6333(a,1,1))].">
      <j1 rule="para" parents="8913 6333"/>
    </justification>
  </clause>

  <clause id="8928">
    <literal><![CDATA[
      a(x,y,x) \ K(x * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(8913(a,1),6334(a,1,1))].">
      <j1 rule="para" parents="8913 6334"/>
    </justification>
  </clause>

  <clause id="8929">
    <literal><![CDATA[
      T(x * y,x) / x = y * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(8913(a,1),6544(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8913 6544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8930">
    <literal><![CDATA[
      R(x,y,x) \ x = a(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(8913(a,1),6733(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8913 6733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8931">
    <literal><![CDATA[
      x \ R(T(x,y),z,x) = K(x,y) * a(x,z,x)
    ]]></literal>
    <justification jstring="[para(8913(a,1),7578(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8913 7578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8932">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(8919(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8919 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8933">
    <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(8919(a,1),232(a,1,1))].">
      <j1 rule="para" parents="8919 232"/>
    </justification>
  </clause>

  <clause id="8934">
    <literal><![CDATA[
      K(x,y) * a(y,x,y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(5109,a,8916,a)].">
      <j1 rule="hyper" parents="5109 8916"/>
    </justification>
  </clause>

  <clause id="8935">
    <literal><![CDATA[
      a(x,y,x) * K(y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(6315,a,8917,a)].">
      <j1 rule="hyper" parents="6315 8917"/>
    </justification>
  </clause>

  <clause id="8936">
    <literal><![CDATA[
      a(x,y,x) * K(x,x * y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8917(a,1),6312(a,1,1))].">
      <j1 rule="para" parents="8917 6312"/>
    </justification>
  </clause>

  <clause id="8937">
    <literal><![CDATA[
      K(x,y) * a(y,x,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(5109,a,8918,a)].">
      <j1 rule="hyper" parents="5109 8918"/>
    </justification>
  </clause>

  <clause id="8938">
    <literal><![CDATA[
      (x * y) * a(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8918,a(flip),b,6695,a)].">
      <j1 rule="hyper" parents="119 8918 6695"/>
    </justification>
  </clause>

  <clause id="8939">
    <literal><![CDATA[
      a(x,y,x) * (y * x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(8918(a,1),6694(a,1,1))].">
      <j1 rule="para" parents="8918 6694"/>
    </justification>
  </clause>

  <clause id="8940">
    <literal><![CDATA[
      K(x,y) * a(x,x \ y,x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),8924(a,1,1,2))].">
      <j1 rule="para" parents="5 8924"/>
    </justification>
  </clause>

  <clause id="8941">
    <literal><![CDATA[
      a(x,y \ 1,x) \ K(y \ x,x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(5324(a,1),8928(a,1,2))].">
      <j1 rule="para" parents="5324 8928"/>
    </justification>
  </clause>

  <clause id="8942">
    <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,1890,a,b,8929,a)].">
      <j1 rule="hyper" parents="58 1890 8929"/>
    </justification>
  </clause>

  <clause id="8943">
    <literal><![CDATA[
      (x \ y) * a(x,x \ y,x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(5(a,1),8929(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 8929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8944">
    <literal><![CDATA[
      T(x * a(y,x,y),y) = y \ T(y * x,y)
    ]]></literal>
    <justification jstring="[para(8929(a,1),107(a,1,1))].">
      <j1 rule="para" parents="8929 107"/>
    </justification>
  </clause>

  <clause id="8945">
    <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(8929(a,2),231(a,1,2,2))].">
      <j1 rule="para" parents="8929 231"/>
    </justification>
  </clause>

  <clause id="8946">
    <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(8929(a,2),476(a,1,2,2))].">
      <j1 rule="para" parents="8929 476"/>
    </justification>
  </clause>

  <clause id="8947">
    <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(8929(a,2),828(a,1,2,2,2))].">
      <j1 rule="para" parents="8929 828"/>
    </justification>
  </clause>

  <clause id="8948">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(5255(a,2),8932(a,1))].">
      <j1 rule="para" parents="5255 8932"/>
    </justification>
  </clause>

  <clause id="8949">
    <literal><![CDATA[
      a(x,y,x) * K(y,x) = K(y * x,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5228,a,b,8935,a),flip(a)].">
      <j1 rule="hyper" parents="320 5228 8935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8950">
    <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(6181(a,1),8935(a,2,1))].">
      <j1 rule="para" parents="6181 8935"/>
    </justification>
  </clause>

  <clause id="8951">
    <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(8938(a,1),942(a,1,1,2))].">
      <j1 rule="para" parents="8938 942"/>
    </justification>
  </clause>

  <clause id="8952">
    <literal><![CDATA[
      a(x,x \ y,x) = T(x,y) \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(4334(a,1),8914(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4334 8914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8953">
    <literal><![CDATA[
      a(x,y,x) * T(x,z) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(8914(a,1),5890(a,1,1))].">
      <j1 rule="para" parents="8914 5890"/>
    </justification>
  </clause>

  <clause id="8954">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = a(x / y,z,x / y) * (x / y)
    ]]></literal>
    <justification jstring="[para(6345(a,1),8953(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6345 8953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8955">
    <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(8922(a,2),8366(a,1))].">
      <j1 rule="para" parents="8922 8366"/>
    </justification>
  </clause>

  <clause id="8956">
    <literal><![CDATA[
      a(x,x \ (y \ x),x) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,8913,a(flip),b,8925,a),flip(a)].">
      <j1 rule="hyper" parents="320 8913 8925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8957">
    <literal><![CDATA[
      T(x,y \ x) \ ((x \ (y \ x)) \ (y \ x)) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8952,a(flip),b,8956,a)].">
      <j1 rule="hyper" parents="58 8952 8956"/>
    </justification>
  </clause>

  <clause id="8958">
    <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(8931(a,1),91(a,1,2,2,1))].">
      <j1 rule="para" parents="8931 91"/>
    </justification>
  </clause>

  <clause id="8959">
    <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(8931(a,1),4081(a,1,1,1))].">
      <j1 rule="para" parents="8931 4081"/>
    </justification>
  </clause>

  <clause id="8960">
    <literal><![CDATA[
      L(K(x,y),K(z,y),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6645,a,8893,a)].">
      <j1 rule="hyper" parents="6645 8893"/>
    </justification>
  </clause>

  <clause id="8961">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * K(z,y) = x * K(u,y)
    ]]></literal>
    <justification jstring="[para(1991(a,2),8893(a,1,1,2))].">
      <j1 rule="para" parents="1991 8893"/>
    </justification>
  </clause>

  <clause id="8962">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,z) = x * (K(y,z) * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,8960,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 8960 13"/>
    </justification>
  </clause>

  <clause id="8963">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = x * (K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(1991(a,2),8895(a,2,2))].">
      <j1 rule="para" parents="1991 8895"/>
    </justification>
  </clause>

  <clause id="8964">
    <literal><![CDATA[
      (x / T(y,z)) * T(y,u) = x * (K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6458,a,8897,a)].">
      <j1 rule="hyper" parents="6458 8897"/>
    </justification>
  </clause>

  <clause id="8965">
    <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(239,a,8897,a,b,631,a)].">
      <j1 rule="hyper" parents="239 8897 631"/>
    </justification>
  </clause>

  <clause id="8966">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(u,y)) = (x / T(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6293(a,1),8897(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6293 8897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8967">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * (K(z,y) * K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(30,a,8893,a,b,8961,a(flip))].">
      <j1 rule="hyper" parents="30 8893 8961"/>
    </justification>
  </clause>

  <clause id="8968">
    <literal><![CDATA[
      (x * K(y,z)) * (K(u,y) * K(z,y)) = x * K(u,y)
    ]]></literal>
    <justification jstring="[hyper(6797,a,8962,a),flip(a)].">
      <j1 rule="hyper" parents="6797 8962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8969">
    <literal><![CDATA[
      R(x,K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(515,a,8963,a)].">
      <j1 rule="hyper" parents="515 8963"/>
    </justification>
  </clause>

  <clause id="8970">
    <literal><![CDATA[
      L(K(x,y),K(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(479,a,8963,a)].">
      <j1 rule="hyper" parents="479 8963"/>
    </justification>
  </clause>

  <clause id="8971">
    <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(2952(a,1),8963(a,1,1))].">
      <j1 rule="para" parents="2952 8963"/>
    </justification>
  </clause>

  <clause id="8972">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * K(u,z)) = x * K(u,z)
    ]]></literal>
    <justification jstring="[para(6300(a,1),8963(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6300 8963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8973">
    <literal><![CDATA[
      R(x / K(y,z),K(u,w),K(v5,u)) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6306,a(flip),b,8969,a),flip(a)].">
      <j1 rule="hyper" parents="320 6306 8969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8974">
    <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(8970(a,1),286(a,1,2))].">
      <j1 rule="para" parents="8970 286"/>
    </justification>
  </clause>

  <clause id="8975">
    <literal><![CDATA[
      L(K(x,T(y,z)),K(y,u),w) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7863(a,1),8970(a,1,2))].">
      <j1 rule="para" parents="7863 8970"/>
    </justification>
  </clause>

  <clause id="8976">
    <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,8975,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 8975 13"/>
    </justification>
  </clause>

  <clause id="8977">
    <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(8973(a,1),1359(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8973 1359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8978">
    <literal><![CDATA[
      (x * y) * (K(y,z) * K(u,y)) = (x * K(u,y)) * T(y,z)
    ]]></literal>
    <justification jstring="[para(6290(a,1),8964(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6290 8964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8979">
    <literal><![CDATA[
      x / (K(y,z) * K(u,y)) = x * (K(z,y) * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(326,a,8967,a),flip(a)].">
      <j1 rule="hyper" parents="326 8967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8980">
    <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(8967(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8967 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8981">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ 1 = K(y,x) * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4933,a(flip),b,8968,a)].">
      <j1 rule="hyper" parents="116 4933 8968"/>
    </justification>
  </clause>

  <clause id="8982">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ 1 = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5605,a,b,8981,a),flip(a)].">
      <j1 rule="hyper" parents="320 5605 8981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8983">
    <literal><![CDATA[
      T(K(x,y) * K(x,z),K(z,x) * K(y,x)) = (K(z,x) * K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(8981(a,1),6852(a,2,1))].">
      <j1 rule="para" parents="8981 6852"/>
    </justification>
  </clause>

  <clause id="8984">
    <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(8972(a,1),4864(a,1,1,1))].">
      <j1 rule="para" parents="8972 4864"/>
    </justification>
  </clause>

  <clause id="8985">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ 1 = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(3919,a,8979,a)].">
      <j1 rule="hyper" parents="3919 8979"/>
    </justification>
  </clause>

  <clause id="8986">
    <literal><![CDATA[
      x / (K(y,z) * K(z,u)) = x * (K(u,z) * K(z,y))
    ]]></literal>
    <justification jstring="[para(1991(a,1),8979(a,1,2))].">
      <j1 rule="para" parents="1991 8979"/>
    </justification>
  </clause>

  <clause id="8987">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = x * (y \ L(y,z,y))
    ]]></literal>
    <justification jstring="[para(5452(a,1),8896(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5452 8896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8988">
    <literal><![CDATA[
      K(x,L(y,z / T(y,u),w)) = L(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[para(7863(a,1),8283(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7863 8283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8989">
    <literal><![CDATA[
      L(K(x,y),y * z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(187(a,1),8988(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="187 8988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8990">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(265(a,1),8988(a,1,2,2))].">
      <j1 rule="para" parents="265 8988"/>
    </justification>
  </clause>

  <clause id="8991">
    <literal><![CDATA[
      L(K(x,y),z * K(y,u),w) = K(x,L(y,z / y,w))
    ]]></literal>
    <justification jstring="[para(6118(a,1),8988(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6118 8988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8993">
    <literal><![CDATA[
      K(x * y,L(x,y,z)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(6088,a,8989,a),flip(a)].">
      <j1 rule="hyper" parents="6088 8989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8994">
    <literal><![CDATA[
      K((x \ y) \ (z * u),L(z,u,x)) = K(y \ (x * (z * u)),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6597,a(flip),b,8989,a),flip(a)].">
      <j1 rule="hyper" parents="58 6597 8989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8995">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(y,z,x)) = x * ((y * z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,8989,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 8989 13"/>
    </justification>
  </clause>

  <clause id="8996">
    <literal><![CDATA[
      L(K(x,y / z),y,u) = K(x,L(y / z,z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),8989(a,1,2))].">
      <j1 rule="para" parents="7 8989"/>
    </justification>
  </clause>

  <clause id="8997">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(x,L(y,K(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(4737(a,1),8989(a,1,2))].">
      <j1 rule="para" parents="4737 8989"/>
    </justification>
  </clause>

  <clause id="8998">
    <literal><![CDATA[
      K(x,L(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y,z),y) = u
    ]]></literal>
    <justification jstring="[para(8989(a,1),8365(a,1))].">
      <j1 rule="para" parents="8989 8365"/>
    </justification>
  </clause>

  <clause id="8999">
    <literal><![CDATA[
      L(K(x,y),z * K(y,u),w) = L(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,6578,a(flip),b,8991,a),flip(a)].">
      <j1 rule="hyper" parents="320 6578 8991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9000">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z * K(x,u),w) = a(w,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8999(a,2),5861(a,1,2))].">
      <j1 rule="para" parents="8999 5861"/>
    </justification>
  </clause>

  <clause id="9001">
    <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(8999(a,2),8573(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8999 8573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9002">
    <literal><![CDATA[
      K(K(x,y) * T(y,z),T(u,z)) = K(y,T(u,T(x,z)))
    ]]></literal>
    <justification jstring="[hyper(320,a,7905,a(flip),b,8285,a),flip(a)].">
      <j1 rule="hyper" parents="320 7905 8285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9003">
    <literal><![CDATA[
      K(K(x,y) * T(y,z),T(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(u,T(x,z))) = w
    ]]></literal>
    <justification jstring="[para(8285(a,2),8229(a,1))].">
      <j1 rule="para" parents="8285 8229"/>
    </justification>
  </clause>

  <clause id="9004">
    <literal><![CDATA[
      T(T(x,K(y,T(z,z))),z \ T(y,z)) = T(x,y / T(z,y))
    ]]></literal>
    <justification jstring="[para(4206(a,1),8298(a,2,2))].">
      <j1 rule="para" parents="4206 8298"/>
    </justification>
  </clause>

  <clause id="9005">
    <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(320,a,8279,a(flip),b,8314,a),flip(a)].">
      <j1 rule="hyper" parents="320 8279 8314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9006">
    <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(7755(a,1),8338(a,2,2))].">
      <j1 rule="para" parents="7755 8338"/>
    </justification>
  </clause>

  <clause id="9007">
    <literal><![CDATA[
      K(x,y) * T(z,T(x * z,y)) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4569(a,2),8343(a,1,2))].">
      <j1 rule="para" parents="4569 8343"/>
    </justification>
  </clause>

  <clause id="9008">
    <literal><![CDATA[
      T(x,(y \ x) \ (z * x)) = T(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4953,a,b,8352,a),flip(a)].">
      <j1 rule="hyper" parents="320 4953 8352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9009">
    <literal><![CDATA[
      T(x,(y \ 1) \ (x \ z)) = x * K(x,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(8432,a,9008,a),flip(a)].">
      <j1 rule="hyper" parents="8432 9008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9010">
    <literal><![CDATA[
      K(x,(y \ 1) \ (x \ z)) = K(x,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(4796,a,9009,a)].">
      <j1 rule="hyper" parents="4796 9009"/>
    </justification>
  </clause>

  <clause id="9011">
    <literal><![CDATA[
      K(x / y,z \ (y \ x)) = K(y \ x,y \ (z \ x))
    ]]></literal>
    <justification jstring="[hyper(8028,a,8484,a)].">
      <j1 rule="hyper" parents="8028 8484"/>
    </justification>
  </clause>

  <clause id="9012">
    <literal><![CDATA[
      K(x \ y,(z * x) \ y) = K(x \ y,x \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8655,a(flip),b,9011,a)].">
      <j1 rule="hyper" parents="58 8655 9011"/>
    </justification>
  </clause>

  <clause id="9013">
    <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),9012(a,2,2))].">
      <j1 rule="para" parents="75 9012"/>
    </justification>
  </clause>

  <clause id="9014">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,x \ (x * y)) = K(z / ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[para(4(a,1),8502(a,2,2))].">
      <j1 rule="para" parents="4 8502"/>
    </justification>
  </clause>

  <clause id="9015">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * y))) = ((z * x) * y) \ ((x * z) * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),8506(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 8506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9016">
    <literal><![CDATA[
      K(T(x,y),z \ T(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ T(T(x,w),y),y)) = u
    ]]></literal>
    <justification jstring="[para(8542(a,1),7679(a,1))].">
      <j1 rule="para" parents="8542 7679"/>
    </justification>
  </clause>

  <clause id="9018">
    <literal><![CDATA[
      K(T(x,y * K(z,y)),u) = K(x * K(T(x,z),y),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,4753,a,b,8586,a),flip(a)].">
      <j1 rule="hyper" parents="320 4753 8586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9019">
    <literal><![CDATA[
      K(T(x * K(x * y,x),z * K(y * x,z)),u) = K((x * K(x * y,x)) * K(x,z),u)
    ]]></literal>
    <justification jstring="[para(5165(a,1),9018(a,2,1,2,1))].">
      <j1 rule="para" parents="5165 9018"/>
    </justification>
  </clause>

  <clause id="9020">
    <literal><![CDATA[
      K(T(x,y * K(z * x,y)),u) = K(x * K(T(x,z),y),u)
    ]]></literal>
    <justification jstring="[para(7117(a,1),9018(a,2,1,2))].">
      <j1 rule="para" parents="7117 9018"/>
    </justification>
  </clause>

  <clause id="9021">
    <literal><![CDATA[
      T(x * (y \ z),K(y,z)) = (y \ z) * T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5545,a(flip),b,8589,a),flip(a)].">
      <j1 rule="hyper" parents="58 5545 8589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9022">
    <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(8614(a,1),490(a,1,1,1))].">
      <j1 rule="para" parents="8614 490"/>
    </justification>
  </clause>

  <clause id="9023">
    <literal><![CDATA[
      K((T(x,y) \ y) \ z,u) = K((x \ T(y,x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(7395,a,8617,a),flip(a)].">
      <j1 rule="hyper" parents="7395 8617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9024">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(x,K(w,z \ (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,7759,a(flip),b,8639,a),flip(a)].">
      <j1 rule="hyper" parents="320 7759 8639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9025">
    <literal><![CDATA[
      K(x,T(y \ T(T(x,z),u),w)) = K(x,T(y \ x,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,8682,a(flip),b,8683,a),flip(a)].">
      <j1 rule="hyper" parents="320 8682 8683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9027">
    <literal><![CDATA[
      T(K(x \ y,x) * z,y) = K(x \ y,x) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6170,a,8754,a),flip(a)].">
      <j1 rule="hyper" parents="6170 8754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9028">
    <literal><![CDATA[
      T(K(x \ (y * x),x) * z,y * x) = K(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(4923(a,1),9027(a,2,1))].">
      <j1 rule="para" parents="4923 9027"/>
    </justification>
  </clause>

  <clause id="9029">
    <literal><![CDATA[
      K(T(x,y \ z),R(y,u,w)) = K(T(x,z),R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(4944,a,8764,a),flip(a)].">
      <j1 rule="hyper" parents="4944 8764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9030">
    <literal><![CDATA[
      K(x,y) * ((y * R(x,z,u)) * x) = (x * y) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(1864(a,2),8771(a,1,2))].">
      <j1 rule="para" parents="1864 8771"/>
    </justification>
  </clause>

  <clause id="9031">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (R(x,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(320,a,7536,a(flip),b,8773,a),flip(a)].">
      <j1 rule="hyper" parents="320 7536 8773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9032">
    <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(320,a,22,a,b,8775,a),flip(a)].">
      <j1 rule="hyper" parents="320 22 8775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9033">
    <literal><![CDATA[
      L(x \ y,z,T(x \ y,u)) = L(x \ y,z,y / x)
    ]]></literal>
    <justification jstring="[hyper(855,a,8776,a),flip(a)].">
      <j1 rule="hyper" parents="855 8776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9034">
    <literal><![CDATA[
      L(x \ y,z,y / x) = L(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7466,a(flip),b,9033,a),flip(a)].">
      <j1 rule="hyper" parents="58 7466 9033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9035">
    <literal><![CDATA[
      L(x \ y,x,x \ y) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(757,a,9034,a),flip(a)].">
      <j1 rule="hyper" parents="757 9034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9036">
    <literal><![CDATA[
      L(T(x \ y,z),x,x \ y) = T(T(y / x,y),z)
    ]]></literal>
    <justification jstring="[para(9035(a,1),20(a,2,1))].">
      <j1 rule="para" parents="9035 20"/>
    </justification>
  </clause>

  <clause id="9037">
    <literal><![CDATA[
      T(x / y,z) * T(y,K(x,z)) = x * K(x / y,z)
    ]]></literal>
    <justification jstring="[para(8018(a,1),8792(a,1,2))].">
      <j1 rule="para" parents="8018 8792"/>
    </justification>
  </clause>

  <clause id="9038">
    <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(4206(a,2),9037(a,2,2,1))].">
      <j1 rule="para" parents="4206 9037"/>
    </justification>
  </clause>

  <clause id="9039">
    <literal><![CDATA[
      R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,8146,a(flip),b,8794,a),flip(a)].">
      <j1 rule="hyper" parents="320 8146 8794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9040">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[para(8146(a,1),9039(a,1,1))].">
      <j1 rule="para" parents="8146 9039"/>
    </justification>
  </clause>

  <clause id="9041">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(y,K(z,R(x,u,w)))
    ]]></literal>
    <justification jstring="[para(8149(a,1),9039(a,1,1))].">
      <j1 rule="para" parents="8149 9039"/>
    </justification>
  </clause>

  <clause id="9042">
    <literal><![CDATA[
      K(x,R(K(y,z),u,w)) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8797,a(flip),b,9040,a)].">
      <j1 rule="hyper" parents="58 8797 9040"/>
    </justification>
  </clause>

  <clause id="9043">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) = K(z,K(x,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,9040,a(flip),b,9041,a),flip(a)].">
      <j1 rule="hyper" parents="58 9040 9041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9044">
    <literal><![CDATA[
      K(x,R(K(y,z),u,w)) = K(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8796,a(flip),b,9041,a)].">
      <j1 rule="hyper" parents="58 8796 9041"/>
    </justification>
  </clause>

  <clause id="9045">
    <literal><![CDATA[
      T(x,R(K(y,z),u,w)) = T(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(118,a,9042,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 9042 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9046">
    <literal><![CDATA[
      T(x,R(K(y,z),u,w)) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(118,a,9044,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 9044 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9047">
    <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(6920(a,1),9044(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6920 9044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9048">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w))) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,9045,a(flip),b,9046,a)].">
      <j1 rule="hyper" parents="58 9045 9046"/>
    </justification>
  </clause>

  <clause id="9049">
    <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(9048(a,1),8805(a,2,2))].">
      <j1 rule="para" parents="9048 8805"/>
    </justification>
  </clause>

  <clause id="9050">
    <literal><![CDATA[
      K(T(x,y),z) * ((y * z) / y) = (y * (z * K(x,z))) / y
    ]]></literal>
    <justification jstring="[hyper(133,a,8860,a)].">
      <j1 rule="hyper" parents="133 8860"/>
    </justification>
  </clause>

  <clause id="9051">
    <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(8867(a,1),6286(a,1,1))].">
      <j1 rule="para" parents="8867 6286"/>
    </justification>
  </clause>

  <clause id="9052">
    <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(8882(a,2),8038(a,1))].">
      <j1 rule="para" parents="8882 8038"/>
    </justification>
  </clause>

  <clause id="9053">
    <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),9052(a,1,2,1))].">
      <j1 rule="para" parents="104 9052"/>
    </justification>
  </clause>

  <clause id="9054">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(y * z,y)) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6618,a(flip),b,8966,a),flip(a)].">
      <j1 rule="hyper" parents="320 6618 8966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9055">
    <literal><![CDATA[
      (x / y) * a(y,z,y) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(8918(a,1),9054(a,1,2))].">
      <j1 rule="para" parents="8918 9054"/>
    </justification>
  </clause>

  <clause id="9056">
    <literal><![CDATA[
      L(x,y,x) \ x = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,6032,a,b,9055,a)].">
      <j1 rule="hyper" parents="29 6032 9055"/>
    </justification>
  </clause>

  <clause id="9057">
    <literal><![CDATA[
      (x * y) / L(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),9055(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 9055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9058">
    <literal><![CDATA[
      L(x,y,x) \ 1 = x \ a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,9056,a(flip),b,1404,a),flip(a)].">
      <j1 rule="hyper" parents="116 9056 1404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9059">
    <literal><![CDATA[
      a(x,y,x) \ x = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(9056(a,1),5918(a,1,1))].">
      <j1 rule="para" parents="9056 5918"/>
    </justification>
  </clause>

  <clause id="9060">
    <literal><![CDATA[
      L(x \ L(y,z,y),x,a(y,z,y)) = (a(y,z,y) * x) \ y
    ]]></literal>
    <justification jstring="[para(9059(a,1),298(a,1,1,2))].">
      <j1 rule="para" parents="9059 298"/>
    </justification>
  </clause>

  <clause id="9061">
    <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(9058(a,1),6723(a,1,1,2))].">
      <j1 rule="para" parents="9058 6723"/>
    </justification>
  </clause>

  <clause id="9062">
    <literal><![CDATA[
      (x / L(y,z,y)) * y = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(1640,a,9057,a)].">
      <j1 rule="hyper" parents="1640 9057"/>
    </justification>
  </clause>

  <clause id="9063">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (x * y) = L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(188,a,9057,a)].">
      <j1 rule="hyper" parents="188 9057"/>
    </justification>
  </clause>

  <clause id="9064">
    <literal><![CDATA[
      x * (L(x,y,x) \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7488,a(flip),b,9062,a)].">
      <j1 rule="hyper" parents="58 7488 9062"/>
    </justification>
  </clause>

  <clause id="9065">
    <literal><![CDATA[
      (x * L(y,z,y)) * a(y,z,y) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),9062(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 9062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9066">
    <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(901(a,1),9063(a,1,2))].">
      <j1 rule="para" parents="901 9063"/>
    </justification>
  </clause>

  <clause id="9067">
    <literal><![CDATA[
      (T(x * y,x) / x) \ (y * x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(8929(a,2),9063(a,1,1))].">
      <j1 rule="para" parents="8929 9063"/>
    </justification>
  </clause>

  <clause id="9068">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = z / a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(573,a,9064,a),flip(a)].">
      <j1 rule="hyper" parents="573 9064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9069">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = u * a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8513,a,b,9064,a)].">
      <j1 rule="hyper" parents="58 8513 9064"/>
    </justification>
  </clause>

  <clause id="9070">
    <literal><![CDATA[
      L(x,y,x) \ (x * z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1403,a,b,9064,a)].">
      <j1 rule="hyper" parents="58 1403 9064"/>
    </justification>
  </clause>

  <clause id="9071">
    <literal><![CDATA[
      K(x,y) * (z * a(x,u,x)) = T(x,y) * (L(x,u,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,9064,a(flip),b,4741,a)].">
      <j1 rule="hyper" parents="119 9064 4741"/>
    </justification>
  </clause>

  <clause id="9072">
    <literal><![CDATA[
      x * a(y,y \ x,y) = y * (T(x,y) / y)
    ]]></literal>
    <justification jstring="[para(4465(a,1),9064(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4465 9064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9073">
    <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(7478(a,1),9064(a,1,2,1))].">
      <j1 rule="para" parents="7478 9064"/>
    </justification>
  </clause>

  <clause id="9074">
    <literal><![CDATA[
      (x / y) \ (x / a(y,z,y)) = L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,9068,a(flip),b,7489,a(flip))].">
      <j1 rule="hyper" parents="116 9068 7489"/>
    </justification>
  </clause>

  <clause id="9075">
    <literal><![CDATA[
      (x \ y) * a(x,z,x) = L(x,z,x) \ y
    ]]></literal>
    <justification jstring="[para(5(a,1),9070(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 9070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9076">
    <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(7929(a,1),9067(a,1,2))].">
      <j1 rule="para" parents="7929 9067"/>
    </justification>
  </clause>

  <clause id="9077">
    <literal><![CDATA[
      x * a(y,y \ x,y) = T(y * (x / y),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4533,a,b,9072,a),flip(a)].">
      <j1 rule="hyper" parents="320 4533 9072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9078">
    <literal><![CDATA[
      K(x,y) * (z * a(y,u,y)) = y * (L(T(y,x),u,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,9069,a(flip),b,5060,a)].">
      <j1 rule="hyper" parents="119 9069 5060"/>
    </justification>
  </clause>

  <clause id="9079">
    <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(9069(a,2),38(a,1))].">
      <j1 rule="para" parents="9069 38"/>
    </justification>
  </clause>

  <clause id="9080">
    <literal><![CDATA[
      (x * y) * (K(y,z) * K(u,y)) = x * (K(u,y) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,6281,a(flip),b,8978,a),flip(a)].">
      <j1 rule="hyper" parents="320 6281 8978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9081">
    <literal><![CDATA[
      a(x,y * K(z,u),K(z,w)) = a(x,y,K(z,w))
    ]]></literal>
    <justification jstring="[hyper(5868,a,9000,a)].">
      <j1 rule="hyper" parents="5868 9000"/>
    </justification>
  </clause>

  <clause id="9082">
    <literal><![CDATA[
      a(x,y * K(z,u),K(u,w)) = a(x,y,K(u,w))
    ]]></literal>
    <justification jstring="[para(6300(a,1),9081(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6300 9081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9083">
    <literal><![CDATA[
      (x * y) \ ((x * (y * K(z,u))) * K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6314,a,b,9082,a)].">
      <j1 rule="hyper" parents="58 6314 9082"/>
    </justification>
  </clause>

  <clause id="9084">
    <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(320,a,7750,a,b,9001,a),flip(a)].">
      <j1 rule="hyper" parents="320 7750 9001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9085">
    <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),9004(a,1,1,2,2))].">
      <j1 rule="para" parents="104 9004"/>
    </justification>
  </clause>

  <clause id="9086">
    <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,9032,a(flip),b,5064,a),flip(a)].">
      <j1 rule="hyper" parents="116 9032 5064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9087">
    <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(9032(a,1),7076(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9032 7076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9088">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z,y))) / x) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(9050(a,1),5104(a,1,2))].">
      <j1 rule="para" parents="9050 5104"/>
    </justification>
  </clause>

  <clause id="9089">
    <literal><![CDATA[
      K(x,x * y) * (z * a(x,y,x)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(320,a,6944,a(flip),b,9071,a),flip(a)].">
      <j1 rule="hyper" parents="320 6944 9071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9090">
    <literal><![CDATA[
      K(x,x * y) * z != K(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      u * a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(9089(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="9089 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9091">
    <literal><![CDATA[
      K(x,y) * (z * L(x,y,x)) = K(x,x * y) * (z * x)
    ]]></literal>
    <justification jstring="[para(9065(a,1),9089(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9065 9089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9092">
    <literal><![CDATA[
      (x * y) * (K(y,z) * K(y * z,y)) = x * R(y,z,y)
    ]]></literal>
    <justification jstring="[para(5054(a,1),9080(a,2,2))].">
      <j1 rule="para" parents="5054 9080"/>
    </justification>
  </clause>

  <clause id="9093">
    <literal><![CDATA[
      (x * y) * a(y,z,y) = x * R(y,z,y)
    ]]></literal>
    <justification jstring="[para(8918(a,1),9092(a,1,2))].">
      <j1 rule="para" parents="8918 9092"/>
    </justification>
  </clause>

  <clause id="9094">
    <literal><![CDATA[
      (x / y) * R(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(326,a,9093,a),flip(a)].">
      <j1 rule="hyper" parents="326 9093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9095">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z,y)) = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,9093,a)].">
      <j1 rule="hyper" parents="123 9093"/>
    </justification>
  </clause>

  <clause id="9096">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,9093,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 9093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9097">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7112,a,b,9094,a)].">
      <j1 rule="hyper" parents="58 7112 9094"/>
    </justification>
  </clause>

  <clause id="9098">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (x * R(y,z,y)) = y
    ]]></literal>
    <justification jstring="[para(9094(a,1),1870(a,1,1))].">
      <j1 rule="para" parents="9094 1870"/>
    </justification>
  </clause>

  <clause id="9099">
    <literal><![CDATA[
      (x / y) * ((y \ z) \ T(z,y)) = x * a(y,y \ z,y)
    ]]></literal>
    <justification jstring="[para(4294(a,1),9094(a,1,2))].">
      <j1 rule="para" parents="4294 9094"/>
    </justification>
  </clause>

  <clause id="9100">
    <literal><![CDATA[
      K(x,y) * ((z / y) * R(y,u,y)) = y * (L(T(y,x),u,y) \ z)
    ]]></literal>
    <justification jstring="[para(9094(a,2),9078(a,1,2))].">
      <j1 rule="para" parents="9094 9078"/>
    </justification>
  </clause>

  <clause id="9101">
    <literal><![CDATA[
      (x * y) * a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x * R(y,z,y) = u
    ]]></literal>
    <justification jstring="[para(9095(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9095 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9102">
    <literal><![CDATA[
      x * (y \ L(y,z,y)) = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8987,a(flip),b,9096,a)].">
      <j1 rule="hyper" parents="58 8987 9096"/>
    </justification>
  </clause>

  <clause id="9103">
    <literal><![CDATA[
      (x * y) * a(x,z,x) = R(x,z,x) * y
    ]]></literal>
    <justification jstring="[hyper(584,a,9097,a),flip(a)].">
      <j1 rule="hyper" parents="584 9097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9104">
    <literal><![CDATA[
      (R(x,y,x) \ z) * a(x,y,x) = x \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,1304,a(flip),b,9097,a),flip(a)].">
      <j1 rule="hyper" parents="58 1304 9097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9105">
    <literal><![CDATA[
      x * (y * a(x,z,x)) = R(x,z,x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,9097,a(flip),b,1303,a)].">
      <j1 rule="hyper" parents="119 9097 1303"/>
    </justification>
  </clause>

  <clause id="9106">
    <literal><![CDATA[
      (x / R(y,z,y)) * a(y,z,y) = x / y
    ]]></literal>
    <justification jstring="[para(9098(a,1),324(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9098 324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9107">
    <literal><![CDATA[
      K(x,T((y \ z) / z,u)) = ((u * x) / u) / ((u * (x * K(y \ 1,x))) / u)
    ]]></literal>
    <justification jstring="[para(5396(a,1),9088(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5396 9088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9108">
    <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(8835(a,1),9088(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8835 9088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9109">
    <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),7116(a,1,2,1,1))].">
      <j1 rule="para" parents="72 7116"/>
    </justification>
  </clause>

  <clause id="9110">
    <literal><![CDATA[
      L(x,T(y,K(x,z)),x) = T(x,x * y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7846(a,1),7125(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7846 7125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9111">
    <literal><![CDATA[
      L(x,T(y,K(x,z)),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5246,a(flip),b,9110,a),flip(a)].">
      <j1 rule="hyper" parents="320 5246 9110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9113">
    <literal><![CDATA[
      L(x,T(y,T(x,z)),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7421,a(flip),b,9111,a)].">
      <j1 rule="hyper" parents="58 7421 9111"/>
    </justification>
  </clause>

  <clause id="9115">
    <literal><![CDATA[
      L(x,y / T(x,z),x) = L(x,T(x,z) \ y,x)
    ]]></literal>
    <justification jstring="[para(107(a,1),9113(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 9113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9116">
    <literal><![CDATA[
      L(K(x,T((y \ z) \ u,w)),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[para(7131(a,2),7135(a,1,1))].">
      <j1 rule="para" parents="7131 7135"/>
    </justification>
  </clause>

  <clause id="9117">
    <literal><![CDATA[
      L(K(x,T(y \ z,u)),y \ z,w) = K(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(7131(a,2),7136(a,1,1))].">
      <j1 rule="para" parents="7131 7136"/>
    </justification>
  </clause>

  <clause id="9119">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * x,x)
    ]]></literal>
    <justification jstring="[para(7314(a,1),7222(a,2,2))].">
      <j1 rule="para" parents="7314 7222"/>
    </justification>
  </clause>

  <clause id="9120">
    <literal><![CDATA[
      R(x,y * K(x,z),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5464,a,9119,a),flip(a)].">
      <j1 rule="hyper" parents="5464 9119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9122">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,9120,a(flip),b,8919,a),flip(a)].">
      <j1 rule="hyper" parents="116 9120 8919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9123">
    <literal><![CDATA[
      a(x,y * K(x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9122(a,2),8932(a,1))].">
      <j1 rule="para" parents="9122 8932"/>
    </justification>
  </clause>

  <clause id="9124">
    <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(5594(a,1),7506(a,1,2,1))].">
      <j1 rule="para" parents="5594 7506"/>
    </justification>
  </clause>

  <clause id="9125">
    <literal><![CDATA[
      T((x \ 1) * y,K(x,z)) = (x \ 1) * T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(837,a,7614,a),flip(a)].">
      <j1 rule="hyper" parents="837 7614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9126">
    <literal><![CDATA[
      K(x,y) * T((x \ 1) * z,K(x,y)) = (x \ 1) * (z * K(x,y))
    ]]></literal>
    <justification jstring="[para(9125(a,2),5980(a,1,2))].">
      <j1 rule="para" parents="9125 5980"/>
    </justification>
  </clause>

  <clause id="9127">
    <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(320,a,7133,a(flip),b,7712,a),flip(a)].">
      <j1 rule="hyper" parents="320 7133 7712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9128">
    <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(5600(a,1),7879(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5600 7879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9129">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = (u * (K(x,y) * z)) / (u * z)
    ]]></literal>
    <justification jstring="[para(7152(a,1),7959(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7152 7959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9130">
    <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(8039,a,8282,a),flip(a)].">
      <j1 rule="hyper" parents="8039 8282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9131">
    <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(7728(a,1),8445(a,1,1))].">
      <j1 rule="para" parents="7728 8445"/>
    </justification>
  </clause>

  <clause id="9132">
    <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(7754(a,1),8445(a,1,1))].">
      <j1 rule="para" parents="7754 8445"/>
    </justification>
  </clause>

  <clause id="9133">
    <literal><![CDATA[
      x * K(y,(x \ 1) * (z * x)) = K(y,L(z,x,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(5284(a,1),8501(a,1,2))].">
      <j1 rule="para" parents="5284 8501"/>
    </justification>
  </clause>

  <clause id="9134">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(6875(a,1),8512(a,1))].">
      <j1 rule="para" parents="6875 8512"/>
    </justification>
  </clause>

  <clause id="9135">
    <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(630(a,1),8537(a,1,2))].">
      <j1 rule="para" parents="630 8537"/>
    </justification>
  </clause>

  <clause id="9136">
    <literal><![CDATA[
      K(x,a(K(x,y),z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,5476,a(flip),b,9135,a),flip(a)].">
      <j1 rule="hyper" parents="58 5476 9135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9137">
    <literal><![CDATA[
      a(K(x,y),z,u) * x = x * a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(5533,a,9136,a),flip(a)].">
      <j1 rule="hyper" parents="5533 9136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9138">
    <literal><![CDATA[
      T(a(K(x,y),z,u),x) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(4913,a,9136,a)].">
      <j1 rule="hyper" parents="4913 9136"/>
    </justification>
  </clause>

  <clause id="9140">
    <literal><![CDATA[
      T(x,a(K(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,9136,a)].">
      <j1 rule="hyper" parents="51 9136"/>
    </justification>
  </clause>

  <clause id="9141">
    <literal><![CDATA[
      T(T(x,y),a(K(x,z),u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(9140(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9140 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9142">
    <literal><![CDATA[
      K(x,y) * a(K(x,z),u,w) = a(K(x,z),u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[para(9140(a,1),7123(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9140 7123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9143">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) * x = x * K(a(K(x,y),z,u),w)
    ]]></literal>
    <justification jstring="[para(9138(a,1),7123(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9138 7123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9144">
    <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(8637(a,1),7730(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8637 7730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9145">
    <literal><![CDATA[
      K(x,L(x,y,y \ 1) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(164(a,1),8679(a,1,2)),flip(a)].">
      <j1 rule="para" parents="164 8679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9147">
    <literal><![CDATA[
      K((x \ 1) \ y,((x \ 1) \ y) \ z) = K((x \ 1) \ y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(2795(a,1),9145(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2795 9145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9148">
    <literal><![CDATA[
      x * K(L(K(y,z),T(z,u),w),x) != v5 * (z \ x)
    ]]></literal>
    <literal><![CDATA[
      T(z,K(y,x)) = v5
    ]]></literal>
    <justification jstring="[para(8714(a,2),39(a,1))].">
      <j1 rule="para" parents="8714 39"/>
    </justification>
  </clause>

  <clause id="9149">
    <literal><![CDATA[
      K(x,y) * (y \ R(y,x,L(y,z,u))) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(5109,a,8717,a)].">
      <j1 rule="hyper" parents="5109 8717"/>
    </justification>
  </clause>

  <clause id="9150">
    <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,8904,a,b,8717,a)].">
      <j1 rule="hyper" parents="58 8904 8717"/>
    </justification>
  </clause>

  <clause id="9151">
    <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(8717(a,1),1993(a,1))].">
      <j1 rule="para" parents="8717 1993"/>
    </justification>
  </clause>

  <clause id="9152">
    <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,8904,a,b,8720,a)].">
      <j1 rule="hyper" parents="58 8904 8720"/>
    </justification>
  </clause>

  <clause id="9153">
    <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(8720(a,1),1993(a,1))].">
      <j1 rule="para" parents="8720 1993"/>
    </justification>
  </clause>

  <clause id="9154">
    <literal><![CDATA[
      K(R(x,y / x,z),u) = K((y * z) / ((y / x) * z),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(7981,a,8873,a)].">
      <j1 rule="hyper" parents="7981 8873"/>
    </justification>
  </clause>

  <clause id="9155">
    <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(477(a,1),8881(a,2,2))].">
      <j1 rule="para" parents="477 8881"/>
    </justification>
  </clause>

  <clause id="9156">
    <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(825,a,8892,a)].">
      <j1 rule="hyper" parents="825 8892"/>
    </justification>
  </clause>

  <clause id="9157">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(y,z,x)) = x * (y * (z * K(u,y)))
    ]]></literal>
    <justification jstring="[para(7028(a,1),8995(a,2,2))].">
      <j1 rule="para" parents="7028 8995"/>
    </justification>
  </clause>

  <clause id="9159">
    <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(320,a,4894,a,b,9083,a)].">
      <j1 rule="hyper" parents="320 4894 9083"/>
    </justification>
  </clause>

  <clause id="9160">
    <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,9083,a(flip),b,155,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 9083 155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9161">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,u)) = K(x,T(z \ (y * x),u))
    ]]></literal>
    <justification jstring="[hyper(6088,a,9116,a)].">
      <j1 rule="hyper" parents="6088 9116"/>
    </justification>
  </clause>

  <clause id="9162">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,y)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,8465,a(flip),b,9161,a),flip(a)].">
      <j1 rule="hyper" parents="320 8465 9161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9163">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(9161(a,2),8485(a,1))].">
      <j1 rule="para" parents="9161 8485"/>
    </justification>
  </clause>

  <clause id="9164">
    <literal><![CDATA[
      K(x,((y * z) / y) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(4(a,1),9162(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4 9162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9165">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,(z / (z / y)) \ x)
    ]]></literal>
    <justification jstring="[para(4302(a,1),9164(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4302 9164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9166">
    <literal><![CDATA[
      K(x,T((y / (z * y)) \ x,z)) = K(x,R(1 / (1 / (1 / z)),z,y) \ x)
    ]]></literal>
    <justification jstring="[para(4367(a,2),9164(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4367 9164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9167">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,u)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(7364,a,9117,a),flip(a)].">
      <j1 rule="hyper" parents="7364 9117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9168">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ y,u)) = w
    ]]></literal>
    <justification jstring="[para(9117(a,1),3637(a,1))].">
      <j1 rule="para" parents="9117 3637"/>
    </justification>
  </clause>

  <clause id="9169">
    <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,7586,a,b,9167,a)].">
      <j1 rule="hyper" parents="58 7586 9167"/>
    </justification>
  </clause>

  <clause id="9170">
    <literal><![CDATA[
      K(x,T(y,z * R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8774,a(flip),b,9127,a)].">
      <j1 rule="hyper" parents="58 8774 9127"/>
    </justification>
  </clause>

  <clause id="9172">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),9170(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 9170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9173">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,7698,a(flip),b,9172,a)].">
      <j1 rule="hyper" parents="58 7698 9172"/>
    </justification>
  </clause>

  <clause id="9175">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(4(a,1),9173(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 9173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9176">
    <literal><![CDATA[
      K(x,T(y,(x * z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(184(a,1),9173(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="184 9173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9177">
    <literal><![CDATA[
      K(x,T(y \ (R(x,z,u) * w),w)) = K(x,(R(x,z,u) * w) / y)
    ]]></literal>
    <justification jstring="[hyper(8262,a,9175,a),flip(a)].">
      <j1 rule="hyper" parents="8262 9175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9178">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,y) * K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,7741,a,b,9175,a),flip(a)].">
      <j1 rule="hyper" parents="320 7741 9175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9179">
    <literal><![CDATA[
      K(x,T(y,(z * x) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8567,a,b,9176,a)].">
      <j1 rule="hyper" parents="58 8567 9176"/>
    </justification>
  </clause>

  <clause id="9180">
    <literal><![CDATA[
      K(x,T(y / ((z * x) * u),z * u)) = K(x,((z * x) * u) \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),9179(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 9179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9181">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(8049,a,9178,a)].">
      <j1 rule="hyper" parents="8049 9178"/>
    </justification>
  </clause>

  <clause id="9182">
    <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(9178(a,2),8044(a,1))].">
      <j1 rule="para" parents="9178 8044"/>
    </justification>
  </clause>

  <clause id="9183">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),9181(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 9181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9184">
    <literal><![CDATA[
      K(x,K(y,(x * z) * u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(101(a,1),9181(a,1,2,2))].">
      <j1 rule="para" parents="101 9181"/>
    </justification>
  </clause>

  <clause id="9185">
    <literal><![CDATA[
      K(x,K(y,z \ R(x,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8189,a,9183,a)].">
      <j1 rule="hyper" parents="8189 9183"/>
    </justification>
  </clause>

  <clause id="9186">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) / w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(75(a,1),9185(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 9185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9187">
    <literal><![CDATA[
      K(x,K(y,z * R(x,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8187,a,9186,a),flip(a)].">
      <j1 rule="hyper" parents="8187 9186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9188">
    <literal><![CDATA[
      K(x,K(y,(y * z) * u)) = K(y,K(x,z * u))
    ]]></literal>
    <justification jstring="[hyper(7756,a,9184,a)].">
      <j1 rule="hyper" parents="7756 9184"/>
    </justification>
  </clause>

  <clause id="9189">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,8732,a(flip),b,9130,a)].">
      <j1 rule="hyper" parents="58 8732 9130"/>
    </justification>
  </clause>

  <clause id="9191">
    <literal><![CDATA[
      K(x,T(y,z * (u * x))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8710,a(flip),b,9189,a)].">
      <j1 rule="hyper" parents="58 8710 9189"/>
    </justification>
  </clause>

  <clause id="9193">
    <literal><![CDATA[
      K(x,T(y,z * (x * u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,7659,a(flip),b,9191,a)].">
      <j1 rule="hyper" parents="58 7659 9191"/>
    </justification>
  </clause>

  <clause id="9194">
    <literal><![CDATA[
      K(x,T(y,z * (u / x))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(7(a,1),9191(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7 9191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9195">
    <literal><![CDATA[
      K(x,T(y,z * u)) * (z * (u * x)) = (z * (u * x)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(9191(a,1),7872(a,1,1))].">
      <j1 rule="para" parents="9191 7872"/>
    </justification>
  </clause>

  <clause id="9196">
    <literal><![CDATA[
      K(x,T(x * y,z * y)) = K(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7130,a(flip),b,9193,a),flip(a)].">
      <j1 rule="hyper" parents="58 7130 9193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9197">
    <literal><![CDATA[
      K(x,T(y,z * (x \ u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(5(a,1),9193(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 9193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9198">
    <literal><![CDATA[
      K(x,T(x * y,z * y)) = K(x,T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,5349,a,b,9196,a),flip(a)].">
      <j1 rule="hyper" parents="320 5349 9196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9199">
    <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(9197(a,1),8033(a,1))].">
      <j1 rule="para" parents="9197 8033"/>
    </justification>
  </clause>

  <clause id="9200">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(7876,a,9133,a)].">
      <j1 rule="hyper" parents="7876 9133"/>
    </justification>
  </clause>

  <clause id="9201">
    <literal><![CDATA[
      R(K(x,T(T(y,z),z)),z,u) = K(R(x,z / x,u),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7987,a(flip),b,9154,a)].">
      <j1 rule="hyper" parents="320 7987 9154"/>
    </justification>
  </clause>

  <clause id="9202">
    <literal><![CDATA[
      K(R(x,y / x,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(7858(a,1),9201(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7858 9201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9204">
    <literal><![CDATA[
      R(K(x,y),z * x,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(6(a,1),9202(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6 9202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9205">
    <literal><![CDATA[
      K(x,R(y,z / y,u)) = w / (R(K(y,x),z,u) * w)
    ]]></literal>
    <justification jstring="[para(9202(a,1),5104(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9202 5104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9206">
    <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(7318(a,1),9204(a,1,1))].">
      <j1 rule="para" parents="7318 9204"/>
    </justification>
  </clause>

  <clause id="9207">
    <literal><![CDATA[
      K(x,R(y,z / y,u)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,6905,a(flip),b,9205,a),flip(a)].">
      <j1 rule="hyper" parents="320 6905 9205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9208">
    <literal><![CDATA[
      K(x,R(y,z / y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(9205(a,2),6909(a,1))].">
      <j1 rule="para" parents="9205 6909"/>
    </justification>
  </clause>

  <clause id="9209">
    <literal><![CDATA[
      K(x,R(y,z / y,u)) = K(x,R(y,y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,6922,a,b,9207,a),flip(a)].">
      <j1 rule="hyper" parents="320 6922 9207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9210">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(6(a,1),9207(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 9207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9211">
    <literal><![CDATA[
      R(K(x,y \ z),z,u) = K(x,R(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),9207(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 9207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9212">
    <literal><![CDATA[
      R(K(x,y),z * T(y,u),w) = K(x,R(y,z * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(6164(a,1),9207(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6164 9207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9213">
    <literal><![CDATA[
      R(K(x,y),z * K(u,y),w) = K(x,R(y,z / T(y,u),w))
    ]]></literal>
    <justification jstring="[para(6313(a,1),9207(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6313 9207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9214">
    <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(7216(a,1),9210(a,1,1))].">
      <j1 rule="para" parents="7216 9210"/>
    </justification>
  </clause>

  <clause id="9215">
    <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(5892(a,1),9211(a,2,2))].">
      <j1 rule="para" parents="5892 9211"/>
    </justification>
  </clause>

  <clause id="9216">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(9209(a,1),9208(a,1))].">
      <j1 rule="para" parents="9209 9208"/>
    </justification>
  </clause>

  <clause id="9217">
    <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(184(a,1),9216(a,1,2,2))].">
      <j1 rule="para" parents="184 9216"/>
    </justification>
  </clause>

  <clause id="9218">
    <literal><![CDATA[
      K(x,R(y,z / T(y,u),w)) = R(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,8820,a(flip),b,9213,a),flip(a)].">
      <j1 rule="hyper" parents="58 8820 9213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9220">
    <literal><![CDATA[
      R(K(x,y),z * T(y,u),w) = K(x,R(y,z,w))
    ]]></literal>
    <justification jstring="[para(6(a,1),9218(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 9218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9221">
    <literal><![CDATA[
      K(x,R(y,z * K(y,u),w)) = K(x,R(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9212,a(flip),b,9220,a)].">
      <j1 rule="hyper" parents="58 9212 9220"/>
    </justification>
  </clause>

  <clause id="9223">
    <literal><![CDATA[
      K(x,R(y,K(y,z) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(7152(a,1),9221(a,1,2,2))].">
      <j1 rule="para" parents="7152 9221"/>
    </justification>
  </clause>

  <clause id="9224">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = (v5 * K(w,R(x,z,u))) \ v5
    ]]></literal>
    <justification jstring="[para(9223(a,1),6309(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9223 6309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9225">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(320,a,6309,a(flip),b,9224,a),flip(a)].">
      <j1 rule="hyper" parents="320 6309 9224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9226">
    <literal><![CDATA[
      R(K(x,y),K(x,z) * u,w) = K(R(x,x \ u,w),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6720,a(flip),b,9225,a)].">
      <j1 rule="hyper" parents="58 6720 9225"/>
    </justification>
  </clause>

  <clause id="9227">
    <literal><![CDATA[
      K(R(x,K(y,x) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(5095(a,1),9225(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5095 9225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9229">
    <literal><![CDATA[
      R(K(x,y),K(x,z) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,6718,a(flip),b,9226,a),flip(a)].">
      <j1 rule="hyper" parents="320 6718 9226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9230">
    <literal><![CDATA[
      R(K(x,y),z / x,u) = R(K(x,y),x \ z,u)
    ]]></literal>
    <justification jstring="[para(4818(a,1),9229(a,1,2))].">
      <j1 rule="para" parents="4818 9229"/>
    </justification>
  </clause>

  <clause id="9231">
    <literal><![CDATA[
      R(K(x,y),z * (K(u,x) * w),v5) = R(K(x,y),z * w,v5)
    ]]></literal>
    <justification jstring="[para(6008(a,1),9229(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6008 9229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9232">
    <literal><![CDATA[
      R(K(x,y),x \ y,z) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(9230(a,1),6907(a,1,1))].">
      <j1 rule="para" parents="9230 6907"/>
    </justification>
  </clause>

  <clause id="9233">
    <literal><![CDATA[
      R(K(x,y),z * (u * K(w,x)),v5) = R(K(x,y),z * u,v5)
    ]]></literal>
    <justification jstring="[para(7261(a,1),9231(a,1,2,2))].">
      <j1 rule="para" parents="7261 9231"/>
    </justification>
  </clause>

  <clause id="9234">
    <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(4587(a,2),9157(a,2,2))].">
      <j1 rule="para" parents="4587 9157"/>
    </justification>
  </clause>

  <clause id="9235">
    <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(9232(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="9232 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9236">
    <literal><![CDATA[
      K(L(x,y,z),R(z,u,w)) = K(x,R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,5485,a(flip),b,7047,a),flip(a)].">
      <j1 rule="hyper" parents="320 5485 7047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9237">
    <literal><![CDATA[
      K((x \ 1) \ y,R(x,z,u)) = K(x * y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(489(a,1),9236(a,1,1)),flip(a)].">
      <j1 rule="para" parents="489 9236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9238">
    <literal><![CDATA[
      K((x \ 1) * y,R(x \ 1,z,u)) = K(x \ y,R(x \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(5936,a,9237,a),flip(a)].">
      <j1 rule="hyper" parents="5936 9237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9239">
    <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(7166(a,2),8408(a,1))].">
      <j1 rule="para" parents="7166 8408"/>
    </justification>
  </clause>

  <clause id="9240">
    <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(7177(a,2),7679(a,1))].">
      <j1 rule="para" parents="7177 7679"/>
    </justification>
  </clause>

  <clause id="9241">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * K(z,w) = (x * K(z,w)) * K(y,T(z,u))
    ]]></literal>
    <justification jstring="[para(7133(a,1),7206(a,1,1,2))].">
      <j1 rule="para" parents="7133 7206"/>
    </justification>
  </clause>

  <clause id="9242">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z * (1 / ((x * y) \ x)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3939,a(flip),b,7346,a)].">
      <j1 rule="hyper" parents="58 3939 7346"/>
    </justification>
  </clause>

  <clause id="9243">
    <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(7349(a,1),7517(a,1,1,1,1,2))].">
      <j1 rule="para" parents="7349 7517"/>
    </justification>
  </clause>

  <clause id="9244">
    <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(7571(a,1),8365(a,1))].">
      <j1 rule="para" parents="7571 8365"/>
    </justification>
  </clause>

  <clause id="9245">
    <literal><![CDATA[
      K(x,(y \ K(x,z)) \ u) = (y \ T(y * u,x)) \ u
    ]]></literal>
    <justification jstring="[para(7622(a,1),6358(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7622 6358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9246">
    <literal><![CDATA[
      K(x,(y \ K(x,z)) \ u) = K(x,(y \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(320,a,6435,a(flip),b,9245,a),flip(a)].">
      <j1 rule="hyper" parents="320 6435 9245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9247">
    <literal><![CDATA[
      K(x,((y \ 1) \ K(x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(320,a,5283,a(flip),b,9246,a),flip(a)].">
      <j1 rule="hyper" parents="320 5283 9246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9248">
    <literal><![CDATA[
      K(x,y) * (z * T(z \ (K(x,y) \ u),x)) = z * T(z \ u,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,453,a(flip),b,7623,a),flip(a)].">
      <j1 rule="hyper" parents="320 453 7623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9249">
    <literal><![CDATA[
      (1 / (x \ y)) * K(y / x,z) = K(y / x,z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(7882(a,1),7977(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7882 7977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9250">
    <literal><![CDATA[
      K(1 / x,y) / (x \ 1) = x * K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(348,a,9249,a),flip(a)].">
      <j1 rule="hyper" parents="348 9249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9251">
    <literal><![CDATA[
      1 / (x \ K(y,1 / x)) = x * K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5849,a(flip),b,9250,a)].">
      <j1 rule="hyper" parents="58 5849 9250"/>
    </justification>
  </clause>

  <clause id="9252">
    <literal><![CDATA[
      1 / ((x * (y \ 1)) / x) = y * K(1 / y,x)
    ]]></literal>
    <justification jstring="[para(4854(a,1),9251(a,1,2))].">
      <j1 rule="para" parents="4854 9251"/>
    </justification>
  </clause>

  <clause id="9253">
    <literal><![CDATA[
      1 / ((x * ((y / z) \ 1)) / x) = (y / z) * K(z / y,x)
    ]]></literal>
    <justification jstring="[para(5391(a,1),9252(a,2,2))].">
      <j1 rule="para" parents="5391 9252"/>
    </justification>
  </clause>

  <clause id="9254">
    <literal><![CDATA[
      x / (K(T(y,z),x) * K(x,z)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(4930(a,1),7996(a,1,2,2))].">
      <j1 rule="para" parents="4930 7996"/>
    </justification>
  </clause>

  <clause id="9255">
    <literal><![CDATA[
      T(x * K(y,x),z) \ x = K(T(z,y),x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(188,a,9254,a)].">
      <j1 rule="hyper" parents="188 9254"/>
    </justification>
  </clause>

  <clause id="9257">
    <literal><![CDATA[
      T((x * y) / x,z) \ y = K(T(z,x),y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(4711(a,2),9255(a,1,1,1))].">
      <j1 rule="para" parents="4711 9255"/>
    </justification>
  </clause>

  <clause id="9258">
    <literal><![CDATA[
      T((x * y) / x,z) \ y = K(y,x) * K(T(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,1991,a,b,9257,a),flip(a)].">
      <j1 rule="hyper" parents="320 1991 9257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9259">
    <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(1617(a,1),9258(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1617 9258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9260">
    <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(8065(a,1),7653(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8065 7653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9261">
    <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(7771(a,1),8067(a,1,1))].">
      <j1 rule="para" parents="7771 8067"/>
    </justification>
  </clause>

  <clause id="9262">
    <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(443(a,1),8255(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="443 8255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9263">
    <literal><![CDATA[
      K(x,(y * z) \ (x \ y)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(8649,a,8257,a)].">
      <j1 rule="hyper" parents="8649 8257"/>
    </justification>
  </clause>

  <clause id="9264">
    <literal><![CDATA[
      K((x * y) \ (z \ x),z) = (u * K(z,y \ (z \ 1))) \ u
    ]]></literal>
    <justification jstring="[para(9263(a,1),6309(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9263 6309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9265">
    <literal><![CDATA[
      K((x * y) \ (z \ x),z) = K(y \ (z \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,6309,a(flip),b,9264,a),flip(a)].">
      <j1 rule="hyper" parents="320 6309 9264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9266">
    <literal><![CDATA[
      K((x \ y) \ (z \ 1),z) = K(y \ (z \ x),z)
    ]]></literal>
    <justification jstring="[para(5(a,1),9265(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 9265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9267">
    <literal><![CDATA[
      (x * (y * K(z,y))) / (x * K(z,y)) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(4828(a,1),8261(a,1,2,2))].">
      <j1 rule="para" parents="4828 8261"/>
    </justification>
  </clause>

  <clause id="9269">
    <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(8275(a,2),4945(a,1))].">
      <j1 rule="para" parents="8275 4945"/>
    </justification>
  </clause>

  <clause id="9270">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = (y / z) \ (x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,5556,a(flip),b,8299,a),flip(a)].">
      <j1 rule="hyper" parents="320 5556 8299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9271">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = K(x,y / z) * K(z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,9270,a(flip),b,4737,a)].">
      <j1 rule="hyper" parents="116 9270 4737"/>
    </justification>
  </clause>

  <clause id="9272">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(29,a,8435,a,b,8426,a),flip(a)].">
      <j1 rule="hyper" parents="29 8435 8426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9273">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7754,a,b,9272,a),flip(a)].">
      <j1 rule="hyper" parents="320 7754 9272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9274">
    <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(1303(a,1),9272(a,1,2,2))].">
      <j1 rule="para" parents="1303 9272"/>
    </justification>
  </clause>

  <clause id="9275">
    <literal><![CDATA[
      K(x,K(y,z \ (y \ u))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(8422(a,1),9272(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8422 9272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9276">
    <literal><![CDATA[
      K(x,K(y,z \ (y * u))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(8423(a,1),9272(a,1,2))].">
      <j1 rule="para" parents="8423 9272"/>
    </justification>
  </clause>

  <clause id="9277">
    <literal><![CDATA[
      K(x,K(y,z \ (u * x))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(7756,a,9273,a)].">
      <j1 rule="hyper" parents="7756 9273"/>
    </justification>
  </clause>

  <clause id="9278">
    <literal><![CDATA[
      K(x,K(y,z \ (u * x))) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8163,a,b,9277,a),flip(a)].">
      <j1 rule="hyper" parents="320 8163 9277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9279">
    <literal><![CDATA[
      T(K(x,y),(z \ (u * x)) \ 1) = K(x,y) * K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(9277(a,1),8164(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9277 8164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9280">
    <literal><![CDATA[
      K(x,K(y,(z * x) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(8189,a,9278,a)].">
      <j1 rule="hyper" parents="8189 9278"/>
    </justification>
  </clause>

  <clause id="9281">
    <literal><![CDATA[
      K(x,K(y,(z / x) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(7(a,1),9280(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 9280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9282">
    <literal><![CDATA[
      K(x,K(y,(x \ z) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8104,a(flip),b,9281,a)].">
      <j1 rule="hyper" parents="58 8104 9281"/>
    </justification>
  </clause>

  <clause id="9283">
    <literal><![CDATA[
      K(x,K(y,z \ (x \ u))) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(8189,a,9282,a)].">
      <j1 rule="hyper" parents="8189 9282"/>
    </justification>
  </clause>

  <clause id="9284">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z \ u)) = K(x,T(y,(x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(9282(a,1),7741(a,1,2))].">
      <j1 rule="para" parents="9282 7741"/>
    </justification>
  </clause>

  <clause id="9285">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(x,K(w,u \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9024,a,b,9283,a)].">
      <j1 rule="hyper" parents="58 9024 9283"/>
    </justification>
  </clause>

  <clause id="9286">
    <literal><![CDATA[
      K(x,K(y,(T(x,z) * u) \ w)) = K(x,K(y,w \ u))
    ]]></literal>
    <justification jstring="[hyper(7796,a,9285,a)].">
      <j1 rule="hyper" parents="7796 9285"/>
    </justification>
  </clause>

  <clause id="9287">
    <literal><![CDATA[
      K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(8044,a,9284,a),flip(a)].">
      <j1 rule="hyper" parents="8044 9284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9288">
    <literal><![CDATA[
      K(x,T(y,z \ (x * u))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8232,a(flip),b,9287,a)].">
      <j1 rule="hyper" parents="58 8232 9287"/>
    </justification>
  </clause>

  <clause id="9289">
    <literal><![CDATA[
      K(x,T(y,(x * z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(4(a,1),9287(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 9287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9290">
    <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),9289(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 9289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9291">
    <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(630(a,1),9290(a,1,2,2))].">
      <j1 rule="para" parents="630 9290"/>
    </justification>
  </clause>

  <clause id="9292">
    <literal><![CDATA[
      K(x,T(y,a(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8036,a,9291,a),flip(a)].">
      <j1 rule="hyper" parents="8036 9291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9293">
    <literal><![CDATA[
      K(x,y / a(x,z,u)) = K(x,a(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(8033,a,9292,a)].">
      <j1 rule="hyper" parents="8033 9292"/>
    </justification>
  </clause>

  <clause id="9295">
    <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,9293,a(flip),b,8471,a)].">
      <j1 rule="hyper" parents="58 9293 8471"/>
    </justification>
  </clause>

  <clause id="9296">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (u * K(y,x))) = T(K(z,x) * u,K(x,y))
    ]]></literal>
    <justification jstring="[para(6300(a,1),8488(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6300 8488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9297">
    <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(6425(a,1),8488(a,1,1,2))].">
      <j1 rule="para" parents="6425 8488"/>
    </justification>
  </clause>

  <clause id="9298">
    <literal><![CDATA[
      K(x,y / z) * K(z \ y,z) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6343,a(flip),b,8490,a),flip(a)].">
      <j1 rule="hyper" parents="58 6343 8490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9299">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * u = (z * K((x \ 1) \ (y \ z),y)) * u
    ]]></literal>
    <justification jstring="[para(3517(a,1),8511(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3517 8511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9300">
    <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(8544(a,1),5329(a,1,2,1))].">
      <j1 rule="para" parents="8544 5329"/>
    </justification>
  </clause>

  <clause id="9301">
    <literal><![CDATA[
      K(x,(K(y \ x,y) * z) \ x) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,6814,a(flip),b,8558,a),flip(a)].">
      <j1 rule="hyper" parents="320 6814 8558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9303">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ x) * x)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6563,a(flip),b,9301,a)].">
      <j1 rule="hyper" parents="58 6563 9301"/>
    </justification>
  </clause>

  <clause id="9304">
    <literal><![CDATA[
      K(x,y \ (z * (x / z))) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(4742(a,1),9303(a,1,2,2))].">
      <j1 rule="para" parents="4742 9303"/>
    </justification>
  </clause>

  <clause id="9305">
    <literal><![CDATA[
      K(x,y \ ((z \ x) * z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(72(a,1),9304(a,1,2,2,2))].">
      <j1 rule="para" parents="72 9304"/>
    </justification>
  </clause>

  <clause id="9306">
    <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(9305(a,1),6603(a,1))].">
      <j1 rule="para" parents="9305 6603"/>
    </justification>
  </clause>

  <clause id="9307">
    <literal><![CDATA[
      T(K(x,y),T(z,u * x)) = T(K(x,y),T(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(8405,a,8593,a),flip(a)].">
      <j1 rule="hyper" parents="8405 8593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9308">
    <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,7425,a(flip),b,9307,a),flip(a)].">
      <j1 rule="hyper" parents="58 7425 9307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9309">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8127,a(flip),b,8601,a),flip(a)].">
      <j1 rule="hyper" parents="320 8127 8601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9310">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(75(a,1),9309(a,1,2,2,1,2))].">
      <j1 rule="para" parents="75 9309"/>
    </justification>
  </clause>

  <clause id="9311">
    <literal><![CDATA[
      K(x,(y \ 1) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5284,a(flip),b,9310,a)].">
      <j1 rule="hyper" parents="58 5284 9310"/>
    </justification>
  </clause>

  <clause id="9312">
    <literal><![CDATA[
      K(T(x,y * (z * K(u,w))),w) = K(x,T(w,y * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7176,a(flip),b,8640,a),flip(a)].">
      <j1 rule="hyper" parents="320 7176 8640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9313">
    <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(8645(a,1),5619(a,1))].">
      <j1 rule="para" parents="8645 5619"/>
    </justification>
  </clause>

  <clause id="9314">
    <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(7131(a,2),8668(a,1,2))].">
      <j1 rule="para" parents="7131 8668"/>
    </justification>
  </clause>

  <clause id="9315">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * y) \ (z \ u),z) = w
    ]]></literal>
    <justification jstring="[para(8680(a,1),6316(a,1))].">
      <j1 rule="para" parents="8680 6316"/>
    </justification>
  </clause>

  <clause id="9316">
    <literal><![CDATA[
      K((x * (y * z)) \ u,y) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * z) \ (y \ u),y) = w
    ]]></literal>
    <justification jstring="[para(8621(a,1),9315(a,1))].">
      <j1 rule="para" parents="8621 9315"/>
    </justification>
  </clause>

  <clause id="9317">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(y,z)) = T(x,1 / T(y / z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7932,a(flip),b,8790,a)].">
      <j1 rule="hyper" parents="58 7932 8790"/>
    </justification>
  </clause>

  <clause id="9318">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(z,z / y)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[para(107(a,1),8790(a,2,2,2))].">
      <j1 rule="para" parents="107 8790"/>
    </justification>
  </clause>

  <clause id="9319">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(y,z)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8177,a(flip),b,9318,a)].">
      <j1 rule="hyper" parents="58 8177 9318"/>
    </justification>
  </clause>

  <clause id="9320">
    <literal><![CDATA[
      T(x,1 / T(y / z,y)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9317,a(flip),b,9319,a)].">
      <j1 rule="hyper" parents="58 9317 9319"/>
    </justification>
  </clause>

  <clause id="9321">
    <literal><![CDATA[
      T(x,T(1 / (y / z),y)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(8789,a,9320,a)].">
      <j1 rule="hyper" parents="8789 9320"/>
    </justification>
  </clause>

  <clause id="9322">
    <literal><![CDATA[
      T(x,1 / ((y \ z) \ z)) = T(x,T(1 / y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),9321(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 9321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9323">
    <literal><![CDATA[
      T(x,T(1 / (y \ z),z)) = T(x,1 / (z / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8344,a(flip),b,9322,a),flip(a)].">
      <j1 rule="hyper" parents="58 8344 9322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9324">
    <literal><![CDATA[
      T(x,K(y,z / y) / (z \ y)) = T(x,1 / (y / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8312,a,b,9323,a)].">
      <j1 rule="hyper" parents="58 8312 9323"/>
    </justification>
  </clause>

  <clause id="9325">
    <literal><![CDATA[
      K(x,y / (z * (K(u,x) / z))) = K(x,y * K(z \ K(u,x),z))
    ]]></literal>
    <justification jstring="[para(6306(a,1),8842(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6306 8842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9326">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = x * K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(9029(a,1),8869(a,2,2))].">
      <j1 rule="para" parents="9029 8869"/>
    </justification>
  </clause>

  <clause id="9327">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = T(x,R(y / (y / z),u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,8099,a,b,9326,a)].">
      <j1 rule="hyper" parents="320 8099 9326"/>
    </justification>
  </clause>

  <clause id="9328">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = T(x,R(T(z,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,8588,a(flip),b,9327,a),flip(a)].">
      <j1 rule="hyper" parents="58 8588 9327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9329">
    <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,8664,a,b,9328,a)].">
      <j1 rule="hyper" parents="58 8664 9328"/>
    </justification>
  </clause>

  <clause id="9330">
    <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),9329(a,1,2,1))].">
      <j1 rule="para" parents="106 9329"/>
    </justification>
  </clause>

  <clause id="9331">
    <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(6658(a,1),9330(a,1,2,1,1))].">
      <j1 rule="para" parents="6658 9330"/>
    </justification>
  </clause>

  <clause id="9332">
    <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(8929(a,1),8942(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8929 8942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9333">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * x) * z) = K(y,R(T(x,z),y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8723,a(flip),b,9015,a),flip(a)].">
      <j1 rule="hyper" parents="58 8723 9015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9334">
    <literal><![CDATA[
      T(K(x,y) * z,x * y) = K(x,y) * T(z,x * y)
    ]]></literal>
    <justification jstring="[para(4923(a,1),9028(a,1,1,1))].">
      <j1 rule="para" parents="4923 9028"/>
    </justification>
  </clause>

  <clause id="9335">
    <literal><![CDATA[
      T(x * K(y,z),z * y) = T(x,z * y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6011,a,9334,a),flip(a)].">
      <j1 rule="hyper" parents="6011 9334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9336">
    <literal><![CDATA[
      (x * (y * z)) * L(K(z,y),T(x,y * z),y * z) = (y * z) * T(x * K(z,y),y * z)
    ]]></literal>
    <justification jstring="[para(9335(a,2),481(a,2,2))].">
      <j1 rule="para" parents="9335 481"/>
    </justification>
  </clause>

  <clause id="9337">
    <literal><![CDATA[
      a(T(x,y),z,T(x,y)) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(9079,a,9073,a),flip(a)].">
      <j1 rule="hyper" parents="9079 9073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9339">
    <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(5652(a,1),9084(a,2,1,1))].">
      <j1 rule="para" parents="5652 9084"/>
    </justification>
  </clause>

  <clause id="9340">
    <literal><![CDATA[
      R(x,y,x) * (T(x,z) \ u) = x * (L(T(x,z),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7709,a(flip),b,9100,a)].">
      <j1 rule="hyper" parents="58 7709 9100"/>
    </justification>
  </clause>

  <clause id="9341">
    <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(9340(a,1),7058(a,1,2))].">
      <j1 rule="para" parents="9340 7058"/>
    </justification>
  </clause>

  <clause id="9342">
    <literal><![CDATA[
      ((x \ 1) * y) * K(x,z) = (x \ 1) * (y * K(x,z))
    ]]></literal>
    <justification jstring="[hyper(284,a,9126,a)].">
      <j1 rule="hyper" parents="284 9126"/>
    </justification>
  </clause>

  <clause id="9344">
    <literal><![CDATA[
      a(x \ 1,y,K(x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,9342,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="115 9342 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9345">
    <literal><![CDATA[
      L(K(x,y),z,y \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5862,a,9344,a)].">
      <j1 rule="hyper" parents="5862 9344"/>
    </justification>
  </clause>

  <clause id="9346">
    <literal><![CDATA[
      a(x,y,K(x \ 1,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,4023,a(flip),b,9344,a)].">
      <j1 rule="hyper" parents="58 4023 9344"/>
    </justification>
  </clause>

  <clause id="9347">
    <literal><![CDATA[
      (x * y) * K(x \ 1,z) = x * (y * K(x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(969,a,9346,a)].">
      <j1 rule="hyper" parents="969 9346"/>
    </justification>
  </clause>

  <clause id="9348">
    <literal><![CDATA[
      L(K(x \ 1,y),z,x) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(47,a,9346,a)].">
      <j1 rule="hyper" parents="47 9346"/>
    </justification>
  </clause>

  <clause id="9349">
    <literal><![CDATA[
      K(L(x,y,z \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(9053,a,9345,a)].">
      <j1 rule="hyper" parents="9053 9345"/>
    </justification>
  </clause>

  <clause id="9352">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (z * (x \ 1)),x) = K(y \ T(z,x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6596,a(flip),b,9345,a)].">
      <j1 rule="hyper" parents="58 6596 9345"/>
    </justification>
  </clause>

  <clause id="9353">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,y)) = K(((x \ 1) \ z) / y,x)
    ]]></literal>
    <justification jstring="[hyper(8228,a,9349,a)].">
      <j1 rule="hyper" parents="8228 9349"/>
    </justification>
  </clause>

  <clause id="9355">
    <literal><![CDATA[
      K(L(x,y,x) \ 1,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(5685,a,9348,a)].">
      <j1 rule="hyper" parents="5685 9348"/>
    </justification>
  </clause>

  <clause id="9357">
    <literal><![CDATA[
      K(R(x,y,x) \ 1,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(4632(a,1),9355(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4632 9355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9358">
    <literal><![CDATA[
      R(K(x,y),z,x \ 1) = K((x \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5673,a(flip),b,9357,a)].">
      <j1 rule="hyper" parents="58 5673 9357"/>
    </justification>
  </clause>

  <clause id="9359">
    <literal><![CDATA[
      (K(x \ 1,y) * z) * x = K(x \ 1,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(9357(a,1),5671(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9357 5671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9360">
    <literal><![CDATA[
      R(K(x,y),z,x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3298,a(flip),b,9358,a),flip(a)].">
      <j1 rule="hyper" parents="320 3298 9358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9361">
    <literal><![CDATA[
      K(x,R(y,z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8823,a,9360,a)].">
      <j1 rule="hyper" parents="8823 9360"/>
    </justification>
  </clause>

  <clause id="9362">
    <literal><![CDATA[
      (K(x,y) * z) * (x \ 1) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[para(9360(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9360 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9363">
    <literal><![CDATA[
      R(x * K(y,x),z,y \ 1) = R(x,z,y \ 1) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,9361,a(flip),b,5485,a),flip(a)].">
      <j1 rule="hyper" parents="119 9361 5485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9364">
    <literal><![CDATA[
      R(x,y,K(x \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(3998,a,9347,a)].">
      <j1 rule="hyper" parents="3998 9347"/>
    </justification>
  </clause>

  <clause id="9365">
    <literal><![CDATA[
      x * (y * K(x \ 1,x * y)) = y / R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5906,a(flip),b,9347,a),flip(a)].">
      <j1 rule="hyper" parents="58 5906 9347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9367">
    <literal><![CDATA[
      R(T(x,y),z,K(x \ 1,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(9364(a,1),22(a,2,1))].">
      <j1 rule="para" parents="9364 22"/>
    </justification>
  </clause>

  <clause id="9369">
    <literal><![CDATA[
      T(x,y * K(x \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5800,a(flip),b,9367,a),flip(a)].">
      <j1 rule="hyper" parents="58 5800 9367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9371">
    <literal><![CDATA[
      K(x,y * K(x \ 1,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,9369,a(flip),b,4714,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 9369 4714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9373">
    <literal><![CDATA[
      T(x,K(y,x \ 1) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(7149(a,1),9369(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7149 9369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9374">
    <literal><![CDATA[
      T(x,K(x \ 1,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(7152(a,1),9369(a,1,2))].">
      <j1 rule="para" parents="7152 9369"/>
    </justification>
  </clause>

  <clause id="9375">
    <literal><![CDATA[
      T(x,K(y,1 / x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(3528(a,2),9373(a,1,2,1))].">
      <j1 rule="para" parents="3528 9373"/>
    </justification>
  </clause>

  <clause id="9376">
    <literal><![CDATA[
      T(x \ 1,K(x,y) * z) = T(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(3298(a,1),9374(a,1,2,1))].">
      <j1 rule="para" parents="3298 9374"/>
    </justification>
  </clause>

  <clause id="9377">
    <literal><![CDATA[
      K(K(x,1 / y) * z,y) = y / T(y,z)
    ]]></literal>
    <justification jstring="[para(9375(a,1),4753(a,2,2))].">
      <j1 rule="para" parents="9375 4753"/>
    </justification>
  </clause>

  <clause id="9378">
    <literal><![CDATA[
      K(x,y * K(x \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4688,a,b,9371,a),flip(a)].">
      <j1 rule="hyper" parents="320 4688 9371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9380">
    <literal><![CDATA[
      K(x,y * K(z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6300(a,1),9378(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6300 9378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9381">
    <literal><![CDATA[
      K(x \ y,z * K(u,y \ x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(6078(a,1),9380(a,1,2,2))].">
      <j1 rule="para" parents="6078 9380"/>
    </justification>
  </clause>

  <clause id="9382">
    <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(9376(a,1),920(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9376 920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9384">
    <literal><![CDATA[
      K(K(x,1 / y) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4753,a,b,9377,a),flip(a)].">
      <j1 rule="hyper" parents="320 4753 9377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9385">
    <literal><![CDATA[
      K(K(x,y) * z,y \ 1) = K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),9384(a,1,1,1,2))].">
      <j1 rule="para" parents="72 9384"/>
    </justification>
  </clause>

  <clause id="9386">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(3528(a,1),9384(a,1,1,1))].">
      <j1 rule="para" parents="3528 9384"/>
    </justification>
  </clause>

  <clause id="9387">
    <literal><![CDATA[
      K(T(x,1 / y) / z,y) = K(x / z,y)
    ]]></literal>
    <justification jstring="[para(5702(a,1),9384(a,1,1))].">
      <j1 rule="para" parents="5702 9384"/>
    </justification>
  </clause>

  <clause id="9389">
    <literal><![CDATA[
      (K(x,y \ 1) * z) * K(z,y) = T(K(x,y \ 1) * z,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,9386,a(flip),b,4688,a(flip))].">
      <j1 rule="hyper" parents="119 9386 4688"/>
    </justification>
  </clause>

  <clause id="9390">
    <literal><![CDATA[
      K(K(x,x \ y) * z,x / y) = K(z,x / y)
    ]]></literal>
    <justification jstring="[para(5176(a,1),9386(a,1,1,1))].">
      <j1 rule="para" parents="5176 9386"/>
    </justification>
  </clause>

  <clause id="9391">
    <literal><![CDATA[
      K(x \ T(y,z \ 1),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(5514(a,1),9386(a,1,1))].">
      <j1 rule="para" parents="5514 9386"/>
    </justification>
  </clause>

  <clause id="9392">
    <literal><![CDATA[
      K(x * K(y,z \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7261(a,1),9386(a,1,1))].">
      <j1 rule="para" parents="7261 9386"/>
    </justification>
  </clause>

  <clause id="9393">
    <literal><![CDATA[
      K(x * K(y,z \ u),u \ z) = K(x,u \ z)
    ]]></literal>
    <justification jstring="[para(6078(a,1),9392(a,1,1,2))].">
      <j1 rule="para" parents="6078 9392"/>
    </justification>
  </clause>

  <clause id="9394">
    <literal><![CDATA[
      K(((x * y) \ x) * z,y) = K(z * ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[para(6154(a,1),9392(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6154 9392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9395">
    <literal><![CDATA[
      K(T(x / (1 / (1 / y)),1 / z) / (1 / y),z) = K((x / y) / (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2714(a,1),9387(a,2,1))].">
      <j1 rule="para" parents="2714 9387"/>
    </justification>
  </clause>

  <clause id="9396">
    <literal><![CDATA[
      K(x \ y,(y \ x) * z) = K(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[para(84(a,1),9381(a,1,2)),flip(a)].">
      <j1 rule="para" parents="84 9381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9397">
    <literal><![CDATA[
      K(x \ y,z * (x / y)) = K(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[para(6071(a,1),9381(a,1,2))].">
      <j1 rule="para" parents="6071 9381"/>
    </justification>
  </clause>

  <clause id="9398">
    <literal><![CDATA[
      K((x / y) \ z,y / x) = K((y \ x) \ z,y / x)
    ]]></literal>
    <justification jstring="[para(5376(a,1),9390(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5376 9390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9399">
    <literal><![CDATA[
      K(x * (y / z),y \ z) = K(x * (z \ y),y \ z)
    ]]></literal>
    <justification jstring="[para(6071(a,1),9393(a,1,1))].">
      <j1 rule="para" parents="6071 9393"/>
    </justification>
  </clause>

  <clause id="9400">
    <literal><![CDATA[
      L(x,y,K(x \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(3988,a,9359,a)].">
      <j1 rule="hyper" parents="3988 9359"/>
    </justification>
  </clause>

  <clause id="9403">
    <literal><![CDATA[
      L(x \ 1,y,K(x,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(3298(a,1),9400(a,1,3))].">
      <j1 rule="para" parents="3298 9400"/>
    </justification>
  </clause>

  <clause id="9404">
    <literal><![CDATA[
      (K(x,y) * (z * x)) \ (K(x,y) * z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[para(9403(a,1),912(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9403 912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9408">
    <literal><![CDATA[
      (x \ 1) * T(K(x,y) * z,x \ 1) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(285,a,9362,a)].">
      <j1 rule="hyper" parents="285 9362"/>
    </justification>
  </clause>

  <clause id="9409">
    <literal><![CDATA[
      T(K(x,y) * z,x \ 1) = K(x,y) * T(z,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(239,a,9362,a,b,5976,a)].">
      <j1 rule="hyper" parents="239 9362 5976"/>
    </justification>
  </clause>

  <clause id="9410">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = z * K(y \ x,z * (y / x))
    ]]></literal>
    <justification jstring="[para(9397(a,2),6253(a,2,2))].">
      <j1 rule="para" parents="9397 6253"/>
    </justification>
  </clause>

  <clause id="9411">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = z * K(z * (y / x),y \ x)
    ]]></literal>
    <justification jstring="[para(9399(a,2),6139(a,2,2))].">
      <j1 rule="para" parents="9399 6139"/>
    </justification>
  </clause>

  <clause id="9412">
    <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),9409(a,2,2))].">
      <j1 rule="para" parents="20 9409"/>
    </justification>
  </clause>

  <clause id="9413">
    <literal><![CDATA[
      x * (((x * y) \ y) * (x * y)) = y / R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(5401(a,2),9365(a,1,2))].">
      <j1 rule="para" parents="5401 9365"/>
    </justification>
  </clause>

  <clause id="9414">
    <literal><![CDATA[
      x * (((x * y) \ y) * (x * y)) = y / (y / (x * y))
    ]]></literal>
    <justification jstring="[para(219(a,1),9413(a,2,2))].">
      <j1 rule="para" parents="219 9413"/>
    </justification>
  </clause>

  <clause id="9415">
    <literal><![CDATA[
      R(x * K(y,x),z,y \ 1) = K(y,x) * R(x,z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,2878,a(flip),b,9363,a),flip(a)].">
      <j1 rule="hyper" parents="320 2878 9363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9416">
    <literal><![CDATA[
      T(K(x,y \ 1) * z,y) = K(x,y \ 1) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6170,a,9389,a),flip(a)].">
      <j1 rule="hyper" parents="6170 9389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9418">
    <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,9415,a,b,5199,a)].">
      <j1 rule="hyper" parents="116 9415 5199"/>
    </justification>
  </clause>

  <clause id="9419">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y * K(w,x),z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9233,a(flip),b,9214,a)].">
      <j1 rule="hyper" parents="58 9233 9214"/>
    </justification>
  </clause>

  <clause id="9421">
    <literal><![CDATA[
      K(x,R(y * K(z,x),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9210,a(flip),b,9419,a),flip(a)].">
      <j1 rule="hyper" parents="58 9210 9419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9422">
    <literal><![CDATA[
      K(x,R(y * K(x,z),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(6300(a,1),9421(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6300 9421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9423">
    <literal><![CDATA[
      K(x,R(K(y,x) * z,u,w)) = K(x,R(z * K(y,x),u,w))
    ]]></literal>
    <justification jstring="[para(7733(a,1),9422(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7733 9422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9424">
    <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(649(a,1),9238(a,1,2)),flip(a)].">
      <j1 rule="para" parents="649 9238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9425">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * K(z,w) = x * (K(z,w) * K(y,T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,8976,a(flip),b,9241,a),flip(a)].">
      <j1 rule="hyper" parents="320 8976 9241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9426">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z * (((x * y) \ x) \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3933,a(flip),b,9242,a),flip(a)].">
      <j1 rule="hyper" parents="320 3933 9242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9427">
    <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),9248(a,1,2,2,1,2))].">
      <j1 rule="para" parents="4 9248"/>
    </justification>
  </clause>

  <clause id="9428">
    <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(58,a,7495,a,b,9261,a)].">
      <j1 rule="hyper" parents="58 7495 9261"/>
    </justification>
  </clause>

  <clause id="9429">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,9298,a(flip),b,9271,a),flip(a)].">
      <j1 rule="hyper" parents="320 9298 9271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9430">
    <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(9274(a,2),8189(a,1))].">
      <j1 rule="para" parents="9274 8189"/>
    </justification>
  </clause>

  <clause id="9431">
    <literal><![CDATA[
      T(K(x,y),(z \ (u * x)) \ 1) = T(K(x,y),z \ u)
    ]]></literal>
    <justification jstring="[hyper(320,a,7738,a(flip),b,9279,a),flip(a)].">
      <j1 rule="hyper" parents="320 7738 9279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9432">
    <literal><![CDATA[
      T(K(x,y),z \ (u * x)) = T(K(x,y),z \ u)
    ]]></literal>
    <justification jstring="[hyper(8332,a,9431,a)].">
      <j1 rule="hyper" parents="8332 9431"/>
    </justification>
  </clause>

  <clause id="9433">
    <literal><![CDATA[
      T(K(x,y),z \ (u / x)) = T(K(x,y),z \ u)
    ]]></literal>
    <justification jstring="[para(7(a,1),9432(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 9432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9434">
    <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(9433(a,1),4723(a,1,2,1))].">
      <j1 rule="para" parents="9433 4723"/>
    </justification>
  </clause>

  <clause id="9435">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),T(y,z)) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8862,a(flip),b,9308,a)].">
      <j1 rule="hyper" parents="58 8862 9308"/>
    </justification>
  </clause>

  <clause id="9436">
    <literal><![CDATA[
      K(x,T(y \ (z * x),T(y,z))) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(7683,a,9435,a)].">
      <j1 rule="hyper" parents="7683 9435"/>
    </justification>
  </clause>

  <clause id="9437">
    <literal><![CDATA[
      K(x,T(y \ (z * x),T(y,z))) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,8464,a(flip),b,9436,a),flip(a)].">
      <j1 rule="hyper" parents="320 8464 9436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9438">
    <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(320,a,6753,a(flip),b,9437,a),flip(a)].">
      <j1 rule="hyper" parents="320 6753 9437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9439">
    <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,5540,a(flip),b,9325,a),flip(a)].">
      <j1 rule="hyper" parents="58 5540 9325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9440">
    <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(5680(a,1),9427(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5680 9427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9441">
    <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(8415,a,9428,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8415 9428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9442">
    <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),7231(a,1,1))].">
      <j1 rule="para" parents="22 7231"/>
    </justification>
  </clause>

  <clause id="9443">
    <literal><![CDATA[
      K(R(x,y,z),u * K(x,w)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,5487,a(flip),b,7322,a),flip(a)].">
      <j1 rule="hyper" parents="320 5487 7322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9444">
    <literal><![CDATA[
      K(R(x,y,z),u * K(w,x)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(6300(a,1),9443(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6300 9443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9445">
    <literal><![CDATA[
      K(L(x,y,z),T(u,x \ w)) = K(L(x,y,z),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(4992,a,7355,a),flip(a)].">
      <j1 rule="hyper" parents="4992 7355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9446">
    <literal><![CDATA[
      K(T(x,y \ z),L(y,u,w)) = 1 / K(L(y,u,w),T(x,z))
    ]]></literal>
    <justification jstring="[para(9445(a,1),4931(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9445 4931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9447">
    <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,7203,a(flip),b,9446,a),flip(a)].">
      <j1 rule="hyper" parents="114 7203 9446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9448">
    <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),9447(a,2,2))].">
      <j1 rule="para" parents="20 9447"/>
    </justification>
  </clause>

  <clause id="9449">
    <literal><![CDATA[
      K(x,T(L(y,z,u),y \ w)) = K(x,L(T(y,w),z,u))
    ]]></literal>
    <justification jstring="[hyper(7679,a,9448,a)].">
      <j1 rule="hyper" parents="7679 9448"/>
    </justification>
  </clause>

  <clause id="9450">
    <literal><![CDATA[
      K(x,L((y \ z) \ z,u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(317(a,1),9449(a,1,2))].">
      <j1 rule="para" parents="317 9449"/>
    </justification>
  </clause>

  <clause id="9451">
    <literal><![CDATA[
      T(x,L((y \ z) \ z,u,w)) = T(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(118,a,9450,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 9450 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9452">
    <literal><![CDATA[
      K(x,L(T(y,z * y),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(4228(a,2),9450(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4228 9450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9453">
    <literal><![CDATA[
      T(x,L(T(y,z * y),u,w)) = T(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(4228(a,2),9451(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4228 9451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9454">
    <literal><![CDATA[
      L(x \ 1,x,K(x,y) * z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9404,a(flip),b,7459,a),flip(a)].">
      <j1 rule="hyper" parents="58 9404 7459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9456">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(7872(a,1),9454(a,1,3))].">
      <j1 rule="para" parents="7872 9454"/>
    </justification>
  </clause>

  <clause id="9457">
    <literal><![CDATA[
      L(x \ 1,T(x,y),z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(6661,a,9456,a)].">
      <j1 rule="hyper" parents="6661 9456"/>
    </justification>
  </clause>

  <clause id="9459">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),z) = T(x,z) * ((y * T(x,z)) \ y)
    ]]></literal>
    <justification jstring="[para(9457(a,1),2132(a,1,1,2))].">
      <j1 rule="para" parents="9457 2132"/>
    </justification>
  </clause>

  <clause id="9462">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = a(x,y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(691,a,7705,a),flip(a)].">
      <j1 rule="hyper" parents="691 7705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9463">
    <literal><![CDATA[
      a(x,y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9462(a,1),9123(a,1))].">
      <j1 rule="para" parents="9462 9123"/>
    </justification>
  </clause>

  <clause id="9464">
    <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),7711(a,2,1))].">
      <j1 rule="para" parents="24 7711"/>
    </justification>
  </clause>

  <clause id="9465">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ ((z * x) * u))) = 1
    ]]></literal>
    <justification jstring="[para(7902(a,1),8051(a,1,2))].">
      <j1 rule="para" parents="7902 8051"/>
    </justification>
  </clause>

  <clause id="9466">
    <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,7930,a(flip),b,6902,a(flip))].">
      <j1 rule="hyper" parents="116 7930 6902"/>
    </justification>
  </clause>

  <clause id="9467">
    <literal><![CDATA[
      R(K(x,T(T(y,z),z * u)),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(7131(a,2),7958(a,1,1))].">
      <j1 rule="para" parents="7131 7958"/>
    </justification>
  </clause>

  <clause id="9468">
    <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(7203(a,1),7964(a,1,1))].">
      <j1 rule="para" parents="7203 7964"/>
    </justification>
  </clause>

  <clause id="9469">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * y) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(320,a,8694,a(flip),b,8425,a),flip(a)].">
      <j1 rule="hyper" parents="320 8694 8425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9470">
    <literal><![CDATA[
      T(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) / z) = u
    ]]></literal>
    <justification jstring="[para(9004(a,1),8444(a,1))].">
      <j1 rule="para" parents="9004 8444"/>
    </justification>
  </clause>

  <clause id="9471">
    <literal><![CDATA[
      x / (x / R(K(y,z),u,w)) = (R(K(y,z),u,w) \ x) \ x
    ]]></literal>
    <justification jstring="[para(8661(a,1),4264(a,1,2))].">
      <j1 rule="para" parents="8661 4264"/>
    </justification>
  </clause>

  <clause id="9472">
    <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(320,a,7128,a(flip),b,8699,a),flip(a)].">
      <j1 rule="hyper" parents="320 7128 8699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9473">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (z * u)) = R(K(x,T(y,z * u)),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,8675,a(flip),b,9109,a),flip(a)].">
      <j1 rule="hyper" parents="58 8675 9109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9474">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = K((u * z) / (u * (x \ z)),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5957,a,b,9129,a),flip(a)].">
      <j1 rule="hyper" parents="320 5957 9129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9475">
    <literal><![CDATA[
      L(T(K(x,T(y,z * u)),u),u,z) = (z * (K(x,y) * u)) / (z * u)
    ]]></literal>
    <justification jstring="[para(7154(a,1),9129(a,1,1))].">
      <j1 rule="para" parents="7154 9129"/>
    </justification>
  </clause>

  <clause id="9476">
    <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(9160(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="9160 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9477">
    <literal><![CDATA[
      K(x,y) * K(L(x,z,u) * y,x) = L(x,y,L(x,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(8605(a,1),9259(a,1,2))].">
      <j1 rule="para" parents="8605 9259"/>
    </justification>
  </clause>

  <clause id="9478">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) * K(x,u) = L(x,u,L(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(1993,a,9477,a)].">
      <j1 rule="hyper" parents="1993 9477"/>
    </justification>
  </clause>

  <clause id="9479">
    <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(2635(a,1),9442(a,2,1,1))].">
      <j1 rule="para" parents="2635 9442"/>
    </justification>
  </clause>

  <clause id="9480">
    <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(8227,a,9464,a)].">
      <j1 rule="hyper" parents="8227 9464"/>
    </justification>
  </clause>

  <clause id="9481">
    <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),9480(a,1,2))].">
      <j1 rule="para" parents="18 9480"/>
    </justification>
  </clause>

  <clause id="9482">
    <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,8765,a(flip),b,9481,a)].">
      <j1 rule="hyper" parents="58 8765 9481"/>
    </justification>
  </clause>

  <clause id="9483">
    <literal><![CDATA[
      K(L(R(x,y,z),u,x),w) = K(R(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(7981,a,9482,a),flip(a)].">
      <j1 rule="hyper" parents="7981 9482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9485">
    <literal><![CDATA[
      K(R(L(x,y,x),z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(24(a,2),9483(a,1,1))].">
      <j1 rule="para" parents="24 9483"/>
    </justification>
  </clause>

  <clause id="9486">
    <literal><![CDATA[
      K(R(x,x \ a(x,y,x),z),u) = K(L(x,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9061,a(flip),b,9485,a),flip(a)].">
      <j1 rule="hyper" parents="58 9061 9485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9487">
    <literal><![CDATA[
      K(R(x,x \ a(x,y,x),z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,7024,a(flip),b,9486,a),flip(a)].">
      <j1 rule="hyper" parents="320 7024 9486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9490">
    <literal><![CDATA[
      (K(x,y) * a(x,z,x)) * u = K(x,y) * (a(x,z,x) * u)
    ]]></literal>
    <justification jstring="[para(9487(a,1),6724(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9487 6724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9491">
    <literal><![CDATA[
      K(x,x * y) * (a(x,y,x) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(8924(a,1),9490(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8924 9490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9492">
    <literal><![CDATA[
      a(x,y,x) * z = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(9090,a,9491,a),flip(a)].">
      <j1 rule="hyper" parents="9090 9491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9493">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(5109,a,9491,a)].">
      <j1 rule="hyper" parents="5109 9491"/>
    </justification>
  </clause>

  <clause id="9494">
    <literal><![CDATA[
      K(x,y) * (a(x,y,x) \ z) = K(x,x * y) * z
    ]]></literal>
    <justification jstring="[hyper(342,a,9491,a),flip(a)].">
      <j1 rule="hyper" parents="342 9491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9495">
    <literal><![CDATA[
      x / a(y,z,y) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(337,a,9492,a)].">
      <j1 rule="hyper" parents="337 9492"/>
    </justification>
  </clause>

  <clause id="9496">
    <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(320,a,9332,a(flip),b,9492,a),flip(a)].">
      <j1 rule="hyper" parents="320 9332 9492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9497">
    <literal><![CDATA[
      a(x,y,x) * (R(x,y,x) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(320,a,9104,a(flip),b,9492,a),flip(a)].">
      <j1 rule="hyper" parents="320 9104 9492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9498">
    <literal><![CDATA[
      a(x,y,x) * (x * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(320,a,9103,a(flip),b,9492,a),flip(a)].">
      <j1 rule="hyper" parents="320 9103 9492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9499">
    <literal><![CDATA[
      a(x,y,x) * (z * x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,9093,a(flip),b,9492,a),flip(a)].">
      <j1 rule="hyper" parents="320 9093 9492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9500">
    <literal><![CDATA[
      a(x,x \ y,x) * y = T(x * (y / x),x)
    ]]></literal>
    <justification jstring="[hyper(320,a,9077,a(flip),b,9492,a),flip(a)].">
      <j1 rule="hyper" parents="320 9077 9492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9501">
    <literal><![CDATA[
      a(x,y,x) * (x \ z) = L(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(320,a,9075,a(flip),b,9492,a),flip(a)].">
      <j1 rule="hyper" parents="320 9075 9492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9502">
    <literal><![CDATA[
      a(x,y,x) * (z / x) = z / L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,9055,a(flip),b,9492,a),flip(a)].">
      <j1 rule="hyper" parents="320 9055 9492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9503">
    <literal><![CDATA[
      (a(x,y,x) \ z) * a(x,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(256,a,9492,a),flip(a)].">
      <j1 rule="hyper" parents="256 9492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9504">
    <literal><![CDATA[
      T(x,a(y,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(242,a,9492,a)].">
      <j1 rule="hyper" parents="242 9492"/>
    </justification>
  </clause>

  <clause id="9505">
    <literal><![CDATA[
      T(a(x,y,x),z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(239,a,9492,a,b,xx)].">
      <j1 rule="hyper" parents="239 9492"/>
    </justification>
  </clause>

  <clause id="9506">
    <literal><![CDATA[
      (x * a(y,z,y)) / x = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,9492,a)].">
      <j1 rule="hyper" parents="131 9492"/>
    </justification>
  </clause>

  <clause id="9507">
    <literal><![CDATA[
      a(x,y,x) \ (z * a(x,y,x)) = z
    ]]></literal>
    <justification jstring="[hyper(123,a,9492,a)].">
      <j1 rule="hyper" parents="123 9492"/>
    </justification>
  </clause>

  <clause id="9508">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,9093,a(flip),b,9492,a)].">
      <j1 rule="hyper" parents="117 9093 9492"/>
    </justification>
  </clause>

  <clause id="9509">
    <literal><![CDATA[
      a(x,y,x) \ (z / x) = z / R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,9106,a(flip),b,9492,a)].">
      <j1 rule="hyper" parents="116 9106 9492"/>
    </justification>
  </clause>

  <clause id="9510">
    <literal><![CDATA[
      a(x,y,x) \ (x \ z) = R(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,9104,a(flip),b,9492,a)].">
      <j1 rule="hyper" parents="116 9104 9492"/>
    </justification>
  </clause>

  <clause id="9511">
    <literal><![CDATA[
      x \ (a(x,y,x) * z) = L(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,9492,a,b,9064,a)].">
      <j1 rule="hyper" parents="116 9492 9064"/>
    </justification>
  </clause>

  <clause id="9512">
    <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,9492,a,b,638,a)].">
      <j1 rule="hyper" parents="116 9492 638"/>
    </justification>
  </clause>

  <clause id="9513">
    <literal><![CDATA[
      K(x,a(y,z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,9492,a,b,84,a),flip(a)].">
      <j1 rule="hyper" parents="115 9492 84"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9514">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = (z * a(x,y,x)) \ u
    ]]></literal>
    <justification jstring="[hyper(56,a,9492,a)].">
      <j1 rule="hyper" parents="56 9492"/>
    </justification>
  </clause>

  <clause id="9515">
    <literal><![CDATA[
      a(x,y,x) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9492(a,2),38(a,1))].">
      <j1 rule="para" parents="9492 38"/>
    </justification>
  </clause>

  <clause id="9516">
    <literal><![CDATA[
      (a(x,y,x) \ z) * a(x,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(9492(a,1),256(a,1))].">
      <j1 rule="para" parents="9492 256"/>
    </justification>
  </clause>

  <clause id="9517">
    <literal><![CDATA[
      (x * y) \ ((x * a(z,u,z)) * y) = R(T(a(z,u,z),x * y),x,y)
    ]]></literal>
    <justification jstring="[para(9492(a,1),630(a,1,2,1))].">
      <j1 rule="para" parents="9492 630"/>
    </justification>
  </clause>

  <clause id="9518">
    <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(9492(a,1),769(a,1,1))].">
      <j1 rule="para" parents="9492 769"/>
    </justification>
  </clause>

  <clause id="9519">
    <literal><![CDATA[
      a(x,y,x) * (z * x) != u
    ]]></literal>
    <literal><![CDATA[
      z * R(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9492(a,2),9101(a,1))].">
      <j1 rule="para" parents="9492 9101"/>
    </justification>
  </clause>

  <clause id="9520">
    <literal><![CDATA[
      a(x,y,x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9504(a,1),284(a,1,2))].">
      <j1 rule="para" parents="9504 284"/>
    </justification>
  </clause>

  <clause id="9521">
    <literal><![CDATA[
      x * K(y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(9513(a,2),128(a,1,2))].">
      <j1 rule="para" parents="9513 128"/>
    </justification>
  </clause>

  <clause id="9522">
    <literal><![CDATA[
      T(a(x,y,x),z) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,8913,a,b,9505,a),flip(a)].">
      <j1 rule="hyper" parents="320 8913 9505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9523">
    <literal><![CDATA[
      x * a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) * x = u
    ]]></literal>
    <justification jstring="[para(9505(a,1),284(a,1,2))].">
      <j1 rule="para" parents="9505 284"/>
    </justification>
  </clause>

  <clause id="9524">
    <literal><![CDATA[
      R(a(x,y,x),z,u) * w = w * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(9505(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9505 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9525">
    <literal><![CDATA[
      x * (y \ L(y,z,y)) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,9102,a,b,9495,a)].">
      <j1 rule="hyper" parents="58 9102 9495"/>
    </justification>
  </clause>

  <clause id="9526">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,9068,a,b,9495,a)].">
      <j1 rule="hyper" parents="58 9068 9495"/>
    </justification>
  </clause>

  <clause id="9527">
    <literal><![CDATA[
      (x / y) \ (a(y,z,y) \ x) = L(y,z,y)
    ]]></literal>
    <justification jstring="[para(9495(a,1),9074(a,1,2))].">
      <j1 rule="para" parents="9495 9074"/>
    </justification>
  </clause>

  <clause id="9528">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) / (x * y) = L(a(z,u,z),y,x)
    ]]></literal>
    <justification jstring="[para(9506(a,1),845(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9506 845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9529">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u != w
    ]]></literal>
    <literal><![CDATA[
      (z * a(x,y,x)) \ u = w
    ]]></literal>
    <justification jstring="[para(9507(a,1),350(a,1,1,2))].">
      <j1 rule="para" parents="9507 350"/>
    </justification>
  </clause>

  <clause id="9530">
    <literal><![CDATA[
      K(x,a(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(2(a,1),9521(a,1))].">
      <j1 rule="para" parents="2 9521"/>
    </justification>
  </clause>

  <clause id="9531">
    <literal><![CDATA[
      T(a(x / y,z,x / y),u) = (x / y) \ R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(7091(a,1),9522(a,2,2))].">
      <j1 rule="para" parents="7091 9522"/>
    </justification>
  </clause>

  <clause id="9533">
    <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(9498(a,1),518(a,1,1,1))].">
      <j1 rule="para" parents="9498 518"/>
    </justification>
  </clause>

  <clause id="9534">
    <literal><![CDATA[
      (x * R(x \ y,z,x \ y)) / y = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(117,a,9499,a(flip),b,151,a(flip))].">
      <j1 rule="hyper" parents="117 9499 151"/>
    </justification>
  </clause>

  <clause id="9535">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) = u
    ]]></literal>
    <justification jstring="[para(9499(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9499 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9536">
    <literal><![CDATA[
      a(x,y,x) \ y = x \ ((x * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4331,a(flip),b,9501,a)].">
      <j1 rule="hyper" parents="116 4331 9501"/>
    </justification>
  </clause>

  <clause id="9537">
    <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),9508(a,1,2))].">
      <j1 rule="para" parents="90 9508"/>
    </justification>
  </clause>

  <clause id="9538">
    <literal><![CDATA[
      a(x,y,x) \ (x * z) = L(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(624,a,9511,a),flip(a)].">
      <j1 rule="hyper" parents="624 9511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9539">
    <literal><![CDATA[
      a(x,y,x) * (L(x,y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(119,a,4,a(flip),b,9511,a),flip(a)].">
      <j1 rule="hyper" parents="119 4 9511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9540">
    <literal><![CDATA[
      L(x,y,x) \ z != x \ u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) * z = u
    ]]></literal>
    <justification jstring="[para(9511(a,1),42(a,1))].">
      <j1 rule="para" parents="9511 42"/>
    </justification>
  </clause>

  <clause id="9541">
    <literal><![CDATA[
      a(x,y,x) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(9525(a,1),255(a,1)),flip(b)].">
      <j1 rule="para" parents="9525 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9542">
    <literal><![CDATA[
      (x / y) * L(y,z,y) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,7489,a(flip),b,9526,a)].">
      <j1 rule="hyper" parents="58 7489 9526"/>
    </justification>
  </clause>

  <clause id="9543">
    <literal><![CDATA[
      (x / y) \ (a(y,z,y) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      L(y,z,y) = u
    ]]></literal>
    <justification jstring="[para(9542(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9542 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9544">
    <literal><![CDATA[
      K(x * y,y) * (K(y,x) * z) = a(y,x,y) * z
    ]]></literal>
    <justification jstring="[para(5228(a,2),9493(a,1,1))].">
      <j1 rule="para" parents="5228 9493"/>
    </justification>
  </clause>

  <clause id="9545">
    <literal><![CDATA[
      K(x,y) * (K(y,y * x) * z) = a(y,x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(5109,a,9494,a)].">
      <j1 rule="hyper" parents="5109 9494"/>
    </justification>
  </clause>

  <clause id="9546">
    <literal><![CDATA[
      K(x * y,y) * (x * (K(y,x) * z)) = a(y,x,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(5219(a,1),9544(a,1,2))].">
      <j1 rule="para" parents="5219 9544"/>
    </justification>
  </clause>

  <clause id="9547">
    <literal><![CDATA[
      K(x,y) * (K(y,x * y) * z) = a(y,x,y) \ z
    ]]></literal>
    <justification jstring="[para(5346(a,2),9545(a,1,2,1))].">
      <j1 rule="para" parents="5346 9545"/>
    </justification>
  </clause>

  <clause id="9548">
    <literal><![CDATA[
      K(x,y) * (K(y,y * x) * z) = (y \ R(y,x,y)) \ z
    ]]></literal>
    <justification jstring="[para(8913(a,2),9545(a,2,1))].">
      <j1 rule="para" parents="8913 9545"/>
    </justification>
  </clause>

  <clause id="9549">
    <literal><![CDATA[
      T(x,R(a(y,z,y),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(242,a,9524,a)].">
      <j1 rule="hyper" parents="242 9524"/>
    </justification>
  </clause>

  <clause id="9550">
    <literal><![CDATA[
      (x * (y * R(z,u,z))) / (x * (y * z)) = L(a(z,u,z),y * z,x)
    ]]></literal>
    <justification jstring="[para(9093(a,1),9528(a,1,1,2))].">
      <j1 rule="para" parents="9093 9528"/>
    </justification>
  </clause>

  <clause id="9551">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ (K(x * y,x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(5095(a,1),9548(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5095 9548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9552">
    <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(9467(a,1),6903(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9467 6903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9553">
    <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(8437(a,1),9475(a,1,1,1))].">
      <j1 rule="para" parents="8437 9475"/>
    </justification>
  </clause>

  <clause id="9554">
    <literal><![CDATA[
      (x * y) \ ((x * a(z,u,z)) * y) = R(a(z,u,z),x,y)
    ]]></literal>
    <justification jstring="[para(9505(a,1),9517(a,2,1))].">
      <j1 rule="para" parents="9505 9517"/>
    </justification>
  </clause>

  <clause id="9555">
    <literal><![CDATA[
      (x * y) \ ((T(z * x,z) / z) * y) = R(a(z,x,z),x,y)
    ]]></literal>
    <justification jstring="[para(8929(a,2),9554(a,1,2,1))].">
      <j1 rule="para" parents="8929 9554"/>
    </justification>
  </clause>

  <clause id="9557">
    <literal><![CDATA[
      T(x * K(y,x),K(x,z) * u) = T(x,u) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[para(7238(a,1),7245(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7238 7245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9558">
    <literal><![CDATA[
      T(x * K(y,x),K(x,z) * u) = T(x * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,5164,a(flip),b,9557,a),flip(a)].">
      <j1 rule="hyper" parents="320 5164 9557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9560">
    <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,5339,a(flip),b,9558,a),flip(a)].">
      <j1 rule="hyper" parents="58 5339 9558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9561">
    <literal><![CDATA[
      K(x * K(L(y,z,u),w),L(y,v5,v6)) = K(x,L(y,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(320,a,4765,a(flip),b,7399,a),flip(a)].">
      <j1 rule="hyper" parents="320 4765 7399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9562">
    <literal><![CDATA[
      K(x * K(y,z),L(y,u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(372(a,1),9561(a,1,1,2,1))].">
      <j1 rule="para" parents="372 9561"/>
    </justification>
  </clause>

  <clause id="9563">
    <literal><![CDATA[
      K(x * y,L(y,z,u)) = K(y * x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(84(a,1),9562(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 9562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9564">
    <literal><![CDATA[
      K(x \ T(y,z),L(z,u,w)) = K(x \ y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(6538(a,1),9562(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6538 9562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9565">
    <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),9564(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 9564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9566">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,L(y,w,v5)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(3988,a,7438,a)].">
      <j1 rule="hyper" parents="3988 7438"/>
    </justification>
  </clause>

  <clause id="9567">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9472,a(flip),b,9566,a)].">
      <j1 rule="hyper" parents="58 9472 9566"/>
    </justification>
  </clause>

  <clause id="9569">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),9567(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 9567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9570">
    <literal><![CDATA[
      K(x,T(y,z * (u * y))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(7398(a,1),9567(a,1,2))].">
      <j1 rule="para" parents="7398 9567"/>
    </justification>
  </clause>

  <clause id="9571">
    <literal><![CDATA[
      K(x,T(y \ z,u * z)) = K(x,T(y \ z,u * y))
    ]]></literal>
    <justification jstring="[para(5(a,1),9570(a,1,2,2,2))].">
      <j1 rule="para" parents="5 9570"/>
    </justification>
  </clause>

  <clause id="9572">
    <literal><![CDATA[
      K(x,T(y,z * (y * u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(7108(a,1),9570(a,1,2))].">
      <j1 rule="para" parents="7108 9570"/>
    </justification>
  </clause>

  <clause id="9573">
    <literal><![CDATA[
      K(x * y,T(x,z * y)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(7699,a,9572,a),flip(a)].">
      <j1 rule="hyper" parents="7699 9572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9575">
    <literal><![CDATA[
      K(x * y,T(y,z * x)) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5857,a,b,9573,a)].">
      <j1 rule="hyper" parents="58 5857 9573"/>
    </justification>
  </clause>

  <clause id="9576">
    <literal><![CDATA[
      K(x,T(y \ x,z * y)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(7699,a,9571,a),flip(a)].">
      <j1 rule="hyper" parents="7699 9571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9577">
    <literal><![CDATA[
      K(x,T(y \ x,z / y)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),9576(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 9576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9578">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8267,a(flip),b,9577,a)].">
      <j1 rule="hyper" parents="58 8267 9577"/>
    </justification>
  </clause>

  <clause id="9579">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9165,a(flip),b,9578,a)].">
      <j1 rule="hyper" parents="58 9165 9578"/>
    </justification>
  </clause>

  <clause id="9580">
    <literal><![CDATA[
      K(x,T(y \ x,x * z)) = K(x,((x * z) / y) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8458,a(flip),b,9579,a),flip(a)].">
      <j1 rule="hyper" parents="58 8458 9579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9581">
    <literal><![CDATA[
      K(x,((x * y) / z) / y) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(7685,a,9580,a),flip(a)].">
      <j1 rule="hyper" parents="7685 9580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9582">
    <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,8760,a(flip),b,9581,a)].">
      <j1 rule="hyper" parents="58 8760 9581"/>
    </justification>
  </clause>

  <clause id="9583">
    <literal><![CDATA[
      R(x,y,T(x * K(z,x),u)) = R(x,y,x * K(z,x))
    ]]></literal>
    <justification jstring="[para(4775(a,1),7507(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4775 7507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9584">
    <literal><![CDATA[
      R(x,y,x * K(z,x)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4775(a,1),9583(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4775 9583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9585">
    <literal><![CDATA[
      R(x \ y,z,y / x) = R(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[para(4735(a,1),9584(a,1,3))].">
      <j1 rule="para" parents="4735 9584"/>
    </justification>
  </clause>

  <clause id="9586">
    <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(4684(a,1),7671(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4684 7671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9587">
    <literal><![CDATA[
      T(x / y,T((y * z) \ x,y)) = T(x / y,T(z \ (y \ x),y))
    ]]></literal>
    <justification jstring="[hyper(7291,a,7718,a),flip(a)].">
      <j1 rule="hyper" parents="7291 7718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9588">
    <literal><![CDATA[
      T(x / y,T(z \ (y \ x),y)) = T(x / y,x / (y * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8010,a(flip),b,9587,a),flip(a)].">
      <j1 rule="hyper" parents="58 8010 9587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9589">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) * (y / u) = T(y,K(x,z)) / u
    ]]></literal>
    <justification jstring="[para(7809(a,1),7787(a,1,1))].">
      <j1 rule="para" parents="7809 7787"/>
    </justification>
  </clause>

  <clause id="9590">
    <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(9589(a,1),103(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9589 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9591">
    <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(9589(a,1),5108(a,1,2))].">
      <j1 rule="para" parents="9589 5108"/>
    </justification>
  </clause>

  <clause id="9592">
    <literal><![CDATA[
      T(x / y,K(((x / y) \ (1 / y)) \ 1,z)) = T(x,K(z,y \ x)) / y
    ]]></literal>
    <justification jstring="[para(6151(a,1),7848(a,2,1))].">
      <j1 rule="para" parents="6151 7848"/>
    </justification>
  </clause>

  <clause id="9593">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,(((y \ 1) \ 1) \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7919,a(flip),b,8001,a)].">
      <j1 rule="hyper" parents="58 7919 8001"/>
    </justification>
  </clause>

  <clause id="9594">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,((y \ 1) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,4412,a(flip),b,9593,a),flip(a)].">
      <j1 rule="hyper" parents="320 4412 9593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9596">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3738,a(flip),b,9594,a),flip(a)].">
      <j1 rule="hyper" parents="320 3738 9594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9597">
    <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,9425,a(flip),b,8013,a)].">
      <j1 rule="hyper" parents="58 9425 8013"/>
    </justification>
  </clause>

  <clause id="9598">
    <literal><![CDATA[
      K(x,K(y,z)) * ((K(x,y) * z) \ u) = (z * K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(6322(a,1),8271(a,2,1))].">
      <j1 rule="para" parents="6322 8271"/>
    </justification>
  </clause>

  <clause id="9599">
    <literal><![CDATA[
      K(x,y * ((K(x,z) * u) \ w)) = K(x,y * ((u * K(x,z)) \ w))
    ]]></literal>
    <justification jstring="[para(9598(a,1),7530(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9598 7530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9600">
    <literal><![CDATA[
      K(1 / T(x,y),z) \ K(K(1 / T(x,y),z),y) = K(z,1 / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4929,a(flip),b,8276,a),flip(a)].">
      <j1 rule="hyper" parents="320 4929 8276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9601">
    <literal><![CDATA[
      K(x,1 / T(T(y,z),z)) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(9269,a,9600,a)].">
      <j1 rule="hyper" parents="9269 9600"/>
    </justification>
  </clause>

  <clause id="9602">
    <literal><![CDATA[
      K(x,1 / ((y * z) / y)) = K(x,1 / T(z,y))
    ]]></literal>
    <justification jstring="[para(224(a,1),9601(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="224 9601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9603">
    <literal><![CDATA[
      K(x,1 / T(y,z / y)) = K(x,1 / (z / (z / y)))
    ]]></literal>
    <justification jstring="[para(244(a,1),9601(a,1,2,2,1))].">
      <j1 rule="para" parents="244 9601"/>
    </justification>
  </clause>

  <clause id="9604">
    <literal><![CDATA[
      K(x,K(y,z) / y) = K(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[para(4911(a,2),9602(a,1,2))].">
      <j1 rule="para" parents="4911 9602"/>
    </justification>
  </clause>

  <clause id="9605">
    <literal><![CDATA[
      K(x,K(1 / y,z) / (1 / y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5474,a(flip),b,9604,a),flip(a)].">
      <j1 rule="hyper" parents="320 5474 9604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9606">
    <literal><![CDATA[
      K(x,1 / (K(y,z \ 1) / z)) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(5234(a,1),9605(a,1,2))].">
      <j1 rule="para" parents="5234 9605"/>
    </justification>
  </clause>

  <clause id="9607">
    <literal><![CDATA[
      K(x,y * K(y \ 1,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6330,a(flip),b,9606,a)].">
      <j1 rule="hyper" parents="58 6330 9606"/>
    </justification>
  </clause>

  <clause id="9608">
    <literal><![CDATA[
      K(x,y * K(1 / y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(3293(a,2),9607(a,1,2,2))].">
      <j1 rule="para" parents="3293 9607"/>
    </justification>
  </clause>

  <clause id="9609">
    <literal><![CDATA[
      T(K(x,y),z / (1 / y)) = K(x,1 / (z / (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(58,a,5474,a(flip),b,9603,a)].">
      <j1 rule="hyper" parents="58 5474 9603"/>
    </justification>
  </clause>

  <clause id="9610">
    <literal><![CDATA[
      K(T(x,y) / y,z) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(29,a,7949,a(flip),b,8303,a)].">
      <j1 rule="hyper" parents="29 7949 8303"/>
    </justification>
  </clause>

  <clause id="9611">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(320,a,8479,a(flip),b,8480,a),flip(a)].">
      <j1 rule="hyper" parents="320 8479 8480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9612">
    <literal><![CDATA[
      K(x,R(x \ y,x,z / y)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,8486,a,b,9611,a)].">
      <j1 rule="hyper" parents="58 8486 9611"/>
    </justification>
  </clause>

  <clause id="9613">
    <literal><![CDATA[
      K(x,R(x \ (y / z),x,y / (y / z))) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(75(a,1),9612(a,2,2,2,1))].">
      <j1 rule="para" parents="75 9612"/>
    </justification>
  </clause>

  <clause id="9614">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,K(x,v5)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7555,a(flip),b,8521,a),flip(a)].">
      <j1 rule="hyper" parents="320 7555 8521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9616">
    <literal><![CDATA[
      K(x,T(1 \ ((y \ z) * x),z)) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,9161,a(flip),b,8549,a)].">
      <j1 rule="hyper" parents="58 9161 8549"/>
    </justification>
  </clause>

  <clause id="9617">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (y \ 1)) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(3517(a,1),8648(a,1,1,2))].">
      <j1 rule="para" parents="3517 8648"/>
    </justification>
  </clause>

  <clause id="9618">
    <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(320,a,7519,a(flip),b,8650,a),flip(a)].">
      <j1 rule="hyper" parents="320 7519 8650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9619">
    <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,8660,a(flip),b,9618,a)].">
      <j1 rule="hyper" parents="58 8660 9618"/>
    </justification>
  </clause>

  <clause id="9620">
    <literal><![CDATA[
      T(x,T(y,z)) \ R(x,y,x) = K(y * x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(8409,a,9619,a),flip(a)].">
      <j1 rule="hyper" parents="8409 9619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9621">
    <literal><![CDATA[
      K(x,T(y,z)) * a(y,x,y) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8955,a,9620,a)].">
      <j1 rule="hyper" parents="8955 9620"/>
    </justification>
  </clause>

  <clause id="9622">
    <literal><![CDATA[
      K(x,T(y,z)) * a(y,x,y) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,5857,a(flip),b,9621,a),flip(a)].">
      <j1 rule="hyper" parents="320 5857 9621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9623">
    <literal><![CDATA[
      K(x / y,z) * a(z,y \ x,z) = K((y \ x) * z,T(z,y))
    ]]></literal>
    <justification jstring="[para(7882(a,1),9621(a,1,1))].">
      <j1 rule="para" parents="7882 9621"/>
    </justification>
  </clause>

  <clause id="9624">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (K(x,T(y,z)) * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(9621(a,1),9063(a,1,1))].">
      <j1 rule="para" parents="9621 9063"/>
    </justification>
  </clause>

  <clause id="9625">
    <literal><![CDATA[
      a(x,y,x) * K(y,T(x,z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(9523,a,9622,a)].">
      <j1 rule="hyper" parents="9523 9622"/>
    </justification>
  </clause>

  <clause id="9626">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(x,T(y,z)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7204,a,9625,a)].">
      <j1 rule="hyper" parents="7204 9625"/>
    </justification>
  </clause>

  <clause id="9627">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (y * K(x,T(y,z))) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(2886(a,1),9624(a,1,2))].">
      <j1 rule="para" parents="2886 9624"/>
    </justification>
  </clause>

  <clause id="9628">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K(y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7201,a,9627,a)].">
      <j1 rule="hyper" parents="7201 9627"/>
    </justification>
  </clause>

  <clause id="9629">
    <literal><![CDATA[
      T(x,T(x * y,z)) * K(y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4569(a,1),9628(a,1,1))].">
      <j1 rule="para" parents="4569 9628"/>
    </justification>
  </clause>

  <clause id="9630">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * (z \ y)) \ u,z) = w
    ]]></literal>
    <justification jstring="[para(8652(a,1),5204(a,1))].">
      <j1 rule="para" parents="8652 5204"/>
    </justification>
  </clause>

  <clause id="9631">
    <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(320,a,4247,a(flip),b,8669,a),flip(a)].">
      <j1 rule="hyper" parents="320 4247 8669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9632">
    <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(320,a,4246,a(flip),b,8670,a),flip(a)].">
      <j1 rule="hyper" parents="320 4246 8670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9633">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) = K((x * y) \ (u * z),z)
    ]]></literal>
    <justification jstring="[hyper(5204,a,8695,a),flip(a)].">
      <j1 rule="hyper" parents="5204 8695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9634">
    <literal><![CDATA[
      K((x * (y \ z)) \ u,y) = K((x * z) \ (u * y),y)
    ]]></literal>
    <justification jstring="[hyper(9630,a,9633,a)].">
      <j1 rule="hyper" parents="9630 9633"/>
    </justification>
  </clause>

  <clause id="9635">
    <literal><![CDATA[
      K((x * (y \ 1)) \ z,y) = K(x \ (z * y),y)
    ]]></literal>
    <justification jstring="[para(3(a,1),9634(a,2,1,1))].">
      <j1 rule="para" parents="3 9634"/>
    </justification>
  </clause>

  <clause id="9636">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6628,a,b,9635,a)].">
      <j1 rule="hyper" parents="58 6628 9635"/>
    </justification>
  </clause>

  <clause id="9637">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(z \ ((z * y) * x),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6607,a,b,9635,a)].">
      <j1 rule="hyper" parents="58 6607 9635"/>
    </justification>
  </clause>

  <clause id="9638">
    <literal><![CDATA[
      K(x \ ((x * y) * z),z) \ K(z * y,z) = a(x,y,K(z * y,z))
    ]]></literal>
    <justification jstring="[para(9637(a,1),1921(a,1,1))].">
      <j1 rule="para" parents="9637 1921"/>
    </justification>
  </clause>

  <clause id="9639">
    <literal><![CDATA[
      L(K(x * y,y),x,z) = K(z \ ((z * x) * y),y)
    ]]></literal>
    <justification jstring="[para(5228(a,2),9637(a,1,1))].">
      <j1 rule="para" parents="5228 9637"/>
    </justification>
  </clause>

  <clause id="9640">
    <literal><![CDATA[
      L(K(x * T(y,z * x),T(y,z * x)),x,z) = K(z \ (y * (z * x)),T(y,z * x))
    ]]></literal>
    <justification jstring="[para(105(a,1),9639(a,2,1,2))].">
      <j1 rule="para" parents="105 9639"/>
    </justification>
  </clause>

  <clause id="9641">
    <literal><![CDATA[
      K(x,y \ ((y * z) * x)) * K(x * z,x) = a(y,z,K(x * z,x))
    ]]></literal>
    <justification jstring="[hyper(5125,a,9638,a)].">
      <j1 rule="hyper" parents="5125 9638"/>
    </justification>
  </clause>

  <clause id="9642">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[hyper(30,a,5859,a,b,9641,a)].">
      <j1 rule="hyper" parents="30 5859 9641"/>
    </justification>
  </clause>

  <clause id="9643">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,y) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[para(5(a,1),9642(a,2,2,2,1))].">
      <j1 rule="para" parents="5 9642"/>
    </justification>
  </clause>

  <clause id="9644">
    <literal><![CDATA[
      L(K(x,y * x),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[para(5346(a,2),9642(a,1,1))].">
      <j1 rule="para" parents="5346 9642"/>
    </justification>
  </clause>

  <clause id="9645">
    <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(296(a,1),9644(a,2,2))].">
      <j1 rule="para" parents="296 9644"/>
    </justification>
  </clause>

  <clause id="9646">
    <literal><![CDATA[
      L(K(L(x,y,z),y * L(x,y,z)),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6593,a(flip),b,9645,a),flip(a)].">
      <j1 rule="hyper" parents="320 6593 9645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9648">
    <literal><![CDATA[
      K(x,(((K(y,x \ z) / y) \ 1) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(5232(a,2),8697(a,1,2,1,1))].">
      <j1 rule="para" parents="5232 8697"/>
    </justification>
  </clause>

  <clause id="9649">
    <literal><![CDATA[
      x / T(x / y,L(y,z,u)) = y * a(u,z * y,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(176(a,1),8759(a,1,2,2))].">
      <j1 rule="para" parents="176 8759"/>
    </justification>
  </clause>

  <clause id="9650">
    <literal><![CDATA[
      K(x,y / ((T(z,u) \ u) / w)) = K(x,y / ((z \ T(u,z)) / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,8841,a(flip),b,8848,a),flip(a)].">
      <j1 rule="hyper" parents="58 8841 8848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9651">
    <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(1999(a,2),8886(a,2,2))].">
      <j1 rule="para" parents="1999 8886"/>
    </justification>
  </clause>

  <clause id="9652">
    <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(6300(a,1),8886(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6300 8886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9653">
    <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(1994(a,1),8888(a,2,2))].">
      <j1 rule="para" parents="1994 8888"/>
    </justification>
  </clause>

  <clause id="9654">
    <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(8954(a,2),39(a,1))].">
      <j1 rule="para" parents="8954 39"/>
    </justification>
  </clause>

  <clause id="9655">
    <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(7759(a,1),9006(a,1,1,1))].">
      <j1 rule="para" parents="7759 9006"/>
    </justification>
  </clause>

  <clause id="9656">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z / ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[para(4(a,1),9014(a,1,2))].">
      <j1 rule="para" parents="4 9014"/>
    </justification>
  </clause>

  <clause id="9657">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) = K(x / ((y * z) \ y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9426,a(flip),b,9656,a)].">
      <j1 rule="hyper" parents="58 9426 9656"/>
    </justification>
  </clause>

  <clause id="9658">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(((y * z) \ y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(9657(a,2),7973(a,1))].">
      <j1 rule="para" parents="9657 7973"/>
    </justification>
  </clause>

  <clause id="9659">
    <literal><![CDATA[
      T(x / T(y,x),z) * T(y,T(x,z)) = x * K(T(x,y) / y,z)
    ]]></literal>
    <justification jstring="[para(7413(a,1),9038(a,1,2))].">
      <j1 rule="para" parents="7413 9038"/>
    </justification>
  </clause>

  <clause id="9660">
    <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(9147(a,1),6254(a,1,2))].">
      <j1 rule="para" parents="9147 6254"/>
    </justification>
  </clause>

  <clause id="9661">
    <literal><![CDATA[
      (x / a(y,z,K(u,w))) * K(u,w) = x * L(K(u,w),z,y)
    ]]></literal>
    <justification jstring="[para(5861(a,1),9156(a,1,1,2))].">
      <j1 rule="para" parents="5861 9156"/>
    </justification>
  </clause>

  <clause id="9662">
    <literal><![CDATA[
      (x * K((y \ 1) \ (z \ x),z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(4622,a,9299,a),flip(a)].">
      <j1 rule="hyper" parents="4622 9299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9663">
    <literal><![CDATA[
      (x * K((y \ z) \ x,z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(8269(a,1),9662(a,1,1,2))].">
      <j1 rule="para" parents="8269 9662"/>
    </justification>
  </clause>

  <clause id="9664">
    <literal><![CDATA[
      x \ R(x * K(y,x),y,y \ 1) = K(y,x) * a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(704(a,1),9418(a,2,2))].">
      <j1 rule="para" parents="704 9418"/>
    </justification>
  </clause>

  <clause id="9665">
    <literal><![CDATA[
      K(x,y) * a(y,x,x \ 1) = y \ ((x * y) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(4889(a,1),9664(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4889 9664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9666">
    <literal><![CDATA[
      K(x,(x \ ((y * x) * (y \ 1))) \ z) = K(x,a(x,y,y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(9665(a,1),8530(a,1,2,1))].">
      <j1 rule="para" parents="9665 8530"/>
    </justification>
  </clause>

  <clause id="9667">
    <literal><![CDATA[
      K(x,((y * x) * (y \ 1)) \ (x * z)) = K(x,a(x,y,y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7005,a(flip),b,9666,a)].">
      <j1 rule="hyper" parents="58 7005 9666"/>
    </justification>
  </clause>

  <clause id="9668">
    <literal><![CDATA[
      T(x / y,K(((x / y) \ (1 / y)) \ 1,z)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8575,a(flip),b,9592,a),flip(a)].">
      <j1 rule="hyper" parents="320 8575 9592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9669">
    <literal><![CDATA[
      T(x / y,K(z,((x / y) \ (1 / y)) \ 1)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(7841,a,9668,a)].">
      <j1 rule="hyper" parents="7841 9668"/>
    </justification>
  </clause>

  <clause id="9670">
    <literal><![CDATA[
      T(x / y,K(z,(1 / y) \ (x / y))) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(6078(a,1),9669(a,1,2))].">
      <j1 rule="para" parents="6078 9669"/>
    </justification>
  </clause>

  <clause id="9671">
    <literal><![CDATA[
      (x / T(y / (y / z),u)) * z = x * (T(y / (y / z),u) \ z)
    ]]></literal>
    <justification jstring="[para(8012(a,1),9597(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8012 9597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9672">
    <literal><![CDATA[
      (x / T(1 / (1 / y),z)) * y = x * (y * (1 / T(y,z)))
    ]]></literal>
    <justification jstring="[para(6777(a,1),9671(a,2,2))].">
      <j1 rule="para" parents="6777 9671"/>
    </justification>
  </clause>

  <clause id="9673">
    <literal><![CDATA[
      K(x,T((y \ z) * x,z)) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[para(60(a,1),9616(a,1,2,1))].">
      <j1 rule="para" parents="60 9616"/>
    </justification>
  </clause>

  <clause id="9674">
    <literal><![CDATA[
      K(x,T(((y \ z) \ 1) \ x,y)) = K(x,T((y \ z) * x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8481,a(flip),b,9673,a)].">
      <j1 rule="hyper" parents="320 8481 9673"/>
    </justification>
  </clause>

  <clause id="9675">
    <literal><![CDATA[
      K(x,T(1 \ ((y \ z) * x),y)) = K(x,T((y \ z) * x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9161,a(flip),b,9674,a)].">
      <j1 rule="hyper" parents="58 9161 9674"/>
    </justification>
  </clause>

  <clause id="9676">
    <literal><![CDATA[
      K(x,T((y \ z) * x,z)) = K(x,T((y \ z) * x,y))
    ]]></literal>
    <justification jstring="[para(60(a,1),9675(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="60 9675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9677">
    <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,6927,a(flip),b,9652,a)].">
      <j1 rule="hyper" parents="117 6927 9652"/>
    </justification>
  </clause>

  <clause id="9678">
    <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(6315,a,9653,a)].">
      <j1 rule="hyper" parents="6315 9653"/>
    </justification>
  </clause>

  <clause id="9679">
    <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(8808(a,1),9655(a,1,1))].">
      <j1 rule="para" parents="8808 9655"/>
    </justification>
  </clause>

  <clause id="9680">
    <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(7759(a,1),9679(a,2,1))].">
      <j1 rule="para" parents="7759 9679"/>
    </justification>
  </clause>

  <clause id="9681">
    <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(7754(a,1),9680(a,2,2))].">
      <j1 rule="para" parents="7754 9680"/>
    </justification>
  </clause>

  <clause id="9682">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * K(w,u) = x * L(K(w,u),z,y)
    ]]></literal>
    <justification jstring="[para(5861(a,1),9678(a,1,1,2))].">
      <j1 rule="para" parents="5861 9678"/>
    </justification>
  </clause>

  <clause id="9683">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) = x * a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(30,a,9661,a,b,9682,a)].">
      <j1 rule="hyper" parents="30 9661 9682"/>
    </justification>
  </clause>

  <clause id="9684">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) \ x = a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(572,a,9683,a)].">
      <j1 rule="hyper" parents="572 9683"/>
    </justification>
  </clause>

  <clause id="9685">
    <literal><![CDATA[
      (T(x,x \ y) * a(z,u,K(w,v5))) \ ((x \ y) \ y) = a(z,u,K(v5,w))
    ]]></literal>
    <justification jstring="[para(9683(a,1),439(a,1,1))].">
      <j1 rule="para" parents="9683 439"/>
    </justification>
  </clause>

  <clause id="9686">
    <literal><![CDATA[
      K(x,y) * T(y,K(z,y) * (x * y)) = L(y,K(z,y) * x,y)
    ]]></literal>
    <justification jstring="[para(7318(a,1),7497(a,1,1))].">
      <j1 rule="para" parents="7318 7497"/>
    </justification>
  </clause>

  <clause id="9687">
    <literal><![CDATA[
      L(x,K(y,x) * z,x) = K(z,x) * T(x,z * x)
    ]]></literal>
    <justification jstring="[para(7243(a,1),9686(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7243 9686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9689">
    <literal><![CDATA[
      L(x,K(y,x) * z,x) = L(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5052,a(flip),b,9687,a),flip(a)].">
      <j1 rule="hyper" parents="320 5052 9687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9691">
    <literal><![CDATA[
      L(x,T(x,y) \ z,x) = L(x,x \ z,x)
    ]]></literal>
    <justification jstring="[para(5093(a,1),9689(a,1,2))].">
      <j1 rule="para" parents="5093 9689"/>
    </justification>
  </clause>

  <clause id="9692">
    <literal><![CDATA[
      L(x,y / T(x,z),x) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9115,a,b,9691,a)].">
      <j1 rule="hyper" parents="58 9115 9691"/>
    </justification>
  </clause>

  <clause id="9694">
    <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,6991,a,b,9692,a)].">
      <j1 rule="hyper" parents="58 6991 9692"/>
    </justification>
  </clause>

  <clause id="9696">
    <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(5892(a,2),7976(a,1,1))].">
      <j1 rule="para" parents="5892 7976"/>
    </justification>
  </clause>

  <clause id="9697">
    <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(320,a,7741,a,b,7982,a)].">
      <j1 rule="hyper" parents="320 7741 7982"/>
    </justification>
  </clause>

  <clause id="9698">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,x) \ z) = ((y * x) / y) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(4076(a,1),8002(a,1,2,1))].">
      <j1 rule="para" parents="4076 8002"/>
    </justification>
  </clause>

  <clause id="9699">
    <literal><![CDATA[
      K(L(x / (y \ 1),y \ 1,y) \ 1,z) = K(T(y * x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,8348,a(flip),b,8320,a),flip(a)].">
      <j1 rule="hyper" parents="320 8348 8320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9700">
    <literal><![CDATA[
      K((x / y) \ z,L(y,u,w)) = K(x \ (z * y),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(4987,a,8431,a),flip(a)].">
      <j1 rule="hyper" parents="4987 8431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9701">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),L(y,u,w)) = K(x \ z,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,4765,a(flip),b,8433,a),flip(a)].">
      <j1 rule="hyper" parents="320 4765 8433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9702">
    <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),9701(a,1,1,2,1))].">
      <j1 rule="para" parents="4 9701"/>
    </justification>
  </clause>

  <clause id="9703">
    <literal><![CDATA[
      (x * y) / (x * (y * K(z,u))) = L(T(K(u,z),x * y),y,x)
    ]]></literal>
    <justification jstring="[para(8399(a,1),8578(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8399 8578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9704">
    <literal><![CDATA[
      (x * y) / (x * (y * K(z,u))) = L(K(u,T(z,x * y)),y,x)
    ]]></literal>
    <justification jstring="[para(7131(a,2),9703(a,2,1))].">
      <j1 rule="para" parents="7131 9703"/>
    </justification>
  </clause>

  <clause id="9706">
    <literal><![CDATA[
      L(K(x,T(x * y,z * y)),y,z) = (z * y) / (z * (x \ T(x * y,x)))
    ]]></literal>
    <justification jstring="[para(6355(a,2),9704(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6355 9704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9707">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = (u * z) / (u * (K(y,x) * z))
    ]]></literal>
    <justification jstring="[para(7123(a,1),9704(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7123 9704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9708">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = (x * y) / (x * (K(u,z) * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9474,a(flip),b,9707,a)].">
      <j1 rule="hyper" parents="58 9474 9707"/>
    </justification>
  </clause>

  <clause id="9709">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = K(z,(x * y) / (x * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(320,a,6014,a,b,9708,a),flip(a)].">
      <j1 rule="hyper" parents="320 6014 9708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9710">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) = (y * (K(x,u) * z)) / (y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5957,a(flip),b,9709,a),flip(a)].">
      <j1 rule="hyper" parents="58 5957 9709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9711">
    <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(9105(a,1),8933(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9105 8933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9712">
    <literal><![CDATA[
      L(T(x,a(y,z,y)),a(y,z,y),y) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,4,a(flip),b,9711,a),flip(a)].">
      <j1 rule="hyper" parents="320 4 9711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9714">
    <literal><![CDATA[
      L(x,a(y,z,y),y) = x
    ]]></literal>
    <justification jstring="[para(9504(a,1),9712(a,1,1))].">
      <j1 rule="para" parents="9504 9712"/>
    </justification>
  </clause>

  <clause id="9716">
    <literal><![CDATA[
      L(x,a(y,z,y),T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(9337(a,1),9714(a,1,2))].">
      <j1 rule="para" parents="9337 9714"/>
    </justification>
  </clause>

  <clause id="9717">
    <literal><![CDATA[
      (T(x,y) * a(x,z,x)) * u = T(x,y) * (a(x,z,x) * u)
    ]]></literal>
    <justification jstring="[hyper(1330,a,9716,a),flip(a)].">
      <j1 rule="hyper" parents="1330 9716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9718">
    <literal><![CDATA[
      T(x,y) * (a(x,z,x) * u) = R(T(x,y),z,x) * u
    ]]></literal>
    <justification jstring="[para(8921(a,1),9717(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8921 9717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9719">
    <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(320,a,7755,a(flip),b,9144,a),flip(a)].">
      <j1 rule="hyper" parents="320 7755 9144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9720">
    <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(7518(a,1),9552(a,1,1))].">
      <j1 rule="para" parents="7518 9552"/>
    </justification>
  </clause>

  <clause id="9721">
    <literal><![CDATA[
      (x * (K(y \ x,y) * z)) / (x * z) = L(K(y \ x,y),z,x)
    ]]></literal>
    <justification jstring="[para(7854(a,1),9553(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7854 9553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9722">
    <literal><![CDATA[
      L(K(x \ y,x),z,y) * (y * z) = y * (K(x \ y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,9721,a)].">
      <j1 rule="hyper" parents="133 9721"/>
    </justification>
  </clause>

  <clause id="9724">
    <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),9722(a,1,1,1,1))].">
      <j1 rule="para" parents="4 9722"/>
    </justification>
  </clause>

  <clause id="9725">
    <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(5118(a,1),9696(a,2,2))].">
      <j1 rule="para" parents="5118 9696"/>
    </justification>
  </clause>

  <clause id="9726">
    <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(9696(a,1),8139(a,2,2))].">
      <j1 rule="para" parents="9696 8139"/>
    </justification>
  </clause>

  <clause id="9727">
    <literal><![CDATA[
      (x * y) / (x * (z \ T(z * y,z))) = L(K(z,T(y * z,x)),y,x)
    ]]></literal>
    <justification jstring="[para(9198(a,1),9706(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9198 9706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9728">
    <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(7796,a,9719,a)].">
      <j1 rule="hyper" parents="7796 9719"/>
    </justification>
  </clause>

  <clause id="9729">
    <literal><![CDATA[
      ((x * y) \ ((x * K(z,u)) * y)) \ 1 = (x * y) \ ((x * K(u,z)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9467,a(flip),b,9720,a),flip(a)].">
      <j1 rule="hyper" parents="58 9467 9720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9730">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) \ 1 = (x * z) \ ((x * K(u,y)) * z)
    ]]></literal>
    <justification jstring="[para(6793(a,2),9729(a,1,1))].">
      <j1 rule="para" parents="6793 9729"/>
    </justification>
  </clause>

  <clause id="9731">
    <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(9730(a,1),4945(a,1))].">
      <j1 rule="para" parents="9730 4945"/>
    </justification>
  </clause>

  <clause id="9732">
    <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(1328(a,1),7344(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1328 7344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9733">
    <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(6898(a,1),7450(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6898 7450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9734">
    <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(320,a,3332,a,b,9733,a),flip(a)].">
      <j1 rule="hyper" parents="320 3332 9733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9735">
    <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(320,a,6648,a,b,8089,a),flip(a)].">
      <j1 rule="hyper" parents="320 6648 8089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9736">
    <literal><![CDATA[
      K(x,K((1 / y) / z,(z * y) / u)) = (T(z * y,K(x,u)) / y) / z
    ]]></literal>
    <justification jstring="[hyper(8184,a,8142,a)].">
      <j1 rule="hyper" parents="8184 8142"/>
    </justification>
  </clause>

  <clause id="9737">
    <literal><![CDATA[
      K(x,K((1 / y) / z,(z * y) / u)) = K(x,K(u,(1 / y) / z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8183,a(flip),b,9736,a),flip(a)].">
      <j1 rule="hyper" parents="320 8183 9736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9738">
    <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(524(a,2),9737(a,1,2,2))].">
      <j1 rule="para" parents="524 9737"/>
    </justification>
  </clause>

  <clause id="9739">
    <literal><![CDATA[
      T((1 / ((x * y) \ x)) * K(y,z),y) = (y \ (1 / ((x * y) \ x))) * T(y,z)
    ]]></literal>
    <justification jstring="[para(6029(a,1),8256(a,2,1))].">
      <j1 rule="para" parents="6029 8256"/>
    </justification>
  </clause>

  <clause id="9740">
    <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(320,a,9651,a(flip),b,8583,a),flip(a)].">
      <j1 rule="hyper" parents="320 9651 8583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9741">
    <literal><![CDATA[
      K(L(x,y,z),(u * (w * x)) \ v5) = K(L(x,y,z),(u * (x * w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(8365,a,8653,a),flip(a)].">
      <j1 rule="hyper" parents="8365 8653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9742">
    <literal><![CDATA[
      K((x * (y * z)) \ (x * ((z * u) * y)),y) = K(L(u,y * z,x),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7046,a(flip),b,8674,a),flip(a)].">
      <j1 rule="hyper" parents="320 7046 8674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9743">
    <literal><![CDATA[
      K((x * y) \ (z \ (x * ((y * u) * z))),z) = K(L(u,z * y,x),z)
    ]]></literal>
    <justification jstring="[hyper(9316,a,9742,a)].">
      <j1 rule="hyper" parents="9316 9742"/>
    </justification>
  </clause>

  <clause id="9745">
    <literal><![CDATA[
      K(L(x,y,z),(u * (x * w)) \ v5) = K(L(x,y,z),(u * w) \ (x \ v5))
    ]]></literal>
    <justification jstring="[hyper(8365,a,8692,a),flip(a)].">
      <j1 rule="hyper" parents="8365 8692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9746">
    <literal><![CDATA[
      K(L(x,y,z),(u * (w * x)) \ v5) = K(L(x,y,z),(u * w) \ (x \ v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,9741,a,b,9745,a)].">
      <j1 rule="hyper" parents="58 9741 9745"/>
    </justification>
  </clause>

  <clause id="9747">
    <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(6744(a,1),8864(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6744 8864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9748">
    <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(7131(a,2),8868(a,1,2))].">
      <j1 rule="para" parents="7131 8868"/>
    </justification>
  </clause>

  <clause id="9749">
    <literal><![CDATA[
      x \ (K(y,z) * (K(u,y) * x)) = T(K(u,y),x) * T(K(y,z),x)
    ]]></literal>
    <justification jstring="[para(7642(a,1),8903(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7642 8903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9751">
    <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(1541(a,1),8945(a,1,2,2))].">
      <j1 rule="para" parents="1541 8945"/>
    </justification>
  </clause>

  <clause id="9752">
    <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(7754(a,1),9051(a,1,1))].">
      <j1 rule="para" parents="7754 9051"/>
    </justification>
  </clause>

  <clause id="9753">
    <literal><![CDATA[
      ((x * y) * a(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(9337(a,1),9066(a,1,1,2))].">
      <j1 rule="para" parents="9337 9066"/>
    </justification>
  </clause>

  <clause id="9754">
    <literal><![CDATA[
      (x * R(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(9093(a,1),9753(a,1,1))].">
      <j1 rule="para" parents="9093 9753"/>
    </justification>
  </clause>

  <clause id="9756">
    <literal><![CDATA[
      (x * R(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7478,a(flip),b,9754,a),flip(a)].">
      <j1 rule="hyper" parents="320 7478 9754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9758">
    <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(9756(a,2),8395(a,1))].">
      <j1 rule="para" parents="9756 8395"/>
    </justification>
  </clause>

  <clause id="9759">
    <literal><![CDATA[
      K(x,T((y \ z) / z,u)) = K(x,T(y \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,9088,a(flip),b,9107,a),flip(a)].">
      <j1 rule="hyper" parents="320 9088 9107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9760">
    <literal><![CDATA[
      T(x,T((y \ z) / z,u)) = T(x,T(y \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,9759,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 9759 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9761">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,u)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(75(a,1),9759(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="75 9759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9762">
    <literal><![CDATA[
      T(x,T((y / z) \ 1,u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(75(a,1),9760(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="75 9760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9763">
    <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(9761(a,1),9626(a,1,1))].">
      <j1 rule="para" parents="9761 9626"/>
    </justification>
  </clause>

  <clause id="9764">
    <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(6195(a,1),9762(a,2,2,1))].">
      <j1 rule="para" parents="6195 9762"/>
    </justification>
  </clause>

  <clause id="9765">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T(y \ x,u)) = K((x \ y) \ z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(9168,a,9169,a)].">
      <j1 rule="hyper" parents="9168 9169"/>
    </justification>
  </clause>

  <clause id="9766">
    <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,8253,a(flip),b,9765,a)].">
      <j1 rule="hyper" parents="58 8253 9765"/>
    </justification>
  </clause>

  <clause id="9767">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),T(z \ y,z)) = K((y \ z) \ x,y / z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7888,a(flip),b,9766,a),flip(a)].">
      <j1 rule="hyper" parents="320 7888 9766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9768">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),y / z) = K((y \ z) \ x,y / z)
    ]]></literal>
    <justification jstring="[hyper(8033,a,9767,a)].">
      <j1 rule="hyper" parents="8033 9767"/>
    </justification>
  </clause>

  <clause id="9769">
    <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(8802(a,2),9297(a,1,1))].">
      <j1 rule="para" parents="8802 9297"/>
    </justification>
  </clause>

  <clause id="9770">
    <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(5002,a,9341,a),flip(a)].">
      <j1 rule="hyper" parents="5002 9341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9771">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (y \ 1),1 / y)
    ]]></literal>
    <justification jstring="[para(3056(a,1),9395(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3056 9395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9772">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3934,a,b,9771,a),flip(a)].">
      <j1 rule="hyper" parents="320 3934 9771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9773">
    <literal><![CDATA[
      K((x / y) / (1 / y),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3934,a,b,9772,a)].">
      <j1 rule="hyper" parents="58 3934 9772"/>
    </justification>
  </clause>

  <clause id="9774">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[para(9773(a,1),4712(a,2,2))].">
      <j1 rule="para" parents="9773 4712"/>
    </justification>
  </clause>

  <clause id="9775">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ (x \ u)) = K(x,(y * (z \ x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6651,a(flip),b,9617,a),flip(a)].">
      <j1 rule="hyper" parents="58 6651 9617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9776">
    <literal><![CDATA[
      K(x,(y * (z \ x)) \ (u * x)) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(8380,a,9775,a),flip(a)].">
      <j1 rule="hyper" parents="8380 9775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9777">
    <literal><![CDATA[
      K(x,(y * ((z \ x) \ 1)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6812,a(flip),b,9776,a),flip(a)].">
      <j1 rule="hyper" parents="58 6812 9776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9778">
    <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(5481(a,1),9777(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5481 9777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9779">
    <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),9631(a,1,1,2,1))].">
      <j1 rule="para" parents="4 9631"/>
    </justification>
  </clause>

  <clause id="9780">
    <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),9632(a,1,1,2,1))].">
      <j1 rule="para" parents="4 9632"/>
    </justification>
  </clause>

  <clause id="9781">
    <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,5288,a,b,9648,a)].">
      <j1 rule="hyper" parents="58 5288 9648"/>
    </justification>
  </clause>

  <clause id="9782">
    <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,7620,a,b,9732,a)].">
      <j1 rule="hyper" parents="58 7620 9732"/>
    </justification>
  </clause>

  <clause id="9783">
    <literal><![CDATA[
      K(x / y,z) * K(K(y \ x,z) * x,x) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4462(a,1),9735(a,2,1))].">
      <j1 rule="para" parents="4462 9735"/>
    </justification>
  </clause>

  <clause id="9784">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,9783,a(flip),b,8089,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 9783 8089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9785">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(T(x,y) / y,z)
    ]]></literal>
    <justification jstring="[para(4206(a,2),9784(a,2,2,1))].">
      <j1 rule="para" parents="4206 9784"/>
    </justification>
  </clause>

  <clause id="9786">
    <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(7205,a,9748,a),flip(a)].">
      <j1 rule="hyper" parents="7205 9748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9787">
    <literal><![CDATA[
      L(a(x,T(y,z),x),T(y,z),z) = (y * z) \ ((T(x * y,x) / x) * z)
    ]]></literal>
    <justification jstring="[para(105(a,1),9751(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 9751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9788">
    <literal><![CDATA[
      L(a(x,T(y,z),x),T(y,z),z) = R(a(x,y,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,9555,a(flip),b,9787,a),flip(a)].">
      <j1 rule="hyper" parents="320 9555 9787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9789">
    <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(4775(a,1),9788(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4775 9788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9790">
    <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(5682(a,1),9752(a,1,2))].">
      <j1 rule="para" parents="5682 9752"/>
    </justification>
  </clause>

  <clause id="9791">
    <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(7804,a,9790,a)].">
      <j1 rule="hyper" parents="7804 9790"/>
    </justification>
  </clause>

  <clause id="9792">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,x) * T(z \ 1,y)) = T(z \ K(z,x),y)
    ]]></literal>
    <justification jstring="[para(8146(a,1),9791(a,1,1))].">
      <j1 rule="para" parents="8146 9791"/>
    </justification>
  </clause>

  <clause id="9793">
    <literal><![CDATA[
      K(x,T(y,z)) * T(x \ 1,z) = T(x \ K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(9132,a,9792,a)].">
      <j1 rule="hyper" parents="9132 9792"/>
    </justification>
  </clause>

  <clause id="9794">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (K(x,y) \ u)) = K(z,x) * u
    ]]></literal>
    <justification jstring="[hyper(7825,a,9769,a),flip(a)].">
      <j1 rule="hyper" parents="7825 9769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9796">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * u) = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(4(a,1),9794(a,1,2,2))].">
      <j1 rule="para" parents="4 9794"/>
    </justification>
  </clause>

  <clause id="9797">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (K(y,x) * u)) = K(z,x) * u
    ]]></literal>
    <justification jstring="[para(5092(a,1),9794(a,1,2,2))].">
      <j1 rule="para" parents="5092 9794"/>
    </justification>
  </clause>

  <clause id="9798">
    <literal><![CDATA[
      T(x,y) \ (T(x,z) * u) = K(x,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(320,a,5196,a,b,9796,a)].">
      <j1 rule="hyper" parents="320 5196 9796"/>
    </justification>
  </clause>

  <clause id="9799">
    <literal><![CDATA[
      K(x,y) * (K(x * y,x) * z) = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(320,a,9493,a(flip),b,9796,a),flip(a)].">
      <j1 rule="hyper" parents="320 9493 9796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9800">
    <literal><![CDATA[
      K(x,y) * (K(y,z) * (K(y,x) * u)) = K(y,z) * u
    ]]></literal>
    <justification jstring="[para(5095(a,1),9796(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5095 9796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9801">
    <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(6584(a,1),9796(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6584 9796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9802">
    <literal><![CDATA[
      a(x,y,x) * (K(x,x * y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(5095(a,1),9799(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5095 9799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9803">
    <literal><![CDATA[
      a(x,x \ y,x) * (K(x,y) * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),9802(a,1,2,1,2))].">
      <j1 rule="para" parents="5 9802"/>
    </justification>
  </clause>

  <clause id="9804">
    <literal><![CDATA[
      K(x,y) * (K(z,y) * u) = K(z,y) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(5109,a,9797,a)].">
      <j1 rule="hyper" parents="5109 9797"/>
    </justification>
  </clause>

  <clause id="9805">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * u) = K(x,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(5109,a,9800,a)].">
      <j1 rule="hyper" parents="5109 9800"/>
    </justification>
  </clause>

  <clause id="9806">
    <literal><![CDATA[
      K(x,y) * (K(y,T(x,z)) * u) = K(y,K(x,z)) * u
    ]]></literal>
    <justification jstring="[para(8491(a,1),9800(a,1,2))].">
      <j1 rule="para" parents="8491 9800"/>
    </justification>
  </clause>

  <clause id="9807">
    <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(9804(a,1),1627(a,1,1,1,1))].">
      <j1 rule="para" parents="9804 1627"/>
    </justification>
  </clause>

  <clause id="9808">
    <literal><![CDATA[
      K(x,y) * (K(x,K(y,z)) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(9131,a,9805,a),flip(a)].">
      <j1 rule="hyper" parents="9131 9805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9809">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(7759(a,2),9805(a,1,1))].">
      <j1 rule="para" parents="7759 9805"/>
    </justification>
  </clause>

  <clause id="9810">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(7759(a,2),9809(a,2,2,1))].">
      <j1 rule="para" parents="7759 9809"/>
    </justification>
  </clause>

  <clause id="9811">
    <literal><![CDATA[
      K(x,y) * (K(z,K(u,x)) * (K(x,y) \ w)) = K(z,K(u,x)) * w
    ]]></literal>
    <justification jstring="[hyper(342,a,9810,a),flip(a)].">
      <j1 rule="hyper" parents="342 9810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9812">
    <literal><![CDATA[
      K(x,y) * (K(z,K(x,u)) * (K(x,y) \ w)) = K(u,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(7759(a,2),9811(a,1,2,1))].">
      <j1 rule="para" parents="7759 9811"/>
    </justification>
  </clause>

  <clause id="9813">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) * y,1 / y)
    ]]></literal>
    <justification jstring="[para(5833(a,1),9774(a,2,2))].">
      <j1 rule="para" parents="5833 9774"/>
    </justification>
  </clause>

  <clause id="9814">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(5843(a,1),9813(a,2,2))].">
      <j1 rule="para" parents="5843 9813"/>
    </justification>
  </clause>

  <clause id="9815">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = K(x,1 / y) / y
    ]]></literal>
    <justification jstring="[hyper(320,a,2340,a(flip),b,9814,a),flip(a)].">
      <j1 rule="hyper" parents="320 2340 9814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9816">
    <literal><![CDATA[
      x / ((y / (x \ y)) / (1 / (x \ y))) = K(y,1 / (x \ y)) / (x \ y)
    ]]></literal>
    <justification jstring="[para(72(a,1),9815(a,1,1))].">
      <j1 rule="para" parents="72 9815"/>
    </justification>
  </clause>

  <clause id="9817">
    <literal><![CDATA[
      K(x,1 / (y \ x)) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(72(a,1),9816(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 9816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9819">
    <literal><![CDATA[
      K(x,y / x) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(5181(a,1),9817(a,1,1))].">
      <j1 rule="para" parents="5181 9817"/>
    </justification>
  </clause>

  <clause id="9820">
    <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(9819(a,2),2057(a,1,2))].">
      <j1 rule="para" parents="9819 2057"/>
    </justification>
  </clause>

  <clause id="9821">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ ((L(y,z,u) * (y \ x)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7458,a(flip),b,9782,a)].">
      <j1 rule="hyper" parents="58 7458 9782"/>
    </justification>
  </clause>

  <clause id="9822">
    <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(320,a,7439,a(flip),b,9786,a),flip(a)].">
      <j1 rule="hyper" parents="320 7439 9786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9823">
    <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(6584(a,1),9801(a,1,1))].">
      <j1 rule="para" parents="6584 9801"/>
    </justification>
  </clause>

  <clause id="9824">
    <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(7160(a,2),9822(a,2,2))].">
      <j1 rule="para" parents="7160 9822"/>
    </justification>
  </clause>

  <clause id="9825">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * (K(y,x) * z)) = T(z,T(u,K(x,y)))
    ]]></literal>
    <justification jstring="[hyper(8095,a,9824,a),flip(a)].">
      <j1 rule="hyper" parents="8095 9824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9826">
    <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(5095(a,1),9825(a,1,2,2))].">
      <j1 rule="para" parents="5095 9825"/>
    </justification>
  </clause>

  <clause id="9827">
    <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(7998(a,1),9826(a,1,2))].">
      <j1 rule="para" parents="7998 9826"/>
    </justification>
  </clause>

  <clause id="9828">
    <literal><![CDATA[
      K((x \ y) \ z,L(x,u,w)) = K(y \ (x * z),L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(5761,a,7447,a),flip(a)].">
      <j1 rule="hyper" parents="5761 7447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9829">
    <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(7447(a,1),5761(a,1))].">
      <j1 rule="para" parents="7447 5761"/>
    </justification>
  </clause>

  <clause id="9830">
    <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,7336,a(flip),b,7552,a)].">
      <j1 rule="hyper" parents="58 7336 7552"/>
    </justification>
  </clause>

  <clause id="9832">
    <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,5339,a(flip),b,9830,a),flip(a)].">
      <j1 rule="hyper" parents="58 5339 9830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9833">
    <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(7884(a,1),9832(a,1,2))].">
      <j1 rule="para" parents="7884 9832"/>
    </justification>
  </clause>

  <clause id="9834">
    <literal><![CDATA[
      K((x * y) \ z,L(y,u,w)) = K(x \ (y \ z),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(5761,a,7574,a),flip(a)].">
      <j1 rule="hyper" parents="5761 7574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9835">
    <literal><![CDATA[
      K(L(x,y,z),u * (K(x,w) * v5)) = K(L(x,y,z),u * v5)
    ]]></literal>
    <justification jstring="[hyper(320,a,5484,a(flip),b,7610,a),flip(a)].">
      <j1 rule="hyper" parents="320 5484 7610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9836">
    <literal><![CDATA[
      K(x * (K(y,z) * u),R(y,w,v5)) = K(x * u,R(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,5485,a(flip),b,7611,a),flip(a)].">
      <j1 rule="hyper" parents="320 5485 7611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9837">
    <literal><![CDATA[
      K(x * y,R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(4806(a,1),9836(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4806 9836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9838">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(7817(a,1),8316(a,1,1,3))].">
      <j1 rule="para" parents="7817 8316"/>
    </justification>
  </clause>

  <clause id="9839">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5092(a,1),9838(a,2,2))].">
      <j1 rule="para" parents="5092 9838"/>
    </justification>
  </clause>

  <clause id="9840">
    <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,6563,a(flip),b,8467,a)].">
      <j1 rule="hyper" parents="58 6563 8467"/>
    </justification>
  </clause>

  <clause id="9841">
    <literal><![CDATA[
      K(x,(y * (z * (u / x))) \ w) = K(x,(y * (z * u)) \ (w * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,9469,a(flip),b,8696,a),flip(a)].">
      <j1 rule="hyper" parents="58 9469 8696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9842">
    <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(7806,a,9047,a)].">
      <j1 rule="hyper" parents="7806 9047"/>
    </justification>
  </clause>

  <clause id="9843">
    <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(8070(a,1),9076(a,1,1))].">
      <j1 rule="para" parents="8070 9076"/>
    </justification>
  </clause>

  <clause id="9844">
    <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(1303(a,1),9438(a,1,2,1))].">
      <j1 rule="para" parents="1303 9438"/>
    </justification>
  </clause>

  <clause id="9845">
    <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(7392(a,1),9560(a,1,1,2))].">
      <j1 rule="para" parents="7392 9560"/>
    </justification>
  </clause>

  <clause id="9846">
    <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,5339,a(flip),b,9845,a),flip(a)].">
      <j1 rule="hyper" parents="58 5339 9845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9848">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = T(y,K(x,z)) / y
    ]]></literal>
    <justification jstring="[hyper(320,a,153,a(flip),b,9590,a),flip(a)].">
      <j1 rule="hyper" parents="320 153 9590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9849">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,4703,a,b,9848,a),flip(a)].">
      <j1 rule="hyper" parents="320 4703 9848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9851">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7754,a,b,9849,a),flip(a)].">
      <j1 rule="hyper" parents="320 7754 9849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9852">
    <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),9724(a,2,2,1,1))].">
      <j1 rule="para" parents="4 9724"/>
    </justification>
  </clause>

  <clause id="9853">
    <literal><![CDATA[
      ((x * y) * (K(y,x) * z)) / ((x * y) * z) = L(K(y,x),z,x * y)
    ]]></literal>
    <justification jstring="[hyper(131,a,9852,a)].">
      <j1 rule="hyper" parents="131 9852"/>
    </justification>
  </clause>

  <clause id="9854">
    <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(9852(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9852 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9856">
    <literal><![CDATA[
      ((x * y) * (K(y,x) * z)) / (z * T(x * y,z)) = L(K(y,x),z,x * y)
    ]]></literal>
    <justification jstring="[para(105(a,2),9853(a,1,2))].">
      <j1 rule="para" parents="105 9853"/>
    </justification>
  </clause>

  <clause id="9857">
    <literal><![CDATA[
      ((K(x,y) * z) * T(y * x,z)) / (z * T(y * x,z)) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[para(8747(a,2),9856(a,1,1))].">
      <j1 rule="para" parents="8747 9856"/>
    </justification>
  </clause>

  <clause id="9858">
    <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(9710(a,2),9854(a,1))].">
      <j1 rule="para" parents="9710 9854"/>
    </justification>
  </clause>

  <clause id="9859">
    <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(9842(a,1),7806(a,1))].">
      <j1 rule="para" parents="9842 7806"/>
    </justification>
  </clause>

  <clause id="9860">
    <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(7929(a,1),9843(a,1,1,2,1))].">
      <j1 rule="para" parents="7929 9843"/>
    </justification>
  </clause>

  <clause id="9861">
    <literal><![CDATA[
      K(x,T(R(y,z,u) * (y \ x),y)) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(172(a,1),9844(a,1,2,2))].">
      <j1 rule="para" parents="172 9844"/>
    </justification>
  </clause>

  <clause id="9862">
    <literal><![CDATA[
      L(K(x,y),z,y * x) != u
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),z,T(y * x,z)) = u
    ]]></literal>
    <justification jstring="[para(9857(a,1),518(a,1))].">
      <j1 rule="para" parents="9857 518"/>
    </justification>
  </clause>

  <clause id="9863">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,1945,a(flip),b,4657,a),flip(a)].">
      <j1 rule="hyper" parents="320 1945 4657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9864">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,4404,a(flip),b,9863,a),flip(a)].">
      <j1 rule="hyper" parents="320 4404 9863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9865">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,y) \ y) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[para(7645(a,1),9864(a,1,2))].">
      <j1 rule="para" parents="7645 9864"/>
    </justification>
  </clause>

  <clause id="9866">
    <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(9865(a,1),717(a,1,2))].">
      <j1 rule="para" parents="9865 717"/>
    </justification>
  </clause>

  <clause id="9867">
    <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(5579(a,1),4940(a,1,2,1))].">
      <j1 rule="para" parents="5579 4940"/>
    </justification>
  </clause>

  <clause id="9868">
    <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(8415,a,9867,a)].">
      <j1 rule="hyper" parents="8415 9867"/>
    </justification>
  </clause>

  <clause id="9869">
    <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(7131(a,2),9868(a,1,2,1))].">
      <j1 rule="para" parents="7131 9868"/>
    </justification>
  </clause>

  <clause id="9870">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,K(u,z)) = y \ (y * x)
    ]]></literal>
    <justification jstring="[para(5095(a,1),5127(a,2,2))].">
      <j1 rule="para" parents="5095 5127"/>
    </justification>
  </clause>

  <clause id="9871">
    <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(9870(a,2),287(a,1))].">
      <j1 rule="para" parents="9870 287"/>
    </justification>
  </clause>

  <clause id="9873">
    <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(238(a,1),5202(a,1,2)),flip(a)].">
      <j1 rule="para" parents="238 5202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9874">
    <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(4929(a,1),9873(a,1,1,2,1))].">
      <j1 rule="para" parents="4929 9873"/>
    </justification>
  </clause>

  <clause id="9875">
    <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(237(a,1),5203(a,1,2)),flip(a)].">
      <j1 rule="para" parents="237 5203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9876">
    <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(4929(a,1),9875(a,1,1,2,1))].">
      <j1 rule="para" parents="4929 9875"/>
    </justification>
  </clause>

  <clause id="9877">
    <literal><![CDATA[
      K(x,y) * (L(K(y,x),z,u) * w) = a(u,z,K(x,y)) * w
    ]]></literal>
    <justification jstring="[para(5861(a,1),9876(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5861 9876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9878">
    <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,9823,a,b,9877,a)].">
      <j1 rule="hyper" parents="58 9823 9877"/>
    </justification>
  </clause>

  <clause id="9879">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (L(K(z,u),y,x) * w) = K(z,u) * w
    ]]></literal>
    <justification jstring="[para(5860(a,1),9877(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5860 9877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9880">
    <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,5095,a(flip),b,9879,a),flip(a)].">
      <j1 rule="hyper" parents="116 5095 9879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9881">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = a(x,y,K(u,z)) * w
    ]]></literal>
    <justification jstring="[hyper(58,a,9878,a(flip),b,9880,a),flip(a)].">
      <j1 rule="hyper" parents="58 9878 9880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9882">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * x) = a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(575,a,9881,a)].">
      <j1 rule="hyper" parents="575 9881"/>
    </justification>
  </clause>

  <clause id="9883">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ K(w,u) = K(w,u) * a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7381,a,b,9881,a),flip(a)].">
      <j1 rule="hyper" parents="320 7381 9881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9884">
    <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,6816,a(flip),b,9881,a)].">
      <j1 rule="hyper" parents="119 6816 9881"/>
    </justification>
  </clause>

  <clause id="9885">
    <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(9883(a,2),38(a,1))].">
      <j1 rule="para" parents="9883 38"/>
    </justification>
  </clause>

  <clause id="9886">
    <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(5783(a,1),5686(a,1,2,2,1,2))].">
      <j1 rule="para" parents="5783 5686"/>
    </justification>
  </clause>

  <clause id="9887">
    <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(3537(a,1),5755(a,1,1))].">
      <j1 rule="para" parents="3537 5755"/>
    </justification>
  </clause>

  <clause id="9888">
    <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(3955(a,1),9887(a,1,1,1))].">
      <j1 rule="para" parents="3955 9887"/>
    </justification>
  </clause>

  <clause id="9889">
    <literal><![CDATA[
      (T(x * (y \ 1),x) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(5383(a,1),5878(a,1,1,1))].">
      <j1 rule="para" parents="5383 5878"/>
    </justification>
  </clause>

  <clause id="9890">
    <literal><![CDATA[
      (x \ R(x,y \ 1,x)) / (T(x * (y \ 1),x) / x) = y
    ]]></literal>
    <justification jstring="[hyper(117,a,8705,a(flip),b,9889,a(flip))].">
      <j1 rule="hyper" parents="117 8705 9889"/>
    </justification>
  </clause>

  <clause id="9891">
    <literal><![CDATA[
      x * T(K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      w * T(K(z,y),u) = x
    ]]></literal>
    <justification jstring="[para(8902(a,1),6824(a,1)),flip(a)].">
      <j1 rule="para" parents="8902 6824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9892">
    <literal><![CDATA[
      K(x,y * (((z * K(u,z)) * u) * w)) = K(x,y * ((u * (1 / (1 / z))) * w))
    ]]></literal>
    <justification jstring="[para(5232(a,1),6826(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5232 6826"/>
    </justification>
  </clause>

  <clause id="9893">
    <literal><![CDATA[
      K(x,y * ((z * (1 / (1 / u))) * w)) = K(x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[para(4733(a,1),9892(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4733 9892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9894">
    <literal><![CDATA[
      ((x \ y) \ y) \ R((x \ y) \ y,z,u) = x \ (y \ ((R(x,z,u) * (x \ y)) * x))
    ]]></literal>
    <justification jstring="[hyper(1177,a,6843,a)].">
      <j1 rule="hyper" parents="1177 6843"/>
    </justification>
  </clause>

  <clause id="9895">
    <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(7863(a,1),7909(a,1,2,2,1))].">
      <j1 rule="para" parents="7863 7909"/>
    </justification>
  </clause>

  <clause id="9897">
    <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,8272,a(flip),b,8274,a),flip(a)].">
      <j1 rule="hyper" parents="58 8272 8274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9898">
    <literal><![CDATA[
      x \ (T((y * x) / y,K(z,u)) * w) = x * (T(T(x,K(z,u)),y) \ w)
    ]]></literal>
    <justification jstring="[para(460(a,1),9897(a,1,2,1))].">
      <j1 rule="para" parents="460 9897"/>
    </justification>
  </clause>

  <clause id="9899">
    <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,7980,a(flip),b,9898,a)].">
      <j1 rule="hyper" parents="58 7980 9898"/>
    </justification>
  </clause>

  <clause id="9900">
    <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(7131(a,2),9899(a,1,2,1,2))].">
      <j1 rule="para" parents="7131 9899"/>
    </justification>
  </clause>

  <clause id="9901">
    <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,3757,a(flip),b,8297,a)].">
      <j1 rule="hyper" parents="58 3757 8297"/>
    </justification>
  </clause>

  <clause id="9902">
    <literal><![CDATA[
      T(x,y / (((z \ 1) \ 1) \ u)) = T(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(8413,a,9901,a),flip(a)].">
      <j1 rule="hyper" parents="8413 9901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9903">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ y) * K(x,K(y,z \ u)) = K(x,y / ((y \ z) \ u))
    ]]></literal>
    <justification jstring="[para(9276(a,1),8355(a,1,2))].">
      <j1 rule="para" parents="9276 8355"/>
    </justification>
  </clause>

  <clause id="9904">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((y \ z) \ u)) = K(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(9276(a,1),8362(a,1,1))].">
      <j1 rule="para" parents="9276 8362"/>
    </justification>
  </clause>

  <clause id="9905">
    <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,8520,a),flip(a)].">
      <j1 rule="hyper" parents="120 8520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9906">
    <literal><![CDATA[
      T((x \ 1) * y,K(z,T(u,x \ y))) = T((x \ 1) * y,K(z,u))
    ]]></literal>
    <justification jstring="[para(3750(a,1),9905(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3750 9905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9907">
    <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(5947,a,9906,a)].">
      <j1 rule="hyper" parents="5947 9906"/>
    </justification>
  </clause>

  <clause id="9908">
    <literal><![CDATA[
      K(T(x,((y \ 1) / ((1 / (y \ 1)) \ z)) \ 1),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,8662,a(flip),b,8663,a),flip(a)].">
      <j1 rule="hyper" parents="320 8662 8663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9910">
    <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),9908(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="72 9908"/>
    </justification>
  </clause>

  <clause id="9912">
    <literal><![CDATA[
      K(T(x,(y \ 1) \ (y \ z)),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,7655,a(flip),b,9910,a)].">
      <j1 rule="hyper" parents="58 7655 9910"/>
    </justification>
  </clause>

  <clause id="9913">
    <literal><![CDATA[
      K(T(x,y \ z),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(8233,a,9912,a)].">
      <j1 rule="hyper" parents="8233 9912"/>
    </justification>
  </clause>

  <clause id="9914">
    <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(320,a,7300,a(flip),b,8718,a),flip(a)].">
      <j1 rule="hyper" parents="320 7300 8718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9916">
    <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(5651(a,1),8809(a,1,1,2))].">
      <j1 rule="para" parents="5651 8809"/>
    </justification>
  </clause>

  <clause id="9917">
    <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(4577,a,9916,a),flip(a)].">
      <j1 rule="hyper" parents="4577 9916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9918">
    <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(5858(a,1),9917(a,1,1))].">
      <j1 rule="para" parents="5858 9917"/>
    </justification>
  </clause>

  <clause id="9919">
    <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(320,a,5858,a(flip),b,9918,a),flip(a)].">
      <j1 rule="hyper" parents="320 5858 9918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9920">
    <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(320,a,236,a(flip),b,9919,a),flip(a)].">
      <j1 rule="hyper" parents="320 236 9919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9921">
    <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,8250,a(flip),b,8871,a)].">
      <j1 rule="hyper" parents="58 8250 8871"/>
    </justification>
  </clause>

  <clause id="9922">
    <literal><![CDATA[
      K(x,L(y,z * K(y,u),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,8810,a(flip),b,8891,a),flip(a)].">
      <j1 rule="hyper" parents="320 8810 8891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9923">
    <literal><![CDATA[
      K(x,L(y,K(y,z) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(7152(a,1),9922(a,1,2,2))].">
      <j1 rule="para" parents="7152 9922"/>
    </justification>
  </clause>

  <clause id="9924">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,8997,a,b,9923,a)].">
      <j1 rule="hyper" parents="58 8997 9923"/>
    </justification>
  </clause>

  <clause id="9926">
    <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(8880(a,1),9924(a,1,1))].">
      <j1 rule="para" parents="8880 9924"/>
    </justification>
  </clause>

  <clause id="9927">
    <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(238(a,1),9087(a,2,1))].">
      <j1 rule="para" parents="238 9087"/>
    </justification>
  </clause>

  <clause id="9928">
    <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,9030,a(flip),b,9927,a),flip(a)].">
      <j1 rule="hyper" parents="58 9030 9927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9929">
    <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(1646(a,1),9150(a,1,2))].">
      <j1 rule="para" parents="1646 9150"/>
    </justification>
  </clause>

  <clause id="9930">
    <literal><![CDATA[
      x \ R(x,y,L(x,z,u)) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(691,a,9929,a),flip(a)].">
      <j1 rule="hyper" parents="691 9929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9931">
    <literal><![CDATA[
      K(x * L(y,z,u),y) * K(y,x) = a(y,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9151,a,9930,a)].">
      <j1 rule="hyper" parents="9151 9930"/>
    </justification>
  </clause>

  <clause id="9932">
    <literal><![CDATA[
      K(x,y) * K(y * L(x,z,u),x) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(8719,a,9930,a)].">
      <j1 rule="hyper" parents="8719 9930"/>
    </justification>
  </clause>

  <clause id="9933">
    <literal><![CDATA[
      K(x,y) * a(y,x,L(y,z,u)) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(9930(a,1),9149(a,1,2))].">
      <j1 rule="para" parents="9930 9149"/>
    </justification>
  </clause>

  <clause id="9934">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) * K(x,u) = a(x,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(7405(a,2),9931(a,1,1))].">
      <j1 rule="para" parents="7405 9931"/>
    </justification>
  </clause>

  <clause id="9935">
    <literal><![CDATA[
      K(x,y) * K(y,x * L(y,z,u)) = a(y,x,L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(9932(a,1),8985(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9932 8985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9936">
    <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(9933(a,1),38(a,1))].">
      <j1 rule="para" parents="9933 38"/>
    </justification>
  </clause>

  <clause id="9937">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) \ x = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9478,a(flip),b,9934,a)].">
      <j1 rule="hyper" parents="58 9478 9934"/>
    </justification>
  </clause>

  <clause id="9938">
    <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(9937(a,1),6802(a,1,1,1))].">
      <j1 rule="para" parents="9937 6802"/>
    </justification>
  </clause>

  <clause id="9939">
    <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(1882(a,1),9152(a,1,2))].">
      <j1 rule="para" parents="1882 9152"/>
    </justification>
  </clause>

  <clause id="9940">
    <literal><![CDATA[
      x * a(x,y,R(x,z,u)) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(693,a,9939,a)].">
      <j1 rule="hyper" parents="693 9939"/>
    </justification>
  </clause>

  <clause id="9941">
    <literal><![CDATA[
      x \ R(x,y,R(x,z,u)) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(691,a,9939,a),flip(a)].">
      <j1 rule="hyper" parents="691 9939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9942">
    <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(9939(a,1),691(a,1))].">
      <j1 rule="para" parents="9939 691"/>
    </justification>
  </clause>

  <clause id="9943">
    <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,9833,a,b,9940,a)].">
      <j1 rule="hyper" parents="116 9833 9940"/>
    </justification>
  </clause>

  <clause id="9944">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,x) = a(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9153,a,9941,a)].">
      <j1 rule="hyper" parents="9153 9941"/>
    </justification>
  </clause>

  <clause id="9945">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) \ x = a(x,y,R(x,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(9941(a,1),6733(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9941 6733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9946">
    <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(9941(a,1),9086(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9941 9086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9947">
    <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(4624(a,1),9945(a,2,1))].">
      <j1 rule="para" parents="4624 9945"/>
    </justification>
  </clause>

  <clause id="9948">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) * K(x,y * R(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(9944(a,1),6312(a,1,1))].">
      <j1 rule="para" parents="9944 6312"/>
    </justification>
  </clause>

  <clause id="9949">
    <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(7409(a,1),9944(a,1,1))].">
      <j1 rule="para" parents="7409 9944"/>
    </justification>
  </clause>

  <clause id="9950">
    <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(9944(a,1),8572(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9944 8572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9951">
    <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),9948(a,1,2,2))].">
      <j1 rule="para" parents="7 9948"/>
    </justification>
  </clause>

  <clause id="9952">
    <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(5186,a,9946,a)].">
      <j1 rule="hyper" parents="5186 9946"/>
    </justification>
  </clause>

  <clause id="9953">
    <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(5043,a,9946,a)].">
      <j1 rule="hyper" parents="5043 9946"/>
    </justification>
  </clause>

  <clause id="9954">
    <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(9953(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9953 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9955">
    <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(872(a,1),9954(a,1))].">
      <j1 rule="para" parents="872 9954"/>
    </justification>
  </clause>

  <clause id="9956">
    <literal><![CDATA[
      ((1 / x) * T((1 / x) \ K(y,z),y)) * u = K(y,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(1587,a,9440,a)].">
      <j1 rule="hyper" parents="1587 9440"/>
    </justification>
  </clause>

  <clause id="9957">
    <literal><![CDATA[
      (K(x,y) * K((1 / z) \ 1,x)) * u = K(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(8260(a,2),9956(a,1,1))].">
      <j1 rule="para" parents="8260 9956"/>
    </justification>
  </clause>

  <clause id="9958">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(75(a,1),9957(a,1,1,2,1))].">
      <j1 rule="para" parents="75 9957"/>
    </justification>
  </clause>

  <clause id="9959">
    <literal><![CDATA[
      L(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,9958,a)].">
      <j1 rule="hyper" parents="479 9958"/>
    </justification>
  </clause>

  <clause id="9960">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(320,a,9796,a(flip),b,9958,a),flip(a)].">
      <j1 rule="hyper" parents="320 9796 9958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9961">
    <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(9958(a,1),288(a,1,2))].">
      <j1 rule="para" parents="9958 288"/>
    </justification>
  </clause>

  <clause id="9963">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(y,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(1991(a,1),9958(a,1,1))].">
      <j1 rule="para" parents="1991 9958"/>
    </justification>
  </clause>

  <clause id="9964">
    <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(9958(a,1),6904(a,1,2))].">
      <j1 rule="para" parents="9958 6904"/>
    </justification>
  </clause>

  <clause id="9967">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ u = K(x,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5732,a(flip),b,9959,a)].">
      <j1 rule="hyper" parents="58 5732 9959"/>
    </justification>
  </clause>

  <clause id="9969">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),K(z,w)) = x
    ]]></literal>
    <justification jstring="[para(7133(a,1),9959(a,1,2))].">
      <j1 rule="para" parents="7133 9959"/>
    </justification>
  </clause>

  <clause id="9970">
    <literal><![CDATA[
      (K(x,y) * K(z,T(x,u))) * w = K(x,y) * (K(z,T(x,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(1330,a,9969,a),flip(a)].">
      <j1 rule="hyper" parents="1330 9969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9971">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(x,y) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(1991(a,1),9960(a,1,1))].">
      <j1 rule="para" parents="1991 9960"/>
    </justification>
  </clause>

  <clause id="9972">
    <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(4725,a,9963,a),flip(a)].">
      <j1 rule="hyper" parents="4725 9963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9973">
    <literal><![CDATA[
      (K(x,y) * z) / (K(u,y) * z) = K(x,y) * K(y,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,9797,a(flip),b,9963,a)].">
      <j1 rule="hyper" parents="117 9797 9963"/>
    </justification>
  </clause>

  <clause id="9974">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) \ u = K(y,x) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(1991(a,1),9967(a,1,1))].">
      <j1 rule="para" parents="1991 9967"/>
    </justification>
  </clause>

  <clause id="9975">
    <literal><![CDATA[
      R(K(x,y),K(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3450,a,9971,a)].">
      <j1 rule="hyper" parents="3450 9971"/>
    </justification>
  </clause>

  <clause id="9976">
    <literal><![CDATA[
      L(x,K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,9971,a)].">
      <j1 rule="hyper" parents="479 9971"/>
    </justification>
  </clause>

  <clause id="9977">
    <literal><![CDATA[
      (K(x,y) * z) / (K(x,u) * z) = K(u,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,9800,a(flip),b,9971,a)].">
      <j1 rule="hyper" parents="117 9800 9971"/>
    </justification>
  </clause>

  <clause id="9978">
    <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,9971,a(flip),b,4733,a)].">
      <j1 rule="hyper" parents="117 9971 4733"/>
    </justification>
  </clause>

  <clause id="9979">
    <literal><![CDATA[
      K(x,y) * (K(y,x * y) * z) = (y \ L(y,x,y)) * z
    ]]></literal>
    <justification jstring="[para(5463(a,1),9971(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5463 9971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9983">
    <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(9975(a,1),3574(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9975 3574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9984">
    <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(7872(a,1),9973(a,1,1))].">
      <j1 rule="para" parents="7872 9973"/>
    </justification>
  </clause>

  <clause id="9985">
    <literal><![CDATA[
      (K(x,T(y,z)) * K(y,u)) \ w = K(y,T(x,z)) * (K(u,y) * w)
    ]]></literal>
    <justification jstring="[para(7133(a,1),9974(a,1,1,1))].">
      <j1 rule="para" parents="7133 9974"/>
    </justification>
  </clause>

  <clause id="9986">
    <literal><![CDATA[
      x / (K(y \ x,z) * (y * (x / y))) = K(z,y \ x) * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4676(a,1),9977(a,1,1))].">
      <j1 rule="para" parents="4676 9977"/>
    </justification>
  </clause>

  <clause id="9987">
    <literal><![CDATA[
      (x \ L(x,y,x)) * z = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,9547,a(flip),b,9979,a),flip(a)].">
      <j1 rule="hyper" parents="58 9547 9979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9988">
    <literal><![CDATA[
      (x \ L(x,y,x)) \ z = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,9507,a(flip),b,9987,a)].">
      <j1 rule="hyper" parents="116 9507 9987"/>
    </justification>
  </clause>

  <clause id="9989">
    <literal><![CDATA[
      (R(x,y,x) \ x) * z = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[para(5741(a,2),9987(a,1,1))].">
      <j1 rule="para" parents="5741 9987"/>
    </justification>
  </clause>

  <clause id="9990">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ z = (R(x,y,x) \ x) * z
    ]]></literal>
    <justification jstring="[para(8913(a,2),9989(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8913 9989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9991">
    <literal><![CDATA[
      (R(x,y,x) \ x) * (K(x * y,x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,9551,a(flip),b,9990,a),flip(a)].">
      <j1 rule="hyper" parents="58 9551 9990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9992">
    <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(9749(a,1),9961(a,1))].">
      <j1 rule="para" parents="9749 9961"/>
    </justification>
  </clause>

  <clause id="9993">
    <literal><![CDATA[
      R(K(x,y),K(z,y),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5112,a,9964,a),flip(a)].">
      <j1 rule="hyper" parents="5112 9964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9995">
    <literal><![CDATA[
      (x * K(y,z)) / (x * K(u,z)) = K(y,T(z,x)) * K(T(z,x),u)
    ]]></literal>
    <justification jstring="[para(7872(a,1),9984(a,1,2))].">
      <j1 rule="para" parents="7872 9984"/>
    </justification>
  </clause>

  <clause id="9996">
    <literal><![CDATA[
      (x * K(y,z)) / (x * K(u,z)) = K(y,T(z,x)) * K(z,T(u,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,7172,a(flip),b,9995,a),flip(a)].">
      <j1 rule="hyper" parents="320 7172 9995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9997">
    <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(215(a,2),9986(a,1,2,2,2))].">
      <j1 rule="para" parents="215 9986"/>
    </justification>
  </clause>

  <clause id="9998">
    <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,9827,a(flip),b,9972,a)].">
      <j1 rule="hyper" parents="58 9827 9972"/>
    </justification>
  </clause>

  <clause id="9999">
    <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(4775(a,1),9789(a,2,2))].">
      <j1 rule="para" parents="4775 9789"/>
    </justification>
  </clause>

  <clause id="10000">
    <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(9846(a,1),9894(a,2,2,2,1,1))].">
      <j1 rule="para" parents="9846 9894"/>
    </justification>
  </clause>

  <clause id="10001">
    <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(9942,a,9943,a)].">
      <j1 rule="hyper" parents="9942 9943"/>
    </justification>
  </clause>

  <clause id="10002">
    <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(9833(a,1),9947(a,1,1))].">
      <j1 rule="para" parents="9833 9947"/>
    </justification>
  </clause>

  <clause id="10003">
    <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(8980,a,9978,a)].">
      <j1 rule="hyper" parents="8980 9978"/>
    </justification>
  </clause>

  <clause id="10004">
    <literal><![CDATA[
      T(x,R(x * K(y,x),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(328,a,4466,a),flip(a)].">
      <j1 rule="hyper" parents="328 4466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10006">
    <literal><![CDATA[
      T(x \ y,R(y / x,z,u)) = x \ y
    ]]></literal>
    <justification jstring="[para(4735(a,1),10004(a,1,2,1))].">
      <j1 rule="para" parents="4735 10004"/>
    </justification>
  </clause>

  <clause id="10007">
    <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(10006(a,1),7168(a,1,2))].">
      <j1 rule="para" parents="10006 7168"/>
    </justification>
  </clause>

  <clause id="10008">
    <literal><![CDATA[
      ((x * (y * ((x \ (z / u)) / y))) * u) / z = K(y,z / ((x * y) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6917,a(flip),b,5726,a),flip(a)].">
      <j1 rule="hyper" parents="58 6917 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10009">
    <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(3581(a,1),5847(a,1,2,1,1))].">
      <j1 rule="para" parents="3581 5847"/>
    </justification>
  </clause>

  <clause id="10010">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(R(x,y,z),u) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3298(a,1),10009(a,1,2))].">
      <j1 rule="para" parents="3298 10009"/>
    </justification>
  </clause>

  <clause id="10011">
    <literal><![CDATA[
      R(K(x,y),R(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5903,a,6016,a)].">
      <j1 rule="hyper" parents="5903 6016"/>
    </justification>
  </clause>

  <clause id="10012">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) = (v5 * K(y,x)) \ v5
    ]]></literal>
    <justification jstring="[para(10011(a,1),6926(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10011 6926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10013">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(10012(a,2),6316(a,1))].">
      <j1 rule="para" parents="10012 6316"/>
    </justification>
  </clause>

  <clause id="10014">
    <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(6918(a,1),10013(a,1))].">
      <j1 rule="para" parents="6918 10013"/>
    </justification>
  </clause>

  <clause id="10015">
    <literal><![CDATA[
      ((x * T(x \ (y / z),y / z)) * z) / y = K(x \ (y / z),(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(5456,a,5907,a),flip(a)].">
      <j1 rule="hyper" parents="5456 5907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10016">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),z / y))) / z = K(x \ (z / y),(y / z) \ 1)
    ]]></literal>
    <justification jstring="[para(1566(a,1),10015(a,1,1))].">
      <j1 rule="para" parents="1566 10015"/>
    </justification>
  </clause>

  <clause id="10017">
    <literal><![CDATA[
      K(((x * y) / z) \ 1,z / y) = K(x \ (z / y),(y / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5491,a(flip),b,10016,a)].">
      <j1 rule="hyper" parents="58 5491 10016"/>
    </justification>
  </clause>

  <clause id="10018">
    <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(1753(a,2),6822(a,1,2))].">
      <j1 rule="para" parents="1753 6822"/>
    </justification>
  </clause>

  <clause id="10019">
    <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(7133(a,1),7965(a,2,1,2))].">
      <j1 rule="para" parents="7133 7965"/>
    </justification>
  </clause>

  <clause id="10020">
    <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(5103(a,1),8063(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5103 8063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10021">
    <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(10020(a,2),7721(a,1))].">
      <j1 rule="para" parents="10020 7721"/>
    </justification>
  </clause>

  <clause id="10022">
    <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(8659(a,1),4987(a,1))].">
      <j1 rule="para" parents="8659 4987"/>
    </justification>
  </clause>

  <clause id="10023">
    <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(4193(a,1),8951(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4193 8951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10024">
    <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(9959(a,1),8965(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9959 8965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10025">
    <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(1991(a,1),10024(a,1,2,2))].">
      <j1 rule="para" parents="1991 10024"/>
    </justification>
  </clause>

  <clause id="10026">
    <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(10025(a,1),6358(a,1,1))].">
      <j1 rule="para" parents="10025 6358"/>
    </justification>
  </clause>

  <clause id="10027">
    <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(6425(a,1),10026(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6425 10026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10028">
    <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),9005(a,1,1,2))].">
      <j1 rule="para" parents="22 9005"/>
    </justification>
  </clause>

  <clause id="10029">
    <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(7759(a,2),9128(a,1,2,1))].">
      <j1 rule="para" parents="7759 9128"/>
    </justification>
  </clause>

  <clause id="10030">
    <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(7131(a,2),9382(a,2,2,1))].">
      <j1 rule="para" parents="7131 9382"/>
    </justification>
  </clause>

  <clause id="10031">
    <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(4992,a,9434,a),flip(a)].">
      <j1 rule="hyper" parents="4992 9434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10032">
    <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(9512(a,1),9518(a,1))].">
      <j1 rule="para" parents="9512 9518"/>
    </justification>
  </clause>

  <clause id="10033">
    <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(9582(a,2),8036(a,1))].">
      <j1 rule="para" parents="9582 8036"/>
    </justification>
  </clause>

  <clause id="10034">
    <literal><![CDATA[
      L(K(x * y,T(y,z * x)),x,z) = K(z \ (y * (z * x)),T(y,z * x))
    ]]></literal>
    <justification jstring="[para(7546(a,1),9640(a,1,1))].">
      <j1 rule="para" parents="7546 9640"/>
    </justification>
  </clause>

  <clause id="10036">
    <literal><![CDATA[
      K(x \ (y * (x * z)),T(y,x * z)) = L(K(y * z,T(y,x)),z,x)
    ]]></literal>
    <justification jstring="[para(9575(a,1),10034(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9575 10034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10037">
    <literal><![CDATA[
      L(K(x * y,T(x,z)),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((z / (z * y)) \ x,x) = u
    ]]></literal>
    <justification jstring="[para(10036(a,1),8301(a,1))].">
      <j1 rule="para" parents="10036 8301"/>
    </justification>
  </clause>

  <clause id="10038">
    <literal><![CDATA[
      L(K(x * y,T(y,z)),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((z / (z * x)) \ y,y) = u
    ]]></literal>
    <justification jstring="[para(5857(a,2),10037(a,1,1))].">
      <j1 rule="para" parents="5857 10037"/>
    </justification>
  </clause>

  <clause id="10039">
    <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(7146(a,1),9949(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7146 9949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10040">
    <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(320,a,9944,a(flip),b,10039,a),flip(a)].">
      <j1 rule="hyper" parents="320 9944 10039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10042">
    <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),10040(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 10040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10043">
    <literal><![CDATA[
      a(x,T(y,x),R(x,z,u)) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(379(a,1),10040(a,1,2,2))].">
      <j1 rule="para" parents="379 10040"/>
    </justification>
  </clause>

  <clause id="10044">
    <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(10042(a,1),9951(a,1,1))].">
      <j1 rule="para" parents="10042 9951"/>
    </justification>
  </clause>

  <clause id="10045">
    <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(320,a,7209,a(flip),b,10044,a),flip(a)].">
      <j1 rule="hyper" parents="320 7209 10044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10046">
    <literal><![CDATA[
      x * (y * (z \ T(z * (y \ (z \ 1)),z))) = (x * K(y \ 1,z)) * (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(286,a,10018,a)].">
      <j1 rule="hyper" parents="286 10018"/>
    </justification>
  </clause>

  <clause id="10047">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * (z \ 1) = x * (K(y \ 1,z) * (z \ 1))
    ]]></literal>
    <justification jstring="[para(5683(a,1),10046(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5683 10046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10048">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * (z \ 1) = x * (T(z,y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(5093(a,1),10047(a,2,2))].">
      <j1 rule="para" parents="5093 10047"/>
    </justification>
  </clause>

  <clause id="10049">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (T(z,(1 / y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),10048(a,1,1,2,1))].">
      <j1 rule="para" parents="75 10048"/>
    </justification>
  </clause>

  <clause id="10050">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (T(z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),10049(a,2,2,1,2))].">
      <j1 rule="para" parents="75 10049"/>
    </justification>
  </clause>

  <clause id="10051">
    <literal><![CDATA[
      x \ T(x * (y \ 1),y) = T(y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(6546,a,10050,a)].">
      <j1 rule="hyper" parents="6546 10050"/>
    </justification>
  </clause>

  <clause id="10052">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (z \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,4916,a(flip),b,10050,a),flip(a)].">
      <j1 rule="hyper" parents="320 4916 10050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10053">
    <literal><![CDATA[
      (x * (y \ 1)) \ (x * (T(y,z) \ 1)) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,10050,a(flip),b,6766,a(flip))].">
      <j1 rule="hyper" parents="116 10050 6766"/>
    </justification>
  </clause>

  <clause id="10056">
    <literal><![CDATA[
      (x * K(y,z)) * (T(y,z) \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(6300(a,1),10050(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6300 10050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10057">
    <literal><![CDATA[
      x \ T(x * (y \ 1),y) = ((y \ x) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,311,a(flip),b,10051,a),flip(a)].">
      <j1 rule="hyper" parents="320 311 10051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10058">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,y) = x * (y \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6766,a(flip),b,10052,a)].">
      <j1 rule="hyper" parents="58 6766 10052"/>
    </justification>
  </clause>

  <clause id="10059">
    <literal><![CDATA[
      L(K(x,y),y \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5136,a,10053,a)].">
      <j1 rule="hyper" parents="5136 10053"/>
    </justification>
  </clause>

  <clause id="10060">
    <literal><![CDATA[
      L(K((x \ y) \ (z \ 1),z),z \ 1,u) = K(y \ (z \ x),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,9266,a(flip),b,10059,a),flip(a)].">
      <j1 rule="hyper" parents="320 9266 10059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10063">
    <literal><![CDATA[
      a(x,y \ 1,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10059,a(flip),b,5865,a),flip(a)].">
      <j1 rule="hyper" parents="115 10059 5865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10064">
    <literal><![CDATA[
      L(K(x,y),x \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(47,a,10063,a)].">
      <j1 rule="hyper" parents="47 10063"/>
    </justification>
  </clause>

  <clause id="10066">
    <literal><![CDATA[
      L(K(x,y),1 / x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3978,a,b,10064,a)].">
      <j1 rule="hyper" parents="58 3978 10064"/>
    </justification>
  </clause>

  <clause id="10067">
    <literal><![CDATA[
      L(K(x \ 1,y),x,z) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3979,a(flip),b,10064,a)].">
      <j1 rule="hyper" parents="58 3979 10064"/>
    </justification>
  </clause>

  <clause id="10068">
    <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(2616(a,1),10066(a,1,2))].">
      <j1 rule="para" parents="2616 10066"/>
    </justification>
  </clause>

  <clause id="10069">
    <literal><![CDATA[
      (x * y) * K(y \ 1,z) = x * (y * K(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,10067,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 10067 13"/>
    </justification>
  </clause>

  <clause id="10070">
    <literal><![CDATA[
      a(x,y,K(z,y \ 1)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10067,a(flip),b,5865,a),flip(a)].">
      <j1 rule="hyper" parents="115 10067 5865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10071">
    <literal><![CDATA[
      (x * y) * K(z,y \ 1) = x * (y * K(z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(969,a,10070,a)].">
      <j1 rule="hyper" parents="969 10070"/>
    </justification>
  </clause>

  <clause id="10072">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y,z) = x / (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,10056,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 10056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10073">
    <literal><![CDATA[
      (x * K(y * K(z,y),z)) * (y \ 1) = x * ((y * K(z,y)) \ 1)
    ]]></literal>
    <justification jstring="[para(4775(a,1),10056(a,1,2,1))].">
      <j1 rule="para" parents="4775 10056"/>
    </justification>
  </clause>

  <clause id="10074">
    <literal><![CDATA[
      T((x \ 1) * y,x) = (((x \ y) \ y) \ 1) * y
    ]]></literal>
    <justification jstring="[para(10057(a,1),4555(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10057 4555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10075">
    <literal><![CDATA[
      (x * T(y,z)) * (y \ K(z,y)) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,6768,a(flip),b,10058,a),flip(a)].">
      <j1 rule="hyper" parents="58 6768 10058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10076">
    <literal><![CDATA[
      L((x / (y \ 1)) / y,z,u) * T(y,w) = L(x,z,u) / (T(y,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(6831,a,10072,a)].">
      <j1 rule="hyper" parents="6831 10072"/>
    </justification>
  </clause>

  <clause id="10077">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * x = x / (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5496,a,b,10072,a)].">
      <j1 rule="hyper" parents="58 5496 10072"/>
    </justification>
  </clause>

  <clause id="10078">
    <literal><![CDATA[
      x / (T(y,x) \ 1) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5823,a(flip),b,10072,a),flip(a)].">
      <j1 rule="hyper" parents="58 5823 10072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10079">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) \ y = (((x \ y) \ y) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,4153,a(flip),b,10074,a)].">
      <j1 rule="hyper" parents="58 4153 10074"/>
    </justification>
  </clause>

  <clause id="10080">
    <literal><![CDATA[
      T(((x / y) \ 1) * x,x / y) = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(75(a,1),10074(a,2,1,1,1))].">
      <j1 rule="para" parents="75 10074"/>
    </justification>
  </clause>

  <clause id="10081">
    <literal><![CDATA[
      x / (y \ K(x,y)) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(4763(a,1),10078(a,1,2))].">
      <j1 rule="para" parents="4763 10078"/>
    </justification>
  </clause>

  <clause id="10082">
    <literal><![CDATA[
      x \ (y / (x \ K(y,x))) = (y / (x \ 1)) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,10081,a,b,xx)].">
      <j1 rule="hyper" parents="116 10081"/>
    </justification>
  </clause>

  <clause id="10083">
    <literal><![CDATA[
      (x * y) * (x \ K(y,x)) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(569,a,10075,a)].">
      <j1 rule="hyper" parents="569 10075"/>
    </justification>
  </clause>

  <clause id="10084">
    <literal><![CDATA[
      R(x,y,K(y \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(515,a,10069,a)].">
      <j1 rule="hyper" parents="515 10069"/>
    </justification>
  </clause>

  <clause id="10085">
    <literal><![CDATA[
      R(x,y \ z,K(y / z,u)) = x
    ]]></literal>
    <justification jstring="[para(7974(a,1),10084(a,1,3))].">
      <j1 rule="para" parents="7974 10084"/>
    </justification>
  </clause>

  <clause id="10086">
    <literal><![CDATA[
      x \ (y * K(x / y,z)) = (x \ y) * K(x / y,z)
    ]]></literal>
    <justification jstring="[para(10085(a,1),505(a,1,1))].">
      <j1 rule="para" parents="10085 505"/>
    </justification>
  </clause>

  <clause id="10087">
    <literal><![CDATA[
      R(x,y,K(z,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(515,a,10071,a)].">
      <j1 rule="hyper" parents="515 10071"/>
    </justification>
  </clause>

  <clause id="10088">
    <literal><![CDATA[
      x / (x * (y * K(z,y \ 1))) = T(x / (x * y),z)
    ]]></literal>
    <justification jstring="[para(10071(a,1),7631(a,1,2))].">
      <j1 rule="para" parents="10071 7631"/>
    </justification>
  </clause>

  <clause id="10090">
    <literal><![CDATA[
      R(x,y \ 1,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(3131(a,1),10087(a,1,3))].">
      <j1 rule="para" parents="3131 10087"/>
    </justification>
  </clause>

  <clause id="10091">
    <literal><![CDATA[
      R(x,y \ z,K(u,z \ y)) = x
    ]]></literal>
    <justification jstring="[para(6078(a,1),10087(a,1,3))].">
      <j1 rule="para" parents="6078 10087"/>
    </justification>
  </clause>

  <clause id="10092">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) * K(x,y)) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(6676,a,10090,a)].">
      <j1 rule="hyper" parents="6676 10090"/>
    </justification>
  </clause>

  <clause id="10093">
    <literal><![CDATA[
      R(x,y \ 1,K(z,T(y,u))) = x
    ]]></literal>
    <justification jstring="[para(7133(a,1),10090(a,1,3))].">
      <j1 rule="para" parents="7133 10090"/>
    </justification>
  </clause>

  <clause id="10094">
    <literal><![CDATA[
      x \ (y * K(z,y \ x)) = (x \ y) * K(z,y \ x)
    ]]></literal>
    <justification jstring="[para(10091(a,1),505(a,1,1))].">
      <j1 rule="para" parents="10091 505"/>
    </justification>
  </clause>

  <clause id="10095">
    <literal><![CDATA[
      R(x,(y * K(z,y)) \ 1,K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(4775(a,1),10093(a,1,3,2))].">
      <j1 rule="para" parents="4775 10093"/>
    </justification>
  </clause>

  <clause id="10096">
    <literal><![CDATA[
      R(x,y \ K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(5171(a,1),10095(a,1,2))].">
      <j1 rule="para" parents="5171 10095"/>
    </justification>
  </clause>

  <clause id="10097">
    <literal><![CDATA[
      (x * K(y,z)) / (z \ 1) = x / (z \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6357,a(flip),b,10096,a)].">
      <j1 rule="hyper" parents="58 6357 10096"/>
    </justification>
  </clause>

  <clause id="10098">
    <literal><![CDATA[
      T(x,y) / (T(y,x) \ 1) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(4760(a,1),10092(a,1,2))].">
      <j1 rule="para" parents="4760 10092"/>
    </justification>
  </clause>

  <clause id="10099">
    <literal><![CDATA[
      (x / (y \ 1)) \ T(x,y) = T(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(188,a,10098,a)].">
      <j1 rule="hyper" parents="188 10098"/>
    </justification>
  </clause>

  <clause id="10100">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = T(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,6691,a,b,10099,a)].">
      <j1 rule="hyper" parents="58 6691 10099"/>
    </justification>
  </clause>

  <clause id="10101">
    <literal><![CDATA[
      ((x / y) / (y \ 1)) \ (y \ x) = T(y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,6808,a(flip),b,10099,a)].">
      <j1 rule="hyper" parents="58 6808 10099"/>
    </justification>
  </clause>

  <clause id="10102">
    <literal><![CDATA[
      (x \ ((y \ 1) \ x)) * x = (T(y,x) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(10100(a,1),4459(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10100 4459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10104">
    <literal><![CDATA[
      T(x,y) / (y \ 1) = x / (y \ K(y,x))
    ]]></literal>
    <justification jstring="[para(4714(a,2),10097(a,1,1))].">
      <j1 rule="para" parents="4714 10097"/>
    </justification>
  </clause>

  <clause id="10105">
    <literal><![CDATA[
      (T(x,y) / (y \ 1)) \ x = y \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(188,a,10104,a(flip))].">
      <j1 rule="hyper" parents="188 10104"/>
    </justification>
  </clause>

  <clause id="10106">
    <literal><![CDATA[
      x \ (x / (y \ K(y,x))) = (x / (y \ 1)) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,10104,a(flip),b,3873,a(flip))].">
      <j1 rule="hyper" parents="116 10104 3873"/>
    </justification>
  </clause>

  <clause id="10107">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = (x \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(10105(a,1),6836(a,1,1))].">
      <j1 rule="para" parents="10105 6836"/>
    </justification>
  </clause>

  <clause id="10108">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = (x \ ((x \ 1) \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,1968,a,b,10107,a),flip(a)].">
      <j1 rule="hyper" parents="320 1968 10107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10109">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = y * (((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3877,a(flip),b,10107,a),flip(a)].">
      <j1 rule="hyper" parents="320 3877 10107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10110">
    <literal><![CDATA[
      x \ ((y \ K(y,x)) \ x) = ((y \ 1) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,10107,a,b,3877,a(flip))].">
      <j1 rule="hyper" parents="116 10107 3877"/>
    </justification>
  </clause>

  <clause id="10111">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) \ y = (y \ (x \ y)) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),10102(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 10102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10112">
    <literal><![CDATA[
      x / ((x \ (y \ x)) * x) = T(1 / y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(197,a,10111,a)].">
      <j1 rule="hyper" parents="197 10111"/>
    </justification>
  </clause>

  <clause id="10113">
    <literal><![CDATA[
      T(1 / (x \ y),y) \ 1 = x \ T(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6709,a,b,10112,a),flip(a)].">
      <j1 rule="hyper" parents="58 6709 10112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10114">
    <literal><![CDATA[
      T(1 / (x / y),x) \ 1 = x / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(75(a,1),10112(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="75 10112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10115">
    <literal><![CDATA[
      (x \ T(y,y \ x)) \ 1 = T((x \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[para(10113(a,1),2153(a,1,1))].">
      <j1 rule="para" parents="10113 2153"/>
    </justification>
  </clause>

  <clause id="10116">
    <literal><![CDATA[
      ((((x / y) \ 1) * x) \ x) \ x = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(75(a,1),10079(a,2,1,1,1))].">
      <j1 rule="para" parents="75 10079"/>
    </justification>
  </clause>

  <clause id="10117">
    <literal><![CDATA[
      ((x / y) \ 1) * (y * (x / y)) = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,1972,a(flip),b,10080,a)].">
      <j1 rule="hyper" parents="58 1972 10080"/>
    </justification>
  </clause>

  <clause id="10118">
    <literal><![CDATA[
      (x \ y) * K(x / y,y) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,1442,a(flip),b,10086,a),flip(a)].">
      <j1 rule="hyper" parents="58 1442 10086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10119">
    <literal><![CDATA[
      T(x \ y,z) * ((y \ x) * K(z,x \ y)) = T((x \ y) * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10094,a(flip),b,5908,a)].">
      <j1 rule="hyper" parents="119 10094 5908"/>
    </justification>
  </clause>

  <clause id="10120">
    <literal><![CDATA[
      (x \ y) / (T(x,x \ y) \ 1) = (y / x) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(197,a,10101,a)].">
      <j1 rule="hyper" parents="197 10101"/>
    </justification>
  </clause>

  <clause id="10121">
    <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(10117(a,1),6569(a,2,2,1))].">
      <j1 rule="para" parents="10117 6569"/>
    </justification>
  </clause>

  <clause id="10122">
    <literal><![CDATA[
      K(x \ (y * (z \ 1)),z) = K(x \ (z \ y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6597,a(flip),b,10060,a)].">
      <j1 rule="hyper" parents="58 6597 10060"/>
    </justification>
  </clause>

  <clause id="10123">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (x \ z),x) = K(y \ T(z,x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9352,a(flip),b,10122,a),flip(a)].">
      <j1 rule="hyper" parents="58 9352 10122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10124">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (x \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,9391,a(flip),b,10123,a),flip(a)].">
      <j1 rule="hyper" parents="320 9391 10123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10125">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,x) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(7694,a,10124,a)].">
      <j1 rule="hyper" parents="7694 10124"/>
    </justification>
  </clause>

  <clause id="10126">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,y) = K((x * y) \ (z * y),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8671,a(flip),b,10125,a)].">
      <j1 rule="hyper" parents="58 8671 10125"/>
    </justification>
  </clause>

  <clause id="10127">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7573,a(flip),b,10126,a),flip(a)].">
      <j1 rule="hyper" parents="320 7573 10126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10128">
    <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(10127(a,1),5341(a,1,2,1,2))].">
      <j1 rule="para" parents="10127 5341"/>
    </justification>
  </clause>

  <clause id="10129">
    <literal><![CDATA[
      (x * K(y,z)) * (y \ 1) = x * ((y * K(z,y)) \ 1)
    ]]></literal>
    <justification jstring="[para(4930(a,1),10073(a,1,1,2))].">
      <j1 rule="para" parents="4930 10073"/>
    </justification>
  </clause>

  <clause id="10130">
    <literal><![CDATA[
      (x * K(y,z)) * (y \ 1) = x * (K(y,z) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(5360(a,1),10129(a,2,2))].">
      <j1 rule="para" parents="5360 10129"/>
    </justification>
  </clause>

  <clause id="10132">
    <literal><![CDATA[
      L(x \ 1,K(x,y),z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(479,a,10130,a)].">
      <j1 rule="hyper" parents="479 10130"/>
    </justification>
  </clause>

  <clause id="10133">
    <literal><![CDATA[
      T((x \ y) * (y \ x),z) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(5449,a,10119,a),flip(a)].">
      <j1 rule="hyper" parents="5449 10119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10134">
    <literal><![CDATA[
      K(x,(y \ z) * (z \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(4784,a,10133,a)].">
      <j1 rule="hyper" parents="4784 10133"/>
    </justification>
  </clause>

  <clause id="10135">
    <literal><![CDATA[
      T(x,(y \ z) * (z \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,10133,a)].">
      <j1 rule="hyper" parents="49 10133"/>
    </justification>
  </clause>

  <clause id="10136">
    <literal><![CDATA[
      K(x,y * ((z * y) \ z)) = 1
    ]]></literal>
    <justification jstring="[para(4(a,1),10134(a,1,2,1))].">
      <j1 rule="para" parents="4 10134"/>
    </justification>
  </clause>

  <clause id="10137">
    <literal><![CDATA[
      T(x,y * ((z * y) \ z)) = x
    ]]></literal>
    <justification jstring="[para(4(a,1),10135(a,1,2,1))].">
      <j1 rule="para" parents="4 10135"/>
    </justification>
  </clause>

  <clause id="10138">
    <literal><![CDATA[
      T(x * ((y * x) \ y),z) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(4913,a,10136,a)].">
      <j1 rule="hyper" parents="4913 10136"/>
    </justification>
  </clause>

  <clause id="10139">
    <literal><![CDATA[
      x / (y * ((z * y) \ z)) = (y * ((z * y) \ z)) \ x
    ]]></literal>
    <justification jstring="[hyper(168,a,4977,a,b,10136,a(flip))].">
      <j1 rule="hyper" parents="168 4977 10136"/>
    </justification>
  </clause>

  <clause id="10140">
    <literal><![CDATA[
      x / (y * ((z * y) \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      (y * ((z * y) \ z)) \ x = u
    ]]></literal>
    <justification jstring="[para(10137(a,1),421(a,1))].">
      <j1 rule="para" parents="10137 421"/>
    </justification>
  </clause>

  <clause id="10141">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),z) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[para(217(a,2),10138(a,1,1,2))].">
      <j1 rule="para" parents="217 10138"/>
    </justification>
  </clause>

  <clause id="10142">
    <literal><![CDATA[
      T(x,y) * ((z * T(x,y)) \ z) = x * ((z * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9459,a(flip),b,10141,a)].">
      <j1 rule="hyper" parents="58 9459 10141"/>
    </justification>
  </clause>

  <clause id="10143">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5441,a(flip),b,10141,a)].">
      <j1 rule="hyper" parents="58 5441 10141"/>
    </justification>
  </clause>

  <clause id="10146">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ T(x,z) = 1 / ((y * T(x,z)) \ y)
    ]]></literal>
    <justification jstring="[para(10142(a,1),1837(a,1,1))].">
      <j1 rule="para" parents="10142 1837"/>
    </justification>
  </clause>

  <clause id="10147">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,T(y,u)) = K(x \ z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(5344,a,10128,a),flip(a)].">
      <j1 rule="hyper" parents="5344 10128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10148">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,T(x,u)) = K((x \ y) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[para(2792(a,1),10147(a,1,1,1))].">
      <j1 rule="para" parents="2792 10147"/>
    </justification>
  </clause>

  <clause id="10149">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,u)) = K((x \ y) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,3946,a(flip),b,10148,a)].">
      <j1 rule="hyper" parents="58 3946 10148"/>
    </justification>
  </clause>

  <clause id="10150">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,u)) = K(y \ (x * z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7587,a(flip),b,10149,a),flip(a)].">
      <j1 rule="hyper" parents="320 7587 10149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10151">
    <literal><![CDATA[
      K(x \ (y * z),T(y,x)) = K(((y \ 1) \ z) / x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9353,a(flip),b,10150,a),flip(a)].">
      <j1 rule="hyper" parents="58 9353 10150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10152">
    <literal><![CDATA[
      K(((x \ 1) \ y) / z,x) = K((x * y) / z,x)
    ]]></literal>
    <justification jstring="[hyper(8034,a,10151,a),flip(a)].">
      <j1 rule="hyper" parents="8034 10151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10153">
    <literal><![CDATA[
      K(((x \ 1) \ y) / z,x) = K((z / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,6739,a(flip),b,10152,a),flip(a)].">
      <j1 rule="hyper" parents="320 6739 10152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10154">
    <literal><![CDATA[
      K((x / ((y \ 1) * z)) \ y,y) = K(z / x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),10153(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 10153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10155">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),z) = K(y \ z,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),10154(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6 10154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10156">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),(z \ 1) \ 1) = K(y \ z,z)
    ]]></literal>
    <justification jstring="[hyper(3525,a,10155,a)].">
      <j1 rule="hyper" parents="3525 10155"/>
    </justification>
  </clause>

  <clause id="10157">
    <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(9314(a,1),10019(a,2,1))].">
      <j1 rule="para" parents="9314 10019"/>
    </justification>
  </clause>

  <clause id="10158">
    <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(320,a,9839,a(flip),b,10157,a),flip(a)].">
      <j1 rule="hyper" parents="320 9839 10157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10159">
    <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(7133(a,1),10158(a,1,1,2))].">
      <j1 rule="para" parents="7133 10158"/>
    </justification>
  </clause>

  <clause id="10160">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * (u * K(z,y)) = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(7872(a,1),10159(a,1,2))].">
      <j1 rule="para" parents="7872 10159"/>
    </justification>
  </clause>

  <clause id="10161">
    <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(9142(a,2),10160(a,1,1))].">
      <j1 rule="para" parents="9142 10160"/>
    </justification>
  </clause>

  <clause id="10162">
    <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(7807(a,1),10028(a,1,2))].">
      <j1 rule="para" parents="7807 10028"/>
    </justification>
  </clause>

  <clause id="10163">
    <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(9041(a,1),10029(a,1,2))].">
      <j1 rule="para" parents="9041 10029"/>
    </justification>
  </clause>

  <clause id="10164">
    <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(9793(a,1),10030(a,2,2))].">
      <j1 rule="para" parents="9793 10030"/>
    </justification>
  </clause>

  <clause id="10165">
    <literal><![CDATA[
      L(x \ 1,T(K(x,y),z),z) * (K(x,y) * z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(320,a,105,a(flip),b,10164,a),flip(a)].">
      <j1 rule="hyper" parents="320 105 10164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10166">
    <literal><![CDATA[
      L(x \ 1,K(x,T(y,z)),z) * (K(x,y) * z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(7131(a,2),10165(a,1,1,2))].">
      <j1 rule="para" parents="7131 10165"/>
    </justification>
  </clause>

  <clause id="10167">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(10132(a,1),10166(a,1,1))].">
      <j1 rule="para" parents="10132 10166"/>
    </justification>
  </clause>

  <clause id="10168">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,5975,a,b,10167,a)].">
      <j1 rule="hyper" parents="58 5975 10167"/>
    </justification>
  </clause>

  <clause id="10169">
    <literal><![CDATA[
      ((x \ 1) * y) / ((x \ K(x,z)) * y) = K(z,x)
    ]]></literal>
    <justification jstring="[para(10167(a,1),5981(a,1,2))].">
      <j1 rule="para" parents="10167 5981"/>
    </justification>
  </clause>

  <clause id="10171">
    <literal><![CDATA[
      L(x,y \ 1,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(3191,a,10168,a)].">
      <j1 rule="hyper" parents="3191 10168"/>
    </justification>
  </clause>

  <clause id="10172">
    <literal><![CDATA[
      L(x,y,K(y \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,3979,a(flip),b,10171,a)].">
      <j1 rule="hyper" parents="58 3979 10171"/>
    </justification>
  </clause>

  <clause id="10173">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,K(y,u)) = x
    ]]></literal>
    <justification jstring="[para(7863(a,1),10171(a,1,3))].">
      <j1 rule="para" parents="7863 10171"/>
    </justification>
  </clause>

  <clause id="10174">
    <literal><![CDATA[
      L(x,y,K(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(10172(a,1),45(a,2))].">
      <j1 rule="para" parents="10172 45"/>
    </justification>
  </clause>

  <clause id="10175">
    <literal><![CDATA[
      L(x,y \ z,K(y / z,u)) = x
    ]]></literal>
    <justification jstring="[para(7974(a,1),10172(a,1,3))].">
      <j1 rule="para" parents="7974 10172"/>
    </justification>
  </clause>

  <clause id="10176">
    <literal><![CDATA[
      L(x,(y * z) \ z,K(y,u)) = x
    ]]></literal>
    <justification jstring="[para(6(a,1),10175(a,1,3,1))].">
      <j1 rule="para" parents="6 10175"/>
    </justification>
  </clause>

  <clause id="10177">
    <literal><![CDATA[
      R(K(x,y),y \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6912,a(flip),b,10169,a)].">
      <j1 rule="hyper" parents="58 6912 10169"/>
    </justification>
  </clause>

  <clause id="10179">
    <literal><![CDATA[
      L(K((x / y) \ x,z),x \ (x / (1 / (1 / y))),u) = K(1 / (x \ (x / y)),z)
    ]]></literal>
    <justification jstring="[para(6237(a,1),10068(a,1,1))].">
      <j1 rule="para" parents="6237 10068"/>
    </justification>
  </clause>

  <clause id="10180">
    <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),10179(a,1,1,1))].">
      <j1 rule="para" parents="75 10179"/>
    </justification>
  </clause>

  <clause id="10182">
    <literal><![CDATA[
      L(K(x,y),1 / (1 / (z \ (z / x))),u) = K(1 / (z \ (z / x)),y)
    ]]></literal>
    <justification jstring="[para(2616(a,2),10180(a,1,2))].">
      <j1 rule="para" parents="2616 10180"/>
    </justification>
  </clause>

  <clause id="10183">
    <literal><![CDATA[
      L(K(x,y),z \ (z / x),u) = K(1 / (z \ (z / x)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3980,a(flip),b,10182,a)].">
      <j1 rule="hyper" parents="58 3980 10182"/>
    </justification>
  </clause>

  <clause id="10184">
    <literal><![CDATA[
      L(K(x,y),z \ (z / x),u) = K((z / x) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6237,a(flip),b,10183,a),flip(a)].">
      <j1 rule="hyper" parents="320 6237 10183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10185">
    <literal><![CDATA[
      L(K(x,y),z \ (z / x),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,674,a(flip),b,10184,a),flip(a)].">
      <j1 rule="hyper" parents="320 674 10184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10187">
    <literal><![CDATA[
      (x / y) \ (x * (K(y,z) * (x \ (x / y)))) = T(K(y,z),x \ (x / y))
    ]]></literal>
    <justification jstring="[para(10185(a,1),791(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10185 791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10188">
    <literal><![CDATA[
      (x / y) \ (x * (K(y,z) * (x \ (x / y)))) = T(K(y,z),1 / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6174,a(flip),b,10187,a),flip(a)].">
      <j1 rule="hyper" parents="320 6174 10187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10190">
    <literal><![CDATA[
      (x / y) \ (x * (K(y,z) * (x \ (x / y)))) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,1288,a(flip),b,10188,a),flip(a)].">
      <j1 rule="hyper" parents="320 1288 10188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10191">
    <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(2889(a,1),10162(a,1,2))].">
      <j1 rule="para" parents="2889 10162"/>
    </justification>
  </clause>

  <clause id="10193">
    <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(10191(a,1),5339(a,1,1,2))].">
      <j1 rule="para" parents="10191 5339"/>
    </justification>
  </clause>

  <clause id="10194">
    <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(5164(a,1),10193(a,1,1))].">
      <j1 rule="para" parents="5164 10193"/>
    </justification>
  </clause>

  <clause id="10195">
    <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,6977,a(flip),b,10194,a),flip(a)].">
      <j1 rule="hyper" parents="58 6977 10194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10196">
    <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(10195(a,1),8721(a,2,1))].">
      <j1 rule="para" parents="10195 8721"/>
    </justification>
  </clause>

  <clause id="10197">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = (x * (u * ((x \ y) / u))) * (y \ z)
    ]]></literal>
    <justification jstring="[para(4582(a,1),4598(a,2,1))].">
      <j1 rule="para" parents="4582 4598"/>
    </justification>
  </clause>

  <clause id="10198">
    <literal><![CDATA[
      ((K(x,y) * z) * (z \ x)) / T(x,y) = a(K(x,y),z,z \ x)
    ]]></literal>
    <justification jstring="[para(9141(a,1),4816(a,1,2))].">
      <j1 rule="para" parents="9141 4816"/>
    </justification>
  </clause>

  <clause id="10200">
    <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(4778(a,1),5147(a,2,2))].">
      <j1 rule="para" parents="4778 5147"/>
    </justification>
  </clause>

  <clause id="10201">
    <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(10200(a,2),482(a,1))].">
      <j1 rule="para" parents="10200 482"/>
    </justification>
  </clause>

  <clause id="10203">
    <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(320,a,4556,a,b,6161,a)].">
      <j1 rule="hyper" parents="320 4556 6161"/>
    </justification>
  </clause>

  <clause id="10204">
    <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(6302(a,1),6361(a,2,1))].">
      <j1 rule="para" parents="6302 6361"/>
    </justification>
  </clause>

  <clause id="10205">
    <literal><![CDATA[
      R(R(x,y,T(z,u)),y * T(z,u),K(u,z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,15,a,b,10204,a),flip(a)].">
      <j1 rule="hyper" parents="320 15 10204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10208">
    <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(223(a,1),10205(a,1,2))].">
      <j1 rule="para" parents="223 10205"/>
    </justification>
  </clause>

  <clause id="10209">
    <literal><![CDATA[
      R(R(x,y / z,z),y,K(z \ y,z)) = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[para(6698(a,1),10208(a,1,1))].">
      <j1 rule="para" parents="6698 10208"/>
    </justification>
  </clause>

  <clause id="10210">
    <literal><![CDATA[
      (T(x,y) / z) / K(((1 / z) / (x / z)) \ 1,y) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,9670,a(flip),b,6807,a),flip(a)].">
      <j1 rule="hyper" parents="320 9670 6807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10211">
    <literal><![CDATA[
      (T(x,y) / z) / K(((z \ 1) / (x / z)) \ 1,y) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(3962(a,1),10210(a,1,2))].">
      <j1 rule="para" parents="3962 10210"/>
    </justification>
  </clause>

  <clause id="10212">
    <literal><![CDATA[
      (T(x,y) / z) * K(y,((z \ 1) / (x / z)) \ 1) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6317,a,10211,a)].">
      <j1 rule="hyper" parents="6317 10211"/>
    </justification>
  </clause>

  <clause id="10213">
    <literal><![CDATA[
      (T(x,y) / z) * K(y,(x / z) / (z \ 1)) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5312(a,1),10212(a,1,2))].">
      <j1 rule="para" parents="5312 10212"/>
    </justification>
  </clause>

  <clause id="10214">
    <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(7131(a,2),10213(a,1,1,1))].">
      <j1 rule="para" parents="7131 10213"/>
    </justification>
  </clause>

  <clause id="10215">
    <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,5016,a,b,6840,a)].">
      <j1 rule="hyper" parents="58 5016 6840"/>
    </justification>
  </clause>

  <clause id="10216">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = (y \ T(y * K(x \ 1,x),z)) / x
    ]]></literal>
    <justification jstring="[para(3968(a,1),10215(a,1,2))].">
      <j1 rule="para" parents="3968 10215"/>
    </justification>
  </clause>

  <clause id="10217">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = ((y \ T(y,z)) * K(x \ 1,x)) / x
    ]]></literal>
    <justification jstring="[para(4609(a,1),10216(a,2,1))].">
      <j1 rule="para" parents="4609 10216"/>
    </justification>
  </clause>

  <clause id="10218">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = (K(y,z) * K(x \ 1,x)) / x
    ]]></literal>
    <justification jstring="[para(4688(a,2),10217(a,2,1,1))].">
      <j1 rule="para" parents="4688 10217"/>
    </justification>
  </clause>

  <clause id="10219">
    <literal><![CDATA[
      K((x * ((y \ 1) / x)) \ 1,z) = x * (K(y,z) / T(x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(6351,a,10218,a),flip(a)].">
      <j1 rule="hyper" parents="6351 10218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10220">
    <literal><![CDATA[
      K((x * ((y \ 1) / x)) \ 1,z) = x * (K(y,z) / ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(106(a,1),10219(a,2,2,2))].">
      <j1 rule="para" parents="106 10219"/>
    </justification>
  </clause>

  <clause id="10221">
    <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(5886(a,1),7707(a,1,1))].">
      <j1 rule="para" parents="5886 7707"/>
    </justification>
  </clause>

  <clause id="10222">
    <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(7051(a,1),7725(a,2,2))].">
      <j1 rule="para" parents="7051 7725"/>
    </justification>
  </clause>

  <clause id="10223">
    <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(320,a,7715,a(flip),b,10222,a),flip(a)].">
      <j1 rule="hyper" parents="320 7715 10222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10225">
    <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(199(a,1),8337(a,1,1))].">
      <j1 rule="para" parents="199 8337"/>
    </justification>
  </clause>

  <clause id="10227">
    <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(6306(a,1),10225(a,1,2))].">
      <j1 rule="para" parents="6306 10225"/>
    </justification>
  </clause>

  <clause id="10228">
    <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(10010(a,1),10227(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10010 10227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10229">
    <literal><![CDATA[
      K(R(x,y,z),u) * (x \ R(x,y,z)) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,2,a(flip),b,10228,a),flip(a)].">
      <j1 rule="hyper" parents="320 2 10228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10230">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (y \ R(T(y,x),z,u)) = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(5109,a,10229,a)].">
      <j1 rule="hyper" parents="5109 10229"/>
    </justification>
  </clause>

  <clause id="10231">
    <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(9044(a,1),10230(a,1,1))].">
      <j1 rule="para" parents="9044 10230"/>
    </justification>
  </clause>

  <clause id="10232">
    <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(7679,a,8624,a)].">
      <j1 rule="hyper" parents="7679 8624"/>
    </justification>
  </clause>

  <clause id="10233">
    <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,9841,a(flip),b,8658,a),flip(a)].">
      <j1 rule="hyper" parents="58 9841 8658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10234">
    <literal><![CDATA[
      K(x,(y * (K(x,z) * u)) \ (y * (u * w))) = K(x,L(w,K(x,z) * u,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7484,a(flip),b,8681,a),flip(a)].">
      <j1 rule="hyper" parents="58 7484 8681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10236">
    <literal><![CDATA[
      K(x,L(y,K(x,z) * u,w)) = K(x,(w * u) \ (w * (u * y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8654,a(flip),b,10234,a),flip(a)].">
      <j1 rule="hyper" parents="58 8654 10234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10238">
    <literal><![CDATA[
      K(x,L(y,K(x,z) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(13(a,2),10236(a,2,2))].">
      <j1 rule="para" parents="13 10236"/>
    </justification>
  </clause>

  <clause id="10239">
    <literal><![CDATA[
      K(x,L(y,K(x,z) \ u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),10238(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 10238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10240">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = (y \ 1) / (y \ K(y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(10238(a,1),5100(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10238 5100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10241">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = K(L(x,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5100,a(flip),b,10240,a),flip(a)].">
      <j1 rule="hyper" parents="320 5100 10240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10242">
    <literal><![CDATA[
      K(L(x,T(y,z),u),z) = K(L(x,y,u),z)
    ]]></literal>
    <justification jstring="[para(4770(a,1),10241(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4770 10241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10243">
    <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,8389,a(flip),b,8837,a),flip(a)].">
      <j1 rule="hyper" parents="58 8389 8837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10245">
    <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),10243(a,1,1))].">
      <j1 rule="para" parents="15 10243"/>
    </justification>
  </clause>

  <clause id="10246">
    <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,8268,a,b,10245,a)].">
      <j1 rule="hyper" parents="58 8268 10245"/>
    </justification>
  </clause>

  <clause id="10247">
    <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,9206,a,b,10246,a)].">
      <j1 rule="hyper" parents="58 9206 10246"/>
    </justification>
  </clause>

  <clause id="10248">
    <literal><![CDATA[
      R(K(x,y),z * x,u) = K(R(x,K(w,y) * z,u),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8821,a(flip),b,10247,a)].">
      <j1 rule="hyper" parents="58 8821 10247"/>
    </justification>
  </clause>

  <clause id="10250">
    <literal><![CDATA[
      K(R(x,K(y,z) * u,w),z) = K(R(x,u,w),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9204,a(flip),b,10248,a),flip(a)].">
      <j1 rule="hyper" parents="58 9204 10248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10251">
    <literal><![CDATA[
      T(x,R(y,K(z,x) * u,w)) = 1 / (x \ K(R(y,u,w),x))
    ]]></literal>
    <justification jstring="[para(10250(a,1),4953(a,2,2,2))].">
      <j1 rule="para" parents="10250 4953"/>
    </justification>
  </clause>

  <clause id="10252">
    <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(10251(a,2),4954(a,1))].">
      <j1 rule="para" parents="10251 4954"/>
    </justification>
  </clause>

  <clause id="10253">
    <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,8379,a(flip),b,8854,a),flip(a)].">
      <j1 rule="hyper" parents="58 8379 8854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10255">
    <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),10253(a,1,2))].">
      <j1 rule="para" parents="15 10253"/>
    </justification>
  </clause>

  <clause id="10256">
    <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,9423,a,b,10255,a)].">
      <j1 rule="hyper" parents="58 9423 10255"/>
    </justification>
  </clause>

  <clause id="10257">
    <literal><![CDATA[
      K(x,R(y,K(z,x) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9421,a(flip),b,10255,a),flip(a)].">
      <j1 rule="hyper" parents="58 9421 10255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10259">
    <literal><![CDATA[
      K(x,R(y,K(x,z) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(5095(a,1),10257(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5095 10257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10260">
    <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(560(a,1),10259(a,1,2)),flip(a)].">
      <j1 rule="para" parents="560 10259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10261">
    <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,10256,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 10256 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10262">
    <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(5093(a,1),10261(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5093 10261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10263">
    <literal><![CDATA[
      T(x,R(T(x,y) \ z,u,w)) = T(x,R(x \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(10252,a,10262,a),flip(a)].">
      <j1 rule="hyper" parents="10252 10262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10265">
    <literal><![CDATA[
      T(x,R(y / T(x,z),u,w)) = T(x,R(x \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(5252,a,10263,a)].">
      <j1 rule="hyper" parents="5252 10263"/>
    </justification>
  </clause>

  <clause id="10266">
    <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(9490(a,1),8958(a,1,2,2))].">
      <j1 rule="para" parents="9490 8958"/>
    </justification>
  </clause>

  <clause id="10267">
    <literal><![CDATA[
      K(T(x,y * K(z * x,y)),T(u,x * z)) = K((x * K(x * z,x)) * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(8230,a,9019,a)].">
      <j1 rule="hyper" parents="8230 9019"/>
    </justification>
  </clause>

  <clause id="10268">
    <literal><![CDATA[
      K(T(x,y * K(z * x,y)),T(u,z)) = K((x * K(x * z,x)) * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,8596,a(flip),b,10267,a)].">
      <j1 rule="hyper" parents="58 8596 10267"/>
    </justification>
  </clause>

  <clause id="10269">
    <literal><![CDATA[
      K((x * K(x * y,x)) * K(x,z),u) = K(x * K(T(x,y),z),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9020,a(flip),b,10268,a),flip(a)].">
      <j1 rule="hyper" parents="58 9020 10268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10270">
    <literal><![CDATA[
      K((x * K(x * y,x)) * K(x,z),u) = K(K(y,x) * T(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,8265,a(flip),b,10269,a),flip(a)].">
      <j1 rule="hyper" parents="320 8265 10269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10271">
    <literal><![CDATA[
      K(K(x * y,x) * T(x,z),u) = K(K(y,x) * T(x,z),u)
    ]]></literal>
    <justification jstring="[para(5433(a,1),10270(a,1,1))].">
      <j1 rule="para" parents="5433 10270"/>
    </justification>
  </clause>

  <clause id="10272">
    <literal><![CDATA[
      K(K(x * y,x) * T(x,z),T(u,z)) = K(x,T(u,T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(320,a,9002,a(flip),b,10271,a),flip(a)].">
      <j1 rule="hyper" parents="320 9002 10271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10273">
    <literal><![CDATA[
      K(x,T(y,T(x * z,u))) = K(x,T(y,T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(9003,a,10272,a)].">
      <j1 rule="hyper" parents="9003 10272"/>
    </justification>
  </clause>

  <clause id="10274">
    <literal><![CDATA[
      K(x,T(x * y,T(y,z))) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(174(a,1),10273(a,1,2)),flip(a)].">
      <j1 rule="para" parents="174 10273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10275">
    <literal><![CDATA[
      K(x,T(x * T(y,z),y)) = K(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[para(7884(a,1),10274(a,1,2))].">
      <j1 rule="para" parents="7884 10274"/>
    </justification>
  </clause>

  <clause id="10276">
    <literal><![CDATA[
      K(x,T(T(x * T(y,z),u),y)) = T(K(x,x * T(y,z)),u)
    ]]></literal>
    <justification jstring="[para(10275(a,1),7154(a,2,1))].">
      <j1 rule="para" parents="10275 7154"/>
    </justification>
  </clause>

  <clause id="10277">
    <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(10276(a,2),7683(a,1))].">
      <j1 rule="para" parents="10276 7683"/>
    </justification>
  </clause>

  <clause id="10278">
    <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(9240,a,9243,a),flip(a)].">
      <j1 rule="hyper" parents="9240 9243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10279">
    <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,8597,a(flip),b,10278,a),flip(a)].">
      <j1 rule="hyper" parents="58 8597 10278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10281">
    <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(447(a,1),9537(a,1,1))].">
      <j1 rule="para" parents="447 9537"/>
    </justification>
  </clause>

  <clause id="10282">
    <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),10197(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 10197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10283">
    <literal><![CDATA[
      (x / y) \ T(x * K(y,z),(x / y) \ 1) = T(x * (y / x),z)
    ]]></literal>
    <justification jstring="[para(3883(a,1),10203(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3883 10203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10284">
    <literal><![CDATA[
      K(x * K(y,z),(x / y) \ 1) = T(x * (y / x),z) / T(y,z)
    ]]></literal>
    <justification jstring="[para(10283(a,1),6162(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10283 6162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10285">
    <literal><![CDATA[
      K(x * K(y,z),(x / y) \ 1) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,5089,a(flip),b,10284,a),flip(a)].">
      <j1 rule="hyper" parents="320 5089 10284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10286">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) = K(z,z \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8587,a(flip),b,10285,a)].">
      <j1 rule="hyper" parents="58 8587 10285"/>
    </justification>
  </clause>

  <clause id="10287">
    <literal><![CDATA[
      ((x \ y) \ R(x \ y,z,x \ y)) * (y / x) = R(y / x,z,x \ y)
    ]]></literal>
    <justification jstring="[para(4735(a,1),10221(a,2,1))].">
      <j1 rule="para" parents="4735 10221"/>
    </justification>
  </clause>

  <clause id="10288">
    <literal><![CDATA[
      a(x \ y,z,x \ y) * (y / x) = R(y / x,z,x \ y)
    ]]></literal>
    <justification jstring="[para(8913(a,1),10287(a,1,1))].">
      <j1 rule="para" parents="8913 10287"/>
    </justification>
  </clause>

  <clause id="10289">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = a(y \ x,z,y \ x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7708,a,b,10288,a)].">
      <j1 rule="hyper" parents="320 7708 10288"/>
    </justification>
  </clause>

  <clause id="10290">
    <literal><![CDATA[
      a(x / y,z,x / y) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(9654,a,10289,a)].">
      <j1 rule="hyper" parents="9654 10289"/>
    </justification>
  </clause>

  <clause id="10291">
    <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(7105(a,1),10232(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7105 10232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10293">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * (u / x)))
    ]]></literal>
    <justification jstring="[hyper(7686,a,10233,a),flip(a)].">
      <j1 rule="hyper" parents="7686 10233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10294">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * u))
    ]]></literal>
    <justification jstring="[hyper(320,a,9194,a(flip),b,10293,a),flip(a)].">
      <j1 rule="hyper" parents="320 9194 10293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10295">
    <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),10294(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 10294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10296">
    <literal><![CDATA[
      K(x,y \ ((z * (x \ u)) * x)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(7717,a,10295,a),flip(a)].">
      <j1 rule="hyper" parents="7717 10295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10297">
    <literal><![CDATA[
      K(x,x \ (y * z)) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(4997,a,10296,a),flip(a)].">
      <j1 rule="hyper" parents="4997 10296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10298">
    <literal><![CDATA[
      K(x,y \ ((x \ y) * z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8424,a(flip),b,10296,a),flip(a)].">
      <j1 rule="hyper" parents="58 8424 10296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10299">
    <literal><![CDATA[
      K(x,x \ (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(10296(a,1),4997(a,1))].">
      <j1 rule="para" parents="10296 4997"/>
    </justification>
  </clause>

  <clause id="10300">
    <literal><![CDATA[
      T(x,x \ (y * z)) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,10297,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 10297 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10301">
    <literal><![CDATA[
      K(x,x \ (y * (x * z))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),10297(a,2,2,2))].">
      <j1 rule="para" parents="4 10297"/>
    </justification>
  </clause>

  <clause id="10302">
    <literal><![CDATA[
      (x * K(y,z * (y \ u))) \ x = K(y \ (z * u),y)
    ]]></literal>
    <justification jstring="[para(10297(a,1),6309(a,1,1,2))].">
      <j1 rule="para" parents="10297 6309"/>
    </justification>
  </clause>

  <clause id="10303">
    <literal><![CDATA[
      K(x,K(y,z * (y \ u))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(10297(a,1),7934(a,1,2))].">
      <j1 rule="para" parents="10297 7934"/>
    </justification>
  </clause>

  <clause id="10304">
    <literal><![CDATA[
      K(x,x \ ((x \ y) \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),10298(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 10298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10305">
    <literal><![CDATA[
      T(x,y * (x \ z)) = (x \ (y * z)) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(428,a,10300,a),flip(a)].">
      <j1 rule="hyper" parents="428 10300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10306">
    <literal><![CDATA[
      K(x,x \ (y * (z * x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8557,a,b,10301,a)].">
      <j1 rule="hyper" parents="58 8557 10301"/>
    </justification>
  </clause>

  <clause id="10307">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[para(4(a,1),10304(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 10304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10308">
    <literal><![CDATA[
      K(x,x \ (y \ (z * x))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(8419,a,10307,a),flip(a)].">
      <j1 rule="hyper" parents="8419 10307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10309">
    <literal><![CDATA[
      K(x,y \ (x \ z)) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(7368,a,10307,a)].">
      <j1 rule="hyper" parents="7368 10307"/>
    </justification>
  </clause>

  <clause id="10310">
    <literal><![CDATA[
      K(x,x \ (y \ (x * z))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(10307(a,1),7366(a,1))].">
      <j1 rule="para" parents="10307 7366"/>
    </justification>
  </clause>

  <clause id="10311">
    <literal><![CDATA[
      K(x,x \ (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(10307(a,1),7368(a,1))].">
      <j1 rule="para" parents="10307 7368"/>
    </justification>
  </clause>

  <clause id="10312">
    <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),10308(a,1,2,2,2))].">
      <j1 rule="para" parents="101 10308"/>
    </justification>
  </clause>

  <clause id="10313">
    <literal><![CDATA[
      K(x,y \ (x \ (y * z))) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(4(a,1),10309(a,2,2,2))].">
      <j1 rule="para" parents="4 10309"/>
    </justification>
  </clause>

  <clause id="10314">
    <literal><![CDATA[
      L(K(x,x \ y),y,z) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(7572,a,10313,a)].">
      <j1 rule="hyper" parents="7572 10313"/>
    </justification>
  </clause>

  <clause id="10315">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4869,a(flip),b,10313,a),flip(a)].">
      <j1 rule="hyper" parents="320 4869 10313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10316">
    <literal><![CDATA[
      (x * y) * K(z,z \ y) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[para(10313(a,1),8508(a,1,2))].">
      <j1 rule="para" parents="10313 8508"/>
    </justification>
  </clause>

  <clause id="10317">
    <literal><![CDATA[
      a(x,y,K(z,z \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10314,a,b,1923,a),flip(a)].">
      <j1 rule="hyper" parents="115 10314 1923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10318">
    <literal><![CDATA[
      L(K(x \ y,x),y,z) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(5862,a,10317,a)].">
      <j1 rule="hyper" parents="5862 10317"/>
    </justification>
  </clause>

  <clause id="10319">
    <literal><![CDATA[
      K(x \ (y \ (x * z)),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(8447,a,10318,a)].">
      <j1 rule="hyper" parents="8447 10318"/>
    </justification>
  </clause>

  <clause id="10320">
    <literal><![CDATA[
      K((x * y) \ z,y) = K(y \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(6829,a,10318,a)].">
      <j1 rule="hyper" parents="6829 10318"/>
    </justification>
  </clause>

  <clause id="10322">
    <literal><![CDATA[
      (x * y) * K(z \ y,z) = x * ((z \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10318,a(flip),b,463,a)].">
      <j1 rule="hyper" parents="119 10318 463"/>
    </justification>
  </clause>

  <clause id="10323">
    <literal><![CDATA[
      K(x,L(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8701,a,10315,a)].">
      <j1 rule="hyper" parents="8701 10315"/>
    </justification>
  </clause>

  <clause id="10324">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8998,a,10323,a)].">
      <j1 rule="hyper" parents="8998 10323"/>
    </justification>
  </clause>

  <clause id="10327">
    <literal><![CDATA[
      T(x,L(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,10323,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 10323 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10329">
    <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(501(a,1),10323(a,1,2))].">
      <j1 rule="para" parents="501 10323"/>
    </justification>
  </clause>

  <clause id="10331">
    <literal><![CDATA[
      K(L(x,y,z),L(u,x,w)) = L(K(x,u),y * x,z)
    ]]></literal>
    <justification jstring="[para(10323(a,1),6586(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10323 6586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10332">
    <literal><![CDATA[
      (x * (y * z)) * K(z,y) = x * (z * y)
    ]]></literal>
    <justification jstring="[para(10323(a,1),6604(a,1,2))].">
      <j1 rule="para" parents="10323 6604"/>
    </justification>
  </clause>

  <clause id="10333">
    <literal><![CDATA[
      (x * (y * z)) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = u
    ]]></literal>
    <justification jstring="[para(10323(a,1),6657(a,1,2))].">
      <j1 rule="para" parents="10323 6657"/>
    </justification>
  </clause>

  <clause id="10334">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(L(x,y,v5),L(y,u,w))
    ]]></literal>
    <justification jstring="[para(10323(a,1),9926(a,1,1))].">
      <j1 rule="para" parents="10323 9926"/>
    </justification>
  </clause>

  <clause id="10335">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,L(y,x,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,10323,a,b,10324,a),flip(a)].">
      <j1 rule="hyper" parents="320 10323 10324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10338">
    <literal><![CDATA[
      L(x,y,z) * T(y,x) = y * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10327,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 10327 17"/>
    </justification>
  </clause>

  <clause id="10339">
    <literal><![CDATA[
      L(x,y,z) = (z * T(y,x)) \ (z * (T(y,x) * x))
    ]]></literal>
    <justification jstring="[para(10327(a,1),6877(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10327 6877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10341">
    <literal><![CDATA[
      K(x,L(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(10335(a,1),7367(a,1))].">
      <j1 rule="para" parents="10335 7367"/>
    </justification>
  </clause>

  <clause id="10343">
    <literal><![CDATA[
      K(x,(y * x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(298(a,1),10341(a,1,2))].">
      <j1 rule="para" parents="298 10341"/>
    </justification>
  </clause>

  <clause id="10344">
    <literal><![CDATA[
      K(x \ (y \ z),y) = K(y \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(5(a,1),10319(a,1,1,2,2))].">
      <j1 rule="para" parents="5 10319"/>
    </justification>
  </clause>

  <clause id="10345">
    <literal><![CDATA[
      K(x \ (y \ (z * x)),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(8400,a,10320,a),flip(a)].">
      <j1 rule="hyper" parents="8400 10320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10346">
    <literal><![CDATA[
      K(x \ (y \ z),x) * z = z * K(z / (y * x),x)
    ]]></literal>
    <justification jstring="[para(10320(a,1),7929(a,1,1))].">
      <j1 rule="para" parents="10320 7929"/>
    </justification>
  </clause>

  <clause id="10347">
    <literal><![CDATA[
      K(x \ (y \ z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x \ z),x) = u
    ]]></literal>
    <justification jstring="[para(10320(a,1),8443(a,1))].">
      <j1 rule="para" parents="10320 8443"/>
    </justification>
  </clause>

  <clause id="10348">
    <literal><![CDATA[
      R(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(833,a,10332,a)].">
      <j1 rule="hyper" parents="833 10332"/>
    </justification>
  </clause>

  <clause id="10349">
    <literal><![CDATA[
      (x / (y * z)) * (z * y) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(326,a,10332,a),flip(a)].">
      <j1 rule="hyper" parents="326 10332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10350">
    <literal><![CDATA[
      K(x,T(y,z * (x * y))) * (z * (y * x)) = z * (x * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,10332,a(flip),b,7896,a)].">
      <j1 rule="hyper" parents="119 10332 7896"/>
    </justification>
  </clause>

  <clause id="10351">
    <literal><![CDATA[
      K(x * (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (z * y),z) = u
    ]]></literal>
    <justification jstring="[para(10332(a,1),7307(a,1,1))].">
      <j1 rule="para" parents="10332 7307"/>
    </justification>
  </clause>

  <clause id="10352">
    <literal><![CDATA[
      R(x,y,T(z,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(6871,a,10348,a)].">
      <j1 rule="hyper" parents="6871 10348"/>
    </justification>
  </clause>

  <clause id="10353">
    <literal><![CDATA[
      R(x,y,K(z \ y,z)) = x
    ]]></literal>
    <justification jstring="[para(5(a,1),10348(a,1,2))].">
      <j1 rule="para" parents="5 10348"/>
    </justification>
  </clause>

  <clause id="10354">
    <literal><![CDATA[
      R(x,y / z,z) = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10209,a(flip),b,10353,a),flip(a)].">
      <j1 rule="hyper" parents="58 10209 10353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10356">
    <literal><![CDATA[
      (x * T(y,z)) / (y * z) = R(x / z,z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,527,a(flip),b,10352,a)].">
      <j1 rule="hyper" parents="58 527 10352"/>
    </justification>
  </clause>

  <clause id="10357">
    <literal><![CDATA[
      R(x,y,z / y) = R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(107(a,1),10352(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 10352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10359">
    <literal><![CDATA[
      R(x,y,z) * (z * y) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(10352(a,1),516(a,1,1))].">
      <j1 rule="para" parents="10352 516"/>
    </justification>
  </clause>

  <clause id="10361">
    <literal><![CDATA[
      R(x,y,K(z,T(u,y))) = R(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(7131(a,2),10352(a,1,3))].">
      <j1 rule="para" parents="7131 10352"/>
    </justification>
  </clause>

  <clause id="10363">
    <literal><![CDATA[
      R(K(x,(y / (z / u)) \ x),u \ z,u) = K(x,z / ((x \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8459,a(flip),b,10354,a),flip(a)].">
      <j1 rule="hyper" parents="58 8459 10354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10364">
    <literal><![CDATA[
      R(K(x,(y / z) / u),z \ y,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6917,a(flip),b,10354,a),flip(a)].">
      <j1 rule="hyper" parents="58 6917 10354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10365">
    <literal><![CDATA[
      R(x / (y / z),z \ y,z) = (x * z) / y
    ]]></literal>
    <justification jstring="[hyper(58,a,525,a(flip),b,10354,a),flip(a)].">
      <j1 rule="hyper" parents="58 525 10354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10368">
    <literal><![CDATA[
      R(x,y \ z,y) * z = (x * (z / y)) * y
    ]]></literal>
    <justification jstring="[para(10354(a,1),508(a,1,1))].">
      <j1 rule="para" parents="10354 508"/>
    </justification>
  </clause>

  <clause id="10369">
    <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(10338(a,1),1405(a,1,2,2))].">
      <j1 rule="para" parents="10338 1405"/>
    </justification>
  </clause>

  <clause id="10370">
    <literal><![CDATA[
      x * K(y \ (z \ u),z) = x * K(z \ (y \ u),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10344,a,b,4,a)].">
      <j1 rule="hyper" parents="119 10344 4"/>
    </justification>
  </clause>

  <clause id="10371">
    <literal><![CDATA[
      (x * T(y,z)) / (y * z) = (x * y) / (z * y)
    ]]></literal>
    <justification jstring="[hyper(117,a,6302,a(flip),b,10349,a),flip(a)].">
      <j1 rule="hyper" parents="117 6302 10349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10372">
    <literal><![CDATA[
      R(R(x,y,x) / x,x,z) = (z * R(x,y,x)) / (z * x)
    ]]></literal>
    <justification jstring="[para(7079(a,1),10356(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7079 10356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10373">
    <literal><![CDATA[
      R(x / ((y * z) / y),z,y) = (x * y) / (y * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),10365(a,1,2))].">
      <j1 rule="para" parents="4 10365"/>
    </justification>
  </clause>

  <clause id="10374">
    <literal><![CDATA[
      K(x,K(y / z,u * z)) = K(x,K(y / z,u * y))
    ]]></literal>
    <justification jstring="[para(75(a,1),10303(a,1,2,2,2))].">
      <j1 rule="para" parents="75 10303"/>
    </justification>
  </clause>

  <clause id="10375">
    <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(10305(a,2),5115(a,1,1))].">
      <j1 rule="para" parents="10305 5115"/>
    </justification>
  </clause>

  <clause id="10378">
    <literal><![CDATA[
      K(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (x \ (u \ y))) = z
    ]]></literal>
    <justification jstring="[para(5(a,1),10299(a,1,2,2))].">
      <j1 rule="para" parents="5 10299"/>
    </justification>
  </clause>

  <clause id="10379">
    <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),10311(a,1,2,2))].">
      <j1 rule="para" parents="17 10311"/>
    </justification>
  </clause>

  <clause id="10380">
    <literal><![CDATA[
      K(L(x,y,z),L(u,x,w)) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,6586,a(flip),b,10331,a),flip(a)].">
      <j1 rule="hyper" parents="320 6586 10331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10381">
    <literal><![CDATA[
      K(L(x,y,z),(u * x) \ (u * w)) = K(L(x,y,z),x \ w)
    ]]></literal>
    <justification jstring="[hyper(6682,a,10380,a)].">
      <j1 rule="hyper" parents="6682 10380"/>
    </justification>
  </clause>

  <clause id="10382">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = w
    ]]></literal>
    <justification jstring="[para(10323(a,2),10333(a,1,2))].">
      <j1 rule="para" parents="10323 10333"/>
    </justification>
  </clause>

  <clause id="10383">
    <literal><![CDATA[
      L(x,T(y,x),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,13,a,b,10339,a)].">
      <j1 rule="hyper" parents="320 13 10339"/>
    </justification>
  </clause>

  <clause id="10385">
    <literal><![CDATA[
      L(x,y / x,z) = L(x,x \ y,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),10383(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 10383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10389">
    <literal><![CDATA[
      L(x,x \ (y \ z),y) = (y * ((y \ z) / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,567,a(flip),b,10385,a),flip(a)].">
      <j1 rule="hyper" parents="58 567 10385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10390">
    <literal><![CDATA[
      L(x,x \ y,z) = (z * (y / x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,94,a(flip),b,10385,a),flip(a)].">
      <j1 rule="hyper" parents="58 94 10385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10391">
    <literal><![CDATA[
      x / L(y,y \ (z \ x),z) = z * ((z \ x) / y)
    ]]></literal>
    <justification jstring="[hyper(366,a,10390,a(flip))].">
      <j1 rule="hyper" parents="366 10390"/>
    </justification>
  </clause>

  <clause id="10392">
    <literal><![CDATA[
      K(x,T(L(y,y \ z,u),u * z)) = K(x,(u * z) / (u * (z / y)))
    ]]></literal>
    <justification jstring="[para(10390(a,2),7865(a,1,2,1))].">
      <j1 rule="para" parents="10390 7865"/>
    </justification>
  </clause>

  <clause id="10393">
    <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(10390(a,2),7963(a,1,1,2))].">
      <j1 rule="para" parents="10390 7963"/>
    </justification>
  </clause>

  <clause id="10394">
    <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),10343(a,1,2))].">
      <j1 rule="para" parents="9 10343"/>
    </justification>
  </clause>

  <clause id="10395">
    <literal><![CDATA[
      ((x * y) * z) / (z * y) = R(x * K(y,z),y,z)
    ]]></literal>
    <justification jstring="[para(6442(a,1),10373(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6442 10373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10396">
    <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(7152(a,1),10395(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7152 10395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10397">
    <literal><![CDATA[
      K(x \ (y * z),x) = K(y * (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(6316,a,10302,a),flip(a)].">
      <j1 rule="hyper" parents="6316 10302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10398">
    <literal><![CDATA[
      K(x \ (y * z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * (x \ z),x) = u
    ]]></literal>
    <justification jstring="[para(10302(a,1),6316(a,1))].">
      <j1 rule="para" parents="10302 6316"/>
    </justification>
  </clause>

  <clause id="10399">
    <literal><![CDATA[
      K(x * (y \ (x \ z)),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),10397(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 10397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10400">
    <literal><![CDATA[
      K(L(x,y,z),L(y,u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9924,a(flip),b,10334,a),flip(a)].">
      <j1 rule="hyper" parents="58 9924 10334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10401">
    <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(10334(a,2),7367(a,1))].">
      <j1 rule="para" parents="10334 7367"/>
    </justification>
  </clause>

  <clause id="10402">
    <literal><![CDATA[
      K((x * y) \ z,L(y,u,w)) = K(y \ (x \ z),L(y,u,w))
    ]]></literal>
    <justification jstring="[para(298(a,1),10400(a,1,1))].">
      <j1 rule="para" parents="298 10400"/>
    </justification>
  </clause>

  <clause id="10403">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) = R(a(y,z,y),y,x)
    ]]></literal>
    <justification jstring="[para(8915(a,1),10372(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8915 10372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10404">
    <literal><![CDATA[
      R(a(x,y,x),x,z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(9535,a,10403,a),flip(a)].">
      <j1 rule="hyper" parents="9535 10403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10406">
    <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,511,a,b,10404,a)].">
      <j1 rule="hyper" parents="58 511 10404"/>
    </justification>
  </clause>

  <clause id="10407">
    <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),10401(a,1,2,1))].">
      <j1 rule="para" parents="104 10401"/>
    </justification>
  </clause>

  <clause id="10408">
    <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),10407(a,1,2))].">
      <j1 rule="para" parents="5 10407"/>
    </justification>
  </clause>

  <clause id="10409">
    <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),10407(a,1,2))].">
      <j1 rule="para" parents="7 10407"/>
    </justification>
  </clause>

  <clause id="10410">
    <literal><![CDATA[
      K(L(x,y,z),u \ (x \ (u * w))) = K(L(x,y,z),x \ w)
    ]]></literal>
    <justification jstring="[hyper(9244,a,10381,a)].">
      <j1 rule="hyper" parents="9244 10381"/>
    </justification>
  </clause>

  <clause id="10412">
    <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),10402(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7 10402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10413">
    <literal><![CDATA[
      K(x \ ((x \ y) \ z),L(x,u,w)) = K(y \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(10022,a,10412,a)].">
      <j1 rule="hyper" parents="10022 10412"/>
    </justification>
  </clause>

  <clause id="10414">
    <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),10392(a,1,2))].">
      <j1 rule="para" parents="20 10392"/>
    </justification>
  </clause>

  <clause id="10415">
    <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(58,a,9746,a(flip),b,10329,a)].">
      <j1 rule="hyper" parents="58 9746 10329"/>
    </justification>
  </clause>

  <clause id="10416">
    <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,10410,a(flip),b,10415,a),flip(a)].">
      <j1 rule="hyper" parents="58 10410 10415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10418">
    <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,10416,a,b,4723,a)].">
      <j1 rule="hyper" parents="119 10416 4723"/>
    </justification>
  </clause>

  <clause id="10419">
    <literal><![CDATA[
      x / L(T(y,y \ x),z,u) = L(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(10418(a,1),4798(a,1,2))].">
      <j1 rule="para" parents="10418 4798"/>
    </justification>
  </clause>

  <clause id="10420">
    <literal><![CDATA[
      x / L(y \ x,z,u) = L(x / y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(642(a,1),10419(a,1,2,1))].">
      <j1 rule="para" parents="642 10419"/>
    </justification>
  </clause>

  <clause id="10422">
    <literal><![CDATA[
      (L(x / y,z,u) \ x) \ x = L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(188,a,10420,a)].">
      <j1 rule="hyper" parents="188 10420"/>
    </justification>
  </clause>

  <clause id="10424">
    <literal><![CDATA[
      L((x \ y) \ y,z,u) = (L(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[para(72(a,1),10422(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 10422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10428">
    <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(10424(a,2),4758(a,1,1))].">
      <j1 rule="para" parents="10424 4758"/>
    </justification>
  </clause>

  <clause id="10429">
    <literal><![CDATA[
      K(L(x,y,z) \ u,L(x,y,z)) = K(x \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(4989,a,10428,a),flip(a)].">
      <j1 rule="hyper" parents="4989 10428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10430">
    <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(10347,a,10429,a)].">
      <j1 rule="hyper" parents="10347 10429"/>
    </justification>
  </clause>

  <clause id="10431">
    <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,7445,a(flip),b,10430,a),flip(a)].">
      <j1 rule="hyper" parents="58 7445 10430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10432">
    <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,10413,a(flip),b,10431,a)].">
      <j1 rule="hyper" parents="58 10413 10431"/>
    </justification>
  </clause>

  <clause id="10433">
    <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),10369(a,1,1,1))].">
      <j1 rule="para" parents="105 10369"/>
    </justification>
  </clause>

  <clause id="10434">
    <literal><![CDATA[
      K(L(x,y,z),x * T(y,x)) = K(x,y * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(1638,a,10433,a),flip(a)].">
      <j1 rule="hyper" parents="1638 10433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10435">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,y * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(105(a,1),10434(a,1,2))].">
      <j1 rule="para" parents="105 10434"/>
    </justification>
  </clause>

  <clause id="10436">
    <literal><![CDATA[
      K(x,y * L(x,y,z)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(8375,a,10435,a),flip(a)].">
      <j1 rule="hyper" parents="8375 10435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10438">
    <literal><![CDATA[
      L(K(x,x * y),z * x,u) = K(L(x,z,u),y * L(x,y,w))
    ]]></literal>
    <justification jstring="[para(10436(a,1),6586(a,1,1))].">
      <j1 rule="para" parents="10436 6586"/>
    </justification>
  </clause>

  <clause id="10439">
    <literal><![CDATA[
      K(L(x,y,z),u * L(x,u,w)) = K(L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(8365,a,10438,a),flip(a)].">
      <j1 rule="hyper" parents="8365 10438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10440">
    <literal><![CDATA[
      L(K(L(x,y,z),x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(10439(a,1),9646(a,1,1))].">
      <j1 rule="para" parents="10439 9646"/>
    </justification>
  </clause>

  <clause id="10441">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(8879(a,1),10440(a,1,1))].">
      <j1 rule="para" parents="8879 10440"/>
    </justification>
  </clause>

  <clause id="10443">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9643,a(flip),b,10441,a)].">
      <j1 rule="hyper" parents="58 9643 10441"/>
    </justification>
  </clause>

  <clause id="10444">
    <literal><![CDATA[
      K(x,y \ ((y * z) * x)) = K(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9642,a(flip),b,10441,a)].">
      <j1 rule="hyper" parents="58 9642 10441"/>
    </justification>
  </clause>

  <clause id="10445">
    <literal><![CDATA[
      1 / L(K(x,x * y),y,z) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(10441(a,2),4931(a,1,2))].">
      <j1 rule="para" parents="10441 4931"/>
    </justification>
  </clause>

  <clause id="10447">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(6576,a,10443,a)].">
      <j1 rule="hyper" parents="6576 10443"/>
    </justification>
  </clause>

  <clause id="10448">
    <literal><![CDATA[
      K(x,x * ((y * z) \ y)) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(6559,a,10443,a),flip(a)].">
      <j1 rule="hyper" parents="6559 10443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10449">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,u) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(320,a,10441,a,b,10443,a)].">
      <j1 rule="hyper" parents="320 10441 10443"/>
    </justification>
  </clause>

  <clause id="10451">
    <literal><![CDATA[
      K(x,y \ ((y * z) * x)) = K(x,z * x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5346,a,b,10444,a),flip(a)].">
      <j1 rule="hyper" parents="320 5346 10444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10452">
    <literal><![CDATA[
      L(K(x,y * x),y,z) = K(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9644,a,b,10451,a)].">
      <j1 rule="hyper" parents="58 9644 10451"/>
    </justification>
  </clause>

  <clause id="10454">
    <literal><![CDATA[
      a(x,y,K(z,y * z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10452,a,b,1923,a),flip(a)].">
      <j1 rule="hyper" parents="115 10452 1923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10455">
    <literal><![CDATA[
      a(x,y,K(y * z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10452,a(flip),b,5865,a),flip(a)].">
      <j1 rule="hyper" parents="115 10452 5865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10456">
    <literal><![CDATA[
      L(K(x * y,y),x,z) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(5862,a,10454,a)].">
      <j1 rule="hyper" parents="5862 10454"/>
    </justification>
  </clause>

  <clause id="10457">
    <literal><![CDATA[
      a(x,y,K(z,y \ z)) = 1
    ]]></literal>
    <justification jstring="[para(5(a,1),10455(a,1,3,1))].">
      <j1 rule="para" parents="5 10455"/>
    </justification>
  </clause>

  <clause id="10458">
    <literal><![CDATA[
      L(K(x * y,y),x,z) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5228,a(flip),b,10456,a),flip(a)].">
      <j1 rule="hyper" parents="320 5228 10456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10459">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(5228(a,1),10458(a,1,1))].">
      <j1 rule="para" parents="5228 10458"/>
    </justification>
  </clause>

  <clause id="10460">
    <literal><![CDATA[
      K((x * (y \ 1)) \ z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(6830,a,10459,a)].">
      <j1 rule="hyper" parents="6830 10459"/>
    </justification>
  </clause>

  <clause id="10461">
    <literal><![CDATA[
      K(x \ (y * z),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9636,a(flip),b,10459,a)].">
      <j1 rule="hyper" parents="58 9636 10459"/>
    </justification>
  </clause>

  <clause id="10462">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(x * (y \ z),x)
    ]]></literal>
    <justification jstring="[hyper(8401,a,10461,a)].">
      <j1 rule="hyper" parents="8401 10461"/>
    </justification>
  </clause>

  <clause id="10463">
    <literal><![CDATA[
      K(x * ((y * x) \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(8400,a,10461,a),flip(a)].">
      <j1 rule="hyper" parents="8400 10461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10464">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(z * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(6610,a,10461,a)].">
      <j1 rule="hyper" parents="6610 10461"/>
    </justification>
  </clause>

  <clause id="10466">
    <literal><![CDATA[
      K(x * (y \ (x \ z)),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7616,a(flip),b,10461,a),flip(a)].">
      <j1 rule="hyper" parents="58 7616 10461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10467">
    <literal><![CDATA[
      K(x,y \ z) * K(x * (y \ z),x) = a(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(10461(a,1),8920(a,1,2))].">
      <j1 rule="para" parents="10461 8920"/>
    </justification>
  </clause>

  <clause id="10468">
    <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,10432,a(flip),b,10462,a),flip(a)].">
      <j1 rule="hyper" parents="58 10432 10462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10469">
    <literal><![CDATA[
      K((x / y) \ z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[para(7(a,1),10463(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 10463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10470">
    <literal><![CDATA[
      1 / ((x * (y \ T(y * z,y))) \ (x * z)) = K(y * z,y)
    ]]></literal>
    <justification jstring="[para(6646(a,2),10445(a,1,2))].">
      <j1 rule="para" parents="6646 10445"/>
    </justification>
  </clause>

  <clause id="10472">
    <literal><![CDATA[
      K((x * (1 / y)) \ z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8620,a,b,10460,a)].">
      <j1 rule="hyper" parents="58 8620 10460"/>
    </justification>
  </clause>

  <clause id="10473">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x * (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(10449(a,1),3637(a,1))].">
      <j1 rule="para" parents="10449 3637"/>
    </justification>
  </clause>

  <clause id="10474">
    <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(1403(a,1),10473(a,1,2))].">
      <j1 rule="para" parents="1403 10473"/>
    </justification>
  </clause>

  <clause id="10475">
    <literal><![CDATA[
      T(K(x * y,T(x,z)),z) = 1 / ((u * (x \ T(x * y,x))) \ (u * y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7854,a,b,10470,a)].">
      <j1 rule="hyper" parents="320 7854 10470"/>
    </justification>
  </clause>

  <clause id="10477">
    <literal><![CDATA[
      a(x,(y \ z) \ 1,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ y,x) = u
    ]]></literal>
    <justification jstring="[para(10467(a,1),8948(a,1))].">
      <j1 rule="para" parents="10467 8948"/>
    </justification>
  </clause>

  <clause id="10478">
    <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(320,a,9828,a(flip),b,10468,a),flip(a)].">
      <j1 rule="hyper" parents="320 9828 10468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10479">
    <literal><![CDATA[
      K(L(x,y,z) * (x \ u),L(x,y,z)) = K(u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,673,a(flip),b,10478,a),flip(a)].">
      <j1 rule="hyper" parents="320 673 10478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10480">
    <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),10479(a,1,1,2))].">
      <j1 rule="para" parents="4 10479"/>
    </justification>
  </clause>

  <clause id="10481">
    <literal><![CDATA[
      K((x \ y) \ z,L(x,u,w)) = K(x * (y \ z),L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,10468,a(flip),b,10480,a)].">
      <j1 rule="hyper" parents="58 10468 10480"/>
    </justification>
  </clause>

  <clause id="10482">
    <literal><![CDATA[
      T(L(x,y,z) * K(x * u,L(x,y,z)),u) = R(L(x,y,z),u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(10480(a,1),5166(a,1,1,2))].">
      <j1 rule="para" parents="10480 5166"/>
    </justification>
  </clause>

  <clause id="10483">
    <literal><![CDATA[
      K((x \ y) \ z,L(x,u,w)) = K((y \ z) * x,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,9563,a,b,10481,a),flip(a)].">
      <j1 rule="hyper" parents="320 9563 10481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10484">
    <literal><![CDATA[
      K(x \ (y * z),L(y,u,w)) = K((x \ z) * y,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(9829,a,10483,a)].">
      <j1 rule="hyper" parents="9829 10483"/>
    </justification>
  </clause>

  <clause id="10485">
    <literal><![CDATA[
      K(x \ (y * z),L(z,u,w)) = K((x \ y) * z,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9702,a,b,10484,a)].">
      <j1 rule="hyper" parents="58 9702 10484"/>
    </justification>
  </clause>

  <clause id="10486">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,L(u,z,x)) = K(y \ (x * (u * z)),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,8994,a(flip),b,10484,a),flip(a)].">
      <j1 rule="hyper" parents="58 8994 10484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10487">
    <literal><![CDATA[
      K((x / y) \ z,L(y,u,w)) = K((x \ z) * y,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9700,a,b,10485,a)].">
      <j1 rule="hyper" parents="58 9700 10485"/>
    </justification>
  </clause>

  <clause id="10488">
    <literal><![CDATA[
      T(K(x,K(y,z)) * K(y * z,y),x) = 1 / ((u * (y \ T(y * z,y))) \ (u * z))
    ]]></literal>
    <justification jstring="[para(7937(a,2),10475(a,1,1))].">
      <j1 rule="para" parents="7937 10475"/>
    </justification>
  </clause>

  <clause id="10489">
    <literal><![CDATA[
      T(L(x * K(x * y,x),z,u),y) = R(L(x,z,u),y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(5478(a,1),10482(a,1,1))].">
      <j1 rule="para" parents="5478 10482"/>
    </justification>
  </clause>

  <clause id="10490">
    <literal><![CDATA[
      R(L(x,y,z),u,L(x,y,z)) = L(T(x * K(x * u,x),u),y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,20,a,b,10489,a),flip(a)].">
      <j1 rule="hyper" parents="58 20 10489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10491">
    <literal><![CDATA[
      R(L(x,y,z),u,L(x,y,z)) = L(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(5166(a,1),10490(a,2,1))].">
      <j1 rule="para" parents="5166 10490"/>
    </justification>
  </clause>

  <clause id="10492">
    <literal><![CDATA[
      R(x,y,L(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(141,a,10491,a)].">
      <j1 rule="hyper" parents="141 10491"/>
    </justification>
  </clause>

  <clause id="10493">
    <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(10491(a,1),7111(a,1,2))].">
      <j1 rule="para" parents="10491 7111"/>
    </justification>
  </clause>

  <clause id="10494">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,4891,a,b,10492,a)].">
      <j1 rule="hyper" parents="320 4891 10492"/>
    </justification>
  </clause>

  <clause id="10495">
    <literal><![CDATA[
      x * R(y,z,L(y,u,w)) = x * R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,10492,a,b,4,a)].">
      <j1 rule="hyper" parents="119 10492 4"/>
    </justification>
  </clause>

  <clause id="10497">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = (w * T(y,x)) \ (w * R(y,x,y))
    ]]></literal>
    <justification jstring="[para(10492(a,1),9914(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10492 9914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10498">
    <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(10492(a,1),10281(a,1,1,2,2))].">
      <j1 rule="para" parents="10492 10281"/>
    </justification>
  </clause>

  <clause id="10499">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7301,a(flip),b,10497,a),flip(a)].">
      <j1 rule="hyper" parents="320 7301 10497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10501">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = K(x,y) * a(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,8937,a,b,10499,a),flip(a)].">
      <j1 rule="hyper" parents="320 8937 10499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10502">
    <literal><![CDATA[
      K(x * (L(x,y,z) \ u),x) = K(u,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7406,a(flip),b,10499,a),flip(a)].">
      <j1 rule="hyper" parents="58 7406 10499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10503">
    <literal><![CDATA[
      K(x * (y * z),z) = K(z * (x * y),z)
    ]]></literal>
    <justification jstring="[para(90(a,1),10499(a,1,1))].">
      <j1 rule="para" parents="90 10499"/>
    </justification>
  </clause>

  <clause id="10505">
    <literal><![CDATA[
      K(L(x,y,z) \ u,x) = K(x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,10466,a(flip),b,10502,a)].">
      <j1 rule="hyper" parents="58 10466 10502"/>
    </justification>
  </clause>

  <clause id="10506">
    <literal><![CDATA[
      K(x / L(y,z,u),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(8236,a,10505,a)].">
      <j1 rule="hyper" parents="8236 10505"/>
    </justification>
  </clause>

  <clause id="10507">
    <literal><![CDATA[
      K(x \ (y * L(x,z,u)),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(6(a,1),10506(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 10506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10508">
    <literal><![CDATA[
      T(x * L(y,z,u),K(x,y)) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(10507(a,1),4683(a,1,2))].">
      <j1 rule="para" parents="10507 4683"/>
    </justification>
  </clause>

  <clause id="10509">
    <literal><![CDATA[
      K(x * (y * z),y) = K(y * (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(10351,a,10503,a)].">
      <j1 rule="hyper" parents="10351 10503"/>
    </justification>
  </clause>

  <clause id="10510">
    <literal><![CDATA[
      a(x,y,L(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(9936,a,10501,a)].">
      <j1 rule="hyper" parents="9936 10501"/>
    </justification>
  </clause>

  <clause id="10511">
    <literal><![CDATA[
      (x / y) * R(y,z,y) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(10510(a,2),9094(a,2,2))].">
      <j1 rule="para" parents="10510 9094"/>
    </justification>
  </clause>

  <clause id="10513">
    <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),10508(a,1,1,2))].">
      <j1 rule="para" parents="92 10508"/>
    </justification>
  </clause>

  <clause id="10514">
    <literal><![CDATA[
      (x / y) * R(y,z,L(y,u,w)) = x * a(y,z,L(y,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,10495,a,b,10511,a)].">
      <j1 rule="hyper" parents="58 10495 10511"/>
    </justification>
  </clause>

  <clause id="10516">
    <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,9550,a(flip),b,10498,a)].">
      <j1 rule="hyper" parents="58 9550 10498"/>
    </justification>
  </clause>

  <clause id="10518">
    <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),10516(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 10516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10519">
    <literal><![CDATA[
      1 / ((x * (y \ T(y * z,y))) \ (x * z)) = K(u,K(y,z)) * K(y * z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(8446,a,10488,a),flip(a)].">
      <j1 rule="hyper" parents="8446 10488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10520">
    <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(4737(a,1),10266(a,1,2))].">
      <j1 rule="para" parents="4737 10266"/>
    </justification>
  </clause>

  <clause id="10521">
    <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(9718(a,1),10520(a,1,2))].">
      <j1 rule="para" parents="9718 10520"/>
    </justification>
  </clause>

  <clause id="10522">
    <literal><![CDATA[
      L(x,y \ R(T(y,z),u,y),y) = x
    ]]></literal>
    <justification jstring="[hyper(341,a,10521,a),flip(a)].">
      <j1 rule="hyper" parents="341 10521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10524">
    <literal><![CDATA[
      L(x,K(y,z) * a(y,u,y),y) = x
    ]]></literal>
    <justification jstring="[para(8931(a,1),10522(a,1,2))].">
      <j1 rule="para" parents="8931 10522"/>
    </justification>
  </clause>

  <clause id="10525">
    <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(6994(a,1),4340(a,2,1))].">
      <j1 rule="para" parents="6994 4340"/>
    </justification>
  </clause>

  <clause id="10526">
    <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(10525(a,2),327(a,1)),flip(b)].">
      <j1 rule="para" parents="10525 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10527">
    <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(5318,a,5674,a),flip(a)].">
      <j1 rule="hyper" parents="5318 5674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10529">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,z / (y * z)) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,5389,a(flip),b,10527,a),flip(a)].">
      <j1 rule="hyper" parents="320 5389 10527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10530">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5318,a,10529,a)].">
      <j1 rule="hyper" parents="5318 10529"/>
    </justification>
  </clause>

  <clause id="10531">
    <literal><![CDATA[
      K(R(1 / x,x,y) / z,x \ 1) = K(y / (z * (x * y)),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(5632,a,10530,a)].">
      <j1 rule="hyper" parents="5632 10530"/>
    </justification>
  </clause>

  <clause id="10533">
    <literal><![CDATA[
      K(x \ R(1 / y,y,z),y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(10007,a,10531,a)].">
      <j1 rule="hyper" parents="10007 10531"/>
    </justification>
  </clause>

  <clause id="10534">
    <literal><![CDATA[
      K(x \ R(y \ 1,y,z),y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3960,a(flip),b,10533,a)].">
      <j1 rule="hyper" parents="58 3960 10533"/>
    </justification>
  </clause>

  <clause id="10535">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ (x / (z * x)),z \ 1)
    ]]></literal>
    <justification jstring="[para(219(a,1),10533(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="219 10533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10536">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ ((z * x) \ x),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,8633,a(flip),b,10535,a),flip(a)].">
      <j1 rule="hyper" parents="320 8633 10535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10537">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),(z \ 1) \ 1) = K(y \ (x / ((z \ 1) * x)),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3523,a(flip),b,10535,a),flip(a)].">
      <j1 rule="hyper" parents="320 3523 10535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10538">
    <literal><![CDATA[
      K(x \ (y / ((z \ 1) * y)),z) = K(x \ z,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10156,a(flip),b,10537,a),flip(a)].">
      <j1 rule="hyper" parents="58 10156 10537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10540">
    <literal><![CDATA[
      K(x \ R(y \ 1,y,z),y \ 1) = K(x \ (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[para(3068(a,2),10538(a,1,1,2))].">
      <j1 rule="para" parents="3068 10538"/>
    </justification>
  </clause>

  <clause id="10541">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ (z \ 1),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,10534,a(flip),b,10540,a)].">
      <j1 rule="hyper" parents="58 10534 10540"/>
    </justification>
  </clause>

  <clause id="10543">
    <literal><![CDATA[
      K(x \ ((y * z) \ z),y \ 1) = K(x \ (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,10536,a(flip),b,10541,a)].">
      <j1 rule="hyper" parents="58 10536 10541"/>
    </justification>
  </clause>

  <clause id="10545">
    <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(6306(a,1),5728(a,1,1,2))].">
      <j1 rule="para" parents="6306 5728"/>
    </justification>
  </clause>

  <clause id="10546">
    <literal><![CDATA[
      L(T(x,y),x \ (z * K(u,x)),x) = T(L(x,x \ z,x),y)
    ]]></literal>
    <justification jstring="[para(9694(a,1),6364(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9694 6364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10547">
    <literal><![CDATA[
      L(T(x,y),x \ (K(z,x) * u),x) = T(L(x,x \ u,x),y)
    ]]></literal>
    <justification jstring="[para(7123(a,1),10546(a,1,2,2))].">
      <j1 rule="para" parents="7123 10546"/>
    </justification>
  </clause>

  <clause id="10549">
    <literal><![CDATA[
      L(T(x,y),x \ (K(z,x) * u),x) = L(T(x,y),x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,20,a,b,10547,a),flip(a)].">
      <j1 rule="hyper" parents="320 20 10547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10550">
    <literal><![CDATA[
      L(T(x,y),T(x,z) \ u,x) = L(T(x,y),x \ u,x)
    ]]></literal>
    <justification jstring="[para(5068(a,1),10549(a,1,2))].">
      <j1 rule="para" parents="5068 10549"/>
    </justification>
  </clause>

  <clause id="10551">
    <literal><![CDATA[
      L(T(x,y),T(z / T(x,u),x),x) = L(T(x,y),x \ z,x)
    ]]></literal>
    <justification jstring="[para(8309(a,2),10550(a,1,2))].">
      <j1 rule="para" parents="8309 10550"/>
    </justification>
  </clause>

  <clause id="10552">
    <literal><![CDATA[
      L(T(x,y),z / T(x,u),x) = L(T(x,y),x \ z,x)
    ]]></literal>
    <justification jstring="[hyper(7582,a,10551,a)].">
      <j1 rule="hyper" parents="7582 10551"/>
    </justification>
  </clause>

  <clause id="10553">
    <literal><![CDATA[
      R(x,x \ 1,y \ R(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,9890,a(flip),b,6545,a),flip(a)].">
      <j1 rule="hyper" parents="320 9890 6545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10555">
    <literal><![CDATA[
      R(x,x \ 1,a(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(8913(a,1),10553(a,1,3))].">
      <j1 rule="para" parents="8913 10553"/>
    </justification>
  </clause>

  <clause id="10556">
    <literal><![CDATA[
      (x \ 1) * a(y,x \ 1,y) = x \ a(y,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(10555(a,1),426(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10555 426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10557">
    <literal><![CDATA[
      T(x \ a(y,x \ 1,y),y) = y \ T(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(10556(a,1),8944(a,1,1))].">
      <j1 rule="para" parents="10556 8944"/>
    </justification>
  </clause>

  <clause id="10558">
    <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(10557(a,1),2103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10557 2103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10559">
    <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(3321(a,1),8086(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3321 8086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10560">
    <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(3321(a,1),10559(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3321 10559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10562">
    <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(10560(a,1),639(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10560 639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10564">
    <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(9187(a,1),8604(a,1,2))].">
      <j1 rule="para" parents="9187 8604"/>
    </justification>
  </clause>

  <clause id="10565">
    <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(7759(a,1),10564(a,1,2))].">
      <j1 rule="para" parents="7759 10564"/>
    </justification>
  </clause>

  <clause id="10567">
    <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(8221(a,1),10565(a,2,1))].">
      <j1 rule="para" parents="8221 10565"/>
    </justification>
  </clause>

  <clause id="10568">
    <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,9950,a(flip),b,10567,a)].">
      <j1 rule="hyper" parents="58 9950 10567"/>
    </justification>
  </clause>

  <clause id="10569">
    <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(9891,a,10568,a)].">
      <j1 rule="hyper" parents="9891 10568"/>
    </justification>
  </clause>

  <clause id="10570">
    <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(9992,a,10569,a)].">
      <j1 rule="hyper" parents="9992 10569"/>
    </justification>
  </clause>

  <clause id="10571">
    <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(7679,a,8769,a),flip(a)].">
      <j1 rule="hyper" parents="7679 8769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10572">
    <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(5598(a,1),9124(a,1,2))].">
      <j1 rule="para" parents="5598 9124"/>
    </justification>
  </clause>

  <clause id="10573">
    <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(320,a,8054,a(flip),b,10572,a),flip(a)].">
      <j1 rule="hyper" parents="320 8054 10572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10575">
    <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),9155(a,1,2,1))].">
      <j1 rule="para" parents="4 9155"/>
    </justification>
  </clause>

  <clause id="10577">
    <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),10575(a,1,2))].">
      <j1 rule="para" parents="13 10575"/>
    </justification>
  </clause>

  <clause id="10578">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(L(z,y,x),x * y,u))
    ]]></literal>
    <justification jstring="[hyper(8414,a,10577,a)].">
      <j1 rule="hyper" parents="8414 10577"/>
    </justification>
  </clause>

  <clause id="10579">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(z,x * y,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7042,a(flip),b,10578,a),flip(a)].">
      <j1 rule="hyper" parents="320 7042 10578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10581">
    <literal><![CDATA[
      K(L(x,(x \ y) * z,u),z) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),10579(a,2,2,2))].">
      <j1 rule="para" parents="5 10579"/>
    </justification>
  </clause>

  <clause id="10582">
    <literal><![CDATA[
      K(x,L(y * ((z * y) \ z),u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,10136,a(flip),b,10581,a),flip(a)].">
      <j1 rule="hyper" parents="58 10136 10581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10583">
    <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(4290(a,1),10581(a,1,1,2))].">
      <j1 rule="para" parents="4290 10581"/>
    </justification>
  </clause>

  <clause id="10584">
    <literal><![CDATA[
      K(x,y \ K(z,L(x,u,w))) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(10581(a,1),7228(a,1,2,2))].">
      <j1 rule="para" parents="10581 7228"/>
    </justification>
  </clause>

  <clause id="10585">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,6635,a(flip),b,10582,a)].">
      <j1 rule="hyper" parents="58 6635 10582"/>
    </justification>
  </clause>

  <clause id="10587">
    <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,6637,a(flip),b,10584,a),flip(a)].">
      <j1 rule="hyper" parents="58 6637 10584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10588">
    <literal><![CDATA[
      K(x,y \ K(z,L(L(x,u,w),v5,v6))) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(10581(a,1),10584(a,1,2,2))].">
      <j1 rule="para" parents="10581 10584"/>
    </justification>
  </clause>

  <clause id="10589">
    <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),10587(a,1,2,1,1))].">
      <j1 rule="para" parents="20 10587"/>
    </justification>
  </clause>

  <clause id="10590">
    <literal><![CDATA[
      K(x,y \ L(T(x,z),u,w)) = K(x,y \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(6136,a,10589,a)].">
      <j1 rule="hyper" parents="6136 10589"/>
    </justification>
  </clause>

  <clause id="10591">
    <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(1154(a,1),10590(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1154 10590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10592">
    <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(1164(a,1),10590(a,1,2,2,1))].">
      <j1 rule="para" parents="1164 10590"/>
    </justification>
  </clause>

  <clause id="10593">
    <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(7111,a,10583,a)].">
      <j1 rule="hyper" parents="7111 10583"/>
    </justification>
  </clause>

  <clause id="10595">
    <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,10242,a(flip),b,10593,a),flip(a)].">
      <j1 rule="hyper" parents="58 10242 10593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10596">
    <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(10595(a,1),10493(a,1))].">
      <j1 rule="para" parents="10595 10493"/>
    </justification>
  </clause>

  <clause id="10597">
    <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(116,a,105,a(flip),b,9336,a)].">
      <j1 rule="hyper" parents="116 105 9336"/>
    </justification>
  </clause>

  <clause id="10598">
    <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(9731,a,10597,a)].">
      <j1 rule="hyper" parents="9731 10597"/>
    </justification>
  </clause>

  <clause id="10599">
    <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(9134,a,10598,a)].">
      <j1 rule="hyper" parents="9134 10598"/>
    </justification>
  </clause>

  <clause id="10600">
    <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),10599(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 10599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10601">
    <literal><![CDATA[
      L(K(x,y),T(z,y * x),y * x) = K(x,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8700,a(flip),b,10600,a),flip(a)].">
      <j1 rule="hyper" parents="320 8700 10600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10602">
    <literal><![CDATA[
      K(x,L(y,x,((y * x) * z) / (y * x))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[para(224(a,1),10601(a,1,2)),flip(a)].">
      <j1 rule="para" parents="224 10601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10603">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = (y * z) * T(x * K(z,y),y * z)
    ]]></literal>
    <justification jstring="[para(10601(a,1),9336(a,1,2))].">
      <j1 rule="para" parents="10601 9336"/>
    </justification>
  </clause>

  <clause id="10604">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10341,a,10602,a),flip(a)].">
      <j1 rule="hyper" parents="10341 10602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10605">
    <literal><![CDATA[
      L(K(x,y),z,y * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(10602(a,1),10341(a,1))].">
      <j1 rule="para" parents="10602 10341"/>
    </justification>
  </clause>

  <clause id="10608">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(10604(a,1),9852(a,1,1))].">
      <j1 rule="para" parents="10604 9852"/>
    </justification>
  </clause>

  <clause id="10610">
    <literal><![CDATA[
      (x * y) * T(z * K(y,x),x * y) = z * (y * x)
    ]]></literal>
    <justification jstring="[hyper(10382,a,10603,a),flip(a)].">
      <j1 rule="hyper" parents="10382 10603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10611">
    <literal><![CDATA[
      (x * K(y,z)) * (z * y) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(284,a,10610,a)].">
      <j1 rule="hyper" parents="284 10610"/>
    </justification>
  </clause>

  <clause id="10612">
    <literal><![CDATA[
      (x * K(y,z)) / (z * y) = (x / (z * y)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,10349,a(flip),b,10611,a)].">
      <j1 rule="hyper" parents="117 10349 10611"/>
    </justification>
  </clause>

  <clause id="10613">
    <literal><![CDATA[
      (x / (y * z)) * K(y,z) = x / (z * y)
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,10611,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 10611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10614">
    <literal><![CDATA[
      ((x * K(y,z)) * z) \ (x * (y * z)) = L(y,z,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,10611,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="116 10611 90"/>
    </justification>
  </clause>

  <clause id="10615">
    <literal><![CDATA[
      (T(x,y) \ 1) * (x * y) = (x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(4760(a,1),10611(a,1,1))].">
      <j1 rule="para" parents="4760 10611"/>
    </justification>
  </clause>

  <clause id="10616">
    <literal><![CDATA[
      (x / y) * K(z,z \ y) = x / ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),10613(a,1,1,2))].">
      <j1 rule="para" parents="5 10613"/>
    </justification>
  </clause>

  <clause id="10617">
    <literal><![CDATA[
      (x / y) * K(y / z,z) = x / (z * (y / z))
    ]]></literal>
    <justification jstring="[para(7(a,1),10613(a,1,1,2))].">
      <j1 rule="para" parents="7 10613"/>
    </justification>
  </clause>

  <clause id="10618">
    <literal><![CDATA[
      (x / (y * z)) * (z * K(y,z)) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(10613(a,1),6060(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10613 6060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10619">
    <literal><![CDATA[
      K(x,y / (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x * z)) = u
    ]]></literal>
    <justification jstring="[para(10613(a,1),7213(a,1,2))].">
      <j1 rule="para" parents="10613 7213"/>
    </justification>
  </clause>

  <clause id="10620">
    <literal><![CDATA[
      K(x / (y * z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / (z * y),y) = u
    ]]></literal>
    <justification jstring="[para(10613(a,1),7307(a,1,1))].">
      <j1 rule="para" parents="10613 7307"/>
    </justification>
  </clause>

  <clause id="10621">
    <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(10615(a,1),6569(a,2,2,2))].">
      <j1 rule="para" parents="10615 6569"/>
    </justification>
  </clause>

  <clause id="10622">
    <literal><![CDATA[
      T(x / ((y \ z) * y),K(y,z)) = K(y,y \ z) * (x / z)
    ]]></literal>
    <justification jstring="[para(10616(a,1),8062(a,1,1))].">
      <j1 rule="para" parents="10616 8062"/>
    </justification>
  </clause>

  <clause id="10623">
    <literal><![CDATA[
      1 / ((x * ((x / y) \ 1)) / x) = x / (x * (y / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,9253,a,b,10617,a)].">
      <j1 rule="hyper" parents="58 9253 10617"/>
    </justification>
  </clause>

  <clause id="10624">
    <literal><![CDATA[
      (x / y) * K(z \ y,z) = x / (z * (y / z))
    ]]></literal>
    <justification jstring="[para(4924(a,1),10617(a,1,2))].">
      <j1 rule="para" parents="4924 10617"/>
    </justification>
  </clause>

  <clause id="10625">
    <literal><![CDATA[
      (x / (y * z)) * ((y * z) / y) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[hyper(4858,a,10618,a)].">
      <j1 rule="hyper" parents="4858 10618"/>
    </justification>
  </clause>

  <clause id="10626">
    <literal><![CDATA[
      (x * ((x / y) \ 1)) / x = (x / (x * (y / x))) \ 1
    ]]></literal>
    <justification jstring="[hyper(188,a,10623,a),flip(a)].">
      <j1 rule="hyper" parents="188 10623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10627">
    <literal><![CDATA[
      x / (x * (((y / x) \ 1) \ 1)) = ((x * ((x / y) \ 1)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(10626(a,2),3062(a,2,1))].">
      <j1 rule="para" parents="10626 3062"/>
    </justification>
  </clause>

  <clause id="10628">
    <literal><![CDATA[
      (x * (y * K(z,y))) \ (x * (z * y)) = L(z,y,x * K(z,y))
    ]]></literal>
    <justification jstring="[para(6060(a,1),10614(a,1,1))].">
      <j1 rule="para" parents="6060 10614"/>
    </justification>
  </clause>

  <clause id="10629">
    <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(9819(a,2),10627(a,2,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9819 10627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10630">
    <literal><![CDATA[
      K((x / y) \ z,R((x / y) \ 1,x / y,y)) = K(((x / y) \ 1) * z,y / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,3531,a(flip),b,9424,a),flip(a)].">
      <j1 rule="hyper" parents="320 3531 9424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10631">
    <literal><![CDATA[
      K((x / y) \ z,T(y / x,x / y)) = K(((x / y) \ 1) * z,y / x)
    ]]></literal>
    <justification jstring="[para(649(a,1),10630(a,1,2))].">
      <j1 rule="para" parents="649 10630"/>
    </justification>
  </clause>

  <clause id="10632">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) = K((x / y) \ z,y / x)
    ]]></literal>
    <justification jstring="[hyper(5747,a,10631,a),flip(a)].">
      <j1 rule="hyper" parents="5747 10631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10633">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) = K((y \ x) \ z,y / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,9398,a(flip),b,10632,a),flip(a)].">
      <j1 rule="hyper" parents="320 9398 10632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10634">
    <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(6900(a,1),9726(a,1,2))].">
      <j1 rule="para" parents="6900 9726"/>
    </justification>
  </clause>

  <clause id="10635">
    <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,9044,a(flip),b,10634,a)].">
      <j1 rule="hyper" parents="58 9044 10634"/>
    </justification>
  </clause>

  <clause id="10636">
    <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),9920(a,1,1))].">
      <j1 rule="para" parents="105 9920"/>
    </justification>
  </clause>

  <clause id="10637">
    <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(10191(a,1),10196(a,1,2,1))].">
      <j1 rule="para" parents="10191 10196"/>
    </justification>
  </clause>

  <clause id="10638">
    <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(5093(a,1),10637(a,1,2))].">
      <j1 rule="para" parents="5093 10637"/>
    </justification>
  </clause>

  <clause id="10640">
    <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(7131(a,2),10231(a,1,2,2,1))].">
      <j1 rule="para" parents="7131 10231"/>
    </justification>
  </clause>

  <clause id="10641">
    <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(7730(a,1),10396(a,1,1,2))].">
      <j1 rule="para" parents="7730 10396"/>
    </justification>
  </clause>

  <clause id="10642">
    <literal><![CDATA[
      x / (y * K(1 / z,z)) = K(z,1 / z) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(3396,a,10545,a)].">
      <j1 rule="hyper" parents="3396 10545"/>
    </justification>
  </clause>

  <clause id="10644">
    <literal><![CDATA[
      K(x,1 / x) * (y / L(x,z,u)) = y / (1 / (1 / L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(5783(a,1),10642(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5783 10642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10645">
    <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(320,a,9569,a(flip),b,10571,a),flip(a)].">
      <j1 rule="hyper" parents="320 9569 10571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10647">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K((L(x,y,z) * w) / u,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,7882,a(flip),b,10645,a),flip(a)].">
      <j1 rule="hyper" parents="320 7882 10645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10648">
    <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(5092(a,1),10640(a,1,2))].">
      <j1 rule="para" parents="5092 10640"/>
    </justification>
  </clause>

  <clause id="10649">
    <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(10648(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="10648 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10650">
    <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(1309(a,1),4429(a,1,1))].">
      <j1 rule="para" parents="1309 4429"/>
    </justification>
  </clause>

  <clause id="10651">
    <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(1329(a,1),10650(a,1,2))].">
      <j1 rule="para" parents="1329 10650"/>
    </justification>
  </clause>

  <clause id="10652">
    <literal><![CDATA[
      a(x,T(y,x),R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(691,a,10651,a),flip(a)].">
      <j1 rule="hyper" parents="691 10651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10653">
    <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,4626,a,b,10652,a)].">
      <j1 rule="hyper" parents="58 4626 10652"/>
    </justification>
  </clause>

  <clause id="10654">
    <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,10001,a(flip),b,10653,a)].">
      <j1 rule="hyper" parents="58 10001 10653"/>
    </justification>
  </clause>

  <clause id="10655">
    <literal><![CDATA[
      a(x,y,R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(4625,a,10654,a)].">
      <j1 rule="hyper" parents="4625 10654"/>
    </justification>
  </clause>

  <clause id="10656">
    <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(10655(a,1),10002(a,2,1))].">
      <j1 rule="para" parents="10655 10002"/>
    </justification>
  </clause>

  <clause id="10657">
    <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,9945,a(flip),b,10656,a)].">
      <j1 rule="hyper" parents="58 9945 10656"/>
    </justification>
  </clause>

  <clause id="10658">
    <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(298(a,1),5790(a,1,2)),flip(a)].">
      <j1 rule="para" parents="298 5790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10659">
    <literal><![CDATA[
      K((x \ (y \ z)) \ 1,L(x \ (y \ z),u,w)) = K(z \ (y * x),(y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,6230,a(flip),b,10658,a),flip(a)].">
      <j1 rule="hyper" parents="320 6230 10658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10660">
    <literal><![CDATA[
      K((x \ (y \ z)) \ 1,(y * x) \ z) = K(z \ (y * x),(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(298(a,1),10659(a,1,2))].">
      <j1 rule="para" parents="298 10659"/>
    </justification>
  </clause>

  <clause id="10661">
    <literal><![CDATA[
      K((x \ (y \ z)) \ 1,(y * x) \ z) = K(z \ (y * x),x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(320,a,6842,a(flip),b,10660,a),flip(a)].">
      <j1 rule="hyper" parents="320 6842 10660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10662">
    <literal><![CDATA[
      x * K(1 \ (y * x),x \ (y \ 1)) = y \ (((y * x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(10661(a,1),5700(a,2,2)),flip(a)].">
      <j1 rule="para" parents="10661 5700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10663">
    <literal><![CDATA[
      x * K(y * x,x \ (y \ 1)) = y \ (((y * x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(60(a,1),10662(a,1,2,1))].">
      <j1 rule="para" parents="60 10662"/>
    </justification>
  </clause>

  <clause id="10664">
    <literal><![CDATA[
      K((1 / x) * y,y \ ((1 / x) \ 1)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(29,a,3346,a(flip),b,10663,a),flip(a)].">
      <j1 rule="hyper" parents="29 3346 10663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10665">
    <literal><![CDATA[
      K((1 / x) * y,y \ x) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(75(a,1),10664(a,1,2,2))].">
      <j1 rule="para" parents="75 10664"/>
    </justification>
  </clause>

  <clause id="10666">
    <literal><![CDATA[
      K((x \ 1) \ y,y \ (x \ 1)) = K(x * y,y \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(72(a,1),10665(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 10665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10667">
    <literal><![CDATA[
      ((x \ 1) \ y) \ K(x * y,y \ (x \ 1)) = 1 / ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,10666,a(flip),b,2383,a)].">
      <j1 rule="hyper" parents="116 10666 2383"/>
    </justification>
  </clause>

  <clause id="10668">
    <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(3262(a,1),6042(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3262 6042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10669">
    <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(6283(a,1),7441(a,2,1))].">
      <j1 rule="para" parents="6283 7441"/>
    </justification>
  </clause>

  <clause id="10670">
    <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(5848(a,1),8870(a,1,1,2))].">
      <j1 rule="para" parents="5848 8870"/>
    </justification>
  </clause>

  <clause id="10671">
    <literal><![CDATA[
      K(x,T(y / ((K(x,z) * u) * w),v5)) = K(x,T(y / (u * w),v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,9088,a(flip),b,9108,a),flip(a)].">
      <j1 rule="hyper" parents="320 9088 9108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10672">
    <literal><![CDATA[
      K(x,T(y / ((z * T(x,u)) * w),v5)) = K(x,T(y / ((z * x) * w),v5))
    ]]></literal>
    <justification jstring="[para(7915(a,1),10671(a,1,2,1,2,1))].">
      <j1 rule="para" parents="7915 10671"/>
    </justification>
  </clause>

  <clause id="10673">
    <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),9660(a,1,2,2,1))].">
      <j1 rule="para" parents="5 9660"/>
    </justification>
  </clause>

  <clause id="10674">
    <literal><![CDATA[
      x \ T(y,((x \ 1) \ (x \ y)) \ z) = x \ T(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(6388,a,10673,a),flip(a)].">
      <j1 rule="hyper" parents="6388 10673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10676">
    <literal><![CDATA[
      K(x,y \ T(z,z \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(10674(a,1),8744(a,1,2))].">
      <j1 rule="para" parents="10674 8744"/>
    </justification>
  </clause>

  <clause id="10677">
    <literal><![CDATA[
      T(x,y \ T(z,z \ x)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(118,a,10676,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 10676 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10678">
    <literal><![CDATA[
      K(x,y \ ((z \ x) \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(106(a,1),10676(a,1,2,2))].">
      <j1 rule="para" parents="106 10676"/>
    </justification>
  </clause>

  <clause id="10679">
    <literal><![CDATA[
      T(x,y \ (x / z)) = T(x,y \ (z \ x))
    ]]></literal>
    <justification jstring="[para(642(a,1),10677(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="642 10677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10680">
    <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(6461,a,10678,a),flip(a)].">
      <j1 rule="hyper" parents="6461 10678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10681">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) = (((x / (1 / (x \ y))) / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,9324,a(flip),b,9820,a)].">
      <j1 rule="hyper" parents="58 9324 9820"/>
    </justification>
  </clause>

  <clause id="10682">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) = (1 / ((x / ((x \ y) \ 1)) / x)) \ 1
    ]]></literal>
    <justification jstring="[para(2629(a,2),10681(a,2,1))].">
      <j1 rule="para" parents="2629 10681"/>
    </justification>
  </clause>

  <clause id="10683">
    <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(10682(a,2),582(a,1))].">
      <j1 rule="para" parents="10682 582"/>
    </justification>
  </clause>

  <clause id="10684">
    <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(320,a,6306,a(flip),b,10669,a),flip(a)].">
      <j1 rule="hyper" parents="320 6306 10669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10685">
    <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(8052(a,1),10670(a,1,2))].">
      <j1 rule="para" parents="8052 10670"/>
    </justification>
  </clause>

  <clause id="10686">
    <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(7754(a,1),10685(a,1,2))].">
      <j1 rule="para" parents="7754 10685"/>
    </justification>
  </clause>

  <clause id="10688">
    <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(10686(a,1),7378(a,1,2,2))].">
      <j1 rule="para" parents="10686 7378"/>
    </justification>
  </clause>

  <clause id="10689">
    <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,7602,a(flip),b,10688,a),flip(a)].">
      <j1 rule="hyper" parents="58 7602 10688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10691">
    <literal><![CDATA[
      K(x,y * (z * (x * (T(T(x,u),u) \ w)))) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[hyper(320,a,8396,a(flip),b,10689,a),flip(a)].">
      <j1 rule="hyper" parents="320 8396 10689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10693">
    <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(6283(a,1),10684(a,1,1,1))].">
      <j1 rule="para" parents="6283 10684"/>
    </justification>
  </clause>

  <clause id="10694">
    <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(2074(a,2),10693(a,1,1))].">
      <j1 rule="para" parents="2074 10693"/>
    </justification>
  </clause>

  <clause id="10695">
    <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(2870(a,1),10694(a,1,1,1,1,2))].">
      <j1 rule="para" parents="2870 10694"/>
    </justification>
  </clause>

  <clause id="10696">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x = (x * (K(w,y) * R(y,z,u))) * K(y,w)
    ]]></literal>
    <justification jstring="[para(9267(a,1),10695(a,1,1,1))].">
      <j1 rule="para" parents="9267 10695"/>
    </justification>
  </clause>

  <clause id="10697">
    <literal><![CDATA[
      (x * (K(y,z) * R(z,u,w))) * K(z,y) = x * R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(883,a,10696,a),flip(a)].">
      <j1 rule="hyper" parents="883 10696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10699">
    <literal><![CDATA[
      (x * (R(y,z,u) * K(w,y))) * K(y,w) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(2878(a,2),10697(a,1,1,2))].">
      <j1 rule="para" parents="2878 10697"/>
    </justification>
  </clause>

  <clause id="10700">
    <literal><![CDATA[
      L(K(x,y),R(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6645,a,10699,a)].">
      <j1 rule="hyper" parents="6645 10699"/>
    </justification>
  </clause>

  <clause id="10701">
    <literal><![CDATA[
      a(x,R(y,z,u),K(y,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10700,a,b,1923,a),flip(a)].">
      <j1 rule="hyper" parents="115 10700 1923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10702">
    <literal><![CDATA[
      K(x,(y \ z) \ R(x,u,w)) = K(x,z \ (y * R(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,6555,a(flip),b,10700,a),flip(a)].">
      <j1 rule="hyper" parents="58 6555 10700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10703">
    <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(5647(a,1),5992(a,1,2))].">
      <j1 rule="para" parents="5647 5992"/>
    </justification>
  </clause>

  <clause id="10704">
    <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(5651(a,1),10703(a,2,3))].">
      <j1 rule="para" parents="5651 10703"/>
    </justification>
  </clause>

  <clause id="10705">
    <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(1684(a,2),6044(a,2,2,1))].">
      <j1 rule="para" parents="1684 6044"/>
    </justification>
  </clause>

  <clause id="10706">
    <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(7759(a,1),6429(a,1,2,2))].">
      <j1 rule="para" parents="7759 6429"/>
    </justification>
  </clause>

  <clause id="10707">
    <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(5447,a,10638,a)].">
      <j1 rule="hyper" parents="5447 10638"/>
    </justification>
  </clause>

  <clause id="10708">
    <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),10705(a,2,2,1,1,2))].">
      <j1 rule="para" parents="61 10705"/>
    </justification>
  </clause>

  <clause id="10709">
    <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),10708(a,2,2))].">
      <j1 rule="para" parents="20 10708"/>
    </justification>
  </clause>

  <clause id="10711">
    <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(320,a,668,a(flip),b,10709,a),flip(a)].">
      <j1 rule="hyper" parents="320 668 10709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10712">
    <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(320,a,1436,a(flip),b,10711,a),flip(a)].">
      <j1 rule="hyper" parents="320 1436 10711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10713">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K(L(x,y,z),u) = x \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3298(a,1),10712(a,1,2))].">
      <j1 rule="para" parents="3298 10712"/>
    </justification>
  </clause>

  <clause id="10714">
    <literal><![CDATA[
      K(x \ L(T(x,y),z,u),x) = K(x \ L(x,z,u),x)
    ]]></literal>
    <justification jstring="[para(10713(a,1),7391(a,1,1))].">
      <j1 rule="para" parents="10713 7391"/>
    </justification>
  </clause>

  <clause id="10715">
    <literal><![CDATA[
      K(x \ L(T(x,y),z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,3494,a(flip),b,10714,a),flip(a)].">
      <j1 rule="hyper" parents="320 3494 10714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10717">
    <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(7131(a,2),10706(a,2,1,1))].">
      <j1 rule="para" parents="7131 10706"/>
    </justification>
  </clause>

  <clause id="10718">
    <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(8366,a,10707,a)].">
      <j1 rule="hyper" parents="8366 10707"/>
    </justification>
  </clause>

  <clause id="10719">
    <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(7170(a,1),10717(a,2,1))].">
      <j1 rule="para" parents="7170 10717"/>
    </justification>
  </clause>

  <clause id="10720">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = K(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8975,a(flip),b,10719,a),flip(a)].">
      <j1 rule="hyper" parents="320 8975 10719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10723">
    <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(5966(a,2),10720(a,1,1))].">
      <j1 rule="para" parents="5966 10720"/>
    </justification>
  </clause>

  <clause id="10724">
    <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(7223(a,1),10723(a,1,2,2))].">
      <j1 rule="para" parents="7223 10723"/>
    </justification>
  </clause>

  <clause id="10725">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) \ K(x,z) = K(y,T(y * K(x,z),x))
    ]]></literal>
    <justification jstring="[hyper(293,a,10724,a)].">
      <j1 rule="hyper" parents="293 10724"/>
    </justification>
  </clause>

  <clause id="10726">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) * K(z,y) = K(x,T(x * K(z,y),z))
    ]]></literal>
    <justification jstring="[hyper(5125,a,10725,a)].">
      <j1 rule="hyper" parents="5125 10725"/>
    </justification>
  </clause>

  <clause id="10727">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,T(y * K(z,x),z))
    ]]></literal>
    <justification jstring="[para(6649(a,1),10726(a,1,1))].">
      <j1 rule="para" parents="6649 10726"/>
    </justification>
  </clause>

  <clause id="10728">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,7563,a(flip),b,10727,a),flip(a)].">
      <j1 rule="hyper" parents="320 7563 10727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10729">
    <literal><![CDATA[
      K(x * K(y,z),x) = K(x,x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6886,a(flip),b,10728,a)].">
      <j1 rule="hyper" parents="58 6886 10728"/>
    </justification>
  </clause>

  <clause id="10730">
    <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(10729(a,1),5629(a,1,1,1,2))].">
      <j1 rule="para" parents="10729 5629"/>
    </justification>
  </clause>

  <clause id="10731">
    <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(4714(a,2),10730(a,1,1,1))].">
      <j1 rule="para" parents="4714 10730"/>
    </justification>
  </clause>

  <clause id="10732">
    <literal><![CDATA[
      R(T(x,K(y,z)),K(z,y),x) = T(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5596,a,10731,a)].">
      <j1 rule="hyper" parents="5596 10731"/>
    </justification>
  </clause>

  <clause id="10733">
    <literal><![CDATA[
      T(x,x * K(y,z)) \ T(K(z,y) * x,x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(10732(a,1),10573(a,1,1))].">
      <j1 rule="para" parents="10732 10573"/>
    </justification>
  </clause>

  <clause id="10734">
    <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(9634(a,1),10733(a,1,1,2,2))].">
      <j1 rule="para" parents="9634 10733"/>
    </justification>
  </clause>

  <clause id="10735">
    <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(5070(a,1),5086(a,1,1))].">
      <j1 rule="para" parents="5070 5086"/>
    </justification>
  </clause>

  <clause id="10736">
    <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(10735(a,1),9286(a,1,2,2))].">
      <j1 rule="para" parents="10735 9286"/>
    </justification>
  </clause>

  <clause id="10737">
    <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(320,a,7262,a(flip),b,6792,a),flip(a)].">
      <j1 rule="hyper" parents="320 7262 6792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10738">
    <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(173(a,1),10737(a,2,1,2))].">
      <j1 rule="para" parents="173 10737"/>
    </justification>
  </clause>

  <clause id="10739">
    <literal><![CDATA[
      L(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1637(a,1),10738(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1637 10738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10740">
    <literal><![CDATA[
      K((x \ 1) * L(y,z,u),y) = K(x \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(6613,a,10739,a),flip(a)].">
      <j1 rule="hyper" parents="6613 10739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10741">
    <literal><![CDATA[
      a(x,L(y,z,u),K(w,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10739,a,b,1923,a),flip(a)].">
      <j1 rule="hyper" parents="115 10739 1923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10742">
    <literal><![CDATA[
      K((x \ y) \ L(z,u,w),z) = K(y \ (x * L(z,u,w)),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6597,a(flip),b,10739,a),flip(a)].">
      <j1 rule="hyper" parents="58 6597 10739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10743">
    <literal><![CDATA[
      L(K(x,y),L(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5862,a,10741,a)].">
      <j1 rule="hyper" parents="5862 10741"/>
    </justification>
  </clause>

  <clause id="10744">
    <literal><![CDATA[
      K(x,(y \ z) \ L(x,u,w)) = K(x,z \ (y * L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,6555,a(flip),b,10743,a),flip(a)].">
      <j1 rule="hyper" parents="58 6555 10743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10745">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,10499,a(flip),b,10740,a),flip(a)].">
      <j1 rule="hyper" parents="58 10499 10740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10747">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5324,a(flip),b,10745,a),flip(a)].">
      <j1 rule="hyper" parents="320 5324 10745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10748">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,y) = w
    ]]></literal>
    <justification jstring="[para(10745(a,2),5938(a,1))].">
      <j1 rule="para" parents="10745 5938"/>
    </justification>
  </clause>

  <clause id="10749">
    <literal><![CDATA[
      (L(x,y,z) * K((u \ x) \ x,x)) * u = (x \ (L(x,y,z) * u)) * x
    ]]></literal>
    <justification jstring="[para(10747(a,1),9663(a,1,1,2))].">
      <j1 rule="para" parents="10747 9663"/>
    </justification>
  </clause>

  <clause id="10750">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K((y \ x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(10748,a,10742,a),flip(a)].">
      <j1 rule="hyper" parents="10748 10742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10752">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,10464,a(flip),b,10750,a),flip(a)].">
      <j1 rule="hyper" parents="320 10464 10750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10753">
    <literal><![CDATA[
      K(x \ (y * L(x,z,u)),x) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = w
    ]]></literal>
    <justification jstring="[para(10750(a,2),6269(a,1))].">
      <j1 rule="para" parents="10750 6269"/>
    </justification>
  </clause>

  <clause id="10754">
    <literal><![CDATA[
      K(x \ (y * (z * x)),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * z,x) = u
    ]]></literal>
    <justification jstring="[para(90(a,1),10753(a,1,1,2))].">
      <j1 rule="para" parents="90 10753"/>
    </justification>
  </clause>

  <clause id="10755">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(u * (x \ (y * z)),u)
    ]]></literal>
    <justification jstring="[para(90(a,1),10752(a,1,1,2))].">
      <j1 rule="para" parents="90 10752"/>
    </justification>
  </clause>

  <clause id="10756">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(y * ((x * y) \ (z * u)),y)
    ]]></literal>
    <justification jstring="[hyper(8443,a,10755,a)].">
      <j1 rule="hyper" parents="8443 10755"/>
    </justification>
  </clause>

  <clause id="10757">
    <literal><![CDATA[
      K(x \ (y * (z * u)),z) = K(z * (x \ (y * u)),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8635,a(flip),b,10755,a)].">
      <j1 rule="hyper" parents="58 8635 10755"/>
    </justification>
  </clause>

  <clause id="10758">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,L(u,z,x)) = K(u * (y \ (x * z)),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,10486,a,b,10757,a)].">
      <j1 rule="hyper" parents="58 10486 10757"/>
    </justification>
  </clause>

  <clause id="10759">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(x \ (z * u),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,10463,a(flip),b,10756,a),flip(a)].">
      <j1 rule="hyper" parents="320 10463 10756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10760">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K((u * z) \ (u * (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9743,a(flip),b,10759,a)].">
      <j1 rule="hyper" parents="58 9743 10759"/>
    </justification>
  </clause>

  <clause id="10761">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(13(a,2),10760(a,2,1))].">
      <j1 rule="para" parents="13 10760"/>
    </justification>
  </clause>

  <clause id="10762">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(10596,a,10761,a),flip(a)].">
      <j1 rule="hyper" parents="10596 10761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10763">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8877,a(flip),b,10762,a)].">
      <j1 rule="hyper" parents="58 8877 10762"/>
    </justification>
  </clause>

  <clause id="10764">
    <literal><![CDATA[
      K(x,L(y,T(x,z),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6223(a,1),10762(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6223 10762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10765">
    <literal><![CDATA[
      K(x,(y * T(x,z)) \ u) = K(x,T(x,z) \ (y \ u))
    ]]></literal>
    <justification jstring="[para(298(a,1),10764(a,1,2))].">
      <j1 rule="para" parents="298 10764"/>
    </justification>
  </clause>

  <clause id="10766">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) = K(x,L(y / z,y,u))
    ]]></literal>
    <justification jstring="[hyper(10409,a,10763,a)].">
      <j1 rule="hyper" parents="10409 10763"/>
    </justification>
  </clause>

  <clause id="10767">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10408,a,10763,a)].">
      <j1 rule="hyper" parents="10408 10763"/>
    </justification>
  </clause>

  <clause id="10768">
    <literal><![CDATA[
      K(x,L(y,z * x,u)) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(8365,a,10763,a),flip(a)].">
      <j1 rule="hyper" parents="8365 10763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10769">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = K(x,L(T(z,u),u,y))
    ]]></literal>
    <justification jstring="[hyper(7235,a,10763,a)].">
      <j1 rule="hyper" parents="7235 10763"/>
    </justification>
  </clause>

  <clause id="10770">
    <literal><![CDATA[
      K(x,(y * ((y \ z) / u)) \ z) = K(x,L(u,y \ z,y))
    ]]></literal>
    <justification jstring="[hyper(6838,a,10763,a)].">
      <j1 rule="hyper" parents="6838 10763"/>
    </justification>
  </clause>

  <clause id="10771">
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(6681,a,10763,a),flip(a)].">
      <j1 rule="hyper" parents="6681 10763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10772">
    <literal><![CDATA[
      K(L(x,y,z),u) \ 1 = L(K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4929,a,b,10763,a)].">
      <j1 rule="hyper" parents="320 4929 10763"/>
    </justification>
  </clause>

  <clause id="10773">
    <literal><![CDATA[
      L(K(x,y \ z),y,u) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,6569,a(flip),b,10763,a),flip(a)].">
      <j1 rule="hyper" parents="320 6569 10763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10775">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6578,a,b,10763,a)].">
      <j1 rule="hyper" parents="58 6578 10763"/>
    </justification>
  </clause>

  <clause id="10776">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5865,a,b,10763,a)].">
      <j1 rule="hyper" parents="58 5865 10763"/>
    </justification>
  </clause>

  <clause id="10777">
    <literal><![CDATA[
      K(x,L(T(y,z),y,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7207,a(flip),b,10763,a),flip(a)].">
      <j1 rule="hyper" parents="58 7207 10763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10778">
    <literal><![CDATA[
      K(x \ y,L(z,y,y \ 1)) = K(((y \ 1) * x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6606,a(flip),b,10763,a),flip(a)].">
      <j1 rule="hyper" parents="58 6606 10763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10779">
    <literal><![CDATA[
      K((x \ y) \ z,L(u,z,x)) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6597,a(flip),b,10763,a),flip(a)].">
      <j1 rule="hyper" parents="58 6597 10763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10780">
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) = K(x,L(y \ z,y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6558,a(flip),b,10763,a),flip(a)].">
      <j1 rule="hyper" parents="58 6558 10763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10781">
    <literal><![CDATA[
      K(x,L((y \ z) \ u,u,y)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6555,a(flip),b,10763,a),flip(a)].">
      <j1 rule="hyper" parents="58 6555 10763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10782">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u)) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5639,a(flip),b,10763,a),flip(a)].">
      <j1 rule="hyper" parents="58 5639 10763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10783">
    <literal><![CDATA[
      x * K(y,L(z,u \ x,u)) = u * ((u \ x) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,10763,a(flip),b,91,a)].">
      <j1 rule="hyper" parents="119 10763 91"/>
    </justification>
  </clause>

  <clause id="10784">
    <literal><![CDATA[
      (x * y) * K(z,L(u,y,x)) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,10763,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 10763 13"/>
    </justification>
  </clause>

  <clause id="10785">
    <literal><![CDATA[
      x \ K(y,L(z,x \ 1,x)) = (x \ 1) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,10763,a(flip),b,257,a)].">
      <j1 rule="hyper" parents="116 10763 257"/>
    </justification>
  </clause>

  <clause id="10787">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),y,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(298(a,1),10763(a,2,2))].">
      <j1 rule="para" parents="298 10763"/>
    </justification>
  </clause>

  <clause id="10788">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),y \ z,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(490(a,1),10763(a,2,2))].">
      <j1 rule="para" parents="490 10763"/>
    </justification>
  </clause>

  <clause id="10789">
    <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(10763(a,1),469(a,1,2,2))].">
      <j1 rule="para" parents="10763 469"/>
    </justification>
  </clause>

  <clause id="10790">
    <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(10763(a,1),1411(a,1,2,1))].">
      <j1 rule="para" parents="10763 1411"/>
    </justification>
  </clause>

  <clause id="10791">
    <literal><![CDATA[
      K(x,L(y,z,u)) * a(u,z,K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(10763(a,1),1923(a,1,1))].">
      <j1 rule="para" parents="10763 1923"/>
    </justification>
  </clause>

  <clause id="10792">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(10763(a,1),5859(a,1,1))].">
      <j1 rule="para" parents="10763 5859"/>
    </justification>
  </clause>

  <clause id="10793">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(10763(a,1),5861(a,1,2))].">
      <j1 rule="para" parents="10763 5861"/>
    </justification>
  </clause>

  <clause id="10794">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(10763(a,1),5868(a,1,2))].">
      <j1 rule="para" parents="10763 5868"/>
    </justification>
  </clause>

  <clause id="10795">
    <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(10763(a,1),5869(a,1,1))].">
      <j1 rule="para" parents="10763 5869"/>
    </justification>
  </clause>

  <clause id="10796">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,L(u,y,x)) = K(z,u)
    ]]></literal>
    <justification jstring="[para(10763(a,1),5923(a,1,2))].">
      <j1 rule="para" parents="10763 5923"/>
    </justification>
  </clause>

  <clause id="10797">
    <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(10763(a,1),6829(a,1))].">
      <j1 rule="para" parents="10763 6829"/>
    </justification>
  </clause>

  <clause id="10798">
    <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(10763(a,1),6837(a,1))].">
      <j1 rule="para" parents="10763 6837"/>
    </justification>
  </clause>

  <clause id="10799">
    <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(10763(a,1),6838(a,1))].">
      <j1 rule="para" parents="10763 6838"/>
    </justification>
  </clause>

  <clause id="10800">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(10763(a,1),7808(a,2,2))].">
      <j1 rule="para" parents="10763 7808"/>
    </justification>
  </clause>

  <clause id="10801">
    <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(10763(a,1),8582(a,1,2))].">
      <j1 rule="para" parents="10763 8582"/>
    </justification>
  </clause>

  <clause id="10802">
    <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(4373(a,2),10767(a,1,2,2))].">
      <j1 rule="para" parents="4373 10767"/>
    </justification>
  </clause>

  <clause id="10803">
    <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(10767(a,1),10393(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10767 10393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10804">
    <literal><![CDATA[
      K(x,K(y,L(z,u * y,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(10768(a,2),7772(a,1,2))].">
      <j1 rule="para" parents="10768 7772"/>
    </justification>
  </clause>

  <clause id="10805">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(34,a,5716,a,b,10772,a)].">
      <j1 rule="hyper" parents="34 5716 10772"/>
    </justification>
  </clause>

  <clause id="10806">
    <literal><![CDATA[
      L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(10772(a,1),4945(a,1))].">
      <j1 rule="para" parents="10772 4945"/>
    </justification>
  </clause>

  <clause id="10807">
    <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(10772(a,1),4946(a,1))].">
      <j1 rule="para" parents="10772 4946"/>
    </justification>
  </clause>

  <clause id="10808">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(y,K(z,L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,7759,a,b,10805,a),flip(a)].">
      <j1 rule="hyper" parents="320 7759 10805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10809">
    <literal><![CDATA[
      K(L(x,y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,10763,a(flip),b,10805,a),flip(a)].">
      <j1 rule="hyper" parents="58 10763 10805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10810">
    <literal><![CDATA[
      L(K((x \ 1) \ y,z),x \ 1,x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(489(a,1),10805(a,2,1))].">
      <j1 rule="para" parents="489 10805"/>
    </justification>
  </clause>

  <clause id="10811">
    <literal><![CDATA[
      K(L(x,y,z),u) * a(z,y,K(x,u)) = K(x,u)
    ]]></literal>
    <justification jstring="[para(10805(a,1),1923(a,1,1))].">
      <j1 rule="para" parents="10805 1923"/>
    </justification>
  </clause>

  <clause id="10812">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(w,K(y,L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(10805(a,2),5584(a,1,1))].">
      <j1 rule="para" parents="10805 5584"/>
    </justification>
  </clause>

  <clause id="10813">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(10805(a,1),5861(a,1,2))].">
      <j1 rule="para" parents="10805 5861"/>
    </justification>
  </clause>

  <clause id="10814">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(y,K(w,L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(10805(a,2),7755(a,1,1))].">
      <j1 rule="para" parents="10805 7755"/>
    </justification>
  </clause>

  <clause id="10815">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w)) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(10805(a,2),7772(a,1,2))].">
      <j1 rule="para" parents="10805 7772"/>
    </justification>
  </clause>

  <clause id="10816">
    <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(10805(a,2),7796(a,1))].">
      <j1 rule="para" parents="10805 7796"/>
    </justification>
  </clause>

  <clause id="10817">
    <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(10805(a,2),7806(a,1,2))].">
      <j1 rule="para" parents="10805 7806"/>
    </justification>
  </clause>

  <clause id="10818">
    <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(10805(a,2),8020(a,1,1))].">
      <j1 rule="para" parents="10805 8020"/>
    </justification>
  </clause>

  <clause id="10819">
    <literal><![CDATA[
      K(x,L(y,z * x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,10768,a,b,10809,a)].">
      <j1 rule="hyper" parents="58 10768 10809"/>
    </justification>
  </clause>

  <clause id="10820">
    <literal><![CDATA[
      L(x,y,z) \ L(T(x,u),y,z) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,4723,a,b,10809,a)].">
      <j1 rule="hyper" parents="58 4723 10809"/>
    </justification>
  </clause>

  <clause id="10821">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (K(y,L(x,z,u)) * w) = w
    ]]></literal>
    <justification jstring="[hyper(118,a,10809,a(flip),b,5104,a),flip(a)].">
      <j1 rule="hyper" parents="118 10809 5104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10822">
    <literal><![CDATA[
      K(x \ (y \ z),L(u,x,y)) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(298(a,1),10809(a,1,1)),flip(a)].">
      <j1 rule="para" parents="298 10809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10823">
    <literal><![CDATA[
      K((x \ 1) \ y,L(z,x \ 1,x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(489(a,1),10809(a,1,1)),flip(a)].">
      <j1 rule="para" parents="489 10809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10824">
    <literal><![CDATA[
      K(x,L(y,z,u)) * L(x,z,u) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(10809(a,1),4803(a,1,1))].">
      <j1 rule="para" parents="10809 4803"/>
    </justification>
  </clause>

  <clause id="10825">
    <literal><![CDATA[
      ((x * y) * K(z,L(u,y,x))) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(10809(a,1),6206(a,1,1,2))].">
      <j1 rule="para" parents="10809 6206"/>
    </justification>
  </clause>

  <clause id="10826">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(z,K(x,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(10809(a,1),7759(a,1,2))].">
      <j1 rule="para" parents="10809 7759"/>
    </justification>
  </clause>

  <clause id="10827">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(10809(a,1),7772(a,1,2))].">
      <j1 rule="para" parents="10809 7772"/>
    </justification>
  </clause>

  <clause id="10828">
    <literal><![CDATA[
      x * K(y,K(z,L(x,u,w))) = T(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(10809(a,1),7769(a,1,2,2))].">
      <j1 rule="para" parents="10809 7769"/>
    </justification>
  </clause>

  <clause id="10829">
    <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(10809(a,1),7806(a,1,2))].">
      <j1 rule="para" parents="10809 7806"/>
    </justification>
  </clause>

  <clause id="10830">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(10775(a,1),6585(a,1))].">
      <j1 rule="para" parents="10775 6585"/>
    </justification>
  </clause>

  <clause id="10831">
    <literal><![CDATA[
      K(x \ y,L(z,y,u)) = K(x \ y,L(z,x,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),10819(a,1,2,2))].">
      <j1 rule="para" parents="5 10819"/>
    </justification>
  </clause>

  <clause id="10832">
    <literal><![CDATA[
      K(x,L(y,z / x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),10819(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 10819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10833">
    <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(5865(a,2),10806(a,1))].">
      <j1 rule="para" parents="5865 10806"/>
    </justification>
  </clause>

  <clause id="10834">
    <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(6558(a,1),10806(a,1))].">
      <j1 rule="para" parents="6558 10806"/>
    </justification>
  </clause>

  <clause id="10835">
    <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(6577(a,2),10806(a,1))].">
      <j1 rule="para" parents="6577 10806"/>
    </justification>
  </clause>

  <clause id="10836">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,L(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(6643(a,2),10806(a,1))].">
      <j1 rule="para" parents="6643 10806"/>
    </justification>
  </clause>

  <clause id="10837">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(10805(a,1),10806(a,1))].">
      <j1 rule="para" parents="10805 10806"/>
    </justification>
  </clause>

  <clause id="10838">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(10809(a,2),10830(a,1))].">
      <j1 rule="para" parents="10809 10830"/>
    </justification>
  </clause>

  <clause id="10839">
    <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(7759(a,2),10838(a,1))].">
      <j1 rule="para" parents="7759 10838"/>
    </justification>
  </clause>

  <clause id="10840">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(u,z) = K(u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7381,a(flip),b,10776,a)].">
      <j1 rule="hyper" parents="58 7381 10776"/>
    </justification>
  </clause>

  <clause id="10841">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,u,z)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[para(496(a,1),10780(a,2,2))].">
      <j1 rule="para" parents="496 10780"/>
    </justification>
  </clause>

  <clause id="10842">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(6583,a,10792,a)].">
      <j1 rule="hyper" parents="6583 10792"/>
    </justification>
  </clause>

  <clause id="10843">
    <literal><![CDATA[
      T(x,L(y,z,u)) * K(y,x) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,10792,a(flip),b,4736,a),flip(a)].">
      <j1 rule="hyper" parents="119 10792 4736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10844">
    <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(10792(a,1),1993(a,1))].">
      <j1 rule="para" parents="10792 1993"/>
    </justification>
  </clause>

  <clause id="10845">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z * x,K(y,x))
    ]]></literal>
    <justification jstring="[para(10819(a,1),10792(a,1,1))].">
      <j1 rule="para" parents="10819 10792"/>
    </justification>
  </clause>

  <clause id="10846">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,z))) = a(x,y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(7759(a,2),10842(a,1,3))].">
      <j1 rule="para" parents="7759 10842"/>
    </justification>
  </clause>

  <clause id="10847">
    <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(10793(a,1),1997(a,1))].">
      <j1 rule="para" parents="10793 1997"/>
    </justification>
  </clause>

  <clause id="10848">
    <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,9001,a,b,10800,a)].">
      <j1 rule="hyper" parents="58 9001 10800"/>
    </justification>
  </clause>

  <clause id="10849">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w)) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,7808,a(flip),b,10800,a)].">
      <j1 rule="hyper" parents="58 7808 10800"/>
    </justification>
  </clause>

  <clause id="10850">
    <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,10808,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 10808 13"/>
    </justification>
  </clause>

  <clause id="10851">
    <literal><![CDATA[
      L(K(x,K(y,y * z)),u,w) = K(x,K(z * x,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(8007(a,1),10808(a,1,1))].">
      <j1 rule="para" parents="8007 10808"/>
    </justification>
  </clause>

  <clause id="10852">
    <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(10811(a,1),5117(a,2,2))].">
      <j1 rule="para" parents="10811 5117"/>
    </justification>
  </clause>

  <clause id="10853">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(6592,a,10813,a)].">
      <j1 rule="hyper" parents="6592 10813"/>
    </justification>
  </clause>

  <clause id="10854">
    <literal><![CDATA[
      T(x,L(y,z,u)) \ T(x,y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(5636,a,10813,a)].">
      <j1 rule="hyper" parents="5636 10813"/>
    </justification>
  </clause>

  <clause id="10855">
    <literal><![CDATA[
      (x * y) / T(x,L(y,z,u)) = y * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(10813(a,1),6340(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10813 6340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10856">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y * u,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(10813(a,1),6592(a,1))].">
      <j1 rule="para" parents="10813 6592"/>
    </justification>
  </clause>

  <clause id="10857">
    <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(10812(a,1),10813(a,1,2))].">
      <j1 rule="para" parents="10812 10813"/>
    </justification>
  </clause>

  <clause id="10858">
    <literal><![CDATA[
      x / T(x / y,L(y,z,u)) = y * a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(10853(a,1),9649(a,2,2))].">
      <j1 rule="para" parents="10853 9649"/>
    </justification>
  </clause>

  <clause id="10859">
    <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,10031,a,b,10814,a)].">
      <j1 rule="hyper" parents="58 10031 10814"/>
    </justification>
  </clause>

  <clause id="10860">
    <literal><![CDATA[
      K(x,1 / L(K(y,z),u,w)) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(5717(a,2),10815(a,1,2))].">
      <j1 rule="para" parents="5717 10815"/>
    </justification>
  </clause>

  <clause id="10861">
    <literal><![CDATA[
      K(x,K(y,L(z,z,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(6072(a,1),10815(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6072 10815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10862">
    <literal><![CDATA[
      K(x,K(y / z,L(u,y,w))) = K(x,K(u,L(y / z,z,w)))
    ]]></literal>
    <justification jstring="[para(8996(a,1),10815(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8996 10815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10863">
    <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,10821,a(flip),b,5223,a),flip(a)].">
      <j1 rule="hyper" parents="119 10821 5223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10864">
    <literal><![CDATA[
      K(x,K(y,L(z \ 1,u,w))) = K(y,K(z,L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(8176,a,10826,a),flip(a)].">
      <j1 rule="hyper" parents="8176 10826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10865">
    <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(10826(a,2),4725(a,1,2))].">
      <j1 rule="para" parents="10826 4725"/>
    </justification>
  </clause>

  <clause id="10866">
    <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(10389(a,1),10831(a,2,2))].">
      <j1 rule="para" parents="10389 10831"/>
    </justification>
  </clause>

  <clause id="10867">
    <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(5564(a,1),10771(a,2,2,2))].">
      <j1 rule="para" parents="5564 10771"/>
    </justification>
  </clause>

  <clause id="10868">
    <literal><![CDATA[
      K(x,(y * z) \ (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z \ u,z,y)) = w
    ]]></literal>
    <justification jstring="[para(10773(a,1),10806(a,1))].">
      <j1 rule="para" parents="10773 10806"/>
    </justification>
  </clause>

  <clause id="10869">
    <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(407(a,1),10781(a,1,2,1,1))].">
      <j1 rule="para" parents="407 10781"/>
    </justification>
  </clause>

  <clause id="10870">
    <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),10784(a,1,2,2))].">
      <j1 rule="para" parents="25 10784"/>
    </justification>
  </clause>

  <clause id="10871">
    <literal><![CDATA[
      (x * y) * z != x * (y * K(u,w))
    ]]></literal>
    <literal><![CDATA[
      K(u,L(w,y,x)) = z
    ]]></literal>
    <justification jstring="[para(10784(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="10784 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10872">
    <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(10784(a,1),322(a,1)),flip(b)].">
      <j1 rule="para" parents="10784 322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10873">
    <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(7181(a,1),10784(a,2,2))].">
      <j1 rule="para" parents="7181 10784"/>
    </justification>
  </clause>

  <clause id="10874">
    <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(10784(a,1),7532(a,2,2,1))].">
      <j1 rule="para" parents="10784 7532"/>
    </justification>
  </clause>

  <clause id="10875">
    <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(10784(a,1),8829(a,2,2,1))].">
      <j1 rule="para" parents="10784 8829"/>
    </justification>
  </clause>

  <clause id="10876">
    <literal><![CDATA[
      (x * y) * K(z,K(u,L(w,y,x))) = x * (y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(10763(a,1),10784(a,1,2,2))].">
      <j1 rule="para" parents="10763 10784"/>
    </justification>
  </clause>

  <clause id="10877">
    <literal><![CDATA[
      (x * (y / z)) * K(z,L(u,y,x)) = x * ((y / z) * K(z,u))
    ]]></literal>
    <justification jstring="[para(10832(a,1),10784(a,1,2))].">
      <j1 rule="para" parents="10832 10784"/>
    </justification>
  </clause>

  <clause id="10878">
    <literal><![CDATA[
      K(x,L(T(y,z),z \ 1,z)) = z * (K(x,y) * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(119,a,8212,a(flip),b,10785,a),flip(a)].">
      <j1 rule="hyper" parents="119 8212 10785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10879">
    <literal><![CDATA[
      L(K((x \ 1) \ (y \ z),y),x \ 1,x) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,10397,a,b,10810,a),flip(a)].">
      <j1 rule="hyper" parents="320 10397 10810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10880">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(10820(a,1),4992(a,1))].">
      <j1 rule="para" parents="10820 4992"/>
    </justification>
  </clause>

  <clause id="10881">
    <literal><![CDATA[
      K((x * ((y \ 1) \ 1)) \ z,u) = K(y \ (x \ z),L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,3951,a,b,10822,a)].">
      <j1 rule="hyper" parents="320 3951 10822"/>
    </justification>
  </clause>

  <clause id="10882">
    <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(10822(a,2),7774(a,1,2))].">
      <j1 rule="para" parents="10822 7774"/>
    </justification>
  </clause>

  <clause id="10883">
    <literal><![CDATA[
      K((x \ 1) \ y,x * z) = K(x * y,(x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(489(a,1),10823(a,1,2))].">
      <j1 rule="para" parents="489 10823"/>
    </justification>
  </clause>

  <clause id="10884">
    <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(10824(a,1),8563(a,1,2,2))].">
      <j1 rule="para" parents="10824 8563"/>
    </justification>
  </clause>

  <clause id="10886">
    <literal><![CDATA[
      K(x,(y * T(x,z)) \ u) = K(x,x \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7251,a(flip),b,10765,a),flip(a)].">
      <j1 rule="hyper" parents="320 7251 10765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10888">
    <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(298(a,1),10804(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="298 10804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10889">
    <literal><![CDATA[
      x * ((x \ y) * K(y,z)) = T(y,L(z,x \ y,x))
    ]]></literal>
    <justification jstring="[hyper(9476,a,10843,a)].">
      <j1 rule="hyper" parents="9476 10843"/>
    </justification>
  </clause>

  <clause id="10890">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,u)) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(7210,a,10843,a)].">
      <j1 rule="hyper" parents="7210 10843"/>
    </justification>
  </clause>

  <clause id="10891">
    <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(4427(a,1),10855(a,1,1))].">
      <j1 rule="para" parents="4427 10855"/>
    </justification>
  </clause>

  <clause id="10892">
    <literal><![CDATA[
      K(x,1 / L(K(y,z),u,w)) = K(x,L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,10849,a,b,10860,a),flip(a)].">
      <j1 rule="hyper" parents="320 10849 10860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10893">
    <literal><![CDATA[
      K(x * y,(x \ 1) \ (x \ z)) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),10883(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 10883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10894">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),u) = T(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(10890(a,1),4829(a,1,1))].">
      <j1 rule="para" parents="10890 4829"/>
    </justification>
  </clause>

  <clause id="10895">
    <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(10890(a,1),4895(a,1,1))].">
      <j1 rule="para" parents="10890 4895"/>
    </justification>
  </clause>

  <clause id="10896">
    <literal><![CDATA[
      K((x \ 1) \ (x \ y),z) = K(y,(x \ 1) \ (x \ z))
    ]]></literal>
    <justification jstring="[para(5(a,1),10893(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 10893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10897">
    <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(6212(a,1),10769(a,1,2,1))].">
      <j1 rule="para" parents="6212 10769"/>
    </justification>
  </clause>

  <clause id="10898">
    <literal><![CDATA[
      K(((x \ y) / z) \ y,L(z,x \ y,x)) = K(((x \ y) / z) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9013,a(flip),b,10770,a),flip(a)].">
      <j1 rule="hyper" parents="58 9013 10770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10899">
    <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,10896,a(flip),b,10778,a)].">
      <j1 rule="hyper" parents="58 10896 10778"/>
    </justification>
  </clause>

  <clause id="10900">
    <literal><![CDATA[
      x \ (y * K(z,y \ (x * u))) = (x \ y) * K(z,(x \ y) \ u)
    ]]></literal>
    <justification jstring="[para(10788(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="10788 474"/>
    </justification>
  </clause>

  <clause id="10901">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(6582(a,1),10794(a,1))].">
      <j1 rule="para" parents="6582 10794"/>
    </justification>
  </clause>

  <clause id="10902">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(10845(a,1),10795(a,1))].">
      <j1 rule="para" parents="10845 10795"/>
    </justification>
  </clause>

  <clause id="10903">
    <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(7754(a,1),10816(a,1,1))].">
      <j1 rule="para" parents="7754 10816"/>
    </justification>
  </clause>

  <clause id="10904">
    <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(10815(a,2),10829(a,1))].">
      <j1 rule="para" parents="10815 10829"/>
    </justification>
  </clause>

  <clause id="10905">
    <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(4155(a,1),10841(a,2,2,1))].">
      <j1 rule="para" parents="4155 10841"/>
    </justification>
  </clause>

  <clause id="10906">
    <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,9339,a(flip),b,10848,a)].">
      <j1 rule="hyper" parents="58 9339 10848"/>
    </justification>
  </clause>

  <clause id="10907">
    <literal><![CDATA[
      K(x,K(y * z,L(y,u,w))) = K(x,K(z * x,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(10903,a,10851,a)].">
      <j1 rule="hyper" parents="10903 10851"/>
    </justification>
  </clause>

  <clause id="10908">
    <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(10858(a,1),9429(a,2,2))].">
      <j1 rule="para" parents="10858 9429"/>
    </justification>
  </clause>

  <clause id="10909">
    <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(497(a,1),10862(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="497 10862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10910">
    <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(10771(a,2),10868(a,1))].">
      <j1 rule="para" parents="10771 10868"/>
    </justification>
  </clause>

  <clause id="10911">
    <literal><![CDATA[
      K(x,K(y * z,L(y,u,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,7943,a(flip),b,10907,a),flip(a)].">
      <j1 rule="hyper" parents="320 7943 10907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10912">
    <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(10876(a,1),10865(a,1))].">
      <j1 rule="para" parents="10876 10865"/>
    </justification>
  </clause>

  <clause id="10913">
    <literal><![CDATA[
      L(K((x \ y) \ z,y),x \ 1,x) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[para(8269(a,1),10879(a,1,1))].">
      <j1 rule="para" parents="8269 10879"/>
    </justification>
  </clause>

  <clause id="10914">
    <literal><![CDATA[
      K(x \ (y \ z),L(u,x,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(10831(a,1),10797(a,1))].">
      <j1 rule="para" parents="10831 10797"/>
    </justification>
  </clause>

  <clause id="10915">
    <literal><![CDATA[
      K((x * ((y \ 1) \ 1)) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * y) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(10881(a,2),10914(a,1))].">
      <j1 rule="para" parents="10881 10914"/>
    </justification>
  </clause>

  <clause id="10916">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(10784(a,1),10825(a,1,1))].">
      <j1 rule="para" parents="10784 10825"/>
    </justification>
  </clause>

  <clause id="10917">
    <literal><![CDATA[
      L(x,y * K(x,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(6211,a,10916,a)].">
      <j1 rule="hyper" parents="6211 10916"/>
    </justification>
  </clause>

  <clause id="10918">
    <literal><![CDATA[
      L(x,y,z) = (z * (y * K(x,y))) \ (z * (x * y))
    ]]></literal>
    <justification jstring="[para(105(a,1),10916(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="105 10916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10919">
    <literal><![CDATA[
      L(x,y \ T(z,x),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(6538(a,1),10917(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6538 10917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10921">
    <literal><![CDATA[
      L(x,K(x,y) * z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(7152(a,1),10917(a,1,2))].">
      <j1 rule="para" parents="7152 10917"/>
    </justification>
  </clause>

  <clause id="10922">
    <literal><![CDATA[
      L(x,T(y,x) \ z,u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(7271(a,1),10917(a,1,2))].">
      <j1 rule="para" parents="7271 10917"/>
    </justification>
  </clause>

  <clause id="10925">
    <literal><![CDATA[
      L(T(x,y),K(x,z) * u,w) = L(T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7863(a,1),10921(a,1,2,1))].">
      <j1 rule="para" parents="7863 10921"/>
    </justification>
  </clause>

  <clause id="10926">
    <literal><![CDATA[
      T(x,y) * L(y,z \ x,z) = z * ((z \ T(x,y)) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,10919,a(flip),b,91,a)].">
      <j1 rule="hyper" parents="119 10919 91"/>
    </justification>
  </clause>

  <clause id="10928">
    <literal><![CDATA[
      L(T(x,y),z / x,u) = L(T(x,y),x \ z,u)
    ]]></literal>
    <justification jstring="[para(4818(a,1),10925(a,1,2))].">
      <j1 rule="para" parents="4818 10925"/>
    </justification>
  </clause>

  <clause id="10929">
    <literal><![CDATA[
      L(T(x,y),T(x,z) \ u,w) = L(T(x,y),x \ u,w)
    ]]></literal>
    <justification jstring="[para(5042(a,1),10925(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5042 10925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10931">
    <literal><![CDATA[
      L(x,y,z * K(x,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,10628,a(flip),b,10918,a)].">
      <j1 rule="hyper" parents="320 10628 10918"/>
    </justification>
  </clause>

  <clause id="10934">
    <literal><![CDATA[
      K(x,L(T(y,z),y \ u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(10929(a,1),10767(a,1,2))].">
      <j1 rule="para" parents="10929 10767"/>
    </justification>
  </clause>

  <clause id="10935">
    <literal><![CDATA[
      K(x,(y * z) / (y * (z / u))) = K(x,L(T(u,y * z),z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,10414,a(flip),b,10934,a)].">
      <j1 rule="hyper" parents="58 10414 10934"/>
    </justification>
  </clause>

  <clause id="10936">
    <literal><![CDATA[
      K(x,L(T(y,z),u / y,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(10928(a,2),10934(a,1,2))].">
      <j1 rule="para" parents="10928 10934"/>
    </justification>
  </clause>

  <clause id="10937">
    <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),10936(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 10936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10938">
    <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(10857(a,1),5603(a,1))].">
      <j1 rule="para" parents="10857 5603"/>
    </justification>
  </clause>

  <clause id="10939">
    <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(10818,a,10859,a)].">
      <j1 rule="hyper" parents="10818 10859"/>
    </justification>
  </clause>

  <clause id="10940">
    <literal><![CDATA[
      K(K(L(x,y,z) \ 1,u) \ 1,w) = K(w,K(x,L(u,y,z)))
    ]]></literal>
    <justification jstring="[hyper(320,a,10864,a(flip),b,10906,a),flip(a)].">
      <j1 rule="hyper" parents="320 10864 10906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10941">
    <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(9699(a,1),10940(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9699 10940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10942">
    <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(9565(a,1),10939(a,1,2))].">
      <j1 rule="para" parents="9565 10939"/>
    </justification>
  </clause>

  <clause id="10943">
    <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(5858(a,1),10801(a,1,1))].">
      <j1 rule="para" parents="5858 10801"/>
    </justification>
  </clause>

  <clause id="10944">
    <literal><![CDATA[
      K(((x \ y) \ y) * z,L(z,x \ y,x)) = K(((x \ y) / z) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10487,a(flip),b,10898,a)].">
      <j1 rule="hyper" parents="58 10487 10898"/>
    </justification>
  </clause>

  <clause id="10945">
    <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(320,a,6640,a(flip),b,10943,a),flip(a)].">
      <j1 rule="hyper" parents="320 6640 10943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10946">
    <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(7826,a,10945,a)].">
      <j1 rule="hyper" parents="7826 10945"/>
    </justification>
  </clause>

  <clause id="10947">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = (L(x,y,z) * K(u,x)) * u
    ]]></literal>
    <justification jstring="[para(6264(a,1),10749(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6264 10749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10948">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,6167,a(flip),b,10947,a),flip(a)].">
      <j1 rule="hyper" parents="320 6167 10947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10949">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[para(1397(a,1),10948(a,1,1))].">
      <j1 rule="para" parents="1397 10948"/>
    </justification>
  </clause>

  <clause id="10950">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ (L(y,z,u) * T(x,y))
    ]]></literal>
    <justification jstring="[para(10949(a,1),9821(a,2,2))].">
      <j1 rule="para" parents="10949 9821"/>
    </justification>
  </clause>

  <clause id="10951">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = T(L(y,z,u) * K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(320,a,6168,a,b,10950,a),flip(a)].">
      <j1 rule="hyper" parents="320 6168 10950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10952">
    <literal><![CDATA[
      (x * (y / z)) * K(u,L(T(z,w),y,x)) = x * (y / T(z,T(u,w)))
    ]]></literal>
    <justification jstring="[para(10936(a,1),10873(a,1,2))].">
      <j1 rule="para" parents="10936 10873"/>
    </justification>
  </clause>

  <clause id="10953">
    <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(9834(a,1),10888(a,1,2))].">
      <j1 rule="para" parents="9834 10888"/>
    </justification>
  </clause>

  <clause id="10954">
    <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,10942,a(flip),b,10953,a)].">
      <j1 rule="hyper" parents="58 10942 10953"/>
    </justification>
  </clause>

  <clause id="10955">
    <literal><![CDATA[
      K(x,K(y,(z * (u * y)) \ w)) = K(y,K(x,(z * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(10882,a,10954,a),flip(a)].">
      <j1 rule="hyper" parents="10882 10954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10956">
    <literal><![CDATA[
      K(x,K(y,(z * (u * x)) \ w)) = K(x,K(y,(z * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(7756,a,10955,a)].">
      <j1 rule="hyper" parents="7756 10955"/>
    </justification>
  </clause>

  <clause id="10957">
    <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,9728,a(flip),b,10956,a)].">
      <j1 rule="hyper" parents="58 9728 10956"/>
    </justification>
  </clause>

  <clause id="10958">
    <literal><![CDATA[
      K(x,K(y,a(z,x,T(u,x)))) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,9465,a(flip),b,10957,a),flip(a)].">
      <j1 rule="hyper" parents="320 9465 10957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10960">
    <literal><![CDATA[
      K(x,K(y,a(z,x,u))) = 1
    ]]></literal>
    <justification jstring="[para(224(a,1),10958(a,1,2,2,3))].">
      <j1 rule="para" parents="224 10958"/>
    </justification>
  </clause>

  <clause id="10962">
    <literal><![CDATA[
      T(a(x,y,z),K(u,y)) = a(x,y,z) * 1
    ]]></literal>
    <justification jstring="[para(10960(a,1),7732(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10960 7732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10963">
    <literal><![CDATA[
      T(a(x,y,z),K(u,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3,a(flip),b,10962,a),flip(a)].">
      <j1 rule="hyper" parents="320 3 10962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10964">
    <literal><![CDATA[
      T(a(x,y \ z,u),K(y,z)) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,8006,a(flip),b,10963,a)].">
      <j1 rule="hyper" parents="58 8006 10963"/>
    </justification>
  </clause>

  <clause id="10965">
    <literal><![CDATA[
      a(x,y \ z,u) * K(y,z) = K(y,z) * a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,10964,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 10964 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10966">
    <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(3665(a,1),10869(a,1,2))].">
      <j1 rule="para" parents="3665 10869"/>
    </justification>
  </clause>

  <clause id="10967">
    <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(4929(a,1),10941(a,2,1))].">
      <j1 rule="para" parents="4929 10941"/>
    </justification>
  </clause>

  <clause id="10968">
    <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(320,a,7730,a(flip),b,10967,a),flip(a)].">
      <j1 rule="hyper" parents="320 7730 10967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10969">
    <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(10968(a,2),8168(a,1))].">
      <j1 rule="para" parents="10968 8168"/>
    </justification>
  </clause>

  <clause id="10970">
    <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(5092(a,1),10790(a,1,2))].">
      <j1 rule="para" parents="5092 10790"/>
    </justification>
  </clause>

  <clause id="10971">
    <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(10809(a,1),10970(a,1,2,1))].">
      <j1 rule="para" parents="10809 10970"/>
    </justification>
  </clause>

  <clause id="10972">
    <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(4740(a,1),10971(a,1,2))].">
      <j1 rule="para" parents="4740 10971"/>
    </justification>
  </clause>

  <clause id="10973">
    <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(10843(a,1),10972(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10843 10972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10974">
    <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(10935(a,1),10803(a,1,2))].">
      <j1 rule="para" parents="10935 10803"/>
    </justification>
  </clause>

  <clause id="10975">
    <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,10952,a(flip),b,10974,a),flip(a)].">
      <j1 rule="hyper" parents="58 10952 10974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10976">
    <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,10483,a(flip),b,10866,a),flip(a)].">
      <j1 rule="hyper" parents="58 10483 10866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10977">
    <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(10951(a,1),10908(a,1,2))].">
      <j1 rule="para" parents="10951 10908"/>
    </justification>
  </clause>

  <clause id="10978">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = K(L(x,z,y),u) * K(u,x)
    ]]></literal>
    <justification jstring="[hyper(7562,a,10977,a),flip(a)].">
      <j1 rule="hyper" parents="7562 10977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10979">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = K(x,L(u,z,y)) * K(u,x)
    ]]></literal>
    <justification jstring="[para(10809(a,1),10978(a,2,1))].">
      <j1 rule="para" parents="10809 10978"/>
    </justification>
  </clause>

  <clause id="10980">
    <literal><![CDATA[
      x * a(y,z,K(x \ u,x)) = x * a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(10852,a,10979,a),flip(a)].">
      <j1 rule="hyper" parents="10852 10979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10981">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,10792,a(flip),b,10979,a),flip(a)].">
      <j1 rule="hyper" parents="320 10792 10979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10982">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(278,a,10980,a),flip(a)].">
      <j1 rule="hyper" parents="278 10980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10985">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),10982(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="4 10982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10986">
    <literal><![CDATA[
      a(x,y,K(z * u,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(4923(a,1),10982(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4923 10982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10987">
    <literal><![CDATA[
      a(x,y,K(z,u \ z)) = a(x,y,K(u,u \ z))
    ]]></literal>
    <justification jstring="[para(4925(a,1),10982(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4925 10982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10988">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u)) = a(x,y,K(z \ u,u))
    ]]></literal>
    <justification jstring="[para(5400(a,1),10982(a,1,3))].">
      <j1 rule="para" parents="5400 10982"/>
    </justification>
  </clause>

  <clause id="10989">
    <literal><![CDATA[
      a(x,y,K(z \ (u * w),w)) = a(x,y,K(z \ u,w))
    ]]></literal>
    <justification jstring="[para(10345(a,1),10982(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10345 10982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10990">
    <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(10985(a,2),9883(a,1,1))].">
      <j1 rule="para" parents="10985 9883"/>
    </justification>
  </clause>

  <clause id="10991">
    <literal><![CDATA[
      a(x,y,K(x * z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,7010,a(flip),b,10986,a),flip(a)].">
      <j1 rule="hyper" parents="320 7010 10986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10992">
    <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(10986(a,1),10973(a,2,2,2))].">
      <j1 rule="para" parents="10986 10973"/>
    </justification>
  </clause>

  <clause id="10993">
    <literal><![CDATA[
      L(K(x * y,y),z,x) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(47,a,10991,a)].">
      <j1 rule="hyper" parents="47 10991"/>
    </justification>
  </clause>

  <clause id="10994">
    <literal><![CDATA[
      x * (y * K(x * z,T(z,x * y))) = K(x * z,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(10993(a,1),7158(a,2,1))].">
      <j1 rule="para" parents="10993 7158"/>
    </justification>
  </clause>

  <clause id="10995">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(10981(a,1),287(a,1)),flip(b)].">
      <j1 rule="para" parents="10981 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10996">
    <literal><![CDATA[
      a(x,y,K(z,z * u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(9885,a,10990,a)].">
      <j1 rule="hyper" parents="9885 10990"/>
    </justification>
  </clause>

  <clause id="10997">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),10996(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5 10996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10998">
    <literal><![CDATA[
      a(x,y,K(z,u * z)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(5346(a,2),10996(a,1,3))].">
      <j1 rule="para" parents="5346 10996"/>
    </justification>
  </clause>

  <clause id="10999">
    <literal><![CDATA[
      a(x,y,K(z,u \ z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,10987,a,b,10997,a)].">
      <j1 rule="hyper" parents="58 10987 10997"/>
    </justification>
  </clause>

  <clause id="11000">
    <literal><![CDATA[
      a(x,y,K(z \ u,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(5158(a,1),10999(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5158 10999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11001">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,10988,a,b,11000,a)].">
      <j1 rule="hyper" parents="58 10988 11000"/>
    </justification>
  </clause>

  <clause id="11002">
    <literal><![CDATA[
      a(x,y,K(z \ u,w)) = a(x,y,K(w,u \ z))
    ]]></literal>
    <justification jstring="[para(6230(a,1),11001(a,1,3))].">
      <j1 rule="para" parents="6230 11001"/>
    </justification>
  </clause>

  <clause id="11003">
    <literal><![CDATA[
      x * (y * K(x * z,T(z,y))) = K(x * z,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(8442(a,1),10994(a,1,2,2))].">
      <j1 rule="para" parents="8442 10994"/>
    </justification>
  </clause>

  <clause id="11004">
    <literal><![CDATA[
      K(x * y,y) * (x * z) = x * (K(x * y,y) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7274,a(flip),b,11003,a),flip(a)].">
      <j1 rule="hyper" parents="58 7274 11003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11005">
    <literal><![CDATA[
      x * (K(x * y,y) * (K(y,x) * z)) = a(y,x,y) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9546,a(flip),b,11004,a),flip(a)].">
      <j1 rule="hyper" parents="58 9546 11004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11006">
    <literal><![CDATA[
      a(x,y,x) * (y * z) = y * (a(x,y,x) * z)
    ]]></literal>
    <justification jstring="[para(9544(a,1),11005(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9544 11005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11007">
    <literal><![CDATA[
      x * (a(y,x,y) * (x \ z)) = a(y,x,y) * z
    ]]></literal>
    <justification jstring="[hyper(342,a,11006,a),flip(a)].">
      <j1 rule="hyper" parents="342 11006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11008">
    <literal><![CDATA[
      K((x \ (y \ z)) \ u,(y * ((y \ z) / x)) \ z) = K(x * (z \ (y * u)),x)
    ]]></literal>
    <justification jstring="[hyper(320,a,10758,a(flip),b,10976,a),flip(a)].">
      <j1 rule="hyper" parents="320 10758 10976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11009">
    <literal><![CDATA[
      K((x \ (y \ z)) \ u,L(x,y \ z,y)) = K(x * (z \ (y * u)),x)
    ]]></literal>
    <justification jstring="[hyper(10835,a,11008,a)].">
      <j1 rule="hyper" parents="10835 11008"/>
    </justification>
  </clause>

  <clause id="11010">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,L(u,x \ y,x)) = K(u * (y \ (x * z)),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,10483,a(flip),b,11009,a)].">
      <j1 rule="hyper" parents="58 10483 11009"/>
    </justification>
  </clause>

  <clause id="11011">
    <literal><![CDATA[
      K(((x \ y) / z) \ y,z) = K(z * (y \ (x * y)),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10944,a(flip),b,11010,a)].">
      <j1 rule="hyper" parents="58 10944 11010"/>
    </justification>
  </clause>

  <clause id="11012">
    <literal><![CDATA[
      K(((x \ y) / z) \ y,z) = K(z * T(x,y),z)
    ]]></literal>
    <justification jstring="[para(17(a,2),11011(a,2,1,2))].">
      <j1 rule="para" parents="17 11011"/>
    </justification>
  </clause>

  <clause id="11013">
    <literal><![CDATA[
      K(x * ((y \ z) \ z),x) = K(x * T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,10469,a(flip),b,11012,a)].">
      <j1 rule="hyper" parents="58 10469 11012"/>
    </justification>
  </clause>

  <clause id="11014">
    <literal><![CDATA[
      K(x,x * ((y \ z) \ z)) = u / (K(x * T(y,z),x) * u)
    ]]></literal>
    <justification jstring="[para(11013(a,1),5104(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11013 5104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11015">
    <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(11013(a,1),10733(a,1,1,2,2))].">
      <j1 rule="para" parents="11013 10733"/>
    </justification>
  </clause>

  <clause id="11016">
    <literal><![CDATA[
      K(x,x * ((y \ z) \ z)) = K(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,5104,a(flip),b,11014,a),flip(a)].">
      <j1 rule="hyper" parents="320 5104 11014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11017">
    <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(320,a,5060,a(flip),b,10992,a),flip(a)].">
      <j1 rule="hyper" parents="320 5060 10992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11018">
    <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(1684(a,2),10899(a,1,2))].">
      <j1 rule="para" parents="1684 10899"/>
    </justification>
  </clause>

  <clause id="11019">
    <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(6771(a,1),6851(a,1,2,2))].">
      <j1 rule="para" parents="6771 6851"/>
    </justification>
  </clause>

  <clause id="11020">
    <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(9466(a,1),6911(a,1,1))].">
      <j1 rule="para" parents="9466 6911"/>
    </justification>
  </clause>

  <clause id="11021">
    <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(6903(a,1),11020(a,2,2))].">
      <j1 rule="para" parents="6903 11020"/>
    </justification>
  </clause>

  <clause id="11022">
    <literal><![CDATA[
      R(T(K(x,y),z),u,w) \ z = z / R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7657(a,1),11021(a,1,1,1))].">
      <j1 rule="para" parents="7657 11021"/>
    </justification>
  </clause>

  <clause id="11023">
    <literal><![CDATA[
      x / (x / R(K(y,z),u,w)) = R(T(K(y,z),x),u,w)
    ]]></literal>
    <justification jstring="[hyper(197,a,11022,a)].">
      <j1 rule="hyper" parents="197 11022"/>
    </justification>
  </clause>

  <clause id="11025">
    <literal><![CDATA[
      (R(K(x,y),z,u) \ w) \ w = R(T(K(x,y),w),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9471,a(flip),b,11023,a)].">
      <j1 rule="hyper" parents="58 9471 11023"/>
    </justification>
  </clause>

  <clause id="11026">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = R(T(K(y,x),z * u),z,u)
    ]]></literal>
    <justification jstring="[para(6906(a,1),11025(a,1,1))].">
      <j1 rule="para" parents="6906 11025"/>
    </justification>
  </clause>

  <clause id="11027">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = R(K(y,T(x,z * u)),z,u)
    ]]></literal>
    <justification jstring="[para(7131(a,2),11026(a,2,1))].">
      <j1 rule="para" parents="7131 11026"/>
    </justification>
  </clause>

  <clause id="11028">
    <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(8284(a,1),11027(a,2,1))].">
      <j1 rule="para" parents="8284 11027"/>
    </justification>
  </clause>

  <clause id="11029">
    <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(6292(a,1),7630(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6292 7630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11030">
    <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(320,a,7722,a(flip),b,11029,a),flip(a)].">
      <j1 rule="hyper" parents="320 7722 11029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11031">
    <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(7589(a,1),11030(a,2,1))].">
      <j1 rule="para" parents="7589 11030"/>
    </justification>
  </clause>

  <clause id="11032">
    <literal><![CDATA[
      T(x,T(y / T(y / z,u),w)) = T(x,T(T(z \ y,u) \ y,w))
    ]]></literal>
    <justification jstring="[para(11031(a,1),8287(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11031 8287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11033">
    <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(4737(a,1),8772(a,1,1))].">
      <j1 rule="para" parents="4737 8772"/>
    </justification>
  </clause>

  <clause id="11034">
    <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(691,a,11033,a),flip(a)].">
      <j1 rule="hyper" parents="691 11033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11035">
    <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(11033(a,1),691(a,1))].">
      <j1 rule="para" parents="11033 691"/>
    </justification>
  </clause>

  <clause id="11036">
    <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(5042(a,1),11034(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5042 11034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11037">
    <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(5092(a,1),8971(a,1,1,1))].">
      <j1 rule="para" parents="5092 8971"/>
    </justification>
  </clause>

  <clause id="11038">
    <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(9996(a,1),8984(a,1,1))].">
      <j1 rule="para" parents="9996 8984"/>
    </justification>
  </clause>

  <clause id="11039">
    <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),9159(a,2,1))].">
      <j1 rule="para" parents="7 9159"/>
    </justification>
  </clause>

  <clause id="11040">
    <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(320,a,6337,a,b,11039,a)].">
      <j1 rule="hyper" parents="320 6337 11039"/>
    </justification>
  </clause>

  <clause id="11041">
    <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(10220(a,2),9439(a,2,2,2))].">
      <j1 rule="para" parents="10220 9439"/>
    </justification>
  </clause>

  <clause id="11042">
    <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(320,a,5300,a(flip),b,9778,a),flip(a)].">
      <j1 rule="hyper" parents="320 5300 9778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11043">
    <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(9975(a,1),9983(a,2,2,1,1))].">
      <j1 rule="para" parents="9975 9983"/>
    </justification>
  </clause>

  <clause id="11044">
    <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(4929(a,1),11043(a,2,2,1))].">
      <j1 rule="para" parents="4929 11043"/>
    </justification>
  </clause>

  <clause id="11046">
    <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(4929(a,1),11044(a,1,1,2,1))].">
      <j1 rule="para" parents="4929 11044"/>
    </justification>
  </clause>

  <clause id="11047">
    <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,5997,a(flip),b,11046,a)].">
      <j1 rule="hyper" parents="58 5997 11046"/>
    </justification>
  </clause>

  <clause id="11048">
    <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(11046(a,1),507(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11046 507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11049">
    <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(11046(a,2),9874(a,1,1))].">
      <j1 rule="para" parents="11046 9874"/>
    </justification>
  </clause>

  <clause id="11051">
    <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(7730(a,1),11049(a,1,1,1,2,1))].">
      <j1 rule="para" parents="7730 11049"/>
    </justification>
  </clause>

  <clause id="11052">
    <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),10282(a,2,2,2,1,1,2))].">
      <j1 rule="para" parents="75 10282"/>
    </justification>
  </clause>

  <clause id="11053">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * u = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[hyper(585,a,11052,a)].">
      <j1 rule="hyper" parents="585 11052"/>
    </justification>
  </clause>

  <clause id="11056">
    <literal><![CDATA[
      ((x * y) * (z * (((x * y) \ u) / z))) / u = K(z,u / ((x * z) * y))
    ]]></literal>
    <justification jstring="[para(11053(a,1),10008(a,1,1))].">
      <j1 rule="para" parents="11053 10008"/>
    </justification>
  </clause>

  <clause id="11057">
    <literal><![CDATA[
      K(x,y / ((z * u) * x)) = K(x,y / ((z * x) * u))
    ]]></literal>
    <justification jstring="[hyper(5881,a,11056,a)].">
      <j1 rule="hyper" parents="5881 11056"/>
    </justification>
  </clause>

  <clause id="11058">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(10619,a,11057,a),flip(a)].">
      <j1 rule="hyper" parents="10619 11057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11059">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) = K(x,1 / (z * x))
    ]]></literal>
    <justification jstring="[hyper(320,a,5314,a(flip),b,11057,a),flip(a)].">
      <j1 rule="hyper" parents="320 5314 11057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11060">
    <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),11057(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="105 11057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11061">
    <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),11057(a,1,2))].">
      <j1 rule="para" parents="102 11057"/>
    </justification>
  </clause>

  <clause id="11062">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / (z * x)) = u
    ]]></literal>
    <justification jstring="[para(11057(a,2),5460(a,1))].">
      <j1 rule="para" parents="11057 5460"/>
    </justification>
  </clause>

  <clause id="11063">
    <literal><![CDATA[
      K(x,1 / ((y / z) * x)) = K(x,z / (y * x))
    ]]></literal>
    <justification jstring="[para(7(a,1),11059(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 11059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11064">
    <literal><![CDATA[
      K(x,((y * x) * z) / (x * (y * (y \ z)))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[hyper(9858,a,11058,a),flip(a)].">
      <j1 rule="hyper" parents="9858 11058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11065">
    <literal><![CDATA[
      K(x,y / ((x * z) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8849,a(flip),b,11058,a)].">
      <j1 rule="hyper" parents="58 8849 11058"/>
    </justification>
  </clause>

  <clause id="11066">
    <literal><![CDATA[
      K(x,(y * x) / ((z * x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,7071,a(flip),b,11061,a),flip(a)].">
      <j1 rule="hyper" parents="58 7071 11061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11068">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,((y * x) * z) / (x * z))
    ]]></literal>
    <justification jstring="[para(5(a,1),11064(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 11064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11069">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[para(15(a,2),11068(a,2,2))].">
      <j1 rule="para" parents="15 11068"/>
    </justification>
  </clause>

  <clause id="11071">
    <literal><![CDATA[
      K(x,R(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10605,a,11069,a),flip(a)].">
      <j1 rule="hyper" parents="10605 11069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11072">
    <literal><![CDATA[
      R(K(x,y),z,T(y * x,z)) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(9862,a,11069,a)].">
      <j1 rule="hyper" parents="9862 11069"/>
    </justification>
  </clause>

  <clause id="11073">
    <literal><![CDATA[
      K(x,R(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(11069(a,1),10605(a,1))].">
      <j1 rule="para" parents="11069 10605"/>
    </justification>
  </clause>

  <clause id="11074">
    <literal><![CDATA[
      R(K(x \ y,x),y,z) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(9216,a,11071,a)].">
      <j1 rule="hyper" parents="9216 11071"/>
    </justification>
  </clause>

  <clause id="11076">
    <literal><![CDATA[
      T(x,R(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,11071,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 11071 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11077">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9613,a(flip),b,11071,a)].">
      <j1 rule="hyper" parents="58 9613 11071"/>
    </justification>
  </clause>

  <clause id="11079">
    <literal><![CDATA[
      K(x,R(R(y,x,z),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(26(a,1),11071(a,1,2))].">
      <j1 rule="para" parents="26 11071"/>
    </justification>
  </clause>

  <clause id="11080">
    <literal><![CDATA[
      K(1 / x,y / (1 / x)) = K(1 / x,y * x)
    ]]></literal>
    <justification jstring="[para(522(a,1),11071(a,1,2)),flip(a)].">
      <j1 rule="para" parents="522 11071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11083">
    <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(533(a,1),11076(a,1,2))].">
      <j1 rule="para" parents="533 11076"/>
    </justification>
  </clause>

  <clause id="11084">
    <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(610(a,1),11073(a,1,2))].">
      <j1 rule="para" parents="610 11073"/>
    </justification>
  </clause>

  <clause id="11085">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(9333(a,2),11073(a,1))].">
      <j1 rule="para" parents="9333 11073"/>
    </justification>
  </clause>

  <clause id="11086">
    <literal><![CDATA[
      K(x / (y * z),y) = K(y \ (x / z),y)
    ]]></literal>
    <justification jstring="[hyper(5943,a,11074,a)].">
      <j1 rule="hyper" parents="5943 11074"/>
    </justification>
  </clause>

  <clause id="11087">
    <literal><![CDATA[
      K(x,y / (x * z)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(10619,a,11077,a)].">
      <j1 rule="hyper" parents="10619 11077"/>
    </justification>
  </clause>

  <clause id="11089">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,11057,a(flip),b,11077,a)].">
      <j1 rule="hyper" parents="58 11057 11077"/>
    </justification>
  </clause>

  <clause id="11090">
    <literal><![CDATA[
      K(x,x \ ((x * y) / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8474,a(flip),b,11077,a),flip(a)].">
      <j1 rule="hyper" parents="58 8474 11077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11091">
    <literal><![CDATA[
      K(x / (y * z),z) = K(z \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(10620,a,11086,a)].">
      <j1 rule="hyper" parents="10620 11086"/>
    </justification>
  </clause>

  <clause id="11092">
    <literal><![CDATA[
      K((x \ y) / z,x) = K(x \ (y / z),x)
    ]]></literal>
    <justification jstring="[hyper(8715,a,11086,a)].">
      <j1 rule="hyper" parents="8715 11086"/>
    </justification>
  </clause>

  <clause id="11093">
    <literal><![CDATA[
      K(x,y / ((x * z) * u)) = K(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,11065,a,b,11087,a)].">
      <j1 rule="hyper" parents="58 11065 11087"/>
    </justification>
  </clause>

  <clause id="11094">
    <literal><![CDATA[
      K(x,x \ ((y \ 1) \ (x * z))) = K(x,z / T(y \ 1,y * (x * z)))
    ]]></literal>
    <justification jstring="[para(4327(a,1),11090(a,1,2,2))].">
      <j1 rule="para" parents="4327 11090"/>
    </justification>
  </clause>

  <clause id="11095">
    <literal><![CDATA[
      K(x \ (y \ z),x) * z = z * K(x \ (z / y),x)
    ]]></literal>
    <justification jstring="[para(11091(a,1),10346(a,2,2))].">
      <j1 rule="para" parents="11091 10346"/>
    </justification>
  </clause>

  <clause id="11096">
    <literal><![CDATA[
      K(x \ (y / z),x) * z = z * K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(11092(a,1),7260(a,1,1))].">
      <j1 rule="para" parents="11092 7260"/>
    </justification>
  </clause>

  <clause id="11097">
    <literal><![CDATA[
      R(K(x,R(y,x,z)),(y * x) * z,u) = K(x,R(y,x * z,u))
    ]]></literal>
    <justification jstring="[hyper(9217,a,11079,a)].">
      <j1 rule="hyper" parents="9217 11079"/>
    </justification>
  </clause>

  <clause id="11098">
    <literal><![CDATA[
      K(x,R(y,x,z)) * ((y * x) * z) = (K(x,y) * z) * T(y * x,z)
    ]]></literal>
    <justification jstring="[para(11072(a,1),516(a,1,1))].">
      <j1 rule="para" parents="11072 516"/>
    </justification>
  </clause>

  <clause id="11099">
    <literal><![CDATA[
      K(x,y * K(1 / y,z * y)) = T(K(x,y),z / (1 / y))
    ]]></literal>
    <justification jstring="[para(11080(a,1),9608(a,1,2,2))].">
      <j1 rule="para" parents="11080 9608"/>
    </justification>
  </clause>

  <clause id="11100">
    <literal><![CDATA[
      K(x,x \ (y / ((x \ z) * u))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8850,a(flip),b,11089,a),flip(a)].">
      <j1 rule="hyper" parents="58 8850 11089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11101">
    <literal><![CDATA[
      T(x,y / ((x * z) * u)) = T(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(118,a,11093,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 11093 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11102">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(7278,a,11096,a)].">
      <j1 rule="hyper" parents="7278 11096"/>
    </justification>
  </clause>

  <clause id="11103">
    <literal><![CDATA[
      K(x \ (y / z),T(x,y)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8438,a(flip),b,11102,a)].">
      <j1 rule="hyper" parents="58 8438 11102"/>
    </justification>
  </clause>

  <clause id="11104">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = (u * K(z \ (x \ y),x)) \ u
    ]]></literal>
    <justification jstring="[para(11103(a,1),6309(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11103 6309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11105">
    <literal><![CDATA[
      K(x,(x * y) / (z * u)) = K(x,y / ((x \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11090,a(flip),b,11100,a),flip(a)].">
      <j1 rule="hyper" parents="58 11090 11100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11106">
    <literal><![CDATA[
      K(x,y / ((x \ z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z * u) / y) \ x) = w
    ]]></literal>
    <justification jstring="[para(11105(a,1),6937(a,1))].">
      <j1 rule="para" parents="11105 6937"/>
    </justification>
  </clause>

  <clause id="11107">
    <literal><![CDATA[
      T(K(x,y),z / (1 / y)) = T(K(x,y),z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9608,a(flip),b,11099,a),flip(a)].">
      <j1 rule="hyper" parents="58 9608 11099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11108">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,1 / (z / (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(58,a,9609,a(flip),b,11107,a),flip(a)].">
      <j1 rule="hyper" parents="58 9609 11107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11109">
    <literal><![CDATA[
      K(x,1 / (y / (y / (1 / z)))) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6189,a(flip),b,11108,a),flip(a)].">
      <j1 rule="hyper" parents="58 6189 11108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11110">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,6309,a(flip),b,11104,a),flip(a)].">
      <j1 rule="hyper" parents="320 6309 11104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11111">
    <literal><![CDATA[
      K(x,T(x \ (y / z),y)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(7679,a,11110,a)].">
      <j1 rule="hyper" parents="7679 11110"/>
    </justification>
  </clause>

  <clause id="11112">
    <literal><![CDATA[
      K(x,(y \ z) \ (x \ z)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),11111(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 11111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11113">
    <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,8397,a,b,11112,a)].">
      <j1 rule="hyper" parents="58 8397 11112"/>
    </justification>
  </clause>

  <clause id="11114">
    <literal><![CDATA[
      R(K(x,y),(y * x) * z,u) = K(x,R(y,x * z,u))
    ]]></literal>
    <justification jstring="[para(11071(a,1),11097(a,1,1))].">
      <j1 rule="para" parents="11071 11097"/>
    </justification>
  </clause>

  <clause id="11116">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (y * (K(x,y) * x)) * z
    ]]></literal>
    <justification jstring="[hyper(6957,a,11098,a),flip(a)].">
      <j1 rule="hyper" parents="6957 11098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11117">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(4806(a,1),11116(a,2,1))].">
      <j1 rule="para" parents="4806 11116"/>
    </justification>
  </clause>

  <clause id="11118">
    <literal><![CDATA[
      (x * y) * (K(y,x) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(8748,a,11117,a)].">
      <j1 rule="hyper" parents="8748 11117"/>
    </justification>
  </clause>

  <clause id="11119">
    <literal><![CDATA[
      (x * y) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(116,a,11117,a(flip),b,8747,a(flip))].">
      <j1 rule="hyper" parents="116 11117 8747"/>
    </justification>
  </clause>

  <clause id="11120">
    <literal><![CDATA[
      ((x \ y) * x) \ (y * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(116,a,148,a(flip),b,11118,a)].">
      <j1 rule="hyper" parents="116 148 11118"/>
    </justification>
  </clause>

  <clause id="11121">
    <literal><![CDATA[
      K(x,y) * ((x * y) \ z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,11118,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 11118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11122">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,10608,a,b,11118,a)].">
      <j1 rule="hyper" parents="58 10608 11118"/>
    </justification>
  </clause>

  <clause id="11123">
    <literal><![CDATA[
      K(x,y) \ ((x * y) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(116,a,11118,a(flip),b,10608,a)].">
      <j1 rule="hyper" parents="116 11118 10608"/>
    </justification>
  </clause>

  <clause id="11125">
    <literal><![CDATA[
      (x * y) * (1 / T(x,y)) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(5138(a,1),11118(a,1,2))].">
      <j1 rule="para" parents="5138 11118"/>
    </justification>
  </clause>

  <clause id="11126">
    <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(11118(a,1),7892(a,1,1,1))].">
      <j1 rule="para" parents="11118 7892"/>
    </justification>
  </clause>

  <clause id="11127">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,T(x,z)) * u) = (z * K(x,y)) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(7163(a,1),11118(a,1,2))].">
      <j1 rule="para" parents="7163 11118"/>
    </justification>
  </clause>

  <clause id="11128">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) = x * ((y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,11121,a(flip),b,5137,a)].">
      <j1 rule="hyper" parents="119 11121 5137"/>
    </justification>
  </clause>

  <clause id="11129">
    <literal><![CDATA[
      ((x * y) / x) \ ((y * x) \ z) = y \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,11121,a(flip),b,5410,a)].">
      <j1 rule="hyper" parents="116 11121 5410"/>
    </justification>
  </clause>

  <clause id="11130">
    <literal><![CDATA[
      ((x * y) \ z) * L(u,(y * x) \ z,K(y,x)) = K(y,x) * (((y * x) \ z) * u)
    ]]></literal>
    <justification jstring="[para(11121(a,1),90(a,1,1))].">
      <j1 rule="para" parents="11121 90"/>
    </justification>
  </clause>

  <clause id="11131">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x * ((y * x) \ z) = u
    ]]></literal>
    <justification jstring="[para(11121(a,1),5224(a,1,2))].">
      <j1 rule="para" parents="11121 5224"/>
    </justification>
  </clause>

  <clause id="11132">
    <literal><![CDATA[
      T((x * y) \ z,K(y,x)) = ((y * x) \ z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(11121(a,1),6311(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11121 6311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11133">
    <literal><![CDATA[
      K(x,y * ((z * x) \ u)) = K(x,y * ((x * z) \ u))
    ]]></literal>
    <justification jstring="[para(11121(a,1),7252(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11121 7252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11134">
    <literal><![CDATA[
      L(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(4966,a,11122,a)].">
      <j1 rule="hyper" parents="4966 11122"/>
    </justification>
  </clause>

  <clause id="11135">
    <literal><![CDATA[
      (x * y) \ (K(x,y) * z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(598,a,11122,a)].">
      <j1 rule="hyper" parents="598 11122"/>
    </justification>
  </clause>

  <clause id="11136">
    <literal><![CDATA[
      (x * y) * ((y * x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(342,a,11122,a),flip(a)].">
      <j1 rule="hyper" parents="342 11122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11137">
    <literal><![CDATA[
      K(x \ y,x) * (y * z) = ((x \ y) * x) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),11122(a,1,2,1))].">
      <j1 rule="para" parents="5 11122"/>
    </justification>
  </clause>

  <clause id="11138">
    <literal><![CDATA[
      K(x,(x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * x) * z) = u
    ]]></literal>
    <justification jstring="[para(11122(a,1),7334(a,1,2))].">
      <j1 rule="para" parents="11122 7334"/>
    </justification>
  </clause>

  <clause id="11139">
    <literal><![CDATA[
      K(x,y \ ((x * z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ ((z * x) * u)) = w
    ]]></literal>
    <justification jstring="[para(11122(a,1),8563(a,1,2,2))].">
      <j1 rule="para" parents="11122 8563"/>
    </justification>
  </clause>

  <clause id="11140">
    <literal><![CDATA[
      K(x \ ((y * z) * u),z) = K(x \ ((z * y) * u),z)
    ]]></literal>
    <justification jstring="[para(11122(a,1),8625(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11122 8625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11142">
    <literal><![CDATA[
      L(x,T(y,z),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(6806,a,11134,a)].">
      <j1 rule="hyper" parents="6806 11134"/>
    </justification>
  </clause>

  <clause id="11143">
    <literal><![CDATA[
      L(x,y,z) = (y * z) \ (z * (T(y,z) * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6804,a(flip),b,11134,a),flip(a)].">
      <j1 rule="hyper" parents="58 6804 11134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11144">
    <literal><![CDATA[
      (x * y) * L(z,x,y) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,11134,a(flip),b,6804,a(flip))].">
      <j1 rule="hyper" parents="119 11134 6804"/>
    </justification>
  </clause>

  <clause id="11145">
    <literal><![CDATA[
      L(x,y * z,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(11134(a,1),45(a,2))].">
      <j1 rule="para" parents="11134 45"/>
    </justification>
  </clause>

  <clause id="11146">
    <literal><![CDATA[
      L(x,T(y,z) * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(4867(a,1),11134(a,1,3))].">
      <j1 rule="para" parents="4867 11134"/>
    </justification>
  </clause>

  <clause id="11147">
    <literal><![CDATA[
      L(L(x,y,z),u * w,K(w,u)) = L(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,11134,a,b,11142,a)].">
      <j1 rule="hyper" parents="320 11134 11142"/>
    </justification>
  </clause>

  <clause id="11148">
    <literal><![CDATA[
      L(x \ y,x,x \ z) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6974,a(flip),b,11142,a),flip(a)].">
      <j1 rule="hyper" parents="58 6974 11142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11149">
    <literal><![CDATA[
      L(x,(y \ z) \ z,y \ z) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1604,a(flip),b,11142,a)].">
      <j1 rule="hyper" parents="58 1604 11142"/>
    </justification>
  </clause>

  <clause id="11150">
    <literal><![CDATA[
      L(T(x,y) \ z,x,y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,496,a(flip),b,11142,a),flip(a)].">
      <j1 rule="hyper" parents="58 496 11142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11151">
    <literal><![CDATA[
      L(x,y / z,z) = L(x,z \ y,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),11142(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 11142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11155">
    <literal><![CDATA[
      L(x,y,T(z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(10201,a,11146,a),flip(a)].">
      <j1 rule="hyper" parents="10201 11146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11156">
    <literal><![CDATA[
      L(x,y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(11146(a,1),10201(a,1))].">
      <j1 rule="para" parents="11146 10201"/>
    </justification>
  </clause>

  <clause id="11157">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) \ z) = L(x,y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(2101,a,11155,a)].">
      <j1 rule="hyper" parents="2101 11155"/>
    </justification>
  </clause>

  <clause id="11158">
    <literal><![CDATA[
      L(x,y,z / y) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(107(a,1),11155(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 11155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11160">
    <literal><![CDATA[
      L(x,y,z \ K(y,z \ 1)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(4839(a,1),11155(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4839 11155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11161">
    <literal><![CDATA[
      L(x,T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(6805(a,1),11145(a,1))].">
      <j1 rule="para" parents="6805 11145"/>
    </justification>
  </clause>

  <clause id="11164">
    <literal><![CDATA[
      x \ ((x / y) * (y * z)) = L(z,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,93,a,b,11158,a)].">
      <j1 rule="hyper" parents="58 93 11158"/>
    </justification>
  </clause>

  <clause id="11165">
    <literal><![CDATA[
      L(T(x,y),y,y \ z) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,695,a(flip),b,11158,a),flip(a)].">
      <j1 rule="hyper" parents="58 695 11158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11166">
    <literal><![CDATA[
      x * L(y,z,z \ x) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,11158,a(flip),b,93,a)].">
      <j1 rule="hyper" parents="119 11158 93"/>
    </justification>
  </clause>

  <clause id="11167">
    <literal><![CDATA[
      (x / y) * (y * T(z,x)) = L(z,y,y \ x) * x
    ]]></literal>
    <justification jstring="[para(11158(a,1),749(a,2,1))].">
      <j1 rule="para" parents="11158 749"/>
    </justification>
  </clause>

  <clause id="11168">
    <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(6095(a,1),11161(a,1,2))].">
      <j1 rule="para" parents="6095 11161"/>
    </justification>
  </clause>

  <clause id="11169">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * z) = (y * x) \ (x * z)
    ]]></literal>
    <justification jstring="[para(4740(a,1),11135(a,1,2))].">
      <j1 rule="para" parents="4740 11135"/>
    </justification>
  </clause>

  <clause id="11170">
    <literal><![CDATA[
      (x * y) \ (R(y,z,u) * T(x,y)) = (y * x) \ (R(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(5845(a,1),11135(a,1,2))].">
      <j1 rule="para" parents="5845 11135"/>
    </justification>
  </clause>

  <clause id="11171">
    <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(320,a,4281,a,b,11136,a)].">
      <j1 rule="hyper" parents="320 4281 11136"/>
    </justification>
  </clause>

  <clause id="11172">
    <literal><![CDATA[
      (x * y) * K(z,L(u,x,y)) = y * (T(x,y) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(10807,a,11143,a)].">
      <j1 rule="hyper" parents="10807 11143"/>
    </justification>
  </clause>

  <clause id="11174">
    <literal><![CDATA[
      (x * (T(y,x) * z)) / L(z,y,x) = y * x
    ]]></literal>
    <justification jstring="[hyper(197,a,11143,a(flip))].">
      <j1 rule="hyper" parents="197 11143"/>
    </justification>
  </clause>

  <clause id="11175">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * (K(x,T(y,z)) * u)) = L(u,K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7131(a,2),11143(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7131 11143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11176">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),T(x,y) \ y) = y \ ((T(y,x) / x) * z)
    ]]></literal>
    <justification jstring="[para(4206(a,2),11148(a,2,2,1))].">
      <j1 rule="para" parents="4206 11148"/>
    </justification>
  </clause>

  <clause id="11177">
    <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(6309(a,1),11148(a,1,3))].">
      <j1 rule="para" parents="6309 11148"/>
    </justification>
  </clause>

  <clause id="11178">
    <literal><![CDATA[
      x * K(y,L(z,u,u \ x)) = (x / u) * (u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,10763,a(flip),b,11164,a)].">
      <j1 rule="hyper" parents="119 10763 11164"/>
    </justification>
  </clause>

  <clause id="11179">
    <literal><![CDATA[
      ((x / y) * (y * z)) \ K(x,L(z,y,y \ x)) = (L(z,y,y \ x) * x) \ 1
    ]]></literal>
    <justification jstring="[para(11166(a,1),5530(a,1,1))].">
      <j1 rule="para" parents="11166 5530"/>
    </justification>
  </clause>

  <clause id="11180">
    <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(1698(a,1),11125(a,2,1))].">
      <j1 rule="para" parents="1698 11125"/>
    </justification>
  </clause>

  <clause id="11181">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * ((y * x) \ z)) = w
    ]]></literal>
    <justification jstring="[para(11128(a,2),536(a,1))].">
      <j1 rule="para" parents="11128 536"/>
    </justification>
  </clause>

  <clause id="11182">
    <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(7837(a,1),11128(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7837 11128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11183">
    <literal><![CDATA[
      K(x,(((x \ y) * x) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(11137(a,1),8562(a,1,2,1))].">
      <j1 rule="para" parents="11137 8562"/>
    </justification>
  </clause>

  <clause id="11184">
    <literal><![CDATA[
      K((x * T(y,x * y)) \ z,x * y) * (z * u) = (((x * y) \ z) * (x * y)) * u
    ]]></literal>
    <justification jstring="[para(8619(a,2),11137(a,1,1))].">
      <j1 rule="para" parents="8619 11137"/>
    </justification>
  </clause>

  <clause id="11185">
    <literal><![CDATA[
      K(x,L(y,T(z,u),u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11147(a,1),7481(a,1,2))].">
      <j1 rule="para" parents="11147 7481"/>
    </justification>
  </clause>

  <clause id="11186">
    <literal><![CDATA[
      K(x,L(y,z / u,u)) = K(x,L(y,u \ z,u))
    ]]></literal>
    <justification jstring="[para(107(a,1),11185(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 11185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11187">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,x) \ z) = x \ ((y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9698,a,b,11129,a)].">
      <j1 rule="hyper" parents="58 9698 11129"/>
    </justification>
  </clause>

  <clause id="11188">
    <literal><![CDATA[
      L(x,y,T((y * x) \ z,K(x,y))) = L(x,y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(11132(a,2),10931(a,1,3))].">
      <j1 rule="para" parents="11132 10931"/>
    </justification>
  </clause>

  <clause id="11189">
    <literal><![CDATA[
      (x / y) * (y * K(z,T(u,y))) = x * K(z,x \ ((x / y) * (u * y)))
    ]]></literal>
    <justification jstring="[para(11165(a,1),11178(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11165 11178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11190">
    <literal><![CDATA[
      a(x,y,x) * (T(x * y,x) \ z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(9540,a,11187,a)].">
      <j1 rule="hyper" parents="9540 11187"/>
    </justification>
  </clause>

  <clause id="11191">
    <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),11170(a,2,2))].">
      <j1 rule="para" parents="101 11170"/>
    </justification>
  </clause>

  <clause id="11192">
    <literal><![CDATA[
      K(x,y / T(z \ 1,z * (x * y))) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(10310,a,11094,a),flip(a)].">
      <j1 rule="hyper" parents="10310 11094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11193">
    <literal><![CDATA[
      x * K(y,x \ ((x / z) * (u * z))) = (x / z) * (K(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7274,a(flip),b,11189,a),flip(a)].">
      <j1 rule="hyper" parents="58 7274 11189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11194">
    <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,11083,a)].">
      <j1 rule="hyper" parents="58 22 11083"/>
    </justification>
  </clause>

  <clause id="11195">
    <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(3740(a,1),11113(a,2,2))].">
      <j1 rule="para" parents="3740 11113"/>
    </justification>
  </clause>

  <clause id="11196">
    <literal><![CDATA[
      K(x,y) * (((x * y) \ y) * z) = ((y * x) \ y) * z
    ]]></literal>
    <justification jstring="[para(10176(a,1),11130(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10176 11130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11197">
    <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(7971(a,1),11177(a,2,2,1))].">
      <j1 rule="para" parents="7971 11177"/>
    </justification>
  </clause>

  <clause id="11198">
    <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,11191,a)].">
      <j1 rule="hyper" parents="119 9 11191"/>
    </justification>
  </clause>

  <clause id="11199">
    <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(320,a,4213,a(flip),b,11194,a),flip(a)].">
      <j1 rule="hyper" parents="320 4213 11194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11200">
    <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(320,a,8608,a(flip),b,11195,a),flip(a)].">
      <j1 rule="hyper" parents="320 8608 11195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11201">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,y \ ((1 / z) \ y))) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8200,a(flip),b,11200,a),flip(a)].">
      <j1 rule="hyper" parents="320 8200 11200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11202">
    <literal><![CDATA[
      K(x,T(x \ y,z)) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(10341,a,11201,a),flip(a)].">
      <j1 rule="hyper" parents="10341 11201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11203">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,u)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,10323,a,b,11202,a)].">
      <j1 rule="hyper" parents="320 10323 11202"/>
    </justification>
  </clause>

  <clause id="11204">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) = K(z,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,10286,a,b,11202,a)].">
      <j1 rule="hyper" parents="320 10286 11202"/>
    </justification>
  </clause>

  <clause id="11205">
    <literal><![CDATA[
      T((x \ y) * x,z) \ T(y,z) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,4579,a,b,11202,a)].">
      <j1 rule="hyper" parents="320 4579 11202"/>
    </justification>
  </clause>

  <clause id="11206">
    <literal><![CDATA[
      K(x,y \ (x \ (z * y))) = K(x,T(x \ z,y))
    ]]></literal>
    <justification jstring="[hyper(10379,a,11202,a(flip))].">
      <j1 rule="hyper" parents="10379 11202"/>
    </justification>
  </clause>

  <clause id="11207">
    <literal><![CDATA[
      K(x,x \ T(x * y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),11202(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 11202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11208">
    <literal><![CDATA[
      K(x,T(y,z) / x) = K(x,T(y / x,z))
    ]]></literal>
    <justification jstring="[para(4532(a,1),11207(a,1,2))].">
      <j1 rule="para" parents="4532 11207"/>
    </justification>
  </clause>

  <clause id="11209">
    <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(2709(a,1),11208(a,2,2,1))].">
      <j1 rule="para" parents="2709 11208"/>
    </justification>
  </clause>

  <clause id="11210">
    <literal><![CDATA[
      K(x,T(x \ y,z)) * (K(y,z) * x) = T(K(y,z) * x,x \ y)
    ]]></literal>
    <justification jstring="[para(11204(a,1),4729(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11204 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11211">
    <literal><![CDATA[
      K(x,T(x \ y,y \ (x * z))) = K(x,(y \ (x * z)) \ z)
    ]]></literal>
    <justification jstring="[para(66(a,1),11206(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="66 11206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11212">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,u)) = K(x,T(x \ y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,8200,a,b,11203,a),flip(a)].">
      <j1 rule="hyper" parents="320 8200 11203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11213">
    <literal><![CDATA[
      T(x,y) * K(z \ x,T(z,y)) = T((z \ x) * z,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,7176,a,b,11205,a)].">
      <j1 rule="hyper" parents="34 7176 11205"/>
    </justification>
  </clause>

  <clause id="11214">
    <literal><![CDATA[
      T(x,y) * K(z \ x,T(z,y)) = (z \ T(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(320,a,4556,a(flip),b,11213,a),flip(a)].">
      <j1 rule="hyper" parents="320 4556 11213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11215">
    <literal><![CDATA[
      K(x \ T(y,z),x) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(29,a,302,a,b,11214,a)].">
      <j1 rule="hyper" parents="29 302 11214"/>
    </justification>
  </clause>

  <clause id="11217">
    <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(11212(a,2),8243(a,1))].">
      <j1 rule="para" parents="11212 8243"/>
    </justification>
  </clause>

  <clause id="11218">
    <literal><![CDATA[
      K(x,T(x \ y,y \ z)) = K(x,(y \ (x * z)) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9288,a(flip),b,11211,a)].">
      <j1 rule="hyper" parents="58 9288 11211"/>
    </justification>
  </clause>

  <clause id="11219">
    <literal><![CDATA[
      K(x,(y \ (x * z)) \ z) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(8722,a,11218,a),flip(a)].">
      <j1 rule="hyper" parents="8722 11218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11220">
    <literal><![CDATA[
      K(x,x \ T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(2444(a,1),11217(a,1,2))].">
      <j1 rule="para" parents="2444 11217"/>
    </justification>
  </clause>

  <clause id="11221">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,T(z \ x,y)) = u
    ]]></literal>
    <justification jstring="[para(10286(a,2),11220(a,1))].">
      <j1 rule="para" parents="10286 11220"/>
    </justification>
  </clause>

  <clause id="11222">
    <literal><![CDATA[
      T(K(x,y) * z,z \ x) = T(z,z \ x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9313,a,11210,a),flip(a)].">
      <j1 rule="hyper" parents="9313 11210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11223">
    <literal><![CDATA[
      (x \ y) * T(K(y,z) * x,x \ y) = (y / x) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(11222(a,2),4523(a,1,2))].">
      <j1 rule="para" parents="11222 4523"/>
    </justification>
  </clause>

  <clause id="11224">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ x) = (x / z) * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(284,a,11223,a)].">
      <j1 rule="hyper" parents="284 11223"/>
    </justification>
  </clause>

  <clause id="11225">
    <literal><![CDATA[
      ((x / y) * (y * K(x,z))) / T(x,z) = a(K(x,z),y,y \ x)
    ]]></literal>
    <justification jstring="[para(11224(a,1),10198(a,1,1))].">
      <j1 rule="para" parents="11224 10198"/>
    </justification>
  </clause>

  <clause id="11226">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = T(a(K(x,z),y,y \ x),x)
    ]]></literal>
    <justification jstring="[para(11225(a,1),11040(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11225 11040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11227">
    <literal><![CDATA[
      K(x \ 1,T(y * x,z)) = K(x \ 1,T(y,z) * x)
    ]]></literal>
    <justification jstring="[para(2710(a,1),11209(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2710 11209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11228">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = a(K(x,z),y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,9138,a(flip),b,11226,a),flip(a)].">
      <j1 rule="hyper" parents="320 9138 11226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11229">
    <literal><![CDATA[
      a(K(x,y),z,z \ x) = a(x / z,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4894,a(flip),b,11228,a),flip(a)].">
      <j1 rule="hyper" parents="58 4894 11228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11230">
    <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),11229(a,2,1))].">
      <j1 rule="para" parents="6 11229"/>
    </justification>
  </clause>

  <clause id="11231">
    <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),11230(a,1,3))].">
      <j1 rule="para" parents="17 11230"/>
    </justification>
  </clause>

  <clause id="11232">
    <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(11231(a,1),4815(a,1,2))].">
      <j1 rule="para" parents="11231 4815"/>
    </justification>
  </clause>

  <clause id="11233">
    <literal><![CDATA[
      (K(x * y,z) * y) * T(x,y) = x * (y * K(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5911,a(flip),b,11232,a),flip(a)].">
      <j1 rule="hyper" parents="58 5911 11232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11234">
    <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(11233(a,2),38(a,1))].">
      <j1 rule="para" parents="11233 38"/>
    </justification>
  </clause>

  <clause id="11235">
    <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(320,a,22,a,b,11199,a),flip(a)].">
      <j1 rule="hyper" parents="320 22 11199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11236">
    <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(11101(a,1),11235(a,1,1))].">
      <j1 rule="para" parents="11101 11235"/>
    </justification>
  </clause>

  <clause id="11237">
    <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),11236(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 11236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11238">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(600,a,11237,a),flip(a)].">
      <j1 rule="hyper" parents="600 11237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11240">
    <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(11237(a,1),5189(a,1,2,1))].">
      <j1 rule="para" parents="11237 5189"/>
    </justification>
  </clause>

  <clause id="11241">
    <literal><![CDATA[
      R((x \ y) \ y,z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,824,a(flip),b,11238,a)].">
      <j1 rule="hyper" parents="58 824 11238"/>
    </justification>
  </clause>

  <clause id="11242">
    <literal><![CDATA[
      (R(x,y,z) \ (x * u)) \ (x * u) = R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11238(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 11238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11243">
    <literal><![CDATA[
      (R(x / y,z,u) \ x) \ x = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(642(a,1),11238(a,1,1)),flip(a)].">
      <j1 rule="para" parents="642 11238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11247">
    <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(5486(a,1),11241(a,2,1))].">
      <j1 rule="para" parents="5486 11241"/>
    </justification>
  </clause>

  <clause id="11249">
    <literal><![CDATA[
      K(x,R(x / y,z,u) \ w) = K(x,R(y \ x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(11243(a,1),6815(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11243 6815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11250">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = (x * u) \ (x * (R(x,y,z) * u))
    ]]></literal>
    <justification jstring="[para(1307(a,1),11242(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1307 11242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11251">
    <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(320,a,232,a(flip),b,11250,a),flip(a)].">
      <j1 rule="hyper" parents="320 232 11250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11252">
    <literal><![CDATA[
      T(x,R(x,y,z) * u) = T(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(964,a,11251,a),flip(a)].">
      <j1 rule="hyper" parents="964 11251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11253">
    <literal><![CDATA[
      T(x,x * (R(x,y,z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),11252(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 11252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11255">
    <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(11252(a,1),4766(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11252 4766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11256">
    <literal><![CDATA[
      T(x,x * ((x \ y) * z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(505(a,1),11253(a,1,2,2))].">
      <j1 rule="para" parents="505 11253"/>
    </justification>
  </clause>

  <clause id="11257">
    <literal><![CDATA[
      T(x,y * K(x \ y,z)) = T(x,x * T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(4714(a,2),11256(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4714 11256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11258">
    <literal><![CDATA[
      K(R(x,y,z) * u,R(x,w,v5)) = K(x * u,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,4766,a(flip),b,11255,a),flip(a)].">
      <j1 rule="hyper" parents="320 4766 11255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11259">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(7394,a,11258,a)].">
      <j1 rule="hyper" parents="7394 11258"/>
    </justification>
  </clause>

  <clause id="11260">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,z,u)) = K(x * y,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,9837,a,b,11259,a),flip(a)].">
      <j1 rule="hyper" parents="320 9837 11259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11261">
    <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(11260(a,1),10494(a,1,1,2))].">
      <j1 rule="para" parents="11260 10494"/>
    </justification>
  </clause>

  <clause id="11262">
    <literal><![CDATA[
      K((L(x,y,x) * y) \ z,y * x) * (z * u) = (((y * x) \ z) * (y * x)) * u
    ]]></literal>
    <justification jstring="[para(4278(a,1),11184(a,1,1,1,1))].">
      <j1 rule="para" parents="4278 11184"/>
    </justification>
  </clause>

  <clause id="11263">
    <literal><![CDATA[
      K(R(x,y,z) \ u,R(x,y,z)) = K(x \ u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(5910,a,11240,a),flip(a)].">
      <j1 rule="hyper" parents="5910 11240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11265">
    <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(11263(a,1),4680(a,1,1,2))].">
      <j1 rule="para" parents="11263 4680"/>
    </justification>
  </clause>

  <clause id="11266">
    <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(5479(a,1),11261(a,1,1))].">
      <j1 rule="para" parents="5479 11261"/>
    </justification>
  </clause>

  <clause id="11267">
    <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(5228(a,1),11266(a,1,1,1,2))].">
      <j1 rule="para" parents="5228 11266"/>
    </justification>
  </clause>

  <clause id="11268">
    <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,11267,a)].">
      <j1 rule="hyper" parents="58 22 11267"/>
    </justification>
  </clause>

  <clause id="11269">
    <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(5166(a,1),11268(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5166 11268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11270">
    <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,10492,a(flip),b,11269,a)].">
      <j1 rule="hyper" parents="58 10492 11269"/>
    </justification>
  </clause>

  <clause id="11271">
    <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(11269(a,1),10514(a,1,2))].">
      <j1 rule="para" parents="11269 10514"/>
    </justification>
  </clause>

  <clause id="11272">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(144,a,11270,a)].">
      <j1 rule="hyper" parents="144 11270"/>
    </justification>
  </clause>

  <clause id="11273">
    <literal><![CDATA[
      (R(x,y,R(x,z,u)) * z) * u = R(R(x,y,x),z,u) * (z * u)
    ]]></literal>
    <justification jstring="[para(11270(a,1),514(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11270 514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11275">
    <literal><![CDATA[
      K(x,R(y,z,R(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11272(a,2),7051(a,1,2))].">
      <j1 rule="para" parents="11272 7051"/>
    </justification>
  </clause>

  <clause id="11276">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,R(z,u,R(T(z,y),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(8040,a,11275,a),flip(a)].">
      <j1 rule="hyper" parents="8040 11275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11277">
    <literal><![CDATA[
      K(x,R(y,z,R(T(y,u),w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8029,a,11276,a),flip(a)].">
      <j1 rule="hyper" parents="8029 11276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11279">
    <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(11277(a,1),10230(a,1,1))].">
      <j1 rule="para" parents="11277 10230"/>
    </justification>
  </clause>

  <clause id="11280">
    <literal><![CDATA[
      (R(x,y,R(x,z,u)) * z) * u = (R(x,y,x) * z) * u
    ]]></literal>
    <justification jstring="[hyper(320,a,101,a(flip),b,11273,a),flip(a)].">
      <j1 rule="hyper" parents="320 101 11273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11281">
    <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(10195(a,1),11280(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10195 11280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11282">
    <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(5142,a,11279,a)].">
      <j1 rule="hyper" parents="5142 11279"/>
    </justification>
  </clause>

  <clause id="11283">
    <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(10195(a,1),11279(a,1,2,2))].">
      <j1 rule="para" parents="10195 11279"/>
    </justification>
  </clause>

  <clause id="11284">
    <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(9942,a,11282,a)].">
      <j1 rule="hyper" parents="9942 11282"/>
    </justification>
  </clause>

  <clause id="11285">
    <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(11282(a,1),9942(a,1))].">
      <j1 rule="para" parents="11282 9942"/>
    </justification>
  </clause>

  <clause id="11286">
    <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(9946(a,1),11283(a,1,2))].">
      <j1 rule="para" parents="9946 11283"/>
    </justification>
  </clause>

  <clause id="11287">
    <literal><![CDATA[
      x \ R(x,y,R(T(x,z),u,w)) = a(x,y,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(5111,a,11286,a),flip(a)].">
      <j1 rule="hyper" parents="5111 11286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11288">
    <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(11286(a,1),5110(a,1)),flip(b)].">
      <j1 rule="para" parents="11286 5110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11289">
    <literal><![CDATA[
      a(T(x,y),z,R(T(x,y),u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(11285,a,11287,a)].">
      <j1 rule="hyper" parents="11285 11287"/>
    </justification>
  </clause>

  <clause id="11292">
    <literal><![CDATA[
      a(R(x,y,z),u,x) \ 1 = a(x,u,R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(11289(a,1),10657(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11289 10657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11293">
    <literal><![CDATA[
      a(R(x,y,z),u,x) = a(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(43,a,11292,a)].">
      <j1 rule="hyper" parents="43 11292"/>
    </justification>
  </clause>

  <clause id="11295">
    <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(320,a,6817,a,b,11293,a)].">
      <j1 rule="hyper" parents="320 6817 11293"/>
    </justification>
  </clause>

  <clause id="11297">
    <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(11284(a,2),11288(a,1))].">
      <j1 rule="para" parents="11284 11288"/>
    </justification>
  </clause>

  <clause id="11298">
    <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(320,a,7133,a(flip),b,11060,a),flip(a)].">
      <j1 rule="hyper" parents="320 7133 11060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11299">
    <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(320,a,6054,a(flip),b,11247,a),flip(a)].">
      <j1 rule="hyper" parents="320 6054 11247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11300">
    <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(6052(a,1),11299(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6052 11299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11301">
    <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(11300(a,1),9099(a,1,2))].">
      <j1 rule="para" parents="11300 9099"/>
    </justification>
  </clause>

  <clause id="11302">
    <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(5479(a,1),11265(a,1,1))].">
      <j1 rule="para" parents="5479 11265"/>
    </justification>
  </clause>

  <clause id="11303">
    <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,11302,a)].">
      <j1 rule="hyper" parents="58 22 11302"/>
    </justification>
  </clause>

  <clause id="11304">
    <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(4680(a,1),11303(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4680 11303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11305">
    <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(320,a,24,a(flip),b,11304,a),flip(a)].">
      <j1 rule="hyper" parents="320 24 11304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11306">
    <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(11305(a,1),1346(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11305 1346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11307">
    <literal><![CDATA[
      K(T(x,y * z),u / ((y * T(x,y * z)) * z)) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7719,a(flip),b,11298,a),flip(a)].">
      <j1 rule="hyper" parents="320 7719 11298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11308">
    <literal><![CDATA[
      K(x,T(y / ((z * T(x,z * u)) * u),z * u)) = K(x,(z * u) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(7679,a,11307,a)].">
      <j1 rule="hyper" parents="7679 11307"/>
    </justification>
  </clause>

  <clause id="11309">
    <literal><![CDATA[
      K(x,T(y / ((z * x) * u),z * u)) = K(x,(z * u) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,10672,a(flip),b,11308,a)].">
      <j1 rule="hyper" parents="58 10672 11308"/>
    </justification>
  </clause>

  <clause id="11311">
    <literal><![CDATA[
      K(x,((y * x) * z) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9180,a(flip),b,11309,a)].">
      <j1 rule="hyper" parents="58 9180 11309"/>
    </justification>
  </clause>

  <clause id="11312">
    <literal><![CDATA[
      K(x,((x \ y) * z) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(11183,a,11311,a),flip(a)].">
      <j1 rule="hyper" parents="11183 11311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11313">
    <literal><![CDATA[
      K(x,((y * x) * (y \ 1)) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(163(a,1),11311(a,2,2))].">
      <j1 rule="para" parents="163 11311"/>
    </justification>
  </clause>

  <clause id="11314">
    <literal><![CDATA[
      K(x,a(x,y,y \ 1) \ z) = K(x,x \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9667,a(flip),b,11313,a)].">
      <j1 rule="hyper" parents="58 9667 11313"/>
    </justification>
  </clause>

  <clause id="11316">
    <literal><![CDATA[
      K(x,a(x,y,y \ 1) \ z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11314(a,2,2))].">
      <j1 rule="para" parents="4 11314"/>
    </justification>
  </clause>

  <clause id="11317">
    <literal><![CDATA[
      K(x,y \ R(x,z,z \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9295,a(flip),b,11316,a),flip(a)].">
      <j1 rule="hyper" parents="58 9295 11316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11318">
    <literal><![CDATA[
      K(x,y \ ((z * x) * (z \ 1))) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(8564,a,11317,a)].">
      <j1 rule="hyper" parents="8564 11317"/>
    </justification>
  </clause>

  <clause id="11320">
    <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,9473,a(flip),b,11318,a)].">
      <j1 rule="hyper" parents="58 9473 11318"/>
    </justification>
  </clause>

  <clause id="11321">
    <literal><![CDATA[
      K(x,((x \ y) * z) \ 1) = K(x,(y * z) \ x)
    ]]></literal>
    <justification jstring="[para(61(a,1),11312(a,1,2,2))].">
      <j1 rule="para" parents="61 11312"/>
    </justification>
  </clause>

  <clause id="11322">
    <literal><![CDATA[
      (x / (1 / y)) * (1 / T(y,y \ (x / (1 / y)))) = (T(x,y) / (1 / y)) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(568,a,11180,a)].">
      <j1 rule="hyper" parents="568 11180"/>
    </justification>
  </clause>

  <clause id="11324">
    <literal><![CDATA[
      (x / (1 / y)) * (1 / T(y,(x / (1 / y)) / y)) = (T(x,y) / (1 / y)) * (1 / y)
    ]]></literal>
    <justification jstring="[para(4213(a,2),11322(a,1,2,2))].">
      <j1 rule="para" parents="4213 11322"/>
    </justification>
  </clause>

  <clause id="11325">
    <literal><![CDATA[
      (T(x,y) / (1 / y)) * (1 / y) = (x / (1 / y)) * (1 / T(y,x))
    ]]></literal>
    <justification jstring="[para(6196(a,1),11324(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6196 11324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11326">
    <literal><![CDATA[
      T(x,y) / (1 / T(y,x)) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(414,a,11325,a)].">
      <j1 rule="hyper" parents="414 11325"/>
    </justification>
  </clause>

  <clause id="11327">
    <literal><![CDATA[
      T(x,y / x) / (1 / (x \ y)) = x / (1 / (y / x))
    ]]></literal>
    <justification jstring="[para(107(a,1),11326(a,1,2,2))].">
      <j1 rule="para" parents="107 11326"/>
    </justification>
  </clause>

  <clause id="11328">
    <literal><![CDATA[
      (x / (1 / (x \ y))) / x = x \ (x / (1 / (y / x)))
    ]]></literal>
    <justification jstring="[para(11327(a,1),4254(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11327 4254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11329">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) = x \ (x / ((y / x) \ 1))
    ]]></literal>
    <justification jstring="[para(11328(a,2),2630(a,1,1))].">
      <j1 rule="para" parents="11328 2630"/>
    </justification>
  </clause>

  <clause id="11330">
    <literal><![CDATA[
      x * ((x / ((x \ y) \ 1)) / x) = x / ((y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(10683,a,11329,a)].">
      <j1 rule="hyper" parents="10683 11329"/>
    </justification>
  </clause>

  <clause id="11331">
    <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,10691,a(flip),b,11019,a)].">
      <j1 rule="hyper" parents="58 10691 11019"/>
    </justification>
  </clause>

  <clause id="11332">
    <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(8579(a,1),11331(a,1,2,2))].">
      <j1 rule="para" parents="8579 11331"/>
    </justification>
  </clause>

  <clause id="11333">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ K(u,x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7554,a(flip),b,11332,a),flip(a)].">
      <j1 rule="hyper" parents="58 7554 11332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11335">
    <literal><![CDATA[
      K(x,y * (z \ K(u,x))) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,5538,a(flip),b,11333,a)].">
      <j1 rule="hyper" parents="58 5538 11333"/>
    </justification>
  </clause>

  <clause id="11336">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,K(z,u)) = K(z,K(u,x * (y \ K(w,u))))
    ]]></literal>
    <justification jstring="[para(11335(a,2),8158(a,2,2))].">
      <j1 rule="para" parents="11335 8158"/>
    </justification>
  </clause>

  <clause id="11337">
    <literal><![CDATA[
      K(x,K(y,z * (u \ K(w,y)))) = K(x,K(y,z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(8171,a,11336,a),flip(a)].">
      <j1 rule="hyper" parents="8171 11336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11338">
    <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(7224(a,1),11337(a,1,2))].">
      <j1 rule="para" parents="7224 11337"/>
    </justification>
  </clause>

  <clause id="11339">
    <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(261(a,1),11338(a,2,2,2))].">
      <j1 rule="para" parents="261 11338"/>
    </justification>
  </clause>

  <clause id="11340">
    <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,9043,a,b,11339,a)].">
      <j1 rule="hyper" parents="58 9043 11339"/>
    </justification>
  </clause>

  <clause id="11341">
    <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(320,a,7754,a,b,11340,a),flip(a)].">
      <j1 rule="hyper" parents="320 7754 11340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11342">
    <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(4472(a,1),11028(a,1,1))].">
      <j1 rule="para" parents="4472 11028"/>
    </justification>
  </clause>

  <clause id="11343">
    <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(2395(a,1),11037(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2395 11037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11344">
    <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(6311(a,1),11343(a,2,1))].">
      <j1 rule="para" parents="6311 11343"/>
    </justification>
  </clause>

  <clause id="11345">
    <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(320,a,8806,a,b,11344,a),flip(a)].">
      <j1 rule="hyper" parents="320 8806 11344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11346">
    <literal><![CDATA[
      (K(x,y) \ z) * (K(x,y) * K(u,x)) = T(z * K(u,x),K(x,y))
    ]]></literal>
    <justification jstring="[para(2398(a,1),11345(a,1,1,1))].">
      <j1 rule="para" parents="2398 11345"/>
    </justification>
  </clause>

  <clause id="11347">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * K(u,y)) = T(z * K(u,y),K(y,x))
    ]]></literal>
    <justification jstring="[para(5092(a,1),11346(a,1,1))].">
      <j1 rule="para" parents="5092 11346"/>
    </justification>
  </clause>

  <clause id="11348">
    <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,10003,a(flip),b,11347,a),flip(a)].">
      <j1 rule="hyper" parents="58 10003 11347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11349">
    <literal><![CDATA[
      x * K(K(y,z) * K(z,u),x) = T(T(x,K(z,u)),K(z,y))
    ]]></literal>
    <justification jstring="[para(7814(a,1),11348(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7814 11348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11350">
    <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,9985,a(flip),b,11038,a),flip(a)].">
      <j1 rule="hyper" parents="58 9985 11038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11351">
    <literal><![CDATA[
      K(x,y * K(((z \ 1) \ 1) \ K(u,x),(z \ 1) \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7217,a(flip),b,11041,a),flip(a)].">
      <j1 rule="hyper" parents="320 7217 11041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11353">
    <literal><![CDATA[
      K(x,y * K(z \ K(u,x),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3112(a,1),11351(a,1,2,2))].">
      <j1 rule="para" parents="3112 11351"/>
    </justification>
  </clause>

  <clause id="11355">
    <literal><![CDATA[
      K(x,y * (K(z,x) / u)) = K(x,y * (u \ K(z,x)))
    ]]></literal>
    <justification jstring="[para(6446(a,1),11353(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6446 11353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11356">
    <literal><![CDATA[
      K(x,y * (K(z,x) / u)) = K(x,y * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,11335,a(flip),b,11355,a),flip(a)].">
      <j1 rule="hyper" parents="320 11335 11355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11358">
    <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),11042(a,2,2,1,2))].">
      <j1 rule="para" parents="72 11042"/>
    </justification>
  </clause>

  <clause id="11360">
    <literal><![CDATA[
      K(x,((1 / (K(y,x \ z) / y)) * z) \ (u * x)) = K(x,(((z \ x) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(6078(a,1),11358(a,1,2,1,1,2,1))].">
      <j1 rule="para" parents="6078 11358"/>
    </justification>
  </clause>

  <clause id="11361">
    <literal><![CDATA[
      K(x,(((y \ x) \ 1) * z) \ u) = K(x,((x \ y) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9781,a(flip),b,11360,a),flip(a)].">
      <j1 rule="hyper" parents="58 9781 11360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11362">
    <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(4391(a,1),11301(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4391 11301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11363">
    <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(7872(a,1),11342(a,1,1,2))].">
      <j1 rule="para" parents="7872 11342"/>
    </justification>
  </clause>

  <clause id="11364">
    <literal><![CDATA[
      R(K(x,L(y,z,L(y,u,w))),L(y,u,w),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8731,a,11363,a),flip(a)].">
      <j1 rule="hyper" parents="8731 11363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11365">
    <literal><![CDATA[
      R(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8768(a,1),11364(a,1,1))].">
      <j1 rule="para" parents="8768 11364"/>
    </justification>
  </clause>

  <clause id="11366">
    <literal><![CDATA[
      K((L(x,y,z) * u) / w,x) = K(L(x,y,z) / (w / u),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6737,a(flip),b,11365,a)].">
      <j1 rule="hyper" parents="58 6737 11365"/>
    </justification>
  </clause>

  <clause id="11368">
    <literal><![CDATA[
      K((L(x,y,z) * u) / w,x) = K((w / u) \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(320,a,6260,a(flip),b,11366,a),flip(a)].">
      <j1 rule="hyper" parents="320 6260 11366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11369">
    <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,10647,a,b,11368,a)].">
      <j1 rule="hyper" parents="58 10647 11368"/>
    </justification>
  </clause>

  <clause id="11370">
    <literal><![CDATA[
      K(x / (L(y,z,u) \ w),y) = K((w / x) \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(8235,a,11369,a)].">
      <j1 rule="hyper" parents="8235 11369"/>
    </justification>
  </clause>

  <clause id="11371">
    <literal><![CDATA[
      K(x / (L(y,z,u) \ w),y) = K((w / x) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,10747,a(flip),b,11370,a),flip(a)].">
      <j1 rule="hyper" parents="320 10747 11370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11373">
    <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(7133(a,1),11350(a,2,2,1))].">
      <j1 rule="para" parents="7133 11350"/>
    </justification>
  </clause>

  <clause id="11374">
    <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),11373(a,2,2))].">
      <j1 rule="para" parents="3 11373"/>
    </justification>
  </clause>

  <clause id="11375">
    <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(4290(a,1),4300(a,2,2,1,1))].">
      <j1 rule="para" parents="4290 4300"/>
    </justification>
  </clause>

  <clause id="11376">
    <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,11375,a)].">
      <j1 rule="hyper" parents="123 11375"/>
    </justification>
  </clause>

  <clause id="11377">
    <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(4844(a,1),4969(a,1,1,1,1))].">
      <j1 rule="para" parents="4844 4969"/>
    </justification>
  </clause>

  <clause id="11378">
    <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(6823(a,1),11377(a,1,1))].">
      <j1 rule="para" parents="6823 11377"/>
    </justification>
  </clause>

  <clause id="11379">
    <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(320,a,5351,a(flip),b,11378,a),flip(a)].">
      <j1 rule="hyper" parents="320 5351 11378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11380">
    <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),11379(a,1,1,2))].">
      <j1 rule="para" parents="25 11379"/>
    </justification>
  </clause>

  <clause id="11381">
    <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,7920,a(flip),b,11380,a)].">
      <j1 rule="hyper" parents="58 7920 11380"/>
    </justification>
  </clause>

  <clause id="11382">
    <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,8220,a(flip),b,11381,a)].">
      <j1 rule="hyper" parents="58 8220 11381"/>
    </justification>
  </clause>

  <clause id="11383">
    <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(11382(a,1),5075(a,1,2,2))].">
      <j1 rule="para" parents="11382 5075"/>
    </justification>
  </clause>

  <clause id="11384">
    <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(7237(a,1),11383(a,1,1))].">
      <j1 rule="para" parents="7237 11383"/>
    </justification>
  </clause>

  <clause id="11385">
    <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(4738(a,1),6888(a,2,2))].">
      <j1 rule="para" parents="4738 6888"/>
    </justification>
  </clause>

  <clause id="11386">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),x \ y,T(x,x \ y)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,6173,a(flip),b,11385,a),flip(a)].">
      <j1 rule="hyper" parents="320 6173 11385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11388">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),y / x,x) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4530,a(flip),b,11386,a)].">
      <j1 rule="hyper" parents="58 4530 11386"/>
    </justification>
  </clause>

  <clause id="11389">
    <literal><![CDATA[
      K((x \ 1) \ (x \ y),L(z,y / x,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(10806,a,11388,a)].">
      <j1 rule="hyper" parents="10806 11388"/>
    </justification>
  </clause>

  <clause id="11390">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ L(z,x / y,y))) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10896,a(flip),b,11389,a)].">
      <j1 rule="hyper" parents="58 10896 11389"/>
    </justification>
  </clause>

  <clause id="11391">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),x / y,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1684(a,2),11390(a,1,2))].">
      <j1 rule="para" parents="1684 11390"/>
    </justification>
  </clause>

  <clause id="11392">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),y \ x,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11186,a(flip),b,11391,a)].">
      <j1 rule="hyper" parents="58 11186 11391"/>
    </justification>
  </clause>

  <clause id="11393">
    <literal><![CDATA[
      K(R(x \ y,z,u),w \ (y / x)) = K(R(x \ y,z,u),w \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(5488,a,8672,a),flip(a)].">
      <j1 rule="hyper" parents="5488 8672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11394">
    <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(4888(a,1),11393(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4888 11393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11395">
    <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(1755(a,2),8946(a,1,2,2))].">
      <j1 rule="para" parents="1755 8946"/>
    </justification>
  </clause>

  <clause id="11396">
    <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(3532(a,1),9763(a,1,1))].">
      <j1 rule="para" parents="3532 9763"/>
    </justification>
  </clause>

  <clause id="11397">
    <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),9807(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6 9807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11399">
    <literal><![CDATA[
      (K(x,y) * K(z,y)) * u = K(z,y) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(9993(a,1),11397(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9993 11397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11401">
    <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(11399(a,1),5663(a,1,2,2))].">
      <j1 rule="para" parents="11399 5663"/>
    </justification>
  </clause>

  <clause id="11402">
    <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(5123(a,1),11401(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5123 11401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11403">
    <literal><![CDATA[
      L(x,T(y,z) \ ((u * y) / u),T(y,z)) = K(y,u) * (K(u,y) * x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5065,a(flip),b,11402,a),flip(a)].">
      <j1 rule="hyper" parents="320 5065 11402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11405">
    <literal><![CDATA[
      L(x,T(y,z) \ ((u * y) / u),T(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,5095,a(flip),b,11403,a),flip(a)].">
      <j1 rule="hyper" parents="320 5095 11403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11407">
    <literal><![CDATA[
      L(x,K(y,z) * K(u,z),T(z,u)) = x
    ]]></literal>
    <justification jstring="[para(5662(a,1),11405(a,1,2))].">
      <j1 rule="para" parents="5662 11405"/>
    </justification>
  </clause>

  <clause id="11408">
    <literal><![CDATA[
      L(x,K(y,z) * K(u,z),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(11407(a,1),45(a,2))].">
      <j1 rule="para" parents="11407 45"/>
    </justification>
  </clause>

  <clause id="11409">
    <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(8926(a,1),10406(a,1,1,1))].">
      <j1 rule="para" parents="8926 10406"/>
    </justification>
  </clause>

  <clause id="11410">
    <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(514(a,1),11409(a,1,1))].">
      <j1 rule="para" parents="514 11409"/>
    </justification>
  </clause>

  <clause id="11411">
    <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(11272(a,1),11410(a,1,1,1,1))].">
      <j1 rule="para" parents="11272 11410"/>
    </justification>
  </clause>

  <clause id="11412">
    <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(11411(a,1),9533(a,1))].">
      <j1 rule="para" parents="11411 9533"/>
    </justification>
  </clause>

  <clause id="11414">
    <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(320,a,1346,a(flip),b,11306,a),flip(a)].">
      <j1 rule="hyper" parents="320 1346 11306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11415">
    <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),11414(a,2,3))].">
      <j1 rule="para" parents="22 11414"/>
    </justification>
  </clause>

  <clause id="11416">
    <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),11395(a,1,2)),flip(a)].">
      <j1 rule="para" parents="90 11395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11417">
    <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(10633(a,1),11396(a,1,1))].">
      <j1 rule="para" parents="10633 11396"/>
    </justification>
  </clause>

  <clause id="11418">
    <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(5389(a,1),11417(a,1,2))].">
      <j1 rule="para" parents="5389 11417"/>
    </justification>
  </clause>

  <clause id="11419">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a((y / x) \ 1,z,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[para(8223(a,1),11418(a,1,2))].">
      <j1 rule="para" parents="8223 11418"/>
    </justification>
  </clause>

  <clause id="11420">
    <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(1185(a,1),5813(a,2,1))].">
      <j1 rule="para" parents="1185 5813"/>
    </justification>
  </clause>

  <clause id="11421">
    <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,11420,a(flip),b,5814,a),flip(a)].">
      <j1 rule="hyper" parents="58 11420 5814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11422">
    <literal><![CDATA[
      T(x \ L(x,y,z),u * x) = T(x \ L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[para(1185(a,1),11421(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1185 11421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11423">
    <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(3606(a,2),5996(a,1,1))].">
      <j1 rule="para" parents="3606 5996"/>
    </justification>
  </clause>

  <clause id="11424">
    <literal><![CDATA[
      x \ ((x / ((y * z) / y)) * ((z \ 1) * ((y * z) / y))) = T(x \ (x / z),(y * z) / y)
    ]]></literal>
    <justification jstring="[para(4717(a,1),6370(a,1,2,2,1))].">
      <j1 rule="para" parents="4717 6370"/>
    </justification>
  </clause>

  <clause id="11426">
    <literal><![CDATA[
      x \ ((x / ((y * z) / y)) * ((T(z,y) \ 1) * z)) = T(x \ (x / z),(y * z) / y)
    ]]></literal>
    <justification jstring="[para(5621(a,1),11424(a,1,2,2))].">
      <j1 rule="para" parents="5621 11424"/>
    </justification>
  </clause>

  <clause id="11427">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * ((T(y,x) \ 1) * y) = T(1 \ (1 / y),(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(165,a,11426,a)].">
      <j1 rule="hyper" parents="165 11426"/>
    </justification>
  </clause>

  <clause id="11428">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * ((T(y,x) \ 1) * y) = T(1 / y,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(60(a,1),11427(a,2,1))].">
      <j1 rule="para" parents="60 11427"/>
    </justification>
  </clause>

  <clause id="11429">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ (y \ 1) = (T(y,x) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(116,a,5168,a(flip),b,11428,a)].">
      <j1 rule="hyper" parents="116 5168 11428"/>
    </justification>
  </clause>

  <clause id="11430">
    <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,8853,a(flip),b,6989,a),flip(a)].">
      <j1 rule="hyper" parents="58 8853 6989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11432">
    <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(6097(a,1),7541(a,2,1))].">
      <j1 rule="para" parents="6097 7541"/>
    </justification>
  </clause>

  <clause id="11433">
    <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),11432(a,2,1,2))].">
      <j1 rule="para" parents="75 11432"/>
    </justification>
  </clause>

  <clause id="11435">
    <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(320,a,7495,a,b,11433,a),flip(a)].">
      <j1 rule="hyper" parents="320 7495 11433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11436">
    <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(320,a,7593,a(flip),b,11435,a),flip(a)].">
      <j1 rule="hyper" parents="320 7593 11435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11437">
    <literal><![CDATA[
      x / (T(y,z) \ R(x,y \ 1,y)) = T((x * (1 / y)) \ x,z)
    ]]></literal>
    <justification jstring="[para(11436(a,1),7632(a,1,2))].">
      <j1 rule="para" parents="11436 7632"/>
    </justification>
  </clause>

  <clause id="11438">
    <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(11016(a,1),11015(a,1,2,1,1))].">
      <j1 rule="para" parents="11016 11015"/>
    </justification>
  </clause>

  <clause id="11439">
    <literal><![CDATA[
      K(x,T(x * ((y \ z) \ z),u)) = K(x,T(x * T(y,z),u))
    ]]></literal>
    <justification jstring="[hyper(58,a,10733,a(flip),b,11438,a),flip(a)].">
      <j1 rule="hyper" parents="58 10733 11438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11440">
    <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(4499(a,1),4336(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4499 4336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11441">
    <literal><![CDATA[
      T(x / T(y,x),z) * T(y,y * T(y \ x,z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(10526,a,11440,a),flip(a)].">
      <j1 rule="hyper" parents="10526 11440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11442">
    <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(5434(a,1),5231(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5434 5231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11443">
    <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(4929(a,1),11442(a,2,1,2))].">
      <j1 rule="para" parents="4929 11442"/>
    </justification>
  </clause>

  <clause id="11445">
    <literal><![CDATA[
      (x * K(y,x)) * (T(x,z) * (x \ K(x,y))) = T(x,z)
    ]]></literal>
    <justification jstring="[para(6300(a,1),11443(a,2,1))].">
      <j1 rule="para" parents="6300 11443"/>
    </justification>
  </clause>

  <clause id="11446">
    <literal><![CDATA[
      T(x,y) / (T(x,y) * (x \ K(x,z))) = x * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,11445,a)].">
      <j1 rule="hyper" parents="131 11445"/>
    </justification>
  </clause>

  <clause id="11447">
    <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(11446(a,1),3066(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11446 3066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11448">
    <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(5793(a,1),11447(a,2,1))].">
      <j1 rule="para" parents="5793 11447"/>
    </justification>
  </clause>

  <clause id="11449">
    <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(5576(a,1),11448(a,1,2,2))].">
      <j1 rule="para" parents="5576 11448"/>
    </justification>
  </clause>

  <clause id="11450">
    <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(8003(a,1),11449(a,1,2))].">
      <j1 rule="para" parents="8003 11449"/>
    </justification>
  </clause>

  <clause id="11451">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ T(x,z) = T(x,z) * T(x \ K(x,y),x)
    ]]></literal>
    <justification jstring="[para(8107(a,1),11450(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8107 11450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11452">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ T(x,z) = (x \ K(x,y)) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,8317,a(flip),b,11451,a),flip(a)].">
      <j1 rule="hyper" parents="320 8317 11451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11454">
    <literal><![CDATA[
      K((T(x,y) \ ((x \ 1) \ K(z,x))) \ 1,((x \ K(x,z)) * T(x,y)) \ 1) = K(((x \ 1) \ K(z,x)) \ T(x,y),T(x,y) \ ((x \ 1) \ K(z,x)))
    ]]></literal>
    <justification jstring="[para(11452(a,1),6094(a,1,2,1))].">
      <j1 rule="para" parents="11452 6094"/>
    </justification>
  </clause>

  <clause id="11455">
    <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(11452(a,2),10667(a,1,2,1))].">
      <j1 rule="para" parents="11452 10667"/>
    </justification>
  </clause>

  <clause id="11456">
    <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(198(a,1),8341(a,1,1,1))].">
      <j1 rule="para" parents="198 8341"/>
    </justification>
  </clause>

  <clause id="11457">
    <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(198(a,1),11456(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="198 11456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11458">
    <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(198(a,1),11457(a,2,2,3,1))].">
      <j1 rule="para" parents="198 11457"/>
    </justification>
  </clause>

  <clause id="11459">
    <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(232(a,1),8487(a,1,1)),flip(a)].">
      <j1 rule="para" parents="232 8487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11460">
    <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(9976(a,1),11459(a,2,1))].">
      <j1 rule="para" parents="9976 11459"/>
    </justification>
  </clause>

  <clause id="11461">
    <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(320,a,7807,a,b,11460,a),flip(a)].">
      <j1 rule="hyper" parents="320 7807 11460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11463">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(u,y) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8898,a,11461,a)].">
      <j1 rule="hyper" parents="8898 11461"/>
    </justification>
  </clause>

  <clause id="11464">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,u)) = T(x,K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(7824,a,11463,a)].">
      <j1 rule="hyper" parents="7824 11463"/>
    </justification>
  </clause>

  <clause id="11466">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(1991(a,2),11463(a,2,2))].">
      <j1 rule="para" parents="1991 11463"/>
    </justification>
  </clause>

  <clause id="11467">
    <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(11463(a,1),9681(a,1,1))].">
      <j1 rule="para" parents="11463 9681"/>
    </justification>
  </clause>

  <clause id="11468">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,u)) = T(x,K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[para(1991(a,2),11464(a,2,2))].">
      <j1 rule="para" parents="1991 11464"/>
    </justification>
  </clause>

  <clause id="11469">
    <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(11464(a,1),7823(a,1))].">
      <j1 rule="para" parents="11464 7823"/>
    </justification>
  </clause>

  <clause id="11470">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(435,a,11466,a)].">
      <j1 rule="hyper" parents="435 11466"/>
    </justification>
  </clause>

  <clause id="11471">
    <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,11349,a,b,11466,a)].">
      <j1 rule="hyper" parents="58 11349 11466"/>
    </justification>
  </clause>

  <clause id="11472">
    <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,9048,a,b,11466,a)].">
      <j1 rule="hyper" parents="58 9048 11466"/>
    </justification>
  </clause>

  <clause id="11473">
    <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(9202(a,1),11468(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9202 11468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11474">
    <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(11468(a,1),10027(a,2,1))].">
      <j1 rule="para" parents="11468 10027"/>
    </justification>
  </clause>

  <clause id="11475">
    <literal><![CDATA[
      T(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,11466,a(flip),b,11470,a)].">
      <j1 rule="hyper" parents="58 11466 11470"/>
    </justification>
  </clause>

  <clause id="11476">
    <literal><![CDATA[
      x * K(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(4817,a,11475,a)].">
      <j1 rule="hyper" parents="4817 11475"/>
    </justification>
  </clause>

  <clause id="11477">
    <literal><![CDATA[
      x * K(K(y,z) * K(u,y),x) = T(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(1991(a,2),11471(a,1,2,1))].">
      <j1 rule="para" parents="1991 11471"/>
    </justification>
  </clause>

  <clause id="11478">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),u) = K(u,K(y,x) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(29,a,11471,a,b,11476,a)].">
      <j1 rule="hyper" parents="29 11471 11476"/>
    </justification>
  </clause>

  <clause id="11479">
    <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(11476(a,1),4725(a,1))].">
      <j1 rule="para" parents="11476 4725"/>
    </justification>
  </clause>

  <clause id="11480">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(x,z) * K(y,x))
    ]]></literal>
    <justification jstring="[para(1991(a,2),11478(a,1,1))].">
      <j1 rule="para" parents="1991 11478"/>
    </justification>
  </clause>

  <clause id="11481">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(y,x) * K(x,z))
    ]]></literal>
    <justification jstring="[para(1991(a,1),11480(a,2,2))].">
      <j1 rule="para" parents="1991 11480"/>
    </justification>
  </clause>

  <clause id="11482">
    <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,11481,a,b,4754,a(flip))].">
      <j1 rule="hyper" parents="117 11481 4754"/>
    </justification>
  </clause>

  <clause id="11483">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(x,y) * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(29,a,4714,a(flip),b,11477,a),flip(a)].">
      <j1 rule="hyper" parents="29 4714 11477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11484">
    <literal><![CDATA[
      K(x,K(y,z) * K(u,y)) = K(x,K(z,y) * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11481,a(flip),b,11483,a),flip(a)].">
      <j1 rule="hyper" parents="58 11481 11483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11485">
    <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(11466(a,2),11479(a,1))].">
      <j1 rule="para" parents="11466 11479"/>
    </justification>
  </clause>

  <clause id="11486">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(K(z,y) * K(y,u),x)
    ]]></literal>
    <justification jstring="[hyper(4786,a,11467,a),flip(a)].">
      <j1 rule="hyper" parents="4786 11467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11487">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,11478,a(flip),b,11486,a),flip(a)].">
      <j1 rule="hyper" parents="320 11478 11486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11488">
    <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(6919(a,1),11486(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6919 11486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11489">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(K(y,z) * K(u,y),x)
    ]]></literal>
    <justification jstring="[hyper(320,a,11483,a,b,11487,a),flip(a)].">
      <j1 rule="hyper" parents="320 11483 11487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11490">
    <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,9812,a,b,11487,a)].">
      <j1 rule="hyper" parents="58 9812 11487"/>
    </justification>
  </clause>

  <clause id="11491">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,u)) = K(x,K(z,y) * K(u,z))
    ]]></literal>
    <justification jstring="[para(7772(a,1),11487(a,1,1))].">
      <j1 rule="para" parents="7772 11487"/>
    </justification>
  </clause>

  <clause id="11492">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,u)) = K(x,K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,11484,a(flip),b,11491,a),flip(a)].">
      <j1 rule="hyper" parents="320 11484 11491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11493">
    <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,11464,a(flip),b,11472,a),flip(a)].">
      <j1 rule="hyper" parents="58 11464 11472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11494">
    <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(320,a,4689,a,b,11474,a),flip(a)].">
      <j1 rule="hyper" parents="320 4689 11474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11495">
    <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(5092(a,1),11494(a,1,2))].">
      <j1 rule="para" parents="5092 11494"/>
    </justification>
  </clause>

  <clause id="11496">
    <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(320,a,11483,a(flip),b,11495,a),flip(a)].">
      <j1 rule="hyper" parents="320 11483 11495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11497">
    <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(11479,a,11493,a)].">
      <j1 rule="hyper" parents="11479 11493"/>
    </justification>
  </clause>

  <clause id="11498">
    <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(320,a,4714,a(flip),b,11497,a)].">
      <j1 rule="hyper" parents="320 4714 11497"/>
    </justification>
  </clause>

  <clause id="11499">
    <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(9046(a,1),11473(a,2,1))].">
      <j1 rule="para" parents="9046 11473"/>
    </justification>
  </clause>

  <clause id="11500">
    <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,4714,a(flip),b,11498,a)].">
      <j1 rule="hyper" parents="29 4714 11498"/>
    </justification>
  </clause>

  <clause id="11501">
    <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(320,a,11470,a(flip),b,11499,a),flip(a)].">
      <j1 rule="hyper" parents="320 11470 11499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11502">
    <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(9202(a,1),11501(a,1,2,2))].">
      <j1 rule="para" parents="9202 11501"/>
    </justification>
  </clause>

  <clause id="11503">
    <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(320,a,11475,a,b,11502,a)].">
      <j1 rule="hyper" parents="320 11475 11502"/>
    </justification>
  </clause>

  <clause id="11504">
    <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,8986,a(flip),b,11482,a)].">
      <j1 rule="hyper" parents="58 8986 11482"/>
    </justification>
  </clause>

  <clause id="11505">
    <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(7754(a,1),11490(a,1,2,2,2))].">
      <j1 rule="para" parents="7754 11490"/>
    </justification>
  </clause>

  <clause id="11506">
    <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(58,a,6531,a(flip),b,11504,a)].">
      <j1 rule="hyper" parents="58 6531 11504"/>
    </justification>
  </clause>

  <clause id="11507">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,u)) = K(z,K(x,y) * K(u,x))
    ]]></literal>
    <justification jstring="[hyper(5374,a,11505,a)].">
      <j1 rule="hyper" parents="5374 11505"/>
    </justification>
  </clause>

  <clause id="11508">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,K(z,u)) = K(z,K(y,x) * K(u,y))
    ]]></literal>
    <justification jstring="[para(7754(a,1),11507(a,1,1))].">
      <j1 rule="para" parents="7754 11507"/>
    </justification>
  </clause>

  <clause id="11509">
    <literal><![CDATA[
      1 / T(K(x,y) * K(y,z),u) = 1 * T(K(y,x) * K(z,y),u)
    ]]></literal>
    <justification jstring="[para(1989(a,1),11506(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1989 11506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11510">
    <literal><![CDATA[
      1 / T(K(x,y) * K(y,z),u) = T(K(y,x) * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,2,a(flip),b,11509,a),flip(a)].">
      <j1 rule="hyper" parents="320 2 11509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11512">
    <literal><![CDATA[
      1 / T(K(x,y) * K(y,z),u) = T(K(z,y) * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(1991(a,1),11510(a,2,1))].">
      <j1 rule="para" parents="1991 11510"/>
    </justification>
  </clause>

  <clause id="11513">
    <literal><![CDATA[
      1 / T(K(x,y) * K(z,x),u) = T(K(y,x) * K(x,z),u)
    ]]></literal>
    <justification jstring="[para(1991(a,2),11512(a,1,2,1))].">
      <j1 rule="para" parents="1991 11512"/>
    </justification>
  </clause>

  <clause id="11514">
    <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(11513(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="11513 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11515">
    <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(9042(a,1),11488(a,2,2))].">
      <j1 rule="para" parents="9042 11488"/>
    </justification>
  </clause>

  <clause id="11516">
    <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(320,a,11486,a(flip),b,11515,a),flip(a)].">
      <j1 rule="hyper" parents="320 11486 11515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11517">
    <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(6919(a,1),11516(a,1,1,2))].">
      <j1 rule="para" parents="6919 11516"/>
    </justification>
  </clause>

  <clause id="11518">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,z),u) * u) = (K(y,x) * (x \ 1)) * u
    ]]></literal>
    <justification jstring="[para(5982(a,1),8822(a,2,1,1))].">
      <j1 rule="para" parents="5982 8822"/>
    </justification>
  </clause>

  <clause id="11519">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,z),u) * u) = (T(x,y) \ 1) * u
    ]]></literal>
    <justification jstring="[para(5093(a,1),11518(a,2,1))].">
      <j1 rule="para" parents="5093 11518"/>
    </justification>
  </clause>

  <clause id="11521">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ 1,z) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(166(a,1),11519(a,1,2,1,2,2))].">
      <j1 rule="para" parents="166 11519"/>
    </justification>
  </clause>

  <clause id="11522">
    <literal><![CDATA[
      (x \ 1) * (K(y,x) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(10177(a,1),11521(a,1,2,1))].">
      <j1 rule="para" parents="10177 11521"/>
    </justification>
  </clause>

  <clause id="11523">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * z) = L(z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(11522(a,1),5984(a,1,2))].">
      <j1 rule="para" parents="11522 5984"/>
    </justification>
  </clause>

  <clause id="11525">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,y) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4492,a(flip),b,11523,a)].">
      <j1 rule="hyper" parents="58 4492 11523"/>
    </justification>
  </clause>

  <clause id="11527">
    <literal><![CDATA[
      L(x,((y \ z) \ z) \ 1,(y \ z) \ z) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4658,a(flip),b,11525,a)].">
      <j1 rule="hyper" parents="58 4658 11525"/>
    </justification>
  </clause>

  <clause id="11530">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z) \ z) = K(x,((((z \ x) \ x) \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(11527(a,1),10680(a,1,2,1))].">
      <j1 rule="para" parents="11527 10680"/>
    </justification>
  </clause>

  <clause id="11531">
    <literal><![CDATA[
      K(x,((((y \ x) \ x) \ 1) * z) \ 1) = K(x,((y \ 1) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(6461,a,11530,a),flip(a)].">
      <j1 rule="hyper" parents="6461 11530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11533">
    <literal><![CDATA[
      K(x,((x \ (y \ x)) * z) \ 1) = K(x,((y \ 1) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,11361,a(flip),b,11531,a)].">
      <j1 rule="hyper" parents="58 11361 11531"/>
    </justification>
  </clause>

  <clause id="11534">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ 1) = K(x,((y \ x) * z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11321,a(flip),b,11533,a),flip(a)].">
      <j1 rule="hyper" parents="58 11321 11533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11535">
    <literal><![CDATA[
      K(x,((y \ x) * (y / z)) \ x) = L(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,6634,a(flip),b,11534,a),flip(a)].">
      <j1 rule="hyper" parents="58 6634 11534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11536">
    <literal><![CDATA[
      L(K(x,y),z,z \ 1) = L(K(x,y),z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(9306,a,11535,a),flip(a)].">
      <j1 rule="hyper" parents="9306 11535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11537">
    <literal><![CDATA[
      L(K(x,y),z,z \ x) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(10806,a,11536,a),flip(a)].">
      <j1 rule="hyper" parents="10806 11536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11538">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) = K(x,L(y,z,z \ x))
    ]]></literal>
    <justification jstring="[hyper(10806,a,11537,a),flip(a)].">
      <j1 rule="hyper" parents="10806 11537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11539">
    <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(11537(a,1),10806(a,1))].">
      <j1 rule="para" parents="11537 10806"/>
    </justification>
  </clause>

  <clause id="11540">
    <literal><![CDATA[
      K(x,L(y,z \ x,(z \ x) \ 1)) = K(x,L(y,z \ x,z))
    ]]></literal>
    <justification jstring="[para(11157(a,1),11538(a,2,2))].">
      <j1 rule="para" parents="11157 11538"/>
    </justification>
  </clause>

  <clause id="11541">
    <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,11018,a(flip),b,11540,a),flip(a)].">
      <j1 rule="hyper" parents="58 11018 11540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11542">
    <literal><![CDATA[
      K((((x \ y) \ 1) * (x \ 1)) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11392,a(flip),b,11541,a),flip(a)].">
      <j1 rule="hyper" parents="58 11392 11541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11543">
    <literal><![CDATA[
      K(((((x \ 1) \ y) \ 1) * x) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(10915,a,11542,a)].">
      <j1 rule="hyper" parents="10915 11542"/>
    </justification>
  </clause>

  <clause id="11545">
    <literal><![CDATA[
      (1 / (x \ y)) * (x \ T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6012,a(flip),b,11542,a)].">
      <j1 rule="hyper" parents="58 6012 11542"/>
    </justification>
  </clause>

  <clause id="11547">
    <literal><![CDATA[
      (1 / x) * (y \ T(y * x,z)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11545(a,1,1,2))].">
      <j1 rule="para" parents="4 11545"/>
    </justification>
  </clause>

  <clause id="11548">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = K(x,y) / z
    ]]></literal>
    <justification jstring="[para(11543(a,1),6887(a,2,1))].">
      <j1 rule="para" parents="11543 6887"/>
    </justification>
  </clause>

  <clause id="11549">
    <literal><![CDATA[
      T(x,y) / ((1 / y) \ x) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4762,a(flip),b,11548,a),flip(a)].">
      <j1 rule="hyper" parents="320 4762 11548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11550">
    <literal><![CDATA[
      (K(x,y) / z) \ T(x,y) = (1 / z) \ x
    ]]></literal>
    <justification jstring="[hyper(188,a,11548,a)].">
      <j1 rule="hyper" parents="188 11548"/>
    </justification>
  </clause>

  <clause id="11551">
    <literal><![CDATA[
      (1 / (x \ K(y,z))) \ y = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(31,a,180,a,b,11548,a),flip(a)].">
      <j1 rule="hyper" parents="31 180 11548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11553">
    <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(10141(a,1),11549(a,2,2))].">
      <j1 rule="para" parents="10141 11549"/>
    </justification>
  </clause>

  <clause id="11554">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / z = u
    ]]></literal>
    <justification jstring="[para(11550(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11550 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11555">
    <literal><![CDATA[
      K(x,((y \ 1) * (z \ 1)) \ 1) = 1 / K(z * y,x)
    ]]></literal>
    <justification jstring="[para(11547(a,1),6013(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11547 6013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11556">
    <literal><![CDATA[
      K(x,((y \ 1) * (z \ 1)) \ 1) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4931,a(flip),b,11555,a),flip(a)].">
      <j1 rule="hyper" parents="320 4931 11555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11557">
    <literal><![CDATA[
      (1 / x) \ K(y,z * x) = x * K(y,(z \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(11556(a,1),6633(a,1,2))].">
      <j1 rule="para" parents="11556 6633"/>
    </justification>
  </clause>

  <clause id="11558">
    <literal><![CDATA[
      x * K(y,((z / x) \ 1) \ x) = (1 / x) \ K(y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),11557(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 11557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11559">
    <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(6624(a,1),11553(a,1,1))].">
      <j1 rule="para" parents="6624 11553"/>
    </justification>
  </clause>

  <clause id="11560">
    <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(9453(a,1),10891(a,1,2))].">
      <j1 rule="para" parents="9453 10891"/>
    </justification>
  </clause>

  <clause id="11561">
    <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(4318(a,1),11560(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4318 11560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11562">
    <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),11561(a,2,2))].">
      <j1 rule="para" parents="18 11561"/>
    </justification>
  </clause>

  <clause id="11563">
    <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(320,a,7539,a(flip),b,11562,a),flip(a)].">
      <j1 rule="hyper" parents="320 7539 11562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11564">
    <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(10809(a,1),11563(a,2,1))].">
      <j1 rule="para" parents="10809 11563"/>
    </justification>
  </clause>

  <clause id="11565">
    <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(320,a,7040,a(flip),b,11564,a),flip(a)].">
      <j1 rule="hyper" parents="320 7040 11564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11566">
    <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(7130(a,1),11565(a,1,2,3))].">
      <j1 rule="para" parents="7130 11565"/>
    </justification>
  </clause>

  <clause id="11567">
    <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(4221(a,1),11566(a,1,2,3))].">
      <j1 rule="para" parents="4221 11566"/>
    </justification>
  </clause>

  <clause id="11568">
    <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,11017,a,b,11567,a)].">
      <j1 rule="hyper" parents="58 11017 11567"/>
    </justification>
  </clause>

  <clause id="11569">
    <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(10763(a,1),11568(a,1,1))].">
      <j1 rule="para" parents="10763 11568"/>
    </justification>
  </clause>

  <clause id="11570">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = K(y * x,L(x,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(2869(a,1),11569(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2869 11569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11571">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = K(L(x,z,u),y * x) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,5092,a(flip),b,11570,a),flip(a)].">
      <j1 rule="hyper" parents="320 5092 11570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11572">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = K(x,L(y * x,z,u)) * x
    ]]></literal>
    <justification jstring="[para(10809(a,1),11571(a,2,1))].">
      <j1 rule="para" parents="10809 11571"/>
    </justification>
  </clause>

  <clause id="11573">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = T(x,L(y * x,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,4729,a,b,11572,a),flip(a)].">
      <j1 rule="hyper" parents="320 4729 11572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11574">
    <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,10895,a,b,11573,a)].">
      <j1 rule="hyper" parents="58 10895 11573"/>
    </justification>
  </clause>

  <clause id="11575">
    <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),11394(a,2,1,1))].">
      <j1 rule="para" parents="4 11394"/>
    </justification>
  </clause>

  <clause id="11576">
    <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(320,a,9444,a(flip),b,11575,a),flip(a)].">
      <j1 rule="hyper" parents="320 9444 11575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11578">
    <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),11576(a,1,1,1))].">
      <j1 rule="para" parents="4 11576"/>
    </justification>
  </clause>

  <clause id="11579">
    <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),11578(a,1,2,2))].">
      <j1 rule="para" parents="4 11578"/>
    </justification>
  </clause>

  <clause id="11580">
    <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(4782(a,1),11579(a,1,2,1,3))].">
      <j1 rule="para" parents="4782 11579"/>
    </justification>
  </clause>

  <clause id="11581">
    <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(320,a,5648,a(flip),b,5352,a),flip(a)].">
      <j1 rule="hyper" parents="320 5648 5352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11582">
    <literal><![CDATA[
      ((x * y) * K(T(z,(1 / y) \ x),x * y)) / y = x * K(z,(x \ (1 / y)) \ 1)
    ]]></literal>
    <justification jstring="[para(4711(a,1),11581(a,1,1))].">
      <j1 rule="para" parents="4711 11581"/>
    </justification>
  </clause>

  <clause id="11583">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(x \ (1 / y)) \ 1)
    ]]></literal>
    <justification jstring="[para(7191(a,1),11582(a,1,1,2))].">
      <j1 rule="para" parents="7191 11582"/>
    </justification>
  </clause>

  <clause id="11584">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(1 / y) \ x)
    ]]></literal>
    <justification jstring="[para(6078(a,1),11583(a,2,2))].">
      <j1 rule="para" parents="6078 11583"/>
    </justification>
  </clause>

  <clause id="11585">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(5285(a,1),11584(a,2,2))].">
      <j1 rule="para" parents="5285 11584"/>
    </justification>
  </clause>

  <clause id="11586">
    <literal><![CDATA[
      (x * K(y,(z \ 1) \ x)) * z = (x * z) * K(y,x * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,11585,a)].">
      <j1 rule="hyper" parents="133 11585"/>
    </justification>
  </clause>

  <clause id="11587">
    <literal><![CDATA[
      (x \ y) * K(z,(x \ 1) \ (x \ y)) = x \ (y * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(30,a,5661,a(flip),b,11586,a),flip(a)].">
      <j1 rule="hyper" parents="30 5661 11586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11588">
    <literal><![CDATA[
      (x \ y) \ (x \ (y * K(z,y))) = K(z,(x \ 1) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(123,a,11587,a)].">
      <j1 rule="hyper" parents="123 11587"/>
    </justification>
  </clause>

  <clause id="11589">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ K(y,T(z,u))) = K(u,(x \ 1) \ (x \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(7811(a,1),11588(a,1,2,2))].">
      <j1 rule="para" parents="7811 11588"/>
    </justification>
  </clause>

  <clause id="11590">
    <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(6972(a,1),6973(a,2,2,1,1))].">
      <j1 rule="para" parents="6972 6973"/>
    </justification>
  </clause>

  <clause id="11591">
    <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),11590(a,2,2,1))].">
      <j1 rule="para" parents="75 11590"/>
    </justification>
  </clause>

  <clause id="11593">
    <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(320,a,5884,a(flip),b,11591,a),flip(a)].">
      <j1 rule="hyper" parents="320 5884 11591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11594">
    <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),11593(a,1,1,2,1))].">
      <j1 rule="para" parents="75 11593"/>
    </justification>
  </clause>

  <clause id="11595">
    <literal><![CDATA[
      T(x \ R(x,y,z),R(x,u,w) \ x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5884(a,1),11594(a,1,1))].">
      <j1 rule="para" parents="5884 11594"/>
    </justification>
  </clause>

  <clause id="11596">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ 1) \ 1 = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(6148,a,11595,a)].">
      <j1 rule="hyper" parents="6148 11595"/>
    </justification>
  </clause>

  <clause id="11597">
    <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(11596(a,1),11423(a,1,1,1))].">
      <j1 rule="para" parents="11596 11423"/>
    </justification>
  </clause>

  <clause id="11598">
    <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(787,a,11597,a)].">
      <j1 rule="hyper" parents="787 11597"/>
    </justification>
  </clause>

  <clause id="11599">
    <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),11598(a,1,1,2))].">
      <j1 rule="para" parents="101 11598"/>
    </justification>
  </clause>

  <clause id="11600">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1 = T(a(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(9(a,2),11599(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 11599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11601">
    <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(7730(a,1),9260(a,2,1))].">
      <j1 rule="para" parents="7730 9260"/>
    </justification>
  </clause>

  <clause id="11602">
    <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,3798,a(flip),b,9331,a),flip(a)].">
      <j1 rule="hyper" parents="58 3798 9331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11604">
    <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(320,a,3612,a(flip),b,11602,a),flip(a)].">
      <j1 rule="hyper" parents="320 3612 11602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11605">
    <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(2168(a,1),11604(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2168 11604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11607">
    <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(9955,a,10000,a)].">
      <j1 rule="hyper" parents="9955 10000"/>
    </justification>
  </clause>

  <clause id="11608">
    <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(11035,a,11607,a)].">
      <j1 rule="hyper" parents="11035 11607"/>
    </justification>
  </clause>

  <clause id="11610">
    <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(9928(a,1),11608(a,2,2,2))].">
      <j1 rule="para" parents="9928 11608"/>
    </justification>
  </clause>

  <clause id="11611">
    <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),11610(a,2,2,2,1))].">
      <j1 rule="para" parents="5 11610"/>
    </justification>
  </clause>

  <clause id="11612">
    <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),11611(a,2,2))].">
      <j1 rule="para" parents="4 11611"/>
    </justification>
  </clause>

  <clause id="11614">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,9941,a(flip),b,11612,a),flip(a)].">
      <j1 rule="hyper" parents="320 9941 11612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11615">
    <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,11036,a(flip),b,11614,a),flip(a)].">
      <j1 rule="hyper" parents="58 11036 11614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11617">
    <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(320,a,7054,a(flip),b,10591,a),flip(a)].">
      <j1 rule="hyper" parents="320 7054 10591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11619">
    <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(11617(a,2),10884(a,1))].">
      <j1 rule="para" parents="11617 10884"/>
    </justification>
  </clause>

  <clause id="11620">
    <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(8694(a,1),10734(a,1,2,1,1))].">
      <j1 rule="para" parents="8694 10734"/>
    </justification>
  </clause>

  <clause id="11621">
    <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(320,a,8491,a(flip),b,11601,a),flip(a)].">
      <j1 rule="hyper" parents="320 8491 11601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11622">
    <literal><![CDATA[
      K(x,T((y * (x \ z)) \ u,w)) = K(x,T((y * z) \ (u * x),w))
    ]]></literal>
    <justification jstring="[hyper(58,a,10733,a(flip),b,11620,a),flip(a)].">
      <j1 rule="hyper" parents="58 10733 11620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11623">
    <literal><![CDATA[
      K(x,T((y * z) \ (u * x),y * z)) = K(x,u / (y * (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(9199,a,11622,a),flip(a)].">
      <j1 rule="hyper" parents="9199 11622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11624">
    <literal><![CDATA[
      K(x,(y * x) / (z * u)) = K(x,y / (z * (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(8033,a,11623,a)].">
      <j1 rule="hyper" parents="8033 11623"/>
    </justification>
  </clause>

  <clause id="11625">
    <literal><![CDATA[
      K(x,y / (z * (x \ u))) = K(x,((z * u) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(8468,a,11624,a),flip(a)].">
      <j1 rule="hyper" parents="8468 11624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11626">
    <literal><![CDATA[
      R(K(x,((y * z) / (u / w)) \ x),w \ u,w) = K(x,u / ((y * (x \ z)) * w))
    ]]></literal>
    <justification jstring="[para(11625(a,1),10364(a,1,1))].">
      <j1 rule="para" parents="11625 10364"/>
    </justification>
  </clause>

  <clause id="11627">
    <literal><![CDATA[
      K(x,y / ((x \ (z * u)) * w)) = K(x,y / ((z * (x \ u)) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,10363,a(flip),b,11626,a)].">
      <j1 rule="hyper" parents="58 10363 11626"/>
    </justification>
  </clause>

  <clause id="11628">
    <literal><![CDATA[
      K(x,y / ((z * (x \ u)) * w)) = K(x,(((z * u) * w) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(11106,a,11627,a),flip(a)].">
      <j1 rule="hyper" parents="11106 11627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11629">
    <literal><![CDATA[
      K(x,(((y * z) * u) / (z * u)) \ x) = R(K(x,y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6990,a(flip),b,11628,a),flip(a)].">
      <j1 rule="hyper" parents="58 6990 11628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11630">
    <literal><![CDATA[
      R(K(x,y \ x),z,u) = K(x,R(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(15(a,2),11629(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15 11629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11631">
    <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(531(a,1),11630(a,2,2,1))].">
      <j1 rule="para" parents="531 11630"/>
    </justification>
  </clause>

  <clause id="11632">
    <literal><![CDATA[
      K(x,R(y \ x,z,u) \ x) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(5158(a,1),11630(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5158 11630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11633">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ x) = R(K(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(5384(a,1),11630(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5384 11630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11634">
    <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(11249(a,1),11630(a,1,1))].">
      <j1 rule="para" parents="11249 11630"/>
    </justification>
  </clause>

  <clause id="11635">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ x) = R(K(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5305,a,b,11633,a)].">
      <j1 rule="hyper" parents="58 5305 11633"/>
    </justification>
  </clause>

  <clause id="11636">
    <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(11632(a,1),11634(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11632 11634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11637">
    <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(5305(a,1),11631(a,1,1))].">
      <j1 rule="para" parents="5305 11631"/>
    </justification>
  </clause>

  <clause id="11638">
    <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),4181(a,1,1,2))].">
      <j1 rule="para" parents="75 4181"/>
    </justification>
  </clause>

  <clause id="11639">
    <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),11638(a,1,1))].">
      <j1 rule="para" parents="20 11638"/>
    </justification>
  </clause>

  <clause id="11640">
    <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(2798(a,1),11639(a,1,1))].">
      <j1 rule="para" parents="2798 11639"/>
    </justification>
  </clause>

  <clause id="11641">
    <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),11640(a,1,2,2,2))].">
      <j1 rule="para" parents="75 11640"/>
    </justification>
  </clause>

  <clause id="11642">
    <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),11641(a,1,2,2))].">
      <j1 rule="para" parents="20 11641"/>
    </justification>
  </clause>

  <clause id="11643">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ ((1 / x) * (y * x))) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(2798(a,1),11642(a,1,2,2))].">
      <j1 rule="para" parents="2798 11642"/>
    </justification>
  </clause>

  <clause id="11644">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * x) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),11643(a,1,2))].">
      <j1 rule="para" parents="4 11643"/>
    </justification>
  </clause>

  <clause id="11646">
    <literal><![CDATA[
      1 / R(T(x,y),x \ 1,y * x) = (L(y,x,x \ 1) \ (x * y)) \ 1
    ]]></literal>
    <justification jstring="[para(11644(a,1),4133(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11644 4133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11647">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = R(T(y,x),y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(188,a,11646,a)].">
      <j1 rule="hyper" parents="188 11646"/>
    </justification>
  </clause>

  <clause id="11648">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) \ (x * y) = R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2806,a(flip),b,11647,a)].">
      <j1 rule="hyper" parents="58 2806 11647"/>
    </justification>
  </clause>

  <clause id="11649">
    <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(7325(a,1),5941(a,1,3))].">
      <j1 rule="para" parents="7325 5941"/>
    </justification>
  </clause>

  <clause id="11651">
    <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(8791(a,1),8504(a,1,1))].">
      <j1 rule="para" parents="8791 8504"/>
    </justification>
  </clause>

  <clause id="11652">
    <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(9958(a,1),8977(a,2,2))].">
      <j1 rule="para" parents="9958 8977"/>
    </justification>
  </clause>

  <clause id="11653">
    <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(5092(a,1),9234(a,1,1,2,2))].">
      <j1 rule="para" parents="5092 9234"/>
    </justification>
  </clause>

  <clause id="11654">
    <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,7768,a(flip),b,10736,a),flip(a)].">
      <j1 rule="hyper" parents="58 7768 10736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11655">
    <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(7756,a,11654,a)].">
      <j1 rule="hyper" parents="7756 11654"/>
    </justification>
  </clause>

  <clause id="11657">
    <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(8641(a,1),11655(a,1,2))].">
      <j1 rule="para" parents="8641 11655"/>
    </justification>
  </clause>

  <clause id="11658">
    <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,9275,a(flip),b,11657,a)].">
      <j1 rule="hyper" parents="58 9275 11657"/>
    </justification>
  </clause>

  <clause id="11659">
    <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(9040(a,1),11051(a,1,1,1,2))].">
      <j1 rule="para" parents="9040 11051"/>
    </justification>
  </clause>

  <clause id="11660">
    <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(6773(a,1),11295(a,1,1,2))].">
      <j1 rule="para" parents="6773 11295"/>
    </justification>
  </clause>

  <clause id="11661">
    <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(634(a,1),11660(a,1,1))].">
      <j1 rule="para" parents="634 11660"/>
    </justification>
  </clause>

  <clause id="11662">
    <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(238(a,1),11661(a,1,2)),flip(a)].">
      <j1 rule="para" parents="238 11661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11663">
    <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(320,a,1346,a(flip),b,11662,a),flip(a)].">
      <j1 rule="hyper" parents="320 1346 11662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11664">
    <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),11663(a,2,3))].">
      <j1 rule="para" parents="22 11663"/>
    </justification>
  </clause>

  <clause id="11665">
    <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,11293,a(flip),b,11664,a)].">
      <j1 rule="hyper" parents="58 11293 11664"/>
    </justification>
  </clause>

  <clause id="11666">
    <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(11297,a,11665,a)].">
      <j1 rule="hyper" parents="11297 11665"/>
    </justification>
  </clause>

  <clause id="11668">
    <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,11615,a(flip),b,11666,a),flip(a)].">
      <j1 rule="hyper" parents="58 11615 11666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11670">
    <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,11415,a,b,11668,a)].">
      <j1 rule="hyper" parents="58 11415 11668"/>
    </justification>
  </clause>

  <clause id="11671">
    <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(9463,a,11670,a)].">
      <j1 rule="hyper" parents="9463 11670"/>
    </justification>
  </clause>

  <clause id="11672">
    <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(11671(a,1),11362(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11671 11362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11673">
    <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),11672(a,2,2,2))].">
      <j1 rule="para" parents="17 11672"/>
    </justification>
  </clause>

  <clause id="11674">
    <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(10043(a,1),11673(a,2,2))].">
      <j1 rule="para" parents="10043 11673"/>
    </justification>
  </clause>

  <clause id="11675">
    <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,11271,a(flip),b,11674,a)].">
      <j1 rule="hyper" parents="58 11271 11674"/>
    </justification>
  </clause>

  <clause id="11676">
    <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(372(a,1),11675(a,1,2,3))].">
      <j1 rule="para" parents="372 11675"/>
    </justification>
  </clause>

  <clause id="11677">
    <literal><![CDATA[
      a(R(x,y,z),u,R(x,y,z)) = a(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(9515,a,11676,a)].">
      <j1 rule="hyper" parents="9515 11676"/>
    </justification>
  </clause>

  <clause id="11678">
    <literal><![CDATA[
      R(a(x,y,x),x * z,u) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(11412,a,11677,a)].">
      <j1 rule="hyper" parents="11412 11677"/>
    </justification>
  </clause>

  <clause id="11679">
    <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,11671,a(flip),b,11677,a),flip(a)].">
      <j1 rule="hyper" parents="58 11671 11677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11680">
    <literal><![CDATA[
      a(x,y,R(x,x \ z,u)) = R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),11678(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 11678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11681">
    <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,11680,a(flip),b,9952,a),flip(a)].">
      <j1 rule="hyper" parents="119 11680 9952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11682">
    <literal><![CDATA[
      R(x,y,R(x,x \ z,u)) = x * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,11680,a(flip),b,9941,a),flip(a)].">
      <j1 rule="hyper" parents="119 11680 9941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11683">
    <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,10195,a(flip),b,11682,a),flip(a)].">
      <j1 rule="hyper" parents="58 10195 11682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11684">
    <literal><![CDATA[
      a(x,x \ y,R(x,z,u)) * K(x,y) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(11679(a,1),10045(a,1,1))].">
      <j1 rule="para" parents="11679 10045"/>
    </justification>
  </clause>

  <clause id="11685">
    <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,10965,a(flip),b,11684,a)].">
      <j1 rule="hyper" parents="58 10965 11684"/>
    </justification>
  </clause>

  <clause id="11686">
    <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(9337(a,1),11683(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9337 11683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11687">
    <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(320,a,11681,a,b,11686,a),flip(a)].">
      <j1 rule="hyper" parents="320 11681 11686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11689">
    <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(11687(a,1),11281(a,2,1,1))].">
      <j1 rule="para" parents="11687 11281"/>
    </justification>
  </clause>

  <clause id="11690">
    <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(7051(a,1),11651(a,1,2))].">
      <j1 rule="para" parents="7051 11651"/>
    </justification>
  </clause>

  <clause id="11692">
    <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(10715(a,1),11690(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10715 11690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11693">
    <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(320,a,3,a(flip),b,11692,a),flip(a)].">
      <j1 rule="hyper" parents="320 3 11692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11695">
    <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,10223,a(flip),b,11693,a),flip(a)].">
      <j1 rule="hyper" parents="58 10223 11693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11696">
    <literal><![CDATA[
      R(T(x,y),z,x) \ T(x,y) = x \ L(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,7451,a(flip),b,11695,a),flip(a)].">
      <j1 rule="hyper" parents="320 7451 11695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11697">
    <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(9296(a,1),11652(a,2,2))].">
      <j1 rule="para" parents="9296 11652"/>
    </justification>
  </clause>

  <clause id="11698">
    <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(320,a,6695,a(flip),b,11697,a),flip(a)].">
      <j1 rule="hyper" parents="320 6695 11697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11699">
    <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(7771(a,1),11698(a,2,1))].">
      <j1 rule="para" parents="7771 11698"/>
    </justification>
  </clause>

  <clause id="11700">
    <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(8100(a,1),11699(a,2,2))].">
      <j1 rule="para" parents="8100 11699"/>
    </justification>
  </clause>

  <clause id="11701">
    <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(320,a,11492,a(flip),b,11700,a),flip(a)].">
      <j1 rule="hyper" parents="320 11492 11700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11703">
    <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(8973(a,1),11701(a,1,2))].">
      <j1 rule="para" parents="8973 11701"/>
    </justification>
  </clause>

  <clause id="11705">
    <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(11703(a,1),11374(a,1,2))].">
      <j1 rule="para" parents="11703 11374"/>
    </justification>
  </clause>

  <clause id="11706">
    <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(5064(a,1),11653(a,1,1,2))].">
      <j1 rule="para" parents="5064 11653"/>
    </justification>
  </clause>

  <clause id="11707">
    <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(10239(a,1),11706(a,1,2))].">
      <j1 rule="para" parents="10239 11706"/>
    </justification>
  </clause>

  <clause id="11708">
    <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(8990(a,1),11707(a,1,2))].">
      <j1 rule="para" parents="8990 11707"/>
    </justification>
  </clause>

  <clause id="11710">
    <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(5092(a,1),11708(a,2,2,1,1))].">
      <j1 rule="para" parents="5092 11708"/>
    </justification>
  </clause>

  <clause id="11711">
    <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(7814(a,1),11710(a,2,2,1))].">
      <j1 rule="para" parents="7814 11710"/>
    </justification>
  </clause>

  <clause id="11712">
    <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(7615(a,2),11711(a,2,2))].">
      <j1 rule="para" parents="7615 11711"/>
    </justification>
  </clause>

  <clause id="11713">
    <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),11712(a,2,2,1))].">
      <j1 rule="para" parents="7 11712"/>
    </justification>
  </clause>

  <clause id="11714">
    <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(11713(a,1),5954(a,1,1,2))].">
      <j1 rule="para" parents="11713 5954"/>
    </justification>
  </clause>

  <clause id="11715">
    <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(11508(a,1),11659(a,1,1,1))].">
      <j1 rule="para" parents="11508 11659"/>
    </justification>
  </clause>

  <clause id="11716">
    <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(3556(a,1),6043(a,1,1))].">
      <j1 rule="para" parents="3556 6043"/>
    </justification>
  </clause>

  <clause id="11717">
    <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(3556(a,1),11716(a,1,2,1,1))].">
      <j1 rule="para" parents="3556 11716"/>
    </justification>
  </clause>

  <clause id="11718">
    <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(6023(a,1),11717(a,1,2,1))].">
      <j1 rule="para" parents="6023 11717"/>
    </justification>
  </clause>

  <clause id="11719">
    <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(320,a,10668,a(flip),b,11718,a),flip(a)].">
      <j1 rule="hyper" parents="320 10668 11718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11720">
    <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(11719(a,1),428(a,1,2))].">
      <j1 rule="para" parents="11719 428"/>
    </justification>
  </clause>

  <clause id="11721">
    <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),6782(a,2,2,1,2))].">
      <j1 rule="para" parents="5 6782"/>
    </justification>
  </clause>

  <clause id="11722">
    <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(320,a,237,a(flip),b,11721,a),flip(a)].">
      <j1 rule="hyper" parents="320 237 11721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11723">
    <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(237(a,1),11722(a,1,2))].">
      <j1 rule="para" parents="237 11722"/>
    </justification>
  </clause>

  <clause id="11724">
    <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(5092(a,1),11723(a,1,2,2))].">
      <j1 rule="para" parents="5092 11723"/>
    </justification>
  </clause>

  <clause id="11725">
    <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(5109,a,11724,a),flip(a)].">
      <j1 rule="hyper" parents="5109 11724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11726">
    <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(320,a,3262,a(flip),b,11724,a),flip(a)].">
      <j1 rule="hyper" parents="320 3262 11724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11727">
    <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(11725(a,2),5110(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11725 5110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11728">
    <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(7004(a,1),11182(a,2,2,1))].">
      <j1 rule="para" parents="7004 11182"/>
    </justification>
  </clause>

  <clause id="11729">
    <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(8962(a,1),11728(a,2,2,1,2))].">
      <j1 rule="para" parents="8962 11728"/>
    </justification>
  </clause>

  <clause id="11730">
    <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(6505(a,1),9866(a,1,1,1))].">
      <j1 rule="para" parents="6505 9866"/>
    </justification>
  </clause>

  <clause id="11731">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,x * (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(4207(a,1),11730(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4207 11730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11732">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7358,a(flip),b,11731,a),flip(a)].">
      <j1 rule="hyper" parents="320 7358 11731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11734">
    <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(320,a,514,a(flip),b,10562,a),flip(a)].">
      <j1 rule="hyper" parents="320 514 10562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11735">
    <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(2099,a,11734,a)].">
      <j1 rule="hyper" parents="2099 11734"/>
    </justification>
  </clause>

  <clause id="11736">
    <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(5105(a,1),11735(a,1,1,2,1))].">
      <j1 rule="para" parents="5105 11735"/>
    </justification>
  </clause>

  <clause id="11737">
    <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(5520(a,1),11736(a,1,1,2,1))].">
      <j1 rule="para" parents="5520 11736"/>
    </justification>
  </clause>

  <clause id="11738">
    <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(7894(a,1),11737(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7894 11737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11739">
    <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,4381,a(flip),b,11738,a),flip(a)].">
      <j1 rule="hyper" parents="58 4381 11738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11741">
    <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(11739(a,1),1320(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11739 1320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11742">
    <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(5092(a,1),11741(a,1,1))].">
      <j1 rule="para" parents="5092 11741"/>
    </justification>
  </clause>

  <clause id="11743">
    <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(9895(a,1),11742(a,1,1))].">
      <j1 rule="para" parents="9895 11742"/>
    </justification>
  </clause>

  <clause id="11744">
    <literal><![CDATA[
      R(K(x,y),R(T(x,z),u,w),v5) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(332,a,11743,a),flip(a)].">
      <j1 rule="hyper" parents="332 11743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11747">
    <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,6915,a(flip),b,11744,a)].">
      <j1 rule="hyper" parents="58 6915 11744"/>
    </justification>
  </clause>

  <clause id="11748">
    <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(320,a,7236,a(flip),b,11747,a),flip(a)].">
      <j1 rule="hyper" parents="320 7236 11747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11749">
    <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,7403,a(flip),b,11748,a),flip(a)].">
      <j1 rule="hyper" parents="58 7403 11748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11750">
    <literal><![CDATA[
      K(x,R(x,y,z) * (u \ 1)) = K(x,u \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(8381,a,11749,a),flip(a)].">
      <j1 rule="hyper" parents="8381 11749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11752">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) = K(x,y \ R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,11749,a,b,11750,a)].">
      <j1 rule="hyper" parents="58 11749 11750"/>
    </justification>
  </clause>

  <clause id="11753">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(8263,a,11752,a)].">
      <j1 rule="hyper" parents="8263 11752"/>
    </justification>
  </clause>

  <clause id="11755">
    <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,7054,a(flip),b,10592,a),flip(a)].">
      <j1 rule="hyper" parents="58 7054 10592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11757">
    <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(4929(a,1),11726(a,2,1,2,1))].">
      <j1 rule="para" parents="4929 11726"/>
    </justification>
  </clause>

  <clause id="11758">
    <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(5861(a,1),11757(a,2,1))].">
      <j1 rule="para" parents="5861 11757"/>
    </justification>
  </clause>

  <clause id="11759">
    <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(5716(a,1),11758(a,1,2,2,2,1))].">
      <j1 rule="para" parents="5716 11758"/>
    </justification>
  </clause>

  <clause id="11760">
    <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(11727,a,11759,a)].">
      <j1 rule="hyper" parents="11727 11759"/>
    </justification>
  </clause>

  <clause id="11761">
    <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,10704,a(flip),b,11760,a)].">
      <j1 rule="hyper" parents="58 10704 11760"/>
    </justification>
  </clause>

  <clause id="11762">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = L(a(x,y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(10763(a,1),11761(a,1,3))].">
      <j1 rule="para" parents="10763 11761"/>
    </justification>
  </clause>

  <clause id="11763">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,146,a(flip),b,11762,a),flip(a)].">
      <j1 rule="hyper" parents="320 146 11762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11765">
    <literal><![CDATA[
      a(x,y,K(z,(u * w) \ v5)) = a(x,y,K(z,w \ (u \ v5)))
    ]]></literal>
    <justification jstring="[para(298(a,1),11763(a,1,3,2))].">
      <j1 rule="para" parents="298 11763"/>
    </justification>
  </clause>

  <clause id="11766">
    <literal><![CDATA[
      a(x,y,K((z \ u) \ w,v5)) = a(x,y,K(u \ (z * w),v5))
    ]]></literal>
    <justification jstring="[para(10779(a,1),11763(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10779 11763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11767">
    <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(8894(a,1),8900(a,1,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="8894 8900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11768">
    <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),11767(a,2,1,2,1))].">
      <j1 rule="para" parents="4 11767"/>
    </justification>
  </clause>

  <clause id="11770">
    <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(8894(a,1),11768(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8894 11768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11771">
    <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(1995(a,1),11770(a,2,2))].">
      <j1 rule="para" parents="1995 11770"/>
    </justification>
  </clause>

  <clause id="11772">
    <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,9677,a,b,11771,a)].">
      <j1 rule="hyper" parents="58 9677 11771"/>
    </justification>
  </clause>

  <clause id="11773">
    <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(328,a,11772,a),flip(a)].">
      <j1 rule="hyper" parents="328 11772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11774">
    <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(5102(a,1),11772(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5102 11772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11775">
    <literal><![CDATA[
      x / a(K(y,z),u,u \ 1) = x * a(K(z,y),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(5102(a,1),11774(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5102 11774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11776">
    <literal><![CDATA[
      a(K(x,y),z,z \ 1) \ 1 = a(K(y,x),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(3919,a,11775,a)].">
      <j1 rule="hyper" parents="3919 11775"/>
    </justification>
  </clause>

  <clause id="11777">
    <literal><![CDATA[
      K(x,a(K(y,z),u,u \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(11776(a,1),10585(a,1,2))].">
      <j1 rule="para" parents="11776 10585"/>
    </justification>
  </clause>

  <clause id="11778">
    <literal><![CDATA[
      T(x,a(K(y,z),u,u \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,11777,a)].">
      <j1 rule="hyper" parents="51 11777"/>
    </justification>
  </clause>

  <clause id="11779">
    <literal><![CDATA[
      T(x,a(K(y,z),u \ 1,u)) = x
    ]]></literal>
    <justification jstring="[para(3666(a,1),11778(a,1,2))].">
      <j1 rule="para" parents="3666 11778"/>
    </justification>
  </clause>

  <clause id="11780">
    <literal><![CDATA[
      T(a(K(x,y),z \ 1,z),u) = a(K(x,y),z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(49,a,11779,a)].">
      <j1 rule="hyper" parents="49 11779"/>
    </justification>
  </clause>

  <clause id="11781">
    <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(320,a,3641,a,b,11780,a),flip(a)].">
      <j1 rule="hyper" parents="320 3641 11780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11782">
    <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(5107(a,2),11781(a,1,1))].">
      <j1 rule="para" parents="5107 11781"/>
    </justification>
  </clause>

  <clause id="11783">
    <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,9869,a,b,11782,a)].">
      <j1 rule="hyper" parents="58 9869 11782"/>
    </justification>
  </clause>

  <clause id="11784">
    <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,7163,a,b,11783,a)].">
      <j1 rule="hyper" parents="58 7163 11783"/>
    </justification>
  </clause>

  <clause id="11785">
    <literal><![CDATA[
      K(x,K(y,R(z,u \ 1,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(10649,a,11784,a)].">
      <j1 rule="hyper" parents="10649 11784"/>
    </justification>
  </clause>

  <clause id="11786">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ 1))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(2597(a,1),11785(a,1,2,2))].">
      <j1 rule="para" parents="2597 11785"/>
    </justification>
  </clause>

  <clause id="11787">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ 1))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7772,a,b,11786,a),flip(a)].">
      <j1 rule="hyper" parents="320 7772 11786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11788">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ K(w,x)))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,11341,a,b,11786,a)].">
      <j1 rule="hyper" parents="58 11341 11786"/>
    </justification>
  </clause>

  <clause id="11789">
    <literal><![CDATA[
      K(x,K(y,z * (u \ 1))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(523(a,1),11787(a,1,2,2))].">
      <j1 rule="para" parents="523 11787"/>
    </justification>
  </clause>

  <clause id="11790">
    <literal><![CDATA[
      T(x,K(y,z * (u \ 1))) = T(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(118,a,11789,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 11789 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11791">
    <literal><![CDATA[
      K(x,K(y,z / (1 / u))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(75(a,1),11789(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="75 11789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11792">
    <literal><![CDATA[
      K(x,K(y,z / (u \ 1))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(5274(a,1),11789(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5274 11789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11793">
    <literal><![CDATA[
      K(x,K(y,z * (1 / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(5277(a,2),11789(a,1,2))].">
      <j1 rule="para" parents="5277 11789"/>
    </justification>
  </clause>

  <clause id="11794">
    <literal><![CDATA[
      T(T(x,y),K(y,z / u)) = T(x,T(y,(z * (u \ 1)) \ 1))
    ]]></literal>
    <justification jstring="[hyper(8182,a,11790,a),flip(a)].">
      <j1 rule="hyper" parents="8182 11790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11795">
    <literal><![CDATA[
      T(x,K(y,z * (x \ 1))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8009,a(flip),b,11790,a),flip(a)].">
      <j1 rule="hyper" parents="320 8009 11790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11796">
    <literal><![CDATA[
      T(x \ 1,K(y,z * x)) = T(x \ 1,K(y,z))
    ]]></literal>
    <justification jstring="[para(5274(a,1),11795(a,1,2))].">
      <j1 rule="para" parents="5274 11795"/>
    </justification>
  </clause>

  <clause id="11797">
    <literal><![CDATA[
      K(x,K(y,(1 / z) / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8240,a,11791,a)].">
      <j1 rule="hyper" parents="8240 11791"/>
    </justification>
  </clause>

  <clause id="11798">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8240,a,11792,a)].">
      <j1 rule="hyper" parents="8240 11792"/>
    </justification>
  </clause>

  <clause id="11799">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(7806,a,11792,a)].">
      <j1 rule="hyper" parents="7806 11792"/>
    </justification>
  </clause>

  <clause id="11800">
    <literal><![CDATA[
      K(x,K(T(y,z),z * u)) = K(x,K(y,(u \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(7119(a,1),11792(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7119 11792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11801">
    <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(11796(a,1),4955(a,1,1))].">
      <j1 rule="para" parents="11796 4955"/>
    </justification>
  </clause>

  <clause id="11802">
    <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(11797(a,1),10846(a,1,3))].">
      <j1 rule="para" parents="11797 10846"/>
    </justification>
  </clause>

  <clause id="11803">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),11798(a,2,2,2))].">
      <j1 rule="para" parents="7 11798"/>
    </justification>
  </clause>

  <clause id="11804">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) = K(x,K(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7772,a,b,11799,a),flip(a)].">
      <j1 rule="hyper" parents="320 7772 11799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11805">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(7756,a,11803,a)].">
      <j1 rule="hyper" parents="7756 11803"/>
    </justification>
  </clause>

  <clause id="11806">
    <literal><![CDATA[
      K(x,K(y * z,L(u,z \ 1,z))) = K(u,K(x,T(z * y,z)))
    ]]></literal>
    <justification jstring="[hyper(10969,a,11804,a),flip(a)].">
      <j1 rule="hyper" parents="10969 11804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11807">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y * z)) = w
    ]]></literal>
    <justification jstring="[para(11804(a,2),7806(a,1))].">
      <j1 rule="para" parents="11804 7806"/>
    </justification>
  </clause>

  <clause id="11808">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8178,a(flip),b,11805,a)].">
      <j1 rule="hyper" parents="58 8178 11805"/>
    </justification>
  </clause>

  <clause id="11810">
    <literal><![CDATA[
      K(x,K(y,z)) * (z / u) = T(z,K(x,y)) / u
    ]]></literal>
    <justification jstring="[para(11808(a,1),9589(a,1,1))].">
      <j1 rule="para" parents="11808 9589"/>
    </justification>
  </clause>

  <clause id="11811">
    <literal><![CDATA[
      R(K(x,K(y,z)),z / u,u) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(11808(a,1),9851(a,1,1))].">
      <j1 rule="para" parents="11808 9851"/>
    </justification>
  </clause>

  <clause id="11812">
    <literal><![CDATA[
      R(K(x,K(y,z)),y / u,u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7772(a,1),11811(a,1,1))].">
      <j1 rule="para" parents="7772 11811"/>
    </justification>
  </clause>

  <clause id="11814">
    <literal><![CDATA[
      K(x,K(y,R(z,x / u,u))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9041,a(flip),b,11812,a)].">
      <j1 rule="hyper" parents="58 9041 11812"/>
    </justification>
  </clause>

  <clause id="11815">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(72(a,1),11814(a,1,2,2,2))].">
      <j1 rule="para" parents="72 11814"/>
    </justification>
  </clause>

  <clause id="11816">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,K(x,y)) / u) = z / u
    ]]></literal>
    <justification jstring="[hyper(7802,a,11810,a)].">
      <j1 rule="hyper" parents="7802 11810"/>
    </justification>
  </clause>

  <clause id="11817">
    <literal><![CDATA[
      T(x,K(y,z)) / (u \ x) = K(y,K(z,x)) * u
    ]]></literal>
    <justification jstring="[para(72(a,1),11810(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 11810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11819">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(x,K(z,y)) / u) = x / u
    ]]></literal>
    <justification jstring="[para(7728(a,1),11816(a,1,1))].">
      <j1 rule="para" parents="7728 11816"/>
    </justification>
  </clause>

  <clause id="11820">
    <literal><![CDATA[
      T(x,K(y,z)) / (u \ x) = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(7759(a,1),11817(a,2,1))].">
      <j1 rule="para" parents="7759 11817"/>
    </justification>
  </clause>

  <clause id="11821">
    <literal><![CDATA[
      K((T(x,y) / z) / (x / z),u) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(9591,a,11819,a)].">
      <j1 rule="hyper" parents="9591 11819"/>
    </justification>
  </clause>

  <clause id="11822">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ T(x,K(y,z)) = u \ x
    ]]></literal>
    <justification jstring="[hyper(188,a,11820,a)].">
      <j1 rule="hyper" parents="188 11820"/>
    </justification>
  </clause>

  <clause id="11823">
    <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(11422(a,1),11821(a,1,1,1,1))].">
      <j1 rule="para" parents="11422 11821"/>
    </justification>
  </clause>

  <clause id="11824">
    <literal><![CDATA[
      L(x \ y,x,K(y,K(z,u))) = x \ y
    ]]></literal>
    <justification jstring="[hyper(4814,a,11822,a)].">
      <j1 rule="hyper" parents="4814 11822"/>
    </justification>
  </clause>

  <clause id="11825">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,u \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(48,a,11824,a)].">
      <j1 rule="hyper" parents="48 11824"/>
    </justification>
  </clause>

  <clause id="11826">
    <literal><![CDATA[
      a(K(x * y,K(z,u)),x,y) = 1
    ]]></literal>
    <justification jstring="[para(4(a,1),11825(a,1,3))].">
      <j1 rule="para" parents="4 11825"/>
    </justification>
  </clause>

  <clause id="11827">
    <literal><![CDATA[
      a(K(K(x,y),z),u,u \ z) = 1
    ]]></literal>
    <justification jstring="[para(5584(a,2),11825(a,1,1))].">
      <j1 rule="para" parents="5584 11825"/>
    </justification>
  </clause>

  <clause id="11828">
    <literal><![CDATA[
      a(K(x,K(y,z * u)),z,u) = 1
    ]]></literal>
    <justification jstring="[para(7728(a,1),11826(a,1,1))].">
      <j1 rule="para" parents="7728 11826"/>
    </justification>
  </clause>

  <clause id="11829">
    <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(320,a,7780,a,b,11827,a),flip(a)].">
      <j1 rule="hyper" parents="320 7780 11827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11831">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (u \ K(w,z)) = K(w,z) * K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(11788(a,1),10163(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11788 10163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11832">
    <literal><![CDATA[
      K(x,K(y,T(z * u,z))) = K(x,K(y,(u \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(7133(a,1),11800(a,1,2))].">
      <j1 rule="para" parents="7133 11800"/>
    </justification>
  </clause>

  <clause id="11833">
    <literal><![CDATA[
      T(x,T(y,(z * (u \ 1)) \ 1)) = T(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(7678,a,11794,a),flip(a)].">
      <j1 rule="hyper" parents="7678 11794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11834">
    <literal><![CDATA[
      T(x,T(y,z * (u \ 1))) = T(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(8194,a,11833,a)].">
      <j1 rule="hyper" parents="8194 11833"/>
    </justification>
  </clause>

  <clause id="11835">
    <literal><![CDATA[
      T(x,T(y,z * (u \ 1))) = x * K(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(320,a,4714,a(flip),b,11834,a),flip(a)].">
      <j1 rule="hyper" parents="320 4714 11834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11836">
    <literal><![CDATA[
      K(x,T(y,z * (u \ 1))) = K(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(4796,a,11835,a)].">
      <j1 rule="hyper" parents="4796 11835"/>
    </justification>
  </clause>

  <clause id="11837">
    <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(11836(a,1),11320(a,1,1))].">
      <j1 rule="para" parents="11836 11320"/>
    </justification>
  </clause>

  <clause id="11838">
    <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),11806(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 11806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11839">
    <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(11815(a,1),11829(a,2,2))].">
      <j1 rule="para" parents="11815 11829"/>
    </justification>
  </clause>

  <clause id="11840">
    <literal><![CDATA[
      K(x,K(y,T(z * (u / z),z))) = K(x,K(u,L(y,z \ 1,z)))
    ]]></literal>
    <justification jstring="[hyper(7756,a,11838,a)].">
      <j1 rule="hyper" parents="7756 11838"/>
    </justification>
  </clause>

  <clause id="11841">
    <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,11832,a(flip),b,11840,a)].">
      <j1 rule="hyper" parents="58 11832 11840"/>
    </justification>
  </clause>

  <clause id="11842">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(z,K(x,L(u,y \ 1,y)))
    ]]></literal>
    <justification jstring="[para(11841(a,1),8798(a,2,2))].">
      <j1 rule="para" parents="11841 8798"/>
    </justification>
  </clause>

  <clause id="11843">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(x,K(z,L(u,y \ 1,y)))
    ]]></literal>
    <justification jstring="[para(7754(a,1),11842(a,2,2))].">
      <j1 rule="para" parents="7754 11842"/>
    </justification>
  </clause>

  <clause id="11844">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (u \ K(y,z)) = T(K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(320,a,7765,a(flip),b,11831,a),flip(a)].">
      <j1 rule="hyper" parents="320 7765 11831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11846">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (u \ K(x,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7759(a,2),11844(a,1,1,1))].">
      <j1 rule="para" parents="7759 11844"/>
    </justification>
  </clause>

  <clause id="11847">
    <literal><![CDATA[
      K(x,T(y,z)) / (u \ K(x,y)) = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(117,a,7131,a,b,11846,a)].">
      <j1 rule="hyper" parents="117 7131 11846"/>
    </justification>
  </clause>

  <clause id="11848">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) / u) = K(x,T(y,z)) / u
    ]]></literal>
    <justification jstring="[para(75(a,1),11847(a,1,2)),flip(a)].">
      <j1 rule="para" parents="75 11847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11849">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,T(y,z)) / u) = K(x,y) / u
    ]]></literal>
    <justification jstring="[hyper(7802,a,11848,a)].">
      <j1 rule="hyper" parents="7802 11848"/>
    </justification>
  </clause>

  <clause id="11850">
    <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(11849(a,1),6322(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11849 6322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11851">
    <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(7730(a,2),11850(a,2,2))].">
      <j1 rule="para" parents="7730 11850"/>
    </justification>
  </clause>

  <clause id="11852">
    <literal><![CDATA[
      K(x,(K(y,z) / u) / (u \ 1)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(29,a,10214,a,b,11851,a)].">
      <j1 rule="hyper" parents="29 10214 11851"/>
    </justification>
  </clause>

  <clause id="11854">
    <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(7759(a,2),11839(a,2,2))].">
      <j1 rule="para" parents="7759 11839"/>
    </justification>
  </clause>

  <clause id="11855">
    <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(5584(a,1),11854(a,1,1))].">
      <j1 rule="para" parents="5584 11854"/>
    </justification>
  </clause>

  <clause id="11856">
    <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(320,a,11487,a(flip),b,11855,a)].">
      <j1 rule="hyper" parents="320 11487 11855"/>
    </justification>
  </clause>

  <clause id="11857">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x)) * K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,11828,a(flip),b,11856,a),flip(a)].">
      <j1 rule="hyper" parents="320 11828 11856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11858">
    <literal><![CDATA[
      K(x,K(y,z) * K(z,R(y,u,u \ x))) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,11500,a(flip),b,11857,a)].">
      <j1 rule="hyper" parents="58 11500 11857"/>
    </justification>
  </clause>

  <clause id="11859">
    <literal><![CDATA[
      K(x * y,K(z,u) * K(u,R(z,x,y))) = 1
    ]]></literal>
    <justification jstring="[para(4(a,1),11858(a,1,2,2,2,3))].">
      <j1 rule="para" parents="4 11858"/>
    </justification>
  </clause>

  <clause id="11860">
    <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(7918(a,1),11837(a,1,1,2))].">
      <j1 rule="para" parents="7918 11837"/>
    </justification>
  </clause>

  <clause id="11861">
    <literal><![CDATA[
      K(x,((y \ (z * x)) * (z \ 1)) \ x) = R(K(x,y),z * x,z \ 1)
    ]]></literal>
    <justification jstring="[para(5152(a,1),11860(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5152 11860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11862">
    <literal><![CDATA[
      K(x,((y \ (z * x)) * (z \ 1)) \ x) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,9204,a(flip),b,11861,a),flip(a)].">
      <j1 rule="hyper" parents="320 9204 11861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11864">
    <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(505(a,1),11862(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="505 11862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11865">
    <literal><![CDATA[
      R(K(R(x,y,y \ 1),z),y,x) = K(x,(((z \ y) * x) * (y \ 1)) \ x)
    ]]></literal>
    <justification jstring="[hyper(9216,a,11864,a)].">
      <j1 rule="hyper" parents="9216 11864"/>
    </justification>
  </clause>

  <clause id="11866">
    <literal><![CDATA[
      K(x,(((y \ z) * x) * (z \ 1)) \ x) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(7074,a,11865,a)].">
      <j1 rule="hyper" parents="7074 11865"/>
    </justification>
  </clause>

  <clause id="11867">
    <literal><![CDATA[
      K(x,((y \ z) * (z \ 1)) \ (x \ x)) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11311,a(flip),b,11866,a)].">
      <j1 rule="hyper" parents="58 11311 11866"/>
    </justification>
  </clause>

  <clause id="11869">
    <literal><![CDATA[
      K(x,((y \ z) * (z \ 1)) \ 1) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[para(61(a,1),11867(a,1,2,2))].">
      <j1 rule="para" parents="61 11867"/>
    </justification>
  </clause>

  <clause id="11870">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6948,a(flip),b,11869,a)].">
      <j1 rule="hyper" parents="58 6948 11869"/>
    </justification>
  </clause>

  <clause id="11872">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) \ 1 = K(y,R(x,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(11870(a,2),4929(a,1,1))].">
      <j1 rule="para" parents="11870 4929"/>
    </justification>
  </clause>

  <clause id="11873">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,R(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(6908,a,11872,a)].">
      <j1 rule="hyper" parents="6908 11872"/>
    </justification>
  </clause>

  <clause id="11874">
    <literal><![CDATA[
      K(x,(y * z) * (z \ 1)) = R(K(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[para(261(a,2),11873(a,2,2)),flip(a)].">
      <j1 rule="para" parents="261 11873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11875">
    <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(5139(a,2),11823(a,1,1))].">
      <j1 rule="para" parents="5139 11823"/>
    </justification>
  </clause>

  <clause id="11876">
    <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(8019,a,11875,a)].">
      <j1 rule="hyper" parents="8019 11875"/>
    </justification>
  </clause>

  <clause id="11877">
    <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(11807,a,11876,a)].">
      <j1 rule="hyper" parents="11807 11876"/>
    </justification>
  </clause>

  <clause id="11878">
    <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),11877(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 11877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11879">
    <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(11878(a,1),7749(a,1))].">
      <j1 rule="para" parents="11878 7749"/>
    </justification>
  </clause>

  <clause id="11880">
    <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(3071(a,1),9262(a,2,1,2))].">
      <j1 rule="para" parents="3071 9262"/>
    </justification>
  </clause>

  <clause id="11881">
    <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(443(a,1),11880(a,1,1,2,2))].">
      <j1 rule="para" parents="443 11880"/>
    </justification>
  </clause>

  <clause id="11882">
    <literal><![CDATA[
      K(x * T((y * z) \ z,y),y \ 1) = K(x * R(y \ 1,y,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(2735(a,1),11881(a,1,1,2))].">
      <j1 rule="para" parents="2735 11881"/>
    </justification>
  </clause>

  <clause id="11883">
    <literal><![CDATA[
      K(x * R(y \ 1,y,z),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3954,a(flip),b,11882,a),flip(a)].">
      <j1 rule="hyper" parents="58 3954 11882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11884">
    <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(7730(a,1),11801(a,1,2,1,2))].">
      <j1 rule="para" parents="7730 11801"/>
    </justification>
  </clause>

  <clause id="11885">
    <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(8139(a,1),11884(a,1,2,1,2))].">
      <j1 rule="para" parents="8139 11884"/>
    </justification>
  </clause>

  <clause id="11886">
    <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(7763(a,1),11885(a,1,2,1,2))].">
      <j1 rule="para" parents="7763 11885"/>
    </justification>
  </clause>

  <clause id="11887">
    <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(7941(a,1),11886(a,1,2,1,2))].">
      <j1 rule="para" parents="7941 11886"/>
    </justification>
  </clause>

  <clause id="11888">
    <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(4692(a,2),11887(a,1,2,1))].">
      <j1 rule="para" parents="4692 11887"/>
    </justification>
  </clause>

  <clause id="11889">
    <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(5635,a,11888,a)].">
      <j1 rule="hyper" parents="5635 11888"/>
    </justification>
  </clause>

  <clause id="11890">
    <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(8169(a,1),11889(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8169 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11891">
    <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(1436(a,1),11890(a,2,2))].">
      <j1 rule="para" parents="1436 11890"/>
    </justification>
  </clause>

  <clause id="11892">
    <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(320,a,7801,a(flip),b,11891,a),flip(a)].">
      <j1 rule="hyper" parents="320 7801 11891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11893">
    <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),6689(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 6689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11894">
    <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(320,a,7138,a(flip),b,11893,a),flip(a)].">
      <j1 rule="hyper" parents="320 7138 11893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11896">
    <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(320,a,9177,a(flip),b,11894,a),flip(a)].">
      <j1 rule="hyper" parents="320 9177 11894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11897">
    <literal><![CDATA[
      K(x,T((R(x,y,z) \ u) \ w,R(x,y,z) * (x \ w))) = K(x,(R(x,y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(7679,a,11896,a)].">
      <j1 rule="hyper" parents="7679 11896"/>
    </justification>
  </clause>

  <clause id="11898">
    <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(58,a,9197,a(flip),b,11897,a)].">
      <j1 rule="hyper" parents="58 9197 11897"/>
    </justification>
  </clause>

  <clause id="11899">
    <literal><![CDATA[
      K(x,T((R(x,y,z) \ u) \ w,w)) = K(x,(R(x,y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(9182,a,11898,a)].">
      <j1 rule="hyper" parents="9182 11898"/>
    </justification>
  </clause>

  <clause id="11900">
    <literal><![CDATA[
      K(x,(R(x,y,z) * u) / w) = K(x,u / (R(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(8262,a,11899,a),flip(a)].">
      <j1 rule="hyper" parents="8262 11899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11902">
    <literal><![CDATA[
      K(x,R(x,y,z) / (u / w)) = K(x,w / (R(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(10014,a,11900,a)].">
      <j1 rule="hyper" parents="10014 11900"/>
    </justification>
  </clause>

  <clause id="11903">
    <literal><![CDATA[
      K(x,y / (R(x,z,u) \ w)) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(6479,a,11902,a),flip(a)].">
      <j1 rule="hyper" parents="6479 11902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11904">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9031,a,b,11903,a)].">
      <j1 rule="hyper" parents="58 9031 11903"/>
    </justification>
  </clause>

  <clause id="11905">
    <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,11430,a,b,11904,a)].">
      <j1 rule="hyper" parents="58 11430 11904"/>
    </justification>
  </clause>

  <clause id="11906">
    <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),11905(a,2,2,1))].">
      <j1 rule="para" parents="15 11905"/>
    </justification>
  </clause>

  <clause id="11907">
    <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,9227,a(flip),b,11906,a),flip(a)].">
      <j1 rule="hyper" parents="58 9227 11906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11909">
    <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(5092(a,1),9725(a,1,1,1))].">
      <j1 rule="para" parents="5092 9725"/>
    </justification>
  </clause>

  <clause id="11910">
    <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(7126(a,1),10905(a,1,2,1,1))].">
      <j1 rule="para" parents="7126 10905"/>
    </justification>
  </clause>

  <clause id="11911">
    <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(11046(a,1),11909(a,1,1))].">
      <j1 rule="para" parents="11046 11909"/>
    </justification>
  </clause>

  <clause id="11912">
    <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,6111,a(flip),b,11911,a)].">
      <j1 rule="hyper" parents="58 6111 11911"/>
    </justification>
  </clause>

  <clause id="11914">
    <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,11517,a(flip),b,11912,a)].">
      <j1 rule="hyper" parents="58 11517 11912"/>
    </justification>
  </clause>

  <clause id="11915">
    <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,11496,a(flip),b,11914,a),flip(a)].">
      <j1 rule="hyper" parents="58 11496 11914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11916">
    <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(320,a,11500,a(flip),b,11915,a),flip(a)].">
      <j1 rule="hyper" parents="320 11500 11915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11917">
    <literal><![CDATA[
      K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,11859,a(flip),b,11916,a),flip(a)].">
      <j1 rule="hyper" parents="320 11859 11916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11919">
    <literal><![CDATA[
      K(a(K(x,y),z,u),K(x,y) * (z * u)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,6111,a(flip),b,11917,a)].">
      <j1 rule="hyper" parents="58 6111 11917"/>
    </justification>
  </clause>

  <clause id="11920">
    <literal><![CDATA[
      1 * (((K(x,y) * z) * u) / (K(x,y) * (z * u))) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(11919(a,1),4960(a,1,1))].">
      <j1 rule="para" parents="11919 4960"/>
    </justification>
  </clause>

  <clause id="11921">
    <literal><![CDATA[
      1 * (K(x,y) * R(K(y,x),z,u)) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(11047(a,1),11920(a,1,2))].">
      <j1 rule="para" parents="11047 11920"/>
    </justification>
  </clause>

  <clause id="11922">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(120,a,11921,a)].">
      <j1 rule="hyper" parents="120 11921"/>
    </justification>
  </clause>

  <clause id="11923">
    <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(7771(a,1),11921(a,1,2,1))].">
      <j1 rule="para" parents="7771 11921"/>
    </justification>
  </clause>

  <clause id="11924">
    <literal><![CDATA[
      K(x,y) * a(K(x,y),z,u) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(5109,a,11922,a)].">
      <j1 rule="hyper" parents="5109 11922"/>
    </justification>
  </clause>

  <clause id="11925">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(y,x) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(2001,a,11922,a)].">
      <j1 rule="hyper" parents="2001 11922"/>
    </justification>
  </clause>

  <clause id="11926">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,R(x,z,u) \ 1) = a(K(y,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(6894(a,1),11922(a,1,2))].">
      <j1 rule="para" parents="6894 11922"/>
    </justification>
  </clause>

  <clause id="11927">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z * x,u)
    ]]></literal>
    <justification jstring="[para(9210(a,1),11922(a,1,2))].">
      <j1 rule="para" parents="9210 11922"/>
    </justification>
  </clause>

  <clause id="11928">
    <literal><![CDATA[
      K(x,y) * (R(K(y,x),z,u) * w) = a(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(11922(a,1),9874(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11922 9874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11929">
    <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(11922(a,1),11503(a,2,2))].">
      <j1 rule="para" parents="11922 11503"/>
    </justification>
  </clause>

  <clause id="11930">
    <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(11922(a,1),11517(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11922 11517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11932">
    <literal><![CDATA[
      (x * a(K(y,z),u,w)) * (K(y,z) * R(K(z,y),u,w)) = x
    ]]></literal>
    <justification jstring="[para(11922(a,1),11773(a,1,1,2))].">
      <j1 rule="para" parents="11922 11773"/>
    </justification>
  </clause>

  <clause id="11933">
    <literal><![CDATA[
      a(K(x,y),K(z,y),u) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,9993,a(flip),b,11924,a),flip(a)].">
      <j1 rule="hyper" parents="115 9993 11924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11934">
    <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(11924(a,1),10161(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11924 10161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11935">
    <literal><![CDATA[
      L(x,K(y,z),K(u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,11933,a)].">
      <j1 rule="hyper" parents="47 11933"/>
    </justification>
  </clause>

  <clause id="11936">
    <literal><![CDATA[
      (K(x,y) * K(z,y)) \ u = K(y,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5732,a(flip),b,11935,a)].">
      <j1 rule="hyper" parents="58 5732 11935"/>
    </justification>
  </clause>

  <clause id="11937">
    <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(11925(a,1),9740(a,2,2))].">
      <j1 rule="para" parents="11925 9740"/>
    </justification>
  </clause>

  <clause id="11938">
    <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,8983,a,b,11936,a)].">
      <j1 rule="hyper" parents="58 8983 11936"/>
    </justification>
  </clause>

  <clause id="11939">
    <literal><![CDATA[
      K(x,y) * (a(K(x,y),z,u) * w) = R(K(x,y),z,u) * w
    ]]></literal>
    <justification jstring="[hyper(5109,a,11928,a)].">
      <j1 rule="hyper" parents="5109 11928"/>
    </justification>
  </clause>

  <clause id="11942">
    <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(58,a,11478,a(flip),b,11930,a)].">
      <j1 rule="hyper" parents="58 11478 11930"/>
    </justification>
  </clause>

  <clause id="11943">
    <literal><![CDATA[
      (x * a(K(y,z),u,w)) * a(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[para(11922(a,1),11932(a,1,2))].">
      <j1 rule="para" parents="11922 11932"/>
    </justification>
  </clause>

  <clause id="11945">
    <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,11943,a)].">
      <j1 rule="hyper" parents="116 106 11943"/>
    </justification>
  </clause>

  <clause id="11946">
    <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,9091,a(flip),b,11939,a)].">
      <j1 rule="hyper" parents="58 9091 11939"/>
    </justification>
  </clause>

  <clause id="11947">
    <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(11942(a,1),11715(a,1,1,1))].">
      <j1 rule="para" parents="11942 11715"/>
    </justification>
  </clause>

  <clause id="11948">
    <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(9041(a,1),11923(a,1,2,2))].">
      <j1 rule="para" parents="9041 11923"/>
    </justification>
  </clause>

  <clause id="11949">
    <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),11938(a,2,2))].">
      <j1 rule="para" parents="3 11938"/>
    </justification>
  </clause>

  <clause id="11950">
    <literal><![CDATA[
      K(K(x,y) * K(x,z),K(z,x) * K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,11949,a)].">
      <j1 rule="hyper" parents="50 11949"/>
    </justification>
  </clause>

  <clause id="11951">
    <literal><![CDATA[
      K(K(x,y) * K(x,z),(K(x,y) * K(x,z)) \ 1) = 1
    ]]></literal>
    <justification jstring="[para(8982(a,2),11950(a,1,2))].">
      <j1 rule="para" parents="8982 11950"/>
    </justification>
  </clause>

  <clause id="11952">
    <literal><![CDATA[
      K((K(x,y) * K(x,z)) \ 1,K(x,y) * K(x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,11951,a,b,4933,a),flip(a)].">
      <j1 rule="hyper" parents="115 11951 4933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11953">
    <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(11952(a,1),3028(a,1,1,2))].">
      <j1 rule="para" parents="11952 3028"/>
    </justification>
  </clause>

  <clause id="11954">
    <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(11508(a,1),11948(a,1,2))].">
      <j1 rule="para" parents="11508 11948"/>
    </justification>
  </clause>

  <clause id="11955">
    <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(9137(a,1),11946(a,1,2))].">
      <j1 rule="para" parents="9137 11946"/>
    </justification>
  </clause>

  <clause id="11956">
    <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(5002,a,11955,a)].">
      <j1 rule="hyper" parents="5002 11955"/>
    </justification>
  </clause>

  <clause id="11957">
    <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(320,a,9734,a,b,11956,a),flip(a)].">
      <j1 rule="hyper" parents="320 9734 11956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11958">
    <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(320,a,11937,a(flip),b,11934,a),flip(a)].">
      <j1 rule="hyper" parents="320 11937 11934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11959">
    <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(383(a,1),11947(a,1,1)),flip(a)].">
      <j1 rule="para" parents="383 11947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11960">
    <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(320,a,9143,a(flip),b,11959,a),flip(a)].">
      <j1 rule="hyper" parents="320 9143 11959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11961">
    <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(7730(a,1),11960(a,1,2,1,1))].">
      <j1 rule="para" parents="7730 11960"/>
    </justification>
  </clause>

  <clause id="11962">
    <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(9040(a,1),11961(a,1,2,1))].">
      <j1 rule="para" parents="9040 11961"/>
    </justification>
  </clause>

  <clause id="11963">
    <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(4729(a,2),11962(a,1,2))].">
      <j1 rule="para" parents="4729 11962"/>
    </justification>
  </clause>

  <clause id="11964">
    <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,9049,a,b,11963,a)].">
      <j1 rule="hyper" parents="58 9049 11963"/>
    </justification>
  </clause>

  <clause id="11965">
    <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(7761(a,1),11964(a,1,1))].">
      <j1 rule="para" parents="7761 11964"/>
    </justification>
  </clause>

  <clause id="11966">
    <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(11485,a,11965,a)].">
      <j1 rule="hyper" parents="11485 11965"/>
    </justification>
  </clause>

  <clause id="11967">
    <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,11929,a(flip),b,11966,a),flip(a)].">
      <j1 rule="hyper" parents="58 11929 11966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11968">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) = K(x,a(K(w,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(29,a,4714,a(flip),b,11967,a),flip(a)].">
      <j1 rule="hyper" parents="29 4714 11967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11969">
    <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,11942,a,b,11968,a)].">
      <j1 rule="hyper" parents="58 11942 11968"/>
    </justification>
  </clause>

  <clause id="11970">
    <literal><![CDATA[
      1 * K(x,a(K(y,z),u,w)) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[para(11969(a,1),11954(a,1,2))].">
      <j1 rule="para" parents="11969 11954"/>
    </justification>
  </clause>

  <clause id="11971">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(y,a(K(z,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(120,a,11970,a),flip(a)].">
      <j1 rule="hyper" parents="120 11970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11972">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,11968,a,b,11971,a),flip(a)].">
      <j1 rule="hyper" parents="320 11968 11971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11973">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(x,a(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(7754(a,1),11971(a,1,1))].">
      <j1 rule="para" parents="7754 11971"/>
    </justification>
  </clause>

  <clause id="11974">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(7754(a,1),11972(a,1,1))].">
      <j1 rule="para" parents="7754 11972"/>
    </justification>
  </clause>

  <clause id="11975">
    <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),11953(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3 11953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11976">
    <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(8981(a,1),11975(a,2,3))].">
      <j1 rule="para" parents="8981 11975"/>
    </justification>
  </clause>

  <clause id="11977">
    <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(8981(a,1),11976(a,1,1))].">
      <j1 rule="para" parents="8981 11976"/>
    </justification>
  </clause>

  <clause id="11978">
    <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,5757,a(flip),b,5345,a),flip(a)].">
      <j1 rule="hyper" parents="58 5757 5345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11980">
    <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,5958,a(flip),b,11978,a)].">
      <j1 rule="hyper" parents="58 5958 11978"/>
    </justification>
  </clause>

  <clause id="11981">
    <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,10017,a(flip),b,11980,a)].">
      <j1 rule="hyper" parents="58 10017 11980"/>
    </justification>
  </clause>

  <clause id="11982">
    <literal><![CDATA[
      K((x \ 1) \ (y / (z * y)),z \ 1) = K(x * (y / (z * y)),z \ 1)
    ]]></literal>
    <justification jstring="[para(6(a,1),11981(a,1,2,1))].">
      <j1 rule="para" parents="6 11981"/>
    </justification>
  </clause>

  <clause id="11983">
    <literal><![CDATA[
      K((x \ 1) \ ((y * z) \ z),y \ 1) = K(x * (z / (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,8633,a(flip),b,11982,a)].">
      <j1 rule="hyper" parents="58 8633 11982"/>
    </justification>
  </clause>

  <clause id="11984">
    <literal><![CDATA[
      K((x \ 1) \ ((y * z) \ z),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,7549,a(flip),b,11983,a),flip(a)].">
      <j1 rule="hyper" parents="320 7549 11983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11985">
    <literal><![CDATA[
      K((x \ 1) \ (y \ 1),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,10543,a(flip),b,11984,a)].">
      <j1 rule="hyper" parents="58 10543 11984"/>
    </justification>
  </clause>

  <clause id="11986">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y \ 1) = K(x * (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(7410,a,11985,a),flip(a)].">
      <j1 rule="hyper" parents="7410 11985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11988">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,6514,a(flip),b,11986,a),flip(a)].">
      <j1 rule="hyper" parents="320 6514 11986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11989">
    <literal><![CDATA[
      K(x * R(y \ 1,y,z),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,11883,a,b,11988,a)].">
      <j1 rule="hyper" parents="58 11883 11988"/>
    </justification>
  </clause>

  <clause id="11991">
    <literal><![CDATA[
      T(K(x \ y,x \ 1) / x,y) = R(1 / x,y,z / (x * z))
    ]]></literal>
    <justification jstring="[para(11989(a,1),9888(a,1,1,1))].">
      <j1 rule="para" parents="11989 9888"/>
    </justification>
  </clause>

  <clause id="11992">
    <literal><![CDATA[
      R(1 / x,y,z / (x * z)) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,6515,a(flip),b,11991,a),flip(a)].">
      <j1 rule="hyper" parents="58 6515 11991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11994">
    <literal><![CDATA[
      R(1 / (x / y),z,(x / y) \ 1) = R(1 / (x / y),z,y / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),11992(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="7 11992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11995">
    <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(11994(a,1),9531(a,2,2))].">
      <j1 rule="para" parents="11994 9531"/>
    </justification>
  </clause>

  <clause id="11996">
    <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(320,a,1207,a(flip),b,11995,a),flip(a)].">
      <j1 rule="hyper" parents="320 1207 11995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11997">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x * R(x \ y,z,y / x)) / y
    ]]></literal>
    <justification jstring="[hyper(320,a,1695,a(flip),b,11996,a),flip(a)].">
      <j1 rule="hyper" parents="320 1695 11996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11998">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x * R(x \ y,z,x \ y)) / y
    ]]></literal>
    <justification jstring="[para(9585(a,1),11997(a,2,1,2))].">
      <j1 rule="para" parents="9585 11997"/>
    </justification>
  </clause>

  <clause id="11999">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,9534,a(flip),b,11998,a),flip(a)].">
      <j1 rule="hyper" parents="320 9534 11998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12000">
    <literal><![CDATA[
      T(a(1 / (x / y),z,(x / y) \ 1),u) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[para(4008(a,1),11999(a,1,1))].">
      <j1 rule="para" parents="4008 11999"/>
    </justification>
  </clause>

  <clause id="12001">
    <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(6763(a,1),6372(a,2,1))].">
      <j1 rule="para" parents="6763 6372"/>
    </justification>
  </clause>

  <clause id="12002">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ T(1 / y,(x * y) / x) = (1 / y) * (1 / (1 / ((x * y) / x)))
    ]]></literal>
    <justification jstring="[para(2940(a,1),12001(a,1,2))].">
      <j1 rule="para" parents="2940 12001"/>
    </justification>
  </clause>

  <clause id="12003">
    <literal><![CDATA[
      (1 / x) * (1 / (1 / ((y * x) / y))) = (1 / ((y * x) / y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(5168(a,1),12002(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5168 12002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12004">
    <literal><![CDATA[
      (1 / x) * (1 / (1 / ((y * x) / y))) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,11429,a(flip),b,12003,a),flip(a)].">
      <j1 rule="hyper" parents="320 11429 12003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12006">
    <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(5006(a,1),5321(a,1,1))].">
      <j1 rule="para" parents="5006 5321"/>
    </justification>
  </clause>

  <clause id="12007">
    <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(5006(a,1),12006(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5006 12006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12008">
    <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(4929(a,1),12007(a,2,2,1))].">
      <j1 rule="para" parents="4929 12007"/>
    </justification>
  </clause>

  <clause id="12009">
    <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(6894(a,1),12008(a,2,2))].">
      <j1 rule="para" parents="6894 12008"/>
    </justification>
  </clause>

  <clause id="12010">
    <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(4705(a,1),12009(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4705 12009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12011">
    <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(6894(a,1),12010(a,2,1,2))].">
      <j1 rule="para" parents="6894 12010"/>
    </justification>
  </clause>

  <clause id="12012">
    <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,11926,a(flip),b,12011,a),flip(a)].">
      <j1 rule="hyper" parents="58 11926 12011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12013">
    <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),2237(a,1,2,1))].">
      <j1 rule="para" parents="7 2237"/>
    </justification>
  </clause>

  <clause id="12014">
    <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),12013(a,1,2))].">
      <j1 rule="para" parents="69 12013"/>
    </justification>
  </clause>

  <clause id="12016">
    <literal><![CDATA[
      (x / (x * L(x \ 1,y,z))) / x = 1 / (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(343,a,12014,a),flip(a)].">
      <j1 rule="hyper" parents="343 12014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12019">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) / x = 1 / (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(3211(a,1),12016(a,1,1))].">
      <j1 rule="para" parents="3211 12016"/>
    </justification>
  </clause>

  <clause id="12020">
    <literal><![CDATA[
      1 / (x * L(x \ 1,y,z)) = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,6026,a(flip),b,12019,a),flip(a)].">
      <j1 rule="hyper" parents="58 6026 12019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12021">
    <literal><![CDATA[
      1 / (x * L(x \ 1,y,z)) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3559,a,b,12020,a),flip(a)].">
      <j1 rule="hyper" parents="320 3559 12020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12022">
    <literal><![CDATA[
      1 / ((x \ 1) * L((x \ 1) \ 1,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(320,a,3561,a(flip),b,12021,a),flip(a)].">
      <j1 rule="hyper" parents="320 3561 12021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12023">
    <literal><![CDATA[
      (1 / (x * L(x \ 1,y,z))) \ (L(x \ 1,y,z) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(12021(a,2),6025(a,1,1))].">
      <j1 rule="para" parents="12021 6025"/>
    </justification>
  </clause>

  <clause id="12024">
    <literal><![CDATA[
      1 / (x \ L(x,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(1185(a,1),12022(a,1,2))].">
      <j1 rule="para" parents="1185 12022"/>
    </justification>
  </clause>

  <clause id="12025">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ 1 = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(188,a,12024,a)].">
      <j1 rule="hyper" parents="188 12024"/>
    </justification>
  </clause>

  <clause id="12026">
    <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(12024(a,1),4702(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12024 4702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12027">
    <literal><![CDATA[
      1 / (L(x,y,z) \ x) = (L(x,y,z) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,3555,a,b,12025,a)].">
      <j1 rule="hyper" parents="320 3555 12025"/>
    </justification>
  </clause>

  <clause id="12028">
    <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(1920(a,1),12025(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1920 12025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12029">
    <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(12028(a,1),3491(a,1,1))].">
      <j1 rule="para" parents="12028 3491"/>
    </justification>
  </clause>

  <clause id="12030">
    <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(320,a,7772,a,b,12026,a),flip(a)].">
      <j1 rule="hyper" parents="320 7772 12026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12031">
    <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(12026(a,2),7806(a,1))].">
      <j1 rule="para" parents="12026 7806"/>
    </justification>
  </clause>

  <clause id="12032">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) / ((y \ 1) \ 1) = 1 / (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(12023(a,1),11559(a,1,2))].">
      <j1 rule="para" parents="12023 11559"/>
    </justification>
  </clause>

  <clause id="12033">
    <literal><![CDATA[
      1 / (x * ((y * x) \ y)) = x \ (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6030,a(flip),b,12032,a),flip(a)].">
      <j1 rule="hyper" parents="58 6030 12032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12034">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) / y = 1 / (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5894,a(flip),b,12032,a)].">
      <j1 rule="hyper" parents="58 5894 12032"/>
    </justification>
  </clause>

  <clause id="12035">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ 1 = x \ (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(10140,a,12033,a)].">
      <j1 rule="hyper" parents="10140 12033"/>
    </justification>
  </clause>

  <clause id="12036">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) / y = (y * ((x * y) \ x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,10139,a(flip),b,12034,a),flip(a)].">
      <j1 rule="hyper" parents="320 10139 12034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12037">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) \ (1 / ((y * x) \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(188,a,12036,a)].">
      <j1 rule="hyper" parents="188 12036"/>
    </justification>
  </clause>

  <clause id="12038">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) * T(x,z) = T(x,z) / (x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[para(12037(a,1),4597(a,1,2,1))].">
      <j1 rule="para" parents="12037 4597"/>
    </justification>
  </clause>

  <clause id="12039">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) * T(x,z) = (x * ((y * x) \ y)) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,10139,a(flip),b,12038,a),flip(a)].">
      <j1 rule="hyper" parents="320 10139 12038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12040">
    <literal><![CDATA[
      (x \ (1 / ((y * x) \ y))) * T(x,z) = (x * ((y * x) \ y)) \ T(x,z)
    ]]></literal>
    <justification jstring="[para(12035(a,1),12039(a,1,1))].">
      <j1 rule="para" parents="12035 12039"/>
    </justification>
  </clause>

  <clause id="12041">
    <literal><![CDATA[
      T((1 / ((x * y) \ x)) * K(y,z),y) = (y * ((x * y) \ x)) \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9739,a,b,12040,a)].">
      <j1 rule="hyper" parents="58 9739 12040"/>
    </justification>
  </clause>

  <clause id="12042">
    <literal><![CDATA[
      T(T(1 / ((x * y) \ x),z),y) = (y * ((x * y) \ x)) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(6236(a,1),12041(a,1,1))].">
      <j1 rule="para" parents="6236 12041"/>
    </justification>
  </clause>

  <clause id="12043">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ T(x,z) = T(1 / ((y * x) \ y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,866,a(flip),b,12042,a),flip(a)].">
      <j1 rule="hyper" parents="58 866 12042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12044">
    <literal><![CDATA[
      1 / ((x * T(y,z)) \ x) = T(1 / ((x * y) \ x),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10146,a(flip),b,12043,a)].">
      <j1 rule="hyper" parents="58 10146 12043"/>
    </justification>
  </clause>

  <clause id="12045">
    <literal><![CDATA[
      T(1 / ((x * y) \ x),z) \ 1 = (x * T(y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(188,a,12044,a)].">
      <j1 rule="hyper" parents="188 12044"/>
    </justification>
  </clause>

  <clause id="12046">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,z) = ((x * T(y,z)) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(12045(a,1),2153(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12045 2153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12047">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) \ 1,u) \ x) = K(x,1 \ (((y * T(z,u)) \ y) * x))
    ]]></literal>
    <justification jstring="[para(12046(a,2),6560(a,1,2,1))].">
      <j1 rule="para" parents="12046 6560"/>
    </justification>
  </clause>

  <clause id="12048">
    <literal><![CDATA[
      K(x,T((((y * z) \ y) \ 1) \ x,u)) = K(x,1 \ (((y * T(z,u)) \ y) * x))
    ]]></literal>
    <justification jstring="[hyper(8706,a,12047,a)].">
      <j1 rule="hyper" parents="8706 12047"/>
    </justification>
  </clause>

  <clause id="12049">
    <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(7131(a,2),8811(a,2,2))].">
      <j1 rule="para" parents="7131 8811"/>
    </justification>
  </clause>

  <clause id="12050">
    <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(8732(a,1),9938(a,1,1,2))].">
      <j1 rule="para" parents="8732 9938"/>
    </justification>
  </clause>

  <clause id="12052">
    <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(8733(a,1),12050(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8733 12050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12053">
    <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,5919,a(flip),b,12052,a),flip(a)].">
      <j1 rule="hyper" parents="58 5919 12052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12055">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = (a(x,y,x) * K(x,w)) \ T(x,w)
    ]]></literal>
    <justification jstring="[para(10510(a,1),12053(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10510 12053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12057">
    <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(7644(a,1),12049(a,2,2))].">
      <j1 rule="para" parents="7644 12049"/>
    </justification>
  </clause>

  <clause id="12058">
    <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(320,a,7203,a(flip),b,12057,a),flip(a)].">
      <j1 rule="hyper" parents="320 7203 12057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12060">
    <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(320,a,7439,a(flip),b,12058,a),flip(a)].">
      <j1 rule="hyper" parents="320 7439 12058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12061">
    <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(320,a,7274,a(flip),b,12060,a),flip(a)].">
      <j1 rule="hyper" parents="320 7274 12060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12062">
    <literal><![CDATA[
      (x * K(y,z * x)) / K(y,z) = K(y,z * x) * (K(z,y) * x)
    ]]></literal>
    <justification jstring="[para(7853(a,1),12061(a,1,2))].">
      <j1 rule="para" parents="7853 12061"/>
    </justification>
  </clause>

  <clause id="12063">
    <literal><![CDATA[
      (x * K(y,z * x)) * K(z,y) = K(y,z * x) * (K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(6317,a,12062,a)].">
      <j1 rule="hyper" parents="6317 12062"/>
    </justification>
  </clause>

  <clause id="12065">
    <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(12063(a,1),8974(a,1))].">
      <j1 rule="para" parents="12063 8974"/>
    </justification>
  </clause>

  <clause id="12066">
    <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(145(a,1),1926(a,1,1))].">
      <j1 rule="para" parents="145 1926"/>
    </justification>
  </clause>

  <clause id="12067">
    <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,145,a(flip),b,12066,a),flip(a)].">
      <j1 rule="hyper" parents="58 145 12066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12070">
    <literal><![CDATA[
      K(x * (y \ T(y * z,y)),K(y * z,L(y,z,x))) / ((x * z) / (x * (y \ T(y * z,y)))) = 1 / ((x * (y \ T(y * z,y))) \ (x * z))
    ]]></literal>
    <justification jstring="[para(10815(a,1),6672(a,1,1))].">
      <j1 rule="para" parents="10815 6672"/>
    </justification>
  </clause>

  <clause id="12071">
    <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(6414(a,1),9997(a,1,2,1))].">
      <j1 rule="para" parents="6414 9997"/>
    </justification>
  </clause>

  <clause id="12072">
    <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(3893(a,1),12071(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3893 12071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12073">
    <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(8085(a,1),12072(a,2,2))].">
      <j1 rule="para" parents="8085 12072"/>
    </justification>
  </clause>

  <clause id="12074">
    <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),12073(a,2,2,1))].">
      <j1 rule="para" parents="4 12073"/>
    </justification>
  </clause>

  <clause id="12075">
    <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(11648(a,1),12074(a,1,1,2))].">
      <j1 rule="para" parents="11648 12074"/>
    </justification>
  </clause>

  <clause id="12076">
    <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(8690(a,1),12075(a,1,1))].">
      <j1 rule="para" parents="8690 12075"/>
    </justification>
  </clause>

  <clause id="12078">
    <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(11648(a,1),12076(a,1,2,1))].">
      <j1 rule="para" parents="11648 12076"/>
    </justification>
  </clause>

  <clause id="12079">
    <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(5280(a,1),12078(a,1,2))].">
      <j1 rule="para" parents="5280 12078"/>
    </justification>
  </clause>

  <clause id="12080">
    <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(7520(a,1),12079(a,1,2))].">
      <j1 rule="para" parents="7520 12079"/>
    </justification>
  </clause>

  <clause id="12081">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x),y) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6727(a,1),12080(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6727 12080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12082">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x) * K(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7612,a,b,12081,a),flip(a)].">
      <j1 rule="hyper" parents="320 7612 12081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12084">
    <literal><![CDATA[
      K(x * (y \ T(y * z,y)),K(y * z,y)) / ((x * z) / (x * (y \ T(y * z,y)))) = 1 / ((x * (y \ T(y * z,y))) \ (x * z))
    ]]></literal>
    <justification jstring="[para(8993(a,1),12070(a,1,1,2))].">
      <j1 rule="para" parents="8993 12070"/>
    </justification>
  </clause>

  <clause id="12085">
    <literal><![CDATA[
      K(x * y,K(z * (x \ T(x * y,x)),x)) / ((z * y) / (z * (x \ T(x * y,x)))) = 1 / ((z * (x \ T(x * y,x))) \ (z * y))
    ]]></literal>
    <justification jstring="[para(7754(a,1),12084(a,1,1))].">
      <j1 rule="para" parents="7754 12084"/>
    </justification>
  </clause>

  <clause id="12087">
    <literal><![CDATA[
      K(x * y,K(z * (x \ (x * y)),x)) / ((z * y) / (z * (x \ T(x * y,x)))) = 1 / ((z * (x \ T(x * y,x))) \ (z * y))
    ]]></literal>
    <justification jstring="[para(7550(a,1),12085(a,1,1,2))].">
      <j1 rule="para" parents="7550 12085"/>
    </justification>
  </clause>

  <clause id="12088">
    <literal><![CDATA[
      K(x * y,K(z * y,x)) / ((z * y) / (z * (x \ T(x * y,x)))) = 1 / ((z * (x \ T(x * y,x))) \ (z * y))
    ]]></literal>
    <justification jstring="[para(4(a,1),12087(a,1,1,2,1,2))].">
      <j1 rule="para" parents="4 12087"/>
    </justification>
  </clause>

  <clause id="12090">
    <literal><![CDATA[
      K(x,K(x * y,z * y)) / ((z * y) / (z * (x \ T(x * y,x)))) = 1 / ((z * (x \ T(x * y,x))) \ (z * y))
    ]]></literal>
    <justification jstring="[para(7759(a,1),12088(a,1,1))].">
      <j1 rule="para" parents="7759 12088"/>
    </justification>
  </clause>

  <clause id="12091">
    <literal><![CDATA[
      K(x,K(y,z * y)) / ((z * y) / (z * (x \ T(x * y,x)))) = 1 / ((z * (x \ T(x * y,x))) \ (z * y))
    ]]></literal>
    <justification jstring="[para(7845(a,1),12090(a,1,1))].">
      <j1 rule="para" parents="7845 12090"/>
    </justification>
  </clause>

  <clause id="12092">
    <literal><![CDATA[
      K(x,K(y,z)) / ((y * z) / (y * (x \ T(x * z,x)))) = 1 / ((y * (x \ T(x * z,x))) \ (y * z))
    ]]></literal>
    <justification jstring="[para(7842(a,1),12091(a,1,1))].">
      <j1 rule="para" parents="7842 12091"/>
    </justification>
  </clause>

  <clause id="12093">
    <literal><![CDATA[
      K(x,K(y,z)) / ((x * z) / (x * (y \ T(y * z,y)))) = 1 / ((x * (y \ T(y * z,y))) \ (x * z))
    ]]></literal>
    <justification jstring="[para(7754(a,1),12092(a,1,1))].">
      <j1 rule="para" parents="7754 12092"/>
    </justification>
  </clause>

  <clause id="12094">
    <literal><![CDATA[
      K(x,K(y,z)) / L(K(y,T(z * y,x)),z,x) = 1 / ((x * (y \ T(y * z,y))) \ (x * z))
    ]]></literal>
    <justification jstring="[para(9727(a,1),12093(a,1,2))].">
      <j1 rule="para" parents="9727 12093"/>
    </justification>
  </clause>

  <clause id="12095">
    <literal><![CDATA[
      K(x,K(y,z)) * L(K(T(z * y,x),y),z,x) = 1 / ((x * (y \ T(y * z,y))) \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(6642,a,12094,a)].">
      <j1 rule="hyper" parents="6642 12094"/>
    </justification>
  </clause>

  <clause id="12096">
    <literal><![CDATA[
      K(x,K(y,z)) * L(K(z * y,T(y,x)),z,x) = 1 / ((x * (y \ T(y * z,y))) \ (x * z))
    ]]></literal>
    <justification jstring="[para(7133(a,1),12095(a,1,2,1))].">
      <j1 rule="para" parents="7133 12095"/>
    </justification>
  </clause>

  <clause id="12097">
    <literal><![CDATA[
      L(K(x * y,T(y,z)),x,z) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(29,a,10519,a(flip),b,12096,a),flip(a)].">
      <j1 rule="hyper" parents="29 10519 12096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12098">
    <literal><![CDATA[
      K((x / (x * y)) \ z,z) = K(z * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(10038,a,12097,a)].">
      <j1 rule="hyper" parents="10038 12097"/>
    </justification>
  </clause>

  <clause id="12100">
    <literal><![CDATA[
      K(x * (y \ z),T(x,y)) = K((y / z) \ x,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),12098(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 12098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12101">
    <literal><![CDATA[
      K((x \ y) * z,T(z,x)) = K((x / y) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5857,a,b,12100,a)].">
      <j1 rule="hyper" parents="58 5857 12100"/>
    </justification>
  </clause>

  <clause id="12102">
    <literal><![CDATA[
      K(x / y,z) * a(z,y \ x,z) = K((y / x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9623,a,b,12101,a)].">
      <j1 rule="hyper" parents="58 9623 12101"/>
    </justification>
  </clause>

  <clause id="12103">
    <literal><![CDATA[
      K(x,y / z) * K((z / y) \ x,x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(5109,a,12102,a)].">
      <j1 rule="hyper" parents="5109 12102"/>
    </justification>
  </clause>

  <clause id="12104">
    <literal><![CDATA[
      T(x,(y / z) \ x) \ T(x,z / y) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(5636,a,12103,a)].">
      <j1 rule="hyper" parents="5636 12103"/>
    </justification>
  </clause>

  <clause id="12105">
    <literal><![CDATA[
      T(x,(y / z) \ x) \ T(x,(y / z) \ 1) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(4415(a,2),12104(a,1,2))].">
      <j1 rule="para" parents="4415 12104"/>
    </justification>
  </clause>

  <clause id="12106">
    <literal><![CDATA[
      T(x,(y / z) \ x) \ ((x \ ((y / z) \ x)) \ ((y / z) \ x)) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(4138(a,2),12105(a,1,2))].">
      <j1 rule="para" parents="4138 12105"/>
    </justification>
  </clause>

  <clause id="12107">
    <literal><![CDATA[
      a(x,(y / z) \ 1,x) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8957,a(flip),b,12106,a)].">
      <j1 rule="hyper" parents="58 8957 12106"/>
    </justification>
  </clause>

  <clause id="12108">
    <literal><![CDATA[
      a(x,(y * z) \ z,x) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(6(a,1),12107(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6 12107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12110">
    <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(8786(a,1),5989(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8786 5989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12111">
    <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(320,a,7579,a,b,12110,a),flip(a)].">
      <j1 rule="hyper" parents="320 7579 12110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12113">
    <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(4740(a,1),12111(a,2,1))].">
      <j1 rule="para" parents="4740 12111"/>
    </justification>
  </clause>

  <clause id="12114">
    <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(320,a,9780,a(flip),b,12113,a),flip(a)].">
      <j1 rule="hyper" parents="320 9780 12113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12115">
    <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(4274(a,2),12114(a,1,2))].">
      <j1 rule="para" parents="4274 12114"/>
    </justification>
  </clause>

  <clause id="12116">
    <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(8782(a,1),12115(a,1,2,1))].">
      <j1 rule="para" parents="8782 12115"/>
    </justification>
  </clause>

  <clause id="12117">
    <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(4266(a,2),12116(a,1,2,1))].">
      <j1 rule="para" parents="4266 12116"/>
    </justification>
  </clause>

  <clause id="12119">
    <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(8786(a,1),5990(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8786 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12120">
    <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(320,a,7579,a,b,12119,a),flip(a)].">
      <j1 rule="hyper" parents="320 7579 12119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12122">
    <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(4740(a,1),12120(a,2,1))].">
      <j1 rule="para" parents="4740 12120"/>
    </justification>
  </clause>

  <clause id="12123">
    <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(8931(a,1),8959(a,1,2))].">
      <j1 rule="para" parents="8931 8959"/>
    </justification>
  </clause>

  <clause id="12124">
    <literal><![CDATA[
      K((x * (K(y,x) / T(x,z))) \ 1,((x \ K(x,y)) * T(x,z)) \ 1) = K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x)))
    ]]></literal>
    <justification jstring="[para(8614(a,1),11454(a,1,1,1))].">
      <j1 rule="para" parents="8614 11454"/>
    </justification>
  </clause>

  <clause id="12125">
    <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(5576(a,1),11455(a,1,1,1))].">
      <j1 rule="para" parents="5576 11455"/>
    </justification>
  </clause>

  <clause id="12126">
    <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(212(a,1),12123(a,1,3)),flip(a)].">
      <j1 rule="para" parents="212 12123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12127">
    <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(320,a,10524,a(flip),b,12126,a),flip(a)].">
      <j1 rule="hyper" parents="320 10524 12126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12129">
    <literal><![CDATA[
      (K(x,y) * a(x,z,x)) \ u = R(T(x,y),z,x) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,4511,a(flip),b,12127,a),flip(a)].">
      <j1 rule="hyper" parents="58 4511 12127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12130">
    <literal><![CDATA[
      (K(x,y) * a(x,z,x)) \ u = x * (R(T(x,y),z,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(320,a,1903,a(flip),b,12129,a),flip(a)].">
      <j1 rule="hyper" parents="320 1903 12129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12131">
    <literal><![CDATA[
      (a(x,y,x) * K(x,z)) \ u = x * (R(T(x,z),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9514,a,b,12130,a)].">
      <j1 rule="hyper" parents="58 9514 12130"/>
    </justification>
  </clause>

  <clause id="12132">
    <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,12055,a,b,12131,a)].">
      <j1 rule="hyper" parents="58 12055 12131"/>
    </justification>
  </clause>

  <clause id="12133">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = x * (x \ L(x,y,x))
    ]]></literal>
    <justification jstring="[para(11696(a,1),12132(a,2,2))].">
      <j1 rule="para" parents="11696 12132"/>
    </justification>
  </clause>

  <clause id="12134">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5,a(flip),b,12133,a),flip(a)].">
      <j1 rule="hyper" parents="320 5 12133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12136">
    <literal><![CDATA[
      L(L(x,y,z),u,L(x,w,v5)) = L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(12134(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12134 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12137">
    <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(12136(a,1),9988(a,1,1,2))].">
      <j1 rule="para" parents="12136 9988"/>
    </justification>
  </clause>

  <clause id="12138">
    <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(11452(a,1),12125(a,1,1))].">
      <j1 rule="para" parents="11452 12125"/>
    </justification>
  </clause>

  <clause id="12139">
    <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(11452(a,1),12138(a,1,2,1))].">
      <j1 rule="para" parents="11452 12138"/>
    </justification>
  </clause>

  <clause id="12140">
    <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(5576(a,1),12139(a,1,2,2,2))].">
      <j1 rule="para" parents="5576 12139"/>
    </justification>
  </clause>

  <clause id="12141">
    <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(10557(a,1),10558(a,2,2,1,1))].">
      <j1 rule="para" parents="10557 10558"/>
    </justification>
  </clause>

  <clause id="12142">
    <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(320,a,1687,a(flip),b,12141,a),flip(a)].">
      <j1 rule="hyper" parents="320 1687 12141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12143">
    <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(2033(a,1),12142(a,2,2))].">
      <j1 rule="para" parents="2033 12142"/>
    </justification>
  </clause>

  <clause id="12144">
    <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(911(a,1),12143(a,2,2,1))].">
      <j1 rule="para" parents="911 12143"/>
    </justification>
  </clause>

  <clause id="12145">
    <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(1199(a,1),12144(a,2,2,1,2))].">
      <j1 rule="para" parents="1199 12144"/>
    </justification>
  </clause>

  <clause id="12146">
    <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(1687(a,1),12145(a,1,1))].">
      <j1 rule="para" parents="1687 12145"/>
    </justification>
  </clause>

  <clause id="12147">
    <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(320,a,9311,a(flip),b,9586,a),flip(a)].">
      <j1 rule="hyper" parents="320 9311 9586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12148">
    <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(320,a,7759,a(flip),b,12147,a),flip(a)].">
      <j1 rule="hyper" parents="320 7759 12147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12150">
    <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(2656(a,1),9479(a,1,1,1,2))].">
      <j1 rule="para" parents="2656 9479"/>
    </justification>
  </clause>

  <clause id="12151">
    <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(320,a,4,a(flip),b,11048,a),flip(a)].">
      <j1 rule="hyper" parents="320 4 11048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12153">
    <literal><![CDATA[
      L(x,K(y,z),K(u,y) * R(K(y,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(11046(a,1),12151(a,1,3))].">
      <j1 rule="para" parents="11046 12151"/>
    </justification>
  </clause>

  <clause id="12155">
    <literal><![CDATA[
      L(x,K(y,z),a(K(y,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(11922(a,1),12153(a,1,3))].">
      <j1 rule="para" parents="11922 12153"/>
    </justification>
  </clause>

  <clause id="12156">
    <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(1330,a,12155,a),flip(a)].">
      <j1 rule="hyper" parents="1330 12155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12157">
    <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,11958,a(flip),b,12156,a),flip(a)].">
      <j1 rule="hyper" parents="58 11958 12156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12158">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) * z = z * a(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(5095(a,1),12157(a,1,2))].">
      <j1 rule="para" parents="5095 12157"/>
    </justification>
  </clause>

  <clause id="12159">
    <literal><![CDATA[
      x * a(K(y,T(z,x)),u,w) = a(K(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(7858(a,1),12158(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7858 12158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12160">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) = T(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(240,a,12159,a),flip(a)].">
      <j1 rule="hyper" parents="240 12159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12161">
    <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(10763(a,1),11714(a,1,2,2))].">
      <j1 rule="para" parents="10763 11714"/>
    </justification>
  </clause>

  <clause id="12163">
    <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(3741(a,1),12150(a,1,1,1))].">
      <j1 rule="para" parents="3741 12150"/>
    </justification>
  </clause>

  <clause id="12164">
    <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),12163(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="104 12163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12168">
    <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(2656(a,1),12164(a,2,1,3,2))].">
      <j1 rule="para" parents="2656 12164"/>
    </justification>
  </clause>

  <clause id="12169">
    <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),12168(a,2,1,3))].">
      <j1 rule="para" parents="4 12168"/>
    </justification>
  </clause>

  <clause id="12173">
    <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(3389(a,1),12169(a,2,1))].">
      <j1 rule="para" parents="3389 12169"/>
    </justification>
  </clause>

  <clause id="12174">
    <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),12173(a,1,1,1,1,2))].">
      <j1 rule="para" parents="72 12173"/>
    </justification>
  </clause>

  <clause id="12176">
    <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(2656(a,1),12174(a,1,1,2))].">
      <j1 rule="para" parents="2656 12174"/>
    </justification>
  </clause>

  <clause id="12177">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ y,z) = K(R(y,y \ x,x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3965,a(flip),b,12176,a)].">
      <j1 rule="hyper" parents="58 3965 12176"/>
    </justification>
  </clause>

  <clause id="12179">
    <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),12177(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="17 12177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12180">
    <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(10143(a,1),12179(a,2,1,1))].">
      <j1 rule="para" parents="10143 12179"/>
    </justification>
  </clause>

  <clause id="12181">
    <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(320,a,7233,a(flip),b,12180,a),flip(a)].">
      <j1 rule="hyper" parents="320 7233 12180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12182">
    <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),12181(a,1,1,3))].">
      <j1 rule="para" parents="17 12181"/>
    </justification>
  </clause>

  <clause id="12183">
    <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(7133(a,1),12182(a,2,1))].">
      <j1 rule="para" parents="7133 12182"/>
    </justification>
  </clause>

  <clause id="12184">
    <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,6718,a(flip),b,12183,a)].">
      <j1 rule="hyper" parents="58 6718 12183"/>
    </justification>
  </clause>

  <clause id="12185">
    <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(12184(a,1),6507(a,2,2))].">
      <j1 rule="para" parents="12184 6507"/>
    </justification>
  </clause>

  <clause id="12186">
    <literal><![CDATA[
      (K(x * y,z) * ((x * y) / x)) * x = x * (y * K(y * x,T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(320,a,90,a(flip),b,12185,a),flip(a)].">
      <j1 rule="hyper" parents="320 90 12185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12187">
    <literal><![CDATA[
      (K(x * y,z) * ((x * y) / x)) * x = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7274,a(flip),b,12186,a),flip(a)].">
      <j1 rule="hyper" parents="320 7274 12186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12188">
    <literal><![CDATA[
      (K(x * y,z) * y) * T(x,y) = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(6462,a,12187,a)].">
      <j1 rule="hyper" parents="6462 12187"/>
    </justification>
  </clause>

  <clause id="12189">
    <literal><![CDATA[
      K(x * y,z) * x = x * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(11234,a,12188,a),flip(a)].">
      <j1 rule="hyper" parents="11234 12188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12190">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(7957,a,12189,a),flip(a)].">
      <j1 rule="hyper" parents="7957 12189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12191">
    <literal><![CDATA[
      K(x * y,T(z,x)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(7278,a,12189,a)].">
      <j1 rule="hyper" parents="7278 12189"/>
    </justification>
  </clause>

  <clause id="12192">
    <literal><![CDATA[
      K(x * (y \ 1),T(z,y)) = K((y \ 1) * x,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,8214,a,b,12189,a)].">
      <j1 rule="hyper" parents="30 8214 12189"/>
    </justification>
  </clause>

  <clause id="12193">
    <literal><![CDATA[
      K((x \ 1) * y,T(z,x)) = K(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(30,a,8212,a(flip),b,12189,a),flip(a)].">
      <j1 rule="hyper" parents="30 8212 12189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12195">
    <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(12189(a,1),9840(a,1,2,2))].">
      <j1 rule="para" parents="12189 9840"/>
    </justification>
  </clause>

  <clause id="12196">
    <literal><![CDATA[
      K((x \ y) * x,z) = K(y,T(z,x \ y))
    ]]></literal>
    <justification jstring="[para(5(a,1),12190(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 12190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12197">
    <literal><![CDATA[
      K(x * (y / x),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(7(a,1),12190(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 12190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12199">
    <literal><![CDATA[
      K(x * y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(12190(a,1),7981(a,1))].">
      <j1 rule="para" parents="12190 7981"/>
    </justification>
  </clause>

  <clause id="12200">
    <literal><![CDATA[
      K((x * y) * (z / (y * x)),u) = K(z * K(x,y),T(u,x * y))
    ]]></literal>
    <justification jstring="[para(10349(a,1),12190(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10349 12190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12201">
    <literal><![CDATA[
      K(x * y,(z * x) \ x) = K(y * x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(8403,a,12191,a)].">
      <j1 rule="hyper" parents="8403 12191"/>
    </justification>
  </clause>

  <clause id="12203">
    <literal><![CDATA[
      K((x \ y) * x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(5(a,1),12191(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 12191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12204">
    <literal><![CDATA[
      K(x * y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(12191(a,1),7981(a,1))].">
      <j1 rule="para" parents="12191 7981"/>
    </justification>
  </clause>

  <clause id="12205">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(4051(a,2),12197(a,1,1))].">
      <j1 rule="para" parents="4051 12197"/>
    </justification>
  </clause>

  <clause id="12206">
    <literal><![CDATA[
      K(x * K((x \ y) \ 1,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[para(5503(a,1),12197(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5503 12197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12207">
    <literal><![CDATA[
      K(x * K(y \ x,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[para(6250(a,1),12197(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6250 12197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12208">
    <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(12197(a,1),8345(a,1,1,2))].">
      <j1 rule="para" parents="12197 8345"/>
    </justification>
  </clause>

  <clause id="12209">
    <literal><![CDATA[
      T(x,(y \ z) * y) = x / K(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(12203(a,1),4764(a,2,2))].">
      <j1 rule="para" parents="12203 4764"/>
    </justification>
  </clause>

  <clause id="12210">
    <literal><![CDATA[
      K((x \ y) * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(12196(a,2),8225(a,1))].">
      <j1 rule="para" parents="12196 8225"/>
    </justification>
  </clause>

  <clause id="12211">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,12191,a(flip),b,12205,a),flip(a)].">
      <j1 rule="hyper" parents="320 12191 12205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12212">
    <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,12211,a(flip),b,4855,a)].">
      <j1 rule="hyper" parents="119 12211 4855"/>
    </justification>
  </clause>

  <clause id="12213">
    <literal><![CDATA[
      T(x,(y \ z) * y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7194,a(flip),b,12209,a),flip(a)].">
      <j1 rule="hyper" parents="320 7194 12209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12214">
    <literal><![CDATA[
      T(x,T(y * z,y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),12213(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 12213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12215">
    <literal><![CDATA[
      T(x,T(T(y * z,u),y)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4555(a,1),12213(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4555 12213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12216">
    <literal><![CDATA[
      T(x,T(y * z,y)) = x * K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4714,a(flip),b,12214,a),flip(a)].">
      <j1 rule="hyper" parents="320 4714 12214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12217">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8015,a,b,12214,a)].">
      <j1 rule="hyper" parents="58 8015 12214"/>
    </justification>
  </clause>

  <clause id="12218">
    <literal><![CDATA[
      K(x / y,y * z) = K(y \ x,z * y)
    ]]></literal>
    <justification jstring="[hyper(8310,a,12216,a)].">
      <j1 rule="hyper" parents="8310 12216"/>
    </justification>
  </clause>

  <clause id="12219">
    <literal><![CDATA[
      K(x,T((y \ 1) * z,y)) = K(x,z * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(8197,a,12216,a)].">
      <j1 rule="hyper" parents="8197 12216"/>
    </justification>
  </clause>

  <clause id="12220">
    <literal><![CDATA[
      K(T(x,y),y * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(7285,a,12216,a)].">
      <j1 rule="hyper" parents="7285 12216"/>
    </justification>
  </clause>

  <clause id="12221">
    <literal><![CDATA[
      T(K(x,y * z),y) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(7282,a,12216,a)].">
      <j1 rule="hyper" parents="7282 12216"/>
    </justification>
  </clause>

  <clause id="12222">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(4796,a,12216,a)].">
      <j1 rule="hyper" parents="4796 12216"/>
    </justification>
  </clause>

  <clause id="12223">
    <literal><![CDATA[
      T(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12216(a,2),4725(a,1))].">
      <j1 rule="para" parents="12216 4725"/>
    </justification>
  </clause>

  <clause id="12224">
    <literal><![CDATA[
      T(x * y,T(z,x)) \ 1 = (x * y) \ K(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(116,a,12220,a(flip),b,4755,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 12220 4755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12225">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) \ u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(12220(a,1),11800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12220 11800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12226">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(7873,a,12221,a)].">
      <j1 rule="hyper" parents="7873 12221"/>
    </justification>
  </clause>

  <clause id="12227">
    <literal><![CDATA[
      L(x,y,K(z,u * y)) = L(x,y,K(z,y * u))
    ]]></literal>
    <justification jstring="[para(12221(a,1),11155(a,1,3))].">
      <j1 rule="para" parents="12221 11155"/>
    </justification>
  </clause>

  <clause id="12228">
    <literal><![CDATA[
      K(x,T((1 / y) * z,y)) = K(x,z * (1 / y))
    ]]></literal>
    <justification jstring="[hyper(8246,a,12222,a)].">
      <j1 rule="hyper" parents="8246 12222"/>
    </justification>
  </clause>

  <clause id="12229">
    <literal><![CDATA[
      K(x,T(y * (z \ x),z)) = K(x,(z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(8245,a,12222,a)].">
      <j1 rule="hyper" parents="8245 12222"/>
    </justification>
  </clause>

  <clause id="12230">
    <literal><![CDATA[
      K(x,(y \ z) * y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(5(a,1),12222(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 12222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12231">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,T(y,z) * z)
    ]]></literal>
    <justification jstring="[para(105(a,1),12222(a,1,2,1))].">
      <j1 rule="para" parents="105 12222"/>
    </justification>
  </clause>

  <clause id="12232">
    <literal><![CDATA[
      K(x,K(y,z * y)) * K(x,z * y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(8060,a,12226,a)].">
      <j1 rule="hyper" parents="8060 12226"/>
    </justification>
  </clause>

  <clause id="12233">
    <literal><![CDATA[
      T(x,T(y * z,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,12226,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 12226 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12234">
    <literal><![CDATA[
      K(x,T(y,z \ y)) = K(x,(z \ y) * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),12226(a,1,2,1))].">
      <j1 rule="para" parents="5 12226"/>
    </justification>
  </clause>

  <clause id="12235">
    <literal><![CDATA[
      K(x,y * (z / y)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),12226(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 12226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12236">
    <literal><![CDATA[
      T(K(x,y * z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12226(a,1),7956(a,1,1))].">
      <j1 rule="para" parents="12226 7956"/>
    </justification>
  </clause>

  <clause id="12237">
    <literal><![CDATA[
      K(x,T(T(y * z,u),y)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4555(a,1),12230(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4555 12230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12238">
    <literal><![CDATA[
      T(x,T(y * z,z \ 1)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(8242,a,12233,a)].">
      <j1 rule="hyper" parents="8242 12233"/>
    </justification>
  </clause>

  <clause id="12239">
    <literal><![CDATA[
      T(x,y * (z / y)) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),12233(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 12233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12240">
    <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(12233(a,1),11910(a,1,2,1,1))].">
      <j1 rule="para" parents="12233 11910"/>
    </justification>
  </clause>

  <clause id="12241">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),z)) = K(x,y / (T(z,y) \ 1))
    ]]></literal>
    <justification jstring="[para(10078(a,2),12235(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10078 12235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12242">
    <literal><![CDATA[
      (x * (y / x)) * T(z,T(y,x)) = z * (x * (y / x))
    ]]></literal>
    <justification jstring="[hyper(119,a,12239,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 12239 17"/>
    </justification>
  </clause>

  <clause id="12243">
    <literal><![CDATA[
      T(x,T(T(y * z,u),z)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4542(a,1),12239(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4542 12239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12244">
    <literal><![CDATA[
      T(T(x,y * z),K(y,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(7823,a,12217,a)].">
      <j1 rule="hyper" parents="7823 12217"/>
    </justification>
  </clause>

  <clause id="12245">
    <literal><![CDATA[
      T(K(x,y) * z,x * y) = T(z * K(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(6308(a,1),12217(a,1,1))].">
      <j1 rule="para" parents="6308 12217"/>
    </justification>
  </clause>

  <clause id="12246">
    <literal><![CDATA[
      K(1 / x,x * T(y,z)) = K(x \ 1,T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,11227,a,b,12218,a),flip(a)].">
      <j1 rule="hyper" parents="320 11227 12218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12247">
    <literal><![CDATA[
      K(1 / x,y * x) = K(1 / x,x * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3293,a,b,12218,a)].">
      <j1 rule="hyper" parents="320 3293 12218"/>
    </justification>
  </clause>

  <clause id="12248">
    <literal><![CDATA[
      K(x,T(y,z) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,12226,a(flip),b,12231,a),flip(a)].">
      <j1 rule="hyper" parents="58 12226 12231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12249">
    <literal><![CDATA[
      T(x,T(y,z) * z) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,12248,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 12248 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12250">
    <literal><![CDATA[
      K(x,y * (z * K(y,z))) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(4775(a,1),12248(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4775 12248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12251">
    <literal><![CDATA[
      T(x,T(y \ z,u) * y) = T(x,y * T(z / y,u))
    ]]></literal>
    <justification jstring="[para(246(a,1),12249(a,1,2,1))].">
      <j1 rule="para" parents="246 12249"/>
    </justification>
  </clause>

  <clause id="12252">
    <literal><![CDATA[
      K(x,(y \ z) * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(12234(a,1),8224(a,1))].">
      <j1 rule="para" parents="12234 8224"/>
    </justification>
  </clause>

  <clause id="12253">
    <literal><![CDATA[
      T(T(x,y * z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12244(a,1),5595(a,1,1))].">
      <j1 rule="para" parents="12244 5595"/>
    </justification>
  </clause>

  <clause id="12254">
    <literal><![CDATA[
      x * K(1 / y,z * y) = x * K(1 / y,y * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,12247,a,b,4,a)].">
      <j1 rule="hyper" parents="119 12247 4"/>
    </justification>
  </clause>

  <clause id="12255">
    <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(4709(a,2),12199(a,1,1))].">
      <j1 rule="para" parents="4709 12199"/>
    </justification>
  </clause>

  <clause id="12256">
    <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(6086(a,1),12204(a,1,1))].">
      <j1 rule="para" parents="6086 12204"/>
    </justification>
  </clause>

  <clause id="12257">
    <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(11135(a,1),12210(a,1,1,1))].">
      <j1 rule="para" parents="11135 12210"/>
    </justification>
  </clause>

  <clause id="12258">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(8015(a,2),12223(a,1))].">
      <j1 rule="para" parents="8015 12223"/>
    </justification>
  </clause>

  <clause id="12259">
    <literal><![CDATA[
      K(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(7131(a,2),12236(a,1))].">
      <j1 rule="para" parents="7131 12236"/>
    </justification>
  </clause>

  <clause id="12260">
    <literal><![CDATA[
      K(x,T(y * z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(8205(a,2),12259(a,1))].">
      <j1 rule="para" parents="8205 12259"/>
    </justification>
  </clause>

  <clause id="12261">
    <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(635(a,1),12260(a,1,2,1))].">
      <j1 rule="para" parents="635 12260"/>
    </justification>
  </clause>

  <clause id="12262">
    <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(11144(a,1),12260(a,1,2,1))].">
      <j1 rule="para" parents="11144 12260"/>
    </justification>
  </clause>

  <clause id="12263">
    <literal><![CDATA[
      K(x,T(y,z) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12231(a,1),12260(a,1))].">
      <j1 rule="para" parents="12231 12260"/>
    </justification>
  </clause>

  <clause id="12264">
    <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(12213(a,1),12263(a,1,2,1))].">
      <j1 rule="para" parents="12213 12263"/>
    </justification>
  </clause>

  <clause id="12265">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) = K(z * ((x \ y) \ 1),x / y)
    ]]></literal>
    <justification jstring="[hyper(5750,a,12192,a),flip(a)].">
      <j1 rule="hyper" parents="5750 12192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12266">
    <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(453(a,1),12192(a,1,1))].">
      <j1 rule="para" parents="453 12192"/>
    </justification>
  </clause>

  <clause id="12267">
    <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(2012(a,1),12193(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2012 12193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12268">
    <literal><![CDATA[
      T(x,y) * K(y * x,y \ 1) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(12201(a,1),6754(a,1,2))].">
      <j1 rule="para" parents="12201 6754"/>
    </justification>
  </clause>

  <clause id="12269">
    <literal><![CDATA[
      T(x,T(T(y * z,y),u)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(18(a,1),12215(a,1,2))].">
      <j1 rule="para" parents="18 12215"/>
    </justification>
  </clause>

  <clause id="12270">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y)) = R(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,11874,a(flip),b,12219,a),flip(a)].">
      <j1 rule="hyper" parents="320 11874 12219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12271">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ 1))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8189,a,12225,a)].">
      <j1 rule="hyper" parents="8189 12225"/>
    </justification>
  </clause>

  <clause id="12272">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,x * y))
    ]]></literal>
    <justification jstring="[para(12225(a,1),7781(a,2,2))].">
      <j1 rule="para" parents="12225 7781"/>
    </justification>
  </clause>

  <clause id="12273">
    <literal><![CDATA[
      K(x \ y,(1 / (y / x)) * z) = K(x \ y,z * (1 / (y / x)))
    ]]></literal>
    <justification jstring="[hyper(8026,a,12228,a)].">
      <j1 rule="hyper" parents="8026 12228"/>
    </justification>
  </clause>

  <clause id="12274">
    <literal><![CDATA[
      K(x,(y \ x) * R(y,z,u)) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,9861,a(flip),b,12229,a),flip(a)].">
      <j1 rule="hyper" parents="58 9861 12229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12275">
    <literal><![CDATA[
      K(x / y,T(z * y,u)) = K(y \ x,T(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(7693,a,12237,a),flip(a)].">
      <j1 rule="hyper" parents="7693 12237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12276">
    <literal><![CDATA[
      K(x,T(y * x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x * y,z)) = u
    ]]></literal>
    <justification jstring="[para(12237(a,1),4927(a,1))].">
      <j1 rule="para" parents="12237 4927"/>
    </justification>
  </clause>

  <clause id="12277">
    <literal><![CDATA[
      T(x,T(T(y * z,z),u)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(18(a,1),12243(a,1,2))].">
      <j1 rule="para" parents="18 12243"/>
    </justification>
  </clause>

  <clause id="12278">
    <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(454(a,1),12243(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="454 12243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12279">
    <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(7975(a,1),12269(a,1,2,1,1))].">
      <j1 rule="para" parents="7975 12269"/>
    </justification>
  </clause>

  <clause id="12280">
    <literal><![CDATA[
      K(x,K(y \ (z * u),z * u)) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8188,a(flip),b,12271,a),flip(a)].">
      <j1 rule="hyper" parents="58 8188 12271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12281">
    <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(453(a,1),12277(a,1,2,1,1))].">
      <j1 rule="para" parents="453 12277"/>
    </justification>
  </clause>

  <clause id="12282">
    <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(6368(a,2),12277(a,2,2,1))].">
      <j1 rule="para" parents="6368 12277"/>
    </justification>
  </clause>

  <clause id="12283">
    <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(7772(a,1),12258(a,1,1,2))].">
      <j1 rule="para" parents="7772 12258"/>
    </justification>
  </clause>

  <clause id="12284">
    <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(7858(a,1),12258(a,1,1,2))].">
      <j1 rule="para" parents="7858 12258"/>
    </justification>
  </clause>

  <clause id="12285">
    <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(7844(a,1),12258(a,1,1,2))].">
      <j1 rule="para" parents="7844 12258"/>
    </justification>
  </clause>

  <clause id="12286">
    <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(320,a,11705,a(flip),b,12224,a),flip(a)].">
      <j1 rule="hyper" parents="320 11705 12224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12287">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z * y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(7752(a,1),12232(a,1,1))].">
      <j1 rule="para" parents="7752 12232"/>
    </justification>
  </clause>

  <clause id="12288">
    <literal><![CDATA[
      K(x,y * z) * K(x,K(z,y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(5603,a,12287,a)].">
      <j1 rule="hyper" parents="5603 12287"/>
    </justification>
  </clause>

  <clause id="12289">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z * x) = K(y,x * z)
    ]]></literal>
    <justification jstring="[para(7754(a,1),12287(a,1,1))].">
      <j1 rule="para" parents="7754 12287"/>
    </justification>
  </clause>

  <clause id="12290">
    <literal><![CDATA[
      K(x,y * z) * K(z,K(y,x)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(7759(a,2),12288(a,1,2))].">
      <j1 rule="para" parents="7759 12288"/>
    </justification>
  </clause>

  <clause id="12291">
    <literal><![CDATA[
      K(x,y / (T(z,y) \ 1)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8209,a(flip),b,12241,a),flip(a)].">
      <j1 rule="hyper" parents="58 8209 12241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12292">
    <literal><![CDATA[
      K(x,(y / z) / (z \ 1)) = K(x,(z \ 1) \ (z \ y))
    ]]></literal>
    <justification jstring="[para(10120(a,1),12291(a,1,2))].">
      <j1 rule="para" parents="10120 12291"/>
    </justification>
  </clause>

  <clause id="12293">
    <literal><![CDATA[
      (x * (y / x)) * z != u * (x * (y / x))
    ]]></literal>
    <literal><![CDATA[
      T(u,T(y,x)) = z
    ]]></literal>
    <justification jstring="[para(12242(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="12242 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12294">
    <literal><![CDATA[
      K(T(K(x,y) * z,x * y),u) = K(z * K(x,y),T(u,y * x))
    ]]></literal>
    <justification jstring="[para(12245(a,2),7133(a,1,1))].">
      <j1 rule="para" parents="12245 7133"/>
    </justification>
  </clause>

  <clause id="12295">
    <literal><![CDATA[
      K(1 / x,T(y * x,z)) = K(1 / x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,3293,a,b,12246,a)].">
      <j1 rule="hyper" parents="320 3293 12246"/>
    </justification>
  </clause>

  <clause id="12296">
    <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(4532(a,1),12251(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4532 12251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12297">
    <literal><![CDATA[
      x * K(1 / (y / z),(y / z) * u) = x * K(z / y,u * (y / z))
    ]]></literal>
    <justification jstring="[para(5391(a,1),12254(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5391 12254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12298">
    <literal><![CDATA[
      x * (y * K(z,K(u,x * y))) = T(x * y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,12272,a)].">
      <j1 rule="hyper" parents="134 12272"/>
    </justification>
  </clause>

  <clause id="12299">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ K(z,u))) = K(z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,11852,a(flip),b,12292,a),flip(a)].">
      <j1 rule="hyper" parents="58 11852 12292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12300">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ K(y,T(z,u))) = K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11589,a,b,12299,a)].">
      <j1 rule="hyper" parents="58 11589 12299"/>
    </justification>
  </clause>

  <clause id="12301">
    <literal><![CDATA[
      (x \ K(y,z)) * K(y,K(z,u)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,12299,a(flip),b,11589,a)].">
      <j1 rule="hyper" parents="119 12299 11589"/>
    </justification>
  </clause>

  <clause id="12302">
    <literal><![CDATA[
      K(1 / x,T(y / (1 / x),z)) = K(1 / x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(11084,a,12295,a)].">
      <j1 rule="hyper" parents="11084 12295"/>
    </justification>
  </clause>

  <clause id="12303">
    <literal><![CDATA[
      K(1 / (x / y),(x / y) * T(z,x)) = K(1 / (y \ x),z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(8600,a,12295,a),flip(a)].">
      <j1 rule="hyper" parents="8600 12295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12304">
    <literal><![CDATA[
      T(1 / x,T(y * x,z)) = T(1 / x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,12295,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 12295 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12305">
    <literal><![CDATA[
      T(x * y,K(z,L(u,y,x))) = T(x * y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(10912,a,12298,a)].">
      <j1 rule="hyper" parents="10912 12298"/>
    </justification>
  </clause>

  <clause id="12306">
    <literal><![CDATA[
      (x * (y * K(z,u))) / T(x * y,K(z,u)) = L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[para(12305(a,1),10789(a,1,2))].">
      <j1 rule="para" parents="12305 10789"/>
    </justification>
  </clause>

  <clause id="12308">
    <literal><![CDATA[
      (x \ K(y,z)) * K(z,K(y,u)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,7754,a,b,12300,a)].">
      <j1 rule="hyper" parents="119 7754 12300"/>
    </justification>
  </clause>

  <clause id="12309">
    <literal><![CDATA[
      (x \ K(y,z)) * K(u,K(y,z)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,7759,a(flip),b,12300,a)].">
      <j1 rule="hyper" parents="119 7759 12300"/>
    </justification>
  </clause>

  <clause id="12310">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,9200,a(flip),b,12270,a),flip(a)].">
      <j1 rule="hyper" parents="58 9200 12270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12311">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,11873,a(flip),b,12310,a)].">
      <j1 rule="hyper" parents="58 11873 12310"/>
    </justification>
  </clause>

  <clause id="12312">
    <literal><![CDATA[
      K(x,L(y / z,z,z \ 1)) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(523(a,1),12311(a,1,2)),flip(a)].">
      <j1 rule="para" parents="523 12311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12313">
    <literal><![CDATA[
      K(x,K(y,L(z,u,u \ 1))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(12311(a,1),11787(a,1,2))].">
      <j1 rule="para" parents="12311 11787"/>
    </justification>
  </clause>

  <clause id="12314">
    <literal><![CDATA[
      K(x,K(y,L(z,u \ 1,u))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(3661(a,1),12313(a,1,2,2))].">
      <j1 rule="para" parents="3661 12313"/>
    </justification>
  </clause>

  <clause id="12315">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(12314(a,1),11843(a,2,2))].">
      <j1 rule="para" parents="12314 11843"/>
    </justification>
  </clause>

  <clause id="12316">
    <literal><![CDATA[
      (x \ y) * K(y,K(z,u)) = x \ T(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),12315(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 12315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12317">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(z,K(u,x))
    ]]></literal>
    <justification jstring="[para(7759(a,2),12315(a,2,2))].">
      <j1 rule="para" parents="7759 12315"/>
    </justification>
  </clause>

  <clause id="12319">
    <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(12306(a,1),107(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12306 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12320">
    <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(12306(a,1),4978(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12306 4978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12321">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) = K((x \ y) \ z,x / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,9768,a(flip),b,12265,a),flip(a)].">
      <j1 rule="hyper" parents="320 9768 12265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12322">
    <literal><![CDATA[
      K(x \ y,(1 / (y / x)) * z) = K(x \ y,z / (y / x))
    ]]></literal>
    <justification jstring="[hyper(320,a,6789,a(flip),b,12273,a),flip(a)].">
      <j1 rule="hyper" parents="320 6789 12273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12323">
    <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(4373(a,2),12322(a,1,1))].">
      <j1 rule="para" parents="4373 12322"/>
    </justification>
  </clause>

  <clause id="12324">
    <literal><![CDATA[
      K(x,K(y * z,(y \ u) \ z)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8141,a,12280,a),flip(a)].">
      <j1 rule="hyper" parents="8141 12280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12325">
    <literal><![CDATA[
      K(x,K(y * z,z \ (y \ u))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8189,a,12324,a)].">
      <j1 rule="hyper" parents="8189 12324"/>
    </justification>
  </clause>

  <clause id="12326">
    <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(5348(a,2),12325(a,2,2))].">
      <j1 rule="para" parents="5348 12325"/>
    </justification>
  </clause>

  <clause id="12327">
    <literal><![CDATA[
      T(x,T(y * T((y * z) / y,u),w)) = T(x,T(T(z,u) * y,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,12215,a(flip),b,12278,a),flip(a)].">
      <j1 rule="hyper" parents="320 12215 12278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12328">
    <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),12327(a,1,2,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 12327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12329">
    <literal><![CDATA[
      x * K(y / z,(z / y) * u) = x * K(y / z,u * (z / y))
    ]]></literal>
    <justification jstring="[para(5391(a,1),12297(a,1,2))].">
      <j1 rule="para" parents="5391 12297"/>
    </justification>
  </clause>

  <clause id="12330">
    <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(320,a,8327,a(flip),b,12329,a),flip(a)].">
      <j1 rule="hyper" parents="320 8327 12329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12331">
    <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(12329(a,1),39(a,2))].">
      <j1 rule="para" parents="12329 39"/>
    </justification>
  </clause>

  <clause id="12332">
    <literal><![CDATA[
      K(1 / (x \ y),z * (y / x)) = K(x / y,(y / x) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(5633,a,12303,a),flip(a)].">
      <j1 rule="hyper" parents="5633 12303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12333">
    <literal><![CDATA[
      K(x / y,(y / x) * T(z,y)) = K(y \ x,z * (y / x))
    ]]></literal>
    <justification jstring="[hyper(6464,a,12332,a),flip(a)].">
      <j1 rule="hyper" parents="6464 12332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12334">
    <literal><![CDATA[
      ((x * y) * ((T(y,x) * x) \ z)) / (x * y) = z / (T(y,x) * x)
    ]]></literal>
    <justification jstring="[hyper(4780,a,12212,a)].">
      <j1 rule="hyper" parents="4780 12212"/>
    </justification>
  </clause>

  <clause id="12335">
    <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,12277,a(flip),b,12282,a),flip(a)].">
      <j1 rule="hyper" parents="58 12277 12282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12336">
    <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(9998(a,1),12286(a,1,1))].">
      <j1 rule="para" parents="9998 12286"/>
    </justification>
  </clause>

  <clause id="12337">
    <literal><![CDATA[
      K(x,T(y,z)) * K(u,T(x,z)) = T(K(x,y) * K(u,x),z)
    ]]></literal>
    <justification jstring="[hyper(11514,a,12336,a),flip(a)].">
      <j1 rule="hyper" parents="11514 12336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12338">
    <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(12337(a,1),9970(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12337 9970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12339">
    <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,10718,a(flip),b,12338,a),flip(a)].">
      <j1 rule="hyper" parents="58 10718 12338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12340">
    <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(453(a,1),12296(a,2,2))].">
      <j1 rule="para" parents="453 12296"/>
    </justification>
  </clause>

  <clause id="12341">
    <literal><![CDATA[
      K(x \ T(x * y,z),T(u,x)) = K((x \ 1) * T(y / (x \ 1),z),u)
    ]]></literal>
    <justification jstring="[para(932(a,1),12266(a,1,1))].">
      <j1 rule="para" parents="932 12266"/>
    </justification>
  </clause>

  <clause id="12342">
    <literal><![CDATA[
      K((x \ 1) * T(y / (x \ 1),z),u) = K(x \ T(y * x,z),u)
    ]]></literal>
    <justification jstring="[hyper(7701,a,12341,a),flip(a)].">
      <j1 rule="hyper" parents="7701 12341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12343">
    <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(320,a,4211,a(flip),b,12319,a),flip(a)].">
      <j1 rule="hyper" parents="320 4211 12319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12344">
    <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(7131(a,2),12343(a,2,1))].">
      <j1 rule="para" parents="7131 12343"/>
    </justification>
  </clause>

  <clause id="12345">
    <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(10570(a,1),12339(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10570 12339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12347">
    <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(12345(a,1),11689(a,2,1))].">
      <j1 rule="para" parents="12345 11689"/>
    </justification>
  </clause>

  <clause id="12348">
    <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(11680(a,1),12347(a,2,1,1))].">
      <j1 rule="para" parents="11680 12347"/>
    </justification>
  </clause>

  <clause id="12350">
    <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(7096(a,1),12348(a,1,1,1))].">
      <j1 rule="para" parents="7096 12348"/>
    </justification>
  </clause>

  <clause id="12352">
    <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(9770(a,1),12350(a,1,1))].">
      <j1 rule="para" parents="9770 12350"/>
    </justification>
  </clause>

  <clause id="12353">
    <literal><![CDATA[
      (R(a(x,y,x),z,u) * z) * u = (z * a(x,y,x)) * u
    ]]></literal>
    <justification jstring="[para(9069(a,1),12352(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9069 12352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12354">
    <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,12353,a(flip),b,692,a)].">
      <j1 rule="hyper" parents="116 12353 692"/>
    </justification>
  </clause>

  <clause id="12355">
    <literal><![CDATA[
      a(R(a(x,y,x),z,u),z,u) = K(z,T(a(x,y,x),u))
    ]]></literal>
    <justification jstring="[hyper(11085,a,12354,a),flip(a)].">
      <j1 rule="hyper" parents="11085 12354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12356">
    <literal><![CDATA[
      a(R(a(x,y,x),z,u),z,u) = K(z,a(x,y,x))
    ]]></literal>
    <justification jstring="[para(9505(a,1),12355(a,2,2))].">
      <j1 rule="para" parents="9505 12355"/>
    </justification>
  </clause>

  <clause id="12357">
    <literal><![CDATA[
      a(R(a(x,y,x),z,u),z,u) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,9513,a(flip),b,12356,a),flip(a)].">
      <j1 rule="hyper" parents="320 9513 12356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12360">
    <literal><![CDATA[
      L(x,y,R(a(z,u,z),y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,12357,a)].">
      <j1 rule="hyper" parents="47 12357"/>
    </justification>
  </clause>

  <clause id="12361">
    <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(12360(a,1),11174(a,1,2))].">
      <j1 rule="para" parents="12360 11174"/>
    </justification>
  </clause>

  <clause id="12362">
    <literal><![CDATA[
      (R(a(x,y,x),z,u) * (z * u)) / u = z * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(9549(a,1),12361(a,1,1,2,1))].">
      <j1 rule="para" parents="9549 12361"/>
    </justification>
  </clause>

  <clause id="12363">
    <literal><![CDATA[
      x * R(a(y,z,y),x,u) = a(y,z,y) * x
    ]]></literal>
    <justification jstring="[hyper(519,a,12362,a),flip(a)].">
      <j1 rule="hyper" parents="519 12362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12364">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,9492,a(flip),b,12363,a),flip(a)].">
      <j1 rule="hyper" parents="29 9492 12363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12366">
    <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,511,a,b,12364,a)].">
      <j1 rule="hyper" parents="58 511 12364"/>
    </justification>
  </clause>

  <clause id="12367">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11678,a(flip),b,12364,a)].">
      <j1 rule="hyper" parents="58 11678 12364"/>
    </justification>
  </clause>

  <clause id="12368">
    <literal><![CDATA[
      a(x,y * K(z,y),x) = L(a(x,y,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9999,a(flip),b,12364,a),flip(a)].">
      <j1 rule="hyper" parents="58 9999 12364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12369">
    <literal><![CDATA[
      (a(x,y,x) * z) * u = a(x,y,x) * (z * u)
    ]]></literal>
    <justification jstring="[para(12364(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12364 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12371">
    <literal><![CDATA[
      a(a(x,y,x),z,u) = 1
    ]]></literal>
    <justification jstring="[para(12364(a,1),12357(a,1,1))].">
      <j1 rule="para" parents="12364 12357"/>
    </justification>
  </clause>

  <clause id="12372">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[para(12364(a,1),12360(a,1,3))].">
      <j1 rule="para" parents="12364 12360"/>
    </justification>
  </clause>

  <clause id="12373">
    <literal><![CDATA[
      a(x,y,x) * ((a(x,y,x) \ z) * u) = z * u
    ]]></literal>
    <justification jstring="[hyper(167,a,81,a,b,12371,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 81 12371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12375">
    <literal><![CDATA[
      (a(x,y,x) * z) \ x = z \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9060,a(flip),b,12372,a)].">
      <j1 rule="hyper" parents="58 9060 12372"/>
    </justification>
  </clause>

  <clause id="12376">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,298,a(flip),b,12372,a)].">
      <j1 rule="hyper" parents="58 298 12372"/>
    </justification>
  </clause>

  <clause id="12377">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(12372(a,1),45(a,2))].">
      <j1 rule="para" parents="12372 45"/>
    </justification>
  </clause>

  <clause id="12378">
    <literal><![CDATA[
      (a(x,y,x) * z) / u = a(x,y,x) * (z / u)
    ]]></literal>
    <justification jstring="[para(12372(a,1),544(a,1,2))].">
      <j1 rule="para" parents="12372 544"/>
    </justification>
  </clause>

  <clause id="12379">
    <literal><![CDATA[
      x \ (a(y,z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,y) \ x) \ u = w
    ]]></literal>
    <justification jstring="[para(12372(a,1),756(a,1)),flip(a)].">
      <j1 rule="para" parents="12372 756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12380">
    <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(12372(a,1),478(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12372 478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12381">
    <literal><![CDATA[
      a(x,y,x) * ((a(x,y,x) \ z) / u) = z / u
    ]]></literal>
    <justification jstring="[para(12372(a,1),10391(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12372 10391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12384">
    <literal><![CDATA[
      K(x,R(x,y,z) \ u) = K(x,u) * a(x,x \ u,x)
    ]]></literal>
    <justification jstring="[para(12367(a,1),11685(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12367 11685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12386">
    <literal><![CDATA[
      (x * y) \ L(y,x,y) = T(y * x,y) \ y
    ]]></literal>
    <justification jstring="[para(8939(a,1),12375(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8939 12375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12388">
    <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(5478(a,1),12368(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5478 12368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12389">
    <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(4605(a,1),12386(a,1,1))].">
      <j1 rule="para" parents="4605 12386"/>
    </justification>
  </clause>

  <clause id="12390">
    <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(12369(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12369 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12391">
    <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(12369(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12369 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12392">
    <literal><![CDATA[
      a(x,y,x) * ((a(x,y,x) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      z * u = w
    ]]></literal>
    <justification jstring="[para(12369(a,1),568(a,1))].">
      <j1 rule="para" parents="12369 568"/>
    </justification>
  </clause>

  <clause id="12393">
    <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(12369(a,1),482(a,1,2,2))].">
      <j1 rule="para" parents="12369 482"/>
    </justification>
  </clause>

  <clause id="12394">
    <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(12369(a,1),615(a,1))].">
      <j1 rule="para" parents="12369 615"/>
    </justification>
  </clause>

  <clause id="12395">
    <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(12369(a,1),691(a,1,1,2))].">
      <j1 rule="para" parents="12369 691"/>
    </justification>
  </clause>

  <clause id="12396">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = a(y,z,y) * (x * u)
    ]]></literal>
    <justification jstring="[para(9492(a,1),12369(a,1,1))].">
      <j1 rule="para" parents="9492 12369"/>
    </justification>
  </clause>

  <clause id="12397">
    <literal><![CDATA[
      (x * a(y,z,y)) \ u = x \ (a(y,z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(9529,a,12376,a)].">
      <j1 rule="hyper" parents="9529 12376"/>
    </justification>
  </clause>

  <clause id="12398">
    <literal><![CDATA[
      (a(x,y,x) * z) / u = (z / u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,9492,a(flip),b,12378,a),flip(a)].">
      <j1 rule="hyper" parents="320 9492 12378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12399">
    <literal><![CDATA[
      a(x,y,x) * (x / z) = R(x,y,x) / z
    ]]></literal>
    <justification jstring="[para(8926(a,1),12378(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8926 12378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12400">
    <literal><![CDATA[
      (x / y) * a(x,z,x) = R(x,z,x) / y
    ]]></literal>
    <justification jstring="[hyper(9520,a,12399,a)].">
      <j1 rule="hyper" parents="9520 12399"/>
    </justification>
  </clause>

  <clause id="12401">
    <literal><![CDATA[
      (a(x,y,x) \ z) / u = a(x,y,x) \ (z / u)
    ]]></literal>
    <justification jstring="[hyper(123,a,12381,a),flip(a)].">
      <j1 rule="hyper" parents="123 12381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12402">
    <literal><![CDATA[
      (x * a(y,x,y)) * z = x * (a(y,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,11006,a(flip),b,12396,a),flip(a)].">
      <j1 rule="hyper" parents="320 11006 12396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12403">
    <literal><![CDATA[
      (x * a(y,z,y)) / u = (x / u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(9492(a,1),12398(a,1,1))].">
      <j1 rule="para" parents="9492 12398"/>
    </justification>
  </clause>

  <clause id="12404">
    <literal><![CDATA[
      a(x,y,x) \ (x / z) = L(x,y,x) / z
    ]]></literal>
    <justification jstring="[para(9059(a,1),12401(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9059 12401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12405">
    <literal><![CDATA[
      K(x,R(x,y,z) \ u) = K(x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(320,a,8940,a(flip),b,12384,a),flip(a)].">
      <j1 rule="hyper" parents="320 8940 12384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12407">
    <literal><![CDATA[
      K(x,x \ ((x * R(T(x,y),z,u)) / w)) = K(x,w \ x)
    ]]></literal>
    <justification jstring="[hyper(10033,a,12405,a),flip(a)].">
      <j1 rule="hyper" parents="10033 12405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12408">
    <literal><![CDATA[
      K(x,x \ ((x * y) * z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(184(a,1),12405(a,1,2)),flip(a)].">
      <j1 rule="para" parents="184 12405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12409">
    <literal><![CDATA[
      K(x,x \ (y * z)) = K(x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[para(505(a,1),12405(a,1,2)),flip(a)].">
      <j1 rule="para" parents="505 12405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12410">
    <literal><![CDATA[
      K(x,y * ((x * y) \ z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(367(a,1),12405(a,1,2))].">
      <j1 rule="para" parents="367 12405"/>
    </justification>
  </clause>

  <clause id="12411">
    <literal><![CDATA[
      K(x,x \ ((y * x) * z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(11139,a,12408,a)].">
      <j1 rule="hyper" parents="11139 12408"/>
    </justification>
  </clause>

  <clause id="12412">
    <literal><![CDATA[
      K(x,y * (x \ (y \ (z * u)))) = K(x,(x \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(10378,a,12409,a)].">
      <j1 rule="hyper" parents="10378 12409"/>
    </justification>
  </clause>

  <clause id="12413">
    <literal><![CDATA[
      K(x,(x \ y) * z) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(10299,a,12409,a),flip(a)].">
      <j1 rule="hyper" parents="10299 12409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12414">
    <literal><![CDATA[
      K(x,y * ((y * x) \ z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11133,a,b,12410,a)].">
      <j1 rule="hyper" parents="58 11133 12410"/>
    </justification>
  </clause>

  <clause id="12415">
    <literal><![CDATA[
      T(x,(x \ y) * z) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,12413,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 12413 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12416">
    <literal><![CDATA[
      K(x,(y * x) * (x \ z)) = K(x,T(y,x) * z)
    ]]></literal>
    <justification jstring="[para(17(a,2),12413(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="17 12413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12417">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ z) = K(x \ y,x * (y \ z))
    ]]></literal>
    <justification jstring="[para(5(a,1),12414(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 12414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12418">
    <literal><![CDATA[
      T(x,(y / x) * z) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(8384,a,12415,a)].">
      <j1 rule="hyper" parents="8384 12415"/>
    </justification>
  </clause>

  <clause id="12419">
    <literal><![CDATA[
      T(x,(x \ y) * z) \ u = T(x,y * (x \ z)) \ u
    ]]></literal>
    <justification jstring="[hyper(56,a,12415,a)].">
      <j1 rule="hyper" parents="56 12415"/>
    </justification>
  </clause>

  <clause id="12420">
    <literal><![CDATA[
      K(x,(y * x) * (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(12416(a,2),8372(a,1))].">
      <j1 rule="para" parents="12416 8372"/>
    </justification>
  </clause>

  <clause id="12421">
    <literal><![CDATA[
      K(x,y * (x \ T(z,y))) = K(x,(x \ z) * y)
    ]]></literal>
    <justification jstring="[para(17(a,2),12412(a,1,2,2,2))].">
      <j1 rule="para" parents="17 12412"/>
    </justification>
  </clause>

  <clause id="12422">
    <literal><![CDATA[
      K((x \ y) * z,x) = K(y * (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(5624,a,12419,a)].">
      <j1 rule="hyper" parents="5624 12419"/>
    </justification>
  </clause>

  <clause id="12423">
    <literal><![CDATA[
      K(x \ (y * z),x) = K((x \ y) * z,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,10397,a,b,12422,a)].">
      <j1 rule="hyper" parents="320 10397 12422"/>
    </justification>
  </clause>

  <clause id="12424">
    <literal><![CDATA[
      K(x \ ((x * y) * z),x) = K(y * z,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),12423(a,2,1,1))].">
      <j1 rule="para" parents="4 12423"/>
    </justification>
  </clause>

  <clause id="12425">
    <literal><![CDATA[
      K(x \ ((y * x) * z),x) = K(y * z,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11140,a,b,12424,a)].">
      <j1 rule="hyper" parents="58 11140 12424"/>
    </justification>
  </clause>

  <clause id="12426">
    <literal><![CDATA[
      K(x * ((x * y) \ z),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),12425(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 12425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12427">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(x * (y \ z),x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),12426(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 12426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12428">
    <literal><![CDATA[
      K((x / y) \ z,y \ x) = K(y * (x \ z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(7404,a,12427,a)].">
      <j1 rule="hyper" parents="7404 12427"/>
    </justification>
  </clause>

  <clause id="12429">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),z \ u)) = a(x,y,K(w,z \ u))
    ]]></literal>
    <justification jstring="[para(12427(a,1),10982(a,1,3))].">
      <j1 rule="para" parents="12427 10982"/>
    </justification>
  </clause>

  <clause id="12430">
    <literal><![CDATA[
      K(x / (y / z),z \ y) = K(z * (y \ x),z \ y)
    ]]></literal>
    <justification jstring="[hyper(8239,a,12428,a)].">
      <j1 rule="hyper" parents="8239 12428"/>
    </justification>
  </clause>

  <clause id="12431">
    <literal><![CDATA[
      a(x,y,x) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      (z * a(x,y,x)) * u = w
    ]]></literal>
    <justification jstring="[para(9507(a,1),12392(a,1,2,1))].">
      <j1 rule="para" parents="9507 12392"/>
    </justification>
  </clause>

  <clause id="12432">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11090,a(flip),b,12407,a)].">
      <j1 rule="hyper" parents="58 11090 12407"/>
    </justification>
  </clause>

  <clause id="12433">
    <literal><![CDATA[
      K(x,y \ R(x,z,u)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11753,a(flip),b,12432,a)].">
      <j1 rule="hyper" parents="58 11753 12432"/>
    </justification>
  </clause>

  <clause id="12436">
    <literal><![CDATA[
      K(R(x,y,z),u \ x) = K(x,R(u,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11907,a(flip),b,12433,a)].">
      <j1 rule="hyper" parents="58 11907 12433"/>
    </justification>
  </clause>

  <clause id="12437">
    <literal><![CDATA[
      K(x,y \ (z * R(x,u,w))) = K(x,(z \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,10702,a(flip),b,12433,a)].">
      <j1 rule="hyper" parents="58 10702 12433"/>
    </justification>
  </clause>

  <clause id="12439">
    <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,11580,a(flip),b,12436,a),flip(a)].">
      <j1 rule="hyper" parents="58 11580 12436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12441">
    <literal><![CDATA[
      K(x,y \ (z * R(x,u,w))) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(320,a,10447,a(flip),b,12437,a),flip(a)].">
      <j1 rule="hyper" parents="320 10447 12437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12442">
    <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(9496(a,1),12366(a,1,1,1))].">
      <j1 rule="para" parents="9496 12366"/>
    </justification>
  </clause>

  <clause id="12443">
    <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,11416,a(flip),b,12388,a)].">
      <j1 rule="hyper" parents="58 11416 12388"/>
    </justification>
  </clause>

  <clause id="12444">
    <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,11636,a(flip),b,12439,a)].">
      <j1 rule="hyper" parents="58 11636 12439"/>
    </justification>
  </clause>

  <clause id="12445">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(5434(a,1),12444(a,1,1))].">
      <j1 rule="para" parents="5434 12444"/>
    </justification>
  </clause>

  <clause id="12446">
    <literal><![CDATA[
      R(K(x,y),K(x,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4378(a,1),12445(a,2,1))].">
      <j1 rule="para" parents="4378 12445"/>
    </justification>
  </clause>

  <clause id="12447">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 = K(y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(12445(a,2),4929(a,1,1))].">
      <j1 rule="para" parents="12445 4929"/>
    </justification>
  </clause>

  <clause id="12449">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) * u = K(x,y) * (K(x,z) * u)
    ]]></literal>
    <justification jstring="[para(12446(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12446 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12450">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(6908,a,12447,a)].">
      <j1 rule="hyper" parents="6908 12447"/>
    </justification>
  </clause>

  <clause id="12451">
    <literal><![CDATA[
      K(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(12447(a,1),6908(a,1))].">
      <j1 rule="para" parents="12447 6908"/>
    </justification>
  </clause>

  <clause id="12452">
    <literal><![CDATA[
      K(x,R(y,z,u)) * 1 = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,3,a,b,12450,a)].">
      <j1 rule="hyper" parents="320 3 12450"/>
    </justification>
  </clause>

  <clause id="12453">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,R(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,12445,a(flip),b,12450,a)].">
      <j1 rule="hyper" parents="58 12445 12450"/>
    </justification>
  </clause>

  <clause id="12454">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(12450(a,1),101(a,1,1))].">
      <j1 rule="para" parents="12450 101"/>
    </justification>
  </clause>

  <clause id="12457">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(12450(a,1),11922(a,1,2))].">
      <j1 rule="para" parents="12450 11922"/>
    </justification>
  </clause>

  <clause id="12458">
    <literal><![CDATA[
      T(x,x * y) * a(K(x,y),z,u) = L(x * K(x,R(y,z,u)),y,x)
    ]]></literal>
    <justification jstring="[para(12450(a,1),11957(a,2,1,2))].">
      <j1 rule="para" parents="12450 11957"/>
    </justification>
  </clause>

  <clause id="12459">
    <literal><![CDATA[
      K(R(x,y,z),R(x * y,y * z,u)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(6965,a,12453,a),flip(a)].">
      <j1 rule="hyper" parents="6965 12453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12461">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(12452(a,1),127(a,1)),flip(b)].">
      <j1 rule="para" parents="12452 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12462">
    <literal><![CDATA[
      K(R(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(12453(a,2),12451(a,1))].">
      <j1 rule="para" parents="12453 12451"/>
    </justification>
  </clause>

  <clause id="12463">
    <literal><![CDATA[
      K(R(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(12445(a,1),12461(a,1))].">
      <j1 rule="para" parents="12445 12461"/>
    </justification>
  </clause>

  <clause id="12464">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,11927,a(flip),b,12457,a)].">
      <j1 rule="hyper" parents="58 11927 12457"/>
    </justification>
  </clause>

  <clause id="12465">
    <literal><![CDATA[
      K(a(K(x,y),z * y,u),w) = a(K(y,K(x,w)),z,u)
    ]]></literal>
    <justification jstring="[para(12464(a,2),11972(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12464 11972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12466">
    <literal><![CDATA[
      ((x * y) * z) / ((K(u,x) * y) * z) = T(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(12454(a,1),5218(a,1,2))].">
      <j1 rule="para" parents="12454 5218"/>
    </justification>
  </clause>

  <clause id="12467">
    <literal><![CDATA[
      L(x,K(y,z),K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,12449,a)].">
      <j1 rule="hyper" parents="479 12449"/>
    </justification>
  </clause>

  <clause id="12468">
    <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(12449(a,1),11977(a,1,2))].">
      <j1 rule="para" parents="12449 11977"/>
    </justification>
  </clause>

  <clause id="12469">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ u = K(z,x) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5732,a(flip),b,12467,a)].">
      <j1 rule="hyper" parents="58 5732 12467"/>
    </justification>
  </clause>

  <clause id="12470">
    <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,11974,a,b,12465,a)].">
      <j1 rule="hyper" parents="58 11974 12465"/>
    </justification>
  </clause>

  <clause id="12471">
    <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,6006,a(flip),b,12469,a),flip(a)].">
      <j1 rule="hyper" parents="58 6006 12469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12472">
    <literal><![CDATA[
      ((x * y) * z) / (T(y,x) * z) = T(R(x,y,z),y)
    ]]></literal>
    <justification jstring="[para(4729(a,2),12466(a,1,2,1))].">
      <j1 rule="para" parents="4729 12466"/>
    </justification>
  </clause>

  <clause id="12473">
    <literal><![CDATA[
      R(T(x,y),T(y,x),z) = T(R(x,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(4235,a,12472,a)].">
      <j1 rule="hyper" parents="4235 12472"/>
    </justification>
  </clause>

  <clause id="12474">
    <literal><![CDATA[
      R(x,T(y,x),z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(140,a,12473,a(flip))].">
      <j1 rule="hyper" parents="140 12473"/>
    </justification>
  </clause>

  <clause id="12480">
    <literal><![CDATA[
      R(x,y,z) \ ((y * x) * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[para(12474(a,1),540(a,1,1))].">
      <j1 rule="para" parents="12474 540"/>
    </justification>
  </clause>

  <clause id="12481">
    <literal><![CDATA[
      R(x,y,T(z,y * x)) \ (z * (y * x)) = T(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(12474(a,1),931(a,1,1))].">
      <j1 rule="para" parents="12474 931"/>
    </justification>
  </clause>

  <clause id="12482">
    <literal><![CDATA[
      K(x,(((y * x) * z) / R(x,y,z)) \ u) = K(x,(T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(12480(a,1),7402(a,2,2,1))].">
      <j1 rule="para" parents="12480 7402"/>
    </justification>
  </clause>

  <clause id="12483">
    <literal><![CDATA[
      K(x,R(R(x * y,y * z,u),y,z)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12463,a,12459,a)].">
      <j1 rule="hyper" parents="12463 12459"/>
    </justification>
  </clause>

  <clause id="12484">
    <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(4714(a,2),12458(a,2,1))].">
      <j1 rule="para" parents="4714 12458"/>
    </justification>
  </clause>

  <clause id="12485">
    <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(12482(a,2),8561(a,1))].">
      <j1 rule="para" parents="12482 8561"/>
    </justification>
  </clause>

  <clause id="12486">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ 1 = K(z,x) * (x * (K(y,x) / x))
    ]]></literal>
    <justification jstring="[para(3342(a,1),12471(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3342 12471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12487">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ 1 = x * (K(z,x) * (K(y,x) / x))
    ]]></literal>
    <justification jstring="[hyper(320,a,5219,a(flip),b,12486,a),flip(a)].">
      <j1 rule="hyper" parents="320 5219 12486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12488">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ 1 = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[para(8305(a,1),12487(a,2,2))].">
      <j1 rule="para" parents="8305 12487"/>
    </justification>
  </clause>

  <clause id="12489">
    <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,x * (K(y,x) / T(x,z)))
    ]]></literal>
    <justification jstring="[para(12488(a,1),12124(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12488 12124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12490">
    <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),12442(a,1,1))].">
      <j1 rule="para" parents="101 12442"/>
    </justification>
  </clause>

  <clause id="12491">
    <literal><![CDATA[
      ((x * (a(y,x,y) * z)) * u) / ((x * z) * u) = a(y,R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(12402(a,1),12490(a,1,1,1))].">
      <j1 rule="para" parents="12402 12490"/>
    </justification>
  </clause>

  <clause id="12492">
    <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),12491(a,1,2,1))].">
      <j1 rule="para" parents="5 12491"/>
    </justification>
  </clause>

  <clause id="12493">
    <literal><![CDATA[
      a(x,R(y,y \ z,u),x) = ((a(x,y,x) * z) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(11007(a,1),12492(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11007 12492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12494">
    <literal><![CDATA[
      a(x,R(y,y \ z,u),x) = R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,15,a,b,12493,a),flip(a)].">
      <j1 rule="hyper" parents="320 15 12493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12495">
    <literal><![CDATA[
      R(a(x,y,x),y * z,u) = a(x,R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),12494(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 12494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12496">
    <literal><![CDATA[
      a(x,R(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12364,a(flip),b,12495,a),flip(a)].">
      <j1 rule="hyper" parents="58 12364 12495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12497">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = a(x,R(y,w,v5),x)
    ]]></literal>
    <justification jstring="[hyper(320,a,12364,a,b,12496,a)].">
      <j1 rule="hyper" parents="320 12364 12496"/>
    </justification>
  </clause>

  <clause id="12498">
    <literal><![CDATA[
      a(x,y,x) * (R(y,z,u) * x) = T(x * R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(12496(a,1),8939(a,1,1))].">
      <j1 rule="para" parents="12496 8939"/>
    </justification>
  </clause>

  <clause id="12499">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = a(x,z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(12496(a,1),8953(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12496 8953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12501">
    <literal><![CDATA[
      a(x,R(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = w
    ]]></literal>
    <justification jstring="[para(12497(a,1),380(a,1)),flip(b)].">
      <j1 rule="para" parents="12497 380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12502">
    <literal><![CDATA[
      a(x,(y \ z) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,T(y,z),x) = u
    ]]></literal>
    <justification jstring="[para(4334(a,1),12501(a,1,2))].">
      <j1 rule="para" parents="4334 12501"/>
    </justification>
  </clause>

  <clause id="12503">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,8953,a(flip),b,12499,a),flip(a)].">
      <j1 rule="hyper" parents="320 8953 12499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12504">
    <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(12503(a,1),12117(a,1,2))].">
      <j1 rule="para" parents="12503 12117"/>
    </justification>
  </clause>

  <clause id="12505">
    <literal><![CDATA[
      R(x,y,z) * R(u,x,u) = T(u * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(9519,a,12498,a)].">
      <j1 rule="hyper" parents="9519 12498"/>
    </justification>
  </clause>

  <clause id="12506">
    <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(12505(a,2),4200(a,1,1))].">
      <j1 rule="para" parents="12505 4200"/>
    </justification>
  </clause>

  <clause id="12507">
    <literal><![CDATA[
      T(x * R(y,z,u),x * y) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(803(a,1),12504(a,1,2)),flip(a)].">
      <j1 rule="para" parents="803 12504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12509">
    <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(12507(a,1),4753(a,2,2)),flip(a)].">
      <j1 rule="para" parents="12507 4753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12510">
    <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,12082,a(flip),b,12509,a)].">
      <j1 rule="hyper" parents="58 12082 12509"/>
    </justification>
  </clause>

  <clause id="12511">
    <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(11927(a,1),12510(a,1,1))].">
      <j1 rule="para" parents="11927 12510"/>
    </justification>
  </clause>

  <clause id="12512">
    <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,12160,a,b,12511,a),flip(a)].">
      <j1 rule="hyper" parents="58 12160 12511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12513">
    <literal><![CDATA[
      K(x * y,x * R(y,z,u)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(172(a,1),12512(a,2,1,2))].">
      <j1 rule="para" parents="172 12512"/>
    </justification>
  </clause>

  <clause id="12514">
    <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(6925,a,12513,a)].">
      <j1 rule="hyper" parents="6925 12513"/>
    </justification>
  </clause>

  <clause id="12515">
    <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),12513(a,1,1))].">
      <j1 rule="para" parents="7 12513"/>
    </justification>
  </clause>

  <clause id="12516">
    <literal><![CDATA[
      K(x,(y \ x) * R(y,z,u)) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,8742,a(flip),b,12515,a)].">
      <j1 rule="hyper" parents="58 8742 12515"/>
    </justification>
  </clause>

  <clause id="12517">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12274,a(flip),b,12516,a)].">
      <j1 rule="hyper" parents="58 12274 12516"/>
    </justification>
  </clause>

  <clause id="12518">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(y \ x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(4924(a,1),12517(a,2,1))].">
      <j1 rule="para" parents="4924 12517"/>
    </justification>
  </clause>

  <clause id="12519">
    <literal><![CDATA[
      L(T(x,R(y,z,u)),y,T(x,w)) = T(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9758,a,12506,a)].">
      <j1 rule="hyper" parents="9758 12506"/>
    </justification>
  </clause>

  <clause id="12520">
    <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(12513(a,1),12514(a,1,1))].">
      <j1 rule="para" parents="12513 12514"/>
    </justification>
  </clause>

  <clause id="12521">
    <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(12369(a,1),12391(a,1,2))].">
      <j1 rule="para" parents="12369 12391"/>
    </justification>
  </clause>

  <clause id="12522">
    <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(828,a,12521,a)].">
      <j1 rule="hyper" parents="828 12521"/>
    </justification>
  </clause>

  <clause id="12523">
    <literal><![CDATA[
      L(x,y,a(z,u,z) * w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(12377,a,12522,a),flip(a)].">
      <j1 rule="hyper" parents="12377 12522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12525">
    <literal><![CDATA[
      L(x,y,a(z,u,z) \ w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),12523(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5 12523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12526">
    <literal><![CDATA[
      L(x,y,R(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(8926(a,1),12523(a,1,3))].">
      <j1 rule="para" parents="8926 12523"/>
    </justification>
  </clause>

  <clause id="12527">
    <literal><![CDATA[
      L(x,y,K(z * u,z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(8935(a,1),12523(a,1,3))].">
      <j1 rule="para" parents="8935 12523"/>
    </justification>
  </clause>

  <clause id="12528">
    <literal><![CDATA[
      L(x,y,K(z,z * u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(8936(a,1),12523(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8936 12523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12529">
    <literal><![CDATA[
      L(x,y,T(z * u,z)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(8939(a,1),12523(a,1,3))].">
      <j1 rule="para" parents="8939 12523"/>
    </justification>
  </clause>

  <clause id="12530">
    <literal><![CDATA[
      L(x,y,K(z,z \ u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(8910(a,1),12523(a,1,3))].">
      <j1 rule="para" parents="8910 12523"/>
    </justification>
  </clause>

  <clause id="12531">
    <literal><![CDATA[
      L(x,y,z * a(u,w,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(9492(a,1),12523(a,1,3))].">
      <j1 rule="para" parents="9492 12523"/>
    </justification>
  </clause>

  <clause id="12532">
    <literal><![CDATA[
      L(x,y,R(z,u,z) \ w) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(9497(a,1),12523(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9497 12523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12533">
    <literal><![CDATA[
      L(x,y,z * R(u,w,u)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(9499(a,1),12523(a,1,3))].">
      <j1 rule="para" parents="9499 12523"/>
    </justification>
  </clause>

  <clause id="12534">
    <literal><![CDATA[
      L(x,y,L(z,u,z) \ w) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(9501(a,1),12523(a,1,3))].">
      <j1 rule="para" parents="9501 12523"/>
    </justification>
  </clause>

  <clause id="12536">
    <literal><![CDATA[
      L(x,y,T(z,z * u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(4344(a,1),12526(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4344 12526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12537">
    <literal><![CDATA[
      L(x,y,T(z,z \ u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(4399(a,1),12526(a,1,3))].">
      <j1 rule="para" parents="4399 12526"/>
    </justification>
  </clause>

  <clause id="12538">
    <literal><![CDATA[
      L(x,y,(z \ u) \ u) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(7504(a,1),12526(a,1,3))].">
      <j1 rule="para" parents="7504 12526"/>
    </justification>
  </clause>

  <clause id="12539">
    <literal><![CDATA[
      L(x,y,K(z \ u,z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(8909(a,1),12525(a,1,3))].">
      <j1 rule="para" parents="8909 12525"/>
    </justification>
  </clause>

  <clause id="12540">
    <literal><![CDATA[
      L(x,y,L(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(9059(a,1),12525(a,1,3))].">
      <j1 rule="para" parents="9059 12525"/>
    </justification>
  </clause>

  <clause id="12541">
    <literal><![CDATA[
      L(x,y,z / R(u,w,u)) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(9509(a,1),12525(a,1,3))].">
      <j1 rule="para" parents="9509 12525"/>
    </justification>
  </clause>

  <clause id="12542">
    <literal><![CDATA[
      L(x,y,T(z / u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(4363(a,1),12540(a,1,3))].">
      <j1 rule="para" parents="4363 12540"/>
    </justification>
  </clause>

  <clause id="12543">
    <literal><![CDATA[
      L(x,y,T(z,u) / u) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(8943(a,1),12531(a,1,3))].">
      <j1 rule="para" parents="8943 12531"/>
    </justification>
  </clause>

  <clause id="12544">
    <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,11649,a(flip),b,12527,a),flip(a)].">
      <j1 rule="hyper" parents="58 11649 12527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12545">
    <literal><![CDATA[
      L(x,y,K(z,u * z)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(5346(a,2),12528(a,1,3))].">
      <j1 rule="para" parents="5346 12528"/>
    </justification>
  </clause>

  <clause id="12546">
    <literal><![CDATA[
      L(x,y,K(z * u,(z * u) * (u \ 1))) = L(x,y,K(u * z,u \ 1))
    ]]></literal>
    <justification jstring="[para(5840(a,1),12528(a,2,3))].">
      <j1 rule="para" parents="5840 12528"/>
    </justification>
  </clause>

  <clause id="12547">
    <literal><![CDATA[
      L(x,y \ z,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(5437,a,12530,a),flip(a)].">
      <j1 rule="hyper" parents="5437 12530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12548">
    <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(320,a,12372,a,b,12530,a)].">
      <j1 rule="hyper" parents="320 12372 12530"/>
    </justification>
  </clause>

  <clause id="12549">
    <literal><![CDATA[
      L(x \ y,z,K(x,y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,7493,a(flip),b,12530,a),flip(a)].">
      <j1 rule="hyper" parents="58 7493 12530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12550">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) * z = K(x,y) * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(1330,a,12547,a),flip(a)].">
      <j1 rule="hyper" parents="1330 12547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12551">
    <literal><![CDATA[
      (K(x,y) * z) / (x \ y) = K(x,y) * (z / (x \ y))
    ]]></literal>
    <justification jstring="[para(12549(a,1),544(a,1,2))].">
      <j1 rule="para" parents="12549 544"/>
    </justification>
  </clause>

  <clause id="12552">
    <literal><![CDATA[
      L(x,y * z,T(y,z)) = L(x,y * z,y)
    ]]></literal>
    <justification jstring="[hyper(11156,a,12536,a),flip(a)].">
      <j1 rule="hyper" parents="11156 12536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12553">
    <literal><![CDATA[
      L(x,y,T(z * u,u \ 1)) = L(x,y,T(z * u,z))
    ]]></literal>
    <justification jstring="[para(6144(a,1),12537(a,1,3))].">
      <j1 rule="para" parents="6144 12537"/>
    </justification>
  </clause>

  <clause id="12554">
    <literal><![CDATA[
      L(x,y / z,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(7266,a,12539,a)].">
      <j1 rule="hyper" parents="7266 12539"/>
    </justification>
  </clause>

  <clause id="12555">
    <literal><![CDATA[
      L(x,y \ z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(4174,a,12539,a),flip(a)].">
      <j1 rule="hyper" parents="4174 12539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12556">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(u,z \ 1))
    ]]></literal>
    <justification jstring="[para(4447(a,1),12539(a,1,3))].">
      <j1 rule="para" parents="4447 12539"/>
    </justification>
  </clause>

  <clause id="12557">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) = L(x,y,K(u,u \ z))
    ]]></literal>
    <justification jstring="[para(4925(a,1),12539(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4925 12539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12558">
    <literal><![CDATA[
      K(x,y) * ((x / y) * z) = (x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(12554(a,1),5236(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12554 5236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12559">
    <literal><![CDATA[
      (K(x,y) * (y \ x)) \ z = (y \ x) \ (K(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,298,a(flip),b,12555,a)].">
      <j1 rule="hyper" parents="58 298 12555"/>
    </justification>
  </clause>

  <clause id="12560">
    <literal><![CDATA[
      L(x,y,y / z) = L(x,y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(11156,a,12542,a)].">
      <j1 rule="hyper" parents="11156 12542"/>
    </justification>
  </clause>

  <clause id="12561">
    <literal><![CDATA[
      L(x,y * z,(y * z) / y) = L(x,y * z,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),12560(a,2,3))].">
      <j1 rule="para" parents="4 12560"/>
    </justification>
  </clause>

  <clause id="12562">
    <literal><![CDATA[
      L(x,y,z / T(u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(4206(a,1),12543(a,1,3))].">
      <j1 rule="para" parents="4206 12543"/>
    </justification>
  </clause>

  <clause id="12563">
    <literal><![CDATA[
      L(x,T(y,z),T(y,z) \ z) = L(x,T(y,z),y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11158,a(flip),b,12562,a)].">
      <j1 rule="hyper" parents="58 11158 12562"/>
    </justification>
  </clause>

  <clause id="12564">
    <literal><![CDATA[
      L(x,y,(z \ T(u,z \ u)) \ w) = L(x,y,(u / z) \ w)
    ]]></literal>
    <justification jstring="[para(4382(a,1),12532(a,1,3,1))].">
      <j1 rule="para" parents="4382 12532"/>
    </justification>
  </clause>

  <clause id="12565">
    <literal><![CDATA[
      L(x,y,z * T(u,u \ w)) = L(x,y,z * T(u,w))
    ]]></literal>
    <justification jstring="[para(4399(a,1),12533(a,1,3,2))].">
      <j1 rule="para" parents="4399 12533"/>
    </justification>
  </clause>

  <clause id="12566">
    <literal><![CDATA[
      L(x,y,T(z / u,z) \ w) = L(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(4363(a,1),12534(a,1,3,1))].">
      <j1 rule="para" parents="4363 12534"/>
    </justification>
  </clause>

  <clause id="12567">
    <literal><![CDATA[
      L(x,y,K(z,u) * (z \ u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(6050(a,1),12541(a,1,3))].">
      <j1 rule="para" parents="6050 12541"/>
    </justification>
  </clause>

  <clause id="12568">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,12530,a(flip),b,12557,a),flip(a)].">
      <j1 rule="hyper" parents="320 12530 12557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12569">
    <literal><![CDATA[
      L(x,y,K(z,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(10174,a,12568,a),flip(a)].">
      <j1 rule="hyper" parents="10174 12568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12571">
    <literal><![CDATA[
      (K(x,y \ 1) * y) * z = K(x,y \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1330,a,12569,a),flip(a)].">
      <j1 rule="hyper" parents="1330 12569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12579">
    <literal><![CDATA[
      K(x,y) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(5109,a,12558,a)].">
      <j1 rule="hyper" parents="5109 12558"/>
    </justification>
  </clause>

  <clause id="12580">
    <literal><![CDATA[
      L(x,y * z,z * K(y,z)) = L(x,y * z,z)
    ]]></literal>
    <justification jstring="[para(4711(a,1),12561(a,1,3))].">
      <j1 rule="para" parents="4711 12561"/>
    </justification>
  </clause>

  <clause id="12581">
    <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,12567,a)].">
      <j1 rule="hyper" parents="58 13 12567"/>
    </justification>
  </clause>

  <clause id="12582">
    <literal><![CDATA[
      R(K(x,y),x \ y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9235,a,12579,a)].">
      <j1 rule="hyper" parents="9235 12579"/>
    </justification>
  </clause>

  <clause id="12583">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),12582(a,1,2))].">
      <j1 rule="para" parents="4 12582"/>
    </justification>
  </clause>

  <clause id="12585">
    <literal><![CDATA[
      K(x,R(y \ 1,y,z) \ x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11633,a,b,12583,a)].">
      <j1 rule="hyper" parents="58 11633 12583"/>
    </justification>
  </clause>

  <clause id="12586">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,12585,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 12585 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12587">
    <literal><![CDATA[
      R(K(x,x * y),y * z,u) = K(x,((z * u) / ((y * z) * u)) \ x)
    ]]></literal>
    <justification jstring="[para(12585(a,1),11637(a,1,1))].">
      <j1 rule="para" parents="12585 11637"/>
    </justification>
  </clause>

  <clause id="12588">
    <literal><![CDATA[
      T(x,(y / (z * y)) \ x) = T(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3751,a(flip),b,12586,a)].">
      <j1 rule="hyper" parents="58 3751 12586"/>
    </justification>
  </clause>

  <clause id="12589">
    <literal><![CDATA[
      T(x,(y / z) \ x) = T(x,x * (z / y))
    ]]></literal>
    <justification jstring="[para(7(a,1),12588(a,1,2,1,2))].">
      <j1 rule="para" parents="7 12588"/>
    </justification>
  </clause>

  <clause id="12590">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,x * (y / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8463,a,b,12589,a)].">
      <j1 rule="hyper" parents="58 8463 12589"/>
    </justification>
  </clause>

  <clause id="12591">
    <literal><![CDATA[
      x * K(x,x * (y / z)) = T(x,(y * x) / z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4714,a(flip),b,12590,a)].">
      <j1 rule="hyper" parents="320 4714 12590"/>
    </justification>
  </clause>

  <clause id="12592">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,x * (y / z))
    ]]></literal>
    <justification jstring="[hyper(29,a,4714,a(flip),b,12591,a)].">
      <j1 rule="hyper" parents="29 4714 12591"/>
    </justification>
  </clause>

  <clause id="12593">
    <literal><![CDATA[
      K(x,(y / z) \ x) = K(x,x * (z / y))
    ]]></literal>
    <justification jstring="[hyper(8468,a,12592,a)].">
      <j1 rule="hyper" parents="8468 12592"/>
    </justification>
  </clause>

  <clause id="12594">
    <literal><![CDATA[
      K(x,x * (y / ((z * x) * u))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11066,a(flip),b,12592,a),flip(a)].">
      <j1 rule="hyper" parents="58 11066 12592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12595">
    <literal><![CDATA[
      (x * K(y,y * (z / u))) \ x = K((u / z) \ y,y)
    ]]></literal>
    <justification jstring="[para(12593(a,1),6309(a,1,1,2))].">
      <j1 rule="para" parents="12593 6309"/>
    </justification>
  </clause>

  <clause id="12596">
    <literal><![CDATA[
      R(K(x,x * (y / z)),x * u,w) = K(R(x,u,w),(z / y) \ x)
    ]]></literal>
    <justification jstring="[para(12593(a,1),6716(a,1,1))].">
      <j1 rule="para" parents="12593 6716"/>
    </justification>
  </clause>

  <clause id="12597">
    <literal><![CDATA[
      L(x,y,T(z * u,u \ 1)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,12529,a(flip),b,12553,a),flip(a)].">
      <j1 rule="hyper" parents="320 12529 12553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12598">
    <literal><![CDATA[
      (x \ y) \ (K(y,x) \ z) = (T(x,y) \ y) \ z
    ]]></literal>
    <justification jstring="[para(5093(a,1),12559(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5093 12559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12599">
    <literal><![CDATA[
      (x \ y) \ (K(x,y) * z) = (T(x,y) \ y) \ z
    ]]></literal>
    <justification jstring="[para(5092(a,1),12598(a,1,2))].">
      <j1 rule="para" parents="5092 12598"/>
    </justification>
  </clause>

  <clause id="12600">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),x \ y) = y \ ((T(y,x) / x) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11176,a(flip),b,12563,a),flip(a)].">
      <j1 rule="hyper" parents="58 11176 12563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12601">
    <literal><![CDATA[
      L(x,y,(z / u) * T(u,w)) = L(x,y,z * K(u,u \ w))
    ]]></literal>
    <justification jstring="[para(6121(a,1),12565(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6121 12565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12602">
    <literal><![CDATA[
      (x * K(y,x \ 1)) * z = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[para(2273(a,1),12571(a,1,1))].">
      <j1 rule="para" parents="2273 12571"/>
    </justification>
  </clause>

  <clause id="12603">
    <literal><![CDATA[
      K((x / y) \ z,z) = K(z * (y / x),z)
    ]]></literal>
    <justification jstring="[hyper(6316,a,12595,a),flip(a)].">
      <j1 rule="hyper" parents="6316 12595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12604">
    <literal><![CDATA[
      K(x / y,z) * a(z,y \ x,z) = K(z * (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,12102,a,b,12603,a)].">
      <j1 rule="hyper" parents="58 12102 12603"/>
    </justification>
  </clause>

  <clause id="12605">
    <literal><![CDATA[
      (x * K(y,x \ 1)) * z = x * (K(y,x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5899,a(flip),b,12602,a),flip(a)].">
      <j1 rule="hyper" parents="320 5899 12602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12606">
    <literal><![CDATA[
      L(x,K(y,z \ 1),z) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,12605,a)].">
      <j1 rule="hyper" parents="479 12605"/>
    </justification>
  </clause>

  <clause id="12612">
    <literal><![CDATA[
      L(x,K(y,z \ u),u \ z) = x
    ]]></literal>
    <justification jstring="[para(6078(a,1),12606(a,1,2))].">
      <j1 rule="para" parents="6078 12606"/>
    </justification>
  </clause>

  <clause id="12613">
    <literal><![CDATA[
      L(x,K(y,z),u \ (u / z)) = x
    ]]></literal>
    <justification jstring="[para(6101(a,1),12606(a,1,2))].">
      <j1 rule="para" parents="6101 12606"/>
    </justification>
  </clause>

  <clause id="12614">
    <literal><![CDATA[
      L(x,K(y,z \ u),u \ z) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(12612(a,1),45(a,2))].">
      <j1 rule="para" parents="12612 45"/>
    </justification>
  </clause>

  <clause id="12615">
    <literal><![CDATA[
      L(x,K(y,z),u \ (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(12613(a,1),45(a,2))].">
      <j1 rule="para" parents="12613 45"/>
    </justification>
  </clause>

  <clause id="12616">
    <literal><![CDATA[
      a(x,y / z,x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,8937,a,b,12604,a)].">
      <j1 rule="hyper" parents="29 8937 12604"/>
    </justification>
  </clause>

  <clause id="12618">
    <literal><![CDATA[
      a(x,y / (z * y),x) = a(x,z \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,12108,a(flip),b,12616,a),flip(a)].">
      <j1 rule="hyper" parents="320 12108 12616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12619">
    <literal><![CDATA[
      a(x,(y \ z) \ z,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),12616(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 12616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12620">
    <literal><![CDATA[
      a(x,T(y,z),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(12502,a,12619,a)].">
      <j1 rule="hyper" parents="12502 12619"/>
    </justification>
  </clause>

  <clause id="12621">
    <literal><![CDATA[
      a(x,y * K(z,y),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(5627(a,1),12619(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5627 12619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12622">
    <literal><![CDATA[
      a(x,T(y / z,u),x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,12616,a(flip),b,12620,a),flip(a)].">
      <j1 rule="hyper" parents="320 12616 12620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12624">
    <literal><![CDATA[
      L(x,T(y,z),x) = a(x,y,x) \ x
    ]]></literal>
    <justification jstring="[para(12620(a,1),9059(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12620 9059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12625">
    <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(12620(a,1),8950(a,1,1))].">
      <j1 rule="para" parents="12620 8950"/>
    </justification>
  </clause>

  <clause id="12626">
    <literal><![CDATA[
      L(a(x,y,x),y,z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12368,a(flip),b,12621,a)].">
      <j1 rule="hyper" parents="58 12368 12621"/>
    </justification>
  </clause>

  <clause id="12629">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,9059,a(flip),b,12624,a),flip(a)].">
      <j1 rule="hyper" parents="320 9059 12624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12630">
    <literal><![CDATA[
      L(x,T(y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(12624(a,2),9541(a,1))].">
      <j1 rule="para" parents="12624 9541"/>
    </justification>
  </clause>

  <clause id="12631">
    <literal><![CDATA[
      L(x,T(y,z),x) = T(x,T(x * y,u)) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,9629,a,b,12629,a),flip(a)].">
      <j1 rule="hyper" parents="320 9629 12629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12634">
    <literal><![CDATA[
      L(x,y / z,x) = L(x,z \ y,x)
    ]]></literal>
    <justification jstring="[para(107(a,1),12629(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 12629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12638">
    <literal><![CDATA[
      L(x,y * K(z,y),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4775(a,1),12629(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4775 12629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12640">
    <literal><![CDATA[
      L(x,R(y * K(z,y),z,u),x) = L(x,(z * u) \ ((z * y) * u),x)
    ]]></literal>
    <justification jstring="[para(4886(a,2),12634(a,1,2))].">
      <j1 rule="para" parents="4886 12634"/>
    </justification>
  </clause>

  <clause id="12641">
    <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(5892(a,2),12634(a,1,2))].">
      <j1 rule="para" parents="5892 12634"/>
    </justification>
  </clause>

  <clause id="12642">
    <literal><![CDATA[
      L(x,R(y * K(z,y),u,w),x) = L(x,R(y,u,w),x)
    ]]></literal>
    <justification jstring="[para(5479(a,1),12638(a,1,2))].">
      <j1 rule="para" parents="5479 12638"/>
    </justification>
  </clause>

  <clause id="12643">
    <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(4012(a,1),12618(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4012 12618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12644">
    <literal><![CDATA[
      a(x,R(y \ z,y,u),x) = a(x,(y * u) \ (z * u),x)
    ]]></literal>
    <justification jstring="[para(647(a,1),12622(a,1,2))].">
      <j1 rule="para" parents="647 12622"/>
    </justification>
  </clause>

  <clause id="12645">
    <literal><![CDATA[
      T(x,T(x * y,z)) = T(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8698,a,12631,a),flip(a)].">
      <j1 rule="hyper" parents="8698 12631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12646">
    <literal><![CDATA[
      T(x,T(x * (x \ y),z)) = T(x,y * K(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,11257,a,b,12645,a),flip(a)].">
      <j1 rule="hyper" parents="320 11257 12645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12647">
    <literal><![CDATA[
      T(x / T(y,x),z) * T(y,T(y * (y \ x),z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(12645(a,2),11441(a,1,2))].">
      <j1 rule="para" parents="12645 11441"/>
    </justification>
  </clause>

  <clause id="12649">
    <literal><![CDATA[
      T(x,y * K(x \ y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),12646(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 12646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12650">
    <literal><![CDATA[
      T(x \ y,y * K(x,T(z,y))) = T(x \ y,T(y,z))
    ]]></literal>
    <justification jstring="[para(7138(a,1),12649(a,1,2,2))].">
      <j1 rule="para" parents="7138 12649"/>
    </justification>
  </clause>

  <clause id="12651">
    <literal><![CDATA[
      T(x \ y,K(x,z) * y) = T(x \ y,T(y,z))
    ]]></literal>
    <justification jstring="[para(7152(a,1),12650(a,1,2))].">
      <j1 rule="para" parents="7152 12650"/>
    </justification>
  </clause>

  <clause id="12652">
    <literal><![CDATA[
      a(x,(y * z) \ (u * z),x) = a(x,y \ u,x)
    ]]></literal>
    <justification jstring="[hyper(12501,a,12644,a),flip(a)].">
      <j1 rule="hyper" parents="12501 12644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12654">
    <literal><![CDATA[
      L(x,(y * z) \ (u * z),x) = (w / x) \ (a(x,y \ u,x) \ w)
    ]]></literal>
    <justification jstring="[para(12652(a,1),9527(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12652 9527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12655">
    <literal><![CDATA[
      L(x,y,K(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(12548(a,1),373(a,1)),flip(b)].">
      <j1 rule="para" parents="12548 373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12656">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(12557(a,2),12655(a,1))].">
      <j1 rule="para" parents="12557 12655"/>
    </justification>
  </clause>

  <clause id="12657">
    <literal><![CDATA[
      L(x,y,z * K(u,u \ w)) = L(x,y,z * K(u,w))
    ]]></literal>
    <justification jstring="[para(6121(a,1),12601(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6121 12601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12658">
    <literal><![CDATA[
      K(R(x,y,z),(u / w) \ x) = K(R(x,y,z),x * (w / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6716,a(flip),b,12596,a),flip(a)].">
      <j1 rule="hyper" parents="58 6716 12596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12659">
    <literal><![CDATA[
      L(x,(y * z) \ (u * z),x) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ u,x) = w
    ]]></literal>
    <justification jstring="[para(12654(a,2),9543(a,1))].">
      <j1 rule="para" parents="12654 9543"/>
    </justification>
  </clause>

  <clause id="12660">
    <literal><![CDATA[
      R(K(x,x * y),y * z,u) = K(x,x * (((y * z) * u) / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,12593,a(flip),b,12587,a),flip(a)].">
      <j1 rule="hyper" parents="320 12593 12587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12662">
    <literal><![CDATA[
      L(x,(y * z) \ ((y * u) * z),x) = L(x,R(u,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12642,a(flip),b,12640,a),flip(a)].">
      <j1 rule="hyper" parents="58 12642 12640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12663">
    <literal><![CDATA[
      L(x,R(y,z,u),x) = L(x,z \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(12659,a,12662,a),flip(a)].">
      <j1 rule="hyper" parents="12659 12662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12665">
    <literal><![CDATA[
      L(x,R(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),12663(a,2,2))].">
      <j1 rule="para" parents="4 12663"/>
    </justification>
  </clause>

  <clause id="12666">
    <literal><![CDATA[
      R(K(x,x * y),y * z,u) = K(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(15(a,2),12660(a,2,2,2))].">
      <j1 rule="para" parents="15 12660"/>
    </justification>
  </clause>

  <clause id="12667">
    <literal><![CDATA[
      K(x,R(x * y,y * z,u)) = K(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12461,a,12666,a)].">
      <j1 rule="hyper" parents="12461 12666"/>
    </justification>
  </clause>

  <clause id="12668">
    <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(261(a,1),12546(a,1,3,2))].">
      <j1 rule="para" parents="261 12546"/>
    </justification>
  </clause>

  <clause id="12669">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(u * z,u))
    ]]></literal>
    <justification jstring="[para(6931(a,1),12668(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6931 12668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12670">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,12527,a(flip),b,12669,a),flip(a)].">
      <j1 rule="hyper" parents="320 12527 12669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12672">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,12556,a(flip),b,12670,a)].">
      <j1 rule="hyper" parents="58 12556 12670"/>
    </justification>
  </clause>

  <clause id="12673">
    <literal><![CDATA[
      L(x,y,K(z \ u,w)) = L(x,y,K(w,u \ z))
    ]]></literal>
    <justification jstring="[para(6078(a,1),12672(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6078 12672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12674">
    <literal><![CDATA[
      L(x,y,K(z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(12673(a,2),12656(a,1))].">
      <j1 rule="para" parents="12673 12656"/>
    </justification>
  </clause>

  <clause id="12675">
    <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),12674(a,1,3,1))].">
      <j1 rule="para" parents="4 12674"/>
    </justification>
  </clause>

  <clause id="12676">
    <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),12647(a,1,2,2,1))].">
      <j1 rule="para" parents="5 12647"/>
    </justification>
  </clause>

  <clause id="12677">
    <literal><![CDATA[
      x * K(T(x,y) / y,z) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9659,a(flip),b,12676,a)].">
      <j1 rule="hyper" parents="58 9659 12676"/>
    </justification>
  </clause>

  <clause id="12678">
    <literal><![CDATA[
      K(T(x,y) / y,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,6084,a(flip),b,12677,a),flip(a)].">
      <j1 rule="hyper" parents="29 6084 12677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12679">
    <literal><![CDATA[
      K(x / T(y,x),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9610,a(flip),b,12678,a)].">
      <j1 rule="hyper" parents="58 9610 12678"/>
    </justification>
  </clause>

  <clause id="12680">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(12678(a,1),9785(a,2,2))].">
      <j1 rule="para" parents="12678 9785"/>
    </justification>
  </clause>

  <clause id="12681">
    <literal><![CDATA[
      (x \ (x * K(y \ x,z))) \ (x * K(x / y,z)) = L(x,K(y \ x,z),x)
    ]]></literal>
    <justification jstring="[para(12680(a,1),9860(a,1,1,2))].">
      <j1 rule="para" parents="12680 9860"/>
    </justification>
  </clause>

  <clause id="12682">
    <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),12681(a,1,1))].">
      <j1 rule="para" parents="4 12681"/>
    </justification>
  </clause>

  <clause id="12683">
    <literal><![CDATA[
      L(x,K(y \ x,z),x) = x
    ]]></literal>
    <justification jstring="[hyper(8088,a,12682,a)].">
      <j1 rule="hyper" parents="8088 12682"/>
    </justification>
  </clause>

  <clause id="12685">
    <literal><![CDATA[
      L(x,K(y,z),x) = x
    ]]></literal>
    <justification jstring="[para(75(a,1),12683(a,1,2,1))].">
      <j1 rule="para" parents="75 12683"/>
    </justification>
  </clause>

  <clause id="12686">
    <literal><![CDATA[
      T(K(x,y) * z,z) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10021,a,12685,a)].">
      <j1 rule="hyper" parents="10021 12685"/>
    </justification>
  </clause>

  <clause id="12689">
    <literal><![CDATA[
      T(x * T(x \ y,z),y) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(4776(a,1),12686(a,1,1))].">
      <j1 rule="para" parents="4776 12686"/>
    </justification>
  </clause>

  <clause id="12690">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1949,a,b,12689,a)].">
      <j1 rule="hyper" parents="58 1949 12689"/>
    </justification>
  </clause>

  <clause id="12691">
    <literal><![CDATA[
      K(T(x,y) \ y,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(6125,a,12690,a)].">
      <j1 rule="hyper" parents="6125 12690"/>
    </justification>
  </clause>

  <clause id="12692">
    <literal><![CDATA[
      K(x / y,z) * a(z,T(y,x) \ x,z) = K(z * (T(y,x) \ x),z)
    ]]></literal>
    <justification jstring="[para(12691(a,1),8937(a,1,1))].">
      <j1 rule="para" parents="12691 8937"/>
    </justification>
  </clause>

  <clause id="12693">
    <literal><![CDATA[
      T(x,y / z) \ R(x,T(z,y) \ y,x) = K(x * (T(z,y) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(8923,a,12692,a)].">
      <j1 rule="hyper" parents="8923 12692"/>
    </justification>
  </clause>

  <clause id="12694">
    <literal><![CDATA[
      T(x,T(y,z) \ z) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(5257,a,12693,a)].">
      <j1 rule="hyper" parents="5257 12693"/>
    </justification>
  </clause>

  <clause id="12695">
    <literal><![CDATA[
      T(x,y \ T(z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6572,a(flip),b,12694,a)].">
      <j1 rule="hyper" parents="58 6572 12694"/>
    </justification>
  </clause>

  <clause id="12696">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / z) = T(x,y / T(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9085,a(flip),b,12695,a),flip(a)].">
      <j1 rule="hyper" parents="58 9085 12695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12697">
    <literal><![CDATA[
      T(x,T(y \ T(z,y),u)) = K(x,u) * T(x * K(u,x),z / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,12695,a(flip),b,8349,a),flip(a)].">
      <j1 rule="hyper" parents="119 12695 8349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12698">
    <literal><![CDATA[
      T(x,y / T(z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(8339,a,12696,a),flip(a)].">
      <j1 rule="hyper" parents="8339 12696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12699">
    <literal><![CDATA[
      T(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(12696(a,1),8339(a,1))].">
      <j1 rule="para" parents="12696 8339"/>
    </justification>
  </clause>

  <clause id="12700">
    <literal><![CDATA[
      T(x,T(y,z) / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(9470,a,12698,a)].">
      <j1 rule="hyper" parents="9470 12698"/>
    </justification>
  </clause>

  <clause id="12701">
    <literal><![CDATA[
      T(x,y / T(T(z,y),u)) = T(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[para(18(a,1),12698(a,1,2,2))].">
      <j1 rule="para" parents="18 12698"/>
    </justification>
  </clause>

  <clause id="12702">
    <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(12698(a,1),12699(a,1,2,2))].">
      <j1 rule="para" parents="12698 12699"/>
    </justification>
  </clause>

  <clause id="12703">
    <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(12651(a,1),12701(a,1,2,2,1))].">
      <j1 rule="para" parents="12651 12701"/>
    </justification>
  </clause>

  <clause id="12704">
    <literal><![CDATA[
      T(x,T(y \ T(z,y),u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,8350,a(flip),b,12697,a),flip(a)].">
      <j1 rule="hyper" parents="320 8350 12697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12705">
    <literal><![CDATA[
      (K(x,y) * ((x \ y) * z)) \ ((K(x,y) * (x \ y)) * (z * u)) = L(u,z,y / x)
    ]]></literal>
    <justification jstring="[para(12550(a,1),12581(a,1,1))].">
      <j1 rule="para" parents="12550 12581"/>
    </justification>
  </clause>

  <clause id="12706">
    <literal><![CDATA[
      (K(x,y) * ((x \ y) * z)) \ (K(x,y) * ((x \ y) * (z * u))) = L(u,z,y / x)
    ]]></literal>
    <justification jstring="[para(12550(a,1),12705(a,1,2))].">
      <j1 rule="para" parents="12550 12705"/>
    </justification>
  </clause>

  <clause id="12707">
    <literal><![CDATA[
      L(L(x,y,z \ u),(z \ u) * y,K(z,u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[hyper(828,a,12706,a)].">
      <j1 rule="hyper" parents="828 12706"/>
    </justification>
  </clause>

  <clause id="12708">
    <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),12641(a,2,2))].">
      <j1 rule="para" parents="9 12641"/>
    </justification>
  </clause>

  <clause id="12709">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),x) = L(x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12665,a(flip),b,12708,a)].">
      <j1 rule="hyper" parents="58 12665 12708"/>
    </justification>
  </clause>

  <clause id="12711">
    <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(12369(a,1),12380(a,2,1))].">
      <j1 rule="para" parents="12369 12380"/>
    </justification>
  </clause>

  <clause id="12712">
    <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(320,a,12378,a(flip),b,12711,a),flip(a)].">
      <j1 rule="hyper" parents="320 12378 12711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12713">
    <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),12712(a,2,2))].">
      <j1 rule="para" parents="15 12712"/>
    </justification>
  </clause>

  <clause id="12714">
    <literal><![CDATA[
      R(a(x,y,x) * z,u,w) = a(x,y,x) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(12372(a,1),12713(a,1,2))].">
      <j1 rule="para" parents="12372 12713"/>
    </justification>
  </clause>

  <clause id="12715">
    <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(12714(a,2),12146(a,1,1,2))].">
      <j1 rule="para" parents="12714 12146"/>
    </justification>
  </clause>

  <clause id="12716">
    <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(12369(a,1),12390(a,1,2,1))].">
      <j1 rule="para" parents="12369 12390"/>
    </justification>
  </clause>

  <clause id="12717">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) = a(u,(x * (y * z)) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(4896(a,1),12443(a,2,2))].">
      <j1 rule="para" parents="4896 12443"/>
    </justification>
  </clause>

  <clause id="12718">
    <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(8947,a,12717,a)].">
      <j1 rule="hyper" parents="8947 12717"/>
    </justification>
  </clause>

  <clause id="12719">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * (z * y)) / (u * z),x)
    ]]></literal>
    <justification jstring="[para(12626(a,1),12718(a,1,1))].">
      <j1 rule="para" parents="12626 12718"/>
    </justification>
  </clause>

  <clause id="12720">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * z) \ (u * (z * y)),x)
    ]]></literal>
    <justification jstring="[hyper(320,a,12616,a(flip),b,12719,a),flip(a)].">
      <j1 rule="hyper" parents="320 12616 12719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12722">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(13(a,2),12720(a,2,2))].">
      <j1 rule="para" parents="13 12720"/>
    </justification>
  </clause>

  <clause id="12723">
    <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(12369(a,1),12716(a,1,2))].">
      <j1 rule="para" parents="12369 12716"/>
    </justification>
  </clause>

  <clause id="12724">
    <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(830,a,12723,a)].">
      <j1 rule="hyper" parents="830 12723"/>
    </justification>
  </clause>

  <clause id="12725">
    <literal><![CDATA[
      a(a(x,y,x) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(12377,a,12724,a),flip(a)].">
      <j1 rule="hyper" parents="12377 12724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12727">
    <literal><![CDATA[
      a(a(x,y,x) \ z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),12725(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 12725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12728">
    <literal><![CDATA[
      a(R(x,y,x),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(8926(a,1),12725(a,1,1))].">
      <j1 rule="para" parents="8926 12725"/>
    </justification>
  </clause>

  <clause id="12729">
    <literal><![CDATA[
      a(T(x * y,x),z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(8939(a,1),12725(a,1,1))].">
      <j1 rule="para" parents="8939 12725"/>
    </justification>
  </clause>

  <clause id="12730">
    <literal><![CDATA[
      a(K(x * y,y),z,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(8949(a,1),12725(a,1,1))].">
      <j1 rule="para" parents="8949 12725"/>
    </justification>
  </clause>

  <clause id="12731">
    <literal><![CDATA[
      a(K(x,x \ y),z,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(8910(a,1),12725(a,1,1))].">
      <j1 rule="para" parents="8910 12725"/>
    </justification>
  </clause>

  <clause id="12732">
    <literal><![CDATA[
      a(x * a(y,z,y),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(9492(a,1),12725(a,1,1))].">
      <j1 rule="para" parents="9492 12725"/>
    </justification>
  </clause>

  <clause id="12733">
    <literal><![CDATA[
      a(R(x,y,x) * z,u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[para(9498(a,1),12725(a,1,1))].">
      <j1 rule="para" parents="9498 12725"/>
    </justification>
  </clause>

  <clause id="12734">
    <literal><![CDATA[
      a(T(x * (y / x),x),z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(9500(a,1),12725(a,1,1))].">
      <j1 rule="para" parents="9500 12725"/>
    </justification>
  </clause>

  <clause id="12735">
    <literal><![CDATA[
      a(T(x,x \ y),z,u) = a(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4399(a,1),12728(a,1,1))].">
      <j1 rule="para" parents="4399 12728"/>
    </justification>
  </clause>

  <clause id="12736">
    <literal><![CDATA[
      a((x \ y) \ y,z,u) = a(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(7504(a,1),12728(a,1,1))].">
      <j1 rule="para" parents="7504 12728"/>
    </justification>
  </clause>

  <clause id="12737">
    <literal><![CDATA[
      a(K(x \ y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(8909(a,1),12727(a,1,1))].">
      <j1 rule="para" parents="8909 12727"/>
    </justification>
  </clause>

  <clause id="12738">
    <literal><![CDATA[
      a(K(x \ 1,y),z,u) = a(K(x \ y,y),z,u)
    ]]></literal>
    <justification jstring="[para(8941(a,1),12727(a,1,1))].">
      <j1 rule="para" parents="8941 12727"/>
    </justification>
  </clause>

  <clause id="12739">
    <literal><![CDATA[
      a(L(x,y,x),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(9059(a,1),12727(a,1,1))].">
      <j1 rule="para" parents="9059 12727"/>
    </justification>
  </clause>

  <clause id="12740">
    <literal><![CDATA[
      a(T(x / y,x),z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(4363(a,1),12739(a,1,1))].">
      <j1 rule="para" parents="4363 12739"/>
    </justification>
  </clause>

  <clause id="12741">
    <literal><![CDATA[
      a(T(x,x \ y),z,u) = a((x \ y) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(6280(a,1),12739(a,1,1))].">
      <j1 rule="para" parents="6280 12739"/>
    </justification>
  </clause>

  <clause id="12742">
    <literal><![CDATA[
      a(T(x,y) / y,z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(8943(a,1),12732(a,1,1))].">
      <j1 rule="para" parents="8943 12732"/>
    </justification>
  </clause>

  <clause id="12743">
    <literal><![CDATA[
      a(K(x,y \ x),z,u) = a(K(y,y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),12730(a,1,1,1))].">
      <j1 rule="para" parents="5 12730"/>
    </justification>
  </clause>

  <clause id="12744">
    <literal><![CDATA[
      a(T(x * y,y \ 1),z,u) = a(T(x * y,x),z,u)
    ]]></literal>
    <justification jstring="[para(6144(a,1),12735(a,1,1))].">
      <j1 rule="para" parents="6144 12735"/>
    </justification>
  </clause>

  <clause id="12745">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12518,a,b,12737,a)].">
      <j1 rule="hyper" parents="58 12518 12737"/>
    </justification>
  </clause>

  <clause id="12746">
    <literal><![CDATA[
      a(T(x,x \ y) * z,u,w) = a(T(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(4399(a,1),12733(a,1,1,1))].">
      <j1 rule="para" parents="4399 12733"/>
    </justification>
  </clause>

  <clause id="12747">
    <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(3869(a,1),12741(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3869 12741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12748">
    <literal><![CDATA[
      a(K(x,y \ x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,12731,a(flip),b,12743,a),flip(a)].">
      <j1 rule="hyper" parents="320 12731 12743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12749">
    <literal><![CDATA[
      a(K(x \ y,y),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5158(a,1),12748(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5158 12748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12750">
    <literal><![CDATA[
      a(K(x \ 1,y),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12738,a,b,12749,a)].">
      <j1 rule="hyper" parents="58 12738 12749"/>
    </justification>
  </clause>

  <clause id="12751">
    <literal><![CDATA[
      a(K(x,y \ 1),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(3298(a,1),12750(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3298 12750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12752">
    <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(11114(a,2),12750(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11114 12750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12753">
    <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,11926,a,b,12751,a)].">
      <j1 rule="hyper" parents="58 11926 12751"/>
    </justification>
  </clause>

  <clause id="12754">
    <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(12453(a,1),12751(a,2,1))].">
      <j1 rule="para" parents="12453 12751"/>
    </justification>
  </clause>

  <clause id="12755">
    <literal><![CDATA[
      a(T(x * y,y \ 1),z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,12729,a(flip),b,12744,a),flip(a)].">
      <j1 rule="hyper" parents="320 12729 12744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12756">
    <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,5573,a,b,12745,a)].">
      <j1 rule="hyper" parents="58 5573 12745"/>
    </justification>
  </clause>

  <clause id="12757">
    <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,12012,a,b,12754,a)].">
      <j1 rule="hyper" parents="58 12012 12754"/>
    </justification>
  </clause>

  <clause id="12758">
    <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(6932(a,1),12752(a,2,1))].">
      <j1 rule="para" parents="6932 12752"/>
    </justification>
  </clause>

  <clause id="12759">
    <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(320,a,12750,a(flip),b,12758,a),flip(a)].">
      <j1 rule="hyper" parents="320 12750 12758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12760">
    <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(11114(a,1),12759(a,1,1))].">
      <j1 rule="para" parents="11114 12759"/>
    </justification>
  </clause>

  <clause id="12761">
    <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(12453(a,1),12760(a,2,1))].">
      <j1 rule="para" parents="12453 12760"/>
    </justification>
  </clause>

  <clause id="12762">
    <literal><![CDATA[
      a(K(x,R(y,z,u)),w,v5) = R(a(K(x,y),w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(12753(a,1),12757(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12753 12757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12763">
    <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(320,a,12520,a(flip),b,12762,a),flip(a)].">
      <j1 rule="hyper" parents="320 12520 12762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12764">
    <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,12761,a(flip),b,12763,a)].">
      <j1 rule="hyper" parents="58 12761 12763"/>
    </justification>
  </clause>

  <clause id="12765">
    <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(12709(a,1),12756(a,1,2))].">
      <j1 rule="para" parents="12709 12756"/>
    </justification>
  </clause>

  <clause id="12766">
    <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(5424,a,12765,a)].">
      <j1 rule="hyper" parents="5424 12765"/>
    </justification>
  </clause>

  <clause id="12767">
    <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),12267(a,2,1,2,2,1,2))].">
      <j1 rule="para" parents="60 12267"/>
    </justification>
  </clause>

  <clause id="12768">
    <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),12767(a,2,1,2))].">
      <j1 rule="para" parents="2 12767"/>
    </justification>
  </clause>

  <clause id="12769">
    <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(12768(a,2),8034(a,1))].">
      <j1 rule="para" parents="12768 8034"/>
    </justification>
  </clause>

  <clause id="12770">
    <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,11399,a(flip),b,12468,a)].">
      <j1 rule="hyper" parents="58 11399 12468"/>
    </justification>
  </clause>

  <clause id="12771">
    <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,5729,a(flip),b,12544,a),flip(a)].">
      <j1 rule="hyper" parents="58 5729 12544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12772">
    <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(7248(a,1),12771(a,1,1,1))].">
      <j1 rule="para" parents="7248 12771"/>
    </justification>
  </clause>

  <clause id="12773">
    <literal><![CDATA[
      (K(x,x * y) \ z) \ T(x * y,x) = (K(x,y) \ z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(4106(a,1),12772(a,1,2,1))].">
      <j1 rule="para" parents="4106 12772"/>
    </justification>
  </clause>

  <clause id="12775">
    <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(5095(a,1),12770(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5095 12770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12776">
    <literal><![CDATA[
      L(x,K(y,z) * K(y,u),K(z,y) * K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,5095,a(flip),b,12775,a),flip(a)].">
      <j1 rule="hyper" parents="320 5095 12775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12779">
    <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),12715(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 12715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12780">
    <literal><![CDATA[
      R(x,y \ R(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(1319,a,12779,a)].">
      <j1 rule="hyper" parents="1319 12779"/>
    </justification>
  </clause>

  <clause id="12781">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[para(12780(a,1),4291(a,1,1))].">
      <j1 rule="para" parents="12780 4291"/>
    </justification>
  </clause>

  <clause id="12782">
    <literal><![CDATA[
      L(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,12709,a(flip),b,12781,a)].">
      <j1 rule="hyper" parents="58 12709 12781"/>
    </justification>
  </clause>

  <clause id="12783">
    <literal><![CDATA[
      R(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(6818,a,12782,a),flip(a)].">
      <j1 rule="hyper" parents="6818 12782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12785">
    <literal><![CDATA[
      L(T(x,y),a(z,u,w),x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7478,a(flip),b,12782,a)].">
      <j1 rule="hyper" parents="58 7478 12782"/>
    </justification>
  </clause>

  <clause id="12786">
    <literal><![CDATA[
      a(x,a(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(48,a,12782,a)].">
      <j1 rule="hyper" parents="48 12782"/>
    </justification>
  </clause>

  <clause id="12787">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = a(y,z,u) * (x / a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,12783,a(flip),b,4382,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 12783 4382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12788">
    <literal><![CDATA[
      a(x,a(y,z,u),x) \ w = w
    ]]></literal>
    <justification jstring="[hyper(280,a,12786,a(flip))].">
      <j1 rule="hyper" parents="280 12786"/>
    </justification>
  </clause>

  <clause id="12789">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ 1 = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,12786,a(flip),b,2211,a(flip))].">
      <j1 rule="hyper" parents="116 12786 2211"/>
    </justification>
  </clause>

  <clause id="12790">
    <literal><![CDATA[
      a(x,a(y,z,u),x) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      w = v5
    ]]></literal>
    <justification jstring="[para(12786(a,2),165(a,1,1))].">
      <j1 rule="para" parents="12786 165"/>
    </justification>
  </clause>

  <clause id="12791">
    <literal><![CDATA[
      x * (y \ L(y,a(z,u,w),y)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,9525,a,b,12788,a)].">
      <j1 rule="hyper" parents="58 9525 12788"/>
    </justification>
  </clause>

  <clause id="12792">
    <literal><![CDATA[
      a(x,y,z) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),12789(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 12789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12793">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12766,a(flip),b,12791,a)].">
      <j1 rule="hyper" parents="58 12766 12791"/>
    </justification>
  </clause>

  <clause id="12794">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(8927(a,1),12790(a,1))].">
      <j1 rule="para" parents="8927 12790"/>
    </justification>
  </clause>

  <clause id="12796">
    <literal><![CDATA[
      a(K(x,K(y,z)),u * y,w) = K(x,K(z,y \ R(y,u,w)))
    ]]></literal>
    <justification jstring="[para(12793(a,1),11973(a,2,2))].">
      <j1 rule="para" parents="12793 11973"/>
    </justification>
  </clause>

  <clause id="12797">
    <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,12787,a,b,4974,a),flip(a)].">
      <j1 rule="hyper" parents="116 12787 4974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12798">
    <literal><![CDATA[
      T(a(x,y,z),x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,11600,a(flip),b,12792,a)].">
      <j1 rule="hyper" parents="320 11600 12792"/>
    </justification>
  </clause>

  <clause id="12799">
    <literal><![CDATA[
      a(x,y,z) * x = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,12798,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 12798 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12800">
    <literal><![CDATA[
      T(a(1 / x,y,z),x \ 1) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(4022(a,2),12798(a,1,1))].">
      <j1 rule="para" parents="4022 12798"/>
    </justification>
  </clause>

  <clause id="12801">
    <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,9884,a(flip),b,12799,a),flip(a)].">
      <j1 rule="hyper" parents="58 9884 12799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12802">
    <literal><![CDATA[
      a((x / y) \ 1,z,(x / y) \ 1) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,12000,a(flip),b,12800,a),flip(a)].">
      <j1 rule="hyper" parents="58 12000 12800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12803">
    <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,12470,a(flip),b,12796,a),flip(a)].">
      <j1 rule="hyper" parents="58 12470 12796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12804">
    <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,9274,a,b,12803,a)].">
      <j1 rule="hyper" parents="58 9274 12803"/>
    </justification>
  </clause>

  <clause id="12805">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11419,a,b,12802,a)].">
      <j1 rule="hyper" parents="58 11419 12802"/>
    </justification>
  </clause>

  <clause id="12806">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(7759(a,2),12804(a,2,1))].">
      <j1 rule="para" parents="7759 12804"/>
    </justification>
  </clause>

  <clause id="12807">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) \ z)) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(9430,a,12806,a)].">
      <j1 rule="hyper" parents="9430 12806"/>
    </justification>
  </clause>

  <clause id="12808">
    <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,9842,a(flip),b,12807,a)].">
      <j1 rule="hyper" parents="58 9842 12807"/>
    </justification>
  </clause>

  <clause id="12809">
    <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(12797(a,2),4797(a,1))].">
      <j1 rule="para" parents="12797 4797"/>
    </justification>
  </clause>

  <clause id="12810">
    <literal><![CDATA[
      K(x,y * (1 / (z * K(x,u)))) = K(x,y * (K(u,x) / z))
    ]]></literal>
    <justification jstring="[para(12801(a,1),9614(a,1,2,2))].">
      <j1 rule="para" parents="12801 9614"/>
    </justification>
  </clause>

  <clause id="12811">
    <literal><![CDATA[
      K(x,y * ((z * K(x,u)) \ 1)) = K(x,y * (K(u,x) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5277,a(flip),b,12810,a)].">
      <j1 rule="hyper" parents="58 5277 12810"/>
    </justification>
  </clause>

  <clause id="12812">
    <literal><![CDATA[
      K(x,y * ((K(x,z) * u) \ 1)) = K(x,y * (K(z,x) / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9599,a,b,12811,a)].">
      <j1 rule="hyper" parents="58 9599 12811"/>
    </justification>
  </clause>

  <clause id="12813">
    <literal><![CDATA[
      K(x,y * ((K(x,z) * u) \ 1)) = K(x,y * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,11356,a(flip),b,12812,a),flip(a)].">
      <j1 rule="hyper" parents="320 11356 12812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12815">
    <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,10260,a,b,12813,a)].">
      <j1 rule="hyper" parents="58 10260 12813"/>
    </justification>
  </clause>

  <clause id="12816">
    <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(7772(a,1),12808(a,2,1))].">
      <j1 rule="para" parents="7772 12808"/>
    </justification>
  </clause>

  <clause id="12817">
    <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(11071(a,1),12816(a,2,1,2))].">
      <j1 rule="para" parents="11071 12816"/>
    </justification>
  </clause>

  <clause id="12818">
    <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(9859,a,12817,a)].">
      <j1 rule="hyper" parents="9859 12817"/>
    </justification>
  </clause>

  <clause id="12821">
    <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,10635,a(flip),b,12818,a)].">
      <j1 rule="hyper" parents="58 10635 12818"/>
    </justification>
  </clause>

  <clause id="12824">
    <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(261(a,1),12815(a,2,2))].">
      <j1 rule="para" parents="261 12815"/>
    </justification>
  </clause>

  <clause id="12825">
    <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(320,a,9422,a(flip),b,12824,a),flip(a)].">
      <j1 rule="hyper" parents="320 9422 12824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12827">
    <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,8859,a(flip),b,12825,a)].">
      <j1 rule="hyper" parents="58 8859 12825"/>
    </justification>
  </clause>

  <clause id="12828">
    <literal><![CDATA[
      K(x,R(y,z,(K(x,u) * z) \ 1)) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,12311,a(flip),b,12827,a),flip(a)].">
      <j1 rule="hyper" parents="320 12311 12827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12830">
    <literal><![CDATA[
      R(K(x,y),z,(K(x,u) * z) \ 1) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(12451,a,12828,a)].">
      <j1 rule="hyper" parents="12451 12828"/>
    </justification>
  </clause>

  <clause id="12831">
    <literal><![CDATA[
      x / (K(y,L(z,u,u \ 1)) * x) = u * ((K(y,z) * u) \ 1)
    ]]></literal>
    <justification jstring="[para(12830(a,1),6955(a,1,2,1))].">
      <j1 rule="para" parents="12830 6955"/>
    </justification>
  </clause>

  <clause id="12832">
    <literal><![CDATA[
      x * ((K(y,z) * x) \ 1) = K(L(z,x,x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(5112,a,12831,a),flip(a)].">
      <j1 rule="hyper" parents="5112 12831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12834">
    <literal><![CDATA[
      x * ((K(y,z) * x) \ 1) = K(z,L(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,10809,a(flip),b,12832,a),flip(a)].">
      <j1 rule="hyper" parents="320 10809 12832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12835">
    <literal><![CDATA[
      x \ K(y,L(z,x,x \ 1)) = (K(z,y) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,10809,a(flip),b,12832,a)].">
      <j1 rule="hyper" parents="116 10809 12832"/>
    </justification>
  </clause>

  <clause id="12836">
    <literal><![CDATA[
      K(x,((K(y,x) * (z \ 1)) \ 1) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(12835(a,1),9247(a,1,2,1))].">
      <j1 rule="para" parents="12835 9247"/>
    </justification>
  </clause>

  <clause id="12837">
    <literal><![CDATA[
      K(x,(((y \ 1) * K(z,x)) \ 1) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(7261(a,1),12836(a,1,2,1,1))].">
      <j1 rule="para" parents="7261 12836"/>
    </justification>
  </clause>

  <clause id="12838">
    <literal><![CDATA[
      K(x,((y * K(z,x)) \ 1) \ u) = K(x,(y \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5536,a(flip),b,12837,a)].">
      <j1 rule="hyper" parents="58 5536 12837"/>
    </justification>
  </clause>

  <clause id="12839">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ u) = K(x,((y / z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1429(a,1),12838(a,1,2,1,1))].">
      <j1 rule="para" parents="1429 12838"/>
    </justification>
  </clause>

  <clause id="12840">
    <literal><![CDATA[
      (T(x,y) / z) \ x = z * K(y,((x / z) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,12839,a(flip),b,8560,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 12839 8560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12841">
    <literal><![CDATA[
      (T(x,y) / z) \ x = (1 / z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,11558,a(flip),b,12840,a),flip(a)].">
      <j1 rule="hyper" parents="320 11558 12840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12842">
    <literal><![CDATA[
      (1 / (x \ T(y,z))) \ K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[para(72(a,1),12841(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 12841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12844">
    <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(12842(a,2),7237(a,2,2)),flip(a)].">
      <j1 rule="para" parents="12842 7237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12845">
    <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(4545(a,1),12747(a,2,1))].">
      <j1 rule="para" parents="4545 12747"/>
    </justification>
  </clause>

  <clause id="12846">
    <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,12736,a(flip),b,12845,a)].">
      <j1 rule="hyper" parents="58 12736 12845"/>
    </justification>
  </clause>

  <clause id="12847">
    <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(10477,a,12643,a)].">
      <j1 rule="hyper" parents="10477 12643"/>
    </justification>
  </clause>

  <clause id="12848">
    <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(320,a,7237,a(flip),b,12844,a),flip(a)].">
      <j1 rule="hyper" parents="320 7237 12844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12849">
    <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),12848(a,1,2,1,2,2))].">
      <j1 rule="para" parents="20 12848"/>
    </justification>
  </clause>

  <clause id="12850">
    <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),12849(a,1,2,1,2,2,1))].">
      <j1 rule="para" parents="20 12849"/>
    </justification>
  </clause>

  <clause id="12851">
    <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,10588,a(flip),b,12850,a)].">
      <j1 rule="hyper" parents="58 10588 12850"/>
    </justification>
  </clause>

  <clause id="12853">
    <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),12851(a,1,2))].">
      <j1 rule="para" parents="75 12851"/>
    </justification>
  </clause>

  <clause id="12854">
    <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,11755,a,b,12853,a)].">
      <j1 rule="hyper" parents="58 11755 12853"/>
    </justification>
  </clause>

  <clause id="12856">
    <literal><![CDATA[
      K(x,y \ L(L(x,z,x),u,w)) = K(x,y \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(11619,a,12854,a),flip(a)].">
      <j1 rule="hyper" parents="11619 12854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12858">
    <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(12856(a,1),11384(a,1,1))].">
      <j1 rule="para" parents="12856 11384"/>
    </justification>
  </clause>

  <clause id="12859">
    <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(10744(a,1),12858(a,1,1))].">
      <j1 rule="para" parents="10744 12858"/>
    </justification>
  </clause>

  <clause id="12861">
    <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),12859(a,1,1,2))].">
      <j1 rule="para" parents="60 12859"/>
    </justification>
  </clause>

  <clause id="12862">
    <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(4736(a,1),12861(a,1,2))].">
      <j1 rule="para" parents="4736 12861"/>
    </justification>
  </clause>

  <clause id="12863">
    <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(12065,a,12862,a)].">
      <j1 rule="hyper" parents="12065 12862"/>
    </justification>
  </clause>

  <clause id="12864">
    <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(1991(a,1),12863(a,1,2))].">
      <j1 rule="para" parents="1991 12863"/>
    </justification>
  </clause>

  <clause id="12865">
    <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(9935(a,1),12864(a,1,2))].">
      <j1 rule="para" parents="9935 12864"/>
    </justification>
  </clause>

  <clause id="12866">
    <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,12865,a)].">
      <j1 rule="hyper" parents="123 12865"/>
    </justification>
  </clause>

  <clause id="12867">
    <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(12866(a,1),12137(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12866 12137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12868">
    <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,12867,a,b,12789,a(flip))].">
      <j1 rule="hyper" parents="114 12867 12789"/>
    </justification>
  </clause>

  <clause id="12869">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z)) = a(x,u,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,10510,a(flip),b,12868,a),flip(a)].">
      <j1 rule="hyper" parents="320 10510 12868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12871">
    <literal><![CDATA[
      L(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,10518,a(flip),b,12869,a)].">
      <j1 rule="hyper" parents="58 10518 12869"/>
    </justification>
  </clause>

  <clause id="12874">
    <literal><![CDATA[
      a(x,L(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12722,a(flip),b,12871,a)].">
      <j1 rule="hyper" parents="58 12722 12871"/>
    </justification>
  </clause>

  <clause id="12875">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,z)) = y * a(z,u,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,12871,a(flip),b,4522,a),flip(a)].">
      <j1 rule="hyper" parents="119 12871 4522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12876">
    <literal><![CDATA[
      (x * y) * a(z,u,z) = x * (y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,12871,a(flip),b,4519,a)].">
      <j1 rule="hyper" parents="119 12871 4519"/>
    </justification>
  </clause>

  <clause id="12878">
    <literal><![CDATA[
      x \ (y * a(z,u,z)) = (x \ y) * a(z,u,z)
    ]]></literal>
    <justification jstring="[para(12871(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="12871 474"/>
    </justification>
  </clause>

  <clause id="12881">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = x * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,12874,a(flip),b,8913,a),flip(a)].">
      <j1 rule="hyper" parents="119 12874 8913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12882">
    <literal><![CDATA[
      a(x,(y * z) \ u,x) = a(x,z \ (y \ u),x)
    ]]></literal>
    <justification jstring="[para(298(a,1),12874(a,1,2))].">
      <j1 rule="para" parents="298 12874"/>
    </justification>
  </clause>

  <clause id="12883">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = a(x,y,x) \ x
    ]]></literal>
    <justification jstring="[para(12874(a,1),9059(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12874 9059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12884">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,8919,a(flip),b,12881,a),flip(a)].">
      <j1 rule="hyper" parents="320 8919 12881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12885">
    <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(12884(a,1),12122(a,1,2,1))].">
      <j1 rule="para" parents="12884 12122"/>
    </justification>
  </clause>

  <clause id="12886">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,9059,a(flip),b,12883,a),flip(a)].">
      <j1 rule="hyper" parents="320 9059 12883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12887">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,x) = L(x,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(1918(a,2),12886(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1918 12886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12888">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,z)) = a(z,u,z) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,9492,a,b,12875,a),flip(a)].">
      <j1 rule="hyper" parents="320 9492 12875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12889">
    <literal><![CDATA[
      x \ (a(y,z,y) * u) = (x \ u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,9492,a,b,12875,a)].">
      <j1 rule="hyper" parents="116 9492 12875"/>
    </justification>
  </clause>

  <clause id="12890">
    <literal><![CDATA[
      (x \ K(y,z)) * a(y,y \ z,y) = x \ K(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,8940,a(flip),b,12875,a),flip(a)].">
      <j1 rule="hyper" parents="116 8940 12875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12891">
    <literal><![CDATA[
      (x \ y) * a(y,z,y) = x \ R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,8919,a(flip),b,12875,a),flip(a)].">
      <j1 rule="hyper" parents="116 8919 12875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12892">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (u * a(x,y,x))
    ]]></literal>
    <justification jstring="[hyper(9523,a,12876,a)].">
      <j1 rule="hyper" parents="9523 12876"/>
    </justification>
  </clause>

  <clause id="12893">
    <literal><![CDATA[
      R(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(3998,a,12876,a)].">
      <j1 rule="hyper" parents="3998 12876"/>
    </justification>
  </clause>

  <clause id="12894">
    <literal><![CDATA[
      x \ (y * (z * a(u,w,u))) = (x \ (y * z)) * a(u,w,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,12876,a(flip),b,12875,a)].">
      <j1 rule="hyper" parents="116 12876 12875"/>
    </justification>
  </clause>

  <clause id="12895">
    <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(12876(a,1),510(a,1,1))].">
      <j1 rule="para" parents="12876 510"/>
    </justification>
  </clause>

  <clause id="12896">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) \ w = (x * y) \ (a(z,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(12876(a,1),12397(a,1,1))].">
      <j1 rule="para" parents="12876 12397"/>
    </justification>
  </clause>

  <clause id="12897">
    <literal><![CDATA[
      a(x * (y * a(z,u,z)),w,v5) = a(x * y,w,v5)
    ]]></literal>
    <justification jstring="[para(12876(a,1),12732(a,1,1))].">
      <j1 rule="para" parents="12876 12732"/>
    </justification>
  </clause>

  <clause id="12898">
    <literal><![CDATA[
      L(T(x,y),y,a(z,u,z)) = T(x,y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(10032,a,12893,a)].">
      <j1 rule="hyper" parents="10032 12893"/>
    </justification>
  </clause>

  <clause id="12900">
    <literal><![CDATA[
      x \ (y * a(z,u,z)) = a(z,u,z) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,9492,a,b,12878,a),flip(a)].">
      <j1 rule="hyper" parents="320 9492 12878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12901">
    <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,12847,a(flip),b,12882,a),flip(a)].">
      <j1 rule="hyper" parents="58 12847 12882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12902">
    <literal><![CDATA[
      (x \ (y * x)) * a(z,u,z) = T(y * a(z,u,z),x)
    ]]></literal>
    <justification jstring="[hyper(239,a,12396,a,b,12888,a),flip(a)].">
      <j1 rule="hyper" parents="239 12396 12888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12904">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ u = (z \ u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(12379,a,12889,a)].">
      <j1 rule="hyper" parents="12379 12889"/>
    </justification>
  </clause>

  <clause id="12905">
    <literal><![CDATA[
      a(x,y,x) \ (z \ (a(x,y,x) * u)) = z \ u
    ]]></literal>
    <justification jstring="[hyper(116,a,12889,a,b,9492,a)].">
      <j1 rule="hyper" parents="116 12889 9492"/>
    </justification>
  </clause>

  <clause id="12906">
    <literal><![CDATA[
      (x * y) / (y * a(z,u,z)) = a(z,u,z) \ x
    ]]></literal>
    <justification jstring="[hyper(12394,a,12892,a)].">
      <j1 rule="hyper" parents="12394 12892"/>
    </justification>
  </clause>

  <clause id="12907">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (a(x,y,x) * u)
    ]]></literal>
    <justification jstring="[para(9492(a,2),12892(a,2,2))].">
      <j1 rule="para" parents="9492 12892"/>
    </justification>
  </clause>

  <clause id="12908">
    <literal><![CDATA[
      a(x,y,x) * (z * (a(x,y,x) \ u)) = z * u
    ]]></literal>
    <justification jstring="[para(9503(a,1),12892(a,2,2))].">
      <j1 rule="para" parents="9503 12892"/>
    </justification>
  </clause>

  <clause id="12909">
    <literal><![CDATA[
      a(x,y,x) * (z \ (a(x,y,x) \ u)) = z \ u
    ]]></literal>
    <justification jstring="[para(9503(a,1),12900(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9503 12900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12910">
    <literal><![CDATA[
      ((a(x,y,x) * z) \ u) * a(x,y,x) = z \ u
    ]]></literal>
    <justification jstring="[para(4(a,1),12904(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 12904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12911">
    <literal><![CDATA[
      a(x,y,x) \ (z \ u) = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),12905(a,1,2,2))].">
      <j1 rule="para" parents="5 12905"/>
    </justification>
  </clause>

  <clause id="12912">
    <literal><![CDATA[
      a(x,y,x) \ (z \ (x * u)) = z \ (L(x,y,x) * u)
    ]]></literal>
    <justification jstring="[para(9539(a,1),12905(a,1,2,2))].">
      <j1 rule="para" parents="9539 12905"/>
    </justification>
  </clause>

  <clause id="12913">
    <literal><![CDATA[
      x / (y * a(z,u,z)) = a(z,u,z) \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(576,a,12906,a)].">
      <j1 rule="hyper" parents="576 12906"/>
    </justification>
  </clause>

  <clause id="12914">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = x * (a(y,z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(12431,a,12907,a)].">
      <j1 rule="hyper" parents="12431 12907"/>
    </justification>
  </clause>

  <clause id="12915">
    <literal><![CDATA[
      a(x,y,x) \ (z * u) = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,12907,a)].">
      <j1 rule="hyper" parents="116 151 12907"/>
    </justification>
  </clause>

  <clause id="12916">
    <literal><![CDATA[
      x \ (y * (a(z,u,z) * w)) = (x \ (y * w)) * a(z,u,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,12907,a(flip),b,12888,a)].">
      <j1 rule="hyper" parents="116 12907 12888"/>
    </justification>
  </clause>

  <clause id="12918">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) \ w = (x * u) \ (a(y,z,y) \ w)
    ]]></literal>
    <justification jstring="[para(12907(a,1),12376(a,1,1))].">
      <j1 rule="para" parents="12907 12376"/>
    </justification>
  </clause>

  <clause id="12919">
    <literal><![CDATA[
      (a(x,y,x) \ z) * u = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(12392,a,12908,a),flip(a)].">
      <j1 rule="hyper" parents="12392 12908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12920">
    <literal><![CDATA[
      a(x,y,x) * (z \ L(x,y,x)) = z \ x
    ]]></literal>
    <justification jstring="[para(9059(a,1),12909(a,1,2,2))].">
      <j1 rule="para" parents="9059 12909"/>
    </justification>
  </clause>

  <clause id="12921">
    <literal><![CDATA[
      a(x,y,x) \ (z \ x) = z \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,12920,a)].">
      <j1 rule="hyper" parents="123 12920"/>
    </justification>
  </clause>

  <clause id="12922">
    <literal><![CDATA[
      a(x \ L(y,z,y),u,w) = a(x \ y,u,w)
    ]]></literal>
    <justification jstring="[para(12920(a,1),12725(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12920 12725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12923">
    <literal><![CDATA[
      (x \ (a(y,z,y) \ u)) * a(y,z,y) != w
    ]]></literal>
    <literal><![CDATA[
      x \ u = w
    ]]></literal>
    <justification jstring="[para(12911(a,1),9516(a,1,1))].">
      <j1 rule="para" parents="12911 9516"/>
    </justification>
  </clause>

  <clause id="12924">
    <literal><![CDATA[
      L(x,y,z / (u * a(w,v5,w))) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(12913(a,2),12525(a,1,3))].">
      <j1 rule="para" parents="12913 12525"/>
    </justification>
  </clause>

  <clause id="12927">
    <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(12914(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12914 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12928">
    <literal><![CDATA[
      a(x * K(y * z,y),u,w) = a(x * K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(8937(a,1),12897(a,1,1,2))].">
      <j1 rule="para" parents="8937 12897"/>
    </justification>
  </clause>

  <clause id="12929">
    <literal><![CDATA[
      a(x * K(y,y \ z),u,w) = a(x * K(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(8940(a,1),12897(a,1,1,2))].">
      <j1 rule="para" parents="8940 12897"/>
    </justification>
  </clause>

  <clause id="12930">
    <literal><![CDATA[
      T(x,y * a(z,u,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(12377,a,12898,a),flip(a)].">
      <j1 rule="hyper" parents="12377 12898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12931">
    <literal><![CDATA[
      T(x,y * a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(12898(a,1),12377(a,1))].">
      <j1 rule="para" parents="12898 12377"/>
    </justification>
  </clause>

  <clause id="12933">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,12930,a(flip),b,4714,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 12930 4714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12934">
    <literal><![CDATA[
      K(x * a(y,z,y),u) = u / T(u,x)
    ]]></literal>
    <justification jstring="[para(12930(a,1),4753(a,2,2))].">
      <j1 rule="para" parents="12930 4753"/>
    </justification>
  </clause>

  <clause id="12935">
    <literal><![CDATA[
      T(x,y * L(z,u,z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(9065(a,1),12930(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9065 12930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12936">
    <literal><![CDATA[
      T(x,y * R(z,u,z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(9093(a,1),12930(a,1,2))].">
      <j1 rule="para" parents="9093 12930"/>
    </justification>
  </clause>

  <clause id="12937">
    <literal><![CDATA[
      T(x,R(y,z,y) * u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(9103(a,1),12930(a,1,2))].">
      <j1 rule="para" parents="9103 12930"/>
    </justification>
  </clause>

  <clause id="12938">
    <literal><![CDATA[
      T(x,y / R(z,u,z)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(9106(a,1),12930(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9106 12930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12939">
    <literal><![CDATA[
      T(x,a(y,z,y) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(9492(a,2),12930(a,1,2))].">
      <j1 rule="para" parents="9492 12930"/>
    </justification>
  </clause>

  <clause id="12940">
    <literal><![CDATA[
      T(x,a(y,z,y) \ u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(9503(a,1),12930(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9503 12930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12941">
    <literal><![CDATA[
      T(x,R(y,z,y) / u) = T(x,y / u)
    ]]></literal>
    <justification jstring="[para(12400(a,1),12930(a,1,2))].">
      <j1 rule="para" parents="12400 12930"/>
    </justification>
  </clause>

  <clause id="12942">
    <literal><![CDATA[
      T(x,y \ R(z,u,z)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(12891(a,1),12930(a,1,2))].">
      <j1 rule="para" parents="12891 12930"/>
    </justification>
  </clause>

  <clause id="12944">
    <literal><![CDATA[
      T(x,T(y * z,y) \ u) = T(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(11190(a,1),12939(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11190 12939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12945">
    <literal><![CDATA[
      T(x,(a(y,z,y) \ u) * w) = T(x,u * w)
    ]]></literal>
    <justification jstring="[para(12373(a,1),12939(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12373 12939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12946">
    <literal><![CDATA[
      T(x,y * (a(z,u,z) * w)) = T(x,y * w)
    ]]></literal>
    <justification jstring="[para(12907(a,1),12939(a,1,2))].">
      <j1 rule="para" parents="12907 12939"/>
    </justification>
  </clause>

  <clause id="12947">
    <literal><![CDATA[
      T(x,(R(y,z,y) \ y) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(9989(a,2),12940(a,1,2))].">
      <j1 rule="para" parents="9989 12940"/>
    </justification>
  </clause>

  <clause id="12948">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4688,a,b,12933,a),flip(a)].">
      <j1 rule="hyper" parents="320 4688 12933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12949">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(12933(a,2),4797(a,1))].">
      <j1 rule="para" parents="12933 4797"/>
    </justification>
  </clause>

  <clause id="12950">
    <literal><![CDATA[
      K(x,T(y,z) / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(8943(a,1),12948(a,1,2))].">
      <j1 rule="para" parents="8943 12948"/>
    </justification>
  </clause>

  <clause id="12951">
    <literal><![CDATA[
      K(x,y / L(z,u,z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(9055(a,1),12948(a,1,2))].">
      <j1 rule="para" parents="9055 12948"/>
    </justification>
  </clause>

  <clause id="12952">
    <literal><![CDATA[
      K(x,y * L(z,u,z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(9065(a,1),12948(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9065 12948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12953">
    <literal><![CDATA[
      K(x,L(y,z,y) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(9075(a,1),12948(a,1,2))].">
      <j1 rule="para" parents="9075 12948"/>
    </justification>
  </clause>

  <clause id="12954">
    <literal><![CDATA[
      K(x,R(y,z,y) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(9103(a,1),12948(a,1,2))].">
      <j1 rule="para" parents="9103 12948"/>
    </justification>
  </clause>

  <clause id="12955">
    <literal><![CDATA[
      K(x,a(y,z,y) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(9492(a,2),12948(a,1,2))].">
      <j1 rule="para" parents="9492 12948"/>
    </justification>
  </clause>

  <clause id="12956">
    <literal><![CDATA[
      K(x,a(y,z,y) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(9503(a,1),12948(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9503 12948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12957">
    <literal><![CDATA[
      K(x,R(y,z,y) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(12400(a,1),12948(a,1,2))].">
      <j1 rule="para" parents="12400 12948"/>
    </justification>
  </clause>

  <clause id="12958">
    <literal><![CDATA[
      K(x,(a(y,z,y) * u) / w) = K(x,u / w)
    ]]></literal>
    <justification jstring="[para(12398(a,2),12948(a,1,2))].">
      <j1 rule="para" parents="12398 12948"/>
    </justification>
  </clause>

  <clause id="12959">
    <literal><![CDATA[
      K(x,y \ R(z,u,z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(12891(a,1),12948(a,1,2))].">
      <j1 rule="para" parents="12891 12948"/>
    </justification>
  </clause>

  <clause id="12960">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(12876(a,1),12948(a,1,2))].">
      <j1 rule="para" parents="12876 12948"/>
    </justification>
  </clause>

  <clause id="12961">
    <literal><![CDATA[
      K(x,y \ (a(z,u,z) * w)) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(12889(a,2),12948(a,1,2))].">
      <j1 rule="para" parents="12889 12948"/>
    </justification>
  </clause>

  <clause id="12962">
    <literal><![CDATA[
      K(x,(a(y,z,y) * u) \ w) = K(x,u \ w)
    ]]></literal>
    <justification jstring="[para(12910(a,1),12948(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12910 12948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12963">
    <literal><![CDATA[
      K(x,L(y,z,y) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(9539(a,1),12955(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9539 12955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12964">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(9803(a,1),12955(a,1,2))].">
      <j1 rule="para" parents="9803 12955"/>
    </justification>
  </clause>

  <clause id="12965">
    <literal><![CDATA[
      K(x,T(y * z,y) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(11190(a,1),12955(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11190 12955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12966">
    <literal><![CDATA[
      K(x,(a(y,z,y) \ u) * w) = K(x,u * w)
    ]]></literal>
    <justification jstring="[para(12373(a,1),12955(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12373 12955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12967">
    <literal><![CDATA[
      K(x,y * (a(z,u,z) * w)) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(12907(a,1),12955(a,1,2))].">
      <j1 rule="para" parents="12907 12955"/>
    </justification>
  </clause>

  <clause id="12968">
    <literal><![CDATA[
      K(x,y * (a(z,u,z) \ w)) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(12908(a,1),12955(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12908 12955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12969">
    <literal><![CDATA[
      K(x,y \ (a(z,u,z) \ w)) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(12909(a,1),12955(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12909 12955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12970">
    <literal><![CDATA[
      K(x,(y \ R(y,z,y)) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(8911(a,1),12956(a,1,2,1))].">
      <j1 rule="para" parents="8911 12956"/>
    </justification>
  </clause>

  <clause id="12971">
    <literal><![CDATA[
      K(x,L(y,z,y) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(12404(a,1),12956(a,1,2))].">
      <j1 rule="para" parents="12404 12956"/>
    </justification>
  </clause>

  <clause id="12972">
    <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),12950(a,1,2,1))].">
      <j1 rule="para" parents="20 12950"/>
    </justification>
  </clause>

  <clause id="12973">
    <literal><![CDATA[
      K(x,y / T(z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4206(a,1),12950(a,1,2))].">
      <j1 rule="para" parents="4206 12950"/>
    </justification>
  </clause>

  <clause id="12974">
    <literal><![CDATA[
      K(x,y / T(z,y)) = K(x,T(y / z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7050,a,b,12973,a),flip(a)].">
      <j1 rule="hyper" parents="320 7050 12973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12975">
    <literal><![CDATA[
      K(x * a(y,z,y),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,4753,a,b,12934,a),flip(a)].">
      <j1 rule="hyper" parents="320 4753 12934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12976">
    <literal><![CDATA[
      K(x * a(y,z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(12934(a,2),4821(a,1))].">
      <j1 rule="para" parents="12934 4821"/>
    </justification>
  </clause>

  <clause id="12981">
    <literal><![CDATA[
      K(a(x,y,x) * z,u) = K(z,u)
    ]]></literal>
    <justification jstring="[para(9492(a,2),12975(a,1,1))].">
      <j1 rule="para" parents="9492 12975"/>
    </justification>
  </clause>

  <clause id="12982">
    <literal><![CDATA[
      K((x * a(y,z,y)) / u,w) = K(x / u,w)
    ]]></literal>
    <justification jstring="[para(12403(a,2),12975(a,1,1))].">
      <j1 rule="para" parents="12403 12975"/>
    </justification>
  </clause>

  <clause id="12983">
    <literal><![CDATA[
      K(x * (y * a(z,u,z)),w) = K(x * y,w)
    ]]></literal>
    <justification jstring="[para(12876(a,1),12975(a,1,1))].">
      <j1 rule="para" parents="12876 12975"/>
    </justification>
  </clause>

  <clause id="12984">
    <literal><![CDATA[
      K(x \ (a(y,z,y) * u),w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[para(12889(a,2),12975(a,1,1))].">
      <j1 rule="para" parents="12889 12975"/>
    </justification>
  </clause>

  <clause id="12985">
    <literal><![CDATA[
      K((a(x,y,x) \ z) \ u,w) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[para(12904(a,2),12975(a,1,1))].">
      <j1 rule="para" parents="12904 12975"/>
    </justification>
  </clause>

  <clause id="12986">
    <literal><![CDATA[
      K(L(x,y,x) * z,u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(9539(a,1),12981(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9539 12981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12987">
    <literal><![CDATA[
      K(T(x * y,x) \ z,u) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(11190(a,1),12981(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11190 12981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12988">
    <literal><![CDATA[
      K((a(x,y,x) \ z) * u,w) = K(z * u,w)
    ]]></literal>
    <justification jstring="[para(12373(a,1),12981(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12373 12981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12989">
    <literal><![CDATA[
      K(x \ L(y,z,y),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(12920(a,1),12981(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12920 12981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12990">
    <literal><![CDATA[
      T(x,y * ((z \ u) \ u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(11732(a,1),12935(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11732 12935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12991">
    <literal><![CDATA[
      T(x,y * T(z,z * u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4344(a,1),12936(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4344 12936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12992">
    <literal><![CDATA[
      T(x,((y \ z) \ z) * u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(7504(a,1),12937(a,1,2,1))].">
      <j1 rule="para" parents="7504 12937"/>
    </justification>
  </clause>

  <clause id="12993">
    <literal><![CDATA[
      T(x,y / T(z,z \ u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(4399(a,1),12938(a,1,2,2))].">
      <j1 rule="para" parents="4399 12938"/>
    </justification>
  </clause>

  <clause id="12994">
    <literal><![CDATA[
      T(x,y / ((z \ u) \ u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(7504(a,1),12938(a,1,2,2))].">
      <j1 rule="para" parents="7504 12938"/>
    </justification>
  </clause>

  <clause id="12995">
    <literal><![CDATA[
      T(x,((y \ z) \ z) / u) = T(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(7504(a,1),12941(a,1,2,1))].">
      <j1 rule="para" parents="7504 12941"/>
    </justification>
  </clause>

  <clause id="12996">
    <literal><![CDATA[
      T(x,y \ T(z,z * u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(4344(a,1),12942(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4344 12942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12997">
    <literal><![CDATA[
      T(x,y \ T(z,z \ u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(4399(a,1),12942(a,1,2,2))].">
      <j1 rule="para" parents="4399 12942"/>
    </justification>
  </clause>

  <clause id="12998">
    <literal><![CDATA[
      T(x,y \ ((z \ u) \ u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(7504(a,1),12942(a,1,2,2))].">
      <j1 rule="para" parents="7504 12942"/>
    </justification>
  </clause>

  <clause id="12999">
    <literal><![CDATA[
      T(x,K(y * z,y) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(9991(a,1),12947(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9991 12947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13000">
    <literal><![CDATA[
      K(x,y / T(z / u,z)) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[para(4363(a,1),12951(a,1,2,2))].">
      <j1 rule="para" parents="4363 12951"/>
    </justification>
  </clause>

  <clause id="13001">
    <literal><![CDATA[
      K(x,y * T(z / u,z)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(4363(a,1),12952(a,1,2,2))].">
      <j1 rule="para" parents="4363 12952"/>
    </justification>
  </clause>

  <clause id="13002">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(11732(a,1),12952(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11732 12952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13003">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,((y \ z) \ z) \ u)
    ]]></literal>
    <justification jstring="[para(6280(a,1),12953(a,1,2,1))].">
      <j1 rule="para" parents="6280 12953"/>
    </justification>
  </clause>

  <clause id="13004">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(11732(a,1),12953(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11732 12953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13006">
    <literal><![CDATA[
      K(x,T(y,y * z) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(4344(a,1),12954(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4344 12954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13007">
    <literal><![CDATA[
      K(x,((y \ z) \ z) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(7504(a,1),12957(a,1,2,1))].">
      <j1 rule="para" parents="7504 12957"/>
    </justification>
  </clause>

  <clause id="13008">
    <literal><![CDATA[
      K(x,y \ T(z,z \ u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(4399(a,1),12959(a,1,2,2))].">
      <j1 rule="para" parents="4399 12959"/>
    </justification>
  </clause>

  <clause id="13009">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(7504(a,1),12959(a,1,2,2))].">
      <j1 rule="para" parents="7504 12959"/>
    </justification>
  </clause>

  <clause id="13010">
    <literal><![CDATA[
      K(x,T(y / z,y) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(4363(a,1),12963(a,1,2,1))].">
      <j1 rule="para" parents="4363 12963"/>
    </justification>
  </clause>

  <clause id="13011">
    <literal><![CDATA[
      K(x,K(y * z,y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(9551(a,1),12970(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9551 12970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13012">
    <literal><![CDATA[
      K(x,T(y / z,y) / u) = K(x,(z \ y) / u)
    ]]></literal>
    <justification jstring="[para(4363(a,1),12971(a,1,2,1))].">
      <j1 rule="para" parents="4363 12971"/>
    </justification>
  </clause>

  <clause id="13013">
    <literal><![CDATA[
      K(x \ T(y / z,y),u) = K(x \ (z \ y),u)
    ]]></literal>
    <justification jstring="[para(4363(a,1),12989(a,1,1,2))].">
      <j1 rule="para" parents="4363 12989"/>
    </justification>
  </clause>

  <clause id="13014">
    <literal><![CDATA[
      T(x,K(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8940(a,1),12931(a,1,2))].">
      <j1 rule="para" parents="8940 12931"/>
    </justification>
  </clause>

  <clause id="13015">
    <literal><![CDATA[
      K(x,K(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8940(a,1),12949(a,1,2))].">
      <j1 rule="para" parents="8940 12949"/>
    </justification>
  </clause>

  <clause id="13016">
    <literal><![CDATA[
      K(x,T(y,z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(8943(a,1),12949(a,1,2))].">
      <j1 rule="para" parents="8943 12949"/>
    </justification>
  </clause>

  <clause id="13017">
    <literal><![CDATA[
      K(x,R(y,z,y) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / u) = w
    ]]></literal>
    <justification jstring="[para(12400(a,1),12949(a,1,2))].">
      <j1 rule="para" parents="12400 12949"/>
    </justification>
  </clause>

  <clause id="13018">
    <literal><![CDATA[
      K(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(12974(a,2),7167(a,1))].">
      <j1 rule="para" parents="12974 7167"/>
    </justification>
  </clause>

  <clause id="13019">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(8909(a,1),12945(a,1,2,1))].">
      <j1 rule="para" parents="8909 12945"/>
    </justification>
  </clause>

  <clause id="13020">
    <literal><![CDATA[
      T(x,y * T(z * u,z)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(8939(a,1),12946(a,1,2,2))].">
      <j1 rule="para" parents="8939 12946"/>
    </justification>
  </clause>

  <clause id="13021">
    <literal><![CDATA[
      K(x,T(y * z,y) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[para(8939(a,1),12958(a,1,2,1))].">
      <j1 rule="para" parents="8939 12958"/>
    </justification>
  </clause>

  <clause id="13022">
    <literal><![CDATA[
      K(x,(y * R(z,u,z)) / w) = K(x,(y * z) / w)
    ]]></literal>
    <justification jstring="[para(9499(a,1),12958(a,1,2,1))].">
      <j1 rule="para" parents="9499 12958"/>
    </justification>
  </clause>

  <clause id="13023">
    <literal><![CDATA[
      K(x,y * K(z,z * u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(8924(a,1),12960(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8924 12960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13024">
    <literal><![CDATA[
      K(x,y * T(z * u,z)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(8938(a,1),12960(a,1,2,2))].">
      <j1 rule="para" parents="8938 12960"/>
    </justification>
  </clause>

  <clause id="13025">
    <literal><![CDATA[
      K(x,y * K(z,z \ u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(8940(a,1),12960(a,1,2,2))].">
      <j1 rule="para" parents="8940 12960"/>
    </justification>
  </clause>

  <clause id="13026">
    <literal><![CDATA[
      K(x,y * (T(z,u) / u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(8943(a,1),12960(a,1,2,2))].">
      <j1 rule="para" parents="8943 12960"/>
    </justification>
  </clause>

  <clause id="13027">
    <literal><![CDATA[
      K(x,y * (z * L(u,w,u))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(9065(a,1),12960(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9065 12960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13028">
    <literal><![CDATA[
      K(x,y * (L(z,u,z) \ w)) = K(x,y * (z \ w))
    ]]></literal>
    <justification jstring="[para(9075(a,1),12960(a,1,2,2))].">
      <j1 rule="para" parents="9075 12960"/>
    </justification>
  </clause>

  <clause id="13029">
    <literal><![CDATA[
      K(x,y * (z \ R(u,w,u))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(12891(a,1),12960(a,1,2,2))].">
      <j1 rule="para" parents="12891 12960"/>
    </justification>
  </clause>

  <clause id="13030">
    <literal><![CDATA[
      K(x,y * (z * (u * a(w,v5,w)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(12876(a,1),12960(a,1,2,2))].">
      <j1 rule="para" parents="12876 12960"/>
    </justification>
  </clause>

  <clause id="13031">
    <literal><![CDATA[
      K(x,y \ T(z * u,z)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(8939(a,1),12961(a,1,2,2))].">
      <j1 rule="para" parents="8939 12961"/>
    </justification>
  </clause>

  <clause id="13032">
    <literal><![CDATA[
      K(x,y \ (z * R(u,w,u))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(9499(a,1),12961(a,1,2,2))].">
      <j1 rule="para" parents="9499 12961"/>
    </justification>
  </clause>

  <clause id="13033">
    <literal><![CDATA[
      K(x,y \ (L(z,u,z) * w)) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(9539(a,1),12961(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9539 12961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13034">
    <literal><![CDATA[
      K(x,K(y * z,y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(8935(a,1),12962(a,1,2,1))].">
      <j1 rule="para" parents="8935 12962"/>
    </justification>
  </clause>

  <clause id="13035">
    <literal><![CDATA[
      K(x,K(y * z,z) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(8949(a,1),12962(a,1,2,1))].">
      <j1 rule="para" parents="8949 12962"/>
    </justification>
  </clause>

  <clause id="13036">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(9539(a,1),12962(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9539 12962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13037">
    <literal><![CDATA[
      K(x,(T(y * z,y) \ u) \ w) = K(x,((z * y) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(11190(a,1),12962(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11190 12962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13038">
    <literal><![CDATA[
      K(x,(y * (z * a(u,w,u))) \ v5) = K(x,(y * z) \ v5)
    ]]></literal>
    <justification jstring="[para(12892(a,1),12962(a,1,2,1))].">
      <j1 rule="para" parents="12892 12962"/>
    </justification>
  </clause>

  <clause id="13039">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(8909(a,1),12966(a,1,2,1))].">
      <j1 rule="para" parents="8909 12966"/>
    </justification>
  </clause>

  <clause id="13040">
    <literal><![CDATA[
      K(x,(R(y,z,y) \ u) * w) = K(x,(y \ u) * w)
    ]]></literal>
    <justification jstring="[para(9510(a,1),12966(a,1,2,1))].">
      <j1 rule="para" parents="9510 12966"/>
    </justification>
  </clause>

  <clause id="13041">
    <literal><![CDATA[
      K(x,y * (K(z,z \ u) * w)) = K(x,y * (K(z,u) * w))
    ]]></literal>
    <justification jstring="[para(9803(a,1),12967(a,1,2,2))].">
      <j1 rule="para" parents="9803 12967"/>
    </justification>
  </clause>

  <clause id="13042">
    <literal><![CDATA[
      K(x,y * (z \ (a(u,w,u) \ v5))) = K(x,y * (z \ v5))
    ]]></literal>
    <justification jstring="[para(12909(a,1),12967(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12909 12967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13043">
    <literal><![CDATA[
      K(x,y * (z \ L(u,w,u))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(12920(a,1),12967(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12920 12967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13044">
    <literal><![CDATA[
      K(x,y * K(z \ u,z)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(8909(a,1),12968(a,1,2,2))].">
      <j1 rule="para" parents="8909 12968"/>
    </justification>
  </clause>

  <clause id="13045">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(z \ u,u))
    ]]></literal>
    <justification jstring="[para(8941(a,1),12969(a,1,2,2))].">
      <j1 rule="para" parents="8941 12969"/>
    </justification>
  </clause>

  <clause id="13046">
    <literal><![CDATA[
      K(T(x * y,x) / z,u) = K((y * x) / z,u)
    ]]></literal>
    <justification jstring="[para(8938(a,1),12982(a,1,1,1))].">
      <j1 rule="para" parents="8938 12982"/>
    </justification>
  </clause>

  <clause id="13047">
    <literal><![CDATA[
      K(x * K(y,y \ z),u) = K(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[para(8940(a,1),12983(a,1,1,2))].">
      <j1 rule="para" parents="8940 12983"/>
    </justification>
  </clause>

  <clause id="13048">
    <literal><![CDATA[
      K(x * (y \ R(z,u,z)),w) = K(x * (y \ z),w)
    ]]></literal>
    <justification jstring="[para(12891(a,1),12983(a,1,1,2))].">
      <j1 rule="para" parents="12891 12983"/>
    </justification>
  </clause>

  <clause id="13049">
    <literal><![CDATA[
      K(x \ T(y * z,y),u) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(8939(a,1),12984(a,1,1,2))].">
      <j1 rule="para" parents="8939 12984"/>
    </justification>
  </clause>

  <clause id="13050">
    <literal><![CDATA[
      K(x \ K(y,y \ z),u) = K(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[para(8910(a,1),12984(a,1,1,2))].">
      <j1 rule="para" parents="8910 12984"/>
    </justification>
  </clause>

  <clause id="13051">
    <literal><![CDATA[
      K((L(x,y,x) * z) \ u,w) = K((x * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(9538(a,1),12985(a,1,1,1))].">
      <j1 rule="para" parents="9538 12985"/>
    </justification>
  </clause>

  <clause id="13052">
    <literal><![CDATA[
      K(K(x * y,x) * z,u) = K(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[para(8928(a,1),12988(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8928 12988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13053">
    <literal><![CDATA[
      T(x,K(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7807(a,1),13014(a,1))].">
      <j1 rule="para" parents="7807 13014"/>
    </justification>
  </clause>

  <clause id="13054">
    <literal><![CDATA[
      K(x,K(y,z / y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(4871(a,2),13015(a,1,2))].">
      <j1 rule="para" parents="4871 13015"/>
    </justification>
  </clause>

  <clause id="13055">
    <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(185(a,1),13054(a,1,2,2))].">
      <j1 rule="para" parents="185 13054"/>
    </justification>
  </clause>

  <clause id="13056">
    <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,12944,a(flip),b,8349,a),flip(a)].">
      <j1 rule="hyper" parents="119 12944 8349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13057">
    <literal><![CDATA[
      T(x,((y \ z) * y) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),12944(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 12944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13058">
    <literal><![CDATA[
      K(x,K(y \ z,y * (z \ u)) * w) = K(x,K(y \ z,u) * w)
    ]]></literal>
    <justification jstring="[para(12417(a,1),12964(a,1,2,1))].">
      <j1 rule="para" parents="12417 12964"/>
    </justification>
  </clause>

  <clause id="13059">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),12965(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 12965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13060">
    <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(12965(a,1),8356(a,1,1,2))].">
      <j1 rule="para" parents="12965 8356"/>
    </justification>
  </clause>

  <clause id="13061">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),12987(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 12987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13062">
    <literal><![CDATA[
      K((x * y) \ 1,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K((y * x) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(12987(a,1),8027(a,1))].">
      <j1 rule="para" parents="12987 8027"/>
    </justification>
  </clause>

  <clause id="13064">
    <literal><![CDATA[
      T(x,y * T(T(z / u,w),z)) = T(x,y * T(u \ z,w))
    ]]></literal>
    <justification jstring="[para(7605(a,1),12990(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7605 12990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13065">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) = x \ T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,12991,a(flip),b,4714,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 12991 4714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13066">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) = x \ T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(116,a,12992,a(flip),b,4714,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 12992 4714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13068">
    <literal><![CDATA[
      T(x,y / T((z \ u) \ u,w)) = T(x,y / T(T(z,w),u))
    ]]></literal>
    <justification jstring="[para(7633(a,2),12994(a,1,2,2))].">
      <j1 rule="para" parents="7633 12994"/>
    </justification>
  </clause>

  <clause id="13069">
    <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(8519(a,1),12994(a,2,2,2))].">
      <j1 rule="para" parents="8519 12994"/>
    </justification>
  </clause>

  <clause id="13070">
    <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(12995(a,1),12263(a,1,2,1))].">
      <j1 rule="para" parents="12995 12263"/>
    </justification>
  </clause>

  <clause id="13071">
    <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,12996,a(flip),b,8349,a),flip(a)].">
      <j1 rule="hyper" parents="119 12996 8349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13072">
    <literal><![CDATA[
      T(x,y \ T(T(z,u),z \ w)) = T(x,y \ T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(7600(a,1),12997(a,1,2,2))].">
      <j1 rule="para" parents="7600 12997"/>
    </justification>
  </clause>

  <clause id="13073">
    <literal><![CDATA[
      T(x \ T(y,y \ z),x \ T(y,z)) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,657,a(flip),b,12998,a),flip(a)].">
      <j1 rule="hyper" parents="58 657 12998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13074">
    <literal><![CDATA[
      T(x,K(y,z) * ((z * y) * u)) = T(x,T(z * y,z) * u)
    ]]></literal>
    <justification jstring="[para(4740(a,1),12999(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4740 12999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13075">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) = w / (K(y * T(z,u),x) * w)
    ]]></literal>
    <justification jstring="[hyper(320,a,5104,a,b,13002,a),flip(a)].">
      <j1 rule="hyper" parents="320 5104 13002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13076">
    <literal><![CDATA[
      K(x,y * T(z,u * z)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4228(a,2),13002(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4228 13002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13077">
    <literal><![CDATA[
      K(x,y * T(T(z / u,w),z)) = K(x,y * T(u \ z,w))
    ]]></literal>
    <justification jstring="[para(7605(a,1),13002(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7605 13002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13078">
    <literal><![CDATA[
      K(x,L(((y \ z) \ z) \ u,w,v5)) = K(L(x,w,v5),T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(10837,a,13004,a)].">
      <j1 rule="hyper" parents="10837 13004"/>
    </justification>
  </clause>

  <clause id="13079">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = (w * K(T(y,z) \ u,x)) \ w
    ]]></literal>
    <justification jstring="[hyper(320,a,6309,a,b,13004,a),flip(a)].">
      <j1 rule="hyper" parents="320 6309 13004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13080">
    <literal><![CDATA[
      K(x,((y \ x) \ x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(13004(a,2),7396(a,1))].">
      <j1 rule="para" parents="13004 7396"/>
    </justification>
  </clause>

  <clause id="13081">
    <literal><![CDATA[
      K(x,T(((y / z) \ 1) * y,y) \ u) = K(x,(((z \ y) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(10116(a,1),13004(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10116 13004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13082">
    <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(10837,a,13006,a)].">
      <j1 rule="hyper" parents="10837 13006"/>
    </justification>
  </clause>

  <clause id="13083">
    <literal><![CDATA[
      K(x,T(y * (1 / z),z) / u) = K(x,T(y * (1 / z),y) / u)
    ]]></literal>
    <justification jstring="[para(6401(a,2),13007(a,1,2,1))].">
      <j1 rule="para" parents="6401 13007"/>
    </justification>
  </clause>

  <clause id="13084">
    <literal><![CDATA[
      K(x,y \ T(z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(8323,a,13008,a),flip(a)].">
      <j1 rule="hyper" parents="8323 13008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13085">
    <literal><![CDATA[
      K(x,y \ T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(13008(a,1),8323(a,1))].">
      <j1 rule="para" parents="13008 8323"/>
    </justification>
  </clause>

  <clause id="13086">
    <literal><![CDATA[
      K(x,T(y,z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(4208(a,2),13085(a,1,2))].">
      <j1 rule="para" parents="4208 13085"/>
    </justification>
  </clause>

  <clause id="13087">
    <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(6095(a,1),13085(a,1,2,2))].">
      <j1 rule="para" parents="6095 13085"/>
    </justification>
  </clause>

  <clause id="13088">
    <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(7954(a,1),13085(a,1,2,2))].">
      <j1 rule="para" parents="7954 13085"/>
    </justification>
  </clause>

  <clause id="13089">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) = x \ T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(116,a,13019,a(flip),b,4714,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 13019 4714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13090">
    <literal><![CDATA[
      K(K(x \ y,x) * z,u) = u / T(u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(13019(a,1),4753(a,2,2))].">
      <j1 rule="para" parents="13019 4753"/>
    </justification>
  </clause>

  <clause id="13091">
    <literal><![CDATA[
      T(x,y * ((z \ u) * z)) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),13020(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13092">
    <literal><![CDATA[
      K(x,((y \ z) * y) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13021(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13093">
    <literal><![CDATA[
      K(x,y * ((z \ u) * z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),13024(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13094">
    <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(10472(a,2),13025(a,2,2,2))].">
      <j1 rule="para" parents="10472 13025"/>
    </justification>
  </clause>

  <clause id="13095">
    <literal><![CDATA[
      K(x,y * (z / T(u,z))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(4206(a,1),13026(a,1,2,2))].">
      <j1 rule="para" parents="4206 13026"/>
    </justification>
  </clause>

  <clause id="13096">
    <literal><![CDATA[
      K(x,K(y \ z,y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13034(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13097">
    <literal><![CDATA[
      K(x,K(y,z \ y) \ u) = K(x,K(z,z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13035(a,1,2,1,1))].">
      <j1 rule="para" parents="5 13035"/>
    </justification>
  </clause>

  <clause id="13098">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ y) \ u)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(5361(a,1),13039(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5361 13039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13099">
    <literal><![CDATA[
      K(x,(y / (z \ u)) * K(u,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(6441(a,1),13044(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6441 13044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13100">
    <literal><![CDATA[
      K(((x \ y) * x) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13046(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13101">
    <literal><![CDATA[
      K(x \ (y * z),T(x,y)) = K(x \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11215,a(flip),b,13049,a)].">
      <j1 rule="hyper" parents="58 11215 13049"/>
    </justification>
  </clause>

  <clause id="13102">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13049(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13103">
    <literal><![CDATA[
      K(x \ K(y,z \ 1),u) = K(x \ K(y,z \ y),u)
    ]]></literal>
    <justification jstring="[para(4973(a,1),13050(a,1,1,2))].">
      <j1 rule="para" parents="4973 13050"/>
    </justification>
  </clause>

  <clause id="13104">
    <literal><![CDATA[
      K(x \ K(y,(z * y) * u),w) = K(x \ K(y,z * u),w)
    ]]></literal>
    <justification jstring="[para(12411(a,1),13050(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12411 13050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13105">
    <literal><![CDATA[
      K(K(x * y,y) * z,u) = K(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5228(a,2),13052(a,1,1,1))].">
      <j1 rule="para" parents="5228 13052"/>
    </justification>
  </clause>

  <clause id="13106">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ y)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(6478,a,13057,a),flip(a)].">
      <j1 rule="hyper" parents="6478 13057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13107">
    <literal><![CDATA[
      K(x,T(T(y * z,u),y) \ w) = K(x,T(z * y,u) \ w)
    ]]></literal>
    <justification jstring="[para(4555(a,1),13059(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4555 13059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13108">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * T(z,u)) = K(x,((u \ z) * u) * y)
    ]]></literal>
    <justification jstring="[hyper(12264,a,13093,a),flip(a)].">
      <j1 rule="hyper" parents="12264 13093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13109">
    <literal><![CDATA[
      K(x,y * T((z \ 1) \ u,z)) = K(x,y * ((z \ K(z,u)) \ u))
    ]]></literal>
    <justification jstring="[para(10108(a,2),13093(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10108 13093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13110">
    <literal><![CDATA[
      K(x \ T(T(y * z,u),y),w) = K(x \ T(z * y,u),w)
    ]]></literal>
    <justification jstring="[para(4555(a,1),13102(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4555 13102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13111">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(13102(a,2),7386(a,1))].">
      <j1 rule="para" parents="13102 7386"/>
    </justification>
  </clause>

  <clause id="13112">
    <literal><![CDATA[
      L(x,y,z / T(u * (w / u),u)) = L(x,y,z / w)
    ]]></literal>
    <justification jstring="[para(9077(a,1),12924(a,1,3,2))].">
      <j1 rule="para" parents="9077 12924"/>
    </justification>
  </clause>

  <clause id="13113">
    <literal><![CDATA[
      K(x,(y * ((z \ u) \ u)) / w) = K(x,(y * T(z,u)) / w)
    ]]></literal>
    <justification jstring="[para(7504(a,1),13022(a,1,2,1,2))].">
      <j1 rule="para" parents="7504 13022"/>
    </justification>
  </clause>

  <clause id="13114">
    <literal><![CDATA[
      K(x,y * (z * L(T(u,w),v5,u))) = K(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(7478(a,1),13027(a,1,2,2,2))].">
      <j1 rule="para" parents="7478 13027"/>
    </justification>
  </clause>

  <clause id="13115">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) \ w)) = K(x,y * (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[para(11732(a,1),13028(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="11732 13028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13116">
    <literal><![CDATA[
      K(x,y * (z \ T(u,u * w))) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(4344(a,1),13029(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4344 13029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13117">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) \ w))) = K(x,y \ (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(7504(a,1),13032(a,1,2,2,2))].">
      <j1 rule="para" parents="7504 13032"/>
    </justification>
  </clause>

  <clause id="13118">
    <literal><![CDATA[
      K(x,y \ (T(z / u,z) * w)) = K(x,y \ ((u \ z) * w))
    ]]></literal>
    <justification jstring="[para(4363(a,1),13033(a,1,2,2,1))].">
      <j1 rule="para" parents="4363 13033"/>
    </justification>
  </clause>

  <clause id="13119">
    <literal><![CDATA[
      K(x,y \ (((z \ u) \ u) * w)) = K(x,y \ (T(z,u) * w))
    ]]></literal>
    <justification jstring="[para(11732(a,1),13033(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="11732 13033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13120">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) \ u) * w) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(7504(a,1),13040(a,1,2,1,1))].">
      <j1 rule="para" parents="7504 13040"/>
    </justification>
  </clause>

  <clause id="13121">
    <literal><![CDATA[
      K(x,y * (z \ T(u / w,u))) = K(x,y * (z \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(4363(a,1),13043(a,1,2,2,2))].">
      <j1 rule="para" parents="4363 13043"/>
    </justification>
  </clause>

  <clause id="13122">
    <literal><![CDATA[
      K(x * (y \ T(z,z * u)),w) = K(x * (y \ T(z,u)),w)
    ]]></literal>
    <justification jstring="[para(4344(a,1),13048(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4344 13048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13123">
    <literal><![CDATA[
      K((x * y) \ z,y * x) * (z * u) = (((y * x) \ z) * (y * x)) * u
    ]]></literal>
    <justification jstring="[para(13051(a,1),11262(a,1,1))].">
      <j1 rule="para" parents="13051 11262"/>
    </justification>
  </clause>

  <clause id="13124">
    <literal><![CDATA[
      K((x \ 1) \ (y \ z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ y) \ z,y) = u
    ]]></literal>
    <justification jstring="[para(8336(a,1),13111(a,1))].">
      <j1 rule="para" parents="8336 13111"/>
    </justification>
  </clause>

  <clause id="13125">
    <literal><![CDATA[
      T(x * a(y,z,y),u) = T(x,u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(17(a,2),12902(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17 12902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13126">
    <literal><![CDATA[
      T(a(x,y,x) * z,u) = T(z,u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(9492(a,2),13125(a,1,1))].">
      <j1 rule="para" parents="9492 13125"/>
    </justification>
  </clause>

  <clause id="13127">
    <literal><![CDATA[
      K(x,T(a(y,z,y) * u,w)) = K(x,T(u,w))
    ]]></literal>
    <justification jstring="[para(13126(a,2),12948(a,1,2))].">
      <j1 rule="para" parents="13126 12948"/>
    </justification>
  </clause>

  <clause id="13128">
    <literal><![CDATA[
      K(x,y * T(a(z,u,z) * w,v5)) = K(x,y * T(w,v5))
    ]]></literal>
    <justification jstring="[para(13126(a,2),12960(a,1,2,2))].">
      <j1 rule="para" parents="13126 12960"/>
    </justification>
  </clause>

  <clause id="13129">
    <literal><![CDATA[
      K(x,T(K(y,y \ z) * u,w)) = K(x,T(K(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(9803(a,1),13127(a,1,2,1))].">
      <j1 rule="para" parents="9803 13127"/>
    </justification>
  </clause>

  <clause id="13130">
    <literal><![CDATA[
      K(x,y * (z \ (L(u,w,u) * v5))) = K(x,y * (z \ (u * v5)))
    ]]></literal>
    <justification jstring="[para(12912(a,1),12968(a,1,2,2))].">
      <j1 rule="para" parents="12912 12968"/>
    </justification>
  </clause>

  <clause id="13131">
    <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(4416(a,1),12972(a,1,2,1,1))].">
      <j1 rule="para" parents="4416 12972"/>
    </justification>
  </clause>

  <clause id="13132">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13065(a,2),4797(a,1))].">
      <j1 rule="para" parents="13065 4797"/>
    </justification>
  </clause>

  <clause id="13133">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(13066(a,2),4797(a,1))].">
      <j1 rule="para" parents="13066 4797"/>
    </justification>
  </clause>

  <clause id="13134">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(13089(a,2),4797(a,1))].">
      <j1 rule="para" parents="13089 4797"/>
    </justification>
  </clause>

  <clause id="13135">
    <literal><![CDATA[
      K(K(x \ y,x) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) * z,u) = w
    ]]></literal>
    <justification jstring="[para(13090(a,2),4821(a,1))].">
      <j1 rule="para" parents="13090 4821"/>
    </justification>
  </clause>

  <clause id="13136">
    <literal><![CDATA[
      L(x,y,(z * (u / z)) \ z) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12562,a(flip),b,13112,a)].">
      <j1 rule="hyper" parents="58 12562 13112"/>
    </justification>
  </clause>

  <clause id="13137">
    <literal><![CDATA[
      L(x,y,z / (u * z)) = L(x,y,(z * u) \ z)
    ]]></literal>
    <justification jstring="[para(6(a,1),13136(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="6 13136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13138">
    <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(4877(a,2),13136(a,2,3))].">
      <j1 rule="para" parents="4877 13136"/>
    </justification>
  </clause>

  <clause id="13139">
    <literal><![CDATA[
      L(x,y,z \ (z / (z / u))) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(5032(a,1),13136(a,1,3))].">
      <j1 rule="para" parents="5032 13136"/>
    </justification>
  </clause>

  <clause id="13140">
    <literal><![CDATA[
      L(x,y,(z \ u) / u) = L(x,y,u \ (u / z))
    ]]></literal>
    <justification jstring="[para(72(a,1),13139(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="72 13139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13141">
    <literal><![CDATA[
      L(x,y,z \ K(u,u \ w)) = L(x,y,z \ K(u,w))
    ]]></literal>
    <justification jstring="[para(12890(a,1),12531(a,1,3))].">
      <j1 rule="para" parents="12890 12531"/>
    </justification>
  </clause>

  <clause id="13142">
    <literal><![CDATA[
      K(x \ K(y,y \ z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(12890(a,1),12976(a,1,1))].">
      <j1 rule="para" parents="12890 12976"/>
    </justification>
  </clause>

  <clause id="13143">
    <literal><![CDATA[
      K(x,y * (z * (T(u,w) / w))) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(8943(a,1),13030(a,1,2,2,2))].">
      <j1 rule="para" parents="8943 13030"/>
    </justification>
  </clause>

  <clause id="13144">
    <literal><![CDATA[
      K(x,y * (z * (u \ K(w,w \ v5)))) = K(x,y * (z * (u \ K(w,v5))))
    ]]></literal>
    <justification jstring="[para(12890(a,1),13030(a,1,2,2,2))].">
      <j1 rule="para" parents="12890 13030"/>
    </justification>
  </clause>

  <clause id="13145">
    <literal><![CDATA[
      K(x,(y * K(z * u,u)) \ w) = K(x,(y * K(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(8934(a,1),13038(a,1,2,1,2))].">
      <j1 rule="para" parents="8934 13038"/>
    </justification>
  </clause>

  <clause id="13146">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,u))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(8909(a,1),13042(a,1,2,2,2))].">
      <j1 rule="para" parents="8909 13042"/>
    </justification>
  </clause>

  <clause id="13147">
    <literal><![CDATA[
      K(x,y * T(T(z * u,z),w)) = K(x,y * T(u * z,w))
    ]]></literal>
    <justification jstring="[para(8939(a,1),13128(a,1,2,2,1))].">
      <j1 rule="para" parents="8939 13128"/>
    </justification>
  </clause>

  <clause id="13148">
    <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(10305(a,2),13133(a,1,2,1))].">
      <j1 rule="para" parents="10305 13133"/>
    </justification>
  </clause>

  <clause id="13149">
    <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(691,a,12894,a),flip(a)].">
      <j1 rule="hyper" parents="691 12894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13150">
    <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),12894(a,2,1))].">
      <j1 rule="para" parents="13 12894"/>
    </justification>
  </clause>

  <clause id="13151">
    <literal><![CDATA[
      (x * (y * (z * a(u,w,u)))) \ v5 = (x * (y * z)) \ (a(u,w,u) \ v5)
    ]]></literal>
    <justification jstring="[para(12876(a,1),12896(a,1,1,2))].">
      <j1 rule="para" parents="12876 12896"/>
    </justification>
  </clause>

  <clause id="13152">
    <literal><![CDATA[
      ((x * (a(y,z,y) * u)) \ (x * (u * w))) * a(y,z,y) = L(w,a(y,z,y) * u,x)
    ]]></literal>
    <justification jstring="[hyper(12393,a,12916,a),flip(a)].">
      <j1 rule="hyper" parents="12393 12916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13153">
    <literal><![CDATA[
      K(x,y * ((z / (z / u)) \ w)) = K(x,y * (K(u,z) * (u \ w)))
    ]]></literal>
    <justification jstring="[para(5363(a,2),13041(a,1,2,2))].">
      <j1 rule="para" parents="5363 13041"/>
    </justification>
  </clause>

  <clause id="13154">
    <literal><![CDATA[
      T(x,T(y * z,y) * u) = T(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(11122(a,1),13074(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11122 13074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13155">
    <literal><![CDATA[
      T(x,((y \ z) * y) * u) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13154(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13156">
    <literal><![CDATA[
      T(x,T(T(y * z,u),y) * w) = T(x,T(z * y,u) * w)
    ]]></literal>
    <justification jstring="[para(4555(a,1),13155(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4555 13155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13157">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13075(a,2),5112(a,1))].">
      <j1 rule="para" parents="13075 5112"/>
    </justification>
  </clause>

  <clause id="13158">
    <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),13157(a,1,2,2))].">
      <j1 rule="para" parents="106 13157"/>
    </justification>
  </clause>

  <clause id="13159">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(13079(a,2),6316(a,1))].">
      <j1 rule="para" parents="13079 6316"/>
    </justification>
  </clause>

  <clause id="13160">
    <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),13159(a,1,2,1))].">
      <j1 rule="para" parents="106 13159"/>
    </justification>
  </clause>

  <clause id="13161">
    <literal><![CDATA[
      K(x,((y \ z) * y) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(12263,a,13108,a),flip(a)].">
      <j1 rule="hyper" parents="12263 13108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13162">
    <literal><![CDATA[
      K(x,y * (z * (u / T(w,u)))) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(4206(a,1),13143(a,1,2,2,2))].">
      <j1 rule="para" parents="4206 13143"/>
    </justification>
  </clause>

  <clause id="13163">
    <literal><![CDATA[
      K(x,y * T((z / u) \ 1,z)) = K(x,y * ((z / u) \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(5398(a,1),13146(a,1,2,2))].">
      <j1 rule="para" parents="5398 13146"/>
    </justification>
  </clause>

  <clause id="13164">
    <literal><![CDATA[
      K(x,y * (z * T(T(u / w,u),v5))) = K(x,y * (z * T(w \ u,v5)))
    ]]></literal>
    <justification jstring="[para(9036(a,1),13114(a,1,2,2,2))].">
      <j1 rule="para" parents="9036 13114"/>
    </justification>
  </clause>

  <clause id="13165">
    <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(13078(a,2),10837(a,1))].">
      <j1 rule="para" parents="13078 10837"/>
    </justification>
  </clause>

  <clause id="13166">
    <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(13082(a,2),10837(a,1))].">
      <j1 rule="para" parents="13082 10837"/>
    </justification>
  </clause>

  <clause id="13167">
    <literal><![CDATA[
      K(x,T(y * (1 / z),z) / u) = K(x,((1 / z) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13021,a(flip),b,13083,a),flip(a)].">
      <j1 rule="hyper" parents="320 13021 13083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13168">
    <literal><![CDATA[
      K(x,T(y * (1 / z),z) / u) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,5542,a(flip),b,13167,a),flip(a)].">
      <j1 rule="hyper" parents="320 5542 13167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13169">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * a(u,w,u)))) = L(z,y,x) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(12876(a,1),13150(a,1,2,2))].">
      <j1 rule="para" parents="12876 13150"/>
    </justification>
  </clause>

  <clause id="13170">
    <literal><![CDATA[
      L(x * a(y,z,y),u,w) = L(x,u,w) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(482,a,13169,a)].">
      <j1 rule="hyper" parents="482 13169"/>
    </justification>
  </clause>

  <clause id="13171">
    <literal><![CDATA[
      L(a(x,y,x) \ z,u,w) = a(x,y,x) \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(3507,a,13170,a),flip(a)].">
      <j1 rule="hyper" parents="3507 13170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13172">
    <literal><![CDATA[
      x * L(y * a(x,z,x),u,w) = R(x,z,x) * L(y,u,w)
    ]]></literal>
    <justification jstring="[para(13170(a,2),9105(a,1,2))].">
      <j1 rule="para" parents="13170 9105"/>
    </justification>
  </clause>

  <clause id="13173">
    <literal><![CDATA[
      K(x,L(y * a(z,u,z),w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(13170(a,2),12948(a,1,2))].">
      <j1 rule="para" parents="13170 12948"/>
    </justification>
  </clause>

  <clause id="13174">
    <literal><![CDATA[
      K(x,L(a(y,z,y) * u,w,v5)) = K(x,L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(9492(a,2),13173(a,1,2,1))].">
      <j1 rule="para" parents="9492 13173"/>
    </justification>
  </clause>

  <clause id="13175">
    <literal><![CDATA[
      K(x,L(T(y * z,y) \ u,w,v5)) = K(x,L((z * y) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(11190(a,1),13174(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11190 13174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13176">
    <literal><![CDATA[
      L(a(x,y,x) \ z,u,w) * a(x,y,x) != v5
    ]]></literal>
    <literal><![CDATA[
      L(z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(13171(a,2),9516(a,1,1))].">
      <j1 rule="para" parents="13171 9516"/>
    </justification>
  </clause>

  <clause id="13177">
    <literal><![CDATA[
      L(a(x,y,x) \ z,u,w) * v5 = L(z,u,w) * (a(x,y,x) \ v5)
    ]]></literal>
    <justification jstring="[para(13171(a,2),12919(a,1,1))].">
      <j1 rule="para" parents="13171 12919"/>
    </justification>
  </clause>

  <clause id="13178">
    <literal><![CDATA[
      R(x,y,x) * L(R(x,y,x) \ z,u,w) = x * L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(9104(a,1),13172(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9104 13172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13179">
    <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(320,a,10776,a,b,13175,a)].">
      <j1 rule="hyper" parents="320 10776 13175"/>
    </justification>
  </clause>

  <clause id="13180">
    <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(12921(a,1),13177(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12921 13177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13181">
    <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,13178,a(flip),b,11376,a),flip(a)].">
      <j1 rule="hyper" parents="119 13178 11376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13183">
    <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(13056(a,2),8351(a,1))].">
      <j1 rule="para" parents="13056 8351"/>
    </justification>
  </clause>

  <clause id="13184">
    <literal><![CDATA[
      T(x,T(y \ T(z,z * u),w)) = T(x,T(y \ T(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(320,a,8350,a(flip),b,13071,a),flip(a)].">
      <j1 rule="hyper" parents="320 8350 13071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13185">
    <literal><![CDATA[
      ((x * y) \ (a(z,u,z) \ (x * (y * w)))) * a(z,u,z) = L(w,a(z,u,z) * y,x)
    ]]></literal>
    <justification jstring="[para(12918(a,1),13152(a,1,1))].">
      <j1 rule="para" parents="12918 13152"/>
    </justification>
  </clause>

  <clause id="13186">
    <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,2126,a(flip),b,13181,a)].">
      <j1 rule="hyper" parents="58 2126 13181"/>
    </justification>
  </clause>

  <clause id="13187">
    <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),13181(a,1,1,1))].">
      <j1 rule="para" parents="5 13181"/>
    </justification>
  </clause>

  <clause id="13189">
    <literal><![CDATA[
      T((x * y) * L((x * y) \ x,z,u),x) = (y * L(y \ 1,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,1839,a(flip),b,13186,a),flip(a)].">
      <j1 rule="hyper" parents="320 1839 13186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13190">
    <literal><![CDATA[
      T(x * (y * L(y \ 1,z,u)),x) = (y * L(y \ 1,z,u)) * x
    ]]></literal>
    <justification jstring="[para(913(a,1),13189(a,1,1))].">
      <j1 rule="para" parents="913 13189"/>
    </justification>
  </clause>

  <clause id="13191">
    <literal><![CDATA[
      R(x,y * L(y \ 1,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(4298,a,13190,a)].">
      <j1 rule="hyper" parents="4298 13190"/>
    </justification>
  </clause>

  <clause id="13192">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[para(1185(a,1),13191(a,1,2))].">
      <j1 rule="para" parents="1185 13191"/>
    </justification>
  </clause>

  <clause id="13193">
    <literal><![CDATA[
      R(T(x,y),z \ L(z,u,w),x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7096,a(flip),b,13192,a)].">
      <j1 rule="hyper" parents="58 7096 13192"/>
    </justification>
  </clause>

  <clause id="13194">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,13192,a(flip),b,8919,a),flip(a)].">
      <j1 rule="hyper" parents="115 13192 8919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13195">
    <literal><![CDATA[
      ((x * y) \ (x * (a(z,u,z) \ (y * w)))) * a(z,u,z) = L(w,a(z,u,z) * y,x)
    ]]></literal>
    <justification jstring="[para(12915(a,1),13185(a,1,1,2))].">
      <j1 rule="para" parents="12915 13185"/>
    </justification>
  </clause>

  <clause id="13196">
    <literal><![CDATA[
      ((x * y) \ (x * (y * (a(z,u,z) \ w)))) * a(z,u,z) = L(w,a(z,u,z) * y,x)
    ]]></literal>
    <justification jstring="[para(12915(a,1),13195(a,1,1,2,2))].">
      <j1 rule="para" parents="12915 13195"/>
    </justification>
  </clause>

  <clause id="13197">
    <literal><![CDATA[
      L(a(x,y,x) \ z,u,w) * a(x,y,x) = L(z,a(x,y,x) * u,w)
    ]]></literal>
    <justification jstring="[para(13(a,2),13196(a,1,1))].">
      <j1 rule="para" parents="13 13196"/>
    </justification>
  </clause>

  <clause id="13198">
    <literal><![CDATA[
      L(x,a(y,z,y) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(13176,a,13197,a),flip(a)].">
      <j1 rule="hyper" parents="13176 13197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13199">
    <literal><![CDATA[
      L(x,a(y,z,y) \ u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),13198(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 13198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13200">
    <literal><![CDATA[
      L(x,R(y,z,y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(8926(a,1),13198(a,1,2))].">
      <j1 rule="para" parents="8926 13198"/>
    </justification>
  </clause>

  <clause id="13201">
    <literal><![CDATA[
      L(x,K(y * z,y),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(8935(a,1),13198(a,1,2))].">
      <j1 rule="para" parents="8935 13198"/>
    </justification>
  </clause>

  <clause id="13202">
    <literal><![CDATA[
      L(x,K(y,y * z),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[para(8936(a,1),13198(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8936 13198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13203">
    <literal><![CDATA[
      L(x,T(y * z,y),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(8939(a,1),13198(a,1,2))].">
      <j1 rule="para" parents="8939 13198"/>
    </justification>
  </clause>

  <clause id="13204">
    <literal><![CDATA[
      L(x,K(y,y \ z),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[para(8910(a,1),13198(a,1,2))].">
      <j1 rule="para" parents="8910 13198"/>
    </justification>
  </clause>

  <clause id="13205">
    <literal><![CDATA[
      L(x,L(y,z,y) \ u,w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(9501(a,1),13198(a,1,2))].">
      <j1 rule="para" parents="9501 13198"/>
    </justification>
  </clause>

  <clause id="13206">
    <literal><![CDATA[
      L(x,y / L(z,u,z),w) = L(x,y / z,w)
    ]]></literal>
    <justification jstring="[para(9502(a,1),13198(a,1,2))].">
      <j1 rule="para" parents="9502 13198"/>
    </justification>
  </clause>

  <clause id="13207">
    <literal><![CDATA[
      L(x,T(y * (z / y),y),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(9500(a,1),13198(a,1,2))].">
      <j1 rule="para" parents="9500 13198"/>
    </justification>
  </clause>

  <clause id="13208">
    <literal><![CDATA[
      L(x,K(y,y \ z) * u,w) = L(x,K(y,z) * u,w)
    ]]></literal>
    <justification jstring="[para(9803(a,1),13198(a,1,2))].">
      <j1 rule="para" parents="9803 13198"/>
    </justification>
  </clause>

  <clause id="13209">
    <literal><![CDATA[
      L(x,T(y,y \ z),u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4399(a,1),13200(a,1,2))].">
      <j1 rule="para" parents="4399 13200"/>
    </justification>
  </clause>

  <clause id="13210">
    <literal><![CDATA[
      L(x,(y \ z) \ z,u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(7504(a,1),13200(a,1,2))].">
      <j1 rule="para" parents="7504 13200"/>
    </justification>
  </clause>

  <clause id="13211">
    <literal><![CDATA[
      L(x,a(y,z,y) \ 1,u) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,372,a(flip),b,13199,a),flip(a)].">
      <j1 rule="hyper" parents="320 372 13199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13212">
    <literal><![CDATA[
      L(x,K(y \ z,y),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(8909(a,1),13199(a,1,2))].">
      <j1 rule="para" parents="8909 13199"/>
    </justification>
  </clause>

  <clause id="13213">
    <literal><![CDATA[
      L(x,R(y,z,y) \ y,u) = x
    ]]></literal>
    <justification jstring="[para(8930(a,2),13211(a,1,2))].">
      <j1 rule="para" parents="8930 13211"/>
    </justification>
  </clause>

  <clause id="13214">
    <literal><![CDATA[
      L((x * y) \ (x * z),R(u,w,u) \ u,v5) = L(y \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,92,a,b,13213,a),flip(a)].">
      <j1 rule="hyper" parents="320 92 13213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13215">
    <literal><![CDATA[
      L(x,K(y * z,(y * z) * (z \ 1)),u) = L(x,K(z * y,z \ 1),u)
    ]]></literal>
    <justification jstring="[para(5840(a,1),13202(a,2,2))].">
      <j1 rule="para" parents="5840 13202"/>
    </justification>
  </clause>

  <clause id="13216">
    <literal><![CDATA[
      L(x,y * z,z) = L(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(11161,a,13203,a),flip(a)].">
      <j1 rule="hyper" parents="11161 13203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13217">
    <literal><![CDATA[
      L(x,(y \ z) * y,u) = L(x,T(z,y),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13203(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13218">
    <literal><![CDATA[
      L(x,K(y,z),z \ y) = x
    ]]></literal>
    <justification jstring="[hyper(12614,a,13204,a),flip(a)].">
      <j1 rule="hyper" parents="12614 13204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13219">
    <literal><![CDATA[
      (x \ y) * (K(y,x) * z) = (x \ T(y,x)) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,13218,a(flip),b,6356,a),flip(a)].">
      <j1 rule="hyper" parents="119 13218 6356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13220">
    <literal><![CDATA[
      L(x,y * (z / T(y,z)),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(4238(a,1),13207(a,1,2))].">
      <j1 rule="para" parents="4238 13207"/>
    </justification>
  </clause>

  <clause id="13221">
    <literal><![CDATA[
      L(x,T(y,z),y \ z) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(11161,a,13209,a),flip(a)].">
      <j1 rule="hyper" parents="11161 13209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13222">
    <literal><![CDATA[
      L(x,T(y * z,z \ 1),u) = L(x,T(y * z,y),u)
    ]]></literal>
    <justification jstring="[para(6144(a,1),13209(a,1,2))].">
      <j1 rule="para" parents="6144 13209"/>
    </justification>
  </clause>

  <clause id="13223">
    <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(13209(a,1),4529(a,1))].">
      <j1 rule="para" parents="13209 4529"/>
    </justification>
  </clause>

  <clause id="13224">
    <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(13209(a,1),11168(a,1))].">
      <j1 rule="para" parents="13209 11168"/>
    </justification>
  </clause>

  <clause id="13225">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ 1),u) = L(x,T(T(y,z),z \ y),u)
    ]]></literal>
    <justification jstring="[para(13106(a,1),13209(a,1,2))].">
      <j1 rule="para" parents="13106 13209"/>
    </justification>
  </clause>

  <clause id="13227">
    <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(13210(a,1),6602(a,1,2))].">
      <j1 rule="para" parents="13210 6602"/>
    </justification>
  </clause>

  <clause id="13228">
    <literal><![CDATA[
      L(x,K(y * z,y \ 1),u) = L(x,K(z,y \ 1),u)
    ]]></literal>
    <justification jstring="[para(4447(a,1),13212(a,1,2))].">
      <j1 rule="para" parents="4447 13212"/>
    </justification>
  </clause>

  <clause id="13229">
    <literal><![CDATA[
      L(x,T(y,z \ y),u) = L(x,z * (y / z),u)
    ]]></literal>
    <justification jstring="[para(4107(a,1),13217(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4107 13217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13230">
    <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,13203,a,b,13220,a)].">
      <j1 rule="hyper" parents="58 13203 13220"/>
    </justification>
  </clause>

  <clause id="13231">
    <literal><![CDATA[
      L(T(x,y) \ z,x,x \ y) = y \ ((T(y,x) / x) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,12600,a(flip),b,13221,a),flip(a)].">
      <j1 rule="hyper" parents="58 12600 13221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13232">
    <literal><![CDATA[
      L(x,T(y / z,y) \ u,w) = L(x,(z \ y) \ u,w)
    ]]></literal>
    <justification jstring="[para(4363(a,1),13205(a,1,2,1))].">
      <j1 rule="para" parents="4363 13205"/>
    </justification>
  </clause>

  <clause id="13233">
    <literal><![CDATA[
      L(x,(y * z) / y,u) = L(x,y * (z / y),u)
    ]]></literal>
    <justification jstring="[para(544(a,1),13206(a,1,2)),flip(a)].">
      <j1 rule="para" parents="544 13206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13234">
    <literal><![CDATA[
      K(x,y) * ((y \ T(x,y)) \ z) = (y \ x) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,13219,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 13219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13235">
    <literal><![CDATA[
      K(x,y) * ((T(y,x) \ x) \ z) = (y \ x) \ z
    ]]></literal>
    <justification jstring="[para(4208(a,2),13234(a,1,2,1))].">
      <j1 rule="para" parents="4208 13234"/>
    </justification>
  </clause>

  <clause id="13236">
    <literal><![CDATA[
      L(x,T(y * z,z \ 1),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13203,a(flip),b,13222,a),flip(a)].">
      <j1 rule="hyper" parents="320 13203 13222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13237">
    <literal><![CDATA[
      L(x,y * z,z \ 1) = L(x,z * y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(11161,a,13236,a)].">
      <j1 rule="hyper" parents="11161 13236"/>
    </justification>
  </clause>

  <clause id="13238">
    <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(13236(a,1),10867(a,1,2))].">
      <j1 rule="para" parents="13236 10867"/>
    </justification>
  </clause>

  <clause id="13239">
    <literal><![CDATA[
      L(x,(x / y) \ z,u) = L(x,(y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,10922,a(flip),b,13232,a)].">
      <j1 rule="hyper" parents="58 10922 13232"/>
    </justification>
  </clause>

  <clause id="13240">
    <literal><![CDATA[
      L(x,T(T(y,z),y / T(z,y)),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(4202(a,1),13230(a,1,2,1))].">
      <j1 rule="para" parents="4202 13230"/>
    </justification>
  </clause>

  <clause id="13241">
    <literal><![CDATA[
      L(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      L(x,T(y,u),x) = z
    ]]></literal>
    <justification jstring="[para(13240(a,1),12630(a,1))].">
      <j1 rule="para" parents="13240 12630"/>
    </justification>
  </clause>

  <clause id="13242">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(12698(a,1),13240(a,1,2))].">
      <j1 rule="para" parents="12698 13240"/>
    </justification>
  </clause>

  <clause id="13243">
    <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(9629(a,2),13241(a,1))].">
      <j1 rule="para" parents="9629 13241"/>
    </justification>
  </clause>

  <clause id="13244">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ 1),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13225,a,b,13242,a)].">
      <j1 rule="hyper" parents="58 13225 13242"/>
    </justification>
  </clause>

  <clause id="13245">
    <literal><![CDATA[
      L(x,T(y,z),z \ 1) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(11161,a,13244,a)].">
      <j1 rule="hyper" parents="11161 13244"/>
    </justification>
  </clause>

  <clause id="13247">
    <literal><![CDATA[
      L(x,y * (z / y),(y \ z) \ 1) = L(x,z,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,13229,a(flip),b,13245,a)].">
      <j1 rule="hyper" parents="58 13229 13245"/>
    </justification>
  </clause>

  <clause id="13248">
    <literal><![CDATA[
      L(x \ y,x,z) != u
    ]]></literal>
    <literal><![CDATA[
      (z * x) \ (z * y) = u
    ]]></literal>
    <justification jstring="[para(13214(a,1),3637(a,1))].">
      <j1 rule="para" parents="13214 3637"/>
    </justification>
  </clause>

  <clause id="13249">
    <literal><![CDATA[
      a(x \ L(y \ z,y,u),w,v5) = a(x \ ((u * y) \ (u * z)),w,v5)
    ]]></literal>
    <justification jstring="[para(13214(a,1),12922(a,1,1,2))].">
      <j1 rule="para" parents="13214 12922"/>
    </justification>
  </clause>

  <clause id="13250">
    <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),13248(a,1,1))].">
      <j1 rule="para" parents="92 13248"/>
    </justification>
  </clause>

  <clause id="13251">
    <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(261(a,1),13215(a,1,2,2))].">
      <j1 rule="para" parents="261 13215"/>
    </justification>
  </clause>

  <clause id="13252">
    <literal><![CDATA[
      L(x,K(y * z,y \ 1),u) = L(x,K(z * y,z),u)
    ]]></literal>
    <justification jstring="[para(6931(a,1),13251(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6931 13251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13253">
    <literal><![CDATA[
      L(x,K(y * z,y \ 1),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13201,a(flip),b,13252,a),flip(a)].">
      <j1 rule="hyper" parents="320 13201 13252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13255">
    <literal><![CDATA[
      L(x,K(y,z),y \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(5430,a,13253,a),flip(a)].">
      <j1 rule="hyper" parents="5430 13253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13256">
    <literal><![CDATA[
      L(x,K(y,z \ 1),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13228,a(flip),b,13253,a)].">
      <j1 rule="hyper" parents="58 13228 13253"/>
    </justification>
  </clause>

  <clause id="13257">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * z) = (K(x,y) / x) * z
    ]]></literal>
    <justification jstring="[para(13255(a,1),6217(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13255 6217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13259">
    <literal><![CDATA[
      L(x,K(y \ 1,z),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(3523(a,1),13256(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3523 13256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13260">
    <literal><![CDATA[
      L(x,K(y,z),u \ (z \ u)) = x
    ]]></literal>
    <justification jstring="[hyper(8024,a,13259,a),flip(a)].">
      <j1 rule="hyper" parents="8024 13259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13261">
    <literal><![CDATA[
      (K(x,y) / x) * ((1 / x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(5978,a,13257,a),flip(a)].">
      <j1 rule="hyper" parents="5978 13257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13262">
    <literal><![CDATA[
      (K(x,y) / x) * (x * z) = (1 / x) * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4740(a,1),13257(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4740 13257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13263">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) / x) * z = u
    ]]></literal>
    <justification jstring="[para(13261(a,1),584(a,1))].">
      <j1 rule="para" parents="13261 584"/>
    </justification>
  </clause>

  <clause id="13264">
    <literal><![CDATA[
      (K(x,y) / x) * (x * (T(y,x) * z)) = (1 / x) * (x * (y * z))
    ]]></literal>
    <justification jstring="[para(4512(a,1),13262(a,2,2))].">
      <j1 rule="para" parents="4512 13262"/>
    </justification>
  </clause>

  <clause id="13265">
    <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(13264(a,2),2807(a,1))].">
      <j1 rule="para" parents="13264 2807"/>
    </justification>
  </clause>

  <clause id="13266">
    <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(12914(a,1),12927(a,1,2,1))].">
      <j1 rule="para" parents="12914 12927"/>
    </justification>
  </clause>

  <clause id="13267">
    <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(6097(a,1),13094(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6097 13094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13268">
    <literal><![CDATA[
      K(x,y * K((z * (1 / u)) \ w,u)) = K(x,y * K(u * (z \ w),w \ z))
    ]]></literal>
    <justification jstring="[para(6078(a,1),13267(a,2,2,2))].">
      <j1 rule="para" parents="6078 13267"/>
    </justification>
  </clause>

  <clause id="13270">
    <literal><![CDATA[
      K(x,y * K(z * (u \ w),w \ u)) = K(x,y * K(z * (u \ w),z))
    ]]></literal>
    <justification jstring="[para(10472(a,1),13268(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10472 13268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13271">
    <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(13151(a,1),13149(a,1,1))].">
      <j1 rule="para" parents="13151 13149"/>
    </justification>
  </clause>

  <clause id="13272">
    <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(13179(a,1),10833(a,1))].">
      <j1 rule="para" parents="13179 10833"/>
    </justification>
  </clause>

  <clause id="13273">
    <literal><![CDATA[
      a(x * a(y,z,y),u,w) = a(x,a(y,z,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(12395,a,13266,a),flip(a)].">
      <j1 rule="hyper" parents="12395 13266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13274">
    <literal><![CDATA[
      a(x,a(y,z,y) * u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,12732,a(flip),b,13273,a),flip(a)].">
      <j1 rule="hyper" parents="58 12732 13273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13276">
    <literal><![CDATA[
      a(x,R(y,z,y),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(8926(a,1),13274(a,1,2))].">
      <j1 rule="para" parents="8926 13274"/>
    </justification>
  </clause>

  <clause id="13277">
    <literal><![CDATA[
      a(x,T(y * z,y),u) = a(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(8939(a,1),13274(a,1,2))].">
      <j1 rule="para" parents="8939 13274"/>
    </justification>
  </clause>

  <clause id="13278">
    <literal><![CDATA[
      a(x,T(y,y \ z),u) = a(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4399(a,1),13276(a,1,2))].">
      <j1 rule="para" parents="4399 13276"/>
    </justification>
  </clause>

  <clause id="13279">
    <literal><![CDATA[
      a(x,(y \ z) * y,u) = a(x,T(z,y),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13277(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13280">
    <literal><![CDATA[
      a(x \ y,T(x,y),z) = a(y / x,x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4616,a(flip),b,13278,a),flip(a)].">
      <j1 rule="hyper" parents="58 4616 13278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13281">
    <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(13279(a,1),4365(a,1,2))].">
      <j1 rule="para" parents="13279 4365"/>
    </justification>
  </clause>

  <clause id="13282">
    <literal><![CDATA[
      a(x,y,z * a(u,w,u)) = (x * (y * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(12923,a,13271,a),flip(a)].">
      <j1 rule="hyper" parents="12923 13271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13283">
    <literal><![CDATA[
      a(x,y,z * a(u,w,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,9,a,b,13282,a),flip(a)].">
      <j1 rule="hyper" parents="320 9 13282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13284">
    <literal><![CDATA[
      a(x,y,a(z,u,z) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(9492(a,2),13283(a,1,3))].">
      <j1 rule="para" parents="9492 13283"/>
    </justification>
  </clause>

  <clause id="13285">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,u) \ v5)) = a(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(12908(a,1),13284(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12908 13284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13286">
    <literal><![CDATA[
      a(x,y,z * K(u,u * w)) = a(x,y,z * K(u,w))
    ]]></literal>
    <justification jstring="[para(8927(a,1),13285(a,1,3,2))].">
      <j1 rule="para" parents="8927 13285"/>
    </justification>
  </clause>

  <clause id="13287">
    <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(12884(a,1),12885(a,1,2,2,1))].">
      <j1 rule="para" parents="12884 12885"/>
    </justification>
  </clause>

  <clause id="13289">
    <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(4266(a,2),13287(a,1,2))].">
      <j1 rule="para" parents="4266 13287"/>
    </justification>
  </clause>

  <clause id="13291">
    <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(12936(a,1),13289(a,1,2))].">
      <j1 rule="para" parents="12936 13289"/>
    </justification>
  </clause>

  <clause id="13292">
    <literal><![CDATA[
      T(T(x,x * y) * L(y,z,u),x) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(802(a,1),13291(a,1,2)),flip(a)].">
      <j1 rule="para" parents="802 13291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13294">
    <literal><![CDATA[
      T(x * L(y,z,u),x * y) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9779,a(flip),b,13292,a)].">
      <j1 rule="hyper" parents="58 9779 13292"/>
    </justification>
  </clause>

  <clause id="13295">
    <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,13294,a(flip),b,4714,a(flip))].">
      <j1 rule="hyper" parents="116 13294 4714"/>
    </justification>
  </clause>

  <clause id="13296">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = K(x,y) * K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(8906,a,13295,a),flip(a)].">
      <j1 rule="hyper" parents="8906 13295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13297">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,10813,a(flip),b,13296,a),flip(a)].">
      <j1 rule="hyper" parents="320 10813 13296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13298">
    <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),13297(a,1,1))].">
      <j1 rule="para" parents="7 13297"/>
    </justification>
  </clause>

  <clause id="13299">
    <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,6954,a(flip),b,13298,a)].">
      <j1 rule="hyper" parents="58 6954 13298"/>
    </justification>
  </clause>

  <clause id="13300">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(10506(a,1),13299(a,2,3))].">
      <j1 rule="para" parents="10506 13299"/>
    </justification>
  </clause>

  <clause id="13301">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,10982,a(flip),b,13300,a),flip(a)].">
      <j1 rule="hyper" parents="320 10982 13300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13303">
    <literal><![CDATA[
      K(x,x * (L(y,z,u) \ y)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(10474,a,13301,a)].">
      <j1 rule="hyper" parents="10474 13301"/>
    </justification>
  </clause>

  <clause id="13304">
    <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,5573,a,b,13303,a)].">
      <j1 rule="hyper" parents="58 5573 13303"/>
    </justification>
  </clause>

  <clause id="13305">
    <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),13303(a,1,2))].">
      <j1 rule="para" parents="7 13303"/>
    </justification>
  </clause>

  <clause id="13306">
    <literal><![CDATA[
      K(x * (L(y,z,u) \ y),x) = w / (a(u,z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(13303(a,1),5104(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13303 5104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13307">
    <literal><![CDATA[
      K(x * (L(y,z,u) \ y),x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,9882,a(flip),b,13306,a),flip(a)].">
      <j1 rule="hyper" parents="320 9882 13306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13308">
    <literal><![CDATA[
      L(x,y,a(z,u,K(w,y))) = x
    ]]></literal>
    <justification jstring="[para(13307(a,1),5435(a,1,3))].">
      <j1 rule="para" parents="13307 5435"/>
    </justification>
  </clause>

  <clause id="13309">
    <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(13307(a,1),10985(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13307 10985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13310">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * u) * w = a(x,y,K(z,u)) * (u * w)
    ]]></literal>
    <justification jstring="[hyper(1330,a,13308,a),flip(a)].">
      <j1 rule="hyper" parents="1330 13308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13311">
    <literal><![CDATA[
      a(x,y,K(L(z,u,w) \ z,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,27,a(flip),b,13309,a),flip(a)].">
      <j1 rule="hyper" parents="320 27 13309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13312">
    <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,11002,a(flip),b,13309,a)].">
      <j1 rule="hyper" parents="58 11002 13309"/>
    </justification>
  </clause>

  <clause id="13314">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(u,w,v5))) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,11002,a(flip),b,13311,a)].">
      <j1 rule="hyper" parents="58 11002 13311"/>
    </justification>
  </clause>

  <clause id="13315">
    <literal><![CDATA[
      T(L(x,y,z) \ x,L(u,w,v5)) = T(L(x,y,z) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(167,a,10854,a,b,13311,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 10854 13311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13316">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = K(a(z,y,x),u) * 1
    ]]></literal>
    <justification jstring="[para(13311(a,1),6631(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13311 6631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13318">
    <literal><![CDATA[
      T(x,L(y \ L(y,z,u),w,v5)) = T(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(167,a,10854,a,b,13314,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 10854 13314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13319">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = K(a(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,3,a(flip),b,13316,a),flip(a)].">
      <j1 rule="hyper" parents="320 3 13316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13321">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = w / (K(a(u,z,y),x) * w)
    ]]></literal>
    <justification jstring="[para(13319(a,1),5104(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13319 5104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13322">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = K(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,5104,a(flip),b,13321,a),flip(a)].">
      <j1 rule="hyper" parents="320 5104 13321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13323">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,13322,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 13322 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13325">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = T(x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6673,a(flip),b,13318,a)].">
      <j1 rule="hyper" parents="58 6673 13318"/>
    </justification>
  </clause>

  <clause id="13327">
    <literal><![CDATA[
      T(x * K(y \ L(y,z,u),x),a(u,z,y) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,4775,a(flip),b,13325,a),flip(a)].">
      <j1 rule="hyper" parents="320 4775 13325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13328">
    <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(13325(a,2),710(a,1,1))].">
      <j1 rule="para" parents="13325 710"/>
    </justification>
  </clause>

  <clause id="13329">
    <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(13327(a,1),4890(a,1,1))].">
      <j1 rule="para" parents="13327 4890"/>
    </justification>
  </clause>

  <clause id="13330">
    <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(6480,a,13305,a)].">
      <j1 rule="hyper" parents="6480 13305"/>
    </justification>
  </clause>

  <clause id="13331">
    <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,10464,a(flip),b,13330,a)].">
      <j1 rule="hyper" parents="58 10464 13330"/>
    </justification>
  </clause>

  <clause id="13332">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K((y / x) \ y,y))
    ]]></literal>
    <justification jstring="[para(11371(a,1),13331(a,2,3))].">
      <j1 rule="para" parents="11371 13331"/>
    </justification>
  </clause>

  <clause id="13333">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),13332(a,2,3,1))].">
      <j1 rule="para" parents="75 13332"/>
    </justification>
  </clause>

  <clause id="13336">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = w / (a(u,z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(13333(a,1),5104(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13333 5104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13337">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,9882,a(flip),b,13336,a),flip(a)].">
      <j1 rule="hyper" parents="320 9882 13336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13338">
    <literal><![CDATA[
      T(x,x * (y \ L(y,z,u))) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,13337,a(flip),b,4688,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 13337 4688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13339">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)),L(w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      x = v7
    ]]></literal>
    <justification jstring="[para(13337(a,1),4473(a,1,2))].">
      <j1 rule="para" parents="13337 4473"/>
    </justification>
  </clause>

  <clause id="13340">
    <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(13337(a,1),4725(a,1,2))].">
      <j1 rule="para" parents="13337 4725"/>
    </justification>
  </clause>

  <clause id="13341">
    <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(12887(a,1),13304(a,1,2))].">
      <j1 rule="para" parents="12887 13304"/>
    </justification>
  </clause>

  <clause id="13342">
    <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(5424,a,13341,a)].">
      <j1 rule="hyper" parents="5424 13341"/>
    </justification>
  </clause>

  <clause id="13343">
    <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(7724,a,13342,a)].">
      <j1 rule="hyper" parents="7724 13342"/>
    </justification>
  </clause>

  <clause id="13344">
    <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(13323(a,1),13343(a,1,2,1))].">
      <j1 rule="para" parents="13323 13343"/>
    </justification>
  </clause>

  <clause id="13345">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(4994,a,13344,a)].">
      <j1 rule="hyper" parents="4994 13344"/>
    </justification>
  </clause>

  <clause id="13346">
    <literal><![CDATA[
      x \ T(x,a(y,z,u)) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(12785(a,1),13344(a,1,2))].">
      <j1 rule="para" parents="12785 13344"/>
    </justification>
  </clause>

  <clause id="13347">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(12794,a,13345,a),flip(a)].">
      <j1 rule="hyper" parents="12794 13345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13348">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,a(x,y,u)) = w
    ]]></literal>
    <justification jstring="[para(13345(a,1),12794(a,1))].">
      <j1 rule="para" parents="13345 12794"/>
    </justification>
  </clause>

  <clause id="13349">
    <literal><![CDATA[
      (x * y) * a(z,u,K(y,w)) = x * T(y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,13347,a,b,6124,a)].">
      <j1 rule="hyper" parents="119 13347 6124"/>
    </justification>
  </clause>

  <clause id="13350">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,13347,a,b,4688,a(flip))].">
      <j1 rule="hyper" parents="119 13347 4688"/>
    </justification>
  </clause>

  <clause id="13352">
    <literal><![CDATA[
      a(x,y,K(z,a(u,w,v5))) = 1
    ]]></literal>
    <justification jstring="[para(13347(a,1),27(a,1,3))].">
      <j1 rule="para" parents="13347 27"/>
    </justification>
  </clause>

  <clause id="13353">
    <literal><![CDATA[
      a(x,y,K(z,u)) != 1
    ]]></literal>
    <literal><![CDATA[
      T(z,a(x,y,u)) = z
    ]]></literal>
    <justification jstring="[para(13347(a,2),51(a,1))].">
      <j1 rule="para" parents="13347 51"/>
    </justification>
  </clause>

  <clause id="13354">
    <literal><![CDATA[
      a(x,y,K(z,u)) * z = T(z,a(x,y,u))
    ]]></literal>
    <justification jstring="[para(13347(a,2),4729(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13347 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13355">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(13347(a,2),4725(a,1,2))].">
      <j1 rule="para" parents="13347 4725"/>
    </justification>
  </clause>

  <clause id="13356">
    <literal><![CDATA[
      a(x,y,K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(13347(a,2),9530(a,1))].">
      <j1 rule="para" parents="13347 9530"/>
    </justification>
  </clause>

  <clause id="13357">
    <literal><![CDATA[
      K(x,a(y,z,a(u,w,v5))) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,13347,a(flip),b,13352,a)].">
      <j1 rule="hyper" parents="58 13347 13352"/>
    </justification>
  </clause>

  <clause id="13358">
    <literal><![CDATA[
      a(x,y,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(6073(a,1),13356(a,1))].">
      <j1 rule="para" parents="6073 13356"/>
    </justification>
  </clause>

  <clause id="13359">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(5533,a,13357,a),flip(a)].">
      <j1 rule="hyper" parents="5533 13357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13360">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) \ v5) * a(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[hyper(5258,a,13357,a)].">
      <j1 rule="hyper" parents="5258 13357"/>
    </justification>
  </clause>

  <clause id="13361">
    <literal><![CDATA[
      T(a(x,y,a(z,u,w)),v5) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(4913,a,13357,a)].">
      <j1 rule="hyper" parents="4913 13357"/>
    </justification>
  </clause>

  <clause id="13362">
    <literal><![CDATA[
      K(x,a(y,z,a(u,w,v5))) = a(v6,v7,K(v8,a(v9,v10,v11)))
    ]]></literal>
    <justification jstring="[hyper(320,a,13352,a,b,13357,a),flip(a)].">
      <j1 rule="hyper" parents="320 13352 13357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13363">
    <literal><![CDATA[
      x / a(y,z,a(u,w,v5)) = a(y,z,a(u,w,v5)) \ x
    ]]></literal>
    <justification jstring="[hyper(168,a,4977,a,b,13357,a(flip))].">
      <j1 rule="hyper" parents="168 4977 13357"/>
    </justification>
  </clause>

  <clause id="13364">
    <literal><![CDATA[
      x * (a(y,z,a(u,w,v5)) * v6) = x * (v6 * a(y,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(167,a,6590,a,b,13357,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 6590 13357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13365">
    <literal><![CDATA[
      a(x,y,K(z,L(y,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      1 = v5
    ]]></literal>
    <justification jstring="[para(10581(a,1),13358(a,1,3))].">
      <j1 rule="para" parents="10581 13358"/>
    </justification>
  </clause>

  <clause id="13366">
    <literal><![CDATA[
      a(x,L(y,z,u),K(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      1 = v5
    ]]></literal>
    <justification jstring="[para(11763(a,1),13358(a,1))].">
      <j1 rule="para" parents="11763 13358"/>
    </justification>
  </clause>

  <clause id="13367">
    <literal><![CDATA[
      T(x,a(y,z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(167,a,13346,a,b,10070,a(flip))].">
      <j1 rule="hyper" parents="167 13346 10070"/>
    </justification>
  </clause>

  <clause id="13368">
    <literal><![CDATA[
      T(x,a(y,z,L(u,w,v5))) = x * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,11763,a(flip),b,13346,a),flip(a)].">
      <j1 rule="hyper" parents="119 11763 13346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13370">
    <literal><![CDATA[
      (a(x,y,y \ 1) \ z) * a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[hyper(2325,a,13367,a)].">
      <j1 rule="hyper" parents="2325 13367"/>
    </justification>
  </clause>

  <clause id="13372">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ u = T(u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9881,a,b,13354,a)].">
      <j1 rule="hyper" parents="58 9881 13354"/>
    </justification>
  </clause>

  <clause id="13373">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(34,a,4749,a(flip),b,13372,a),flip(a)].">
      <j1 rule="hyper" parents="34 4749 13372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13374">
    <literal><![CDATA[
      (x / y) * a(z,u,K(w,y)) = x / T(y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,13373,a,b,6335,a)].">
      <j1 rule="hyper" parents="119 13373 6335"/>
    </justification>
  </clause>

  <clause id="13375">
    <literal><![CDATA[
      K(x,a(y,z,u) \ x) = a(y,z,K(u,a(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(12809,a,13373,a(flip))].">
      <j1 rule="hyper" parents="12809 13373"/>
    </justification>
  </clause>

  <clause id="13376">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u * a(x,y,z)) = a(x,y,z) * u
    ]]></literal>
    <justification jstring="[para(13373(a,2),4772(a,1,1))].">
      <j1 rule="para" parents="13373 4772"/>
    </justification>
  </clause>

  <clause id="13377">
    <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(13373(a,2),4730(a,1,1))].">
      <j1 rule="para" parents="13373 4730"/>
    </justification>
  </clause>

  <clause id="13378">
    <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(13373(a,2),4742(a,1,1))].">
      <j1 rule="para" parents="13373 4742"/>
    </justification>
  </clause>

  <clause id="13379">
    <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(13373(a,2),5142(a,1,1))].">
      <j1 rule="para" parents="13373 5142"/>
    </justification>
  </clause>

  <clause id="13380">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(y,z,a(u,w,v5)) * x = v6
    ]]></literal>
    <justification jstring="[para(13361(a,1),284(a,1,2))].">
      <j1 rule="para" parents="13361 284"/>
    </justification>
  </clause>

  <clause id="13381">
    <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(11001(a,1),13355(a,1,2))].">
      <j1 rule="para" parents="11001 13355"/>
    </justification>
  </clause>

  <clause id="13382">
    <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(13368(a,2),13355(a,1))].">
      <j1 rule="para" parents="13368 13355"/>
    </justification>
  </clause>

  <clause id="13383">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * v6) = v5 * (v6 * a(x,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,346,a(flip),b,13359,a),flip(a)].">
      <j1 rule="hyper" parents="320 346 13359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13384">
    <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(13359(a,1),691(a,1,2,1))].">
      <j1 rule="para" parents="13359 691"/>
    </justification>
  </clause>

  <clause id="13385">
    <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,13360,a(flip),b,889,a),flip(a)].">
      <j1 rule="hyper" parents="116 13360 889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13386">
    <literal><![CDATA[
      a(x,y,K(z,a(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      1 = v6
    ]]></literal>
    <justification jstring="[para(13362(a,1),9530(a,1))].">
      <j1 rule="para" parents="13362 9530"/>
    </justification>
  </clause>

  <clause id="13387">
    <literal><![CDATA[
      a(x,y,a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      1 = v6
    ]]></literal>
    <justification jstring="[para(13347(a,2),13386(a,1,3))].">
      <j1 rule="para" parents="13347 13386"/>
    </justification>
  </clause>

  <clause id="13388">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      1 = v6
    ]]></literal>
    <justification jstring="[para(13312(a,2),13387(a,1))].">
      <j1 rule="para" parents="13312 13387"/>
    </justification>
  </clause>

  <clause id="13389">
    <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(13363(a,1),1357(a,1,1,2))].">
      <j1 rule="para" parents="13363 1357"/>
    </justification>
  </clause>

  <clause id="13390">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * v6) = v5 * (a(x,y,a(z,u,w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(320,a,13364,a,b,13383,a),flip(a)].">
      <j1 rule="hyper" parents="320 13364 13383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13391">
    <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(1925(a,1),13383(a,2,2))].">
      <j1 rule="para" parents="1925 13383"/>
    </justification>
  </clause>

  <clause id="13392">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 \ (a(x,y,a(z,u,w)) \ v6)) = v5 \ v6
    ]]></literal>
    <justification jstring="[hyper(13380,a,13385,a)].">
      <j1 rule="hyper" parents="13380 13385"/>
    </justification>
  </clause>

  <clause id="13393">
    <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,13390,a)].">
      <j1 rule="hyper" parents="116 151 13390"/>
    </justification>
  </clause>

  <clause id="13394">
    <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(13390(a,2),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13390 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13395">
    <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="[hyper(116,a,13,a,b,13392,a),flip(a)].">
      <j1 rule="hyper" parents="116 13 13392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13396">
    <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,12029,a(flip),b,13391,a)].">
      <j1 rule="hyper" parents="117 12029 13391"/>
    </justification>
  </clause>

  <clause id="13397">
    <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(320,a,13338,a(flip),b,13328,a),flip(a)].">
      <j1 rule="hyper" parents="320 13338 13328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13398">
    <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(13393(a,1),13395(a,1,2))].">
      <j1 rule="para" parents="13393 13395"/>
    </justification>
  </clause>

  <clause id="13399">
    <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(13393(a,1),13398(a,1,2,2))].">
      <j1 rule="para" parents="13393 13398"/>
    </justification>
  </clause>

  <clause id="13400">
    <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(625,a,13399,a)].">
      <j1 rule="hyper" parents="625 13399"/>
    </justification>
  </clause>

  <clause id="13401">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) \ v5,v6,v7) = a(x,y,a(z,u,w)) \ L(v5,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(482,a,13399,a)].">
      <j1 rule="hyper" parents="482 13399"/>
    </justification>
  </clause>

  <clause id="13402">
    <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,13400,a(flip),b,3504,a),flip(a)].">
      <j1 rule="hyper" parents="119 13400 3504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13403">
    <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(12876(a,1),12895(a,1,2))].">
      <j1 rule="para" parents="12876 12895"/>
    </justification>
  </clause>

  <clause id="13404">
    <literal><![CDATA[
      R(R(x,y,z),y * z,a(u,w,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z * a(u,w,u)) = v5
    ]]></literal>
    <justification jstring="[para(13403(a,1),518(a,1))].">
      <j1 rule="para" parents="13403 518"/>
    </justification>
  </clause>

  <clause id="13405">
    <literal><![CDATA[
      R(x,y,z * a(u,w,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(13404,a,12893,a)].">
      <j1 rule="hyper" parents="13404 12893"/>
    </justification>
  </clause>

  <clause id="13406">
    <literal><![CDATA[
      R(x,y,z \ R(u,w,u)) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(12891(a,1),13405(a,1,3))].">
      <j1 rule="para" parents="12891 13405"/>
    </justification>
  </clause>

  <clause id="13407">
    <literal><![CDATA[
      R(x,y,z \ ((u \ w) \ w)) = R(x,y,z \ T(u,w))
    ]]></literal>
    <justification jstring="[para(7504(a,1),13406(a,1,3,2))].">
      <j1 rule="para" parents="7504 13406"/>
    </justification>
  </clause>

  <clause id="13408">
    <literal><![CDATA[
      L(x,y,((z \ u) * z) \ (u * (1 / z))) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[para(5970(a,1),13138(a,1,3,1))].">
      <j1 rule="para" parents="5970 13138"/>
    </justification>
  </clause>

  <clause id="13409">
    <literal><![CDATA[
      L(x,y,K(z,z \ u) * (1 / z)) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[para(11120(a,1),13408(a,1,3))].">
      <j1 rule="para" parents="11120 13408"/>
    </justification>
  </clause>

  <clause id="13410">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1) / u) = L(x,y,K(u,u \ z) / u)
    ]]></literal>
    <justification jstring="[para(6216(a,1),13409(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6216 13409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13411">
    <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),13187(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13412">
    <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(13402(a,2),13396(a,1,2))].">
      <j1 rule="para" parents="13402 13396"/>
    </justification>
  </clause>

  <clause id="13413">
    <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(12029(a,1),13412(a,1,2,1))].">
      <j1 rule="para" parents="12029 13412"/>
    </justification>
  </clause>

  <clause id="13414">
    <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(13413(a,1),5920(a,1,1))].">
      <j1 rule="para" parents="13413 5920"/>
    </justification>
  </clause>

  <clause id="13415">
    <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),12901(a,1,2,2))].">
      <j1 rule="para" parents="13 12901"/>
    </justification>
  </clause>

  <clause id="13416">
    <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(3513(a,1),13415(a,1,2))].">
      <j1 rule="para" parents="3513 13415"/>
    </justification>
  </clause>

  <clause id="13417">
    <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(4016,a,13416,a)].">
      <j1 rule="hyper" parents="4016 13416"/>
    </justification>
  </clause>

  <clause id="13418">
    <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(320,a,12616,a(flip),b,13417,a)].">
      <j1 rule="hyper" parents="320 12616 13417"/>
    </justification>
  </clause>

  <clause id="13420">
    <literal><![CDATA[
      a(x,a(y,z,u) \ 1,x) = a(x,u \ L(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(201(a,1),13418(a,1,2,2))].">
      <j1 rule="para" parents="201 13418"/>
    </justification>
  </clause>

  <clause id="13421">
    <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(13420(a,1),10023(a,1,1,2))].">
      <j1 rule="para" parents="13420 10023"/>
    </justification>
  </clause>

  <clause id="13422">
    <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(13203(a,1),13227(a,1,2))].">
      <j1 rule="para" parents="13203 13227"/>
    </justification>
  </clause>

  <clause id="13423">
    <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(13384,a,13394,a)].">
      <j1 rule="hyper" parents="13384 13394"/>
    </justification>
  </clause>

  <clause id="13424">
    <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),12326(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13 12326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13425">
    <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(12538(a,1),12240(a,1,2))].">
      <j1 rule="para" parents="12538 12240"/>
    </justification>
  </clause>

  <clause id="13428">
    <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(190(a,1),12323(a,1,2,1))].">
      <j1 rule="para" parents="190 12323"/>
    </justification>
  </clause>

  <clause id="13429">
    <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(7679,a,13428,a),flip(a)].">
      <j1 rule="hyper" parents="7679 13428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13432">
    <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(320,a,12275,a,b,13429,a),flip(a)].">
      <j1 rule="hyper" parents="320 12275 13429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13434">
    <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(320,a,12295,a(flip),b,13432,a),flip(a)].">
      <j1 rule="hyper" parents="320 12295 13432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13436">
    <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(320,a,5391,a(flip),b,13434,a),flip(a)].">
      <j1 rule="hyper" parents="320 5391 13434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13438">
    <literal><![CDATA[
      K((((x / y) \ 1) \ y) \ y,z / (y / (((x / y) \ 1) \ y))) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(320,a,12333,a(flip),b,13436,a),flip(a)].">
      <j1 rule="hyper" parents="320 12333 13436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13440">
    <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),13438(a,1,2,2))].">
      <j1 rule="para" parents="72 13438"/>
    </justification>
  </clause>

  <clause id="13442">
    <literal><![CDATA[
      K((((x / y) \ 1) \ y) \ y,z / (1 / (x / y))) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,5278,a,b,13440,a)].">
      <j1 rule="hyper" parents="58 5278 13440"/>
    </justification>
  </clause>

  <clause id="13443">
    <literal><![CDATA[
      K((x / y) \ 1,T(z / (1 / (x / y)),y)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(7684,a,13442,a)].">
      <j1 rule="hyper" parents="7684 13442"/>
    </justification>
  </clause>

  <clause id="13444">
    <literal><![CDATA[
      K(1 / (x / y),T(z / (1 / (x / y)),y)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(5244,a,13443,a)].">
      <j1 rule="hyper" parents="5244 13443"/>
    </justification>
  </clause>

  <clause id="13445">
    <literal><![CDATA[
      K(1 / (x / y),(x / y) * T(z,y)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,12302,a(flip),b,13444,a)].">
      <j1 rule="hyper" parents="58 12302 13444"/>
    </justification>
  </clause>

  <clause id="13446">
    <literal><![CDATA[
      K(x / y,(y / x) * T(z,x)) = K(y \ x,z * (y / x))
    ]]></literal>
    <justification jstring="[hyper(5633,a,13445,a)].">
      <j1 rule="hyper" parents="5633 13445"/>
    </justification>
  </clause>

  <clause id="13447">
    <literal><![CDATA[
      K((x / y) \ x,z * ((x / y) / x)) = K(y,T(((x / y) / x) * T(z,x),x))
    ]]></literal>
    <justification jstring="[hyper(7913,a,13446,a),flip(a)].">
      <j1 rule="hyper" parents="7913 13446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13448">
    <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(4070(a,1),13446(a,2,1))].">
      <j1 rule="para" parents="4070 13446"/>
    </justification>
  </clause>

  <clause id="13449">
    <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(13447(a,1),6274(a,1))].">
      <j1 rule="para" parents="13447 6274"/>
    </justification>
  </clause>

  <clause id="13450">
    <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(13389(a,1),1358(a,1))].">
      <j1 rule="para" parents="13389 1358"/>
    </justification>
  </clause>

  <clause id="13451">
    <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(320,a,6865,a(flip),b,12489,a),flip(a)].">
      <j1 rule="hyper" parents="320 6865 12489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13452">
    <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,145,a(flip),b,13414,a),flip(a)].">
      <j1 rule="hyper" parents="58 145 13414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13453">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),v5,v6)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(691,a,13452,a)].">
      <j1 rule="hyper" parents="691 13452"/>
    </justification>
  </clause>

  <clause id="13455">
    <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,4010,a(flip),b,13453,a)].">
      <j1 rule="hyper" parents="58 4010 13453"/>
    </justification>
  </clause>

  <clause id="13456">
    <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(320,a,13453,a,b,13455,a)].">
      <j1 rule="hyper" parents="320 13453 13455"/>
    </justification>
  </clause>

  <clause id="13457">
    <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(8865(a,1),13451(a,2,1,2))].">
      <j1 rule="para" parents="8865 13451"/>
    </justification>
  </clause>

  <clause id="13458">
    <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(7017(a,1),13457(a,2,1))].">
      <j1 rule="para" parents="7017 13457"/>
    </justification>
  </clause>

  <clause id="13459">
    <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(3308(a,1),13458(a,2,1,1))].">
      <j1 rule="para" parents="3308 13458"/>
    </justification>
  </clause>

  <clause id="13460">
    <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(6296(a,1),13459(a,2,2))].">
      <j1 rule="para" parents="6296 13459"/>
    </justification>
  </clause>

  <clause id="13461">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,11950,a(flip),b,13460,a),flip(a)].">
      <j1 rule="hyper" parents="320 11950 13460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13463">
    <literal><![CDATA[
      K((x \ K(x,y)) * T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = 1
    ]]></literal>
    <justification jstring="[para(11452(a,1),13461(a,1,1))].">
      <j1 rule="para" parents="11452 13461"/>
    </justification>
  </clause>

  <clause id="13464">
    <literal><![CDATA[
      1 / (((x \ K(x,y)) \ 1) \ T(x,z)) = ((x \ K(x,y)) * T(x,z)) \ 1
    ]]></literal>
    <justification jstring="[para(13463(a,1),12140(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13463 12140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13465">
    <literal><![CDATA[
      1 / (((x \ K(x,y)) \ 1) \ T(x,z)) = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,12488,a(flip),b,13464,a),flip(a)].">
      <j1 rule="hyper" parents="320 12488 13464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13467">
    <literal><![CDATA[
      1 / (((x \ 1) \ K(y,x)) \ T(x,z)) = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[para(5576(a,1),13465(a,1,2,1))].">
      <j1 rule="para" parents="5576 13465"/>
    </justification>
  </clause>

  <clause id="13468">
    <literal><![CDATA[
      1 / ((x \ K(x,y)) * T(x,z)) = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[para(11452(a,1),13467(a,1,2))].">
      <j1 rule="para" parents="11452 13467"/>
    </justification>
  </clause>

  <clause id="13469">
    <literal><![CDATA[
      (x * (K(y,x) / T(x,z))) \ 1 = (x \ K(x,y)) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(188,a,13468,a)].">
      <j1 rule="hyper" parents="188 13468"/>
    </justification>
  </clause>

  <clause id="13470">
    <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(13469(a,1),3664(a,1,1,1))].">
      <j1 rule="para" parents="13469 3664"/>
    </justification>
  </clause>

  <clause id="13471">
    <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(186(a,1),12320(a,2,2))].">
      <j1 rule="para" parents="186 12320"/>
    </justification>
  </clause>

  <clause id="13472">
    <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(320,a,4703,a,b,13471,a),flip(a)].">
      <j1 rule="hyper" parents="320 4703 13471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13474">
    <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(320,a,7759,a,b,13472,a),flip(a)].">
      <j1 rule="hyper" parents="320 7759 13472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13475">
    <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(12344(a,1),13474(a,1,2))].">
      <j1 rule="para" parents="12344 13474"/>
    </justification>
  </clause>

  <clause id="13476">
    <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(10904,a,13475,a)].">
      <j1 rule="hyper" parents="10904 13475"/>
    </justification>
  </clause>

  <clause id="13477">
    <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(7756,a,13476,a)].">
      <j1 rule="hyper" parents="7756 13476"/>
    </justification>
  </clause>

  <clause id="13478">
    <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,7208,a(flip),b,13477,a)].">
      <j1 rule="hyper" parents="58 7208 13477"/>
    </justification>
  </clause>

  <clause id="13480">
    <literal><![CDATA[
      K(x,K(y * z,L(u,z,y))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[para(4870(a,1),13478(a,1,2))].">
      <j1 rule="para" parents="4870 13478"/>
    </justification>
  </clause>

  <clause id="13481">
    <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(10290(a,1),12625(a,1,1))].">
      <j1 rule="para" parents="10290 12625"/>
    </justification>
  </clause>

  <clause id="13483">
    <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,12317,a(flip),b,12161,a)].">
      <j1 rule="hyper" parents="58 12317 12161"/>
    </justification>
  </clause>

  <clause id="13484">
    <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(9835(a,1),13483(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9835 13483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13485">
    <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(7772(a,1),13484(a,2,2))].">
      <j1 rule="para" parents="7772 13484"/>
    </justification>
  </clause>

  <clause id="13487">
    <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(13480(a,1),13485(a,2,2))].">
      <j1 rule="para" parents="13480 13485"/>
    </justification>
  </clause>

  <clause id="13488">
    <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(7754(a,1),13487(a,2,2))].">
      <j1 rule="para" parents="7754 13487"/>
    </justification>
  </clause>

  <clause id="13489">
    <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(10763(a,1),13488(a,1,1,2))].">
      <j1 rule="para" parents="10763 13488"/>
    </justification>
  </clause>

  <clause id="13490">
    <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,10636,a,b,13489,a)].">
      <j1 rule="hyper" parents="58 10636 13489"/>
    </justification>
  </clause>

  <clause id="13491">
    <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(11713(a,1),13490(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11713 13490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13492">
    <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(13491(a,1),536(a,1))].">
      <j1 rule="para" parents="13491 536"/>
    </justification>
  </clause>

  <clause id="13493">
    <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(12488(a,1),13470(a,1,1))].">
      <j1 rule="para" parents="12488 13470"/>
    </justification>
  </clause>

  <clause id="13494">
    <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(13469(a,1),13493(a,1,2,2))].">
      <j1 rule="para" parents="13469 13493"/>
    </justification>
  </clause>

  <clause id="13495">
    <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(8566(a,1),13494(a,1,2))].">
      <j1 rule="para" parents="8566 13494"/>
    </justification>
  </clause>

  <clause id="13496">
    <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(6007(a,1),13495(a,1,2))].">
      <j1 rule="para" parents="6007 13495"/>
    </justification>
  </clause>

  <clause id="13497">
    <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(12776(a,1),13496(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12776 13496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13498">
    <literal><![CDATA[
      ((((x \ K(x,y)) * T(x,z)) \ 1) \ 1) * u = (x * (K(y,x) / T(x,z))) \ u
    ]]></literal>
    <justification jstring="[para(13469(a,1),13497(a,1,1,1,1))].">
      <j1 rule="para" parents="13469 13497"/>
    </justification>
  </clause>

  <clause id="13499">
    <literal><![CDATA[
      ((x * (K(y,x) / T(x,z))) \ 1) * u = (x * (K(y,x) / T(x,z))) \ u
    ]]></literal>
    <justification jstring="[para(12488(a,1),13498(a,1,1,1))].">
      <j1 rule="para" parents="12488 13498"/>
    </justification>
  </clause>

  <clause id="13500">
    <literal><![CDATA[
      (x * (K(y,x) / T(x,z))) \ u = ((x \ K(x,y)) * T(x,z)) * u
    ]]></literal>
    <justification jstring="[para(13469(a,1),13499(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13469 13499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13501">
    <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(13500(a,1),9022(a,1,1))].">
      <j1 rule="para" parents="13500 9022"/>
    </justification>
  </clause>

  <clause id="13502">
    <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(8614(a,1),13501(a,1,2))].">
      <j1 rule="para" parents="8614 13501"/>
    </justification>
  </clause>

  <clause id="13503">
    <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,9747,a(flip),b,13502,a)].">
      <j1 rule="hyper" parents="58 9747 13502"/>
    </justification>
  </clause>

  <clause id="13504">
    <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(4777(a,1),13503(a,1,2))].">
      <j1 rule="para" parents="4777 13503"/>
    </justification>
  </clause>

  <clause id="13505">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ (T(x,z) * u) = ((x \ K(x,y)) * T(x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(11408,a,13504,a),flip(a)].">
      <j1 rule="hyper" parents="11408 13504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13507">
    <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(5576(a,1),9300(a,1,1,1))].">
      <j1 rule="para" parents="5576 9300"/>
    </justification>
  </clause>

  <clause id="13508">
    <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(13505(a,1),13507(a,1,1))].">
      <j1 rule="para" parents="13505 13507"/>
    </justification>
  </clause>

  <clause id="13509">
    <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(5522(a,1),13508(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5522 13508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13510">
    <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(5281(a,1),13509(a,2,2))].">
      <j1 rule="para" parents="5281 13509"/>
    </justification>
  </clause>

  <clause id="13511">
    <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(5850(a,1),13510(a,2,2))].">
      <j1 rule="para" parents="5850 13510"/>
    </justification>
  </clause>

  <clause id="13512">
    <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(8688(a,1),13511(a,2,2))].">
      <j1 rule="para" parents="8688 13511"/>
    </justification>
  </clause>

  <clause id="13513">
    <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),13512(a,2,2,1))].">
      <j1 rule="para" parents="4 13512"/>
    </justification>
  </clause>

  <clause id="13514">
    <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(320,a,6086,a(flip),b,13513,a),flip(a)].">
      <j1 rule="hyper" parents="320 6086 13513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13516">
    <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(320,a,9007,a(flip),b,13514,a),flip(a)].">
      <j1 rule="hyper" parents="320 9007 13514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13517">
    <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(5576(a,1),13516(a,1,1,1))].">
      <j1 rule="para" parents="5576 13516"/>
    </justification>
  </clause>

  <clause id="13518">
    <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(13505(a,1),13517(a,1,1))].">
      <j1 rule="para" parents="13505 13517"/>
    </justification>
  </clause>

  <clause id="13519">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,x \ 1) * z) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(5522(a,1),13518(a,1,1,1))].">
      <j1 rule="para" parents="5522 13518"/>
    </justification>
  </clause>

  <clause id="13520">
    <literal><![CDATA[
      T(K(x,y) * z,x * z) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3737,a(flip),b,13519,a)].">
      <j1 rule="hyper" parents="58 3737 13519"/>
    </justification>
  </clause>

  <clause id="13521">
    <literal><![CDATA[
      T(K(x,y) * z,x * z) = T(z,z * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4266(a,1),13520(a,2,1))].">
      <j1 rule="para" parents="4266 13520"/>
    </justification>
  </clause>

  <clause id="13522">
    <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(13337(a,1),13521(a,2,2))].">
      <j1 rule="para" parents="13337 13521"/>
    </justification>
  </clause>

  <clause id="13523">
    <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(13337(a,1),13522(a,1,1,1))].">
      <j1 rule="para" parents="13337 13522"/>
    </justification>
  </clause>

  <clause id="13524">
    <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(1677(a,1),13421(a,2,1))].">
      <j1 rule="para" parents="1677 13421"/>
    </justification>
  </clause>

  <clause id="13525">
    <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(320,a,12893,a(flip),b,13524,a),flip(a)].">
      <j1 rule="hyper" parents="320 12893 13524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13527">
    <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(9093(a,1),13525(a,1,1))].">
      <j1 rule="para" parents="9093 13525"/>
    </justification>
  </clause>

  <clause id="13528">
    <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,9756,a(flip),b,13527,a)].">
      <j1 rule="hyper" parents="58 9756 13527"/>
    </justification>
  </clause>

  <clause id="13529">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x * a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,13397,a(flip),b,13528,a),flip(a)].">
      <j1 rule="hyper" parents="58 13397 13528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13530">
    <literal><![CDATA[
      T(T(x,a(y,z,u) \ x),x * u) = T(x,L(u * x,z,y))
    ]]></literal>
    <justification jstring="[para(13529(a,2),11574(a,1,1))].">
      <j1 rule="para" parents="13529 11574"/>
    </justification>
  </clause>

  <clause id="13531">
    <literal><![CDATA[
      T(T(x,x * y),a(z,u,y) \ x) = T(x,L(y * x,u,z))
    ]]></literal>
    <justification jstring="[hyper(435,a,13530,a)].">
      <j1 rule="hyper" parents="435 13530"/>
    </justification>
  </clause>

  <clause id="13532">
    <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(5302(a,1),8092(a,1,1))].">
      <j1 rule="para" parents="5302 8092"/>
    </justification>
  </clause>

  <clause id="13533">
    <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(261(a,1),13532(a,1,1,2,2))].">
      <j1 rule="para" parents="261 13532"/>
    </justification>
  </clause>

  <clause id="13534">
    <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(3393(a,1),9886(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3393 9886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13535">
    <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(2236(a,1),13534(a,2,2,2))].">
      <j1 rule="para" parents="2236 13534"/>
    </justification>
  </clause>

  <clause id="13537">
    <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(12004(a,1),13535(a,2,2))].">
      <j1 rule="para" parents="12004 13535"/>
    </justification>
  </clause>

  <clause id="13538">
    <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(320,a,5092,a(flip),b,13537,a),flip(a)].">
      <j1 rule="hyper" parents="320 5092 13537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13539">
    <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(320,a,5715,a(flip),b,13538,a),flip(a)].">
      <j1 rule="hyper" parents="320 5715 13538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13540">
    <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(3393(a,1),13539(a,1,2,2,2))].">
      <j1 rule="para" parents="3393 13539"/>
    </justification>
  </clause>

  <clause id="13542">
    <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(5092(a,1),13540(a,1,2,2))].">
      <j1 rule="para" parents="5092 13540"/>
    </justification>
  </clause>

  <clause id="13543">
    <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(10644(a,1),13542(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10644 13542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13544">
    <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(320,a,11109,a(flip),b,13543,a),flip(a)].">
      <j1 rule="hyper" parents="320 11109 13543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13545">
    <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(198(a,1),13544(a,2,2))].">
      <j1 rule="para" parents="198 13544"/>
    </justification>
  </clause>

  <clause id="13546">
    <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(3487(a,1),9907(a,1,2,1,2,2,2))].">
      <j1 rule="para" parents="3487 9907"/>
    </justification>
  </clause>

  <clause id="13547">
    <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(3733(a,1),13546(a,1,2,1,2,2))].">
      <j1 rule="para" parents="3733 13546"/>
    </justification>
  </clause>

  <clause id="13548">
    <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(7754(a,1),13547(a,1,2,1))].">
      <j1 rule="para" parents="7754 13547"/>
    </justification>
  </clause>

  <clause id="13549">
    <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(8594(a,1),13548(a,1,2,1,2))].">
      <j1 rule="para" parents="8594 13548"/>
    </justification>
  </clause>

  <clause id="13550">
    <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(7510(a,1),13549(a,1,2,1,2))].">
      <j1 rule="para" parents="7510 13549"/>
    </justification>
  </clause>

  <clause id="13552">
    <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(8165(a,1),13550(a,1,2,1))].">
      <j1 rule="para" parents="8165 13550"/>
    </justification>
  </clause>

  <clause id="13553">
    <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(3487(a,1),13552(a,1,2,2,1,2,1,2,2))].">
      <j1 rule="para" parents="3487 13552"/>
    </justification>
  </clause>

  <clause id="13554">
    <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(3733(a,1),13553(a,1,2,2,1,2,1,2))].">
      <j1 rule="para" parents="3733 13553"/>
    </justification>
  </clause>

  <clause id="13555">
    <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(7730(a,1),13554(a,1,2,2,1,2))].">
      <j1 rule="para" parents="7730 13554"/>
    </justification>
  </clause>

  <clause id="13556">
    <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(9913(a,1),13555(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="9913 13555"/>
    </justification>
  </clause>

  <clause id="13557">
    <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(7259(a,1),13556(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="7259 13556"/>
    </justification>
  </clause>

  <clause id="13559">
    <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(8149(a,1),13557(a,1,2,2,1,2))].">
      <j1 rule="para" parents="8149 13557"/>
    </justification>
  </clause>

  <clause id="13560">
    <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(4692(a,2),13559(a,1,2,2,1))].">
      <j1 rule="para" parents="4692 13559"/>
    </justification>
  </clause>

  <clause id="13561">
    <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(9412(a,2),13560(a,1,2))].">
      <j1 rule="para" parents="9412 13560"/>
    </justification>
  </clause>

  <clause id="13562">
    <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,9408,a(flip),b,13561,a)].">
      <j1 rule="hyper" parents="58 9408 13561"/>
    </justification>
  </clause>

  <clause id="13563">
    <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(1436(a,1),13562(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1436 13562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13564">
    <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(320,a,7801,a(flip),b,13563,a),flip(a)].">
      <j1 rule="hyper" parents="320 7801 13563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13565">
    <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(1185(a,1),13564(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1185 13564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13566">
    <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,11892,a,b,13565,a)].">
      <j1 rule="hyper" parents="58 11892 13565"/>
    </justification>
  </clause>

  <clause id="13567">
    <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(1185(a,1),13566(a,1,1))].">
      <j1 rule="para" parents="1185 13566"/>
    </justification>
  </clause>

  <clause id="13568">
    <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(13567(a,1),12030(a,1,2))].">
      <j1 rule="para" parents="13567 12030"/>
    </justification>
  </clause>

  <clause id="13569">
    <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(12031,a,13568,a),flip(a)].">
      <j1 rule="hyper" parents="12031 13568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13570">
    <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(320,a,7759,a,b,13569,a),flip(a)].">
      <j1 rule="hyper" parents="320 7759 13569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13571">
    <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,11878,a(flip),b,13570,a)].">
      <j1 rule="hyper" parents="58 11878 13570"/>
    </justification>
  </clause>

  <clause id="13572">
    <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(320,a,7754,a,b,13571,a),flip(a)].">
      <j1 rule="hyper" parents="320 7754 13571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13573">
    <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(11879,a,13572,a)].">
      <j1 rule="hyper" parents="11879 13572"/>
    </justification>
  </clause>

  <clause id="13574">
    <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,13424,a,b,13573,a)].">
      <j1 rule="hyper" parents="58 13424 13573"/>
    </justification>
  </clause>

  <clause id="13575">
    <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(320,a,11658,a(flip),b,13574,a),flip(a)].">
      <j1 rule="hyper" parents="320 11658 13574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13576">
    <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(8023,a,13575,a)].">
      <j1 rule="hyper" parents="8023 13575"/>
    </justification>
  </clause>

  <clause id="13577">
    <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(13575(a,1),8023(a,1))].">
      <j1 rule="para" parents="13575 8023"/>
    </justification>
  </clause>

  <clause id="13578">
    <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(13055,a,13576,a)].">
      <j1 rule="hyper" parents="13055 13576"/>
    </justification>
  </clause>

  <clause id="13579">
    <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,12148,a,b,13578,a)].">
      <j1 rule="hyper" parents="58 12148 13578"/>
    </justification>
  </clause>

  <clause id="13580">
    <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(9239,a,13579,a)].">
      <j1 rule="hyper" parents="9239 13579"/>
    </justification>
  </clause>

  <clause id="13581">
    <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,12821,a(flip),b,13580,a)].">
      <j1 rule="hyper" parents="58 12821 13580"/>
    </justification>
  </clause>

  <clause id="13582">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = a(K(y,K(x,z * u)),z,u)
    ]]></literal>
    <justification jstring="[para(9188(a,1),13581(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9188 13581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13583">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,11828,a(flip),b,13582,a),flip(a)].">
      <j1 rule="hyper" parents="320 11828 13582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13584">
    <literal><![CDATA[
      K(x,K(a(y,z,u),y * (z * u))) = 1
    ]]></literal>
    <justification jstring="[hyper(13577,a,13583,a)].">
      <j1 rule="hyper" parents="13577 13583"/>
    </justification>
  </clause>

  <clause id="13587">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,a(y,z,u)) * 1
    ]]></literal>
    <justification jstring="[para(13584(a,1),9697(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13584 9697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13588">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,3,a(flip),b,13587,a),flip(a)].">
      <j1 rule="hyper" parents="320 3 13587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13590">
    <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,9215,a,b,13588,a)].">
      <j1 rule="hyper" parents="58 9215 13588"/>
    </justification>
  </clause>

  <clause id="13591">
    <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(12793(a,2),13590(a,1,1))].">
      <j1 rule="para" parents="12793 13590"/>
    </justification>
  </clause>

  <clause id="13592">
    <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,12762,a,b,13591,a)].">
      <j1 rule="hyper" parents="58 12762 13591"/>
    </justification>
  </clause>

  <clause id="13593">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12764,a(flip),b,13592,a)].">
      <j1 rule="hyper" parents="58 12764 13592"/>
    </justification>
  </clause>

  <clause id="13595">
    <literal><![CDATA[
      a(K(x,y),z,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12464,a(flip),b,13593,a)].">
      <j1 rule="hyper" parents="58 12464 13593"/>
    </justification>
  </clause>

  <clause id="13596">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,13347,a,b,13595,a),flip(a)].">
      <j1 rule="hyper" parents="320 13347 13595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13597">
    <literal><![CDATA[
      a(K(x,y),z,z \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,10457,a(flip),b,13596,a),flip(a)].">
      <j1 rule="hyper" parents="320 10457 13596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13598">
    <literal><![CDATA[
      a(K(x * y,z),x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,10455,a(flip),b,13596,a),flip(a)].">
      <j1 rule="hyper" parents="320 10455 13596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13599">
    <literal><![CDATA[
      x * a(K(y,z),u,w) = x * a(z,u,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,13596,a,b,4,a)].">
      <j1 rule="hyper" parents="119 13596 4"/>
    </justification>
  </clause>

  <clause id="13600">
    <literal><![CDATA[
      a(x,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,5436,a(flip),b,13596,a),flip(a)].">
      <j1 rule="hyper" parents="58 5436 13596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13601">
    <literal><![CDATA[
      a(x,y,K(z,u)) != 1
    ]]></literal>
    <literal><![CDATA[
      L(u,y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(13596(a,1),47(a,1))].">
      <j1 rule="para" parents="13596 47"/>
    </justification>
  </clause>

  <clause id="13602">
    <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(13596(a,1),11945(a,1,1,2))].">
      <j1 rule="para" parents="13596 11945"/>
    </justification>
  </clause>

  <clause id="13603">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(13596(a,2),13348(a,1))].">
      <j1 rule="para" parents="13596 13348"/>
    </justification>
  </clause>

  <clause id="13604">
    <literal><![CDATA[
      a(x * y,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(10901,a,13600,a)].">
      <j1 rule="hyper" parents="10901 13600"/>
    </justification>
  </clause>

  <clause id="13605">
    <literal><![CDATA[
      L(K(x,y),z,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5862,a,13600,a)].">
      <j1 rule="hyper" parents="5862 13600"/>
    </justification>
  </clause>

  <clause id="13608">
    <literal><![CDATA[
      a(x,y,K(z,x * y)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,11230,a(flip),b,13597,a)].">
      <j1 rule="hyper" parents="58 11230 13597"/>
    </justification>
  </clause>

  <clause id="13609">
    <literal><![CDATA[
      L(x \ y,x,K(y,z)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(47,a,13597,a)].">
      <j1 rule="hyper" parents="47 13597"/>
    </justification>
  </clause>

  <clause id="13610">
    <literal><![CDATA[
      (x / y) * (y * K(x,z)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(168,a,11225,a,b,13597,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="168 11225 13597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13611">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(168,a,10198,a,b,13597,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="168 10198 13597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13612">
    <literal><![CDATA[
      L(x,y,K(y * x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,13598,a)].">
      <j1 rule="hyper" parents="47 13598"/>
    </justification>
  </clause>

  <clause id="13613">
    <literal><![CDATA[
      K(x,(y \ z) \ y) = K(x,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6555,a(flip),b,13605,a),flip(a)].">
      <j1 rule="hyper" parents="58 6555 13605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13614">
    <literal><![CDATA[
      (x * y) * K(z,x * y) = x * (y * K(z,x * y))
    ]]></literal>
    <justification jstring="[hyper(969,a,13608,a)].">
      <j1 rule="hyper" parents="969 13608"/>
    </justification>
  </clause>

  <clause id="13616">
    <literal><![CDATA[
      a(x,y,K(x * y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,11001,a(flip),b,13608,a)].">
      <j1 rule="hyper" parents="58 11001 13608"/>
    </justification>
  </clause>

  <clause id="13617">
    <literal><![CDATA[
      a(x,x \ y,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[para(5(a,1),13608(a,1,3,2))].">
      <j1 rule="para" parents="5 13608"/>
    </justification>
  </clause>

  <clause id="13618">
    <literal><![CDATA[
      a(x,y,K(z,y * x)) = 1
    ]]></literal>
    <justification jstring="[para(12220(a,1),13608(a,1,3))].">
      <j1 rule="para" parents="12220 13608"/>
    </justification>
  </clause>

  <clause id="13619">
    <literal><![CDATA[
      L(x,y,K(z,y * x)) = x
    ]]></literal>
    <justification jstring="[hyper(12656,a,13612,a)].">
      <j1 rule="hyper" parents="12656 13612"/>
    </justification>
  </clause>

  <clause id="13620">
    <literal><![CDATA[
      T(x * y,L(z,y,x)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(167,a,10854,a,b,13616,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 10854 13616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13621">
    <literal><![CDATA[
      a(x,x \ y,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[para(5(a,1),13616(a,1,3,1))].">
      <j1 rule="para" parents="5 13616"/>
    </justification>
  </clause>

  <clause id="13622">
    <literal><![CDATA[
      a(x,y,K(y * x,z)) = 1
    ]]></literal>
    <justification jstring="[para(12190(a,1),13616(a,1,3))].">
      <j1 rule="para" parents="12190 13616"/>
    </justification>
  </clause>

  <clause id="13623">
    <literal><![CDATA[
      x * ((x \ y) * K(z,y)) = y * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(167,a,81,a,b,13617,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 81 13617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13624">
    <literal><![CDATA[
      (x * y) * K(z,y * x) = x * (y * K(z,y * x))
    ]]></literal>
    <justification jstring="[hyper(969,a,13618,a)].">
      <j1 rule="hyper" parents="969 13618"/>
    </justification>
  </clause>

  <clause id="13625">
    <literal><![CDATA[
      a(x,y,K(z,z * (y * x))) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,10996,a,b,13618,a)].">
      <j1 rule="hyper" parents="58 10996 13618"/>
    </justification>
  </clause>

  <clause id="13626">
    <literal><![CDATA[
      L(x,y,K(z,x * y)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,12227,a,b,13619,a)].">
      <j1 rule="hyper" parents="58 12227 13619"/>
    </justification>
  </clause>

  <clause id="13627">
    <literal><![CDATA[
      L(x \ y,x,K(z,y)) = x \ y
    ]]></literal>
    <justification jstring="[para(5(a,1),13619(a,1,3,2))].">
      <j1 rule="para" parents="5 13619"/>
    </justification>
  </clause>

  <clause id="13628">
    <literal><![CDATA[
      T(x,L(y,z \ x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(167,a,10854,a,b,13621,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 10854 13621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13629">
    <literal><![CDATA[
      T(x * y,L(z,x,y)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(167,a,10854,a,b,13622,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 10854 13622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13630">
    <literal><![CDATA[
      L(x,x \ y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(5(a,1),13626(a,1,3,2))].">
      <j1 rule="para" parents="5 13626"/>
    </justification>
  </clause>

  <clause id="13631">
    <literal><![CDATA[
      (K(x,y) * z) \ T(x,y) = z \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,4809,a(flip),b,13609,a)].">
      <j1 rule="hyper" parents="58 4809 13609"/>
    </justification>
  </clause>

  <clause id="13632">
    <literal><![CDATA[
      L(x \ (y \ z),x,K(y,z)) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(12656,a,13627,a)].">
      <j1 rule="hyper" parents="12656 13627"/>
    </justification>
  </clause>

  <clause id="13633">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,13627,a(flip),b,2880,a(flip))].">
      <j1 rule="hyper" parents="119 13627 2880"/>
    </justification>
  </clause>

  <clause id="13634">
    <literal><![CDATA[
      (x \ y) * K(y,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,13628,a(flip),b,10889,a),flip(a)].">
      <j1 rule="hyper" parents="116 13628 10889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13635">
    <literal><![CDATA[
      T(x,(y \ x) \ z) = T(x,x \ (y * z))
    ]]></literal>
    <justification jstring="[para(490(a,1),13628(a,1,2)),flip(a)].">
      <j1 rule="para" parents="490 13628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13636">
    <literal><![CDATA[
      K(x,T(y,z) * L(z,u \ y,u)) = K(x,L(z,u \ y,u) * y)
    ]]></literal>
    <justification jstring="[para(13628(a,1),12248(a,1,2,1))].">
      <j1 rule="para" parents="13628 12248"/>
    </justification>
  </clause>

  <clause id="13637">
    <literal><![CDATA[
      T(x,y) / (z * K(x,y)) = x / z
    ]]></literal>
    <justification jstring="[hyper(131,a,13610,a)].">
      <j1 rule="hyper" parents="131 13610"/>
    </justification>
  </clause>

  <clause id="13639">
    <literal><![CDATA[
      T(x,y) / (z \ x) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(117,a,13610,a(flip),b,11224,a)].">
      <j1 rule="hyper" parents="117 13610 11224"/>
    </justification>
  </clause>

  <clause id="13640">
    <literal><![CDATA[
      T(x,y) * K(x * y,z) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,13610,a(flip),b,4517,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 13610 4517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13641">
    <literal><![CDATA[
      x * (y * K(x * y,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),13610(a,1,1))].">
      <j1 rule="para" parents="6 13610"/>
    </justification>
  </clause>

  <clause id="13642">
    <literal><![CDATA[
      (x / (y / z)) * (y / T(z,x)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(6293(a,1),13610(a,1,2))].">
      <j1 rule="para" parents="6293 13610"/>
    </justification>
  </clause>

  <clause id="13643">
    <literal><![CDATA[
      K(x,y) * (x / z) = T(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(353,a,13611,a),flip(a)].">
      <j1 rule="hyper" parents="353 13611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13645">
    <literal><![CDATA[
      (T(x,y) \ z) * ((x \ z) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[para(5093(a,1),13611(a,1,1))].">
      <j1 rule="para" parents="5093 13611"/>
    </justification>
  </clause>

  <clause id="13647">
    <literal><![CDATA[
      K(x,y) * (1 / z) = K(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(34,a,11550,a,b,13631,a),flip(a)].">
      <j1 rule="hyper" parents="34 11550 13631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13648">
    <literal><![CDATA[
      (K(x,y) \ z) \ T(y,x) = z \ y
    ]]></literal>
    <justification jstring="[para(5092(a,2),13631(a,1,1))].">
      <j1 rule="para" parents="5092 13631"/>
    </justification>
  </clause>

  <clause id="13649">
    <literal><![CDATA[
      (K(x,y) * z) \ y = z \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5095(a,1),13631(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5095 13631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13650">
    <literal><![CDATA[
      (T(x,y) * z) \ y = (x * z) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4778(a,1),13631(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4778 13631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13651">
    <literal><![CDATA[
      ((x / T(y,x)) * z) \ T(x,y) = ((x / y) * z) \ x
    ]]></literal>
    <justification jstring="[para(12558(a,1),13631(a,1,1))].">
      <j1 rule="para" parents="12558 13631"/>
    </justification>
  </clause>

  <clause id="13652">
    <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(13631(a,1),13407(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="13631 13407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13653">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ x) = z \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(8713,a,13634,a)].">
      <j1 rule="hyper" parents="8713 13634"/>
    </justification>
  </clause>

  <clause id="13654">
    <literal><![CDATA[
      x \ T(y,T(z,x)) = K(y,z) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(8215,a,13634,a),flip(a)].">
      <j1 rule="hyper" parents="8215 13634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13655">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(6315,a,13634,a)].">
      <j1 rule="hyper" parents="6315 13634"/>
    </justification>
  </clause>

  <clause id="13657">
    <literal><![CDATA[
      (x \ y) \ (x \ T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,13634,a)].">
      <j1 rule="hyper" parents="123 13634"/>
    </justification>
  </clause>

  <clause id="13659">
    <literal><![CDATA[
      (x \ T(y,z)) / (x \ y) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(117,a,13634,a(flip),b,8216,a)].">
      <j1 rule="hyper" parents="117 13634 8216"/>
    </justification>
  </clause>

  <clause id="13660">
    <literal><![CDATA[
      (x \ T(y,z)) / T(y,z) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,13634,a(flip),b,6121,a)].">
      <j1 rule="hyper" parents="117 13634 6121"/>
    </justification>
  </clause>

  <clause id="13661">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K(x * y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),13634(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 13634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13663">
    <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),13634(a,2,2))].">
      <j1 rule="para" parents="20 13634"/>
    </justification>
  </clause>

  <clause id="13665">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(K(x,y),z \ x) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(13634(a,1),5530(a,2,1))].">
      <j1 rule="para" parents="13634 5530"/>
    </justification>
  </clause>

  <clause id="13668">
    <literal><![CDATA[
      T(x \ T(y,z),K(z,y)) = K(y,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(13634(a,1),6308(a,1,1))].">
      <j1 rule="para" parents="13634 6308"/>
    </justification>
  </clause>

  <clause id="13669">
    <literal><![CDATA[
      K(x * (y \ T(z,u)),z) = K(x * (y \ z),z)
    ]]></literal>
    <justification jstring="[para(13634(a,1),7390(a,1,1,2))].">
      <j1 rule="para" parents="13634 7390"/>
    </justification>
  </clause>

  <clause id="13670">
    <literal><![CDATA[
      (x \ y) / (x \ T(y,z)) = K(z,T(y,x \ y))
    ]]></literal>
    <justification jstring="[para(13634(a,1),7971(a,1,2))].">
      <j1 rule="para" parents="13634 7971"/>
    </justification>
  </clause>

  <clause id="13671">
    <literal><![CDATA[
      x / (y * K(z,x)) = T(x,z) / y
    ]]></literal>
    <justification jstring="[para(6300(a,1),13637(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6300 13637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13674">
    <literal><![CDATA[
      K(x,y) * (1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / z = u
    ]]></literal>
    <justification jstring="[para(13639(a,1),11554(a,1))].">
      <j1 rule="para" parents="13639 11554"/>
    </justification>
  </clause>

  <clause id="13675">
    <literal><![CDATA[
      K(x,y) \ (y / z) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(5129,a,13643,a)].">
      <j1 rule="hyper" parents="5129 13643"/>
    </justification>
  </clause>

  <clause id="13676">
    <literal><![CDATA[
      K(x,y) * (T(y,x) / z) = y / z
    ]]></literal>
    <justification jstring="[hyper(5109,a,13643,a)].">
      <j1 rule="hyper" parents="5109 13643"/>
    </justification>
  </clause>

  <clause id="13678">
    <literal><![CDATA[
      (x / y) \ (T(x,z) / y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,13643,a(flip),b,8565,a)].">
      <j1 rule="hyper" parents="116 13643 8565"/>
    </justification>
  </clause>

  <clause id="13679">
    <literal><![CDATA[
      (T(x,y) / z) \ K(K(x,y),x / z) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(13643(a,1),5530(a,1,1))].">
      <j1 rule="para" parents="13643 5530"/>
    </justification>
  </clause>

  <clause id="13680">
    <literal><![CDATA[
      T(T(x,y) / z,K(x,y)) = (x / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(13643(a,1),6322(a,1,1))].">
      <j1 rule="para" parents="13643 6322"/>
    </justification>
  </clause>

  <clause id="13681">
    <literal><![CDATA[
      K(x,y) * (K(y,x) / z) = 1 / z
    ]]></literal>
    <justification jstring="[hyper(5109,a,13647,a)].">
      <j1 rule="hyper" parents="5109 13647"/>
    </justification>
  </clause>

  <clause id="13682">
    <literal><![CDATA[
      K(x,T(y,z)) / z = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8219,a(flip),b,13647,a),flip(a)].">
      <j1 rule="hyper" parents="58 8219 13647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13683">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2726,a,13647,a(flip))].">
      <j1 rule="hyper" parents="2726 13647"/>
    </justification>
  </clause>

  <clause id="13684">
    <literal><![CDATA[
      (x * y) * (K(y,x) / z) = (y * x) * (1 / z)
    ]]></literal>
    <justification jstring="[hyper(119,a,13647,a(flip),b,11119,a)].">
      <j1 rule="hyper" parents="119 13647 11119"/>
    </justification>
  </clause>

  <clause id="13685">
    <literal><![CDATA[
      K(x,y) / (z \ 1) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(72(a,1),13647(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 13647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13686">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(13647(a,1),6322(a,1,1))].">
      <j1 rule="para" parents="13647 6322"/>
    </justification>
  </clause>

  <clause id="13687">
    <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(13647(a,1),5854(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13647 5854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13688">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(12461,a,13683,a)].">
      <j1 rule="hyper" parents="12461 13683"/>
    </justification>
  </clause>

  <clause id="13689">
    <literal><![CDATA[
      K(R(x,y,y \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,12445,a(flip),b,13683,a)].">
      <j1 rule="hyper" parents="58 12445 13683"/>
    </justification>
  </clause>

  <clause id="13690">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,12310,a(flip),b,13683,a)].">
      <j1 rule="hyper" parents="58 12310 13683"/>
    </justification>
  </clause>

  <clause id="13691">
    <literal><![CDATA[
      (K(x,y) * z) \ K(x,y) = z \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,13683,a(flip),b,261,a)].">
      <j1 rule="hyper" parents="116 13683 261"/>
    </justification>
  </clause>

  <clause id="13693">
    <literal><![CDATA[
      T(x,R(y,z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,13688,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 13688 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13694">
    <literal><![CDATA[
      K(x,y * (z \ 1)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(523(a,1),13688(a,1,2))].">
      <j1 rule="para" parents="523 13688"/>
    </justification>
  </clause>

  <clause id="13698">
    <literal><![CDATA[
      K(x * (y \ 1),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(523(a,1),13689(a,1,1))].">
      <j1 rule="para" parents="523 13689"/>
    </justification>
  </clause>

  <clause id="13699">
    <literal><![CDATA[
      K(x,L(y,z,z \ x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11539,a,13690,a)].">
      <j1 rule="hyper" parents="11539 13690"/>
    </justification>
  </clause>

  <clause id="13700">
    <literal><![CDATA[
      K(L(x,y,y \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(10880,a,13690,a)].">
      <j1 rule="hyper" parents="10880 13690"/>
    </justification>
  </clause>

  <clause id="13701">
    <literal><![CDATA[
      L(K(x,y),z,z \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10830,a,13690,a)].">
      <j1 rule="hyper" parents="10830 13690"/>
    </justification>
  </clause>

  <clause id="13703">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,L(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,13683,a,b,13690,a)].">
      <j1 rule="hyper" parents="320 13683 13690"/>
    </justification>
  </clause>

  <clause id="13705">
    <literal><![CDATA[
      T(x,L(y,z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,13690,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 13690 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13706">
    <literal><![CDATA[
      a(x \ 1,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,13690,a,b,10791,a),flip(a)].">
      <j1 rule="hyper" parents="115 13690 10791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13707">
    <literal><![CDATA[
      K(x,L(y,z \ x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11540,a(flip),b,13690,a)].">
      <j1 rule="hyper" parents="58 11540 13690"/>
    </justification>
  </clause>

  <clause id="13708">
    <literal><![CDATA[
      (K(x,y) * z) \ 1 = z \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,13690,a(flip),b,12834,a),flip(a)].">
      <j1 rule="hyper" parents="116 13690 12834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13709">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2792(a,1),13690(a,1,2))].">
      <j1 rule="para" parents="2792 13690"/>
    </justification>
  </clause>

  <clause id="13710">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(2795(a,1),13690(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2795 13690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13711">
    <literal><![CDATA[
      K(x,L((1 / y) * z,u,w)) = K(x,L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(2800(a,1),13690(a,1,2))].">
      <j1 rule="para" parents="2800 13690"/>
    </justification>
  </clause>

  <clause id="13712">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3661(a,1),13690(a,1,2))].">
      <j1 rule="para" parents="3661 13690"/>
    </justification>
  </clause>

  <clause id="13714">
    <literal><![CDATA[
      T(x,a(y \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(13353,a,13706,a)].">
      <j1 rule="hyper" parents="13353 13706"/>
    </justification>
  </clause>

  <clause id="13715">
    <literal><![CDATA[
      a(1 / x,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,4022,a,b,13706,a)].">
      <j1 rule="hyper" parents="58 4022 13706"/>
    </justification>
  </clause>

  <clause id="13716">
    <literal><![CDATA[
      a(x,x \ 1,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,4023,a(flip),b,13706,a)].">
      <j1 rule="hyper" parents="58 4023 13706"/>
    </justification>
  </clause>

  <clause id="13717">
    <literal><![CDATA[
      x / a(y \ 1,y,z) = a(y \ 1,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(2431,a,13714,a),flip(a)].">
      <j1 rule="hyper" parents="2431 13714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13720">
    <literal><![CDATA[
      L(K(x,y),z \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5862,a,13716,a)].">
      <j1 rule="hyper" parents="5862 13716"/>
    </justification>
  </clause>

  <clause id="13722">
    <literal><![CDATA[
      R(x,y,y \ 1) * T(z,x) = z * R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,13693,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 13693 17"/>
    </justification>
  </clause>

  <clause id="13723">
    <literal><![CDATA[
      T(x,y * (z \ 1)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(523(a,1),13693(a,1,2))].">
      <j1 rule="para" parents="523 13693"/>
    </justification>
  </clause>

  <clause id="13724">
    <literal><![CDATA[
      T(x,R(y,z \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2653(a,1),13693(a,1,2))].">
      <j1 rule="para" parents="2653 13693"/>
    </justification>
  </clause>

  <clause id="13726">
    <literal><![CDATA[
      ((x / y) * (y * z)) \ K(x,z) = (L(z,y,y \ x) * x) \ 1
    ]]></literal>
    <justification jstring="[para(13699(a,1),11179(a,1,2))].">
      <j1 rule="para" parents="13699 11179"/>
    </justification>
  </clause>

  <clause id="13727">
    <literal><![CDATA[
      K((1 / x) * y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2792(a,1),13700(a,1,1))].">
      <j1 rule="para" parents="2792 13700"/>
    </justification>
  </clause>

  <clause id="13729">
    <literal><![CDATA[
      K((x \ 1) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(2795(a,1),13700(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2795 13700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13731">
    <literal><![CDATA[
      K(x,y) / (z * K(x,y)) = 1 / z
    ]]></literal>
    <justification jstring="[hyper(117,a,13701,a(flip),b,2797,a)].">
      <j1 rule="hyper" parents="117 13701 2797"/>
    </justification>
  </clause>

  <clause id="13735">
    <literal><![CDATA[
      L(x,y,y \ 1) * T(z,x) = z * L(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,13705,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 13705 17"/>
    </justification>
  </clause>

  <clause id="13736">
    <literal><![CDATA[
      T(x,(1 / y) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2792(a,1),13705(a,1,2))].">
      <j1 rule="para" parents="2792 13705"/>
    </justification>
  </clause>

  <clause id="13737">
    <literal><![CDATA[
      T(x,(y \ 1) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(2795(a,1),13705(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2795 13705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13738">
    <literal><![CDATA[
      T(x,T((1 / y) * z,u)) = T(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(2799(a,1),13705(a,1,2))].">
      <j1 rule="para" parents="2799 13705"/>
    </justification>
  </clause>

  <clause id="13739">
    <literal><![CDATA[
      K(x,(y * z) \ x) = K(x,z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(10798,a,13707,a)].">
      <j1 rule="hyper" parents="10798 13707"/>
    </justification>
  </clause>

  <clause id="13741">
    <literal><![CDATA[
      K(x * y,L(z,y,x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),13707(a,1,2,2))].">
      <j1 rule="para" parents="4 13707"/>
    </justification>
  </clause>

  <clause id="13742">
    <literal><![CDATA[
      K(x,(y \ x) \ z) = K(x,x \ (y * z))
    ]]></literal>
    <justification jstring="[para(490(a,1),13707(a,1,2)),flip(a)].">
      <j1 rule="para" parents="490 13707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13743">
    <literal><![CDATA[
      K(x,(y * z) \ 1) = K(x,z \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(10798,a,13712,a)].">
      <j1 rule="hyper" parents="10798 13712"/>
    </justification>
  </clause>

  <clause id="13745">
    <literal><![CDATA[
      x \ K(y,T(z,x)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,13712,a(flip),b,10878,a(flip))].">
      <j1 rule="hyper" parents="116 13712 10878"/>
    </justification>
  </clause>

  <clause id="13746">
    <literal><![CDATA[
      K(x,T((y \ 1) \ z,u)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(607(a,1),13712(a,1,2)),flip(a)].">
      <j1 rule="para" parents="607 13712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13747">
    <literal><![CDATA[
      (x \ 1) * K(y,z) = x \ K(y,z)
    ]]></literal>
    <justification jstring="[para(13712(a,1),10785(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13712 10785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13748">
    <literal><![CDATA[
      L(K(x,y),z \ 1,z) = u \ (u * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,4,a,b,13720,a),flip(a)].">
      <j1 rule="hyper" parents="320 4 13720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13749">
    <literal><![CDATA[
      K((x \ y) \ z,y) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,10913,a(flip),b,13720,a),flip(a)].">
      <j1 rule="hyper" parents="58 10913 13720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13750">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(2593(a,1),13724(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2593 13724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13751">
    <literal><![CDATA[
      (K(x,y) \ z) \ (y * x) = z \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,12773,a(flip),b,13648,a)].">
      <j1 rule="hyper" parents="58 12773 13648"/>
    </justification>
  </clause>

  <clause id="13752">
    <literal><![CDATA[
      T(x \ T(y,z),(K(z,y) * x) \ y) = (K(z,y) * x) \ y
    ]]></literal>
    <justification jstring="[hyper(444,a,xx,b,13649,a)].">
      <j1 rule="hyper" parents="444 13649"/>
    </justification>
  </clause>

  <clause id="13753">
    <literal><![CDATA[
      1 / (x \ K(y,z)) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(34,a,11551,a,b,13649,a)].">
      <j1 rule="hyper" parents="34 11551 13649"/>
    </justification>
  </clause>

  <clause id="13754">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = (T(K(x,y),z) * z) \ y
    ]]></literal>
    <justification jstring="[para(4051(a,2),13649(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4051 13649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13756">
    <literal><![CDATA[
      (((x * y) \ y) * z) \ T(y,x) = (((y * x) \ y) * z) \ y
    ]]></literal>
    <justification jstring="[para(11196(a,1),13649(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11196 13649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13757">
    <literal><![CDATA[
      (x * K(y * x,z)) \ z = x \ T(z,x * y)
    ]]></literal>
    <justification jstring="[para(12189(a,1),13649(a,1,1))].">
      <j1 rule="para" parents="12189 13649"/>
    </justification>
  </clause>

  <clause id="13758">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y = K(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(116,a,4,a(flip),b,13655,a)].">
      <j1 rule="hyper" parents="116 4 13655"/>
    </justification>
  </clause>

  <clause id="13762">
    <literal><![CDATA[
      T(x,y) \ (y \ T(x * y,z)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(17(a,2),13657(a,1,1))].">
      <j1 rule="para" parents="17 13657"/>
    </justification>
  </clause>

  <clause id="13763">
    <literal><![CDATA[
      T(x,y) / (1 / y) = x / (K(y,x) / y)
    ]]></literal>
    <justification jstring="[para(6193(a,1),13671(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6193 13671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13765">
    <literal><![CDATA[
      x / (y * K(x,z)) = K(z,x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,13637,a(flip),b,13675,a),flip(a)].">
      <j1 rule="hyper" parents="119 13637 13675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13766">
    <literal><![CDATA[
      T(x,(T(y,z) / u) \ 1) = T(x,(y / u) \ K(z,y))
    ]]></literal>
    <justification jstring="[para(13675(a,1),6095(a,1,2,1))].">
      <j1 rule="para" parents="13675 6095"/>
    </justification>
  </clause>

  <clause id="13767">
    <literal><![CDATA[
      K(x \ y,x) * (((x \ y) \ y) / z) = x / z
    ]]></literal>
    <justification jstring="[para(106(a,1),13676(a,1,2,1))].">
      <j1 rule="para" parents="106 13676"/>
    </justification>
  </clause>

  <clause id="13768">
    <literal><![CDATA[
      K(x,y) * (x / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) / z = u
    ]]></literal>
    <justification jstring="[para(13676(a,1),5110(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13676 5110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13769">
    <literal><![CDATA[
      (T(x,y) \ z) \ 1 = (x \ z) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(5042(a,1),13691(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5042 13691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13771">
    <literal><![CDATA[
      ((x * y) \ z) \ K(y,x) = ((y * x) \ z) \ 1
    ]]></literal>
    <justification jstring="[para(11121(a,1),13691(a,1,1))].">
      <j1 rule="para" parents="11121 13691"/>
    </justification>
  </clause>

  <clause id="13773">
    <literal><![CDATA[
      K(x,y * (z \ K(u,x))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11335,a,b,13694,a)].">
      <j1 rule="hyper" parents="58 11335 13694"/>
    </justification>
  </clause>

  <clause id="13774">
    <literal><![CDATA[
      K(x,y * (1 / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5277,a,b,13694,a)].">
      <j1 rule="hyper" parents="58 5277 13694"/>
    </justification>
  </clause>

  <clause id="13775">
    <literal><![CDATA[
      K(x,y / (z \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5274,a(flip),b,13694,a),flip(a)].">
      <j1 rule="hyper" parents="58 5274 13694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13776">
    <literal><![CDATA[
      K(x,y / (1 / z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(75(a,1),13694(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 13694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13777">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3933,a,b,13698,a)].">
      <j1 rule="hyper" parents="58 3933 13698"/>
    </justification>
  </clause>

  <clause id="13778">
    <literal><![CDATA[
      K(x / (y \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3935,a(flip),b,13698,a),flip(a)].">
      <j1 rule="hyper" parents="58 3935 13698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13779">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),13698(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 13698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13781">
    <literal><![CDATA[
      x \ K(y,z) != u \ 1
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * x = u
    ]]></literal>
    <justification jstring="[para(13708(a,1),43(a,1))].">
      <j1 rule="para" parents="13708 43"/>
    </justification>
  </clause>

  <clause id="13784">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,y * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(13708(a,1),13694(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13708 13694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13785">
    <literal><![CDATA[
      K(x,(y \ 1) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5284,a(flip),b,13709,a)].">
      <j1 rule="hyper" parents="58 5284 13709"/>
    </justification>
  </clause>

  <clause id="13786">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,z \ y)) = K(x,u / ((y \ z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(13087,a,13710,a),flip(a)].">
      <j1 rule="hyper" parents="13087 13710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13787">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,12222,a,b,13710,a)].">
      <j1 rule="hyper" parents="320 12222 13710"/>
    </justification>
  </clause>

  <clause id="13788">
    <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,13131,a,b,13710,a)].">
      <j1 rule="hyper" parents="58 13131 13710"/>
    </justification>
  </clause>

  <clause id="13789">
    <literal><![CDATA[
      K(x,(1 / y) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5285,a,b,13710,a)].">
      <j1 rule="hyper" parents="58 5285 13710"/>
    </justification>
  </clause>

  <clause id="13790">
    <literal><![CDATA[
      K(x,(y \ x) \ z) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9010,a(flip),b,13710,a)].">
      <j1 rule="hyper" parents="58 9010 13710"/>
    </justification>
  </clause>

  <clause id="13791">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(13710(a,1),10763(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13710 10763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13792">
    <literal><![CDATA[
      T(x,y * (1 / z)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3735,a,b,13723,a)].">
      <j1 rule="hyper" parents="58 3735 13723"/>
    </justification>
  </clause>

  <clause id="13793">
    <literal><![CDATA[
      L(x,y \ 1,z) * (z * (y \ 1)) = z * ((y \ 1) * T(x,z / y))
    ]]></literal>
    <justification jstring="[para(13723(a,1),631(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13723 631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13794">
    <literal><![CDATA[
      T(x,y / (K(z,u) * w)) = T(x,y * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(13708(a,1),13723(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13708 13723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13795">
    <literal><![CDATA[
      K((x \ 1) * y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3939,a(flip),b,13727,a)].">
      <j1 rule="hyper" parents="58 3939 13727"/>
    </justification>
  </clause>

  <clause id="13797">
    <literal><![CDATA[
      K((x \ y) \ z,y) = K(x * (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(13124,a,13729,a)].">
      <j1 rule="hyper" parents="13124 13729"/>
    </justification>
  </clause>

  <clause id="13798">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(5937,a,13729,a)].">
      <j1 rule="hyper" parents="5937 13729"/>
    </justification>
  </clause>

  <clause id="13803">
    <literal><![CDATA[
      K((x \ 1) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(13729(a,1),5936(a,1))].">
      <j1 rule="para" parents="13729 5936"/>
    </justification>
  </clause>

  <clause id="13804">
    <literal><![CDATA[
      (x * K(y * x,z)) * y = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(13729(a,1),6501(a,1,1,2))].">
      <j1 rule="para" parents="13729 6501"/>
    </justification>
  </clause>

  <clause id="13805">
    <literal><![CDATA[
      T(x * K(y * x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(13729(a,1),6502(a,1,1,2))].">
      <j1 rule="para" parents="13729 6502"/>
    </justification>
  </clause>

  <clause id="13809">
    <literal><![CDATA[
      (x * K(y * (z \ x),z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(13729(a,1),9662(a,1,1,2))].">
      <j1 rule="para" parents="13729 9662"/>
    </justification>
  </clause>

  <clause id="13810">
    <literal><![CDATA[
      K(x,y) / ((L(z,u,w) \ z) * K(x,y)) = (L(z,u,w) \ z) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,12027,a(flip),b,13731,a),flip(a)].">
      <j1 rule="hyper" parents="320 12027 13731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13811">
    <literal><![CDATA[
      1 / (x * K(y,z)) = K(z,y) / x
    ]]></literal>
    <justification jstring="[para(6300(a,1),13731(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6300 13731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13813">
    <literal><![CDATA[
      T(x,(y \ 1) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3739,a(flip),b,13736,a)].">
      <j1 rule="hyper" parents="58 3739 13736"/>
    </justification>
  </clause>

  <clause id="13814">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3740,a,b,13737,a)].">
      <j1 rule="hyper" parents="58 3740 13737"/>
    </justification>
  </clause>

  <clause id="13815">
    <literal><![CDATA[
      T(x,(y \ K(z,u)) \ w) = T(x,(K(u,z) * y) * w)
    ]]></literal>
    <justification jstring="[para(13708(a,1),13737(a,1,2,1))].">
      <j1 rule="para" parents="13708 13737"/>
    </justification>
  </clause>

  <clause id="13816">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ 1) = z \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8712,a,13747,a)].">
      <j1 rule="hyper" parents="8712 13747"/>
    </justification>
  </clause>

  <clause id="13821">
    <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(13747(a,1),687(a,2,2))].">
      <j1 rule="para" parents="13747 687"/>
    </justification>
  </clause>

  <clause id="13824">
    <literal><![CDATA[
      T(x,y * ((1 / z) * K(u,w))) = T(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(13747(a,1),3756(a,2,2,2))].">
      <j1 rule="para" parents="13747 3756"/>
    </justification>
  </clause>

  <clause id="13826">
    <literal><![CDATA[
      (x \ K(y,z)) * y = (x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[para(13747(a,1),6167(a,1,1))].">
      <j1 rule="para" parents="13747 6167"/>
    </justification>
  </clause>

  <clause id="13827">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ 1) = K(z,y)
    ]]></literal>
    <justification jstring="[para(13747(a,1),6309(a,1,1))].">
      <j1 rule="para" parents="13747 6309"/>
    </justification>
  </clause>

  <clause id="13829">
    <literal><![CDATA[
      T(x \ K(y,z),K(z,y)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(13747(a,1),6308(a,1,1))].">
      <j1 rule="para" parents="13747 6308"/>
    </justification>
  </clause>

  <clause id="13832">
    <literal><![CDATA[
      (K(x,y) * z) \ K(u,w) = (z \ K(y,x)) * K(u,w)
    ]]></literal>
    <justification jstring="[para(13708(a,1),13747(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13708 13747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13833">
    <literal><![CDATA[
      T(x,y / (z \ 1)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(3914,a,13750,a)].">
      <j1 rule="hyper" parents="3914 13750"/>
    </justification>
  </clause>

  <clause id="13837">
    <literal><![CDATA[
      K(((x \ K(y,z)) \ 1) * u,w) = K((K(z,y) * x) * u,w)
    ]]></literal>
    <justification jstring="[para(13753(a,1),3939(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13753 3939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13838">
    <literal><![CDATA[
      K(x / (x / y),z / u) = K(y,T(z * (1 / u),x))
    ]]></literal>
    <justification jstring="[hyper(7913,a,13774,a),flip(a)].">
      <j1 rule="hyper" parents="7913 13774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13840">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * K(u,y / z)) = K(x,T(y * (1 / z),u))
    ]]></literal>
    <justification jstring="[para(13774(a,1),7891(a,1,2,2))].">
      <j1 rule="para" parents="13774 7891"/>
    </justification>
  </clause>

  <clause id="13841">
    <literal><![CDATA[
      K(x,y * z) * (z \ T(z * y,x)) = y
    ]]></literal>
    <justification jstring="[para(13775(a,1),5075(a,1,1))].">
      <j1 rule="para" parents="13775 5075"/>
    </justification>
  </clause>

  <clause id="13842">
    <literal><![CDATA[
      K(x,L(y / (z \ 1),u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(13775(a,1),10763(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13775 10763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13844">
    <literal><![CDATA[
      K((x * (y \ 1)) * y,z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),13778(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 13778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13845">
    <literal><![CDATA[
      K(x / (1 / y),z) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,13729,a,b,13779,a),flip(a)].">
      <j1 rule="hyper" parents="320 13729 13779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13848">
    <literal><![CDATA[
      K(x,y * ((1 / y) * z)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),13789(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 13789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13849">
    <literal><![CDATA[
      K(x,y * (T(1 / y,z) * u)) = K(x,K(1 / y,z) * u)
    ]]></literal>
    <justification jstring="[para(4736(a,1),13789(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4736 13789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13850">
    <literal><![CDATA[
      K(x,L((1 / y) \ z,u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(13789(a,1),10763(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13789 10763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13854">
    <literal><![CDATA[
      T(x,y / (z \ K(u,w))) = T(x,y * (K(w,u) * z))
    ]]></literal>
    <justification jstring="[para(13753(a,1),13792(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13753 13792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13858">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z) = K(y,T(z,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,12197,a(flip),b,13795,a),flip(a)].">
      <j1 rule="hyper" parents="58 12197 13795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13859">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),13795(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13860">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K(y * x,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,12190,a,b,13798,a),flip(a)].">
      <j1 rule="hyper" parents="320 12190 13798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13861">
    <literal><![CDATA[
      K((x \ K(y,z)) * y,u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(11551(a,1),13798(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11551 13798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13862">
    <literal><![CDATA[
      (K(x,y) / z) \ 1 = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(188,a,13811,a)].">
      <j1 rule="hyper" parents="188 13811"/>
    </justification>
  </clause>

  <clause id="13863">
    <literal><![CDATA[
      T(K(x,y) / z,z * K(y,x)) = (z * K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(13811(a,1),107(a,1,1))].">
      <j1 rule="para" parents="13811 107"/>
    </justification>
  </clause>

  <clause id="13868">
    <literal><![CDATA[
      K(x,y * (z / ((u * K(w,v5)) \ 1))) = K(x,y * (z / (K(v5,w) / u)))
    ]]></literal>
    <justification jstring="[para(13811(a,1),5295(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13811 5295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13869">
    <literal><![CDATA[
      K(x,(y / (1 / (K(z,u) / w))) * v5) = K(x,(y / (w * K(u,z))) * v5)
    ]]></literal>
    <justification jstring="[para(13811(a,1),5883(a,1,2,1,2,2))].">
      <j1 rule="para" parents="13811 5883"/>
    </justification>
  </clause>

  <clause id="13870">
    <literal><![CDATA[
      1 / T(x * K(y,z),y) = K(z,y) / T(x,y)
    ]]></literal>
    <justification jstring="[para(7412(a,2),13811(a,1,2))].">
      <j1 rule="para" parents="7412 13811"/>
    </justification>
  </clause>

  <clause id="13871">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) = K(x,y * (K(w,u) / z))
    ]]></literal>
    <justification jstring="[para(13811(a,1),13774(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13811 13774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13872">
    <literal><![CDATA[
      K(x,y / (K(z,u) / w)) = K(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(13811(a,1),13776(a,1,2,2))].">
      <j1 rule="para" parents="13811 13776"/>
    </justification>
  </clause>

  <clause id="13874">
    <literal><![CDATA[
      T(x,(y \ 1) / z) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,13723,a(flip),b,13813,a)].">
      <j1 rule="hyper" parents="58 13723 13813"/>
    </justification>
  </clause>

  <clause id="13875">
    <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(13813(a,1),8033(a,1,2))].">
      <j1 rule="para" parents="13813 8033"/>
    </justification>
  </clause>

  <clause id="13876">
    <literal><![CDATA[
      K(x,T(y,(z \ 1) / u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[para(13833(a,1),8210(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13833 8210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13877">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(12204,a,13844,a)].">
      <j1 rule="hyper" parents="12204 13844"/>
    </justification>
  </clause>

  <clause id="13878">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z)) = K(x,u * ((1 / u) * y))
    ]]></literal>
    <justification jstring="[hyper(320,a,13712,a,b,13848,a)].">
      <j1 rule="hyper" parents="320 13712 13848"/>
    </justification>
  </clause>

  <clause id="13879">
    <literal><![CDATA[
      K(x,(y \ z) * K(z,u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(11545(a,1),13848(a,1,2,2))].">
      <j1 rule="para" parents="11545 13848"/>
    </justification>
  </clause>

  <clause id="13883">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = K(K(u,u \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3936,a,b,13859,a),flip(a)].">
      <j1 rule="hyper" parents="320 3936 13859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13884">
    <literal><![CDATA[
      ((x * ((x \ y) * K(x / y,y))) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(13862(a,1),10629(a,1,1,1,2))].">
      <j1 rule="para" parents="13862 10629"/>
    </justification>
  </clause>

  <clause id="13885">
    <literal><![CDATA[
      L(x,y / x,z) \ (z * y) = T(z * (y / x),x)
    ]]></literal>
    <justification jstring="[hyper(767,a,13620,a)].">
      <j1 rule="hyper" parents="767 13620"/>
    </justification>
  </clause>

  <clause id="13886">
    <literal><![CDATA[
      L(x \ y,x,z) \ (z * y) = T(z * x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(605,a,13620,a)].">
      <j1 rule="hyper" parents="605 13620"/>
    </justification>
  </clause>

  <clause id="13887">
    <literal><![CDATA[
      L(x,y,z) \ (z * (y * x)) = T(z * y,x)
    ]]></literal>
    <justification jstring="[hyper(546,a,13620,a)].">
      <j1 rule="hyper" parents="546 13620"/>
    </justification>
  </clause>

  <clause id="13888">
    <literal><![CDATA[
      L(x,y,z) * T(z * y,x) = z * (y * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,13620,a(flip),b,470,a)].">
      <j1 rule="hyper" parents="119 13620 470"/>
    </justification>
  </clause>

  <clause id="13889">
    <literal><![CDATA[
      L(x,y,z) = (z * (y * x)) / T(z * y,x)
    ]]></literal>
    <justification jstring="[para(13620(a,1),469(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13620 469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13890">
    <literal><![CDATA[
      T(x,(y \ z) \ y) = T(x,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(118,a,13613,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 13613 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13891">
    <literal><![CDATA[
      K(x,L(y,z \ y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10872,a,13623,a)].">
      <j1 rule="hyper" parents="10872 13623"/>
    </justification>
  </clause>

  <clause id="13892">
    <literal><![CDATA[
      (x / y) * (y * K(z,x)) = x * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(5768,a,13623,a)].">
      <j1 rule="hyper" parents="5768 13623"/>
    </justification>
  </clause>

  <clause id="13893">
    <literal><![CDATA[
      x \ (y * K(z,y)) = (x \ y) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,13623,a)].">
      <j1 rule="hyper" parents="123 13623"/>
    </justification>
  </clause>

  <clause id="13894">
    <literal><![CDATA[
      x \ ((y * z) / y) = (x \ z) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,4711,a,b,13623,a)].">
      <j1 rule="hyper" parents="116 4711 13623"/>
    </justification>
  </clause>

  <clause id="13896">
    <literal><![CDATA[
      (x \ (y \ z)) * K(y,y \ z) = x \ (z / y)
    ]]></literal>
    <justification jstring="[hyper(116,a,4735,a(flip),b,13623,a),flip(a)].">
      <j1 rule="hyper" parents="116 4735 13623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13897">
    <literal><![CDATA[
      K(x,L(y * z,z,y)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),13891(a,1,2,2))].">
      <j1 rule="para" parents="4 13891"/>
    </justification>
  </clause>

  <clause id="13898">
    <literal><![CDATA[
      K((x * y) \ z,x * y) = K(y \ (x \ z),x * y)
    ]]></literal>
    <justification jstring="[hyper(10914,a,13897,a)].">
      <j1 rule="hyper" parents="10914 13897"/>
    </justification>
  </clause>

  <clause id="13899">
    <literal><![CDATA[
      (K(x,y) * (y / z)) * z = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(585,a,13633,a)].">
      <j1 rule="hyper" parents="585 13633"/>
    </justification>
  </clause>

  <clause id="13900">
    <literal><![CDATA[
      (x * K(y,x)) / z = K(y,x) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(353,a,13633,a)].">
      <j1 rule="hyper" parents="353 13633"/>
    </justification>
  </clause>

  <clause id="13901">
    <literal><![CDATA[
      (1 / x) * ((K(y,z) / x) \ y) = y * K(z,y)
    ]]></literal>
    <justification jstring="[para(13681(a,1),13633(a,1,1))].">
      <j1 rule="para" parents="13681 13633"/>
    </justification>
  </clause>

  <clause id="13902">
    <literal><![CDATA[
      T(T(x,x \ (y * z)),u) \ T(x,u) = K((y \ x) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[para(13635(a,1),4756(a,1,1,1))].">
      <j1 rule="para" parents="13635 4756"/>
    </justification>
  </clause>

  <clause id="13904">
    <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(440,a,6308,a(flip),b,13642,a)].">
      <j1 rule="hyper" parents="440 6308 13642"/>
    </justification>
  </clause>

  <clause id="13906">
    <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(5918(a,1),13645(a,1,2,1))].">
      <j1 rule="para" parents="5918 13645"/>
    </justification>
  </clause>

  <clause id="13908">
    <literal><![CDATA[
      (x * ((x * y) / x)) \ y = (x * y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4051(a,1),13650(a,1,1))].">
      <j1 rule="para" parents="4051 13650"/>
    </justification>
  </clause>

  <clause id="13909">
    <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(7816(a,1),13650(a,2,2))].">
      <j1 rule="para" parents="7816 13650"/>
    </justification>
  </clause>

  <clause id="13910">
    <literal><![CDATA[
      K(x / y,z) * (y \ (y \ x)) = y \ T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(7882(a,1),13653(a,1,1))].">
      <j1 rule="para" parents="7882 13653"/>
    </justification>
  </clause>

  <clause id="13912">
    <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(13654(a,1),12251(a,1,2,1,1))].">
      <j1 rule="para" parents="13654 12251"/>
    </justification>
  </clause>

  <clause id="13913">
    <literal><![CDATA[
      (x \ T(y * x,z)) / (x \ (y * x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,12190,a(flip),b,13659,a),flip(a)].">
      <j1 rule="hyper" parents="320 12190 13659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13914">
    <literal><![CDATA[
      L(x * K(y * x,z),y,z) = (z * y) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(13661(a,1),450(a,1,1))].">
      <j1 rule="para" parents="13661 450"/>
    </justification>
  </clause>

  <clause id="13916">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x * y) = u
    ]]></literal>
    <justification jstring="[para(13661(a,2),6316(a,1,1))].">
      <j1 rule="para" parents="13661 6316"/>
    </justification>
  </clause>

  <clause id="13919">
    <literal><![CDATA[
      K(x * K(y * x,z),T(u,y)) = K(y \ T(x * y,z),u)
    ]]></literal>
    <justification jstring="[para(13661(a,1),7192(a,1,1))].">
      <j1 rule="para" parents="13661 7192"/>
    </justification>
  </clause>

  <clause id="13921">
    <literal><![CDATA[
      x \ T(x * y,T(z,y)) = y * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(12190(a,1),13661(a,2,2))].">
      <j1 rule="para" parents="12190 13661"/>
    </justification>
  </clause>

  <clause id="13922">
    <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(13678(a,1),5531(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13678 5531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13923">
    <literal><![CDATA[
      (1 / x) * K(y,z / x) = K(y,x \ z) / x
    ]]></literal>
    <justification jstring="[para(107(a,1),13682(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 13682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13924">
    <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(13682(a,2),687(a,2,2))].">
      <j1 rule="para" parents="13682 687"/>
    </justification>
  </clause>

  <clause id="13925">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = K(y,T(z,x)) / T(x,u)
    ]]></literal>
    <justification jstring="[para(13682(a,1),6293(a,1,1))].">
      <j1 rule="para" parents="13682 6293"/>
    </justification>
  </clause>

  <clause id="13926">
    <literal><![CDATA[
      T(x,(y * z) \ x) = T(x,z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(118,a,13739,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 13739 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13927">
    <literal><![CDATA[
      K(x,x \ ((y \ x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(13742(a,1),13080(a,1))].">
      <j1 rule="para" parents="13742 13080"/>
    </justification>
  </clause>

  <clause id="13928">
    <literal><![CDATA[
      T(x,(y * z) \ 1) = T(x,z \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(118,a,13743,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 13743 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13929">
    <literal><![CDATA[
      (x \ K(y,T(z,x))) \ 1 = (x \ 1) \ K(z,y)
    ]]></literal>
    <justification jstring="[para(13745(a,2),13708(a,1,1))].">
      <j1 rule="para" parents="13745 13708"/>
    </justification>
  </clause>

  <clause id="13930">
    <literal><![CDATA[
      K(x \ ((y \ x) * z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(8757,a,13749,a),flip(a)].">
      <j1 rule="hyper" parents="8757 13749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13933">
    <literal><![CDATA[
      (x * y) / (z \ (y * x)) = K(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(197,a,13751,a)].">
      <j1 rule="hyper" parents="197 13751"/>
    </justification>
  </clause>

  <clause id="13934">
    <literal><![CDATA[
      (K(x,y) * z) \ (x * y) = z \ (y * x)
    ]]></literal>
    <justification jstring="[para(4(a,1),13751(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 13751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13935">
    <literal><![CDATA[
      (T(x,y) * z) \ (x * y) = (x * z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(4741(a,1),13751(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4741 13751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13936">
    <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(13765(a,1),9764(a,1,2,1,1))].">
      <j1 rule="para" parents="13765 9764"/>
    </justification>
  </clause>

  <clause id="13937">
    <literal><![CDATA[
      K(x,y) * (y / (z \ 1)) = y / (z \ K(y,x))
    ]]></literal>
    <justification jstring="[para(13747(a,1),13765(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13747 13765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13938">
    <literal><![CDATA[
      K((x \ y) \ K(x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ T(x,z),u) = w
    ]]></literal>
    <justification jstring="[para(13769(a,1),6396(a,1,1))].">
      <j1 rule="para" parents="13769 6396"/>
    </justification>
  </clause>

  <clause id="13939">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ K(z,w))) = K(x,y / (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[para(13769(a,1),13694(a,1,2,2))].">
      <j1 rule="para" parents="13769 13694"/>
    </justification>
  </clause>

  <clause id="13940">
    <literal><![CDATA[
      T(x,y * ((z \ u) \ K(z,w))) = T(x,y / (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[para(13769(a,1),13723(a,1,2,2))].">
      <j1 rule="para" parents="13769 13723"/>
    </justification>
  </clause>

  <clause id="13941">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(13787(a,1),12259(a,1))].">
      <j1 rule="para" parents="13787 12259"/>
    </justification>
  </clause>

  <clause id="13942">
    <literal><![CDATA[
      K(x,(y \ x) * (x \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(13080,a,13790,a),flip(a)].">
      <j1 rule="hyper" parents="13080 13790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13943">
    <literal><![CDATA[
      x * (y * K(x * (z \ y),z)) = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(13797(a,1),6386(a,1,2,2))].">
      <j1 rule="para" parents="13797 6386"/>
    </justification>
  </clause>

  <clause id="13944">
    <literal><![CDATA[
      (x * K(y,z)) * (y / x) = T(x * (y / x),z)
    ]]></literal>
    <justification jstring="[para(7(a,1),13804(a,1,1,2,1))].">
      <j1 rule="para" parents="7 13804"/>
    </justification>
  </clause>

  <clause id="13947">
    <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(440,a,6448,a,b,13841,a)].">
      <j1 rule="hyper" parents="440 6448 13841"/>
    </justification>
  </clause>

  <clause id="13948">
    <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(440,a,6160,a,b,13841,a)].">
      <j1 rule="hyper" parents="440 6160 13841"/>
    </justification>
  </clause>

  <clause id="13949">
    <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(440,a,3950,a,b,13841,a)].">
      <j1 rule="hyper" parents="440 3950 13841"/>
    </justification>
  </clause>

  <clause id="13950">
    <literal><![CDATA[
      K((1 / x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(13860(a,2),12204(a,1))].">
      <j1 rule="para" parents="13860 12204"/>
    </justification>
  </clause>

  <clause id="13951">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z) = K(y,T(z,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,8200,a,b,13877,a),flip(a)].">
      <j1 rule="hyper" parents="320 8200 13877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13952">
    <literal><![CDATA[
      ((x \ y) / z) \ (y / x) = z * K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,4735,a(flip),b,13892,a)].">
      <j1 rule="hyper" parents="116 4735 13892"/>
    </justification>
  </clause>

  <clause id="13954">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,y * z) = x \ (L(z,y,z) * y)
    ]]></literal>
    <justification jstring="[para(4332(a,1),13894(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4332 13894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13956">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) / z) = (y / x) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,4735,a(flip),b,13899,a),flip(a)].">
      <j1 rule="hyper" parents="117 4735 13899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13957">
    <literal><![CDATA[
      T(K(x,y) * (y / T(z,K(x,y))),z) = z \ (y * T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(13900(a,1),6347(a,1,1))].">
      <j1 rule="para" parents="13900 6347"/>
    </justification>
  </clause>

  <clause id="13958">
    <literal><![CDATA[
      K(x \ (y * z),z) = K((x \ z) * y,z)
    ]]></literal>
    <justification jstring="[hyper(10754,a,13930,a),flip(a)].">
      <j1 rule="hyper" parents="10754 13930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13959">
    <literal><![CDATA[
      (x * y) / (z \ (y * x)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(320,a,5092,a(flip),b,13933,a),flip(a)].">
      <j1 rule="hyper" parents="320 5092 13933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13960">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * (y * x)) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,11644,a(flip),b,13934,a),flip(a)].">
      <j1 rule="hyper" parents="34 11644 13934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13961">
    <literal><![CDATA[
      (K(x,x \ y) * z) \ y = z \ ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(5(a,1),13934(a,1,2))].">
      <j1 rule="para" parents="5 13934"/>
    </justification>
  </clause>

  <clause id="13962">
    <literal><![CDATA[
      K(x,K(y,(z \ y) * u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(13942(a,1),10303(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13942 10303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13963">
    <literal><![CDATA[
      K((x \ y) * z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,10461,a(flip),b,13958,a),flip(a)].">
      <j1 rule="hyper" parents="58 10461 13958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13964">
    <literal><![CDATA[
      K(x,y) * ((y * x) / z) = (x * y) / z
    ]]></literal>
    <justification jstring="[para(75(a,1),13959(a,1,2)),flip(a)].">
      <j1 rule="para" parents="75 13959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13965">
    <literal><![CDATA[
      K((x / y) * z,x) = K(x * (y \ z),x)
    ]]></literal>
    <justification jstring="[hyper(8758,a,13963,a)].">
      <j1 rule="hyper" parents="8758 13963"/>
    </justification>
  </clause>

  <clause id="13966">
    <literal><![CDATA[
      ((x * y) / z) \ T(x,y) = ((y * x) / z) \ x
    ]]></literal>
    <justification jstring="[para(13964(a,1),13631(a,1,1))].">
      <j1 rule="para" parents="13964 13631"/>
    </justification>
  </clause>

  <clause id="13967">
    <literal><![CDATA[
      ((x * y) / z) \ K(x,y) = ((y * x) / z) \ 1
    ]]></literal>
    <justification jstring="[para(13964(a,1),13691(a,1,1))].">
      <j1 rule="para" parents="13964 13691"/>
    </justification>
  </clause>

  <clause id="13968">
    <literal><![CDATA[
      K((x * y) * (T(x,y) \ z),x * y) = K(y * z,x * y)
    ]]></literal>
    <justification jstring="[para(187(a,1),13965(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="187 13965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13969">
    <literal><![CDATA[
      L(a(x,y,z),u,K(w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(13601,a,13352,a)].">
      <j1 rule="hyper" parents="13601 13352"/>
    </justification>
  </clause>

  <clause id="13971">
    <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,10735,a,b,13969,a)].">
      <j1 rule="hyper" parents="58 10735 13969"/>
    </justification>
  </clause>

  <clause id="13972">
    <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,8084,a,b,13969,a)].">
      <j1 rule="hyper" parents="58 8084 13969"/>
    </justification>
  </clause>

  <clause id="13973">
    <literal><![CDATA[
      (T(x,y) * (z * u)) \ (K(x,y) * ((x * z) * u)) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5085,a,b,13969,a)].">
      <j1 rule="hyper" parents="58 5085 13969"/>
    </justification>
  </clause>

  <clause id="13974">
    <literal><![CDATA[
      (K(x,y) * z) * a(u,w,v5) = K(x,y) * (z * a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(119,a,13969,a(flip),b,3975,a(flip))].">
      <j1 rule="hyper" parents="119 13969 3975"/>
    </justification>
  </clause>

  <clause id="13975">
    <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(13969(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13969 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13976">
    <literal><![CDATA[
      (K(x,y) * z) / a(u,w,v5) = K(x,y) * (z / a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(13969(a,1),544(a,1,2))].">
      <j1 rule="para" parents="13969 544"/>
    </justification>
  </clause>

  <clause id="13978">
    <literal><![CDATA[
      (K(x,y) * z) \ (x \ ((x * y) / x)) = z \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5359,a(flip),b,13632,a)].">
      <j1 rule="hyper" parents="58 5359 13632"/>
    </justification>
  </clause>

  <clause id="13979">
    <literal><![CDATA[
      L(x \ (T(y,z) \ z),x,K(T(y,z),z)) = x \ (y \ T(z,y))
    ]]></literal>
    <justification jstring="[para(4208(a,1),13632(a,2,2))].">
      <j1 rule="para" parents="4208 13632"/>
    </justification>
  </clause>

  <clause id="13980">
    <literal><![CDATA[
      K(x,y) * (K(z,u) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / T(u,z) = w
    ]]></literal>
    <justification jstring="[para(4762(a,2),13674(a,1,2))].">
      <j1 rule="para" parents="4762 13674"/>
    </justification>
  </clause>

  <clause id="13981">
    <literal><![CDATA[
      L(K(x,y),z \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(13748(a,2),287(a,1)),flip(b)].">
      <j1 rule="para" parents="13748 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13983">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(10763(a,1),13981(a,1))].">
      <j1 rule="para" parents="10763 13981"/>
    </justification>
  </clause>

  <clause id="13984">
    <literal><![CDATA[
      K(L(x,y \ 1,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(10805(a,1),13981(a,1))].">
      <j1 rule="para" parents="10805 13981"/>
    </justification>
  </clause>

  <clause id="13985">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2841(a,1),13983(a,1,2))].">
      <j1 rule="para" parents="2841 13983"/>
    </justification>
  </clause>

  <clause id="13986">
    <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(6031(a,1),13983(a,1,2))].">
      <j1 rule="para" parents="6031 13983"/>
    </justification>
  </clause>

  <clause id="13987">
    <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(6031(a,1),13984(a,1,1))].">
      <j1 rule="para" parents="6031 13984"/>
    </justification>
  </clause>

  <clause id="13988">
    <literal><![CDATA[
      K(x,(1 / y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(2792(a,1),13985(a,1,2))].">
      <j1 rule="para" parents="2792 13985"/>
    </justification>
  </clause>

  <clause id="13989">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(12311(a,2),13985(a,1))].">
      <j1 rule="para" parents="12311 13985"/>
    </justification>
  </clause>

  <clause id="13990">
    <literal><![CDATA[
      K(x,y * (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(12312(a,1),13985(a,1))].">
      <j1 rule="para" parents="12312 13985"/>
    </justification>
  </clause>

  <clause id="13991">
    <literal><![CDATA[
      K(x,T(y * (z \ 1),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(611(a,1),13989(a,1,2))].">
      <j1 rule="para" parents="611 13989"/>
    </justification>
  </clause>

  <clause id="13992">
    <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(4226(a,1),13768(a,1,2))].">
      <j1 rule="para" parents="4226 13768"/>
    </justification>
  </clause>

  <clause id="13993">
    <literal><![CDATA[
      K((1 / x) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(3939(a,2),13803(a,1))].">
      <j1 rule="para" parents="3939 13803"/>
    </justification>
  </clause>

  <clause id="13994">
    <literal><![CDATA[
      K((x \ K(y,z)) * y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ T(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(13826(a,2),13803(a,1,1))].">
      <j1 rule="para" parents="13826 13803"/>
    </justification>
  </clause>

  <clause id="13995">
    <literal><![CDATA[
      (x * (y * z)) / T(x * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(13887(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13887 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13997">
    <literal><![CDATA[
      L(x,y,z) * (x \ (z * y)) = (z * (y * x)) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,13888,a(flip),b,10949,a),flip(a)].">
      <j1 rule="hyper" parents="117 13888 10949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13999">
    <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(6293(a,1),13888(a,2,2))].">
      <j1 rule="para" parents="6293 13888"/>
    </justification>
  </clause>

  <clause id="14000">
    <literal><![CDATA[
      (x * (y * z)) * K(z,x * y) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(13888(a,1),6302(a,1,1))].">
      <j1 rule="para" parents="13888 6302"/>
    </justification>
  </clause>

  <clause id="14002">
    <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(4352(a,2),13941(a,1,2))].">
      <j1 rule="para" parents="4352 13941"/>
    </justification>
  </clause>

  <clause id="14003">
    <literal><![CDATA[
      K(x,(1 / y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(5285(a,2),13941(a,1))].">
      <j1 rule="para" parents="5285 13941"/>
    </justification>
  </clause>

  <clause id="14004">
    <literal><![CDATA[
      K(x,y / T(z \ 1,z * (x * y))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(11192(a,2),13941(a,1))].">
      <j1 rule="para" parents="11192 13941"/>
    </justification>
  </clause>

  <clause id="14005">
    <literal><![CDATA[
      K((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(3940(a,1),13950(a,1))].">
      <j1 rule="para" parents="3940 13950"/>
    </justification>
  </clause>

  <clause id="14006">
    <literal><![CDATA[
      K(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(5284(a,1),13988(a,1))].">
      <j1 rule="para" parents="5284 13988"/>
    </justification>
  </clause>

  <clause id="14007">
    <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(13753(a,1),13988(a,1,2,1))].">
      <j1 rule="para" parents="13753 13988"/>
    </justification>
  </clause>

  <clause id="14008">
    <literal><![CDATA[
      K(x,y * (z \ K(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(4763(a,1),13990(a,1,2,2))].">
      <j1 rule="para" parents="4763 13990"/>
    </justification>
  </clause>

  <clause id="14009">
    <literal><![CDATA[
      K(x,y * (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(5277(a,2),13990(a,1))].">
      <j1 rule="para" parents="5277 13990"/>
    </justification>
  </clause>

  <clause id="14010">
    <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(13769(a,1),13990(a,1,2,2))].">
      <j1 rule="para" parents="13769 13990"/>
    </justification>
  </clause>

  <clause id="14011">
    <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(1942(a,1),14003(a,1,2))].">
      <j1 rule="para" parents="1942 14003"/>
    </justification>
  </clause>

  <clause id="14012">
    <literal><![CDATA[
      K(x / (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(13845(a,2),14005(a,1))].">
      <j1 rule="para" parents="13845 14005"/>
    </justification>
  </clause>

  <clause id="14013">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(13710(a,2),14006(a,1))].">
      <j1 rule="para" parents="13710 14006"/>
    </justification>
  </clause>

  <clause id="14014">
    <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(13862(a,1),14006(a,1,2,1))].">
      <j1 rule="para" parents="13862 14006"/>
    </justification>
  </clause>

  <clause id="14015">
    <literal><![CDATA[
      K(x / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ 1),z) = u
    ]]></literal>
    <justification jstring="[para(72(a,1),14012(a,1,1,2))].">
      <j1 rule="para" parents="72 14012"/>
    </justification>
  </clause>

  <clause id="14016">
    <literal><![CDATA[
      K(x * (1 / (1 / y)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(13777(a,2),14012(a,1))].">
      <j1 rule="para" parents="13777 14012"/>
    </justification>
  </clause>

  <clause id="14017">
    <literal><![CDATA[
      K(x * (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ 1),z) = u
    ]]></literal>
    <justification jstring="[para(13777(a,2),14015(a,1))].">
      <j1 rule="para" parents="13777 14015"/>
    </justification>
  </clause>

  <clause id="14018">
    <literal><![CDATA[
      T(x,y) * (z * K(x * y,z)) = (y \ T(x * y,z)) * z
    ]]></literal>
    <justification jstring="[para(13640(a,1),6060(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13640 6060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14019">
    <literal><![CDATA[
      (x \ y) / (x \ T(y,z)) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,8206,a(flip),b,13670,a),flip(a)].">
      <j1 rule="hyper" parents="320 8206 13670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14020">
    <literal><![CDATA[
      K(x,y * ((1 / z) * K(u,w))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(13686(a,1),13001(a,1,2,2))].">
      <j1 rule="para" parents="13686 13001"/>
    </justification>
  </clause>

  <clause id="14021">
    <literal><![CDATA[
      T(1 / (x * K(y,z)),K(z,y)) = (1 / x) * K(z,y)
    ]]></literal>
    <justification jstring="[para(13811(a,2),13686(a,1,1))].">
      <j1 rule="para" parents="13811 13686"/>
    </justification>
  </clause>

  <clause id="14025">
    <literal><![CDATA[
      T(x,T((y \ 1) * z,u)) = T(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,4611,a(flip),b,13738,a)].">
      <j1 rule="hyper" parents="58 4611 13738"/>
    </justification>
  </clause>

  <clause id="14026">
    <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,12048,a(flip),b,13746,a)].">
      <j1 rule="hyper" parents="58 12048 13746"/>
    </justification>
  </clause>

  <clause id="14027">
    <literal><![CDATA[
      ((x * K(y,z)) \ u) \ K(x,K(y,z)) = ((K(y,z) * x) \ u) \ 1
    ]]></literal>
    <justification jstring="[para(7771(a,1),13771(a,1,2))].">
      <j1 rule="para" parents="7771 13771"/>
    </justification>
  </clause>

  <clause id="14028">
    <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(4278(a,1),13805(a,1,1,2,1))].">
      <j1 rule="para" parents="4278 13805"/>
    </justification>
  </clause>

  <clause id="14029">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = y \ T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(12190(a,1),13805(a,1,1,2))].">
      <j1 rule="para" parents="12190 13805"/>
    </justification>
  </clause>

  <clause id="14030">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(13858(a,2),8243(a,1))].">
      <j1 rule="para" parents="13858 8243"/>
    </justification>
  </clause>

  <clause id="14032">
    <literal><![CDATA[
      K(x,y / (T(z \ (u \ w),x) * K(u,u \ w))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[para(13896(a,1),8843(a,2,2,2))].">
      <j1 rule="para" parents="13896 8843"/>
    </justification>
  </clause>

  <clause id="14034">
    <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(13901(a,1),10841(a,2,2,1))].">
      <j1 rule="para" parents="13901 10841"/>
    </justification>
  </clause>

  <clause id="14036">
    <literal><![CDATA[
      (x \ 1) \ K(y,T(z,x)) = (x \ K(z,y)) \ 1
    ]]></literal>
    <justification jstring="[para(7863(a,1),13929(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7863 13929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14037">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(13951(a,2),8243(a,1))].">
      <j1 rule="para" parents="13951 8243"/>
    </justification>
  </clause>

  <clause id="14039">
    <literal><![CDATA[
      ((x \ y) * z) \ ((x \ y) * x) = ((y / x) * z) \ y
    ]]></literal>
    <justification jstring="[para(5421(a,1),13961(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5421 13961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14040">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ z) * K(x,K(z,y \ u)) = K(x,z / ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(13962(a,1),8347(a,1,2))].">
      <j1 rule="para" parents="13962 8347"/>
    </justification>
  </clause>

  <clause id="14041">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((z \ y) * u)) = K(x,((z \ y) * u) / y)
    ]]></literal>
    <justification jstring="[para(13962(a,1),8358(a,1,1))].">
      <j1 rule="para" parents="13962 8358"/>
    </justification>
  </clause>

  <clause id="14042">
    <literal><![CDATA[
      ((x * T(y,x)) / z) \ T(x,T(y,x)) = ((y * ((y * x) / y)) / z) \ x
    ]]></literal>
    <justification jstring="[para(4051(a,1),13966(a,2,1,1))].">
      <j1 rule="para" parents="4051 13966"/>
    </justification>
  </clause>

  <clause id="14043">
    <literal><![CDATA[
      K(x,(((y * z) / u) \ T(K(y,z),x)) \ w) = K(x,(((z * y) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(13967(a,1),8525(a,2,2,1))].">
      <j1 rule="para" parents="13967 8525"/>
    </justification>
  </clause>

  <clause id="14044">
    <literal><![CDATA[
      T(x,T((y \ 1) * z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(14025(a,2),4333(a,1))].">
      <j1 rule="para" parents="14025 4333"/>
    </justification>
  </clause>

  <clause id="14045">
    <literal><![CDATA[
      ((x \ 1) \ K(y,z)) * K(x,K(y,z)) = (x \ K(z,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,12309,a,b,14036,a)].">
      <j1 rule="hyper" parents="58 12309 14036"/>
    </justification>
  </clause>

  <clause id="14046">
    <literal><![CDATA[
      K(x,y * ((1 / y) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(13878(a,1),6470(a,1))].">
      <j1 rule="para" parents="13878 6470"/>
    </justification>
  </clause>

  <clause id="14047">
    <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(5220(a,1),14046(a,1,2,2))].">
      <j1 rule="para" parents="5220 14046"/>
    </justification>
  </clause>

  <clause id="14048">
    <literal><![CDATA[
      K(x,(y \ z) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(11545(a,1),14046(a,1,2,2))].">
      <j1 rule="para" parents="11545 14046"/>
    </justification>
  </clause>

  <clause id="14049">
    <literal><![CDATA[
      L(x,x \ y,z) \ (z * y) = T(z * (y / x),x)
    ]]></literal>
    <justification jstring="[para(10385(a,1),13885(a,1,1))].">
      <j1 rule="para" parents="10385 13885"/>
    </justification>
  </clause>

  <clause id="14050">
    <literal><![CDATA[
      K(x,T(y * z,z \ u)) = K(x,T(y * z,y * u))
    ]]></literal>
    <justification jstring="[para(13886(a,1),7115(a,1,2))].">
      <j1 rule="para" parents="13886 7115"/>
    </justification>
  </clause>

  <clause id="14051">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(13927,a,10306,a)].">
      <j1 rule="hyper" parents="13927 10306"/>
    </justification>
  </clause>

  <clause id="14052">
    <literal><![CDATA[
      K(x,(y \ x) * z) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(10473,a,14051,a),flip(a)].">
      <j1 rule="hyper" parents="10473 14051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14054">
    <literal><![CDATA[
      T(x,(y \ x) * z) = T(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,14052,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 14052 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14056">
    <literal><![CDATA[
      (K(x,y) / x) * (y * x) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(13263,a,13960,a)].">
      <j1 rule="hyper" parents="13263 13960"/>
    </justification>
  </clause>

  <clause id="14057">
    <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(2153(a,1),14013(a,1,2,1))].">
      <j1 rule="para" parents="2153 14013"/>
    </justification>
  </clause>

  <clause id="14058">
    <literal><![CDATA[
      T(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(4193(a,1),14044(a,1))].">
      <j1 rule="para" parents="4193 14044"/>
    </justification>
  </clause>

  <clause id="14059">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(13737(a,2),14058(a,1))].">
      <j1 rule="para" parents="13737 14058"/>
    </justification>
  </clause>

  <clause id="14060">
    <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(13862(a,1),14058(a,1,2,1))].">
      <j1 rule="para" parents="13862 14058"/>
    </justification>
  </clause>

  <clause id="14061">
    <literal><![CDATA[
      L(x,x \ (x * y),z) \ (z * (x * y)) = T(z * (y * K(x,y)),x)
    ]]></literal>
    <justification jstring="[para(4711(a,1),14049(a,2,1,2))].">
      <j1 rule="para" parents="4711 14049"/>
    </justification>
  </clause>

  <clause id="14062">
    <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(6433(a,1),14049(a,1,2))].">
      <j1 rule="para" parents="6433 14049"/>
    </justification>
  </clause>

  <clause id="14063">
    <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(2631(a,1),14059(a,1,2,1))].">
      <j1 rule="para" parents="2631 14059"/>
    </justification>
  </clause>

  <clause id="14064">
    <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(3052(a,2),14059(a,1,2,1))].">
      <j1 rule="para" parents="3052 14059"/>
    </justification>
  </clause>

  <clause id="14065">
    <literal><![CDATA[
      K(x,y * (z * K(u,y * z))) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(13614(a,1),7891(a,1,2))].">
      <j1 rule="para" parents="13614 7891"/>
    </justification>
  </clause>

  <clause id="14066">
    <literal><![CDATA[
      L(x \ y,x,z / T(y,z)) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(4230,a,13651,a)].">
      <j1 rule="hyper" parents="4230 13651"/>
    </justification>
  </clause>

  <clause id="14067">
    <literal><![CDATA[
      L(x \ y,x,y \ z) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,12562,a(flip),b,14066,a)].">
      <j1 rule="hyper" parents="58 12562 14066"/>
    </justification>
  </clause>

  <clause id="14068">
    <literal><![CDATA[
      x / L(y \ z,y,z \ x) = (x / z) * y
    ]]></literal>
    <justification jstring="[hyper(197,a,14067,a(flip))].">
      <j1 rule="hyper" parents="197 14067"/>
    </justification>
  </clause>

  <clause id="14070">
    <literal><![CDATA[
      x / L(y,z,(z * y) \ x) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(4(a,1),14068(a,1,2,1))].">
      <j1 rule="para" parents="4 14068"/>
    </justification>
  </clause>

  <clause id="14071">
    <literal><![CDATA[
      (x \ y) / (K(z,x) \ y) = ((x \ y) / y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(13260(a,1),14068(a,1,2))].">
      <j1 rule="para" parents="13260 14068"/>
    </justification>
  </clause>

  <clause id="14072">
    <literal><![CDATA[
      x / K(y,L(z,u,(u * K(y,z)) \ x)) = (x / (u * K(y,z))) * u
    ]]></literal>
    <justification jstring="[para(10763(a,1),14070(a,1,2))].">
      <j1 rule="para" parents="10763 14070"/>
    </justification>
  </clause>

  <clause id="14073">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) = K(x,L(y * z,u,w))
    ]]></literal>
    <justification jstring="[para(72(a,1),13711(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="72 13711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14074">
    <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(2154(a,1),13711(a,1,2,1,1))].">
      <j1 rule="para" parents="2154 13711"/>
    </justification>
  </clause>

  <clause id="14075">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,z \ 1) = R(x,z,z \ 1) * y
    ]]></literal>
    <justification jstring="[para(224(a,1),13722(a,1,2)),flip(a)].">
      <j1 rule="para" parents="224 13722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14076">
    <literal><![CDATA[
      ((x * y) / x) * L(x,z,z \ 1) = L(x,z,z \ 1) * y
    ]]></literal>
    <justification jstring="[para(224(a,1),13735(a,1,2)),flip(a)].">
      <j1 rule="para" parents="224 13735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14077">
    <literal><![CDATA[
      T(x,(y / z) \ K(u,y)) = T(x,z / T(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,4415,a(flip),b,13766,a),flip(a)].">
      <j1 rule="hyper" parents="58 4415 13766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14078">
    <literal><![CDATA[
      T(x,(y \ z) / T(z,u)) = T(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),14077(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 14077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14079">
    <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(13791(a,2),10806(a,1))].">
      <j1 rule="para" parents="13791 10806"/>
    </justification>
  </clause>

  <clause id="14080">
    <literal><![CDATA[
      (x \ (y * z)) * K(x * (y \ (x \ (y * z))),y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(30,a,4621,a(flip),b,13809,a),flip(a)].">
      <j1 rule="hyper" parents="30 4621 13809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14081">
    <literal><![CDATA[
      (K(x,y) * z) \ K(x,K(y,u)) = z \ K(y,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,12308,a(flip),b,13832,a),flip(a)].">
      <j1 rule="hyper" parents="320 12308 13832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14082">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u)) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(7913,a,13838,a),flip(a)].">
      <j1 rule="hyper" parents="7913 13838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14083">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(13838(a,1),7913(a,1))].">
      <j1 rule="para" parents="13838 7913"/>
    </justification>
  </clause>

  <clause id="14084">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),u)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),14082(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 14082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14085">
    <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(13842(a,2),10806(a,1))].">
      <j1 rule="para" parents="13842 10806"/>
    </justification>
  </clause>

  <clause id="14086">
    <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(13850(a,2),10806(a,1))].">
      <j1 rule="para" parents="13850 10806"/>
    </justification>
  </clause>

  <clause id="14089">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(13883(a,2),7330(a,1))].">
      <j1 rule="para" parents="13883 7330"/>
    </justification>
  </clause>

  <clause id="14090">
    <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(6117(a,1),14089(a,1,1,2))].">
      <j1 rule="para" parents="6117 14089"/>
    </justification>
  </clause>

  <clause id="14091">
    <literal><![CDATA[
      (x \ T(y * x,z)) / T(y,x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(17(a,2),13913(a,1,2))].">
      <j1 rule="para" parents="17 13913"/>
    </justification>
  </clause>

  <clause id="14092">
    <literal><![CDATA[
      K(x * y,z) * T(y,x) = x \ T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,14091,a)].">
      <j1 rule="hyper" parents="133 14091"/>
    </justification>
  </clause>

  <clause id="14093">
    <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(14091(a,1),530(a,1,1))].">
      <j1 rule="para" parents="14091 530"/>
    </justification>
  </clause>

  <clause id="14094">
    <literal><![CDATA[
      T(x,y * (T(z,u) \ K(w,u * z))) = T(x,y / (u \ T(z * u,w)))
    ]]></literal>
    <justification jstring="[para(14092(a,1),13794(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14092 13794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14095">
    <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(7872(a,1),13995(a,1,1,2))].">
      <j1 rule="para" parents="7872 13995"/>
    </justification>
  </clause>

  <clause id="14096">
    <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(11118(a,1),13995(a,1,2,1))].">
      <j1 rule="para" parents="11118 13995"/>
    </justification>
  </clause>

  <clause id="14097">
    <literal><![CDATA[
      1 / (K(x,y) * z) = (1 / z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8199,a(flip),b,14021,a)].">
      <j1 rule="hyper" parents="58 8199 14021"/>
    </justification>
  </clause>

  <clause id="14098">
    <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(14097(a,1),13674(a,1,2))].">
      <j1 rule="para" parents="14097 13674"/>
    </justification>
  </clause>

  <clause id="14099">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) \ x = K(u,L(z,y,y \ x))
    ]]></literal>
    <justification jstring="[hyper(10836,a,14039,a),flip(a)].">
      <j1 rule="hyper" parents="10836 14039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14100">
    <literal><![CDATA[
      K(x,y * (((z * y) \ u) * K(z,z \ u))) = K(x,T(y * ((z * y) \ u),z))
    ]]></literal>
    <justification jstring="[para(12410(a,1),14065(a,1,2,2,2))].">
      <j1 rule="para" parents="12410 14065"/>
    </justification>
  </clause>

  <clause id="14101">
    <literal><![CDATA[
      (x \ y) / (K(x,z) * y) = ((x \ y) / y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(5092(a,1),14071(a,1,2))].">
      <j1 rule="para" parents="5092 14071"/>
    </justification>
  </clause>

  <clause id="14102">
    <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,10802,a(flip),b,14073,a),flip(a)].">
      <j1 rule="hyper" parents="58 10802 14073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14103">
    <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(3528(a,1),13938(a,1,1,2))].">
      <j1 rule="para" parents="3528 13938"/>
    </justification>
  </clause>

  <clause id="14104">
    <literal><![CDATA[
      K(T(x / y,T(y,x)) \ K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ T(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(4077(a,2),13938(a,1,1,1))].">
      <j1 rule="para" parents="4077 13938"/>
    </justification>
  </clause>

  <clause id="14105">
    <literal><![CDATA[
      L(a(x,y,z),u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(13975(a,1),9871(a,1)),flip(b)].">
      <j1 rule="para" parents="13975 9871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14107">
    <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(14099(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14099 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14108">
    <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(6123(a,1),13752(a,1,2,1))].">
      <j1 rule="para" parents="6123 13752"/>
    </justification>
  </clause>

  <clause id="14109">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,z \ y)) = K(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(320,a,13775,a(flip),b,13786,a),flip(a)].">
      <j1 rule="hyper" parents="320 13775 13786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14110">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) * (z \ y)) = K(x,(z \ y) * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(176(a,1),14109(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="176 14109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14111">
    <literal><![CDATA[
      K(x,y * (T(1 / y,z) * u)) = K(x,K(y \ 1,z) * u)
    ]]></literal>
    <justification jstring="[para(3293(a,1),13849(a,2,2,1))].">
      <j1 rule="para" parents="3293 13849"/>
    </justification>
  </clause>

  <clause id="14112">
    <literal><![CDATA[
      (K(x,y) * (z \ 1)) \ K(z,K(y,x)) = (z \ K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,13832,a,b,14045,a)].">
      <j1 rule="hyper" parents="58 13832 14045"/>
    </justification>
  </clause>

  <clause id="14113">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,z \ 1) = y * R(T(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,238,a,b,14075,a),flip(a)].">
      <j1 rule="hyper" parents="320 238 14075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14114">
    <literal><![CDATA[
      (L(x,y,y \ 1) * z) / L(x,y,y \ 1) = (x * z) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,14076,a)].">
      <j1 rule="hyper" parents="131 14076"/>
    </justification>
  </clause>

  <clause id="14115">
    <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(13655(a,1),14114(a,2,1))].">
      <j1 rule="para" parents="13655 14114"/>
    </justification>
  </clause>

  <clause id="14117">
    <literal><![CDATA[
      K(x,y) * ((y / z) * (z * x)) = L(x,z,z \ y) * y
    ]]></literal>
    <justification jstring="[hyper(13781,a,13726,a)].">
      <j1 rule="hyper" parents="13781 13726"/>
    </justification>
  </clause>

  <clause id="14120">
    <literal><![CDATA[
      (x * (y * z)) \ (K(x,y) * ((x * T(y,x)) * z)) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4512(a,1),13973(a,1,1))].">
      <j1 rule="para" parents="4512 13973"/>
    </justification>
  </clause>

  <clause id="14121">
    <literal><![CDATA[
      L(x \ (T(y,z) \ z),x,K(y,z)) = x \ (y \ T(z,y))
    ]]></literal>
    <justification jstring="[para(4918(a,1),13979(a,1,3))].">
      <j1 rule="para" parents="4918 13979"/>
    </justification>
  </clause>

  <clause id="14122">
    <literal><![CDATA[
      (K(x,y) * z) \ (x \ y) = z \ (x \ T(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5188,a(flip),b,14121,a)].">
      <j1 rule="hyper" parents="58 5188 14121"/>
    </justification>
  </clause>

  <clause id="14123">
    <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(10115(a,1),14085(a,1,2,1,2))].">
      <j1 rule="para" parents="10115 14085"/>
    </justification>
  </clause>

  <clause id="14124">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * u) = K(x,z * ((z \ T(u,y)) * y))
    ]]></literal>
    <justification jstring="[para(10926(a,1),13636(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10926 13636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14125">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(x,K(y,z \ x)) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(7730(a,1),13665(a,1,2))].">
      <j1 rule="para" parents="7730 13665"/>
    </justification>
  </clause>

  <clause id="14126">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,x / z)) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(7730(a,1),13679(a,1,2))].">
      <j1 rule="para" parents="7730 13679"/>
    </justification>
  </clause>

  <clause id="14127">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = (z * K(x,y)) \ y
    ]]></literal>
    <justification jstring="[para(7838(a,1),13754(a,2,1))].">
      <j1 rule="para" parents="7838 13754"/>
    </justification>
  </clause>

  <clause id="14128">
    <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(13840(a,2),14083(a,1))].">
      <j1 rule="para" parents="13840 14083"/>
    </justification>
  </clause>

  <clause id="14129">
    <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(13902(a,1),4986(a,1))].">
      <j1 rule="para" parents="13902 4986"/>
    </justification>
  </clause>

  <clause id="14130">
    <literal><![CDATA[
      K(x \ (y * z),T(x,y)) = K(z / (y \ x),x)
    ]]></literal>
    <justification jstring="[hyper(14129,a,8217,a)].">
      <j1 rule="hyper" parents="14129 8217"/>
    </justification>
  </clause>

  <clause id="14131">
    <literal><![CDATA[
      K(x / (y \ z),z) = K(z \ (x * y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,13101,a(flip),b,14130,a),flip(a)].">
      <j1 rule="hyper" parents="58 13101 14130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14132">
    <literal><![CDATA[
      K(x \ (y * (x / z)),x) = K(y / z,x)
    ]]></literal>
    <justification jstring="[para(75(a,1),14131(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 14131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14133">
    <literal><![CDATA[
      K(x / (y \ z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (z \ y),z) = u
    ]]></literal>
    <justification jstring="[para(14131(a,2),10398(a,1))].">
      <j1 rule="para" parents="14131 10398"/>
    </justification>
  </clause>

  <clause id="14134">
    <literal><![CDATA[
      T(K(x,y) * T(y / z,K(x,y)),z) = z \ (y * T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(8326(a,1),13957(a,1,1,2))].">
      <j1 rule="para" parents="8326 13957"/>
    </justification>
  </clause>

  <clause id="14136">
    <literal><![CDATA[
      ((x * K(y,z)) \ 1) \ K(x,K(y,z)) = (x \ K(z,y)) \ 1
    ]]></literal>
    <justification jstring="[para(13708(a,1),14027(a,2,1))].">
      <j1 rule="para" parents="13708 14027"/>
    </justification>
  </clause>

  <clause id="14137">
    <literal><![CDATA[
      (x * K(y,z)) \ 1 = K(z,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,14112,a,b,14136,a),flip(a)].">
      <j1 rule="hyper" parents="34 14112 14136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14138">
    <literal><![CDATA[
      T(K(x,y) / z,z * K(y,x)) = K(x,y) * (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,13863,a,b,14137,a)].">
      <j1 rule="hyper" parents="58 13863 14137"/>
    </justification>
  </clause>

  <clause id="14140">
    <literal><![CDATA[
      K(x,y \ (R(x,z,u) * w)) = K(x,y \ (w * R(x,z,u)))
    ]]></literal>
    <justification jstring="[para(14080(a,1),7535(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14080 7535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14141">
    <literal><![CDATA[
      (x \ (y * z)) * K(y \ (y * z),y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(10399(a,1),14080(a,1,2))].">
      <j1 rule="para" parents="10399 14080"/>
    </justification>
  </clause>

  <clause id="14142">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),14141(a,1,2,1))].">
      <j1 rule="para" parents="4 14141"/>
    </justification>
  </clause>

  <clause id="14144">
    <literal><![CDATA[
      ((x * y) / z) \ (y * x) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(619,a,14142,a),flip(a)].">
      <j1 rule="hyper" parents="619 14142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14145">
    <literal><![CDATA[
      (x \ (y * z)) / (y * z) = (x \ (z * y)) / (z * y)
    ]]></literal>
    <justification jstring="[hyper(117,a,14142,a(flip),b,10349,a)].">
      <j1 rule="hyper" parents="117 14142 10349"/>
    </justification>
  </clause>

  <clause id="14146">
    <literal><![CDATA[
      (x \ y) * K(z \ y,z) = x \ ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),14142(a,1,1,2))].">
      <j1 rule="para" parents="5 14142"/>
    </justification>
  </clause>

  <clause id="14148">
    <literal><![CDATA[
      (x * y) / (z * K(x,y)) = (y * x) / z
    ]]></literal>
    <justification jstring="[hyper(197,a,14144,a)].">
      <j1 rule="hyper" parents="197 14144"/>
    </justification>
  </clause>

  <clause id="14149">
    <literal><![CDATA[
      x / (y * K(x / z,z)) = (z * (x / z)) / y
    ]]></literal>
    <justification jstring="[para(14144(a,1),324(a,1,2))].">
      <j1 rule="para" parents="14144 324"/>
    </justification>
  </clause>

  <clause id="14150">
    <literal><![CDATA[
      (x * y) / (z * K(y,x)) = K(x,y) * ((x * y) / z)
    ]]></literal>
    <justification jstring="[para(14144(a,1),13959(a,1,2))].">
      <j1 rule="para" parents="14144 13959"/>
    </justification>
  </clause>

  <clause id="14151">
    <literal><![CDATA[
      (x * y) / (z * K(y,T(x,y))) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[para(105(a,1),14148(a,1,1))].">
      <j1 rule="para" parents="105 14148"/>
    </justification>
  </clause>

  <clause id="14152">
    <literal><![CDATA[
      (x * y) / (z * T(x,y)) = (y * x) / (z * x)
    ]]></literal>
    <justification jstring="[para(6086(a,1),14148(a,1,2))].">
      <j1 rule="para" parents="6086 14148"/>
    </justification>
  </clause>

  <clause id="14153">
    <literal><![CDATA[
      x / (y * K(z \ x,z)) = (z * (x / z)) / y
    ]]></literal>
    <justification jstring="[para(4924(a,1),14149(a,1,2,2))].">
      <j1 rule="para" parents="4924 14149"/>
    </justification>
  </clause>

  <clause id="14154">
    <literal><![CDATA[
      R(x,y,z) = (z * (x * y)) / (y * T(z,x * y))
    ]]></literal>
    <justification jstring="[hyper(320,a,15,a,b,14152,a)].">
      <j1 rule="hyper" parents="320 15 14152"/>
    </justification>
  </clause>

  <clause id="14155">
    <literal><![CDATA[
      (x * (y / x)) / (z * (y / x)) = y / (z * (x \ y))
    ]]></literal>
    <justification jstring="[para(6446(a,1),14153(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6446 14153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14156">
    <literal><![CDATA[
      R(x,y,z) \ (z * (x * y)) = y * T(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(188,a,14154,a(flip))].">
      <j1 rule="hyper" parents="188 14154"/>
    </justification>
  </clause>

  <clause id="14157">
    <literal><![CDATA[
      (x * y) / (z * K(y,x)) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[para(4867(a,1),14151(a,1,2,2))].">
      <j1 rule="para" parents="4867 14151"/>
    </justification>
  </clause>

  <clause id="14158">
    <literal><![CDATA[
      K(x,y) * ((x * y) / z) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[hyper(58,a,14150,a(flip),b,14157,a)].">
      <j1 rule="hyper" parents="58 14150 14157"/>
    </justification>
  </clause>

  <clause id="14159">
    <literal><![CDATA[
      K(x,y \ (R(x,z,u) * w)) = K(x,x * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(320,a,12441,a(flip),b,14140,a),flip(a)].">
      <j1 rule="hyper" parents="320 12441 14140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14161">
    <literal><![CDATA[
      K(x,(R(x,y,z) \ u) \ w) = K(x,x * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,8734,a,b,14159,a)].">
      <j1 rule="hyper" parents="58 8734 14159"/>
    </justification>
  </clause>

  <clause id="14162">
    <literal><![CDATA[
      K(x,x * (R(x,y,z) \ u)) = K(x,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),14159(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 14159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14164">
    <literal><![CDATA[
      K(x,(x * y) * z) = K(x,x * (y * z))
    ]]></literal>
    <justification jstring="[para(184(a,1),14162(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="184 14162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14165">
    <literal><![CDATA[
      K(x,(y * x) * z) = K(x,x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(11138,a,14164,a)].">
      <j1 rule="hyper" parents="11138 14164"/>
    </justification>
  </clause>

  <clause id="14167">
    <literal><![CDATA[
      K(x,(y / R(x,z,u)) \ w) = K(x,x * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,7402,a,b,14161,a)].">
      <j1 rule="hyper" parents="58 7402 14161"/>
    </justification>
  </clause>

  <clause id="14169">
    <literal><![CDATA[
      K(x,x * (((y * x) * z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(14167(a,1),12485(a,1))].">
      <j1 rule="para" parents="14167 12485"/>
    </justification>
  </clause>

  <clause id="14171">
    <literal><![CDATA[
      T(x,y) * a(x,z,z \ 1) = R(T(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(4659,a,14113,a)].">
      <j1 rule="hyper" parents="4659 14113"/>
    </justification>
  </clause>

  <clause id="14172">
    <literal><![CDATA[
      a(T(x,y),z,z \ 1) = a(x,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(29,a,705,a,b,14171,a)].">
      <j1 rule="hyper" parents="29 705 14171"/>
    </justification>
  </clause>

  <clause id="14173">
    <literal><![CDATA[
      a(x / y,z,z \ 1) = a(y \ x,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,12740,a(flip),b,14172,a),flip(a)].">
      <j1 rule="hyper" parents="58 12740 14172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14174">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(x,K(y,z)) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8135(a,1),14125(a,1,2))].">
      <j1 rule="para" parents="8135 14125"/>
    </justification>
  </clause>

  <clause id="14175">
    <literal><![CDATA[
      (x \ y) \ K(z,T(y,x)) = (x \ T(y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,14081,a(flip),b,14174,a)].">
      <j1 rule="hyper" parents="58 14081 14174"/>
    </justification>
  </clause>

  <clause id="14176">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8129(a,1),14126(a,1,2))].">
      <j1 rule="para" parents="8129 14126"/>
    </justification>
  </clause>

  <clause id="14177">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) = K(y,x) * ((x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,14137,a(flip),b,14176,a),flip(a)].">
      <j1 rule="hyper" parents="320 14137 14176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14178">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = y \ (x * T(K(z,x),y))
    ]]></literal>
    <justification jstring="[para(105(a,1),14134(a,1,1))].">
      <j1 rule="para" parents="105 14134"/>
    </justification>
  </clause>

  <clause id="14179">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = y \ (x * K(z,T(x,y)))
    ]]></literal>
    <justification jstring="[para(7131(a,2),14178(a,2,2,2))].">
      <j1 rule="para" parents="7131 14178"/>
    </justification>
  </clause>

  <clause id="14180">
    <literal><![CDATA[
      L(x,y,z) \ (z * (x * y)) = T(z * (y * K(x,y)),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),14061(a,1,1,2))].">
      <j1 rule="para" parents="4 14061"/>
    </justification>
  </clause>

  <clause id="14181">
    <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(13614(a,2),14180(a,1,2))].">
      <j1 rule="para" parents="13614 14180"/>
    </justification>
  </clause>

  <clause id="14182">
    <literal><![CDATA[
      (x * (y * z)) \ (K(x,y) * ((y * x) * z)) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(105(a,1),14120(a,1,2,2,1))].">
      <j1 rule="para" parents="105 14120"/>
    </justification>
  </clause>

  <clause id="14183">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(11122(a,1),14182(a,1,2))].">
      <j1 rule="para" parents="11122 14182"/>
    </justification>
  </clause>

  <clause id="14184">
    <literal><![CDATA[
      a(x,T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(691,a,14183,a),flip(a)].">
      <j1 rule="hyper" parents="691 14183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14185">
    <literal><![CDATA[
      a(x,T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(14183(a,1),691(a,1))].">
      <j1 rule="para" parents="14183 691"/>
    </justification>
  </clause>

  <clause id="14186">
    <literal><![CDATA[
      a(x,y * x,z) = a(x,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,13277,a(flip),b,14184,a)].">
      <j1 rule="hyper" parents="58 13277 14184"/>
    </justification>
  </clause>

  <clause id="14187">
    <literal><![CDATA[
      a(x / y,y,z) = a(y \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4616,a(flip),b,14184,a)].">
      <j1 rule="hyper" parents="58 4616 14184"/>
    </justification>
  </clause>

  <clause id="14188">
    <literal><![CDATA[
      a(x / y,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(y \ x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4616(a,1),14185(a,1))].">
      <j1 rule="para" parents="4616 14185"/>
    </justification>
  </clause>

  <clause id="14189">
    <literal><![CDATA[
      a(x,y * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,x * y,z) = u
    ]]></literal>
    <justification jstring="[para(13277(a,1),14185(a,1))].">
      <j1 rule="para" parents="13277 14185"/>
    </justification>
  </clause>

  <clause id="14190">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9685,a(flip),b,13602,a),flip(a)].">
      <j1 rule="hyper" parents="58 9685 13602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14191">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(13603,a,14190,a),flip(a)].">
      <j1 rule="hyper" parents="13603 14190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14192">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(K(u,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,13596,a,b,14190,a),flip(a)].">
      <j1 rule="hyper" parents="320 13596 14190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14193">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = a(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,11763,a,b,14190,a)].">
      <j1 rule="hyper" parents="320 11763 14190"/>
    </justification>
  </clause>

  <clause id="14194">
    <literal><![CDATA[
      a(K(x,a(y,z,u)),w,v5) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,13352,a(flip),b,14190,a),flip(a)].">
      <j1 rule="hyper" parents="320 13352 14190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14195">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13596,a(flip),b,14190,a),flip(a)].">
      <j1 rule="hyper" parents="58 13596 14190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14196">
    <literal><![CDATA[
      (K(x,y) * (z * u)) * a(x,z,K(u,y)) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(119,a,14190,a(flip),b,9,a(flip))].">
      <j1 rule="hyper" parents="119 14190 9"/>
    </justification>
  </clause>

  <clause id="14197">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) = x * a(w,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(14190(a,1),13599(a,1,2))].">
      <j1 rule="para" parents="14190 13599"/>
    </justification>
  </clause>

  <clause id="14198">
    <literal><![CDATA[
      a(a(x,y,z),u,K(w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,13596,a(flip),b,14194,a)].">
      <j1 rule="hyper" parents="58 13596 14194"/>
    </justification>
  </clause>

  <clause id="14199">
    <literal><![CDATA[
      a(a(x,y,K(z,u)),w,v5) = 1
    ]]></literal>
    <justification jstring="[para(13347(a,2),14194(a,1,1))].">
      <j1 rule="para" parents="13347 14194"/>
    </justification>
  </clause>

  <clause id="14200">
    <literal><![CDATA[
      L(K(x,y),z,a(u,w,v5)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5862,a,14198,a)].">
      <j1 rule="hyper" parents="5862 14198"/>
    </justification>
  </clause>

  <clause id="14201">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) * v5 = a(x,y,K(z,u)) * (w * v5)
    ]]></literal>
    <justification jstring="[hyper(6622,a,14199,a)].">
      <j1 rule="hyper" parents="6622 14199"/>
    </justification>
  </clause>

  <clause id="14202">
    <literal><![CDATA[
      L(x,y,a(z,u,K(w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,14199,a)].">
      <j1 rule="hyper" parents="47 14199"/>
    </justification>
  </clause>

  <clause id="14203">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) \ v5 = w \ (a(x,y,K(z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,298,a(flip),b,14202,a)].">
      <j1 rule="hyper" parents="58 298 14202"/>
    </justification>
  </clause>

  <clause id="14204">
    <literal><![CDATA[
      L(x,y,a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      x = v6
    ]]></literal>
    <justification jstring="[para(14202(a,1),45(a,2))].">
      <j1 rule="para" parents="14202 45"/>
    </justification>
  </clause>

  <clause id="14205">
    <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(14202(a,1),476(a,1,2,2,1))].">
      <j1 rule="para" parents="14202 476"/>
    </justification>
  </clause>

  <clause id="14207">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,13322,a,b,14191,a)].">
      <j1 rule="hyper" parents="320 13322 14191"/>
    </justification>
  </clause>

  <clause id="14208">
    <literal><![CDATA[
      (x * y) * a(y,z,K(u,w)) = x * T(y,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,14191,a,b,6124,a)].">
      <j1 rule="hyper" parents="119 14191 6124"/>
    </justification>
  </clause>

  <clause id="14209">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,14191,a,b,4688,a(flip))].">
      <j1 rule="hyper" parents="119 14191 4688"/>
    </justification>
  </clause>

  <clause id="14210">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) / x = T(1 / x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(117,a,14191,a,b,5008,a)].">
      <j1 rule="hyper" parents="117 14191 5008"/>
    </justification>
  </clause>

  <clause id="14211">
    <literal><![CDATA[
      K(x * y,(x * y) \ (z \ ((z * x) * y))) = a(x * y,x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(10394,a,14191,a(flip))].">
      <j1 rule="hyper" parents="10394 14191"/>
    </justification>
  </clause>

  <clause id="14212">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(14191(a,2),4729(a,2,1)),flip(a)].">
      <j1 rule="para" parents="14191 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14213">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(14191(a,2),4725(a,1,2))].">
      <j1 rule="para" parents="14191 4725"/>
    </justification>
  </clause>

  <clause id="14214">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(14191(a,2),4730(a,1,1))].">
      <j1 rule="para" parents="14191 4730"/>
    </justification>
  </clause>

  <clause id="14215">
    <literal><![CDATA[
      (x / y) \ (x * a(y,z,K(u,w))) = T(y,a(w,z,u))
    ]]></literal>
    <justification jstring="[para(14191(a,2),6119(a,1,2,2))].">
      <j1 rule="para" parents="14191 6119"/>
    </justification>
  </clause>

  <clause id="14216">
    <literal><![CDATA[
      L(a(x,y,K(z,u)),w,v5) = K(x,L(a(u,y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(14191(a,2),10763(a,1,1))].">
      <j1 rule="para" parents="14191 10763"/>
    </justification>
  </clause>

  <clause id="14217">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(z,K(x,a(w,y,u)))
    ]]></literal>
    <justification jstring="[para(14191(a,1),13347(a,2,2))].">
      <j1 rule="para" parents="14191 13347"/>
    </justification>
  </clause>

  <clause id="14218">
    <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(14191(a,2),13943(a,1,2,2))].">
      <j1 rule="para" parents="14191 13943"/>
    </justification>
  </clause>

  <clause id="14219">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,14190,a(flip),b,14192,a),flip(a)].">
      <j1 rule="hyper" parents="320 14190 14192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14220">
    <literal><![CDATA[
      a(x \ y,x,K(z,u)) = a(u,x,K(y / x,z))
    ]]></literal>
    <justification jstring="[hyper(14188,a,14195,a)].">
      <j1 rule="hyper" parents="14188 14195"/>
    </justification>
  </clause>

  <clause id="14221">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,K(w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(13388,a,14195,a),flip(a)].">
      <j1 rule="hyper" parents="13388 14195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14222">
    <literal><![CDATA[
      a(x,L(x,y,z),K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(13366,a,14195,a),flip(a)].">
      <j1 rule="hyper" parents="13366 14195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14223">
    <literal><![CDATA[
      a(L(x,y,z),x,K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(13365,a,14195,a),flip(a)].">
      <j1 rule="hyper" parents="13365 14195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14224">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(10995,a,14195,a)].">
      <j1 rule="hyper" parents="10995 14195"/>
    </justification>
  </clause>

  <clause id="14225">
    <literal><![CDATA[
      a(x,y * x,K(z,u)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(10902,a,14195,a),flip(a)].">
      <j1 rule="hyper" parents="10902 14195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14226">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(10856,a,14195,a)].">
      <j1 rule="hyper" parents="10856 14195"/>
    </justification>
  </clause>

  <clause id="14227">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(10847,a,14195,a)].">
      <j1 rule="hyper" parents="10847 14195"/>
    </justification>
  </clause>

  <clause id="14228">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(10844,a,14195,a)].">
      <j1 rule="hyper" parents="10844 14195"/>
    </justification>
  </clause>

  <clause id="14229">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,13337,a,b,14195,a)].">
      <j1 rule="hyper" parents="320 13337 14195"/>
    </justification>
  </clause>

  <clause id="14230">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,10997,a,b,14195,a)].">
      <j1 rule="hyper" parents="320 10997 14195"/>
    </justification>
  </clause>

  <clause id="14231">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * x) = a(w,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,9882,a,b,14195,a)].">
      <j1 rule="hyper" parents="320 9882 14195"/>
    </justification>
  </clause>

  <clause id="14232">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,x) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,5859,a,b,14195,a)].">
      <j1 rule="hyper" parents="320 5859 14195"/>
    </justification>
  </clause>

  <clause id="14233">
    <literal><![CDATA[
      a((x \ y) \ z,u,K(w,v5)) = a(v5,u,K(y \ (x * z),w))
    ]]></literal>
    <justification jstring="[hyper(320,a,11766,a(flip),b,14195,a),flip(a)].">
      <j1 rule="hyper" parents="320 11766 14195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14234">
    <literal><![CDATA[
      a(x \ y,z,K(u,w)) = a(w,z,K(u,y \ x))
    ]]></literal>
    <justification jstring="[hyper(320,a,11002,a(flip),b,14195,a),flip(a)].">
      <j1 rule="hyper" parents="320 11002 14195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14235">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,11001,a(flip),b,14195,a),flip(a)].">
      <j1 rule="hyper" parents="320 11001 14195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14236">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,14195,a,b,5864,a)].">
      <j1 rule="hyper" parents="119 14195 5864"/>
    </justification>
  </clause>

  <clause id="14237">
    <literal><![CDATA[
      a(x \ y,z,K(u,w)) = a(u,z,K(y \ x,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,11002,a,b,14195,a),flip(a)].">
      <j1 rule="hyper" parents="58 11002 14195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14238">
    <literal><![CDATA[
      a(x,y,K(z,u \ z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,10999,a,b,14195,a)].">
      <j1 rule="hyper" parents="58 10999 14195"/>
    </justification>
  </clause>

  <clause id="14239">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,10997,a,b,14195,a)].">
      <j1 rule="hyper" parents="58 10997 14195"/>
    </justification>
  </clause>

  <clause id="14240">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,10985,a,b,14195,a)].">
      <j1 rule="hyper" parents="58 10985 14195"/>
    </justification>
  </clause>

  <clause id="14241">
    <literal><![CDATA[
      a((x * y) \ z,u,K(w,v5)) = a(w,u,K(v5,y \ (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,11765,a(flip),b,14195,a),flip(a)].">
      <j1 rule="hyper" parents="58 11765 14195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14242">
    <literal><![CDATA[
      a(L(x,y,z),u,K(w,v5)) = a(w,u,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,11763,a(flip),b,14195,a),flip(a)].">
      <j1 rule="hyper" parents="58 11763 14195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14243">
    <literal><![CDATA[
      a(x * y,z,K(u,x)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,10996,a(flip),b,14195,a),flip(a)].">
      <j1 rule="hyper" parents="58 10996 14195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14244">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,14195,a(flip),b,13346,a)].">
      <j1 rule="hyper" parents="119 14195 13346"/>
    </justification>
  </clause>

  <clause id="14245">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (a(z,y,K(x,u)) * w) = w
    ]]></literal>
    <justification jstring="[hyper(118,a,14195,a(flip),b,9882,a),flip(a)].">
      <j1 rule="hyper" parents="118 14195 9882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14246">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(w,y,K(x,K(z,u)))
    ]]></literal>
    <justification jstring="[para(7730(a,1),14195(a,1,3))].">
      <j1 rule="para" parents="7730 14195"/>
    </justification>
  </clause>

  <clause id="14247">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,y,K(x,K(w,z)))
    ]]></literal>
    <justification jstring="[para(7755(a,1),14195(a,1,3))].">
      <j1 rule="para" parents="7755 14195"/>
    </justification>
  </clause>

  <clause id="14248">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = a(u,y,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(14195(a,2),9881(a,1,1))].">
      <j1 rule="para" parents="14195 9881"/>
    </justification>
  </clause>

  <clause id="14249">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u,y)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14195(a,1),10776(a,1,2))].">
      <j1 rule="para" parents="14195 10776"/>
    </justification>
  </clause>

  <clause id="14250">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14195(a,2),10776(a,1,2))].">
      <j1 rule="para" parents="14195 10776"/>
    </justification>
  </clause>

  <clause id="14251">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,L(z,y,u)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(14195(a,2),10796(a,1,1))].">
      <j1 rule="para" parents="14195 10796"/>
    </justification>
  </clause>

  <clause id="14252">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[para(14195(a,1),10840(a,1,1))].">
      <j1 rule="para" parents="14195 10840"/>
    </justification>
  </clause>

  <clause id="14253">
    <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(14195(a,1),10833(a,1,2))].">
      <j1 rule="para" parents="14195 10833"/>
    </justification>
  </clause>

  <clause id="14254">
    <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(14195(a,2),10833(a,1,2))].">
      <j1 rule="para" parents="14195 10833"/>
    </justification>
  </clause>

  <clause id="14255">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(14195(a,1),13354(a,1,1))].">
      <j1 rule="para" parents="14195 13354"/>
    </justification>
  </clause>

  <clause id="14256">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x * a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(14195(a,1),13529(a,2,2))].">
      <j1 rule="para" parents="14195 13529"/>
    </justification>
  </clause>

  <clause id="14257">
    <literal><![CDATA[
      L(K(x,y),L(z,u,w),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5862,a,14222,a)].">
      <j1 rule="hyper" parents="5862 14222"/>
    </justification>
  </clause>

  <clause id="14258">
    <literal><![CDATA[
      L(K(x,y),z,L(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5862,a,14223,a)].">
      <j1 rule="hyper" parents="5862 14223"/>
    </justification>
  </clause>

  <clause id="14259">
    <literal><![CDATA[
      K(x,(a(y,z,u) \ w) \ v5) = K(x,w \ (a(y,z,u) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,10788,a(flip),b,14200,a),flip(a)].">
      <j1 rule="hyper" parents="58 10788 14200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14260">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,a(w,v5,v6))) = z
    ]]></literal>
    <justification jstring="[para(14200(a,1),10401(a,1))].">
      <j1 rule="para" parents="14200 10401"/>
    </justification>
  </clause>

  <clause id="14262">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(x,y) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,1921,a,b,14219,a)].">
      <j1 rule="hyper" parents="320 1921 14219"/>
    </justification>
  </clause>

  <clause id="14263">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) * K(w,v5) = (x \ L(x,y,z)) * (u * K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(969,a,14221,a)].">
      <j1 rule="hyper" parents="969 14221"/>
    </justification>
  </clause>

  <clause id="14264">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10806,a,14257,a)].">
      <j1 rule="hyper" parents="10806 14257"/>
    </justification>
  </clause>

  <clause id="14265">
    <literal><![CDATA[
      K(x,L(y,z,L(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10806,a,14258,a)].">
      <j1 rule="hyper" parents="10806 14258"/>
    </justification>
  </clause>

  <clause id="14266">
    <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(14207(a,1),6375(a,1,1,1))].">
      <j1 rule="para" parents="14207 6375"/>
    </justification>
  </clause>

  <clause id="14267">
    <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(14207(a,1),6772(a,1,1,1))].">
      <j1 rule="para" parents="14207 6772"/>
    </justification>
  </clause>

  <clause id="14268">
    <literal><![CDATA[
      T(x,a(y * z,u,y)) = x * a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[para(10996(a,1),14209(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10996 14209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14269">
    <literal><![CDATA[
      a(x,x * y,K(z,u)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(14189,a,14225,a)].">
      <j1 rule="hyper" parents="14189 14225"/>
    </justification>
  </clause>

  <clause id="14270">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(14226(a,1),10902(a,1))].">
      <j1 rule="para" parents="14226 10902"/>
    </justification>
  </clause>

  <clause id="14271">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) = x * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(14226(a,1),14209(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14226 14209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14272">
    <literal><![CDATA[
      a(x,y,K(z \ (u * x),w)) = a(w,y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[para(10308(a,1),14230(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10308 14230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14273">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14195,a(flip),b,14235,a),flip(a)].">
      <j1 rule="hyper" parents="320 14195 14235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14274">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[para(14235(a,1),10776(a,1,2))].">
      <j1 rule="para" parents="14235 10776"/>
    </justification>
  </clause>

  <clause id="14275">
    <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(14235(a,1),10833(a,1,2))].">
      <j1 rule="para" parents="14235 10833"/>
    </justification>
  </clause>

  <clause id="14276">
    <literal><![CDATA[
      a(x,y,K(z,x * u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14195,a(flip),b,14240,a)].">
      <j1 rule="hyper" parents="58 14195 14240"/>
    </justification>
  </clause>

  <clause id="14277">
    <literal><![CDATA[
      a(x * y,z,K(u,x)) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,14195,a(flip),b,14243,a),flip(a)].">
      <j1 rule="hyper" parents="320 14195 14243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14278">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,y)) = x \ T(y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,14244,a(flip),b,702,a),flip(a)].">
      <j1 rule="hyper" parents="116 14244 702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14279">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),y) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14244(a,1),10894(a,1,1))].">
      <j1 rule="para" parents="14244 10894"/>
    </justification>
  </clause>

  <clause id="14280">
    <literal><![CDATA[
      T(x * (y * z),a(x,y,z)) = (x * (y * z)) * 1
    ]]></literal>
    <justification jstring="[para(13625(a,1),14244(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13625 14244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14281">
    <literal><![CDATA[
      T(x,a(x * y,z,u)) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14240(a,1),14244(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14240 14244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14282">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = a(y,z,K(u,x)) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,13323,a,b,14255,a)].">
      <j1 rule="hyper" parents="320 13323 14255"/>
    </justification>
  </clause>

  <clause id="14283">
    <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(11763(a,1),14255(a,1,1))].">
      <j1 rule="para" parents="11763 14255"/>
    </justification>
  </clause>

  <clause id="14284">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u * w) = T(u,a(z,y,x)) * w
    ]]></literal>
    <justification jstring="[para(14255(a,1),13310(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14255 13310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14285">
    <literal><![CDATA[
      a(x,y * z,K(u,y)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,14195,a,b,14269,a)].">
      <j1 rule="hyper" parents="58 14195 14269"/>
    </justification>
  </clause>

  <clause id="14286">
    <literal><![CDATA[
      a(K(x,y) / z,u,K(w,v5)) = a(z * K(y,x),u,K(v5,w))
    ]]></literal>
    <justification jstring="[para(13862(a,1),14273(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13862 14273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14287">
    <literal><![CDATA[
      (x * y) * a(y,z,K(u,x)) = T(x * y,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(14277(a,1),14209(a,1,2))].">
      <j1 rule="para" parents="14277 14209"/>
    </justification>
  </clause>

  <clause id="14288">
    <literal><![CDATA[
      T(T(x,y),a(y,z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(435,a,14279,a)].">
      <j1 rule="hyper" parents="435 14279"/>
    </justification>
  </clause>

  <clause id="14289">
    <literal><![CDATA[
      T(x,a(y,z,u)) * y = y * T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,14279,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 14279 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14290">
    <literal><![CDATA[
      a(x,y \ z,K(u,y)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(5(a,1),14285(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 14285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14291">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,14195,a(flip),b,14290,a)].">
      <j1 rule="hyper" parents="58 14195 14290"/>
    </justification>
  </clause>

  <clause id="14292">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14195,a,b,14291,a),flip(a)].">
      <j1 rule="hyper" parents="320 14195 14291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14293">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14195,a(flip),b,14291,a),flip(a)].">
      <j1 rule="hyper" parents="320 14195 14291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14294">
    <literal><![CDATA[
      a(x,y \ z,K(y,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14195,a(flip),b,14292,a)].">
      <j1 rule="hyper" parents="58 14195 14292"/>
    </justification>
  </clause>

  <clause id="14295">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(y,x) \ a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(116,a,14293,a(flip),b,10793,a),flip(a)].">
      <j1 rule="hyper" parents="116 14293 10793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14296">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(x,y) * a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[para(14293(a,1),10776(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14293 10776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14297">
    <literal><![CDATA[
      T(x,a(y,x \ z,u)) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14293(a,1),14209(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14293 14209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14298">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = x * a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[para(14293(a,1),14244(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14293 14244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14299">
    <literal><![CDATA[
      a(x,y * z,K(y,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),14294(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 14294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14300">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,y))) = a(x,z,K(y,K(u,w)))
    ]]></literal>
    <justification jstring="[para(7759(a,2),14299(a,1,3))].">
      <j1 rule="para" parents="7759 14299"/>
    </justification>
  </clause>

  <clause id="14301">
    <literal><![CDATA[
      a(L(x,y,z),u,K(w,v5)) = a(x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,14195,a(flip),b,14242,a),flip(a)].">
      <j1 rule="hyper" parents="320 14195 14242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14302">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,v5))) = K(x,y) * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(14242(a,1),10776(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14242 10776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14303">
    <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(11002(a,1),14270(a,1))].">
      <j1 rule="para" parents="11002 14270"/>
    </justification>
  </clause>

  <clause id="14304">
    <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(13249(a,1),14270(a,1))].">
      <j1 rule="para" parents="13249 14270"/>
    </justification>
  </clause>

  <clause id="14305">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(13596(a,2),14270(a,1))].">
      <j1 rule="para" parents="13596 14270"/>
    </justification>
  </clause>

  <clause id="14306">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(14190(a,2),14270(a,1))].">
      <j1 rule="para" parents="14190 14270"/>
    </justification>
  </clause>

  <clause id="14307">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(x,z)) = w
    ]]></literal>
    <justification jstring="[para(14195(a,1),14270(a,1))].">
      <j1 rule="para" parents="14195 14270"/>
    </justification>
  </clause>

  <clause id="14308">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(14224(a,2),14270(a,1))].">
      <j1 rule="para" parents="14224 14270"/>
    </justification>
  </clause>

  <clause id="14309">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(14273(a,2),14270(a,1))].">
      <j1 rule="para" parents="14273 14270"/>
    </justification>
  </clause>

  <clause id="14310">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(x,z)) = w
    ]]></literal>
    <justification jstring="[para(14291(a,2),14270(a,1))].">
      <j1 rule="para" parents="14291 14270"/>
    </justification>
  </clause>

  <clause id="14311">
    <literal><![CDATA[
      a((x * y) \ z,u,K(w,v5)) = a(y \ (x \ z),u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(298(a,1),14301(a,1,1))].">
      <j1 rule="para" parents="298 14301"/>
    </justification>
  </clause>

  <clause id="14312">
    <literal><![CDATA[
      a((x \ y) \ z,u,K(w,v5)) = a(y \ (x * z),u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(490(a,1),14301(a,1,1)),flip(a)].">
      <j1 rule="para" parents="490 14301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14313">
    <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(14193(a,2),14305(a,1))].">
      <j1 rule="para" parents="14193 14305"/>
    </justification>
  </clause>

  <clause id="14314">
    <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(13333(a,2),14307(a,1))].">
      <j1 rule="para" parents="13333 14307"/>
    </justification>
  </clause>

  <clause id="14315">
    <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(14132(a,1),14307(a,1,3))].">
      <j1 rule="para" parents="14132 14307"/>
    </justification>
  </clause>

  <clause id="14316">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(u,K(x,a(w,y,z)))
    ]]></literal>
    <justification jstring="[para(7754(a,1),14217(a,1,3))].">
      <j1 rule="para" parents="7754 14217"/>
    </justification>
  </clause>

  <clause id="14317">
    <literal><![CDATA[
      a(x,y,K((y * z) / y,u)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[para(4(a,1),14220(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 14220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14318">
    <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,14229,a(flip),b,8927,a)].">
      <j1 rule="hyper" parents="119 14229 8927"/>
    </justification>
  </clause>

  <clause id="14319">
    <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(14231(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="14231 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14320">
    <literal><![CDATA[
      K(L(x,y,z),u) * K(u,x) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[para(10805(a,1),14232(a,1,1))].">
      <j1 rule="para" parents="10805 14232"/>
    </justification>
  </clause>

  <clause id="14321">
    <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(14234(a,2),14307(a,1))].">
      <j1 rule="para" parents="14234 14307"/>
    </justification>
  </clause>

  <clause id="14322">
    <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(8186(a,1),14236(a,1,2,3))].">
      <j1 rule="para" parents="8186 14236"/>
    </justification>
  </clause>

  <clause id="14323">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(5927,a,14245,a),flip(a)].">
      <j1 rule="hyper" parents="5927 14245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14324">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(w,y,K(z,K(x,u)))
    ]]></literal>
    <justification jstring="[para(7754(a,1),14246(a,2,3))].">
      <j1 rule="para" parents="7754 14246"/>
    </justification>
  </clause>

  <clause id="14325">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,y,K(z,K(x,w)))
    ]]></literal>
    <justification jstring="[para(7759(a,1),14247(a,2,3))].">
      <j1 rule="para" parents="7759 14247"/>
    </justification>
  </clause>

  <clause id="14326">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) / w)) = K(x,y) * a(x,z,K(u \ 1,y))
    ]]></literal>
    <justification jstring="[para(5396(a,1),14249(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="5396 14249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14327">
    <literal><![CDATA[
      K(x,L(y,z,K(y,u) * w)) = K(x,y) * a(x,z,K(w,y))
    ]]></literal>
    <justification jstring="[para(7316(a,1),14249(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="7316 14249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14328">
    <literal><![CDATA[
      K(x,L(y,R(z,u,w),z)) = K(x,y) * 1
    ]]></literal>
    <justification jstring="[para(10701(a,1),14249(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10701 14249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14329">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,z,u \ y))
    ]]></literal>
    <justification jstring="[para(11000(a,1),14249(a,1,2))].">
      <j1 rule="para" parents="11000 14249"/>
    </justification>
  </clause>

  <clause id="14330">
    <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(11086(a,1),14249(a,1,2,3))].">
      <j1 rule="para" parents="11086 14249"/>
    </justification>
  </clause>

  <clause id="14331">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u * w,y)) = K(x,L(y,z,u / (w \ 1)))
    ]]></literal>
    <justification jstring="[para(13778(a,1),14249(a,1,2,3))].">
      <j1 rule="para" parents="13778 14249"/>
    </justification>
  </clause>

  <clause id="14332">
    <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(13669(a,1),14249(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="13669 14249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14333">
    <literal><![CDATA[
      K(x,L(y,R(z,u,w),z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(14328(a,2),127(a,1)),flip(b)].">
      <j1 rule="para" parents="14328 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14334">
    <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(8843(a,1),14250(a,1,2,3))].">
      <j1 rule="para" parents="8843 14250"/>
    </justification>
  </clause>

  <clause id="14335">
    <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(14250(a,2),10830(a,1))].">
      <j1 rule="para" parents="14250 10830"/>
    </justification>
  </clause>

  <clause id="14336">
    <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(10886(a,1),14250(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="10886 14250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14337">
    <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(13872(a,1),14250(a,1,2,3))].">
      <j1 rule="para" parents="13872 14250"/>
    </justification>
  </clause>

  <clause id="14338">
    <literal><![CDATA[
      K(x,a(y,z,u) \ x) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(4796,a,14256,a)].">
      <j1 rule="hyper" parents="4796 14256"/>
    </justification>
  </clause>

  <clause id="14339">
    <literal><![CDATA[
      a(x,y,K(z,a(x,y,z) \ u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13375,a(flip),b,14338,a)].">
      <j1 rule="hyper" parents="58 13375 14338"/>
    </justification>
  </clause>

  <clause id="14340">
    <literal><![CDATA[
      T(x,a(y * z,u,y)) = T(x,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,14209,a(flip),b,14268,a),flip(a)].">
      <j1 rule="hyper" parents="320 14209 14268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14341">
    <literal><![CDATA[
      T(x,a(y \ z,u,y)) = T(x,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(5(a,1),14340(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 14340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14342">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,13350,a(flip),b,14271,a),flip(a)].">
      <j1 rule="hyper" parents="320 13350 14271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14343">
    <literal><![CDATA[
      T(x,a(y,y * z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(14186(a,1),14342(a,1,2))].">
      <j1 rule="para" parents="14186 14342"/>
    </justification>
  </clause>

  <clause id="14344">
    <literal><![CDATA[
      T(x,a(y,(z \ y) * u,z)) = T(x,a(z \ y,u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14341,a(flip),b,14343,a)].">
      <j1 rule="hyper" parents="58 14341 14343"/>
    </justification>
  </clause>

  <clause id="14345">
    <literal><![CDATA[
      T(x,a(x * y,z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14209,a(flip),b,14281,a),flip(a)].">
      <j1 rule="hyper" parents="320 14209 14281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14346">
    <literal><![CDATA[
      T(x,a(x \ y,z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),14345(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 14345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14347">
    <literal><![CDATA[
      T(x,a(y,x \ z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14209,a(flip),b,14297,a),flip(a)].">
      <j1 rule="hyper" parents="320 14209 14297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14348">
    <literal><![CDATA[
      T(T(x,y),a(z,x \ u,w)) = T(T(x,a(z,u,w)),y)
    ]]></literal>
    <justification jstring="[para(14347(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14347 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14349">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14244,a(flip),b,14298,a),flip(a)].">
      <j1 rule="hyper" parents="320 14244 14298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14350">
    <literal><![CDATA[
      T(x,a(y,z * u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),14349(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 14349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14351">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(z,K(w,a(u,y,x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14246,a,b,14316,a)].">
      <j1 rule="hyper" parents="58 14246 14316"/>
    </justification>
  </clause>

  <clause id="14352">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(x,K(z,a(u,y,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14247,a(flip),b,14316,a)].">
      <j1 rule="hyper" parents="58 14247 14316"/>
    </justification>
  </clause>

  <clause id="14353">
    <literal><![CDATA[
      a(x,y,K(z,T(u,y))) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[para(7883(a,1),14317(a,1,3))].">
      <j1 rule="para" parents="7883 14317"/>
    </justification>
  </clause>

  <clause id="14354">
    <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(14320(a,1),5110(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14320 5110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14355">
    <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(320,a,10808,a(flip),b,14323,a),flip(a)].">
      <j1 rule="hyper" parents="320 10808 14323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14356">
    <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(14323(a,1),39(a,1))].">
      <j1 rule="para" parents="14323 39"/>
    </justification>
  </clause>

  <clause id="14357">
    <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(14323(a,2),10816(a,1))].">
      <j1 rule="para" parents="14323 10816"/>
    </justification>
  </clause>

  <clause id="14358">
    <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(10938,a,14325,a)].">
      <j1 rule="hyper" parents="10938 14325"/>
    </justification>
  </clause>

  <clause id="14359">
    <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,14301,a,b,14351,a)].">
      <j1 rule="hyper" parents="58 14301 14351"/>
    </justification>
  </clause>

  <clause id="14360">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u != w
    ]]></literal>
    <literal><![CDATA[
      T(u,a(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(14195(a,2),14214(a,1,1))].">
      <j1 rule="para" parents="14195 14214"/>
    </justification>
  </clause>

  <clause id="14361">
    <literal><![CDATA[
      T(x * (y * z),a(x,y,z)) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3,a(flip),b,14280,a),flip(a)].">
      <j1 rule="hyper" parents="320 3 14280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14363">
    <literal><![CDATA[
      a(x,y,z) * (x * (y * z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,14361,a(flip),b,684,a(flip))].">
      <j1 rule="hyper" parents="119 14361 684"/>
    </justification>
  </clause>

  <clause id="14364">
    <literal><![CDATA[
      a(x,y,z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(14361(a,1),685(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14361 685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14365">
    <literal><![CDATA[
      (x * (y * z)) / (y * (z * T(x,y * z))) = a(y,z,T(x,y * z))
    ]]></literal>
    <justification jstring="[hyper(117,a,105,a(flip),b,14363,a)].">
      <j1 rule="hyper" parents="117 105 14363"/>
    </justification>
  </clause>

  <clause id="14367">
    <literal><![CDATA[
      a(x,y,z) = (z * (x * y)) / ((x * (y * z)) * K(z,x * y))
    ]]></literal>
    <justification jstring="[hyper(320,a,14148,a,b,14364,a),flip(a)].">
      <j1 rule="hyper" parents="320 14148 14364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14368">
    <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(13450,a,14364,a(flip))].">
      <j1 rule="hyper" parents="13450 14364"/>
    </justification>
  </clause>

  <clause id="14369">
    <literal><![CDATA[
      ((x * y) * z) / (y * (T(x,y) * z)) = a(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[para(105(a,1),14364(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="105 14364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14371">
    <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(10344(a,2),14308(a,1,3))].">
      <j1 rule="para" parents="10344 14308"/>
    </justification>
  </clause>

  <clause id="14372">
    <literal><![CDATA[
      a(x,y,K(z,x \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(14195(a,1),14308(a,1))].">
      <j1 rule="para" parents="14195 14308"/>
    </justification>
  </clause>

  <clause id="14373">
    <literal><![CDATA[
      a(x,y \ z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(14195(a,1),14310(a,1))].">
      <j1 rule="para" parents="14195 14310"/>
    </justification>
  </clause>

  <clause id="14374">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = a(z,y,u) * (x / a(z,y,u))
    ]]></literal>
    <justification jstring="[para(14339(a,1),13378(a,1,1))].">
      <j1 rule="para" parents="14339 13378"/>
    </justification>
  </clause>

  <clause id="14375">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u * z) != w
    ]]></literal>
    <literal><![CDATA[
      T(u * z,a(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(10998(a,1),14360(a,1,1))].">
      <j1 rule="para" parents="10998 14360"/>
    </justification>
  </clause>

  <clause id="14376">
    <literal><![CDATA[
      T(1 / x,a(y,z,u)) = a(x,z,K(y,u)) / x
    ]]></literal>
    <justification jstring="[para(14273(a,1),14210(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14273 14210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14377">
    <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,11762,a,b,14216,a)].">
      <j1 rule="hyper" parents="58 11762 14216"/>
    </justification>
  </clause>

  <clause id="14378">
    <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(7031(a,1),14274(a,1,2,3))].">
      <j1 rule="para" parents="7031 14274"/>
    </justification>
  </clause>

  <clause id="14379">
    <literal><![CDATA[
      T(x,a(y,z,u)) * a(u,z,y) = a(u,z,y) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,13376,a(flip),b,14284,a),flip(a)].">
      <j1 rule="hyper" parents="58 13376 14284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14380">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),a(u,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(239,a,14284,a(flip),b,13376,a(flip))].">
      <j1 rule="hyper" parents="239 14284 13376"/>
    </justification>
  </clause>

  <clause id="14381">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),L(u,z,y)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(14380(a,1),14279(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14380 14279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14382">
    <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(14381(a,1),12211(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14381 12211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14383">
    <literal><![CDATA[
      T(x * y,a(x,z,u)) = x * T(y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14208,a(flip),b,14287,a),flip(a)].">
      <j1 rule="hyper" parents="58 14208 14287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14384">
    <literal><![CDATA[
      T(x,a(y,z,u)) / y = T(x / y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(4543,a,14383,a)].">
      <j1 rule="hyper" parents="4543 14383"/>
    </justification>
  </clause>

  <clause id="14385">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,10776,a(flip),b,14296,a),flip(a)].">
      <j1 rule="hyper" parents="320 10776 14296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14386">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(14296(a,2),10833(a,1))].">
      <j1 rule="para" parents="14296 10833"/>
    </justification>
  </clause>

  <clause id="14387">
    <literal><![CDATA[
      K(x,(y * ((y \ z) / u)) \ z) = K(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(10799,a,14385,a)].">
      <j1 rule="hyper" parents="10799 14385"/>
    </justification>
  </clause>

  <clause id="14388">
    <literal><![CDATA[
      K(x,L(y \ (z \ u),u,z)) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(10798,a,14385,a),flip(a)].">
      <j1 rule="hyper" parents="10798 14385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14389">
    <literal><![CDATA[
      T(x,L(y,z \ u,z)) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,14385,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 14385 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14390">
    <literal><![CDATA[
      K(x,L(y,z * u,z)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),14385(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 14385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14391">
    <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(704(a,1),14385(a,1,2,2))].">
      <j1 rule="para" parents="704 14385"/>
    </justification>
  </clause>

  <clause id="14392">
    <literal><![CDATA[
      K(x,L((y \ z) \ u,z,y)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(490(a,1),14385(a,1,2)),flip(a)].">
      <j1 rule="para" parents="490 14385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14393">
    <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(4025(a,1),14385(a,1,2,2))].">
      <j1 rule="para" parents="4025 14385"/>
    </justification>
  </clause>

  <clause id="14394">
    <literal><![CDATA[
      K(x,L(y \ z,u,y \ u)) = K(x,u \ ((u / y) * z))
    ]]></literal>
    <justification jstring="[para(6975(a,1),14385(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6975 14385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14395">
    <literal><![CDATA[
      x * K(y,L(z,x,u)) = u * ((u \ x) * K(y,z))
    ]]></literal>
    <justification jstring="[para(14385(a,1),10783(a,1,2))].">
      <j1 rule="para" parents="14385 10783"/>
    </justification>
  </clause>

  <clause id="14396">
    <literal><![CDATA[
      K(x,L(y,z,u \ z)) = K(x,L(y,u,u \ z))
    ]]></literal>
    <justification jstring="[para(11149(a,1),14385(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11149 14385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14397">
    <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(13762(a,1),14389(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13762 14389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14398">
    <literal><![CDATA[
      K(x,L(y,z * u,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(13216(a,2),14390(a,1,2))].">
      <j1 rule="para" parents="13216 14390"/>
    </justification>
  </clause>

  <clause id="14399">
    <literal><![CDATA[
      K(x,y \ ((y / z) * (u * z))) = K(x,L(T(u,z),y,z \ y))
    ]]></literal>
    <justification jstring="[para(11165(a,1),14396(a,2,2)),flip(a)].">
      <j1 rule="para" parents="11165 14396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14400">
    <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(13952(a,1),14396(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="13952 14396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14401">
    <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(11149(a,1),14386(a,1,2))].">
      <j1 rule="para" parents="11149 14386"/>
    </justification>
  </clause>

  <clause id="14402">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(14387(a,1),10835(a,1))].">
      <j1 rule="para" parents="14387 10835"/>
    </justification>
  </clause>

  <clause id="14403">
    <literal><![CDATA[
      K(x,(y * z) \ L(y,u,w)) = K(x,z \ (y \ L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14264,a(flip),b,14388,a),flip(a)].">
      <j1 rule="hyper" parents="58 14264 14388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14404">
    <literal><![CDATA[
      K(x,(y \ R(y,z,u)) \ w) = K(x,R(y,z,u) \ (y * w))
    ]]></literal>
    <justification jstring="[hyper(14333,a,14392,a)].">
      <j1 rule="hyper" parents="14333 14392"/>
    </justification>
  </clause>

  <clause id="14405">
    <literal><![CDATA[
      x \ (K(y,L(z,u,x)) * u) = (x \ u) * K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(8500,a,14395,a)].">
      <j1 rule="hyper" parents="8500 14395"/>
    </justification>
  </clause>

  <clause id="14406">
    <literal><![CDATA[
      x \ (y * K(z,L(u,y,x))) = (x \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(536,a,14395,a)].">
      <j1 rule="hyper" parents="536 14395"/>
    </justification>
  </clause>

  <clause id="14407">
    <literal><![CDATA[
      x \ (y * K(z,T(y,u))) = (x \ y) * K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(10777(a,1),14406(a,1,2,2))].">
      <j1 rule="para" parents="10777 14406"/>
    </justification>
  </clause>

  <clause id="14408">
    <literal><![CDATA[
      L(x,y,z) \ (x * K(u,w)) = (L(x,y,z) \ x) * K(u,w)
    ]]></literal>
    <justification jstring="[para(14265(a,1),14406(a,1,2,2))].">
      <j1 rule="para" parents="14265 14406"/>
    </justification>
  </clause>

  <clause id="14409">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,y))) = a(x,z,K(u,K(w,y)))
    ]]></literal>
    <justification jstring="[para(7759(a,2),14300(a,2,3))].">
      <j1 rule="para" parents="7759 14300"/>
    </justification>
  </clause>

  <clause id="14410">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = K(x,L(y,z,u \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,14274,a(flip),b,14329,a)].">
      <j1 rule="hyper" parents="58 14274 14329"/>
    </justification>
  </clause>

  <clause id="14411">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u \ w,y)) = K(x,L(y,z,(w \ u) \ y))
    ]]></literal>
    <justification jstring="[para(11002(a,2),14329(a,1,2))].">
      <j1 rule="para" parents="11002 14329"/>
    </justification>
  </clause>

  <clause id="14412">
    <literal><![CDATA[
      T(x,a(y,(z \ y) * u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14341,a(flip),b,14344,a),flip(a)].">
      <j1 rule="hyper" parents="320 14341 14344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14413">
    <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(14377(a,1),14313(a,1))].">
      <j1 rule="para" parents="14377 14313"/>
    </justification>
  </clause>

  <clause id="14414">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = (y \ x) * K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,14179,a,b,14407,a)].">
      <j1 rule="hyper" parents="58 14179 14407"/>
    </justification>
  </clause>

  <clause id="14415">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = K(z,x) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,8218,a(flip),b,14414,a),flip(a)].">
      <j1 rule="hyper" parents="320 8218 14414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14416">
    <literal><![CDATA[
      T(x * K(y,z),x \ z) = K(y,z) * ((x \ z) \ z)
    ]]></literal>
    <justification jstring="[para(72(a,1),14415(a,1,1,1))].">
      <j1 rule="para" parents="72 14415"/>
    </justification>
  </clause>

  <clause id="14417">
    <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(11000(a,1),14253(a,1,2))].">
      <j1 rule="para" parents="11000 14253"/>
    </justification>
  </clause>

  <clause id="14418">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,v5))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14250,a(flip),b,14302,a),flip(a)].">
      <j1 rule="hyper" parents="320 14250 14302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14419">
    <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(14302(a,2),14254(a,1))].">
      <j1 rule="para" parents="14302 14254"/>
    </justification>
  </clause>

  <clause id="14420">
    <literal><![CDATA[
      K(x,L(y,z \ 1,L(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,13712,a(flip),b,14418,a),flip(a)].">
      <j1 rule="hyper" parents="320 13712 14418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14421">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ u)) = K(x,L(y,z,w \ 1))
    ]]></literal>
    <justification jstring="[para(217(a,1),14418(a,1,2,3))].">
      <j1 rule="para" parents="217 14418"/>
    </justification>
  </clause>

  <clause id="14422">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ v5)) = K(x,L(y,z,w \ (u \ v5)))
    ]]></literal>
    <justification jstring="[para(298(a,1),14418(a,1,2,3))].">
      <j1 rule="para" parents="298 14418"/>
    </justification>
  </clause>

  <clause id="14423">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ 1)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[para(390(a,1),14418(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="390 14418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14424">
    <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(2491(a,1),14420(a,1,2))].">
      <j1 rule="para" parents="2491 14420"/>
    </justification>
  </clause>

  <clause id="14425">
    <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(217(a,1),14419(a,1,2,3))].">
      <j1 rule="para" parents="217 14419"/>
    </justification>
  </clause>

  <clause id="14426">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ y)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14410,a(flip),b,14423,a)].">
      <j1 rule="hyper" parents="58 14410 14423"/>
    </justification>
  </clause>

  <clause id="14427">
    <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(14314,a,13968,a),flip(a)].">
      <j1 rule="hyper" parents="14314 13968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14428">
    <literal><![CDATA[
      a(x,y,z) = ((y * x) * z) / (x * (T(y,x) * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14184,a(flip),b,14369,a)].">
      <j1 rule="hyper" parents="320 14184 14369"/>
    </justification>
  </clause>

  <clause id="14429">
    <literal><![CDATA[
      a(x,y,z) \ ((y * x) * z) = x * (T(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(188,a,14428,a(flip))].">
      <j1 rule="hyper" parents="188 14428"/>
    </justification>
  </clause>

  <clause id="14430">
    <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(320,a,631,a(flip),b,14429,a),flip(a)].">
      <j1 rule="hyper" parents="320 631 14429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14431">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (K(u,z) * w) = K(u,L(z,y,x)) * w
    ]]></literal>
    <justification jstring="[para(10840(a,1),14201(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10840 14201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14432">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) \ v5 = w \ (a(u,y,K(z,x)) * v5)
    ]]></literal>
    <justification jstring="[para(14248(a,1),14203(a,2,2))].">
      <j1 rule="para" parents="14248 14203"/>
    </justification>
  </clause>

  <clause id="14433">
    <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(14233(a,2),14270(a,1))].">
      <j1 rule="para" parents="14233 14270"/>
    </justification>
  </clause>

  <clause id="14434">
    <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(14241(a,2),14307(a,1))].">
      <j1 rule="para" parents="14241 14307"/>
    </justification>
  </clause>

  <clause id="14435">
    <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(320,a,20,a,b,14283,a),flip(a)].">
      <j1 rule="hyper" parents="320 20 14283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14436">
    <literal><![CDATA[
      K(x,L(y,z,K(y,u) * w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,14249,a(flip),b,14327,a),flip(a)].">
      <j1 rule="hyper" parents="320 14249 14327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14437">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ (y * u)) = K(x,a(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(704(a,1),14404(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="704 14404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14438">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(u,w) = x * (L(x,y,z) \ K(u,w))
    ]]></literal>
    <justification jstring="[hyper(1413,a,14408,a),flip(a)].">
      <j1 rule="hyper" parents="1413 14408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14439">
    <literal><![CDATA[
      x / K(y,L(z,u,K(y,z) \ (u \ x))) = (x / (u * K(y,z))) * u
    ]]></literal>
    <justification jstring="[para(14422(a,1),14072(a,1,2))].">
      <j1 rule="para" parents="14422 14072"/>
    </justification>
  </clause>

  <clause id="14440">
    <literal><![CDATA[
      K(x,y) / (z * (L(z,u,w) \ K(x,y))) = (L(z,u,w) \ z) \ 1
    ]]></literal>
    <justification jstring="[para(14438(a,1),13810(a,1,2))].">
      <j1 rule="para" parents="14438 13810"/>
    </justification>
  </clause>

  <clause id="14441">
    <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(14196(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="14196 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14442">
    <literal><![CDATA[
      a(x,y,z) = (z * (x * y)) / (L(z,y,x) * (x * y))
    ]]></literal>
    <justification jstring="[para(14000(a,1),14367(a,2,2))].">
      <j1 rule="para" parents="14000 14367"/>
    </justification>
  </clause>

  <clause id="14443">
    <literal><![CDATA[
      a(x,y,z) \ (z * (x * y)) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(188,a,14442,a(flip))].">
      <j1 rule="hyper" parents="188 14442"/>
    </justification>
  </clause>

  <clause id="14444">
    <literal><![CDATA[
      (x * (y * z)) / (L(x,z,y) * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,x) = u
    ]]></literal>
    <justification jstring="[para(14443(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14443 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14445">
    <literal><![CDATA[
      T(x * y,a(y,z,u)) = T(x,a(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(14375,a,14284,a)].">
      <j1 rule="hyper" parents="14375 14284"/>
    </justification>
  </clause>

  <clause id="14446">
    <literal><![CDATA[
      T(x * y,a(y,z,u)) = y * T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14289,a(flip),b,14445,a),flip(a)].">
      <j1 rule="hyper" parents="320 14289 14445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14447">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u \ x)) = (x / u) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(14399(a,1),11193(a,1,2))].">
      <j1 rule="para" parents="14399 11193"/>
    </justification>
  </clause>

  <clause id="14448">
    <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(14396(a,1),14425(a,1))].">
      <j1 rule="para" parents="14396 14425"/>
    </justification>
  </clause>

  <clause id="14449">
    <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(13681(a,1),14447(a,2,2))].">
      <j1 rule="para" parents="13681 14447"/>
    </justification>
  </clause>

  <clause id="14450">
    <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(14326(a,2),14253(a,1))].">
      <j1 rule="para" parents="14326 14253"/>
    </justification>
  </clause>

  <clause id="14451">
    <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(14331(a,1),14253(a,1))].">
      <j1 rule="para" parents="14331 14253"/>
    </justification>
  </clause>

  <clause id="14452">
    <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),14355(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="91 14355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14453">
    <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(7754(a,1),14355(a,1,1,3))].">
      <j1 rule="para" parents="7754 14355"/>
    </justification>
  </clause>

  <clause id="14454">
    <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(8148(a,1),14355(a,1,1,3))].">
      <j1 rule="para" parents="8148 14355"/>
    </justification>
  </clause>

  <clause id="14455">
    <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(7772(a,1),14358(a,1,2))].">
      <j1 rule="para" parents="7772 14358"/>
    </justification>
  </clause>

  <clause id="14456">
    <literal><![CDATA[
      K(x,L(y,a(z,u,u \ 1),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14333,a,14391,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14333 14391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14457">
    <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(10910,a,14456,a)].">
      <j1 rule="hyper" parents="10910 14456"/>
    </justification>
  </clause>

  <clause id="14458">
    <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(14411(a,1),14253(a,1))].">
      <j1 rule="para" parents="14411 14253"/>
    </justification>
  </clause>

  <clause id="14459">
    <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(14410(a,2),14458(a,1))].">
      <j1 rule="para" parents="14410 14458"/>
    </justification>
  </clause>

  <clause id="14460">
    <literal><![CDATA[
      a(T(x,y),z,K(u,x * y)) = K(L(x,z,u) * y,x * y)
    ]]></literal>
    <justification jstring="[para(237(a,1),14427(a,1,1)),flip(a)].">
      <j1 rule="para" parents="237 14427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14461">
    <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,11489,a(flip),b,14455,a)].">
      <j1 rule="hyper" parents="58 11489 14455"/>
    </justification>
  </clause>

  <clause id="14462">
    <literal><![CDATA[
      K(a(x,y * z,K(z,u)),w) = a(z,y,K(w,K(x,u)))
    ]]></literal>
    <justification jstring="[para(6581(a,1),14461(a,1,1))].">
      <j1 rule="para" parents="6581 14461"/>
    </justification>
  </clause>

  <clause id="14463">
    <literal><![CDATA[
      K(a(x,y * z,K(z,u)),w) = a(z,y,K(w,K(u,x)))
    ]]></literal>
    <justification jstring="[para(7772(a,1),14462(a,2,3))].">
      <j1 rule="para" parents="7772 14462"/>
    </justification>
  </clause>

  <clause id="14464">
    <literal><![CDATA[
      K(x * y,(x * y) \ (z \ ((z * x) * y))) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,13604,a(flip),b,14211,a),flip(a)].">
      <j1 rule="hyper" parents="320 13604 14211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14466">
    <literal><![CDATA[
      K(x * y,z \ R(z,x,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,10312,a(flip),b,14464,a)].">
      <j1 rule="hyper" parents="58 10312 14464"/>
    </justification>
  </clause>

  <clause id="14467">
    <literal><![CDATA[
      T(x \ R(x,y,z),y * z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(4913,a,14466,a)].">
      <j1 rule="hyper" parents="4913 14466"/>
    </justification>
  </clause>

  <clause id="14468">
    <literal><![CDATA[
      (x * (y * z)) / (L(x,z,y) * (y * z)) = a(y,z,T(x,y * z))
    ]]></literal>
    <justification jstring="[para(631(a,1),14365(a,1,2))].">
      <j1 rule="para" parents="631 14365"/>
    </justification>
  </clause>

  <clause id="14469">
    <literal><![CDATA[
      a(x,y,T(z,x * y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(14444,a,14468,a),flip(a)].">
      <j1 rule="hyper" parents="14444 14468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14470">
    <literal><![CDATA[
      x / K(y,L(z,u,K(z,y) * (u \ x))) = (x / (u * K(y,z))) * u
    ]]></literal>
    <justification jstring="[para(5092(a,1),14439(a,1,2,2,3))].">
      <j1 rule="para" parents="5092 14439"/>
    </justification>
  </clause>

  <clause id="14471">
    <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(14421(a,1),14448(a,1))].">
      <j1 rule="para" parents="14421 14448"/>
    </justification>
  </clause>

  <clause id="14472">
    <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(13237(a,1),14471(a,1,2))].">
      <j1 rule="para" parents="13237 14471"/>
    </justification>
  </clause>

  <clause id="14473">
    <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(14410(a,1),14471(a,1))].">
      <j1 rule="para" parents="14410 14471"/>
    </justification>
  </clause>

  <clause id="14474">
    <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(14421(a,2),14471(a,1))].">
      <j1 rule="para" parents="14421 14471"/>
    </justification>
  </clause>

  <clause id="14475">
    <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(14472,a,13422,a)].">
      <j1 rule="hyper" parents="14472 13422"/>
    </justification>
  </clause>

  <clause id="14476">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,L((y * z) \ u,z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(14472,a,10780,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14472 10780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14477">
    <literal><![CDATA[
      K(x,L(y,z * u,z \ 1)) = K(x,L(y,u,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(14472,a,xx),flip(a)].">
      <j1 rule="hyper" parents="14472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14478">
    <literal><![CDATA[
      K(x,L(y,z \ u,z \ 1)) = K(x,L(y,u,z \ 1))
    ]]></literal>
    <justification jstring="[para(5(a,1),14477(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 14477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14479">
    <literal><![CDATA[
      K(x,(y * z) \ R(y,u,u \ 1)) = K(x,z \ a(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[para(706(a,1),14457(a,1,2))].">
      <j1 rule="para" parents="706 14457"/>
    </justification>
  </clause>

  <clause id="14480">
    <literal><![CDATA[
      x / K(y,L(z,u,u \ x)) = (x / (u * K(y,z))) * u
    ]]></literal>
    <justification jstring="[para(14436(a,1),14470(a,1,2))].">
      <j1 rule="para" parents="14436 14470"/>
    </justification>
  </clause>

  <clause id="14481">
    <literal><![CDATA[
      (x / (y * K(z,u))) * y = (x / y) * (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(14107,a,14480,a),flip(a)].">
      <j1 rule="hyper" parents="14107 14480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14483">
    <literal><![CDATA[
      ((x * y) / (y * K(z,u))) * y = x * (y * K(u,z))
    ]]></literal>
    <justification jstring="[para(6(a,1),14481(a,2,1))].">
      <j1 rule="para" parents="6 14481"/>
    </justification>
  </clause>

  <clause id="14484">
    <literal><![CDATA[
      (x / y) * (y * K(z,T(u,y))) = (x / (K(u,z) * y)) * y
    ]]></literal>
    <justification jstring="[para(7123(a,1),14481(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7123 14481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14485">
    <literal><![CDATA[
      (x / ((y \ 1) * K(z,u))) * (y \ 1) = (x / (y \ 1)) * (y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(13747(a,1),14481(a,2,2))].">
      <j1 rule="para" parents="13747 14481"/>
    </justification>
  </clause>

  <clause id="14486">
    <literal><![CDATA[
      (x * (y * K(z,u))) / y = (x * y) / (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,14483,a)].">
      <j1 rule="hyper" parents="131 14483"/>
    </justification>
  </clause>

  <clause id="14487">
    <literal><![CDATA[
      (x * (y * K(z,u))) / y != w
    ]]></literal>
    <literal><![CDATA[
      (x * y) / (y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(14483(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="14483 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14488">
    <literal><![CDATA[
      (x / (K(y,z) * u)) * u = (x / u) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7274,a(flip),b,14484,a),flip(a)].">
      <j1 rule="hyper" parents="58 7274 14484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14489">
    <literal><![CDATA[
      (x / (K(y,z) * (1 / u))) * (1 / u) = (x / (1 / u)) * (K(z,y) / u)
    ]]></literal>
    <justification jstring="[para(13647(a,1),14488(a,2,2))].">
      <j1 rule="para" parents="13647 14488"/>
    </justification>
  </clause>

  <clause id="14490">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) * (v5 \ 1)))) = K(x,y * (z / (K(u,w) / v5)))
    ]]></literal>
    <justification jstring="[para(14137(a,1),13868(a,1,2,2,2))].">
      <j1 rule="para" parents="14137 13868"/>
    </justification>
  </clause>

  <clause id="14491">
    <literal><![CDATA[
      T(x,T((y / z) \ K(y,u),w)) = T(x,T((z / y) * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(13708(a,1),13936(a,1,2,1))].">
      <j1 rule="para" parents="13708 13936"/>
    </justification>
  </clause>

  <clause id="14492">
    <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),14026(a,1,2)),flip(a)].">
      <j1 rule="para" parents="60 14026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14493">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) * x,u)) = K(x,x * ((y * T(z,u)) \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,5346,a(flip),b,14492,a),flip(a)].">
      <j1 rule="hyper" parents="320 5346 14492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14494">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) * x,u)) = K(x,T(z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,10448,a(flip),b,14493,a),flip(a)].">
      <j1 rule="hyper" parents="320 10448 14493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14496">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) * x,u)) = K(x,T(z \ x,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,8541,a,b,14494,a),flip(a)].">
      <j1 rule="hyper" parents="320 8541 14494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14497">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,u)) = K(x,T((z \ y) * x,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),14496(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 14496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14498">
    <literal><![CDATA[
      K(x,T((y \ z) * x,z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(9163,a,14497,a),flip(a)].">
      <j1 rule="hyper" parents="9163 14497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14499">
    <literal><![CDATA[
      K(x,T(x * (y \ z),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(12276,a,14498,a)].">
      <j1 rule="hyper" parents="12276 14498"/>
    </justification>
  </clause>

  <clause id="14500">
    <literal><![CDATA[
      K(x,T((y \ z) * x,y)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9676,a(flip),b,14498,a)].">
      <j1 rule="hyper" parents="58 9676 14498"/>
    </justification>
  </clause>

  <clause id="14501">
    <literal><![CDATA[
      K(x,T(x * T(y,z),z)) = K(x,((y \ z) / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11439,a(flip),b,14499,a)].">
      <j1 rule="hyper" parents="58 11439 14499"/>
    </justification>
  </clause>

  <clause id="14502">
    <literal><![CDATA[
      K(x,(y / (y * z)) \ x) = K(x,T(z * x,y))
    ]]></literal>
    <justification jstring="[para(4(a,1),14500(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4 14500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14503">
    <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(9016,a,14502,a)].">
      <j1 rule="hyper" parents="9016 14502"/>
    </justification>
  </clause>

  <clause id="14504">
    <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(14501(a,2),6716(a,1,1))].">
      <j1 rule="para" parents="14501 6716"/>
    </justification>
  </clause>

  <clause id="14505">
    <literal><![CDATA[
      ((x * ((x * y) / x)) / z) \ y = ((x * y) / z) \ T(y,T(x,y))
    ]]></literal>
    <justification jstring="[para(105(a,1),14042(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="105 14042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14506">
    <literal><![CDATA[
      ((x * ((x * y) / x)) / z) \ y = ((x * y) / z) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4193(a,1),14505(a,2,2))].">
      <j1 rule="para" parents="4193 14505"/>
    </justification>
  </clause>

  <clause id="14507">
    <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(9536(a,2),14110(a,1,2,2))].">
      <j1 rule="para" parents="9536 14110"/>
    </justification>
  </clause>

  <clause id="14508">
    <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(10114(a,1),14110(a,1,2,1,1))].">
      <j1 rule="para" parents="10114 14110"/>
    </justification>
  </clause>

  <clause id="14509">
    <literal><![CDATA[
      K(x,L(y,z,u \ L(u,w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10871,a,14263,a)].">
      <j1 rule="hyper" parents="10871 14263"/>
    </justification>
  </clause>

  <clause id="14510">
    <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(14509(a,2),14260(a,1))].">
      <j1 rule="para" parents="14509 14260"/>
    </justification>
  </clause>

  <clause id="14511">
    <literal><![CDATA[
      K(x,y \ L(y,z,u)) = 1 * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(13194(a,1),14318(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13194 14318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14513">
    <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(14322(a,1),14335(a,1))].">
      <j1 rule="para" parents="14322 14335"/>
    </justification>
  </clause>

  <clause id="14514">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u / w,y)) = K(x,L(y,z,u / (y * w)))
    ]]></literal>
    <justification jstring="[para(10982(a,1),14330(a,1,2))].">
      <j1 rule="para" parents="10982 14330"/>
    </justification>
  </clause>

  <clause id="14515">
    <literal><![CDATA[
      K(x,L(L(y,z,u),z,u \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14354,a,14378,a),flip(a)].">
      <j1 rule="hyper" parents="14354 14378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14516">
    <literal><![CDATA[
      K(x,L(L(y,z,u \ 1),z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(25(a,1),14515(a,1,2))].">
      <j1 rule="para" parents="25 14515"/>
    </justification>
  </clause>

  <clause id="14517">
    <literal><![CDATA[
      K(x,L((y * z) \ u,z,y \ 1)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(298(a,1),14515(a,1,2,1))].">
      <j1 rule="para" parents="298 14515"/>
    </justification>
  </clause>

  <clause id="14518">
    <literal><![CDATA[
      x * (y * K(z,L(u,y,x \ 1))) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14515(a,1),10870(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14515 10870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14519">
    <literal><![CDATA[
      (x \ y) * K(z,L(u,y,x \ 1)) = x \ (y * K(z,u))
    ]]></literal>
    <justification jstring="[para(14516(a,1),14406(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14516 14406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14520">
    <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),14517(a,1,2,1))].">
      <j1 rule="para" parents="17 14517"/>
    </justification>
  </clause>

  <clause id="14521">
    <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),14517(a,1,2,1))].">
      <j1 rule="para" parents="81 14517"/>
    </justification>
  </clause>

  <clause id="14522">
    <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,7152,a(flip),b,14518,a),flip(a)].">
      <j1 rule="hyper" parents="116 7152 14518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14524">
    <literal><![CDATA[
      x * (y * K(z,L(u,y,x \ u))) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14410(a,1),14518(a,1,2,2))].">
      <j1 rule="para" parents="14410 14518"/>
    </justification>
  </clause>

  <clause id="14525">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(29,a,10900,a(flip),b,14519,a),flip(a)].">
      <j1 rule="hyper" parents="29 10900 14519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14527">
    <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(14056(a,1),14524(a,2,1))].">
      <j1 rule="para" parents="14056 14524"/>
    </justification>
  </clause>

  <clause id="14528">
    <literal><![CDATA[
      x * K(y,x \ (z \ (u * (z * x)))) = z \ (K(y,u) * (z * x))
    ]]></literal>
    <justification jstring="[para(14520(a,1),14522(a,1,2))].">
      <j1 rule="para" parents="14520 14522"/>
    </justification>
  </clause>

  <clause id="14529">
    <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),14528(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="101 14528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14530">
    <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(9683(a,1),14441(a,1))].">
      <j1 rule="para" parents="9683 14441"/>
    </justification>
  </clause>

  <clause id="14531">
    <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,14453,a(flip),b,14454,a),flip(a)].">
      <j1 rule="hyper" parents="58 14453 14454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14532">
    <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),14531(a,1,2,2,3)),flip(a)].">
      <j1 rule="para" parents="75 14531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14533">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14517,a(flip),b,14476,a),flip(a)].">
      <j1 rule="hyper" parents="320 14517 14476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14534">
    <literal><![CDATA[
      (x / (K(y,z) / u)) * (1 / u) = (x / (1 / u)) * (K(z,y) / u)
    ]]></literal>
    <justification jstring="[para(13647(a,1),14489(a,1,1,2))].">
      <j1 rule="para" parents="13647 14489"/>
    </justification>
  </clause>

  <clause id="14536">
    <literal><![CDATA[
      ((x * (y * z)) * K(z,u)) \ ((x * y) * T(z,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(9195(a,1),13972(a,1,1))].">
      <j1 rule="para" parents="9195 13972"/>
    </justification>
  </clause>

  <clause id="14537">
    <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(10763(a,1),13999(a,1,1))].">
      <j1 rule="para" parents="10763 13999"/>
    </justification>
  </clause>

  <clause id="14538">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),T(x,z)) = K(y * K((x \ 1) \ y,z),x)
    ]]></literal>
    <justification jstring="[hyper(14090,a,11215,a),flip(a)].">
      <j1 rule="hyper" parents="14090 11215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14539">
    <literal><![CDATA[
      K(x * K((y \ 1) \ x,z),y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(14089,a,14538,a),flip(a)].">
      <j1 rule="hyper" parents="14089 14538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14541">
    <literal><![CDATA[
      K(x * K(y * x,z),y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(13729(a,1),14539(a,1,1,2))].">
      <j1 rule="para" parents="13729 14539"/>
    </justification>
  </clause>

  <clause id="14542">
    <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,14541,a(flip),b,5247,a(flip))].">
      <j1 rule="hyper" parents="119 14541 5247"/>
    </justification>
  </clause>

  <clause id="14543">
    <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(7754(a,1),14357(a,1,1,3))].">
      <j1 rule="para" parents="7754 14357"/>
    </justification>
  </clause>

  <clause id="14544">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) \ w) = K(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(13983,a,14424,a)].">
      <j1 rule="hyper" parents="13983 14424"/>
    </justification>
  </clause>

  <clause id="14546">
    <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(3485(a,1),14544(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3485 14544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14547">
    <literal><![CDATA[
      x * K(y,x \ (z \ ((u * z) * x))) = z \ ((K(y,u) * z) * x)
    ]]></literal>
    <justification jstring="[para(12454(a,1),14529(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12454 14529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14548">
    <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,14547,a(flip),b,4205,a)].">
      <j1 rule="hyper" parents="116 14547 4205"/>
    </justification>
  </clause>

  <clause id="14549">
    <literal><![CDATA[
      K(x,L(y,z,u)) * T(u * (z / y),K(x,y)) = u * (z / T(y,x))
    ]]></literal>
    <justification jstring="[para(10775(a,1),14537(a,1,1))].">
      <j1 rule="para" parents="10775 14537"/>
    </justification>
  </clause>

  <clause id="14550">
    <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(7414(a,1),13652(a,1,3,2))].">
      <j1 rule="para" parents="7414 13652"/>
    </justification>
  </clause>

  <clause id="14551">
    <literal><![CDATA[
      K(x,(((y * z) / u) \ K(y,T(z,x))) \ w) = K(x,(((z * y) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(7131(a,2),14043(a,1,2,1,2))].">
      <j1 rule="para" parents="7131 14043"/>
    </justification>
  </clause>

  <clause id="14552">
    <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(14074(a,2),14086(a,1))].">
      <j1 rule="para" parents="14074 14086"/>
    </justification>
  </clause>

  <clause id="14553">
    <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(14239(a,1),14336(a,2,2))].">
      <j1 rule="para" parents="14239 14336"/>
    </justification>
  </clause>

  <clause id="14554">
    <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(14553(a,2),10833(a,1))].">
      <j1 rule="para" parents="14553 10833"/>
    </justification>
  </clause>

  <clause id="14555">
    <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),14554(a,1,2,3,1,2))].">
      <j1 rule="para" parents="104 14554"/>
    </justification>
  </clause>

  <clause id="14556">
    <literal><![CDATA[
      K(x,L(y,z,(u * x) \ w)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(14555,a,xx),flip(a)].">
      <j1 rule="hyper" parents="14555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14557">
    <literal><![CDATA[
      K(x \ 1,L(y,z,x \ u)) = K(x \ 1,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(163(a,1),14556(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="163 14556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14558">
    <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,9025,a(flip),b,14503,a),flip(a)].">
      <j1 rule="hyper" parents="58 9025 14503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14559">
    <literal><![CDATA[
      K(x,T(T(y * T(x,z),u),z)) = K(x,T((u / (u * y)) \ x,z))
    ]]></literal>
    <justification jstring="[hyper(7679,a,14558,a)].">
      <j1 rule="hyper" parents="7679 14558"/>
    </justification>
  </clause>

  <clause id="14561">
    <literal><![CDATA[
      K(x,T((y / (y * z)) \ x,u)) = K(x,T(T(x * z,y),u))
    ]]></literal>
    <justification jstring="[hyper(58,a,10279,a(flip),b,14559,a),flip(a)].">
      <j1 rule="hyper" parents="58 10279 14559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14563">
    <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),14561(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="105 14561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14564">
    <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(320,a,9166,a(flip),b,14563,a),flip(a)].">
      <j1 rule="hyper" parents="320 9166 14563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14565">
    <literal><![CDATA[
      K(x,T(x * T(y,z),z)) = K(x,R(1 / (1 / (1 / y)),y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(10277,a,14564,a)].">
      <j1 rule="hyper" parents="10277 14564"/>
    </justification>
  </clause>

  <clause id="14566">
    <literal><![CDATA[
      K(x,T(x * T(y,z),z)) = K(x,R((1 / (1 / y)) \ 1,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5305,a(flip),b,14565,a),flip(a)].">
      <j1 rule="hyper" parents="320 5305 14565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14567">
    <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),14566(a,2,2,1,1))].">
      <j1 rule="para" parents="75 14566"/>
    </justification>
  </clause>

  <clause id="14568">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,T(x * T(y,z),z))
    ]]></literal>
    <justification jstring="[hyper(320,a,11635,a(flip),b,14567,a)].">
      <j1 rule="hyper" parents="320 11635 14567"/>
    </justification>
  </clause>

  <clause id="14570">
    <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(14568(a,2),6716(a,1,1))].">
      <j1 rule="para" parents="14568 6716"/>
    </justification>
  </clause>

  <clause id="14571">
    <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,6719,a(flip),b,14570,a)].">
      <j1 rule="hyper" parents="58 6719 14570"/>
    </justification>
  </clause>

  <clause id="14572">
    <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,6716,a(flip),b,14504,a)].">
      <j1 rule="hyper" parents="58 6716 14504"/>
    </justification>
  </clause>

  <clause id="14573">
    <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(320,a,12658,a(flip),b,14572,a),flip(a)].">
      <j1 rule="hyper" parents="320 12658 14572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14574">
    <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),14573(a,2,2,2))].">
      <j1 rule="para" parents="72 14573"/>
    </justification>
  </clause>

  <clause id="14576">
    <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,14571,a,b,14574,a)].">
      <j1 rule="hyper" parents="58 14571 14574"/>
    </justification>
  </clause>

  <clause id="14578">
    <literal><![CDATA[
      R(K(x,R(x * y,z,u)),y,w) = K(R(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(12453(a,1),14576(a,1,1))].">
      <j1 rule="para" parents="12453 14576"/>
    </justification>
  </clause>

  <clause id="14579">
    <literal><![CDATA[
      K(x,R(R(x * y,z,u),y,w)) = K(R(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(12461,a,14578,a)].">
      <j1 rule="hyper" parents="12461 14578"/>
    </justification>
  </clause>

  <clause id="14580">
    <literal><![CDATA[
      K(x,R(R(x * y,z,u),y,w)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,12453,a(flip),b,14579,a),flip(a)].">
      <j1 rule="hyper" parents="320 12453 14579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14581">
    <literal><![CDATA[
      K(x,R(x * y,y * z,u)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12483,a(flip),b,14580,a),flip(a)].">
      <j1 rule="hyper" parents="58 12483 14580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14583">
    <literal><![CDATA[
      K(x,R(x * y,z,u)) = K(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12667,a(flip),b,14581,a),flip(a)].">
      <j1 rule="hyper" parents="58 12667 14581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14584">
    <literal><![CDATA[
      T(x,R(x * y,z,u)) = T(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,14583,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 14583 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14585">
    <literal><![CDATA[
      L(T(x,R(y,z,u)),y,T(x,w)) = T(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,12519,a,b,14584,a)].">
      <j1 rule="hyper" parents="320 12519 14584"/>
    </justification>
  </clause>

  <clause id="14586">
    <literal><![CDATA[
      L(T(x,R(y,z,u)),y,x) = T(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(11156,a,14585,a)].">
      <j1 rule="hyper" parents="11156 14585"/>
    </justification>
  </clause>

  <clause id="14587">
    <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,12484,a,b,14586,a)].">
      <j1 rule="hyper" parents="58 12484 14586"/>
    </justification>
  </clause>

  <clause id="14588">
    <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(3116(a,2),14586(a,2,2,1))].">
      <j1 rule="para" parents="3116 14586"/>
    </justification>
  </clause>

  <clause id="14589">
    <literal><![CDATA[
      T(x,x * y) * a(x,z,K(u,y)) = T(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[para(14190(a,1),14587(a,1,2))].">
      <j1 rule="para" parents="14190 14587"/>
    </justification>
  </clause>

  <clause id="14590">
    <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,13523,a,b,14589,a)].">
      <j1 rule="hyper" parents="58 13523 14589"/>
    </justification>
  </clause>

  <clause id="14591">
    <literal><![CDATA[
      T(x * a(x,y,K(z,u)),u * x) = T(x,R(x * u,y,z))
    ]]></literal>
    <justification jstring="[para(12799(a,1),14590(a,1,1))].">
      <j1 rule="para" parents="12799 14590"/>
    </justification>
  </clause>

  <clause id="14592">
    <literal><![CDATA[
      T(T(x,a(y,z,u) \ x),u * x) = T(x,R(x * u,z,y))
    ]]></literal>
    <justification jstring="[para(14256(a,2),14591(a,1,1))].">
      <j1 rule="para" parents="14256 14591"/>
    </justification>
  </clause>

  <clause id="14593">
    <literal><![CDATA[
      T(T(x,x * y),a(z,u,y) \ x) = T(x,R(x * y,u,z))
    ]]></literal>
    <justification jstring="[hyper(4371,a,14592,a)].">
      <j1 rule="hyper" parents="4371 14592"/>
    </justification>
  </clause>

  <clause id="14594">
    <literal><![CDATA[
      T(x,R(x * y,z,u)) = T(x,L(y * x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,13531,a(flip),b,14593,a),flip(a)].">
      <j1 rule="hyper" parents="58 13531 14593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14595">
    <literal><![CDATA[
      K(x,(y * L(y \ 1,z,u)) \ w) = K(x,y \ (L(y \ 1,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(14006,a,14546,a),flip(a)].">
      <j1 rule="hyper" parents="14006 14546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14596">
    <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(4266(a,1),14028(a,1,1,1))].">
      <j1 rule="para" parents="4266 14028"/>
    </justification>
  </clause>

  <clause id="14597">
    <literal><![CDATA[
      K(x,L(y,a(z \ 1,z,u),L(u,z,z \ 1))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,14265,a(flip),b,14393,a),flip(a)].">
      <j1 rule="hyper" parents="320 14265 14393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14598">
    <literal><![CDATA[
      K(x,L(y,a(z \ 1,z,u),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14419,a,14597,a)].">
      <j1 rule="hyper" parents="14419 14597"/>
    </justification>
  </clause>

  <clause id="14600">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) * (y \ u)) = K(x,a(z \ 1,z,y) \ u)
    ]]></literal>
    <justification jstring="[para(4031(a,1),14597(a,1,2))].">
      <j1 rule="para" parents="4031 14597"/>
    </justification>
  </clause>

  <clause id="14602">
    <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(13641(a,1),14542(a,1,1,2))].">
      <j1 rule="para" parents="13641 14542"/>
    </justification>
  </clause>

  <clause id="14603">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,y * K(x * y,u),x)
    ]]></literal>
    <justification jstring="[hyper(13243,a,14602,a)].">
      <j1 rule="hyper" parents="13243 14602"/>
    </justification>
  </clause>

  <clause id="14605">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,x \ T(x * y,u),x)
    ]]></literal>
    <justification jstring="[para(13661(a,2),14603(a,2,2))].">
      <j1 rule="para" parents="13661 14603"/>
    </justification>
  </clause>

  <clause id="14606">
    <literal><![CDATA[
      L(x,x \ T(x * y,z),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(12630,a,14605,a),flip(a)].">
      <j1 rule="hyper" parents="12630 14605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14607">
    <literal><![CDATA[
      L(x,x \ T(y,z),x) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),14606(a,1,2,2,1))].">
      <j1 rule="para" parents="5 14606"/>
    </justification>
  </clause>

  <clause id="14609">
    <literal><![CDATA[
      L(x,x \ (y / z),x) = L(x,x \ (z \ y),x)
    ]]></literal>
    <justification jstring="[para(107(a,1),14607(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 14607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14610">
    <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(14609(a,1),12389(a,1,2))].">
      <j1 rule="para" parents="14609 12389"/>
    </justification>
  </clause>

  <clause id="14611">
    <literal><![CDATA[
      T(T(x,x * y) * K(x * y,z),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(12986(a,1),14596(a,1,1,2))].">
      <j1 rule="para" parents="12986 14596"/>
    </justification>
  </clause>

  <clause id="14612">
    <literal><![CDATA[
      T(T(x * K(x * y,z),x * y),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(7412(a,2),14611(a,1,1))].">
      <j1 rule="para" parents="7412 14611"/>
    </justification>
  </clause>

  <clause id="14614">
    <literal><![CDATA[
      T(T(x * K(x * y,z),y),x * y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[hyper(435,a,14612,a)].">
      <j1 rule="hyper" parents="435 14612"/>
    </justification>
  </clause>

  <clause id="14615">
    <literal><![CDATA[
      T(T(x * K(x * y,z),y),x * y) = y \ T(T(x,x * y) * y,z)
    ]]></literal>
    <justification jstring="[para(4266(a,1),14614(a,2,2,1,1))].">
      <j1 rule="para" parents="4266 14614"/>
    </justification>
  </clause>

  <clause id="14616">
    <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),14102(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 14102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14617">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,z,u)) = K(x,L(y,(y / z) \ 1,u))
    ]]></literal>
    <justification jstring="[para(10383(a,1),14616(a,2,2))].">
      <j1 rule="para" parents="10383 14616"/>
    </justification>
  </clause>

  <clause id="14618">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,z,u)) = K(x,L(y,(z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(13239(a,1),14617(a,2,2))].">
      <j1 rule="para" parents="13239 14617"/>
    </justification>
  </clause>

  <clause id="14619">
    <literal><![CDATA[
      K(x,L((y / z) * z,z,u)) = K(x,L(y,(z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(14079,a,14618,a)].">
      <j1 rule="hyper" parents="14079 14618"/>
    </justification>
  </clause>

  <clause id="14620">
    <literal><![CDATA[
      K(x,L(y,(z \ y) \ 1,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),14619(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 14619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14621">
    <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(14187(a,1),13821(a,1,2))].">
      <j1 rule="para" parents="14187 13821"/>
    </justification>
  </clause>

  <clause id="14622">
    <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(14294(a,1),14452(a,2,1))].">
      <j1 rule="para" parents="14294 14452"/>
    </justification>
  </clause>

  <clause id="14623">
    <literal><![CDATA[
      K(x,K(y,z \ (u * ((u \ z) * w)))) = K(x,K(y,L(w,z,u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,14355,a(flip),b,14622,a),flip(a)].">
      <j1 rule="hyper" parents="320 14355 14622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14624">
    <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),14623(a,1,2,2))].">
      <j1 rule="para" parents="91 14623"/>
    </justification>
  </clause>

  <clause id="14625">
    <literal><![CDATA[
      K(x,K(y,L(z,u / w,w))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(11151(a,2),14624(a,1,2,2))].">
      <j1 rule="para" parents="11151 14624"/>
    </justification>
  </clause>

  <clause id="14626">
    <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(13643(a,1),13922(a,2,1))].">
      <j1 rule="para" parents="13643 13922"/>
    </justification>
  </clause>

  <clause id="14627">
    <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(13678(a,1),14626(a,1,2,2))].">
      <j1 rule="para" parents="13678 14626"/>
    </justification>
  </clause>

  <clause id="14628">
    <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(7754(a,1),14627(a,1,2))].">
      <j1 rule="para" parents="7754 14627"/>
    </justification>
  </clause>

  <clause id="14629">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(z \ x,y)) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(7186(a,1),14628(a,1,2,2))].">
      <j1 rule="para" parents="7186 14628"/>
    </justification>
  </clause>

  <clause id="14630">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(z,y)) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(8140(a,1),14629(a,1,2))].">
      <j1 rule="para" parents="8140 14629"/>
    </justification>
  </clause>

  <clause id="14631">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(7772(a,1),14630(a,1,2))].">
      <j1 rule="para" parents="7772 14630"/>
    </justification>
  </clause>

  <clause id="14632">
    <literal><![CDATA[
      (T(x,T(y,z)) / z) \ 1 = K(y,x) * ((x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,14177,a(flip),b,14631,a),flip(a)].">
      <j1 rule="hyper" parents="58 14177 14631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14633">
    <literal><![CDATA[
      K(x * y,L(z,u,u \ 1)) = (x \ T(y * x,z)) * (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(14093,a,13703,a),flip(a)].">
      <j1 rule="hyper" parents="14093 13703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14634">
    <literal><![CDATA[
      (x \ T(y * x,z)) * (T(y,x) \ 1) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(14093,a,13683,a)].">
      <j1 rule="hyper" parents="14093 13683"/>
    </justification>
  </clause>

  <clause id="14635">
    <literal><![CDATA[
      (x \ T(y * x,z)) * (T(y,x) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(14633(a,1),6470(a,1))].">
      <j1 rule="para" parents="14633 6470"/>
    </justification>
  </clause>

  <clause id="14636">
    <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(13165,a,14475,a)].">
      <j1 rule="hyper" parents="13165 14475"/>
    </justification>
  </clause>

  <clause id="14637">
    <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(13272,a,14636,a)].">
      <j1 rule="hyper" parents="13272 14636"/>
    </justification>
  </clause>

  <clause id="14638">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ ((z \ 1) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14517,a(flip),b,14637,a),flip(a)].">
      <j1 rule="hyper" parents="58 14517 14637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14639">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ ((z \ 1) * u)) = K(x,(y / z) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(523(a,1),14638(a,1,2,1))].">
      <j1 rule="para" parents="523 14638"/>
    </justification>
  </clause>

  <clause id="14640">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ ((z \ 1) * (z * u))) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(4(a,1),14639(a,2,2,2))].">
      <j1 rule="para" parents="4 14639"/>
    </justification>
  </clause>

  <clause id="14641">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ L(u,z,z \ 1)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5693,a(flip),b,14640,a)].">
      <j1 rule="hyper" parents="58 5693 14640"/>
    </justification>
  </clause>

  <clause id="14642">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (y \ (z * u))) = a(x,y \ z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(14413,a,14521,a),flip(a)].">
      <j1 rule="hyper" parents="14413 14521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14643">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (y \ (z * u))) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,14290,a(flip),b,14642,a),flip(a)].">
      <j1 rule="hyper" parents="320 14290 14642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14644">
    <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(9414(a,1),14643(a,1,2,1))].">
      <j1 rule="para" parents="9414 14643"/>
    </justification>
  </clause>

  <clause id="14645">
    <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(4018(a,1),13924(a,1,2))].">
      <j1 rule="para" parents="4018 13924"/>
    </justification>
  </clause>

  <clause id="14646">
    <literal><![CDATA[
      ((x * ((y * (x / y)) \ y)) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(10118(a,1),13884(a,1,1,1,2))].">
      <j1 rule="para" parents="10118 13884"/>
    </justification>
  </clause>

  <clause id="14647">
    <literal><![CDATA[
      x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(5357(a,1),14646(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5357 14646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14648">
    <literal><![CDATA[
      x / (x * ((1 / ((x / ((x \ y) \ 1)) / x)) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(2629(a,2),14647(a,1,2,2,1))].">
      <j1 rule="para" parents="2629 14647"/>
    </justification>
  </clause>

  <clause id="14649">
    <literal><![CDATA[
      x / (x * ((x / ((x \ y) \ 1)) / x)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),14648(a,1,2,2))].">
      <j1 rule="para" parents="75 14648"/>
    </justification>
  </clause>

  <clause id="14651">
    <literal><![CDATA[
      x / (x / ((y / x) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(11330(a,1),14649(a,1,2))].">
      <j1 rule="para" parents="11330 14649"/>
    </justification>
  </clause>

  <clause id="14652">
    <literal><![CDATA[
      1 / (x / (x / ((y / x) \ 1))) = (x / (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(197,a,14651,a(flip))].">
      <j1 rule="hyper" parents="197 14651"/>
    </justification>
  </clause>

  <clause id="14653">
    <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(12657(a,1),14400(a,2,2))].">
      <j1 rule="para" parents="12657 14400"/>
    </justification>
  </clause>

  <clause id="14654">
    <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(13952(a,1),14653(a,1,2,3))].">
      <j1 rule="para" parents="13952 14653"/>
    </justification>
  </clause>

  <clause id="14655">
    <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(11142(a,1),14430(a,2,1))].">
      <j1 rule="para" parents="11142 14430"/>
    </justification>
  </clause>

  <clause id="14656">
    <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),14655(a,2,2))].">
      <j1 rule="para" parents="105 14655"/>
    </justification>
  </clause>

  <clause id="14657">
    <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),14656(a,1,1,3,2))].">
      <j1 rule="para" parents="105 14656"/>
    </justification>
  </clause>

  <clause id="14658">
    <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),14610(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="62 14610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14659">
    <literal><![CDATA[
      ((x * (y * z)) / x) \ L(z,y,z) = T((x * (z * y)) / x,z) \ z
    ]]></literal>
    <justification jstring="[para(5(a,1),14658(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 14658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14661">
    <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(13393(a,1),14368(a,1,2))].">
      <j1 rule="para" parents="13393 14368"/>
    </justification>
  </clause>

  <clause id="14662">
    <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(1363(a,1),14661(a,1,2,2))].">
      <j1 rule="para" parents="1363 14661"/>
    </justification>
  </clause>

  <clause id="14663">
    <literal><![CDATA[
      a(x,y,z * a(u,w,a(v5,v6,v7))) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(13360(a,1),14662(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13360 14662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14664">
    <literal><![CDATA[
      a(x,y,z * a(u,w,a(v5,v6,v7))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,14364,a,b,14663,a),flip(a)].">
      <j1 rule="hyper" parents="320 14364 14663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14666">
    <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(14664(a,2),969(a,1))].">
      <j1 rule="para" parents="14664 969"/>
    </justification>
  </clause>

  <clause id="14667">
    <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(6306(a,1),13904(a,1,1,2))].">
      <j1 rule="para" parents="6306 13904"/>
    </justification>
  </clause>

  <clause id="14668">
    <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(11605(a,1),14588(a,1,1))].">
      <j1 rule="para" parents="11605 14588"/>
    </justification>
  </clause>

  <clause id="14669">
    <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),14668(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="75 14668"/>
    </justification>
  </clause>

  <clause id="14670">
    <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(10265(a,1),14669(a,1,1))].">
      <j1 rule="para" parents="10265 14669"/>
    </justification>
  </clause>

  <clause id="14671">
    <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,3987,a(flip),b,14670,a)].">
      <j1 rule="hyper" parents="58 3987 14670"/>
    </justification>
  </clause>

  <clause id="14673">
    <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),14671(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="75 14671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14674">
    <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(320,a,10552,a(flip),b,14673,a),flip(a)].">
      <j1 rule="hyper" parents="320 10552 14673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14676">
    <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(320,a,14586,a(flip),b,14674,a),flip(a)].">
      <j1 rule="hyper" parents="320 14586 14674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14677">
    <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),14676(a,2,2,1))].">
      <j1 rule="para" parents="5 14676"/>
    </justification>
  </clause>

  <clause id="14678">
    <literal><![CDATA[
      T(x,R(x * (y / T(1 / (1 / x),z)),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(3116(a,1),14677(a,1,2,1))].">
      <j1 rule="para" parents="3116 14677"/>
    </justification>
  </clause>

  <clause id="14679">
    <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,14594,a(flip),b,14678,a)].">
      <j1 rule="hyper" parents="58 14594 14678"/>
    </justification>
  </clause>

  <clause id="14680">
    <literal><![CDATA[
      T(x,L(y * (x * (1 / T(x,z))),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(9672(a,1),14679(a,1,2,1))].">
      <j1 rule="para" parents="9672 14679"/>
    </justification>
  </clause>

  <clause id="14681">
    <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,3758,a(flip),b,14680,a)].">
      <j1 rule="hyper" parents="58 3758 14680"/>
    </justification>
  </clause>

  <clause id="14682">
    <literal><![CDATA[
      T(x,L(y * K(z,x),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(4755(a,2),14681(a,1,2,1,2))].">
      <j1 rule="para" parents="4755 14681"/>
    </justification>
  </clause>

  <clause id="14683">
    <literal><![CDATA[
      T(x,R(y,z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(178(a,1),14682(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="178 14682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14685">
    <literal><![CDATA[
      R(x,y,z) * T(u,L(x,y,z)) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,14683,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 14683 17"/>
    </justification>
  </clause>

  <clause id="14686">
    <literal><![CDATA[
      T(x,L(y / z,z,u)) = T(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[para(102(a,1),14683(a,1,2)),flip(a)].">
      <j1 rule="para" parents="102 14683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14687">
    <literal><![CDATA[
      T(x,L((y / z) / u,u,z)) = T(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(301(a,1),14683(a,1,2)),flip(a)].">
      <j1 rule="para" parents="301 14683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14688">
    <literal><![CDATA[
      x / T(x,L(y,z,u)) = K(R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(14683(a,1),4753(a,2,2)),flip(a)].">
      <j1 rule="para" parents="14683 4753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14689">
    <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(14683(a,1),8262(a,1,2))].">
      <j1 rule="para" parents="14683 8262"/>
    </justification>
  </clause>

  <clause id="14690">
    <literal><![CDATA[
      T(x,L(y / (z / u),u \ z,u)) = T(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(10365(a,1),14683(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10365 14683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14691">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(4821,a,14688,a),flip(a)].">
      <j1 rule="hyper" parents="4821 14688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14692">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,10809,a(flip),b,14691,a),flip(a)].">
      <j1 rule="hyper" parents="320 10809 14691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14693">
    <literal><![CDATA[
      K(L(x / y,y,z),u) = K((x * z) / (y * z),u)
    ]]></literal>
    <justification jstring="[para(102(a,1),14691(a,1,1)),flip(a)].">
      <j1 rule="para" parents="102 14691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14694">
    <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(14691(a,1),7702(a,1))].">
      <j1 rule="para" parents="14691 7702"/>
    </justification>
  </clause>

  <clause id="14695">
    <literal><![CDATA[
      K(x,R(y,z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12463,a,14692,a)].">
      <j1 rule="hyper" parents="12463 14692"/>
    </justification>
  </clause>

  <clause id="14696">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12462,a,14692,a)].">
      <j1 rule="hyper" parents="12462 14692"/>
    </justification>
  </clause>

  <clause id="14697">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,10763,a,b,14695,a)].">
      <j1 rule="hyper" parents="320 10763 14695"/>
    </justification>
  </clause>

  <clause id="14698">
    <literal><![CDATA[
      ((x * y) * z) / ((T(x,u) * y) * z) = K(u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5951,a,b,14695,a)].">
      <j1 rule="hyper" parents="58 5951 14695"/>
    </justification>
  </clause>

  <clause id="14699">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[para(102(a,1),14695(a,1,2)),flip(a)].">
      <j1 rule="para" parents="102 14695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14700">
    <literal><![CDATA[
      K(x,L((y / z) / u,u,z)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(301(a,1),14695(a,1,2)),flip(a)].">
      <j1 rule="para" parents="301 14695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14701">
    <literal><![CDATA[
      K(x,L(y \ (z / u),y,u)) = K(x,T(z / (y * u),y))
    ]]></literal>
    <justification jstring="[para(648(a,1),14695(a,1,2)),flip(a)].">
      <j1 rule="para" parents="648 14695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14702">
    <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(14695(a,1),9738(a,1,2))].">
      <j1 rule="para" parents="14695 9738"/>
    </justification>
  </clause>

  <clause id="14703">
    <literal><![CDATA[
      K(x,L(y / (z / u),u \ z,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(10365(a,1),14695(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10365 14695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14704">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(14695(a,1),12454(a,1,1))].">
      <j1 rule="para" parents="14695 12454"/>
    </justification>
  </clause>

  <clause id="14705">
    <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(14695(a,1),14250(a,1,2,3))].">
      <j1 rule="para" parents="14695 14250"/>
    </justification>
  </clause>

  <clause id="14706">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(6951,a,14696,a)].">
      <j1 rule="hyper" parents="6951 14696"/>
    </justification>
  </clause>

  <clause id="14707">
    <literal><![CDATA[
      K(x,L(y / z,y,u)) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[hyper(6916,a,14696,a),flip(a)].">
      <j1 rule="hyper" parents="6916 14696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14708">
    <literal><![CDATA[
      R(K(x,y),z,u) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,10763,a,b,14696,a),flip(a)].">
      <j1 rule="hyper" parents="320 10763 14696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14709">
    <literal><![CDATA[
      K(x,L(y / (z / u),y,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6918,a(flip),b,14696,a),flip(a)].">
      <j1 rule="hyper" parents="58 6918 14696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14710">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u)) = K(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,6894,a(flip),b,14696,a),flip(a)].">
      <j1 rule="hyper" parents="58 6894 14696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14711">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) = K(x \ 1,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5667,a(flip),b,14696,a)].">
      <j1 rule="hyper" parents="58 5667 14696"/>
    </justification>
  </clause>

  <clause id="14712">
    <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(14696(a,1),700(a,1,1))].">
      <j1 rule="para" parents="14696 700"/>
    </justification>
  </clause>

  <clause id="14713">
    <literal><![CDATA[
      (K(x,T(y,z * u)) * z) * u = (z * u) * K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14696(a,1),7878(a,2,2))].">
      <j1 rule="para" parents="14696 7878"/>
    </justification>
  </clause>

  <clause id="14714">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (u * z) = (K(x,y) * z) * T(u,z)
    ]]></literal>
    <justification jstring="[para(14696(a,1),10359(a,1,1))].">
      <j1 rule="para" parents="14696 10359"/>
    </justification>
  </clause>

  <clause id="14715">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) * u = (K(x,y) * (u / z)) * z
    ]]></literal>
    <justification jstring="[para(14696(a,1),10368(a,1,1))].">
      <j1 rule="para" parents="14696 10368"/>
    </justification>
  </clause>

  <clause id="14716">
    <literal><![CDATA[
      K(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(14697(a,1),10806(a,1))].">
      <j1 rule="para" parents="14697 10806"/>
    </justification>
  </clause>

  <clause id="14717">
    <literal><![CDATA[
      L(K(x / (y / z),u),x,z) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6737,a(flip),b,14708,a),flip(a)].">
      <j1 rule="hyper" parents="58 6737 14708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14718">
    <literal><![CDATA[
      T(L(K(x,y),z,u),w) * (z * u) = (T(K(x,y),w) * z) * u
    ]]></literal>
    <justification jstring="[para(14708(a,1),512(a,1,1,1))].">
      <j1 rule="para" parents="14708 512"/>
    </justification>
  </clause>

  <clause id="14720">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(14708(a,2),10806(a,1))].">
      <j1 rule="para" parents="14708 10806"/>
    </justification>
  </clause>

  <clause id="14721">
    <literal><![CDATA[
      L(K(x,y),z,u) \ (u * (K(x,y) * z)) = z * T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(14708(a,1),14156(a,1,1))].">
      <j1 rule="para" parents="14708 14156"/>
    </justification>
  </clause>

  <clause id="14722">
    <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),14716(a,1,2))].">
      <j1 rule="para" parents="102 14716"/>
    </justification>
  </clause>

  <clause id="14723">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(6919(a,2),14720(a,1))].">
      <j1 rule="para" parents="6919 14720"/>
    </justification>
  </clause>

  <clause id="14724">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,10782,a(flip),b,14710,a),flip(a)].">
      <j1 rule="hyper" parents="58 10782 14710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14725">
    <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,7543,a(flip),b,14711,a),flip(a)].">
      <j1 rule="hyper" parents="58 7543 14711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14726">
    <literal><![CDATA[
      K(T(x / y,z) \ 1,L(u,y,y \ z)) = K((z \ (x * (y \ z))) \ 1,u)
    ]]></literal>
    <justification jstring="[para(955(a,1),14711(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="955 14711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14727">
    <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(765(a,1),14724(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="765 14724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14729">
    <literal><![CDATA[
      R(x,y,z) * T(y * z,x) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(13629(a,1),14685(a,1,2))].">
      <j1 rule="para" parents="13629 14685"/>
    </justification>
  </clause>

  <clause id="14730">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(((x \ z) * x) / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(8228,a,14693,a)].">
      <j1 rule="hyper" parents="8228 14693"/>
    </justification>
  </clause>

  <clause id="14731">
    <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(14693(a,1),8228(a,1))].">
      <j1 rule="para" parents="14693 8228"/>
    </justification>
  </clause>

  <clause id="14732">
    <literal><![CDATA[
      K(x,T((y * z) \ u,z)) = K(x,((y \ u) * y) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7985,a(flip),b,14699,a)].">
      <j1 rule="hyper" parents="58 7985 14699"/>
    </justification>
  </clause>

  <clause id="14733">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,y / z,z))) = K(x,K(w,y / (u * z)))
    ]]></literal>
    <justification jstring="[para(14700(a,1),10862(a,2,2))].">
      <j1 rule="para" parents="14700 10862"/>
    </justification>
  </clause>

  <clause id="14734">
    <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(14704(a,1),6102(a,2,2,1))].">
      <j1 rule="para" parents="14704 6102"/>
    </justification>
  </clause>

  <clause id="14735">
    <literal><![CDATA[
      (K(x,L(y,z,u \ 1)) * z) * u = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(14516(a,1),14704(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14516 14704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14736">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,((y * z) * (z \ 1)) / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(14471,a,14707,a)].">
      <j1 rule="hyper" parents="14471 14707"/>
    </justification>
  </clause>

  <clause id="14737">
    <literal><![CDATA[
      K(x,(y * (y \ z)) / (u * (y \ z))) = K(x,L(y / u,z,y \ z))
    ]]></literal>
    <justification jstring="[hyper(14401,a,14707,a),flip(a)].">
      <j1 rule="hyper" parents="14401 14707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14738">
    <literal><![CDATA[
      K(x,L(y * z,y,u)) = K(x,(y * u) / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(14085,a,14707,a)].">
      <j1 rule="hyper" parents="14085 14707"/>
    </justification>
  </clause>

  <clause id="14739">
    <literal><![CDATA[
      K(x,(y * z) / (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y / u),y,z) = w
    ]]></literal>
    <justification jstring="[para(14707(a,1),10830(a,1))].">
      <j1 rule="para" parents="14707 10830"/>
    </justification>
  </clause>

  <clause id="14740">
    <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,14709,a(flip),b,14252,a)].">
      <j1 rule="hyper" parents="116 14709 14252"/>
    </justification>
  </clause>

  <clause id="14741">
    <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(7710,a,14717,a)].">
      <j1 rule="hyper" parents="7710 14717"/>
    </justification>
  </clause>

  <clause id="14742">
    <literal><![CDATA[
      ((x * y) * z) * a(z,x,y) = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11198,a,b,14729,a)].">
      <j1 rule="hyper" parents="58 11198 14729"/>
    </justification>
  </clause>

  <clause id="14743">
    <literal><![CDATA[
      a(x,y,z) = ((y * z) * x) \ ((y * z) * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,14729,a(flip),b,11198,a),flip(a)].">
      <j1 rule="hyper" parents="116 14729 11198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14744">
    <literal><![CDATA[
      x * a(x,y,a(z,u,w)) = R(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(894,a,14742,a)].">
      <j1 rule="hyper" parents="894 14742"/>
    </justification>
  </clause>

  <clause id="14745">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = R(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(826,a,14742,a)].">
      <j1 rule="hyper" parents="826 14742"/>
    </justification>
  </clause>

  <clause id="14746">
    <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(7152(a,1),14742(a,1,1,1))].">
      <j1 rule="para" parents="7152 14742"/>
    </justification>
  </clause>

  <clause id="14747">
    <literal><![CDATA[
      R(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(14745(a,1),14213(a,1))].">
      <j1 rule="para" parents="14745 14213"/>
    </justification>
  </clause>

  <clause id="14748">
    <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,3810,a,b,14744,a)].">
      <j1 rule="hyper" parents="29 3810 14744"/>
    </justification>
  </clause>

  <clause id="14749">
    <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(14744(a,1),476(a,1,2,2))].">
      <j1 rule="para" parents="14744 476"/>
    </justification>
  </clause>

  <clause id="14750">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * x) = v5 * R(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(14744(a,1),13383(a,2,2))].">
      <j1 rule="para" parents="14744 13383"/>
    </justification>
  </clause>

  <clause id="14751">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,y * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,92,a,b,14743,a),flip(a)].">
      <j1 rule="hyper" parents="320 92 14743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14752">
    <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(14743(a,2),495(a,2,1))].">
      <j1 rule="para" parents="14743 495"/>
    </justification>
  </clause>

  <clause id="14753">
    <literal><![CDATA[
      L(x,y,z * u) != a(y,z,u)
    ]]></literal>
    <literal><![CDATA[
      y \ R(y,z,u) = x
    ]]></literal>
    <justification jstring="[para(14751(a,2),45(a,1)),flip(a)].">
      <j1 rule="para" parents="14751 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14755">
    <literal><![CDATA[
      T(x,L(y / (z / u),z,u)) = T(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,14389,a(flip),b,14690,a)].">
      <j1 rule="hyper" parents="58 14389 14690"/>
    </justification>
  </clause>

  <clause id="14756">
    <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(14091(a,1),14755(a,1,2,1,2))].">
      <j1 rule="para" parents="14091 14755"/>
    </justification>
  </clause>

  <clause id="14757">
    <literal><![CDATA[
      K(L(x,y,z),u) * ((x * y) * z) = (T(x,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(31,a,5104,a,b,14698,a)].">
      <j1 rule="hyper" parents="31 5104 14698"/>
    </justification>
  </clause>

  <clause id="14758">
    <literal><![CDATA[
      K(x,L(y,z,(T(y,x) * z) \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(14698(a,1),323(a,1,1))].">
      <j1 rule="para" parents="14698 323"/>
    </justification>
  </clause>

  <clause id="14759">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),z \ u)) = K(x,u \ (z * (y / z)))
    ]]></literal>
    <justification jstring="[para(490(a,1),14701(a,1,2)),flip(a)].">
      <j1 rule="para" parents="490 14701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14760">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,(z * y) \ K(z,1 / z))
    ]]></literal>
    <justification jstring="[para(497(a,1),14701(a,1,2)),flip(a)].">
      <j1 rule="para" parents="497 14701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14761">
    <literal><![CDATA[
      K(x,L(y / (z / u),z,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(14386,a,14703,a)].">
      <j1 rule="hyper" parents="14386 14703"/>
    </justification>
  </clause>

  <clause id="14762">
    <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,14598,a(flip),b,14761,a),flip(a)].">
      <j1 rule="hyper" parents="58 14598 14761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14763">
    <literal><![CDATA[
      K(x,L(y,z,u)) * z = (K(x,y) * (z / u)) * u
    ]]></literal>
    <justification jstring="[para(14385(a,1),14715(a,1,1))].">
      <j1 rule="para" parents="14385 14715"/>
    </justification>
  </clause>

  <clause id="14764">
    <literal><![CDATA[
      (x * K(y,L(z,x,u))) / u = K(y,T(z,x)) * (x / u)
    ]]></literal>
    <justification jstring="[hyper(8584,a,14763,a)].">
      <j1 rule="hyper" parents="8584 14763"/>
    </justification>
  </clause>

  <clause id="14765">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * z) / u = K(x,y) * (z / u)
    ]]></literal>
    <justification jstring="[hyper(537,a,14763,a)].">
      <j1 rule="hyper" parents="537 14763"/>
    </justification>
  </clause>

  <clause id="14766">
    <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(14763(a,1),537(a,1))].">
      <j1 rule="para" parents="14763 537"/>
    </justification>
  </clause>

  <clause id="14767">
    <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(440,a,14765,a(flip),b,13997,a)].">
      <j1 rule="hyper" parents="440 14765 13997"/>
    </justification>
  </clause>

  <clause id="14768">
    <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(14486(a,1),14765(a,2,2))].">
      <j1 rule="para" parents="14486 14765"/>
    </justification>
  </clause>

  <clause id="14769">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) * (z / u) = (K(x,y) * z) / u
    ]]></literal>
    <justification jstring="[para(14516(a,1),14765(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14516 14765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14771">
    <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(10083(a,1),14735(a,2,2))].">
      <j1 rule="para" parents="10083 14735"/>
    </justification>
  </clause>

  <clause id="14772">
    <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(5226(a,1),14738(a,2,2,1))].">
      <j1 rule="para" parents="5226 14738"/>
    </justification>
  </clause>

  <clause id="14773">
    <literal><![CDATA[
      a(x,y,K(y * z,u)) * K(x,(y * u) / ((z \ 1) * u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(14738(a,1),14251(a,1,2))].">
      <j1 rule="para" parents="14738 14251"/>
    </justification>
  </clause>

  <clause id="14774">
    <literal><![CDATA[
      K(x,y) * ((x * y) * z) = (T(x,y) * y) * z
    ]]></literal>
    <justification jstring="[para(10324(a,1),14757(a,1,1))].">
      <j1 rule="para" parents="10324 14757"/>
    </justification>
  </clause>

  <clause id="14775">
    <literal><![CDATA[
      K(x,L(y,z,u)) * ((x * z) * u) = (T(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(10809(a,1),14757(a,1,1))].">
      <j1 rule="para" parents="10809 14757"/>
    </justification>
  </clause>

  <clause id="14776">
    <literal><![CDATA[
      ((x * y) / x) \ ((y * x) * z) = y \ ((T(y,x) * x) * z)
    ]]></literal>
    <justification jstring="[hyper(116,a,14774,a(flip),b,4773,a),flip(a)].">
      <j1 rule="hyper" parents="116 14774 4773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14777">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(T(z,x) / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13100,a(flip),b,14730,a),flip(a)].">
      <j1 rule="hyper" parents="320 13100 14730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14778">
    <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,13876,a(flip),b,14777,a)].">
      <j1 rule="hyper" parents="58 13876 14777"/>
    </justification>
  </clause>

  <clause id="14779">
    <literal><![CDATA[
      K(T(x,y),(z * y) \ u) = K(x,((z \ u) * z) / (y * z))
    ]]></literal>
    <justification jstring="[hyper(7283,a,14732,a)].">
      <j1 rule="hyper" parents="7283 14732"/>
    </justification>
  </clause>

  <clause id="14780">
    <literal><![CDATA[
      K(x,T((y * z) \ u,z)) = K(x,T(u,y) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(320,a,13092,a(flip),b,14732,a),flip(a)].">
      <j1 rule="hyper" parents="320 13092 14732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14781">
    <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(5564(a,1),14780(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5564 14780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14782">
    <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(6892(a,2),14780(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6892 14780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14783">
    <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(320,a,3574,a(flip),b,14750,a),flip(a)].">
      <j1 rule="hyper" parents="320 3574 14750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14784">
    <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,14750,a(flip),b,13359,a(flip))].">
      <j1 rule="hyper" parents="116 14750 13359"/>
    </justification>
  </clause>

  <clause id="14785">
    <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(14779(a,1),7679(a,1))].">
      <j1 rule="para" parents="14779 7679"/>
    </justification>
  </clause>

  <clause id="14786">
    <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(14784(a,1),92(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14784 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14787">
    <literal><![CDATA[
      T(K(x,T(y,z * u)) * z,u) = T(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(239,a,14713,a,b,11172,a(flip))].">
      <j1 rule="hyper" parents="239 14713 11172"/>
    </justification>
  </clause>

  <clause id="14788">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,x * y)) = T(K(z,u) * x,y)
    ]]></literal>
    <justification jstring="[para(7858(a,1),14787(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7858 14787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14789">
    <literal><![CDATA[
      K((T(x,y) * K(z,u)) \ 1,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((K(z,T(u,x * y)) * x) \ 1,T(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(14787(a,1),7687(a,1,1,1))].">
      <j1 rule="para" parents="14787 7687"/>
    </justification>
  </clause>

  <clause id="14790">
    <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(14788(a,2),766(a,1))].">
      <j1 rule="para" parents="14788 766"/>
    </justification>
  </clause>

  <clause id="14791">
    <literal><![CDATA[
      K(x,y * T(K(x,z) * u,w)) = K(x,y * T(u,w))
    ]]></literal>
    <justification jstring="[para(14788(a,1),7378(a,1,2,2))].">
      <j1 rule="para" parents="14788 7378"/>
    </justification>
  </clause>

  <clause id="14792">
    <literal><![CDATA[
      x * K(L(K(y,z),T(z,y),z \ x),x) = (T(K(y,z),x) * T(z,y)) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6516,a(flip),b,14718,a)].">
      <j1 rule="hyper" parents="58 6516 14718"/>
    </justification>
  </clause>

  <clause id="14793">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) \ L(R(a(x,y,a(z,u,w)),v5,v6),v7,v8),a(x,y,a(z,u,w)),v5 * v6) = L(a(a(x,y,a(z,u,w)),v5,v6),v7,v8)
    ]]></literal>
    <justification jstring="[para(13401(a,1),14752(a,1,1))].">
      <j1 rule="para" parents="13401 14752"/>
    </justification>
  </clause>

  <clause id="14794">
    <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(14705(a,1),14254(a,1))].">
      <j1 rule="para" parents="14705 14254"/>
    </justification>
  </clause>

  <clause id="14795">
    <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(14794,a,10966,a)].">
      <j1 rule="hyper" parents="14794 10966"/>
    </justification>
  </clause>

  <clause id="14796">
    <literal><![CDATA[
      L(K(x,y),z,u) * (u * (K(y,x) * z)) = z * T(u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(5863,a,14721,a)].">
      <j1 rule="hyper" parents="5863 14721"/>
    </justification>
  </clause>

  <clause id="14797">
    <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(13100(a,1),14731(a,1))].">
      <j1 rule="para" parents="13100 14731"/>
    </justification>
  </clause>

  <clause id="14798">
    <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(13779(a,1),14733(a,1,2))].">
      <j1 rule="para" parents="13779 14733"/>
    </justification>
  </clause>

  <clause id="14799">
    <literal><![CDATA[
      K(x,L(y / z,u,y \ u)) = K(x,u / (z * (y \ u)))
    ]]></literal>
    <justification jstring="[para(5(a,1),14737(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 14737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14800">
    <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(4314(a,2),14799(a,2,2,2,2))].">
      <j1 rule="para" parents="4314 14799"/>
    </justification>
  </clause>

  <clause id="14801">
    <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(13092(a,1),14785(a,1))].">
      <j1 rule="para" parents="13092 14785"/>
    </justification>
  </clause>

  <clause id="14802">
    <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,10946,a,b,14796,a)].">
      <j1 rule="hyper" parents="58 10946 14796"/>
    </justification>
  </clause>

  <clause id="14803">
    <literal><![CDATA[
      K(T(x / y,z) \ 1,L(u,y,y \ z)) = K((x * (y \ z)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,6230,a(flip),b,14726,a),flip(a)].">
      <j1 rule="hyper" parents="320 6230 14726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14804">
    <literal><![CDATA[
      K((x / y) \ 1,T(L(z,y,y \ u),u)) = K((x * (y \ u)) \ u,z)
    ]]></literal>
    <justification jstring="[hyper(7687,a,14803,a)].">
      <j1 rule="hyper" parents="7687 14803"/>
    </justification>
  </clause>

  <clause id="14805">
    <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),14804(a,1,2))].">
      <j1 rule="para" parents="20 14804"/>
    </justification>
  </clause>

  <clause id="14806">
    <literal><![CDATA[
      a(x,y,K(z,(u / y) \ z)) \ K(x,(y * z) / u) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(8455(a,1),14740(a,1,1,3))].">
      <j1 rule="para" parents="8455 14740"/>
    </justification>
  </clause>

  <clause id="14807">
    <literal><![CDATA[
      a(x,y,K(z,u / y)) \ K(z,(y * x) / u) = K(z,y / (u / x))
    ]]></literal>
    <justification jstring="[para(14238(a,1),14806(a,1,1))].">
      <j1 rule="para" parents="14238 14806"/>
    </justification>
  </clause>

  <clause id="14808">
    <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(320,a,7142,a,b,14727,a),flip(a)].">
      <j1 rule="hyper" parents="320 7142 14727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14809">
    <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(261(a,1),14736(a,2,2,1))].">
      <j1 rule="para" parents="261 14736"/>
    </justification>
  </clause>

  <clause id="14810">
    <literal><![CDATA[
      T(K(x,y),z) * T(y,x) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(9148,a,14792,a),flip(a)].">
      <j1 rule="hyper" parents="9148 14792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14811">
    <literal><![CDATA[
      K(x,y / z) * T(z \ y,x) = T(z \ y,K(x,y))
    ]]></literal>
    <justification jstring="[para(7856(a,1),14810(a,1,1))].">
      <j1 rule="para" parents="7856 14810"/>
    </justification>
  </clause>

  <clause id="14813">
    <literal><![CDATA[
      T(x \ y,K(z,y)) = T(y / x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7599,a(flip),b,14811,a),flip(a)].">
      <j1 rule="hyper" parents="58 7599 14811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14814">
    <literal><![CDATA[
      (x \ y) / T(y / x,T(x,z)) = K(K(z,y),x \ y)
    ]]></literal>
    <justification jstring="[para(14813(a,1),4753(a,2,2)),flip(a)].">
      <j1 rule="para" parents="14813 4753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14815">
    <literal><![CDATA[
      (x \ y) / T(y / x,T(x,z)) = K(z,K(y,x \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7730,a(flip),b,14814,a),flip(a)].">
      <j1 rule="hyper" parents="320 7730 14814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14816">
    <literal><![CDATA[
      (x \ y) / T(y / x,T(x,z)) = K(z,K(y,y / x))
    ]]></literal>
    <justification jstring="[para(5159(a,2),14815(a,2,2))].">
      <j1 rule="para" parents="5159 14815"/>
    </justification>
  </clause>

  <clause id="14817">
    <literal><![CDATA[
      (x \ y) / T(y / x,T(x,z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,8128,a(flip),b,14816,a),flip(a)].">
      <j1 rule="hyper" parents="320 8128 14816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14818">
    <literal><![CDATA[
      (x \ y) / T(y / x,T(x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7759,a(flip),b,14817,a),flip(a)].">
      <j1 rule="hyper" parents="320 7759 14817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14819">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,z \ (R(1 / y,y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(14419,a,14795,a)].">
      <j1 rule="hyper" parents="14419 14795"/>
    </justification>
  </clause>

  <clause id="14821">
    <literal><![CDATA[
      K(x,y \ (R(1 / z,z,y) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14533,a(flip),b,14819,a),flip(a)].">
      <j1 rule="hyper" parents="58 14533 14819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14822">
    <literal><![CDATA[
      K(x,y \ ((y / (z * y)) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(219(a,1),14821(a,1,2,2,1))].">
      <j1 rule="para" parents="219 14821"/>
    </justification>
  </clause>

  <clause id="14823">
    <literal><![CDATA[
      K(x,y \ ((z / y) \ u)) = K(x,y \ ((y / z) * u))
    ]]></literal>
    <justification jstring="[para(409(a,1),14821(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="409 14821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14824">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z \ ((z / u) * w)) = K(y,T(z \ ((u / z) \ w),x))
    ]]></literal>
    <justification jstring="[hyper(14030,a,14823,a),flip(a)].">
      <j1 rule="hyper" parents="14030 14823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14825">
    <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(14824(a,1),14030(a,1))].">
      <j1 rule="para" parents="14824 14030"/>
    </justification>
  </clause>

  <clause id="14826">
    <literal><![CDATA[
      K(x,L((y / z) \ u,y / z,z) \ 1) = K(x,T(y / (u * z),y / z))
    ]]></literal>
    <justification jstring="[hyper(320,a,9761,a(flip),b,14808,a),flip(a)].">
      <j1 rule="hyper" parents="320 9761 14808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14827">
    <literal><![CDATA[
      K(x,T(y / (z * u),y / u)) = K(x,(u * z) \ (u * (y / u)))
    ]]></literal>
    <justification jstring="[hyper(6453,a,14826,a),flip(a)].">
      <j1 rule="hyper" parents="6453 14826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14828">
    <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(320,a,13059,a(flip),b,14827,a),flip(a)].">
      <j1 rule="hyper" parents="320 13059 14827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14829">
    <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(5703(a,1),14827(a,2,2,1))].">
      <j1 rule="para" parents="5703 14827"/>
    </justification>
  </clause>

  <clause id="14830">
    <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(320,a,145,a(flip),b,14786,a),flip(a)].">
      <j1 rule="hyper" parents="320 145 14786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14832">
    <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(1624(a,1),14830(a,1,2))].">
      <j1 rule="para" parents="1624 14830"/>
    </justification>
  </clause>

  <clause id="14833">
    <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(11713(a,1),14802(a,1,1))].">
      <j1 rule="para" parents="11713 14802"/>
    </justification>
  </clause>

  <clause id="14834">
    <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(7807(a,1),14833(a,1,1,2))].">
      <j1 rule="para" parents="7807 14833"/>
    </justification>
  </clause>

  <clause id="14835">
    <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(13492,a,14834,a)].">
      <j1 rule="hyper" parents="13492 14834"/>
    </justification>
  </clause>

  <clause id="14836">
    <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(766,a,14834,a)].">
      <j1 rule="hyper" parents="766 14834"/>
    </justification>
  </clause>

  <clause id="14837">
    <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(8057(a,2),14835(a,1,2,2))].">
      <j1 rule="para" parents="8057 14835"/>
    </justification>
  </clause>

  <clause id="14838">
    <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(8897(a,2),14837(a,1,2))].">
      <j1 rule="para" parents="8897 14837"/>
    </justification>
  </clause>

  <clause id="14839">
    <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(7846(a,2),14838(a,1,2,2,2))].">
      <j1 rule="para" parents="7846 14838"/>
    </justification>
  </clause>

  <clause id="14840">
    <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),14828(a,1,2,1,2))].">
      <j1 rule="para" parents="5 14828"/>
    </justification>
  </clause>

  <clause id="14841">
    <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(3638(a,1),14772(a,1,2))].">
      <j1 rule="para" parents="3638 14772"/>
    </justification>
  </clause>

  <clause id="14842">
    <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(13245(a,1),14841(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13245 14841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14843">
    <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,5539,a(flip),b,14842,a)].">
      <j1 rule="hyper" parents="58 5539 14842"/>
    </justification>
  </clause>

  <clause id="14844">
    <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(14353(a,1),14746(a,1,2))].">
      <j1 rule="para" parents="14353 14746"/>
    </justification>
  </clause>

  <clause id="14845">
    <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(14530,a,14844,a),flip(a)].">
      <j1 rule="hyper" parents="14530 14844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14846">
    <literal><![CDATA[
      (K(x,y) * z) * R(u,z,K(x,T(y,z))) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(7152(a,1),14845(a,1,1))].">
      <j1 rule="para" parents="7152 14845"/>
    </justification>
  </clause>

  <clause id="14847">
    <literal><![CDATA[
      (K(x,y) * z) * R(u,z,K(x,y)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(10361(a,1),14846(a,1,2))].">
      <j1 rule="para" parents="10361 14846"/>
    </justification>
  </clause>

  <clause id="14848">
    <literal><![CDATA[
      R(x,y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(479,a,14847,a),flip(a)].">
      <j1 rule="hyper" parents="479 14847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14849">
    <literal><![CDATA[
      L(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(14747,a,14848,a),flip(a)].">
      <j1 rule="hyper" parents="14747 14848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14850">
    <literal><![CDATA[
      L((x * K(y,z)) / u,u,K(z,y)) = x / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6326,a,14848,a),flip(a)].">
      <j1 rule="hyper" parents="6326 14848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14851">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) = (y * K(z,u)) / ((x \ y) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(874,a,14848,a),flip(a)].">
      <j1 rule="hyper" parents="874 14848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14852">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14745,a,b,14848,a)].">
      <j1 rule="hyper" parents="58 14745 14848"/>
    </justification>
  </clause>

  <clause id="14853">
    <literal><![CDATA[
      x \ L(x,y,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,14848,a(flip),b,14745,a)].">
      <j1 rule="hyper" parents="116 14848 14745"/>
    </justification>
  </clause>

  <clause id="14854">
    <literal><![CDATA[
      L(x,y,K(z,u)) * (y * K(z,u)) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14848(a,1),101(a,1,1))].">
      <j1 rule="para" parents="14848 101"/>
    </justification>
  </clause>

  <clause id="14855">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) \ (y * K(z,u)) = (x \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14848(a,1),505(a,1,1))].">
      <j1 rule="para" parents="14848 505"/>
    </justification>
  </clause>

  <clause id="14856">
    <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(14848(a,1),6871(a,1))].">
      <j1 rule="para" parents="14848 6871"/>
    </justification>
  </clause>

  <clause id="14857">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(14848(a,1),14747(a,1))].">
      <j1 rule="para" parents="14848 14747"/>
    </justification>
  </clause>

  <clause id="14858">
    <literal><![CDATA[
      T(x,a(y,(z \ y) * u,z)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,14412,a,b,14849,a)].">
      <j1 rule="hyper" parents="320 14412 14849"/>
    </justification>
  </clause>

  <clause id="14859">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,14349,a,b,14849,a)].">
      <j1 rule="hyper" parents="320 14349 14849"/>
    </justification>
  </clause>

  <clause id="14860">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14244,a,b,14849,a)].">
      <j1 rule="hyper" parents="320 14244 14849"/>
    </justification>
  </clause>

  <clause id="14861">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14212,a,b,14849,a)].">
      <j1 rule="hyper" parents="320 14212 14849"/>
    </justification>
  </clause>

  <clause id="14862">
    <literal><![CDATA[
      a(x,y,K(z,u)) * z = L(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,13354,a,b,14849,a)].">
      <j1 rule="hyper" parents="320 13354 14849"/>
    </justification>
  </clause>

  <clause id="14863">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,13350,a,b,14849,a)].">
      <j1 rule="hyper" parents="320 13350 14849"/>
    </justification>
  </clause>

  <clause id="14864">
    <literal><![CDATA[
      L(1 / x,y,K(z,u)) = a(x,y,K(u,z)) / x
    ]]></literal>
    <justification jstring="[hyper(320,a,14376,a(flip),b,14849,a),flip(a)].">
      <j1 rule="hyper" parents="320 14376 14849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14865">
    <literal><![CDATA[
      L(T(x,y),x \ z,K(u,w)) = T(T(x,a(w,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,14348,a(flip),b,14849,a),flip(a)].">
      <j1 rule="hyper" parents="320 14348 14849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14866">
    <literal><![CDATA[
      L(T(x,y),z,K(u,y)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14288,a(flip),b,14849,a),flip(a)].">
      <j1 rule="hyper" parents="320 14288 14849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14867">
    <literal><![CDATA[
      L(x / a(y,z,u),z,K(u,y)) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(320,a,107,a(flip),b,14849,a),flip(a)].">
      <j1 rule="hyper" parents="320 107 14849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14868">
    <literal><![CDATA[
      (x / y) * L(y,z,K(u,w)) = x * a(y,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,14849,a,b,14215,a)].">
      <j1 rule="hyper" parents="119 14849 14215"/>
    </justification>
  </clause>

  <clause id="14869">
    <literal><![CDATA[
      x \ L(x,y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,14849,a,b,13350,a)].">
      <j1 rule="hyper" parents="116 14849 13350"/>
    </justification>
  </clause>

  <clause id="14870">
    <literal><![CDATA[
      T(L(x,y,K(z,u)),a(z,y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,14380,a(flip),b,14849,a),flip(a)].">
      <j1 rule="hyper" parents="36 14380 14849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14871">
    <literal><![CDATA[
      L(x,y,K(L(z,u,w),v5)) = T(x,a(v5,y,z))
    ]]></literal>
    <justification jstring="[hyper(13382,a,14849,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="13382 14849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14872">
    <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(14849(a,2),421(a,1))].">
      <j1 rule="para" parents="14849 421"/>
    </justification>
  </clause>

  <clause id="14873">
    <literal><![CDATA[
      (x * y) * a(z,u,K(y,w)) = x * L(y,u,K(w,z))
    ]]></literal>
    <justification jstring="[para(14849(a,2),13349(a,2,2))].">
      <j1 rule="para" parents="14849 13349"/>
    </justification>
  </clause>

  <clause id="14874">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,y)) = x \ L(y,u,K(z,w))
    ]]></literal>
    <justification jstring="[para(14849(a,2),14278(a,2,2))].">
      <j1 rule="para" parents="14849 14278"/>
    </justification>
  </clause>

  <clause id="14875">
    <literal><![CDATA[
      L(x,y,K(z,u)) * a(z,y,u) = a(z,y,u) * x
    ]]></literal>
    <justification jstring="[para(14849(a,2),14379(a,1,1))].">
      <j1 rule="para" parents="14849 14379"/>
    </justification>
  </clause>

  <clause id="14876">
    <literal><![CDATA[
      L(x,y,K(z,u)) / u = T(x / u,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(14849(a,2),14384(a,1,1))].">
      <j1 rule="para" parents="14849 14384"/>
    </justification>
  </clause>

  <clause id="14877">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,K(u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,14849,a,b,14870,a)].">
      <j1 rule="hyper" parents="58 14849 14870"/>
    </justification>
  </clause>

  <clause id="14878">
    <literal><![CDATA[
      T((K(x,y) * z) \ u,a(x,z,y)) = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(5115(a,1),14870(a,1,1))].">
      <j1 rule="para" parents="5115 14870"/>
    </justification>
  </clause>

  <clause id="14879">
    <literal><![CDATA[
      L((K(x,y) * z) \ u,z,K(y,x)) = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(5734,a,14877,a),flip(a)].">
      <j1 rule="hyper" parents="5734 14877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14880">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(14853(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14853 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14881">
    <literal><![CDATA[
      L(x,y \ z,K(y,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14849,a,b,14859,a)].">
      <j1 rule="hyper" parents="58 14849 14859"/>
    </justification>
  </clause>

  <clause id="14882">
    <literal><![CDATA[
      a(x,y,z) * (u / a(x,y,z)) = L(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14374,a(flip),b,14861,a)].">
      <j1 rule="hyper" parents="58 14374 14861"/>
    </justification>
  </clause>

  <clause id="14883">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (z * w) = L(z,y,K(u,x)) * w
    ]]></literal>
    <justification jstring="[para(14862(a,1),14201(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14862 14201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14884">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ x = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(14863(a,1),9684(a,1,1))].">
      <j1 rule="para" parents="14863 9684"/>
    </justification>
  </clause>

  <clause id="14885">
    <literal><![CDATA[
      L(x,y * z,K(y,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),14881(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 14881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14886">
    <literal><![CDATA[
      L(L(x,y,z),y,K(z,u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(6846,a,14885,a),flip(a)].">
      <j1 rule="hyper" parents="6846 14885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14887">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,z) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(14885(a,1),6847(a,1,1))].">
      <j1 rule="para" parents="14885 6847"/>
    </justification>
  </clause>

  <clause id="14888">
    <literal><![CDATA[
      L(x,y,K(z,L(u,w,v5))) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(10581(a,1),14871(a,1,3))].">
      <j1 rule="para" parents="10581 14871"/>
    </justification>
  </clause>

  <clause id="14889">
    <literal><![CDATA[
      L(x,T(y,z),T(u,y)) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(6942,a,14886,a),flip(a)].">
      <j1 rule="hyper" parents="6942 14886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14891">
    <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(14886(a,1),1397(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14886 1397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14892">
    <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(14886(a,1),14884(a,1,1))].">
      <j1 rule="para" parents="14886 14884"/>
    </justification>
  </clause>

  <clause id="14893">
    <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(14889(a,1),13223(a,1))].">
      <j1 rule="para" parents="14889 13223"/>
    </justification>
  </clause>

  <clause id="14894">
    <literal><![CDATA[
      L(L(x,y,K(z * u,u \ 1)),y,z * u) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,12597,a(flip),b,14887,a),flip(a)].">
      <j1 rule="hyper" parents="320 12597 14887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14895">
    <literal><![CDATA[
      L(x,y,K(z,L(u,w,v5))) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14849,a,b,14888,a),flip(a)].">
      <j1 rule="hyper" parents="320 14849 14888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14896">
    <literal><![CDATA[
      L(x,(y \ z) * u,K(y,z)) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14849,a,b,14858,a)].">
      <j1 rule="hyper" parents="58 14849 14858"/>
    </justification>
  </clause>

  <clause id="14898">
    <literal><![CDATA[
      L(x / y,z,K(u,y)) = L(x,z,K(u,y)) / y
    ]]></literal>
    <justification jstring="[hyper(320,a,14849,a,b,14876,a)].">
      <j1 rule="hyper" parents="320 14849 14876"/>
    </justification>
  </clause>

  <clause id="14899">
    <literal><![CDATA[
      L(L(x,y,z \ u),y,K(z,u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,12707,a(flip),b,14896,a),flip(a)].">
      <j1 rule="hyper" parents="58 12707 14896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14900">
    <literal><![CDATA[
      L(x * y,z,K(u,x)) = x * L(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(876,a,14898,a),flip(a)].">
      <j1 rule="hyper" parents="876 14898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14901">
    <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(440,a,14867,a,b,14406,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="440 14867 14406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14902">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(14195(a,2),14880(a,1,2))].">
      <j1 rule="para" parents="14195 14880"/>
    </justification>
  </clause>

  <clause id="14903">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(14209(a,1),14880(a,1))].">
      <j1 rule="para" parents="14209 14880"/>
    </justification>
  </clause>

  <clause id="14904">
    <literal><![CDATA[
      R(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(14745(a,1),14880(a,1))].">
      <j1 rule="para" parents="14745 14880"/>
    </justification>
  </clause>

  <clause id="14905">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(14342(a,2),14903(a,1))].">
      <j1 rule="para" parents="14342 14903"/>
    </justification>
  </clause>

  <clause id="14906">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z \ y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(14859(a,1),14903(a,1))].">
      <j1 rule="para" parents="14859 14903"/>
    </justification>
  </clause>

  <clause id="14907">
    <literal><![CDATA[
      L(x,y,K(z,u)) / a(u,y,z) = a(u,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,14877,a(flip),b,14882,a),flip(a)].">
      <j1 rule="hyper" parents="116 14877 14882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14908">
    <literal><![CDATA[
      x / a(y,z,x) = a(y,z,x) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,7493,a(flip),b,14882,a),flip(a)].">
      <j1 rule="hyper" parents="116 7493 14882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14909">
    <literal><![CDATA[
      L(T(x,y),x \ z,K(u,w)) = T(L(x,z,K(u,w)),y)
    ]]></literal>
    <justification jstring="[para(14849(a,2),14865(a,2,1))].">
      <j1 rule="para" parents="14849 14865"/>
    </justification>
  </clause>

  <clause id="14910">
    <literal><![CDATA[
      L(T(x,y),x \ z,K(u,w)) = L(T(x,y),z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,20,a,b,14909,a),flip(a)].">
      <j1 rule="hyper" parents="320 20 14909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14911">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,14909,a(flip))].">
      <j1 rule="hyper" parents="139 14909"/>
    </justification>
  </clause>

  <clause id="14912">
    <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(14911(a,1),14062(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14911 14062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14913">
    <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(6801(a,1),14854(a,1,2))].">
      <j1 rule="para" parents="6801 14854"/>
    </justification>
  </clause>

  <clause id="14914">
    <literal><![CDATA[
      x \ (K(y,z) * ((K(z,y) * x) * u)) = T(u,a(z,x,y))
    ]]></literal>
    <justification jstring="[para(4(a,1),14878(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 14878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14915">
    <literal><![CDATA[
      (K(x,y) * (x * y)) \ z = (x * y) \ (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(11145,a,14879,a)].">
      <j1 rule="hyper" parents="11145 14879"/>
    </justification>
  </clause>

  <clause id="14916">
    <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(704(a,1),14879(a,1,1)),flip(a)].">
      <j1 rule="para" parents="704 14879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14917">
    <literal><![CDATA[
      (x * y) \ (K(y,x) * z) = (T(x,y) * y) \ z
    ]]></literal>
    <justification jstring="[para(4740(a,1),14915(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4740 14915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14918">
    <literal><![CDATA[
      K(x,y) * ((K(y,x) * z) * u) = z * L(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,14849,a,b,14914,a),flip(a)].">
      <j1 rule="hyper" parents="119 14849 14914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14919">
    <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(440,a,14918,a,b,1634,a)].">
      <j1 rule="hyper" parents="440 14918 1634"/>
    </justification>
  </clause>

  <clause id="14920">
    <literal><![CDATA[
      (x * y) * (z * L(u,z,K(y,x))) = (y * x) * ((K(x,y) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(119,a,14918,a(flip),b,11119,a)].">
      <j1 rule="hyper" parents="119 14918 11119"/>
    </justification>
  </clause>

  <clause id="14921">
    <literal><![CDATA[
      L(x,y,T(z,u)) \ L(x,y,z) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,11763,a(flip),b,14892,a),flip(a)].">
      <j1 rule="hyper" parents="320 11763 14892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14923">
    <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(14921(a,1),490(a,1,1,1))].">
      <j1 rule="para" parents="14921 490"/>
    </justification>
  </clause>

  <clause id="14924">
    <literal><![CDATA[
      (x * K(y,z)) / ((u \ x) * K(y,z)) = L(u,x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14911,a(flip),b,14851,a),flip(a)].">
      <j1 rule="hyper" parents="58 14911 14851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14925">
    <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(14851(a,2),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="14851 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14926">
    <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(5926(a,1),14924(a,1,2,1))].">
      <j1 rule="para" parents="5926 14924"/>
    </justification>
  </clause>

  <clause id="14927">
    <literal><![CDATA[
      L(x,x \ y,K(z,z \ y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(4974(a,1),14855(a,1,2))].">
      <j1 rule="para" parents="4974 14855"/>
    </justification>
  </clause>

  <clause id="14928">
    <literal><![CDATA[
      L(L(x,y,K(z,u * z)),y,u * z) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(12672(a,1),14894(a,1,1))].">
      <j1 rule="para" parents="12672 14894"/>
    </justification>
  </clause>

  <clause id="14929">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,u * z) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(12545(a,1),14928(a,1,1))].">
      <j1 rule="para" parents="12545 14928"/>
    </justification>
  </clause>

  <clause id="14930">
    <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,13889,a(flip),b,14929,a)].">
      <j1 rule="hyper" parents="58 13889 14929"/>
    </justification>
  </clause>

  <clause id="14931">
    <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(14062(a,1),14925(a,1))].">
      <j1 rule="para" parents="14062 14925"/>
    </justification>
  </clause>

  <clause id="14932">
    <literal><![CDATA[
      T(x * a(y,x,K(z,u)),y) = y \ (K(z,u) * ((K(u,z) * x) * y))
    ]]></literal>
    <justification jstring="[para(14868(a,1),14919(a,1,1))].">
      <j1 rule="para" parents="14868 14919"/>
    </justification>
  </clause>

  <clause id="14933">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) * u)) / u = z * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(249,a,14932,a)].">
      <j1 rule="hyper" parents="249 14932"/>
    </justification>
  </clause>

  <clause id="14934">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) * (u \ 1))) / (u \ 1) = z * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(14273(a,1),14933(a,2,2))].">
      <j1 rule="para" parents="14273 14933"/>
    </justification>
  </clause>

  <clause id="14935">
    <literal><![CDATA[
      L(x,x \ y,K(z,y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(12530(a,1),14927(a,1,1))].">
      <j1 rule="para" parents="12530 14927"/>
    </justification>
  </clause>

  <clause id="14936">
    <literal><![CDATA[
      (x \ y) * K(z,z \ y) = x \ (z * (y / z))
    ]]></literal>
    <justification jstring="[para(13630(a,1),14935(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13630 14935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14937">
    <literal><![CDATA[
      K(x,y * ((z * y) \ (z * (u / z)))) = K(x,T(y * ((z * y) \ u),z))
    ]]></literal>
    <justification jstring="[para(14936(a,1),14100(a,1,2,2))].">
      <j1 rule="para" parents="14936 14100"/>
    </justification>
  </clause>

  <clause id="14938">
    <literal><![CDATA[
      T(K(x,y) * ((x \ y) / z),z) = z \ ((x \ y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(12547(a,1),14912(a,2,1))].">
      <j1 rule="para" parents="12547 14912"/>
    </justification>
  </clause>

  <clause id="14939">
    <literal><![CDATA[
      T(K(x,y) * ((x \ y) / z),z) = z \ (K(x,y) * (x \ y))
    ]]></literal>
    <justification jstring="[para(6433(a,2),14938(a,2,2))].">
      <j1 rule="para" parents="6433 14938"/>
    </justification>
  </clause>

  <clause id="14940">
    <literal><![CDATA[
      x \ (K(y,z) * (y \ z)) = (x \ (y \ z)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(14931,a,14939,a),flip(a)].">
      <j1 rule="hyper" parents="14931 14939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14941">
    <literal><![CDATA[
      x \ (y \ ((y * z) / y)) = (x \ (y \ z)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5358,a,b,14940,a)].">
      <j1 rule="hyper" parents="58 5358 14940"/>
    </justification>
  </clause>

  <clause id="14942">
    <literal><![CDATA[
      (K(x,y) * z) \ (x \ ((x * y) / x)) = (z \ (x \ T(y,x))) * K(x,y)
    ]]></literal>
    <justification jstring="[para(14122(a,1),14941(a,2,1))].">
      <j1 rule="para" parents="14122 14941"/>
    </justification>
  </clause>

  <clause id="14943">
    <literal><![CDATA[
      (x \ (y \ T(z,y))) * K(y,z) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,13978,a(flip),b,14942,a),flip(a)].">
      <j1 rule="hyper" parents="58 13978 14942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14944">
    <literal><![CDATA[
      (x \ (y \ z)) * K(z,y) = x \ (y \ T(z,y))
    ]]></literal>
    <justification jstring="[hyper(6315,a,14943,a)].">
      <j1 rule="hyper" parents="6315 14943"/>
    </justification>
  </clause>

  <clause id="14945">
    <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(14886(a,1),14891(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14886 14891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14946">
    <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(3978(a,1),14913(a,1,1))].">
      <j1 rule="para" parents="3978 14913"/>
    </justification>
  </clause>

  <clause id="14947">
    <literal><![CDATA[
      (x * (1 / T(y,z))) * K(y,u) = x * (K(y,u) / T(y,z))
    ]]></literal>
    <justification jstring="[para(10173(a,1),14946(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10173 14946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14948">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = x * (K(y,z) / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6713,a,b,14947,a)].">
      <j1 rule="hyper" parents="58 6713 14947"/>
    </justification>
  </clause>

  <clause id="14949">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(4715(a,1),14948(a,2,2))].">
      <j1 rule="para" parents="4715 14948"/>
    </justification>
  </clause>

  <clause id="14950">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2594,a,14949,a),flip(a)].">
      <j1 rule="hyper" parents="2594 14949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14952">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,T(y,z)) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(6714,a,14950,a)].">
      <j1 rule="hyper" parents="6714 14950"/>
    </justification>
  </clause>

  <clause id="14953">
    <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(14952(a,1),11458(a,2,2))].">
      <j1 rule="para" parents="14952 11458"/>
    </justification>
  </clause>

  <clause id="14954">
    <literal><![CDATA[
      x / (T(y,z) \ R(x,y \ 1,y)) = (x * (1 / T(T(y,1),z))) \ x
    ]]></literal>
    <justification jstring="[para(14953(a,1),8342(a,1,2))].">
      <j1 rule="para" parents="14953 8342"/>
    </justification>
  </clause>

  <clause id="14956">
    <literal><![CDATA[
      (x * (1 / T(T(y,1),z))) \ x = T((x * (1 / y)) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11437,a(flip),b,14954,a),flip(a)].">
      <j1 rule="hyper" parents="58 11437 14954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14957">
    <literal><![CDATA[
      T((x * (1 / y)) \ x,z) = (x * (1 / T(y,z))) \ x
    ]]></literal>
    <justification jstring="[para(198(a,1),14956(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="198 14956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14958">
    <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(14957(a,2),13009(a,1,2,2,1))].">
      <j1 rule="para" parents="14957 13009"/>
    </justification>
  </clause>

  <clause id="14959">
    <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(320,a,13969,a(flip),b,14916,a),flip(a)].">
      <j1 rule="hyper" parents="320 13969 14916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14961">
    <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(14920(a,1),14930(a,1,1))].">
      <j1 rule="para" parents="14920 14930"/>
    </justification>
  </clause>

  <clause id="14962">
    <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),14782(a,2,2,1,1))].">
      <j1 rule="para" parents="7 14782"/>
    </justification>
  </clause>

  <clause id="14963">
    <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(320,a,13746,a(flip),b,14962,a),flip(a)].">
      <j1 rule="hyper" parents="320 13746 14962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14965">
    <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(13874(a,1),14963(a,1,2,1))].">
      <j1 rule="para" parents="13874 14963"/>
    </justification>
  </clause>

  <clause id="14966">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) / (u * ((z \ 1) / u))) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(6892(a,1),14965(a,1,2,2))].">
      <j1 rule="para" parents="6892 14965"/>
    </justification>
  </clause>

  <clause id="14967">
    <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(7137(a,2),14839(a,1,2,2))].">
      <j1 rule="para" parents="7137 14839"/>
    </justification>
  </clause>

  <clause id="14968">
    <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(4956(a,2),14771(a,1,1,1,2,3))].">
      <j1 rule="para" parents="4956 14771"/>
    </justification>
  </clause>

  <clause id="14969">
    <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),14832(a,1,1))].">
      <j1 rule="para" parents="68 14832"/>
    </justification>
  </clause>

  <clause id="14970">
    <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(14748(a,1),14969(a,1,2,1))].">
      <j1 rule="para" parents="14748 14969"/>
    </justification>
  </clause>

  <clause id="14971">
    <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(288,a,14970,a)].">
      <j1 rule="hyper" parents="288 14970"/>
    </justification>
  </clause>

  <clause id="14972">
    <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,13361,a(flip),b,14971,a),flip(a)].">
      <j1 rule="hyper" parents="58 13361 14971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14974">
    <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(3663(a,1),14968(a,1,1,1,2))].">
      <j1 rule="para" parents="3663 14968"/>
    </justification>
  </clause>

  <clause id="14975">
    <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(12552(a,1),14974(a,1,1,1,2))].">
      <j1 rule="para" parents="12552 14974"/>
    </justification>
  </clause>

  <clause id="14976">
    <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(14390(a,1),14975(a,1,1,1))].">
      <j1 rule="para" parents="14390 14975"/>
    </justification>
  </clause>

  <clause id="14977">
    <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(14714(a,1),14976(a,1,1))].">
      <j1 rule="para" parents="14714 14976"/>
    </justification>
  </clause>

  <clause id="14978">
    <literal><![CDATA[
      R(K(x,y) * z,u,u \ 1) = K(x,y) * R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,10075,a(flip),b,14977,a)].">
      <j1 rule="hyper" parents="58 10075 14977"/>
    </justification>
  </clause>

  <clause id="14980">
    <literal><![CDATA[
      R(K(x,y) * (z / u),u,u \ 1) = K(x,y) * (z * (u \ 1))
    ]]></literal>
    <justification jstring="[para(523(a,1),14978(a,2,2))].">
      <j1 rule="para" parents="523 14978"/>
    </justification>
  </clause>

  <clause id="14981">
    <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(14978(a,2),14959(a,1,2))].">
      <j1 rule="para" parents="14978 14959"/>
    </justification>
  </clause>

  <clause id="14982">
    <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(14980(a,1),559(a,1,1))].">
      <j1 rule="para" parents="14980 559"/>
    </justification>
  </clause>

  <clause id="14983">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) / u)) * u = z * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(14982,a,14934,a)].">
      <j1 rule="hyper" parents="14982 14934"/>
    </justification>
  </clause>

  <clause id="14984">
    <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(13959(a,1),14983(a,1,1,2))].">
      <j1 rule="para" parents="13959 14983"/>
    </justification>
  </clause>

  <clause id="14985">
    <literal><![CDATA[
      a(K(x,y) * z,u,u \ 1) = z \ R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(5095(a,1),14981(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5095 14981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14986">
    <literal><![CDATA[
      a(K(x,y) * z,u,u \ 1) = a(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,704,a(flip),b,14985,a),flip(a)].">
      <j1 rule="hyper" parents="320 704 14985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14987">
    <literal><![CDATA[
      a(x * K(y,z),u,u \ 1) = a(x,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(7261(a,1),14986(a,1,1))].">
      <j1 rule="para" parents="7261 14986"/>
    </justification>
  </clause>

  <clause id="14988">
    <literal><![CDATA[
      a(x \ (y / z),u,u \ 1) = a(x \ (z \ y),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(13896(a,1),14987(a,1,1))].">
      <j1 rule="para" parents="13896 14987"/>
    </justification>
  </clause>

  <clause id="14989">
    <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(7758(a,1),14984(a,1,1,2,1))].">
      <j1 rule="para" parents="7758 14984"/>
    </justification>
  </clause>

  <clause id="14990">
    <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(6306(a,1),14756(a,1,2,1))].">
      <j1 rule="para" parents="6306 14756"/>
    </justification>
  </clause>

  <clause id="14991">
    <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(14764(a,1),14901(a,1,2,1))].">
      <j1 rule="para" parents="14764 14901"/>
    </justification>
  </clause>

  <clause id="14992">
    <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(5125,a,14991,a)].">
      <j1 rule="hyper" parents="5125 14991"/>
    </justification>
  </clause>

  <clause id="14993">
    <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(447(a,1),14749(a,1,2)),flip(a)].">
      <j1 rule="para" parents="447 14749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14994">
    <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(320,a,14830,a(flip),b,14993,a),flip(a)].">
      <j1 rule="hyper" parents="320 14830 14993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14995">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,v5,v6)) = a(x,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(893,a,14994,a),flip(a)].">
      <j1 rule="hyper" parents="893 14994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14998">
    <literal><![CDATA[
      a((x * y) \ z,u,a(w,v5,v6)) = a(y \ (x \ z),u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(298(a,1),14995(a,1,1))].">
      <j1 rule="para" parents="298 14995"/>
    </justification>
  </clause>

  <clause id="14999">
    <literal><![CDATA[
      a((x \ y) \ 1,z,a(u,w,v5)) = a(y \ x,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(390(a,1),14995(a,1,1)),flip(a)].">
      <j1 rule="para" parents="390 14995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15000">
    <literal><![CDATA[
      a(x \ ((x / y) * z),u,a(w,v5,v6)) = a(y \ z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(492(a,1),14995(a,1,1))].">
      <j1 rule="para" parents="492 14995"/>
    </justification>
  </clause>

  <clause id="15001">
    <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(2533(a,1),14995(a,1,1))].">
      <j1 rule="para" parents="2533 14995"/>
    </justification>
  </clause>

  <clause id="15002">
    <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(13935(a,2),15000(a,1,1))].">
      <j1 rule="para" parents="13935 15000"/>
    </justification>
  </clause>

  <clause id="15003">
    <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,14995,a(flip),b,15001,a),flip(a)].">
      <j1 rule="hyper" parents="58 14995 15001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15005">
    <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(320,a,14998,a(flip),b,15003,a),flip(a)].">
      <j1 rule="hyper" parents="320 14998 15003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15006">
    <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),15005(a,2,1,2))].">
      <j1 rule="para" parents="4 15005"/>
    </justification>
  </clause>

  <clause id="15007">
    <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(320,a,14998,a(flip),b,15006,a),flip(a)].">
      <j1 rule="hyper" parents="320 14998 15006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15008">
    <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),15007(a,2,1,2))].">
      <j1 rule="para" parents="61 15007"/>
    </justification>
  </clause>

  <clause id="15009">
    <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),15008(a,1,1,1))].">
      <j1 rule="para" parents="2 15008"/>
    </justification>
  </clause>

  <clause id="15011">
    <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(12238(a,1),14781(a,2,2))].">
      <j1 rule="para" parents="12238 14781"/>
    </justification>
  </clause>

  <clause id="15012">
    <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(7654(a,1),15011(a,1,2,1))].">
      <j1 rule="para" parents="7654 15011"/>
    </justification>
  </clause>

  <clause id="15013">
    <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(5563(a,1),15012(a,1,2,2))].">
      <j1 rule="para" parents="5563 15012"/>
    </justification>
  </clause>

  <clause id="15014">
    <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(9416(a,2),15013(a,1,2,2))].">
      <j1 rule="para" parents="9416 15013"/>
    </justification>
  </clause>

  <clause id="15015">
    <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(12189(a,1),15014(a,1,2,2,1))].">
      <j1 rule="para" parents="12189 15014"/>
    </justification>
  </clause>

  <clause id="15016">
    <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(13805(a,1),15015(a,1,2,2))].">
      <j1 rule="para" parents="13805 15015"/>
    </justification>
  </clause>

  <clause id="15017">
    <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(14248(a,1),14923(a,1,1))].">
      <j1 rule="para" parents="14248 14923"/>
    </justification>
  </clause>

  <clause id="15018">
    <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(14921(a,1),15017(a,1,2))].">
      <j1 rule="para" parents="14921 15017"/>
    </justification>
  </clause>

  <clause id="15019">
    <literal><![CDATA[
      L(x,y,z) \ (L(x,y,T(z,u)) * w) = a(x,y,K(z,u)) * w
    ]]></literal>
    <justification jstring="[hyper(13339,a,15018,a),flip(a)].">
      <j1 rule="hyper" parents="13339 15018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15020">
    <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,14945,a(flip),b,15019,a)].">
      <j1 rule="hyper" parents="58 14945 15019"/>
    </justification>
  </clause>

  <clause id="15021">
    <literal><![CDATA[
      L(x,y,T(z,u)) * (L(x,y,z) \ u) = T(u,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,14282,a,b,15020,a),flip(a)].">
      <j1 rule="hyper" parents="320 14282 15020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15022">
    <literal><![CDATA[
      T(L(x,y,z) \ x,u) \ x = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(30,a,13906,a,b,15021,a)].">
      <j1 rule="hyper" parents="30 13906 15021"/>
    </justification>
  </clause>

  <clause id="15023">
    <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),14829(a,1,2,1,2))].">
      <j1 rule="para" parents="7 14829"/>
    </justification>
  </clause>

  <clause id="15024">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(5562(a,2),14967(a,1,2))].">
      <j1 rule="para" parents="5562 14967"/>
    </justification>
  </clause>

  <clause id="15025">
    <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),15024(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15026">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(u,z)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[para(7807(a,1),15024(a,1,2,1,2))].">
      <j1 rule="para" parents="7807 15024"/>
    </justification>
  </clause>

  <clause id="15027">
    <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(8159(a,1),15024(a,1,2,1,2))].">
      <j1 rule="para" parents="8159 15024"/>
    </justification>
  </clause>

  <clause id="15028">
    <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(8181(a,1),15024(a,1,2,1,2))].">
      <j1 rule="para" parents="8181 15024"/>
    </justification>
  </clause>

  <clause id="15029">
    <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(15024(a,1),8618(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15024 8618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15030">
    <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(15024(a,1),13013(a,2,1,2))].">
      <j1 rule="para" parents="15024 13013"/>
    </justification>
  </clause>

  <clause id="15031">
    <literal><![CDATA[
      T(x / T(y,K(z,u)),K(z,u) \ y) = y \ T(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(5092(a,2),15025(a,1,2))].">
      <j1 rule="para" parents="5092 15025"/>
    </justification>
  </clause>

  <clause id="15032">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[para(7807(a,1),15026(a,1,2))].">
      <j1 rule="para" parents="7807 15026"/>
    </justification>
  </clause>

  <clause id="15033">
    <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(6336(a,2),15031(a,1,1))].">
      <j1 rule="para" parents="6336 15031"/>
    </justification>
  </clause>

  <clause id="15034">
    <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,15032,a),flip(a)].">
      <j1 rule="hyper" parents="134 15032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15035">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15024,a(flip),b,15032,a)].">
      <j1 rule="hyper" parents="58 15024 15032"/>
    </justification>
  </clause>

  <clause id="15036">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,u) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(11469,a,15035,a)].">
      <j1 rule="hyper" parents="11469 15035"/>
    </justification>
  </clause>

  <clause id="15037">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13019,a,b,15035,a)].">
      <j1 rule="hyper" parents="320 13019 15035"/>
    </justification>
  </clause>

  <clause id="15038">
    <literal><![CDATA[
      T(x,K(y,y * z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(320,a,12999,a(flip),b,15035,a),flip(a)].">
      <j1 rule="hyper" parents="320 12999 15035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15039">
    <literal><![CDATA[
      x \ T(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(116,a,15035,a,b,4714,a(flip))].">
      <j1 rule="hyper" parents="116 15035 4714"/>
    </justification>
  </clause>

  <clause id="15040">
    <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),15035(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 15035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15041">
    <literal><![CDATA[
      T(x,K(y,z) * (z * u)) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(4740(a,1),15035(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4740 15035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15042">
    <literal><![CDATA[
      T(x,K(y,z) * (K(y,z) * u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(5095(a,1),15035(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5095 15035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15043">
    <literal><![CDATA[
      T(x,K(y,z) * (y \ u)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5093(a,1),15035(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5093 15035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15044">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * (((y \ u) / u) \ w)) = T(x,T((y \ u) / u,z) \ w)
    ]]></literal>
    <justification jstring="[para(5313(a,1),15035(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5313 15035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15045">
    <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(15035(a,1),13086(a,1,2,1))].">
      <j1 rule="para" parents="15035 13086"/>
    </justification>
  </clause>

  <clause id="15046">
    <literal><![CDATA[
      T(x,K(y,z) * (z / u)) = T(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(13643(a,1),15035(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13643 15035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15047">
    <literal><![CDATA[
      T(x,y * (T(T(y,z),z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(5848(a,1),15042(a,1,2))].">
      <j1 rule="para" parents="5848 15042"/>
    </justification>
  </clause>

  <clause id="15048">
    <literal><![CDATA[
      T(x,T(T(y,z),z) * u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(4(a,1),15047(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 15047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15049">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,y * T(T(z,u),u))
    ]]></literal>
    <justification jstring="[hyper(12284,a,15048,a),flip(a)].">
      <j1 rule="hyper" parents="12284 15048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15050">
    <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(12285,a,15038,a),flip(a)].">
      <j1 rule="hyper" parents="12285 15038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15051">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(4797,a,15039,a)].">
      <j1 rule="hyper" parents="4797 15039"/>
    </justification>
  </clause>

  <clause id="15052">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15039(a,1),4797(a,1))].">
      <j1 rule="para" parents="15039 4797"/>
    </justification>
  </clause>

  <clause id="15053">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(13134,a,15051,a),flip(a)].">
      <j1 rule="hyper" parents="13134 15051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15054">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * w) = K(x,K(y \ z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(320,a,13058,a(flip),b,15051,a),flip(a)].">
      <j1 rule="hyper" parents="320 13058 15051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15055">
    <literal><![CDATA[
      K(x,K(y,z) * (z * u)) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(4740(a,1),15051(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4740 15051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15056">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(5092(a,2),15051(a,1,2))].">
      <j1 rule="para" parents="5092 15051"/>
    </justification>
  </clause>

  <clause id="15057">
    <literal><![CDATA[
      K(x,K(y,z) * (T(z,y) \ u)) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(5042(a,1),15051(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5042 15051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15058">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ u)) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5093(a,1),15051(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5093 15051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15059">
    <literal><![CDATA[
      K(x,K(y,z \ u) * (u / z)) = K(x,T(u / z,T(y,z)))
    ]]></literal>
    <justification jstring="[para(7290(a,1),15051(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7290 15051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15060">
    <literal><![CDATA[
      K(x,K(y,z) * (z / u)) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(13643(a,1),15051(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13643 15051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15061">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5092(a,2),15056(a,2,2))].">
      <j1 rule="para" parents="5092 15056"/>
    </justification>
  </clause>

  <clause id="15062">
    <literal><![CDATA[
      K(x,K(y,y \ z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13096,a(flip),b,15061,a),flip(a)].">
      <j1 rule="hyper" parents="320 13096 15061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15063">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = K(x,K(L(z,u,w),y) \ v5)
    ]]></literal>
    <justification jstring="[para(10763(a,2),15061(a,1,2,1))].">
      <j1 rule="para" parents="10763 15061"/>
    </justification>
  </clause>

  <clause id="15064">
    <literal><![CDATA[
      T(x,((y * z) / y) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5049(a,2),15043(a,1,2))].">
      <j1 rule="para" parents="5049 15043"/>
    </justification>
  </clause>

  <clause id="15065">
    <literal><![CDATA[
      T(x,T(y \ z,y) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(5361(a,1),15043(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5361 15043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15066">
    <literal><![CDATA[
      T(x,T(y \ z,y) / u) = T(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[para(13956(a,1),15046(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13956 15046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15067">
    <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),15053(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 15053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15068">
    <literal><![CDATA[
      K(x,y * (K(z,y) * u)) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(5219(a,1),15055(a,1,2))].">
      <j1 rule="para" parents="5219 15055"/>
    </justification>
  </clause>

  <clause id="15069">
    <literal><![CDATA[
      K(x,((y * z) / y) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5404(a,1),15055(a,1,2))].">
      <j1 rule="para" parents="5404 15055"/>
    </justification>
  </clause>

  <clause id="15070">
    <literal><![CDATA[
      K(x,T(y \ z,y) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(5421(a,1),15055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5421 15055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15071">
    <literal><![CDATA[
      K(x,T(T(y,z),z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(5201(a,1),15057(a,1,2))].">
      <j1 rule="para" parents="5201 15057"/>
    </justification>
  </clause>

  <clause id="15072">
    <literal><![CDATA[
      K(x,T(y * z,z) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13107,a(flip),b,15071,a)].">
      <j1 rule="hyper" parents="58 13107 15071"/>
    </justification>
  </clause>

  <clause id="15073">
    <literal><![CDATA[
      K(x,T(y \ z,y) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(107(a,1),15071(a,1,2,1,1))].">
      <j1 rule="para" parents="107 15071"/>
    </justification>
  </clause>

  <clause id="15074">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,(z / (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(4305(a,1),15071(a,1,2,1,1))].">
      <j1 rule="para" parents="4305 15071"/>
    </justification>
  </clause>

  <clause id="15075">
    <literal><![CDATA[
      K(x,(y * K(z,y)) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(13900(a,2),15060(a,1,2))].">
      <j1 rule="para" parents="13900 15060"/>
    </justification>
  </clause>

  <clause id="15076">
    <literal><![CDATA[
      K(x,T(y \ z,y) / u) = K(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[para(13956(a,1),15060(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13956 15060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15077">
    <literal><![CDATA[
      T(x,K(y,y \ z) \ u) = T(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15062,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 15062 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15078">
    <literal><![CDATA[
      K(x,K(y,z \ y) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13097,a,b,15062,a)].">
      <j1 rule="hyper" parents="58 13097 15062"/>
    </justification>
  </clause>

  <clause id="15079">
    <literal><![CDATA[
      K(x,K(y \ z,z) \ u) = K(x,K(z,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(4973(a,1),15062(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4973 15062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15080">
    <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(13767(a,1),15064(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="13767 15064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15081">
    <literal><![CDATA[
      T(x,T((y / (z \ 1)) / y,y) \ u) = T(x,((y / (z \ K(z,y))) / y) \ u)
    ]]></literal>
    <justification jstring="[para(10106(a,1),15065(a,1,2,1,1))].">
      <j1 rule="para" parents="10106 15065"/>
    </justification>
  </clause>

  <clause id="15082">
    <literal><![CDATA[
      K(x,T(T(y,z),z) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(225(a,1),15069(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="225 15069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15083">
    <literal><![CDATA[
      K(x,T(L(y \ z,u,w),y) * v5) = K(x,L(z / y,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(643(a,1),15069(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="643 15069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15084">
    <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),15082(a,2,2))].">
      <j1 rule="para" parents="101 15082"/>
    </justification>
  </clause>

  <clause id="15085">
    <literal><![CDATA[
      K(x,T(y,z * u) / (z * u)) = K(x,T(u * z,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,12950,a,b,15072,a)].">
      <j1 rule="hyper" parents="320 12950 15072"/>
    </justification>
  </clause>

  <clause id="15086">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(7(a,1),15072(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 15072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15087">
    <literal><![CDATA[
      K(x,T(T(y,z),z) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(4710(a,1),15075(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4710 15075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15088">
    <literal><![CDATA[
      K(x,((y * z) / y) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(4711(a,2),15075(a,1,2,1))].">
      <j1 rule="para" parents="4711 15075"/>
    </justification>
  </clause>

  <clause id="15089">
    <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(12599(a,1),15076(a,1,2,1,1))].">
      <j1 rule="para" parents="12599 15076"/>
    </justification>
  </clause>

  <clause id="15090">
    <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(12694(a,1),15076(a,1,2,1))].">
      <j1 rule="para" parents="12694 15076"/>
    </justification>
  </clause>

  <clause id="15091">
    <literal><![CDATA[
      K(x,K(y \ z,z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15061,a,b,15078,a)].">
      <j1 rule="hyper" parents="58 15061 15078"/>
    </justification>
  </clause>

  <clause id="15092">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,w,v5)) = K(L(x,w,v5),T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(10837,a,15086,a)].">
      <j1 rule="hyper" parents="10837 15086"/>
    </justification>
  </clause>

  <clause id="15093">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ u) = K(x,(y * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13059,a,b,15086,a)].">
      <j1 rule="hyper" parents="320 13059 15086"/>
    </justification>
  </clause>

  <clause id="15094">
    <literal><![CDATA[
      K(x,T(y \ z,z) \ u) = K(x,(y \ T(z,y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(3871(a,2),15086(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3871 15086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15095">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15053(a,2),15052(a,1))].">
      <j1 rule="para" parents="15053 15052"/>
    </justification>
  </clause>

  <clause id="15096">
    <literal><![CDATA[
      T(x,K(y,z) * K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(7825,a,15036,a),flip(a)].">
      <j1 rule="hyper" parents="7825 15036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15097">
    <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(15096(a,1),13024(a,1,2,2))].">
      <j1 rule="para" parents="15096 13024"/>
    </justification>
  </clause>

  <clause id="15098">
    <literal><![CDATA[
      T(x,y * K(z,u)) = T(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(7822(a,1),15040(a,1,2))].">
      <j1 rule="para" parents="7822 15040"/>
    </justification>
  </clause>

  <clause id="15099">
    <literal><![CDATA[
      x / T(x,y * K(z,u)) = K(y * K(u,z),x)
    ]]></literal>
    <justification jstring="[para(15098(a,1),4753(a,2,2)),flip(a)].">
      <j1 rule="para" parents="15098 4753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15100">
    <literal><![CDATA[
      T(x,(y / z) * K(z,u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(6293(a,1),15098(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6293 15098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15101">
    <literal><![CDATA[
      K(x * K(y,z),u) = K(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(4821,a,15099,a)].">
      <j1 rule="hyper" parents="4821 15099"/>
    </justification>
  </clause>

  <clause id="15102">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(15099(a,1),4821(a,1))].">
      <j1 rule="para" parents="15099 4821"/>
    </justification>
  </clause>

  <clause id="15103">
    <literal><![CDATA[
      K((1 / x) * K(y,z),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(13993,a,15101,a),flip(a)].">
      <j1 rule="hyper" parents="13993 15101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15104">
    <literal><![CDATA[
      K((x * K(y,z)) * K(y,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(6300(a,1),15101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6300 15101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15105">
    <literal><![CDATA[
      K((x / y) * K(y,z),u) = K(x / T(y,z),u)
    ]]></literal>
    <justification jstring="[para(6293(a,1),15101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6293 15101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15106">
    <literal><![CDATA[
      K((x \ y) * K(z,y),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(13634(a,1),15101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13634 15101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15107">
    <literal><![CDATA[
      K(x * (K(y,z) * K(y,z)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(8962(a,1),15104(a,1,1))].">
      <j1 rule="para" parents="8962 15104"/>
    </justification>
  </clause>

  <clause id="15108">
    <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(15107(a,1),4729(a,2,1)),flip(a)].">
      <j1 rule="para" parents="15107 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15109">
    <literal><![CDATA[
      T(x,y / ((z * u) / z)) = T(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(6368(a,2),15100(a,1,2))].">
      <j1 rule="para" parents="6368 15100"/>
    </justification>
  </clause>

  <clause id="15110">
    <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(6165(a,1),15100(a,1,2,1))].">
      <j1 rule="para" parents="6165 15100"/>
    </justification>
  </clause>

  <clause id="15112">
    <literal><![CDATA[
      K(x \ K(y,z),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(13993,a,15103,a)].">
      <j1 rule="hyper" parents="13993 15103"/>
    </justification>
  </clause>

  <clause id="15113">
    <literal><![CDATA[
      K(x \ K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(15103(a,1),13993(a,1))].">
      <j1 rule="para" parents="15103 13993"/>
    </justification>
  </clause>

  <clause id="15114">
    <literal><![CDATA[
      K(x \ K(y \ z,y),u) = K(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(13142,a,15112,a),flip(a)].">
      <j1 rule="hyper" parents="13142 15112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15115">
    <literal><![CDATA[
      (x \ K(y \ K(z,u),w)) \ (x \ 1) = K(w,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(15112(a,1),13827(a,1,1,2))].">
      <j1 rule="para" parents="15112 13827"/>
    </justification>
  </clause>

  <clause id="15116">
    <literal><![CDATA[
      K((x \ y) \ K(z,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ T(x,z),u) = w
    ]]></literal>
    <justification jstring="[para(15112(a,1),13938(a,1))].">
      <j1 rule="para" parents="15112 13938"/>
    </justification>
  </clause>

  <clause id="15117">
    <literal><![CDATA[
      K(x / ((y * z) / y),u) = K(x / T(z,y),u)
    ]]></literal>
    <justification jstring="[para(6368(a,2),15105(a,1,1))].">
      <j1 rule="para" parents="6368 15105"/>
    </justification>
  </clause>

  <clause id="15119">
    <literal><![CDATA[
      K(x \ (y * K(z,y)),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(13893(a,2),15106(a,1,1))].">
      <j1 rule="para" parents="13893 15106"/>
    </justification>
  </clause>

  <clause id="15121">
    <literal><![CDATA[
      T(x,y / T(T(z \ u,w),z)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[para(457(a,1),15109(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="457 15109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15122">
    <literal><![CDATA[
      T(x,y / ((z * u) / T(z,w))) = T(x,y / T(u * K(w,z),z))
    ]]></literal>
    <justification jstring="[para(7430(a,1),15109(a,1,2,2))].">
      <j1 rule="para" parents="7430 15109"/>
    </justification>
  </clause>

  <clause id="15123">
    <literal><![CDATA[
      T(x,y / (((z * u) / z) * K(z,w))) = T(x,y / T(u * K(z,w),z))
    ]]></literal>
    <justification jstring="[para(7012(a,1),15109(a,1,2,2))].">
      <j1 rule="para" parents="7012 15109"/>
    </justification>
  </clause>

  <clause id="15124">
    <literal><![CDATA[
      K(x \ K(y \ z,z),u) = K(x \ K(y,y \ z),u)
    ]]></literal>
    <justification jstring="[para(4925(a,1),15114(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4925 15114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15127">
    <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(15117(a,1),7413(a,1,2))].">
      <j1 rule="para" parents="15117 7413"/>
    </justification>
  </clause>

  <clause id="15128">
    <literal><![CDATA[
      K(x \ T(T(y,z),z),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(4710(a,1),15119(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4710 15119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15129">
    <literal><![CDATA[
      K(x \ T(y * z,z),u) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13110,a(flip),b,15128,a)].">
      <j1 rule="hyper" parents="58 13110 15128"/>
    </justification>
  </clause>

  <clause id="15130">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) = 1 / K(y \ z,x)
    ]]></literal>
    <justification jstring="[para(15128(a,1),4931(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15128 4931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15131">
    <literal><![CDATA[
      K(x \ (y * (z / y)),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[para(7(a,1),15129(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15132">
    <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(15129(a,1),10776(a,1,2,3))].">
      <j1 rule="para" parents="15129 10776"/>
    </justification>
  </clause>

  <clause id="15133">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4931,a(flip),b,15130,a),flip(a)].">
      <j1 rule="hyper" parents="320 4931 15130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15134">
    <literal><![CDATA[
      T(x,y \ T(T(z,u),u)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(118,a,15133,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 15133 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15135">
    <literal><![CDATA[
      K(x,y \ T(z \ u,z)) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[para(107(a,1),15133(a,1,2,2,1))].">
      <j1 rule="para" parents="107 15133"/>
    </justification>
  </clause>

  <clause id="15136">
    <literal><![CDATA[
      K(x,y \ T(z * (u / T(z,u)),z)) = K(x,y \ (z * (u / z)))
    ]]></literal>
    <justification jstring="[para(4238(a,1),15133(a,1,2,2,1))].">
      <j1 rule="para" parents="4238 15133"/>
    </justification>
  </clause>

  <clause id="15137">
    <literal><![CDATA[
      K(x,y \ (z * K(u,z))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(4775(a,1),15133(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4775 15133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15138">
    <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(15133(a,1),12287(a,1,1,2))].">
      <j1 rule="para" parents="15133 12287"/>
    </justification>
  </clause>

  <clause id="15139">
    <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(7538(a,1),15135(a,1,2,2,1))].">
      <j1 rule="para" parents="7538 15135"/>
    </justification>
  </clause>

  <clause id="15140">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(6575,a,15137,a)].">
      <j1 rule="hyper" parents="6575 15137"/>
    </justification>
  </clause>

  <clause id="15141">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u \ 1,y)) = K(x,z \ T(y,1 / u))
    ]]></literal>
    <justification jstring="[para(2936(a,2),15140(a,2,2,2))].">
      <j1 rule="para" parents="2936 15140"/>
    </justification>
  </clause>

  <clause id="15142">
    <literal><![CDATA[
      T(x,y * T(T(z,u),u)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(12258,a,15049,a),flip(a)].">
      <j1 rule="hyper" parents="12258 15049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15143">
    <literal><![CDATA[
      T(x,y * ((z * u) / z)) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(224(a,1),15142(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="224 15142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15144">
    <literal><![CDATA[
      T(x,y * (z * K(u,z))) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4775(a,1),15142(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4775 15142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15145">
    <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(15142(a,1),12248(a,1,2,1))].">
      <j1 rule="para" parents="15142 12248"/>
    </justification>
  </clause>

  <clause id="15146">
    <literal><![CDATA[
      T(x,y * ((z * u) / z)) = x * K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,4714,a(flip),b,15143,a),flip(a)].">
      <j1 rule="hyper" parents="320 4714 15143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15147">
    <literal><![CDATA[
      K(x * ((y * z) / y),u) = u / T(u,x * T(z,y))
    ]]></literal>
    <justification jstring="[para(15143(a,1),4753(a,2,2))].">
      <j1 rule="para" parents="15143 4753"/>
    </justification>
  </clause>

  <clause id="15148">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(13160,a,15074,a),flip(a)].">
      <j1 rule="hyper" parents="13160 15074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15149">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(15074(a,1),13160(a,1))].">
      <j1 rule="para" parents="15074 13160"/>
    </justification>
  </clause>

  <clause id="15150">
    <literal><![CDATA[
      T(x,(y / (y / z)) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15148,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 15148 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15151">
    <literal><![CDATA[
      K(x,T(y \ z,z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(72(a,1),15148(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 15148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15152">
    <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(15150(a,1),12263(a,1,2,1))].">
      <j1 rule="para" parents="15150 12263"/>
    </justification>
  </clause>

  <clause id="15153">
    <literal><![CDATA[
      K(x,(y / z) \ T(u,y / z)) = K(x,u / T(z \ y,y))
    ]]></literal>
    <justification jstring="[hyper(13088,a,15151,a),flip(a)].">
      <j1 rule="hyper" parents="13088 15151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15154">
    <literal><![CDATA[
      K(x,K(y,z \ 1) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15091,a(flip),b,15079,a),flip(a)].">
      <j1 rule="hyper" parents="58 15091 15079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15155">
    <literal><![CDATA[
      K(x,T(y,z \ 1) \ u) = K(x,K(y,z) \ (y \ u))
    ]]></literal>
    <justification jstring="[para(5048(a,1),15154(a,1,2))].">
      <j1 rule="para" parents="5048 15154"/>
    </justification>
  </clause>

  <clause id="15156">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ u) \ 1 = K(((y \ z) * y) \ u,x)
    ]]></literal>
    <justification jstring="[para(15093(a,1),4929(a,1,1))].">
      <j1 rule="para" parents="15093 4929"/>
    </justification>
  </clause>

  <clause id="15157">
    <literal><![CDATA[
      K(x \ K(y \ z,z),u) = K(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13050,a(flip),b,15124,a),flip(a)].">
      <j1 rule="hyper" parents="320 13050 15124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15158">
    <literal><![CDATA[
      K(x \ K(y,z \ y),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(15113,a,15157,a)].">
      <j1 rule="hyper" parents="15113 15157"/>
    </justification>
  </clause>

  <clause id="15159">
    <literal><![CDATA[
      K(x \ K(y,z \ 1),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13103,a,b,15158,a)].">
      <j1 rule="hyper" parents="58 13103 15158"/>
    </justification>
  </clause>

  <clause id="15160">
    <literal><![CDATA[
      K((x \ y) \ K(z,x),u) = K(y \ T(x,1 / z),u)
    ]]></literal>
    <justification jstring="[hyper(14103,a,15159,a),flip(a)].">
      <j1 rule="hyper" parents="14103 15159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15161">
    <literal><![CDATA[
      K(x,y * ((z * u) / z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(4796,a,15146,a)].">
      <j1 rule="hyper" parents="4796 15146"/>
    </justification>
  </clause>

  <clause id="15162">
    <literal><![CDATA[
      K(x,y * T(z \ u,z)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(5(a,1),15161(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 15161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15163">
    <literal><![CDATA[
      K(x,y * T(T(z,u),u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(225(a,1),15161(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="225 15161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15164">
    <literal><![CDATA[
      K(x,y * (z * K(u,z))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4711(a,1),15161(a,1,2,2))].">
      <j1 rule="para" parents="4711 15161"/>
    </justification>
  </clause>

  <clause id="15165">
    <literal><![CDATA[
      K(x,(y / (z * u)) * T(u,z)) = K(x,(y / (u * z)) * u)
    ]]></literal>
    <justification jstring="[para(10625(a,1),15161(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10625 15161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15166">
    <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(13767(a,1),15161(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="13767 15161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15167">
    <literal><![CDATA[
      K(x,T(y,z \ u) * (u \ z)) = K(x,(u \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,14109,a(flip),b,15163,a)].">
      <j1 rule="hyper" parents="58 14109 15163"/>
    </justification>
  </clause>

  <clause id="15168">
    <literal><![CDATA[
      K(x,y * T(z * u,u)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13147,a(flip),b,15163,a)].">
      <j1 rule="hyper" parents="58 13147 15163"/>
    </justification>
  </clause>

  <clause id="15169">
    <literal><![CDATA[
      K(x,y * T(z \ u,u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13077,a(flip),b,15163,a)].">
      <j1 rule="hyper" parents="58 13077 15163"/>
    </justification>
  </clause>

  <clause id="15170">
    <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),15163(a,2,2))].">
      <j1 rule="para" parents="90 15163"/>
    </justification>
  </clause>

  <clause id="15171">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) \ u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(4199(a,1),15162(a,1,2,2))].">
      <j1 rule="para" parents="4199 15162"/>
    </justification>
  </clause>

  <clause id="15172">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ (u \ z))) = K(x,y * ((u \ z) / z))
    ]]></literal>
    <justification jstring="[para(4314(a,1),15162(a,1,2,2))].">
      <j1 rule="para" parents="4314 15162"/>
    </justification>
  </clause>

  <clause id="15173">
    <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(14446(a,2),15162(a,1,2))].">
      <j1 rule="para" parents="14446 15162"/>
    </justification>
  </clause>

  <clause id="15174">
    <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(4156(a,1),15164(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4156 15164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15175">
    <literal><![CDATA[
      K(x,y * (z * (u / z))) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),15168(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15176">
    <literal><![CDATA[
      K(x,L(y * T(z \ u,u),w,v5)) = K(L(x,w,v5),y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(10837,a,15169,a)].">
      <j1 rule="hyper" parents="10837 15169"/>
    </justification>
  </clause>

  <clause id="15177">
    <literal><![CDATA[
      K(x,y * (z * ((z * u) / z))) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,13024,a(flip),b,15175,a),flip(a)].">
      <j1 rule="hyper" parents="320 13024 15175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15178">
    <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),15175(a,2,2,2))].">
      <j1 rule="para" parents="18 15175"/>
    </justification>
  </clause>

  <clause id="15179">
    <literal><![CDATA[
      K(x * ((y * z) / y),u) = K(x * T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,4753,a,b,15147,a),flip(a)].">
      <j1 rule="hyper" parents="320 4753 15147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15180">
    <literal><![CDATA[
      K(x * (y * K(z,y)),u) = K(x * T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4711(a,1),15179(a,1,1,2))].">
      <j1 rule="para" parents="4711 15179"/>
    </justification>
  </clause>

  <clause id="15181">
    <literal><![CDATA[
      K(x,T(y,z \ 1) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5048(a,1),15155(a,2,2))].">
      <j1 rule="para" parents="5048 15155"/>
    </justification>
  </clause>

  <clause id="15182">
    <literal><![CDATA[
      K(x,T(y * (z \ 1),z) \ u) = K(x,((z \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15072,a(flip),b,15181,a),flip(a)].">
      <j1 rule="hyper" parents="58 15072 15181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15183">
    <literal><![CDATA[
      K(x,y * (T(z,u) \ u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13115,a(flip),b,15171,a)].">
      <j1 rule="hyper" parents="58 13115 15171"/>
    </justification>
  </clause>

  <clause id="15184">
    <literal><![CDATA[
      K(x,y * (z \ T(u,z))) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(4208(a,1),15183(a,1,2,2))].">
      <j1 rule="para" parents="4208 15183"/>
    </justification>
  </clause>

  <clause id="15185">
    <literal><![CDATA[
      K(x,x * (((y * x) * z) \ T(u,(y * x) * z))) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,12594,a(flip),b,15184,a),flip(a)].">
      <j1 rule="hyper" parents="320 12594 15184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15186">
    <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(5131(a,1),15184(a,2,2,2))].">
      <j1 rule="para" parents="5131 15184"/>
    </justification>
  </clause>

  <clause id="15187">
    <literal><![CDATA[
      K(x,y * (T(z,u) * u)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(225(a,1),15177(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="225 15177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15188">
    <literal><![CDATA[
      K(x,T((y * z) * u,y * z)) = K(x,u * (T(z,y) * y))
    ]]></literal>
    <justification jstring="[hyper(320,a,12222,a,b,15187,a)].">
      <j1 rule="hyper" parents="320 12222 15187"/>
    </justification>
  </clause>

  <clause id="15189">
    <literal><![CDATA[
      T(x,y * (T(z,u) * u)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(118,a,15187,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 15187 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15190">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * ((w * u) / w))) = K(x,y * (((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[para(7918(a,1),15187(a,1,2,2,1))].">
      <j1 rule="para" parents="7918 15187"/>
    </justification>
  </clause>

  <clause id="15191">
    <literal><![CDATA[
      T(x,y * (T(z \ u,w) * z)) = T(x,y * (z * T(u / z,w)))
    ]]></literal>
    <justification jstring="[para(246(a,1),15189(a,1,2,2,1))].">
      <j1 rule="para" parents="246 15189"/>
    </justification>
  </clause>

  <clause id="15192">
    <literal><![CDATA[
      K(x \ T(y,1 / z),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(15116,a,15160,a),flip(a)].">
      <j1 rule="hyper" parents="15116 15160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15193">
    <literal><![CDATA[
      K(x \ T(y,z \ 1),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(72(a,1),15192(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 15192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15194">
    <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(15193(a,1),10776(a,1,2,3))].">
      <j1 rule="para" parents="15193 10776"/>
    </justification>
  </clause>

  <clause id="15195">
    <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(15034(a,2),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="15034 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15196">
    <literal><![CDATA[
      K(x,T(y * z,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(15085(a,1),13016(a,1))].">
      <j1 rule="para" parents="15085 13016"/>
    </justification>
  </clause>

  <clause id="15197">
    <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(13081(a,1),15196(a,1))].">
      <j1 rule="para" parents="13081 15196"/>
    </justification>
  </clause>

  <clause id="15198">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15151,a(flip),b,15094,a),flip(a)].">
      <j1 rule="hyper" parents="58 15151 15094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15199">
    <literal><![CDATA[
      K(x,y \ K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15115(a,1),6365(a,1))].">
      <j1 rule="para" parents="15115 6365"/>
    </justification>
  </clause>

  <clause id="15200">
    <literal><![CDATA[
      T(x,y / T(((z \ u) \ u) \ u,w)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[para(4311(a,1),15121(a,1,2,2))].">
      <j1 rule="para" parents="4311 15121"/>
    </justification>
  </clause>

  <clause id="15201">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(15153(a,1),13085(a,1))].">
      <j1 rule="para" parents="15153 13085"/>
    </justification>
  </clause>

  <clause id="15202">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,u) = K((x * (y / x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(4945,a,15156,a),flip(a)].">
      <j1 rule="hyper" parents="4945 15156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15203">
    <literal><![CDATA[
      K((x * (y / x)) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13061,a(flip),b,15202,a),flip(a)].">
      <j1 rule="hyper" parents="58 13061 15202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15204">
    <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,14778,a(flip),b,15203,a),flip(a)].">
      <j1 rule="hyper" parents="58 14778 15203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15205">
    <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,15070,a,b,15165,a)].">
      <j1 rule="hyper" parents="58 15070 15165"/>
    </justification>
  </clause>

  <clause id="15206">
    <literal><![CDATA[
      K(x,y * T(z * (u / z),w)) = K(x,y * T(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(4533(a,2),15178(a,1,2,2))].">
      <j1 rule="para" parents="4533 15178"/>
    </justification>
  </clause>

  <clause id="15207">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) \ u) = K(x,R(z,y,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(784(a,1),15182(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="784 15182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15208">
    <literal><![CDATA[
      K(x,y * (T(z,u) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (u * z)) = w
    ]]></literal>
    <justification jstring="[para(15188(a,1),12259(a,1))].">
      <j1 rule="para" parents="15188 12259"/>
    </justification>
  </clause>

  <clause id="15209">
    <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(12239(a,1),15208(a,1,2,2,1))].">
      <j1 rule="para" parents="12239 15208"/>
    </justification>
  </clause>

  <clause id="15210">
    <literal><![CDATA[
      T(x,y * T(z * (u / z),w)) = T(x,y * T(T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(118,a,15206,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 15206 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15211">
    <literal><![CDATA[
      K(x,R(T(T(y,z),z),u,w) * (u * w)) = K(x,(y * u) * w)
    ]]></literal>
    <justification jstring="[para(819(a,2),15084(a,1,2,1))].">
      <j1 rule="para" parents="819 15084"/>
    </justification>
  </clause>

  <clause id="15212">
    <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),15170(a,1,2,2,1))].">
      <j1 rule="para" parents="20 15170"/>
    </justification>
  </clause>

  <clause id="15213">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ u) = K(x,L(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5535,a(flip),b,15207,a),flip(a)].">
      <j1 rule="hyper" parents="58 5535 15207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15214">
    <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,14437,a(flip),b,15213,a),flip(a)].">
      <j1 rule="hyper" parents="58 14437 15213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15215">
    <literal><![CDATA[
      K(x,(T(T(y,z),z) * u) * w) = K(x,(y * u) * w)
    ]]></literal>
    <justification jstring="[para(101(a,1),15211(a,1,2))].">
      <j1 rule="para" parents="101 15211"/>
    </justification>
  </clause>

  <clause id="15216">
    <literal><![CDATA[
      K(x,(((y * z) / y) * u) * w) = K(x,(T(z,y) * u) * w)
    ]]></literal>
    <justification jstring="[para(224(a,1),15215(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="224 15215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15217">
    <literal><![CDATA[
      K(x,(T(y,z) * z) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(7(a,1),15216(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15218">
    <literal><![CDATA[
      K(x,(y * (K(z,y) * u)) * w) = K(x,(T(y,z) * u) * w)
    ]]></literal>
    <justification jstring="[para(5366(a,1),15216(a,1,2,1))].">
      <j1 rule="para" parents="5366 15216"/>
    </justification>
  </clause>

  <clause id="15219">
    <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(7418(a,1),15217(a,1,2,1,1))].">
      <j1 rule="para" parents="7418 15217"/>
    </justification>
  </clause>

  <clause id="15220">
    <literal><![CDATA[
      K(x,(y * (K(z,y) * (u / y))) * w) = K(x,((T(y,z) \ u) * y) * w)
    ]]></literal>
    <justification jstring="[para(7592(a,1),15217(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7592 15217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15221">
    <literal><![CDATA[
      K(x,((y \ z) * (y * K(u,y))) * w) = K(x,(y * (z / T(y,u))) * w)
    ]]></literal>
    <justification jstring="[para(7576(a,1),15217(a,1,2,1))].">
      <j1 rule="para" parents="7576 15217"/>
    </justification>
  </clause>

  <clause id="15222">
    <literal><![CDATA[
      K(x,y * (z * T(T(u,w),w))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(449(a,1),15212(a,1,2))].">
      <j1 rule="para" parents="449 15212"/>
    </justification>
  </clause>

  <clause id="15223">
    <literal><![CDATA[
      K(x,y * (z * T(u \ w,w))) = K(x,y * (z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13164,a(flip),b,15222,a)].">
      <j1 rule="hyper" parents="58 13164 15222"/>
    </justification>
  </clause>

  <clause id="15224">
    <literal><![CDATA[
      K(x,y * (z * ((u * w) / u))) = K(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[para(224(a,1),15222(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="224 15222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15225">
    <literal><![CDATA[
      T(x,y * K(z,z * u)) = T(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(12283,a,15050,a),flip(a)].">
      <j1 rule="hyper" parents="12283 15050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15226">
    <literal><![CDATA[
      K(x,K(y,z) * T(u,K(z,y))) = K(x,u * K(z,z \ y))
    ]]></literal>
    <justification jstring="[para(8006(a,1),15067(a,1,2,2))].">
      <j1 rule="para" parents="8006 15067"/>
    </justification>
  </clause>

  <clause id="15227">
    <literal><![CDATA[
      K(x,y * K(z,z \ u)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(7822(a,1),15226(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7822 15226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15228">
    <literal><![CDATA[
      K(x,y * K(z,u)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13025,a(flip),b,15227,a)].">
      <j1 rule="hyper" parents="58 13025 15227"/>
    </justification>
  </clause>

  <clause id="15230">
    <literal><![CDATA[
      K(x,(y / z) * K(z,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(6293(a,1),15228(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6293 15228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15231">
    <literal><![CDATA[
      K(x,(y \ z) * K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15228(a,1),14048(a,1))].">
      <j1 rule="para" parents="15228 14048"/>
    </justification>
  </clause>

  <clause id="15233">
    <literal><![CDATA[
      K(x,y / T(z \ u,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(6441(a,1),15230(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6441 15230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15235">
    <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(3950(a,1),15231(a,1,2,2))].">
      <j1 rule="para" parents="3950 15231"/>
    </justification>
  </clause>

  <clause id="15236">
    <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(15092(a,2),10837(a,1))].">
      <j1 rule="para" parents="15092 10837"/>
    </justification>
  </clause>

  <clause id="15237">
    <literal><![CDATA[
      K(x,y \ ((z / T(u,z)) * u)) = K(x,y \ (u * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13031,a(flip),b,15136,a)].">
      <j1 rule="hyper" parents="58 13031 15136"/>
    </justification>
  </clause>

  <clause id="15238">
    <literal><![CDATA[
      K(x,y \ (z * (u / z))) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(4202(a,1),15237(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4202 15237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15239">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),z \ u)) = K(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14759,a,b,15238,a)].">
      <j1 rule="hyper" parents="58 14759 15238"/>
    </justification>
  </clause>

  <clause id="15240">
    <literal><![CDATA[
      K(x,y \ T(z * u,u)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(6(a,1),15238(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6 15238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15241">
    <literal><![CDATA[
      K(x,y \ T(z \ u,u)) = K(x,y \ (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(3871(a,2),15238(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3871 15238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15242">
    <literal><![CDATA[
      K(x,y \ T(z * u,z)) = K(x,y \ (T(z,u) * u))
    ]]></literal>
    <justification jstring="[para(4051(a,2),15238(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4051 15238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15243">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * u)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13031,a(flip),b,15242,a),flip(a)].">
      <j1 rule="hyper" parents="58 13031 15242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15244">
    <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(12233(a,1),15243(a,1,2,2,1))].">
      <j1 rule="para" parents="12233 15243"/>
    </justification>
  </clause>

  <clause id="15245">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * ((u \ 1) \ w))) = K(x,y \ (((u \ 1) \ w) * z))
    ]]></literal>
    <justification jstring="[para(13737(a,1),15243(a,1,2,2,1))].">
      <j1 rule="para" parents="13737 15243"/>
    </justification>
  </clause>

  <clause id="15246">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * ((1 / u) \ w))) = K(x,y \ (((1 / u) \ w) * z))
    ]]></literal>
    <justification jstring="[para(13814(a,1),15243(a,1,2,2,1))].">
      <j1 rule="para" parents="13814 15243"/>
    </justification>
  </clause>

  <clause id="15247">
    <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(15176(a,2),10837(a,1))].">
      <j1 rule="para" parents="15176 10837"/>
    </justification>
  </clause>

  <clause id="15248">
    <literal><![CDATA[
      T(x,y / T(T(z \ u,w),u)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13068,a(flip),b,15200,a)].">
      <j1 rule="hyper" parents="58 13068 15200"/>
    </justification>
  </clause>

  <clause id="15249">
    <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),15248(a,1,2,2))].">
      <j1 rule="para" parents="18 15248"/>
    </justification>
  </clause>

  <clause id="15250">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,a(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1403(a,1),15214(a,1,2))].">
      <j1 rule="para" parents="1403 15214"/>
    </justification>
  </clause>

  <clause id="15251">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15024(a,1),15195(a,1))].">
      <j1 rule="para" parents="15024 15195"/>
    </justification>
  </clause>

  <clause id="15252">
    <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(15032(a,2),15251(a,1))].">
      <j1 rule="para" parents="15032 15251"/>
    </justification>
  </clause>

  <clause id="15253">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15037(a,2),15251(a,1))].">
      <j1 rule="para" parents="15037 15251"/>
    </justification>
  </clause>

  <clause id="15255">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u \ 1,z) * x)
    ]]></literal>
    <justification jstring="[para(8159(a,1),15027(a,1,2))].">
      <j1 rule="para" parents="8159 15027"/>
    </justification>
  </clause>

  <clause id="15256">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(15252,a,15255,a),flip(a)].">
      <j1 rule="hyper" parents="15252 15255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15257">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15255(a,1),15252(a,1))].">
      <j1 rule="para" parents="15255 15252"/>
    </justification>
  </clause>

  <clause id="15258">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = x \ T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(116,a,15256,a(flip),b,4714,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 15256 4714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15259">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(320,a,4688,a,b,15258,a),flip(a)].">
      <j1 rule="hyper" parents="320 4688 15258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15260">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15258(a,2),4797(a,1))].">
      <j1 rule="para" parents="15258 4797"/>
    </justification>
  </clause>

  <clause id="15261">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(15052,a,15259,a)].">
      <j1 rule="hyper" parents="15052 15259"/>
    </justification>
  </clause>

  <clause id="15262">
    <literal><![CDATA[
      K(x,y * (T(1 / y,z) * u)) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,14111,a,b,15259,a)].">
      <j1 rule="hyper" parents="58 14111 15259"/>
    </justification>
  </clause>

  <clause id="15263">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[para(6230(a,1),15259(a,1,2,1))].">
      <j1 rule="para" parents="6230 15259"/>
    </justification>
  </clause>

  <clause id="15264">
    <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(15259(a,1),6699(a,1,1))].">
      <j1 rule="para" parents="15259 6699"/>
    </justification>
  </clause>

  <clause id="15265">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(320,a,15051,a,b,15261,a),flip(a)].">
      <j1 rule="hyper" parents="320 15051 15261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15266">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(u,z \ y) * w)
    ]]></literal>
    <justification jstring="[para(6078(a,1),15261(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6078 15261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15267">
    <literal><![CDATA[
      K(x,K(y,z) * T(u,K(z,y))) = K(x,u * K(z,y \ 1))
    ]]></literal>
    <justification jstring="[para(8180(a,1),15261(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8180 15261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15268">
    <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(15261(a,1),6700(a,1,1))].">
      <j1 rule="para" parents="15261 6700"/>
    </justification>
  </clause>

  <clause id="15269">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) = K(x,K(z,y) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(13986,a,15265,a)].">
      <j1 rule="hyper" parents="13986 15265"/>
    </justification>
  </clause>

  <clause id="15270">
    <literal><![CDATA[
      T(x,K(y,z \ 1) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15265,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 15265 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15271">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,u) = u / T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(15270(a,1),4753(a,2,2))].">
      <j1 rule="para" parents="15270 4753"/>
    </justification>
  </clause>

  <clause id="15272">
    <literal><![CDATA[
      K(x,y * (K(1 / z,y) * u)) = K(x,K(z,y) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(14047,a,15262,a)].">
      <j1 rule="hyper" parents="14047 15262"/>
    </justification>
  </clause>

  <clause id="15273">
    <literal><![CDATA[
      K(x,K(y \ z,z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(13134,a,15263,a),flip(a)].">
      <j1 rule="hyper" parents="13134 15263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15274">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * w) = K(x,K(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(320,a,15054,a,b,15263,a)].">
      <j1 rule="hyper" parents="320 15054 15263"/>
    </justification>
  </clause>

  <clause id="15275">
    <literal><![CDATA[
      K(x,K(y \ z,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15263(a,1),13134(a,1))].">
      <j1 rule="para" parents="15263 13134"/>
    </justification>
  </clause>

  <clause id="15276">
    <literal><![CDATA[
      T(x,K(y \ z,z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15273,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 15273 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15277">
    <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,15059,a(flip),b,15273,a)].">
      <j1 rule="hyper" parents="58 15059 15273"/>
    </justification>
  </clause>

  <clause id="15278">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ u) = K(x,K(z,y) * (y \ u))
    ]]></literal>
    <justification jstring="[para(5093(a,1),15273(a,1,2))].">
      <j1 rule="para" parents="5093 15273"/>
    </justification>
  </clause>

  <clause id="15279">
    <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(15276(a,1),13086(a,1,2,1))].">
      <j1 rule="para" parents="15276 13086"/>
    </justification>
  </clause>

  <clause id="15280">
    <literal><![CDATA[
      K(x,K(y,z \ y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15266(a,1),13134(a,1))].">
      <j1 rule="para" parents="15266 13134"/>
    </justification>
  </clause>

  <clause id="15281">
    <literal><![CDATA[
      K(x,K(y \ (z \ 1),u) * w) = K(x,K(u,z * y) * w)
    ]]></literal>
    <justification jstring="[para(13710(a,1),15266(a,2,2,1))].">
      <j1 rule="para" parents="13710 15266"/>
    </justification>
  </clause>

  <clause id="15282">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(320,a,15055,a(flip),b,15269,a),flip(a)].">
      <j1 rule="hyper" parents="320 15055 15269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15283">
    <literal><![CDATA[
      K(x,T(1 / y,z) \ u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(14057,a,15282,a)].">
      <j1 rule="hyper" parents="14057 15282"/>
    </justification>
  </clause>

  <clause id="15284">
    <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(10837,a,15282,a)].">
      <j1 rule="hyper" parents="10837 15282"/>
    </justification>
  </clause>

  <clause id="15285">
    <literal><![CDATA[
      T(x,T(y \ 1,z) \ u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15282,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 15282 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15286">
    <literal><![CDATA[
      T(x,T(1 / y,z) \ u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15283,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 15283 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15287">
    <literal><![CDATA[
      K(x,T(y \ 1,z) * u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(72(a,1),15283(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="72 15283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15288">
    <literal><![CDATA[
      T(x,T(y \ 1,z) * u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(72(a,1),15286(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="72 15286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15289">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w) \ v5) = T(x,T(u \ K(z,y),w) * v5)
    ]]></literal>
    <justification jstring="[para(13753(a,1),15286(a,1,2,1,1))].">
      <j1 rule="para" parents="13753 15286"/>
    </justification>
  </clause>

  <clause id="15290">
    <literal><![CDATA[
      T(x,T(K(y,z) / u,w) \ v5) = T(x,T(u * K(z,y),w) * v5)
    ]]></literal>
    <justification jstring="[para(13811(a,1),15286(a,1,2,1,1))].">
      <j1 rule="para" parents="13811 15286"/>
    </justification>
  </clause>

  <clause id="15291">
    <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(13769(a,1),15288(a,1,2,1,1))].">
      <j1 rule="para" parents="13769 15288"/>
    </justification>
  </clause>

  <clause id="15292">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,u) = K(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,4753,a,b,15271,a),flip(a)].">
      <j1 rule="hyper" parents="320 4753 15271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15293">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(K(y,x) * (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(13987,a,15292,a)].">
      <j1 rule="hyper" parents="13987 15292"/>
    </justification>
  </clause>

  <clause id="15294">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5093(a,1),15278(a,2,2))].">
      <j1 rule="para" parents="5093 15278"/>
    </justification>
  </clause>

  <clause id="15295">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(x * (K(y,x) * z),u)
    ]]></literal>
    <justification jstring="[para(5219(a,1),15293(a,2,1))].">
      <j1 rule="para" parents="5219 15293"/>
    </justification>
  </clause>

  <clause id="15296">
    <literal><![CDATA[
      K(x,y * K(z,u \ 1)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(7822(a,1),15267(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7822 15267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15297">
    <literal><![CDATA[
      K(x,y * K(z \ 1,u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15228,a,b,15296,a)].">
      <j1 rule="hyper" parents="58 15228 15296"/>
    </justification>
  </clause>

  <clause id="15298">
    <literal><![CDATA[
      K(x * K(y,z \ 1),u) = 1 / K(u,x * K(z,y))
    ]]></literal>
    <justification jstring="[para(15296(a,1),4931(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15296 4931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15299">
    <literal><![CDATA[
      T(x,y * K(z \ 1,u)) = T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,15297,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 15297 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15300">
    <literal><![CDATA[
      K(x * K(y,z \ 1),u) = K(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,4931,a(flip),b,15298,a),flip(a)].">
      <j1 rule="hyper" parents="320 4931 15298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15301">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) = K(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(15102,a,15300,a)].">
      <j1 rule="hyper" parents="15102 15300"/>
    </justification>
  </clause>

  <clause id="15302">
    <literal><![CDATA[
      K(((x * (y \ z)) / x) * y,u) = K(z * K(z \ y,x),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(12255,a,15300,a)].">
      <j1 rule="hyper" parents="12255 15300"/>
    </justification>
  </clause>

  <clause id="15303">
    <literal><![CDATA[
      K(x * K(x \ y,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12206,a(flip),b,15301,a),flip(a)].">
      <j1 rule="hyper" parents="58 12206 15301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15304">
    <literal><![CDATA[
      K(x,y * (K(1 / z,y) * u)) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(320,a,15055,a(flip),b,15272,a),flip(a)].">
      <j1 rule="hyper" parents="320 15055 15272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15305">
    <literal><![CDATA[
      K(x,y * (K(z \ 1,y) * u)) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(3293(a,1),15304(a,1,2,2,1))].">
      <j1 rule="para" parents="3293 15304"/>
    </justification>
  </clause>

  <clause id="15306">
    <literal><![CDATA[
      K(x,T(y,z \ 1) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15068,a(flip),b,15305,a)].">
      <j1 rule="hyper" parents="58 15068 15305"/>
    </justification>
  </clause>

  <clause id="15307">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) * w) = K(x,T(y,u * z) * w)
    ]]></literal>
    <justification jstring="[para(13928(a,1),15306(a,1,2,1))].">
      <j1 rule="para" parents="13928 15306"/>
    </justification>
  </clause>

  <clause id="15308">
    <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(320,a,10809,a(flip),b,15284,a),flip(a)].">
      <j1 rule="hyper" parents="320 10809 15284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15309">
    <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(15284(a,2),10837(a,1))].">
      <j1 rule="para" parents="15284 10837"/>
    </justification>
  </clause>

  <clause id="15310">
    <literal><![CDATA[
      K(((x * (y \ z)) / x) * y,u) = K(y * T(z / y,x),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,15303,a(flip),b,15302,a),flip(a)].">
      <j1 rule="hyper" parents="320 15303 15302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15311">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) = K((z \ 1) * T((z \ y) / (z \ 1),x),u)
    ]]></literal>
    <justification jstring="[hyper(12769,a,15310,a)].">
      <j1 rule="hyper" parents="12769 15310"/>
    </justification>
  </clause>

  <clause id="15312">
    <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),15308(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 15308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15313">
    <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(15312(a,1),14552(a,1))].">
      <j1 rule="para" parents="15312 14552"/>
    </justification>
  </clause>

  <clause id="15314">
    <literal><![CDATA[
      T(x * (K(y,z) * K(y,z)),u) = T(x,u) * (K(y,z) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5002,a,15108,a),flip(a)].">
      <j1 rule="hyper" parents="5002 15108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15315">
    <literal><![CDATA[
      K(x,(y * z) \ T(u,(y * x) * z)) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(14169,a,15185,a)].">
      <j1 rule="hyper" parents="14169 15185"/>
    </justification>
  </clause>

  <clause id="15316">
    <literal><![CDATA[
      K(x,((T(y,z) \ u) * y) * w) = K(x,(T(y,z) * (u / y)) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15218,a(flip),b,15220,a),flip(a)].">
      <j1 rule="hyper" parents="58 15218 15220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15317">
    <literal><![CDATA[
      K(x,T(y / z,T(u \ (z \ y),z))) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(320,a,15059,a(flip),b,15277,a),flip(a)].">
      <j1 rule="hyper" parents="320 15059 15277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15318">
    <literal><![CDATA[
      K(x,T(y / z,y / (z * u))) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[para(9588(a,1),15317(a,1,2))].">
      <j1 rule="para" parents="9588 15317"/>
    </justification>
  </clause>

  <clause id="15319">
    <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,15023,a(flip),b,15318,a)].">
      <j1 rule="hyper" parents="58 15023 15318"/>
    </justification>
  </clause>

  <clause id="15320">
    <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(5879(a,1),15318(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5879 15318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15321">
    <literal><![CDATA[
      K(x \ T((x \ y) * x,z),u) = K(((z * y) / z) / x,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,12342,a(flip),b,15311,a)].">
      <j1 rule="hyper" parents="320 12342 15311"/>
    </justification>
  </clause>

  <clause id="15322">
    <literal><![CDATA[
      K(T(x \ T(y,z),x),u) = K(((z * y) / z) / x,u)
    ]]></literal>
    <justification jstring="[para(4566(a,1),15321(a,1,1))].">
      <j1 rule="para" parents="4566 15321"/>
    </justification>
  </clause>

  <clause id="15323">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(8237,a,15322,a),flip(a)].">
      <j1 rule="hyper" parents="8237 15322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15324">
    <literal><![CDATA[
      K(T(T(x,y),y) / z,u) = K(x / z,u)
    ]]></literal>
    <justification jstring="[para(225(a,1),15323(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="225 15323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15325">
    <literal><![CDATA[
      K((x * y) \ T(z,x),T(u,y)) = K(z / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(14797,a,15324,a)].">
      <j1 rule="hyper" parents="14797 15324"/>
    </justification>
  </clause>

  <clause id="15326">
    <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(13921(a,1),15325(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13921 15325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15327">
    <literal><![CDATA[
      T(x,K(y,z) * (((y \ u) / u) \ w)) = T(x,T((y \ u) / u,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(15257,a,15044,a)].">
      <j1 rule="hyper" parents="15257 15044"/>
    </justification>
  </clause>

  <clause id="15328">
    <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),15081(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 15081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15329">
    <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,15222,a(flip),b,15145,a)].">
      <j1 rule="hyper" parents="58 15222 15145"/>
    </justification>
  </clause>

  <clause id="15330">
    <literal><![CDATA[
      K(x,(y * T(T(z,u),u)) * w) = K(x,(y * z) * w)
    ]]></literal>
    <justification jstring="[hyper(12263,a,15329,a),flip(a)].">
      <j1 rule="hyper" parents="12263 15329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15332">
    <literal><![CDATA[
      K(x,(y * (z * K(u,z))) * w) = K(x,(y * T(z,u)) * w)
    ]]></literal>
    <justification jstring="[para(4775(a,1),15330(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4775 15330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15333">
    <literal><![CDATA[
      T(x,(y * (z * K(u,z))) * w) = T(x,(y * T(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(118,a,15332,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 15332 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15334">
    <literal><![CDATA[
      K(x,((y \ z) * T(y,u)) * w) = K(x,(y * (z / T(y,u))) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15221,a(flip),b,15332,a),flip(a)].">
      <j1 rule="hyper" parents="58 15221 15332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15335">
    <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,15224,a(flip),b,15190,a)].">
      <j1 rule="hyper" parents="58 15224 15190"/>
    </justification>
  </clause>

  <clause id="15336">
    <literal><![CDATA[
      K(x,y * (((z * u) / z) * w)) = K(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(15208,a,15335,a),flip(a)].">
      <j1 rule="hyper" parents="15208 15335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15337">
    <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(15335(a,1),15208(a,1))].">
      <j1 rule="para" parents="15335 15208"/>
    </justification>
  </clause>

  <clause id="15338">
    <literal><![CDATA[
      K(x,y * (T(T(z,u),u) * w)) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(225(a,1),15336(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="225 15336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15339">
    <literal><![CDATA[
      K(x,y * (z * (T(T(z,u),u) \ w))) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(5(a,1),15338(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 15338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15340">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (K(z,u) * w))) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(5848(a,2),15339(a,1,2,2))].">
      <j1 rule="para" parents="5848 15339"/>
    </justification>
  </clause>

  <clause id="15341">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (z \ w))) = K(x,y * (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[para(5042(a,1),15340(a,1,2,2,2))].">
      <j1 rule="para" parents="5042 15340"/>
    </justification>
  </clause>

  <clause id="15342">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * K(z,u)) * w)) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(11399(a,2),15340(a,1,2,2))].">
      <j1 rule="para" parents="11399 15340"/>
    </justification>
  </clause>

  <clause id="15343">
    <literal><![CDATA[
      K(x,y * (z * (K(u,w) * K(u,w)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15097,a(flip),b,15342,a)].">
      <j1 rule="hyper" parents="58 15097 15342"/>
    </justification>
  </clause>

  <clause id="15345">
    <literal><![CDATA[
      K(x,y * (z * K(u,w))) = K(x,y * (z * K(w,u)))
    ]]></literal>
    <justification jstring="[para(8968(a,1),15343(a,1,2,2))].">
      <j1 rule="para" parents="8968 15343"/>
    </justification>
  </clause>

  <clause id="15346">
    <literal><![CDATA[
      K(x,y * ((z / u) * K(u,w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[para(6293(a,1),15345(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6293 15345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15347">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(w,u))) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(13634(a,1),15345(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13634 15345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15348">
    <literal><![CDATA[
      K(x,y * ((z / (z / u)) \ w)) = K(x,y * (T(u,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13153,a,b,15341,a)].">
      <j1 rule="hyper" parents="58 13153 15341"/>
    </justification>
  </clause>

  <clause id="15349">
    <literal><![CDATA[
      K(x,y * (z / T(u,u \ w))) = K(x,y * (z / (w / (w / u))))
    ]]></literal>
    <justification jstring="[para(6444(a,2),15346(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6444 15346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15350">
    <literal><![CDATA[
      K(x,y * (z \ ((u * w) / u))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[para(13894(a,2),15347(a,1,2,2))].">
      <j1 rule="para" parents="13894 15347"/>
    </justification>
  </clause>

  <clause id="15351">
    <literal><![CDATA[
      K(x,y * (z \ (L(u,w,u) * w))) = K(x,y * (z \ T(w * u,u)))
    ]]></literal>
    <justification jstring="[para(13954(a,1),15347(a,1,2,2))].">
      <j1 rule="para" parents="13954 15347"/>
    </justification>
  </clause>

  <clause id="15352">
    <literal><![CDATA[
      K(x,y * (z \ T(T(u,w),w))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(225(a,1),15350(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="225 15350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15353">
    <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(320,a,12287,a,b,15352,a),flip(a)].">
      <j1 rule="hyper" parents="320 12287 15352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15354">
    <literal><![CDATA[
      K(x,y * (z \ T(u * w,w))) = K(x,y * (z \ (w * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13130,a(flip),b,15351,a),flip(a)].">
      <j1 rule="hyper" parents="58 13130 15351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15356">
    <literal><![CDATA[
      K(x,y * (z \ (u * (w / u)))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[para(7(a,1),15354(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15357">
    <literal><![CDATA[
      K(x,T(y * ((z * y) \ u),z)) = K(x,y * ((z * y) \ T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14937,a(flip),b,15356,a)].">
      <j1 rule="hyper" parents="58 14937 15356"/>
    </justification>
  </clause>

  <clause id="15358">
    <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,5298,a(flip),b,15246,a)].">
      <j1 rule="hyper" parents="58 5298 15246"/>
    </justification>
  </clause>

  <clause id="15359">
    <literal><![CDATA[
      K(x,y \ (((1 / z) \ u) * w)) = K(x,y \ (((z \ 1) \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15245,a(flip),b,15358,a),flip(a)].">
      <j1 rule="hyper" parents="58 15245 15358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15360">
    <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(7730(a,1),15033(a,1,1,1,2))].">
      <j1 rule="para" parents="7730 15033"/>
    </justification>
  </clause>

  <clause id="15361">
    <literal><![CDATA[
      K(x,(K(y,z \ K(z,u)) * u) \ w) = K(x,(u * K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(6839,a,15264,a),flip(a)].">
      <j1 rule="hyper" parents="6839 15264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15362">
    <literal><![CDATA[
      K(x,(y * K(z,u \ 1)) \ w) = K(x,(y * K(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(5882(a,1),15361(a,1,2,1))].">
      <j1 rule="para" parents="5882 15361"/>
    </justification>
  </clause>

  <clause id="15363">
    <literal><![CDATA[
      K(x,(K(y \ K(y,z),u) * z) \ w) = K(x,(z * K(u,y)) \ w)
    ]]></literal>
    <justification jstring="[hyper(6839,a,15268,a),flip(a)].">
      <j1 rule="hyper" parents="6839 15268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15364">
    <literal><![CDATA[
      K(x,(y * K(z \ 1,u)) \ w) = K(x,(y * K(u,z)) \ w)
    ]]></literal>
    <justification jstring="[para(6655(a,1),15363(a,1,2,1))].">
      <j1 rule="para" parents="6655 15363"/>
    </justification>
  </clause>

  <clause id="15365">
    <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(7766(a,1),15364(a,2,2))].">
      <j1 rule="para" parents="7766 15364"/>
    </justification>
  </clause>

  <clause id="15366">
    <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(15109(a,1),15127(a,1,1))].">
      <j1 rule="para" parents="15109 15127"/>
    </justification>
  </clause>

  <clause id="15367">
    <literal><![CDATA[
      T(x,T(y / ((z * u) / z),w)) = T(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(7678,a,15366,a),flip(a)].">
      <j1 rule="hyper" parents="7678 15366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15368">
    <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,12335,a(flip),b,15367,a)].">
      <j1 rule="hyper" parents="58 12335 15367"/>
    </justification>
  </clause>

  <clause id="15369">
    <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,14491,a,b,15368,a)].">
      <j1 rule="hyper" parents="58 14491 15368"/>
    </justification>
  </clause>

  <clause id="15370">
    <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(6306(a,1),15080(a,2,2,1))].">
      <j1 rule="para" parents="6306 15080"/>
    </justification>
  </clause>

  <clause id="15371">
    <literal><![CDATA[
      K(x,(y \ T(T(z,u),u)) * w) = K(x,(y \ z) * w)
    ]]></literal>
    <justification jstring="[hyper(29,a,15353,a(flip),b,15138,a),flip(a)].">
      <j1 rule="hyper" parents="29 15353 15138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15372">
    <literal><![CDATA[
      K(x,(y \ ((z * u) / z)) * w) = K(x,(y \ T(u,z)) * w)
    ]]></literal>
    <justification jstring="[para(224(a,1),15371(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="224 15371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15374">
    <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(6306(a,1),15166(a,2,2,2))].">
      <j1 rule="para" parents="6306 15166"/>
    </justification>
  </clause>

  <clause id="15375">
    <literal><![CDATA[
      K(x,y * ((((1 / z) * u) \ u) \ u)) = K(x,y * (((1 / z) * u) * K(z,z \ u)))
    ]]></literal>
    <justification jstring="[para(13709(a,1),15174(a,2,2,2,2))].">
      <j1 rule="para" parents="13709 15174"/>
    </justification>
  </clause>

  <clause id="15376">
    <literal><![CDATA[
      K(x,y * ((((1 / z) * u) \ u) \ u)) = K(x,y * ((1 / z) * (z * (u / z))))
    ]]></literal>
    <justification jstring="[para(10316(a,1),15375(a,2,2,2))].">
      <j1 rule="para" parents="10316 15375"/>
    </justification>
  </clause>

  <clause id="15377">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * ((((1 / u) * z) \ z) \ z))
    ]]></literal>
    <justification jstring="[para(2797(a,1),15376(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2797 15376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15378">
    <literal><![CDATA[
      K(x,y * T((1 / z) * u,u)) = K(x,y * L(u / z,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,13002,a(flip),b,15377,a)].">
      <j1 rule="hyper" parents="320 13002 15377"/>
    </justification>
  </clause>

  <clause id="15379">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * (z * (1 / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15168,a(flip),b,15378,a),flip(a)].">
      <j1 rule="hyper" parents="58 15168 15378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15380">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(320,a,5294,a(flip),b,15379,a),flip(a)].">
      <j1 rule="hyper" parents="320 5294 15379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15381">
    <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,15362,a(flip),b,15319,a)].">
      <j1 rule="hyper" parents="58 15362 15319"/>
    </justification>
  </clause>

  <clause id="15382">
    <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,13145,a(flip),b,15381,a)].">
      <j1 rule="hyper" parents="58 13145 15381"/>
    </justification>
  </clause>

  <clause id="15383">
    <literal><![CDATA[
      K(x,T(y,z) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y)))
    ]]></literal>
    <justification jstring="[para(4714(a,2),15382(a,1,2,1))].">
      <j1 rule="para" parents="4714 15382"/>
    </justification>
  </clause>

  <clause id="15384">
    <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(4193(a,1),15383(a,1,2,1))].">
      <j1 rule="para" parents="4193 15383"/>
    </justification>
  </clause>

  <clause id="15385">
    <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(7548(a,1),15326(a,2,1,2))].">
      <j1 rule="para" parents="7548 15326"/>
    </justification>
  </clause>

  <clause id="15387">
    <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),15384(a,1,2,2,1))].">
      <j1 rule="para" parents="105 15384"/>
    </justification>
  </clause>

  <clause id="15388">
    <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),15387(a,1,2,2,2,2))].">
      <j1 rule="para" parents="105 15387"/>
    </justification>
  </clause>

  <clause id="15389">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z * y) * (u / (z * y)))) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[para(7884(a,1),15388(a,2,2))].">
      <j1 rule="para" parents="7884 15388"/>
    </justification>
  </clause>

  <clause id="15390">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,z * y)) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15238,a(flip),b,15389,a)].">
      <j1 rule="hyper" parents="58 15238 15389"/>
    </justification>
  </clause>

  <clause id="15392">
    <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(5811(a,1),15390(a,1,2,2,2))].">
      <j1 rule="para" parents="5811 15390"/>
    </justification>
  </clause>

  <clause id="15393">
    <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(15152,a,15348,a),flip(a)].">
      <j1 rule="hyper" parents="15152 15348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15394">
    <literal><![CDATA[
      K(x,((y / (y / z)) \ u) * w) = K(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(12263,a,15393,a),flip(a)].">
      <j1 rule="hyper" parents="12263 15393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15395">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(75(a,1),15394(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 15394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15396">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(4208(a,1),15395(a,1,2,1))].">
      <j1 rule="para" parents="4208 15395"/>
    </justification>
  </clause>

  <clause id="15397">
    <literal><![CDATA[
      K(x,(T(y,T(z,u)) \ (u * (z / u))) * w) = K(x,((u * (z / u)) / y) * w)
    ]]></literal>
    <justification jstring="[para(12239(a,1),15395(a,1,2,1,1))].">
      <j1 rule="para" parents="12239 15395"/>
    </justification>
  </clause>

  <clause id="15398">
    <literal><![CDATA[
      K(x,(T(y,z) / z) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15371,a(flip),b,15396,a),flip(a)].">
      <j1 rule="hyper" parents="58 15371 15396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15399">
    <literal><![CDATA[
      K(x,(y / T(z,y)) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(4206(a,1),15398(a,1,2,1))].">
      <j1 rule="para" parents="4206 15398"/>
    </justification>
  </clause>

  <clause id="15400">
    <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(13794(a,1),15399(a,1,2,1,2))].">
      <j1 rule="para" parents="13794 15399"/>
    </justification>
  </clause>

  <clause id="15401">
    <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(320,a,9312,a(flip),b,15029,a),flip(a)].">
      <j1 rule="hyper" parents="320 9312 15029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15403">
    <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(15035(a,1),15401(a,2,2))].">
      <j1 rule="para" parents="15035 15401"/>
    </justification>
  </clause>

  <clause id="15404">
    <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(15240(a,1),15132(a,1,1))].">
      <j1 rule="para" parents="15240 15132"/>
    </justification>
  </clause>

  <clause id="15405">
    <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(15404(a,1),10833(a,1))].">
      <j1 rule="para" parents="15404 10833"/>
    </justification>
  </clause>

  <clause id="15406">
    <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(9902(a,1),15320(a,2,2))].">
      <j1 rule="para" parents="9902 15320"/>
    </justification>
  </clause>

  <clause id="15407">
    <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(7919(a,1),15406(a,1,2))].">
      <j1 rule="para" parents="7919 15406"/>
    </justification>
  </clause>

  <clause id="15408">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(y / z,u \ 1))
    ]]></literal>
    <justification jstring="[para(9596(a,1),15407(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9596 15407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15409">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,8200,a(flip),b,15408,a),flip(a)].">
      <j1 rule="hyper" parents="320 8200 15408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15411">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z \ y) * (u / (z \ y)))) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14840,a(flip),b,15409,a)].">
      <j1 rule="hyper" parents="58 14840 15409"/>
    </justification>
  </clause>

  <clause id="15412">
    <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(4237(a,1),15411(a,1,2,2,1))].">
      <j1 rule="para" parents="4237 15411"/>
    </justification>
  </clause>

  <clause id="15413">
    <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(7306(a,1),15365(a,1,2,2,2))].">
      <j1 rule="para" parents="7306 15365"/>
    </justification>
  </clause>

  <clause id="15415">
    <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(7759(a,2),15413(a,1,2,2))].">
      <j1 rule="para" parents="7759 15413"/>
    </justification>
  </clause>

  <clause id="15416">
    <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(8166(a,1),15415(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8166 15415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15417">
    <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(320,a,6110,a(flip),b,15416,a),flip(a)].">
      <j1 rule="hyper" parents="320 6110 15416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15418">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,13036,a(flip),b,15417,a)].">
      <j1 rule="hyper" parents="58 13036 15417"/>
    </justification>
  </clause>

  <clause id="15419">
    <literal><![CDATA[
      K(x,y \ K(z,u \ 1)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(6455,a,15418,a),flip(a)].">
      <j1 rule="hyper" parents="6455 15418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15423">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(15199,a,15419,a)].">
      <j1 rule="hyper" parents="15199 15419"/>
    </justification>
  </clause>

  <clause id="15424">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(3523(a,1),15419(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3523 15419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15425">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,1 / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15141,a(flip),b,15423,a),flip(a)].">
      <j1 rule="hyper" parents="58 15141 15423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15426">
    <literal><![CDATA[
      K(x,y \ K(z \ u,u)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13045,a(flip),b,15424,a)].">
      <j1 rule="hyper" parents="58 13045 15424"/>
    </justification>
  </clause>

  <clause id="15427">
    <literal><![CDATA[
      K(x,y \ K(z,u \ z)) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(15199,a,15426,a)].">
      <j1 rule="hyper" parents="15199 15426"/>
    </justification>
  </clause>

  <clause id="15428">
    <literal><![CDATA[
      K(x,y \ T(z,1 / u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15140,a(flip),b,15425,a),flip(a)].">
      <j1 rule="hyper" parents="58 15140 15425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15429">
    <literal><![CDATA[
      K(x,y \ T(z,u \ 1)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),15428(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="72 15428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15430">
    <literal><![CDATA[
      K(x,y \ T(z * (u \ 1),u)) = K(x,y \ ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15240,a(flip),b,15429,a),flip(a)].">
      <j1 rule="hyper" parents="58 15240 15429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15431">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w \ u))) = K(x,y \ T(z,T(w,u)))
    ]]></literal>
    <justification jstring="[para(7638(a,1),15429(a,1,2,2))].">
      <j1 rule="para" parents="7638 15429"/>
    </justification>
  </clause>

  <clause id="15432">
    <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(15429(a,1),15194(a,1,1))].">
      <j1 rule="para" parents="15429 15194"/>
    </justification>
  </clause>

  <clause id="15433">
    <literal><![CDATA[
      K(x,y \ ((z \ 1) * (z * u))) = K(x,y \ R(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(784(a,1),15430(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="784 15430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15434">
    <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(10868,a,15433,a)].">
      <j1 rule="hyper" parents="10868 15433"/>
    </justification>
  </clause>

  <clause id="15435">
    <literal><![CDATA[
      K(x,y \ R(z,u,u \ 1)) = K(x,y \ L(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,5693,a(flip),b,15433,a),flip(a)].">
      <j1 rule="hyper" parents="58 5693 15433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15436">
    <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,14479,a(flip),b,15435,a),flip(a)].">
      <j1 rule="hyper" parents="58 14479 15435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15437">
    <literal><![CDATA[
      K(x,y \ L(z / u,u,u \ 1)) = K(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(523(a,1),15435(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="523 15435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15438">
    <literal><![CDATA[
      K(x,y \ (z \ L(z,u,u \ 1))) = K(x,y \ a(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,14403,a(flip),b,15436,a)].">
      <j1 rule="hyper" parents="58 14403 15436"/>
    </justification>
  </clause>

  <clause id="15439">
    <literal><![CDATA[
      K(x,(y \ 1) \ a(z,u,u \ 1)) = K(x,y * (z \ L(z,u,u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(13941,a,15438,a),flip(a)].">
      <j1 rule="hyper" parents="13941 15438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15440">
    <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(15439(a,1),13941(a,1))].">
      <j1 rule="para" parents="15439 13941"/>
    </justification>
  </clause>

  <clause id="15441">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ R(u,y,y \ 1)) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,14525,a(flip),b,15434,a),flip(a)].">
      <j1 rule="hyper" parents="58 14525 15434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15442">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ L(u,y,y \ 1)) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15435,a(flip),b,15441,a)].">
      <j1 rule="hyper" parents="58 15435 15441"/>
    </justification>
  </clause>

  <clause id="15443">
    <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(15432(a,1),10833(a,1))].">
      <j1 rule="para" parents="15432 10833"/>
    </justification>
  </clause>

  <clause id="15444">
    <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(8545(a,1),15412(a,1,2,1))].">
      <j1 rule="para" parents="8545 15412"/>
    </justification>
  </clause>

  <clause id="15445">
    <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(4237(a,1),15444(a,1,2,2,2,2))].">
      <j1 rule="para" parents="4237 15444"/>
    </justification>
  </clause>

  <clause id="15447">
    <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,15294,a(flip),b,15445,a)].">
      <j1 rule="hyper" parents="58 15294 15445"/>
    </justification>
  </clause>

  <clause id="15448">
    <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(12700(a,1),15447(a,2,2))].">
      <j1 rule="para" parents="12700 15447"/>
    </justification>
  </clause>

  <clause id="15449">
    <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,15238,a(flip),b,15448,a)].">
      <j1 rule="hyper" parents="58 15238 15448"/>
    </justification>
  </clause>

  <clause id="15450">
    <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,13003,a(flip),b,15392,a)].">
      <j1 rule="hyper" parents="58 13003 15392"/>
    </justification>
  </clause>

  <clause id="15451">
    <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(15299(a,1),15450(a,1,2,2))].">
      <j1 rule="para" parents="15299 15450"/>
    </justification>
  </clause>

  <clause id="15452">
    <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(5346(a,1),15451(a,1,2,2,2,2))].">
      <j1 rule="para" parents="5346 15451"/>
    </justification>
  </clause>

  <clause id="15453">
    <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(15225(a,1),15452(a,1,2,2))].">
      <j1 rule="para" parents="15225 15452"/>
    </justification>
  </clause>

  <clause id="15454">
    <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(4714(a,2),15453(a,1,2,2,2))].">
      <j1 rule="para" parents="4714 15453"/>
    </justification>
  </clause>

  <clause id="15455">
    <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(13159,a,15454,a),flip(a)].">
      <j1 rule="hyper" parents="13159 15454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15456">
    <literal><![CDATA[
      K(x,T(y / (z * u),(z * u) \ u)) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(320,a,15072,a(flip),b,15455,a),flip(a)].">
      <j1 rule="hyper" parents="320 15072 15455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15457">
    <literal><![CDATA[
      K(x,T(y / (z * u),u \ (z \ u))) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[para(7654(a,1),15456(a,1,2))].">
      <j1 rule="para" parents="7654 15456"/>
    </justification>
  </clause>

  <clause id="15458">
    <literal><![CDATA[
      K(x,T(y / (z * u),T(z,u))) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(8248,a,15457,a)].">
      <j1 rule="hyper" parents="8248 15457"/>
    </justification>
  </clause>

  <clause id="15459">
    <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(5013(a,1),15458(a,2,2,1))].">
      <j1 rule="para" parents="5013 15458"/>
    </justification>
  </clause>

  <clause id="15460">
    <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(14201(a,1),14205(a,1,2))].">
      <j1 rule="para" parents="14201 14205"/>
    </justification>
  </clause>

  <clause id="15461">
    <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(828,a,15460,a)].">
      <j1 rule="hyper" parents="828 15460"/>
    </justification>
  </clause>

  <clause id="15462">
    <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(14204,a,15461,a),flip(a)].">
      <j1 rule="hyper" parents="14204 15461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15464">
    <literal><![CDATA[
      L(x,y,a(z,u,K(w,v5)) * v6) = L(x,y,v6)
    ]]></literal>
    <justification jstring="[para(14202(a,1),15462(a,1,2))].">
      <j1 rule="para" parents="14202 15462"/>
    </justification>
  </clause>

  <clause id="15465">
    <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(13180(a,1),14507(a,1,2))].">
      <j1 rule="para" parents="13180 14507"/>
    </justification>
  </clause>

  <clause id="15466">
    <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(14659(a,1),15465(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="14659 15465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15467">
    <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(224(a,1),15466(a,2,2,1,1,1))].">
      <j1 rule="para" parents="224 15466"/>
    </justification>
  </clause>

  <clause id="15469">
    <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(15467(a,2),14011(a,1))].">
      <j1 rule="para" parents="15467 14011"/>
    </justification>
  </clause>

  <clause id="15470">
    <literal><![CDATA[
      L(a(a(x,y,a(z,u,w)),v5,v6),v7,v8) = L(a(x,y,a(z,u,w)) \ R(a(x,y,a(z,u,w)),v5,v6),a(x,y,a(z,u,w)),v5 * v6)
    ]]></literal>
    <justification jstring="[para(892(a,1),14793(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="892 14793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15471">
    <literal><![CDATA[
      L(a(a(x,y,a(z,u,w)),v5,v6),v7,v8) = a(a(x,y,a(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(320,a,14751,a,b,15470,a),flip(a)].">
      <j1 rule="hyper" parents="320 14751 15470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15473">
    <literal><![CDATA[
      L(a(x,a(y,z,a(u,w,v5)),v6),v7,v8) = a(a(y,z,a(u,w,v5)),x,v6)
    ]]></literal>
    <justification jstring="[para(13423(a,1),15471(a,1,1))].">
      <j1 rule="para" parents="13423 15471"/>
    </justification>
  </clause>

  <clause id="15474">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ R(a(x,y,a(z,u,w)),v5,v6) = a(v5,a(x,y,a(z,u,w)),v6)
    ]]></literal>
    <justification jstring="[hyper(14753,a,15473,a)].">
      <j1 rule="hyper" parents="14753 15473"/>
    </justification>
  </clause>

  <clause id="15475">
    <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),14508(a,1,2,2))].">
      <j1 rule="para" parents="60 14508"/>
    </justification>
  </clause>

  <clause id="15476">
    <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(14895(a,1),14767(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14895 14767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15477">
    <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(14398(a,1),15476(a,2,2,2,1))].">
      <j1 rule="para" parents="14398 15476"/>
    </justification>
  </clause>

  <clause id="15479">
    <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(14405(a,1),15477(a,2,2))].">
      <j1 rule="para" parents="14405 15477"/>
    </justification>
  </clause>

  <clause id="15480">
    <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(7917(a,1),15459(a,2,2,2))].">
      <j1 rule="para" parents="7917 15459"/>
    </justification>
  </clause>

  <clause id="15481">
    <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(8124(a,1),15480(a,2,2,2))].">
      <j1 rule="para" parents="8124 15480"/>
    </justification>
  </clause>

  <clause id="15482">
    <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(320,a,15431,a(flip),b,15481,a),flip(a)].">
      <j1 rule="hyper" parents="320 15431 15481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15483">
    <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(320,a,15364,a(flip),b,15482,a),flip(a)].">
      <j1 rule="hyper" parents="320 15364 15482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15484">
    <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(320,a,13145,a(flip),b,15483,a),flip(a)].">
      <j1 rule="hyper" parents="320 13145 15483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15485">
    <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(4714(a,2),15484(a,2,2,1))].">
      <j1 rule="para" parents="4714 15484"/>
    </justification>
  </clause>

  <clause id="15486">
    <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(320,a,15449,a(flip),b,15485,a),flip(a)].">
      <j1 rule="hyper" parents="320 15449 15485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15487">
    <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),15486(a,1,2,1,2))].">
      <j1 rule="para" parents="5 15486"/>
    </justification>
  </clause>

  <clause id="15488">
    <literal><![CDATA[
      K(x,T(y / z,T(z * u,z))) = K(x,T(y / z,u \ z))
    ]]></literal>
    <justification jstring="[para(7081(a,1),15487(a,1,2))].">
      <j1 rule="para" parents="7081 15487"/>
    </justification>
  </clause>

  <clause id="15489">
    <literal><![CDATA[
      K(x,T(y / z,u \ z)) = K(x,T(y / z,u * z))
    ]]></literal>
    <justification jstring="[para(12214(a,1),15488(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12214 15488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15490">
    <literal><![CDATA[
      K(x,T((y * z) / z,u * z)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6(a,1),15489(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6 15489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15491">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(6(a,1),15490(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6 15490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15492">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8244,a,15491,a)].">
      <j1 rule="hyper" parents="8244 15491"/>
    </justification>
  </clause>

  <clause id="15493">
    <literal><![CDATA[
      K(x \ y,T(z,y * x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(8037,a,15491,a),flip(a)].">
      <j1 rule="hyper" parents="8037 15491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15495">
    <literal><![CDATA[
      K(x,T(y,z * u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15491,a(flip),b,15492,a)].">
      <j1 rule="hyper" parents="58 15491 15492"/>
    </justification>
  </clause>

  <clause id="15496">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),u * z)) = K(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15239,a(flip),b,15492,a),flip(a)].">
      <j1 rule="hyper" parents="58 15239 15492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15497">
    <literal><![CDATA[
      T(x * K(y,T(x,z * u)),y) = T(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(15492(a,1),8106(a,1,1,2))].">
      <j1 rule="para" parents="15492 8106"/>
    </justification>
  </clause>

  <clause id="15498">
    <literal><![CDATA[
      K(x,T((y \ z) * u,z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (y \ z)) = w
    ]]></literal>
    <justification jstring="[para(15492(a,1),12259(a,1))].">
      <j1 rule="para" parents="15492 12259"/>
    </justification>
  </clause>

  <clause id="15499">
    <literal><![CDATA[
      K(x,T(y * (z \ u),u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ u) * y) = w
    ]]></literal>
    <justification jstring="[para(15492(a,1),12260(a,1))].">
      <j1 rule="para" parents="15492 12260"/>
    </justification>
  </clause>

  <clause id="15500">
    <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(15492(a,1),13875(a,1))].">
      <j1 rule="para" parents="15492 13875"/>
    </justification>
  </clause>

  <clause id="15501">
    <literal><![CDATA[
      K(x * (y * z),T(u,z * y)) = K((y * z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(12204,a,15495,a),flip(a)].">
      <j1 rule="hyper" parents="12204 15495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15502">
    <literal><![CDATA[
      K(x,T(y,z * (u * y))) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,9570,a,b,15495,a)].">
      <j1 rule="hyper" parents="320 9570 15495"/>
    </justification>
  </clause>

  <clause id="15503">
    <literal><![CDATA[
      x * K(y,T(z,u * w)) = x * K(y,T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(119,a,15495,a,b,4,a)].">
      <j1 rule="hyper" parents="119 15495 4"/>
    </justification>
  </clause>

  <clause id="15506">
    <literal><![CDATA[
      (x * y) * K(z,T(u,y * x)) = K(z,u) * (x * y)
    ]]></literal>
    <justification jstring="[para(15495(a,1),7152(a,1,2))].">
      <j1 rule="para" parents="15495 7152"/>
    </justification>
  </clause>

  <clause id="15508">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,y * x)) = T(K(z,u) * x,y)
    ]]></literal>
    <justification jstring="[para(15495(a,1),14788(a,1,2))].">
      <j1 rule="para" parents="15495 14788"/>
    </justification>
  </clause>

  <clause id="15509">
    <literal><![CDATA[
      T(x * K(y,T(x,z * u)),y) = T(x,K(y,u * (x * z)))
    ]]></literal>
    <justification jstring="[para(15502(a,1),8119(a,1,1,2))].">
      <j1 rule="para" parents="15502 8119"/>
    </justification>
  </clause>

  <clause id="15510">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8322,a,15497,a),flip(a)].">
      <j1 rule="hyper" parents="8322 15497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15511">
    <literal><![CDATA[
      T(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(15497(a,1),8322(a,1))].">
      <j1 rule="para" parents="15497 8322"/>
    </justification>
  </clause>

  <clause id="15512">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(8192,a,15510,a)].">
      <j1 rule="hyper" parents="8192 15510"/>
    </justification>
  </clause>

  <clause id="15513">
    <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(15510(a,1),15028(a,1,2,1,2))].">
      <j1 rule="para" parents="15510 15028"/>
    </justification>
  </clause>

  <clause id="15514">
    <literal><![CDATA[
      x * K(x,K(y,z * u)) = T(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,4714,a(flip),b,15512,a)].">
      <j1 rule="hyper" parents="320 4714 15512"/>
    </justification>
  </clause>

  <clause id="15515">
    <literal><![CDATA[
      T(x,K(y,z * u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15510,a(flip),b,15512,a)].">
      <j1 rule="hyper" parents="58 15510 15512"/>
    </justification>
  </clause>

  <clause id="15516">
    <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(15515(a,1),15252(a,1,2,1,2))].">
      <j1 rule="para" parents="15515 15252"/>
    </justification>
  </clause>

  <clause id="15517">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(29,a,4714,a(flip),b,15514,a)].">
      <j1 rule="hyper" parents="29 4714 15514"/>
    </justification>
  </clause>

  <clause id="15518">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8189,a,15517,a)].">
      <j1 rule="hyper" parents="8189 15517"/>
    </justification>
  </clause>

  <clause id="15519">
    <literal><![CDATA[
      K(x,K(y,z * u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15517,a(flip),b,15518,a)].">
      <j1 rule="hyper" parents="58 15517 15518"/>
    </justification>
  </clause>

  <clause id="15520">
    <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(15518(a,1),7748(a,1,1))].">
      <j1 rule="para" parents="15518 7748"/>
    </justification>
  </clause>

  <clause id="15521">
    <literal><![CDATA[
      K(x * y,K(z,u)) = K(z,K(u,y * x))
    ]]></literal>
    <justification jstring="[hyper(7774,a,15519,a)].">
      <j1 rule="hyper" parents="7774 15519"/>
    </justification>
  </clause>

  <clause id="15524">
    <literal><![CDATA[
      K(x,K(y,(1 / z) * u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[hyper(320,a,11793,a(flip),b,15519,a),flip(a)].">
      <j1 rule="hyper" parents="320 11793 15519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15525">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,u * z)) = w
    ]]></literal>
    <justification jstring="[para(15519(a,1),7756(a,1))].">
      <j1 rule="para" parents="15519 7756"/>
    </justification>
  </clause>

  <clause id="15526">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,y * x))
    ]]></literal>
    <justification jstring="[para(15519(a,1),12272(a,2,2))].">
      <j1 rule="para" parents="15519 12272"/>
    </justification>
  </clause>

  <clause id="15529">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(15521(a,1),7796(a,1))].">
      <j1 rule="para" parents="15521 7796"/>
    </justification>
  </clause>

  <clause id="15530">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(13709(a,1),15524(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13709 15524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15531">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(8240,a,15530,a)].">
      <j1 rule="hyper" parents="8240 15530"/>
    </justification>
  </clause>

  <clause id="15532">
    <literal><![CDATA[
      K(x,K(y \ (1 / z),L(y / u,u,z))) = K(x,K(y / u,K(z,1 / z) / (z * y)))
    ]]></literal>
    <justification jstring="[hyper(320,a,10909,a,b,15530,a)].">
      <j1 rule="hyper" parents="320 10909 15530"/>
    </justification>
  </clause>

  <clause id="15533">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z / y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7772,a,b,15530,a)].">
      <j1 rule="hyper" parents="320 7772 15530"/>
    </justification>
  </clause>

  <clause id="15534">
    <literal><![CDATA[
      T(x,K(y,z / u)) = T(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,15530,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 15530 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15535">
    <literal><![CDATA[
      K(x,K(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z \ u)) = w
    ]]></literal>
    <justification jstring="[para(15530(a,2),8189(a,1))].">
      <j1 rule="para" parents="15530 8189"/>
    </justification>
  </clause>

  <clause id="15536">
    <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),15531(a,2,2,2))].">
      <j1 rule="para" parents="13 15531"/>
    </justification>
  </clause>

  <clause id="15537">
    <literal><![CDATA[
      K(x,K(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(15531(a,2),8189(a,1))].">
      <j1 rule="para" parents="15531 8189"/>
    </justification>
  </clause>

  <clause id="15538">
    <literal><![CDATA[
      K(x,K(y \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z / y,u)) = w
    ]]></literal>
    <justification jstring="[para(15533(a,2),7806(a,1))].">
      <j1 rule="para" parents="15533 7806"/>
    </justification>
  </clause>

  <clause id="15539">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(w,y,z))) = K(x,K(w,u / (z * y)))
    ]]></literal>
    <justification jstring="[para(10822(a,2),15533(a,1,2))].">
      <j1 rule="para" parents="10822 15533"/>
    </justification>
  </clause>

  <clause id="15541">
    <literal><![CDATA[
      T(x,K(y,(z * u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15534(a,1),8241(a,1))].">
      <j1 rule="para" parents="15534 8241"/>
    </justification>
  </clause>

  <clause id="15542">
    <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),15529(a,1,2,2))].">
      <j1 rule="para" parents="101 15529"/>
    </justification>
  </clause>

  <clause id="15543">
    <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(524(a,2),15537(a,1,2,2))].">
      <j1 rule="para" parents="524 15537"/>
    </justification>
  </clause>

  <clause id="15544">
    <literal><![CDATA[
      T(x,K(y,z * (u * z))) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(15541,a,15510,a),flip(a)].">
      <j1 rule="hyper" parents="15541 15510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15545">
    <literal><![CDATA[
      K((x * y) * T(z,y),T(u,y * z)) = K((z * y) * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(10359(a,1),15501(a,1,1))].">
      <j1 rule="para" parents="10359 15501"/>
    </justification>
  </clause>

  <clause id="15546">
    <literal><![CDATA[
      T(x,y) \ T(K(z,u) * x,y) = K(z,T(u,y * x))
    ]]></literal>
    <justification jstring="[hyper(14790,a,15503,a)].">
      <j1 rule="hyper" parents="14790 15503"/>
    </justification>
  </clause>

  <clause id="15548">
    <literal><![CDATA[
      (x * (y / x)) * K(z,T(u,y)) = K(z,u) * (x * (y / x))
    ]]></literal>
    <justification jstring="[para(7(a,1),15506(a,1,2,2,2))].">
      <j1 rule="para" parents="7 15506"/>
    </justification>
  </clause>

  <clause id="15549">
    <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(15508(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="15508 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15550">
    <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(14900(a,2),15546(a,2,2,2))].">
      <j1 rule="para" parents="14900 15546"/>
    </justification>
  </clause>

  <clause id="15551">
    <literal><![CDATA[
      T(x,K(y,z * (x * u))) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8322,a,15509,a),flip(a)].">
      <j1 rule="hyper" parents="8322 15509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15552">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(12293,a,15548,a)].">
      <j1 rule="hyper" parents="12293 15548"/>
    </justification>
  </clause>

  <clause id="15553">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,y)) = K(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(12236,a,15552,a),flip(a)].">
      <j1 rule="hyper" parents="12236 15552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15554">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7683,a,15552,a)].">
      <j1 rule="hyper" parents="7683 15552"/>
    </justification>
  </clause>

  <clause id="15555">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = T(K(x,y),T(z,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,15552,a,b,15552,a)].">
      <j1 rule="hyper" parents="320 15552 15552"/>
    </justification>
  </clause>

  <clause id="15558">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7131,a(flip),b,15552,a),flip(a)].">
      <j1 rule="hyper" parents="320 7131 15552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15559">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7884,a(flip),b,15552,a),flip(a)].">
      <j1 rule="hyper" parents="58 7884 15552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15560">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,x)) = K(z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,15552,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 15552 17"/>
    </justification>
  </clause>

  <clause id="15561">
    <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(15552(a,1),11621(a,1,2))].">
      <j1 rule="para" parents="15552 11621"/>
    </justification>
  </clause>

  <clause id="15564">
    <literal><![CDATA[
      K(x \ y,T(z,T(y,u))) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7864,a(flip),b,15554,a),flip(a)].">
      <j1 rule="hyper" parents="320 7864 15554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15565">
    <literal><![CDATA[
      T(x,T(y,T(z,u))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,15554,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 15554 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15566">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(107(a,1),15554(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 15554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15568">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(x,T(y,T(z,u))) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(15554(a,1),9626(a,1,1))].">
      <j1 rule="para" parents="15554 9626"/>
    </justification>
  </clause>

  <clause id="15569">
    <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(15554(a,1),12199(a,1))].">
      <j1 rule="para" parents="15554 12199"/>
    </justification>
  </clause>

  <clause id="15570">
    <literal><![CDATA[
      T(K(x,y),K(z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7928,a,15558,a)].">
      <j1 rule="hyper" parents="7928 15558"/>
    </justification>
  </clause>

  <clause id="15572">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15558(a,2),7683(a,1))].">
      <j1 rule="para" parents="15558 7683"/>
    </justification>
  </clause>

  <clause id="15573">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(12236,a,15570,a),flip(a)].">
      <j1 rule="hyper" parents="12236 15570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15574">
    <literal><![CDATA[
      K(x,T(T(y,K(z,u)),w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(8080,a,15570,a)].">
      <j1 rule="hyper" parents="8080 15570"/>
    </justification>
  </clause>

  <clause id="15575">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7956,a,15570,a),flip(a)].">
      <j1 rule="hyper" parents="7956 15570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15576">
    <literal><![CDATA[
      K(T(x,K(y,z)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(7385,a,15570,a)].">
      <j1 rule="hyper" parents="7385 15570"/>
    </justification>
  </clause>

  <clause id="15578">
    <literal><![CDATA[
      K(x,K(y,z) / u) = K(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6456,a,15570,a),flip(a)].">
      <j1 rule="hyper" parents="6456 15570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15582">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ K(z,u) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6427,a,b,15570,a)].">
      <j1 rule="hyper" parents="58 6427 15570"/>
    </justification>
  </clause>

  <clause id="15583">
    <literal><![CDATA[
      K(x,y) \ K(z,u) = K(z,u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,15570,a(flip),b,5094,a),flip(a)].">
      <j1 rule="hyper" parents="119 15570 5094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15584">
    <literal><![CDATA[
      K(x,y) * K(z,u) = K(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,15570,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 15570 17"/>
    </justification>
  </clause>

  <clause id="15585">
    <literal><![CDATA[
      K(x,y) / (K(x,y) * K(z,u)) = K(u,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,15570,a(flip),b,7819,a)].">
      <j1 rule="hyper" parents="117 15570 7819"/>
    </justification>
  </clause>

  <clause id="15586">
    <literal><![CDATA[
      T(x \ K(y,z),K(u,x)) = x \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,15570,a(flip),b,8108,a),flip(a)].">
      <j1 rule="hyper" parents="116 15570 8108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15587">
    <literal><![CDATA[
      K(x,K(y,K(z,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,15570,a(flip),b,10567,a),flip(a)].">
      <j1 rule="hyper" parents="115 15570 10567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15588">
    <literal><![CDATA[
      K(x,K(K(y,z),u)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,15570,a(flip),b,7785,a),flip(a)].">
      <j1 rule="hyper" parents="115 15570 7785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15589">
    <literal><![CDATA[
      T(L(K(x,y),z,u),K(w,v5)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(15570(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15570 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15597">
    <literal><![CDATA[
      x * (K(y,z) * K(x,u)) = T(x,u) * K(y,z)
    ]]></literal>
    <justification jstring="[para(15570(a,1),5039(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15570 5039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15598">
    <literal><![CDATA[
      T(K(x,y),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(15570(a,1),5595(a,1,1))].">
      <j1 rule="para" parents="15570 5595"/>
    </justification>
  </clause>

  <clause id="15599">
    <literal><![CDATA[
      T(x * K(y,z),K(x,u)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(15570(a,1),7567(a,2,2))].">
      <j1 rule="para" parents="15570 7567"/>
    </justification>
  </clause>

  <clause id="15600">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(15570(a,1),7956(a,1))].">
      <j1 rule="para" parents="15570 7956"/>
    </justification>
  </clause>

  <clause id="15602">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15570(a,1),12236(a,1))].">
      <j1 rule="para" parents="15570 12236"/>
    </justification>
  </clause>

  <clause id="15604">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5533,a,15587,a),flip(a)].">
      <j1 rule="hyper" parents="5533 15587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15605">
    <literal><![CDATA[
      T(K(x,K(y,z)),u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(4913,a,15587,a)].">
      <j1 rule="hyper" parents="4913 15587"/>
    </justification>
  </clause>

  <clause id="15607">
    <literal><![CDATA[
      T(x,K(y,K(z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,15587,a)].">
      <j1 rule="hyper" parents="51 15587"/>
    </justification>
  </clause>

  <clause id="15608">
    <literal><![CDATA[
      K(x,T(K(y,z),u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8043,a,15588,a)].">
      <j1 rule="hyper" parents="8043 15588"/>
    </justification>
  </clause>

  <clause id="15609">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(12253,a,15607,a)].">
      <j1 rule="hyper" parents="12253 15607"/>
    </justification>
  </clause>

  <clause id="15610">
    <literal><![CDATA[
      T(x,K(y,z) / u) = T(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8292,a,15607,a)].">
      <j1 rule="hyper" parents="8292 15607"/>
    </justification>
  </clause>

  <clause id="15611">
    <literal><![CDATA[
      x * (y * K(x,K(z,u))) = T(x,K(z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(8277,a,15607,a)].">
      <j1 rule="hyper" parents="8277 15607"/>
    </justification>
  </clause>

  <clause id="15612">
    <literal><![CDATA[
      T(x,T(K(y,z),u)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7833,a,15607,a)].">
      <j1 rule="hyper" parents="7833 15607"/>
    </justification>
  </clause>

  <clause id="15613">
    <literal><![CDATA[
      T(x,T(y,K(z,u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(7678,a,15607,a)].">
      <j1 rule="hyper" parents="7678 15607"/>
    </justification>
  </clause>

  <clause id="15614">
    <literal><![CDATA[
      (x * y) * K(x,K(z,u)) = T(x,K(z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(6521,a,15607,a)].">
      <j1 rule="hyper" parents="6521 15607"/>
    </justification>
  </clause>

  <clause id="15615">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * x) = u * T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8064,a(flip),b,15607,a)].">
      <j1 rule="hyper" parents="58 8064 15607"/>
    </justification>
  </clause>

  <clause id="15616">
    <literal><![CDATA[
      T(x,K(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(15607(a,1),44(a,2))].">
      <j1 rule="para" parents="15607 44"/>
    </justification>
  </clause>

  <clause id="15617">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * K(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15607(a,1),284(a,1,2))].">
      <j1 rule="para" parents="15607 284"/>
    </justification>
  </clause>

  <clause id="15618">
    <literal><![CDATA[
      L(x,y,z) * K(u,K(w,v5)) = K(u,K(w,v5)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(15607(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15607 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15620">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15607(a,1),12258(a,1,1))].">
      <j1 rule="para" parents="15607 12258"/>
    </justification>
  </clause>

  <clause id="15621">
    <literal><![CDATA[
      x \ T(y * x,K(z,K(u,w))) = T(y,K(K(u,w),z) * x)
    ]]></literal>
    <justification jstring="[para(15607(a,1),15024(a,1,2,1,2))].">
      <j1 rule="para" parents="15607 15024"/>
    </justification>
  </clause>

  <clause id="15622">
    <literal><![CDATA[
      K((K(x,y) * z) \ 1,u) = K((z * K(x,y)) \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(13062,a,15575,a)].">
      <j1 rule="hyper" parents="13062 15575"/>
    </justification>
  </clause>

  <clause id="15623">
    <literal><![CDATA[
      K(K(x,y) * (z * x),u) = K(z * T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(12256,a,15575,a)].">
      <j1 rule="hyper" parents="12256 15575"/>
    </justification>
  </clause>

  <clause id="15624">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(12204,a,15575,a)].">
      <j1 rule="hyper" parents="12204 15575"/>
    </justification>
  </clause>

  <clause id="15628">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(6305(a,1),15575(a,1,2))].">
      <j1 rule="para" parents="6305 15575"/>
    </justification>
  </clause>

  <clause id="15630">
    <literal><![CDATA[
      K(x,y * (z * K(y,u))) = K(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[para(7009(a,1),15575(a,1,2))].">
      <j1 rule="para" parents="7009 15575"/>
    </justification>
  </clause>

  <clause id="15631">
    <literal><![CDATA[
      x * (K(y,z) * K(u,w)) = x * (K(u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[para(15575(a,1),7274(a,1,2,2))].">
      <j1 rule="para" parents="15575 7274"/>
    </justification>
  </clause>

  <clause id="15632">
    <literal><![CDATA[
      K(T(x,K(y,z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(15575(a,1),8029(a,1))].">
      <j1 rule="para" parents="15575 8029"/>
    </justification>
  </clause>

  <clause id="15634">
    <literal><![CDATA[
      K(x,K(y,z) * (u * y)) = K(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[para(8064(a,1),15575(a,1,2))].">
      <j1 rule="para" parents="8064 15575"/>
    </justification>
  </clause>

  <clause id="15637">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * x,u) = w
    ]]></literal>
    <justification jstring="[para(15575(a,1),12204(a,1))].">
      <j1 rule="para" parents="15575 12204"/>
    </justification>
  </clause>

  <clause id="15638">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(15575(a,1),12260(a,1))].">
      <j1 rule="para" parents="15575 12260"/>
    </justification>
  </clause>

  <clause id="15639">
    <literal><![CDATA[
      K(T(1 / x,K(y,z)),u) = K(1 / L(x,w,x),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,8728,a,b,15576,a),flip(a)].">
      <j1 rule="hyper" parents="320 8728 15576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15641">
    <literal><![CDATA[
      K(L((x \ y) * K(z,u),K(u,z),x),w) = K((x * K(u,z)) \ y,w)
    ]]></literal>
    <justification jstring="[para(8066(a,2),15576(a,1,1))].">
      <j1 rule="para" parents="8066 15576"/>
    </justification>
  </clause>

  <clause id="15643">
    <literal><![CDATA[
      T(x * K(y,z),T(u,x)) = T(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(8708,a,15613,a)].">
      <j1 rule="hyper" parents="8708 15613"/>
    </justification>
  </clause>

  <clause id="15644">
    <literal><![CDATA[
      T(x,T(T(y,K(z,u)),w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(18(a,1),15613(a,1,2))].">
      <j1 rule="para" parents="18 15613"/>
    </justification>
  </clause>

  <clause id="15645">
    <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(647(a,1),15613(a,1,2))].">
      <j1 rule="para" parents="647 15613"/>
    </justification>
  </clause>

  <clause id="15646">
    <literal><![CDATA[
      T(x,K(y,z) \ u) = T(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(6305(a,1),15613(a,1,2))].">
      <j1 rule="para" parents="6305 15613"/>
    </justification>
  </clause>

  <clause id="15647">
    <literal><![CDATA[
      T(x,K(y,z) * (u / z)) = T(x,u / T(z,y))
    ]]></literal>
    <justification jstring="[para(6191(a,1),15613(a,1,2))].">
      <j1 rule="para" parents="6191 15613"/>
    </justification>
  </clause>

  <clause id="15648">
    <literal><![CDATA[
      T(x,K(y,z) * (u * y)) = T(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[para(8064(a,1),15613(a,1,2))].">
      <j1 rule="para" parents="8064 15613"/>
    </justification>
  </clause>

  <clause id="15650">
    <literal><![CDATA[
      T(x,(y / z) * K(y,u)) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[para(13680(a,1),15613(a,1,2))].">
      <j1 rule="para" parents="13680 15613"/>
    </justification>
  </clause>

  <clause id="15651">
    <literal><![CDATA[
      x * K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,u)) * x = w
    ]]></literal>
    <justification jstring="[para(6322(a,1),15616(a,1))].">
      <j1 rule="para" parents="6322 15616"/>
    </justification>
  </clause>

  <clause id="15652">
    <literal><![CDATA[
      T(x,T(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(7413(a,1),15616(a,1))].">
      <j1 rule="para" parents="7413 15616"/>
    </justification>
  </clause>

  <clause id="15654">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15559(a,2),7683(a,1))].">
      <j1 rule="para" parents="15559 7683"/>
    </justification>
  </clause>

  <clause id="15655">
    <literal><![CDATA[
      T(x,T(T(y,z) / u,y)) = T(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7229,a,15565,a),flip(a)].">
      <j1 rule="hyper" parents="7229 15565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15657">
    <literal><![CDATA[
      T(x,T(T(y,z) \ u,y)) = T(x,u / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7917,a(flip),b,15565,a),flip(a)].">
      <j1 rule="hyper" parents="58 7917 15565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15659">
    <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(15565(a,1),7420(a,1))].">
      <j1 rule="para" parents="15565 7420"/>
    </justification>
  </clause>

  <clause id="15660">
    <literal><![CDATA[
      T(x,y) * K(x / T(y,x),z) = y * T(y \ T(x,y),T(z,x))
    ]]></literal>
    <justification jstring="[para(15565(a,1),8303(a,2,2))].">
      <j1 rule="para" parents="15565 8303"/>
    </justification>
  </clause>

  <clause id="15661">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8032,a,15605,a)].">
      <j1 rule="hyper" parents="8032 15605"/>
    </justification>
  </clause>

  <clause id="15664">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(8021,a,15608,a)].">
      <j1 rule="hyper" parents="8021 15608"/>
    </justification>
  </clause>

  <clause id="15665">
    <literal><![CDATA[
      K(x,T(K(y,z),u)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,7759,a,b,15608,a),flip(a)].">
      <j1 rule="hyper" parents="320 7759 15608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15666">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,w) = T(u,w) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,15608,a(flip),b,15546,a),flip(a)].">
      <j1 rule="hyper" parents="119 15608 15546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15667">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) * K(x,K(y,z)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(119,a,15608,a(flip),b,7716,a)].">
      <j1 rule="hyper" parents="119 15608 7716"/>
    </justification>
  </clause>

  <clause id="15668">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7118(a,2),15608(a,1,2))].">
      <j1 rule="para" parents="7118 15608"/>
    </justification>
  </clause>

  <clause id="15669">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ x) = u \ T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(15608(a,1),13653(a,1,1))].">
      <j1 rule="para" parents="15608 13653"/>
    </justification>
  </clause>

  <clause id="15670">
    <literal><![CDATA[
      T(x,K(y,T(z,u))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6189(a,1),15612(a,1,2))].">
      <j1 rule="para" parents="6189 15612"/>
    </justification>
  </clause>

  <clause id="15671">
    <literal><![CDATA[
      T(x,K(T(y,z),u)) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7118(a,2),15612(a,1,2))].">
      <j1 rule="para" parents="7118 15612"/>
    </justification>
  </clause>

  <clause id="15672">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(7756,a,15661,a)].">
      <j1 rule="hyper" parents="7756 15661"/>
    </justification>
  </clause>

  <clause id="15673">
    <literal><![CDATA[
      K(K(x,y),T(z,u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7737,a,15661,a)].">
      <j1 rule="hyper" parents="7737 15661"/>
    </justification>
  </clause>

  <clause id="15675">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7759,a(flip),b,15661,a),flip(a)].">
      <j1 rule="hyper" parents="320 7759 15661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15676">
    <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,8061,a(flip),b,15661,a)].">
      <j1 rule="hyper" parents="58 8061 15661"/>
    </justification>
  </clause>

  <clause id="15677">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(15661(a,2),7774(a,1))].">
      <j1 rule="para" parents="15661 7774"/>
    </justification>
  </clause>

  <clause id="15678">
    <literal><![CDATA[
      K(x,K(y,L(z / u,u,w))) = K(x,K(y,(w * u) \ (w * z)))
    ]]></literal>
    <justification jstring="[para(7984(a,1),15661(a,1,2))].">
      <j1 rule="para" parents="7984 15661"/>
    </justification>
  </clause>

  <clause id="15679">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ (u * (y / u)),z) = K((u * (y / u)) / x,z)
    ]]></literal>
    <justification jstring="[para(15661(a,1),12208(a,1,1))].">
      <j1 rule="para" parents="15661 12208"/>
    </justification>
  </clause>

  <clause id="15682">
    <literal><![CDATA[
      T(x,K(y,T(z,u))) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,15664,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 15664 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15683">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(15664(a,1),7280(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15664 7280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15684">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15664(a,2),7806(a,1))].">
      <j1 rule="para" parents="15664 7806"/>
    </justification>
  </clause>

  <clause id="15685">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ T(y,u),z) = K(T(y,u) / x,z)
    ]]></literal>
    <justification jstring="[para(15664(a,1),8353(a,1,1))].">
      <j1 rule="para" parents="15664 8353"/>
    </justification>
  </clause>

  <clause id="15686">
    <literal><![CDATA[
      K(x,K(y,(z \ u) * z)) = K(x,K(u,y))
    ]]></literal>
    <justification jstring="[para(12230(a,2),15664(a,1,2))].">
      <j1 rule="para" parents="12230 15664"/>
    </justification>
  </clause>

  <clause id="15688">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) * K(y,K(z,x)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(119,a,15665,a(flip),b,7716,a)].">
      <j1 rule="hyper" parents="119 15665 7716"/>
    </justification>
  </clause>

  <clause id="15690">
    <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(15668(a,1),10641(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="15668 10641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15693">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,u) \ y) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(15670(a,1),8293(a,1,1))].">
      <j1 rule="para" parents="15670 8293"/>
    </justification>
  </clause>

  <clause id="15695">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,u) * y) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(15670(a,1),12217(a,1,1))].">
      <j1 rule="para" parents="15670 12217"/>
    </justification>
  </clause>

  <clause id="15696">
    <literal><![CDATA[
      T(K(x,T(y,z)) * u,K(y,x)) = u * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7828,a,15671,a),flip(a)].">
      <j1 rule="hyper" parents="7828 15671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15697">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u,K(y,x)) = u * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(15671(a,1),7822(a,1,2))].">
      <j1 rule="para" parents="15671 7822"/>
    </justification>
  </clause>

  <clause id="15699">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(15672(a,1),7280(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15672 7280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15700">
    <literal><![CDATA[
      K(x,y) * (K(z,K(y,u)) * w) = y * (T(T(y,K(z,u)),x) \ w)
    ]]></literal>
    <justification jstring="[para(15672(a,1),9900(a,1,2,1))].">
      <j1 rule="para" parents="15672 9900"/>
    </justification>
  </clause>

  <clause id="15703">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(y,K(z,x))) = u
    ]]></literal>
    <justification jstring="[para(15673(a,1),7264(a,1,2,2))].">
      <j1 rule="para" parents="15673 7264"/>
    </justification>
  </clause>

  <clause id="15704">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,y)) = u * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(15673(a,1),7915(a,1,1))].">
      <j1 rule="para" parents="15673 7915"/>
    </justification>
  </clause>

  <clause id="15705">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) = K(y,K(u,T(x,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,15668,a,b,15675,a)].">
      <j1 rule="hyper" parents="320 15668 15675"/>
    </justification>
  </clause>

  <clause id="15707">
    <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(15682(a,1),8413(a,1,1))].">
      <j1 rule="para" parents="15682 8413"/>
    </justification>
  </clause>

  <clause id="15708">
    <literal><![CDATA[
      K(x,y / K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) \ y) = w
    ]]></literal>
    <justification jstring="[para(7874(a,1),15598(a,1))].">
      <j1 rule="para" parents="7874 15598"/>
    </justification>
  </clause>

  <clause id="15709">
    <literal><![CDATA[
      K(x,K(y,z) * (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(z,y)) = w
    ]]></literal>
    <justification jstring="[para(6191(a,1),15600(a,1,2))].">
      <j1 rule="para" parents="6191 15600"/>
    </justification>
  </clause>

  <clause id="15710">
    <literal><![CDATA[
      K(x,y * (z * K(y,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) * z) = w
    ]]></literal>
    <justification jstring="[para(7009(a,1),15600(a,1,2))].">
      <j1 rule="para" parents="7009 15600"/>
    </justification>
  </clause>

  <clause id="15711">
    <literal><![CDATA[
      K(x,y) / (K(x,y) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,z) = w
    ]]></literal>
    <justification jstring="[para(7971(a,2),15600(a,1))].">
      <j1 rule="para" parents="7971 15600"/>
    </justification>
  </clause>

  <clause id="15712">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) \ y) = w
    ]]></literal>
    <justification jstring="[para(7834(a,1),15600(a,1,2))].">
      <j1 rule="para" parents="7834 15600"/>
    </justification>
  </clause>

  <clause id="15713">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(8289(a,1),15600(a,1,2))].">
      <j1 rule="para" parents="8289 15600"/>
    </justification>
  </clause>

  <clause id="15714">
    <literal><![CDATA[
      K(x,K(y,z) * (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(8064(a,1),15600(a,1,2))].">
      <j1 rule="para" parents="8064 15600"/>
    </justification>
  </clause>

  <clause id="15715">
    <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(7703(a,1),15600(a,1,2))].">
      <j1 rule="para" parents="7703 15600"/>
    </justification>
  </clause>

  <clause id="15716">
    <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(10513(a,1),15600(a,1,2))].">
      <j1 rule="para" parents="10513 15600"/>
    </justification>
  </clause>

  <clause id="15717">
    <literal><![CDATA[
      K(x,T(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(12244(a,1),15600(a,1,2))].">
      <j1 rule="para" parents="12244 15600"/>
    </justification>
  </clause>

  <clause id="15718">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(13668(a,1),15600(a,1,2))].">
      <j1 rule="para" parents="13668 15600"/>
    </justification>
  </clause>

  <clause id="15719">
    <literal><![CDATA[
      K(x,(y / z) * K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) / z) = w
    ]]></literal>
    <justification jstring="[para(13680(a,1),15600(a,1,2))].">
      <j1 rule="para" parents="13680 15600"/>
    </justification>
  </clause>

  <clause id="15720">
    <literal><![CDATA[
      K(L((x \ y) * K(z,u),K(u,z),x),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((x * K(u,z)) \ y,w) = v5
    ]]></literal>
    <justification jstring="[para(8066(a,2),15632(a,1,1))].">
      <j1 rule="para" parents="8066 15632"/>
    </justification>
  </clause>

  <clause id="15721">
    <literal><![CDATA[
      T(x,K(y,z) * (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u / T(z,y)) = w
    ]]></literal>
    <justification jstring="[para(6191(a,1),15652(a,1,2))].">
      <j1 rule="para" parents="6191 15652"/>
    </justification>
  </clause>

  <clause id="15722">
    <literal><![CDATA[
      T(x,T(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(7413(a,1),15652(a,1,2))].">
      <j1 rule="para" parents="7413 15652"/>
    </justification>
  </clause>

  <clause id="15723">
    <literal><![CDATA[
      T(x,K(y,z) * (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(8064(a,1),15652(a,1,2))].">
      <j1 rule="para" parents="8064 15652"/>
    </justification>
  </clause>

  <clause id="15724">
    <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(7813(a,1),15652(a,1,2))].">
      <j1 rule="para" parents="7813 15652"/>
    </justification>
  </clause>

  <clause id="15725">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(13668(a,1),15652(a,1,2))].">
      <j1 rule="para" parents="13668 15652"/>
    </justification>
  </clause>

  <clause id="15730">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),T(z,v5)) = w
    ]]></literal>
    <justification jstring="[para(15555(a,1),7551(a,1))].">
      <j1 rule="para" parents="15555 7551"/>
    </justification>
  </clause>

  <clause id="15735">
    <literal><![CDATA[
      T(x,y) * K(z \ x,u) = K(x / z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(15564(a,1),7872(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15564 7872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15736">
    <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(320,a,14741,a,b,15566,a)].">
      <j1 rule="hyper" parents="320 14741 15566"/>
    </justification>
  </clause>

  <clause id="15737">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,15491,a(flip),b,15566,a),flip(a)].">
      <j1 rule="hyper" parents="320 15491 15566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15739">
    <literal><![CDATA[
      K(x,y * K(z,u \ z)) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(15280,a,15573,a),flip(a)].">
      <j1 rule="hyper" parents="15280 15573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15740">
    <literal><![CDATA[
      K(x,y * K(z \ 1,u)) = K(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(15260,a,15573,a),flip(a)].">
      <j1 rule="hyper" parents="15260 15573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15741">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(15052,a,15573,a)].">
      <j1 rule="hyper" parents="15052 15573"/>
    </justification>
  </clause>

  <clause id="15742">
    <literal><![CDATA[
      K(x,K(y,z) * (u / y)) = K(x,u / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,15230,a(flip),b,15573,a),flip(a)].">
      <j1 rule="hyper" parents="320 15230 15573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15743">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,13025,a(flip),b,15573,a),flip(a)].">
      <j1 rule="hyper" parents="320 13025 15573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15744">
    <literal><![CDATA[
      K(x,(y * z) * K(u,y)) = K(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15055,a(flip),b,15573,a),flip(a)].">
      <j1 rule="hyper" parents="58 15055 15573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15745">
    <literal><![CDATA[
      K(x,y * K(z * u,z)) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,13011,a(flip),b,15573,a),flip(a)].">
      <j1 rule="hyper" parents="58 13011 15573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15746">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (w * u)) = K(x,w * (u * K(y,z)))
    ]]></literal>
    <justification jstring="[para(10784(a,1),15573(a,2,2))].">
      <j1 rule="para" parents="10784 15573"/>
    </justification>
  </clause>

  <clause id="15747">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(15573(a,1),15052(a,1))].">
      <j1 rule="para" parents="15573 15052"/>
    </justification>
  </clause>

  <clause id="15748">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u / z),w)) = K(x,T(u / T(z,y),w))
    ]]></literal>
    <justification jstring="[para(6191(a,1),15574(a,1,2,1))].">
      <j1 rule="para" parents="6191 15574"/>
    </justification>
  </clause>

  <clause id="15749">
    <literal><![CDATA[
      K(x,T(K(y,y \ z) * (u / z),w)) = K(x,T(u / ((y \ z) * y),w))
    ]]></literal>
    <justification jstring="[para(10622(a,1),15574(a,1,2,1))].">
      <j1 rule="para" parents="10622 15574"/>
    </justification>
  </clause>

  <clause id="15750">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,K(z,1 / z) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(320,a,14760,a,b,15578,a)].">
      <j1 rule="hyper" parents="320 14760 15578"/>
    </justification>
  </clause>

  <clause id="15751">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ w != K(y,x)
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = w
    ]]></literal>
    <justification jstring="[para(15582(a,1),42(a,1)),flip(a)].">
      <j1 rule="para" parents="15582 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15753">
    <literal><![CDATA[
      K(x,y) \ K(z,u) = K(u,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5092,a,b,15583,a)].">
      <j1 rule="hyper" parents="320 5092 15583"/>
    </justification>
  </clause>

  <clause id="15756">
    <literal><![CDATA[
      R(K(x,y) \ (z / K(u,w)),K(x,y),K(u,w)) = T(z / (K(u,w) * K(x,y)),K(x,y))
    ]]></literal>
    <justification jstring="[para(15584(a,1),648(a,2,1,2))].">
      <j1 rule="para" parents="15584 648"/>
    </justification>
  </clause>

  <clause id="15758">
    <literal><![CDATA[
      K(x,y) * K(z / (z / u),w) = K(u,T(w,z)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7893(a,1),15584(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7893 15584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15762">
    <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(15586(a,1),15026(a,1,2,1,2))].">
      <j1 rule="para" parents="15586 15026"/>
    </justification>
  </clause>

  <clause id="15763">
    <literal><![CDATA[
      T((x * K(y,z)) * u,K(x,u)) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(15599(a,1),8087(a,2,1))].">
      <j1 rule="para" parents="15599 8087"/>
    </justification>
  </clause>

  <clause id="15764">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,K(y,u)) = K(x,T(y,u)) * z
    ]]></literal>
    <justification jstring="[hyper(9131,a,15604,a),flip(a)].">
      <j1 rule="hyper" parents="9131 15604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15765">
    <literal><![CDATA[
      K(x,K(y,z)) \ u = u * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7805,a,15604,a)].">
      <j1 rule="hyper" parents="7805 15604"/>
    </justification>
  </clause>

  <clause id="15766">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[hyper(7803,a,15604,a),flip(a)].">
      <j1 rule="hyper" parents="7803 15604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15767">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,K(y,z))) = u
    ]]></literal>
    <justification jstring="[hyper(7802,a,15604,a)].">
      <j1 rule="hyper" parents="7802 15604"/>
    </justification>
  </clause>

  <clause id="15768">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ K(y,z)) = u \ K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,12309,a(flip),b,15604,a),flip(a)].">
      <j1 rule="hyper" parents="320 12309 15604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15769">
    <literal><![CDATA[
      x \ (y * K(x,K(z,u))) = T(x,K(z,u)) \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,15604,a(flip),b,7800,a)].">
      <j1 rule="hyper" parents="116 15604 7800"/>
    </justification>
  </clause>

  <clause id="15770">
    <literal><![CDATA[
      x * K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,u)) * w = x
    ]]></literal>
    <justification jstring="[para(15604(a,1),7802(a,1))].">
      <j1 rule="para" parents="15604 7802"/>
    </justification>
  </clause>

  <clause id="15771">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * K(x,K(y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(15604(a,1),7803(a,1))].">
      <j1 rule="para" parents="15604 7803"/>
    </justification>
  </clause>

  <clause id="15773">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(15251,a,15609,a)].">
      <j1 rule="hyper" parents="15251 15609"/>
    </justification>
  </clause>

  <clause id="15774">
    <literal><![CDATA[
      T(x,(y / z) * K(u,y)) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15046,a(flip),b,15609,a),flip(a)].">
      <j1 rule="hyper" parents="58 15046 15609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15775">
    <literal><![CDATA[
      T(x,(y \ z) * K(y,u)) = T(x,T(y,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15043,a(flip),b,15609,a),flip(a)].">
      <j1 rule="hyper" parents="58 15043 15609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15776">
    <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,15609,a(flip),b,15032,a),flip(a)].">
      <j1 rule="hyper" parents="119 15609 15032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15777">
    <literal><![CDATA[
      T(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(15609(a,1),15251(a,1))].">
      <j1 rule="para" parents="15609 15251"/>
    </justification>
  </clause>

  <clause id="15778">
    <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(15610(a,1),14449(a,1,2,2,1))].">
      <j1 rule="para" parents="15610 14449"/>
    </justification>
  </clause>

  <clause id="15779">
    <literal><![CDATA[
      K(x * K(y \ z,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(8752,a,15624,a),flip(a)].">
      <j1 rule="hyper" parents="8752 15624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15780">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,15101,a,b,15624,a),flip(a)].">
      <j1 rule="hyper" parents="320 15101 15624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15781">
    <literal><![CDATA[
      K(x * K(y * z,y),u) = K(K(z,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13052,a(flip),b,15624,a),flip(a)].">
      <j1 rule="hyper" parents="58 13052 15624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15782">
    <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(15624(a,1),7689(a,1))].">
      <j1 rule="para" parents="15624 7689"/>
    </justification>
  </clause>

  <clause id="15783">
    <literal><![CDATA[
      K(x * K(y \ z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) * x,u) = w
    ]]></literal>
    <justification jstring="[para(15624(a,1),13135(a,1))].">
      <j1 rule="para" parents="15624 13135"/>
    </justification>
  </clause>

  <clause id="15784">
    <literal><![CDATA[
      K(x / (y / z),y) = K(x / (z \ y),y)
    ]]></literal>
    <justification jstring="[para(6441(a,1),15779(a,1,1))].">
      <j1 rule="para" parents="6441 15779"/>
    </justification>
  </clause>

  <clause id="15785">
    <literal><![CDATA[
      K(x * (y / z),y) = K(x * (z \ y),y)
    ]]></literal>
    <justification jstring="[para(6446(a,1),15779(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6446 15779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15786">
    <literal><![CDATA[
      K(x,K(y,y \ z) \ (u / z)) = K(x,u / (y * (z / y)))
    ]]></literal>
    <justification jstring="[para(10624(a,1),15628(a,2,2))].">
      <j1 rule="para" parents="10624 15628"/>
    </justification>
  </clause>

  <clause id="15787">
    <literal><![CDATA[
      K(x,K(y \ K(z,u),w) * v5) = K(x,K(w,y * K(u,z)) * v5)
    ]]></literal>
    <justification jstring="[para(15628(a,1),15266(a,2,2,1))].">
      <j1 rule="para" parents="15628 15266"/>
    </justification>
  </clause>

  <clause id="15788">
    <literal><![CDATA[
      T(x,T(T(y,T(z,u)) * u,w)) = T(x,T(T(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(7926(a,1),15644(a,1,2,1))].">
      <j1 rule="para" parents="7926 15644"/>
    </justification>
  </clause>

  <clause id="15789">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,K(x,u)) = K(x,T(y,u)) * z
    ]]></literal>
    <justification jstring="[hyper(9132,a,15683,a),flip(a)].">
      <j1 rule="hyper" parents="9132 15683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15790">
    <literal><![CDATA[
      K(x,K(y / z,(z \ u) * y)) = K(x,K(u,y / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,10374,a(flip),b,15686,a)].">
      <j1 rule="hyper" parents="58 10374 15686"/>
    </justification>
  </clause>

  <clause id="15791">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * K(y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(15703(a,1),7803(a,1,2))].">
      <j1 rule="para" parents="15703 7803"/>
    </justification>
  </clause>

  <clause id="15792">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (y \ z))) = K(x,u / (z / y))
    ]]></literal>
    <justification jstring="[hyper(320,a,13099,a(flip),b,15741,a),flip(a)].">
      <j1 rule="hyper" parents="320 13099 15741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15794">
    <literal><![CDATA[
      K(x,K(y,z) * (u * z)) = K(x,u * T(z,y))
    ]]></literal>
    <justification jstring="[para(6086(a,1),15741(a,2,2))].">
      <j1 rule="para" parents="6086 15741"/>
    </justification>
  </clause>

  <clause id="15795">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(w,v5) = K(v5,w) \ K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(10763(a,2),15753(a,1,1))].">
      <j1 rule="para" parents="10763 15753"/>
    </justification>
  </clause>

  <clause id="15796">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,x) = x \ (u * T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(320,a,7017,a,b,15765,a),flip(a)].">
      <j1 rule="hyper" parents="320 7017 15765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15797">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u / T(x,K(y,z))) != w
    ]]></literal>
    <literal><![CDATA[
      u / x = w
    ]]></literal>
    <justification jstring="[para(15765(a,2),6169(a,1))].">
      <j1 rule="para" parents="15765 6169"/>
    </justification>
  </clause>

  <clause id="15798">
    <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(15765(a,2),15360(a,1,1,1))].">
      <j1 rule="para" parents="15765 15360"/>
    </justification>
  </clause>

  <clause id="15799">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      w * K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(15767(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="15767 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15801">
    <literal><![CDATA[
      x \ T(y,K(z,u) * w) = x \ T(y,w * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,15773,a,b,5,a)].">
      <j1 rule="hyper" parents="116 15773 5"/>
    </justification>
  </clause>

  <clause id="15803">
    <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(15773(a,2),421(a,1))].">
      <j1 rule="para" parents="15773 421"/>
    </justification>
  </clause>

  <clause id="15804">
    <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(6084(a,2),15773(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6084 15773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15805">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ z)) = T(x,u \ T(z,y))
    ]]></literal>
    <justification jstring="[para(13634(a,1),15773(a,2,2))].">
      <j1 rule="para" parents="13634 15773"/>
    </justification>
  </clause>

  <clause id="15807">
    <literal><![CDATA[
      K(x * K(y,z),x \ z) = K(x,T(x \ z,y))
    ]]></literal>
    <justification jstring="[hyper(11221,a,15780,a),flip(a)].">
      <j1 rule="hyper" parents="11221 15780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15808">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,15624,a,b,15780,a)].">
      <j1 rule="hyper" parents="320 15624 15780"/>
    </justification>
  </clause>

  <clause id="15809">
    <literal><![CDATA[
      K(K(x \ y,x) * z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13047,a(flip),b,15780,a),flip(a)].">
      <j1 rule="hyper" parents="320 13047 15780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15810">
    <literal><![CDATA[
      K(K(x,y) * (z * (x * y)),u) = K(z * (y * x),u)
    ]]></literal>
    <justification jstring="[para(10332(a,1),15780(a,2,1))].">
      <j1 rule="para" parents="10332 15780"/>
    </justification>
  </clause>

  <clause id="15811">
    <literal><![CDATA[
      K(x / ((y \ z) \ z),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),15784(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 15784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15812">
    <literal><![CDATA[
      K(K(x,y) * (T(x,y) * z),u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(4778(a,1),15808(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4778 15808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15813">
    <literal><![CDATA[
      K(x * (y \ (z \ y)),y) = K(x / z,y)
    ]]></literal>
    <justification jstring="[hyper(14133,a,15811,a)].">
      <j1 rule="hyper" parents="14133 15811"/>
    </justification>
  </clause>

  <clause id="15814">
    <literal><![CDATA[
      x / (K(y / z,u) * x) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,y * (u \ (z \ u))) = w
    ]]></literal>
    <justification jstring="[para(15813(a,1),5112(a,1,2,1))].">
      <j1 rule="para" parents="15813 5112"/>
    </justification>
  </clause>

  <clause id="15815">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(12213(a,2),15654(a,1,2))].">
      <j1 rule="para" parents="12213 15654"/>
    </justification>
  </clause>

  <clause id="15816">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(15705(a,2),15677(a,1))].">
      <j1 rule="para" parents="15705 15677"/>
    </justification>
  </clause>

  <clause id="15817">
    <literal><![CDATA[
      K(x,K(y * z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z * y,u)) = w
    ]]></literal>
    <justification jstring="[para(12190(a,1),15684(a,1,2))].">
      <j1 rule="para" parents="12190 15684"/>
    </justification>
  </clause>

  <clause id="15819">
    <literal><![CDATA[
      T(x,y) * K(z / x,u) = K(x \ z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7882(a,1),15560(a,1,2))].">
      <j1 rule="para" parents="7882 15560"/>
    </justification>
  </clause>

  <clause id="15820">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) * T(z,w) = T(z,w) * K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(7871(a,1),15560(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7871 15560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15821">
    <literal><![CDATA[
      T(x,y) * K(z * x,u) = K(x * z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(12191(a,1),15560(a,1,2))].">
      <j1 rule="para" parents="12191 15560"/>
    </justification>
  </clause>

  <clause id="15822">
    <literal><![CDATA[
      T(L(K(x,y),z,u),w / v5) = T(L(K(x,y),z,u),v5 \ w)
    ]]></literal>
    <justification jstring="[para(15589(a,1),8290(a,1,1))].">
      <j1 rule="para" parents="15589 8290"/>
    </justification>
  </clause>

  <clause id="15823">
    <literal><![CDATA[
      T(x,K(y,z)) * (u / T(x,K(y,z))) = x * (u / x)
    ]]></literal>
    <justification jstring="[para(6159(a,1),15611(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6159 15611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15824">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u * x) = x \ (u * T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(116,a,15615,a(flip),b,7800,a),flip(a)].">
      <j1 rule="hyper" parents="116 15615 7800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15826">
    <literal><![CDATA[
      K(K(x,y) * (z * (x * y)),u) = K(z * T(x * y,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13105,a(flip),b,15623,a)].">
      <j1 rule="hyper" parents="58 13105 15623"/>
    </justification>
  </clause>

  <clause id="15828">
    <literal><![CDATA[
      K(x,y * (z * K(u,y))) = K(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15345,a,b,15630,a)].">
      <j1 rule="hyper" parents="58 15345 15630"/>
    </justification>
  </clause>

  <clause id="15829">
    <literal><![CDATA[
      K(x * y,z * T(x,y)) = K(x * y,z * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8740,a(flip),b,15634,a),flip(a)].">
      <j1 rule="hyper" parents="58 8740 15634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15830">
    <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(8296(a,1),15634(a,2,2,2))].">
      <j1 rule="para" parents="8296 15634"/>
    </justification>
  </clause>

  <clause id="15832">
    <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,7919,a(flip),b,15643,a)].">
      <j1 rule="hyper" parents="58 7919 15643"/>
    </justification>
  </clause>

  <clause id="15834">
    <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(7216(a,1),15647(a,1,2,1))].">
      <j1 rule="para" parents="7216 15647"/>
    </justification>
  </clause>

  <clause id="15835">
    <literal><![CDATA[
      T(x,K(y,z) \ (z / u)) = T(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15646,a,b,15650,a)].">
      <j1 rule="hyper" parents="58 15646 15650"/>
    </justification>
  </clause>

  <clause id="15836">
    <literal><![CDATA[
      T(x,T(y * z,u) / T(y,w)) = T(x,T(y,w) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[para(8254(a,1),15657(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8254 15657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15837">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (w * u)) = K(x,w * (u * K(y \ 1,z)))
    ]]></literal>
    <justification jstring="[para(10784(a,1),15740(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10784 15740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15838">
    <literal><![CDATA[
      K(x,K(y,z \ (y \ u)) * w) = K(x,w * K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(10309(a,2),15743(a,1,2,1))].">
      <j1 rule="para" parents="10309 15743"/>
    </justification>
  </clause>

  <clause id="15839">
    <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(7430(a,1),15774(a,1,2,1))].">
      <j1 rule="para" parents="7430 15774"/>
    </justification>
  </clause>

  <clause id="15840">
    <literal><![CDATA[
      K(x * K(y * (z * u),z),w) = K(K(y * u,z) * x,w)
    ]]></literal>
    <justification jstring="[para(10509(a,2),15781(a,1,1,2))].">
      <j1 rule="para" parents="10509 15781"/>
    </justification>
  </clause>

  <clause id="15841">
    <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(4872(a,1),15794(a,1,2,1))].">
      <j1 rule="para" parents="4872 15794"/>
    </justification>
  </clause>

  <clause id="15842">
    <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(15807(a,1),15100(a,1,2,2))].">
      <j1 rule="para" parents="15807 15100"/>
    </justification>
  </clause>

  <clause id="15843">
    <literal><![CDATA[
      K(((x \ y) \ z) * K(x,y),u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[para(5361(a,1),15809(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5361 15809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15844">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) * x,u) = w
    ]]></literal>
    <justification jstring="[para(15809(a,1),13135(a,1))].">
      <j1 rule="para" parents="15809 13135"/>
    </justification>
  </clause>

  <clause id="15845">
    <literal><![CDATA[
      K(T(T(x,y),y) * z,u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(5088(a,1),15812(a,1,1))].">
      <j1 rule="para" parents="5088 15812"/>
    </justification>
  </clause>

  <clause id="15846">
    <literal><![CDATA[
      K(((x * y) / x) * z,u) = K(T(y,x) * z,u)
    ]]></literal>
    <justification jstring="[para(224(a,1),15845(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="224 15845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15847">
    <literal><![CDATA[
      K(x,T(y,z) * (u * z)) = K(x,y * (u * T(z,y)))
    ]]></literal>
    <justification jstring="[para(6086(a,1),15828(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6086 15828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15848">
    <literal><![CDATA[
      K(x * (y \ z),(1 / (z \ y)) * x) = K(x * (y \ z),x * (1 / (z \ y)))
    ]]></literal>
    <justification jstring="[para(6142(a,1),15829(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6142 15829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15849">
    <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(7634(a,2),15835(a,2,2,1))].">
      <j1 rule="para" parents="7634 15835"/>
    </justification>
  </clause>

  <clause id="15850">
    <literal><![CDATA[
      K(x * (K(y,x) * z),u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5366(a,1),15846(a,1,1))].">
      <j1 rule="para" parents="5366 15846"/>
    </justification>
  </clause>

  <clause id="15851">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15295,a,b,15850,a)].">
      <j1 rule="hyper" parents="58 15295 15850"/>
    </justification>
  </clause>

  <clause id="15852">
    <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,15204,a(flip),b,15851,a)].">
      <j1 rule="hyper" parents="58 15204 15851"/>
    </justification>
  </clause>

  <clause id="15853">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15741(a,1),15602(a,1))].">
      <j1 rule="para" parents="15741 15602"/>
    </justification>
  </clause>

  <clause id="15854">
    <literal><![CDATA[
      K(x,y * K(z,u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15739(a,2),15602(a,1))].">
      <j1 rule="para" parents="15739 15602"/>
    </justification>
  </clause>

  <clause id="15855">
    <literal><![CDATA[
      K(x,y * K(z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15745(a,2),15602(a,1))].">
      <j1 rule="para" parents="15745 15602"/>
    </justification>
  </clause>

  <clause id="15856">
    <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(13091(a,1),15620(a,1))].">
      <j1 rule="para" parents="13091 15620"/>
    </justification>
  </clause>

  <clause id="15857">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(15035(a,1),15620(a,1))].">
      <j1 rule="para" parents="15035 15620"/>
    </justification>
  </clause>

  <clause id="15858">
    <literal><![CDATA[
      T(x,K(y * K(z,u),w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5 * K(K(u,z) * y,w)) = v6
    ]]></literal>
    <justification jstring="[para(15780(a,1),15620(a,1,2,1))].">
      <j1 rule="para" parents="15780 15620"/>
    </justification>
  </clause>

  <clause id="15859">
    <literal><![CDATA[
      K(T(1 / (x \ y),K(z,u)),w) = K(1 / L(x \ y,v5,y / x),w)
    ]]></literal>
    <justification jstring="[para(9034(a,2),15639(a,2,1,2))].">
      <j1 rule="para" parents="9034 15639"/>
    </justification>
  </clause>

  <clause id="15860">
    <literal><![CDATA[
      x * K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,u)) * x = w
    ]]></literal>
    <justification jstring="[para(7754(a,1),15651(a,1,2))].">
      <j1 rule="para" parents="7754 15651"/>
    </justification>
  </clause>

  <clause id="15861">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(15741(a,2),15712(a,1))].">
      <j1 rule="para" parents="15741 15712"/>
    </justification>
  </clause>

  <clause id="15862">
    <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(11166(a,1),15717(a,1,2,2))].">
      <j1 rule="para" parents="11166 15717"/>
    </justification>
  </clause>

  <clause id="15863">
    <literal><![CDATA[
      K(x,T(y,z / (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(13750(a,2),15717(a,1,2))].">
      <j1 rule="para" parents="13750 15717"/>
    </justification>
  </clause>

  <clause id="15864">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(15492(a,2),15717(a,1))].">
      <j1 rule="para" parents="15492 15717"/>
    </justification>
  </clause>

  <clause id="15865">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(15737(a,2),15717(a,1))].">
      <j1 rule="para" parents="15737 15717"/>
    </justification>
  </clause>

  <clause id="15869">
    <literal><![CDATA[
      K(x,y * K(z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(13023(a,2),15853(a,1))].">
      <j1 rule="para" parents="13023 15853"/>
    </justification>
  </clause>

  <clause id="15870">
    <literal><![CDATA[
      K((x * K(y,z)) \ 1,u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(6474,a,15622,a),flip(a)].">
      <j1 rule="hyper" parents="6474 15622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15871">
    <literal><![CDATA[
      K((K(x,T(y,z * u)) * z) \ 1,T(w,u)) = K(T(z,u) \ K(y,x),w)
    ]]></literal>
    <justification jstring="[hyper(14789,a,15870,a)].">
      <j1 rule="hyper" parents="14789 15870"/>
    </justification>
  </clause>

  <clause id="15872">
    <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(14766,a,15631,a)].">
      <j1 rule="hyper" parents="14766 15631"/>
    </justification>
  </clause>

  <clause id="15873">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,w) = K(x,K(y,z)) * T(u,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,15604,a,b,15666,a),flip(a)].">
      <j1 rule="hyper" parents="320 15604 15666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15874">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),w) = T(x,w) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(15604(a,1),15666(a,1,1))].">
      <j1 rule="para" parents="15604 15666"/>
    </justification>
  </clause>

  <clause id="15875">
    <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(7603(a,1),15693(a,2,2))].">
      <j1 rule="para" parents="7603 15693"/>
    </justification>
  </clause>

  <clause id="15876">
    <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,12251,a(flip),b,15695,a)].">
      <j1 rule="hyper" parents="58 12251 15695"/>
    </justification>
  </clause>

  <clause id="15877">
    <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(15696(a,1),236(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15696 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15878">
    <literal><![CDATA[
      K(x,T(y,z)) * (u * K(y,T(x,z))) = T(u,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,15697,a(flip),b,7197,a)].">
      <j1 rule="hyper" parents="119 15697 7197"/>
    </justification>
  </clause>

  <clause id="15879">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,y)) = u * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7151,a,b,15704,a),flip(a)].">
      <j1 rule="hyper" parents="320 7151 15704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15880">
    <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(440,a,15763,a,b,13841,a)].">
      <j1 rule="hyper" parents="440 15763 13841"/>
    </justification>
  </clause>

  <clause id="15881">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) * K(y,K(x,z)) = z \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,13653,a(flip),b,15789,a),flip(a)].">
      <j1 rule="hyper" parents="320 13653 15789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15882">
    <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),15796(a,2,2,2))].">
      <j1 rule="para" parents="107 15796"/>
    </justification>
  </clause>

  <clause id="15883">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,z) = z \ (u * T(z,K(x,y)))
    ]]></literal>
    <justification jstring="[para(7759(a,2),15796(a,1,1))].">
      <j1 rule="para" parents="7759 15796"/>
    </justification>
  </clause>

  <clause id="15884">
    <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(15801(a,1),7533(a,2,2,1))].">
      <j1 rule="para" parents="15801 7533"/>
    </justification>
  </clause>

  <clause id="15885">
    <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(15819(a,2),14686(a,2,2,2))].">
      <j1 rule="para" parents="15819 14686"/>
    </justification>
  </clause>

  <clause id="15886">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),w) / y = y \ T(T(y,K(z,u)) * x,w)
    ]]></literal>
    <justification jstring="[hyper(4563,a,15823,a),flip(a)].">
      <j1 rule="hyper" parents="4563 15823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15887">
    <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(7834(a,1),15824(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7834 15824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15888">
    <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(15847(a,2),7377(a,1))].">
      <j1 rule="para" parents="15847 7377"/>
    </justification>
  </clause>

  <clause id="15890">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),w) = K(y,K(z,u)) * T(x,w)
    ]]></literal>
    <justification jstring="[para(15604(a,1),15873(a,1,1))].">
      <j1 rule="para" parents="15604 15873"/>
    </justification>
  </clause>

  <clause id="15891">
    <literal><![CDATA[
      T(K(x,K(y,z)) \ u,w) = K(x,K(y,z)) \ T(u,w)
    ]]></literal>
    <justification jstring="[hyper(4577,a,15874,a),flip(a)].">
      <j1 rule="hyper" parents="4577 15874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15892">
    <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(15874(a,2),7788(a,1,1))].">
      <j1 rule="para" parents="15874 7788"/>
    </justification>
  </clause>

  <clause id="15893">
    <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(15878(a,1),11175(a,1,2,2))].">
      <j1 rule="para" parents="15878 11175"/>
    </justification>
  </clause>

  <clause id="15894">
    <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(15879(a,2),38(a,1))].">
      <j1 rule="para" parents="15879 38"/>
    </justification>
  </clause>

  <clause id="15895">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(y,z)) = u * K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(7759(a,1),15879(a,1,1))].">
      <j1 rule="para" parents="7759 15879"/>
    </justification>
  </clause>

  <clause id="15896">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(z,y) = K(z,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(30,a,15688,a,b,15881,a)].">
      <j1 rule="hyper" parents="30 15688 15881"/>
    </justification>
  </clause>

  <clause id="15897">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = K(y,x) * (z \ y)
    ]]></literal>
    <justification jstring="[para(7836(a,2),15896(a,1,1))].">
      <j1 rule="para" parents="7836 15896"/>
    </justification>
  </clause>

  <clause id="15898">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(y,z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = w
    ]]></literal>
    <justification jstring="[para(15895(a,2),38(a,1))].">
      <j1 rule="para" parents="15895 38"/>
    </justification>
  </clause>

  <clause id="15899">
    <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(7866(a,1),15568(a,1,1))].">
      <j1 rule="para" parents="7866 15568"/>
    </justification>
  </clause>

  <clause id="15900">
    <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),15569(a,1,2))].">
      <j1 rule="para" parents="18 15569"/>
    </justification>
  </clause>

  <clause id="15901">
    <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(15659,a,14025,a)].">
      <j1 rule="hyper" parents="15659 14025"/>
    </justification>
  </clause>

  <clause id="15902">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(5092(a,2),15709(a,1,2))].">
      <j1 rule="para" parents="5092 15709"/>
    </justification>
  </clause>

  <clause id="15903">
    <literal><![CDATA[
      K(x,K(y,z) * (u / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15051(a,1),15709(a,1))].">
      <j1 rule="para" parents="15051 15709"/>
    </justification>
  </clause>

  <clause id="15904">
    <literal><![CDATA[
      K(x,(y / z) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15741(a,1),15709(a,1))].">
      <j1 rule="para" parents="15741 15709"/>
    </justification>
  </clause>

  <clause id="15905">
    <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(7318(a,1),15714(a,1,2,1))].">
      <j1 rule="para" parents="7318 15714"/>
    </justification>
  </clause>

  <clause id="15906">
    <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(9385(a,1),15714(a,1,2,1))].">
      <j1 rule="para" parents="9385 15714"/>
    </justification>
  </clause>

  <clause id="15907">
    <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(13944(a,1),15723(a,1,2,2))].">
      <j1 rule="para" parents="13944 15723"/>
    </justification>
  </clause>

  <clause id="15908">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(z,y)) = w
    ]]></literal>
    <justification jstring="[para(15035(a,1),15725(a,1))].">
      <j1 rule="para" parents="15035 15725"/>
    </justification>
  </clause>

  <clause id="15909">
    <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(13739(a,1),15854(a,1,2,2))].">
      <j1 rule="para" parents="13739 15854"/>
    </justification>
  </clause>

  <clause id="15910">
    <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(13270(a,2),15855(a,1))].">
      <j1 rule="para" parents="13270 15855"/>
    </justification>
  </clause>

  <clause id="15911">
    <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(14165(a,2),15869(a,1,2,2))].">
      <j1 rule="para" parents="14165 15869"/>
    </justification>
  </clause>

  <clause id="15912">
    <literal><![CDATA[
      K(x,y / ((z * u) / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(6368(a,2),15904(a,1,2))].">
      <j1 rule="para" parents="6368 15904"/>
    </justification>
  </clause>

  <clause id="15913">
    <literal><![CDATA[
      T(x,K(K(y,z),u) * w) = w \ (x * w)
    ]]></literal>
    <justification jstring="[para(15607(a,1),15621(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15607 15621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15914">
    <literal><![CDATA[
      T(x,K(K(y,z),u) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,17,a,b,15913,a),flip(a)].">
      <j1 rule="hyper" parents="320 17 15913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15916">
    <literal><![CDATA[
      T(x,y \ T(z,K(u,w))) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(15908,a,15914,a)].">
      <j1 rule="hyper" parents="15908 15914"/>
    </justification>
  </clause>

  <clause id="15917">
    <literal><![CDATA[
      T(x,y * K(z,K(u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(15857,a,15914,a)].">
      <j1 rule="hyper" parents="15857 15914"/>
    </justification>
  </clause>

  <clause id="15918">
    <literal><![CDATA[
      T(x,y / T(z,K(u,w))) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(15721,a,15914,a)].">
      <j1 rule="hyper" parents="15721 15914"/>
    </justification>
  </clause>

  <clause id="15919">
    <literal><![CDATA[
      T(x,K(y,K(z,u)) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(15251,a,15914,a)].">
      <j1 rule="hyper" parents="15251 15914"/>
    </justification>
  </clause>

  <clause id="15920">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) / w) = T(x,y / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15046,a(flip),b,15914,a)].">
      <j1 rule="hyper" parents="58 15046 15914"/>
    </justification>
  </clause>

  <clause id="15921">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) * w) = T(x,y * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15041,a(flip),b,15914,a)].">
      <j1 rule="hyper" parents="58 15041 15914"/>
    </justification>
  </clause>

  <clause id="15922">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) \ w) = T(x,y \ w)
    ]]></literal>
    <justification jstring="[para(5093(a,1),15914(a,1,2))].">
      <j1 rule="para" parents="5093 15914"/>
    </justification>
  </clause>

  <clause id="15923">
    <literal><![CDATA[
      T(x,y * (K(z,u) * w)) = T(x,y * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(10350(a,1),15914(a,1,2))].">
      <j1 rule="para" parents="10350 15914"/>
    </justification>
  </clause>

  <clause id="15924">
    <literal><![CDATA[
      T(x,(K(y,z) * u) * w) = T(x,(u * K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(11122(a,1),15914(a,1,2))].">
      <j1 rule="para" parents="11122 15914"/>
    </justification>
  </clause>

  <clause id="15925">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) = x \ T(x,w)
    ]]></literal>
    <justification jstring="[para(15914(a,1),15039(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15914 15039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15926">
    <literal><![CDATA[
      T(x,y * T(z,K(u,w))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(1423(a,1),15917(a,1,2))].">
      <j1 rule="para" parents="1423 15917"/>
    </justification>
  </clause>

  <clause id="15927">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) = w / T(w,x)
    ]]></literal>
    <justification jstring="[para(15917(a,1),4753(a,2,2))].">
      <j1 rule="para" parents="15917 4753"/>
    </justification>
  </clause>

  <clause id="15928">
    <literal><![CDATA[
      T(x,y * (z * T(u,K(w,v5)))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(5960(a,1),15917(a,1,2))].">
      <j1 rule="para" parents="5960 15917"/>
    </justification>
  </clause>

  <clause id="15929">
    <literal><![CDATA[
      T(x,y / (K(z,u) * w)) = T(x,y / (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(10613(a,1),15917(a,1,2))].">
      <j1 rule="para" parents="10613 15917"/>
    </justification>
  </clause>

  <clause id="15930">
    <literal><![CDATA[
      T(x,y * (z * K(u,K(w,v5)))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(10850(a,1),15917(a,1,2))].">
      <j1 rule="para" parents="10850 15917"/>
    </justification>
  </clause>

  <clause id="15931">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) = T(x,K(y,z) * w)
    ]]></literal>
    <justification jstring="[para(15764(a,1),15917(a,1,2))].">
      <j1 rule="para" parents="15764 15917"/>
    </justification>
  </clause>

  <clause id="15932">
    <literal><![CDATA[
      K(K(x,K(y,z)) * u,w) = w / T(w,u)
    ]]></literal>
    <justification jstring="[para(15919(a,1),4753(a,2,2))].">
      <j1 rule="para" parents="15919 4753"/>
    </justification>
  </clause>

  <clause id="15933">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w))) = T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(15879(a,1),15919(a,1,2))].">
      <j1 rule="para" parents="15879 15919"/>
    </justification>
  </clause>

  <clause id="15934">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w))) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(7413(a,1),15916(a,1,2,2))].">
      <j1 rule="para" parents="7413 15916"/>
    </justification>
  </clause>

  <clause id="15935">
    <literal><![CDATA[
      T(x,y / T(z,T(u,w))) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(7413(a,1),15918(a,1,2,2))].">
      <j1 rule="para" parents="7413 15918"/>
    </justification>
  </clause>

  <clause id="15936">
    <literal><![CDATA[
      T(x,y / T(T(z,T(u,w)),v5)) = T(x,y / T(T(z,u),v5))
    ]]></literal>
    <justification jstring="[para(7417(a,1),15918(a,1,2,2))].">
      <j1 rule="para" parents="7417 15918"/>
    </justification>
  </clause>

  <clause id="15937">
    <literal><![CDATA[
      T(x,T(y,T(z,u)) / w) = T(x,T(y,z) / w)
    ]]></literal>
    <justification jstring="[para(7413(a,1),15920(a,1,2,1))].">
      <j1 rule="para" parents="7413 15920"/>
    </justification>
  </clause>

  <clause id="15939">
    <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,13156,a(flip),b,15921,a),flip(a)].">
      <j1 rule="hyper" parents="58 13156 15921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15940">
    <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,14108,a(flip),b,15922,a),flip(a)].">
      <j1 rule="hyper" parents="58 14108 15922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15941">
    <literal><![CDATA[
      T(x,T(y,T(z,u)) \ w) = T(x,T(y,z) \ w)
    ]]></literal>
    <justification jstring="[para(7413(a,1),15922(a,1,2,1))].">
      <j1 rule="para" parents="7413 15922"/>
    </justification>
  </clause>

  <clause id="15942">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,4688,a,b,15925,a),flip(a)].">
      <j1 rule="hyper" parents="320 4688 15925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15943">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(15925(a,2),4797(a,1))].">
      <j1 rule="para" parents="15925 4797"/>
    </justification>
  </clause>

  <clause id="15944">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(15903,a,15942,a)].">
      <j1 rule="hyper" parents="15903 15942"/>
    </justification>
  </clause>

  <clause id="15945">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) \ w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(15861,a,15942,a)].">
      <j1 rule="hyper" parents="15861 15942"/>
    </justification>
  </clause>

  <clause id="15946">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(15718,a,15942,a)].">
      <j1 rule="hyper" parents="15718 15942"/>
    </justification>
  </clause>

  <clause id="15947">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(15714,a,15942,a)].">
      <j1 rule="hyper" parents="15714 15942"/>
    </justification>
  </clause>

  <clause id="15948">
    <literal><![CDATA[
      K(x,y * K(z,K(u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15602,a,15942,a)].">
      <j1 rule="hyper" parents="15602 15942"/>
    </justification>
  </clause>

  <clause id="15949">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ w) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15058,a(flip),b,15942,a)].">
      <j1 rule="hyper" parents="58 15058 15942"/>
    </justification>
  </clause>

  <clause id="15950">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) * w) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(4740(a,1),15942(a,1,2))].">
      <j1 rule="para" parents="4740 15942"/>
    </justification>
  </clause>

  <clause id="15951">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) / w) = K(x,y / w)
    ]]></literal>
    <justification jstring="[para(5702(a,1),15942(a,1,2))].">
      <j1 rule="para" parents="5702 15942"/>
    </justification>
  </clause>

  <clause id="15952">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,(u * K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(9598(a,1),15942(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9598 15942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15953">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,(u * K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(11122(a,1),15942(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11122 15942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15954">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,(u * K(y,z)) / w)
    ]]></literal>
    <justification jstring="[para(13964(a,1),15942(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13964 15942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15955">
    <literal><![CDATA[
      K(x,y \ K(z,T(u,w))) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[para(15768(a,1),15942(a,1,2))].">
      <j1 rule="para" parents="15768 15942"/>
    </justification>
  </clause>

  <clause id="15956">
    <literal><![CDATA[
      K(x,y * K(z,T(u,w))) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(15879(a,1),15942(a,1,2))].">
      <j1 rule="para" parents="15879 15942"/>
    </justification>
  </clause>

  <clause id="15957">
    <literal><![CDATA[
      K(x,y * (z * T(u,K(w,v5)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(5960(a,1),15948(a,1,2))].">
      <j1 rule="para" parents="5960 15948"/>
    </justification>
  </clause>

  <clause id="15958">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(8103(a,1),15948(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8103 15948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15959">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,y / (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(10613(a,1),15948(a,1,2))].">
      <j1 rule="para" parents="10613 15948"/>
    </justification>
  </clause>

  <clause id="15960">
    <literal><![CDATA[
      K(x,y * (z * K(u,K(w,v5)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(10850(a,1),15948(a,1,2))].">
      <j1 rule="para" parents="10850 15948"/>
    </justification>
  </clause>

  <clause id="15961">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,y \ (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(14080(a,1),15948(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14080 15948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15962">
    <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,13064,a(flip),b,15926,a),flip(a)].">
      <j1 rule="hyper" parents="58 13064 15926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15965">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,4753,a,b,15927,a),flip(a)].">
      <j1 rule="hyper" parents="320 4753 15927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15966">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(15927(a,2),4821(a,1))].">
      <j1 rule="para" parents="15927 4821"/>
    </justification>
  </clause>

  <clause id="15967">
    <literal><![CDATA[
      K(x \ T(y,K(z,u)),w) = K(x \ y,w)
    ]]></literal>
    <justification jstring="[para(1420(a,1),15965(a,1,1))].">
      <j1 rule="para" parents="1420 15965"/>
    </justification>
  </clause>

  <clause id="15968">
    <literal><![CDATA[
      K(x * (K(y,z) * u),w) = K(x * (u * K(y,z)),w)
    ]]></literal>
    <justification jstring="[para(8103(a,1),15965(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8103 15965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15969">
    <literal><![CDATA[
      K(x \ K(y,T(z,u)),w) = K(x \ K(y,z),w)
    ]]></literal>
    <justification jstring="[para(12301(a,1),15965(a,1,1))].">
      <j1 rule="para" parents="12301 15965"/>
    </justification>
  </clause>

  <clause id="15970">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K(x \ (u * K(y,z)),w)
    ]]></literal>
    <justification jstring="[para(14080(a,1),15965(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14080 15965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15971">
    <literal><![CDATA[
      K(K(x,K(y,z)) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,w) = v5
    ]]></literal>
    <justification jstring="[para(15932(a,2),4821(a,1))].">
      <j1 rule="para" parents="15932 4821"/>
    </justification>
  </clause>

  <clause id="15972">
    <literal><![CDATA[
      K(x,y \ T(z,y)) = K(x,z / T(y,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,13084,a,b,15944,a)].">
      <j1 rule="hyper" parents="320 13084 15944"/>
    </justification>
  </clause>

  <clause id="15973">
    <literal><![CDATA[
      K(x,y / T(z,u / w)) = K(x,y / T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(7923(a,1),15944(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7923 15944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15974">
    <literal><![CDATA[
      K(x,y \ T(z,u / w)) = K(x,y \ T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(7923(a,1),15946(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7923 15946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15976">
    <literal><![CDATA[
      K(x,y * T(z,T(u,w))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(7413(a,1),15947(a,1,2,2))].">
      <j1 rule="para" parents="7413 15947"/>
    </justification>
  </clause>

  <clause id="15977">
    <literal><![CDATA[
      K(x,y * T(z,u / w)) = K(x,y * T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(7923(a,1),15947(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7923 15947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15978">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ z))) = K(x,y * (w \ T(z,u)))
    ]]></literal>
    <justification jstring="[para(13668(a,1),15947(a,1,2,2))].">
      <j1 rule="para" parents="13668 15947"/>
    </justification>
  </clause>

  <clause id="15979">
    <literal><![CDATA[
      K(x,y * ((z / u) * K(z,w))) = K(x,y * (T(z,w) / u))
    ]]></literal>
    <justification jstring="[para(13680(a,1),15947(a,1,2,2))].">
      <j1 rule="para" parents="13680 15947"/>
    </justification>
  </clause>

  <clause id="15980">
    <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(15949(a,1),15196(a,1))].">
      <j1 rule="para" parents="15949 15196"/>
    </justification>
  </clause>

  <clause id="15981">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * w) = K(x,T(y,z) * w)
    ]]></literal>
    <justification jstring="[para(7413(a,1),15950(a,1,2,1))].">
      <j1 rule="para" parents="7413 15950"/>
    </justification>
  </clause>

  <clause id="15982">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) / w) = K(x,T(y,z) / w)
    ]]></literal>
    <justification jstring="[para(7413(a,1),15951(a,1,2,1))].">
      <j1 rule="para" parents="7413 15951"/>
    </justification>
  </clause>

  <clause id="15983">
    <literal><![CDATA[
      K(x,T(y,z / u) / w) = K(x,T(y,u \ z) / w)
    ]]></literal>
    <justification jstring="[para(7923(a,1),15951(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7923 15951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15984">
    <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,15403,a(flip),b,15967,a),flip(a)].">
      <j1 rule="hyper" parents="58 15403 15967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15985">
    <literal><![CDATA[
      K(x \ T(y,T(z,u)),w) = K(x \ T(y,z),w)
    ]]></literal>
    <justification jstring="[para(7413(a,1),15967(a,1,1,2))].">
      <j1 rule="para" parents="7413 15967"/>
    </justification>
  </clause>

  <clause id="15986">
    <literal><![CDATA[
      K(x \ T(y,z * u),w) = K(x \ T(y,u * z),w)
    ]]></literal>
    <justification jstring="[para(12244(a,1),15967(a,1,1,2))].">
      <j1 rule="para" parents="12244 15967"/>
    </justification>
  </clause>

  <clause id="15987">
    <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(15967(a,1),13861(a,1,1,1,2))].">
      <j1 rule="para" parents="15967 13861"/>
    </justification>
  </clause>

  <clause id="15988">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * w) = v5
    ]]></literal>
    <justification jstring="[para(4740(a,1),15943(a,1,2))].">
      <j1 rule="para" parents="4740 15943"/>
    </justification>
  </clause>

  <clause id="15989">
    <literal><![CDATA[
      K(x,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,K(w,v5)) \ z) = u
    ]]></literal>
    <justification jstring="[para(5042(a,1),15943(a,1,2))].">
      <j1 rule="para" parents="5042 15943"/>
    </justification>
  </clause>

  <clause id="15990">
    <literal><![CDATA[
      K(x,K(K(y,z),u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(5584(a,2),15943(a,1,2,1))].">
      <j1 rule="para" parents="5584 15943"/>
    </justification>
  </clause>

  <clause id="15991">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v5
    ]]></literal>
    <justification jstring="[para(5516(a,1),15943(a,1,2))].">
      <j1 rule="para" parents="5516 15943"/>
    </justification>
  </clause>

  <clause id="15992">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = v5
    ]]></literal>
    <justification jstring="[para(5514(a,1),15943(a,1,2))].">
      <j1 rule="para" parents="5514 15943"/>
    </justification>
  </clause>

  <clause id="15993">
    <literal><![CDATA[
      K(x,y * K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(7261(a,1),15943(a,1,2))].">
      <j1 rule="para" parents="7261 15943"/>
    </justification>
  </clause>

  <clause id="15994">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ w) = v5
    ]]></literal>
    <justification jstring="[para(7747(a,1),15943(a,1,2))].">
      <j1 rule="para" parents="7747 15943"/>
    </justification>
  </clause>

  <clause id="15995">
    <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(13964(a,1),15943(a,1,2))].">
      <j1 rule="para" parents="13964 15943"/>
    </justification>
  </clause>

  <clause id="15996">
    <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(14757(a,1),15943(a,1,2))].">
      <j1 rule="para" parents="14757 15943"/>
    </justification>
  </clause>

  <clause id="15997">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = v5
    ]]></literal>
    <justification jstring="[para(15742(a,1),15943(a,1))].">
      <j1 rule="para" parents="15742 15943"/>
    </justification>
  </clause>

  <clause id="15998">
    <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(15768(a,1),15943(a,1,2))].">
      <j1 rule="para" parents="15768 15943"/>
    </justification>
  </clause>

  <clause id="15999">
    <literal><![CDATA[
      K(x \ T(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,w) = v5
    ]]></literal>
    <justification jstring="[para(1420(a,1),15966(a,1,1))].">
      <j1 rule="para" parents="1420 15966"/>
    </justification>
  </clause>

  <clause id="16000">
    <literal><![CDATA[
      K(T(x,K(y,z)) / u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x / u,w) = v5
    ]]></literal>
    <justification jstring="[para(1429(a,1),15966(a,1,1))].">
      <j1 rule="para" parents="1429 15966"/>
    </justification>
  </clause>

  <clause id="16001">
    <literal><![CDATA[
      K(x \ K(y,T(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ K(y,z),w) = v5
    ]]></literal>
    <justification jstring="[para(12301(a,1),15966(a,1,1))].">
      <j1 rule="para" parents="12301 15966"/>
    </justification>
  </clause>

  <clause id="16002">
    <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(11121(a,1),15971(a,1,1))].">
      <j1 rule="para" parents="11121 15971"/>
    </justification>
  </clause>

  <clause id="16003">
    <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(15810(a,1),15971(a,1))].">
      <j1 rule="para" parents="15810 15971"/>
    </justification>
  </clause>

  <clause id="16004">
    <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(10350(a,1),15990(a,1,2))].">
      <j1 rule="para" parents="10350 15990"/>
    </justification>
  </clause>

  <clause id="16005">
    <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(11122(a,1),15990(a,1,2))].">
      <j1 rule="para" parents="11122 15990"/>
    </justification>
  </clause>

  <clause id="16006">
    <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(5960(a,1),15993(a,1,2))].">
      <j1 rule="para" parents="5960 15993"/>
    </justification>
  </clause>

  <clause id="16007">
    <literal><![CDATA[
      K(x,y * (z * K(u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v6
    ]]></literal>
    <justification jstring="[para(10850(a,1),15993(a,1,2))].">
      <j1 rule="para" parents="10850 15993"/>
    </justification>
  </clause>

  <clause id="16008">
    <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(14080(a,1),15993(a,1,2))].">
      <j1 rule="para" parents="14080 15993"/>
    </justification>
  </clause>

  <clause id="16009">
    <literal><![CDATA[
      T(x,y * K(z / u,w)) = T(x,y * K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(8363(a,1),15930(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8363 15930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16010">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) = T(x,K(z,y) * w)
    ]]></literal>
    <justification jstring="[hyper(320,a,15035,a,b,15931,a),flip(a)].">
      <j1 rule="hyper" parents="320 15035 15931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16011">
    <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(15931(a,1),15908(a,1))].">
      <j1 rule="para" parents="15931 15908"/>
    </justification>
  </clause>

  <clause id="16012">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w))) = T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,15773,a,b,15933,a),flip(a)].">
      <j1 rule="hyper" parents="320 15773 15933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16013">
    <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(15933(a,2),15777(a,1))].">
      <j1 rule="para" parents="15933 15777"/>
    </justification>
  </clause>

  <clause id="16014">
    <literal><![CDATA[
      T(x,T(y * K(y * z,u),z)) = T(x,z \ T(y * z,u))
    ]]></literal>
    <justification jstring="[para(14029(a,2),15934(a,1,2))].">
      <j1 rule="para" parents="14029 15934"/>
    </justification>
  </clause>

  <clause id="16015">
    <literal><![CDATA[
      T(x,y / T(z,T(u,w))) = T(x,y / T(z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,12993,a,b,15935,a),flip(a)].">
      <j1 rule="hyper" parents="320 12993 15935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16016">
    <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(15935(a,1),12699(a,1))].">
      <j1 rule="para" parents="15935 12699"/>
    </justification>
  </clause>

  <clause id="16017">
    <literal><![CDATA[
      T(x,T(T(y,z) \ u,y) / w) = T(x,(u / T(y,z)) / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15066,a(flip),b,15937,a),flip(a)].">
      <j1 rule="hyper" parents="58 15066 15937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16018">
    <literal><![CDATA[
      K(x,y \ K(z / u,w)) = K(x,y \ K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(7144(a,1),15955(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7144 15955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16019">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * w) = K(x,w * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(15638,a,15956,a)].">
      <j1 rule="hyper" parents="15638 15956"/>
    </justification>
  </clause>

  <clause id="16020">
    <literal><![CDATA[
      K(x,y * K(z,u / w)) = K(x,y * K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(107(a,1),15956(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="107 15956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16021">
    <literal><![CDATA[
      K(x,y * K(z,u * w)) = K(x,y * K(z,w * u))
    ]]></literal>
    <justification jstring="[para(12222(a,1),15956(a,1,2,2))].">
      <j1 rule="para" parents="12222 15956"/>
    </justification>
  </clause>

  <clause id="16022">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,w)) = K(x,T(u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[para(14788(a,1),15956(a,1,2))].">
      <j1 rule="para" parents="14788 15956"/>
    </justification>
  </clause>

  <clause id="16023">
    <literal><![CDATA[
      K(x,y * (z / T(u,K(w,v5)))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15346,a(flip),b,15960,a)].">
      <j1 rule="hyper" parents="58 15346 15960"/>
    </justification>
  </clause>

  <clause id="16024">
    <literal><![CDATA[
      K(x,y * (z \ T(u,K(w,v5)))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(1420(a,1),15960(a,1,2,2))].">
      <j1 rule="para" parents="1420 15960"/>
    </justification>
  </clause>

  <clause id="16025">
    <literal><![CDATA[
      K(x,y * (T(z,K(u,w)) / v5)) = K(x,y * (z / v5))
    ]]></literal>
    <justification jstring="[para(1429(a,1),15960(a,1,2,2))].">
      <j1 rule="para" parents="1429 15960"/>
    </justification>
  </clause>

  <clause id="16026">
    <literal><![CDATA[
      K(x,y * (T(z,K(u,w)) * v5)) = K(x,y * (z * v5))
    ]]></literal>
    <justification jstring="[para(5500(a,1),15960(a,1,2,2))].">
      <j1 rule="para" parents="5500 15960"/>
    </justification>
  </clause>

  <clause id="16028">
    <literal><![CDATA[
      K(x,y * (K(z,T(u,w)) * v5)) = K(x,y * (K(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(15764(a,1),15960(a,1,2,2))].">
      <j1 rule="para" parents="15764 15960"/>
    </justification>
  </clause>

  <clause id="16029">
    <literal><![CDATA[
      K(x \ K(y,z * u),w) = K(x \ K(y,u * z),w)
    ]]></literal>
    <justification jstring="[para(12222(a,1),15969(a,1,1,2))].">
      <j1 rule="para" parents="12222 15969"/>
    </justification>
  </clause>

  <clause id="16030">
    <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,13448,a(flip),b,15976,a),flip(a)].">
      <j1 rule="hyper" parents="58 13448 15976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16031">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,12248,a(flip),b,15981,a),flip(a)].">
      <j1 rule="hyper" parents="320 12248 15981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16032">
    <literal><![CDATA[
      K(x,T(T(y,z) / u,y) * w) = K(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,13010,a(flip),b,15981,a),flip(a)].">
      <j1 rule="hyper" parents="58 13010 15981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16033">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * z)) = K(x,(u * z) * y)
    ]]></literal>
    <justification jstring="[para(12214(a,1),16031(a,1,2,1))].">
      <j1 rule="para" parents="12214 16031"/>
    </justification>
  </clause>

  <clause id="16034">
    <literal><![CDATA[
      K(x,T(T(y,z) / u,y) / w) = K(x,(u \ T(y,z)) / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,13012,a(flip),b,15982,a),flip(a)].">
      <j1 rule="hyper" parents="58 13012 15982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16035">
    <literal><![CDATA[
      K(T(x * K(x * y,z),y),u) = K(y \ T(x * y,z),u)
    ]]></literal>
    <justification jstring="[para(14029(a,2),15985(a,1,1))].">
      <j1 rule="para" parents="14029 15985"/>
    </justification>
  </clause>

  <clause id="16036">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z) * w) = v5
    ]]></literal>
    <justification jstring="[para(16010(a,2),15251(a,1))].">
      <j1 rule="para" parents="16010 15251"/>
    </justification>
  </clause>

  <clause id="16037">
    <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,15479,a,b,16012,a)].">
      <j1 rule="hyper" parents="58 15479 16012"/>
    </justification>
  </clause>

  <clause id="16038">
    <literal><![CDATA[
      K(x,K(y * z,u) * w) = K(x,w * K(z * y,u))
    ]]></literal>
    <justification jstring="[para(12190(a,1),16019(a,1,2,1))].">
      <j1 rule="para" parents="12190 16019"/>
    </justification>
  </clause>

  <clause id="16039">
    <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(16019(a,2),15747(a,1))].">
      <j1 rule="para" parents="16019 15747"/>
    </justification>
  </clause>

  <clause id="16040">
    <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(7923(a,1),15988(a,1,2,1))].">
      <j1 rule="para" parents="7923 15988"/>
    </justification>
  </clause>

  <clause id="16041">
    <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(8289(a,1),15991(a,1,2,2))].">
      <j1 rule="para" parents="8289 15991"/>
    </justification>
  </clause>

  <clause id="16042">
    <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(8064(a,1),15991(a,1,2,2))].">
      <j1 rule="para" parents="8064 15991"/>
    </justification>
  </clause>

  <clause id="16043">
    <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(13668(a,1),15991(a,1,2,2))].">
      <j1 rule="para" parents="13668 15991"/>
    </justification>
  </clause>

  <clause id="16044">
    <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(13680(a,1),15991(a,1,2,2))].">
      <j1 rule="para" parents="13680 15991"/>
    </justification>
  </clause>

  <clause id="16045">
    <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(15169(a,1),15991(a,1))].">
      <j1 rule="para" parents="15169 15991"/>
    </justification>
  </clause>

  <clause id="16046">
    <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(8289(a,1),15992(a,1,2,2))].">
      <j1 rule="para" parents="8289 15992"/>
    </justification>
  </clause>

  <clause id="16047">
    <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(12244(a,1),15992(a,1,2,2))].">
      <j1 rule="para" parents="12244 15992"/>
    </justification>
  </clause>

  <clause id="16048">
    <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),15997(a,1,2,2))].">
      <j1 rule="para" parents="20 15997"/>
    </justification>
  </clause>

  <clause id="16049">
    <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(13668(a,1),15997(a,1,2,2))].">
      <j1 rule="para" parents="13668 15997"/>
    </justification>
  </clause>

  <clause id="16050">
    <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(6308(a,1),15999(a,1,1,2))].">
      <j1 rule="para" parents="6308 15999"/>
    </justification>
  </clause>

  <clause id="16051">
    <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(7413(a,1),15999(a,1,1,2))].">
      <j1 rule="para" parents="7413 15999"/>
    </justification>
  </clause>

  <clause id="16052">
    <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(8289(a,1),16000(a,1,1,1))].">
      <j1 rule="para" parents="8289 16000"/>
    </justification>
  </clause>

  <clause id="16053">
    <literal><![CDATA[
      T(x,y * (z * T(u,w / v5))) = T(x,y * (z * T(u,v5 \ w)))
    ]]></literal>
    <justification jstring="[para(7923(a,1),15928(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7923 15928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16054">
    <literal><![CDATA[
      T(x,y / (z * K(u,w))) = T(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13794,a(flip),b,15929,a),flip(a)].">
      <j1 rule="hyper" parents="58 13794 15929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16056">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15952(a,1),6455(a,1))].">
      <j1 rule="para" parents="15952 6455"/>
    </justification>
  </clause>

  <clause id="16057">
    <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(14704(a,1),15954(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14704 15954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16058">
    <literal><![CDATA[
      K(x,y * (z * (K(u,w) / v5))) = K(x,y * (z * (v5 \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(58,a,15223,a(flip),b,15957,a)].">
      <j1 rule="hyper" parents="58 15223 15957"/>
    </justification>
  </clause>

  <clause id="16059">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(320,a,15345,a,b,15958,a),flip(a)].">
      <j1 rule="hyper" parents="320 15345 15958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16060">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w / z))) = K(x,y * (w / T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,15346,a(flip),b,15958,a),flip(a)].">
      <j1 rule="hyper" parents="320 15346 15958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16061">
    <literal><![CDATA[
      K(x,y * (z * K(u,u \ w))) = K(x,y * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13041,a(flip),b,15958,a),flip(a)].">
      <j1 rule="hyper" parents="58 13041 15958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16062">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13784,a(flip),b,15959,a),flip(a)].">
      <j1 rule="hyper" parents="58 13784 15959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16063">
    <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(14704(a,1),15961(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14704 15961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16064">
    <literal><![CDATA[
      K(x * (((y * z) / y) \ u),w) = K(x * ((z \ u) * K(z,y)),w)
    ]]></literal>
    <justification jstring="[para(5049(a,2),15968(a,1,1,2))].">
      <j1 rule="para" parents="5049 15968"/>
    </justification>
  </clause>

  <clause id="16065">
    <literal><![CDATA[
      K(x,(y / z) / T(u,z \ y)) = K(x,u \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(13018,a,15973,a),flip(a)].">
      <j1 rule="hyper" parents="13018 15973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16066">
    <literal><![CDATA[
      K(x,(y / z) / T(u,z \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (y / z)) = w
    ]]></literal>
    <justification jstring="[para(15973(a,1),13018(a,1))].">
      <j1 rule="para" parents="15973 13018"/>
    </justification>
  </clause>

  <clause id="16068">
    <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,15090,a(flip),b,15983,a),flip(a)].">
      <j1 rule="hyper" parents="58 15090 15983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16069">
    <literal><![CDATA[
      K(x,T(y,z \ u) / (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u / z) \ y) = w
    ]]></literal>
    <justification jstring="[para(15983(a,1),13016(a,1))].">
      <j1 rule="para" parents="15983 13016"/>
    </justification>
  </clause>

  <clause id="16070">
    <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(15986(a,1),6685(a,1))].">
      <j1 rule="para" parents="15986 6685"/>
    </justification>
  </clause>

  <clause id="16071">
    <literal><![CDATA[
      T(x,((y / z) \ u) * K(z \ y,w)) = T(x,T(y / z,w) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15775,a(flip),b,16009,a),flip(a)].">
      <j1 rule="hyper" parents="58 15775 16009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16072">
    <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,15110,a(flip),b,16009,a),flip(a)].">
      <j1 rule="hyper" parents="58 15110 16009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16073">
    <literal><![CDATA[
      T(x,y \ K(z / u,w)) = T(x,y \ K(u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(118,a,16018,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 16018 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16074">
    <literal><![CDATA[
      K(x,(y * z) * K(u,z * y)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(7997,a,16021,a),flip(a)].">
      <j1 rule="hyper" parents="7997 16021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16075">
    <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(16021(a,1),15747(a,1))].">
      <j1 rule="para" parents="16021 15747"/>
    </justification>
  </clause>

  <clause id="16076">
    <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(16021(a,1),15853(a,1))].">
      <j1 rule="para" parents="16021 15853"/>
    </justification>
  </clause>

  <clause id="16077">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,w)) = K(x,K(y,z) * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,15573,a,b,16022,a),flip(a)].">
      <j1 rule="hyper" parents="320 15573 16022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16078">
    <literal><![CDATA[
      K(x,y * (z / T(u,u \ w))) = K(x,y * (z / ((u \ w) \ w)))
    ]]></literal>
    <justification jstring="[para(3319(a,1),16023(a,1,2,2,2))].">
      <j1 rule="para" parents="3319 16023"/>
    </justification>
  </clause>

  <clause id="16079">
    <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(14836(a,1),16024(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14836 16024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16080">
    <literal><![CDATA[
      K(x,y * (T(z,u / w) / v5)) = K(x,y * (T(z,w \ u) / v5))
    ]]></literal>
    <justification jstring="[para(7923(a,1),16025(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7923 16025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16081">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * v5)) = K(x,y * (T(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(7413(a,1),16026(a,1,2,2,1))].">
      <j1 rule="para" parents="7413 16026"/>
    </justification>
  </clause>

  <clause id="16082">
    <literal><![CDATA[
      K(x,y * (T(z,u / w) * v5)) = K(x,y * (T(z,w \ u) * v5))
    ]]></literal>
    <justification jstring="[para(7923(a,1),16026(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7923 16026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16083">
    <literal><![CDATA[
      K(x \ K(y,z * (u * y)),w) = K(x \ K(y,u * z),w)
    ]]></literal>
    <justification jstring="[hyper(320,a,13104,a(flip),b,16029,a),flip(a)].">
      <j1 rule="hyper" parents="320 13104 16029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16084">
    <literal><![CDATA[
      K(x,T(y,(z / y) * u) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[para(10368(a,2),16033(a,2,2))].">
      <j1 rule="para" parents="10368 16033"/>
    </justification>
  </clause>

  <clause id="16085">
    <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(16038(a,2),15747(a,1))].">
      <j1 rule="para" parents="16038 15747"/>
    </justification>
  </clause>

  <clause id="16086">
    <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,15123,a(flip),b,16054,a),flip(a)].">
      <j1 rule="hyper" parents="58 15123 16054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16087">
    <literal><![CDATA[
      T(x,y * (z \ K(y,u))) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[para(13671(a,1),16054(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13671 16054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16088">
    <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(15180(a,1),16087(a,1,2,2,2))].">
      <j1 rule="para" parents="15180 16087"/>
    </justification>
  </clause>

  <clause id="16089">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w * u))) = K(x,y * (w * T(u,z)))
    ]]></literal>
    <justification jstring="[para(6086(a,1),16059(a,2,2,2))].">
      <j1 rule="para" parents="6086 16059"/>
    </justification>
  </clause>

  <clause id="16090">
    <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,14032,a(flip),b,16062,a),flip(a)].">
      <j1 rule="hyper" parents="58 14032 16062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16091">
    <literal><![CDATA[
      K(x,y * ((z * u) \ K(w,u))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(6086(a,1),16062(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6086 16062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16092">
    <literal><![CDATA[
      K(x,y * ((z / u) \ K(u,w))) = K(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[para(6293(a,1),16062(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6293 16062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16093">
    <literal><![CDATA[
      K(x,y / (z * ((u * w) / u))) = K(x,y * ((z * w) \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(6067(a,1),16062(a,1,2,2))].">
      <j1 rule="para" parents="6067 16062"/>
    </justification>
  </clause>

  <clause id="16094">
    <literal><![CDATA[
      K(x,y * ((z \ (u \ w)) \ K(u,w))) = K(x,y / (z \ (u \ T(w,u))))
    ]]></literal>
    <justification jstring="[para(14944(a,1),16062(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14944 16062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16095">
    <literal><![CDATA[
      K(x,y * (z * K(u,z * y))) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(13624(a,1),16074(a,1,2))].">
      <j1 rule="para" parents="13624 16074"/>
    </justification>
  </clause>

  <clause id="16096">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,K(y,z) * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(118,a,16077,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 16077 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16097">
    <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(14146(a,1),16095(a,1,2,2))].">
      <j1 rule="para" parents="14146 16095"/>
    </justification>
  </clause>

  <clause id="16098">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,T(u,w) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,15773,a(flip),b,16096,a),flip(a)].">
      <j1 rule="hyper" parents="320 15773 16096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16099">
    <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(7865(a,1),15998(a,1,2,2))].">
      <j1 rule="para" parents="7865 15998"/>
    </justification>
  </clause>

  <clause id="16100">
    <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(1420(a,1),16007(a,1,2,2))].">
      <j1 rule="para" parents="1420 16007"/>
    </justification>
  </clause>

  <clause id="16101">
    <literal><![CDATA[
      K(x,y * (K(z,K(u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * v5) = v6
    ]]></literal>
    <justification jstring="[para(7123(a,1),16007(a,1,2,2))].">
      <j1 rule="para" parents="7123 16007"/>
    </justification>
  </clause>

  <clause id="16102">
    <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(7744(a,1),16007(a,1,2,2))].">
      <j1 rule="para" parents="7744 16007"/>
    </justification>
  </clause>

  <clause id="16103">
    <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(12301(a,1),16007(a,1,2,2))].">
      <j1 rule="para" parents="12301 16007"/>
    </justification>
  </clause>

  <clause id="16104">
    <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(15874(a,2),16007(a,1,2,2))].">
      <j1 rule="para" parents="15874 16007"/>
    </justification>
  </clause>

  <clause id="16105">
    <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(15144(a,1),16016(a,1,2,2))].">
      <j1 rule="para" parents="15144 16016"/>
    </justification>
  </clause>

  <clause id="16106">
    <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(12190(a,1),16036(a,1,2,1))].">
      <j1 rule="para" parents="12190 16036"/>
    </justification>
  </clause>

  <clause id="16107">
    <literal><![CDATA[
      K(x,((y * z) / y) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u / z) \ K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(6445(a,1),16056(a,1))].">
      <j1 rule="para" parents="6445 16056"/>
    </justification>
  </clause>

  <clause id="16108">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,1 / (z * y))
    ]]></literal>
    <justification jstring="[hyper(320,a,5306,a(flip),b,15750,a),flip(a)].">
      <j1 rule="hyper" parents="320 5306 15750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16110">
    <literal><![CDATA[
      K(x,y / (y * (y * z))) = K(x,1 / (z * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8113,a(flip),b,16108,a)].">
      <j1 rule="hyper" parents="58 8113 16108"/>
    </justification>
  </clause>

  <clause id="16111">
    <literal><![CDATA[
      K(x / (x / y),z * ((x / y) / x)) = K(y,T(((x / y) / x) * z,x))
    ]]></literal>
    <justification jstring="[hyper(12331,a,15758,a)].">
      <j1 rule="hyper" parents="12331 15758"/>
    </justification>
  </clause>

  <clause id="16112">
    <literal><![CDATA[
      T(x * T(y,x * K(z,u)),K(z,u)) = y * T(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(7826,a,15776,a)].">
      <j1 rule="hyper" parents="7826 15776"/>
    </justification>
  </clause>

  <clause id="16114">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / y)) = K(x,u / (z * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15062,a(flip),b,15786,a)].">
      <j1 rule="hyper" parents="58 15062 15786"/>
    </justification>
  </clause>

  <clause id="16115">
    <literal><![CDATA[
      K(x,y / (z * (u / z))) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(15902,a,16114,a),flip(a)].">
      <j1 rule="hyper" parents="15902 16114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16116">
    <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,14966,a(flip),b,16115,a),flip(a)].">
      <j1 rule="hyper" parents="58 14966 16115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16117">
    <literal><![CDATA[
      K(x,y / T(z * u,u)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(6(a,1),16115(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6 16115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16118">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) = K(x,y / (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(3871(a,2),16115(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3871 16115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16119">
    <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,12279,a,b,15788,a)].">
      <j1 rule="hyper" parents="58 12279 15788"/>
    </justification>
  </clause>

  <clause id="16120">
    <literal><![CDATA[
      K(x,y) \ K(L(x,z,u),y) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,14262,a(flip),b,15795,a),flip(a)].">
      <j1 rule="hyper" parents="58 14262 15795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16121">
    <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(320,a,15503,a,b,15820,a),flip(a)].">
      <j1 rule="hyper" parents="320 15503 15820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16122">
    <literal><![CDATA[
      T(L(K(x,y),z \ u,z),u / z) = u \ (z * (K(x,y) * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,791,a(flip),b,15822,a),flip(a)].">
      <j1 rule="hyper" parents="320 791 15822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16123">
    <literal><![CDATA[
      K(x * T(y * z,z),u) = K(x * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15810,a(flip),b,15826,a),flip(a)].">
      <j1 rule="hyper" parents="58 15810 15826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16124">
    <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,15385,a,b,15840,a)].">
      <j1 rule="hyper" parents="58 15385 15840"/>
    </justification>
  </clause>

  <clause id="16125">
    <literal><![CDATA[
      (x * K(y,z)) \ z = K(z,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,14127,a(flip),b,15897,a)].">
      <j1 rule="hyper" parents="58 14127 15897"/>
    </justification>
  </clause>

  <clause id="16126">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ z = K(z,T(y,u)) * (x \ z)
    ]]></literal>
    <justification jstring="[para(7133(a,1),16125(a,1,1,2))].">
      <j1 rule="para" parents="7133 16125"/>
    </justification>
  </clause>

  <clause id="16127">
    <literal><![CDATA[
      K(x,y) * ((z \ T(x,y)) \ x) = (z \ x) \ x
    ]]></literal>
    <justification jstring="[para(13655(a,1),16125(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13655 16125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16128">
    <literal><![CDATA[
      K(x,y) * ((z \ y) \ y) = (z \ T(y,x)) \ y
    ]]></literal>
    <justification jstring="[hyper(5109,a,16127,a)].">
      <j1 rule="hyper" parents="5109 16127"/>
    </justification>
  </clause>

  <clause id="16129">
    <literal><![CDATA[
      T(x * K(y,z),x \ z) = (x \ T(z,y)) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,14416,a,b,16128,a)].">
      <j1 rule="hyper" parents="58 14416 16128"/>
    </justification>
  </clause>

  <clause id="16130">
    <literal><![CDATA[
      (x * K(y,T(z \ u,z))) \ (z \ u) = K(u / z,y) * (x \ (z \ u))
    ]]></literal>
    <justification jstring="[para(7882(a,1),16126(a,2,1))].">
      <j1 rule="para" parents="7882 16126"/>
    </justification>
  </clause>

  <clause id="16131">
    <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,12703,a(flip),b,15936,a),flip(a)].">
      <j1 rule="hyper" parents="58 12703 15936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16132">
    <literal><![CDATA[
      K(x,y * (K(z / u,w) * v5)) = K(x,y * (K(u \ z,w) * v5))
    ]]></literal>
    <justification jstring="[para(7144(a,1),16028(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7144 16028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16133">
    <literal><![CDATA[
      K(x,T(y * ((y / z) / y),y) / u) = K(x,(z \ T(y,z \ 1)) / u)
    ]]></literal>
    <justification jstring="[para(3868(a,1),16034(a,1,2,1,1))].">
      <j1 rule="para" parents="3868 16034"/>
    </justification>
  </clause>

  <clause id="16134">
    <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(16035(a,1),7679(a,1))].">
      <j1 rule="para" parents="16035 7679"/>
    </justification>
  </clause>

  <clause id="16135">
    <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,15374,a,b,16061,a)].">
      <j1 rule="hyper" parents="58 15374 16061"/>
    </justification>
  </clause>

  <clause id="16136">
    <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,13758,a,b,16061,a)].">
      <j1 rule="hyper" parents="58 13758 16061"/>
    </justification>
  </clause>

  <clause id="16137">
    <literal><![CDATA[
      K(x,y * (z / (u / (u / w)))) = K(x,y * (K(w,u) * (z / w)))
    ]]></literal>
    <justification jstring="[para(6444(a,2),16061(a,1,2,2))].">
      <j1 rule="para" parents="6444 16061"/>
    </justification>
  </clause>

  <clause id="16138">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w * u))) = K(x,y * (w * (z * (u / z))))
    ]]></literal>
    <justification jstring="[para(10316(a,1),16061(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10316 16061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16139">
    <literal><![CDATA[
      K(x,y * (T(z,u) * (w * (u / w)))) = K(x,y * ((w * (u / w)) * z))
    ]]></literal>
    <justification jstring="[hyper(15209,a,16081,a),flip(a)].">
      <j1 rule="hyper" parents="15209 16081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16140">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(u,w))) = K(x,y * (T(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(15208,a,16081,a),flip(a)].">
      <j1 rule="hyper" parents="15208 16081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16141">
    <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(16081(a,1),15208(a,1))].">
      <j1 rule="para" parents="16081 15208"/>
    </justification>
  </clause>

  <clause id="16142">
    <literal><![CDATA[
      K(x,y * T((z / u) \ 1,z)) = K(x,y / (z / T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13163,a,b,16092,a)].">
      <j1 rule="hyper" parents="58 13163 16092"/>
    </justification>
  </clause>

  <clause id="16143">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(16118(a,1),15201(a,1))].">
      <j1 rule="para" parents="16118 15201"/>
    </justification>
  </clause>

  <clause id="16144">
    <literal><![CDATA[
      K(x,K((y \ z) / u,L(w,u,y))) = K(x,K(w,z / (y * u)))
    ]]></literal>
    <justification jstring="[hyper(15538,a,15539,a)].">
      <j1 rule="hyper" parents="15538 15539"/>
    </justification>
  </clause>

  <clause id="16145">
    <literal><![CDATA[
      K(x,K(y,L(z / u,u,w))) = K(x,K(y,(w * z) / (w * u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,15530,a,b,15678,a),flip(a)].">
      <j1 rule="hyper" parents="320 15530 15678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16146">
    <literal><![CDATA[
      K(x,y * (x \ (z \ x))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(15814,a,15585,a)].">
      <j1 rule="hyper" parents="15814 15585"/>
    </justification>
  </clause>

  <clause id="16147">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(12420,a,16146,a),flip(a)].">
      <j1 rule="hyper" parents="12420 16146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16148">
    <literal><![CDATA[
      K(x,y / (x \ z)) = K(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(8417,a,16147,a)].">
      <j1 rule="hyper" parents="8417 16147"/>
    </justification>
  </clause>

  <clause id="16149">
    <literal><![CDATA[
      T(x,y / (x \ z)) = T(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(118,a,16148,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 16148 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16150">
    <literal><![CDATA[
      x / (K(y,z * (u \ y)) * x) = K(z / (y \ u),y)
    ]]></literal>
    <justification jstring="[para(16148(a,1),5104(a,1,2,1))].">
      <j1 rule="para" parents="16148 5104"/>
    </justification>
  </clause>

  <clause id="16151">
    <literal><![CDATA[
      T(x,(x * y) / z) = T(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,8461,a,b,16149,a)].">
      <j1 rule="hyper" parents="58 8461 16149"/>
    </justification>
  </clause>

  <clause id="16152">
    <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(16151(a,1),15002(a,1,1,1,1))].">
      <j1 rule="para" parents="16151 15002"/>
    </justification>
  </clause>

  <clause id="16153">
    <literal><![CDATA[
      K(x / (y \ z),y) = K(x * (z \ y),y)
    ]]></literal>
    <justification jstring="[hyper(15711,a,16150,a),flip(a)].">
      <j1 rule="hyper" parents="15711 16150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16154">
    <literal><![CDATA[
      K(x * (y \ z),z) * ((z * x) / y) = T((z * x) / y,z)
    ]]></literal>
    <justification jstring="[para(16153(a,1),8518(a,1,1))].">
      <j1 rule="para" parents="16153 8518"/>
    </justification>
  </clause>

  <clause id="16155">
    <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(6308(a,1),15996(a,1,2,1,1))].">
      <j1 rule="para" parents="6308 15996"/>
    </justification>
  </clause>

  <clause id="16156">
    <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(15219(a,1),15996(a,1))].">
      <j1 rule="para" parents="15219 15996"/>
    </justification>
  </clause>

  <clause id="16158">
    <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(16059(a,1),16004(a,1))].">
      <j1 rule="para" parents="16059 16004"/>
    </justification>
  </clause>

  <clause id="16159">
    <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(7923(a,1),16006(a,1,2,2,2))].">
      <j1 rule="para" parents="7923 16006"/>
    </justification>
  </clause>

  <clause id="16160">
    <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(13871(a,2),16045(a,1))].">
      <j1 rule="para" parents="13871 16045"/>
    </justification>
  </clause>

  <clause id="16161">
    <literal><![CDATA[
      K(x,(y * z) \ T(u,z * (y * x))) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(16047,a,15315,a)].">
      <j1 rule="hyper" parents="16047 15315"/>
    </justification>
  </clause>

  <clause id="16162">
    <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(15941(a,1),16066(a,1,2,2))].">
      <j1 rule="para" parents="15941 16066"/>
    </justification>
  </clause>

  <clause id="16163">
    <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(6308(a,1),16100(a,1,2,2,2))].">
      <j1 rule="para" parents="6308 16100"/>
    </justification>
  </clause>

  <clause id="16164">
    <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(7413(a,1),16100(a,1,2,2,2))].">
      <j1 rule="para" parents="7413 16100"/>
    </justification>
  </clause>

  <clause id="16165">
    <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(13829(a,1),16100(a,1,2,2,2))].">
      <j1 rule="para" parents="13829 16100"/>
    </justification>
  </clause>

  <clause id="16166">
    <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(7413(a,1),16102(a,1,2,2,2))].">
      <j1 rule="para" parents="7413 16102"/>
    </justification>
  </clause>

  <clause id="16167">
    <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(13829(a,1),16102(a,1,2,2,2))].">
      <j1 rule="para" parents="13829 16102"/>
    </justification>
  </clause>

  <clause id="16168">
    <literal><![CDATA[
      K(x,(y / z) \ K(u,z)) = K(x,T(z,u) / y)
    ]]></literal>
    <justification jstring="[hyper(16107,a,15088,a)].">
      <j1 rule="hyper" parents="16107 15088"/>
    </justification>
  </clause>

  <clause id="16169">
    <literal><![CDATA[
      K(x,(y / z) \ K(z,u)) = K(x,T(z,u) / y)
    ]]></literal>
    <justification jstring="[hyper(15199,a,16168,a)].">
      <j1 rule="hyper" parents="15199 16168"/>
    </justification>
  </clause>

  <clause id="16170">
    <literal><![CDATA[
      K(x,(y / z) \ K(z,u \ w)) = K(x,T(z,w / u) / y)
    ]]></literal>
    <justification jstring="[hyper(16099,a,16169,a)].">
      <j1 rule="hyper" parents="16099 16169"/>
    </justification>
  </clause>

  <clause id="16171">
    <literal><![CDATA[
      K(x,T(y,y / z) / u) = K(x,(u / y) \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15427,a(flip),b,16170,a),flip(a)].">
      <j1 rule="hyper" parents="58 15427 16170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16172">
    <literal><![CDATA[
      K(x,T(y,y / z) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,16169,a(flip),b,16171,a),flip(a)].">
      <j1 rule="hyper" parents="320 16169 16171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16173">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,u)) = K(x,T(y,z) / (u * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(14801,a,16172,a)].">
      <j1 rule="hyper" parents="14801 16172"/>
    </justification>
  </clause>

  <clause id="16174">
    <literal><![CDATA[
      K(x,T(y,z \ y) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15983,a(flip),b,16172,a)].">
      <j1 rule="hyper" parents="58 15983 16172"/>
    </justification>
  </clause>

  <clause id="16175">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ y)) / w) = K(x,T(y,u * z) / w)
    ]]></literal>
    <justification jstring="[para(13926(a,1),16174(a,1,2,1))].">
      <j1 rule="para" parents="13926 16174"/>
    </justification>
  </clause>

  <clause id="16176">
    <literal><![CDATA[
      K(x,T(y,z \ (y / u)) / w) = K(x,T(y,u * z) / w)
    ]]></literal>
    <justification jstring="[para(10679(a,2),16175(a,1,2,1))].">
      <j1 rule="para" parents="10679 16175"/>
    </justification>
  </clause>

  <clause id="16177">
    <literal><![CDATA[
      K(x,T(y,z * u) / ((y / z) / u)) = K(x,((y / z) / u) \ y)
    ]]></literal>
    <justification jstring="[hyper(16069,a,16176,a),flip(a)].">
      <j1 rule="hyper" parents="16069 16176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16178">
    <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(16143,a,15016,a)].">
      <j1 rule="hyper" parents="16143 15016"/>
    </justification>
  </clause>

  <clause id="16179">
    <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),16144(a,1,2,1,1))].">
      <j1 rule="para" parents="17 16144"/>
    </justification>
  </clause>

  <clause id="16180">
    <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),16145(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6 16145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16181">
    <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(7986(a,2),16145(a,1,2))].">
      <j1 rule="para" parents="7986 16145"/>
    </justification>
  </clause>

  <clause id="16182">
    <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(15959(a,2),16160(a,1))].">
      <j1 rule="para" parents="15959 16160"/>
    </justification>
  </clause>

  <clause id="16183">
    <literal><![CDATA[
      K(x,K(y * z,y * (u * z))) = K(x,K(y * z,L(u,z,y)))
    ]]></literal>
    <justification jstring="[hyper(13054,a,16180,a)].">
      <j1 rule="hyper" parents="13054 16180"/>
    </justification>
  </clause>

  <clause id="16184">
    <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(16183(a,1),8364(a,1,1))].">
      <j1 rule="para" parents="16183 8364"/>
    </justification>
  </clause>

  <clause id="16185">
    <literal><![CDATA[
      T(x * T(x \ y,T(z,y)),x) = T(y,x) * K(y / T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,1536,a,b,15660,a)].">
      <j1 rule="hyper" parents="320 1536 15660"/>
    </justification>
  </clause>

  <clause id="16188">
    <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(5655(a,1),15676(a,2,2))].">
      <j1 rule="para" parents="5655 15676"/>
    </justification>
  </clause>

  <clause id="16189">
    <literal><![CDATA[
      K(x,T(L(K(y,z),u,w),v5)) = K(x,L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,10892,a(flip),b,16188,a),flip(a)].">
      <j1 rule="hyper" parents="320 10892 16188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16190">
    <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(16189(a,2),10817(a,1))].">
      <j1 rule="para" parents="16189 10817"/>
    </justification>
  </clause>

  <clause id="16191">
    <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(15700(a,1),14989(a,1,1))].">
      <j1 rule="para" parents="15700 14989"/>
    </justification>
  </clause>

  <clause id="16193">
    <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(15832(a,1),15139(a,1,2,2))].">
      <j1 rule="para" parents="15832 15139"/>
    </justification>
  </clause>

  <clause id="16194">
    <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(15886(a,1),15030(a,1,1,2,1))].">
      <j1 rule="para" parents="15886 15030"/>
    </justification>
  </clause>

  <clause id="16195">
    <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(15764(a,1),15892(a,1,1,1))].">
      <j1 rule="para" parents="15764 15892"/>
    </justification>
  </clause>

  <clause id="16196">
    <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,13687,a,b,16058,a)].">
      <j1 rule="hyper" parents="58 13687 16058"/>
    </justification>
  </clause>

  <clause id="16197">
    <literal><![CDATA[
      K(x * (((y * z) / y) \ u),w) = K(x * (K(z,y) * (z \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(320,a,15968,a,b,16064,a),flip(a)].">
      <j1 rule="hyper" parents="320 15968 16064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16198">
    <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(16082(a,1),15208(a,1))].">
      <j1 rule="para" parents="16082 15208"/>
    </justification>
  </clause>

  <clause id="16199">
    <literal><![CDATA[
      K(x,y * (z / (u / (u / w)))) = K(x,y * (z / T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,16060,a(flip),b,16137,a),flip(a)].">
      <j1 rule="hyper" parents="320 16060 16137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16200">
    <literal><![CDATA[
      K(x,y * (z / T(u,u \ w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15349,a,b,16199,a)].">
      <j1 rule="hyper" parents="58 15349 16199"/>
    </justification>
  </clause>

  <clause id="16201">
    <literal><![CDATA[
      K(x,y * (z / ((u \ w) \ w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16078,a(flip),b,16200,a)].">
      <j1 rule="hyper" parents="58 16078 16200"/>
    </justification>
  </clause>

  <clause id="16202">
    <literal><![CDATA[
      T(x,y * (z / ((u \ w) \ w))) = T(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(118,a,16201,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 16201 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16203">
    <literal><![CDATA[
      K(x,y * (z * (u * (w / u)))) = K(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16089,a(flip),b,16138,a),flip(a)].">
      <j1 rule="hyper" parents="58 16089 16138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16204">
    <literal><![CDATA[
      K(x,y * (z * T(u * w,w))) = K(x,y * (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(6(a,1),16203(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6 16203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16205">
    <literal><![CDATA[
      K(x,y * ((z * u) * u)) = K(x,y * (u * (u * z)))
    ]]></literal>
    <justification jstring="[para(105(a,1),16204(a,1,2,2))].">
      <j1 rule="para" parents="105 16204"/>
    </justification>
  </clause>

  <clause id="16206">
    <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(7500(a,2),16205(a,2,2,2,2))].">
      <j1 rule="para" parents="7500 16205"/>
    </justification>
  </clause>

  <clause id="16207">
    <literal><![CDATA[
      T(x,y) * K(x / T(y,x),z) = T(x * K(x / y,z),y)
    ]]></literal>
    <justification jstring="[para(7949(a,1),16185(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7949 16185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16208">
    <literal><![CDATA[
      T(x * K(x / y,z),y) = T(x,y) * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(12679(a,1),16207(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12679 16207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16209">
    <literal><![CDATA[
      T(x * K(x / y,z),y) = K(x / y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,15735,a(flip),b,16208,a),flip(a)].">
      <j1 rule="hyper" parents="320 15735 16208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16210">
    <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(5092(a,1),15645(a,1,2,1))].">
      <j1 rule="para" parents="5092 15645"/>
    </justification>
  </clause>

  <clause id="16211">
    <literal><![CDATA[
      K(x,y * (z * K(u \ 1,w))) = K(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15746,a(flip),b,15837,a),flip(a)].">
      <j1 rule="hyper" parents="58 15746 15837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16212">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * (u * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,7706,a,b,16211,a)].">
      <j1 rule="hyper" parents="58 7706 16211"/>
    </justification>
  </clause>

  <clause id="16213">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(4714(a,2),16212(a,2,2,2))].">
      <j1 rule="para" parents="4714 16212"/>
    </justification>
  </clause>

  <clause id="16214">
    <literal><![CDATA[
      K(x,y / ((z * (u \ 1)) / z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(13990,a,16213,a)].">
      <j1 rule="hyper" parents="13990 16213"/>
    </justification>
  </clause>

  <clause id="16215">
    <literal><![CDATA[
      K(x,y / T(z \ 1,u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(15912,a,16214,a)].">
      <j1 rule="hyper" parents="15912 16214"/>
    </justification>
  </clause>

  <clause id="16216">
    <literal><![CDATA[
      K(x,y * T(z,z * (x * y))) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(14004,a,16215,a),flip(a)].">
      <j1 rule="hyper" parents="14004 16215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16217">
    <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(10837,a,16215,a)].">
      <j1 rule="hyper" parents="10837 16215"/>
    </justification>
  </clause>

  <clause id="16218">
    <literal><![CDATA[
      T(x,y / T(z \ 1,u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,16215,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 16215 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16219">
    <literal><![CDATA[
      K(x,y / T(1 / z,u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,5544,a,b,16215,a)].">
      <j1 rule="hyper" parents="58 5544 16215"/>
    </justification>
  </clause>

  <clause id="16220">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) * T(z,u)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16116,a(flip),b,16215,a),flip(a)].">
      <j1 rule="hyper" parents="58 16116 16215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16221">
    <literal><![CDATA[
      K(x,y * T(1 / z,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(75(a,1),16215(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="75 16215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16222">
    <literal><![CDATA[
      K(x,y * T(z,x * y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(13132,a,16216,a)].">
      <j1 rule="hyper" parents="13132 16216"/>
    </justification>
  </clause>

  <clause id="16223">
    <literal><![CDATA[
      T(x,y * T(z,x * y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,16222,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 16222 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16224">
    <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,15026,a,b,16223,a)].">
      <j1 rule="hyper" parents="58 15026 16223"/>
    </justification>
  </clause>

  <clause id="16225">
    <literal><![CDATA[
      T(x,y / T(1 / z,u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,5707,a,b,16218,a)].">
      <j1 rule="hyper" parents="58 5707 16218"/>
    </justification>
  </clause>

  <clause id="16226">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),v5)) = T(x,y * T(K(w,u) / z,v5))
    ]]></literal>
    <justification jstring="[para(13862(a,1),16218(a,1,2,2,1))].">
      <j1 rule="para" parents="13862 16218"/>
    </justification>
  </clause>

  <clause id="16227">
    <literal><![CDATA[
      K(x,y * T(z \ 1,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),16219(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="72 16219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16228">
    <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,15475,a(flip),b,16221,a),flip(a)].">
      <j1 rule="hyper" parents="58 15475 16221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16229">
    <literal><![CDATA[
      T(x,y / T(K(z,u) * w,v5)) = T(x,y * T(w \ K(u,z),v5))
    ]]></literal>
    <justification jstring="[para(13753(a,1),16225(a,1,2,2,1))].">
      <j1 rule="para" parents="13753 16225"/>
    </justification>
  </clause>

  <clause id="16230">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y / T(z / u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16142,a(flip),b,16227,a)].">
      <j1 rule="hyper" parents="58 16142 16227"/>
    </justification>
  </clause>

  <clause id="16231">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(320,a,13000,a(flip),b,16230,a),flip(a)].">
      <j1 rule="hyper" parents="320 13000 16230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16232">
    <literal><![CDATA[
      K(x,y / (T(z,u) / u)) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8762,a,b,16231,a)].">
      <j1 rule="hyper" parents="58 8762 16231"/>
    </justification>
  </clause>

  <clause id="16233">
    <literal><![CDATA[
      K(x,T(y,z * u) * T(u,z)) = K(x,T(u * y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15307,a(flip),b,16220,a)].">
      <j1 rule="hyper" parents="58 15307 16220"/>
    </justification>
  </clause>

  <clause id="16234">
    <literal><![CDATA[
      K(x,T(y * ((z * y) \ u),z)) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15205,a(flip),b,16233,a),flip(a)].">
      <j1 rule="hyper" parents="58 15205 16233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16235">
    <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(5815(a,1),16233(a,1,2,1))].">
      <j1 rule="para" parents="5815 16233"/>
    </justification>
  </clause>

  <clause id="16236">
    <literal><![CDATA[
      K(x,y * ((z * y) \ T(u,z))) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15357,a(flip),b,16234,a)].">
      <j1 rule="hyper" parents="58 15357 16234"/>
    </justification>
  </clause>

  <clause id="16237">
    <literal><![CDATA[
      K(x,y * ((T(z,u) * y) \ u)) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[para(13650(a,2),16236(a,1,2,2))].">
      <j1 rule="para" parents="13650 16236"/>
    </justification>
  </clause>

  <clause id="16238">
    <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(320,a,10809,a(flip),b,16217,a),flip(a)].">
      <j1 rule="hyper" parents="320 10809 16217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16239">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),v5)) = T(x,y * T(z \ K(w,u),v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,15962,a(flip),b,16226,a),flip(a)].">
      <j1 rule="hyper" parents="320 15962 16226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16240">
    <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(14123,a,16238,a)].">
      <j1 rule="hyper" parents="14123 16238"/>
    </justification>
  </clause>

  <clause id="16241">
    <literal><![CDATA[
      T(x,((y \ z) * y) * K(u,w)) = T(x,T(K(u,w) * z,y))
    ]]></literal>
    <justification jstring="[hyper(15856,a,16096,a(flip))].">
      <j1 rule="hyper" parents="15856 16096"/>
    </justification>
  </clause>

  <clause id="16242">
    <literal><![CDATA[
      L(K(x \ y,z),u,x / y) = K(T(1 / (y \ x),K(w,v5)),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,6257,a(flip),b,15859,a)].">
      <j1 rule="hyper" parents="320 6257 15859"/>
    </justification>
  </clause>

  <clause id="16243">
    <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),16242(a,1,1,1))].">
      <j1 rule="para" parents="4 16242"/>
    </justification>
  </clause>

  <clause id="16244">
    <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(16132(a,1),16042(a,1))].">
      <j1 rule="para" parents="16132 16042"/>
    </justification>
  </clause>

  <clause id="16245">
    <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(16059(a,1),16043(a,1))].">
      <j1 rule="para" parents="16059 16043"/>
    </justification>
  </clause>

  <clause id="16246">
    <literal><![CDATA[
      T(L(K(x,y),z / u,u),z / u) = z \ (u * (K(x,y) * (u \ z)))
    ]]></literal>
    <justification jstring="[para(11151(a,2),16122(a,1,1))].">
      <j1 rule="para" parents="11151 16122"/>
    </justification>
  </clause>

  <clause id="16247">
    <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(7917(a,1),16141(a,1,2,2,2))].">
      <j1 rule="para" parents="7917 16141"/>
    </justification>
  </clause>

  <clause id="16248">
    <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(16203(a,2),16141(a,1))].">
      <j1 rule="para" parents="16203 16141"/>
    </justification>
  </clause>

  <clause id="16249">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ T(z / u,z))) = K(x,y * (z \ (z / u)))
    ]]></literal>
    <justification jstring="[hyper(16164,a,15186,a)].">
      <j1 rule="hyper" parents="16164 15186"/>
    </justification>
  </clause>

  <clause id="16250">
    <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(13921(a,1),16164(a,1,2,2))].">
      <j1 rule="para" parents="13921 16164"/>
    </justification>
  </clause>

  <clause id="16251">
    <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,14683,a(flip),b,16210,a)].">
      <j1 rule="hyper" parents="58 14683 16210"/>
    </justification>
  </clause>

  <clause id="16252">
    <literal><![CDATA[
      L(K(x,y),z,u / (u * x)) = K(1 / ((u * x) \ u),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,15576,a(flip),b,16243,a),flip(a)].">
      <j1 rule="hyper" parents="320 15576 16243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16253">
    <literal><![CDATA[
      L(K(x,y),z,u / (u * x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(16252(a,2),6275(a,1))].">
      <j1 rule="para" parents="16252 6275"/>
    </justification>
  </clause>

  <clause id="16254">
    <literal><![CDATA[
      K((x * (y / x)) / z,u) = K(z,K(y,u)) * K(z \ T(y,x),u)
    ]]></literal>
    <justification jstring="[para(15131(a,1),15679(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15131 15679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16256">
    <literal><![CDATA[
      K((x * (y / x)) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,15685,a(flip),b,16254,a),flip(a)].">
      <j1 rule="hyper" parents="320 15685 16254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16257">
    <literal><![CDATA[
      K(T(x * y,y) / z,u) = K((y * x) / z,u)
    ]]></literal>
    <justification jstring="[para(6(a,1),16256(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6 16256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16258">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) = (w * K((z * y) / u,x)) \ w
    ]]></literal>
    <justification jstring="[para(16257(a,1),6309(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="16257 6309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16259">
    <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(14056(a,1),16257(a,2,1,1))].">
      <j1 rule="para" parents="14056 16257"/>
    </justification>
  </clause>

  <clause id="16260">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,15582,a(flip),b,16258,a),flip(a)].">
      <j1 rule="hyper" parents="320 15582 16258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16261">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) / u) = w
    ]]></literal>
    <justification jstring="[para(16258(a,2),6316(a,1))].">
      <j1 rule="para" parents="16258 6316"/>
    </justification>
  </clause>

  <clause id="16262">
    <literal><![CDATA[
      K(x,(y * (z / y)) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(7(a,1),16260(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 16260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16263">
    <literal><![CDATA[
      K(x,(y * ((y * z) / y)) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13021,a(flip),b,16262,a),flip(a)].">
      <j1 rule="hyper" parents="320 13021 16262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16264">
    <literal><![CDATA[
      K(x,T(y,z) / (u * (y / z))) = K(x,y / (u * (z \ y)))
    ]]></literal>
    <justification jstring="[para(14155(a,1),16262(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14155 16262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16265">
    <literal><![CDATA[
      K(x,(T(y,z) * z) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[para(225(a,1),16263(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="225 16263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16266">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,u,z)) = K(x,(z * y) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(14722,a,16265,a)].">
      <j1 rule="hyper" parents="14722 16265"/>
    </justification>
  </clause>

  <clause id="16267">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,u)) = K(x,y / (u * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16173,a,b,16264,a)].">
      <j1 rule="hyper" parents="58 16173 16264"/>
    </justification>
  </clause>

  <clause id="16268">
    <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,13129,a(flip),b,15749,a),flip(a)].">
      <j1 rule="hyper" parents="58 13129 15749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16269">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),w)) = K(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(320,a,15748,a(flip),b,16268,a),flip(a)].">
      <j1 rule="hyper" parents="320 15748 16268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16270">
    <literal><![CDATA[
      K(x,T(y / T(z,u),z * u)) = K(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15496,a(flip),b,16269,a),flip(a)].">
      <j1 rule="hyper" parents="58 15496 16269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16271">
    <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),15852(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 15852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16272">
    <literal><![CDATA[
      K(T(x,y) * z,T(u,y * x)) = K(T(z,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13778,a(flip),b,16271,a),flip(a)].">
      <j1 rule="hyper" parents="320 13778 16271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16274">
    <literal><![CDATA[
      K(x * T(y,z),T(u,z * y)) = K(T(x,z) * y,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(15900,a,16272,a)].">
      <j1 rule="hyper" parents="15900 16272"/>
    </justification>
  </clause>

  <clause id="16275">
    <literal><![CDATA[
      K(x * T(y,z),T(u,z * y)) = K(y * T(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,12190,a(flip),b,16274,a),flip(a)].">
      <j1 rule="hyper" parents="320 12190 16274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16276">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) = K(x * T(z * y,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15545,a(flip),b,16275,a)].">
      <j1 rule="hyper" parents="58 15545 16275"/>
    </justification>
  </clause>

  <clause id="16277">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) = K(x * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,16123,a(flip),b,16276,a),flip(a)].">
      <j1 rule="hyper" parents="320 16123 16276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16278">
    <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,16277,a(flip),b,8042,a)].">
      <j1 rule="hyper" parents="116 16277 8042"/>
    </justification>
  </clause>

  <clause id="16279">
    <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),16277(a,1,1,2))].">
      <j1 rule="para" parents="99 16277"/>
    </justification>
  </clause>

  <clause id="16280">
    <literal><![CDATA[
      K(x \ K(T(y,x * z),u),T(w,z)) = K(T(x,z) \ K(y,u),w)
    ]]></literal>
    <justification jstring="[hyper(6474,a,15871,a)].">
      <j1 rule="hyper" parents="6474 15871"/>
    </justification>
  </clause>

  <clause id="16281">
    <literal><![CDATA[
      K(x \ K(y,T(z,x * u)),T(w,u)) = K(T(x,u) \ K(y,z),w)
    ]]></literal>
    <justification jstring="[para(7133(a,1),16280(a,1,1,2))].">
      <j1 rule="para" parents="7133 16280"/>
    </justification>
  </clause>

  <clause id="16282">
    <literal><![CDATA[
      K(T(x,y) \ K(z,u),w) = K(x \ K(z,u),T(w,y))
    ]]></literal>
    <justification jstring="[hyper(16001,a,16281,a),flip(a)].">
      <j1 rule="hyper" parents="16001 16281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16284">
    <literal><![CDATA[
      K(T(x,y) \ K(z,u),w) = T(K(x \ K(z,u),w),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7131,a(flip),b,16282,a),flip(a)].">
      <j1 rule="hyper" parents="320 7131 16282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16285">
    <literal><![CDATA[
      T(K((x / y) \ K(y,z),u),T(y,x)) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(14104,a,16284,a),flip(a)].">
      <j1 rule="hyper" parents="14104 16284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16287">
    <literal><![CDATA[
      T(K(x \ T(y,z),u),T(y,x)) = K((x / y) \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(7859,a,16285,a)].">
      <j1 rule="hyper" parents="7859 16285"/>
    </justification>
  </clause>

  <clause id="16288">
    <literal><![CDATA[
      T(K(x \ T(y,z),u),T(y,w)) = K((x / y) \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(15730,a,16287,a)].">
      <j1 rule="hyper" parents="15730 16287"/>
    </justification>
  </clause>

  <clause id="16289">
    <literal><![CDATA[
      K((x / y) \ K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(y,z) / x,u) = w
    ]]></literal>
    <justification jstring="[para(16288(a,1),8030(a,1))].">
      <j1 rule="para" parents="16288 8030"/>
    </justification>
  </clause>

  <clause id="16290">
    <literal><![CDATA[
      K((x / y) \ K(z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(y,z) / x,u) = w
    ]]></literal>
    <justification jstring="[para(15112(a,1),16289(a,1))].">
      <j1 rule="para" parents="15112 16289"/>
    </justification>
  </clause>

  <clause id="16291">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z \ y,u) \ y) = T(x,T(y / z,u) \ y)
    ]]></literal>
    <justification jstring="[para(8145(a,1),15875(a,1,1))].">
      <j1 rule="para" parents="8145 15875"/>
    </justification>
  </clause>

  <clause id="16292">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y \ z,u) \ z) = T(x,T(z / y,u) \ z)
    ]]></literal>
    <justification jstring="[para(7807(a,1),16291(a,1,1))].">
      <j1 rule="para" parents="7807 16291"/>
    </justification>
  </clause>

  <clause id="16293">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z / y,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(8006(a,1),15876(a,1,1))].">
      <j1 rule="para" parents="8006 15876"/>
    </justification>
  </clause>

  <clause id="16294">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * T(y / z,u)) = T(x,z * T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(7807(a,1),16293(a,1,1))].">
      <j1 rule="para" parents="7807 16293"/>
    </justification>
  </clause>

  <clause id="16296">
    <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,10291,a(flip),b,15984,a)].">
      <j1 rule="hyper" parents="58 10291 15984"/>
    </justification>
  </clause>

  <clause id="16297">
    <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(6168(a,2),16079(a,1,2,2))].">
      <j1 rule="para" parents="6168 16079"/>
    </justification>
  </clause>

  <clause id="16298">
    <literal><![CDATA[
      K(x,T(((y / x) / y) * z,y)) = K(x,T(z * ((y / x) / y),y))
    ]]></literal>
    <justification jstring="[hyper(7913,a,16111,a),flip(a)].">
      <j1 rule="hyper" parents="7913 16111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16299">
    <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(320,a,12328,a(flip),b,16119,a),flip(a)].">
      <j1 rule="hyper" parents="320 12328 16119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16300">
    <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(7890(a,1),16121(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7890 16121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16301">
    <literal><![CDATA[
      (x * K(y,z / u)) \ (u \ z) = K(z / u,y) * (x \ (u \ z))
    ]]></literal>
    <justification jstring="[para(7888(a,1),16130(a,1,1,2))].">
      <j1 rule="para" parents="7888 16130"/>
    </justification>
  </clause>

  <clause id="16302">
    <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(16301(a,1),13069(a,1,2,2,1))].">
      <j1 rule="para" parents="16301 13069"/>
    </justification>
  </clause>

  <clause id="16303">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) / u) = K(x,(((z / y) / z) * z) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13021,a(flip),b,16133,a),flip(a)].">
      <j1 rule="hyper" parents="58 13021 16133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16304">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) / u) = K(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[para(7(a,1),16303(a,2,2,1))].">
      <j1 rule="para" parents="7 16303"/>
    </justification>
  </clause>

  <clause id="16306">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ (u \ z))) = K(x,y * (z \ (z / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13121,a(flip),b,16249,a)].">
      <j1 rule="hyper" parents="58 13121 16249"/>
    </justification>
  </clause>

  <clause id="16307">
    <literal><![CDATA[
      K(x,y * ((z \ u) / u)) = K(x,y * (u \ (u / z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15172,a(flip),b,16306,a)].">
      <j1 rule="hyper" parents="58 15172 16306"/>
    </justification>
  </clause>

  <clause id="16308">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(15966,a,16296,a),flip(a)].">
      <j1 rule="hyper" parents="15966 16296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16309">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16296(a,1),15966(a,1))].">
      <j1 rule="para" parents="16296 15966"/>
    </justification>
  </clause>

  <clause id="16311">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(15717,a,16308,a)].">
      <j1 rule="hyper" parents="15717 16308"/>
    </justification>
  </clause>

  <clause id="16315">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = T(K(x,y),w)
    ]]></literal>
    <justification jstring="[hyper(320,a,7131,a(flip),b,16308,a),flip(a)].">
      <j1 rule="hyper" parents="320 7131 16308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16316">
    <literal><![CDATA[
      T(x,T(y,K(z,u) * w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(118,a,16308,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 16308 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16317">
    <literal><![CDATA[
      K(x,T(y,z / K(u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15737,a,b,16308,a)].">
      <j1 rule="hyper" parents="58 15737 16308"/>
    </justification>
  </clause>

  <clause id="16318">
    <literal><![CDATA[
      K(x,T(y,T(z,u) * w)) = K(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(4740(a,1),16308(a,1,2,2))].">
      <j1 rule="para" parents="4740 16308"/>
    </justification>
  </clause>

  <clause id="16319">
    <literal><![CDATA[
      K(x,T(y,T(z,u) \ w)) = K(x,T(y,z \ w))
    ]]></literal>
    <justification jstring="[para(5042(a,1),16308(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5042 16308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16320">
    <literal><![CDATA[
      K(x,T(y,(z / u) * w)) = K(x,T(y,(u \ z) * w))
    ]]></literal>
    <justification jstring="[para(5405(a,1),16308(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5405 16308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16321">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(5370(a,1),16308(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5370 16308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16322">
    <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(16308(a,1),7157(a,1,2))].">
      <j1 rule="para" parents="16308 7157"/>
    </justification>
  </clause>

  <clause id="16326">
    <literal><![CDATA[
      T(K(x,y),z * K(u,w)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8404,a,16311,a)].">
      <j1 rule="hyper" parents="8404 16311"/>
    </justification>
  </clause>

  <clause id="16329">
    <literal><![CDATA[
      K(x,T(y,K(z,u) / w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15737,a,b,16311,a)].">
      <j1 rule="hyper" parents="58 15737 16311"/>
    </justification>
  </clause>

  <clause id="16331">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) = K(x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(6192(a,1),16311(a,1,2,2))].">
      <j1 rule="para" parents="6192 16311"/>
    </justification>
  </clause>

  <clause id="16332">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,w)) * v5)) = K(x,T(y,z * v5))
    ]]></literal>
    <justification jstring="[para(6791(a,1),16311(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6791 16311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16333">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(u,w)) = (z * K(u,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(16311(a,1),7872(a,1,1))].">
      <j1 rule="para" parents="16311 7872"/>
    </justification>
  </clause>

  <clause id="16337">
    <literal><![CDATA[
      K(x,T(y,z \ (u / w))) = K(x,T(y,z \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(13896(a,1),16311(a,1,2,2))].">
      <j1 rule="para" parents="13896 16311"/>
    </justification>
  </clause>

  <clause id="16338">
    <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(16311(a,1),14694(a,1))].">
      <j1 rule="para" parents="16311 14694"/>
    </justification>
  </clause>

  <clause id="16339">
    <literal><![CDATA[
      K(x,T(y,K(z,u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16311(a,1),15815(a,1))].">
      <j1 rule="para" parents="16311 15815"/>
    </justification>
  </clause>

  <clause id="16340">
    <literal><![CDATA[
      T(K(x,y),K(z,u) * w) = T(K(x,y),w)
    ]]></literal>
    <justification jstring="[hyper(8404,a,16315,a)].">
      <j1 rule="hyper" parents="8404 16315"/>
    </justification>
  </clause>

  <clause id="16341">
    <literal><![CDATA[
      T(x,T(y,K(z,u) \ w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),16316(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 16316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16342">
    <literal><![CDATA[
      T(x,T(y,T(z,u) * w)) = T(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(4740(a,1),16316(a,1,2,2))].">
      <j1 rule="para" parents="4740 16316"/>
    </justification>
  </clause>

  <clause id="16343">
    <literal><![CDATA[
      T(x,T(y,(z * u) * w)) = T(x,T(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[para(11122(a,1),16316(a,1,2,2))].">
      <j1 rule="para" parents="11122 16316"/>
    </justification>
  </clause>

  <clause id="16344">
    <literal><![CDATA[
      T(x,T(y,(T(z,u) * w) * v5)) = T(x,T(y,(z * w) * v5))
    ]]></literal>
    <justification jstring="[para(14757(a,1),16316(a,1,2,2))].">
      <j1 rule="para" parents="14757 16316"/>
    </justification>
  </clause>

  <clause id="16345">
    <literal><![CDATA[
      T(x,T(y,z / K(u,w))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,16317,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 16317 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16346">
    <literal><![CDATA[
      T(K(x,y),z * K(u,w)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7131,a(flip),b,16326,a),flip(a)].">
      <j1 rule="hyper" parents="320 7131 16326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16348">
    <literal><![CDATA[
      (K(x,T(y,z)) * z) * K(x,y) = (x * y) * ((y * x) \ (K(x,y) * z))
    ]]></literal>
    <justification jstring="[para(16326(a,1),11171(a,1,1,1))].">
      <j1 rule="para" parents="16326 11171"/>
    </justification>
  </clause>

  <clause id="16350">
    <literal><![CDATA[
      (K(x,T(y,z)) * u) \ (z * K(x,y)) = (K(x,y) * u) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(16326(a,1),13909(a,1,1,1))].">
      <j1 rule="para" parents="16326 13909"/>
    </justification>
  </clause>

  <clause id="16351">
    <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(16326(a,1),14667(a,1,2,2))].">
      <j1 rule="para" parents="16326 14667"/>
    </justification>
  </clause>

  <clause id="16352">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(u,w) / z) = (K(u,w) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(16329(a,1),7872(a,1,1))].">
      <j1 rule="para" parents="16329 7872"/>
    </justification>
  </clause>

  <clause id="16355">
    <literal><![CDATA[
      T(K(x,y),K(z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16340(a,2),7683(a,1))].">
      <j1 rule="para" parents="16340 7683"/>
    </justification>
  </clause>

  <clause id="16357">
    <literal><![CDATA[
      T(x,T((K(y,z) \ u) \ w,u)) = T(x,w / (K(y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,7917,a(flip),b,16341,a),flip(a)].">
      <j1 rule="hyper" parents="58 7917 16341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16358">
    <literal><![CDATA[
      K(x,K(y,z / K(u,w))) = (x \ y) / T(y / x,T(x,z))
    ]]></literal>
    <justification jstring="[para(16345(a,1),14818(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16345 14818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16361">
    <literal><![CDATA[
      T(K(x,y),z * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(16346(a,2),7683(a,1))].">
      <j1 rule="para" parents="16346 7683"/>
    </justification>
  </clause>

  <clause id="16364">
    <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(16319(a,1),12199(a,1))].">
      <j1 rule="para" parents="16319 12199"/>
    </justification>
  </clause>

  <clause id="16365">
    <literal><![CDATA[
      K(x,T(y,z \ (u / (u / w)))) = K(x,T(y,z \ w))
    ]]></literal>
    <justification jstring="[para(244(a,1),16321(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="244 16321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16366">
    <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(1577(a,1),16309(a,1,2,2))].">
      <j1 rule="para" parents="1577 16309"/>
    </justification>
  </clause>

  <clause id="16367">
    <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(4740(a,1),16309(a,1,2,2))].">
      <j1 rule="para" parents="4740 16309"/>
    </justification>
  </clause>

  <clause id="16368">
    <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(5516(a,1),16309(a,1,2,2))].">
      <j1 rule="para" parents="5516 16309"/>
    </justification>
  </clause>

  <clause id="16369">
    <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(5514(a,1),16309(a,1,2,2))].">
      <j1 rule="para" parents="5514 16309"/>
    </justification>
  </clause>

  <clause id="16370">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(7261(a,1),16309(a,1,2,2))].">
      <j1 rule="para" parents="7261 16309"/>
    </justification>
  </clause>

  <clause id="16371">
    <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(11122(a,1),16309(a,1,2,2))].">
      <j1 rule="para" parents="11122 16309"/>
    </justification>
  </clause>

  <clause id="16372">
    <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(12190(a,1),16309(a,1))].">
      <j1 rule="para" parents="12190 16309"/>
    </justification>
  </clause>

  <clause id="16373">
    <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(6192(a,1),16370(a,1,2,2))].">
      <j1 rule="para" parents="6192 16370"/>
    </justification>
  </clause>

  <clause id="16374">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z / (u / w))) = K(x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(8048,a,16331,a)].">
      <j1 rule="hyper" parents="8048 16331"/>
    </justification>
  </clause>

  <clause id="16375">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * K(u,w)) = T(z * K(u,w),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(239,a,16333,a(flip),b,9808,a),flip(a)].">
      <j1 rule="hyper" parents="239 16333 9808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16376">
    <literal><![CDATA[
      K(x,y) * ((1 / y) * K(z,u)) = ((1 / y) * K(z,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(3530(a,1),16333(a,1,1))].">
      <j1 rule="para" parents="3530 16333"/>
    </justification>
  </clause>

  <clause id="16377">
    <literal><![CDATA[
      T(x,T(y,(z * T(u,w)) * v5)) = T(x,T(y,(u * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,16343,a,b,16344,a)].">
      <j1 rule="hyper" parents="58 16343 16344"/>
    </justification>
  </clause>

  <clause id="16378">
    <literal><![CDATA[
      K(x,T(y,z)) / T(z,u) = (K(u,z) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(13980,a,16352,a)].">
      <j1 rule="hyper" parents="13980 16352"/>
    </justification>
  </clause>

  <clause id="16379">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = (K(u,x) / x) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,13925,a,b,16378,a)].">
      <j1 rule="hyper" parents="58 13925 16378"/>
    </justification>
  </clause>

  <clause id="16380">
    <literal><![CDATA[
      K(x,K(y,z / K(u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14818,a(flip),b,16358,a),flip(a)].">
      <j1 rule="hyper" parents="320 14818 16358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16381">
    <literal><![CDATA[
      K(x,K(y,K(z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(15537,a,16380,a)].">
      <j1 rule="hyper" parents="15537 16380"/>
    </justification>
  </clause>

  <clause id="16382">
    <literal><![CDATA[
      K(x,K(y,z \ K(u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(15535,a,16380,a)].">
      <j1 rule="hyper" parents="15535 16380"/>
    </justification>
  </clause>

  <clause id="16383">
    <literal><![CDATA[
      K(x,K(y,K(z,u) / w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(8240,a,16380,a)].">
      <j1 rule="hyper" parents="8240 16380"/>
    </justification>
  </clause>

  <clause id="16384">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6(a,1),16380(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 16380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16385">
    <literal><![CDATA[
      K(x,K(y,z / T(u,w))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(6297(a,1),16380(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6297 16380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16386">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(7258(a,1),16380(a,1,2,2))].">
      <j1 rule="para" parents="7258 16380"/>
    </justification>
  </clause>

  <clause id="16389">
    <literal><![CDATA[
      K(x,K(y,(z * u) * w)) = K(x,K(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[para(11123(a,1),16381(a,1,2,2))].">
      <j1 rule="para" parents="11123 16381"/>
    </justification>
  </clause>

  <clause id="16390">
    <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(16381(a,1),15883(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16381 15883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16391">
    <literal><![CDATA[
      T(x,K(y,z \ K(u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,16382,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 16382 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16392">
    <literal><![CDATA[
      K(x,K(y,K(z,u) / w)) = K(x,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7772,a,b,16383,a),flip(a)].">
      <j1 rule="hyper" parents="320 7772 16383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16394">
    <literal><![CDATA[
      T(x,K(y,z * K(u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,16384,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 16384 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16396">
    <literal><![CDATA[
      K(x,K(y,z / ((u * w) / u))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[para(6063(a,1),16384(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6063 16384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16397">
    <literal><![CDATA[
      K(x,K(y,z / (u / w))) = K(x,K(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(6192(a,1),16384(a,1,2,2))].">
      <j1 rule="para" parents="6192 16384"/>
    </justification>
  </clause>

  <clause id="16398">
    <literal><![CDATA[
      K(x,K(y,z / (u / (u / w)))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[para(6443(a,2),16384(a,1,2,2))].">
      <j1 rule="para" parents="6443 16384"/>
    </justification>
  </clause>

  <clause id="16399">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) * v5)) = K(x,K(y,z * v5))
    ]]></literal>
    <justification jstring="[para(6791(a,1),16384(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6791 16384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16400">
    <literal><![CDATA[
      K(x,K(y,z / (u * w))) = K(x,K(y,z / (w * u)))
    ]]></literal>
    <justification jstring="[para(10613(a,1),16384(a,1,2,2))].">
      <j1 rule="para" parents="10613 16384"/>
    </justification>
  </clause>

  <clause id="16401">
    <literal><![CDATA[
      K(x,K(y,z \ (u / w))) = K(x,K(y,z \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(13896(a,1),16384(a,1,2,2))].">
      <j1 rule="para" parents="13896 16384"/>
    </justification>
  </clause>

  <clause id="16402">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) = T(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(118,a,16386,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 16386 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16403">
    <literal><![CDATA[
      K(x,K(y,((z * u) / z) * w)) = K(x,K(y,u * w))
    ]]></literal>
    <justification jstring="[para(5332(a,1),16386(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5332 16386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16405">
    <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(16386(a,1),12289(a,1,1))].">
      <j1 rule="para" parents="16386 12289"/>
    </justification>
  </clause>

  <clause id="16406">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[para(13964(a,1),16386(a,1,2,2))].">
      <j1 rule="para" parents="13964 16386"/>
    </justification>
  </clause>

  <clause id="16407">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) * w) * v5)) = K(x,K(y,(z * w) * v5))
    ]]></literal>
    <justification jstring="[para(14757(a,1),16386(a,1,2,2))].">
      <j1 rule="para" parents="14757 16386"/>
    </justification>
  </clause>

  <clause id="16408">
    <literal><![CDATA[
      K(x,K(y,(K(z,u) * w) / v5)) = K(x,K(y,w / v5))
    ]]></literal>
    <justification jstring="[para(14769(a,1),16386(a,1,2,2))].">
      <j1 rule="para" parents="14769 16386"/>
    </justification>
  </clause>

  <clause id="16409">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,K(w,v5) * z)) = u
    ]]></literal>
    <justification jstring="[para(16391(a,1),15511(a,1))].">
      <j1 rule="para" parents="16391 15511"/>
    </justification>
  </clause>

  <clause id="16410">
    <literal><![CDATA[
      K(x,K(y * K(z,u),w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(8190,a,16392,a),flip(a)].">
      <j1 rule="hyper" parents="8190 16392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16411">
    <literal><![CDATA[
      K(x,K(K(y,z) / u,w)) = K(x,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(7806,a,16392,a)].">
      <j1 rule="hyper" parents="7806 16392"/>
    </justification>
  </clause>

  <clause id="16412">
    <literal><![CDATA[
      K(x,K(y * K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16392(a,1),8190(a,1))].">
      <j1 rule="para" parents="16392 8190"/>
    </justification>
  </clause>

  <clause id="16413">
    <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(10809(a,1),16392(a,1,2))].">
      <j1 rule="para" parents="10809 16392"/>
    </justification>
  </clause>

  <clause id="16415">
    <literal><![CDATA[
      T(x,K(y,z * (u * K(w,v5)))) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(10784(a,1),16394(a,1,2,2))].">
      <j1 rule="para" parents="10784 16394"/>
    </justification>
  </clause>

  <clause id="16416">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u * K(w,v5))) = T(y,K(u * K(w,v5),z) * x)
    ]]></literal>
    <justification jstring="[para(16394(a,1),15024(a,1,2,1,2))].">
      <j1 rule="para" parents="16394 15024"/>
    </justification>
  </clause>

  <clause id="16417">
    <literal><![CDATA[
      T(x,K(y,z \ K(u,w))) = T(x,K(y,K(v5,v6) * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,16391,a,b,16402,a)].">
      <j1 rule="hyper" parents="320 16391 16402"/>
    </justification>
  </clause>

  <clause id="16418">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) = T(x,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7807,a,b,16402,a),flip(a)].">
      <j1 rule="hyper" parents="320 7807 16402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16419">
    <literal><![CDATA[
      T(x,K(y,(z / u) \ w)) = T(x,K(y,(u \ z) \ w))
    ]]></literal>
    <justification jstring="[para(5361(a,1),16402(a,1,2,2))].">
      <j1 rule="para" parents="5361 16402"/>
    </justification>
  </clause>

  <clause id="16420">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(16402(a,2),7841(a,1))].">
      <j1 rule="para" parents="16402 7841"/>
    </justification>
  </clause>

  <clause id="16421">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w)) = K(x,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(15817,a,16410,a)].">
      <j1 rule="hyper" parents="15817 16410"/>
    </justification>
  </clause>

  <clause id="16422">
    <literal><![CDATA[
      K(x,K(T(y,z) / u,w)) = K(x,K(y / u,w))
    ]]></literal>
    <justification jstring="[para(1429(a,1),16410(a,1,2,1))].">
      <j1 rule="para" parents="1429 16410"/>
    </justification>
  </clause>

  <clause id="16425">
    <literal><![CDATA[
      K(x,K(K(y,z) / u,w)) = K(x,K(u * K(v5,v6),w))
    ]]></literal>
    <justification jstring="[hyper(320,a,16410,a,b,16411,a),flip(a)].">
      <j1 rule="hyper" parents="320 16410 16411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16426">
    <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(10829,a,16421,a)].">
      <j1 rule="hyper" parents="10829 16421"/>
    </justification>
  </clause>

  <clause id="16427">
    <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,16179,a(flip),b,16422,a),flip(a)].">
      <j1 rule="hyper" parents="58 16179 16422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16428">
    <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(16391(a,2),16409(a,1))].">
      <j1 rule="para" parents="16391 16409"/>
    </justification>
  </clause>

  <clause id="16429">
    <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(16397(a,2),10808(a,1,1))].">
      <j1 rule="para" parents="16397 10808"/>
    </justification>
  </clause>

  <clause id="16430">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) / w) * v5)) = K(x,K(y,(z / w) * v5))
    ]]></literal>
    <justification jstring="[para(1429(a,1),16399(a,1,2,2,1))].">
      <j1 rule="para" parents="1429 16399"/>
    </justification>
  </clause>

  <clause id="16431">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * v5)) = K(x,K(y,((u \ z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(6495(a,1),16399(a,1,2,2,1))].">
      <j1 rule="para" parents="6495 16399"/>
    </justification>
  </clause>

  <clause id="16432">
    <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(16399(a,2),15529(a,1))].">
      <j1 rule="para" parents="16399 15529"/>
    </justification>
  </clause>

  <clause id="16433">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,w / (u * z)))
    ]]></literal>
    <justification jstring="[hyper(8240,a,16400,a)].">
      <j1 rule="hyper" parents="8240 16400"/>
    </justification>
  </clause>

  <clause id="16434">
    <literal><![CDATA[
      K(x,K(y,((z * u) * w) / (w * u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,16180,a(flip),b,16406,a),flip(a)].">
      <j1 rule="hyper" parents="320 16180 16406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16435">
    <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(948(a,1),16406(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="948 16406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16436">
    <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(16406(a,1),8240(a,1))].">
      <j1 rule="para" parents="16406 8240"/>
    </justification>
  </clause>

  <clause id="16437">
    <literal><![CDATA[
      K(x,K(y,z / (K(u,w) * v5))) = K(x,K(y,v5 / z))
    ]]></literal>
    <justification jstring="[hyper(8240,a,16408,a)].">
      <j1 rule="hyper" parents="8240 16408"/>
    </justification>
  </clause>

  <clause id="16438">
    <literal><![CDATA[
      K(x,K(y,(z * T(u,w)) / v5)) = K(x,K(y,(z * u) / v5))
    ]]></literal>
    <justification jstring="[para(5516(a,1),16408(a,1,2,2,1))].">
      <j1 rule="para" parents="5516 16408"/>
    </justification>
  </clause>

  <clause id="16439">
    <literal><![CDATA[
      T(x,K(y,z * (u \ T(w,v5)))) = T(x,K(y,z * (u \ w)))
    ]]></literal>
    <justification jstring="[para(1420(a,1),16415(a,1,2,2,2))].">
      <j1 rule="para" parents="1420 16415"/>
    </justification>
  </clause>

  <clause id="16440">
    <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,16417,a(flip),b,8108,a),flip(a)].">
      <j1 rule="hyper" parents="116 16417 8108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16441">
    <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(16417(a,1),7833(a,1))].">
      <j1 rule="para" parents="16417 7833"/>
    </justification>
  </clause>

  <clause id="16442">
    <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,10862,a(flip),b,16425,a),flip(a)].">
      <j1 rule="hyper" parents="58 10862 16425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16443">
    <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(16433(a,1),8240(a,1))].">
      <j1 rule="para" parents="16433 8240"/>
    </justification>
  </clause>

  <clause id="16444">
    <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(16433(a,2),8240(a,1))].">
      <j1 rule="para" parents="16433 8240"/>
    </justification>
  </clause>

  <clause id="16445">
    <literal><![CDATA[
      K(x,K(y,z / ((K(u,w) * v5) * v6))) = K(x,K(y,(v5 * v6) / z))
    ]]></literal>
    <justification jstring="[para(6724(a,1),16437(a,1,2,2,2))].">
      <j1 rule="para" parents="6724 16437"/>
    </justification>
  </clause>

  <clause id="16446">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) / v5)) = K(x,K(y,v5 / z))
    ]]></literal>
    <justification jstring="[para(7912(a,1),16437(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7912 16437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16447">
    <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(16446(a,1),15879(a,1,1))].">
      <j1 rule="para" parents="16446 15879"/>
    </justification>
  </clause>

  <clause id="16448">
    <literal><![CDATA[
      T(x * K(y,z),K(u,w)) = T(x,K(u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(7784,a,16375,a),flip(a)].">
      <j1 rule="hyper" parents="7784 16375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16449">
    <literal><![CDATA[
      T(K(x,y) * z,K(u,w)) = K(x,y) * T(z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(6005,a,16448,a),flip(a)].">
      <j1 rule="hyper" parents="6005 16448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16455">
    <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,8266,a(flip),b,16377,a),flip(a)].">
      <j1 rule="hyper" parents="58 8266 16377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16456">
    <literal><![CDATA[
      K(x,K(y,z * (T(u,w) * v5))) = K(x,K(y,(u * v5) * z))
    ]]></literal>
    <justification jstring="[hyper(15529,a,16407,a)].">
      <j1 rule="hyper" parents="15529 16407"/>
    </justification>
  </clause>

  <clause id="16457">
    <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(320,a,10827,a,b,16413,a),flip(a)].">
      <j1 rule="hyper" parents="320 10827 16413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16458">
    <literal><![CDATA[
      K(x,K(y,((z / (z / u)) / w) * v5)) = K(x,K(y,(u / w) * v5))
    ]]></literal>
    <justification jstring="[para(244(a,1),16430(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="244 16430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16459">
    <literal><![CDATA[
      K(x,K(y,z / (T(u,w) * v5))) = K(x,K(y,(v5 * u) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16433,a(flip),b,16438,a)].">
      <j1 rule="hyper" parents="58 16433 16438"/>
    </justification>
  </clause>

  <clause id="16460">
    <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),16459(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="107 16459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16461">
    <literal><![CDATA[
      K(x,T(y,T(z * u,w) * v5)) = K(x,T(y,(u * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(16371,a,16318,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16371 16318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16463">
    <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,14624,a(flip),b,16427,a)].">
      <j1 rule="hyper" parents="58 14624 16427"/>
    </justification>
  </clause>

  <clause id="16464">
    <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(7835(a,1),16427(a,1,2,1))].">
      <j1 rule="para" parents="7835 16427"/>
    </justification>
  </clause>

  <clause id="16465">
    <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(6167(a,1),16432(a,1,2,2))].">
      <j1 rule="para" parents="6167 16432"/>
    </justification>
  </clause>

  <clause id="16466">
    <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(6293(a,1),16432(a,1,2,2,1))].">
      <j1 rule="para" parents="6293 16432"/>
    </justification>
  </clause>

  <clause id="16467">
    <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(15519(a,1),16432(a,1))].">
      <j1 rule="para" parents="15519 16432"/>
    </justification>
  </clause>

  <clause id="16468">
    <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),16467(a,1,2,2,2))].">
      <j1 rule="para" parents="84 16467"/>
    </justification>
  </clause>

  <clause id="16469">
    <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(8508(a,1),16467(a,1,2,2,2))].">
      <j1 rule="para" parents="8508 16467"/>
    </justification>
  </clause>

  <clause id="16470">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = K(u,x) / (K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(14098,a,16376,a),flip(a)].">
      <j1 rule="hyper" parents="14098 16376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16471">
    <literal><![CDATA[
      K(x,y) / (K(z,u) * y) = (K(x,y) / y) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,16379,a(flip),b,16470,a),flip(a)].">
      <j1 rule="hyper" parents="58 16379 16470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16472">
    <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(16471(a,2),6581(a,2,2))].">
      <j1 rule="para" parents="16471 6581"/>
    </justification>
  </clause>

  <clause id="16473">
    <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(858(a,1),16431(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="858 16431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16474">
    <literal><![CDATA[
      K(x,K(y,z / ((K(u,w) * v5) * v6))) = K(x,K(y,z / (v5 * v6)))
    ]]></literal>
    <justification jstring="[hyper(320,a,8162,a,b,16445,a),flip(a)].">
      <j1 rule="hyper" parents="320 8162 16445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16475">
    <literal><![CDATA[
      K(x,K(y,z * ((u / (u / w)) / v5))) = K(x,K(y,(w / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(15529,a,16458,a)].">
      <j1 rule="hyper" parents="15529 16458"/>
    </justification>
  </clause>

  <clause id="16476">
    <literal><![CDATA[
      K(x,K(y,z / (u * (K(w,v5) * v6)))) = K(x,K(y,z / (v6 * u)))
    ]]></literal>
    <justification jstring="[hyper(16443,a,16474,a)].">
      <j1 rule="hyper" parents="16443 16474"/>
    </justification>
  </clause>

  <clause id="16477">
    <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),16475(a,1,2,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 16475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16478">
    <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(16475(a,1),15529(a,1))].">
      <j1 rule="para" parents="16475 15529"/>
    </justification>
  </clause>

  <clause id="16479">
    <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(16476(a,2),16443(a,1))].">
      <j1 rule="para" parents="16476 16443"/>
    </justification>
  </clause>

  <clause id="16480">
    <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(16297(a,1),16104(a,1))].">
      <j1 rule="para" parents="16297 16104"/>
    </justification>
  </clause>

  <clause id="16481">
    <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(5516(a,1),16480(a,1,2,2,2))].">
      <j1 rule="para" parents="5516 16480"/>
    </justification>
  </clause>

  <clause id="16482">
    <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(7261(a,1),16480(a,1,2,2,2))].">
      <j1 rule="para" parents="7261 16480"/>
    </justification>
  </clause>

  <clause id="16483">
    <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(13896(a,1),16482(a,1,2,2,2))].">
      <j1 rule="para" parents="13896 16482"/>
    </justification>
  </clause>

  <clause id="16484">
    <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,14788,a(flip),b,16300,a),flip(a)].">
      <j1 rule="hyper" parents="58 14788 16300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16485">
    <literal><![CDATA[
      K(x,T(y,z * u)) * T(u,z) = T(u * K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7872(a,1),16484(a,2,1))].">
      <j1 rule="para" parents="7872 16484"/>
    </justification>
  </clause>

  <clause id="16486">
    <literal><![CDATA[
      T(x * K(x \ y,z),y) = K(x \ y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(15493(a,1),16485(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15493 16485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16487">
    <literal><![CDATA[
      K(x,T(y,z * u)) * T(z,u) = T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(15495(a,1),16485(a,1,1))].">
      <j1 rule="para" parents="15495 16485"/>
    </justification>
  </clause>

  <clause id="16488">
    <literal><![CDATA[
      T(x * K(x \ y,z),y) = T(x,y) * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,15819,a,b,16486,a),flip(a)].">
      <j1 rule="hyper" parents="320 15819 16486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16489">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = K(x * y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4867(a,1),16487(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4867 16487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16490">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = T(x,y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,15821,a,b,16489,a),flip(a)].">
      <j1 rule="hyper" parents="320 15821 16489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16491">
    <literal><![CDATA[
      T(x * y,z) / T(y,x) = T(x * K(x * y,z),y)
    ]]></literal>
    <justification jstring="[hyper(13992,a,16489,a(flip))].">
      <j1 rule="hyper" parents="13992 16489"/>
    </justification>
  </clause>

  <clause id="16492">
    <literal><![CDATA[
      T(x * K(x * y,y \ 1),y) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[hyper(320,a,12268,a(flip),b,16490,a),flip(a)].">
      <j1 rule="hyper" parents="320 12268 16490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16493">
    <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(16491(a,2),7198(a,2,2))].">
      <j1 rule="para" parents="16491 7198"/>
    </justification>
  </clause>

  <clause id="16494">
    <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(16491(a,1),15655(a,1,2,1))].">
      <j1 rule="para" parents="16491 15655"/>
    </justification>
  </clause>

  <clause id="16495">
    <literal><![CDATA[
      x \ T(y * x,x \ 1) = (y * x) * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6550,a(flip),b,16492,a)].">
      <j1 rule="hyper" parents="58 6550 16492"/>
    </justification>
  </clause>

  <clause id="16496">
    <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(16495(a,2),14707(a,2,2,1))].">
      <j1 rule="para" parents="16495 14707"/>
    </justification>
  </clause>

  <clause id="16497">
    <literal><![CDATA[
      (x * y) * ((y * x) \ (K(x,y) * z)) = (z * K(x,y)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7872(a,1),16348(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7872 16348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16499">
    <literal><![CDATA[
      (x * y) * ((y * x) \ (K(x,y) * z)) = z * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,8962,a(flip),b,16497,a),flip(a)].">
      <j1 rule="hyper" parents="320 8962 16497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16500">
    <literal><![CDATA[
      (x * y) * ((T(y,x) * x) \ z) = z * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(14917(a,1),16499(a,1,2))].">
      <j1 rule="para" parents="14917 16499"/>
    </justification>
  </clause>

  <clause id="16501">
    <literal><![CDATA[
      (x * (K(y,z) * K(y,z))) / (y * z) = x / (T(z,y) * y)
    ]]></literal>
    <justification jstring="[para(16500(a,1),12334(a,1,1))].">
      <j1 rule="para" parents="16500 12334"/>
    </justification>
  </clause>

  <clause id="16503">
    <literal><![CDATA[
      K(x,(y * (T(z,y) * K(u,w))) / v5) = K(x,((K(u,w) * z) * y) / v5)
    ]]></literal>
    <justification jstring="[para(11172(a,1),16057(a,1,2,1))].">
      <j1 rule="para" parents="11172 16057"/>
    </justification>
  </clause>

  <clause id="16504">
    <literal><![CDATA[
      K(x,y \ (z * (T(u,z) * K(w,v5)))) = K(x,y \ ((K(w,v5) * u) * z))
    ]]></literal>
    <justification jstring="[para(11172(a,1),16063(a,1,2,2))].">
      <j1 rule="para" parents="11172 16063"/>
    </justification>
  </clause>

  <clause id="16505">
    <literal><![CDATA[
      K(x,T(y,z * (y \ u)) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[para(12418(a,1),16084(a,1,2,1))].">
      <j1 rule="para" parents="12418 16084"/>
    </justification>
  </clause>

  <clause id="16506">
    <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(16139(a,1),16248(a,1))].">
      <j1 rule="para" parents="16139 16248"/>
    </justification>
  </clause>

  <clause id="16507">
    <literal><![CDATA[
      K(x,T(y,z * u) * z) = K(x,y * (u \ T(u * z,y)))
    ]]></literal>
    <justification jstring="[hyper(16250,a,15828,a),flip(a)].">
      <j1 rule="hyper" parents="16250 15828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16508">
    <literal><![CDATA[
      K(x,T(y,z * x) * z) = K(x,(x \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,12421,a(flip),b,16507,a),flip(a)].">
      <j1 rule="hyper" parents="320 12421 16507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16509">
    <literal><![CDATA[
      K(x,T(y,z * x) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),16508(a,2,2,1))].">
      <j1 rule="para" parents="4 16508"/>
    </justification>
  </clause>

  <clause id="16510">
    <literal><![CDATA[
      K(x,y * T(z,y * x)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15082,a(flip),b,16509,a),flip(a)].">
      <j1 rule="hyper" parents="58 15082 16509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16511">
    <literal><![CDATA[
      K(T(x,y),z * T(u,z * x)) = K(T(x,y),u * z)
    ]]></literal>
    <justification jstring="[hyper(16481,a,16510,a)].">
      <j1 rule="hyper" parents="16481 16510"/>
    </justification>
  </clause>

  <clause id="16512">
    <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(4958(a,1),16479(a,1,2,2,2,2))].">
      <j1 rule="para" parents="4958 16479"/>
    </justification>
  </clause>

  <clause id="16513">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[hyper(13148,a,16505,a)].">
      <j1 rule="hyper" parents="13148 16505"/>
    </justification>
  </clause>

  <clause id="16514">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * (z / y))) = K(x,(u * (z / y)) * y)
    ]]></literal>
    <justification jstring="[para(10368(a,1),16513(a,2,2))].">
      <j1 rule="para" parents="10368 16513"/>
    </justification>
  </clause>

  <clause id="16515">
    <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(15510(a,1),15513(a,1,2))].">
      <j1 rule="para" parents="15510 15513"/>
    </justification>
  </clause>

  <clause id="16516">
    <literal><![CDATA[
      K(x * (y \ z),x * (1 / (z \ y))) = K(x * (y \ z),(z \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(13988,a,15848,a),flip(a)].">
      <j1 rule="hyper" parents="13988 15848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16517">
    <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(16516(a,1),14009(a,1))].">
      <j1 rule="para" parents="16516 14009"/>
    </justification>
  </clause>

  <clause id="16518">
    <literal><![CDATA[
      K(x,T(y,L(z,u,u \ w) * w)) = K(x,T(y,(u \ w) * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(15862,a,16320,a)].">
      <j1 rule="hyper" parents="15862 16320"/>
    </justification>
  </clause>

  <clause id="16520">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),(x * y) \ y) = T(x * y,K(y,z)) \ y
    ]]></literal>
    <justification jstring="[para(6123(a,1),15940(a,2,1))].">
      <j1 rule="para" parents="6123 15940"/>
    </justification>
  </clause>

  <clause id="16521">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),(x * y) \ y) = T((x * y) \ y,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8329,a,b,16520,a),flip(a)].">
      <j1 rule="hyper" parents="320 8329 16520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16522">
    <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,15089,a(flip),b,16068,a)].">
      <j1 rule="hyper" parents="58 15089 16068"/>
    </justification>
  </clause>

  <clause id="16523">
    <literal><![CDATA[
      K(x,(K(y,z) * (u / (y \ z))) / w) = K(x,(u / (T(y,z) \ z)) / w)
    ]]></literal>
    <justification jstring="[para(12551(a,1),16522(a,1,2,1))].">
      <j1 rule="para" parents="12551 16522"/>
    </justification>
  </clause>

  <clause id="16524">
    <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(12189(a,1),16124(a,2,1))].">
      <j1 rule="para" parents="12189 16124"/>
    </justification>
  </clause>

  <clause id="16525">
    <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),16178(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 16178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16526">
    <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(6317,a,16195,a),flip(a)].">
      <j1 rule="hyper" parents="6317 16195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16527">
    <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(16240(a,2),15247(a,1))].">
      <j1 rule="para" parents="16240 15247"/>
    </justification>
  </clause>

  <clause id="16528">
    <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(320,a,16457,a(flip),b,16442,a),flip(a)].">
      <j1 rule="hyper" parents="320 16457 16442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16530">
    <literal><![CDATA[
      K(x,K(y * K(z,u),L(w,K(v5,v6),v7))) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,10861,a(flip),b,16528,a),flip(a)].">
      <j1 rule="hyper" parents="320 10861 16528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16531">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w),v5))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(16412,a,16530,a)].">
      <j1 rule="hyper" parents="16412 16530"/>
    </justification>
  </clause>

  <clause id="16533">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,w)) / v5)) = K(x,T(y,v5 / z))
    ]]></literal>
    <justification jstring="[hyper(15894,a,16447,a),flip(a)].">
      <j1 rule="hyper" parents="15894 16447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16534">
    <literal><![CDATA[
      K(x,T(y,(z / T(u,w)) / v5)) = K(x,T(y,v5 / (z / u)))
    ]]></literal>
    <justification jstring="[para(6293(a,1),16533(a,1,2,2,1))].">
      <j1 rule="para" parents="6293 16533"/>
    </justification>
  </clause>

  <clause id="16535">
    <literal><![CDATA[
      K(x,T(y,z / (u / T(w,v5)))) = K(x,T(y,z / (u / w)))
    ]]></literal>
    <justification jstring="[hyper(8247,a,16534,a)].">
      <j1 rule="hyper" parents="8247 16534"/>
    </justification>
  </clause>

  <clause id="16536">
    <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(320,a,8451,a(flip),b,16535,a),flip(a)].">
      <j1 rule="hyper" parents="320 8451 16535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16537">
    <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),16535(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="107 16535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16538">
    <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(16535(a,1),4863(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16535 4863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16539">
    <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(13155(a,1),16455(a,1,2))].">
      <j1 rule="para" parents="13155 16455"/>
    </justification>
  </clause>

  <clause id="16540">
    <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(14615(a,1),16494(a,1,2))].">
      <j1 rule="para" parents="14615 16494"/>
    </justification>
  </clause>

  <clause id="16541">
    <literal><![CDATA[
      K(((T(x,y) * z) * y) / (z * T(x,y)),u) = K(z \ T(y * z,x),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13919,a(flip),b,16524,a),flip(a)].">
      <j1 rule="hyper" parents="320 13919 16524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16542">
    <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(11126,a,16541,a)].">
      <j1 rule="hyper" parents="11126 16541"/>
    </justification>
  </clause>

  <clause id="16543">
    <literal><![CDATA[
      K(x * K(y,z),T(u,z * T(y,x))) = K(z \ T(x * z,y),u)
    ]]></literal>
    <justification jstring="[para(7911(a,1),16542(a,1,1))].">
      <j1 rule="para" parents="7911 16542"/>
    </justification>
  </clause>

  <clause id="16544">
    <literal><![CDATA[
      K(x * K(y,z),T(u,z * y)) = K(z \ T(x * z,y),u)
    ]]></literal>
    <justification jstring="[hyper(16368,a,16543,a)].">
      <j1 rule="hyper" parents="16368 16543"/>
    </justification>
  </clause>

  <clause id="16545">
    <literal><![CDATA[
      K(T(K(x,y) * z,x * y),u) = K(y \ T(z * y,x),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12294,a,b,16544,a)].">
      <j1 rule="hyper" parents="58 12294 16544"/>
    </justification>
  </clause>

  <clause id="16546">
    <literal><![CDATA[
      K(K(x,y) * z,T(u,x * y)) = K(y \ T(z * y,x),u)
    ]]></literal>
    <justification jstring="[hyper(7679,a,16545,a)].">
      <j1 rule="hyper" parents="7679 16545"/>
    </justification>
  </clause>

  <clause id="16547">
    <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(7131(a,2),16526(a,1,2))].">
      <j1 rule="para" parents="7131 16526"/>
    </justification>
  </clause>

  <clause id="16548">
    <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(7205,a,16547,a),flip(a)].">
      <j1 rule="hyper" parents="7205 16547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16549">
    <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,15877,a(flip),b,16548,a),flip(a)].">
      <j1 rule="hyper" parents="58 15877 16548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16550">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u * K(y,x),w) = K(x,y) * T(u * K(y,T(x,z)),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15561,a(flip),b,16549,a)].">
      <j1 rule="hyper" parents="58 15561 16549"/>
    </justification>
  </clause>

  <clause id="16551">
    <literal><![CDATA[
      T(K(x,K(y,z)) \ u,K(x,y) \ z) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(383(a,1),15798(a,1,1))].">
      <j1 rule="para" parents="383 15798"/>
    </justification>
  </clause>

  <clause id="16552">
    <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,15891,a(flip),b,16551,a)].">
      <j1 rule="hyper" parents="58 15891 16551"/>
    </justification>
  </clause>

  <clause id="16553">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) / v5))) = K(x,y * (z / (v5 \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(16167,a,14490,a),flip(a)].">
      <j1 rule="hyper" parents="16167 14490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16554">
    <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(3489(a,2),16553(a,1,2))].">
      <j1 rule="para" parents="3489 16553"/>
    </justification>
  </clause>

  <clause id="16555">
    <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(7169(a,1),16181(a,1,2))].">
      <j1 rule="para" parents="7169 16181"/>
    </justification>
  </clause>

  <clause id="16556">
    <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(16555(a,1),16190(a,1))].">
      <j1 rule="para" parents="16555 16190"/>
    </justification>
  </clause>

  <clause id="16557">
    <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(16418(a,1),16441(a,1))].">
      <j1 rule="para" parents="16418 16441"/>
    </justification>
  </clause>

  <clause id="16558">
    <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(5093(a,1),15762(a,2,2))].">
      <j1 rule="para" parents="5093 15762"/>
    </justification>
  </clause>

  <clause id="16559">
    <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,7533,a(flip),b,15884,a)].">
      <j1 rule="hyper" parents="58 7533 15884"/>
    </justification>
  </clause>

  <clause id="16560">
    <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,16098,a,b,16072,a)].">
      <j1 rule="hyper" parents="58 16098 16072"/>
    </justification>
  </clause>

  <clause id="16562">
    <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,15249,a(flip),b,16131,a)].">
      <j1 rule="hyper" parents="58 15249 16131"/>
    </justification>
  </clause>

  <clause id="16563">
    <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(13643(a,1),16135(a,2,2,2))].">
      <j1 rule="para" parents="13643 16135"/>
    </justification>
  </clause>

  <clause id="16564">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) / w)) = K(x,y * (T(z,u) / w))
    ]]></literal>
    <justification jstring="[hyper(15991,a,16563,a)].">
      <j1 rule="hyper" parents="15991 16563"/>
    </justification>
  </clause>

  <clause id="16565">
    <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(13070,a,16564,a),flip(a)].">
      <j1 rule="hyper" parents="13070 16564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16567">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) / u) * w) = K(x,(T(y,z) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(12263,a,16565,a),flip(a)].">
      <j1 rule="hyper" parents="12263 16565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16568">
    <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(7424(a,1),16193(a,1,2,2))].">
      <j1 rule="para" parents="7424 16193"/>
    </justification>
  </clause>

  <clause id="16569">
    <literal><![CDATA[
      K(x,y \ (z / T(z / u,w))) = K(x,y \ (T(u \ z,w) \ z))
    ]]></literal>
    <justification jstring="[para(7589(a,1),16568(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7589 16568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16570">
    <literal><![CDATA[
      T(x,K(y * K(z,u),w) * v5) = v5 \ T(x * T(v5,K(w,y)),K(w,y))
    ]]></literal>
    <justification jstring="[para(16394(a,1),16416(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16394 16416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16571">
    <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="[hyper(16106,a,16570,a)].">
      <j1 rule="hyper" parents="16106 16570"/>
    </justification>
  </clause>

  <clause id="16572">
    <literal><![CDATA[
      T(x,K(y * K(z,u),w) * v5) = T(x,K(y,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(320,a,15024,a(flip),b,16570,a),flip(a)].">
      <j1 rule="hyper" parents="320 15024 16570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16574">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) = T(x,K(u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(16106,a,16572,a)].">
      <j1 rule="hyper" parents="16106 16572"/>
    </justification>
  </clause>

  <clause id="16575">
    <literal><![CDATA[
      T(x,y * K(K(z,u) * w,v5)) = T(x,K(w,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(15858,a,16572,a)].">
      <j1 rule="hyper" parents="15858 16572"/>
    </justification>
  </clause>

  <clause id="16576">
    <literal><![CDATA[
      T(x,y * K(z,u * K(w,v5))) = T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(15857,a,16572,a)].">
      <j1 rule="hyper" parents="15857 16572"/>
    </justification>
  </clause>

  <clause id="16578">
    <literal><![CDATA[
      T(x,K(T(y,z) \ u,w) * v5) = T(x,K(y \ u,w) * v5)
    ]]></literal>
    <justification jstring="[para(7271(a,1),16572(a,1,2,1,1))].">
      <j1 rule="para" parents="7271 16572"/>
    </justification>
  </clause>

  <clause id="16579">
    <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,15043,a(flip),b,16574,a),flip(a)].">
      <j1 rule="hyper" parents="58 15043 16574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16580">
    <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,16575,a(flip),b,14467,a(flip))].">
      <j1 rule="hyper" parents="119 16575 14467"/>
    </justification>
  </clause>

  <clause id="16581">
    <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(16576(a,1),4797(a,1,2))].">
      <j1 rule="para" parents="16576 4797"/>
    </justification>
  </clause>

  <clause id="16582">
    <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(16576(a,1),4821(a,1,2))].">
      <j1 rule="para" parents="16576 4821"/>
    </justification>
  </clause>

  <clause id="16583">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w) * v5)) = T(x,K(u * v5,z) * y)
    ]]></literal>
    <justification jstring="[para(5500(a,1),16576(a,1,2,2,2))].">
      <j1 rule="para" parents="5500 16576"/>
    </justification>
  </clause>

  <clause id="16584">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w) \ v5)) = T(x,K(u \ v5,z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(15908,a,16578,a)].">
      <j1 rule="hyper" parents="15908 16578"/>
    </justification>
  </clause>

  <clause id="16585">
    <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(16578(a,1),15908(a,1))].">
      <j1 rule="para" parents="16578 15908"/>
    </justification>
  </clause>

  <clause id="16586">
    <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(16584(a,2),15908(a,1))].">
      <j1 rule="para" parents="16584 15908"/>
    </justification>
  </clause>

  <clause id="16587">
    <literal><![CDATA[
      K(x,y * K(z,u * K(w,v5))) = K(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(16581,a,15039,a)].">
      <j1 rule="hyper" parents="16581 15039"/>
    </justification>
  </clause>

  <clause id="16588">
    <literal><![CDATA[
      K(x,y * K(z,u * K(w,v5))) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(16581,a,4688,a(flip))].">
      <j1 rule="hyper" parents="16581 4688"/>
    </justification>
  </clause>

  <clause id="16589">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) = K(x,K(w,u) * v5)
    ]]></literal>
    <justification jstring="[hyper(16075,a,16587,a)].">
      <j1 rule="hyper" parents="16075 16587"/>
    </justification>
  </clause>

  <clause id="16590">
    <literal><![CDATA[
      K(x,y * K(z * K(u,w),v5)) = K(x,K(v5,z) * y)
    ]]></literal>
    <justification jstring="[hyper(15853,a,16587,a)].">
      <j1 rule="hyper" parents="15853 16587"/>
    </justification>
  </clause>

  <clause id="16591">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * v5) = K(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(15638,a,16587,a)].">
      <j1 rule="hyper" parents="15638 16587"/>
    </justification>
  </clause>

  <clause id="16592">
    <literal><![CDATA[
      K(x,y * K(K(z,u) * w,v5)) = K(x,K(w,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(16076,a,16588,a)].">
      <j1 rule="hyper" parents="16076 16588"/>
    </justification>
  </clause>

  <clause id="16593">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) = K(x,K(u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(16075,a,16588,a)].">
      <j1 rule="hyper" parents="16075 16588"/>
    </justification>
  </clause>

  <clause id="16594">
    <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(16588(a,1),15638(a,1))].">
      <j1 rule="para" parents="16588 15638"/>
    </justification>
  </clause>

  <clause id="16595">
    <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(16589(a,2),15052(a,1))].">
      <j1 rule="para" parents="16589 15052"/>
    </justification>
  </clause>

  <clause id="16596">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * v5) = K(x,v5 * K(z,y))
    ]]></literal>
    <justification jstring="[para(6300(a,1),16590(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6300 16590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16597">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w) * v5) = K(x,v5 * K(w,y))
    ]]></literal>
    <justification jstring="[para(7121(a,1),16590(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7121 16590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16598">
    <literal><![CDATA[
      K(x,K(y \ K(z,u),w) * v5) = K(x,K(w,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,15787,a,b,16591,a)].">
      <j1 rule="hyper" parents="58 15787 16591"/>
    </justification>
  </clause>

  <clause id="16599">
    <literal><![CDATA[
      K(x,K(y,z) * (u / ((K(w,v5) * y) \ z))) = K(x,u / (z / (K(w,v5) * y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15792,a(flip),b,16593,a),flip(a)].">
      <j1 rule="hyper" parents="58 15792 16593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16601">
    <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(16597(a,2),15747(a,1))].">
      <j1 rule="para" parents="16597 15747"/>
    </justification>
  </clause>

  <clause id="16602">
    <literal><![CDATA[
      K(x,K(y,z \ K(u,w)) * v5) = K(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(15052,a,16598,a)].">
      <j1 rule="hyper" parents="15052 16598"/>
    </justification>
  </clause>

  <clause id="16604">
    <literal><![CDATA[
      T(x,K(y,z \ K(u,w)) * v5) = T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(118,a,16602,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 16602 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16605">
    <literal><![CDATA[
      T(x,y * K(z \ K(u,w),v5)) = T(x,K(v5,z) * y)
    ]]></literal>
    <justification jstring="[hyper(15857,a,16604,a)].">
      <j1 rule="hyper" parents="15857 16604"/>
    </justification>
  </clause>

  <clause id="16606">
    <literal><![CDATA[
      T(x,y * K(z \ K(u,w),v5)) = T(x,K(z,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,15035,a,b,16605,a),flip(a)].">
      <j1 rule="hyper" parents="320 15035 16605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16607">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) = T(x,v5 * K(u \ K(v6,v7),w))
    ]]></literal>
    <justification jstring="[hyper(320,a,16574,a,b,16606,a)].">
      <j1 rule="hyper" parents="320 16574 16606"/>
    </justification>
  </clause>

  <clause id="16608">
    <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,16071,a(flip),b,16606,a),flip(a)].">
      <j1 rule="hyper" parents="58 16071 16606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16609">
    <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(4818(a,1),16595(a,1,2,1,1))].">
      <j1 rule="para" parents="4818 16595"/>
    </justification>
  </clause>

  <clause id="16610">
    <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(5092(a,2),16609(a,1,2))].">
      <j1 rule="para" parents="5092 16609"/>
    </justification>
  </clause>

  <clause id="16611">
    <literal><![CDATA[
      T(x,K(y \ K(z,u),w) * v5) = T(x,K(K(v6,v7) * y,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(320,a,15609,a,b,16607,a)].">
      <j1 rule="hyper" parents="320 15609 16607"/>
    </justification>
  </clause>

  <clause id="16612">
    <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,15804,a(flip),b,16611,a),flip(a)].">
      <j1 rule="hyper" parents="58 15804 16611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16613">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w)),v5) = K(K(z,y) * x,v5)
    ]]></literal>
    <justification jstring="[hyper(16582,a,4753,a(flip))].">
      <j1 rule="hyper" parents="16582 4753"/>
    </justification>
  </clause>

  <clause id="16614">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w)),v5) = K(x * K(y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(320,a,15780,a(flip),b,16613,a),flip(a)].">
      <j1 rule="hyper" parents="320 15780 16613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16615">
    <literal><![CDATA[
      K(x * K(y,T(z,u) * w),v5) = K(x * K(y,z * w),v5)
    ]]></literal>
    <justification jstring="[para(5500(a,1),16614(a,1,1,2,2))].">
      <j1 rule="para" parents="5500 16614"/>
    </justification>
  </clause>

  <clause id="16616">
    <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(16571(a,2),15252(a,1))].">
      <j1 rule="para" parents="16571 15252"/>
    </justification>
  </clause>

  <clause id="16617">
    <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(320,a,15289,a(flip),b,16579,a),flip(a)].">
      <j1 rule="hyper" parents="320 15289 16579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16619">
    <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(16612(a,1),16616(a,1))].">
      <j1 rule="para" parents="16612 16616"/>
    </justification>
  </clause>

  <clause id="16620">
    <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(8306(a,1),16560(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8306 16560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16621">
    <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(320,a,11032,a(flip),b,16620,a),flip(a)].">
      <j1 rule="hyper" parents="320 11032 16620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16622">
    <literal><![CDATA[
      T(x,K(y \ z,u) * w) = T(x,K(z * y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(15516,a,16515,a),flip(a)].">
      <j1 rule="hyper" parents="15516 16515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16623">
    <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(16515(a,1),15516(a,1))].">
      <j1 rule="para" parents="16515 15516"/>
    </justification>
  </clause>

  <clause id="16624">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w) \ v5)) = T(x,K(v5 * u,z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(16585,a,16622,a)].">
      <j1 rule="hyper" parents="16585 16622"/>
    </justification>
  </clause>

  <clause id="16625">
    <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(16622(a,1),14634(a,1,1,2))].">
      <j1 rule="para" parents="16622 14634"/>
    </justification>
  </clause>

  <clause id="16626">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w) \ v5)) = T(x,y \ T(z,v5 * u))
    ]]></literal>
    <justification jstring="[hyper(320,a,15805,a(flip),b,16624,a),flip(a)].">
      <j1 rule="hyper" parents="320 15805 16624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16627">
    <literal><![CDATA[
      T(x,y \ T(z,u \ w)) = T(x,y \ T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(16586,a,16626,a)].">
      <j1 rule="hyper" parents="16586 16626"/>
    </justification>
  </clause>

  <clause id="16628">
    <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(16627(a,1),14634(a,1,1,2))].">
      <j1 rule="para" parents="16627 14634"/>
    </justification>
  </clause>

  <clause id="16629">
    <literal><![CDATA[
      K(x,K(y \ (1 / z),L(y / u,u,z))) = K(x,K(z * y,y / u))
    ]]></literal>
    <justification jstring="[hyper(320,a,16392,a(flip),b,15532,a),flip(a)].">
      <j1 rule="hyper" parents="320 16392 15532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16630">
    <literal><![CDATA[
      K(x,K((1 / y) / z,L(z / u,u,y))) = K(x,K(y * z,z / u))
    ]]></literal>
    <justification jstring="[hyper(15538,a,16629,a)].">
      <j1 rule="hyper" parents="15538 16629"/>
    </justification>
  </clause>

  <clause id="16632">
    <literal><![CDATA[
      K(x,K((y \ z) * u,u / y)) = K(x,K(z,(1 / (y \ z)) / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14702,a(flip),b,16630,a),flip(a)].">
      <j1 rule="hyper" parents="58 14702 16630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16633">
    <literal><![CDATA[
      K(x,K(y / z,(z \ u) * y)) = K(x,K(u,(1 / (z \ u)) / y))
    ]]></literal>
    <justification jstring="[hyper(7806,a,16632,a)].">
      <j1 rule="hyper" parents="7806 16632"/>
    </justification>
  </clause>

  <clause id="16634">
    <literal><![CDATA[
      K(x,K(y,(1 / (z \ y)) / u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15790,a(flip),b,16633,a),flip(a)].">
      <j1 rule="hyper" parents="58 15790 16633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16635">
    <literal><![CDATA[
      K(x,K(y,(1 / z) / u)) = K(x,K(y,u / (y / z)))
    ]]></literal>
    <justification jstring="[para(75(a,1),16634(a,1,2,2,1,2))].">
      <j1 rule="para" parents="75 16634"/>
    </justification>
  </clause>

  <clause id="16636">
    <literal><![CDATA[
      K(x,K(y,z / (y / u))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11797,a(flip),b,16635,a),flip(a)].">
      <j1 rule="hyper" parents="58 11797 16635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16637">
    <literal><![CDATA[
      K(x,K(y,z * (y / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16398,a(flip),b,16636,a),flip(a)].">
      <j1 rule="hyper" parents="58 16398 16636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16638">
    <literal><![CDATA[
      K(x,K(y,z * x)) * K(y / x,(y / x) \ z) = K(x \ y,z / (y / x))
    ]]></literal>
    <justification jstring="[para(16636(a,1),8346(a,1,1))].">
      <j1 rule="para" parents="16636 8346"/>
    </justification>
  </clause>

  <clause id="16639">
    <literal><![CDATA[
      K(x,K(y,z * (x / u))) = K(y,K(x,z / u))
    ]]></literal>
    <justification jstring="[hyper(7756,a,16637,a)].">
      <j1 rule="hyper" parents="7756 16637"/>
    </justification>
  </clause>

  <clause id="16640">
    <literal><![CDATA[
      K(x,K(y,z * (x / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7754,a,b,16639,a),flip(a)].">
      <j1 rule="hyper" parents="320 7754 16639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16641">
    <literal><![CDATA[
      K(x,K(y,z / y)) * K(y / x,(x / y) * z) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[para(16640(a,1),12330(a,1,1))].">
      <j1 rule="para" parents="16640 12330"/>
    </justification>
  </clause>

  <clause id="16642">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,(z / x) \ y) = K(x \ z,y / (z / x))
    ]]></literal>
    <justification jstring="[para(7852(a,1),16638(a,1,1))].">
      <j1 rule="para" parents="7852 16638"/>
    </justification>
  </clause>

  <clause id="16643">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,y / (z / x)) = K(x \ z,y / (z / x))
    ]]></literal>
    <justification jstring="[para(4871(a,2),16642(a,1,2))].">
      <j1 rule="para" parents="4871 16642"/>
    </justification>
  </clause>

  <clause id="16644">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y / x,(x / y) * z) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[para(7843(a,1),16641(a,1,1))].">
      <j1 rule="para" parents="7843 16641"/>
    </justification>
  </clause>

  <clause id="16645">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,(x / z) * y) = K(x \ z,y * (x / z))
    ]]></literal>
    <justification jstring="[para(7772(a,1),16644(a,1,1))].">
      <j1 rule="para" parents="7772 16644"/>
    </justification>
  </clause>

  <clause id="16647">
    <literal><![CDATA[
      R(K(x,y) \ (z * K(u,w)),K(x,y),K(w,u)) = T(z / (K(w,u) * K(x,y)),K(x,y))
    ]]></literal>
    <justification jstring="[para(6306(a,1),15756(a,1,1,2))].">
      <j1 rule="para" parents="6306 15756"/>
    </justification>
  </clause>

  <clause id="16648">
    <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(13684(a,1),16259(a,1,1,1,1))].">
      <j1 rule="para" parents="13684 16259"/>
    </justification>
  </clause>

  <clause id="16649">
    <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(16052,a,16648,a)].">
      <j1 rule="hyper" parents="16052 16648"/>
    </justification>
  </clause>

  <clause id="16650">
    <literal><![CDATA[
      R(K(x,y) * (z * K(u,w)),K(y,x),K(w,u)) = T(z / (K(w,u) * K(y,x)),K(y,x))
    ]]></literal>
    <justification jstring="[para(5092(a,1),16647(a,1,1))].">
      <j1 rule="para" parents="5092 16647"/>
    </justification>
  </clause>

  <clause id="16651">
    <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(6261(a,1),15736(a,1,2,2))].">
      <j1 rule="para" parents="6261 15736"/>
    </justification>
  </clause>

  <clause id="16652">
    <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(16013,a,15842,a)].">
      <j1 rule="hyper" parents="16013 15842"/>
    </justification>
  </clause>

  <clause id="16653">
    <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(15253,a,16652,a),flip(a)].">
      <j1 rule="hyper" parents="15253 16652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16655">
    <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(7251(a,1),15849(a,1,2,1))].">
      <j1 rule="para" parents="7251 15849"/>
    </justification>
  </clause>

  <clause id="16656">
    <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,15077,a(flip),b,16655,a),flip(a)].">
      <j1 rule="hyper" parents="58 15077 16655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16658">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * (z * K(y,x))) = (z * K(y,x)) \ (u * (K(x,y) \ z))
    ]]></literal>
    <justification jstring="[para(7834(a,1),15887(a,1,2,2))].">
      <j1 rule="para" parents="7834 15887"/>
    </justification>
  </clause>

  <clause id="16659">
    <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(320,a,7917,a(flip),b,15901,a),flip(a)].">
      <j1 rule="hyper" parents="320 7917 15901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16660">
    <literal><![CDATA[
      T(((x \ 1) * y) \ z,K(y * (x \ 1),x)) = T(z / ((x \ 1) * y),y / x)
    ]]></literal>
    <justification jstring="[para(12190(a,1),16659(a,1,2))].">
      <j1 rule="para" parents="12190 16659"/>
    </justification>
  </clause>

  <clause id="16661">
    <literal><![CDATA[
      T(((x \ 1) * y) \ z,K(x \ y,x)) = T(z / ((x \ 1) * y),y / x)
    ]]></literal>
    <justification jstring="[para(5830(a,1),16660(a,1,2))].">
      <j1 rule="para" parents="5830 16660"/>
    </justification>
  </clause>

  <clause id="16662">
    <literal><![CDATA[
      T(x / ((y \ 1) * z),z / y) = T(((y \ 1) * z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(13053,a,16661,a),flip(a)].">
      <j1 rule="hyper" parents="13053 16661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16663">
    <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(6160(a,2),16136(a,1,2))].">
      <j1 rule="para" parents="6160 16136"/>
    </justification>
  </clause>

  <clause id="16664">
    <literal><![CDATA[
      K(x,y * (((z * (u / z)) / z) * (w \ 1))) = K(x,y * ((u / z) * (w \ K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(320,a,13144,a(flip),b,16196,a),flip(a)].">
      <j1 rule="hyper" parents="320 13144 16196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16665">
    <literal><![CDATA[
      K(x,y * (T(z / u,u) * (w \ 1))) = K(x,y * ((z / u) * (w \ K(u,z))))
    ]]></literal>
    <justification jstring="[hyper(15337,a,16664,a)].">
      <j1 rule="hyper" parents="15337 16664"/>
    </justification>
  </clause>

  <clause id="16666">
    <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),16665(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="107 16665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16667">
    <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(13133,a,16235,a)].">
      <j1 rule="hyper" parents="13133 16235"/>
    </justification>
  </clause>

  <clause id="16668">
    <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,15287,a(flip),b,16667,a),flip(a)].">
      <j1 rule="hyper" parents="58 15287 16667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16669">
    <literal><![CDATA[
      K(x,T(y * ((z \ (u * y)) \ 1),u)) = K(x,((u * y) / z) \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,15073,a(flip),b,16668,a),flip(a)].">
      <j1 rule="hyper" parents="320 15073 16668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16670">
    <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(16669(a,1),13991(a,1))].">
      <j1 rule="para" parents="16669 13991"/>
    </justification>
  </clause>

  <clause id="16671">
    <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,12200,a(flip),b,16279,a)].">
      <j1 rule="hyper" parents="58 12200 16279"/>
    </justification>
  </clause>

  <clause id="16672">
    <literal><![CDATA[
      T(x,y / ((z \ T(z \ u,w)) \ (z \ u))) = T(x,y / (T(z \ u,w) \ u))
    ]]></literal>
    <justification jstring="[para(13910(a,1),16302(a,1,2,2,1))].">
      <j1 rule="para" parents="13910 16302"/>
    </justification>
  </clause>

  <clause id="16673">
    <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(7834(a,1),16390(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7834 16390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16674">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * (z * K(y,x))) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16552,a(flip),b,16673,a),flip(a)].">
      <j1 rule="hyper" parents="58 16552 16673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16675">
    <literal><![CDATA[
      (x * K(y,z)) \ (u * (K(z,y) \ x)) = x \ T(u * x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16658,a(flip),b,16674,a)].">
      <j1 rule="hyper" parents="58 16658 16674"/>
    </justification>
  </clause>

  <clause id="16676">
    <literal><![CDATA[
      (x * K(y,z)) \ (u * (K(z,y) \ x)) = x \ T(u * x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7807(a,1),16675(a,2,2))].">
      <j1 rule="para" parents="7807 16675"/>
    </justification>
  </clause>

  <clause id="16677">
    <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(16428,a,16440,a)].">
      <j1 rule="hyper" parents="16428 16440"/>
    </justification>
  </clause>

  <clause id="16678">
    <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,16342,a(flip),b,16539,a)].">
      <j1 rule="hyper" parents="58 16342 16539"/>
    </justification>
  </clause>

  <clause id="16680">
    <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,12281,a(flip),b,16678,a),flip(a)].">
      <j1 rule="hyper" parents="58 12281 16678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16681">
    <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(14848(a,1),16580(a,1,2,1,2))].">
      <j1 rule="para" parents="14848 16580"/>
    </justification>
  </clause>

  <clause id="16682">
    <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(16625(a,1),14635(a,1))].">
      <j1 rule="para" parents="16625 14635"/>
    </justification>
  </clause>

  <clause id="16683">
    <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(16628(a,1),14635(a,1))].">
      <j1 rule="para" parents="16628 14635"/>
    </justification>
  </clause>

  <clause id="16684">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,y / x)) = y \ (y * K((x * (z / x)) \ y,u))
    ]]></literal>
    <justification jstring="[para(6627(a,1),16651(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6627 16651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16685">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,y / x)) = K((x * (z / x)) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,4,a(flip),b,16684,a),flip(a)].">
      <j1 rule="hyper" parents="320 4 16684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16686">
    <literal><![CDATA[
      K((x * ((y * ((x \ z) * x)) / x)) \ z,u) = K(1 / y,T(u,z / x))
    ]]></literal>
    <justification jstring="[hyper(5402,a,16685,a),flip(a)].">
      <j1 rule="hyper" parents="5402 16685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16688">
    <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(16685(a,1),5402(a,1))].">
      <j1 rule="para" parents="16685 5402"/>
    </justification>
  </clause>

  <clause id="16689">
    <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(10320(a,1),16671(a,1,1,2))].">
      <j1 rule="para" parents="10320 16671"/>
    </justification>
  </clause>

  <clause id="16691">
    <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(16418(a,1),16677(a,2,2))].">
      <j1 rule="para" parents="16418 16677"/>
    </justification>
  </clause>

  <clause id="16692">
    <literal><![CDATA[
      T((x \ K(y,z)) \ u,K(x,w)) = (x \ K(y,z)) \ T(u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(16420,a,16691,a)].">
      <j1 rule="hyper" parents="16420 16691"/>
    </justification>
  </clause>

  <clause id="16693">
    <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(320,a,16558,a(flip),b,16692,a),flip(a)].">
      <j1 rule="hyper" parents="320 16558 16692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16694">
    <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),16693(a,1,1))].">
      <j1 rule="para" parents="17 16693"/>
    </justification>
  </clause>

  <clause id="16695">
    <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(16694(a,1),16557(a,1))].">
      <j1 rule="para" parents="16694 16557"/>
    </justification>
  </clause>

  <clause id="16696">
    <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(14869(a,1),16681(a,1,2,1))].">
      <j1 rule="para" parents="14869 16681"/>
    </justification>
  </clause>

  <clause id="16697">
    <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(8539(a,1),15778(a,1,2,2,1))].">
      <j1 rule="para" parents="8539 15778"/>
    </justification>
  </clause>

  <clause id="16699">
    <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(247(a,1),15841(a,2,2,2))].">
      <j1 rule="para" parents="247 15841"/>
    </justification>
  </clause>

  <clause id="16700">
    <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(15906,a,15265,a),flip(a)].">
      <j1 rule="hyper" parents="15906 15265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16701">
    <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(15905,a,16700,a),flip(a)].">
      <j1 rule="hyper" parents="15905 16700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16702">
    <literal><![CDATA[
      K(x,y * T(K(x,z) * u,z)) = K(x,y * T(u,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,14791,a(flip),b,16701,a),flip(a)].">
      <j1 rule="hyper" parents="58 14791 16701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16703">
    <literal><![CDATA[
      K(x,y * T(z,u \ 1)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14791,a(flip),b,16702,a),flip(a)].">
      <j1 rule="hyper" parents="58 14791 16702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16705">
    <literal><![CDATA[
      T(x,y * T(z,u \ 1)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,16703,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 16703 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16706">
    <literal><![CDATA[
      K(x,y * T((z \ 1) \ u,z)) = K(x,y * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15162,a(flip),b,16703,a),flip(a)].">
      <j1 rule="hyper" parents="58 15162 16703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16707">
    <literal><![CDATA[
      T(x,(y * ((z \ 1) * K(u,z \ 1))) * u) = T(x,(y * (z \ 1)) * T(u,z))
    ]]></literal>
    <justification jstring="[para(6214(a,2),16705(a,1,2))].">
      <j1 rule="para" parents="6214 16705"/>
    </justification>
  </clause>

  <clause id="16708">
    <literal><![CDATA[
      K(x,y * ((z \ K(z,u)) \ u)) = K(x,y * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13109,a(flip),b,16706,a)].">
      <j1 rule="hyper" parents="58 13109 16706"/>
    </justification>
  </clause>

  <clause id="16709">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,(y * (z \ 1)) * T(u,z))
    ]]></literal>
    <justification jstring="[para(2909(a,1),16707(a,1,2,1,2))].">
      <j1 rule="para" parents="2909 16707"/>
    </justification>
  </clause>

  <clause id="16710">
    <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(15907,a,15210,a),flip(a)].">
      <j1 rule="hyper" parents="15907 15210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16711">
    <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,16096,a,b,16710,a)].">
      <j1 rule="hyper" parents="58 16096 16710"/>
    </justification>
  </clause>

  <clause id="16712">
    <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(16209(a,2),16711(a,1,2,1))].">
      <j1 rule="para" parents="16209 16711"/>
    </justification>
  </clause>

  <clause id="16713">
    <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,16299,a(flip),b,16712,a),flip(a)].">
      <j1 rule="hyper" parents="58 16299 16712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16714">
    <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(12430(a,1),15830(a,1,2,1))].">
      <j1 rule="para" parents="12430 15830"/>
    </justification>
  </clause>

  <clause id="16715">
    <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(15828(a,1),15839(a,1,2,2))].">
      <j1 rule="para" parents="15828 15839"/>
    </justification>
  </clause>

  <clause id="16716">
    <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,16583,a(flip),b,16715,a)].">
      <j1 rule="hyper" parents="58 16583 16715"/>
    </justification>
  </clause>

  <clause id="16718">
    <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(13643(a,1),16716(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13643 16716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16719">
    <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(320,a,15836,a(flip),b,16718,a),flip(a)].">
      <j1 rule="hyper" parents="320 15836 16718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16720">
    <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,7999,a(flip),b,16719,a)].">
      <j1 rule="hyper" parents="58 7999 16719"/>
    </justification>
  </clause>

  <clause id="16721">
    <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(6060(a,1),16720(a,1,2,2,1))].">
      <j1 rule="para" parents="6060 16720"/>
    </justification>
  </clause>

  <clause id="16722">
    <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,15333,a(flip),b,16088,a)].">
      <j1 rule="hyper" parents="58 15333 16088"/>
    </justification>
  </clause>

  <clause id="16723">
    <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,16087,a(flip),b,16722,a),flip(a)].">
      <j1 rule="hyper" parents="58 16087 16722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16724">
    <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,14998,a(flip),b,16152,a)].">
      <j1 rule="hyper" parents="58 14998 16152"/>
    </justification>
  </clause>

  <clause id="16725">
    <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),16224(a,1,2,1,2))].">
      <j1 rule="para" parents="18 16224"/>
    </justification>
  </clause>

  <clause id="16726">
    <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(16277(a,1),16278(a,1,1))].">
      <j1 rule="para" parents="16277 16278"/>
    </justification>
  </clause>

  <clause id="16727">
    <literal><![CDATA[
      K(x,(y * z) * R(u,z,y)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(8050,a,16726,a),flip(a)].">
      <j1 rule="hyper" parents="8050 16726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16728">
    <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(741(a,1),16727(a,2,2))].">
      <j1 rule="para" parents="741 16727"/>
    </justification>
  </clause>

  <clause id="16729">
    <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(11167(a,1),16727(a,2,2))].">
      <j1 rule="para" parents="11167 16727"/>
    </justification>
  </clause>

  <clause id="16730">
    <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),16728(a,1,2,1))].">
      <j1 rule="para" parents="5 16728"/>
    </justification>
  </clause>

  <clause id="16732">
    <literal><![CDATA[
      K(x,R(y,z \ u,z) * u) = K(x,L(y,z \ u,z) * u)
    ]]></literal>
    <justification jstring="[para(238(a,1),16730(a,1,2))].">
      <j1 rule="para" parents="238 16730"/>
    </justification>
  </clause>

  <clause id="16733">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * u) = K(x,(y * (u / z)) * z)
    ]]></literal>
    <justification jstring="[para(10368(a,1),16732(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10368 16732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16734">
    <literal><![CDATA[
      K(x,y * ((y \ T(z,u)) * u)) = K(x,(u * (z / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,14124,a(flip),b,16733,a)].">
      <j1 rule="hyper" parents="58 14124 16733"/>
    </justification>
  </clause>

  <clause id="16735">
    <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),16729(a,1,2,1))].">
      <j1 rule="para" parents="7 16729"/>
    </justification>
  </clause>

  <clause id="16737">
    <literal><![CDATA[
      K(x,y * R(T(z,y),u,u \ y)) = K(x,L(z,u,u \ y) * y)
    ]]></literal>
    <justification jstring="[para(10357(a,1),16735(a,1,2,2))].">
      <j1 rule="para" parents="10357 16735"/>
    </justification>
  </clause>

  <clause id="16738">
    <literal><![CDATA[
      K(x,L(y,z,z \ u) * u) = K(x,(y * z) * (z \ u))
    ]]></literal>
    <justification jstring="[para(726(a,1),16737(a,1,2)),flip(a)].">
      <j1 rule="para" parents="726 16737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16739">
    <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(320,a,14217,a,b,16435,a),flip(a)].">
      <j1 rule="hyper" parents="320 14217 16435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16740">
    <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,15274,a(flip),b,16714,a)].">
      <j1 rule="hyper" parents="58 15274 16714"/>
    </justification>
  </clause>

  <clause id="16741">
    <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(5137(a,1),16724(a,1,1,2))].">
      <j1 rule="para" parents="5137 16724"/>
    </justification>
  </clause>

  <clause id="16742">
    <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(16154(a,1),16741(a,1,1,2))].">
      <j1 rule="para" parents="16154 16741"/>
    </justification>
  </clause>

  <clause id="16743">
    <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(7807(a,1),16725(a,1,2))].">
      <j1 rule="para" parents="7807 16725"/>
    </justification>
  </clause>

  <clause id="16744">
    <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(15533(a,1),16739(a,2,3))].">
      <j1 rule="para" parents="15533 16739"/>
    </justification>
  </clause>

  <clause id="16745">
    <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(16112(a,1),16743(a,1,2))].">
      <j1 rule="para" parents="16112 16743"/>
    </justification>
  </clause>

  <clause id="16746">
    <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,9798,a(flip),b,16745,a)].">
      <j1 rule="hyper" parents="58 9798 16745"/>
    </justification>
  </clause>

  <clause id="16747">
    <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(16449(a,2),16746(a,1,2))].">
      <j1 rule="para" parents="16449 16746"/>
    </justification>
  </clause>

  <clause id="16748">
    <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(12189(a,1),16747(a,1,2,1))].">
      <j1 rule="para" parents="12189 16747"/>
    </justification>
  </clause>

  <clause id="16749">
    <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(13805(a,1),16748(a,1,2))].">
      <j1 rule="para" parents="13805 16748"/>
    </justification>
  </clause>

  <clause id="16750">
    <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(5092(a,1),16749(a,1,2))].">
      <j1 rule="para" parents="5092 16749"/>
    </justification>
  </clause>

  <clause id="16751">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u * K(y,x),z) = T(u,z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(8445,a,16750,a)].">
      <j1 rule="hyper" parents="8445 16750"/>
    </justification>
  </clause>

  <clause id="16752">
    <literal><![CDATA[
      K(x,y) * T(z * K(y,T(x,u)),u) = T(z,u * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,16550,a(flip),b,16751,a)].">
      <j1 rule="hyper" parents="58 16550 16751"/>
    </justification>
  </clause>

  <clause id="16753">
    <literal><![CDATA[
      T(x * K(y,T(z,u)),u) = K(y,z) * T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5109,a,16752,a),flip(a)].">
      <j1 rule="hyper" parents="5109 16752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16754">
    <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(16753(a,2),14154(a,2,2)),flip(a)].">
      <j1 rule="para" parents="16753 14154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16755">
    <literal><![CDATA[
      L(x,K(y,T(z,x)),u) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(14095,a,16754,a)].">
      <j1 rule="hyper" parents="14095 16754"/>
    </justification>
  </clause>

  <clause id="16756">
    <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,16385,a(flip),b,16744,a)].">
      <j1 rule="hyper" parents="58 16385 16744"/>
    </justification>
  </clause>

  <clause id="16758">
    <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),15550(a,1,1))].">
      <j1 rule="para" parents="20 15550"/>
    </justification>
  </clause>

  <clause id="16759">
    <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(7415(a,1),16191(a,1,1,2,1))].">
      <j1 rule="para" parents="7415 16191"/>
    </justification>
  </clause>

  <clause id="16760">
    <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(4777(a,1),16759(a,1,1))].">
      <j1 rule="para" parents="4777 16759"/>
    </justification>
  </clause>

  <clause id="16761">
    <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),16473(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4 16473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16762">
    <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(15542,a,16761,a)].">
      <j1 rule="hyper" parents="15542 16761"/>
    </justification>
  </clause>

  <clause id="16764">
    <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),16762(a,1,2,2,2))].">
      <j1 rule="para" parents="24 16762"/>
    </justification>
  </clause>

  <clause id="16765">
    <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(14866(a,1),16758(a,1,1))].">
      <j1 rule="para" parents="14866 16758"/>
    </justification>
  </clause>

  <clause id="16767">
    <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,8613,a(flip),b,16030,a),flip(a)].">
      <j1 rule="hyper" parents="58 8613 16030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16769">
    <literal><![CDATA[
      K((x * y) / x,z * ((x / y) / T(x,y))) = K(y,((x / y) / x) * T(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,8096,a(flip),b,16767,a),flip(a)].">
      <j1 rule="hyper" parents="320 8096 16767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16770">
    <literal><![CDATA[
      K(x,T(y * ((z / x) / T(z,x)),z)) = K(x,((z / x) / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7892,a,16769,a)].">
      <j1 rule="hyper" parents="7892 16769"/>
    </justification>
  </clause>

  <clause id="16771">
    <literal><![CDATA[
      K(x,T(y * ((z / x) / z),z)) = K(x,((z / x) / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8651,a(flip),b,16770,a)].">
      <j1 rule="hyper" parents="58 8651 16770"/>
    </justification>
  </clause>

  <clause id="16772">
    <literal><![CDATA[
      K(x,T(((y / x) / y) * z,y)) = K(x,((y / x) / y) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16298,a,b,16771,a)].">
      <j1 rule="hyper" parents="58 16298 16771"/>
    </justification>
  </clause>

  <clause id="16773">
    <literal><![CDATA[
      K(x,((y / x) / y) * T(T(z,y),y)) = K(x,z * ((y / x) / y))
    ]]></literal>
    <justification jstring="[hyper(13449,a,16772,a),flip(a)].">
      <j1 rule="hyper" parents="13449 16772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16774">
    <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(4051(a,1),16773(a,2,2))].">
      <j1 rule="para" parents="4051 16773"/>
    </justification>
  </clause>

  <clause id="16775">
    <literal><![CDATA[
      K(x,T(T(y,z),z) * ((z / x) / z)) = K(x,y * ((y * ((z / x) / z)) / y))
    ]]></literal>
    <justification jstring="[para(452(a,1),16774(a,1,2))].">
      <j1 rule="para" parents="452 16774"/>
    </justification>
  </clause>

  <clause id="16776">
    <literal><![CDATA[
      K(x,T(y * ((z / x) / z),y)) = K(x,T(T(y,z),z) * ((z / x) / z))
    ]]></literal>
    <justification jstring="[hyper(320,a,12235,a(flip),b,16775,a)].">
      <j1 rule="hyper" parents="320 12235 16775"/>
    </justification>
  </clause>

  <clause id="16777">
    <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(16776(a,1),12259(a,1))].">
      <j1 rule="para" parents="16776 12259"/>
    </justification>
  </clause>

  <clause id="16778">
    <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(13741(a,1),16184(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13741 16184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16779">
    <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(10911(a,1),16778(a,2,1))].">
      <j1 rule="para" parents="10911 16778"/>
    </justification>
  </clause>

  <clause id="16780">
    <literal><![CDATA[
      K(x,(y * z) \ (y * (L(y,u,w) * z))) = K(x,T(L(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7791,a(flip),b,16779,a),flip(a)].">
      <j1 rule="hyper" parents="320 7791 16779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16781">
    <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(709(a,1),16780(a,1,2))].">
      <j1 rule="para" parents="709 16780"/>
    </justification>
  </clause>

  <clause id="16782">
    <literal><![CDATA[
      K(x,T(L(y,z,u),y * w)) = K(x,T(L(y,z,u),w))
    ]]></literal>
    <justification jstring="[para(966(a,1),16781(a,1,2))].">
      <j1 rule="para" parents="966 16781"/>
    </justification>
  </clause>

  <clause id="16783">
    <literal><![CDATA[
      K(x,T(L(y,z,u),w / y)) = K(x,T(L(y,z,u),w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15737,a,b,16782,a)].">
      <j1 rule="hyper" parents="58 15737 16782"/>
    </justification>
  </clause>

  <clause id="16784">
    <literal><![CDATA[
      K(x,L(y / (y / z),u,w)) = K(x,T(L(z,u,w),y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7986,a(flip),b,16783,a)].">
      <j1 rule="hyper" parents="58 7986 16783"/>
    </justification>
  </clause>

  <clause id="16785">
    <literal><![CDATA[
      K(x,T(L(y,z / y,u),z)) = K(x,(z * u) / ((z / y) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14699,a(flip),b,16784,a),flip(a)].">
      <j1 rule="hyper" parents="58 14699 16784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16786">
    <literal><![CDATA[
      K(x,(y * z) / ((y / u) * z)) = T(L(K(x,u),y,z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7169,a(flip),b,16785,a),flip(a)].">
      <j1 rule="hyper" parents="58 7169 16785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16787">
    <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),16786(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 16786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16788">
    <literal><![CDATA[
      K(x,y / (((y / z) / u) * z)) = y \ (z * (K(x,u) * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16246,a(flip),b,16787,a),flip(a)].">
      <j1 rule="hyper" parents="58 16246 16787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16789">
    <literal><![CDATA[
      K(x,(y / x) / ((((y / x) / y) / z) * y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,10190,a(flip),b,16788,a),flip(a)].">
      <j1 rule="hyper" parents="320 10190 16788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16790">
    <literal><![CDATA[
      K(x,y / (((((y / x) / y) / z) * y) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7073,a(flip),b,16789,a)].">
      <j1 rule="hyper" parents="58 7073 16789"/>
    </justification>
  </clause>

  <clause id="16791">
    <literal><![CDATA[
      K(x,1 / ((((y / x) / y) / z) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(11062,a,16790,a)].">
      <j1 rule="hyper" parents="11062 16790"/>
    </justification>
  </clause>

  <clause id="16793">
    <literal><![CDATA[
      K(x,y / (((z / x) / z) * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11063,a(flip),b,16791,a)].">
      <j1 rule="hyper" parents="58 11063 16791"/>
    </justification>
  </clause>

  <clause id="16794">
    <literal><![CDATA[
      K(x,y / (x * ((z / x) / z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10619,a,16793,a)].">
      <j1 rule="hyper" parents="10619 16793"/>
    </justification>
  </clause>

  <clause id="16795">
    <literal><![CDATA[
      L(K(x,y / x),y,(z / x) / z) = K(x,y * ((z / x) / z))
    ]]></literal>
    <justification jstring="[hyper(14739,a,16794,a)].">
      <j1 rule="hyper" parents="14739 16794"/>
    </justification>
  </clause>

  <clause id="16796">
    <literal><![CDATA[
      L(K(x,y / x),y,z / (z * x)) = K(x,y * ((z / x) / z))
    ]]></literal>
    <justification jstring="[hyper(14513,a,16795,a)].">
      <j1 rule="hyper" parents="14513 16795"/>
    </justification>
  </clause>

  <clause id="16797">
    <literal><![CDATA[
      K(x,y * ((z / x) / z)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(16253,a,16796,a),flip(a)].">
      <j1 rule="hyper" parents="16253 16796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16798">
    <literal><![CDATA[
      K(x,T(T(y,z),z) / x) = K(x,((z / x) / z) * y)
    ]]></literal>
    <justification jstring="[hyper(16777,a,16797,a),flip(a)].">
      <j1 rule="hyper" parents="16777 16797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16799">
    <literal><![CDATA[
      K(x,((y / x) / y) * z) = K(x,z / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,15087,a(flip),b,16798,a),flip(a)].">
      <j1 rule="hyper" parents="58 15087 16798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16801">
    <literal><![CDATA[
      K(x / y,z / (x / y)) = K(x / y,(y / x) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8251,a(flip),b,16799,a),flip(a)].">
      <j1 rule="hyper" parents="58 8251 16799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16802">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,(x / z) * y) = K(x \ z,y / (z / x))
    ]]></literal>
    <justification jstring="[para(16801(a,1),16643(a,1,2))].">
      <j1 rule="para" parents="16801 16643"/>
    </justification>
  </clause>

  <clause id="16803">
    <literal><![CDATA[
      K(x \ y,z / (y / x)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16645,a(flip),b,16802,a),flip(a)].">
      <j1 rule="hyper" parents="58 16645 16802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16804">
    <literal><![CDATA[
      x * K(y \ z,x * (y / z)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[para(16803(a,1),8497(a,1,2))].">
      <j1 rule="para" parents="16803 8497"/>
    </justification>
  </clause>

  <clause id="16805">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = (y \ x) * (z / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,9410,a,b,16804,a)].">
      <j1 rule="hyper" parents="58 9410 16804"/>
    </justification>
  </clause>

  <clause id="16806">
    <literal><![CDATA[
      x * K(y \ z,x * (z \ y)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[para(9397(a,1),16804(a,1,2))].">
      <j1 rule="para" parents="9397 16804"/>
    </justification>
  </clause>

  <clause id="16807">
    <literal><![CDATA[
      x * K(y \ z,(z \ y) * x) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[para(9396(a,2),16806(a,1,2))].">
      <j1 rule="para" parents="9396 16806"/>
    </justification>
  </clause>

  <clause id="16808">
    <literal><![CDATA[
      (((x \ y) * z) \ z) * ((x \ y) * z) = (y \ x) * (z / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6251,a,b,16807,a)].">
      <j1 rule="hyper" parents="58 6251 16807"/>
    </justification>
  </clause>

  <clause id="16809">
    <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(7299(a,1),16206(a,1,2,2,1))].">
      <j1 rule="para" parents="7299 16206"/>
    </justification>
  </clause>

  <clause id="16810">
    <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(10815(a,1),16472(a,1,1))].">
      <j1 rule="para" parents="10815 16472"/>
    </justification>
  </clause>

  <clause id="16811">
    <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(6306(a,1),15885(a,1,2,1))].">
      <j1 rule="para" parents="6306 15885"/>
    </justification>
  </clause>

  <clause id="16812">
    <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(12321(a,1),15899(a,1,1))].">
      <j1 rule="para" parents="12321 15899"/>
    </justification>
  </clause>

  <clause id="16813">
    <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(6230(a,1),16812(a,1,2))].">
      <j1 rule="para" parents="6230 16812"/>
    </justification>
  </clause>

  <clause id="16814">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(15564(a,1),16813(a,1,2))].">
      <j1 rule="para" parents="15564 16813"/>
    </justification>
  </clause>

  <clause id="16815">
    <literal><![CDATA[
      a((x \ y) \ 1,z,(x \ y) \ 1) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12805,a(flip),b,16814,a),flip(a)].">
      <j1 rule="hyper" parents="58 12805 16814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16816">
    <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(16815(a,1),13481(a,1,1))].">
      <j1 rule="para" parents="16815 13481"/>
    </justification>
  </clause>

  <clause id="16817">
    <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(13137(a,1),16496(a,1,2))].">
      <j1 rule="para" parents="13137 16496"/>
    </justification>
  </clause>

  <clause id="16818">
    <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(14474,a,16817,a),flip(a)].">
      <j1 rule="hyper" parents="14474 16817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16819">
    <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,16304,a(flip),b,16818,a)].">
      <j1 rule="hyper" parents="58 16304 16818"/>
    </justification>
  </clause>

  <clause id="16820">
    <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),16819(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6 16819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16822">
    <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(320,a,20,a,b,16037,a),flip(a)].">
      <j1 rule="hyper" parents="320 20 16037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16823">
    <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(7203(a,1),16351(a,1,2))].">
      <j1 rule="para" parents="7203 16351"/>
    </justification>
  </clause>

  <clause id="16825">
    <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(14398(a,1),16822(a,1,1,2,1))].">
      <j1 rule="para" parents="14398 16822"/>
    </justification>
  </clause>

  <clause id="16826">
    <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(14405(a,1),16825(a,1,1))].">
      <j1 rule="para" parents="14405 16825"/>
    </justification>
  </clause>

  <clause id="16827">
    <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),16826(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 16826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16828">
    <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(16013,a,16823,a)].">
      <j1 rule="hyper" parents="16013 16823"/>
    </justification>
  </clause>

  <clause id="16829">
    <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(15803,a,16828,a),flip(a)].">
      <j1 rule="hyper" parents="15803 16828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16831">
    <literal><![CDATA[
      (x / K(y,T(z,u))) \ (K(z,y) * u) = (x * K(z,y)) \ (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(16326(a,1),16829(a,1,1,2))].">
      <j1 rule="para" parents="16326 16829"/>
    </justification>
  </clause>

  <clause id="16832">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ (K(y,z) * u) = (x * K(y,z)) \ (u * K(y,z))
    ]]></literal>
    <justification jstring="[para(7203(a,1),16831(a,1,1))].">
      <j1 rule="para" parents="7203 16831"/>
    </justification>
  </clause>

  <clause id="16834">
    <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,16827,a,b,16832,a)].">
      <j1 rule="hyper" parents="58 16827 16832"/>
    </justification>
  </clause>

  <clause id="16835">
    <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(16051,a,16194,a)].">
      <j1 rule="hyper" parents="16051 16194"/>
    </justification>
  </clause>

  <clause id="16837">
    <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(15926(a,1),16835(a,1,1,2))].">
      <j1 rule="para" parents="15926 16835"/>
    </justification>
  </clause>

  <clause id="16839">
    <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),16816(a,1,1,1))].">
      <j1 rule="para" parents="4 16816"/>
    </justification>
  </clause>

  <clause id="16840">
    <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),16839(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="4 16839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16841">
    <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(6093(a,1),16840(a,2,2))].">
      <j1 rule="para" parents="6093 16840"/>
    </justification>
  </clause>

  <clause id="16842">
    <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),16841(a,2,2,2))].">
      <j1 rule="para" parents="4 16841"/>
    </justification>
  </clause>

  <clause id="16843">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = a(z,x,z) * K(x,z)
    ]]></literal>
    <justification jstring="[para(4918(a,1),16842(a,2,2))].">
      <j1 rule="para" parents="4918 16842"/>
    </justification>
  </clause>

  <clause id="16844">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,8935,a(flip),b,16843,a),flip(a)].">
      <j1 rule="hyper" parents="320 8935 16843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16845">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),y \ (y * z)) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(6454,a,16844,a)].">
      <j1 rule="hyper" parents="6454 16844"/>
    </justification>
  </clause>

  <clause id="16846">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),z) = K(z * x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),16845(a,1,2))].">
      <j1 rule="para" parents="4 16845"/>
    </justification>
  </clause>

  <clause id="16847">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(14017,a,16846,a)].">
      <j1 rule="hyper" parents="14017 16846"/>
    </justification>
  </clause>

  <clause id="16848">
    <literal><![CDATA[
      K(((x * y) \ x) \ z,y) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(9658,a,16847,a)].">
      <j1 rule="hyper" parents="9658 16847"/>
    </justification>
  </clause>

  <clause id="16849">
    <literal><![CDATA[
      K(((x * y) \ x) \ (y \ z),y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),16848(a,2,1))].">
      <j1 rule="para" parents="5 16848"/>
    </justification>
  </clause>

  <clause id="16850">
    <literal><![CDATA[
      K(((x * y) \ x) * z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,10319,a(flip),b,16849,a),flip(a)].">
      <j1 rule="hyper" parents="58 10319 16849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16851">
    <literal><![CDATA[
      K(x * ((y * z) \ y),z) = K(z \ x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9394,a(flip),b,16850,a)].">
      <j1 rule="hyper" parents="58 9394 16850"/>
    </justification>
  </clause>

  <clause id="16852">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K((y \ x) * z,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),16850(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 16850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16854">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(z * (y \ x),x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),16851(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 16851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16855">
    <literal><![CDATA[
      x * K((y \ z) * x,z \ y) = ((z \ y) \ x) * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,16852,a(flip),b,85,a)].">
      <j1 rule="hyper" parents="119 16852 85"/>
    </justification>
  </clause>

  <clause id="16856">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(z * (x / y),x \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,9399,a,b,16854,a),flip(a)].">
      <j1 rule="hyper" parents="320 9399 16854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16857">
    <literal><![CDATA[
      x * K(x * (y / z),y \ z) = ((y \ z) \ x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,16856,a(flip),b,85,a)].">
      <j1 rule="hyper" parents="119 16856 85"/>
    </justification>
  </clause>

  <clause id="16858">
    <literal><![CDATA[
      (((x \ y) \ 1) \ z) * ((x \ y) \ 1) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6107,a,b,16855,a)].">
      <j1 rule="hyper" parents="58 6107 16855"/>
    </justification>
  </clause>

  <clause id="16859">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9411,a,b,16857,a)].">
      <j1 rule="hyper" parents="58 9411 16857"/>
    </justification>
  </clause>

  <clause id="16860">
    <literal><![CDATA[
      ((x \ y) * z) * (z / ((x \ y) * z)) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3886,a(flip),b,16858,a)].">
      <j1 rule="hyper" parents="58 3886 16858"/>
    </justification>
  </clause>

  <clause id="16861">
    <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(16859(a,1),16686(a,1,1,1,2,1,2))].">
      <j1 rule="para" parents="16859 16686"/>
    </justification>
  </clause>

  <clause id="16862">
    <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(16805(a,1),16861(a,1,1,1))].">
      <j1 rule="para" parents="16805 16861"/>
    </justification>
  </clause>

  <clause id="16863">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u \ w)))) = K(1 / x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(16688,a,16862,a),flip(a)].">
      <j1 rule="hyper" parents="16688 16862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16864">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u \ w)))) = K(1 / x,T(y,z / (u / w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,16331,a,b,16863,a),flip(a)].">
      <j1 rule="hyper" parents="320 16331 16863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16865">
    <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,16537,a,b,16864,a)].">
      <j1 rule="hyper" parents="58 16537 16864"/>
    </justification>
  </clause>

  <clause id="16866">
    <literal><![CDATA[
      K(1 / x,T(y,z / (u / w))) = K(1 / x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(15863,a,16865,a),flip(a)].">
      <j1 rule="hyper" parents="15863 16865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16867">
    <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(16866(a,1),16538(a,2,1))].">
      <j1 rule="para" parents="16866 16538"/>
    </justification>
  </clause>

  <clause id="16868">
    <literal><![CDATA[
      T(1 / x,T(y,z / (u / T(w,v5)))) = T(1 / x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,4863,a(flip),b,16867,a),flip(a)].">
      <j1 rule="hyper" parents="320 4863 16867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16869">
    <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(16868(a,1),3303(a,1,1))].">
      <j1 rule="para" parents="16868 3303"/>
    </justification>
  </clause>

  <clause id="16870">
    <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,3303,a(flip),b,16869,a),flip(a)].">
      <j1 rule="hyper" parents="58 3303 16869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16871">
    <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(16870(a,1),13545(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="16870 13545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16872">
    <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(320,a,13545,a(flip),b,16871,a),flip(a)].">
      <j1 rule="hyper" parents="320 13545 16871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16873">
    <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(320,a,7133,a(flip),b,16872,a),flip(a)].">
      <j1 rule="hyper" parents="320 7133 16872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16874">
    <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(7679,a,16873,a)].">
      <j1 rule="hyper" parents="7679 16873"/>
    </justification>
  </clause>

  <clause id="16875">
    <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,16535,a(flip),b,16874,a)].">
      <j1 rule="hyper" parents="58 16535 16874"/>
    </justification>
  </clause>

  <clause id="16876">
    <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,16536,a(flip),b,16875,a),flip(a)].">
      <j1 rule="hyper" parents="58 16536 16875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16877">
    <literal><![CDATA[
      K(x,T(y,(T(z,u) / w) * v5)) = K(x,T(y,v5 / (w / z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8451,a(flip),b,16876,a)].">
      <j1 rule="hyper" parents="58 8451 16876"/>
    </justification>
  </clause>

  <clause id="16878">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) = K(x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[para(104(a,1),16877(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="104 16877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16879">
    <literal><![CDATA[
      K(x,T(y,z / (u \ w))) = K(x,T(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(16373,a,16878,a)].">
      <j1 rule="hyper" parents="16373 16878"/>
    </justification>
  </clause>

  <clause id="16881">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,(z / u) * w)) = K(x,T(y,w / (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,7741,a,b,16879,a)].">
      <j1 rule="hyper" parents="320 7741 16879"/>
    </justification>
  </clause>

  <clause id="16882">
    <literal><![CDATA[
      K(x,K(y,z / (u / w))) = K(x,K(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(29,a,16374,a,b,16881,a)].">
      <j1 rule="hyper" parents="29 16374 16881"/>
    </justification>
  </clause>

  <clause id="16883">
    <literal><![CDATA[
      K(x,K(y,(z / u) / w)) = K(x,K(y,(u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(8240,a,16882,a)].">
      <j1 rule="hyper" parents="8240 16882"/>
    </justification>
  </clause>

  <clause id="16884">
    <literal><![CDATA[
      K(x,K(y,((z / u) / z) * w)) = K(x,K(y,w / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16398,a(flip),b,16882,a),flip(a)].">
      <j1 rule="hyper" parents="58 16398 16882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16885">
    <literal><![CDATA[
      K(x,K(y,(z / (z * u)) * w)) = K(x,K(y,w / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16396,a(flip),b,16882,a),flip(a)].">
      <j1 rule="hyper" parents="58 16396 16882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16886">
    <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(16882(a,1),16429(a,1,1))].">
      <j1 rule="para" parents="16882 16429"/>
    </justification>
  </clause>

  <clause id="16887">
    <literal><![CDATA[
      K(x,K(y,z * (u / (u * w)))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[hyper(15529,a,16885,a)].">
      <j1 rule="hyper" parents="15529 16885"/>
    </justification>
  </clause>

  <clause id="16888">
    <literal><![CDATA[
      K(x,K(y,z / (u \ w))) = K(x,K(y,z * (u / w)))
    ]]></literal>
    <justification jstring="[para(5(a,1),16887(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 16887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16889">
    <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(10816,a,16886,a),flip(a)].">
      <j1 rule="hyper" parents="10816 16886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16890">
    <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,16463,a(flip),b,16889,a),flip(a)].">
      <j1 rule="hyper" parents="58 16463 16889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16891">
    <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),16889(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="75 16889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16892">
    <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(15817,a,16891,a)].">
      <j1 rule="hyper" parents="15817 16891"/>
    </justification>
  </clause>

  <clause id="16893">
    <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),16890(a,2,2,2,2))].">
      <j1 rule="para" parents="5 16890"/>
    </justification>
  </clause>

  <clause id="16894">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(y * u) / z))
    ]]></literal>
    <justification jstring="[hyper(320,a,16406,a,b,16893,a),flip(a)].">
      <j1 rule="hyper" parents="320 16406 16893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16895">
    <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(16893(a,2),16444(a,1))].">
      <j1 rule="para" parents="16893 16444"/>
    </justification>
  </clause>

  <clause id="16896">
    <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,16892,a(flip),b,16894,a)].">
      <j1 rule="hyper" parents="58 16892 16894"/>
    </justification>
  </clause>

  <clause id="16897">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,z,y))) = K(x,K(w,(y * (1 / u)) / z))
    ]]></literal>
    <justification jstring="[para(13777(a,1),16894(a,1,2))].">
      <j1 rule="para" parents="13777 16894"/>
    </justification>
  </clause>

  <clause id="16898">
    <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(16894(a,2),16444(a,1))].">
      <j1 rule="para" parents="16894 16444"/>
    </justification>
  </clause>

  <clause id="16899">
    <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,16897,a(flip),b,16896,a),flip(a)].">
      <j1 rule="hyper" parents="58 16897 16896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16900">
    <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(3875(a,2),16896(a,2,2,2,1))].">
      <j1 rule="para" parents="3875 16896"/>
    </justification>
  </clause>

  <clause id="16901">
    <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(13779(a,1),16900(a,1,2))].">
      <j1 rule="para" parents="13779 16900"/>
    </justification>
  </clause>

  <clause id="16902">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) / (1 / u)) / w)) = K(x,K(y,(z * u) / w))
    ]]></literal>
    <justification jstring="[hyper(16895,a,16901,a),flip(a)].">
      <j1 rule="hyper" parents="16895 16901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16903">
    <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,16883,a(flip),b,16902,a)].">
      <j1 rule="hyper" parents="58 16883 16902"/>
    </justification>
  </clause>

  <clause id="16904">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) / w))) = K(x,K(y,(w * u) / z))
    ]]></literal>
    <justification jstring="[hyper(16466,a,16903,a)].">
      <j1 rule="hyper" parents="16466 16903"/>
    </justification>
  </clause>

  <clause id="16905">
    <literal><![CDATA[
      K(x,K(y,((z \ 1) / u) * w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,16477,a,b,16904,a)].">
      <j1 rule="hyper" parents="58 16477 16904"/>
    </justification>
  </clause>

  <clause id="16906">
    <literal><![CDATA[
      K(x,K(y,(z * (1 / u)) / w)) = K(x,K(y,(u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,16475,a(flip),b,16904,a),flip(a)].">
      <j1 rule="hyper" parents="58 16475 16904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16907">
    <literal><![CDATA[
      K(x,K(y,((z / (z / (u \ 1))) / w) * v5)) = K(x,K(y,(w * u) / v5))
    ]]></literal>
    <justification jstring="[hyper(16478,a,16905,a)].">
      <j1 rule="hyper" parents="16478 16905"/>
    </justification>
  </clause>

  <clause id="16908">
    <literal><![CDATA[
      K(x,K(y,z / ((1 / u) * w))) = K(x,K(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(16436,a,16906,a)].">
      <j1 rule="hyper" parents="16436 16906"/>
    </justification>
  </clause>

  <clause id="16909">
    <literal><![CDATA[
      K(x,K(y,(z * ((u / w) / u)) / v5)) = K(x,K(y,(w / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,16899,a,b,16906,a)].">
      <j1 rule="hyper" parents="58 16899 16906"/>
    </justification>
  </clause>

  <clause id="16910">
    <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,15536,a(flip),b,16906,a),flip(a)].">
      <j1 rule="hyper" parents="58 15536 16906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16911">
    <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,14798,a,b,16908,a)].">
      <j1 rule="hyper" parents="58 14798 16908"/>
    </justification>
  </clause>

  <clause id="16912">
    <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(8186(a,1),16908(a,1,2))].">
      <j1 rule="para" parents="8186 16908"/>
    </justification>
  </clause>

  <clause id="16913">
    <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(14652(a,1),16908(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14652 16908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16914">
    <literal><![CDATA[
      K(x,K(y,z / (((u / w) / u) * v5))) = K(x,K(y,(w / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(16436,a,16909,a)].">
      <j1 rule="hyper" parents="16436 16909"/>
    </justification>
  </clause>

  <clause id="16915">
    <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,14625,a(flip),b,16911,a)].">
      <j1 rule="hyper" parents="58 14625 16911"/>
    </justification>
  </clause>

  <clause id="16916">
    <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(16110(a,1),16912(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16110 16912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16917">
    <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(320,a,16914,a(flip),b,16913,a),flip(a)].">
      <j1 rule="hyper" parents="320 16914 16913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16919">
    <literal><![CDATA[
      K(x,K(y,(z * (u / w)) / v5)) = K(x,K(y,((w / u) / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,16907,a(flip),b,16917,a)].">
      <j1 rule="hyper" parents="58 16907 16917"/>
    </justification>
  </clause>

  <clause id="16920">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) / v5)) = K(x,K(y,((u / z) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(16444,a,16919,a)].">
      <j1 rule="hyper" parents="16444 16919"/>
    </justification>
  </clause>

  <clause id="16922">
    <literal><![CDATA[
      K(x,K(y,z / ((u \ w) * v5))) = K(x,K(y,((u / w) / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16460,a(flip),b,16919,a)].">
      <j1 rule="hyper" parents="58 16460 16919"/>
    </justification>
  </clause>

  <clause id="16923">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * w) / v5)) = K(x,K(y,((z / u) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(8240,a,16922,a)].">
      <j1 rule="hyper" parents="8240 16922"/>
    </justification>
  </clause>

  <clause id="16924">
    <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),16922(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="105 16922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16925">
    <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,16756,a(flip),b,16923,a),flip(a)].">
      <j1 rule="hyper" parents="58 16756 16923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16926">
    <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(15525,a,16925,a)].">
      <j1 rule="hyper" parents="15525 16925"/>
    </justification>
  </clause>

  <clause id="16927">
    <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(320,a,14409,a,b,16925,a),flip(a)].">
      <j1 rule="hyper" parents="320 14409 16925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16928">
    <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(16925(a,1),7756(a,1))].">
      <j1 rule="para" parents="16925 7756"/>
    </justification>
  </clause>

  <clause id="16929">
    <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),16926(a,1,2,2,2,2))].">
      <j1 rule="para" parents="7 16926"/>
    </justification>
  </clause>

  <clause id="16930">
    <literal><![CDATA[
      K(x,K(y,z / (u * (w \ v5)))) = K(x,K(y,z * ((w / v5) / u)))
    ]]></literal>
    <justification jstring="[hyper(16466,a,16924,a),flip(a)].">
      <j1 rule="hyper" parents="16466 16924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16931">
    <literal><![CDATA[
      K(x,K(y,z / (u * (w / v5)))) = K(x,K(y,z * ((v5 / w) / u)))
    ]]></literal>
    <justification jstring="[hyper(16512,a,16930,a)].">
      <j1 rule="hyper" parents="16512 16930"/>
    </justification>
  </clause>

  <clause id="16932">
    <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(16931(a,1),16556(a,1))].">
      <j1 rule="para" parents="16931 16556"/>
    </justification>
  </clause>

  <clause id="16933">
    <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),16927(a,2,2))].">
      <j1 rule="para" parents="7 16927"/>
    </justification>
  </clause>

  <clause id="16934">
    <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(320,a,8160,a(flip),b,16916,a),flip(a)].">
      <j1 rule="hyper" parents="320 8160 16916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16935">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) * w))) = K(x,K(y,(u / w) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16887,a(flip),b,16934,a),flip(a)].">
      <j1 rule="hyper" parents="58 16887 16934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16937">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) * w))) = K(x,K(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,16883,a(flip),b,16935,a),flip(a)].">
      <j1 rule="hyper" parents="320 16883 16935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16938">
    <literal><![CDATA[
      K(x,K(y,z * (u * (1 / w)))) = K(x,K(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(16468,a,16937,a)].">
      <j1 rule="hyper" parents="16468 16937"/>
    </justification>
  </clause>

  <clause id="16939">
    <literal><![CDATA[
      K(x,K(y,z * L(u,w,1 / w))) = K(x,K(y,((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[para(259(a,1),16937(a,1,2,2,2))].">
      <j1 rule="para" parents="259 16937"/>
    </justification>
  </clause>

  <clause id="16940">
    <literal><![CDATA[
      K(x,K(y,z * L(u,w,1 / w))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,16403,a(flip),b,16939,a),flip(a)].">
      <j1 rule="hyper" parents="320 16403 16939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16942">
    <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,16764,a(flip),b,16940,a),flip(a)].">
      <j1 rule="hyper" parents="58 16764 16940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16944">
    <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),16942(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="101 16942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16945">
    <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,16389,a,b,16944,a)].">
      <j1 rule="hyper" parents="58 16389 16944"/>
    </justification>
  </clause>

  <clause id="16946">
    <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(16465,a,16945,a),flip(a)].">
      <j1 rule="hyper" parents="16465 16945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16947">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((w / u) * z) * (1 / v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,11793,a(flip),b,16945,a)].">
      <j1 rule="hyper" parents="58 11793 16945"/>
    </justification>
  </clause>

  <clause id="16948">
    <literal><![CDATA[
      K(x,K(y,z * (u * ((1 / w) * v5)))) = K(x,K(y,z * ((v5 / w) * u)))
    ]]></literal>
    <justification jstring="[hyper(16465,a,16946,a),flip(a)].">
      <j1 rule="hyper" parents="16465 16946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16949">
    <literal><![CDATA[
      K(x,K(y,z * (((u / (1 / w)) / w) * v5))) = K(x,K(y,z * (v5 * u)))
    ]]></literal>
    <justification jstring="[hyper(16469,a,16948,a),flip(a)].">
      <j1 rule="hyper" parents="16469 16948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16950">
    <literal><![CDATA[
      K(x,K(y,z * (((1 / u) * w) * v5))) = K(x,K(y,z * ((w / u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(16468,a,16948,a)].">
      <j1 rule="hyper" parents="16468 16948"/>
    </justification>
  </clause>

  <clause id="16951">
    <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,16910,a(flip),b,16948,a),flip(a)].">
      <j1 rule="hyper" parents="58 16910 16948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16952">
    <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,16938,a(flip),b,16951,a)].">
      <j1 rule="hyper" parents="58 16938 16951"/>
    </justification>
  </clause>

  <clause id="16953">
    <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(320,a,16456,a(flip),b,16949,a),flip(a)].">
      <j1 rule="hyper" parents="320 16456 16949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16954">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((w / u) * z) / v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,11793,a(flip),b,16947,a),flip(a)].">
      <j1 rule="hyper" parents="320 11793 16947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16955">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((u / w) / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,16920,a(flip),b,16954,a),flip(a)].">
      <j1 rule="hyper" parents="320 16920 16954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16956">
    <literal><![CDATA[
      K(x,K(y,z / (u * ((1 / w) * v5)))) = K(x,K(y,((w / v5) / u) * z))
    ]]></literal>
    <justification jstring="[hyper(8240,a,16955,a)].">
      <j1 rule="hyper" parents="8240 16955"/>
    </justification>
  </clause>

  <clause id="16957">
    <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(13588(a,1),16956(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13588 16956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16958">
    <literal><![CDATA[
      K(x,K(y,z * ((u / (1 / w)) * K(w,v5)))) = K(x,K(y,(w * u) * z))
    ]]></literal>
    <justification jstring="[para(6121(a,1),16953(a,1,2,2,2))].">
      <j1 rule="para" parents="6121 16953"/>
    </justification>
  </clause>

  <clause id="16959">
    <literal><![CDATA[
      K(x,K(y,z * (u / (1 / w)))) = K(x,K(y,(w * u) * z))
    ]]></literal>
    <justification jstring="[hyper(16467,a,16958,a)].">
      <j1 rule="hyper" parents="16467 16958"/>
    </justification>
  </clause>

  <clause id="16960">
    <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,16959,a(flip),b,16952,a)].">
      <j1 rule="hyper" parents="58 16959 16952"/>
    </justification>
  </clause>

  <clause id="16961">
    <literal><![CDATA[
      K(x,K(y,L(z,1 / u,1 / w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(16932,a,16960,a),flip(a)].">
      <j1 rule="hyper" parents="16932 16960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16962">
    <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,14532,a(flip),b,16961,a)].">
      <j1 rule="hyper" parents="58 14532 16961"/>
    </justification>
  </clause>

  <clause id="16963">
    <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(320,a,14352,a,b,16957,a),flip(a)].">
      <j1 rule="hyper" parents="320 14352 16957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16964">
    <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,13000,a(flip),b,16228,a),flip(a)].">
      <j1 rule="hyper" parents="58 13000 16228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16965">
    <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),16964(a,1,2,1))].">
      <j1 rule="para" parents="60 16964"/>
    </justification>
  </clause>

  <clause id="16966">
    <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(15816,a,16464,a),flip(a)].">
      <j1 rule="hyper" parents="15816 16464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16968">
    <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(14692(a,1),16966(a,2,2))].">
      <j1 rule="para" parents="14692 16966"/>
    </justification>
  </clause>

  <clause id="16969">
    <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(320,a,16531,a(flip),b,16968,a),flip(a)].">
      <j1 rule="hyper" parents="320 16531 16968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16970">
    <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(16479,a,16969,a)].">
      <j1 rule="hyper" parents="16479 16969"/>
    </justification>
  </clause>

  <clause id="16972">
    <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,16434,a(flip),b,16970,a)].">
      <j1 rule="hyper" parents="58 16434 16970"/>
    </justification>
  </clause>

  <clause id="16973">
    <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,16426,a(flip),b,16972,a),flip(a)].">
      <j1 rule="hyper" parents="58 16426 16972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16974">
    <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(10839,a,16973,a)].">
      <j1 rule="hyper" parents="10839 16973"/>
    </justification>
  </clause>

  <clause id="16976">
    <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(13647(a,1),16973(a,1,2,2,2))].">
      <j1 rule="para" parents="13647 16973"/>
    </justification>
  </clause>

  <clause id="16977">
    <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(320,a,14355,a,b,16974,a),flip(a)].">
      <j1 rule="hyper" parents="320 14355 16974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16978">
    <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(320,a,16962,a(flip),b,16976,a),flip(a)].">
      <j1 rule="hyper" parents="320 16962 16976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16979">
    <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(16978(a,1),16810(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16978 16810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16980">
    <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(14356,a,16977,a)].">
      <j1 rule="hyper" parents="14356 16977"/>
    </justification>
  </clause>

  <clause id="16981">
    <literal><![CDATA[
      a(x,y * (z / y),K(u,K(w,v5))) = a(x,z,K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(4676(a,1),16980(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4676 16980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16982">
    <literal><![CDATA[
      a(x,y / z,K(u,K(w,v5))) = a(x,z \ y,K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(4818(a,1),16980(a,1,2))].">
      <j1 rule="para" parents="4818 16980"/>
    </justification>
  </clause>

  <clause id="16983">
    <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,11802,a(flip),b,16981,a),flip(a)].">
      <j1 rule="hyper" parents="58 11802 16981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16984">
    <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(7759(a,2),16983(a,2,3))].">
      <j1 rule="para" parents="7759 16983"/>
    </justification>
  </clause>

  <clause id="16985">
    <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(11797(a,1),16984(a,2,3))].">
      <j1 rule="para" parents="11797 16984"/>
    </justification>
  </clause>

  <clause id="16986">
    <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),16985(a,1,3,2,2))].">
      <j1 rule="para" parents="5 16985"/>
    </justification>
  </clause>

  <clause id="16987">
    <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(7759(a,1),16986(a,1,3))].">
      <j1 rule="para" parents="7759 16986"/>
    </justification>
  </clause>

  <clause id="16988">
    <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),16987(a,2,3,2,2))].">
      <j1 rule="para" parents="5 16987"/>
    </justification>
  </clause>

  <clause id="16989">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(z,K(u,w))) = a(x,y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(7759(a,1),16988(a,2,3))].">
      <j1 rule="para" parents="7759 16988"/>
    </justification>
  </clause>

  <clause id="16990">
    <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),16989(a,1,2,2))].">
      <j1 rule="para" parents="75 16989"/>
    </justification>
  </clause>

  <clause id="16991">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,w / y,K(w,K(z,u)))
    ]]></literal>
    <justification jstring="[para(7759(a,2),16990(a,1,3))].">
      <j1 rule="para" parents="7759 16990"/>
    </justification>
  </clause>

  <clause id="16992">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,w / y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(7759(a,2),16991(a,2,3))].">
      <j1 rule="para" parents="7759 16991"/>
    </justification>
  </clause>

  <clause id="16993">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,u / y,K(z,K(x,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14324,a,b,16992,a)].">
      <j1 rule="hyper" parents="58 14324 16992"/>
    </justification>
  </clause>

  <clause id="16994">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,u / y,K(z,K(u,x)))
    ]]></literal>
    <justification jstring="[para(7772(a,1),16993(a,2,3))].">
      <j1 rule="para" parents="7772 16993"/>
    </justification>
  </clause>

  <clause id="16995">
    <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(7771(a,1),16979(a,2,2))].">
      <j1 rule="para" parents="7771 16979"/>
    </justification>
  </clause>

  <clause id="16997">
    <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(320,a,11489,a(flip),b,16995,a),flip(a)].">
      <j1 rule="hyper" parents="320 11489 16995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16998">
    <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(6581(a,1),16997(a,2,1))].">
      <j1 rule="para" parents="6581 16997"/>
    </justification>
  </clause>

  <clause id="16999">
    <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(320,a,14463,a(flip),b,16998,a),flip(a)].">
      <j1 rule="hyper" parents="320 14463 16998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17000">
    <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(16471(a,1),16999(a,1,2))].">
      <j1 rule="para" parents="16471 16999"/>
    </justification>
  </clause>

  <clause id="17001">
    <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(7771(a,1),17000(a,1,3))].">
      <j1 rule="para" parents="7771 17000"/>
    </justification>
  </clause>

  <clause id="17002">
    <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(10902,a,17001,a)].">
      <j1 rule="hyper" parents="10902 17001"/>
    </justification>
  </clause>

  <clause id="17003">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,y,K(z,K(u,x)))
    ]]></literal>
    <justification jstring="[para(166(a,1),17002(a,1,2,1))].">
      <j1 rule="para" parents="166 17002"/>
    </justification>
  </clause>

  <clause id="17004">
    <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,16963,a,b,17003,a)].">
      <j1 rule="hyper" parents="58 16963 17003"/>
    </justification>
  </clause>

  <clause id="17005">
    <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,16994,a(flip),b,17003,a)].">
      <j1 rule="hyper" parents="58 16994 17003"/>
    </justification>
  </clause>

  <clause id="17006">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) = a(y,z,K(u,K(x,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,14325,a,b,17005,a),flip(a)].">
      <j1 rule="hyper" parents="320 14325 17005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17007">
    <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(7759(a,1),17004(a,2,3))].">
      <j1 rule="para" parents="7759 17004"/>
    </justification>
  </clause>

  <clause id="17008">
    <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(5481(a,1),17007(a,1,2,2,2,1))].">
      <j1 rule="para" parents="5481 17007"/>
    </justification>
  </clause>

  <clause id="17009">
    <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(13862(a,1),16554(a,1,2,2,1,2))].">
      <j1 rule="para" parents="13862 16554"/>
    </justification>
  </clause>

  <clause id="17010">
    <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(14138(a,1),17009(a,1,2,2,1))].">
      <j1 rule="para" parents="14138 17009"/>
    </justification>
  </clause>

  <clause id="17011">
    <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(9893(a,1),17008(a,1,2))].">
      <j1 rule="para" parents="9893 17008"/>
    </justification>
  </clause>

  <clause id="17012">
    <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(13869(a,1),17011(a,1,2))].">
      <j1 rule="para" parents="13869 17011"/>
    </justification>
  </clause>

  <clause id="17013">
    <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(6412(a,1),17012(a,1,2,2,1))].">
      <j1 rule="para" parents="6412 17012"/>
    </justification>
  </clause>

  <clause id="17014">
    <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,16950,a(flip),b,17013,a)].">
      <j1 rule="hyper" parents="58 16950 17013"/>
    </justification>
  </clause>

  <clause id="17015">
    <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(16432,a,17014,a)].">
      <j1 rule="hyper" parents="16432 17014"/>
    </justification>
  </clause>

  <clause id="17016">
    <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(6330(a,1),17015(a,2,3,2))].">
      <j1 rule="para" parents="6330 17015"/>
    </justification>
  </clause>

  <clause id="17017">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * ((u / w) / z))) = a(w,u,K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(16384(a,1),17016(a,2,3))].">
      <j1 rule="para" parents="16384 17016"/>
    </justification>
  </clause>

  <clause id="17018">
    <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,16929,a(flip),b,17017,a)].">
      <j1 rule="hyper" parents="58 16929 17017"/>
    </justification>
  </clause>

  <clause id="17020">
    <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),17018(a,1,3,2,1))].">
      <j1 rule="para" parents="72 17018"/>
    </justification>
  </clause>

  <clause id="17021">
    <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(16888(a,1),17020(a,1,3))].">
      <j1 rule="para" parents="16888 17020"/>
    </justification>
  </clause>

  <clause id="17022">
    <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(7754(a,1),17021(a,1,3))].">
      <j1 rule="para" parents="7754 17021"/>
    </justification>
  </clause>

  <clause id="17023">
    <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(16640(a,1),17022(a,1,3))].">
      <j1 rule="para" parents="16640 17022"/>
    </justification>
  </clause>

  <clause id="17024">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(w,z))) = a(u,z,K(y,K(w,x / z)))
    ]]></literal>
    <justification jstring="[hyper(14373,a,17023,a),flip(a)].">
      <j1 rule="hyper" parents="14373 17023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17025">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(z,w))) = a(u,z,K(y,K(w,x / z)))
    ]]></literal>
    <justification jstring="[para(7772(a,1),17024(a,1,3))].">
      <j1 rule="para" parents="7772 17024"/>
    </justification>
  </clause>

  <clause id="17026">
    <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,16982,a,b,17025,a)].">
      <j1 rule="hyper" parents="58 16982 17025"/>
    </justification>
  </clause>

  <clause id="17027">
    <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,17006,a(flip),b,17026,a),flip(a)].">
      <j1 rule="hyper" parents="58 17006 17026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17028">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(y,z,K(w,K(x,u)))
    ]]></literal>
    <justification jstring="[para(7754(a,1),17027(a,2,3))].">
      <j1 rule="para" parents="7754 17027"/>
    </justification>
  </clause>

  <clause id="17029">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(z,y,K(u,K(x,w)))
    ]]></literal>
    <justification jstring="[hyper(16928,a,17028,a)].">
      <j1 rule="hyper" parents="16928 17028"/>
    </justification>
  </clause>

  <clause id="17030">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(z,y,K(x,K(w,u)))
    ]]></literal>
    <justification jstring="[para(7759(a,2),17029(a,2,3))].">
      <j1 rule="para" parents="7759 17029"/>
    </justification>
  </clause>

  <clause id="17031">
    <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,16933,a(flip),b,17030,a)].">
      <j1 rule="hyper" parents="58 16933 17030"/>
    </justification>
  </clause>

  <clause id="17032">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(w,x,K(z,K(u,y)))
    ]]></literal>
    <justification jstring="[para(8162(a,1),17031(a,1,3))].">
      <j1 rule="para" parents="8162 17031"/>
    </justification>
  </clause>

  <clause id="17033">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(w,x,K(z,K(y,u)))
    ]]></literal>
    <justification jstring="[para(7772(a,1),17032(a,2,3))].">
      <j1 rule="para" parents="7772 17032"/>
    </justification>
  </clause>

  <clause id="17034">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,z,K(x,K(y,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17028,a(flip),b,17033,a),flip(a)].">
      <j1 rule="hyper" parents="58 17028 17033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17035">
    <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(17034(a,1),14323(a,1,1))].">
      <j1 rule="para" parents="17034 14323"/>
    </justification>
  </clause>

  <clause id="17036">
    <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(7754(a,1),17035(a,1,2))].">
      <j1 rule="para" parents="7754 17035"/>
    </justification>
  </clause>

  <clause id="17037">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(z,L(y,w,u)))
    ]]></literal>
    <justification jstring="[hyper(14543,a,17036,a),flip(a)].">
      <j1 rule="hyper" parents="14543 17036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17038">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,L(z,w,u)))
    ]]></literal>
    <justification jstring="[hyper(10903,a,17037,a)].">
      <j1 rule="hyper" parents="10903 17037"/>
    </justification>
  </clause>

  <clause id="17039">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(320,a,16915,a(flip),b,17038,a),flip(a)].">
      <j1 rule="hyper" parents="320 16915 17038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17040">
    <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(697(a,1),17038(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="697 17038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17041">
    <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(6671(a,1),17038(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6671 17038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17042">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,(z / w) * u))
    ]]></literal>
    <justification jstring="[hyper(16898,a,17039,a)].">
      <j1 rule="hyper" parents="16898 17039"/>
    </justification>
  </clause>

  <clause id="17043">
    <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(17041(a,2),8185(a,1))].">
      <j1 rule="para" parents="17041 8185"/>
    </justification>
  </clause>

  <clause id="17044">
    <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(320,a,15530,a,b,17040,a),flip(a)].">
      <j1 rule="hyper" parents="320 15530 17040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17045">
    <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(320,a,17042,a(flip),b,17044,a),flip(a)].">
      <j1 rule="hyper" parents="320 17042 17044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17046">
    <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(320,a,16884,a(flip),b,17045,a),flip(a)].">
      <j1 rule="hyper" parents="320 16884 17045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17049">
    <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(7983(a,1),17046(a,2,2))].">
      <j1 rule="para" parents="7983 17046"/>
    </justification>
  </clause>

  <clause id="17050">
    <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(320,a,15661,a(flip),b,17049,a),flip(a)].">
      <j1 rule="hyper" parents="320 15661 17049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17053">
    <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,14625,a(flip),b,17050,a)].">
      <j1 rule="hyper" parents="58 14625 17050"/>
    </justification>
  </clause>

  <clause id="17054">
    <literal><![CDATA[
      K(x,K(y,L(1 / z,z,u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(17043,a,17053,a),flip(a)].">
      <j1 rule="hyper" parents="17043 17053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17057">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,1 / z))
    ]]></literal>
    <justification jstring="[para(6471(a,1),17054(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6471 17054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17059">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,8173,a(flip),b,17057,a),flip(a)].">
      <j1 rule="hyper" parents="320 8173 17057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17060">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8160,a(flip),b,17057,a),flip(a)].">
      <j1 rule="hyper" parents="320 8160 17057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17062">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(10839,a,17059,a)].">
      <j1 rule="hyper" parents="10839 17059"/>
    </justification>
  </clause>

  <clause id="17064">
    <literal><![CDATA[
      K(L(x,y,z),K(u,w)) = K(x,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(7774,a,17059,a)].">
      <j1 rule="hyper" parents="7774 17059"/>
    </justification>
  </clause>

  <clause id="17067">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = x * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(17059(a,1),10828(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17059 10828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17068">
    <literal><![CDATA[
      (x * y) * K(z,K(u,w)) = x * (y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(17059(a,1),10850(a,1,2))].">
      <j1 rule="para" parents="17059 10850"/>
    </justification>
  </clause>

  <clause id="17077">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,17060,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 17060 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17078">
    <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(17060(a,1),8361(a,1,1))].">
      <j1 rule="para" parents="17060 8361"/>
    </justification>
  </clause>

  <clause id="17081">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(14695(a,2),17060(a,1,2))].">
      <j1 rule="para" parents="14695 17060"/>
    </justification>
  </clause>

  <clause id="17084">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,17062,a,b,1923,a),flip(a)].">
      <j1 rule="hyper" parents="115 17062 1923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17086">
    <literal><![CDATA[
      a(K(x,y),z,K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,17062,a(flip),b,14236,a),flip(a)].">
      <j1 rule="hyper" parents="115 17062 14236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17087">
    <literal><![CDATA[
      x \ (y * K(z,K(u,w))) = (x \ y) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[para(17062(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="17062 474"/>
    </justification>
  </clause>

  <clause id="17088">
    <literal><![CDATA[
      L(K(x,y),z,K(u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(13601,a,17084,a)].">
      <j1 rule="hyper" parents="13601 17084"/>
    </justification>
  </clause>

  <clause id="17089">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(13353,a,17084,a)].">
      <j1 rule="hyper" parents="13353 17084"/>
    </justification>
  </clause>

  <clause id="17092">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,14190,a,b,17084,a)].">
      <j1 rule="hyper" parents="58 14190 17084"/>
    </justification>
  </clause>

  <clause id="17093">
    <literal><![CDATA[
      K(x,K(y,a(z,u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,14359,a(flip),b,17084,a)].">
      <j1 rule="hyper" parents="58 14359 17084"/>
    </justification>
  </clause>

  <clause id="17095">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(167,a,14853,a,b,17084,a(flip))].">
      <j1 rule="hyper" parents="167 14853 17084"/>
    </justification>
  </clause>

  <clause id="17096">
    <literal><![CDATA[
      L(K(x,y),z,K(u,w)) = K(x,y) * 1
    ]]></literal>
    <justification jstring="[para(17084(a,1),14236(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17084 14236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17098">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,w) = K(x,y) * (z * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(969,a,17086,a)].">
      <j1 rule="hyper" parents="969 17086"/>
    </justification>
  </clause>

  <clause id="17100">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(167,a,16120,a,b,17086,a(flip))].">
      <j1 rule="hyper" parents="167 16120 17086"/>
    </justification>
  </clause>

  <clause id="17101">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(167,a,14921,a,b,17086,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 14921 17086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17102">
    <literal><![CDATA[
      T(x,L(y,z,K(u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(167,a,10854,a,b,17086,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 10854 17086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17103">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = w * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(2326,a,17089,a),flip(a)].">
      <j1 rule="hyper" parents="2326 17089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17105">
    <literal><![CDATA[
      T(a(x,y,K(z,u)),w) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(49,a,17089,a)].">
      <j1 rule="hyper" parents="49 17089"/>
    </justification>
  </clause>

  <clause id="17106">
    <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(17089(a,1),284(a,1,2))].">
      <j1 rule="para" parents="17089 284"/>
    </justification>
  </clause>

  <clause id="17107">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w))) = x
    ]]></literal>
    <justification jstring="[para(13347(a,1),17089(a,1,2))].">
      <j1 rule="para" parents="13347 17089"/>
    </justification>
  </clause>

  <clause id="17108">
    <literal><![CDATA[
      T(x,K(a(y,z,u),w)) = x
    ]]></literal>
    <justification jstring="[para(13373(a,1),17089(a,1,2))].">
      <j1 rule="para" parents="13373 17089"/>
    </justification>
  </clause>

  <clause id="17109">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w) \ z)) = x
    ]]></literal>
    <justification jstring="[para(14207(a,2),17089(a,1,2))].">
      <j1 rule="para" parents="14207 17089"/>
    </justification>
  </clause>

  <clause id="17111">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * w = K(x,K(y,z)) * (u * w)
    ]]></literal>
    <justification jstring="[hyper(14666,a,17092,a)].">
      <j1 rule="hyper" parents="14666 17092"/>
    </justification>
  </clause>

  <clause id="17117">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8043,a,17093,a)].">
      <j1 rule="hyper" parents="8043 17093"/>
    </justification>
  </clause>

  <clause id="17124">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = u \ (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(756,a,17095,a)].">
      <j1 rule="hyper" parents="756 17095"/>
    </justification>
  </clause>

  <clause id="17126">
    <literal><![CDATA[
      L(x,y,K(z,u) / w) = L(x,y,w \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14899,a(flip),b,17095,a)].">
      <j1 rule="hyper" parents="58 14899 17095"/>
    </justification>
  </clause>

  <clause id="17127">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      v5 = x
    ]]></literal>
    <justification jstring="[para(17095(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="17095 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17128">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(17095(a,1),45(a,2))].">
      <j1 rule="para" parents="17095 45"/>
    </justification>
  </clause>

  <clause id="17129">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * w) = (K(x,K(y,z)) \ u) * w
    ]]></literal>
    <justification jstring="[para(17095(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="17095 474"/>
    </justification>
  </clause>

  <clause id="17130">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) / w = K(x,K(y,z)) * (u / w)
    ]]></literal>
    <justification jstring="[para(17095(a,1),544(a,1,2))].">
      <j1 rule="para" parents="17095 544"/>
    </justification>
  </clause>

  <clause id="17131">
    <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(17095(a,1),477(a,2,1))].">
      <j1 rule="para" parents="17095 477"/>
    </justification>
  </clause>

  <clause id="17132">
    <literal><![CDATA[
      L(x,y,K(z,u) * w) = L(x,y,w * K(z,u))
    ]]></literal>
    <justification jstring="[para(17095(a,1),14929(a,1,1))].">
      <j1 rule="para" parents="17095 14929"/>
    </justification>
  </clause>

  <clause id="17133">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) = T(x,w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12253,a,17107,a)].">
      <j1 rule="hyper" parents="12253 17107"/>
    </justification>
  </clause>

  <clause id="17135">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(17107(a,1),44(a,2))].">
      <j1 rule="para" parents="17107 44"/>
    </justification>
  </clause>

  <clause id="17136">
    <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(17107(a,1),15026(a,1,2,1,2))].">
      <j1 rule="para" parents="17107 15026"/>
    </justification>
  </clause>

  <clause id="17138">
    <literal><![CDATA[
      T(K(x,y),a(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14857,a,17088,a)].">
      <j1 rule="hyper" parents="14857 17088"/>
    </justification>
  </clause>

  <clause id="17139">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10806,a,17088,a)].">
      <j1 rule="hyper" parents="10806 17088"/>
    </justification>
  </clause>

  <clause id="17141">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K(z \ (K(y,x) * u),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,6600,a(flip),b,17088,a),flip(a)].">
      <j1 rule="hyper" parents="58 6600 17088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17142">
    <literal><![CDATA[
      L(x * K(y,z),u,K(w,x)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(17088(a,1),14900(a,2,2))].">
      <j1 rule="para" parents="17088 14900"/>
    </justification>
  </clause>

  <clause id="17145">
    <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(16338,a,17100,a)].">
      <j1 rule="hyper" parents="16338 17100"/>
    </justification>
  </clause>

  <clause id="17148">
    <literal><![CDATA[
      T(x,T((K(y,z) * u) \ w,v5)) = T(x,T(u \ (K(y,z) \ w),v5))
    ]]></literal>
    <justification jstring="[para(564(a,1),17102(a,1,2))].">
      <j1 rule="para" parents="564 17102"/>
    </justification>
  </clause>

  <clause id="17149">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) = T(x,u \ (K(z,y) * w))
    ]]></literal>
    <justification jstring="[para(5115(a,1),17102(a,1,2))].">
      <j1 rule="para" parents="5115 17102"/>
    </justification>
  </clause>

  <clause id="17150">
    <literal><![CDATA[
      T(x,L(y,z,T(u,w))) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(6845(a,1),17102(a,1,2))].">
      <j1 rule="para" parents="6845 17102"/>
    </justification>
  </clause>

  <clause id="17151">
    <literal><![CDATA[
      ((x * y) * ((K(y,x) * z) * u)) / T((y * x) * z,u) = L(u,z,x * y)
    ]]></literal>
    <justification jstring="[para(17102(a,1),14961(a,1,2))].">
      <j1 rule="para" parents="17102 14961"/>
    </justification>
  </clause>

  <clause id="17152">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w) \ z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8321,a,17109,a)].">
      <j1 rule="hyper" parents="8321 17109"/>
    </justification>
  </clause>

  <clause id="17153">
    <literal><![CDATA[
      T(x,K(y,z \ L(z,u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(8192,a,17109,a)].">
      <j1 rule="hyper" parents="8192 17109"/>
    </justification>
  </clause>

  <clause id="17154">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      T(y,K(z,L(u,w,v5) \ u)) = x
    ]]></literal>
    <justification jstring="[para(17109(a,1),7826(a,1))].">
      <j1 rule="para" parents="17109 7826"/>
    </justification>
  </clause>

  <clause id="17157">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ w) * y) = K(x,y * (w / L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15173,a(flip),b,17117,a),flip(a)].">
      <j1 rule="hyper" parents="58 15173 17117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17158">
    <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(17117(a,1),7157(a,1,2))].">
      <j1 rule="para" parents="17117 7157"/>
    </justification>
  </clause>

  <clause id="17159">
    <literal><![CDATA[
      T(K(x,y),a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(17117(a,1),7956(a,1,1))].">
      <j1 rule="para" parents="17117 7956"/>
    </justification>
  </clause>

  <clause id="17160">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(17117(a,1),7981(a,1))].">
      <j1 rule="para" parents="17117 7981"/>
    </justification>
  </clause>

  <clause id="17161">
    <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(17117(a,1),12199(a,1))].">
      <j1 rule="para" parents="17117 12199"/>
    </justification>
  </clause>

  <clause id="17162">
    <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(17117(a,1),12260(a,1))].">
      <j1 rule="para" parents="17117 12260"/>
    </justification>
  </clause>

  <clause id="17163">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(14288(a,1),17117(a,1,2))].">
      <j1 rule="para" parents="14288 17117"/>
    </justification>
  </clause>

  <clause id="17165">
    <literal><![CDATA[
      T(a(x,y,z),K(u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(49,a,17138,a)].">
      <j1 rule="hyper" parents="49 17138"/>
    </justification>
  </clause>

  <clause id="17166">
    <literal><![CDATA[
      T(K(x,y) * z,a(z,u,w)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(17138(a,1),14445(a,2,1))].">
      <j1 rule="para" parents="17138 14445"/>
    </justification>
  </clause>

  <clause id="17168">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(6845(a,1),17139(a,1,2))].">
      <j1 rule="para" parents="6845 17139"/>
    </justification>
  </clause>

  <clause id="17169">
    <literal><![CDATA[
      K(x,L(y,z,u / w)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[para(12707(a,1),17139(a,1,2))].">
      <j1 rule="para" parents="12707 17139"/>
    </justification>
  </clause>

  <clause id="17170">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,y / (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(14850(a,1),17139(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14850 17139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17171">
    <literal><![CDATA[
      K(x,T(y,z \ L(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8321,a,17153,a)].">
      <j1 rule="hyper" parents="8321 17153"/>
    </justification>
  </clause>

  <clause id="17172">
    <literal><![CDATA[
      L(x,y,(y * x) \ z) = L(x,y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11188,a(flip),b,17101,a),flip(a)].">
      <j1 rule="hyper" parents="58 11188 17101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17173">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(6845(a,1),17127(a,1)),flip(b)].">
      <j1 rule="para" parents="6845 17127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17174">
    <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(12707(a,1),17127(a,1)),flip(b)].">
      <j1 rule="para" parents="12707 17127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17175">
    <literal><![CDATA[
      T(x,T(y,a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(7413(a,1),17135(a,1))].">
      <j1 rule="para" parents="7413 17135"/>
    </justification>
  </clause>

  <clause id="17176">
    <literal><![CDATA[
      K(x,K(y,z)) * L(x,u,w) = L(T(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(17064(a,1),4803(a,1,1))].">
      <j1 rule="para" parents="17064 4803"/>
    </justification>
  </clause>

  <clause id="17178">
    <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(17077(a,1),284(a,1,2))].">
      <j1 rule="para" parents="17077 284"/>
    </justification>
  </clause>

  <clause id="17179">
    <literal><![CDATA[
      T(x,K(y,(z \ u) \ w)) = T(x,K(y,u \ (z * w)))
    ]]></literal>
    <justification jstring="[para(490(a,1),17077(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="490 17077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17181">
    <literal><![CDATA[
      K(x,K(y,z \ (u * (w \ z)))) = K(x,K(y,u / w))
    ]]></literal>
    <justification jstring="[hyper(15543,a,17081,a)].">
      <j1 rule="hyper" parents="15543 17081"/>
    </justification>
  </clause>

  <clause id="17188">
    <literal><![CDATA[
      L(K(x,y),z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(17096(a,2),127(a,1)),flip(b)].">
      <j1 rule="para" parents="17096 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17189">
    <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,14050,a(flip),b,17152,a)].">
      <j1 rule="hyper" parents="58 14050 17152"/>
    </justification>
  </clause>

  <clause id="17190">
    <literal><![CDATA[
      K(x,T(y \ R(z,u,w),z)) = K(x,R(z,u,w) / y)
    ]]></literal>
    <justification jstring="[hyper(14689,a,17163,a),flip(a)].">
      <j1 rule="hyper" parents="14689 17163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17191">
    <literal><![CDATA[
      K(x,T(y * (L(y,z,u) \ w),y)) = K(x,(y * w) / L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8238,a,17163,a),flip(a)].">
      <j1 rule="hyper" parents="8238 17163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17193">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ w)) = K(x,T(y,u \ (z \ w)))
    ]]></literal>
    <justification jstring="[para(298(a,1),17163(a,1,2,2))].">
      <j1 rule="para" parents="298 17163"/>
    </justification>
  </clause>

  <clause id="17195">
    <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(17163(a,1),12262(a,1))].">
      <j1 rule="para" parents="17163 12262"/>
    </justification>
  </clause>

  <clause id="17196">
    <literal><![CDATA[
      K(x,T(y,(z / u) / w)) = K(x,T(y,z / (w * u)))
    ]]></literal>
    <justification jstring="[para(14687(a,1),17163(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14687 17163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17197">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) = K(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(12260,a,17171,a)].">
      <j1 rule="hyper" parents="12260 17171"/>
    </justification>
  </clause>

  <clause id="17198">
    <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(17171(a,1),12259(a,1))].">
      <j1 rule="para" parents="17171 12259"/>
    </justification>
  </clause>

  <clause id="17199">
    <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,14990,a(flip),b,17150,a),flip(a)].">
      <j1 rule="hyper" parents="58 14990 17150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17200">
    <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,14397,a(flip),b,17150,a),flip(a)].">
      <j1 rule="hyper" parents="58 14397 17150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17201">
    <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(7874(a,1),17159(a,1))].">
      <j1 rule="para" parents="7874 17159"/>
    </justification>
  </clause>

  <clause id="17202">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(14288(a,1),17160(a,1,2))].">
      <j1 rule="para" parents="14288 17160"/>
    </justification>
  </clause>

  <clause id="17203">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(14849(a,2),17160(a,1,2))].">
      <j1 rule="para" parents="14849 17160"/>
    </justification>
  </clause>

  <clause id="17204">
    <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,13425,a(flip),b,17168,a),flip(a)].">
      <j1 rule="hyper" parents="58 13425 17168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17205">
    <literal><![CDATA[
      K(x,L(y,z,u * w)) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[para(12529(a,1),17168(a,1,2))].">
      <j1 rule="para" parents="12529 17168"/>
    </justification>
  </clause>

  <clause id="17207">
    <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(14878(a,1),17175(a,1,2))].">
      <j1 rule="para" parents="14878 17175"/>
    </justification>
  </clause>

  <clause id="17208">
    <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(6114(a,2),17188(a,1))].">
      <j1 rule="para" parents="6114 17188"/>
    </justification>
  </clause>

  <clause id="17209">
    <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(6805(a,1),17203(a,1,2))].">
      <j1 rule="para" parents="6805 17203"/>
    </justification>
  </clause>

  <clause id="17210">
    <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(6845(a,1),17203(a,1,2))].">
      <j1 rule="para" parents="6845 17203"/>
    </justification>
  </clause>

  <clause id="17211">
    <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(12707(a,1),17203(a,1,2))].">
      <j1 rule="para" parents="12707 17203"/>
    </justification>
  </clause>

  <clause id="17212">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(17067(a,2),4725(a,1))].">
      <j1 rule="para" parents="17067 4725"/>
    </justification>
  </clause>

  <clause id="17214">
    <literal><![CDATA[
      T(x * K(y,z),a(u,w,x)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(17142(a,1),14870(a,1,1))].">
      <j1 rule="para" parents="17142 14870"/>
    </justification>
  </clause>

  <clause id="17215">
    <literal><![CDATA[
      L(K(x,y) * z,u,K(w,z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(14905,a,17166,a)].">
      <j1 rule="hyper" parents="14905 17166"/>
    </justification>
  </clause>

  <clause id="17216">
    <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(8064(a,1),17173(a,1,3))].">
      <j1 rule="para" parents="8064 17173"/>
    </justification>
  </clause>

  <clause id="17217">
    <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(17214(a,1),13870(a,2,2))].">
      <j1 rule="para" parents="17214 13870"/>
    </justification>
  </clause>

  <clause id="17218">
    <literal><![CDATA[
      (K(x,y) * z) / a(u,w,z) = a(u,w,z) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(116,a,17215,a(flip),b,14882,a),flip(a)].">
      <j1 rule="hyper" parents="116 17215 14882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17219">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,x)) = T(x,a(z,u,w)) \ y
    ]]></literal>
    <justification jstring="[hyper(13379,a,17103,a),flip(a)].">
      <j1 rule="hyper" parents="13379 17103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17220">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = w * a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,14197,a,b,17103,a),flip(a)].">
      <j1 rule="hyper" parents="320 14197 17103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17221">
    <literal><![CDATA[
      x \ (y * a(z,u,K(w,v5))) = a(z,u,K(w,v5)) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,752,a,b,17103,a)].">
      <j1 rule="hyper" parents="320 752 17103"/>
    </justification>
  </clause>

  <clause id="17222">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * x) = w * T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14208,a(flip),b,17103,a),flip(a)].">
      <j1 rule="hyper" parents="320 14208 17103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17223">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = w * a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14197,a(flip),b,17103,a),flip(a)].">
      <j1 rule="hyper" parents="320 14197 17103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17224">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * v5) = w * (v5 * a(x,y,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,347,a(flip),b,17103,a),flip(a)].">
      <j1 rule="hyper" parents="320 347 17103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17226">
    <literal><![CDATA[
      K(x,a(y,z,u)) * w = w * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14191(a,1),17103(a,1,1))].">
      <j1 rule="para" parents="14191 17103"/>
    </justification>
  </clause>

  <clause id="17227">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * v5 = a(y,z,K(u,w)) * (x * v5)
    ]]></literal>
    <justification jstring="[para(17103(a,1),14201(a,1,1))].">
      <j1 rule="para" parents="17103 14201"/>
    </justification>
  </clause>

  <clause id="17228">
    <literal><![CDATA[
      L(x,y,z * a(u,w,K(v5,v6))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(17103(a,1),15464(a,1,3))].">
      <j1 rule="para" parents="17103 15464"/>
    </justification>
  </clause>

  <clause id="17229">
    <literal><![CDATA[
      L(x,y,z \ K(z,z \ u)) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,13410,a,b,17126,a),flip(a)].">
      <j1 rule="hyper" parents="58 13410 17126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17230">
    <literal><![CDATA[
      L(x,y,z * K(u,u \ w)) = L(x,y,K(u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,12657,a,b,17132,a)].">
      <j1 rule="hyper" parents="320 12657 17132"/>
    </justification>
  </clause>

  <clause id="17231">
    <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(17133(a,1),16270(a,1,2,1,2))].">
      <j1 rule="para" parents="17133 16270"/>
    </justification>
  </clause>

  <clause id="17232">
    <literal><![CDATA[
      K(x,L(y,z,(u \ 1) \ w)) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[hyper(14451,a,17169,a),flip(a)].">
      <j1 rule="hyper" parents="14451 17169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17233">
    <literal><![CDATA[
      K(x,L(y,z,u \ (w \ u))) = K(x,L(y,z,w \ 1))
    ]]></literal>
    <justification jstring="[hyper(14450,a,17169,a),flip(a)].">
      <j1 rule="hyper" parents="14450 17169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17234">
    <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(17169(a,1),14450(a,1))].">
      <j1 rule="para" parents="17169 14450"/>
    </justification>
  </clause>

  <clause id="17236">
    <literal><![CDATA[
      x / L(y,z,(y * z) \ x) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(17172(a,1),14070(a,1,2))].">
      <j1 rule="para" parents="17172 14070"/>
    </justification>
  </clause>

  <clause id="17237">
    <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(298(a,1),17202(a,1,2,2))].">
      <j1 rule="para" parents="298 17202"/>
    </justification>
  </clause>

  <clause id="17238">
    <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(14525(a,1),17212(a,1,2))].">
      <j1 rule="para" parents="14525 17212"/>
    </justification>
  </clause>

  <clause id="17239">
    <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,14435,a(flip),b,17220,a),flip(a)].">
      <j1 rule="hyper" parents="58 14435 17220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17240">
    <literal><![CDATA[
      (x * y) * a(z,u,K(x,w)) = T(x,a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,14284,a(flip),b,17220,a),flip(a)].">
      <j1 rule="hyper" parents="58 14284 17220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17241">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w \ z) = w \ L(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,14874,a(flip),b,17223,a),flip(a)].">
      <j1 rule="hyper" parents="320 14874 17223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17242">
    <literal><![CDATA[
      (x / y) * a(x,z,K(u,w)) = T(x,a(w,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(13768,a,17226,a),flip(a)].">
      <j1 rule="hyper" parents="13768 17226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17243">
    <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(10766(a,2),17209(a,1))].">
      <j1 rule="para" parents="10766 17209"/>
    </justification>
  </clause>

  <clause id="17244">
    <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(4528(a,1),17210(a,1,2))].">
      <j1 rule="para" parents="4528 17210"/>
    </justification>
  </clause>

  <clause id="17245">
    <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(12529(a,1),17210(a,1,2))].">
      <j1 rule="para" parents="12529 17210"/>
    </justification>
  </clause>

  <clause id="17246">
    <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(14632(a,2),17236(a,1,2,3,1))].">
      <j1 rule="para" parents="14632 17236"/>
    </justification>
  </clause>

  <clause id="17247">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (w * K(y,K(x,z)))
    ]]></literal>
    <justification jstring="[hyper(15860,a,17068,a)].">
      <j1 rule="hyper" parents="15860 17068"/>
    </justification>
  </clause>

  <clause id="17248">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (w * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(15651,a,17068,a)].">
      <j1 rule="hyper" parents="15651 17068"/>
    </justification>
  </clause>

  <clause id="17251">
    <literal><![CDATA[
      x \ (y * K(z,K(u,w))) = K(z,K(u,w)) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,15604,a,b,17087,a),flip(a)].">
      <j1 rule="hyper" parents="320 15604 17087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17252">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,K(u,w)) = x \ (y * T(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(6086(a,1),17087(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6086 17087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17253">
    <literal><![CDATA[
      (x \ (y * z)) * K(y,K(u,w)) = x \ (T(y,K(u,w)) * z)
    ]]></literal>
    <justification jstring="[para(15614(a,1),17087(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15614 17087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17254">
    <literal><![CDATA[
      x \ T(K(y,K(z,u)) * w,v5) = (x \ T(w,v5)) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(15666(a,2),17087(a,1,2))].">
      <j1 rule="para" parents="15666 17087"/>
    </justification>
  </clause>

  <clause id="17255">
    <literal><![CDATA[
      x \ (y * (z * K(u,K(w,v5)))) = (x \ (y * z)) * K(u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(17068(a,1),17087(a,1,2))].">
      <j1 rule="para" parents="17068 17087"/>
    </justification>
  </clause>

  <clause id="17256">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,T(w,z)) = K(x,y) * (K(u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7274,a(flip),b,17098,a),flip(a)].">
      <j1 rule="hyper" parents="320 7274 17098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17257">
    <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(17098(a,1),15(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="17098 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17262">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,y) * u) = T(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[para(7513(a,1),17111(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7513 17111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17263">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = K(y,K(z,u)) * (x * w)
    ]]></literal>
    <justification jstring="[para(15604(a,1),17111(a,1,1))].">
      <j1 rule="para" parents="15604 17111"/>
    </justification>
  </clause>

  <clause id="17264">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ (K(x,K(y,z)) \ w) = u \ w
    ]]></literal>
    <justification jstring="[para(5(a,1),17124(a,2,2))].">
      <j1 rule="para" parents="5 17124"/>
    </justification>
  </clause>

  <clause id="17265">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ w = u \ (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(7799(a,1),17124(a,1,1))].">
      <j1 rule="para" parents="7799 17124"/>
    </justification>
  </clause>

  <clause id="17266">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) / w = K(x,K(y,z)) * (u / w)
    ]]></literal>
    <justification jstring="[para(7799(a,2),17130(a,1,1))].">
      <j1 rule="para" parents="7799 17130"/>
    </justification>
  </clause>

  <clause id="17267">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K(x \ (K(z,y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(16002,a,17141,a)].">
      <j1 rule="hyper" parents="16002 17141"/>
    </justification>
  </clause>

  <clause id="17269">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,u / (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(15995,a,17170,a)].">
      <j1 rule="hyper" parents="15995 17170"/>
    </justification>
  </clause>

  <clause id="17270">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,y * (w \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,16062,a(flip),b,17170,a),flip(a)].">
      <j1 rule="hyper" parents="320 16062 17170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17271">
    <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,17176,a(flip),b,7800,a),flip(a)].">
      <j1 rule="hyper" parents="116 17176 7800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17272">
    <literal><![CDATA[
      T(T(x,(y \ z) \ u),K(w,z \ (y * u))) = T(x,T((y \ z) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(7833,a,17179,a),flip(a)].">
      <j1 rule="hyper" parents="7833 17179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17273">
    <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(17179(a,1),8192(a,1))].">
      <j1 rule="para" parents="17179 8192"/>
    </justification>
  </clause>

  <clause id="17274">
    <literal><![CDATA[
      K(x,K(y,z \ (u * (w \ z)))) = K(x,K(y,w \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,15530,a(flip),b,17181,a),flip(a)].">
      <j1 rule="hyper" parents="320 15530 17181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17275">
    <literal><![CDATA[
      K(x,T(y,z / (u * w))) = K(x,T(y,u \ (z / w)))
    ]]></literal>
    <justification jstring="[hyper(15713,a,17196,a),flip(a)].">
      <j1 rule="hyper" parents="15713 17196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17276">
    <literal><![CDATA[
      T(x \ 1,a(y,z,u)) = T(x,a(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(13381,a,17219,a)].">
      <j1 rule="hyper" parents="13381 17219"/>
    </justification>
  </clause>

  <clause id="17277">
    <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(17276(a,2),13685(a,1,2))].">
      <j1 rule="para" parents="17276 13685"/>
    </justification>
  </clause>

  <clause id="17278">
    <literal><![CDATA[
      L(x,y,K(z,u) * (w * (z \ u))) = L(x,y,w * (u / z))
    ]]></literal>
    <justification jstring="[para(6071(a,1),17230(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6071 17230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17279">
    <literal><![CDATA[
      L(x,y,K(z,u) * (w / (u / z))) = L(x,y,w / (z \ u))
    ]]></literal>
    <justification jstring="[para(6369(a,1),17230(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6369 17230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17280">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,u * y)) = K(x,u \ ((u / (y \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14394,a(flip),b,17232,a),flip(a)].">
      <j1 rule="hyper" parents="58 14394 17232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17281">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ w)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,14422,a,b,17233,a)].">
      <j1 rule="hyper" parents="58 14422 17233"/>
    </justification>
  </clause>

  <clause id="17282">
    <literal><![CDATA[
      (x \ y) * K(z,L(u,y,x \ 1)) = ((x \ y) / y) * (y * K(z,u))
    ]]></literal>
    <justification jstring="[para(17233(a,1),11178(a,1,2))].">
      <j1 rule="para" parents="17233 11178"/>
    </justification>
  </clause>

  <clause id="17283">
    <literal><![CDATA[
      (x / y) * a(x,z,K(u,w)) = L(x,z,K(u,w)) / y
    ]]></literal>
    <justification jstring="[para(14849(a,2),17242(a,2,1))].">
      <j1 rule="para" parents="14849 17242"/>
    </justification>
  </clause>

  <clause id="17284">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(15699(a,2),17247(a,2,2))].">
      <j1 rule="para" parents="15699 17247"/>
    </justification>
  </clause>

  <clause id="17285">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * w = u * (w * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17111,a,b,17248,a)].">
      <j1 rule="hyper" parents="58 17111 17248"/>
    </justification>
  </clause>

  <clause id="17286">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * (w \ x)) = u * (w \ T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(12316(a,1),17248(a,2,2))].">
      <j1 rule="para" parents="12316 17248"/>
    </justification>
  </clause>

  <clause id="17287">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * (w * v5)) = u * (w * (v5 * K(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(17068(a,1),17248(a,2,2))].">
      <j1 rule="para" parents="17068 17248"/>
    </justification>
  </clause>

  <clause id="17288">
    <literal><![CDATA[
      x \ (K(y,K(z,u)) * w) = K(y,K(z,u)) * (x \ w)
    ]]></literal>
    <justification jstring="[para(15604(a,2),17251(a,1,2))].">
      <j1 rule="para" parents="15604 17251"/>
    </justification>
  </clause>

  <clause id="17289">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ (K(x,K(y,z)) * w)) = u \ w
    ]]></literal>
    <justification jstring="[para(15766(a,1),17251(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15766 17251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17290">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ (T(x,K(y,z)) \ w)) = u \ (x \ w)
    ]]></literal>
    <justification jstring="[para(15667(a,1),17251(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15667 17251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17291">
    <literal><![CDATA[
      x \ T(K(y,K(z,u)) * w,v5) = K(y,K(z,u)) * (x \ T(w,v5))
    ]]></literal>
    <justification jstring="[para(15666(a,2),17251(a,1,2))].">
      <j1 rule="para" parents="15666 17251"/>
    </justification>
  </clause>

  <clause id="17292">
    <literal><![CDATA[
      x \ T(y * K(z,K(u,w)),v5) = K(z,K(u,w)) * (x \ T(y,v5))
    ]]></literal>
    <justification jstring="[para(15874(a,2),17251(a,1,2))].">
      <j1 rule="para" parents="15874 17251"/>
    </justification>
  </clause>

  <clause id="17293">
    <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(17262(a,1),16101(a,1,2,2))].">
      <j1 rule="para" parents="17262 16101"/>
    </justification>
  </clause>

  <clause id="17294">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = x * (w * K(y,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,17248,a(flip),b,17263,a),flip(a)].">
      <j1 rule="hyper" parents="320 17248 17263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17295">
    <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(17266(a,2),7805(a,1))].">
      <j1 rule="para" parents="17266 7805"/>
    </justification>
  </clause>

  <clause id="17296">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K(x \ (u * K(z,y)),w)
    ]]></literal>
    <justification jstring="[hyper(320,a,15970,a(flip),b,17267,a),flip(a)].">
      <j1 rule="hyper" parents="320 15970 17267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17297">
    <literal><![CDATA[
      K(L((x \ y) * K(z,u),K(u,z),x),w) = K(x \ (K(z,u) * y),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15641,a,b,17267,a)].">
      <j1 rule="hyper" parents="58 15641 17267"/>
    </justification>
  </clause>

  <clause id="17298">
    <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(17267(a,2),16050(a,1))].">
      <j1 rule="para" parents="17267 16050"/>
    </justification>
  </clause>

  <clause id="17299">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(320,a,16062,a(flip),b,17269,a),flip(a)].">
      <j1 rule="hyper" parents="320 16062 17269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17300">
    <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(17269(a,2),16160(a,1))].">
      <j1 rule="para" parents="17269 16160"/>
    </justification>
  </clause>

  <clause id="17301">
    <literal><![CDATA[
      T(x,(y * K(z,u)) / w) = T(x,y * (w \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(118,a,17270,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 17270 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17302">
    <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,10875,a(flip),b,17270,a),flip(a)].">
      <j1 rule="hyper" parents="58 10875 17270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17303">
    <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,8830,a(flip),b,17270,a),flip(a)].">
      <j1 rule="hyper" parents="58 8830 17270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17304">
    <literal><![CDATA[
      K(x,(y / z) * (u \ K(w,z))) = K(x,(y / T(z,w)) / u)
    ]]></literal>
    <justification jstring="[para(6293(a,1),17270(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6293 17270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17305">
    <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(17270(a,1),15995(a,1))].">
      <j1 rule="para" parents="17270 15995"/>
    </justification>
  </clause>

  <clause id="17306">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ (w * u))) = K(x,K(y,z \ w))
    ]]></literal>
    <justification jstring="[para(4(a,1),17274(a,1,2,2,2,2))].">
      <j1 rule="para" parents="4 17274"/>
    </justification>
  </clause>

  <clause id="17307">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ w)) = K(x,T(y,z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(15713,a,17275,a)].">
      <j1 rule="hyper" parents="15713 17275"/>
    </justification>
  </clause>

  <clause id="17309">
    <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,13238,a(flip),b,17281,a),flip(a)].">
      <j1 rule="hyper" parents="58 13238 17281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17310">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,((u / (z * u)) * y) \ u)
    ]]></literal>
    <justification jstring="[para(14067(a,1),17281(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14067 17281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17311">
    <literal><![CDATA[
      ((x * y) \ y) * ((((x * y) \ y) \ z) * K(u,w)) = z * K(u,L(w,z,x \ 1))
    ]]></literal>
    <justification jstring="[para(17281(a,1),14395(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17281 14395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17313">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * w) = u * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(7805,a,17284,a)].">
      <j1 rule="hyper" parents="7805 17284"/>
    </justification>
  </clause>

  <clause id="17315">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = x * (K(y,K(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17263,a,b,17284,a)].">
      <j1 rule="hyper" parents="58 17263 17284"/>
    </justification>
  </clause>

  <clause id="17317">
    <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(17284(a,1),16101(a,1,2,2))].">
      <j1 rule="para" parents="17284 16101"/>
    </justification>
  </clause>

  <clause id="17318">
    <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(17285(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="17285 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17319">
    <literal><![CDATA[
      (K(x,y) * z) * (u * K(x,K(y,w))) = (K(x,T(y,w)) * z) * u
    ]]></literal>
    <justification jstring="[para(8491(a,1),17285(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8491 17285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17320">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ w = K(x,K(y,z)) * (u \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17265,a,b,17288,a)].">
      <j1 rule="hyper" parents="58 17265 17288"/>
    </justification>
  </clause>

  <clause id="17321">
    <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(17294(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17294 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17322">
    <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(17294(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="17294 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17323">
    <literal><![CDATA[
      K((x \ 1) \ (y * K(z,u)),w) = K((x \ K(u,z)) \ y,w)
    ]]></literal>
    <justification jstring="[para(13747(a,1),17296(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13747 17296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17324">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / w) = T(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(118,a,17299,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 17299 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17325">
    <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,16523,a(flip),b,17299,a),flip(a)].">
      <j1 rule="hyper" parents="58 16523 17299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17326">
    <literal><![CDATA[
      K(x,(y * z) * (u \ K(y,w))) = K(x,(T(y,w) * z) / u)
    ]]></literal>
    <justification jstring="[para(4740(a,1),17299(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4740 17299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17327">
    <literal><![CDATA[
      K(x,(y \ z) * (u \ K(w,y))) = K(x,(T(y,w) \ z) / u)
    ]]></literal>
    <justification jstring="[para(5093(a,1),17299(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5093 17299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17328">
    <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,16621,a(flip),b,17301,a),flip(a)].">
      <j1 rule="hyper" parents="58 16621 17301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17329">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ w)) = K(x,K(y,z \ (w / u)))
    ]]></literal>
    <justification jstring="[para(7(a,1),17306(a,1,2,2,2))].">
      <j1 rule="para" parents="7 17306"/>
    </justification>
  </clause>

  <clause id="17330">
    <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(15782,a,17307,a),flip(a)].">
      <j1 rule="hyper" parents="15782 17307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17331">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ w))) = K(x,T(y,u \ (w / z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17193,a(flip),b,17307,a)].">
      <j1 rule="hyper" parents="58 17193 17307"/>
    </justification>
  </clause>

  <clause id="17332">
    <literal><![CDATA[
      R(x,K(y,K(z,u)),w) = x
    ]]></literal>
    <justification jstring="[hyper(3450,a,17315,a)].">
      <j1 rule="hyper" parents="3450 17315"/>
    </justification>
  </clause>

  <clause id="17333">
    <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,17315,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 17315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17334">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) * v5 = (x * y) * (K(z,K(u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(17068(a,1),17315(a,1,1))].">
      <j1 rule="para" parents="17068 17315"/>
    </justification>
  </clause>

  <clause id="17335">
    <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(17332(a,1),511(a,1,1,1,2))].">
      <j1 rule="para" parents="17332 511"/>
    </justification>
  </clause>

  <clause id="17336">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = K(x,K(y,z)) \ (u \ w)
    ]]></literal>
    <justification jstring="[hyper(116,a,155,a(flip),b,17320,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 155 17320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17337">
    <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(17320(a,2),15617(a,1))].">
      <j1 rule="para" parents="17320 15617"/>
    </justification>
  </clause>

  <clause id="17338">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) \ v5 = K(y,K(z,u)) * ((x * w) \ v5)
    ]]></literal>
    <justification jstring="[para(17284(a,1),17320(a,1,1))].">
      <j1 rule="para" parents="17284 17320"/>
    </justification>
  </clause>

  <clause id="17339">
    <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,16562,a(flip),b,17324,a)].">
      <j1 rule="hyper" parents="58 16562 17324"/>
    </justification>
  </clause>

  <clause id="17340">
    <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(17324(a,1),15399(a,1,2,1,2))].">
      <j1 rule="para" parents="17324 15399"/>
    </justification>
  </clause>

  <clause id="17341">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ w)) = K(x,K(y,z \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,16401,a(flip),b,17329,a),flip(a)].">
      <j1 rule="hyper" parents="320 16401 17329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17342">
    <literal><![CDATA[
      K(x,T(y,(z / u) \ w)) = K(x,T(y,u \ (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(320,a,8211,a,b,17331,a)].">
      <j1 rule="hyper" parents="320 8211 17331"/>
    </justification>
  </clause>

  <clause id="17343">
    <literal><![CDATA[
      K(x,T(y,(z / u) \ (w \ z))) = K(x,T(y,w \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,16365,a(flip),b,17331,a),flip(a)].">
      <j1 rule="hyper" parents="320 16365 17331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17344">
    <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),17331(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="17 17331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17345">
    <literal><![CDATA[
      x / (K(y,K(z,u)) * w) = K(y,K(z,u)) * (x / w)
    ]]></literal>
    <justification jstring="[hyper(15770,a,17333,a),flip(a)].">
      <j1 rule="hyper" parents="15770 17333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17346">
    <literal><![CDATA[
      x / (K(y,K(z,u)) * w) = K(y,K(z,u)) \ (x / w)
    ]]></literal>
    <justification jstring="[hyper(116,a,17333,a(flip),b,15604,a),flip(a)].">
      <j1 rule="hyper" parents="116 17333 15604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17347">
    <literal><![CDATA[
      K(x,(K(y,K(z,u)) \ w) \ v5) = K(x,w \ v5)
    ]]></literal>
    <justification jstring="[para(17336(a,2),15945(a,1,2))].">
      <j1 rule="para" parents="17336 15945"/>
    </justification>
  </clause>

  <clause id="17348">
    <literal><![CDATA[
      K(x,y \ (K(z,K(u,w)) \ v5)) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[para(17264(a,1),17347(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17264 17347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17349">
    <literal><![CDATA[
      K(x,y \ (T(z,K(u,w)) * v5)) = K(x,y \ (z * v5))
    ]]></literal>
    <justification jstring="[para(4741(a,1),17348(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4741 17348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17350">
    <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(15882(a,1),17348(a,1,2,2))].">
      <j1 rule="para" parents="15882 17348"/>
    </justification>
  </clause>

  <clause id="17351">
    <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(17341(a,1),8356(a,1,1))].">
      <j1 rule="para" parents="17341 8356"/>
    </justification>
  </clause>

  <clause id="17352">
    <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(17341(a,1),13060(a,1,1))].">
      <j1 rule="para" parents="17341 13060"/>
    </justification>
  </clause>

  <clause id="17353">
    <literal><![CDATA[
      K(x,T(y,z \ ((u \ w) \ w))) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,17342,a(flip),b,17343,a)].">
      <j1 rule="hyper" parents="58 17342 17343"/>
    </justification>
  </clause>

  <clause id="17354">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ (z * w)))) = K(x,T(y,u \ w))
    ]]></literal>
    <justification jstring="[para(6(a,1),17343(a,1,2,2,1))].">
      <j1 rule="para" parents="6 17343"/>
    </justification>
  </clause>

  <clause id="17355">
    <literal><![CDATA[
      K(x,K(y,z)) * (u / (w \ x)) = u / (w \ T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(15669(a,1),17345(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15669 17345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17356">
    <literal><![CDATA[
      x / T(y * K(z,K(u,w)),v5) = K(z,K(u,w)) * (x / T(y,v5))
    ]]></literal>
    <justification jstring="[para(15890(a,2),17345(a,1,2))].">
      <j1 rule="para" parents="15890 17345"/>
    </justification>
  </clause>

  <clause id="17357">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u / (K(x,K(y,z)) \ w)) = u / w
    ]]></literal>
    <justification jstring="[para(5(a,1),17346(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 17346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17358">
    <literal><![CDATA[
      K(x,y \ (T(z,T(u,w)) * v5)) = K(x,y \ (T(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(7413(a,1),17349(a,1,2,2,1))].">
      <j1 rule="para" parents="7413 17349"/>
    </justification>
  </clause>

  <clause id="17359">
    <literal><![CDATA[
      K(x,T(y,z \ (K(u,w) * v5))) = K(x,T(y,z \ v5))
    ]]></literal>
    <justification jstring="[hyper(16339,a,17354,a)].">
      <j1 rule="hyper" parents="16339 17354"/>
    </justification>
  </clause>

  <clause id="17360">
    <literal><![CDATA[
      K(x,T(y,z \ (T(u,w) \ v5))) = K(x,T(y,z \ (u \ v5)))
    ]]></literal>
    <justification jstring="[para(5042(a,1),17359(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5042 17359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17361">
    <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(14195(a,2),17106(a,1,1))].">
      <j1 rule="para" parents="14195 17106"/>
    </justification>
  </clause>

  <clause id="17362">
    <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(17223(a,1),17106(a,1))].">
      <j1 rule="para" parents="17223 17106"/>
    </justification>
  </clause>

  <clause id="17363">
    <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(14762(a,1),17201(a,1))].">
      <j1 rule="para" parents="14762 17201"/>
    </justification>
  </clause>

  <clause id="17365">
    <literal><![CDATA[
      K(x,L(y,z,u) * T(w,y)) = K(x,w * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(13294(a,1),17189(a,1,2))].">
      <j1 rule="para" parents="13294 17189"/>
    </justification>
  </clause>

  <clause id="17366">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) * T(y,z)) = K(x,y * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(13158,a,17365,a)].">
      <j1 rule="hyper" parents="13158 17365"/>
    </justification>
  </clause>

  <clause id="17368">
    <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(17197(a,2),15440(a,1))].">
      <j1 rule="para" parents="17197 15440"/>
    </justification>
  </clause>

  <clause id="17369">
    <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(14734(a,1),17208(a,1))].">
      <j1 rule="para" parents="14734 17208"/>
    </justification>
  </clause>

  <clause id="17370">
    <literal><![CDATA[
      a(x,y,z) \ (K(u,w) * z) = K(u,w) * (z / a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13976,a(flip),b,17218,a),flip(a)].">
      <j1 rule="hyper" parents="58 13976 17218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17371">
    <literal><![CDATA[
      x \ (a(y,z,K(u,w)) * v5) = a(y,z,K(u,w)) * (x \ v5)
    ]]></literal>
    <justification jstring="[para(17103(a,2),17221(a,1,2))].">
      <j1 rule="para" parents="17103 17221"/>
    </justification>
  </clause>

  <clause id="17372">
    <literal><![CDATA[
      x * (y * a(z,u,K(x,w))) = L(x,u,K(w,z)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,14883,a(flip),b,17224,a),flip(a)].">
      <j1 rule="hyper" parents="58 14883 17224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17373">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * v5) = w * (a(x,y,K(z,u)) * v5)
    ]]></literal>
    <justification jstring="[para(17103(a,2),17224(a,2,2))].">
      <j1 rule="para" parents="17103 17224"/>
    </justification>
  </clause>

  <clause id="17374">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1) / u) = L(x,y,u \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13141,a(flip),b,17229,a),flip(a)].">
      <j1 rule="hyper" parents="58 13141 17229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17375">
    <literal><![CDATA[
      L(x,y,z \ K(u,z \ 1)) = L(x,y,z \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(17174,a,17374,a)].">
      <j1 rule="hyper" parents="17174 17374"/>
    </justification>
  </clause>

  <clause id="17376">
    <literal><![CDATA[
      L(x,y,z \ K(z,y)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,11160,a(flip),b,17375,a),flip(a)].">
      <j1 rule="hyper" parents="58 11160 17375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17377">
    <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(14175(a,1),17376(a,1,3))].">
      <j1 rule="para" parents="14175 17376"/>
    </justification>
  </clause>

  <clause id="17378">
    <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(14235(a,1),17239(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14235 17239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17379">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u \ (w * x)) = x \ (u \ (w * T(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(17252(a,1),15769(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17252 15769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17380">
    <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(17252(a,1),15993(a,1,2))].">
      <j1 rule="para" parents="17252 15993"/>
    </justification>
  </clause>

  <clause id="17381">
    <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(17253(a,1),16007(a,1,2,2))].">
      <j1 rule="para" parents="17253 16007"/>
    </justification>
  </clause>

  <clause id="17382">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * w) = K(z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[hyper(16322,a,17256,a)].">
      <j1 rule="hyper" parents="16322 17256"/>
    </justification>
  </clause>

  <clause id="17387">
    <literal><![CDATA[
      (K(x,y) * z) / (K(x,y) * (K(u,w) * z)) = K(w,u)
    ]]></literal>
    <justification jstring="[para(17382(a,1),5104(a,1,2))].">
      <j1 rule="para" parents="17382 5104"/>
    </justification>
  </clause>

  <clause id="17389">
    <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(17286(a,1),15971(a,1,1))].">
      <j1 rule="para" parents="17286 15971"/>
    </justification>
  </clause>

  <clause id="17390">
    <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(17323(a,1),14005(a,1))].">
      <j1 rule="para" parents="17323 14005"/>
    </justification>
  </clause>

  <clause id="17391">
    <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(17344(a,2),16369(a,1))].">
      <j1 rule="para" parents="17344 16369"/>
    </justification>
  </clause>

  <clause id="17392">
    <literal><![CDATA[
      K(x,y / (z \ T(u,K(w,v5)))) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[para(17355(a,1),15942(a,1,2))].">
      <j1 rule="para" parents="17355 15942"/>
    </justification>
  </clause>

  <clause id="17393">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * v5))) = K(x,y / (z \ (v5 * K(u,w))))
    ]]></literal>
    <justification jstring="[para(6308(a,1),17392(a,1,2,2,2))].">
      <j1 rule="para" parents="6308 17392"/>
    </justification>
  </clause>

  <clause id="17394">
    <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(14836(a,1),17392(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14836 17392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17395">
    <literal><![CDATA[
      K(x,(y * T(z,u)) \ (T(y,z) * w)) = K(x,(T(z,u) * y) \ (y * w))
    ]]></literal>
    <justification jstring="[para(11169(a,1),17358(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11169 17358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17396">
    <literal><![CDATA[
      a(x,y,z) \ (K(u,w) * z) = K(u,w) * (a(x,y,z) \ z)
    ]]></literal>
    <justification jstring="[para(14908(a,1),17370(a,2,2))].">
      <j1 rule="para" parents="14908 17370"/>
    </justification>
  </clause>

  <clause id="17397">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) \ v5 = a(u,y,K(z,x)) * (w \ v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,14432,a,b,17371,a)].">
      <j1 rule="hyper" parents="58 14432 17371"/>
    </justification>
  </clause>

  <clause id="17398">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * v5 = x * (a(y,z,K(u,w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,17227,a,b,17373,a)].">
      <j1 rule="hyper" parents="58 17227 17373"/>
    </justification>
  </clause>

  <clause id="17399">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) \ v5 = a(w,z,K(u,y)) * (x \ v5)
    ]]></literal>
    <justification jstring="[para(17103(a,1),17397(a,1,1))].">
      <j1 rule="para" parents="17103 17397"/>
    </justification>
  </clause>

  <clause id="17400">
    <literal><![CDATA[
      (x * (y * a(z,u,K(w,v5)))) \ v6 = a(v5,u,K(w,z)) * ((x * y) \ v6)
    ]]></literal>
    <justification jstring="[para(17224(a,1),17397(a,1,1))].">
      <j1 rule="para" parents="17224 17397"/>
    </justification>
  </clause>

  <clause id="17401">
    <literal><![CDATA[
      R(x,a(y,z,K(u,w)),v5) = x
    ]]></literal>
    <justification jstring="[hyper(3450,a,17398,a)].">
      <j1 rule="hyper" parents="3450 17398"/>
    </justification>
  </clause>

  <clause id="17402">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)),v5) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,17398,a)].">
      <j1 rule="hyper" parents="479 17398"/>
    </justification>
  </clause>

  <clause id="17403">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (((x * y) * K(z,u)) \ w) = (x * (y * K(z,u))) \ w
    ]]></literal>
    <justification jstring="[para(17401(a,1),758(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17401 758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17406">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) \ v5) = (x / v5) * a(y,z,K(u,w))
    ]]></literal>
    <justification jstring="[para(17402(a,1),498(a,1,2))].">
      <j1 rule="para" parents="17402 498"/>
    </justification>
  </clause>

  <clause id="17407">
    <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(17402(a,1),476(a,1,2,2,1))].">
      <j1 rule="para" parents="17402 476"/>
    </justification>
  </clause>

  <clause id="17408">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * v5) = (x / v5) * a(w,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14248(a,1),17406(a,1,2))].">
      <j1 rule="para" parents="14248 17406"/>
    </justification>
  </clause>

  <clause id="17409">
    <literal><![CDATA[
      (x / y) * a(z,u,K(y,w)) = x / L(y,u,K(z,w))
    ]]></literal>
    <justification jstring="[para(14862(a,1),17408(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14862 17408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17410">
    <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(16419(a,2),17238(a,1))].">
      <j1 rule="para" parents="16419 17238"/>
    </justification>
  </clause>

  <clause id="17411">
    <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(17389,a,15987,a),flip(a)].">
      <j1 rule="hyper" parents="17389 15987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17412">
    <literal><![CDATA[
      K(((x \ K(y,z)) \ 1) * u,w) = K(x * (u * K(z,y)),w)
    ]]></literal>
    <justification jstring="[hyper(17390,a,13795,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="17390 13795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17413">
    <literal><![CDATA[
      K((K(x,y) * z) * u,w) = K(z * (u * K(x,y)),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,13837,a(flip),b,17412,a)].">
      <j1 rule="hyper" parents="58 13837 17412"/>
    </justification>
  </clause>

  <clause id="17414">
    <literal><![CDATA[
      K((x \ y) * (z * K(u,x)),w) = K((T(x,u) \ y) * z,w)
    ]]></literal>
    <justification jstring="[para(5093(a,1),17413(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5093 17413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17415">
    <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(16337(a,1),17391(a,1))].">
      <j1 rule="para" parents="16337 17391"/>
    </justification>
  </clause>

  <clause id="17416">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) = v5 \ (x * v5)
    ]]></literal>
    <justification jstring="[para(17108(a,1),17136(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17108 17136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17417">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) = T(x,v5)
    ]]></literal>
    <justification jstring="[hyper(320,a,17,a,b,17416,a),flip(a)].">
      <j1 rule="hyper" parents="320 17 17416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17418">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(17416(a,2),288(a,1))].">
      <j1 rule="para" parents="17416 288"/>
    </justification>
  </clause>

  <clause id="17420">
    <literal><![CDATA[
      T(x,T(a(y,z,u),w) * v5) = T(x,a(y,z,u) * v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,15041,a(flip),b,17417,a)].">
      <j1 rule="hyper" parents="58 15041 17417"/>
    </justification>
  </clause>

  <clause id="17421">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w)) * v5) = T(x,v5)
    ]]></literal>
    <justification jstring="[para(13347(a,2),17417(a,1,2,1))].">
      <j1 rule="para" parents="13347 17417"/>
    </justification>
  </clause>

  <clause id="17422">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) = v5 / T(v5,w)
    ]]></literal>
    <justification jstring="[para(17421(a,1),4753(a,2,2))].">
      <j1 rule="para" parents="17421 4753"/>
    </justification>
  </clause>

  <clause id="17423">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) * v5) = T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(9879(a,1),17421(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9879 17421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17424">
    <literal><![CDATA[
      T(x,(y * z) * K(u,w)) = T(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(14363(a,1),17421(a,1,2))].">
      <j1 rule="para" parents="14363 17421"/>
    </justification>
  </clause>

  <clause id="17425">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) * v5) = T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(14431(a,1),17421(a,1,2))].">
      <j1 rule="para" parents="14431 17421"/>
    </justification>
  </clause>

  <clause id="17426">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) = K(w,v5)
    ]]></literal>
    <justification jstring="[hyper(320,a,4753,a,b,17422,a),flip(a)].">
      <j1 rule="hyper" parents="320 4753 17422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17427">
    <literal><![CDATA[
      K(x * a(y,z,K(u,w)),v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(17161,a,17426,a)].">
      <j1 rule="hyper" parents="17161 17426"/>
    </justification>
  </clause>

  <clause id="17428">
    <literal><![CDATA[
      K((x * y) * K(z,u),w) = K(x * (y * K(z,u)),w)
    ]]></literal>
    <justification jstring="[para(14363(a,1),17426(a,1,1))].">
      <j1 rule="para" parents="14363 17426"/>
    </justification>
  </clause>

  <clause id="17429">
    <literal><![CDATA[
      K(x * T(y,a(z,u,w)),v5) = K(x * y,v5)
    ]]></literal>
    <justification jstring="[para(17222(a,1),17426(a,1,1))].">
      <j1 rule="para" parents="17222 17426"/>
    </justification>
  </clause>

  <clause id="17430">
    <literal><![CDATA[
      K(x \ (y * a(z,u,K(w,v5))),v6) = K(x \ y,v6)
    ]]></literal>
    <justification jstring="[para(17221(a,2),17426(a,1,1))].">
      <j1 rule="para" parents="17221 17426"/>
    </justification>
  </clause>

  <clause id="17431">
    <literal><![CDATA[
      K(x * a(y,z,K(u,w)),v5) = (v6 * K(v5,x)) \ v6
    ]]></literal>
    <justification jstring="[hyper(320,a,6309,a,b,17427,a),flip(a)].">
      <j1 rule="hyper" parents="320 6309 17427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17432">
    <literal><![CDATA[
      K(T(x,y) * L(y,z,u),w) = K(L(y,z,u) * x,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,14382,a(flip),b,17429,a)].">
      <j1 rule="hyper" parents="58 14382 17429"/>
    </justification>
  </clause>

  <clause id="17433">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(13347(a,2),17418(a,1,2,1))].">
      <j1 rule="para" parents="13347 17418"/>
    </justification>
  </clause>

  <clause id="17434">
    <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(14363(a,1),17433(a,1,2))].">
      <j1 rule="para" parents="14363 17433"/>
    </justification>
  </clause>

  <clause id="17435">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ v5) = T(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[para(5858(a,2),17423(a,1,2))].">
      <j1 rule="para" parents="5858 17423"/>
    </justification>
  </clause>

  <clause id="17436">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) * v5) = T(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(320,a,15035,a,b,17425,a),flip(a)].">
      <j1 rule="hyper" parents="320 15035 17425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17437">
    <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),17430(a,1,1,2))].">
      <j1 rule="para" parents="80 17430"/>
    </justification>
  </clause>

  <clause id="17438">
    <literal><![CDATA[
      K(x,y * a(z,u,K(w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15751,a,17431,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="15751 17431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17439">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) * v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(17162,a,17438,a)].">
      <j1 rule="hyper" parents="17162 17438"/>
    </justification>
  </clause>

  <clause id="17440">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) = K(x,y * a(v5,v6,K(v7,v8)))
    ]]></literal>
    <justification jstring="[hyper(320,a,17117,a,b,17438,a)].">
      <j1 rule="hyper" parents="320 17117 17438"/>
    </justification>
  </clause>

  <clause id="17441">
    <literal><![CDATA[
      K(x,(y * z) * K(u,w)) = K(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(80(a,1),17438(a,1,2))].">
      <j1 rule="para" parents="80 17438"/>
    </justification>
  </clause>

  <clause id="17442">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,K(v5,v6)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(347(a,1),17438(a,1,2))].">
      <j1 rule="para" parents="347 17438"/>
    </justification>
  </clause>

  <clause id="17443">
    <literal><![CDATA[
      K(x,y * T(z,a(u,w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(13349(a,1),17438(a,1,2))].">
      <j1 rule="para" parents="13349 17438"/>
    </justification>
  </clause>

  <clause id="17444">
    <literal><![CDATA[
      K(x,y / T(z,a(u,w,v5))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(13374(a,1),17438(a,1,2))].">
      <j1 rule="para" parents="13374 17438"/>
    </justification>
  </clause>

  <clause id="17445">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[para(14196(a,1),17438(a,1,2))].">
      <j1 rule="para" parents="14196 17438"/>
    </justification>
  </clause>

  <clause id="17446">
    <literal><![CDATA[
      K(x,y * L(z,u,K(w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(14873(a,1),17438(a,1,2))].">
      <j1 rule="para" parents="14873 17438"/>
    </justification>
  </clause>

  <clause id="17447">
    <literal><![CDATA[
      K(x,y \ L(z,u,K(w,v5))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(14874(a,1),17438(a,1,2))].">
      <j1 rule="para" parents="14874 17438"/>
    </justification>
  </clause>

  <clause id="17448">
    <literal><![CDATA[
      K(x,y / L(z,u,K(w,v5))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(17409(a,1),17438(a,1,2))].">
      <j1 rule="para" parents="17409 17438"/>
    </justification>
  </clause>

  <clause id="17449">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) * v6) = K(x,v5 * v6)
    ]]></literal>
    <justification jstring="[para(14201(a,2),17439(a,1,2))].">
      <j1 rule="para" parents="14201 17439"/>
    </justification>
  </clause>

  <clause id="17450">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * v5) = K(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(14431(a,1),17439(a,1,2))].">
      <j1 rule="para" parents="14431 17439"/>
    </justification>
  </clause>

  <clause id="17451">
    <literal><![CDATA[
      K(x,(y * a(z,u,K(w,v5))) * v6) = K(x,y * v6)
    ]]></literal>
    <justification jstring="[para(17227(a,2),17439(a,1,2))].">
      <j1 rule="para" parents="17227 17439"/>
    </justification>
  </clause>

  <clause id="17452">
    <literal><![CDATA[
      K(x,y * (a(z,u,K(w,v5)) * v6)) = K(x,y * v6)
    ]]></literal>
    <justification jstring="[para(17373(a,1),17439(a,1,2))].">
      <j1 rule="para" parents="17373 17439"/>
    </justification>
  </clause>

  <clause id="17453">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) \ v6) = K(x,v5 \ v6)
    ]]></literal>
    <justification jstring="[para(17397(a,2),17439(a,1,2))].">
      <j1 rule="para" parents="17397 17439"/>
    </justification>
  </clause>

  <clause id="17454">
    <literal><![CDATA[
      K(x,y * T(z,L(u,w,v5))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(14288(a,1),17443(a,1,2,2))].">
      <j1 rule="para" parents="14288 17443"/>
    </justification>
  </clause>

  <clause id="17455">
    <literal><![CDATA[
      K(x,y / (a(z,u,w) / v5)) = K(x,y / (v5 \ a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(15201,a,17444,a)].">
      <j1 rule="hyper" parents="15201 17444"/>
    </justification>
  </clause>

  <clause id="17456">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) \ v5)) = K(x,y / (w \ (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[para(14878(a,1),17444(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14878 17444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17457">
    <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(566(a,1),17446(a,1,2,2))].">
      <j1 rule="para" parents="566 17446"/>
    </justification>
  </clause>

  <clause id="17458">
    <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(13914(a,1),17446(a,1,2,2))].">
      <j1 rule="para" parents="13914 17446"/>
    </justification>
  </clause>

  <clause id="17459">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ (K(z,w) * v5))) = K(x,y \ ((T(z,w) \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(5187(a,1),17447(a,1,2,2))].">
      <j1 rule="para" parents="5187 17447"/>
    </justification>
  </clause>

  <clause id="17460">
    <literal><![CDATA[
      K(x,y \ T(z,L(u,w,v5))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(14866(a,1),17447(a,1,2,2))].">
      <j1 rule="para" parents="14866 17447"/>
    </justification>
  </clause>

  <clause id="17461">
    <literal><![CDATA[
      K(x,y / ((z * ((K(u,w) * z) \ v5)) / z)) = K(x,y / ((K(u,w) \ v5) / z))
    ]]></literal>
    <justification jstring="[para(857(a,1),17448(a,1,2,2))].">
      <j1 rule="para" parents="857 17448"/>
    </justification>
  </clause>

  <clause id="17462">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ v5) = T(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(5092(a,2),17435(a,2,2))].">
      <j1 rule="para" parents="5092 17435"/>
    </justification>
  </clause>

  <clause id="17463">
    <literal><![CDATA[
      T(x,(K(y,z) * u) * w) = T(x,K(z,y) * (u * w))
    ]]></literal>
    <justification jstring="[para(14704(a,1),17436(a,1,2))].">
      <j1 rule="para" parents="14704 17436"/>
    </justification>
  </clause>

  <clause id="17465">
    <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),17442(a,1,2,2))].">
      <j1 rule="para" parents="80 17442"/>
    </justification>
  </clause>

  <clause id="17466">
    <literal><![CDATA[
      K(x,y * (z * (u * a(w,v5,K(v6,v7))))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(347(a,1),17442(a,1,2,2))].">
      <j1 rule="para" parents="347 17442"/>
    </justification>
  </clause>

  <clause id="17467">
    <literal><![CDATA[
      K(x,y * (z / L(u,w,K(v5,v6)))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(17409(a,1),17442(a,1,2,2))].">
      <j1 rule="para" parents="17409 17442"/>
    </justification>
  </clause>

  <clause id="17468">
    <literal><![CDATA[
      K(x,(y \ L(z,u,K(w,v5))) * v6) = K(x,(y \ z) * v6)
    ]]></literal>
    <justification jstring="[para(17241(a,1),17449(a,1,2,1))].">
      <j1 rule="para" parents="17241 17449"/>
    </justification>
  </clause>

  <clause id="17469">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * v5) = K(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(320,a,15051,a,b,17450,a),flip(a)].">
      <j1 rule="hyper" parents="320 15051 17450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17470">
    <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,16699,a(flip),b,17450,a),flip(a)].">
      <j1 rule="hyper" parents="58 16699 17450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17471">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (w * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15746,a(flip),b,17450,a),flip(a)].">
      <j1 rule="hyper" parents="58 15746 17450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17472">
    <literal><![CDATA[
      K(x,K((y \ z) \ u,w) * v5) = K(x,K(z \ (y * u),w) * v5)
    ]]></literal>
    <justification jstring="[para(10779(a,1),17450(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10779 17450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17473">
    <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(17450(a,2),15052(a,1))].">
      <j1 rule="para" parents="17450 15052"/>
    </justification>
  </clause>

  <clause id="17474">
    <literal><![CDATA[
      K(x,(L(y,z,K(u,w)) / v5) * v6) = K(x,(y / v5) * v6)
    ]]></literal>
    <justification jstring="[para(17283(a,1),17451(a,1,2,1))].">
      <j1 rule="para" parents="17283 17451"/>
    </justification>
  </clause>

  <clause id="17475">
    <literal><![CDATA[
      K(x,y * (z \ (a(u,w,K(v5,v6)) * v7))) = K(x,y * (z \ v7))
    ]]></literal>
    <justification jstring="[para(17371(a,2),17452(a,1,2,2))].">
      <j1 rule="para" parents="17371 17452"/>
    </justification>
  </clause>

  <clause id="17476">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = K(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(5923(a,1),17453(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5923 17453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17477">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w)) \ v5) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[para(14861(a,1),17453(a,1,2,1))].">
      <j1 rule="para" parents="14861 17453"/>
    </justification>
  </clause>

  <clause id="17478">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w)) \ v5) = K(x,T(y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(14866(a,1),17477(a,1,2,1))].">
      <j1 rule="para" parents="14866 17477"/>
    </justification>
  </clause>

  <clause id="17479">
    <literal><![CDATA[
      K(x,y \ (z * K(u,w))) = K(x,(y \ z) * K(u,w))
    ]]></literal>
    <justification jstring="[para(14855(a,1),17477(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14855 17477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17480">
    <literal><![CDATA[
      K(x,y * T(z,L(u / w,v5,v6))) = K(x,y * T(z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,15977,a(flip),b,17454,a),flip(a)].">
      <j1 rule="hyper" parents="320 15977 17454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17481">
    <literal><![CDATA[
      K(x,y \ T(z,L(u / w,v5,v6))) = K(x,y \ T(z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,15974,a(flip),b,17460,a),flip(a)].">
      <j1 rule="hyper" parents="320 15974 17460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17482">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = x \ T(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(116,a,17462,a(flip),b,4714,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 17462 4714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17483">
    <literal><![CDATA[
      K(x,y * K(z,L(u,w,v5))) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(15602,a,17469,a)].">
      <j1 rule="hyper" parents="15602 17469"/>
    </justification>
  </clause>

  <clause id="17484">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15746,a(flip),b,17469,a),flip(a)].">
      <j1 rule="hyper" parents="58 15746 17469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17485">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,K(z,y) * (u * w))
    ]]></literal>
    <justification jstring="[para(14704(a,1),17469(a,1,2))].">
      <j1 rule="para" parents="14704 17469"/>
    </justification>
  </clause>

  <clause id="17486">
    <literal><![CDATA[
      K(x,K(y,z) * ((z * u) * w)) = K(x,(T(z,y) * u) * w)
    ]]></literal>
    <justification jstring="[para(14775(a,1),17469(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14775 17469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17487">
    <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(17469(a,2),15052(a,1))].">
      <j1 rule="para" parents="17469 15052"/>
    </justification>
  </clause>

  <clause id="17488">
    <literal><![CDATA[
      K(x,T(y,z) \ L(z,u,w)) = K(x,L(z,u,w) / y)
    ]]></literal>
    <justification jstring="[hyper(13086,a,17478,a),flip(a)].">
      <j1 rule="hyper" parents="13086 17478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17489">
    <literal><![CDATA[
      K(x,y * K(z,L(u,w,v5))) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,15573,a(flip),b,17483,a),flip(a)].">
      <j1 rule="hyper" parents="320 15573 17483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17490">
    <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(17483(a,2),15602(a,1))].">
      <j1 rule="para" parents="17483 15602"/>
    </justification>
  </clause>

  <clause id="17491">
    <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(17489(a,2),15638(a,1))].">
      <j1 rule="para" parents="17489 15638"/>
    </justification>
  </clause>

  <clause id="17492">
    <literal><![CDATA[
      T(x,T(a(y,z,u),w) * v5) = T(x,v5 * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,17133,a(flip),b,17420,a),flip(a)].">
      <j1 rule="hyper" parents="320 17133 17420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17493">
    <literal><![CDATA[
      T(x,(y \ z) * (y * K(u,w))) = T(x,T(K(u,w) * z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16241,a(flip),b,17424,a),flip(a)].">
      <j1 rule="hyper" parents="58 16241 17424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17494">
    <literal><![CDATA[
      K(K(x,y) * (z * u),w) = K(z * (u * K(y,x)),w)
    ]]></literal>
    <justification jstring="[hyper(15844,a,17428,a)].">
      <j1 rule="hyper" parents="15844 17428"/>
    </justification>
  </clause>

  <clause id="17495">
    <literal><![CDATA[
      K(K(x,y) * (z * u),w) = K(z * (u * K(x,y)),w)
    ]]></literal>
    <justification jstring="[hyper(15637,a,17428,a)].">
      <j1 rule="hyper" parents="15637 17428"/>
    </justification>
  </clause>

  <clause id="17496">
    <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(17428(a,1),15637(a,1))].">
      <j1 rule="para" parents="17428 15637"/>
    </justification>
  </clause>

  <clause id="17498">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = K(u * L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,8756,a(flip),b,17432,a),flip(a)].">
      <j1 rule="hyper" parents="58 8756 17432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17499">
    <literal><![CDATA[
      K(x,y * a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v6
    ]]></literal>
    <justification jstring="[para(17440(a,1),17160(a,1))].">
      <j1 rule="para" parents="17440 17160"/>
    </justification>
  </clause>

  <clause id="17500">
    <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),17499(a,1,2))].">
      <j1 rule="para" parents="80 17499"/>
    </justification>
  </clause>

  <clause id="17501">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) = K(x,u * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(15712,a,17441,a)].">
      <j1 rule="hyper" parents="15712 17441"/>
    </justification>
  </clause>

  <clause id="17502">
    <literal><![CDATA[
      K(x,y * ((1 / z) * K(u,y / z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(14128,a,17441,a),flip(a)].">
      <j1 rule="hyper" parents="14128 17441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17503">
    <literal><![CDATA[
      K(x,(y * z) * K(u,w)) = K(x,y * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,15958,a,b,17441,a),flip(a)].">
      <j1 rule="hyper" parents="320 15958 17441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17504">
    <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(16854(a,1),17441(a,1,2,2))].">
      <j1 rule="para" parents="16854 17441"/>
    </justification>
  </clause>

  <clause id="17505">
    <literal><![CDATA[
      K(x,(K(y,L(z,u,w)) * v5) * v6) = K(x,K(y,z) * (v5 * v6))
    ]]></literal>
    <justification jstring="[hyper(320,a,17450,a(flip),b,17445,a),flip(a)].">
      <j1 rule="hyper" parents="320 17450 17445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17506">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) * w)) = K(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[para(5093(a,1),17445(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5093 17445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17507">
    <literal><![CDATA[
      K(x,K(y,z) * ((y / u) * w)) = K(x,(T(y,z) / u) * w)
    ]]></literal>
    <justification jstring="[para(13643(a,1),17445(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13643 17445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17508">
    <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(17445(a,2),15052(a,1))].">
      <j1 rule="para" parents="17445 15052"/>
    </justification>
  </clause>

  <clause id="17509">
    <literal><![CDATA[
      T(x,(y \ K(z,u)) \ w) = T(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13815,a,b,17463,a)].">
      <j1 rule="hyper" parents="58 13815 17463"/>
    </justification>
  </clause>

  <clause id="17510">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * w) = T(x,K(u,z) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15924,a(flip),b,17463,a)].">
      <j1 rule="hyper" parents="58 15924 17463"/>
    </justification>
  </clause>

  <clause id="17511">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (K(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(320,a,16059,a,b,17471,a),flip(a)].">
      <j1 rule="hyper" parents="320 16059 17471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17512">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (K(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(320,a,15958,a,b,17471,a),flip(a)].">
      <j1 rule="hyper" parents="320 15958 17471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17513">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (1 / w))) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(320,a,14020,a(flip),b,17471,a),flip(a)].">
      <j1 rule="hyper" parents="320 14020 17471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17515">
    <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(17471(a,2),16158(a,1))].">
      <j1 rule="para" parents="17471 16158"/>
    </justification>
  </clause>

  <clause id="17516">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,(y \ w) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(16008,a,17479,a)].">
      <j1 rule="hyper" parents="16008 17479"/>
    </justification>
  </clause>

  <clause id="17517">
    <literal><![CDATA[
      K(x,y \ (z * K(u,w))) = K(x,K(u,w) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(320,a,15573,a,b,17479,a),flip(a)].">
      <j1 rule="hyper" parents="320 15573 17479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17518">
    <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(10784(a,1),17479(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10784 17479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17519">
    <literal><![CDATA[
      K(x,K(y,z * u) * (w * v5)) = K(x,w * (v5 * K(y,u * z)))
    ]]></literal>
    <justification jstring="[hyper(16085,a,17484,a)].">
      <j1 rule="hyper" parents="16085 17484"/>
    </justification>
  </clause>

  <clause id="17520">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (z / w))) = K(x,u * (T(z,y) / w))
    ]]></literal>
    <justification jstring="[hyper(320,a,15979,a(flip),b,17484,a),flip(a)].">
      <j1 rule="hyper" parents="320 15979 17484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17521">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (1 / w))) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(320,a,14020,a(flip),b,17484,a),flip(a)].">
      <j1 rule="hyper" parents="320 14020 17484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17522">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * w) = K(x,K(u,z) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(16005,a,17485,a)].">
      <j1 rule="hyper" parents="16005 17485"/>
    </justification>
  </clause>

  <clause id="17523">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) \ w) = K(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(14007,a,17485,a)].">
      <j1 rule="hyper" parents="14007 17485"/>
    </justification>
  </clause>

  <clause id="17524">
    <literal><![CDATA[
      K(x,K(y,z) * ((z / u) * w)) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[para(13643(a,1),17485(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13643 17485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17525">
    <literal><![CDATA[
      K(x,K(y,z) * (((z * y) / u) * w)) = K(x,((T(z,y) * y) / u) * w)
    ]]></literal>
    <justification jstring="[para(14158(a,1),17485(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14158 17485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17526">
    <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(17485(a,1),16405(a,1,2))].">
      <j1 rule="para" parents="17485 16405"/>
    </justification>
  </clause>

  <clause id="17527">
    <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(593(a,1),17488(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="593 17488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17528">
    <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(17492(a,1),15707(a,1,2,1))].">
      <j1 rule="para" parents="17492 15707"/>
    </justification>
  </clause>

  <clause id="17529">
    <literal><![CDATA[
      K((K(x,y) * z) * u,w) = K(K(y,x) * (z * u),w)
    ]]></literal>
    <justification jstring="[hyper(320,a,17413,a,b,17494,a)].">
      <j1 rule="hyper" parents="320 17413 17494"/>
    </justification>
  </clause>

  <clause id="17530">
    <literal><![CDATA[
      K(K(x,y) * ((y \ z) * u),w) = K((T(y,x) \ z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,17414,a(flip),b,17495,a),flip(a)].">
      <j1 rule="hyper" parents="320 17414 17495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17531">
    <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(10763(a,2),17501(a,2,2,2,2))].">
      <j1 rule="para" parents="10763 17501"/>
    </justification>
  </clause>

  <clause id="17532">
    <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,17483,a(flip),b,17503,a),flip(a)].">
      <j1 rule="hyper" parents="58 17483 17503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17533">
    <literal><![CDATA[
      K(x,y * (K(z,x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * u) = w
    ]]></literal>
    <justification jstring="[para(17503(a,1),8369(a,1))].">
      <j1 rule="para" parents="17503 8369"/>
    </justification>
  </clause>

  <clause id="17534">
    <literal><![CDATA[
      K(x,y * (T(z,x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * u)) = w
    ]]></literal>
    <justification jstring="[para(4740(a,1),17533(a,1,2,2))].">
      <j1 rule="para" parents="4740 17533"/>
    </justification>
  </clause>

  <clause id="17535">
    <literal><![CDATA[
      K(x,y * (T(z,x) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ u)) = w
    ]]></literal>
    <justification jstring="[para(15341(a,1),17533(a,1))].">
      <j1 rule="para" parents="15341 17533"/>
    </justification>
  </clause>

  <clause id="17536">
    <literal><![CDATA[
      T(x,(K(y,z) / u) \ w) = T(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(14060,a,17510,a)].">
      <j1 rule="hyper" parents="14060 17510"/>
    </justification>
  </clause>

  <clause id="17537">
    <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,16713,a(flip),b,17510,a),flip(a)].">
      <j1 rule="hyper" parents="58 16713 17510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17538">
    <literal><![CDATA[
      T(x,K(y,z) * (u * w)) = T(x,u * (K(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(118,a,17511,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 17511 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17539">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(320,a,15741,a,b,17516,a),flip(a)].">
      <j1 rule="hyper" parents="320 15741 17516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17540">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(320,a,15573,a,b,17516,a),flip(a)].">
      <j1 rule="hyper" parents="320 15573 17516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17541">
    <literal><![CDATA[
      T(x,y \ (z * K(u,w))) = T(x,K(u,w) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,17517,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 17517 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17542">
    <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,12195,a(flip),b,17517,a)].">
      <j1 rule="hyper" parents="58 12195 17517"/>
    </justification>
  </clause>

  <clause id="17543">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * y))) = K(x,u \ (w * T(y,z)))
    ]]></literal>
    <justification jstring="[para(6086(a,1),17517(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6086 17517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17544">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u \ (w / (y \ z)))) = K(x,u \ (w / (z / y)))
    ]]></literal>
    <justification jstring="[para(6441(a,1),17517(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6441 17517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17545">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (u \ (w * z))) = K(x,u \ (w * (y * (z / y))))
    ]]></literal>
    <justification jstring="[para(10316(a,1),17517(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10316 17517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17546">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u \ (w * z))) = K(x,u \ (w * ((y \ z) * y)))
    ]]></literal>
    <justification jstring="[para(10322(a,1),17517(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10322 17517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17547">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w \ y))) = K(x,u \ (w \ T(y,z)))
    ]]></literal>
    <justification jstring="[para(13634(a,1),17517(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13634 17517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17548">
    <literal><![CDATA[
      K(x,(K(y,z) / u) \ w) = K(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(14014,a,17522,a)].">
      <j1 rule="hyper" parents="14014 17522"/>
    </justification>
  </clause>

  <clause id="17549">
    <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,10874,a(flip),b,17522,a),flip(a)].">
      <j1 rule="hyper" parents="58 10874 17522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17550">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ z) * w)) = K(x,(u \ T(z,y)) * w)
    ]]></literal>
    <justification jstring="[para(13634(a,1),17522(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13634 17522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17551">
    <literal><![CDATA[
      K(x,K(y \ z,y) * ((u \ z) * w)) = K(x,(u \ (y * (z / y))) * w)
    ]]></literal>
    <justification jstring="[para(14936(a,1),17522(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14936 17522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17552">
    <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,14551,a(flip),b,17523,a),flip(a)].">
      <j1 rule="hyper" parents="58 14551 17523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17553">
    <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(17523(a,1),15158(a,1,1,2))].">
      <j1 rule="para" parents="17523 15158"/>
    </justification>
  </clause>

  <clause id="17554">
    <literal><![CDATA[
      K(x * (K(y,z) * u),T(w,u)) = K(K(z,y) * (u * x),w)
    ]]></literal>
    <justification jstring="[hyper(16372,a,17529,a)].">
      <j1 rule="hyper" parents="16372 17529"/>
    </justification>
  </clause>

  <clause id="17555">
    <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(17536(a,1),14034(a,1,2,1,1))].">
      <j1 rule="para" parents="17536 14034"/>
    </justification>
  </clause>

  <clause id="17556">
    <literal><![CDATA[
      T(x,(y \ K(z,u)) \ w) = T(x,y * (K(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17509,a,b,17538,a)].">
      <j1 rule="hyper" parents="58 17509 17538"/>
    </justification>
  </clause>

  <clause id="17558">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (z * w))) = K(x,u \ (T(z,y) * w))
    ]]></literal>
    <justification jstring="[para(4740(a,1),17539(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4740 17539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17559">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (u \ (z * w))) = K(x,u \ (((y \ z) * y) * w))
    ]]></literal>
    <justification jstring="[para(11137(a,1),17539(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11137 17539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17560">
    <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(15279,a,17540,a),flip(a)].">
      <j1 rule="hyper" parents="15279 17540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17561">
    <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(15045,a,17540,a),flip(a)].">
      <j1 rule="hyper" parents="15045 17540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17562">
    <literal><![CDATA[
      T(x,y \ (K(z,u) * w)) = T(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(118,a,17540,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 17540 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17563">
    <literal><![CDATA[
      x * K(x,K(y,z) * (u \ w)) = T(x,u \ (K(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(119,a,17540,a(flip),b,4688,a(flip))].">
      <j1 rule="hyper" parents="119 17540 4688"/>
    </justification>
  </clause>

  <clause id="17564">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (y * w))) = K(x,u \ (T(y,z) * w))
    ]]></literal>
    <justification jstring="[para(4740(a,1),17540(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4740 17540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17565">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (z \ w))) = K(x,u \ (T(z,y) \ w))
    ]]></literal>
    <justification jstring="[para(5093(a,1),17540(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5093 17540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17566">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,z) * w))) = K(x,K(u,z) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[para(5219(a,1),17540(a,1,2,2))].">
      <j1 rule="para" parents="5219 17540"/>
    </justification>
  </clause>

  <clause id="17567">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u \ ((z / y) * w))) = K(x,u \ ((y \ z) * w))
    ]]></literal>
    <justification jstring="[para(5405(a,1),17540(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5405 17540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17568">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((z * y) * w))) = K(x,u \ ((y * z) * w))
    ]]></literal>
    <justification jstring="[para(11122(a,1),17540(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11122 17540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17569">
    <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(17541(a,1),15972(a,1,2,2))].">
      <j1 rule="para" parents="17541 15972"/>
    </justification>
  </clause>

  <clause id="17570">
    <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,17010,a(flip),b,17548,a)].">
      <j1 rule="hyper" parents="58 17010 17548"/>
    </justification>
  </clause>

  <clause id="17571">
    <literal><![CDATA[
      T(x,(y \ z) * (K(u,z \ y) * w)) = T(x,T((y \ z) \ 1,u) \ w)
    ]]></literal>
    <justification jstring="[para(6242(a,1),17556(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6242 17556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17572">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) = T(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(17207,a,17562,a)].">
      <j1 rule="hyper" parents="17207 17562"/>
    </justification>
  </clause>

  <clause id="17573">
    <literal><![CDATA[
      T(x,K(y,z) * ((z / u) \ w)) = T(x,(T(z,y) / u) \ w)
    ]]></literal>
    <justification jstring="[para(13643(a,1),17572(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13643 17572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17574">
    <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(17572(a,1),16015(a,2,2,2))].">
      <j1 rule="para" parents="17572 16015"/>
    </justification>
  </clause>

  <clause id="17575">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * w) / v5)) = K(x,y * (K(z,u) * (w / v5)))
    ]]></literal>
    <justification jstring="[para(544(a,1),17467(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="544 17467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17576">
    <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(4896(a,1),17468(a,1,2,1,2))].">
      <j1 rule="para" parents="4896 17468"/>
    </justification>
  </clause>

  <clause id="17577">
    <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(564(a,1),17474(a,1,2,1,1))].">
      <j1 rule="para" parents="564 17474"/>
    </justification>
  </clause>

  <clause id="17578">
    <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(17482(a,2),4797(a,1))].">
      <j1 rule="para" parents="17482 4797"/>
    </justification>
  </clause>

  <clause id="17579">
    <literal><![CDATA[
      K(x,(T(y,z) * (u / y)) * w) = K(x,K(z,y) * (T(u,y) * w))
    ]]></literal>
    <justification jstring="[hyper(16506,a,17486,a),flip(a)].">
      <j1 rule="hyper" parents="16506 17486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17580">
    <literal><![CDATA[
      K(x,y * (K(z,u \ y) / u)) = K(x,T(y / u,z))
    ]]></literal>
    <justification jstring="[para(13923(a,1),17502(a,1,2,2))].">
      <j1 rule="para" parents="13923 17502"/>
    </justification>
  </clause>

  <clause id="17581">
    <literal><![CDATA[
      K(x,y * (z \ K(u,z \ y))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(16045,a,17580,a)].">
      <j1 rule="hyper" parents="16045 17580"/>
    </justification>
  </clause>

  <clause id="17582">
    <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(8643(a,1),17581(a,1,2,2,2))].">
      <j1 rule="para" parents="8643 17581"/>
    </justification>
  </clause>

  <clause id="17583">
    <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(11206(a,1),17581(a,1,2,2,2))].">
      <j1 rule="para" parents="11206 17581"/>
    </justification>
  </clause>

  <clause id="17584">
    <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(11219(a,1),17581(a,1,2,2,2))].">
      <j1 rule="para" parents="11219 17581"/>
    </justification>
  </clause>

  <clause id="17585">
    <literal><![CDATA[
      K(x,(y \ z) * (u * K(w,y))) = K(x,(T(y,w) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,17471,a(flip),b,17506,a)].">
      <j1 rule="hyper" parents="58 17471 17506"/>
    </justification>
  </clause>

  <clause id="17586">
    <literal><![CDATA[
      K(x,K(y,z) * ((y / u) * w)) = K(x,(T(y,K(v5,v6) * z) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(16601,a,17507,a)].">
      <j1 rule="hyper" parents="16601 17507"/>
    </justification>
  </clause>

  <clause id="17587">
    <literal><![CDATA[
      K(x,(K(y,z) * (z / u)) * w) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17485,a,b,17507,a)].">
      <j1 rule="hyper" parents="58 17485 17507"/>
    </justification>
  </clause>

  <clause id="17588">
    <literal><![CDATA[
      K(x,y * (z \ K(u,L(w,v5,v6)))) = K(x,K(w,u) * (y * (1 / z)))
    ]]></literal>
    <justification jstring="[hyper(17473,a,17513,a),flip(a)].">
      <j1 rule="hyper" parents="17473 17513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17589">
    <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,16740,a(flip),b,17520,a),flip(a)].">
      <j1 rule="hyper" parents="58 16740 17520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17590">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17513,a(flip),b,17521,a)].">
      <j1 rule="hyper" parents="58 17513 17521"/>
    </justification>
  </clause>

  <clause id="17591">
    <literal><![CDATA[
      K(x,y * (z \ K(z,u))) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(14008,a,17590,a),flip(a)].">
      <j1 rule="hyper" parents="14008 17590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17592">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,u))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,13146,a,b,17590,a)].">
      <j1 rule="hyper" parents="320 13146 17590"/>
    </justification>
  </clause>

  <clause id="17593">
    <literal><![CDATA[
      K(x,(y \ z) * (u \ K(y,w))) = K(x,(T(y,w) \ z) / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,17327,a(flip),b,17590,a),flip(a)].">
      <j1 rule="hyper" parents="320 17327 17590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17594">
    <literal><![CDATA[
      K(x,(y * z) * (u \ K(w,y))) = K(x,(T(y,w) * z) / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,17326,a(flip),b,17590,a),flip(a)].">
      <j1 rule="hyper" parents="320 17326 17590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17595">
    <literal><![CDATA[
      K(x,(y / z) * (u \ K(z,w))) = K(x,(y / T(z,w)) / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,17304,a(flip),b,17590,a),flip(a)].">
      <j1 rule="hyper" parents="320 17304 17590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17596">
    <literal><![CDATA[
      K(x,y * ((z / u) \ K(w,u))) = K(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,16092,a(flip),b,17590,a),flip(a)].">
      <j1 rule="hyper" parents="320 16092 17590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17597">
    <literal><![CDATA[
      K(x,y * ((z * u) \ K(u,w))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,16091,a(flip),b,17590,a),flip(a)].">
      <j1 rule="hyper" parents="320 16091 17590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17598">
    <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(5877(a,2),17591(a,2,2,2))].">
      <j1 rule="para" parents="5877 17591"/>
    </justification>
  </clause>

  <clause id="17599">
    <literal><![CDATA[
      K(x,(T(y,x) / z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / z) * u) = w
    ]]></literal>
    <justification jstring="[para(17524(a,1),7334(a,1))].">
      <j1 rule="para" parents="17524 7334"/>
    </justification>
  </clause>

  <clause id="17600">
    <literal><![CDATA[
      K(x,L(y,z,z \ u) * u) = K(x,(T(u,y) / z) * (z * y))
    ]]></literal>
    <justification jstring="[para(14117(a,1),17524(a,1,2))].">
      <j1 rule="para" parents="14117 17524"/>
    </justification>
  </clause>

  <clause id="17601">
    <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),17599(a,1,2,1,1))].">
      <j1 rule="para" parents="18 17599"/>
    </justification>
  </clause>

  <clause id="17602">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * z))) = K(x,u \ (w * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(15052,a,17543,a)].">
      <j1 rule="hyper" parents="15052 17543"/>
    </justification>
  </clause>

  <clause id="17603">
    <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(17547(a,1),15943(a,1))].">
      <j1 rule="para" parents="17547 15943"/>
    </justification>
  </clause>

  <clause id="17604">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) * w)) = K(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(15052,a,17550,a)].">
      <j1 rule="hyper" parents="15052 17550"/>
    </justification>
  </clause>

  <clause id="17605">
    <literal><![CDATA[
      K(x,(y \ T(z,x)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ z) * u) = w
    ]]></literal>
    <justification jstring="[para(17550(a,1),7334(a,1))].">
      <j1 rule="para" parents="17550 7334"/>
    </justification>
  </clause>

  <clause id="17606">
    <literal><![CDATA[
      K(K(x,y) * (z * u),T(w,z)) = K(u * (K(y,x) * z),w)
    ]]></literal>
    <justification jstring="[hyper(7981,a,17554,a),flip(a)].">
      <j1 rule="hyper" parents="7981 17554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17607">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (z * x))) = K(x,u \ (x * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(320,a,8423,a(flip),b,17558,a),flip(a)].">
      <j1 rule="hyper" parents="320 8423 17558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17608">
    <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(17563(a,1),4725(a,1))].">
      <j1 rule="para" parents="17563 4725"/>
    </justification>
  </clause>

  <clause id="17609">
    <literal><![CDATA[
      K(x,T(y,z) \ (z \ u)) = K(x,y \ (T(z,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15058,a(flip),b,17565,a)].">
      <j1 rule="hyper" parents="58 15058 17565"/>
    </justification>
  </clause>

  <clause id="17610">
    <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(17609(a,2),8118(a,1,2))].">
      <j1 rule="para" parents="17609 8118"/>
    </justification>
  </clause>

  <clause id="17611">
    <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(15063(a,1),17578(a,1))].">
      <j1 rule="para" parents="15063 17578"/>
    </justification>
  </clause>

  <clause id="17612">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * (w \ (y * z))) = K(x,(y \ u) * (w \ (z * y)))
    ]]></literal>
    <justification jstring="[para(14142(a,1),17585(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14142 17585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17613">
    <literal><![CDATA[
      K(x,(T(y,z) / (u \ 1)) * w) = K(x,(y / (u \ K(y,z))) * w)
    ]]></literal>
    <justification jstring="[para(13937(a,1),17587(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13937 17587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17614">
    <literal><![CDATA[
      K(x,(T(y \ z,y) / u) * w) = K(x,((z / y) / u) * w)
    ]]></literal>
    <justification jstring="[para(13956(a,1),17587(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13956 17587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17615">
    <literal><![CDATA[
      K(x,(K(y \ z,y) * u) / w) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(17305,a,17592,a)].">
      <j1 rule="hyper" parents="17305 17592"/>
    </justification>
  </clause>

  <clause id="17616">
    <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,16090,a(flip),b,17592,a),flip(a)].">
      <j1 rule="hyper" parents="58 16090 17592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17617">
    <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(320,a,16260,a,b,17594,a)].">
      <j1 rule="hyper" parents="320 16260 17594"/>
    </justification>
  </clause>

  <clause id="17618">
    <literal><![CDATA[
      T(x,y * ((z / u) \ K(w,u))) = T(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(118,a,17596,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 17596 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17619">
    <literal><![CDATA[
      K(x,y / (z * ((u * w) / u))) = K(x,y / (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16093,a,b,17597,a)].">
      <j1 rule="hyper" parents="58 16093 17597"/>
    </justification>
  </clause>

  <clause id="17620">
    <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,17530,a(flip),b,17606,a)].">
      <j1 rule="hyper" parents="58 17530 17606"/>
    </justification>
  </clause>

  <clause id="17621">
    <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(15035(a,1),17614(a,1,2,1,1))].">
      <j1 rule="para" parents="15035 17614"/>
    </justification>
  </clause>

  <clause id="17622">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (u \ K(z,y))) = K(x,T(y * (1 / z),z) / u)
    ]]></literal>
    <justification jstring="[para(5832(a,1),17615(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5832 17615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17623">
    <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,16086,a(flip),b,17618,a),flip(a)].">
      <j1 rule="hyper" parents="58 16086 17618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17624">
    <literal><![CDATA[
      K(x,y / (z * T(u \ w,u))) = K(x,y / (z * (w / u)))
    ]]></literal>
    <justification jstring="[para(5(a,1),17619(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 17619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17625">
    <literal><![CDATA[
      K(x,y / (z * T(T(u,w),w))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(225(a,1),17619(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="225 17619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17626">
    <literal><![CDATA[
      K(x,y * (z * ((K(u,w) * v5) * v6))) = K(x,y * (z * (K(u,w) * (v5 * v6))))
    ]]></literal>
    <justification jstring="[para(14196(a,1),17466(a,1,2,2,2))].">
      <j1 rule="para" parents="14196 17466"/>
    </justification>
  </clause>

  <clause id="17627">
    <literal><![CDATA[
      K(x,y * (z \ ((u * w) * K(v5,v6)))) = K(x,y * (z \ (u * (w * K(v5,v6)))))
    ]]></literal>
    <justification jstring="[para(14363(a,1),17475(a,1,2,2,2))].">
      <j1 rule="para" parents="14363 17475"/>
    </justification>
  </clause>

  <clause id="17628">
    <literal><![CDATA[
      K(x,y * T(z,u / (w * v5))) = K(x,y * T(z,w \ (u / v5)))
    ]]></literal>
    <justification jstring="[para(14687(a,1),17480(a,1,2,2))].">
      <j1 rule="para" parents="14687 17480"/>
    </justification>
  </clause>

  <clause id="17629">
    <literal><![CDATA[
      K(x,y \ T(z,u / (w * v5))) = K(x,y \ T(z,w \ (u / v5)))
    ]]></literal>
    <justification jstring="[para(14687(a,1),17481(a,1,2,2))].">
      <j1 rule="para" parents="14687 17481"/>
    </justification>
  </clause>

  <clause id="17630">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) * v5) = K(x,K(y,z) * ((u * w) * v5))
    ]]></literal>
    <justification jstring="[para(14704(a,1),17505(a,1,2,1))].">
      <j1 rule="para" parents="14704 17505"/>
    </justification>
  </clause>

  <clause id="17631">
    <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(15953(a,1),17508(a,1))].">
      <j1 rule="para" parents="15953 17508"/>
    </justification>
  </clause>

  <clause id="17632">
    <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(16596(a,1),17515(a,1))].">
      <j1 rule="para" parents="16596 17515"/>
    </justification>
  </clause>

  <clause id="17633">
    <literal><![CDATA[
      K(x,y * (K(z,L(u,w,v5)) * v6)) = K(x,y * (K(u,z) * v6))
    ]]></literal>
    <justification jstring="[hyper(320,a,17512,a(flip),b,17532,a),flip(a)].">
      <j1 rule="hyper" parents="320 17512 17532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17634">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * (u * z)) = K(x,(z * u) * (u \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16738,a(flip),b,17600,a),flip(a)].">
      <j1 rule="hyper" parents="58 16738 17600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17635">
    <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(10109(a,2),17634(a,1,2,2))].">
      <j1 rule="para" parents="10109 17634"/>
    </justification>
  </clause>

  <clause id="17636">
    <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(17149(a,2),17608(a,1))].">
      <j1 rule="para" parents="17149 17608"/>
    </justification>
  </clause>

  <clause id="17637">
    <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(10863(a,1),17633(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10863 17633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17638">
    <literal><![CDATA[
      T(x,T((K(y,z) \ u) \ w,v5)) = T(x,T(u \ (K(z,y) \ w),v5))
    ]]></literal>
    <justification jstring="[para(5092(a,2),17148(a,1,2,1,1))].">
      <j1 rule="para" parents="5092 17148"/>
    </justification>
  </clause>

  <clause id="17639">
    <literal><![CDATA[
      K(x,(y * z) / L(y,u,w)) = K(x,(L(y,u,w) \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(12259,a,17191,a),flip(a)].">
      <j1 rule="hyper" parents="12259 17191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17640">
    <literal><![CDATA[
      K(x,(y * z) / L(y,u,w)) = K(x,y * (z / L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,17157,a(flip),b,17639,a),flip(a)].">
      <j1 rule="hyper" parents="320 17157 17639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17641">
    <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(17254(a,2),15651(a,1))].">
      <j1 rule="para" parents="17254 15651"/>
    </justification>
  </clause>

  <clause id="17642">
    <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(691,a,17255,a),flip(a)].">
      <j1 rule="hyper" parents="691 17255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17643">
    <literal><![CDATA[
      x \ (y * (K(z,K(u,w)) * v5)) = (x \ (y * v5)) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[para(15604(a,2),17255(a,1,2,2))].">
      <j1 rule="para" parents="15604 17255"/>
    </justification>
  </clause>

  <clause id="17644">
    <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(14849(a,2),17277(a,1,2))].">
      <j1 rule="para" parents="14849 17277"/>
    </justification>
  </clause>

  <clause id="17645">
    <literal><![CDATA[
      (x * (y * (z * K(u,K(w,v5))))) \ v6 = K(u,K(w,v5)) * ((x * (y * z)) \ v6)
    ]]></literal>
    <justification jstring="[para(17287(a,1),17320(a,1,1))].">
      <j1 rule="para" parents="17287 17320"/>
    </justification>
  </clause>

  <clause id="17646">
    <literal><![CDATA[
      (K(x,T(y,z)) * u) * z = (K(x,y) * u) * T(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(7732(a,1),17319(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7732 17319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17647">
    <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),17338(a,2,2,1))].">
      <j1 rule="para" parents="90 17338"/>
    </justification>
  </clause>

  <clause id="17648">
    <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(17356(a,2),15943(a,1,2))].">
      <j1 rule="para" parents="17356 15943"/>
    </justification>
  </clause>

  <clause id="17649">
    <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(10082(a,1),17366(a,1,2,1,1))].">
      <j1 rule="para" parents="10082 17366"/>
    </justification>
  </clause>

  <clause id="17650">
    <literal><![CDATA[
      T(x,a(y \ 1,z,u)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,17239,a(flip),b,17378,a),flip(a)].">
      <j1 rule="hyper" parents="36 17239 17378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17651">
    <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,16809,a(flip),b,17465,a)].">
      <j1 rule="hyper" parents="58 16809 17465"/>
    </justification>
  </clause>

  <clause id="17652">
    <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(17465(a,1),15710(a,1))].">
      <j1 rule="para" parents="17465 15710"/>
    </justification>
  </clause>

  <clause id="17653">
    <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,15281,a(flip),b,17472,a),flip(a)].">
      <j1 rule="hyper" parents="58 15281 17472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17654">
    <literal><![CDATA[
      K(x,y * (z * K((u * w) \ y,u * w))) = K(x,(((w * u) \ y) * (w * u)) * z)
    ]]></literal>
    <justification jstring="[para(13123(a,1),17519(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13123 17519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17655">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * (v5 \ ((y * z) * v6))) = K(x,v5 \ ((z * y) * v6))
    ]]></literal>
    <justification jstring="[hyper(16594,a,17568,a)].">
      <j1 rule="hyper" parents="16594 17568"/>
    </justification>
  </clause>

  <clause id="17656">
    <literal><![CDATA[
      K(x,((y \ z) * T(y,u)) * w) = K(x,K(u,y) * (T(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(16156,a,17579,a)].">
      <j1 rule="hyper" parents="16156 17579"/>
    </justification>
  </clause>

  <clause id="17657">
    <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,15316,a,b,17579,a)].">
      <j1 rule="hyper" parents="58 15316 17579"/>
    </justification>
  </clause>

  <clause id="17658">
    <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,15122,a(flip),b,17623,a)].">
      <j1 rule="hyper" parents="58 15122 17623"/>
    </justification>
  </clause>

  <clause id="17659">
    <literal><![CDATA[
      K(x,y * T(z,(u * w) \ v5)) = K(x,y * T(z,u \ (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(16041,a,17628,a)].">
      <j1 rule="hyper" parents="16041 17628"/>
    </justification>
  </clause>

  <clause id="17660">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) \ v5)) = K(x,y \ T(z,u \ (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(16046,a,17629,a)].">
      <j1 rule="hyper" parents="16046 17629"/>
    </justification>
  </clause>

  <clause id="17661">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) * v5) = K(x,K(z,y) * ((u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,15051,a,b,17630,a),flip(a)].">
      <j1 rule="hyper" parents="320 15051 17630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17662">
    <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),17637(a,2,2,1))].">
      <j1 rule="para" parents="20 17637"/>
    </justification>
  </clause>

  <clause id="17663">
    <literal><![CDATA[
      T(x,T(y \ (K(z,u) \ w),y)) = T(x,w / (K(u,z) \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16357,a(flip),b,17638,a),flip(a)].">
      <j1 rule="hyper" parents="58 16357 17638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17664">
    <literal><![CDATA[
      T(x,(K(y,z) \ u) / w) = T(x,u / (K(z,y) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,7917,a(flip),b,17663,a)].">
      <j1 rule="hyper" parents="58 7917 17663"/>
    </justification>
  </clause>

  <clause id="17665">
    <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(14849(a,2),17644(a,2,2))].">
      <j1 rule="para" parents="14849 17644"/>
    </justification>
  </clause>

  <clause id="17666">
    <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,15334,a(flip),b,17656,a)].">
      <j1 rule="hyper" parents="58 15334 17656"/>
    </justification>
  </clause>

  <clause id="17667">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),w)) = T(x,y * T(K(u,w) / z,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,16226,a(flip),b,17658,a),flip(a)].">
      <j1 rule="hyper" parents="320 16226 17658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17668">
    <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(17659(a,2),16483(a,1))].">
      <j1 rule="para" parents="17659 16483"/>
    </justification>
  </clause>

  <clause id="17669">
    <literal><![CDATA[
      K(x,((y * K(z,u)) * w) * v5) = K(x,K(u,z) * ((y * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(16155,a,17661,a)].">
      <j1 rule="hyper" parents="16155 17661"/>
    </justification>
  </clause>

  <clause id="17670">
    <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,13041,a(flip),b,17662,a)].">
      <j1 rule="hyper" parents="58 13041 17662"/>
    </justification>
  </clause>

  <clause id="17671">
    <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,15834,a,b,17667,a)].">
      <j1 rule="hyper" parents="58 15834 17667"/>
    </justification>
  </clause>

  <clause id="17672">
    <literal><![CDATA[
      (x * (y / z)) * K(u,L(z,y,x)) = x * (y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(17178,a,14549,a)].">
      <j1 rule="hyper" parents="17178 14549"/>
    </justification>
  </clause>

  <clause id="17673">
    <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(17672(a,1),15345(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="17672 15345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17674">
    <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(17672(a,1),16592(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17672 16592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17675">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,y,z)) = K(x,(z * y) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(17243,a,16266,a)].">
      <j1 rule="hyper" parents="17243 16266"/>
    </justification>
  </clause>

  <clause id="17676">
    <literal><![CDATA[
      K(x,L(y * z,u,u * y)) = K(x,u \ ((u / (y \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(14079,a,17280,a)].">
      <j1 rule="hyper" parents="14079 17280"/>
    </justification>
  </clause>

  <clause id="17677">
    <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(6000(a,1),17280(a,2,2,2,1))].">
      <j1 rule="para" parents="6000 17280"/>
    </justification>
  </clause>

  <clause id="17678">
    <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),17676(a,1,2,3))].">
      <j1 rule="para" parents="105 17676"/>
    </justification>
  </clause>

  <clause id="17679">
    <literal><![CDATA[
      ((x \ y) / y) * (y * K(z,u)) = x \ (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14519,a(flip),b,17282,a),flip(a)].">
      <j1 rule="hyper" parents="58 14519 17282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17680">
    <literal><![CDATA[
      (x \ (y * K(z,u))) / (y * K(z,u)) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,14519,a(flip),b,17282,a(flip))].">
      <j1 rule="hyper" parents="117 14519 17282"/>
    </justification>
  </clause>

  <clause id="17681">
    <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(17679(a,1),7532(a,2,2,1))].">
      <j1 rule="para" parents="17679 7532"/>
    </justification>
  </clause>

  <clause id="17682">
    <literal><![CDATA[
      (x \ (K(y,z) * u)) / (K(y,z) * u) = (x \ u) / u
    ]]></literal>
    <justification jstring="[hyper(58,a,14145,a,b,17680,a)].">
      <j1 rule="hyper" parents="58 14145 17680"/>
    </justification>
  </clause>

  <clause id="17683">
    <literal><![CDATA[
      (x \ y) / (K(x,z) * y) = (T(x,z) \ y) / y
    ]]></literal>
    <justification jstring="[para(5041(a,1),17682(a,1,1))].">
      <j1 rule="para" parents="5041 17682"/>
    </justification>
  </clause>

  <clause id="17684">
    <literal><![CDATA[
      ((x \ y) / y) * K(z,x) = (T(x,z) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(58,a,14101,a(flip),b,17683,a)].">
      <j1 rule="hyper" parents="58 14101 17683"/>
    </justification>
  </clause>

  <clause id="17685">
    <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(17684(a,1),5116(a,2,1))].">
      <j1 rule="para" parents="17684 5116"/>
    </justification>
  </clause>

  <clause id="17686">
    <literal><![CDATA[
      K(x,((y / (z * y)) * u) \ y) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,14525,a(flip),b,17310,a),flip(a)].">
      <j1 rule="hyper" parents="58 14525 17310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17687">
    <literal><![CDATA[
      K(x,((y / z) \ u) \ z) = K(x,((z / y) * u) \ z)
    ]]></literal>
    <justification jstring="[para(7(a,1),17686(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 17686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17688">
    <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(17687(a,2),14037(a,1))].">
      <j1 rule="para" parents="17687 14037"/>
    </justification>
  </clause>

  <clause id="17689">
    <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(8359(a,1),17317(a,1,2,2,2))].">
      <j1 rule="para" parents="8359 17317"/>
    </justification>
  </clause>

  <clause id="17690">
    <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(8249(a,1),17601(a,1))].">
      <j1 rule="para" parents="8249 17601"/>
    </justification>
  </clause>

  <clause id="17691">
    <literal><![CDATA[
      K((x * K(y,z)) \ ((x * u) * K(y,z)),w) = K(u,T(T(w,x),x))
    ]]></literal>
    <justification jstring="[hyper(320,a,7905,a(flip),b,17145,a),flip(a)].">
      <j1 rule="hyper" parents="320 7905 17145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17692">
    <literal><![CDATA[
      K((x * K(y,z)) \ ((x * u) * K(y,z)),w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,7858,a(flip),b,17691,a),flip(a)].">
      <j1 rule="hyper" parents="320 7858 17691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17694">
    <literal><![CDATA[
      K((x * K(y,z)) \ (x * (u * K(y,z))),w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17437,a(flip),b,17692,a)].">
      <j1 rule="hyper" parents="58 17437 17692"/>
    </justification>
  </clause>

  <clause id="17695">
    <literal><![CDATA[
      K(L(T(x,K(y,z)),K(y,z),u),w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(232(a,1),17694(a,1,1))].">
      <j1 rule="para" parents="232 17694"/>
    </justification>
  </clause>

  <clause id="17696">
    <literal><![CDATA[
      K(L(x,K(y,z),u),T(w,K(y,z))) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(7681,a,17695,a)].">
      <j1 rule="hyper" parents="7681 17695"/>
    </justification>
  </clause>

  <clause id="17697">
    <literal><![CDATA[
      K(L(x,K(y,z),u),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(15600,a,17696,a)].">
      <j1 rule="hyper" parents="15600 17696"/>
    </justification>
  </clause>

  <clause id="17698">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K((x \ u) * K(z,y),w)
    ]]></literal>
    <justification jstring="[hyper(15720,a,17697,a)].">
      <j1 rule="hyper" parents="15720 17697"/>
    </justification>
  </clause>

  <clause id="17699">
    <literal><![CDATA[
      L(K(x,y),K(z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10838,a,17697,a)].">
      <j1 rule="hyper" parents="10838 17697"/>
    </justification>
  </clause>

  <clause id="17700">
    <literal><![CDATA[
      K(x,L(y,K(z,u),w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10837,a,17697,a)].">
      <j1 rule="hyper" parents="10837 17697"/>
    </justification>
  </clause>

  <clause id="17704">
    <literal><![CDATA[
      a(x,K(y,z),K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,17697,a,b,10811,a),flip(a)].">
      <j1 rule="hyper" parents="115 17697 10811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17706">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K((x \ u) * K(y,z),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17297,a(flip),b,17697,a)].">
      <j1 rule="hyper" parents="58 17297 17697"/>
    </justification>
  </clause>

  <clause id="17709">
    <literal><![CDATA[
      L(x,K(y,z),K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(13601,a,17704,a)].">
      <j1 rule="hyper" parents="13601 17704"/>
    </justification>
  </clause>

  <clause id="17710">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = x * (K(y,z) * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(969,a,17704,a)].">
      <j1 rule="hyper" parents="969 17704"/>
    </justification>
  </clause>

  <clause id="17712">
    <literal><![CDATA[
      L(x,K(y,z),T(u,w)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(167,a,14921,a,b,17704,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 14921 17704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17713">
    <literal><![CDATA[
      T(x,L(y,K(z,u),w)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(167,a,10854,a,b,17704,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 10854 17704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17718">
    <literal><![CDATA[
      R(x,K(y,z),K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,14848,a,b,17709,a)].">
      <j1 rule="hyper" parents="58 14848 17709"/>
    </justification>
  </clause>

  <clause id="17719">
    <literal><![CDATA[
      L(x,K(y,z),u / w) = L(x,K(y,z),w \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,14899,a(flip),b,17709,a)].">
      <j1 rule="hyper" parents="58 14899 17709"/>
    </justification>
  </clause>

  <clause id="17722">
    <literal><![CDATA[
      L(x,K(y,z),K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      v5 = x
    ]]></literal>
    <justification jstring="[para(17709(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="17709 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17727">
    <literal><![CDATA[
      T(x / (K(y,z) * K(u,w)),K(u,w)) = K(w,u) * (x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16650,a(flip),b,17718,a)].">
      <j1 rule="hyper" parents="58 16650 17718"/>
    </justification>
  </clause>

  <clause id="17736">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,K(z,u) \ (y \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,10787,a(flip),b,17699,a)].">
      <j1 rule="hyper" parents="58 10787 17699"/>
    </justification>
  </clause>

  <clause id="17737">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,w)) = K(x,z \ (y * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,6555,a(flip),b,17699,a),flip(a)].">
      <j1 rule="hyper" parents="58 6555 17699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17739">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,z) * K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(17699(a,1),286(a,1,2))].">
      <j1 rule="para" parents="17699 286"/>
    </justification>
  </clause>

  <clause id="17741">
    <literal><![CDATA[
      L(K(x,y),L(K(z,u),w,v5),v6) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5641(a,1),17699(a,1,2))].">
      <j1 rule="para" parents="5641 17699"/>
    </justification>
  </clause>

  <clause id="17743">
    <literal><![CDATA[
      K(x,(y / z) / K(u,w)) = K(x,y / (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14700,a(flip),b,17700,a),flip(a)].">
      <j1 rule="hyper" parents="58 14700 17700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17744">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[para(5116(a,1),17700(a,1,2))].">
      <j1 rule="para" parents="5116 17700"/>
    </justification>
  </clause>

  <clause id="17746">
    <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,16811,a(flip),b,17713,a)].">
      <j1 rule="hyper" parents="58 16811 17713"/>
    </justification>
  </clause>

  <clause id="17747">
    <literal><![CDATA[
      T(x,(y * K(z,u)) \ w) = T(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[para(5116(a,1),17713(a,1,2))].">
      <j1 rule="para" parents="5116 17713"/>
    </justification>
  </clause>

  <clause id="17748">
    <literal><![CDATA[
      T(x,L(y,K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(14866(a,1),17722(a,1)),flip(b)].">
      <j1 rule="para" parents="14866 17722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17749">
    <literal><![CDATA[
      L(x,K(y,z),(u \ w) \ w) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(2101,a,17712,a)].">
      <j1 rule="hyper" parents="2101 17712"/>
    </justification>
  </clause>

  <clause id="17750">
    <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,10787,a(flip),b,17741,a)].">
      <j1 rule="hyper" parents="58 10787 17741"/>
    </justification>
  </clause>

  <clause id="17752">
    <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(16251(a,1),17748(a,1))].">
      <j1 rule="para" parents="16251 17748"/>
    </justification>
  </clause>

  <clause id="17753">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),w) = K((x \ y) * K(z,u),w)
    ]]></literal>
    <justification jstring="[hyper(17298,a,17698,a)].">
      <j1 rule="hyper" parents="17298 17698"/>
    </justification>
  </clause>

  <clause id="17755">
    <literal><![CDATA[
      K(((x \ y) \ z) * K(u,y),w) = K((x \ T(y,u)) \ z,w)
    ]]></literal>
    <justification jstring="[para(13634(a,1),17698(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13634 17698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17756">
    <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(17698(a,1),14237(a,2,3))].">
      <j1 rule="para" parents="17698 14237"/>
    </justification>
  </clause>

  <clause id="17758">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K(K(z,y) * (x \ u),w)
    ]]></literal>
    <justification jstring="[hyper(320,a,15780,a,b,17706,a),flip(a)].">
      <j1 rule="hyper" parents="320 15780 17706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17759">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = x * (K(u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,15631,a,b,17710,a),flip(a)].">
      <j1 rule="hyper" parents="320 15631 17710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17760">
    <literal><![CDATA[
      (L(K(x,y) * K(z,u),w,K(v5,v6)) * a(v5,w,v6)) / K(z,u) = a(v5,w,v6) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,14875,a,b,17710,a)].">
      <j1 rule="hyper" parents="117 14875 17710"/>
    </justification>
  </clause>

  <clause id="17761">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(u,w)) = z * (K(u,w) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16333,a,b,17710,a)].">
      <j1 rule="hyper" parents="58 16333 17710"/>
    </justification>
  </clause>

  <clause id="17762">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) / (u * w) = (x * K(y,z)) / (w * u)
    ]]></literal>
    <justification jstring="[hyper(117,a,17710,a(flip),b,10349,a)].">
      <j1 rule="hyper" parents="117 17710 10349"/>
    </justification>
  </clause>

  <clause id="17764">
    <literal><![CDATA[
      T(x * (K(y,z) * K(u,w)),K(w,u)) = K(u,w) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(17710(a,1),6308(a,1,1))].">
      <j1 rule="para" parents="17710 6308"/>
    </justification>
  </clause>

  <clause id="17765">
    <literal><![CDATA[
      K(x,K(y,z) \ ((u / z) \ w)) = K(x,(u / T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(6293(a,1),17736(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6293 17736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17766">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,w)) = K(x,K(u,w) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,17517,a(flip),b,17737,a),flip(a)].">
      <j1 rule="hyper" parents="320 17517 17737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17767">
    <literal><![CDATA[
      K(x,(y / z) / K(u,w)) = K(x,y / (K(w,u) \ z))
    ]]></literal>
    <justification jstring="[para(5092(a,2),17743(a,2,2,2))].">
      <j1 rule="para" parents="5092 17743"/>
    </justification>
  </clause>

  <clause id="17768">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,(y / w) * K(u,z))
    ]]></literal>
    <justification jstring="[para(6306(a,1),17743(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6306 17743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17769">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(15980,a,17744,a)].">
      <j1 rule="hyper" parents="15980 17744"/>
    </justification>
  </clause>

  <clause id="17770">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ z) \ w)) = K(x,(u \ T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(13634(a,1),17744(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13634 17744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17771">
    <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,15370,a,b,17747,a)].">
      <j1 rule="hyper" parents="58 15370 17747"/>
    </justification>
  </clause>

  <clause id="17772">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * z) \ w)) = T(x,(u * T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(6086(a,1),17747(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6086 17747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17773">
    <literal><![CDATA[
      T(x,K(y,z) * ((u / y) \ w)) = T(x,(u / T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(6293(a,1),17747(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6293 17747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17774">
    <literal><![CDATA[
      T(x,K(y \ z,y) * ((u \ (y \ z)) \ w)) = T(x,(u \ (z / y)) \ w)
    ]]></literal>
    <justification jstring="[para(13896(a,1),17747(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13896 17747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17775">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),w) = K(K(u,z) * (x \ y),w)
    ]]></literal>
    <justification jstring="[hyper(320,a,15780,a,b,17753,a),flip(a)].">
      <j1 rule="hyper" parents="320 15780 17753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17776">
    <literal><![CDATA[
      K(K(x,y) * (z \ (K(x,y) * u)),w) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[para(5095(a,1),17758(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5095 17758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17782">
    <literal><![CDATA[
      K(x,(y \ z) \ K(z,u)) = K(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,15058,a(flip),b,17766,a),flip(a)].">
      <j1 rule="hyper" parents="320 15058 17766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17783">
    <literal><![CDATA[
      T(x,(y \ z) \ K(z,u)) = T(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(118,a,17782,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 17782 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17784">
    <literal><![CDATA[
      T(x,(y \ (z / u)) \ K(u \ z,w)) = T(x,T(z / u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16073,a(flip),b,17783,a)].">
      <j1 rule="hyper" parents="58 16073 17783"/>
    </justification>
  </clause>

  <clause id="17785">
    <literal><![CDATA[
      K(x,y / (K(z,u) \ w)) = K(x,K(u,z) \ (y / w))
    ]]></literal>
    <justification jstring="[hyper(15708,a,17767,a),flip(a)].">
      <j1 rule="hyper" parents="15708 17767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17786">
    <literal><![CDATA[
      K(x,(y / z) * K(u,w)) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(16182,a,17768,a),flip(a)].">
      <j1 rule="hyper" parents="16182 17768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17787">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,K(u,z) * (y / w))
    ]]></literal>
    <justification jstring="[hyper(320,a,15573,a,b,17768,a),flip(a)].">
      <j1 rule="hyper" parents="320 15573 17768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17788">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,z) * x))) = K(x,K(u,z) * ((z \ y) \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6686,a(flip),b,17769,a)].">
      <j1 rule="hyper" parents="58 6686 17769"/>
    </justification>
  </clause>

  <clause id="17789">
    <literal><![CDATA[
      K(x,K(y,z) * ((y \ u) \ w)) = K(x,(T(y,z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(5093(a,1),17769(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5093 17769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17790">
    <literal><![CDATA[
      K(K(x,y) * (z \ (u * K(x,y))),w) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[para(6300(a,1),17775(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6300 17775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17791">
    <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(17776(a,1),17500(a,1,2,2))].">
      <j1 rule="para" parents="17776 17500"/>
    </justification>
  </clause>

  <clause id="17792">
    <literal><![CDATA[
      T(x,y / (K(z,u) \ w)) = T(x,K(u,z) \ (y / w))
    ]]></literal>
    <justification jstring="[hyper(118,a,17785,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 17785 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17793">
    <literal><![CDATA[
      K(x,y * (z \ K(u,K(w,v5)))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(15993,a,17786,a),flip(a)].">
      <j1 rule="hyper" parents="15993 17786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17794">
    <literal><![CDATA[
      K(x,K(y,z) * (u / w)) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(15747,a,17786,a)].">
      <j1 rule="hyper" parents="15747 17786"/>
    </justification>
  </clause>

  <clause id="17795">
    <literal><![CDATA[
      K(x,K(y,z) * (u / w)) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(15638,a,17786,a)].">
      <j1 rule="hyper" parents="15638 17786"/>
    </justification>
  </clause>

  <clause id="17796">
    <literal><![CDATA[
      K(x,y * (z \ K(y,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) / z) = w
    ]]></literal>
    <justification jstring="[para(17786(a,1),15719(a,1))].">
      <j1 rule="para" parents="17786 15719"/>
    </justification>
  </clause>

  <clause id="17797">
    <literal><![CDATA[
      K(x,(y / T(z,K(u,w))) / v5) = K(x,(y / z) / v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,17595,a(flip),b,17793,a)].">
      <j1 rule="hyper" parents="58 17595 17793"/>
    </justification>
  </clause>

  <clause id="17798">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (w \ z))) = K(x,u / (w \ T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(16049,a,17787,a),flip(a)].">
      <j1 rule="hyper" parents="16049 17787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17799">
    <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(17787(a,1),16182(a,1))].">
      <j1 rule="para" parents="17787 16182"/>
    </justification>
  </clause>

  <clause id="17800">
    <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(17790(a,2),8369(a,1))].">
      <j1 rule="para" parents="17790 8369"/>
    </justification>
  </clause>

  <clause id="17801">
    <literal><![CDATA[
      T(x,(K(y,z) \ u) / w) = T(x,K(y,z) \ (u / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17664,a,b,17792,a)].">
      <j1 rule="hyper" parents="58 17664 17792"/>
    </justification>
  </clause>

  <clause id="17802">
    <literal><![CDATA[
      T(x,K(y,z) * (u / w)) = T(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(118,a,17794,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 17794 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17803">
    <literal><![CDATA[
      T(x,K(y,z) * (u / w)) = T(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(118,a,17795,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 17795 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17805">
    <literal><![CDATA[
      K(x,(y / T(z,T(u,w))) / v5) = K(x,(y / T(z,u)) / v5)
    ]]></literal>
    <justification jstring="[para(7413(a,1),17797(a,1,2,1,2))].">
      <j1 rule="para" parents="7413 17797"/>
    </justification>
  </clause>

  <clause id="17806">
    <literal><![CDATA[
      T(x,K(y,z) \ ((T(z,y) \ u) / w)) = T(x,(z \ u) / w)
    ]]></literal>
    <justification jstring="[para(5091(a,1),17801(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5091 17801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17807">
    <literal><![CDATA[
      T(x,K(y * z,u) * (w / T(z,y))) = T(x,w / (y \ T(z * y,u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,14094,a(flip),b,17802,a),flip(a)].">
      <j1 rule="hyper" parents="320 14094 17802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17808">
    <literal><![CDATA[
      T(x,K(y,z) * (u / (y \ w))) = T(x,u / (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(320,a,13940,a(flip),b,17803,a),flip(a)].">
      <j1 rule="hyper" parents="320 13940 17803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17809">
    <literal><![CDATA[
      K(x,y * (z \ K(u,y))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) / z) = w
    ]]></literal>
    <justification jstring="[para(17590(a,1),17796(a,1))].">
      <j1 rule="para" parents="17590 17796"/>
    </justification>
  </clause>

  <clause id="17810">
    <literal><![CDATA[
      K((x \ T(y,x)) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15843,a(flip),b,17755,a),flip(a)].">
      <j1 rule="hyper" parents="58 15843 17755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17811">
    <literal><![CDATA[
      K((T(x,y) \ y) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9023,a,b,17810,a)].">
      <j1 rule="hyper" parents="58 9023 17810"/>
    </justification>
  </clause>

  <clause id="17812">
    <literal><![CDATA[
      x * (y * (K(x,z) * K(x,z))) = T(x,z) * (K(x,z) * y)
    ]]></literal>
    <justification jstring="[para(17761(a,1),7165(a,1,2))].">
      <j1 rule="para" parents="17761 7165"/>
    </justification>
  </clause>

  <clause id="17813">
    <literal><![CDATA[
      K(x,(y / T(z,z \ u)) \ w) = K(x,K(u,z) \ ((y / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13096,a(flip),b,17765,a),flip(a)].">
      <j1 rule="hyper" parents="58 13096 17765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17814">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) \ w)) = K(x,(u \ T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(15052,a,17770,a)].">
      <j1 rule="hyper" parents="15052 17770"/>
    </justification>
  </clause>

  <clause id="17815">
    <literal><![CDATA[
      T(x,(y * T(z,u)) \ T(z,w)) = T(x,(y * z) \ T(T(z,w),u))
    ]]></literal>
    <justification jstring="[hyper(16011,a,17772,a),flip(a)].">
      <j1 rule="hyper" parents="16011 17772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17816">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * y) \ w)) = T(x,(u * T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(15251,a,17772,a)].">
      <j1 rule="hyper" parents="15251 17772"/>
    </justification>
  </clause>

  <clause id="17817">
    <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,16608,a(flip),b,17773,a),flip(a)].">
      <j1 rule="hyper" parents="58 16608 17773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17818">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ w)) = K(x,(T(z,y) \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(15052,a,17789,a)].">
      <j1 rule="hyper" parents="15052 17789"/>
    </justification>
  </clause>

  <clause id="17819">
    <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,16599,a(flip),b,17798,a),flip(a)].">
      <j1 rule="hyper" parents="58 16599 17798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17820">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z))) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15792,a(flip),b,17798,a),flip(a)].">
      <j1 rule="hyper" parents="58 15792 17798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17821">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ u)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(4208(a,2),17820(a,1,2,2))].">
      <j1 rule="para" parents="4208 17820"/>
    </justification>
  </clause>

  <clause id="17822">
    <literal><![CDATA[
      K(x,(y / z) \ T(u,y / z)) = K(x,u / (T(z,y) \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,13084,a,b,17821,a)].">
      <j1 rule="hyper" parents="320 13084 17821"/>
    </justification>
  </clause>

  <clause id="17823">
    <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(16162,a,17805,a)].">
      <j1 rule="hyper" parents="16162 17805"/>
    </justification>
  </clause>

  <clause id="17824">
    <literal><![CDATA[
      T(x,(((y \ T(z,y)) \ z) \ z) / u) = T(x,(y \ z) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16656,a,b,17806,a)].">
      <j1 rule="hyper" parents="58 16656 17806"/>
    </justification>
  </clause>

  <clause id="17825">
    <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,16202,a(flip),b,17808,a)].">
      <j1 rule="hyper" parents="58 16202 17808"/>
    </justification>
  </clause>

  <clause id="17826">
    <literal><![CDATA[
      x * (y * (K(x,z) * K(x,z))) = T(T(x,z),z) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,5058,a(flip),b,17812,a),flip(a)].">
      <j1 rule="hyper" parents="320 5058 17812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17827">
    <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(17826(a,1),11729(a,2,2,1))].">
      <j1 rule="para" parents="17826 11729"/>
    </justification>
  </clause>

  <clause id="17828">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ y) \ w)) = T(x,(u \ T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(118,a,17814,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 17814 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17829">
    <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,16617,a(flip),b,17816,a),flip(a)].">
      <j1 rule="hyper" parents="58 16617 17816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17830">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13098,a(flip),b,17818,a),flip(a)].">
      <j1 rule="hyper" parents="58 13098 17818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17831">
    <literal><![CDATA[
      T(x,(T(y,z) \ z) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,17830,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 17830 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17832">
    <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(7917(a,1),17831(a,1,2,1,1))].">
      <j1 rule="para" parents="7917 17831"/>
    </justification>
  </clause>

  <clause id="17833">
    <literal><![CDATA[
      K(x,(y / (T(z,u) \ u)) / T(w,(u / z) \ y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w \ (y / (T(z,u) \ u))) = v5
    ]]></literal>
    <justification jstring="[para(17831(a,1),16066(a,1,2,2))].">
      <j1 rule="para" parents="17831 16066"/>
    </justification>
  </clause>

  <clause id="17834">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(17822(a,1),13085(a,1))].">
      <j1 rule="para" parents="17822 13085"/>
    </justification>
  </clause>

  <clause id="17835">
    <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(12695(a,1),17834(a,1,2,2,1))].">
      <j1 rule="para" parents="12695 17834"/>
    </justification>
  </clause>

  <clause id="17837">
    <literal><![CDATA[
      T(x,T(T(y,z) \ z,y) / u) = T(x,(y \ z) / u)
    ]]></literal>
    <justification jstring="[para(7634(a,1),17824(a,1,2,1))].">
      <j1 rule="para" parents="7634 17824"/>
    </justification>
  </clause>

  <clause id="17838">
    <literal><![CDATA[
      T(x,(y / T(z,y)) / u) = T(x,(z \ y) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16017,a(flip),b,17837,a)].">
      <j1 rule="hyper" parents="58 16017 17837"/>
    </justification>
  </clause>

  <clause id="17839">
    <literal><![CDATA[
      T(x,(y \ z) / T(u,y \ z)) = T(x,u \ (z / T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(12702,a,17838,a),flip(a)].">
      <j1 rule="hyper" parents="12702 17838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17840">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ y) \ w)) = T(x,((u \ T(y,z)) \ 1) * w)
    ]]></literal>
    <justification jstring="[hyper(320,a,13813,a,b,17828,a),flip(a)].">
      <j1 rule="hyper" parents="320 13813 17828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17841">
    <literal><![CDATA[
      T(x,y \ (z / T(u,z))) = T(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(12699,a,17839,a),flip(a)].">
      <j1 rule="hyper" parents="12699 17839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17842">
    <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(17841(a,1),5004(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="17841 5004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17843">
    <literal><![CDATA[
      x * (K(y,z) * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (K(u,w) * K(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(17759(a,1),17739(a,1))].">
      <j1 rule="para" parents="17759 17739"/>
    </justification>
  </clause>

  <clause id="17844">
    <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(13794(a,1),17752(a,1))].">
      <j1 rule="para" parents="13794 17752"/>
    </justification>
  </clause>

  <clause id="17845">
    <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(15184(a,2),17799(a,1))].">
      <j1 rule="para" parents="15184 17799"/>
    </justification>
  </clause>

  <clause id="17846">
    <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(17794(a,1),17799(a,1))].">
      <j1 rule="para" parents="17794 17799"/>
    </justification>
  </clause>

  <clause id="17847">
    <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(13146(a,2),17846(a,1))].">
      <j1 rule="para" parents="13146 17846"/>
    </justification>
  </clause>

  <clause id="17848">
    <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(17513(a,2),17846(a,1))].">
      <j1 rule="para" parents="17513 17846"/>
    </justification>
  </clause>

  <clause id="17849">
    <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(17592(a,2),17846(a,1))].">
      <j1 rule="para" parents="17592 17846"/>
    </justification>
  </clause>

  <clause id="17851">
    <literal><![CDATA[
      (x * K(y,z)) / (z * y) = x / (T(z,y) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16501,a(flip),b,17762,a),flip(a)].">
      <j1 rule="hyper" parents="58 16501 17762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17852">
    <literal><![CDATA[
      (x / (y * z)) * K(z,y) = x / (T(y,z) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10612,a(flip),b,17851,a)].">
      <j1 rule="hyper" parents="58 10612 17851"/>
    </justification>
  </clause>

  <clause id="17853">
    <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(440,a,14486,a,b,17852,a),flip(a)].">
      <j1 rule="hyper" parents="440 14486 17852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17854">
    <literal><![CDATA[
      x / (K(y,z) * K(u,w)) = x * (K(z,y) * K(w,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,17727,a,b,17764,a)].">
      <j1 rule="hyper" parents="35 17727 17764"/>
    </justification>
  </clause>

  <clause id="17857">
    <literal><![CDATA[
      x / (K(y,z) * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (K(w,u) * K(z,y)) = v5
    ]]></literal>
    <justification jstring="[para(17854(a,2),17843(a,1))].">
      <j1 rule="para" parents="17854 17843"/>
    </justification>
  </clause>

  <clause id="17858">
    <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(15584(a,1),17857(a,1,2))].">
      <j1 rule="para" parents="15584 17857"/>
    </justification>
  </clause>

  <clause id="17859">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ x)) = K(x,K(y,z) * (u \ (z * x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17566,a(flip),b,17788,a),flip(a)].">
      <j1 rule="hyper" parents="58 17566 17788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17860">
    <literal><![CDATA[
      K(x,(y / T(z,z \ u)) \ w) = K(x,(y / T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(320,a,17765,a(flip),b,17813,a),flip(a)].">
      <j1 rule="hyper" parents="320 17765 17813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17861">
    <literal><![CDATA[
      K(x,(y / T(z,y)) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(265(a,1),17860(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="265 17860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17862">
    <literal><![CDATA[
      T(x,(y / T(z,y)) \ u) = T(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,17861,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 17861 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17863">
    <literal><![CDATA[
      K(x,(T(y,z) / z) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4206(a,2),17861(a,1,2,1))].">
      <j1 rule="para" parents="4206 17861"/>
    </justification>
  </clause>

  <clause id="17864">
    <literal><![CDATA[
      T(x,(T(y,z) / z) \ u) = T(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4206(a,2),17862(a,1,2,1))].">
      <j1 rule="para" parents="4206 17862"/>
    </justification>
  </clause>

  <clause id="17865">
    <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,13073,a(flip),b,17815,a),flip(a)].">
      <j1 rule="hyper" parents="58 13073 17815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17866">
    <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,17536,a(flip),b,17817,a),flip(a)].">
      <j1 rule="hyper" parents="58 17536 17817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17867">
    <literal><![CDATA[
      T(x,T(y \ K(z,u),w) * v5) = T(x,K(z,u) * (T(y,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(17636,a,17829,a),flip(a)].">
      <j1 rule="hyper" parents="17636 17829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17868">
    <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(17840(a,2),14058(a,1))].">
      <j1 rule="para" parents="17840 14058"/>
    </justification>
  </clause>

  <clause id="17869">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ x)) = K(x,u \ (x * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(320,a,17607,a(flip),b,17859,a),flip(a)].">
      <j1 rule="hyper" parents="320 17607 17859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17870">
    <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,15290,a(flip),b,17866,a)].">
      <j1 rule="hyper" parents="58 15290 17866"/>
    </justification>
  </clause>

  <clause id="17871">
    <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,15291,a(flip),b,17867,a),flip(a)].">
      <j1 rule="hyper" parents="58 15291 17867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17872">
    <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,15939,a,b,17870,a)].">
      <j1 rule="hyper" parents="58 15939 17870"/>
    </justification>
  </clause>

  <clause id="17873">
    <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,13912,a(flip),b,17872,a),flip(a)].">
      <j1 rule="hyper" parents="58 13912 17872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17874">
    <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(17588(a,2),17848(a,1))].">
      <j1 rule="para" parents="17588 17848"/>
    </justification>
  </clause>

  <clause id="17875">
    <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(17590(a,1),17849(a,1))].">
      <j1 rule="para" parents="17590 17849"/>
    </justification>
  </clause>

  <clause id="17878">
    <literal><![CDATA[
      T(x,L(y,z \ T(u * z,w),u)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(17200(a,2),17748(a,1))].">
      <j1 rule="para" parents="17200 17748"/>
    </justification>
  </clause>

  <clause id="17879">
    <literal><![CDATA[
      T(T(x,y \ (z * z)),K(u,y \ (z * z))) = T(x,T((z \ y) \ z,u))
    ]]></literal>
    <justification jstring="[para(13890(a,1),17272(a,1,1))].">
      <j1 rule="para" parents="13890 17272"/>
    </justification>
  </clause>

  <clause id="17880">
    <literal><![CDATA[
      K(x * K(y,z),T(u,w / x)) = K(K(y,z) * x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(16339,a,17330,a)].">
      <j1 rule="hyper" parents="16339 17330"/>
    </justification>
  </clause>

  <clause id="17881">
    <literal><![CDATA[
      K(x * K(y,z),T(u,x \ w)) = K(K(y,z) * x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(15713,a,17880,a)].">
      <j1 rule="hyper" parents="15713 17880"/>
    </justification>
  </clause>

  <clause id="17882">
    <literal><![CDATA[
      L(x,T(y,z),(y / z) \ 1) = L(x,T(y,z),(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,12564,a(flip),b,17377,a)].">
      <j1 rule="hyper" parents="58 12564 17377"/>
    </justification>
  </clause>

  <clause id="17883">
    <literal><![CDATA[
      L(x,T(y,z),(z \ y) \ 1) = L(x,y,(y / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(14893,a,17882,a),flip(a)].">
      <j1 rule="hyper" parents="14893 17882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17884">
    <literal><![CDATA[
      L(x,y,(y / z) \ 1) = L(x,y,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(13224,a,17883,a),flip(a)].">
      <j1 rule="hyper" parents="13224 17883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17885">
    <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(1493(a,1),17884(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1493 17884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17886">
    <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(6168(a,2),17394(a,1,2,2))].">
      <j1 rule="para" parents="6168 17394"/>
    </justification>
  </clause>

  <clause id="17887">
    <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(15791,a,17526,a)].">
      <j1 rule="hyper" parents="15791 17526"/>
    </justification>
  </clause>

  <clause id="17888">
    <literal><![CDATA[
      K(x,y * (z * L(K(u,w),v5,v6))) = K(x,K(u,w) \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(17611,a,17531,a),flip(a)].">
      <j1 rule="hyper" parents="17611 17531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17889">
    <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(17888(a,2),8374(a,1))].">
      <j1 rule="para" parents="17888 8374"/>
    </justification>
  </clause>

  <clause id="17890">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ K(u,x))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = w
    ]]></literal>
    <justification jstring="[para(11332(a,1),17889(a,1))].">
      <j1 rule="para" parents="11332 17889"/>
    </justification>
  </clause>

  <clause id="17891">
    <literal><![CDATA[
      K(x,y / (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(13773(a,1),17890(a,1))].">
      <j1 rule="para" parents="13773 17890"/>
    </justification>
  </clause>

  <clause id="17892">
    <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(4027(a,1),17891(a,1,2,2))].">
      <j1 rule="para" parents="4027 17891"/>
    </justification>
  </clause>

  <clause id="17893">
    <literal><![CDATA[
      K(x,y / (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(5278(a,2),17891(a,1))].">
      <j1 rule="para" parents="5278 17891"/>
    </justification>
  </clause>

  <clause id="17894">
    <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(13788(a,1),17891(a,1))].">
      <j1 rule="para" parents="13788 17891"/>
    </justification>
  </clause>

  <clause id="17895">
    <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(13811(a,1),17893(a,1,2,2))].">
      <j1 rule="para" parents="13811 17893"/>
    </justification>
  </clause>

  <clause id="17896">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ (u / (z \ y)))
    ]]></literal>
    <justification jstring="[para(5377(a,1),17544(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5377 17544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17897">
    <literal><![CDATA[
      K(x,y \ (z * (u * (w / u)))) = K(x,K(u,w) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(15095,a,17545,a),flip(a)].">
      <j1 rule="hyper" parents="15095 17545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17898">
    <literal><![CDATA[
      K(x,y \ (z * (u * (w / u)))) = K(x,y \ (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,17602,a(flip),b,17897,a),flip(a)].">
      <j1 rule="hyper" parents="320 17602 17897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17899">
    <literal><![CDATA[
      K(x,y \ (z * T(u * w,w))) = K(x,y \ (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(6(a,1),17898(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6 17898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17900">
    <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,15244,a(flip),b,17899,a),flip(a)].">
      <j1 rule="hyper" parents="58 15244 17899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17901">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) * u))) = K(x,K(w,u) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(13134,a,17546,a),flip(a)].">
      <j1 rule="hyper" parents="13134 17546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17902">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) * u))) = K(x,y \ (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,17543,a(flip),b,17901,a),flip(a)].">
      <j1 rule="hyper" parents="320 17543 17901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17903">
    <literal><![CDATA[
      K(x,y \ (z * T(u * w,u))) = K(x,y \ (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(4(a,1),17902(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 17902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17904">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) * w)) = K(x,(u \ (z * (y / z))) * w)
    ]]></literal>
    <justification jstring="[hyper(13134,a,17551,a)].">
      <j1 rule="hyper" parents="13134 17551"/>
    </justification>
  </clause>

  <clause id="17905">
    <literal><![CDATA[
      K(x,(y \ (z * (u / z))) * w) = K(x,(y \ T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17604,a(flip),b,17904,a),flip(a)].">
      <j1 rule="hyper" parents="58 17604 17904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17906">
    <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,15397,a(flip),b,17905,a),flip(a)].">
      <j1 rule="hyper" parents="58 15397 17905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17907">
    <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,16083,a(flip),b,17553,a),flip(a)].">
      <j1 rule="hyper" parents="58 16083 17553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17908">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * z) * w)) = K(x,K(z,u) * (y \ (u * w)))
    ]]></literal>
    <justification jstring="[hyper(15095,a,17559,a),flip(a)].">
      <j1 rule="hyper" parents="15095 17559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17909">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * z) * w)) = K(x,y \ (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(320,a,17558,a(flip),b,17908,a),flip(a)].">
      <j1 rule="hyper" parents="320 17558 17908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17910">
    <literal><![CDATA[
      K(x,y \ ((z / (T(u,z) \ 1)) * w)) = K(x,y \ (T(z / (u \ 1),z) * w))
    ]]></literal>
    <justification jstring="[para(10077(a,1),17909(a,1,2,2,1))].">
      <j1 rule="para" parents="10077 17909"/>
    </justification>
  </clause>

  <clause id="17911">
    <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(320,a,17299,a(flip),b,17561,a),flip(a)].">
      <j1 rule="hyper" parents="320 17299 17561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17912">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y / z) * w))) = K(x,u \ ((z \ y) * w))
    ]]></literal>
    <justification jstring="[hyper(13134,a,17567,a)].">
      <j1 rule="hyper" parents="13134 17567"/>
    </justification>
  </clause>

  <clause id="17913">
    <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,15923,a(flip),b,17571,a)].">
      <j1 rule="hyper" parents="58 15923 17571"/>
    </justification>
  </clause>

  <clause id="17914">
    <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,17507,a(flip),b,17586,a),flip(a)].">
      <j1 rule="hyper" parents="58 17507 17586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17915">
    <literal><![CDATA[
      K(x,y * ((z \ (u \ w)) \ K(u,w))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(17535,a,17616,a)].">
      <j1 rule="hyper" parents="17535 17616"/>
    </justification>
  </clause>

  <clause id="17916">
    <literal><![CDATA[
      K(x,y / (z \ (u \ T(w,u)))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16094,a(flip),b,17915,a)].">
      <j1 rule="hyper" parents="58 16094 17915"/>
    </justification>
  </clause>

  <clause id="17917">
    <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(17617(a,1),16261(a,1))].">
      <j1 rule="para" parents="17617 16261"/>
    </justification>
  </clause>

  <clause id="17918">
    <literal><![CDATA[
      K(x * (K(y,z) * (y \ u)),w) = K(x * (T(y,z) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(16364,a,17620,a),flip(a)].">
      <j1 rule="hyper" parents="16364 17620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17919">
    <literal><![CDATA[
      K(x * ((y \ z) * K(y,u)),w) = K(x * (T(y,u) \ z),w)
    ]]></literal>
    <justification jstring="[hyper(16003,a,17918,a)].">
      <j1 rule="hyper" parents="16003 17918"/>
    </justification>
  </clause>

  <clause id="17920">
    <literal><![CDATA[
      K(x * (((y * z) / y) \ u),w) = K(x * (T(z,y) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,16197,a,b,17918,a)].">
      <j1 rule="hyper" parents="58 16197 17918"/>
    </justification>
  </clause>

  <clause id="17921">
    <literal><![CDATA[
      K(K(x,y) * (z * (x \ u)),w) = K(z * (T(x,y) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(17496,a,17919,a)].">
      <j1 rule="hyper" parents="17496 17919"/>
    </justification>
  </clause>

  <clause id="17922">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (u \ K(z,y))) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13168,a(flip),b,17622,a),flip(a)].">
      <j1 rule="hyper" parents="320 13168 17622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17923">
    <literal><![CDATA[
      K(x,(T(y,z) * (1 / z)) / u) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(17917,a,17922,a)].">
      <j1 rule="hyper" parents="17917 17922"/>
    </justification>
  </clause>

  <clause id="17924">
    <literal><![CDATA[
      K(x,(y * (1 / T(z,y))) / u) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[para(5226(a,1),17923(a,1,2,1))].">
      <j1 rule="para" parents="5226 17923"/>
    </justification>
  </clause>

  <clause id="17925">
    <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,14843,a(flip),b,17924,a)].">
      <j1 rule="hyper" parents="58 14843 17924"/>
    </justification>
  </clause>

  <clause id="17926">
    <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,17653,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 17653 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17927">
    <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(320,a,15962,a(flip),b,17671,a),flip(a)].">
      <j1 rule="hyper" parents="320 15962 17671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17928">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) \ v6) = K(x,K(z,u) \ (y \ v6))
    ]]></literal>
    <justification jstring="[hyper(320,a,17476,a(flip),b,17750,a),flip(a)].">
      <j1 rule="hyper" parents="320 17476 17750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17930">
    <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),17928(a,1,2,1))].">
      <j1 rule="para" parents="90 17928"/>
    </justification>
  </clause>

  <clause id="17931">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) \ v5) = K(x,((y * z) \ v5) * K(w,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,15628,a(flip),b,17930,a),flip(a)].">
      <j1 rule="hyper" parents="320 15628 17930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17932">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) \ v5) = K(x,K(w,u) * ((y * z) \ v5))
    ]]></literal>
    <justification jstring="[para(5092(a,1),17930(a,2,2))].">
      <j1 rule="para" parents="5092 17930"/>
    </justification>
  </clause>

  <clause id="17933">
    <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(17931(a,2),15638(a,1))].">
      <j1 rule="para" parents="17931 15638"/>
    </justification>
  </clause>

  <clause id="17934">
    <literal><![CDATA[
      T(x,(y \ T(z \ u,z)) \ w) = T(x,(y \ (u / z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(17868,a,17774,a)].">
      <j1 rule="hyper" parents="17868 17774"/>
    </justification>
  </clause>

  <clause id="17935">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * T(v5,z)))) = K(x,y / (v5 / (K(w,u) * z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17456,a(flip),b,17819,a)].">
      <j1 rule="hyper" parents="58 17456 17819"/>
    </justification>
  </clause>

  <clause id="17936">
    <literal><![CDATA[
      T(x,K(y * z,u) * (w / T(z,y))) = T(x,w / (T(z \ y,u) \ y))
    ]]></literal>
    <justification jstring="[hyper(16623,a,17825,a)].">
      <j1 rule="hyper" parents="16623 17825"/>
    </justification>
  </clause>

  <clause id="17937">
    <literal><![CDATA[
      T(x,T((y \ z) \ y,u)) = T(x,T(z \ (y * y),u))
    ]]></literal>
    <justification jstring="[hyper(7833,a,17879,a),flip(a)].">
      <j1 rule="hyper" parents="7833 17879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17938">
    <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(13661(a,1),17937(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="13661 17937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17939">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w) * v5)) = K(x,y / T(z,v5))
    ]]></literal>
    <justification jstring="[hyper(17648,a,17886,a),flip(a)].">
      <j1 rule="hyper" parents="17648 17886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17941">
    <literal><![CDATA[
      T(x,y / T(z,K(u,w) * v5)) = T(x,y / T(z,v5))
    ]]></literal>
    <justification jstring="[hyper(118,a,17939,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 17939 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17942">
    <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,15233,a(flip),b,17939,a),flip(a)].">
      <j1 rule="hyper" parents="58 15233 17939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17943">
    <literal><![CDATA[
      T(x,y \ K(K(z,u) * w,v5)) = T(x,(y \ v5) / T(v5,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,14078,a(flip),b,17941,a)].">
      <j1 rule="hyper" parents="58 14078 17941"/>
    </justification>
  </clause>

  <clause id="17944">
    <literal><![CDATA[
      T(x,y / T(z,u * T(w,v5))) = T(x,y / T(z,u * w))
    ]]></literal>
    <justification jstring="[para(5516(a,1),17941(a,1,2,2,2))].">
      <j1 rule="para" parents="5516 17941"/>
    </justification>
  </clause>

  <clause id="17945">
    <literal><![CDATA[
      T(x,y \ K(K(z,u) * w,v5)) = T(x,y \ K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,14078,a(flip),b,17943,a),flip(a)].">
      <j1 rule="hyper" parents="320 14078 17943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17946">
    <literal><![CDATA[
      T(x,y \ K(T(z,u) \ w,v5)) = T(x,y \ K(z \ w,v5))
    ]]></literal>
    <justification jstring="[para(5042(a,1),17945(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5042 17945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17947">
    <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(16105,a,17944,a),flip(a)].">
      <j1 rule="hyper" parents="16105 17944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17948">
    <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(17944(a,1),16016(a,1))].">
      <j1 rule="para" parents="17944 16016"/>
    </justification>
  </clause>

  <clause id="17949">
    <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,17784,a(flip),b,17946,a),flip(a)].">
      <j1 rule="hyper" parents="58 17784 17946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17950">
    <literal><![CDATA[
      K(x,y \ (T(z * u,u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15243,a(flip),b,17900,a),flip(a)].">
      <j1 rule="hyper" parents="58 15243 17900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17951">
    <literal><![CDATA[
      K(x,((y * (z / y)) / u) * w) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15395,a(flip),b,17906,a),flip(a)].">
      <j1 rule="hyper" parents="58 15395 17906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17952">
    <literal><![CDATA[
      K(x,(T(y * z,y) / u) * w) = K(x,((T(y,z) * z) / u) * w)
    ]]></literal>
    <justification jstring="[para(4051(a,2),17951(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4051 17951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17953">
    <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(15052,a,17911,a)].">
      <j1 rule="hyper" parents="15052 17911"/>
    </justification>
  </clause>

  <clause id="17954">
    <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,17493,a(flip),b,17913,a)].">
      <j1 rule="hyper" parents="58 17493 17913"/>
    </justification>
  </clause>

  <clause id="17955">
    <literal><![CDATA[
      T(x,T(y * K(z,y \ u),u)) = T(x,T((u \ y) \ 1,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(15724,a,17954,a)].">
      <j1 rule="hyper" parents="15724 17954"/>
    </justification>
  </clause>

  <clause id="17956">
    <literal><![CDATA[
      T(x,T((y \ z) \ 1,u) \ y) = T(x,T(z \ y,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(7691,a,17955,a),flip(a)].">
      <j1 rule="hyper" parents="7691 17955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17957">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ z) = T(x,T(z \ y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15285,a(flip),b,17956,a),flip(a)].">
      <j1 rule="hyper" parents="58 15285 17956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17958">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ z) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,12251,a(flip),b,17957,a),flip(a)].">
      <j1 rule="hyper" parents="320 12251 17957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17959">
    <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,16292,a(flip),b,17958,a),flip(a)].">
      <j1 rule="hyper" parents="58 16292 17958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17960">
    <literal><![CDATA[
      T(x,T(y / z,u) \ y) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16294,a(flip),b,17959,a),flip(a)].">
      <j1 rule="hyper" parents="58 16294 17959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17961">
    <literal><![CDATA[
      T(x,y * K(z,u \ (w * (v5 \ 1)))) = T(x,K(z,v5 * (w \ u)) * y)
    ]]></literal>
    <justification jstring="[hyper(15857,a,17926,a)].">
      <j1 rule="hyper" parents="15857 17926"/>
    </justification>
  </clause>

  <clause id="17962">
    <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,16653,a,b,17927,a)].">
      <j1 rule="hyper" parents="58 16653 17927"/>
    </justification>
  </clause>

  <clause id="17963">
    <literal><![CDATA[
      T(x,y / (T(z \ u,w) \ u)) = T(x,y / (u \ T(z * u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17807,a(flip),b,17936,a),flip(a)].">
      <j1 rule="hyper" parents="58 17807 17936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17964">
    <literal><![CDATA[
      T(x,y / ((z \ T(u,w)) \ u)) = T(x,y * T(z \ K(w,u),u))
    ]]></literal>
    <justification jstring="[para(16129(a,1),17962(a,1,2,2))].">
      <j1 rule="para" parents="16129 17962"/>
    </justification>
  </clause>

  <clause id="17965">
    <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,16672,a(flip),b,17964,a),flip(a)].">
      <j1 rule="hyper" parents="58 16672 17964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17966">
    <literal><![CDATA[
      L(x,K(y,z) * u,z * y) = L(x,u,z * y)
    ]]></literal>
    <justification jstring="[hyper(14096,a,17151,a)].">
      <j1 rule="hyper" parents="14096 17151"/>
    </justification>
  </clause>

  <clause id="17968">
    <literal><![CDATA[
      L(x,K(y,z / y) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[para(7(a,1),17966(a,1,3))].">
      <j1 rule="para" parents="7 17966"/>
    </justification>
  </clause>

  <clause id="17969">
    <literal><![CDATA[
      L(x,K(y,y \ z) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[para(4871(a,1),17968(a,1,2,1))].">
      <j1 rule="para" parents="4871 17968"/>
    </justification>
  </clause>

  <clause id="17970">
    <literal><![CDATA[
      L(x,K(y,z) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,13208,a(flip),b,17969,a)].">
      <j1 rule="hyper" parents="58 13208 17969"/>
    </justification>
  </clause>

  <clause id="17971">
    <literal><![CDATA[
      L(x,K(y,z) * u,z) = L(x,u,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),17970(a,2,3))].">
      <j1 rule="para" parents="7 17970"/>
    </justification>
  </clause>

  <clause id="17972">
    <literal><![CDATA[
      L(x,K(y,z) * u,y) = L(x,u,y)
    ]]></literal>
    <justification jstring="[para(5095(a,1),17971(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5095 17971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17977">
    <literal><![CDATA[
      L(x,y \ K(z,u),z) = L(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(13816(a,1),17972(a,1,2))].">
      <j1 rule="para" parents="13816 17972"/>
    </justification>
  </clause>

  <clause id="17978">
    <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(6086(a,1),17403(a,2,1,2))].">
      <j1 rule="para" parents="6086 17403"/>
    </justification>
  </clause>

  <clause id="17979">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,v5)))) = K(x,K(v5,w) * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(17491,a,17518,a),flip(a)].">
      <j1 rule="hyper" parents="17491 17518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17980">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,v5)))) = K(x,(y \ (z * u)) * K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(17490,a,17518,a),flip(a)].">
      <j1 rule="hyper" parents="17490 17518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17982">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,v5)))) = K(x,K(w,v5) * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,15051,a,b,17979,a),flip(a)].">
      <j1 rule="hyper" parents="320 15051 17979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17983">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * (v5 \ z)))) = K(x,u \ (w * (v5 \ T(z,y))))
    ]]></literal>
    <justification jstring="[para(13634(a,1),17979(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13634 17979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17984">
    <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,16504,a(flip),b,17980,a),flip(a)].">
      <j1 rule="hyper" parents="58 16504 17980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17985">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * (w \ (v5 * u))) = K(x,w \ (v5 * (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[para(7152(a,1),17982(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7152 17982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17986">
    <literal><![CDATA[
      K(x,T(y,z) \ (u * (w \ y))) = K(x,y \ (u * (w \ T(y,z))))
    ]]></literal>
    <justification jstring="[para(5093(a,1),17983(a,1,2))].">
      <j1 rule="para" parents="5093 17983"/>
    </justification>
  </clause>

  <clause id="17987">
    <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),17984(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="105 17984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17988">
    <literal><![CDATA[
      K(x,y \ ((K(z,u) * w) * v5)) = K(x,K(z,u) * (y \ (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(320,a,15741,a,b,17987,a),flip(a)].">
      <j1 rule="hyper" parents="320 15741 17987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17989">
    <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),17987(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13 17987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17990">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y * w) * v5))) = K(x,u \ ((T(y,z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(4740(a,1),17988(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4740 17988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17991">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y / z) * w))) = K(x,u \ ((T(y,z) / z) * w))
    ]]></literal>
    <justification jstring="[para(5212(a,1),17988(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5212 17988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17993">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,w) * v5))) = K(x,K(w,u) * (y \ (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(16039,a,17985,a),flip(a)].">
      <j1 rule="hyper" parents="16039 17985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17994">
    <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(17985(a,1),16039(a,1))].">
      <j1 rule="para" parents="17985 16039"/>
    </justification>
  </clause>

  <clause id="17996">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) / u) * w)) = K(x,y \ ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17912,a(flip),b,17991,a),flip(a)].">
      <j1 rule="hyper" parents="58 17912 17991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17997">
    <literal><![CDATA[
      K(x,T(y / (z \ u),x) * (w \ K(z,u))) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(17847,a,17303,a)].">
      <j1 rule="hyper" parents="17847 17303"/>
    </justification>
  </clause>

  <clause id="17998">
    <literal><![CDATA[
      K(x,(y / (z \ u)) * (w \ K(z,u))) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(8372,a,17997,a)].">
      <j1 rule="hyper" parents="8372 17997"/>
    </justification>
  </clause>

  <clause id="17999">
    <literal><![CDATA[
      K(x,(y / (T(z,u) \ u)) / w) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17325,a(flip),b,17998,a)].">
      <j1 rule="hyper" parents="58 17325 17998"/>
    </justification>
  </clause>

  <clause id="18000">
    <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(320,a,17328,a(flip),b,17339,a),flip(a)].">
      <j1 rule="hyper" parents="320 17328 17339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18001">
    <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(17608,a,18000,a)].">
      <j1 rule="hyper" parents="17608 18000"/>
    </justification>
  </clause>

  <clause id="18002">
    <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,17871,a(flip),b,18001,a),flip(a)].">
      <j1 rule="hyper" parents="58 17871 18001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18003">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,w)) = T(x,z * T(T(y,w) / z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,17958,a(flip),b,18002,a),flip(a)].">
      <j1 rule="hyper" parents="320 17958 18002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18004">
    <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(17411(a,2),13994(a,1))].">
      <j1 rule="para" parents="17411 13994"/>
    </justification>
  </clause>

  <clause id="18005">
    <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(18004,a,16837,a)].">
      <j1 rule="hyper" parents="18004 16837"/>
    </justification>
  </clause>

  <clause id="18006">
    <literal><![CDATA[
      K(x,y / T((K(z,u) * w) \ v5,w)) = K(x,y / ((K(z,u) \ v5) / w))
    ]]></literal>
    <justification jstring="[hyper(15912,a,17461,a)].">
      <j1 rule="hyper" parents="15912 17461"/>
    </justification>
  </clause>

  <clause id="18007">
    <literal><![CDATA[
      K(x,y / ((K(z,u) \ w) / v5)) = K(x,y / (w / (K(z,u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17942,a(flip),b,18006,a),flip(a)].">
      <j1 rule="hyper" parents="58 17942 18006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18008">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) / v5)) = K(x,y / (w / (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[para(5092(a,1),18007(a,1,2,2,1))].">
      <j1 rule="para" parents="5092 18007"/>
    </justification>
  </clause>

  <clause id="18009">
    <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(15095,a,17470,a)].">
      <j1 rule="hyper" parents="15095 17470"/>
    </justification>
  </clause>

  <clause id="18011">
    <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,17506,a(flip),b,18009,a)].">
      <j1 rule="hyper" parents="58 17506 18009"/>
    </justification>
  </clause>

  <clause id="18012">
    <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(6440(a,1),18009(a,1,2,2,2,1))].">
      <j1 rule="para" parents="6440 18009"/>
    </justification>
  </clause>

  <clause id="18013">
    <literal><![CDATA[
      K(x,K(y,z) * (((z * y) / u) * w)) = K(x,(((y * z) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[hyper(16039,a,17552,a)].">
      <j1 rule="hyper" parents="16039 17552"/>
    </justification>
  </clause>

  <clause id="18014">
    <literal><![CDATA[
      K(x,(((y * z) / u) \ 1) \ w) = K(x,((T(z,y) * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17525,a(flip),b,18013,a),flip(a)].">
      <j1 rule="hyper" parents="58 17525 18013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18015">
    <literal><![CDATA[
      K(x,((T(y,z) * z) / u) * w) = K(x,((z * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(13941,a,18014,a),flip(a)].">
      <j1 rule="hyper" parents="13941 18014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18016">
    <literal><![CDATA[
      K(x,(T(y * z,y) / u) * w) = K(x,((z * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17952,a,b,18015,a)].">
      <j1 rule="hyper" parents="58 17952 18015"/>
    </justification>
  </clause>

  <clause id="18017">
    <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(17589(a,2),15991(a,1))].">
      <j1 rule="para" parents="17589 15991"/>
    </justification>
  </clause>

  <clause id="18019">
    <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,17990,a(flip),b,17655,a)].">
      <j1 rule="hyper" parents="58 17990 17655"/>
    </justification>
  </clause>

  <clause id="18020">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) * u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(178(a,1),18019(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="178 18019"/>
    </justification>
  </clause>

  <clause id="18021">
    <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(16101,a,17670,a),flip(a)].">
      <j1 rule="hyper" parents="16101 17670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18023">
    <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(16488(a,2),17746(a,1,2,2))].">
      <j1 rule="para" parents="16488 17746"/>
    </justification>
  </clause>

  <clause id="18024">
    <literal><![CDATA[
      K(x,y \ (z / T(u,T(w,v5)))) = K(x,y \ (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,16065,a(flip),b,17823,a),flip(a)].">
      <j1 rule="hyper" parents="320 16065 17823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18025">
    <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,17934,a(flip),b,17832,a)].">
      <j1 rule="hyper" parents="58 17934 17832"/>
    </justification>
  </clause>

  <clause id="18026">
    <literal><![CDATA[
      T(x,(T(y \ z,y) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17831,a(flip),b,18025,a),flip(a)].">
      <j1 rule="hyper" parents="58 17831 18025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18027">
    <literal><![CDATA[
      T(x,((((y \ z) \ z) \ z) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[para(4199(a,1),18026(a,1,2,1,1))].">
      <j1 rule="para" parents="4199 18026"/>
    </justification>
  </clause>

  <clause id="18028">
    <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,15191,a(flip),b,17873,a)].">
      <j1 rule="hyper" parents="58 15191 17873"/>
    </justification>
  </clause>

  <clause id="18029">
    <literal><![CDATA[
      K(x,y \ ((z / (T(u,z) \ 1)) * w)) = K(x,y \ (((u \ 1) \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(320,a,13118,a(flip),b,17910,a),flip(a)].">
      <j1 rule="hyper" parents="320 13118 17910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18030">
    <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,17678,a,b,18029,a)].">
      <j1 rule="hyper" parents="58 17678 18029"/>
    </justification>
  </clause>

  <clause id="18031">
    <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(13757(a,1),17938(a,2,2,1))].">
      <j1 rule="para" parents="13757 17938"/>
    </justification>
  </clause>

  <clause id="18032">
    <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(4266(a,1),18031(a,2,2,1,2))].">
      <j1 rule="para" parents="4266 18031"/>
    </justification>
  </clause>

  <clause id="18033">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ (y * y),u)) = T(x,T(z \ T(y,z),u))
    ]]></literal>
    <justification jstring="[hyper(320,a,13184,a(flip),b,18032,a),flip(a)].">
      <j1 rule="hyper" parents="320 13184 18032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18034">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ (y * y),u)) = T(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,12704,a(flip),b,18033,a),flip(a)].">
      <j1 rule="hyper" parents="320 12704 18033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18035">
    <literal><![CDATA[
      T(x,T((y * z) \ (z * z),u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(13183,a,18034,a)].">
      <j1 rule="hyper" parents="13183 18034"/>
    </justification>
  </clause>

  <clause id="18036">
    <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(440,a,18035,a,b,13841,a)].">
      <j1 rule="hyper" parents="440 18035 13841"/>
    </justification>
  </clause>

  <clause id="18037">
    <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,15395,a(flip),b,18011,a)].">
      <j1 rule="hyper" parents="58 15395 18011"/>
    </justification>
  </clause>

  <clause id="18038">
    <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,15083,a(flip),b,18021,a)].">
      <j1 rule="hyper" parents="58 15083 18021"/>
    </justification>
  </clause>

  <clause id="18039">
    <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,16239,a(flip),b,18023,a)].">
      <j1 rule="hyper" parents="58 16239 18023"/>
    </justification>
  </clause>

  <clause id="18040">
    <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,17537,a(flip),b,18028,a),flip(a)].">
      <j1 rule="hyper" parents="58 17537 18028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18041">
    <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,18003,a,b,18040,a)].">
      <j1 rule="hyper" parents="58 18003 18040"/>
    </justification>
  </clause>

  <clause id="18042">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,w)) = T(x,T(z * T(y / z,u),w))
    ]]></literal>
    <justification jstring="[hyper(15722,a,18041,a)].">
      <j1 rule="hyper" parents="15722 18041"/>
    </justification>
  </clause>

  <clause id="18044">
    <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,18003,a(flip),b,18042,a),flip(a)].">
      <j1 rule="hyper" parents="58 18003 18042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18046">
    <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(18044(a,1),15722(a,1))].">
      <j1 rule="para" parents="18044 15722"/>
    </justification>
  </clause>

  <clause id="18047">
    <literal><![CDATA[
      K(x,T(y * z,x) * (u \ K(w,v5))) = K(x,(y * (z * K(w,v5))) / u)
    ]]></literal>
    <justification jstring="[hyper(17874,a,17302,a)].">
      <j1 rule="hyper" parents="17874 17302"/>
    </justification>
  </clause>

  <clause id="18048">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) / v5) = K(x,(y * z) * (v5 \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(8372,a,18047,a),flip(a)].">
      <j1 rule="hyper" parents="8372 18047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18049">
    <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,16503,a(flip),b,18048,a),flip(a)].">
      <j1 rule="hyper" parents="58 16503 18048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18050">
    <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),18049(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="105 18049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18051">
    <literal><![CDATA[
      (x / (y * x)) * ((y * x) * K(z,u)) = x * K(z,L(u,x,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(5768,a,17311,a)].">
      <j1 rule="hyper" parents="5768 17311"/>
    </justification>
  </clause>

  <clause id="18052">
    <literal><![CDATA[
      K(x,y / (z \ a(u \ 1,u,z))) = K(x,a(u \ 1,u,z) \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(17363,a,17455,a),flip(a)].">
      <j1 rule="hyper" parents="17363 17455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18053">
    <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(18052(a,1),17892(a,1))].">
      <j1 rule="para" parents="18052 17892"/>
    </justification>
  </clause>

  <clause id="18054">
    <literal><![CDATA[
      K(x,(x * y) \ (x * T(z,y * x))) = K(x,R(z,z \ (x * y),z) / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,17869,a(flip),b,17542,a)].">
      <j1 rule="hyper" parents="320 17869 17542"/>
    </justification>
  </clause>

  <clause id="18055">
    <literal><![CDATA[
      K(x,R(y,y \ (x * z),y) / z) = K(x,z \ T(y,z * x))
    ]]></literal>
    <justification jstring="[hyper(7366,a,18054,a),flip(a)].">
      <j1 rule="hyper" parents="7366 18054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18056">
    <literal><![CDATA[
      K(x,y \ T(z,y * x)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(13017,a,18055,a),flip(a)].">
      <j1 rule="hyper" parents="13017 18055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18058">
    <literal><![CDATA[
      K(x,(1 / y) \ T(T(z,y),(1 / y) * x)) = K(x,z / (K(y,z) / y))
    ]]></literal>
    <justification jstring="[para(13763(a,1),18056(a,2,2))].">
      <j1 rule="para" parents="13763 18056"/>
    </justification>
  </clause>

  <clause id="18059">
    <literal><![CDATA[
      K(x,(1 / y) \ T(T(z,y),y \ x)) = K(x,z / (K(y,z) / y))
    ]]></literal>
    <justification jstring="[para(13736(a,1),18058(a,1,2,2))].">
      <j1 rule="para" parents="13736 18058"/>
    </justification>
  </clause>

  <clause id="18060">
    <literal><![CDATA[
      K(x,y / (K(z,y) / z)) = K(x,z * T(T(y,z),z \ x))
    ]]></literal>
    <justification jstring="[hyper(14003,a,18059,a),flip(a)].">
      <j1 rule="hyper" parents="14003 18059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18061">
    <literal><![CDATA[
      K(x,y / (K(z,y) / z)) = K(x,T(y,z \ x) * z)
    ]]></literal>
    <justification jstring="[para(236(a,1),18060(a,2,2))].">
      <j1 rule="para" parents="236 18060"/>
    </justification>
  </clause>

  <clause id="18062">
    <literal><![CDATA[
      K(x,T(y,z \ x) * z) = K(x,y * (z * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(17895,a,18061,a),flip(a)].">
      <j1 rule="hyper" parents="17895 18061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18063">
    <literal><![CDATA[
      K(x,T(y,z \ x) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,12250,a(flip),b,18062,a),flip(a)].">
      <j1 rule="hyper" parents="320 12250 18062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18064">
    <literal><![CDATA[
      K(x,T(y,(x * z) \ x) * (x * z)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7531,a,b,18063,a),flip(a)].">
      <j1 rule="hyper" parents="320 7531 18063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18065">
    <literal><![CDATA[
      K(x,T(y,z \ 1) * (x * z)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[para(6144(a,1),18064(a,1,2,1))].">
      <j1 rule="para" parents="6144 18064"/>
    </justification>
  </clause>

  <clause id="18066">
    <literal><![CDATA[
      K(x,T(y,z) * (x * z)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15306,a(flip),b,18065,a)].">
      <j1 rule="hyper" parents="58 15306 18065"/>
    </justification>
  </clause>

  <clause id="18068">
    <literal><![CDATA[
      K(x,y * (T(z,y) * x)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(15888,a,18066,a)].">
      <j1 rule="hyper" parents="15888 18066"/>
    </justification>
  </clause>

  <clause id="18069">
    <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(18068(a,1),7891(a,1,2,2))].">
      <j1 rule="para" parents="18068 7891"/>
    </justification>
  </clause>

  <clause id="18070">
    <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(10809(a,1),17549(a,1,2,1))].">
      <j1 rule="para" parents="10809 17549"/>
    </justification>
  </clause>

  <clause id="18071">
    <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(10809(a,1),17673(a,1,2,2,2))].">
      <j1 rule="para" parents="10809 17673"/>
    </justification>
  </clause>

  <clause id="18072">
    <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(10975(a,1),17674(a,1,2))].">
      <j1 rule="para" parents="10975 17674"/>
    </justification>
  </clause>

  <clause id="18073">
    <literal><![CDATA[
      K(x,y * (z / T(u,K(w,v5) * v6))) = K(x,y * (z / T(u,v6)))
    ]]></literal>
    <justification jstring="[hyper(16166,a,18072,a),flip(a)].">
      <j1 rule="hyper" parents="16166 18072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18074">
    <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,13095,a(flip),b,18073,a),flip(a)].">
      <j1 rule="hyper" parents="58 13095 18073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18075">
    <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,17575,a(flip),b,18074,a)].">
      <j1 rule="hyper" parents="58 17575 18074"/>
    </justification>
  </clause>

  <clause id="18076">
    <literal><![CDATA[
      K(x,y * (z \ (K(u,w) * v5))) = K(x,y * (K(u,w) * (z \ v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13162,a(flip),b,18075,a),flip(a)].">
      <j1 rule="hyper" parents="58 13162 18075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18077">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ (v5 \ 1)))) = K(x,y * (w \ (v5 \ K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(16165,a,18076,a),flip(a)].">
      <j1 rule="hyper" parents="16165 18076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18078">
    <literal><![CDATA[
      K(x,y * (z \ (u * K(w,v5)))) = K(x,y * (K(w,v5) * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(16163,a,18076,a)].">
      <j1 rule="hyper" parents="16163 18076"/>
    </justification>
  </clause>

  <clause id="18079">
    <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,17627,a(flip),b,18078,a)].">
      <j1 rule="hyper" parents="58 17627 18078"/>
    </justification>
  </clause>

  <clause id="18080">
    <literal><![CDATA[
      K(x,y * ((T(z,u) \ u) \ (w \ K(u,z)))) = K(x,y * ((z \ u) \ (w \ 1)))
    ]]></literal>
    <justification jstring="[para(13235(a,1),18077(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13235 18077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18081">
    <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(178(a,1),17800(a,1,2))].">
      <j1 rule="para" parents="178 17800"/>
    </justification>
  </clause>

  <clause id="18082">
    <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),18046(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="104 18046"/>
    </justification>
  </clause>

  <clause id="18083">
    <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(18028(a,2),18046(a,1))].">
      <j1 rule="para" parents="18028 18046"/>
    </justification>
  </clause>

  <clause id="18084">
    <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(17534,a,18070,a)].">
      <j1 rule="hyper" parents="17534 18070"/>
    </justification>
  </clause>

  <clause id="18085">
    <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(18084(a,1),17487(a,1))].">
      <j1 rule="para" parents="18084 17487"/>
    </justification>
  </clause>

  <clause id="18086">
    <literal><![CDATA[
      K(x,y * (z * ((u / w) * K(w,v5)))) = K(x,y * (z * (u / T(w,v5))))
    ]]></literal>
    <justification jstring="[para(10877(a,1),18071(a,1,2,2))].">
      <j1 rule="para" parents="10877 18071"/>
    </justification>
  </clause>

  <clause id="18087">
    <literal><![CDATA[
      K(x,T(y,z) * (u * (w / y))) = K(x,y * (u * (w / T(y,z))))
    ]]></literal>
    <justification jstring="[hyper(17652,a,18086,a)].">
      <j1 rule="hyper" parents="17652 18086"/>
    </justification>
  </clause>

  <clause id="18088">
    <literal><![CDATA[
      K(x,y * (z * (u / T(y,u * z)))) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16514,a(flip),b,18087,a),flip(a)].">
      <j1 rule="hyper" parents="58 16514 18087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18089">
    <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(17510(a,2),18083(a,1))].">
      <j1 rule="para" parents="17510 18083"/>
    </justification>
  </clause>

  <clause id="18090">
    <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(16712(a,2),18089(a,1))].">
      <j1 rule="para" parents="16712 18089"/>
    </justification>
  </clause>

  <clause id="18091">
    <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(16119(a,1),18090(a,1))].">
      <j1 rule="para" parents="16119 18090"/>
    </justification>
  </clause>

  <clause id="18092">
    <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(12269(a,2),18091(a,1))].">
      <j1 rule="para" parents="12269 18091"/>
    </justification>
  </clause>

  <clause id="18093">
    <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(16680(a,1),18092(a,1))].">
      <j1 rule="para" parents="16680 18092"/>
    </justification>
  </clause>

  <clause id="18094">
    <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(6306(a,1),17350(a,1,2,2,1))].">
      <j1 rule="para" parents="6306 17350"/>
    </justification>
  </clause>

  <clause id="18095">
    <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(17516(a,1),17369(a,1))].">
      <j1 rule="para" parents="17516 17369"/>
    </justification>
  </clause>

  <clause id="18096">
    <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(5092(a,1),17457(a,2,2,2,1,2))].">
      <j1 rule="para" parents="5092 17457"/>
    </justification>
  </clause>

  <clause id="18097">
    <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(320,a,13789,a(flip),b,17527,a),flip(a)].">
      <j1 rule="hyper" parents="320 13789 17527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18098">
    <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(18097(a,1),17893(a,1))].">
      <j1 rule="para" parents="18097 17893"/>
    </justification>
  </clause>

  <clause id="18099">
    <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(18037(a,1),18098(a,1))].">
      <j1 rule="para" parents="18037 18098"/>
    </justification>
  </clause>

  <clause id="18100">
    <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(15275,a,17560,a)].">
      <j1 rule="hyper" parents="15275 17560"/>
    </justification>
  </clause>

  <clause id="18101">
    <literal><![CDATA[
      K(x,(K(y \ z,z) * u) / w) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17953,a(flip),b,18100,a),flip(a)].">
      <j1 rule="hyper" parents="58 17953 18100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18102">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(17300,a,18101,a)].">
      <j1 rule="hyper" parents="17300 18101"/>
    </justification>
  </clause>

  <clause id="18103">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w \ u))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(6264(a,1),18102(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6264 18102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18104">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * (u \ K(z,y \ z))) = K(x,T((y \ (z * u)) / u,z))
    ]]></literal>
    <justification jstring="[hyper(16103,a,17582,a)].">
      <j1 rule="hyper" parents="16103 17582"/>
    </justification>
  </clause>

  <clause id="18105">
    <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,18103,a(flip),b,18104,a)].">
      <j1 rule="hyper" parents="58 18103 18104"/>
    </justification>
  </clause>

  <clause id="18106">
    <literal><![CDATA[
      K(x,(T(y,z) \ (z * u)) / u) = K(x,T((y \ (z * u)) / u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,17593,a(flip),b,18105,a)].">
      <j1 rule="hyper" parents="58 17593 18105"/>
    </justification>
  </clause>

  <clause id="18107">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * (u \ K(y,y \ z))) = K(x,T((y \ (z * u)) / u,y))
    ]]></literal>
    <justification jstring="[hyper(16103,a,17583,a)].">
      <j1 rule="hyper" parents="16103 17583"/>
    </justification>
  </clause>

  <clause id="18108">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * (u \ K(z,y))) = K(x,T((y \ (z * u)) / u,y))
    ]]></literal>
    <justification jstring="[hyper(17875,a,18107,a)].">
      <j1 rule="hyper" parents="17875 18107"/>
    </justification>
  </clause>

  <clause id="18109">
    <literal><![CDATA[
      K(x,T((y \ (z * u)) / u,y)) = K(x,(T(y,z) \ (z * u)) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,17327,a(flip),b,18108,a),flip(a)].">
      <j1 rule="hyper" parents="58 17327 18108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18110">
    <literal><![CDATA[
      K(x,T((y \ (z * u)) / u,z)) = K(x,T((y \ (z * u)) / u,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,18106,a(flip),b,18109,a)].">
      <j1 rule="hyper" parents="320 18106 18109"/>
    </justification>
  </clause>

  <clause id="18111">
    <literal><![CDATA[
      K(x,y * ((z \ (u * y)) \ K(u,u \ z))) = K(x,T(y / (z \ (u * y)),u))
    ]]></literal>
    <justification jstring="[hyper(16103,a,17584,a)].">
      <j1 rule="hyper" parents="16103 17584"/>
    </justification>
  </clause>

  <clause id="18112">
    <literal><![CDATA[
      K(x,y * ((z \ (u * y)) \ K(z,u))) = K(x,T(y / (z \ (u * y)),u))
    ]]></literal>
    <justification jstring="[hyper(17875,a,18111,a)].">
      <j1 rule="hyper" parents="17875 18111"/>
    </justification>
  </clause>

  <clause id="18113">
    <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(18112(a,1),14010(a,1))].">
      <j1 rule="para" parents="18112 14010"/>
    </justification>
  </clause>

  <clause id="18114">
    <literal><![CDATA[
      K(x,y * (z * K((u * w) \ y,u * w))) = K(x,T(y,w * u) * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,13161,a(flip),b,17654,a),flip(a)].">
      <j1 rule="hyper" parents="320 13161 17654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18115">
    <literal><![CDATA[
      K(x,y * (z * K(u \ (w \ y),w * u))) = K(x,T(y,u * w) * z)
    ]]></literal>
    <justification jstring="[para(13898(a,1),18114(a,1,2,2,2))].">
      <j1 rule="para" parents="13898 18114"/>
    </justification>
  </clause>

  <clause id="18116">
    <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(18085,a,17681,a)].">
      <j1 rule="hyper" parents="18085 17681"/>
    </justification>
  </clause>

  <clause id="18117">
    <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(4736(a,1),18005(a,1,1,2,1))].">
      <j1 rule="para" parents="4736 18005"/>
    </justification>
  </clause>

  <clause id="18118">
    <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(17291(a,1),18117(a,1,1))].">
      <j1 rule="para" parents="17291 18117"/>
    </justification>
  </clause>

  <clause id="18119">
    <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,13122,a(flip),b,18118,a)].">
      <j1 rule="hyper" parents="58 13122 18118"/>
    </justification>
  </clause>

  <clause id="18120">
    <literal><![CDATA[
      K(x \ T(y,K(z,u) * w),v5) = K(x \ T(y,w),v5)
    ]]></literal>
    <justification jstring="[hyper(15971,a,18119,a),flip(a)].">
      <j1 rule="hyper" parents="15971 18119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18121">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) = K(y \ K(x,z * K(w,v5)),u)
    ]]></literal>
    <justification jstring="[hyper(16070,a,18120,a),flip(a)].">
      <j1 rule="hyper" parents="16070 18120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18122">
    <literal><![CDATA[
      K(x \ K(y,z * K(u,w)),v5) = K(x \ K(y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(6685,a,18121,a),flip(a)].">
      <j1 rule="hyper" parents="6685 18121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18123">
    <literal><![CDATA[
      K(x \ K(y \ K(z,u),w),v5) = K(x \ K(w,y),v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,17907,a,b,18122,a)].">
      <j1 rule="hyper" parents="58 17907 18122"/>
    </justification>
  </clause>

  <clause id="18124">
    <literal><![CDATA[
      K((x / y) \ K(y,z),u) = K(T(y,z \ K(w,v5)) / x,u)
    ]]></literal>
    <justification jstring="[hyper(16290,a,18123,a),flip(a)].">
      <j1 rule="hyper" parents="16290 18123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18126">
    <literal><![CDATA[
      K(T(x,y \ K(z,u)) / w,v5) = K(T(x,y) / w,v5)
    ]]></literal>
    <justification jstring="[hyper(16289,a,18124,a),flip(a)].">
      <j1 rule="hyper" parents="16289 18124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18127">
    <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,16649,a(flip),b,18126,a),flip(a)].">
      <j1 rule="hyper" parents="58 16649 18126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18128">
    <literal><![CDATA[
      K(T(x,y \ T(z,u)) / w,v5) = K(T(x,z \ y) / w,v5)
    ]]></literal>
    <justification jstring="[para(6529(a,1),18126(a,1,1,1))].">
      <j1 rule="para" parents="6529 18126"/>
    </justification>
  </clause>

  <clause id="18129">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w)) / v5) = (v6 * K(T(y,u \ z) / v5,x)) \ v6
    ]]></literal>
    <justification jstring="[para(18128(a,1),6309(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="18128 6309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18131">
    <literal><![CDATA[
      K(((x * y) * (1 / y)) / z,u) = K(L(x,y,y \ 1) / z,u)
    ]]></literal>
    <justification jstring="[para(2324(a,1),18127(a,1,1,1))].">
      <j1 rule="para" parents="2324 18127"/>
    </justification>
  </clause>

  <clause id="18132">
    <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(18131(a,1),13533(a,1,2,2))].">
      <j1 rule="para" parents="18131 13533"/>
    </justification>
  </clause>

  <clause id="18133">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w)) / v5) = K(x,T(y,u \ z) / v5)
    ]]></literal>
    <justification jstring="[hyper(320,a,15582,a(flip),b,18129,a),flip(a)].">
      <j1 rule="hyper" parents="320 15582 18129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18134">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / w) = K(x,T(y,u) / w)
    ]]></literal>
    <justification jstring="[para(7080(a,1),18133(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7080 18133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18135">
    <literal><![CDATA[
      K(x,T(T(y,z) \ u,z * y)) = K(x,T(u,z) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16525,a,b,18134,a)].">
      <j1 rule="hyper" parents="58 16525 18134"/>
    </justification>
  </clause>

  <clause id="18137">
    <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(5555(a,1),18135(a,1,2,1))].">
      <j1 rule="para" parents="5555 18135"/>
    </justification>
  </clause>

  <clause id="18138">
    <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(15911,a,18069,a)].">
      <j1 rule="hyper" parents="15911 18069"/>
    </justification>
  </clause>

  <clause id="18139">
    <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(17500,a,18138,a)].">
      <j1 rule="hyper" parents="17500 18138"/>
    </justification>
  </clause>

  <clause id="18140">
    <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,17465,a(flip),b,18139,a)].">
      <j1 rule="hyper" parents="58 17465 18139"/>
    </justification>
  </clause>

  <clause id="18141">
    <literal><![CDATA[
      K(x,y * ((y \ T(z * y,u)) * u)) = K(x,T(y * (T(z,y) * u),u))
    ]]></literal>
    <justification jstring="[para(14018(a,1),18140(a,1,2,2))].">
      <j1 rule="para" parents="14018 18140"/>
    </justification>
  </clause>

  <clause id="18142">
    <literal><![CDATA[
      K(x,T(y * (T(z,y) * u),u)) = K(x,(u * ((z * y) / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16734,a(flip),b,18141,a),flip(a)].">
      <j1 rule="hyper" parents="58 16734 18141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18143">
    <literal><![CDATA[
      K(x,T(y * (T(z,y) * u),u)) = K(x,(u * z) * y)
    ]]></literal>
    <justification jstring="[para(6(a,1),18142(a,2,2,1,2))].">
      <j1 rule="para" parents="6 18142"/>
    </justification>
  </clause>

  <clause id="18144">
    <literal><![CDATA[
      K(x,L(y,z,u) * (z * u)) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(17195,a,18143,a)].">
      <j1 rule="hyper" parents="17195 18143"/>
    </justification>
  </clause>

  <clause id="18145">
    <literal><![CDATA[
      T(x,L(y,z,u) * (z * u)) = T(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(118,a,18144,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 18144 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18146">
    <literal><![CDATA[
      K(x,((y * z) \ (z * u)) * (y * z)) = K(x,((T(y,z) \ u) * y) * z)
    ]]></literal>
    <justification jstring="[para(11150(a,1),18144(a,1,2,1))].">
      <j1 rule="para" parents="11150 18144"/>
    </justification>
  </clause>

  <clause id="18147">
    <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(4907(a,1),18145(a,1,2,2))].">
      <j1 rule="para" parents="4907 18145"/>
    </justification>
  </clause>

  <clause id="18148">
    <literal><![CDATA[
      K(x,((T(y,z) \ u) * y) * z) = K(x,T(z * u,y * z))
    ]]></literal>
    <justification jstring="[hyper(12252,a,18146,a),flip(a)].">
      <j1 rule="hyper" parents="12252 18146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18149">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,z) * y)) = K(x,T(y * u,z * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,17657,a(flip),b,18148,a)].">
      <j1 rule="hyper" parents="58 17657 18148"/>
    </justification>
  </clause>

  <clause id="18150">
    <literal><![CDATA[
      K(x,T(y * z,u * y)) = K(x,T(z,u) * T(y,u))
    ]]></literal>
    <justification jstring="[hyper(15714,a,18149,a),flip(a)].">
      <j1 rule="hyper" parents="15714 18149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18151">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z * y)) = K(x,(u / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,15070,a(flip),b,18150,a),flip(a)].">
      <j1 rule="hyper" parents="320 15070 18150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18152">
    <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(16676(a,1),18094(a,1,2,2))].">
      <j1 rule="para" parents="16676 18094"/>
    </justification>
  </clause>

  <clause id="18153">
    <literal><![CDATA[
      K(x,y \ T(z,u / K(w,v5))) = K(x,y \ (u \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(17603,a,18152,a),flip(a)].">
      <j1 rule="hyper" parents="17603 18152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18154">
    <literal><![CDATA[
      K(x,y \ T(z,u / K(w,v5))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(17(a,2),18153(a,2,2,2))].">
      <j1 rule="para" parents="17 18153"/>
    </justification>
  </clause>

  <clause id="18155">
    <literal><![CDATA[
      K(x,y \ T(z,u * T(w,v5))) = K(x,y \ T(z,u * w))
    ]]></literal>
    <justification jstring="[para(6320(a,1),18154(a,1,2,2,2))].">
      <j1 rule="para" parents="6320 18154"/>
    </justification>
  </clause>

  <clause id="18156">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w / v5))) = K(x,y \ T(z,u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(6481(a,1),18154(a,1,2,2,2))].">
      <j1 rule="para" parents="6481 18154"/>
    </justification>
  </clause>

  <clause id="18157">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w) * v5)) = K(x,y \ T(z,v5))
    ]]></literal>
    <justification jstring="[para(7258(a,1),18154(a,1,2,2,2))].">
      <j1 rule="para" parents="7258 18154"/>
    </justification>
  </clause>

  <clause id="18158">
    <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(504(a,1),18157(a,1,2)),flip(a)].">
      <j1 rule="para" parents="504 18157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18159">
    <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(18155(a,2),16047(a,1))].">
      <j1 rule="para" parents="18155 16047"/>
    </justification>
  </clause>

  <clause id="18160">
    <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(17489(a,1),18095(a,1))].">
      <j1 rule="para" parents="17489 18095"/>
    </justification>
  </clause>

  <clause id="18162">
    <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(453(a,1),18116(a,1,2,2,1))].">
      <j1 rule="para" parents="453 18116"/>
    </justification>
  </clause>

  <clause id="18163">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,y \ z) / y) = K(x,T(y \ ((z / y) \ u),z))
    ]]></literal>
    <justification jstring="[hyper(15815,a,18137,a),flip(a)].">
      <j1 rule="hyper" parents="15815 18137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18164">
    <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(18163(a,2),14825(a,1))].">
      <j1 rule="para" parents="18163 14825"/>
    </justification>
  </clause>

  <clause id="18165">
    <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,17645,a,b,17647,a),flip(a)].">
      <j1 rule="hyper" parents="34 17645 17647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18166">
    <literal><![CDATA[
      L(x * K(y,K(z,u)),w,v5) = K(y,K(z,u)) * L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(479,a,18165,a)].">
      <j1 rule="hyper" parents="479 18165"/>
    </justification>
  </clause>

  <clause id="18167">
    <literal><![CDATA[
      L(x * K(y,K(z,u)),w,v5) = L(x,w,v5) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,15618,a,b,18166,a),flip(a)].">
      <j1 rule="hyper" parents="320 15618 18166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18168">
    <literal><![CDATA[
      L(x * K(y,K(z,u)),w,v5) * K(y,K(z,u)) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(15799,a,18166,a(flip))].">
      <j1 rule="hyper" parents="15799 18166"/>
    </justification>
  </clause>

  <clause id="18169">
    <literal><![CDATA[
      K(x,L(y * K(z,K(u,w)),v5,v6)) = K(x,L(y,v5,v6))
    ]]></literal>
    <justification jstring="[para(18166(a,2),15942(a,1,2))].">
      <j1 rule="para" parents="18166 15942"/>
    </justification>
  </clause>

  <clause id="18170">
    <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(18166(a,2),16101(a,1,2,2))].">
      <j1 rule="para" parents="18166 16101"/>
    </justification>
  </clause>

  <clause id="18171">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)) \ w,v5,v6)) = K(x,L(y \ w,v5,v6))
    ]]></literal>
    <justification jstring="[para(15667(a,1),18169(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15667 18169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18172">
    <literal><![CDATA[
      L(K(x,K(y,z)) * u,w,v5) = L(u,w,v5) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(15604(a,2),18167(a,1,1))].">
      <j1 rule="para" parents="15604 18167"/>
    </justification>
  </clause>

  <clause id="18173">
    <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),18168(a,1,1))].">
      <j1 rule="para" parents="13 18168"/>
    </justification>
  </clause>

  <clause id="18174">
    <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(7413(a,1),18171(a,1,2,1,1))].">
      <j1 rule="para" parents="7413 18171"/>
    </justification>
  </clause>

  <clause id="18175">
    <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(18172(a,2),15960(a,1,2,2))].">
      <j1 rule="para" parents="18172 15960"/>
    </justification>
  </clause>

  <clause id="18176">
    <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(5361(a,1),18175(a,1,2,2,1))].">
      <j1 rule="para" parents="5361 18175"/>
    </justification>
  </clause>

  <clause id="18177">
    <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(6306(a,1),18176(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6306 18176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18178">
    <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,13140,a(flip),b,17685,a)].">
      <j1 rule="hyper" parents="58 13140 17685"/>
    </justification>
  </clause>

  <clause id="18179">
    <literal><![CDATA[
      K(x,y / (T(z,u / w) \ (u / w))) = K(x,y / ((w \ T(u,w)) / z))
    ]]></literal>
    <justification jstring="[hyper(17835,a,17916,a),flip(a)].">
      <j1 rule="hyper" parents="17835 17916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18180">
    <literal><![CDATA[
      K(x,y / ((z \ T(u,z)) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(17834,a,18179,a),flip(a)].">
      <j1 rule="hyper" parents="17834 18179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18181">
    <literal><![CDATA[
      K(x,y / ((T(z,u) \ u) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9650,a,b,18180,a)].">
      <j1 rule="hyper" parents="58 9650 18180"/>
    </justification>
  </clause>

  <clause id="18182">
    <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(320,a,9,a,b,17978,a),flip(a)].">
      <j1 rule="hyper" parents="320 9 17978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18183">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,(v5 * z) \ (v5 * (z * y)))
    ]]></literal>
    <justification jstring="[hyper(18160,a,17989,a),flip(a)].">
      <j1 rule="hyper" parents="18160 17989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18184">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,L(y,z,v5))
    ]]></literal>
    <justification jstring="[para(13(a,2),18183(a,2,2))].">
      <j1 rule="para" parents="13 18183"/>
    </justification>
  </clause>

  <clause id="18185">
    <literal><![CDATA[
      K(x,L(y,z,u * K(w,v5))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(17245,a,18184,a)].">
      <j1 rule="hyper" parents="17245 18184"/>
    </justification>
  </clause>

  <clause id="18186">
    <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(14402,a,18184,a)].">
      <j1 rule="hyper" parents="14402 18184"/>
    </justification>
  </clause>

  <clause id="18187">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,(z * v5) / ((y \ z) * v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,14706,a,b,18184,a),flip(a)].">
      <j1 rule="hyper" parents="320 14706 18184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18189">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w) \ v5)) = K(x,L(y,z,u \ v5))
    ]]></literal>
    <justification jstring="[para(5042(a,1),18184(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="5042 18184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18191">
    <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(18184(a,1),14704(a,1,1))].">
      <j1 rule="para" parents="18184 14704"/>
    </justification>
  </clause>

  <clause id="18192">
    <literal><![CDATA[
      K(x,L(y,z,u * (w / v5))) = K(x,L(y,z,u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(17278(a,1),18184(a,1,2))].">
      <j1 rule="para" parents="17278 18184"/>
    </justification>
  </clause>

  <clause id="18193">
    <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,14654,a(flip),b,18185,a),flip(a)].">
      <j1 rule="hyper" parents="58 14654 18185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18194">
    <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(13663(a,1),18185(a,1,2,3))].">
      <j1 rule="para" parents="13663 18185"/>
    </justification>
  </clause>

  <clause id="18195">
    <literal><![CDATA[
      a(x,y,K(z * K(u,w),v5)) = K(v5,x) * K(x,L(v5,y,z))
    ]]></literal>
    <justification jstring="[para(18185(a,1),14228(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18185 14228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18196">
    <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(18185(a,1),14704(a,1,1))].">
      <j1 rule="para" parents="18185 14704"/>
    </justification>
  </clause>

  <clause id="18197">
    <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(18185(a,1),15872(a,1,1,1))].">
      <j1 rule="para" parents="18185 15872"/>
    </justification>
  </clause>

  <clause id="18198">
    <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,14800,a(flip),b,18189,a),flip(a)].">
      <j1 rule="hyper" parents="58 14800 18189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18199">
    <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,10621,a(flip),b,18189,a),flip(a)].">
      <j1 rule="hyper" parents="58 10621 18189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18200">
    <literal><![CDATA[
      a(x,y,K(z * K(u,w),v5)) = a(x,y,K(z,v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,14228,a(flip),b,18195,a),flip(a)].">
      <j1 rule="hyper" parents="320 14228 18195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18201">
    <literal><![CDATA[
      a(x * K(y,z),u,K(w,v5)) = a(v5,u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(14270,a,18200,a)].">
      <j1 rule="hyper" parents="14270 18200"/>
    </justification>
  </clause>

  <clause id="18202">
    <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,17756,a,b,18200,a)].">
      <j1 rule="hyper" parents="58 17756 18200"/>
    </justification>
  </clause>

  <clause id="18203">
    <literal><![CDATA[
      a(x,y,K(z * u,w)) = a(x,y,K(u * z,w))
    ]]></literal>
    <justification jstring="[para(84(a,1),18200(a,1,3,1))].">
      <j1 rule="para" parents="84 18200"/>
    </justification>
  </clause>

  <clause id="18204">
    <literal><![CDATA[
      a(x,y,K(z / u,w)) = a(x,y,K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(4735(a,1),18200(a,1,3,1))].">
      <j1 rule="para" parents="4735 18200"/>
    </justification>
  </clause>

  <clause id="18205">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(7905(a,1),18200(a,1,3))].">
      <j1 rule="para" parents="7905 18200"/>
    </justification>
  </clause>

  <clause id="18206">
    <literal><![CDATA[
      a(x,y,K(z \ (u / w),v5)) = a(x,y,K(z \ (w \ u),v5))
    ]]></literal>
    <justification jstring="[para(13896(a,1),18200(a,1,3,1))].">
      <j1 rule="para" parents="13896 18200"/>
    </justification>
  </clause>

  <clause id="18207">
    <literal><![CDATA[
      a(x,y,K((z / u) \ w,v5)) = a(x,y,K((u \ z) \ w,v5))
    ]]></literal>
    <justification jstring="[para(15843(a,1),18200(a,1,3))].">
      <j1 rule="para" parents="15843 18200"/>
    </justification>
  </clause>

  <clause id="18208">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,14195,a,b,18205,a),flip(a)].">
      <j1 rule="hyper" parents="320 14195 18205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18209">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14195,a(flip),b,18205,a),flip(a)].">
      <j1 rule="hyper" parents="320 14195 18205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18210">
    <literal><![CDATA[
      a(x,y,K(z,u / w)) = a(x,y,K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(107(a,1),18205(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="107 18205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18211">
    <literal><![CDATA[
      a(x,y,K(z,u * w)) = a(x,y,K(z,w * u))
    ]]></literal>
    <justification jstring="[para(12222(a,1),18205(a,1,3))].">
      <j1 rule="para" parents="12222 18205"/>
    </justification>
  </clause>

  <clause id="18212">
    <literal><![CDATA[
      T(x,a(y,z,T(u,w))) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,18208,a(flip),b,13346,a),flip(a)].">
      <j1 rule="hyper" parents="119 18208 13346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18215">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(w,z,K(y * x,u))
    ]]></literal>
    <justification jstring="[para(12190(a,1),18208(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12190 18208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18217">
    <literal><![CDATA[
      a(T(x,y),z,K(u,w)) = a(x,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(14307,a,18209,a)].">
      <j1 rule="hyper" parents="14307 18209"/>
    </justification>
  </clause>

  <clause id="18219">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(u,z,K(w,y * x))
    ]]></literal>
    <justification jstring="[para(12222(a,1),18209(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12222 18209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18220">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = a(x,y,K(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14460,a(flip),b,18217,a)].">
      <j1 rule="hyper" parents="58 14460 18217"/>
    </justification>
  </clause>

  <clause id="18221">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(y * x,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,12755,a(flip),b,18217,a)].">
      <j1 rule="hyper" parents="58 12755 18217"/>
    </justification>
  </clause>

  <clause id="18222">
    <literal><![CDATA[
      a(x / y,z,K(u,w)) = a(y \ x,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,12740,a(flip),b,18217,a),flip(a)].">
      <j1 rule="hyper" parents="58 12740 18217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18223">
    <literal><![CDATA[
      a(x * K(y,z),u,K(w,v5)) = a(w,u,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,14195,a(flip),b,18201,a),flip(a)].">
      <j1 rule="hyper" parents="320 14195 18201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18224">
    <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(18201(a,1),14864(a,2,1))].">
      <j1 rule="para" parents="18201 14864"/>
    </justification>
  </clause>

  <clause id="18225">
    <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(18203(a,1),14270(a,1))].">
      <j1 rule="para" parents="18203 14270"/>
    </justification>
  </clause>

  <clause id="18226">
    <literal><![CDATA[
      a(x,y,K(z,x \ (u * (x / w)))) = a(z,y,K(w \ u,x))
    ]]></literal>
    <justification jstring="[hyper(14315,a,18204,a)].">
      <j1 rule="hyper" parents="14315 18204"/>
    </justification>
  </clause>

  <clause id="18227">
    <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(18204(a,1),14274(a,1,2))].">
      <j1 rule="para" parents="18204 14274"/>
    </justification>
  </clause>

  <clause id="18228">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u \ w,y)) = K(x,L(y,z,w / (y * u)))
    ]]></literal>
    <justification jstring="[para(18204(a,1),14514(a,1,2))].">
      <j1 rule="para" parents="18204 14514"/>
    </justification>
  </clause>

  <clause id="18229">
    <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(18210(a,1),14334(a,1,2))].">
      <j1 rule="para" parents="18210 14334"/>
    </justification>
  </clause>

  <clause id="18230">
    <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(18210(a,1),14773(a,1,1))].">
      <j1 rule="para" parents="18210 14773"/>
    </justification>
  </clause>

  <clause id="18231">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) \ K(z,(y * x) / u) = K(z,y / (u / x))
    ]]></literal>
    <justification jstring="[para(18210(a,1),14807(a,1,1))].">
      <j1 rule="para" parents="18210 14807"/>
    </justification>
  </clause>

  <clause id="18232">
    <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(18211(a,1),14307(a,1))].">
      <j1 rule="para" parents="18211 14307"/>
    </justification>
  </clause>

  <clause id="18233">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w) * (v5 * v6))) = a(x,y,K(z,v6 * (v5 * K(w,u))))
    ]]></literal>
    <justification jstring="[para(17522(a,1),18211(a,1,3))].">
      <j1 rule="para" parents="17522 18211"/>
    </justification>
  </clause>

  <clause id="18234">
    <literal><![CDATA[
      T(x,a(y,z,T(u,w))) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14209,a(flip),b,18212,a),flip(a)].">
      <j1 rule="hyper" parents="320 14209 18212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18235">
    <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(18212(a,2),14213(a,1))].">
      <j1 rule="para" parents="18212 14213"/>
    </justification>
  </clause>

  <clause id="18236">
    <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,17214,a(flip),b,18234,a),flip(a)].">
      <j1 rule="hyper" parents="58 17214 18234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18237">
    <literal><![CDATA[
      T(x,a(y,T(z,u),u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(6621(a,1),18234(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6621 18234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18238">
    <literal><![CDATA[
      T(x,a(y,z * u,u)) = T(x,a(y,u * z,u))
    ]]></literal>
    <justification jstring="[para(13277(a,1),18237(a,1,2))].">
      <j1 rule="para" parents="13277 18237"/>
    </justification>
  </clause>

  <clause id="18239">
    <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(18215(a,2),14270(a,1))].">
      <j1 rule="para" parents="18215 14270"/>
    </justification>
  </clause>

  <clause id="18240">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w) * v5)) = a(z,y,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,18201,a(flip),b,18219,a),flip(a)].">
      <j1 rule="hyper" parents="58 18201 18219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18241">
    <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(18219(a,1),14270(a,1))].">
      <j1 rule="para" parents="18219 14270"/>
    </justification>
  </clause>

  <clause id="18242">
    <literal><![CDATA[
      a(K(x,y),z,u \ w) = a(w / u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,14219,a,b,18222,a)].">
      <j1 rule="hyper" parents="320 14219 18222"/>
    </justification>
  </clause>

  <clause id="18243">
    <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(18222(a,1),14645(a,1,2))].">
      <j1 rule="para" parents="18222 14645"/>
    </justification>
  </clause>

  <clause id="18244">
    <literal><![CDATA[
      a(x,y,K(z,u * K(w,v5))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(14270,a,18223,a)].">
      <j1 rule="hyper" parents="14270 18223"/>
    </justification>
  </clause>

  <clause id="18245">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w) * v5)) = a(x,y,K(z,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,18219,a(flip),b,18223,a)].">
      <j1 rule="hyper" parents="58 18219 18223"/>
    </justification>
  </clause>

  <clause id="18246">
    <literal><![CDATA[
      T(x,a(y * K(z,u),w,v5)) = x * a(x,w,K(v5,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,18223,a(flip),b,13346,a),flip(a)].">
      <j1 rule="hyper" parents="119 18223 13346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18247">
    <literal><![CDATA[
      a(x,y,K(z,u * K(w,v5))) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[para(6300(a,1),18223(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6300 18223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18248">
    <literal><![CDATA[
      T(x,a(y,z * u,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14350,a(flip),b,18238,a),flip(a)].">
      <j1 rule="hyper" parents="320 14350 18238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18249">
    <literal><![CDATA[
      L(x,y * z,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(14903,a,18248,a)].">
      <j1 rule="hyper" parents="14903 18248"/>
    </justification>
  </clause>

  <clause id="18250">
    <literal><![CDATA[
      L(x,y * z,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14849,a,b,18249,a),flip(a)].">
      <j1 rule="hyper" parents="320 14849 18249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18252">
    <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,7666,a(flip),b,18250,a)].">
      <j1 rule="hyper" parents="58 7666 18250"/>
    </justification>
  </clause>

  <clause id="18253">
    <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(18250(a,1),14856(a,1))].">
      <j1 rule="para" parents="18250 14856"/>
    </justification>
  </clause>

  <clause id="18254">
    <literal><![CDATA[
      T(x,a(K(y,z) * u,w,v5)) = x * a(v5,w,K(u,x))
    ]]></literal>
    <justification jstring="[para(18240(a,1),14209(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18240 14209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18255">
    <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(18240(a,1),16696(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18240 16696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18257">
    <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(18242(a,1),14306(a,1))].">
      <j1 rule="para" parents="18242 14306"/>
    </justification>
  </clause>

  <clause id="18258">
    <literal><![CDATA[
      a(x,y,K(z,(u / w) * v5)) = a(x,y,K(z,(w \ u) * v5))
    ]]></literal>
    <justification jstring="[para(6495(a,1),18244(a,1,3,2))].">
      <j1 rule="para" parents="6495 18244"/>
    </justification>
  </clause>

  <clause id="18259">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(v5,x)) = v6
    ]]></literal>
    <justification jstring="[para(18245(a,2),14270(a,1))].">
      <j1 rule="para" parents="18245 14270"/>
    </justification>
  </clause>

  <clause id="18260">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,v5)) = a(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,18219,a,b,18247,a)].">
      <j1 rule="hyper" parents="58 18219 18247"/>
    </justification>
  </clause>

  <clause id="18261">
    <literal><![CDATA[
      a(T(x,y) \ z,u,K(w,v5)) = a(x \ z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(5042(a,1),18260(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5042 18260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18262">
    <literal><![CDATA[
      a(x \ T(y,z),u,K(w,v5)) = a(x \ y,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(5370(a,1),18260(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5370 18260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18263">
    <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(18260(a,2),14307(a,1))].">
      <j1 rule="para" parents="18260 14307"/>
    </justification>
  </clause>

  <clause id="18265">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14276,a(flip),b,18220,a),flip(a)].">
      <j1 rule="hyper" parents="320 14276 18220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18266">
    <literal><![CDATA[
      K(x * L(y,z,u),y * x) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,17498,a(flip),b,18265,a)].">
      <j1 rule="hyper" parents="58 17498 18265"/>
    </justification>
  </clause>

  <clause id="18267">
    <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(2391(a,1),18266(a,1,1,2))].">
      <j1 rule="para" parents="2391 18266"/>
    </justification>
  </clause>

  <clause id="18268">
    <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(18246(a,2),14213(a,1))].">
      <j1 rule="para" parents="18246 14213"/>
    </justification>
  </clause>

  <clause id="18272">
    <literal><![CDATA[
      T(x * y,a(K(z,u) * y,w,v5)) = (x * y) * a(v5,w,K(y,x))
    ]]></literal>
    <justification jstring="[para(10998(a,1),18254(a,2,2))].">
      <j1 rule="para" parents="10998 18254"/>
    </justification>
  </clause>

  <clause id="18273">
    <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),18261(a,1,1,1))].">
      <j1 rule="para" parents="20 18261"/>
    </justification>
  </clause>

  <clause id="18274">
    <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),18262(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 18262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18275">
    <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(17920(a,1),18225(a,1,3))].">
      <j1 rule="para" parents="17920 18225"/>
    </justification>
  </clause>

  <clause id="18276">
    <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(14286(a,1),18257(a,1))].">
      <j1 rule="para" parents="14286 18257"/>
    </justification>
  </clause>

  <clause id="18277">
    <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(13896(a,1),18268(a,1,2,1))].">
      <j1 rule="para" parents="13896 18268"/>
    </justification>
  </clause>

  <clause id="18279">
    <literal><![CDATA[
      x * a(y,z,K(u \ (w \ v5),x)) = T(x,a(u \ (v5 / w),z,y))
    ]]></literal>
    <justification jstring="[para(18206(a,1),14244(a,1,2))].">
      <j1 rule="para" parents="18206 14244"/>
    </justification>
  </clause>

  <clause id="18280">
    <literal><![CDATA[
      a(x,y,K(z * (u / w),u)) = a(x,y,K(w \ z,u))
    ]]></literal>
    <justification jstring="[hyper(14372,a,18226,a)].">
      <j1 rule="hyper" parents="14372 18226"/>
    </justification>
  </clause>

  <clause id="18281">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),w)) = a(x,y,K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(15785(a,1),18280(a,1,3))].">
      <j1 rule="para" parents="15785 18280"/>
    </justification>
  </clause>

  <clause id="18282">
    <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(18281(a,1),14332(a,2,2))].">
      <j1 rule="para" parents="18281 14332"/>
    </justification>
  </clause>

  <clause id="18283">
    <literal><![CDATA[
      a((x * y) \ (z \ u),w,K(v5,v6)) = a(y \ (x \ (u / z)),w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(14434,a,18274,a),flip(a)].">
      <j1 rule="hyper" parents="14434 18274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18284">
    <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(18187(a,2),14723(a,1))].">
      <j1 rule="para" parents="18187 14723"/>
    </justification>
  </clause>

  <clause id="18285">
    <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(5093(a,1),18284(a,1,2,3))].">
      <j1 rule="para" parents="5093 18284"/>
    </justification>
  </clause>

  <clause id="18286">
    <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(7261(a,1),18284(a,1,2,3))].">
      <j1 rule="para" parents="7261 18284"/>
    </justification>
  </clause>

  <clause id="18287">
    <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(11121(a,1),18284(a,1,2,3))].">
      <j1 rule="para" parents="11121 18284"/>
    </justification>
  </clause>

  <clause id="18288">
    <literal><![CDATA[
      K(x,L(y,(K(z,u) * w) \ v5,w)) = K(x,L(y,v5,w))
    ]]></literal>
    <justification jstring="[hyper(18284,a,18186,a)].">
      <j1 rule="hyper" parents="18284 18186"/>
    </justification>
  </clause>

  <clause id="18290">
    <literal><![CDATA[
      K(x,L(y,z \ (u \ w),z)) = K(x,L(y,w / u,z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(17244,a,18193,a)].">
      <j1 rule="hyper" parents="17244 18193"/>
    </justification>
  </clause>

  <clause id="18292">
    <literal><![CDATA[
      K(x,L(y,z,u / (y * w))) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(14253,a,18228,a),flip(a)].">
      <j1 rule="hyper" parents="14253 18228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18293">
    <literal><![CDATA[
      K(x,L(y,z,(y * u) \ w)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(17211,a,18292,a)].">
      <j1 rule="hyper" parents="17211 18292"/>
    </justification>
  </clause>

  <clause id="18294">
    <literal><![CDATA[
      T(x * y,a(K(z,u) * y,w,v5)) = x * T(y,a(v5,w,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,13349,a(flip),b,18272,a),flip(a)].">
      <j1 rule="hyper" parents="320 13349 18272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18295">
    <literal><![CDATA[
      T(x,a(x \ ((y * x) / z),u,w)) = x * a(w,u,K(z \ y,x))
    ]]></literal>
    <justification jstring="[para(10345(a,1),18279(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="10345 18279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18296">
    <literal><![CDATA[
      K(x,L(y,z / u,w * K(u,z))) = K(x,L(y,u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(14386,a,18290,a),flip(a)].">
      <j1 rule="hyper" parents="14386 18290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18297">
    <literal><![CDATA[
      K(x,L(y,z / u,w)) = K(x,L(y,u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(18286,a,18296,a)].">
      <j1 rule="hyper" parents="18286 18296"/>
    </justification>
  </clause>

  <clause id="18299">
    <literal><![CDATA[
      K(x,L(y,(z * u) / z,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(4(a,1),18297(a,2,2,2))].">
      <j1 rule="para" parents="4 18297"/>
    </justification>
  </clause>

  <clause id="18300">
    <literal><![CDATA[
      K(x,L(y,T(z,u),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[para(225(a,1),18299(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="225 18299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18304">
    <literal><![CDATA[
      K(x,L(y,z * u,w)) = K(x,L(y,u * z,w))
    ]]></literal>
    <justification jstring="[para(13203(a,1),18300(a,1,2))].">
      <j1 rule="para" parents="13203 18300"/>
    </justification>
  </clause>

  <clause id="18305">
    <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(14878(a,1),18300(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14878 18300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18306">
    <literal><![CDATA[
      T(x,a(x \ ((y * x) / z),u,w)) = T(x,a(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,14244,a(flip),b,18295,a),flip(a)].">
      <j1 rule="hyper" parents="320 14244 18295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18307">
    <literal><![CDATA[
      a(x \ y,x,K(z,u)) * K(z,(x * u) / y) = K(z,x / (y / u))
    ]]></literal>
    <justification jstring="[hyper(14319,a,18231,a)].">
      <j1 rule="hyper" parents="14319 18231"/>
    </justification>
  </clause>

  <clause id="18308">
    <literal><![CDATA[
      a(x \ K(y,z),u,K(w,v5)) = a(w,u,K(x,v5))
    ]]></literal>
    <justification jstring="[hyper(18276,a,18201,a)].">
      <j1 rule="hyper" parents="18276 18201"/>
    </justification>
  </clause>

  <clause id="18309">
    <literal><![CDATA[
      T(x,a(x \ (y \ (z * x)),u,w)) = T(x,a(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(18277,a,18306,a)].">
      <j1 rule="hyper" parents="18277 18306"/>
    </justification>
  </clause>

  <clause id="18310">
    <literal><![CDATA[
      T(x,a(y \ (z * x),u,w)) = T(x,a(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,14346,a(flip),b,18309,a)].">
      <j1 rule="hyper" parents="58 14346 18309"/>
    </justification>
  </clause>

  <clause id="18311">
    <literal><![CDATA[
      T(x,a(y \ 1,z,u)) = T(x,a(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(2(a,1),18310(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2 18310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18312">
    <literal><![CDATA[
      T(x,a(y \ x,z,u)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,17650,a(flip),b,18311,a),flip(a)].">
      <j1 rule="hyper" parents="58 17650 18311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18313">
    <literal><![CDATA[
      L(x,y,K(z,u \ x)) = T(x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(14903,a,18312,a)].">
      <j1 rule="hyper" parents="14903 18312"/>
    </justification>
  </clause>

  <clause id="18314">
    <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(5137(a,1),18312(a,1,2,1))].">
      <j1 rule="para" parents="5137 18312"/>
    </justification>
  </clause>

  <clause id="18315">
    <literal><![CDATA[
      L(x,y,K(z,u \ x)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14849,a,b,18313,a),flip(a)].">
      <j1 rule="hyper" parents="320 14849 18313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18316">
    <literal><![CDATA[
      L(x,y,K(x \ z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12673,a,b,18315,a)].">
      <j1 rule="hyper" parents="58 12673 18315"/>
    </justification>
  </clause>

  <clause id="18317">
    <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(18314(a,2),18235(a,1))].">
      <j1 rule="para" parents="18314 18235"/>
    </justification>
  </clause>

  <clause id="18318">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ v5)) = K(x,L(y,z,u \ (w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(18287,a,14422,a)].">
      <j1 rule="hyper" parents="18287 14422"/>
    </justification>
  </clause>

  <clause id="18319">
    <literal><![CDATA[
      K(x \ 1,L(y,z,(x * u) \ w)) = K(x \ 1,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(320,a,14557,a(flip),b,18318,a),flip(a)].">
      <j1 rule="hyper" parents="320 14557 18318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18320">
    <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,14725,a(flip),b,18319,a),flip(a)].">
      <j1 rule="hyper" parents="58 14725 18319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18321">
    <literal><![CDATA[
      a(x,y,K(z \ y,u)) * K(x,(y * u) / z) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[para(14237(a,1),18307(a,1,1))].">
      <j1 rule="para" parents="14237 18307"/>
    </justification>
  </clause>

  <clause id="18322">
    <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(18208(a,1),18307(a,1,1))].">
      <j1 rule="para" parents="18208 18307"/>
    </justification>
  </clause>

  <clause id="18323">
    <literal><![CDATA[
      T(x * y,a(z,u,x)) = x * T(y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(18317,a,18294,a)].">
      <j1 rule="hyper" parents="18317 18294"/>
    </justification>
  </clause>

  <clause id="18324">
    <literal><![CDATA[
      T(x * y,a(z,u,x)) = x * L(y,u,K(x,z))
    ]]></literal>
    <justification jstring="[para(14849(a,2),18323(a,2,2))].">
      <j1 rule="para" parents="14849 18323"/>
    </justification>
  </clause>

  <clause id="18325">
    <literal><![CDATA[
      L(x * y,z,K(x,u)) = x * L(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(14903,a,18324,a)].">
      <j1 rule="hyper" parents="14903 18324"/>
    </justification>
  </clause>

  <clause id="18326">
    <literal><![CDATA[
      K(x \ (y * (((z / y) * y) \ x)),u) = K((z * (y \ x)) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,14805,a(flip),b,18320,a),flip(a)].">
      <j1 rule="hyper" parents="58 14805 18320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18327">
    <literal><![CDATA[
      K((x * (y \ z)) \ z,u) = K(z \ (y * (x \ z)),u)
    ]]></literal>
    <justification jstring="[para(7(a,1),18326(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 18326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18329">
    <literal><![CDATA[
      x / (K(y \ (z * (u \ y)),w) * x) = K(w,(u * (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[para(18327(a,1),5104(a,1,2,1))].">
      <j1 rule="para" parents="18327 5104"/>
    </justification>
  </clause>

  <clause id="18330">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (z * (y \ u))) = w
    ]]></literal>
    <justification jstring="[para(18329(a,1),5112(a,1))].">
      <j1 rule="para" parents="18329 5112"/>
    </justification>
  </clause>

  <clause id="18331">
    <literal><![CDATA[
      K(x,(y * z) / u) * a(z,y,K(x,u \ y)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(17361,a,18321,a)].">
      <j1 rule="hyper" parents="17361 18321"/>
    </justification>
  </clause>

  <clause id="18332">
    <literal><![CDATA[
      K(x,(y * z) / u) * a(x,y,K(u \ y,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(17158,a,18321,a)].">
      <j1 rule="hyper" parents="17158 18321"/>
    </justification>
  </clause>

  <clause id="18333">
    <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(12599(a,1),18321(a,1,1,3,1))].">
      <j1 rule="para" parents="12599 18321"/>
    </justification>
  </clause>

  <clause id="18334">
    <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,14799,a(flip),b,18194,a),flip(a)].">
      <j1 rule="hyper" parents="58 14799 18194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18335">
    <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(13811(a,1),18224(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13811 18224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18336">
    <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(10989(a,1),18227(a,1,2))].">
      <j1 rule="para" parents="10989 18227"/>
    </justification>
  </clause>

  <clause id="18337">
    <literal><![CDATA[
      a(x,y,K(z,u * (w * K(v5,v6)))) = a(z,y,K(w * u,x))
    ]]></literal>
    <justification jstring="[hyper(18259,a,18233,a),flip(a)].">
      <j1 rule="hyper" parents="18259 18233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18339">
    <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(18337(a,1),14337(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18337 14337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18340">
    <literal><![CDATA[
      R(x,y,K(K(z,u) * w,v5)) = x * a(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[para(17105(a,1),18255(a,2,2))].">
      <j1 rule="para" parents="17105 18255"/>
    </justification>
  </clause>

  <clause id="18342">
    <literal><![CDATA[
      R(x,y,K(K(z,u) * w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,14852,a(flip),b,18340,a),flip(a)].">
      <j1 rule="hyper" parents="320 14852 18340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18344">
    <literal><![CDATA[
      L(x,y,K(K(z,u) * w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(14904,a,18342,a)].">
      <j1 rule="hyper" parents="14904 18342"/>
    </justification>
  </clause>

  <clause id="18345">
    <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(14906,a,18344,a)].">
      <j1 rule="hyper" parents="14906 18344"/>
    </justification>
  </clause>

  <clause id="18346">
    <literal><![CDATA[
      L(x,y,K(z / u,w)) = L(x,y,K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(4818(a,1),18344(a,1,3,1))].">
      <j1 rule="para" parents="4818 18344"/>
    </justification>
  </clause>

  <clause id="18347">
    <literal><![CDATA[
      L(x,y,K(z / x,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,18316,a(flip),b,18346,a),flip(a)].">
      <j1 rule="hyper" parents="320 18316 18346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18348">
    <literal><![CDATA[
      L(x,y,K(z * x,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(6(a,1),18347(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="6 18347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18349">
    <literal><![CDATA[
      L(x,(K(y,z) * u) \ w,K(u,v5)) = L(x,w,K(u,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,18344,a(flip),b,18345,a)].">
      <j1 rule="hyper" parents="58 18344 18345"/>
    </justification>
  </clause>

  <clause id="18351">
    <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(319(a,1),18273(a,1,1,1,1))].">
      <j1 rule="para" parents="319 18273"/>
    </justification>
  </clause>

  <clause id="18352">
    <literal><![CDATA[
      K(x,L(y,z,u * (w \ T(y,v5)))) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14249,a(flip),b,18282,a),flip(a)].">
      <j1 rule="hyper" parents="320 14249 18282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18353">
    <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(18283(a,1),14434(a,1))].">
      <j1 rule="para" parents="18283 14434"/>
    </justification>
  </clause>

  <clause id="18354">
    <literal><![CDATA[
      K(x,L(y,z \ (K(u,w) * v5),z)) = K(x,L(y,v5,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18288,a(flip),b,18305,a),flip(a)].">
      <j1 rule="hyper" parents="58 18288 18305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18355">
    <literal><![CDATA[
      K(x,L(y,K(z,u) * w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(14386,a,18354,a)].">
      <j1 rule="hyper" parents="14386 18354"/>
    </justification>
  </clause>

  <clause id="18356">
    <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,18354,a(flip),b,14295,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 18354 14295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18362">
    <literal><![CDATA[
      K(x,L(y,z * (K(u,w) * v5),v6)) = K(x,L(y,z * v5,v6))
    ]]></literal>
    <justification jstring="[para(6008(a,1),18355(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6008 18355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18363">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = a(v5,u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,14228,a(flip),b,18356,a),flip(a)].">
      <j1 rule="hyper" parents="320 14228 18356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18364">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = a(x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,10793,a(flip),b,18356,a),flip(a)].">
      <j1 rule="hyper" parents="320 10793 18356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18365">
    <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,18363,a)].">
      <j1 rule="hyper" parents="52 18363"/>
    </justification>
  </clause>

  <clause id="18367">
    <literal><![CDATA[
      a(x,y * z,K(u,w)) = a(x,z * y,K(u,w))
    ]]></literal>
    <justification jstring="[para(4772(a,1),18364(a,1,2))].">
      <j1 rule="para" parents="4772 18364"/>
    </justification>
  </clause>

  <clause id="18371">
    <literal><![CDATA[
      x * a(x,y * z,K(u,w)) = L(x,z * y,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,18367,a,b,14853,a)].">
      <j1 rule="hyper" parents="119 18367 14853"/>
    </justification>
  </clause>

  <clause id="18372">
    <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(18371(a,1),14880(a,1))].">
      <j1 rule="para" parents="18371 14880"/>
    </justification>
  </clause>

  <clause id="18373">
    <literal><![CDATA[
      L(x,y * (y \ z),K(u,w)) = L(x,T(z,y),K(u,w))
    ]]></literal>
    <justification jstring="[hyper(18372,a,13217,a)].">
      <j1 rule="hyper" parents="18372 13217"/>
    </justification>
  </clause>

  <clause id="18374">
    <literal><![CDATA[
      L(x,T(y,z),K(u,w)) = L(x,y,K(u,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),18373(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 18373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18375">
    <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(14878(a,1),18374(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14878 18374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18376">
    <literal><![CDATA[
      K(x,L(y,z * (K(u,w) * v5),v6)) = K(x,L(y,v5 * z,v6))
    ]]></literal>
    <justification jstring="[hyper(320,a,18304,a,b,18362,a),flip(a)].">
      <j1 rule="hyper" parents="320 18304 18362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18377">
    <literal><![CDATA[
      K(x,L(y,z * (u * K(w,v5)),v6)) = K(x,L(y,u * z,v6))
    ]]></literal>
    <justification jstring="[para(7261(a,1),18376(a,1,2,2,2))].">
      <j1 rule="para" parents="7261 18376"/>
    </justification>
  </clause>

  <clause id="18378">
    <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(18377(a,1),14768(a,1,1,1))].">
      <j1 rule="para" parents="18377 14768"/>
    </justification>
  </clause>

  <clause id="18379">
    <literal><![CDATA[
      K(x,L(y,z,u / (K(w,v5) / v6))) = K(x,L(y,z,v6 * u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14249,a(flip),b,18339,a),flip(a)].">
      <j1 rule="hyper" parents="320 14249 18339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18381">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),K(y,v5)) = L(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,18349,a(flip),b,18375,a),flip(a)].">
      <j1 rule="hyper" parents="58 18349 18375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18382">
    <literal><![CDATA[
      L(x,K(y,z) * u,K(w,v5)) = L(x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,14881,a(flip),b,18381,a)].">
      <j1 rule="hyper" parents="58 14881 18381"/>
    </justification>
  </clause>

  <clause id="18383">
    <literal><![CDATA[
      L(x,y * K(z,u),K(w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(18372,a,18382,a)].">
      <j1 rule="hyper" parents="18372 18382"/>
    </justification>
  </clause>

  <clause id="18385">
    <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,11197,a(flip),b,18383,a),flip(a)].">
      <j1 rule="hyper" parents="58 11197 18383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18386">
    <literal><![CDATA[
      L(x,y \ (z * K(u,w)),K(v5,v6)) = L(x,y \ z,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(14519(a,1),18383(a,1,2))].">
      <j1 rule="para" parents="14519 18383"/>
    </justification>
  </clause>

  <clause id="18387">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),K(v5,v6)) = L(x,y \ w,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(7121(a,1),18386(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7121 18386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18388">
    <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,10375,a(flip),b,18387,a),flip(a)].">
      <j1 rule="hyper" parents="58 10375 18387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18390">
    <literal><![CDATA[
      K(x,L(y,z,u / (T(w,x) * v5))) = K(x,L(y,z,(w * v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(14254,a,18229,a),flip(a)].">
      <j1 rule="hyper" parents="14254 18229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18391">
    <literal><![CDATA[
      K(x,L(y,z,(T(u,x) * w) \ v5)) = K(x,L(y,z,(u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(17211,a,18390,a)].">
      <j1 rule="hyper" parents="17211 18390"/>
    </justification>
  </clause>

  <clause id="18392">
    <literal><![CDATA[
      K(x,L(y,z,(y * z) \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(18391(a,1),14758(a,1,1))].">
      <j1 rule="para" parents="18391 14758"/>
    </justification>
  </clause>

  <clause id="18393">
    <literal><![CDATA[
      K(x,L(y,z,z \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(18293(a,1),18392(a,1,1))].">
      <j1 rule="para" parents="18293 18392"/>
    </justification>
  </clause>

  <clause id="18394">
    <literal><![CDATA[
      (x * y) * ((T(x,z) * y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      (K(z,x) * y) * (y \ u) = w
    ]]></literal>
    <justification jstring="[para(18393(a,1),14712(a,1))].">
      <j1 rule="para" parents="18393 14712"/>
    </justification>
  </clause>

  <clause id="18395">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18332,a(flip),b,18336,a),flip(a)].">
      <j1 rule="hyper" parents="58 18332 18336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18396">
    <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(14123,a,18395,a)].">
      <j1 rule="hyper" parents="14123 18395"/>
    </justification>
  </clause>

  <clause id="18397">
    <literal><![CDATA[
      K(x,L((y * z) * u,y,z \ 1)) = K(x,y / ((u \ 1) / z))
    ]]></literal>
    <justification jstring="[hyper(14085,a,18395,a)].">
      <j1 rule="hyper" parents="14085 18395"/>
    </justification>
  </clause>

  <clause id="18398">
    <literal><![CDATA[
      K(x,y / (z * (y / (u * y)))) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16820,a(flip),b,18395,a)].">
      <j1 rule="hyper" parents="58 16820 18395"/>
    </justification>
  </clause>

  <clause id="18399">
    <literal><![CDATA[
      K(x,(y \ z) / (u * ((y \ z) / z))) = K(x,(y \ z) / (u / y))
    ]]></literal>
    <justification jstring="[para(5(a,1),18398(a,1,2,2,2,2))].">
      <j1 rule="para" parents="5 18398"/>
    </justification>
  </clause>

  <clause id="18400">
    <literal><![CDATA[
      K(x,y) * (((x \ z) / z) \ u) = ((T(x,y) \ z) / z) \ u
    ]]></literal>
    <justification jstring="[hyper(12615,a,18178,a)].">
      <j1 rule="hyper" parents="12615 18178"/>
    </justification>
  </clause>

  <clause id="18402">
    <literal><![CDATA[
      T(x,((T(y,z) \ u) / u) \ w) = T(x,T((y \ u) / u,z) \ w)
    ]]></literal>
    <justification jstring="[para(18400(a,1),15327(a,1,2))].">
      <j1 rule="para" parents="18400 15327"/>
    </justification>
  </clause>

  <clause id="18403">
    <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(10834,a,18199,a),flip(a)].">
      <j1 rule="hyper" parents="10834 18199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18405">
    <literal><![CDATA[
      K(x,((T(y,z) \ 1) * u) \ ((y \ 1) * (z * y))) = K(x,(y \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,14525,a(flip),b,18199,a),flip(a)].">
      <j1 rule="hyper" parents="58 14525 18199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18406">
    <literal><![CDATA[
      K(x * (1 / (1 / (y \ z))),(z \ y) \ x) = a(1 / (z \ y),z \ y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(13988,a,18267,a)].">
      <j1 rule="hyper" parents="13988 18267"/>
    </justification>
  </clause>

  <clause id="18407">
    <literal><![CDATA[
      K(x * (y \ z),(z \ y) \ x) = a(1 / (z \ y),z \ y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(14016,a,18406,a)].">
      <j1 rule="hyper" parents="14016 18406"/>
    </justification>
  </clause>

  <clause id="18408">
    <literal><![CDATA[
      K(x * (y \ z),(z \ y) \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,13715,a(flip),b,18407,a),flip(a)].">
      <j1 rule="hyper" parents="320 13715 18407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18409">
    <literal><![CDATA[
      K(x * (y \ z),x / (z \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(16517,a,18408,a)].">
      <j1 rule="hyper" parents="16517 18408"/>
    </justification>
  </clause>

  <clause id="18412">
    <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,14910,a(flip),b,18388,a)].">
      <j1 rule="hyper" parents="58 14910 18388"/>
    </justification>
  </clause>

  <clause id="18413">
    <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,16834,a(flip),b,18412,a),flip(a)].">
      <j1 rule="hyper" parents="58 16834 18412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18414">
    <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(18413(a,1),14879(a,1,1))].">
      <j1 rule="para" parents="18413 14879"/>
    </justification>
  </clause>

  <clause id="18415">
    <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,18078,a(flip),b,17458,a)].">
      <j1 rule="hyper" parents="58 18078 17458"/>
    </justification>
  </clause>

  <clause id="18416">
    <literal><![CDATA[
      K(x,y * (z * K((u \ w) \ v5,u \ w))) = K(x,(y * z) * K(w \ u,v5))
    ]]></literal>
    <justification jstring="[hyper(15910,a,17504,a),flip(a)].">
      <j1 rule="hyper" parents="15910 17504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18417">
    <literal><![CDATA[
      K(x,y * (z * K((u \ w) \ y,u \ w))) = K(x,T(y,w \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,15744,a(flip),b,18416,a),flip(a)].">
      <j1 rule="hyper" parents="320 15744 18416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18418">
    <literal><![CDATA[
      K(x,y * (z * K(u * (w \ y),u \ w))) = K(x,T(y,w \ u) * z)
    ]]></literal>
    <justification jstring="[para(12427(a,1),18417(a,1,2,2,2))].">
      <j1 rule="para" parents="12427 18417"/>
    </justification>
  </clause>

  <clause id="18419">
    <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(320,a,17941,a(flip),b,17574,a),flip(a)].">
      <j1 rule="hyper" parents="320 17941 17574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18421">
    <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(320,a,16229,a(flip),b,18419,a),flip(a)].">
      <j1 rule="hyper" parents="320 16229 18419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18422">
    <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,15935,a(flip),b,18421,a),flip(a)].">
      <j1 rule="hyper" parents="58 15935 18421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18423">
    <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(320,a,16229,a(flip),b,18422,a),flip(a)].">
      <j1 rule="hyper" parents="320 16229 18422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18424">
    <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,17965,a(flip),b,18423,a),flip(a)].">
      <j1 rule="hyper" parents="58 17965 18423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18425">
    <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,18039,a(flip),b,18424,a),flip(a)].">
      <j1 rule="hyper" parents="58 18039 18424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18426">
    <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,17963,a(flip),b,18425,a)].">
      <j1 rule="hyper" parents="58 17963 18425"/>
    </justification>
  </clause>

  <clause id="18427">
    <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(5092(a,1),17577(a,2,2,1,1,1,2))].">
      <j1 rule="para" parents="5092 17577"/>
    </justification>
  </clause>

  <clause id="18428">
    <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(5326(a,1),17598(a,1,2,2,2))].">
      <j1 rule="para" parents="5326 17598"/>
    </justification>
  </clause>

  <clause id="18429">
    <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,18102,a(flip),b,18428,a),flip(a)].">
      <j1 rule="hyper" parents="58 18102 18428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18430">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K(u,z))) = K(x,y / T((z \ 1) * u,u))
    ]]></literal>
    <justification jstring="[para(5877(a,1),18429(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5877 18429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18431">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(320,a,16117,a(flip),b,18430,a),flip(a)].">
      <j1 rule="hyper" parents="320 16117 18430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18432">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * T(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17597,a(flip),b,18431,a)].">
      <j1 rule="hyper" parents="58 17597 18431"/>
    </justification>
  </clause>

  <clause id="18433">
    <literal><![CDATA[
      K(x,y / (T(z,u) * (u \ 1))) = K(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,17625,a(flip),b,18432,a),flip(a)].">
      <j1 rule="hyper" parents="58 17625 18432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18434">
    <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(320,a,13019,a(flip),b,17771,a),flip(a)].">
      <j1 rule="hyper" parents="320 13019 17771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18435">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) / u) \ w) = T(x,K(z,y) * ((y / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15922,a(flip),b,18434,a)].">
      <j1 rule="hyper" parents="58 15922 18434"/>
    </justification>
  </clause>

  <clause id="18436">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) / u) \ w) = T(x,(T(y,z) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(320,a,17573,a(flip),b,18435,a),flip(a)].">
      <j1 rule="hyper" parents="320 17573 18435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18438">
    <literal><![CDATA[
      T(x,(T(y \ z,z) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18027,a(flip),b,18436,a),flip(a)].">
      <j1 rule="hyper" parents="58 18027 18436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18439">
    <literal><![CDATA[
      T(x,((y / z) / y) \ u) = T(x,(y \ (z \ y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,17864,a(flip),b,18438,a),flip(a)].">
      <j1 rule="hyper" parents="58 17864 18438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18440">
    <literal><![CDATA[
      T(x,(y \ ((z \ K(z,y)) \ y)) \ u) = T(x,(y \ (y / (z \ 1))) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15328,a(flip),b,18439,a),flip(a)].">
      <j1 rule="hyper" parents="58 15328 18439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18441">
    <literal><![CDATA[
      T(x,(((y \ 1) \ z) / z) \ u) = T(x,(z \ (z / (y \ 1))) \ u)
    ]]></literal>
    <justification jstring="[para(10110(a,1),18440(a,1,2,1))].">
      <j1 rule="para" parents="10110 18440"/>
    </justification>
  </clause>

  <clause id="18442">
    <literal><![CDATA[
      T(x,(y \ (y / ((z \ 1) \ 1))) \ u) = T(x,((z \ y) / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(14064,a,18441,a),flip(a)].">
      <j1 rule="hyper" parents="14064 18441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18443">
    <literal><![CDATA[
      T(x,((y \ z) / z) \ u) = T(x,(z \ (z / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(14063,a,18442,a),flip(a)].">
      <j1 rule="hyper" parents="14063 18442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18444">
    <literal><![CDATA[
      T(x,T((y \ z) / z,u) \ w) = T(x,(z \ (z / T(y,u))) \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18402,a(flip),b,18443,a)].">
      <j1 rule="hyper" parents="58 18402 18443"/>
    </justification>
  </clause>

  <clause id="18445">
    <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(320,a,17949,a(flip),b,18444,a),flip(a)].">
      <j1 rule="hyper" parents="320 17949 18444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18446">
    <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(16695,a,18445,a)].">
      <j1 rule="hyper" parents="16695 18445"/>
    </justification>
  </clause>

  <clause id="18447">
    <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,15369,a(flip),b,18446,a)].">
      <j1 rule="hyper" parents="58 15369 18446"/>
    </justification>
  </clause>

  <clause id="18448">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,T(y / T(z,w),u) \ y)
    ]]></literal>
    <justification jstring="[para(7603(a,1),18447(a,1,2,1))].">
      <j1 rule="para" parents="7603 18447"/>
    </justification>
  </clause>

  <clause id="18449">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,y * T(y \ T(z,w),u))
    ]]></literal>
    <justification jstring="[hyper(320,a,17960,a(flip),b,18448,a),flip(a)].">
      <j1 rule="hyper" parents="320 17960 18448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18450">
    <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(320,a,12340,a,b,18449,a)].">
      <j1 rule="hyper" parents="320 12340 18449"/>
    </justification>
  </clause>

  <clause id="18451">
    <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(18082,a,18450,a)].">
      <j1 rule="hyper" parents="18082 18450"/>
    </justification>
  </clause>

  <clause id="18452">
    <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,12327,a(flip),b,18451,a),flip(a)].">
      <j1 rule="hyper" parents="58 12327 18451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18453">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,T(y * T(y \ z,u),w))
    ]]></literal>
    <justification jstring="[para(453(a,1),18452(a,2,2,1))].">
      <j1 rule="para" parents="453 18452"/>
    </justification>
  </clause>

  <clause id="18454">
    <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,18449,a(flip),b,18453,a),flip(a)].">
      <j1 rule="hyper" parents="58 18449 18453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18455">
    <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(320,a,13233,a(flip),b,17885,a),flip(a)].">
      <j1 rule="hyper" parents="320 13233 17885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18456">
    <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,16723,a(flip),b,17947,a)].">
      <j1 rule="hyper" parents="58 16723 17947"/>
    </justification>
  </clause>

  <clause id="18457">
    <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(18456(a,1),17948(a,1))].">
      <j1 rule="para" parents="18456 17948"/>
    </justification>
  </clause>

  <clause id="18458">
    <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(16721(a,1),18457(a,1))].">
      <j1 rule="para" parents="16721 18457"/>
    </justification>
  </clause>

  <clause id="18459">
    <literal><![CDATA[
      L(x,(y * z) / y,(y \ z) \ 1) = L(x,y * (z / y),(z / y) \ 1)
    ]]></literal>
    <justification jstring="[para(4079(a,1),18455(a,1,3,1))].">
      <j1 rule="para" parents="4079 18455"/>
    </justification>
  </clause>

  <clause id="18460">
    <literal><![CDATA[
      L(x,y * (z / y),(z / y) \ 1) = L(x,y * (z / y),(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,13233,a(flip),b,18459,a),flip(a)].">
      <j1 rule="hyper" parents="58 13233 18459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18461">
    <literal><![CDATA[
      L(x,y * (z / y),(z / y) \ 1) = L(x,z,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,13247,a(flip),b,18460,a),flip(a)].">
      <j1 rule="hyper" parents="320 13247 18460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18462">
    <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(18461(a,1),10121(a,1,2))].">
      <j1 rule="para" parents="18461 10121"/>
    </justification>
  </clause>

  <clause id="18463">
    <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(17313(a,2),17131(a,1,1))].">
      <j1 rule="para" parents="17313 17131"/>
    </justification>
  </clause>

  <clause id="18464">
    <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(13373(a,2),17217(a,1,2,1,2))].">
      <j1 rule="para" parents="13373 17217"/>
    </justification>
  </clause>

  <clause id="18465">
    <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(14472,a,17309,a)].">
      <j1 rule="hyper" parents="14472 17309"/>
    </justification>
  </clause>

  <clause id="18467">
    <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(15443,a,18465,a)].">
      <j1 rule="hyper" parents="15443 18465"/>
    </justification>
  </clause>

  <clause id="18468">
    <literal><![CDATA[
      K(x,(((y * z) \ z) * u) \ T(z,y)) = K(x,L(u \ (y * z),z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(15405,a,18467,a),flip(a)].">
      <j1 rule="hyper" parents="15405 18467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18469">
    <literal><![CDATA[
      K(x,L(y \ (z * u),u,z \ 1)) = K(x,(((u * z) \ u) * y) \ u)
    ]]></literal>
    <justification jstring="[para(13756(a,1),18468(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13756 18468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18470">
    <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(17285(a,1),17318(a,1,2))].">
      <j1 rule="para" parents="17285 17318"/>
    </justification>
  </clause>

  <clause id="18471">
    <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(17690,a,17666,a),flip(a)].">
      <j1 rule="hyper" parents="17690 17666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18472">
    <literal><![CDATA[
      K(x,T(T(y,x) / (z \ 1),y) * u) = K(x,(T(y,z) / (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(7334,a,18471,a)].">
      <j1 rule="hyper" parents="7334 18471"/>
    </justification>
  </clause>

  <clause id="18474">
    <literal><![CDATA[
      K(x,((y \ 1) \ T(z,x)) * u) = K(x,(T(z,y) / (y \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16032,a(flip),b,18472,a)].">
      <j1 rule="hyper" parents="58 16032 18472"/>
    </justification>
  </clause>

  <clause id="18475">
    <literal><![CDATA[
      K(x,(T(y,z) / (z \ 1)) * u) = K(x,((z \ 1) \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(17605,a,18474,a),flip(a)].">
      <j1 rule="hyper" parents="17605 18474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18476">
    <literal><![CDATA[
      K(x,(y / (z \ K(y,z))) * u) = K(x,((z \ 1) \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,17613,a(flip),b,18475,a)].">
      <j1 rule="hyper" parents="58 17613 18475"/>
    </justification>
  </clause>

  <clause id="18477">
    <literal><![CDATA[
      K(x,(y / (z / u)) / T(w,(z / u) \ y)) = K(x,w \ (y / (T(u,z) \ z)))
    ]]></literal>
    <justification jstring="[hyper(17833,a,17999,a),flip(a)].">
      <j1 rule="hyper" parents="17833 17999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18478">
    <literal><![CDATA[
      K(x,y \ (z / (T(u,w) \ w))) = K(x,y \ (z / (w / u)))
    ]]></literal>
    <justification jstring="[hyper(16066,a,18477,a),flip(a)].">
      <j1 rule="hyper" parents="16066 18477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18479">
    <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(18477(a,1),16066(a,1))].">
      <j1 rule="para" parents="18477 16066"/>
    </justification>
  </clause>

  <clause id="18480">
    <literal><![CDATA[
      K(x,y \ (z / (z / u))) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),18478(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 18478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18481">
    <literal><![CDATA[
      K(x,y \ T(z \ u,u)) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[para(72(a,1),18480(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="72 18480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18482">
    <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(10088(a,1),18480(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10088 18480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18483">
    <literal><![CDATA[
      K(x,y \ (z \ T(u,z \ 1))) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15241,a(flip),b,18481,a)].">
      <j1 rule="hyper" parents="58 15241 18481"/>
    </justification>
  </clause>

  <clause id="18484">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ ((z \ y) \ T(u,(y / z) \ 1)))
    ]]></literal>
    <justification jstring="[para(5565(a,1),18483(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5565 18483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18485">
    <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(320,a,16569,a(flip),b,18482,a),flip(a)].">
      <j1 rule="hyper" parents="320 16569 18482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18486">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ ((z \ y) \ T(u,z / y)))
    ]]></literal>
    <justification jstring="[para(4415(a,1),18484(a,2,2,2,2))].">
      <j1 rule="para" parents="4415 18484"/>
    </justification>
  </clause>

  <clause id="18487">
    <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,13031,a(flip),b,18485,a),flip(a)].">
      <j1 rule="hyper" parents="58 13031 18485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18488">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,y \ (u * (K(w,u \ 1) * z)))
    ]]></literal>
    <justification jstring="[para(12605(a,1),18487(a,2,2,2))].">
      <j1 rule="para" parents="12605 18487"/>
    </justification>
  </clause>

  <clause id="18489">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,K(u \ 1,w) * (y \ (u * z)))
    ]]></literal>
    <justification jstring="[hyper(320,a,17993,a(flip),b,18488,a),flip(a)].">
      <j1 rule="hyper" parents="320 17993 18488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18490">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,K(u,w) * (y \ (u * z)))
    ]]></literal>
    <justification jstring="[hyper(320,a,15259,a(flip),b,18489,a),flip(a)].">
      <j1 rule="hyper" parents="320 15259 18489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18491">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,y \ (T(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,17564,a(flip),b,18490,a),flip(a)].">
      <j1 rule="hyper" parents="320 17564 18490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18492">
    <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,14958,a(flip),b,18491,a)].">
      <j1 rule="hyper" parents="58 14958 18491"/>
    </justification>
  </clause>

  <clause id="18493">
    <literal><![CDATA[
      K(x,y \ T(z * (1 / T(u,w)),z)) = K(x,y \ (T(u \ 1,w) * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,5705,a(flip),b,18492,a),flip(a)].">
      <j1 rule="hyper" parents="320 5705 18492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18494">
    <literal><![CDATA[
      K(x,y \ ((1 / T(z,u)) * w)) = K(x,y \ (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13031,a(flip),b,18493,a)].">
      <j1 rule="hyper" parents="58 13031 18493"/>
    </justification>
  </clause>

  <clause id="18495">
    <literal><![CDATA[
      K(x,y \ (T(z \ 1,u) * w)) = K(x,y \ ((T(z,u) \ 1) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,5293,a(flip),b,18494,a),flip(a)].">
      <j1 rule="hyper" parents="58 5293 18494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18496">
    <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(320,a,10897,a(flip),b,18495,a),flip(a)].">
      <j1 rule="hyper" parents="320 10897 18495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18497">
    <literal><![CDATA[
      K(x,y \ (z / T(u,z))) = K(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(320,a,5004,a(flip),b,17842,a),flip(a)].">
      <j1 rule="hyper" parents="320 5004 17842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18498">
    <literal><![CDATA[
      K(x,y \ (T(z,u) / u)) = K(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[para(4206(a,2),18497(a,1,2,2))].">
      <j1 rule="para" parents="4206 18497"/>
    </justification>
  </clause>

  <clause id="18499">
    <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(12694(a,1),18498(a,1,2,2,1))].">
      <j1 rule="para" parents="12694 18498"/>
    </justification>
  </clause>

  <clause id="18500">
    <literal><![CDATA[
      K(x,y \ (T(z,u / w) / (u / w))) = K(x,y \ ((T(w,u) \ u) \ z))
    ]]></literal>
    <justification jstring="[hyper(18479,a,18499,a)].">
      <j1 rule="hyper" parents="18479 18499"/>
    </justification>
  </clause>

  <clause id="18501">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) \ u) \ w)) = K(x,y \ ((u / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,18498,a(flip),b,18500,a),flip(a)].">
      <j1 rule="hyper" parents="58 18498 18500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18502">
    <literal><![CDATA[
      K(x,(y \ 1) \ ((z / u) \ w)) = K(x,y * ((u \ T(z,u)) \ w))
    ]]></literal>
    <justification jstring="[hyper(14002,a,18501,a),flip(a)].">
      <j1 rule="hyper" parents="14002 18501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18503">
    <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(18502(a,1),13941(a,1))].">
      <j1 rule="para" parents="18502 13941"/>
    </justification>
  </clause>

  <clause id="18504">
    <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(4208(a,2),18503(a,1,2,2,1))].">
      <j1 rule="para" parents="4208 18503"/>
    </justification>
  </clause>

  <clause id="18505">
    <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(18080(a,1),18504(a,1))].">
      <j1 rule="para" parents="18080 18504"/>
    </justification>
  </clause>

  <clause id="18506">
    <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(17977(a,1),18147(a,1,2,1))].">
      <j1 rule="para" parents="17977 18147"/>
    </justification>
  </clause>

  <clause id="18507">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,u * ((z \ 1) * T(y,u / z)))
    ]]></literal>
    <justification jstring="[para(13793(a,1),18506(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13793 18506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18509">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,u * ((z \ 1) * T(y,z \ u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,16053,a(flip),b,18507,a),flip(a)].">
      <j1 rule="hyper" parents="320 16053 18507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18510">
    <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,16709,a(flip),b,18509,a),flip(a)].">
      <j1 rule="hyper" parents="58 16709 18509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18511">
    <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(17139(a,1),18197(a,1,1,1))].">
      <j1 rule="para" parents="17139 18197"/>
    </justification>
  </clause>

  <clause id="18513">
    <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(17858,a,18511,a)].">
      <j1 rule="hyper" parents="17858 18511"/>
    </justification>
  </clause>

  <clause id="18515">
    <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(17854(a,1),18513(a,2,2))].">
      <j1 rule="para" parents="17854 18513"/>
    </justification>
  </clause>

  <clause id="18516">
    <literal><![CDATA[
      L(K(x,y) * K(z,u),w,K(v5,v6)) = K(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3988,a,18515,a)].">
      <j1 rule="hyper" parents="3988 18515"/>
    </justification>
  </clause>

  <clause id="18517">
    <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(18516(a,1),17760(a,1,1,1))].">
      <j1 rule="para" parents="18516 17760"/>
    </justification>
  </clause>

  <clause id="18518">
    <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(13974(a,1),18517(a,1,1))].">
      <j1 rule="para" parents="13974 18517"/>
    </justification>
  </clause>

  <clause id="18520">
    <literal><![CDATA[
      T(K(x,y) * a(z,u,w),K(v5,v6)) = a(z,u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7839,a,18518,a)].">
      <j1 rule="hyper" parents="7839 18518"/>
    </justification>
  </clause>

  <clause id="18521">
    <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(12429(a,1),18230(a,1,1))].">
      <j1 rule="para" parents="12429 18230"/>
    </justification>
  </clause>

  <clause id="18522">
    <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(4024(a,1),18243(a,1,2))].">
      <j1 rule="para" parents="4024 18243"/>
    </justification>
  </clause>

  <clause id="18523">
    <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(14390(a,1),18378(a,1,1,1))].">
      <j1 rule="para" parents="14390 18378"/>
    </justification>
  </clause>

  <clause id="18525">
    <literal><![CDATA[
      ((K(x,y) * z) * (u * K(w,v5))) / u = K(x,y) * ((z * u) / (u * K(v5,w)))
    ]]></literal>
    <justification jstring="[para(18196(a,1),18523(a,1,1))].">
      <j1 rule="para" parents="18196 18523"/>
    </justification>
  </clause>

  <clause id="18526">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (u * K(w,v5)) = K(x,y) * ((z * u) / (u * K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(14487,a,18525,a)].">
      <j1 rule="hyper" parents="14487 18525"/>
    </justification>
  </clause>

  <clause id="18527">
    <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(16527,a,18396,a)].">
      <j1 rule="hyper" parents="16527 18396"/>
    </justification>
  </clause>

  <clause id="18528">
    <literal><![CDATA[
      K(x,y / (T((z \ u) \ 1,u) / w)) = K(x,y / (((u / z) \ 1) / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,18397,a(flip),b,18527,a),flip(a)].">
      <j1 rule="hyper" parents="58 18397 18527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18529">
    <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(444,a,18331,a,b,18528,a)].">
      <j1 rule="hyper" parents="444 18331 18528"/>
    </justification>
  </clause>

  <clause id="18530">
    <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(320,a,14477,a(flip),b,18403,a),flip(a)].">
      <j1 rule="hyper" parents="320 14477 18403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18531">
    <literal><![CDATA[
      K(x,L(y \ (z * u),u,z \ 1)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,18405,a(flip),b,18530,a),flip(a)].">
      <j1 rule="hyper" parents="58 18405 18530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18532">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * u) \ y) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,18469,a(flip),b,18531,a)].">
      <j1 rule="hyper" parents="58 18469 18531"/>
    </justification>
  </clause>

  <clause id="18533">
    <literal><![CDATA[
      K(x,y \ (z * (((y * u) \ y) \ y))) = K(x,(u \ (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(18330,a,18532,a)].">
      <j1 rule="hyper" parents="18330 18532"/>
    </justification>
  </clause>

  <clause id="18534">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * T(u,z \ 1)) \ y) = K(x,(u / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,15198,a(flip),b,18532,a),flip(a)].">
      <j1 rule="hyper" parents="320 15198 18532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18535">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ y) = K(x,((z \ y) * u) \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),18532(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 18532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18536">
    <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(14406(a,1),18532(a,2,2,1))].">
      <j1 rule="para" parents="14406 18532"/>
    </justification>
  </clause>

  <clause id="18537">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * u) \ y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ u,K(v5,v6)) \ y) = w
    ]]></literal>
    <justification jstring="[para(18532(a,2),15989(a,1))].">
      <j1 rule="para" parents="18532 15989"/>
    </justification>
  </clause>

  <clause id="18538">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ z) * K(x,K(z,y \ u)) = K(x,z / ((z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(18535(a,1),9903(a,1,1))].">
      <j1 rule="para" parents="18535 9903"/>
    </justification>
  </clause>

  <clause id="18539">
    <literal><![CDATA[
      K(x,y \ (z * T(y * u,y))) = K(x,(u \ (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,13117,a(flip),b,18533,a)].">
      <j1 rule="hyper" parents="58 13117 18533"/>
    </justification>
  </clause>

  <clause id="18540">
    <literal><![CDATA[
      K(x,(y \ (z \ u)) \ u) = K(x,u \ (z * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17903,a(flip),b,18539,a),flip(a)].">
      <j1 rule="hyper" parents="58 17903 18539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18541">
    <literal><![CDATA[
      K(x,y \ ((y / z) * (u * y))) = K(x,(u \ z) \ y)
    ]]></literal>
    <justification jstring="[para(75(a,1),18540(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="75 18540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18542">
    <literal><![CDATA[
      K(x,(y \ (z * u)) \ u) = K(x,u \ (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14822,a(flip),b,18541,a),flip(a)].">
      <j1 rule="hyper" parents="58 14822 18541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18544">
    <literal><![CDATA[
      K(x,((y / z) \ u) \ z) = K(x,z \ ((z / u) * y))
    ]]></literal>
    <justification jstring="[para(7(a,1),18541(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7 18541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18545">
    <literal><![CDATA[
      T(K(x,y \ (z \ (u * y))),y) = K(x,y / (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(18542(a,1),7856(a,1,1))].">
      <j1 rule="para" parents="18542 7856"/>
    </justification>
  </clause>

  <clause id="18546">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z \ ((z / u) * w)) = K(y,T(((z / w) * u) \ z,x))
    ]]></literal>
    <justification jstring="[hyper(17688,a,18544,a),flip(a)].">
      <j1 rule="hyper" parents="17688 18544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18547">
    <literal><![CDATA[
      K(x,(y \ (z * u)) / u) = K(x,u / (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(8025,a,18545,a)].">
      <j1 rule="hyper" parents="8025 18545"/>
    </justification>
  </clause>

  <clause id="18548">
    <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,14548,a,b,18545,a)].">
      <j1 rule="hyper" parents="58 14548 18545"/>
    </justification>
  </clause>

  <clause id="18549">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z / (u \ (w * z))) = K(y,T((w \ (u * z)) / z,x))
    ]]></literal>
    <justification jstring="[hyper(14037,a,18547,a),flip(a)].">
      <j1 rule="hyper" parents="14037 18547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18550">
    <literal><![CDATA[
      K(x,y / (z \ (T(u,z) * y))) = K(x,T((u \ (z * y)) / y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18106,a(flip),b,18547,a),flip(a)].">
      <j1 rule="hyper" parents="58 18106 18547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18551">
    <literal><![CDATA[
      K(x,(y * ((z * u) \ z)) \ z) = K(x,(y / u) \ z)
    ]]></literal>
    <justification jstring="[para(6178(a,1),18534(a,1,2,1))].">
      <j1 rule="para" parents="6178 18534"/>
    </justification>
  </clause>

  <clause id="18552">
    <literal><![CDATA[
      K(x,y \ ((y * z) * (u \ y))) = K(x,(u / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(18330,a,18551,a)].">
      <j1 rule="hyper" parents="18330 18551"/>
    </justification>
  </clause>

  <clause id="18553">
    <literal><![CDATA[
      K(x,((y / z) / u) \ y) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[para(75(a,1),18552(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="75 18552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18554">
    <literal><![CDATA[
      K(x,y \ ((z * y) * (u \ y))) = K(x,(u / T(z,y)) \ y)
    ]]></literal>
    <justification jstring="[para(105(a,1),18552(a,1,2,2,1))].">
      <j1 rule="para" parents="105 18552"/>
    </justification>
  </clause>

  <clause id="18555">
    <literal><![CDATA[
      K(x,((y * ((y * z) / y)) / u) \ z) = K(x,z \ ((z * u) * ((y * z) \ T(z,y))))
    ]]></literal>
    <justification jstring="[para(13908(a,1),18552(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13908 18552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18556">
    <literal><![CDATA[
      K(x,T(y,z * u) / ((y / z) / u)) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16177,a,b,18553,a)].">
      <j1 rule="hyper" parents="58 16177 18553"/>
    </justification>
  </clause>

  <clause id="18557">
    <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(5925(a,1),18554(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5925 18554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18558">
    <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(18537,a,17932,a)].">
      <j1 rule="hyper" parents="18537 17932"/>
    </justification>
  </clause>

  <clause id="18559">
    <literal><![CDATA[
      K(x,y / ((y \ z) \ u)) = K(x,y / ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14040,a(flip),b,18538,a),flip(a)].">
      <j1 rule="hyper" parents="58 14040 18538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18560">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,w)) = K(x,T(y \ ((y / u) * z),w))
    ]]></literal>
    <justification jstring="[hyper(14037,a,18546,a),flip(a)].">
      <j1 rule="hyper" parents="14037 18546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18561">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,y / (z * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16267,a(flip),b,18560,a),flip(a)].">
      <j1 rule="hyper" parents="58 16267 18560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18562">
    <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(18549(a,1),14037(a,1))].">
      <j1 rule="para" parents="18549 14037"/>
    </justification>
  </clause>

  <clause id="18563">
    <literal><![CDATA[
      K(x,T((y \ (z * u)) / u,y)) = K(x,T(u / (z \ (y * u)),z))
    ]]></literal>
    <justification jstring="[hyper(18562,a,18110,a),flip(a)].">
      <j1 rule="hyper" parents="18562 18110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18564">
    <literal><![CDATA[
      K(x,y / (z \ (T(u,z) * y))) = K(x,T(y / (z \ (u * y)),z))
    ]]></literal>
    <justification jstring="[hyper(18562,a,18550,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18562 18550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18565">
    <literal><![CDATA[
      K(x,T(y / (z \ (u * y)),u)) = K(x,T(y / (z \ (u * y)),z))
    ]]></literal>
    <justification jstring="[hyper(18562,a,18563,a)].">
      <j1 rule="hyper" parents="18562 18563"/>
    </justification>
  </clause>

  <clause id="18566">
    <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(17933,a,18536,a)].">
      <j1 rule="hyper" parents="17933 18536"/>
    </justification>
  </clause>

  <clause id="18567">
    <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(10809(a,1),18566(a,1,2,1))].">
      <j1 rule="para" parents="10809 18566"/>
    </justification>
  </clause>

  <clause id="18568">
    <literal><![CDATA[
      K(x,K(y,z) * ((((u * w) \ u) * v5) \ u)) = K(x,((w \ v5) * K(z,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(17487,a,18567,a)].">
      <j1 rule="hyper" parents="17487 18567"/>
    </justification>
  </clause>

  <clause id="18569">
    <literal><![CDATA[
      K(x,K(y,z) * ((((u * w) \ u) * v5) \ u)) = K(x,K(y,z) * ((w \ v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,17744,a(flip),b,18568,a),flip(a)].">
      <j1 rule="hyper" parents="320 17744 18568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18571">
    <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(320,a,18569,a(flip),b,18558,a),flip(a)].">
      <j1 rule="hyper" parents="320 18569 18558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18572">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ v5) = K(x,K(w,u) * ((y \ z) \ v5))
    ]]></literal>
    <justification jstring="[hyper(15994,a,18571,a)].">
      <j1 rule="hyper" parents="15994 18571"/>
    </justification>
  </clause>

  <clause id="18573">
    <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(17313(a,2),18463(a,1,2))].">
      <j1 rule="para" parents="17313 18463"/>
    </justification>
  </clause>

  <clause id="18574">
    <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(17240(a,1),18464(a,1,2,1))].">
      <j1 rule="para" parents="17240 18464"/>
    </justification>
  </clause>

  <clause id="18575">
    <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(18236(a,1),18574(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18236 18574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18576">
    <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(320,a,13811,a(flip),b,18575,a),flip(a)].">
      <j1 rule="hyper" parents="320 13811 18575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18578">
    <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(14191(a,2),18576(a,1,1))].">
      <j1 rule="para" parents="14191 18576"/>
    </justification>
  </clause>

  <clause id="18579">
    <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(14849(a,2),18578(a,2,2))].">
      <j1 rule="para" parents="14849 18578"/>
    </justification>
  </clause>

  <clause id="18580">
    <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,18335,a(flip),b,18579,a)].">
      <j1 rule="hyper" parents="58 18335 18579"/>
    </justification>
  </clause>

  <clause id="18581">
    <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(320,a,17665,a(flip),b,18580,a),flip(a)].">
      <j1 rule="hyper" parents="320 17665 18580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18582">
    <literal><![CDATA[
      L(K(x,y) * z,u,K(w,v5)) = K(x,y) * L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(13685(a,1),18581(a,1,1))].">
      <j1 rule="para" parents="13685 18581"/>
    </justification>
  </clause>

  <clause id="18583">
    <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(320,a,14992,a(flip),b,18582,a),flip(a)].">
      <j1 rule="hyper" parents="320 14992 18582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18584">
    <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(18582(a,2),16765(a,1,2,1))].">
      <j1 rule="para" parents="18582 16765"/>
    </justification>
  </clause>

  <clause id="18585">
    <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(17068(a,1),18470(a,1,2,2))].">
      <j1 rule="para" parents="17068 18470"/>
    </justification>
  </clause>

  <clause id="18586">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,T(u,y)) / y) = (x / (y \ 1)) * (y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14621,a(flip),b,18522,a),flip(a)].">
      <j1 rule="hyper" parents="58 14621 18522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18587">
    <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,5780,a(flip),b,18573,a)].">
      <j1 rule="hyper" parents="58 5780 18573"/>
    </justification>
  </clause>

  <clause id="18588">
    <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(7730(a,1),18587(a,1,3))].">
      <j1 rule="para" parents="7730 18587"/>
    </justification>
  </clause>

  <clause id="18589">
    <literal><![CDATA[
      L(x,K(y,K(z,u)) * w,v5) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(17128,a,18588,a),flip(a)].">
      <j1 rule="hyper" parents="17128 18588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18590">
    <literal><![CDATA[
      L(x,K(y,K(z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(18588(a,1),17127(a,1)),flip(b)].">
      <j1 rule="para" parents="18588 17127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18593">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),w) = L(x,K(y,z),w)
    ]]></literal>
    <justification jstring="[para(7139(a,1),18589(a,1,2))].">
      <j1 rule="para" parents="7139 18589"/>
    </justification>
  </clause>

  <clause id="18594">
    <literal><![CDATA[
      R(x,K(y,z),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16755,a(flip),b,18593,a)].">
      <j1 rule="hyper" parents="58 16755 18593"/>
    </justification>
  </clause>

  <clause id="18595">
    <literal><![CDATA[
      L((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(6327,a,18594,a),flip(a)].">
      <j1 rule="hyper" parents="6327 18594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18597">
    <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,15690,a,b,18594,a)].">
      <j1 rule="hyper" parents="58 15690 18594"/>
    </justification>
  </clause>

  <clause id="18598">
    <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,9468,a(flip),b,18594,a),flip(a)].">
      <j1 rule="hyper" parents="58 9468 18594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18599">
    <literal><![CDATA[
      L(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(18594(a,1),9839(a,1,1))].">
      <j1 rule="para" parents="18594 9839"/>
    </justification>
  </clause>

  <clause id="18600">
    <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(7139(a,1),18590(a,1,2))].">
      <j1 rule="para" parents="7139 18590"/>
    </justification>
  </clause>

  <clause id="18601">
    <literal><![CDATA[
      R(x,K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(16755(a,1),18600(a,1))].">
      <j1 rule="para" parents="16755 18600"/>
    </justification>
  </clause>

  <clause id="18602">
    <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(17257(a,2),18601(a,1))].">
      <j1 rule="para" parents="17257 18601"/>
    </justification>
  </clause>

  <clause id="18603">
    <literal><![CDATA[
      L(x * K(y,z),K(z,y),u) = (x * u) / (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(6(a,1),18595(a,1,1,1))].">
      <j1 rule="para" parents="6 18595"/>
    </justification>
  </clause>

  <clause id="18604">
    <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(18603(a,1),6424(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18603 6424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18605">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,y),u) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(18600,a,18598,a)].">
      <j1 rule="hyper" parents="18600 18598"/>
    </justification>
  </clause>

  <clause id="18606">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,y),u) = (x * (u * K(y,z))) / u
    ]]></literal>
    <justification jstring="[hyper(320,a,14486,a,b,18605,a),flip(a)].">
      <j1 rule="hyper" parents="320 14486 18605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18608">
    <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(18606(a,2),14487(a,1))].">
      <j1 rule="para" parents="18606 14487"/>
    </justification>
  </clause>

  <clause id="18609">
    <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(15893(a,2),18608(a,1))].">
      <j1 rule="para" parents="15893 18608"/>
    </justification>
  </clause>

  <clause id="18610">
    <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(320,a,18593,a(flip),b,18597,a),flip(a)].">
      <j1 rule="hyper" parents="320 18593 18597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18612">
    <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,18526,a(flip),b,18610,a)].">
      <j1 rule="hyper" parents="58 18526 18610"/>
    </justification>
  </clause>

  <clause id="18613">
    <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(9806(a,1),18583(a,1,1))].">
      <j1 rule="para" parents="9806 18583"/>
    </justification>
  </clause>

  <clause id="18614">
    <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(11810(a,1),18613(a,1,1))].">
      <j1 rule="para" parents="11810 18613"/>
    </justification>
  </clause>

  <clause id="18615">
    <literal><![CDATA[
      T(a(x,y,z) \ u,K(w,v5)) = a(x,y,z) \ T(u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(14872,a,18614,a),flip(a)].">
      <j1 rule="hyper" parents="14872 18614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18616">
    <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(320,a,15526,a(flip),b,18615,a),flip(a)].">
      <j1 rule="hyper" parents="320 15526 18615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18617">
    <literal><![CDATA[
      x * K(y,K(z,x * a(u,w,v5))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),18616(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 18616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18618">
    <literal><![CDATA[
      K(x,K(y,z * a(u,w,v5))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(29,a,7769,a,b,18617,a),flip(a)].">
      <j1 rule="hyper" parents="29 7769 18617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18619">
    <literal><![CDATA[
      T(a(x,y,z) * u,K(w,v5)) = a(x,y,z) * T(u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(119,a,18617,a(flip),b,15526,a),flip(a)].">
      <j1 rule="hyper" parents="119 18617 15526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18620">
    <literal><![CDATA[
      T(x,K(y,z * a(u,w,v5))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,18618,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 18618 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18621">
    <literal><![CDATA[
      T(x,K(y,(z * u) * w)) = T(x,K(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(80(a,1),18620(a,1,2,2))].">
      <j1 rule="para" parents="80 18620"/>
    </justification>
  </clause>

  <clause id="18622">
    <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(18620(a,1),15024(a,1,2,1,2))].">
      <j1 rule="para" parents="18620 15024"/>
    </justification>
  </clause>

  <clause id="18623">
    <literal><![CDATA[
      x \ T(a(y,z,u) * (a(y,z,u) \ x),K(w,v5)) = K(w,K(v5,a(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(116,a,18619,a,b,7782,a(flip))].">
      <j1 rule="hyper" parents="116 18619 7782"/>
    </justification>
  </clause>

  <clause id="18624">
    <literal><![CDATA[
      K(x,K(y,a(z,u,w) \ v5)) = v5 \ T(v5,K(x,y))
    ]]></literal>
    <justification jstring="[para(5(a,1),18623(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 18623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18625">
    <literal><![CDATA[
      K(x,K(y,a(z,u,w) \ v5)) = K(v5,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,4688,a,b,18624,a),flip(a)].">
      <j1 rule="hyper" parents="320 4688 18624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18626">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(y,z)) = u * K(y,T(z,a(w,v5,v6) \ x))
    ]]></literal>
    <justification jstring="[para(18625(a,1),15879(a,1,1))].">
      <j1 rule="para" parents="18625 15879"/>
    </justification>
  </clause>

  <clause id="18627">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w) \ v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(15898,a,18626,a),flip(a)].">
      <j1 rule="hyper" parents="15898 18626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18628">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w) * v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(15864,a,18627,a)].">
      <j1 rule="hyper" parents="15864 18627"/>
    </justification>
  </clause>

  <clause id="18629">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w)) = K(x,T(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(14363(a,1),18628(a,1,2,2))].">
      <j1 rule="para" parents="14363 18628"/>
    </justification>
  </clause>

  <clause id="18630">
    <literal><![CDATA[
      K(x,T(y,T(z * u,w) * v5)) = K(x,T(y,u * (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16461,a,b,18629,a)].">
      <j1 rule="hyper" parents="58 16461 18629"/>
    </justification>
  </clause>

  <clause id="18632">
    <literal><![CDATA[
      K(x,T(y,T(z * a(u,w,v5),v6) * v7)) = K(x,T(y,z * v7))
    ]]></literal>
    <justification jstring="[hyper(320,a,18628,a(flip),b,18630,a),flip(a)].">
      <j1 rule="hyper" parents="320 18628 18630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18633">
    <literal><![CDATA[
      K(x,T(y,(z * a(u,w,v5)) * v6)) = K(x,T(y,z * v6))
    ]]></literal>
    <justification jstring="[hyper(16367,a,18632,a)].">
      <j1 rule="hyper" parents="16367 18632"/>
    </justification>
  </clause>

  <clause id="18634">
    <literal><![CDATA[
      K(x,T(y,z * (a(u,w,v5) * v6))) = K(x,T(y,z * v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,18629,a(flip),b,18633,a)].">
      <j1 rule="hyper" parents="58 18629 18633"/>
    </justification>
  </clause>

  <clause id="18635">
    <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(18620(a,1),18622(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18620 18622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18636">
    <literal><![CDATA[
      T(x,K(y * a(z,u,w),v5) * v6) = T(x,K(y,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(320,a,15024,a(flip),b,18635,a),flip(a)].">
      <j1 rule="hyper" parents="320 15024 18635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18638">
    <literal><![CDATA[
      T(x,T(y,z * a(u,w,v5)) \ v6) = T(x,K(z,y) * (y \ v6))
    ]]></literal>
    <justification jstring="[para(5093(a,1),18636(a,1,2))].">
      <j1 rule="para" parents="5093 18636"/>
    </justification>
  </clause>

  <clause id="18639">
    <literal><![CDATA[
      T(x,T(y,z * a(u,w,v5)) \ v6) = T(x,T(y,z) \ v6)
    ]]></literal>
    <justification jstring="[para(5093(a,1),18638(a,2,2))].">
      <j1 rule="para" parents="5093 18638"/>
    </justification>
  </clause>

  <clause id="18640">
    <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),18584(a,1,2))].">
      <j1 rule="para" parents="20 18584"/>
    </justification>
  </clause>

  <clause id="18641">
    <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(17248(a,2),18585(a,1,1))].">
      <j1 rule="para" parents="17248 18585"/>
    </justification>
  </clause>

  <clause id="18642">
    <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(14866(a,1),18640(a,1,2))].">
      <j1 rule="para" parents="14866 18640"/>
    </justification>
  </clause>

  <clause id="18643">
    <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(15549,a,18642,a),flip(a)].">
      <j1 rule="hyper" parents="15549 18642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18644">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w) * v5)) = K(x,T(y,z * v5))
    ]]></literal>
    <justification jstring="[hyper(17202,a,18643,a),flip(a)].">
      <j1 rule="hyper" parents="17202 18643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18645">
    <literal><![CDATA[
      K(x,T(y,z * L(u,w,v5))) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(15717,a,18644,a)].">
      <j1 rule="hyper" parents="15717 18644"/>
    </justification>
  </clause>

  <clause id="18647">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * (z * w))) = K(x,T(y,w * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16518,a(flip),b,18644,a)].">
      <j1 rule="hyper" parents="58 16518 18644"/>
    </justification>
  </clause>

  <clause id="18648">
    <literal><![CDATA[
      K(x,T(y,z * L(u,w,v5))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(320,a,15495,a,b,18645,a),flip(a)].">
      <j1 rule="hyper" parents="320 15495 18645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18649">
    <literal><![CDATA[
      T(x * K(y,T(x,z * u)),y) = T(x,K(y,z * L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(18648(a,1),8106(a,1,1,2))].">
      <j1 rule="para" parents="18648 8106"/>
    </justification>
  </clause>

  <clause id="18650">
    <literal><![CDATA[
      K(x,T(y,(z * u) * (z \ w))) = K(x,T(y,u * w))
    ]]></literal>
    <justification jstring="[hyper(15717,a,18647,a)].">
      <j1 rule="hyper" parents="15717 18647"/>
    </justification>
  </clause>

  <clause id="18652">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * w)) = K(x,T(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[para(5(a,1),18650(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 18650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18653">
    <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,16689,a(flip),b,18652,a),flip(a)].">
      <j1 rule="hyper" parents="58 16689 18652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18654">
    <literal><![CDATA[
      T(x,K(y,z * L(u,w,v5))) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(8322,a,18649,a),flip(a)].">
      <j1 rule="hyper" parents="8322 18649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18655">
    <literal><![CDATA[
      T(x,K(y,z * ((u * w) \ v5))) = T(x,K(y,z * (w \ (u \ v5))))
    ]]></literal>
    <justification jstring="[para(298(a,1),18654(a,1,2,2,2))].">
      <j1 rule="para" parents="298 18654"/>
    </justification>
  </clause>

  <clause id="18656">
    <literal><![CDATA[
      T(x,K(y,z * ((u * z) \ w))) = T(x,K(y,u \ w))
    ]]></literal>
    <justification jstring="[para(5(a,1),18655(a,2,2,2))].">
      <j1 rule="para" parents="5 18655"/>
    </justification>
  </clause>

  <clause id="18657">
    <literal><![CDATA[
      T(x,K(y,(z / u) \ w)) = T(x,K(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[para(7(a,1),18656(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 18656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18658">
    <literal><![CDATA[
      T(x,K(y,z \ (u * w))) = T(x,K(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(17410,a,18657,a)].">
      <j1 rule="hyper" parents="17410 18657"/>
    </justification>
  </clause>

  <clause id="18659">
    <literal><![CDATA[
      T(x,K(y,z \ (u \ w))) = T(x,K(y,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(17273,a,18658,a)].">
      <j1 rule="hyper" parents="17273 18658"/>
    </justification>
  </clause>

  <clause id="18660">
    <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,17610,a(flip),b,18659,a),flip(a)].">
      <j1 rule="hyper" parents="58 17610 18659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18661">
    <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,16439,a(flip),b,18660,a)].">
      <j1 rule="hyper" parents="58 16439 18660"/>
    </justification>
  </clause>

  <clause id="18663">
    <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,8118,a(flip),b,18661,a),flip(a)].">
      <j1 rule="hyper" parents="58 8118 18661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18664">
    <literal><![CDATA[
      x * K(y,T(x,z \ (u \ w))) = x * K(y,T(x,u * (w \ z)))
    ]]></literal>
    <justification jstring="[para(17360(a,1),18663(a,1,2))].">
      <j1 rule="para" parents="17360 18663"/>
    </justification>
  </clause>

  <clause id="18665">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ w))) = K(x,T(y,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(278,a,18664,a),flip(a)].">
      <j1 rule="hyper" parents="278 18664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18668">
    <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(18665(a,1),17415(a,1))].">
      <j1 rule="para" parents="18665 17415"/>
    </justification>
  </clause>

  <clause id="18669">
    <literal><![CDATA[
      K(x * K(y \ (z \ x),y),T(u,x \ z)) = K(((z * y) \ x) * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(18668,a,18653,a)].">
      <j1 rule="hyper" parents="18668 18653"/>
    </justification>
  </clause>

  <clause id="18670">
    <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,17881,a(flip),b,18669,a)].">
      <j1 rule="hyper" parents="58 17881 18669"/>
    </justification>
  </clause>

  <clause id="18671">
    <literal><![CDATA[
      K(x * K(y \ (x / z),y),T(u,z)) = K(((z * y) \ x) * (y * z),u)
    ]]></literal>
    <justification jstring="[para(11095(a,1),18670(a,1,1))].">
      <j1 rule="para" parents="11095 18670"/>
    </justification>
  </clause>

  <clause id="18672">
    <literal><![CDATA[
      K(K(x / y,z) * x,T(u,y)) = K(((y * z) \ x) * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(15783,a,18671,a)].">
      <j1 rule="hyper" parents="15783 18671"/>
    </justification>
  </clause>

  <clause id="18673">
    <literal><![CDATA[
      K(((x * y) \ z) * (y * x),u) = K(z * K(x \ z,y),T(u,x))
    ]]></literal>
    <justification jstring="[para(6261(a,1),18672(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6261 18672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18674">
    <literal><![CDATA[
      K(((x * y) \ z) * (y * x),u) = K(x * T(z / x,y),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,12207,a(flip),b,18673,a),flip(a)].">
      <j1 rule="hyper" parents="320 12207 18673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18675">
    <literal><![CDATA[
      K(K(x,y) * z,T(u,x * y)) = K(y * T(z / y,x),u)
    ]]></literal>
    <justification jstring="[hyper(12257,a,18674,a)].">
      <j1 rule="hyper" parents="12257 18674"/>
    </justification>
  </clause>

  <clause id="18676">
    <literal><![CDATA[
      K(x \ T(y * x,z),u) = K(x * T(y / x,z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16546,a(flip),b,18675,a)].">
      <j1 rule="hyper" parents="58 16546 18675"/>
    </justification>
  </clause>

  <clause id="18677">
    <literal><![CDATA[
      K(x * K(x * y,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[hyper(16134,a,18676,a)].">
      <j1 rule="hyper" parents="16134 18676"/>
    </justification>
  </clause>

  <clause id="18678">
    <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(18677(a,1),16493(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18677 16493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18679">
    <literal><![CDATA[
      T(x,T(y * z,u) / T(z,y)) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,5216,a(flip),b,18678,a),flip(a)].">
      <j1 rule="hyper" parents="320 5216 18678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18680">
    <literal><![CDATA[
      T(x,T(y * K(y * z,u),z)) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[para(16491(a,1),18679(a,1,2))].">
      <j1 rule="para" parents="16491 18679"/>
    </justification>
  </clause>

  <clause id="18681">
    <literal><![CDATA[
      T(x,y \ T(z * y,u)) = T(x,y * T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16014,a(flip),b,18680,a)].">
      <j1 rule="hyper" parents="58 16014 18680"/>
    </justification>
  </clause>

  <clause id="18682">
    <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,16540,a(flip),b,18681,a),flip(a)].">
      <j1 rule="hyper" parents="58 16540 18681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18683">
    <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(18082,a,18682,a)].">
      <j1 rule="hyper" parents="18082 18682"/>
    </justification>
  </clause>

  <clause id="18684">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),y)) = T(x,T(y,z) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(18093,a,18683,a)].">
      <j1 rule="hyper" parents="18093 18683"/>
    </justification>
  </clause>

  <clause id="18685">
    <literal><![CDATA[
      T(x,T(y,z) \ T(z * y,u)) = T(x,T(z / y,u) * y)
    ]]></literal>
    <justification jstring="[hyper(12223,a,18684,a),flip(a)].">
      <j1 rule="hyper" parents="12223 18684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18686">
    <literal><![CDATA[
      T(x,T(y,z) \ T(z * y,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(453(a,1),18685(a,2,2))].">
      <j1 rule="para" parents="453 18685"/>
    </justification>
  </clause>

  <clause id="18687">
    <literal><![CDATA[
      T(x,y \ T(z * T(y,z),u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(18458,a,18686,a)].">
      <j1 rule="hyper" parents="18458 18686"/>
    </justification>
  </clause>

  <clause id="18688">
    <literal><![CDATA[
      T(x,y \ T(y * z,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(105(a,1),18687(a,1,2,2,1))].">
      <j1 rule="para" parents="105 18687"/>
    </justification>
  </clause>

  <clause id="18689">
    <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(17337,a,18641,a)].">
      <j1 rule="hyper" parents="17337 18641"/>
    </justification>
  </clause>

  <clause id="18690">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w)) * v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,18173,a(flip),b,18689,a),flip(a)].">
      <j1 rule="hyper" parents="58 18173 18689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18691">
    <literal><![CDATA[
      L(x,y,z * T(u,K(w,v5))) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(17216,a,18690,a)].">
      <j1 rule="hyper" parents="17216 18690"/>
    </justification>
  </clause>

  <clause id="18693">
    <literal><![CDATA[
      L(x,y,z / (K(u,w) / v5)) = L(x,y,z / (v5 \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17279,a(flip),b,18690,a),flip(a)].">
      <j1 rule="hyper" parents="58 17279 18690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18694">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w)) \ v5) = L(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(5042(a,1),18690(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5042 18690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18696">
    <literal><![CDATA[
      L(x,y,z * (T(u,T(w,v5)) / v5)) = L(x,y,z * (T(u,w) / v5))
    ]]></literal>
    <justification jstring="[para(8120(a,1),18691(a,1,3,2))].">
      <j1 rule="para" parents="8120 18691"/>
    </justification>
  </clause>

  <clause id="18697">
    <literal><![CDATA[
      L(x,y,(K(z,u) / w) \ v5) = L(x,y,(w \ K(z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,12566,a(flip),b,18694,a),flip(a)].">
      <j1 rule="hyper" parents="58 12566 18694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18698">
    <literal><![CDATA[
      K(x,L(y,z,u / (w \ K(v5,v6)))) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[para(18693(a,1),18379(a,1,2))].">
      <j1 rule="para" parents="18693 18379"/>
    </justification>
  </clause>

  <clause id="18699">
    <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(18697(a,1),14527(a,1,2,2,2))].">
      <j1 rule="para" parents="18697 14527"/>
    </justification>
  </clause>

  <clause id="18700">
    <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(18697(a,1),16697(a,1,2,2))].">
      <j1 rule="para" parents="18697 16697"/>
    </justification>
  </clause>

  <clause id="18701">
    <literal><![CDATA[
      K(x,L(y,z,(u \ K(w,v5)) \ v6)) = K(x,L(y,z,u * v6))
    ]]></literal>
    <justification jstring="[hyper(17211,a,18698,a)].">
      <j1 rule="hyper" parents="17211 18698"/>
    </justification>
  </clause>

  <clause id="18702">
    <literal><![CDATA[
      K(x,L(y,z,(u \ K(w,v5)) \ v6)) = K(x,L(y,z,v6 * u))
    ]]></literal>
    <justification jstring="[hyper(320,a,17205,a,b,18701,a),flip(a)].">
      <j1 rule="hyper" parents="320 17205 18701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18703">
    <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(18702(a,2),17245(a,1))].">
      <j1 rule="para" parents="18702 17245"/>
    </justification>
  </clause>

  <clause id="18704">
    <literal><![CDATA[
      x * K(y,L(T(z,u \ 1),x,u * x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(18701(a,1),18700(a,1,2))].">
      <j1 rule="para" parents="18701 18700"/>
    </justification>
  </clause>

  <clause id="18705">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u * x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(8602(a,1),18704(a,1,2))].">
      <j1 rule="para" parents="8602 18704"/>
    </justification>
  </clause>

  <clause id="18707">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u * x)) = (x / (1 / u)) * (K(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,14534,a(flip),b,18705,a),flip(a)].">
      <j1 rule="hyper" parents="320 14534 18705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18708">
    <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(13037(a,1),17352(a,1,2))].">
      <j1 rule="para" parents="13037 17352"/>
    </justification>
  </clause>

  <clause id="18709">
    <literal><![CDATA[
      K(x,y / (T(z * u,z) \ w)) = K(x,y / ((u * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17351,a(flip),b,18708,a),flip(a)].">
      <j1 rule="hyper" parents="58 17351 18708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18710">
    <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,18427,a(flip),b,17621,a)].">
      <j1 rule="hyper" parents="58 18427 17621"/>
    </justification>
  </clause>

  <clause id="18711">
    <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,13072,a(flip),b,17865,a)].">
      <j1 rule="hyper" parents="58 13072 17865"/>
    </justification>
  </clause>

  <clause id="18712">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) * a(x,y,z) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(14536(a,1),18182(a,1,2))].">
      <j1 rule="para" parents="14536 18182"/>
    </justification>
  </clause>

  <clause id="18713">
    <literal><![CDATA[
      a(x,y,K(z,u)) * a(x,y,z) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(10842(a,1),18712(a,1,1))].">
      <j1 rule="para" parents="10842 18712"/>
    </justification>
  </clause>

  <clause id="18715">
    <literal><![CDATA[
      a(x,y,T(z,u)) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(13377,a,18713,a),flip(a)].">
      <j1 rule="hyper" parents="13377 18713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18716">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,T(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,18713,a(flip),b,17103,a(flip))].">
      <j1 rule="hyper" parents="116 18713 17103"/>
    </justification>
  </clause>

  <clause id="18717">
    <literal><![CDATA[
      a(x,y,T(z,K(u,w))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,17165,a(flip),b,18715,a),flip(a)].">
      <j1 rule="hyper" parents="320 17165 18715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18719">
    <literal><![CDATA[
      T(x,a(y,z,u)) / a(y,z,u) = x / a(y,z,T(u,x))
    ]]></literal>
    <justification jstring="[para(18715(a,2),4206(a,2,2))].">
      <j1 rule="para" parents="18715 4206"/>
    </justification>
  </clause>

  <clause id="18720">
    <literal><![CDATA[
      a(x,y,T(z,T(u,w))) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(7413(a,1),18717(a,1,3))].">
      <j1 rule="para" parents="7413 18717"/>
    </justification>
  </clause>

  <clause id="18721">
    <literal><![CDATA[
      a(x,y,T(z,T(x * y,u))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,14469,a(flip),b,18720,a),flip(a)].">
      <j1 rule="hyper" parents="320 14469 18720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18722">
    <literal><![CDATA[
      a(x,y,T(z,y * x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(12214(a,1),18721(a,1,3))].">
      <j1 rule="para" parents="12214 18721"/>
    </justification>
  </clause>

  <clause id="18723">
    <literal><![CDATA[
      a(x,y,z) \ ((y * x) * T(z,x * T(y,x))) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(18722(a,1),14657(a,1,1))].">
      <j1 rule="para" parents="18722 14657"/>
    </justification>
  </clause>

  <clause id="18724">
    <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),18723(a,1,2,2,2))].">
      <j1 rule="para" parents="105 18723"/>
    </justification>
  </clause>

  <clause id="18725">
    <literal><![CDATA[
      a(x,y,z) \ (z * (y * x)) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(105(a,1),18724(a,1,2))].">
      <j1 rule="para" parents="105 18724"/>
    </justification>
  </clause>

  <clause id="18726">
    <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,17914,a(flip),b,18710,a)].">
      <j1 rule="hyper" parents="58 17914 18710"/>
    </justification>
  </clause>

  <clause id="18728">
    <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,17614,a(flip),b,18726,a)].">
      <j1 rule="hyper" parents="58 17614 18726"/>
    </justification>
  </clause>

  <clause id="18730">
    <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(17199(a,1),17878(a,1))].">
      <j1 rule="para" parents="17199 17878"/>
    </justification>
  </clause>

  <clause id="18731">
    <literal><![CDATA[
      T(x,y * K(z,u \ w)) = T(x,y * K(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(18730,a,18426,a),flip(a)].">
      <j1 rule="hyper" parents="18730 18426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18732">
    <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(18731(a,1),14634(a,1,1,2))].">
      <j1 rule="para" parents="18731 14634"/>
    </justification>
  </clause>

  <clause id="18733">
    <literal><![CDATA[
      K(x * y,z * K(u,w \ v5)) = K(x * y,z * K(u,v5 * w))
    ]]></literal>
    <justification jstring="[hyper(14635,a,18732,a),flip(a)].">
      <j1 rule="hyper" parents="14635 18732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18734">
    <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(18732(a,1),14635(a,1))].">
      <j1 rule="para" parents="18732 14635"/>
    </justification>
  </clause>

  <clause id="18735">
    <literal><![CDATA[
      K(K(x,y) * (z \ (u * K(x,y))),w * K(v5,u * z)) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[hyper(17800,a,18733,a),flip(a)].">
      <j1 rule="hyper" parents="17800 18733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18736">
    <literal><![CDATA[
      K(x \ y,z * K(u,y * x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(18081,a,18735,a)].">
      <j1 rule="hyper" parents="18081 18735"/>
    </justification>
  </clause>

  <clause id="18737">
    <literal><![CDATA[
      K(x * K(y,z * u),u \ z) = w / (K(u \ z,x) * w)
    ]]></literal>
    <justification jstring="[para(18736(a,1),5104(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18736 5104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18738">
    <literal><![CDATA[
      K(x * K(y,z * u),u \ z) = K(x,u \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,17387,a(flip),b,18737,a),flip(a)].">
      <j1 rule="hyper" parents="320 17387 18737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18739">
    <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(16683,a,18738,a)].">
      <j1 rule="hyper" parents="16683 18738"/>
    </justification>
  </clause>

  <clause id="18740">
    <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(16047,a,18738,a)].">
      <j1 rule="hyper" parents="16047 18738"/>
    </justification>
  </clause>

  <clause id="18741">
    <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(10370(a,1),18738(a,1,1,2,2))].">
      <j1 rule="para" parents="10370 18738"/>
    </justification>
  </clause>

  <clause id="18742">
    <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(16020(a,1),18738(a,1,1,2))].">
      <j1 rule="para" parents="16020 18738"/>
    </justification>
  </clause>

  <clause id="18743">
    <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,16615,a(flip),b,18739,a)].">
      <j1 rule="hyper" parents="58 16615 18739"/>
    </justification>
  </clause>

  <clause id="18746">
    <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,16615,a(flip),b,18740,a)].">
      <j1 rule="hyper" parents="58 16615 18740"/>
    </justification>
  </clause>

  <clause id="18748">
    <literal><![CDATA[
      K(x,y \ T(z,u \ w)) = K(x,y \ T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,18743,a(flip),b,18746,a)].">
      <j1 rule="hyper" parents="58 18743 18746"/>
    </justification>
  </clause>

  <clause id="18749">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w / v5))) = K(x,y \ T(z,(u * v5) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17660,a(flip),b,18748,a)].">
      <j1 rule="hyper" parents="58 17660 18748"/>
    </justification>
  </clause>

  <clause id="18750">
    <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(18725(a,1),18748(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="18725 18748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18751">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) * v5)) = K(x,y \ T(z,u * (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18748,a(flip),b,18749,a),flip(a)].">
      <j1 rule="hyper" parents="58 18748 18749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18752">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) * v5)) = K(x,y \ T(z,u * (w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(320,a,18156,a(flip),b,18751,a),flip(a)].">
      <j1 rule="hyper" parents="320 18156 18751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18753">
    <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(18145(a,1),18750(a,2,2,2))].">
      <j1 rule="para" parents="18145 18750"/>
    </justification>
  </clause>

  <clause id="18754">
    <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(320,a,18752,a(flip),b,18753,a),flip(a)].">
      <j1 rule="hyper" parents="320 18752 18753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18755">
    <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,18634,a(flip),b,17231,a)].">
      <j1 rule="hyper" parents="58 18634 17231"/>
    </justification>
  </clause>

  <clause id="18757">
    <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(17294(a,2),17321(a,1,2,1))].">
      <j1 rule="para" parents="17294 17321"/>
    </justification>
  </clause>

  <clause id="18758">
    <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(17334(a,1),17321(a,1,2))].">
      <j1 rule="para" parents="17334 17321"/>
    </justification>
  </clause>

  <clause id="18759">
    <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(17068(a,1),17322(a,1,1,2))].">
      <j1 rule="para" parents="17068 17322"/>
    </justification>
  </clause>

  <clause id="18760">
    <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(17528,a,18639,a),flip(a)].">
      <j1 rule="hyper" parents="17528 18639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18761">
    <literal><![CDATA[
      T(x,y / T(z,T(a(u,w,v5),v6) * v7)) = T(x,y / T(z,v7))
    ]]></literal>
    <justification jstring="[hyper(15707,a,18760,a),flip(a)].">
      <j1 rule="hyper" parents="15707 18760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18762">
    <literal><![CDATA[
      T(x,y / T(z,u * a(w,v5,v6))) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(12249(a,1),18761(a,1,2,2))].">
      <j1 rule="para" parents="12249 18761"/>
    </justification>
  </clause>

  <clause id="18763">
    <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(18762(a,1),7175(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18762 7175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18764">
    <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(18763(a,2),7682(a,1))].">
      <j1 rule="para" parents="18763 7682"/>
    </justification>
  </clause>

  <clause id="18765">
    <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(18764,a,18755,a)].">
      <j1 rule="hyper" parents="18764 18755"/>
    </justification>
  </clause>

  <clause id="18766">
    <literal><![CDATA[
      K(x,y \ T(z,a(u,w,v5) * v6)) = K(x,y \ T(z,v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,16270,a(flip),b,18765,a),flip(a)].">
      <j1 rule="hyper" parents="58 16270 18765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18767">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w \ v5))) = K(x,y \ T(z,u * (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18754,a(flip),b,18766,a)].">
      <j1 rule="hyper" parents="58 18754 18766"/>
    </justification>
  </clause>

  <clause id="18769">
    <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,17643,a,b,17642,a)].">
      <j1 rule="hyper" parents="58 17643 17642"/>
    </justification>
  </clause>

  <clause id="18770">
    <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(17645(a,1),17642(a,1,1))].">
      <j1 rule="para" parents="17645 17642"/>
    </justification>
  </clause>

  <clause id="18771">
    <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(17234,a,18198,a)].">
      <j1 rule="hyper" parents="17234 18198"/>
    </justification>
  </clause>

  <clause id="18774">
    <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,14478,a(flip),b,18771,a),flip(a)].">
      <j1 rule="hyper" parents="58 14478 18771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18775">
    <literal><![CDATA[
      K(x,(y \ z) / (u * T(z \ (y \ z),z))) = K(x,((y \ 1) * z) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(320,a,17675,a(flip),b,18774,a),flip(a)].">
      <j1 rule="hyper" parents="320 17675 18774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18776">
    <literal><![CDATA[
      K(x,(y \ z) / (u * ((y \ z) / z))) = K(x,((y \ 1) * z) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17624,a(flip),b,18775,a)].">
      <j1 rule="hyper" parents="58 17624 18775"/>
    </justification>
  </clause>

  <clause id="18777">
    <literal><![CDATA[
      K(x,((y \ 1) * z) / (u * (y \ 1))) = K(x,(y \ z) / (u / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,18399,a(flip),b,18776,a),flip(a)].">
      <j1 rule="hyper" parents="58 18399 18776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18778">
    <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,17925,a,b,18777,a)].">
      <j1 rule="hyper" parents="58 17925 18777"/>
    </justification>
  </clause>

  <clause id="18779">
    <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(14459,a,18462,a)].">
      <j1 rule="hyper" parents="14459 18462"/>
    </justification>
  </clause>

  <clause id="18780">
    <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(15236,a,18779,a),flip(a)].">
      <j1 rule="hyper" parents="15236 18779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18781">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u)) = K(x,y \ ((T(y,z) / z) * u))
    ]]></literal>
    <justification jstring="[para(13231(a,1),18780(a,2,2))].">
      <j1 rule="para" parents="13231 18780"/>
    </justification>
  </clause>

  <clause id="18782">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(320,a,17996,a(flip),b,18781,a),flip(a)].">
      <j1 rule="hyper" parents="320 17996 18781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18783">
    <literal><![CDATA[
      K(x,(y * ((y / z) \ 1)) \ (((y / z) \ 1) * u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(15197,a,18782,a)].">
      <j1 rule="hyper" parents="15197 18782"/>
    </justification>
  </clause>

  <clause id="18784">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ ((y / z) \ u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14639,a(flip),b,18783,a)].">
      <j1 rule="hyper" parents="58 14639 18783"/>
    </justification>
  </clause>

  <clause id="18785">
    <literal><![CDATA[
      K(x,y \ ((y \ z) \ u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[para(5565(a,1),18784(a,1,2))].">
      <j1 rule="para" parents="5565 18784"/>
    </justification>
  </clause>

  <clause id="18786">
    <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,18486,a,b,18785,a)].">
      <j1 rule="hyper" parents="58 18486 18785"/>
    </justification>
  </clause>

  <clause id="18787">
    <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,17459,a(flip),b,18785,a),flip(a)].">
      <j1 rule="hyper" parents="58 17459 18785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18788">
    <literal><![CDATA[
      K(x,y \ (((K(z,y) * u) \ y) * w)) = K(x,y \ ((T(y,z) \ u) \ w))
    ]]></literal>
    <justification jstring="[para(5068(a,1),18785(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5068 18785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18789">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((z \ y) * u)) = K(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(18785(a,1),9904(a,1,2))].">
      <j1 rule="para" parents="18785 9904"/>
    </justification>
  </clause>

  <clause id="18790">
    <literal><![CDATA[
      K(x,K(y,z) * (z \ ((u \ z) * w))) = K(x,z \ ((T(z,y) \ u) \ w))
    ]]></literal>
    <justification jstring="[hyper(17994,a,18787,a)].">
      <j1 rule="hyper" parents="17994 18787"/>
    </justification>
  </clause>

  <clause id="18791">
    <literal><![CDATA[
      K(x,y \ ((T(y,z) \ u) \ w)) = K(x,y \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[para(13649(a,1),18788(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="13649 18788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18792">
    <literal><![CDATA[
      K(x,T(y,z) \ ((u \ y) * w)) = K(x,y \ ((T(y,z) \ u) \ w))
    ]]></literal>
    <justification jstring="[para(5093(a,1),18790(a,1,2))].">
      <j1 rule="para" parents="5093 18790"/>
    </justification>
  </clause>

  <clause id="18793">
    <literal><![CDATA[
      K(x,T(y,z) \ ((u \ y) * w)) = K(x,y \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[hyper(320,a,18791,a(flip),b,18792,a),flip(a)].">
      <j1 rule="hyper" parents="320 18791 18792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18794">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ T(u * (y \ z),K(y,z)))
    ]]></literal>
    <justification jstring="[para(9021(a,2),18786(a,2,2,2))].">
      <j1 rule="para" parents="9021 18786"/>
    </justification>
  </clause>

  <clause id="18795">
    <literal><![CDATA[
      K(x,((y \ z) \ u) / y) = K(x,((z \ y) * u) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,14041,a(flip),b,18789,a),flip(a)].">
      <j1 rule="hyper" parents="58 14041 18789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18796">
    <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(4154(a,1),18795(a,2,2,1))].">
      <j1 rule="para" parents="4154 18795"/>
    </justification>
  </clause>

  <clause id="18797">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ (u * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(320,a,15946,a(flip),b,18794,a),flip(a)].">
      <j1 rule="hyper" parents="320 15946 18794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18799">
    <literal><![CDATA[
      K(x,y \ (z / (y \ u))) = K(x,y \ (z * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17896,a(flip),b,18797,a)].">
      <j1 rule="hyper" parents="58 17896 18797"/>
    </justification>
  </clause>

  <clause id="18800">
    <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(8499(a,1),18799(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8499 18799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18801">
    <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(14155(a,1),18521(a,1,2,2))].">
      <j1 rule="para" parents="14155 18521"/>
    </justification>
  </clause>

  <clause id="18802">
    <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,18757,a(flip),b,18759,a),flip(a)].">
      <j1 rule="hyper" parents="58 18757 18759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18803">
    <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(320,a,18758,a,b,18802,a)].">
      <j1 rule="hyper" parents="320 18758 18802"/>
    </justification>
  </clause>

  <clause id="18804">
    <literal><![CDATA[
      a(x,y,z * K(u,K(w,v5))) = (x * (y * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(15771,a,18770,a),flip(a)].">
      <j1 rule="hyper" parents="15771 18770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18806">
    <literal><![CDATA[
      a(x,y,z * K(u,K(w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,9,a,b,18804,a),flip(a)].">
      <j1 rule="hyper" parents="320 9 18804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18807">
    <literal><![CDATA[
      a(x,y,z * K(u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(18804(a,2),691(a,1))].">
      <j1 rule="para" parents="18804 691"/>
    </justification>
  </clause>

  <clause id="18808">
    <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),18807(a,1,3))].">
      <j1 rule="para" parents="84 18807"/>
    </justification>
  </clause>

  <clause id="18809">
    <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(13286(a,2),18808(a,1))].">
      <j1 rule="para" parents="13286 18808"/>
    </justification>
  </clause>

  <clause id="18810">
    <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,18769,a(flip),b,18803,a),flip(a)].">
      <j1 rule="hyper" parents="58 18769 18803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18811">
    <literal><![CDATA[
      a(x * K(y,K(z,u)),w,v5) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(320,a,18806,a(flip),b,18810,a),flip(a)].">
      <j1 rule="hyper" parents="320 18806 18810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18813">
    <literal><![CDATA[
      a(K(x,y) * z,u,w) = a(z * K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(84(a,1),18811(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 18811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18814">
    <literal><![CDATA[
      a(T(x,K(y,z)),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(1021(a,2),18811(a,1,1))].">
      <j1 rule="para" parents="1021 18811"/>
    </justification>
  </clause>

  <clause id="18815">
    <literal><![CDATA[
      a(T(x,K(y,z)) \ u,w,v5) = a(x \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(15667(a,1),18811(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15667 18811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18816">
    <literal><![CDATA[
      a(K(x,y) * (z \ x),u,w) = a(z \ T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(15881(a,1),18811(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15881 18811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18817">
    <literal><![CDATA[
      a(T(x,T(y,z)),u,w) = a(T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7413(a,1),18814(a,1,1))].">
      <j1 rule="para" parents="7413 18814"/>
    </justification>
  </clause>

  <clause id="18818">
    <literal><![CDATA[
      a(T(x / T(y,z),y),u,w) = a(T(y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(7927(a,1),18814(a,1,1))].">
      <j1 rule="para" parents="7927 18814"/>
    </justification>
  </clause>

  <clause id="18819">
    <literal><![CDATA[
      a(K(x,y) * (z \ 1),u,w) = a(z \ K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(13829(a,1),18814(a,1,1))].">
      <j1 rule="para" parents="13829 18814"/>
    </justification>
  </clause>

  <clause id="18821">
    <literal><![CDATA[
      a(T(x * ((x / y) / x),x),z,u) = a(x * ((y \ x) / x),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12846,a(flip),b,18817,a),flip(a)].">
      <j1 rule="hyper" parents="58 12846 18817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18822">
    <literal><![CDATA[
      a(K(x,x \ y) * z,u,w) = a(z * K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,12929,a(flip),b,18813,a),flip(a)].">
      <j1 rule="hyper" parents="320 12929 18813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18823">
    <literal><![CDATA[
      a(L(x \ 1,x,y) \ z,u,w) = a(((y * x) \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(1284(a,1),18815(a,1,1,1))].">
      <j1 rule="para" parents="1284 18815"/>
    </justification>
  </clause>

  <clause id="18824">
    <literal><![CDATA[
      a(K(x * y,y \ 1) * z,u,w) = a(z * K(x * y,x),u,w)
    ]]></literal>
    <justification jstring="[para(6097(a,1),18822(a,1,1,1))].">
      <j1 rule="para" parents="6097 18822"/>
    </justification>
  </clause>

  <clause id="18826">
    <literal><![CDATA[
      a(x * ((y \ x) / x),z,u) = a(x / y,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12734,a(flip),b,18821,a),flip(a)].">
      <j1 rule="hyper" parents="58 12734 18821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18828">
    <literal><![CDATA[
      a(T(x,y) * ((z \ x) / x),u,w) = a(T(x,y) / z,u,w)
    ]]></literal>
    <justification jstring="[para(13660(a,1),18826(a,1,1,2))].">
      <j1 rule="para" parents="13660 18826"/>
    </justification>
  </clause>

  <clause id="18829">
    <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,12746,a(flip),b,18828,a)].">
      <j1 rule="hyper" parents="58 12746 18828"/>
    </justification>
  </clause>

  <clause id="18830">
    <literal><![CDATA[
      a(K(x * y,y \ 1) * z,u,w) = a(z * K(y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,12928,a(flip),b,18824,a),flip(a)].">
      <j1 rule="hyper" parents="320 12928 18824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18831">
    <literal><![CDATA[
      a(K(x * y,x \ 1) * z,u,w) = a(z * K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(5840(a,1),18830(a,1,1,1))].">
      <j1 rule="para" parents="5840 18830"/>
    </justification>
  </clause>

  <clause id="18832">
    <literal><![CDATA[
      a(T(x,x \ y) / z,u,w) = a(T(x,y) / z,u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18828,a(flip),b,18829,a),flip(a)].">
      <j1 rule="hyper" parents="58 18828 18829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18833">
    <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(18832(a,1),13281(a,1,2))].">
      <j1 rule="para" parents="18832 13281"/>
    </justification>
  </clause>

  <clause id="18834">
    <literal><![CDATA[
      (x * y) / a(z \ x,T(z,x),y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(12742(a,1),18833(a,1,2))].">
      <j1 rule="para" parents="12742 18833"/>
    </justification>
  </clause>

  <clause id="18835">
    <literal><![CDATA[
      (x * y) / a(x / z,z,y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(13280(a,1),18834(a,1,2))].">
      <j1 rule="para" parents="13280 18834"/>
    </justification>
  </clause>

  <clause id="18836">
    <literal><![CDATA[
      (x / ((x \ y) * x)) * (((x \ y) * x) * z) = (x / y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(890,a,18835,a),flip(a)].">
      <j1 rule="hyper" parents="890 18835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18837">
    <literal><![CDATA[
      ((x / ((x \ y) * x)) * (((x \ y) * x) * z)) * u = ((x / y) * (y * z)) * u
    ]]></literal>
    <justification jstring="[hyper(52,a,18836,a)].">
      <j1 rule="hyper" parents="52 18836"/>
    </justification>
  </clause>

  <clause id="18838">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * w = (x * K(z,L(u,x,(x \ y) \ 1))) * w
    ]]></literal>
    <justification jstring="[para(18051(a,1),18837(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18051 18837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18839">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * w = (x * K(z,L(u,x,y \ x))) * w
    ]]></literal>
    <justification jstring="[para(14423(a,1),18838(a,2,1,2))].">
      <j1 rule="para" parents="14423 18838"/>
    </justification>
  </clause>

  <clause id="18840">
    <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(320,a,17710,a(flip),b,18839,a),flip(a)].">
      <j1 rule="hyper" parents="320 17710 18839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18841">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = x * a(z,x,K(y \ x,u))
    ]]></literal>
    <justification jstring="[para(14227(a,1),18840(a,2,2))].">
      <j1 rule="para" parents="14227 18840"/>
    </justification>
  </clause>

  <clause id="18842">
    <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,18728,a(flip),b,17340,a)].">
      <j1 rule="hyper" parents="58 18728 17340"/>
    </justification>
  </clause>

  <clause id="18843">
    <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,18157,a(flip),b,17569,a)].">
      <j1 rule="hyper" parents="58 18157 17569"/>
    </justification>
  </clause>

  <clause id="18845">
    <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(18843(a,2),15997(a,1))].">
      <j1 rule="para" parents="18843 15997"/>
    </justification>
  </clause>

  <clause id="18846">
    <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(18748(a,1),18845(a,1))].">
      <j1 rule="para" parents="18748 18845"/>
    </justification>
  </clause>

  <clause id="18847">
    <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(18572(a,1),18846(a,1))].">
      <j1 rule="para" parents="18572 18846"/>
    </justification>
  </clause>

  <clause id="18848">
    <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(5428(a,1),17651(a,2,2,2,2))].">
      <j1 rule="para" parents="5428 17651"/>
    </justification>
  </clause>

  <clause id="18849">
    <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(7940(a,1),18548(a,1,1))].">
      <j1 rule="para" parents="7940 18548"/>
    </justification>
  </clause>

  <clause id="18850">
    <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(15510(a,1),18849(a,1,1))].">
      <j1 rule="para" parents="15510 18849"/>
    </justification>
  </clause>

  <clause id="18851">
    <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(18621(a,1),18850(a,1,1))].">
      <j1 rule="para" parents="18621 18850"/>
    </justification>
  </clause>

  <clause id="18852">
    <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(15551(a,1),18851(a,1,1))].">
      <j1 rule="para" parents="15551 18851"/>
    </justification>
  </clause>

  <clause id="18853">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u \ ((K(y,z) * u) * x)) = K(y,x / ((z * u) \ (u * x)))
    ]]></literal>
    <justification jstring="[para(15544(a,1),18852(a,1,1))].">
      <j1 rule="para" parents="15544 18852"/>
    </justification>
  </clause>

  <clause id="18854">
    <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,17379,a(flip),b,18853,a)].">
      <j1 rule="hyper" parents="58 17379 18853"/>
    </justification>
  </clause>

  <clause id="18856">
    <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(14426(a,1),18699(a,1,2,2))].">
      <j1 rule="para" parents="14426 18699"/>
    </justification>
  </clause>

  <clause id="18857">
    <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(4935(a,1),18856(a,1,2,2,2,3))].">
      <j1 rule="para" parents="4935 18856"/>
    </justification>
  </clause>

  <clause id="18858">
    <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(12580(a,1),18857(a,1,2,2,2))].">
      <j1 rule="para" parents="12580 18857"/>
    </justification>
  </clause>

  <clause id="18859">
    <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(14398(a,1),18858(a,1,2,2))].">
      <j1 rule="para" parents="14398 18858"/>
    </justification>
  </clause>

  <clause id="18861">
    <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(11172(a,1),18859(a,1,2))].">
      <j1 rule="para" parents="11172 18859"/>
    </justification>
  </clause>

  <clause id="18862">
    <literal><![CDATA[
      L(x * K(y,z),u,u \ 1) = L(x,u,u \ 1) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(13265,a,18861,a)].">
      <j1 rule="hyper" parents="13265 18861"/>
    </justification>
  </clause>

  <clause id="18863">
    <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(18862(a,2),14115(a,1,1))].">
      <j1 rule="para" parents="18862 14115"/>
    </justification>
  </clause>

  <clause id="18864">
    <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(18862(a,2),14926(a,1,2))].">
      <j1 rule="para" parents="18862 14926"/>
    </justification>
  </clause>

  <clause id="18865">
    <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(5921,a,18864,a)].">
      <j1 rule="hyper" parents="5921 18864"/>
    </justification>
  </clause>

  <clause id="18866">
    <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(18865(a,1),4028(a,1))].">
      <j1 rule="para" parents="18865 4028"/>
    </justification>
  </clause>

  <clause id="18867">
    <literal><![CDATA[
      a(x \ 1,x,y * K(z,u)) = a(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(18866,a,13969,a)].">
      <j1 rule="hyper" parents="18866 13969"/>
    </justification>
  </clause>

  <clause id="18868">
    <literal><![CDATA[
      a(x \ 1,x,K(y,z) * u) = a(x \ 1,x,u)
    ]]></literal>
    <justification jstring="[hyper(18809,a,18867,a)].">
      <j1 rule="hyper" parents="18809 18867"/>
    </justification>
  </clause>

  <clause id="18870">
    <literal><![CDATA[
      a(x \ 1,x,y) \ (K(z,u) * y) = L(K(z,u) * y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(18868(a,1),5926(a,1,1))].">
      <j1 rule="para" parents="18868 5926"/>
    </justification>
  </clause>

  <clause id="18871">
    <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,17396,a(flip),b,18870,a)].">
      <j1 rule="hyper" parents="58 17396 18870"/>
    </justification>
  </clause>

  <clause id="18872">
    <literal><![CDATA[
      L(K(x,y) * z,u,u \ 1) = K(x,y) * L(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(5926(a,1),18871(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5926 18871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18873">
    <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,18872,a,b,5137,a)].">
      <j1 rule="hyper" parents="119 18872 5137"/>
    </justification>
  </clause>

  <clause id="18874">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ z,u,u \ 1) = x * L(x \ z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(5093(a,1),18873(a,1,2,1))].">
      <j1 rule="para" parents="5093 18873"/>
    </justification>
  </clause>

  <clause id="18875">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,z \ 1),u) = L(x \ T(y,u),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(2130,a,18874,a)].">
      <j1 rule="hyper" parents="2130 18874"/>
    </justification>
  </clause>

  <clause id="18876">
    <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(18875(a,1),14019(a,1,2))].">
      <j1 rule="para" parents="18875 14019"/>
    </justification>
  </clause>

  <clause id="18877">
    <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(13044(a,1),18741(a,1,1,2))].">
      <j1 rule="para" parents="13044 18741"/>
    </justification>
  </clause>

  <clause id="18878">
    <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(5092(a,1),18877(a,1,2))].">
      <j1 rule="para" parents="5092 18877"/>
    </justification>
  </clause>

  <clause id="18879">
    <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,15838,a(flip),b,18878,a)].">
      <j1 rule="hyper" parents="58 15838 18878"/>
    </justification>
  </clause>

  <clause id="18880">
    <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(18734,a,18879,a)].">
      <j1 rule="hyper" parents="18734 18879"/>
    </justification>
  </clause>

  <clause id="18881">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),z) \ w) = K(x,w * K(z,u * y))
    ]]></literal>
    <justification jstring="[hyper(7967,a,18880,a),flip(a)].">
      <j1 rule="hyper" parents="7967 18880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18882">
    <literal><![CDATA[
      K(x,K(y,z \ (y \ u)) * w) = K(x,w * K(y,u * z))
    ]]></literal>
    <justification jstring="[para(5092(a,1),18881(a,1,2))].">
      <j1 rule="para" parents="5092 18881"/>
    </justification>
  </clause>

  <clause id="18883">
    <literal><![CDATA[
      K(x,y * K(z,u \ w)) = K(x,y * K(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15838,a(flip),b,18882,a)].">
      <j1 rule="hyper" parents="58 15838 18882"/>
    </justification>
  </clause>

  <clause id="18884">
    <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(17632,a,18883,a)].">
      <j1 rule="hyper" parents="17632 18883"/>
    </justification>
  </clause>

  <clause id="18885">
    <literal><![CDATA[
      K(x,y * K(z,(u \ z) * w)) = K(x,y * K(u * w,z))
    ]]></literal>
    <justification jstring="[hyper(15909,a,18883,a),flip(a)].">
      <j1 rule="hyper" parents="15909 18883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18886">
    <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(18883(a,1),18742(a,1,1,2))].">
      <j1 rule="para" parents="18883 18742"/>
    </justification>
  </clause>

  <clause id="18887">
    <literal><![CDATA[
      K(x,y * K(z,z * (u \ w))) = K(x,y * K(u * w,z))
    ]]></literal>
    <justification jstring="[para(14052(a,1),18885(a,1,2,2))].">
      <j1 rule="para" parents="14052 18885"/>
    </justification>
  </clause>

  <clause id="18888">
    <literal><![CDATA[
      K(x,y * K(z \ u,w)) = K(x,y * K(z * u,w))
    ]]></literal>
    <justification jstring="[hyper(15869,a,18887,a)].">
      <j1 rule="hyper" parents="15869 18887"/>
    </justification>
  </clause>

  <clause id="18889">
    <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(17791,a,18888,a)].">
      <j1 rule="hyper" parents="17791 18888"/>
    </justification>
  </clause>

  <clause id="18890">
    <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(320,a,17441,a(flip),b,18884,a),flip(a)].">
      <j1 rule="hyper" parents="320 17441 18884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18891">
    <literal><![CDATA[
      K(x,y * (z * K(u,w \ v5))) = K(x,y * (z * K(u,v5 * w)))
    ]]></literal>
    <justification jstring="[para(178(a,1),18890(a,1,2,2,2,1))].">
      <j1 rule="para" parents="178 18890"/>
    </justification>
  </clause>

  <clause id="18892">
    <literal><![CDATA[
      K(x,y * (z * K(u,w / v5))) = K(x,y * (z * K(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(17689,a,18891,a)].">
      <j1 rule="hyper" parents="17689 18891"/>
    </justification>
  </clause>

  <clause id="18893">
    <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,18418,a(flip),b,18891,a),flip(a)].">
      <j1 rule="hyper" parents="58 18418 18891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18894">
    <literal><![CDATA[
      K(x,y * ((z / u) * K(z,w * v5))) = K(x,y * (T(z,w / v5) / u))
    ]]></literal>
    <justification jstring="[hyper(16044,a,18892,a),flip(a)].">
      <j1 rule="hyper" parents="16044 18892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18895">
    <literal><![CDATA[
      K(x,y * (T(z,u / w) / v5)) = K(x,y * (T(z,u * w) / v5))
    ]]></literal>
    <justification jstring="[hyper(16044,a,18894,a),flip(a)].">
      <j1 rule="hyper" parents="16044 18894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18896">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) / v5)) = K(x,y * (T(z,w * u) / v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,16080,a(flip),b,18895,a)].">
      <j1 rule="hyper" parents="58 16080 18895"/>
    </justification>
  </clause>

  <clause id="18897">
    <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(18896(a,1),18017(a,1))].">
      <j1 rule="para" parents="18896 18017"/>
    </justification>
  </clause>

  <clause id="18898">
    <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(16610,a,18886,a)].">
      <j1 rule="hyper" parents="16610 18886"/>
    </justification>
  </clause>

  <clause id="18899">
    <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(16682,a,18898,a)].">
      <j1 rule="hyper" parents="16682 18898"/>
    </justification>
  </clause>

  <clause id="18900">
    <literal><![CDATA[
      K(x,K(y,z / u) \ w) = K(x,K(z * u,y) * w)
    ]]></literal>
    <justification jstring="[hyper(7967,a,18899,a),flip(a)].">
      <j1 rule="hyper" parents="7967 18899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18901">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(z * y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(16610,a,18900,a)].">
      <j1 rule="hyper" parents="16610 18900"/>
    </justification>
  </clause>

  <clause id="18902">
    <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(18901(a,1),17887(a,1,1))].">
      <j1 rule="para" parents="18901 17887"/>
    </justification>
  </clause>

  <clause id="18903">
    <literal><![CDATA[
      K(x,y * (K(z,u \ w) * v5)) = K(x,y * (K(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,17887,a(flip),b,18902,a),flip(a)].">
      <j1 rule="hyper" parents="58 17887 18902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18904">
    <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(16244,a,18903,a),flip(a)].">
      <j1 rule="hyper" parents="16244 18903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18905">
    <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(320,a,17441,a(flip),b,18889,a),flip(a)].">
      <j1 rule="hyper" parents="320 17441 18889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18906">
    <literal><![CDATA[
      K(x,y * (z * T(u / w,v5 \ v6))) = K(x,y * (z * T(u / w,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(16244,a,18904,a),flip(a)].">
      <j1 rule="hyper" parents="16244 18904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18907">
    <literal><![CDATA[
      K(x,y * (z * K(u \ w,v5))) = K(x,y * (z * K(u * w,v5)))
    ]]></literal>
    <justification jstring="[para(17289(a,1),18905(a,1,2,2,2,1))].">
      <j1 rule="para" parents="17289 18905"/>
    </justification>
  </clause>

  <clause id="18908">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(w * v5,u))) = K(x,y * (z \ T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(16245,a,18907,a),flip(a)].">
      <j1 rule="hyper" parents="16245 18907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18909">
    <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,18115,a(flip),b,18907,a),flip(a)].">
      <j1 rule="hyper" parents="58 18115 18907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18910">
    <literal><![CDATA[
      K(x,y * (z \ T(u,w \ v5))) = K(x,y * (z \ T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(16245,a,18908,a),flip(a)].">
      <j1 rule="hyper" parents="16245 18908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18911">
    <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(17845,a,18910,a),flip(a)].">
      <j1 rule="hyper" parents="17845 18910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18912">
    <literal><![CDATA[
      K(x,T(y,z \ u) * w) = K(x,T(y,u * z) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18893,a(flip),b,18909,a)].">
      <j1 rule="hyper" parents="58 18893 18909"/>
    </justification>
  </clause>

  <clause id="18913">
    <literal><![CDATA[
      K(x,T(y,z / u) * w) = K(x,T(y,z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(16040,a,18912,a)].">
      <j1 rule="hyper" parents="16040 18912"/>
    </justification>
  </clause>

  <clause id="18914">
    <literal><![CDATA[
      K(x,T(y,z * u) * (z \ u)) = K(x,(z \ u) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15167,a(flip),b,18912,a),flip(a)].">
      <j1 rule="hyper" parents="58 15167 18912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18915">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,y * z)) = K(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15082,a(flip),b,18914,a),flip(a)].">
      <j1 rule="hyper" parents="58 15082 18914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18916">
    <literal><![CDATA[
      K(x,y / (z \ (u * K(w,v5)))) = K(x,y * ((z \ u) \ K(v5,w)))
    ]]></literal>
    <justification jstring="[hyper(18847,a,18911,a)].">
      <j1 rule="hyper" parents="18847 18911"/>
    </justification>
  </clause>

  <clause id="18917">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * v5))) = K(x,y * ((z \ v5) \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17393,a,b,18916,a)].">
      <j1 rule="hyper" parents="58 17393 18916"/>
    </justification>
  </clause>

  <clause id="18919">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,z)) \ K(w,v5))) = K(x,y / (u / (K(w,v5) * z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17935,a(flip),b,18917,a),flip(a)].">
      <j1 rule="hyper" parents="58 17935 18917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18920">
    <literal><![CDATA[
      K(x,y / (z / (K(u,w) * v5))) = K(x,y * ((z / v5) \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(18503,a,18919,a),flip(a)].">
      <j1 rule="hyper" parents="18503 18919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18921">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) / v5)) = K(x,y * ((w / v5) \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18008,a,b,18920,a)].">
      <j1 rule="hyper" parents="58 18008 18920"/>
    </justification>
  </clause>

  <clause id="18922">
    <literal><![CDATA[
      K(x,y * (((z \ u) / w) \ K(z,v5))) = K(x,y / ((T(z,v5) \ u) / w))
    ]]></literal>
    <justification jstring="[para(5093(a,1),18921(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5093 18921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18923">
    <literal><![CDATA[
      K(x,y * (((z / u) / w) \ K(v5,z))) = K(x,y / ((T(z,v5) / u) / w))
    ]]></literal>
    <justification jstring="[para(13643(a,1),18921(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="13643 18921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18924">
    <literal><![CDATA[
      K(x,T(y,z) / ((y / u) / w)) = K(x,y / ((T(y,z) / u) / w))
    ]]></literal>
    <justification jstring="[hyper(17809,a,18923,a)].">
      <j1 rule="hyper" parents="17809 18923"/>
    </justification>
  </clause>

  <clause id="18925">
    <literal><![CDATA[
      K(x,y / ((T(y,z * u) / z) / u)) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18556,a(flip),b,18924,a),flip(a)].">
      <j1 rule="hyper" parents="58 18556 18924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18926">
    <literal><![CDATA[
      K(x,((((y \ z) * u) \ u) \ u) / z) = K(x,((z \ y) \ (((z \ y) \ u) * (z \ y))) / z)
    ]]></literal>
    <justification jstring="[para(16860(a,1),18796(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="16860 18796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18927">
    <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),18926(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="17 18926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18928">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,((((z \ y) * u) \ u) \ u) / y)
    ]]></literal>
    <justification jstring="[hyper(18164,a,18927,a)].">
      <j1 rule="hyper" parents="18164 18927"/>
    </justification>
  </clause>

  <clause id="18929">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,T((z \ y) * u,u) / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,13007,a(flip),b,18928,a),flip(a)].">
      <j1 rule="hyper" parents="320 13007 18928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18930">
    <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(18929(a,2),16261(a,1))].">
      <j1 rule="para" parents="18929 16261"/>
    </justification>
  </clause>

  <clause id="18931">
    <literal><![CDATA[
      K(x,(y * (z \ u)) / u) = K(x,u / (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(18930,a,18561,a)].">
      <j1 rule="hyper" parents="18930 18561"/>
    </justification>
  </clause>

  <clause id="18932">
    <literal><![CDATA[
      K(x,y / ((z \ y) * (u \ y))) = K(x,(u * T(z,y)) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,13113,a(flip),b,18931,a),flip(a)].">
      <j1 rule="hyper" parents="58 13113 18931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18933">
    <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(17271(a,2),18931(a,2,2,2,2))].">
      <j1 rule="para" parents="17271 18931"/>
    </justification>
  </clause>

  <clause id="18934">
    <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(14440(a,1),18932(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14440 18932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18935">
    <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,15400,a(flip),b,18842,a),flip(a)].">
      <j1 rule="hyper" parents="58 15400 18842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18936">
    <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(15314(a,2),18848(a,2,2,2,2))].">
      <j1 rule="para" parents="15314 18848"/>
    </justification>
  </clause>

  <clause id="18937">
    <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(13655(a,1),18863(a,1,1,1))].">
      <j1 rule="para" parents="13655 18863"/>
    </justification>
  </clause>

  <clause id="18938">
    <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(320,a,14019,a(flip),b,18937,a),flip(a)].">
      <j1 rule="hyper" parents="320 14019 18937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18940">
    <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(6492(a,1),18936(a,2,2,2,2,1))].">
      <j1 rule="para" parents="6492 18936"/>
    </justification>
  </clause>

  <clause id="18941">
    <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,17626,a(flip),b,18940,a)].">
      <j1 rule="hyper" parents="58 17626 18940"/>
    </justification>
  </clause>

  <clause id="18942">
    <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,15340,a(flip),b,18941,a),flip(a)].">
      <j1 rule="hyper" parents="58 15340 18941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18944">
    <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(4829(a,2),18942(a,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4829 18942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18945">
    <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(320,a,18906,a(flip),b,18944,a),flip(a)].">
      <j1 rule="hyper" parents="320 18906 18944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18946">
    <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(320,a,18942,a(flip),b,18945,a),flip(a)].">
      <j1 rule="hyper" parents="320 18942 18945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18947">
    <literal><![CDATA[
      K(x,y * (z * T(u,w \ v5))) = K(x,y * (z * T(u,v5 * w)))
    ]]></literal>
    <justification jstring="[para(4775(a,1),18946(a,1,2,2,2,1))].">
      <j1 rule="para" parents="4775 18946"/>
    </justification>
  </clause>

  <clause id="18948">
    <literal><![CDATA[
      K(x,y * (z * T(u,w / v5))) = K(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(16159,a,18947,a)].">
      <j1 rule="hyper" parents="16159 18947"/>
    </justification>
  </clause>

  <clause id="18949">
    <literal><![CDATA[
      T(x,y * (z * T(u,w \ v5))) = T(x,y * (z * T(u,v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(118,a,18947,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 18947 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18950">
    <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(16247,a,18948,a)].">
      <j1 rule="hyper" parents="16247 18948"/>
    </justification>
  </clause>

  <clause id="18951">
    <literal><![CDATA[
      T(x,y * (z * T(u,w / v5))) = T(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(118,a,18948,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 18948 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18952">
    <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,18510,a(flip),b,18949,a),flip(a)].">
      <j1 rule="hyper" parents="58 18510 18949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18953">
    <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(18951(a,1),16161(a,1,2,2))].">
      <j1 rule="para" parents="18951 16161"/>
    </justification>
  </clause>

  <clause id="18954">
    <literal><![CDATA[
      K(x,y * (T(z,T(u \ w,u)) * v5)) = K(x,y * (T(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,16140,a(flip),b,18950,a),flip(a)].">
      <j1 rule="hyper" parents="320 16140 18950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18955">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) * v5)) = K(x,y * (T(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(17293,a,18954,a)].">
      <j1 rule="hyper" parents="17293 18954"/>
    </justification>
  </clause>

  <clause id="18957">
    <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(18955(a,1),16198(a,1))].">
      <j1 rule="para" parents="18955 16198"/>
    </justification>
  </clause>

  <clause id="18958">
    <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(18952(a,1),18953(a,1,2,2))].">
      <j1 rule="para" parents="18952 18953"/>
    </justification>
  </clause>

  <clause id="18959">
    <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(15309,a,17204,a)].">
      <j1 rule="hyper" parents="15309 17204"/>
    </justification>
  </clause>

  <clause id="18961">
    <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(4266(a,1),18959(a,1,2,1,1))].">
      <j1 rule="para" parents="4266 18959"/>
    </justification>
  </clause>

  <clause id="18962">
    <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(13166,a,18961,a)].">
      <j1 rule="hyper" parents="13166 18961"/>
    </justification>
  </clause>

  <clause id="18963">
    <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,17395,a(flip),b,18496,a),flip(a)].">
      <j1 rule="hyper" parents="58 17395 18496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18964">
    <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(320,a,14639,a(flip),b,18963,a),flip(a)].">
      <j1 rule="hyper" parents="320 14639 18963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18965">
    <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(320,a,17863,a(flip),b,18964,a),flip(a)].">
      <j1 rule="hyper" parents="320 17863 18964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18966">
    <literal><![CDATA[
      K(x,(y \ (z \ u)) \ (y \ u)) = K(x,L(T(z,u),u,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(18285,a,18965,a),flip(a)].">
      <j1 rule="hyper" parents="18285 18965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18967">
    <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(444,a,10937,a(flip),b,18966,a)].">
      <j1 rule="hyper" parents="444 10937 18966"/>
    </justification>
  </clause>

  <clause id="18969">
    <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(13753(a,1),17570(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13753 17570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18970">
    <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(320,a,18038,a(flip),b,18969,a),flip(a)].">
      <j1 rule="hyper" parents="320 18038 18969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18971">
    <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(4412(a,1),17635(a,1,2,1,1))].">
      <j1 rule="para" parents="4412 17635"/>
    </justification>
  </clause>

  <clause id="18972">
    <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(2939(a,1),18971(a,1,2,1,1))].">
      <j1 rule="para" parents="2939 18971"/>
    </justification>
  </clause>

  <clause id="18974">
    <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,16708,a(flip),b,18972,a)].">
      <j1 rule="hyper" parents="58 16708 18972"/>
    </justification>
  </clause>

  <clause id="18975">
    <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),18974(a,2,2,1))].">
      <j1 rule="para" parents="7 18974"/>
    </justification>
  </clause>

  <clause id="18976">
    <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,9921,a(flip),b,18975,a)].">
      <j1 rule="hyper" parents="58 9921 18975"/>
    </justification>
  </clause>

  <clause id="18978">
    <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,5537,a(flip),b,18976,a),flip(a)].">
      <j1 rule="hyper" parents="58 5537 18976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18979">
    <literal><![CDATA[
      K(x,(((y \ 1) \ 1) \ z) * (z \ (u * y))) = K(x,(T(u * y,u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(320,a,16567,a(flip),b,18978,a),flip(a)].">
      <j1 rule="hyper" parents="320 16567 18978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18980">
    <literal><![CDATA[
      K(x,(((y \ 1) \ 1) \ z) * (z \ (u * y))) = K(x,((y * u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(320,a,18016,a(flip),b,18979,a),flip(a)].">
      <j1 rule="hyper" parents="320 18016 18979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18981">
    <literal><![CDATA[
      K(x,(T(y,1) \ z) * (z \ (u * y))) = K(x,((y * u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,13120,a(flip),b,18980,a)].">
      <j1 rule="hyper" parents="58 13120 18980"/>
    </justification>
  </clause>

  <clause id="18982">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,(y \ u) * (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(198(a,1),18981(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="198 18981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18983">
    <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(18394,a,17827,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18394 17827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18984">
    <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(4867(a,1),18983(a,2,1,1))].">
      <j1 rule="para" parents="4867 18983"/>
    </justification>
  </clause>

  <clause id="18985">
    <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(4740(a,1),18984(a,1,2,1))].">
      <j1 rule="para" parents="4740 18984"/>
    </justification>
  </clause>

  <clause id="18986">
    <literal><![CDATA[
      (K(x,y) * (z * K(y,x))) * ((z * K(y,x)) \ u) = (K(x,y) * z) * (z \ u)
    ]]></literal>
    <justification jstring="[hyper(18394,a,18985,a)].">
      <j1 rule="hyper" parents="18394 18985"/>
    </justification>
  </clause>

  <clause id="18987">
    <literal><![CDATA[
      T(x,K(y,z)) * ((x * K(y,z)) \ u) = (K(z,y) * x) * (x \ u)
    ]]></literal>
    <justification jstring="[para(5103(a,1),18986(a,1,1))].">
      <j1 rule="para" parents="5103 18986"/>
    </justification>
  </clause>

  <clause id="18988">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * ((K(y,x) * z) \ u)) = z \ u
    ]]></literal>
    <justification jstring="[hyper(11181,a,18987,a)].">
      <j1 rule="hyper" parents="11181 18987"/>
    </justification>
  </clause>

  <clause id="18989">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ u) != w
    ]]></literal>
    <literal><![CDATA[
      z * ((K(y,x) * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(18987(a,1),11131(a,1))].">
      <j1 rule="para" parents="18987 11131"/>
    </justification>
  </clause>

  <clause id="18990">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * u) = z \ ((K(y,x) * z) * u)
    ]]></literal>
    <justification jstring="[para(4(a,1),18988(a,1,2,2))].">
      <j1 rule="para" parents="4 18988"/>
    </justification>
  </clause>

  <clause id="18991">
    <literal><![CDATA[
      x \ ((K(y,z) * x) * T(u,K(z,y))) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(18609,a,18990,a),flip(a)].">
      <j1 rule="hyper" parents="18609 18990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18992">
    <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,11175,a(flip),b,18990,a),flip(a)].">
      <j1 rule="hyper" parents="58 11175 18990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18993">
    <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(18990(a,1),18415(a,1,2,2,2))].">
      <j1 rule="para" parents="18990 18415"/>
    </justification>
  </clause>

  <clause id="18994">
    <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(18989,a,16760,a),flip(a)].">
      <j1 rule="hyper" parents="18989 16760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18995">
    <literal><![CDATA[
      x \ ((x * K(y,z)) * (K(z,y) * u)) = L(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[para(11127(a,1),18992(a,1,2))].">
      <j1 rule="para" parents="11127 18992"/>
    </justification>
  </clause>

  <clause id="18996">
    <literal><![CDATA[
      L(x,K(y,z),u * K(z,y)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(6319,a,18995,a)].">
      <j1 rule="hyper" parents="6319 18995"/>
    </justification>
  </clause>

  <clause id="18997">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * u) = x * L(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(134,a,18995,a),flip(a)].">
      <j1 rule="hyper" parents="134 18995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18998">
    <literal><![CDATA[
      L(x,K(y,z),u \ T(z,y)) = L(x,K(y,z),u \ z)
    ]]></literal>
    <justification jstring="[para(13634(a,1),18996(a,1,3))].">
      <j1 rule="para" parents="13634 18996"/>
    </justification>
  </clause>

  <clause id="18999">
    <literal><![CDATA[
      L(x,K(y,z),u) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(18996(a,1),18599(a,1,1))].">
      <j1 rule="para" parents="18996 18599"/>
    </justification>
  </clause>

  <clause id="19000">
    <literal><![CDATA[
      x * L(K(y,z) * u,K(z,y),x) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(5095(a,1),18997(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5095 18997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19001">
    <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(6311(a,1),18999(a,2,1))].">
      <j1 rule="para" parents="6311 18999"/>
    </justification>
  </clause>

  <clause id="19002">
    <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(19000(a,1),15354(a,1,2,2,2,1))].">
      <j1 rule="para" parents="19000 15354"/>
    </justification>
  </clause>

  <clause id="19003">
    <literal><![CDATA[
      x \ ((K(y,z) * x) * T(u,K(y,z))) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(7807(a,1),18991(a,1,2,2))].">
      <j1 rule="para" parents="7807 18991"/>
    </justification>
  </clause>

  <clause id="19004">
    <literal><![CDATA[
      x \ ((K(y,T(z,u)) * x) * u) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(17646(a,2),18991(a,1,2))].">
      <j1 rule="para" parents="17646 18991"/>
    </justification>
  </clause>

  <clause id="19005">
    <literal><![CDATA[
      (x * y) / (y * K(z,T(u,x))) = y \ ((K(u,z) * y) * x)
    ]]></literal>
    <justification jstring="[para(7863(a,1),19004(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7863 19004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19006">
    <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(19005(a,1),18612(a,1,2))].">
      <j1 rule="para" parents="19005 18612"/>
    </justification>
  </clause>

  <clause id="19007">
    <literal><![CDATA[
      K(x,y / ((z * u) \ (u * y))) = y \ ((y * u) / (u * K(z,x)))
    ]]></literal>
    <justification jstring="[para(19003(a,1),18854(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19003 18854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19008">
    <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(16350(a,1),18994(a,2,2))].">
      <j1 rule="para" parents="16350 18994"/>
    </justification>
  </clause>

  <clause id="19009">
    <literal><![CDATA[
      x * a(y,x,K(x \ z,u)) = z * ((K(y,u) * z) \ (K(y,u) * x))
    ]]></literal>
    <justification jstring="[para(18202(a,1),19008(a,1,2))].">
      <j1 rule="para" parents="18202 19008"/>
    </justification>
  </clause>

  <clause id="19010">
    <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(7653(a,1),19009(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7653 19009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19012">
    <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(14272(a,1),19010(a,2,2))].">
      <j1 rule="para" parents="14272 19010"/>
    </justification>
  </clause>

  <clause id="19013">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,x,K(y,u)) = z * a(u,z,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(18252(a,1),19012(a,1,2))].">
      <j1 rule="para" parents="18252 19012"/>
    </justification>
  </clause>

  <clause id="19014">
    <literal><![CDATA[
      x * a(y,x,K(z,x \ u)) = u * (z * L(z \ (u \ x),u,K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(1081,a,19013,a),flip(a)].">
      <j1 rule="hyper" parents="1081 19013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19015">
    <literal><![CDATA[
      x * L(y * (y \ (x \ z)),x,K(y,u)) = z * a(u,z,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(18325(a,2),19014(a,2,2)),flip(a)].">
      <j1 rule="para" parents="18325 19014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19016">
    <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),19015(a,1,2,1))].">
      <j1 rule="para" parents="5 19015"/>
    </justification>
  </clause>

  <clause id="19018">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = y * a(u,y,K(x \ y,z))
    ]]></literal>
    <justification jstring="[para(11002(a,2),19016(a,2,2))].">
      <j1 rule="para" parents="11002 19016"/>
    </justification>
  </clause>

  <clause id="19019">
    <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(19006(a,1),18993(a,1,2,2))].">
      <j1 rule="para" parents="19006 18993"/>
    </justification>
  </clause>

  <clause id="19020">
    <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(18170,a,19019,a),flip(a)].">
      <j1 rule="hyper" parents="18170 19019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19021">
    <literal><![CDATA[
      K(x,y * L(z,K(u,w),v5)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(16007,a,19020,a),flip(a)].">
      <j1 rule="hyper" parents="16007 19020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19022">
    <literal><![CDATA[
      K(x,y * L(z,K(u,w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v6
    ]]></literal>
    <justification jstring="[para(19020(a,1),16007(a,1))].">
      <j1 rule="para" parents="19020 16007"/>
    </justification>
  </clause>

  <clause id="19024">
    <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(566(a,1),19021(a,1,2,2))].">
      <j1 rule="para" parents="566 19021"/>
    </justification>
  </clause>

  <clause id="19025">
    <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(6318(a,1),19022(a,1,2))].">
      <j1 rule="para" parents="6318 19022"/>
    </justification>
  </clause>

  <clause id="19026">
    <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(5092(a,1),19024(a,2,2,2,1))].">
      <j1 rule="para" parents="5092 19024"/>
    </justification>
  </clause>

  <clause id="19027">
    <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,18177,a,b,19026,a)].">
      <j1 rule="hyper" parents="58 18177 19026"/>
    </justification>
  </clause>

  <clause id="19028">
    <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(5092(a,1),19027(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5092 19027"/>
    </justification>
  </clause>

  <clause id="19029">
    <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,18096,a(flip),b,19028,a)].">
      <j1 rule="hyper" parents="58 18096 19028"/>
    </justification>
  </clause>

  <clause id="19030">
    <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(15716,a,19029,a),flip(a)].">
      <j1 rule="hyper" parents="15716 19029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19031">
    <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),19030(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4 19030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19032">
    <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(16609,a,18012,a)].">
      <j1 rule="hyper" parents="16609 18012"/>
    </justification>
  </clause>

  <clause id="19033">
    <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,15134,a(flip),b,18711,a)].">
      <j1 rule="hyper" parents="58 15134 18711"/>
    </justification>
  </clause>

  <clause id="19034">
    <literal><![CDATA[
      T((x * y) \ y,K(y,y \ z)) = (x * T(y,y \ z)) \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,16521,a(flip),b,19033,a)].">
      <j1 rule="hyper" parents="58 16521 19033"/>
    </justification>
  </clause>

  <clause id="19035">
    <literal><![CDATA[
      (x * T(y,y \ z)) \ ((y \ z) \ z) = T((x * y) \ y,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(13014,a,19034,a),flip(a)].">
      <j1 rule="hyper" parents="13014 19034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19036">
    <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(18159,a,18958,a)].">
      <j1 rule="hyper" parents="18159 18958"/>
    </justification>
  </clause>

  <clause id="19037">
    <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),19032(a,1,2,1,1))].">
      <j1 rule="para" parents="4 19032"/>
    </justification>
  </clause>

  <clause id="19039">
    <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(14510,a,18334,a)].">
      <j1 rule="hyper" parents="14510 18334"/>
    </justification>
  </clause>

  <clause id="19040">
    <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(19039(a,1),6470(a,1))].">
      <j1 rule="para" parents="19039 6470"/>
    </justification>
  </clause>

  <clause id="19041">
    <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,18387,a(flip),b,18414,a)].">
      <j1 rule="hyper" parents="58 18387 18414"/>
    </justification>
  </clause>

  <clause id="19043">
    <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,18385,a(flip),b,19041,a)].">
      <j1 rule="hyper" parents="58 18385 19041"/>
    </justification>
  </clause>

  <clause id="19044">
    <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(15492(a,1),19043(a,1,2,1))].">
      <j1 rule="para" parents="15492 19043"/>
    </justification>
  </clause>

  <clause id="19045">
    <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(9441(a,2),19044(a,1,2))].">
      <j1 rule="para" parents="9441 19044"/>
    </justification>
  </clause>

  <clause id="19046">
    <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(7759(a,2),19045(a,1,2,1,1))].">
      <j1 rule="para" parents="7759 19045"/>
    </justification>
  </clause>

  <clause id="19047">
    <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(17641,a,19046,a)].">
      <j1 rule="hyper" parents="17641 19046"/>
    </justification>
  </clause>

  <clause id="19048">
    <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(15520,a,19047,a)].">
      <j1 rule="hyper" parents="15520 19047"/>
    </justification>
  </clause>

  <clause id="19049">
    <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(19048(a,2),13407(a,1,3,2))].">
      <j1 rule="para" parents="19048 13407"/>
    </justification>
  </clause>

  <clause id="19050">
    <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(15035(a,1),19049(a,2,3,2))].">
      <j1 rule="para" parents="15035 19049"/>
    </justification>
  </clause>

  <clause id="19051">
    <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),18876(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 18876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19052">
    <literal><![CDATA[
      K(x,T(y * L(y \ z,u,u \ 1),y)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,18938,a(flip),b,19051,a),flip(a)].">
      <j1 rule="hyper" parents="320 18938 19051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19054">
    <literal><![CDATA[
      K(x,y * L(z / y,u,u \ 1)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(12261,a,19052,a)].">
      <j1 rule="hyper" parents="12261 19052"/>
    </justification>
  </clause>

  <clause id="19056">
    <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(17313(a,2),17335(a,1,1))].">
      <j1 rule="para" parents="17313 17335"/>
    </justification>
  </clause>

  <clause id="19057">
    <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(13854(a,1),17649(a,1,2,2))].">
      <j1 rule="para" parents="13854 17649"/>
    </justification>
  </clause>

  <clause id="19058">
    <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),17677(a,1,2,3))].">
      <j1 rule="para" parents="5 17677"/>
    </justification>
  </clause>

  <clause id="19059">
    <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(58,a,14265,a(flip),b,19058,a),flip(a)].">
      <j1 rule="hyper" parents="58 14265 19058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19062">
    <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(320,a,13710,a(flip),b,19059,a),flip(a)].">
      <j1 rule="hyper" parents="320 13710 19059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19063">
    <literal><![CDATA[
      K(x,y \ (((L(y,z,u) \ y) \ y) * w)) = K(x,(y \ L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(3556(a,1),19062(a,1,2,2,1,1))].">
      <j1 rule="para" parents="3556 19062"/>
    </justification>
  </clause>

  <clause id="19064">
    <literal><![CDATA[
      K(x,y \ (L(y,z,u) * w)) = K(x,(y \ L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(5918(a,1),19063(a,1,2,2,1))].">
      <j1 rule="para" parents="5918 19063"/>
    </justification>
  </clause>

  <clause id="19065">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) = K(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[para(1397(a,1),19064(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1397 19064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19066">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) * (y \ u)) = K(x,u * a(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(17368,a,19065,a),flip(a)].">
      <j1 rule="hyper" parents="17368 19065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19067">
    <literal><![CDATA[
      K(x,L(y,z,u) * (y \ w)) = K(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(17198,a,19065,a),flip(a)].">
      <j1 rule="hyper" parents="17198 19065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19068">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) * w) = T(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(118,a,19065,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 19065 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19069">
    <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,18915,a(flip),b,19065,a),flip(a)].">
      <j1 rule="hyper" parents="58 18915 19065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19070">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ w)) = T(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(118,a,19067,a,b,5368,a),flip(a)].">
      <j1 rule="hyper" parents="118 19067 5368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19071">
    <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(19068(a,1),803(a,1,1))].">
      <j1 rule="para" parents="19068 803"/>
    </justification>
  </clause>

  <clause id="19072">
    <literal><![CDATA[
      K(x,a(y \ 1,y,z) \ u) = K(x,u * a(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,14600,a(flip),b,19066,a)].">
      <j1 rule="hyper" parents="58 14600 19066"/>
    </justification>
  </clause>

  <clause id="19073">
    <literal><![CDATA[
      K(x,(y * z) * a(z,u,u \ 1)) = K(x,y * L(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(18053,a,19072,a),flip(a)].">
      <j1 rule="hyper" parents="18053 19072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19074">
    <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(19072(a,1),18053(a,1))].">
      <j1 rule="para" parents="19072 18053"/>
    </justification>
  </clause>

  <clause id="19075">
    <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(10081(a,2),19073(a,1,2,1))].">
      <j1 rule="para" parents="10081 19073"/>
    </justification>
  </clause>

  <clause id="19076">
    <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(320,a,18024,a(flip),b,18800,a),flip(a)].">
      <j1 rule="hyper" parents="320 18024 18800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19078">
    <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(320,a,13004,a(flip),b,19076,a),flip(a)].">
      <j1 rule="hyper" parents="320 13004 19076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19079">
    <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(19035(a,1),19078(a,1,2,2,2))].">
      <j1 rule="para" parents="19035 19078"/>
    </justification>
  </clause>

  <clause id="19080">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * ((w * y) \ y))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(17380,a,19079,a)].">
      <j1 rule="hyper" parents="17380 19079"/>
    </justification>
  </clause>

  <clause id="19081">
    <literal><![CDATA[
      K(x,T(y,z) \ (u * ((w * y) \ y))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(13159,a,19080,a)].">
      <j1 rule="hyper" parents="13159 19080"/>
    </justification>
  </clause>

  <clause id="19082">
    <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,17986,a(flip),b,19081,a)].">
      <j1 rule="hyper" parents="58 17986 19081"/>
    </justification>
  </clause>

  <clause id="19083">
    <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,18555,a,b,19082,a),flip(a)].">
      <j1 rule="hyper" parents="58 18555 19082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19084">
    <literal><![CDATA[
      K(x,((y * ((y * z) / y)) / u) \ z) = K(x,z \ ((z * u) / y))
    ]]></literal>
    <justification jstring="[hyper(15715,a,19083,a),flip(a)].">
      <j1 rule="hyper" parents="15715 19083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19085">
    <literal><![CDATA[
      K(x,((y * z) / u) \ T(z,y)) = K(x,z \ ((z * u) / y))
    ]]></literal>
    <justification jstring="[para(14506(a,1),19084(a,1,2))].">
      <j1 rule="para" parents="14506 19084"/>
    </justification>
  </clause>

  <clause id="19086">
    <literal><![CDATA[
      K(x,T(y / (z \ (u * y)),u)) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(16670,a,19085,a)].">
      <j1 rule="hyper" parents="16670 19085"/>
    </justification>
  </clause>

  <clause id="19087">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ (u * y))) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(18113,a,19086,a)].">
      <j1 rule="hyper" parents="18113 19086"/>
    </justification>
  </clause>

  <clause id="19088">
    <literal><![CDATA[
      K(x,T(y / (z \ (u * y)),z)) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18565,a(flip),b,19086,a)].">
      <j1 rule="hyper" parents="58 18565 19086"/>
    </justification>
  </clause>

  <clause id="19089">
    <literal><![CDATA[
      K(x,y / ((z * u) \ (u * y))) = K(x,y \ ((y * (u * z)) / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18709,a(flip),b,19087,a)].">
      <j1 rule="hyper" parents="58 18709 19087"/>
    </justification>
  </clause>

  <clause id="19090">
    <literal><![CDATA[
      K(x,y / (z \ (T(u,z) * y))) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18564,a,b,19088,a)].">
      <j1 rule="hyper" parents="58 18564 19088"/>
    </justification>
  </clause>

  <clause id="19091">
    <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(320,a,6078,a(flip),b,18934,a),flip(a)].">
      <j1 rule="hyper" parents="320 6078 18934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19092">
    <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,14511,a(flip),b,19091,a),flip(a)].">
      <j1 rule="hyper" parents="114 14511 19091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19093">
    <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(320,a,18308,a(flip),b,19092,a),flip(a)].">
      <j1 rule="hyper" parents="320 18308 19092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19095">
    <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(6306(a,1),19093(a,1,2))].">
      <j1 rule="para" parents="6306 19093"/>
    </justification>
  </clause>

  <clause id="19096">
    <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(17500,a,19095,a)].">
      <j1 rule="hyper" parents="17500 19095"/>
    </justification>
  </clause>

  <clause id="19097">
    <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(5594(a,1),19096(a,1,2,2))].">
      <j1 rule="para" parents="5594 19096"/>
    </justification>
  </clause>

  <clause id="19098">
    <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,18970,a,b,19097,a)].">
      <j1 rule="hyper" parents="58 18970 19097"/>
    </justification>
  </clause>

  <clause id="19100">
    <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(15765(a,2),19056(a,1,2,1))].">
      <j1 rule="para" parents="15765 19056"/>
    </justification>
  </clause>

  <clause id="19101">
    <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(7528(a,1),19057(a,1,2,2))].">
      <j1 rule="para" parents="7528 19057"/>
    </justification>
  </clause>

  <clause id="19103">
    <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(10076(a,1),19101(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10076 19101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19104">
    <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(320,a,13775,a(flip),b,19103,a),flip(a)].">
      <j1 rule="hyper" parents="320 13775 19103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19105">
    <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(320,a,13076,a(flip),b,19104,a),flip(a)].">
      <j1 rule="hyper" parents="320 13076 19104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19106">
    <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(320,a,17365,a(flip),b,19105,a),flip(a)].">
      <j1 rule="hyper" parents="320 17365 19105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19107">
    <literal><![CDATA[
      K(x,y * L((z / (y \ 1)) / y,u,w)) = K(x,y * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(10082(a,1),19106(a,1,2,2,1))].">
      <j1 rule="para" parents="10082 19106"/>
    </justification>
  </clause>

  <clause id="19108">
    <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(18875(a,2),19107(a,2,2,2))].">
      <j1 rule="para" parents="18875 19107"/>
    </justification>
  </clause>

  <clause id="19109">
    <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(14173(a,1),19075(a,1,2,2))].">
      <j1 rule="para" parents="14173 19075"/>
    </justification>
  </clause>

  <clause id="19110">
    <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(17129(a,2),19100(a,1,2))].">
      <j1 rule="para" parents="17129 19100"/>
    </justification>
  </clause>

  <clause id="19111">
    <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,19054,a(flip),b,19108,a)].">
      <j1 rule="hyper" parents="58 19054 19108"/>
    </justification>
  </clause>

  <clause id="19113">
    <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,14084,a(flip),b,19111,a)].">
      <j1 rule="hyper" parents="58 14084 19111"/>
    </justification>
  </clause>

  <clause id="19114">
    <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(12260,a,19113,a),flip(a)].">
      <j1 rule="hyper" parents="12260 19113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19115">
    <literal><![CDATA[
      K(x,y * L(z \ T(u,w),v5,v5 \ 1)) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(18875(a,1),19114(a,1,2,2))].">
      <j1 rule="para" parents="18875 19114"/>
    </justification>
  </clause>

  <clause id="19116">
    <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(14988(a,1),19109(a,1,2,2))].">
      <j1 rule="para" parents="14988 19109"/>
    </justification>
  </clause>

  <clause id="19117">
    <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(17295,a,19110,a)].">
      <j1 rule="hyper" parents="17295 19110"/>
    </justification>
  </clause>

  <clause id="19118">
    <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,18476,a(flip),b,19116,a)].">
      <j1 rule="hyper" parents="58 18476 19116"/>
    </justification>
  </clause>

  <clause id="19119">
    <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(320,a,19107,a(flip),b,19118,a),flip(a)].">
      <j1 rule="hyper" parents="320 19107 19118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19120">
    <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,17357,a(flip),b,19117,a),flip(a)].">
      <j1 rule="hyper" parents="58 17357 19117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19122">
    <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(320,a,15,a,b,19120,a),flip(a)].">
      <j1 rule="hyper" parents="320 15 19120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19123">
    <literal><![CDATA[
      R(x,y,K(z,K(u,w)) * v5) = R(x,y,v5)
    ]]></literal>
    <justification jstring="[para(17332(a,1),19122(a,1,2))].">
      <j1 rule="para" parents="17332 19122"/>
    </justification>
  </clause>

  <clause id="19125">
    <literal><![CDATA[
      R(x,y,z \ (T(u,K(w,v5)) \ v6)) = R(x,y,z \ (u \ v6))
    ]]></literal>
    <justification jstring="[para(17290(a,1),19123(a,1,3)),flip(a)].">
      <j1 rule="para" parents="17290 19123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19126">
    <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,19050,a(flip),b,19125,a),flip(a)].">
      <j1 rule="hyper" parents="58 19050 19125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19128">
    <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,14550,a,b,19126,a)].">
      <j1 rule="hyper" parents="58 14550 19126"/>
    </justification>
  </clause>

  <clause id="19129">
    <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(17292(a,1),19128(a,1,3))].">
      <j1 rule="para" parents="17292 19128"/>
    </justification>
  </clause>

  <clause id="19130">
    <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,19123,a(flip),b,19129,a),flip(a)].">
      <j1 rule="hyper" parents="58 19123 19129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19132">
    <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(19130(a,1),18158(a,1,2,1))].">
      <j1 rule="para" parents="19130 18158"/>
    </justification>
  </clause>

  <clause id="19133">
    <literal><![CDATA[
      K(x,y * (z \ T(u,K(w,v5) * v6))) = K(x,y * (z \ T(u,v6)))
    ]]></literal>
    <justification jstring="[para(504(a,1),19132(a,1,2)),flip(a)].">
      <j1 rule="para" parents="504 19132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19135">
    <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(10763(a,1),17246(a,1,2))].">
      <j1 rule="para" parents="10763 17246"/>
    </justification>
  </clause>

  <clause id="19136">
    <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(13239(a,1),19135(a,1,2,2))].">
      <j1 rule="para" parents="13239 19135"/>
    </justification>
  </clause>

  <clause id="19137">
    <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(17232(a,1),19136(a,1,2))].">
      <j1 rule="para" parents="17232 19136"/>
    </justification>
  </clause>

  <clause id="19138">
    <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(18696(a,1),19137(a,1,2,2))].">
      <j1 rule="para" parents="18696 19137"/>
    </justification>
  </clause>

  <clause id="19139">
    <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(18192(a,1),19138(a,1,2))].">
      <j1 rule="para" parents="18192 19138"/>
    </justification>
  </clause>

  <clause id="19140">
    <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(18352(a,1),19139(a,1,2))].">
      <j1 rule="para" parents="18352 19139"/>
    </justification>
  </clause>

  <clause id="19141">
    <literal><![CDATA[
      x / K(y,L(z,u,u \ x)) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(14620(a,1),19140(a,1,2))].">
      <j1 rule="para" parents="14620 19140"/>
    </justification>
  </clause>

  <clause id="19143">
    <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(19141(a,1),14107(a,1))].">
      <j1 rule="para" parents="19141 14107"/>
    </justification>
  </clause>

  <clause id="19144">
    <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(14485(a,1),19143(a,1))].">
      <j1 rule="para" parents="14485 19143"/>
    </justification>
  </clause>

  <clause id="19145">
    <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(15648(a,1),17555(a,1,2,1,1))].">
      <j1 rule="para" parents="15648 17555"/>
    </justification>
  </clause>

  <clause id="19146">
    <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(12304(a,2),19145(a,1,2,1,1))].">
      <j1 rule="para" parents="12304 19145"/>
    </justification>
  </clause>

  <clause id="19147">
    <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(18697(a,1),19146(a,1,2))].">
      <j1 rule="para" parents="18697 19146"/>
    </justification>
  </clause>

  <clause id="19148">
    <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(18703,a,19147,a)].">
      <j1 rule="hyper" parents="18703 19147"/>
    </justification>
  </clause>

  <clause id="19150">
    <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,18174,a(flip),b,19148,a)].">
      <j1 rule="hyper" parents="58 18174 19148"/>
    </justification>
  </clause>

  <clause id="19151">
    <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(15313,a,19150,a)].">
      <j1 rule="hyper" parents="15313 19150"/>
    </justification>
  </clause>

  <clause id="19153">
    <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(4266(a,1),19151(a,1,2,1,1))].">
      <j1 rule="para" parents="4266 19151"/>
    </justification>
  </clause>

  <clause id="19154">
    <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(13166,a,19153,a)].">
      <j1 rule="hyper" parents="13166 19153"/>
    </justification>
  </clause>

  <clause id="19155">
    <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(320,a,17744,a(flip),b,19154,a),flip(a)].">
      <j1 rule="hyper" parents="320 17744 19154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19156">
    <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(320,a,15058,a(flip),b,19155,a),flip(a)].">
      <j1 rule="hyper" parents="320 15058 19155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19157">
    <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(320,a,18793,a(flip),b,19156,a),flip(a)].">
      <j1 rule="hyper" parents="320 18793 19156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19158">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,z \ (((1 / y) \ z) * u))
    ]]></literal>
    <justification jstring="[para(11550(a,1),19157(a,2,2,2,1))].">
      <j1 rule="para" parents="11550 19157"/>
    </justification>
  </clause>

  <clause id="19159">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(320,a,15359,a(flip),b,19158,a),flip(a)].">
      <j1 rule="hyper" parents="320 15359 19158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19160">
    <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,18962,a(flip),b,19159,a)].">
      <j1 rule="hyper" parents="58 18962 19159"/>
    </justification>
  </clause>

  <clause id="19161">
    <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,13119,a(flip),b,19160,a)].">
      <j1 rule="hyper" parents="58 13119 19160"/>
    </justification>
  </clause>

  <clause id="19162">
    <literal><![CDATA[
      K(x,((y * z) * (y \ 1)) \ ((z * y) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,17950,a(flip),b,19161,a)].">
      <j1 rule="hyper" parents="58 17950 19161"/>
    </justification>
  </clause>

  <clause id="19163">
    <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(17398(a,1),17407(a,1,2))].">
      <j1 rule="para" parents="17398 17407"/>
    </justification>
  </clause>

  <clause id="19164">
    <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(10371(a,1),17853(a,2,1))].">
      <j1 rule="para" parents="10371 17853"/>
    </justification>
  </clause>

  <clause id="19165">
    <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(320,a,7807,a,b,19164,a),flip(a)].">
      <j1 rule="hyper" parents="320 7807 19164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19166">
    <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(320,a,15607,a(flip),b,19165,a),flip(a)].">
      <j1 rule="hyper" parents="320 15607 19165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19168">
    <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(7771(a,1),19166(a,1,1))].">
      <j1 rule="para" parents="7771 19166"/>
    </justification>
  </clause>

  <clause id="19169">
    <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(5594(a,1),19168(a,1,2,1,2))].">
      <j1 rule="para" parents="5594 19168"/>
    </justification>
  </clause>

  <clause id="19170">
    <literal><![CDATA[
      (x * (K(y,z) * u)) / u = (x * u) / (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(15797,a,19169,a)].">
      <j1 rule="hyper" parents="15797 19169"/>
    </justification>
  </clause>

  <clause id="19171">
    <literal><![CDATA[
      (x * (y / z)) / (K(u,y) * (y / z)) = (x * (T(y,u) / z)) / (y / z)
    ]]></literal>
    <justification jstring="[para(13643(a,1),19170(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13643 19170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19172">
    <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(19170(a,1),14765(a,2,2))].">
      <j1 rule="para" parents="19170 14765"/>
    </justification>
  </clause>

  <clause id="19173">
    <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(18376(a,1),19172(a,1,1,1))].">
      <j1 rule="para" parents="18376 19172"/>
    </justification>
  </clause>

  <clause id="19174">
    <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(14390(a,1),19173(a,1,1,1))].">
      <j1 rule="para" parents="14390 19173"/>
    </justification>
  </clause>

  <clause id="19176">
    <literal><![CDATA[
      ((K(x,y) * z) * (K(u,w) * v5)) / v5 = K(x,y) * ((z * v5) / (K(w,u) * v5))
    ]]></literal>
    <justification jstring="[para(18191(a,1),19174(a,1,1))].">
      <j1 rule="para" parents="18191 19174"/>
    </justification>
  </clause>

  <clause id="19177">
    <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,19170,a(flip),b,19176,a)].">
      <j1 rule="hyper" parents="58 19170 19176"/>
    </justification>
  </clause>

  <clause id="19178">
    <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(18602,a,19177,a),flip(a)].">
      <j1 rule="hyper" parents="18602 19177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19179">
    <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),19178(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15 19178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19180">
    <literal><![CDATA[
      L(K(x,y) * z,K(u,w),v5) = K(x,y) * L(z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[para(18594(a,1),19179(a,2,2))].">
      <j1 rule="para" parents="18594 19179"/>
    </justification>
  </clause>

  <clause id="19181">
    <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(320,a,18604,a(flip),b,19180,a),flip(a)].">
      <j1 rule="hyper" parents="320 18604 19180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19182">
    <literal><![CDATA[
      ((x * y) / (K(z,u) * y)) * K(z,u) = L(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(5095(a,1),19181(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5095 19181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19183">
    <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(13676(a,1),19182(a,1,1,2))].">
      <j1 rule="para" parents="13676 19182"/>
    </justification>
  </clause>

  <clause id="19184">
    <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(320,a,17719,a(flip),b,19183,a),flip(a)].">
      <j1 rule="hyper" parents="320 17719 19183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19185">
    <literal><![CDATA[
      ((x * (T(y,z) / u)) / (y / u)) * K(z,y) = L(x,K(z,y),u \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,18998,a(flip),b,19184,a),flip(a)].">
      <j1 rule="hyper" parents="320 18998 19184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19186">
    <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(17713(a,1),19002(a,1,2,2,2))].">
      <j1 rule="para" parents="17713 19002"/>
    </justification>
  </clause>

  <clause id="19187">
    <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,19133,a(flip),b,19186,a)].">
      <j1 rule="hyper" parents="58 19133 19186"/>
    </justification>
  </clause>

  <clause id="19190">
    <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,15354,a(flip),b,19187,a),flip(a)].">
      <j1 rule="hyper" parents="58 15354 19187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19191">
    <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(320,a,18079,a(flip),b,19190,a),flip(a)].">
      <j1 rule="hyper" parents="320 18079 19190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19192">
    <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(19001(a,1),19191(a,1,2,2,2))].">
      <j1 rule="para" parents="19001 19191"/>
    </justification>
  </clause>

  <clause id="19193">
    <literal><![CDATA[
      K(x,y * (z \ (u * (K(w,v5) * v6)))) = K(x,y * (K(w,v5) * (z \ (u * v6))))
    ]]></literal>
    <justification jstring="[hyper(17381,a,19192,a)].">
      <j1 rule="hyper" parents="17381 19192"/>
    </justification>
  </clause>

  <clause id="19194">
    <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,19031,a(flip),b,19193,a),flip(a)].">
      <j1 rule="hyper" parents="58 19031 19193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19195">
    <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),19194(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13 19194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19196">
    <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(19025,a,19195,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19025 19195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19197">
    <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(17631,a,19196,a)].">
      <j1 rule="hyper" parents="17631 19196"/>
    </justification>
  </clause>

  <clause id="19198">
    <literal><![CDATA[
      K(x,y * L(y \ 1,z,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19098,a(flip),b,19197,a),flip(a)].">
      <j1 rule="hyper" parents="58 19098 19197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19199">
    <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,19037,a(flip),b,19197,a)].">
      <j1 rule="hyper" parents="58 19037 19197"/>
    </justification>
  </clause>

  <clause id="19200">
    <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,16965,a(flip),b,19198,a)].">
      <j1 rule="hyper" parents="58 16965 19198"/>
    </justification>
  </clause>

  <clause id="19201">
    <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(15469,a,19199,a),flip(a)].">
      <j1 rule="hyper" parents="15469 19199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19203">
    <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(7133(a,1),19200(a,2,3))].">
      <j1 rule="para" parents="7133 19200"/>
    </justification>
  </clause>

  <clause id="19204">
    <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(5391(a,1),19203(a,2,3))].">
      <j1 rule="para" parents="5391 19203"/>
    </justification>
  </clause>

  <clause id="19205">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / (z \ y)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[para(7186(a,1),19204(a,2,3))].">
      <j1 rule="para" parents="7186 19204"/>
    </justification>
  </clause>

  <clause id="19206">
    <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,15372,a(flip),b,19201,a)].">
      <j1 rule="hyper" parents="58 15372 19201"/>
    </justification>
  </clause>

  <clause id="19207">
    <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,15396,a(flip),b,19206,a)].">
      <j1 rule="hyper" parents="58 15396 19206"/>
    </justification>
  </clause>

  <clause id="19208">
    <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),19207(a,1,2,1))].">
      <j1 rule="para" parents="6 19207"/>
    </justification>
  </clause>

  <clause id="19209">
    <literal><![CDATA[
      K(x,L(y / (z * y),u,w) * z) = K(x,z * L((y * z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(17894,a,19208,a)].">
      <j1 rule="hyper" parents="17894 19208"/>
    </justification>
  </clause>

  <clause id="19210">
    <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(828,a,19163,a)].">
      <j1 rule="hyper" parents="828 19163"/>
    </justification>
  </clause>

  <clause id="19211">
    <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(14202(a,1),19210(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14202 19210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19212">
    <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(17402(a,1),19211(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17402 19211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19213">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)) * v5,v6) = L(x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(320,a,17228,a(flip),b,19212,a),flip(a)].">
      <j1 rule="hyper" parents="320 17228 19212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19215">
    <literal><![CDATA[
      L(x,L(y,z,K(u,w)),v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[para(14861(a,1),19213(a,1,2))].">
      <j1 rule="para" parents="14861 19213"/>
    </justification>
  </clause>

  <clause id="19216">
    <literal><![CDATA[
      L(x,y * a(z,u,K(w,v5)),v6) = L(x,y,v6)
    ]]></literal>
    <justification jstring="[para(17103(a,1),19213(a,1,2))].">
      <j1 rule="para" parents="17103 19213"/>
    </justification>
  </clause>

  <clause id="19218">
    <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(13250,a,19216,a),flip(a)].">
      <j1 rule="hyper" parents="13250 19216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19219">
    <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(320,a,17400,a(flip),b,19218,a),flip(a)].">
      <j1 rule="hyper" parents="320 17400 19218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19220">
    <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),19219(a,2,2))].">
      <j1 rule="para" parents="13 19219"/>
    </justification>
  </clause>

  <clause id="19221">
    <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(14248(a,1),19220(a,1,1,1))].">
      <j1 rule="para" parents="14248 19220"/>
    </justification>
  </clause>

  <clause id="19222">
    <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(17402(a,1),19221(a,1,1))].">
      <j1 rule="para" parents="17402 19221"/>
    </justification>
  </clause>

  <clause id="19223">
    <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(19222(a,2),17373(a,2,2))].">
      <j1 rule="para" parents="19222 17373"/>
    </justification>
  </clause>

  <clause id="19225">
    <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(17811(a,1),18333(a,1,1,3))].">
      <j1 rule="para" parents="17811 18333"/>
    </justification>
  </clause>

  <clause id="19226">
    <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(18207(a,1),19225(a,1,1))].">
      <j1 rule="para" parents="18207 19225"/>
    </justification>
  </clause>

  <clause id="19227">
    <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,18365,a(flip),b,19226,a)].">
      <j1 rule="hyper" parents="58 18365 19226"/>
    </justification>
  </clause>

  <clause id="19229">
    <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(18050(a,1),19227(a,1,2))].">
      <j1 rule="para" parents="18050 19227"/>
    </justification>
  </clause>

  <clause id="19230">
    <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(13939(a,1),19229(a,1,2))].">
      <j1 rule="para" parents="13939 19229"/>
    </justification>
  </clause>

  <clause id="19231">
    <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(17821(a,1),19230(a,1,2))].">
      <j1 rule="para" parents="17821 19230"/>
    </justification>
  </clause>

  <clause id="19232">
    <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(320,a,17299,a(flip),b,19231,a),flip(a)].">
      <j1 rule="hyper" parents="320 17299 19231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19233">
    <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(320,a,18922,a(flip),b,19232,a),flip(a)].">
      <j1 rule="hyper" parents="320 18922 19232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19234">
    <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(320,a,18181,a(flip),b,19233,a),flip(a)].">
      <j1 rule="hyper" parents="320 18181 19233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19235">
    <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(9452(a,1),18967(a,1,1))].">
      <j1 rule="para" parents="9452 18967"/>
    </justification>
  </clause>

  <clause id="19236">
    <literal><![CDATA[
      K(x,(y \ (z \ (u * z))) \ (y \ (u * z))) = K(x,L(T(z,u),u,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(15598,a,19235,a),flip(a)].">
      <j1 rule="hyper" parents="15598 19235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19238">
    <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),19236(a,1,2,1,2))].">
      <j1 rule="para" parents="17 19236"/>
    </justification>
  </clause>

  <clause id="19239">
    <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(16048,a,18933,a),flip(a)].">
      <j1 rule="hyper" parents="16048 18933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19240">
    <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(320,a,17640,a(flip),b,19239,a),flip(a)].">
      <j1 rule="hyper" parents="320 17640 19239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19241">
    <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(17271(a,1),19240(a,1,2,2,2))].">
      <j1 rule="para" parents="17271 19240"/>
    </justification>
  </clause>

  <clause id="19242">
    <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(19040,a,19241,a),flip(a)].">
      <j1 rule="hyper" parents="19040 19241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19243">
    <literal><![CDATA[
      K(x,y * ((z \ L(y,u,w)) / L(y,u,w))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(1292(a,1),19242(a,1,2,2,1,2,1))].">
      <j1 rule="para" parents="1292 19242"/>
    </justification>
  </clause>

  <clause id="19244">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ (L(y,z,u) / w))) = K(x,y / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,16307,a(flip),b,19243,a)].">
      <j1 rule="hyper" parents="58 16307 19243"/>
    </justification>
  </clause>

  <clause id="19245">
    <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(16808(a,1),14644(a,1,2,2,2,2))].">
      <j1 rule="para" parents="16808 14644"/>
    </justification>
  </clause>

  <clause id="19246">
    <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),19245(a,1,2,2))].">
      <j1 rule="para" parents="91 19245"/>
    </justification>
  </clause>

  <clause id="19247">
    <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(15149,a,19246,a)].">
      <j1 rule="hyper" parents="15149 19246"/>
    </justification>
  </clause>

  <clause id="19248">
    <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(15196,a,19247,a)].">
      <j1 rule="hyper" parents="15196 19247"/>
    </justification>
  </clause>

  <clause id="19249">
    <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(16808(a,1),19248(a,2,3,1))].">
      <j1 rule="para" parents="16808 19248"/>
    </justification>
  </clause>

  <clause id="19250">
    <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(12197(a,1),19249(a,2,3))].">
      <j1 rule="para" parents="12197 19249"/>
    </justification>
  </clause>

  <clause id="19251">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ L(y / (u \ z),u \ z,u)) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,18205,a(flip),b,19250,a),flip(a)].">
      <j1 rule="hyper" parents="320 18205 19250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19253">
    <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,17078,a,b,19251,a)].">
      <j1 rule="hyper" parents="58 17078 19251"/>
    </justification>
  </clause>

  <clause id="19254">
    <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(18409(a,1),19253(a,1,1,2))].">
      <j1 rule="para" parents="18409 19253"/>
    </justification>
  </clause>

  <clause id="19255">
    <literal><![CDATA[
      K(x,L(y / (z \ u),z \ u,z) / (y * (u \ z))) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(205,a,19254,a)].">
      <j1 rule="hyper" parents="205 19254"/>
    </justification>
  </clause>

  <clause id="19257">
    <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(17522(a,1),13947(a,1,1))].">
      <j1 rule="para" parents="17522 13947"/>
    </justification>
  </clause>

  <clause id="19258">
    <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(17522(a,1),13948(a,1,1))].">
      <j1 rule="para" parents="17522 13948"/>
    </justification>
  </clause>

  <clause id="19259">
    <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(12964(a,1),19257(a,1,1))].">
      <j1 rule="para" parents="12964 19257"/>
    </justification>
  </clause>

  <clause id="19260">
    <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(7683,a,19259,a)].">
      <j1 rule="hyper" parents="7683 19259"/>
    </justification>
  </clause>

  <clause id="19261">
    <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(16369,a,19260,a)].">
      <j1 rule="hyper" parents="16369 19260"/>
    </justification>
  </clause>

  <clause id="19263">
    <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),19261(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 19261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19264">
    <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(320,a,16311,a(flip),b,19263,a),flip(a)].">
      <j1 rule="hyper" parents="320 16311 19263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19267">
    <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(13039(a,1),19258(a,1,1))].">
      <j1 rule="para" parents="13039 19258"/>
    </justification>
  </clause>

  <clause id="19268">
    <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(7683,a,19267,a)].">
      <j1 rule="hyper" parents="7683 19267"/>
    </justification>
  </clause>

  <clause id="19269">
    <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(16369,a,19268,a)].">
      <j1 rule="hyper" parents="16369 19268"/>
    </justification>
  </clause>

  <clause id="19271">
    <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),19269(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 19269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19272">
    <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(320,a,16311,a(flip),b,19271,a),flip(a)].">
      <j1 rule="hyper" parents="320 16311 19271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19275">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),u)) = K(x,w * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16663,a(flip),b,19272,a),flip(a)].">
      <j1 rule="hyper" parents="58 16663 19272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19276">
    <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,19264,a,b,19275,a)].">
      <j1 rule="hyper" parents="58 19264 19275"/>
    </justification>
  </clause>

  <clause id="19277">
    <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(6448(a,1),19276(a,1,2))].">
      <j1 rule="para" parents="6448 19276"/>
    </justification>
  </clause>

  <clause id="19278">
    <literal><![CDATA[
      K(x,y * (z * K(u \ w,u))) = K(x,y * (K(w,u) * z))
    ]]></literal>
    <justification jstring="[hyper(13916,a,19277,a)].">
      <j1 rule="hyper" parents="13916 19277"/>
    </justification>
  </clause>

  <clause id="19279">
    <literal><![CDATA[
      K(x,y * (z \ ((u \ w) * u))) = K(x,y * (K(w,u) * (z \ w)))
    ]]></literal>
    <justification jstring="[para(14146(a,1),19278(a,1,2,2))].">
      <j1 rule="para" parents="14146 19278"/>
    </justification>
  </clause>

  <clause id="19280">
    <literal><![CDATA[
      K(x,y * (z \ ((u \ w) * u))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,15978,a(flip),b,19279,a),flip(a)].">
      <j1 rule="hyper" parents="320 15978 19279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19281">
    <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,16097,a(flip),b,19280,a)].">
      <j1 rule="hyper" parents="58 16097 19280"/>
    </justification>
  </clause>

  <clause id="19282">
    <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(14054(a,1),19281(a,2,2,2,2))].">
      <j1 rule="para" parents="14054 19281"/>
    </justification>
  </clause>

  <clause id="19283">
    <literal><![CDATA[
      K(x,T(y * (z \ u),((z \ u) * y) \ u)) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(320,a,13116,a(flip),b,19282,a),flip(a)].">
      <j1 rule="hyper" parents="320 13116 19282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19284">
    <literal><![CDATA[
      K(x,T(y * (z \ u),y \ ((z \ u) \ u))) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(17237,a,19283,a)].">
      <j1 rule="hyper" parents="17237 19283"/>
    </justification>
  </clause>

  <clause id="19285">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z \ y)) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17353,a(flip),b,19284,a)].">
      <j1 rule="hyper" parents="58 17353 19284"/>
    </justification>
  </clause>

  <clause id="19286">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z * y)) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(15864,a,19285,a)].">
      <j1 rule="hyper" parents="15864 19285"/>
    </justification>
  </clause>

  <clause id="19288">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z * y)) = K(x,y * (z \ T(u,z * y)))
    ]]></literal>
    <justification jstring="[hyper(320,a,18910,a(flip),b,19286,a),flip(a)].">
      <j1 rule="hyper" parents="320 18910 19286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19289">
    <literal><![CDATA[
      K(x,y * (z \ T(u,z * y))) = K(x,(u / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18151,a(flip),b,19288,a),flip(a)].">
      <j1 rule="hyper" parents="58 18151 19288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19290">
    <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,19069,a(flip),b,19289,a),flip(a)].">
      <j1 rule="hyper" parents="58 19069 19289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19291">
    <literal><![CDATA[
      K(x,(y / z) * L(z,u,w)) = K(x,y * (z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(176(a,1),19290(a,1,2,2))].">
      <j1 rule="para" parents="176 19290"/>
    </justification>
  </clause>

  <clause id="19292">
    <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,19115,a(flip),b,19291,a),flip(a)].">
      <j1 rule="hyper" parents="58 19115 19291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19293">
    <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),19292(a,2,2))].">
      <j1 rule="para" parents="7 19292"/>
    </justification>
  </clause>

  <clause id="19294">
    <literal><![CDATA[
      K(x,y * a(z \ T(u,w),v5,v5 \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15440,a,19293,a)].">
      <j1 rule="hyper" parents="15440 19293"/>
    </justification>
  </clause>

  <clause id="19297">
    <literal><![CDATA[
      K(x,y * a(z,u,u \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),19294(a,1,2,2,1))].">
      <j1 rule="para" parents="75 19294"/>
    </justification>
  </clause>

  <clause id="19298">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(19074,a,19297,a)].">
      <j1 rule="hyper" parents="19074 19297"/>
    </justification>
  </clause>

  <clause id="19299">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,19119,a(flip),b,19297,a)].">
      <j1 rule="hyper" parents="58 19119 19297"/>
    </justification>
  </clause>

  <clause id="19300">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(13370(a,1),19297(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13370 19297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19302">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15250,a,b,19300,a)].">
      <j1 rule="hyper" parents="58 15250 19300"/>
    </justification>
  </clause>

  <clause id="19305">
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15380,a(flip),b,19298,a)].">
      <j1 rule="hyper" parents="58 15380 19298"/>
    </justification>
  </clause>

  <clause id="19307">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ u) = K(x,w * (L(w,v5,v5 \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,19300,a,b,19302,a)].">
      <j1 rule="hyper" parents="320 19300 19302"/>
    </justification>
  </clause>

  <clause id="19308">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,19244,a(flip),b,19302,a),flip(a)].">
      <j1 rule="hyper" parents="58 19244 19302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19310">
    <literal><![CDATA[
      K(x,y * (z / (u \ 1))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,5297,a(flip),b,19305,a),flip(a)].">
      <j1 rule="hyper" parents="58 5297 19305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19312">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = w
    ]]></literal>
    <justification jstring="[para(19299(a,2),13941(a,1))].">
      <j1 rule="para" parents="19299 13941"/>
    </justification>
  </clause>

  <clause id="19313">
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z / u)) = w
    ]]></literal>
    <justification jstring="[para(15380(a,1),19312(a,1))].">
      <j1 rule="para" parents="15380 19312"/>
    </justification>
  </clause>

  <clause id="19314">
    <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(16666(a,2),19313(a,1))].">
      <j1 rule="para" parents="16666 19313"/>
    </justification>
  </clause>

  <clause id="19315">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) \ (y * u)) = K(x,a(w,v5,v5 \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1403(a,2),19307(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1403 19307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19316">
    <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,18557,a,b,19315,a),flip(a)].">
      <j1 rule="hyper" parents="58 18557 19315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19321">
    <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(5928(a,1),19316(a,2,2,1,2))].">
      <j1 rule="para" parents="5928 19316"/>
    </justification>
  </clause>

  <clause id="19322">
    <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(13717(a,1),19321(a,2,2,1))].">
      <j1 rule="para" parents="13717 19321"/>
    </justification>
  </clause>

  <clause id="19323">
    <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(320,a,14259,a(flip),b,19322,a),flip(a)].">
      <j1 rule="hyper" parents="320 14259 19322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19324">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ (u \ L(w,v5,v5 \ 1))) = K(x,u \ w)
    ]]></literal>
    <justification jstring="[para(5925(a,1),19323(a,2,2,2))].">
      <j1 rule="para" parents="5925 19323"/>
    </justification>
  </clause>

  <clause id="19325">
    <literal><![CDATA[
      K(x,y \ L(z,u,u \ 1)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,19300,a(flip),b,19324,a)].">
      <j1 rule="hyper" parents="58 19300 19324"/>
    </justification>
  </clause>

  <clause id="19327">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15442,a(flip),b,19325,a),flip(a)].">
      <j1 rule="hyper" parents="58 15442 19325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19328">
    <literal><![CDATA[
      K(x,y \ (z * (u \ 1))) = K(x,y \ (z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15437,a(flip),b,19325,a)].">
      <j1 rule="hyper" parents="58 15437 19325"/>
    </justification>
  </clause>

  <clause id="19329">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ u) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,14641,a(flip),b,19325,a),flip(a)].">
      <j1 rule="hyper" parents="58 14641 19325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19333">
    <literal><![CDATA[
      K(x,((y * z) / y) \ ((z * y) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19162,a(flip),b,19329,a),flip(a)].">
      <j1 rule="hyper" parents="58 19162 19329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19334">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,y \ ((T(y,z) * z) * u))
    ]]></literal>
    <justification jstring="[para(14776(a,1),19333(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14776 19333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19335">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,y \ ((z * y) * u))
    ]]></literal>
    <justification jstring="[hyper(320,a,18020,a(flip),b,19334,a),flip(a)].">
      <j1 rule="hyper" parents="320 18020 19334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19336">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y * z)) = K(x,z \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18030,a,b,19335,a)].">
      <j1 rule="hyper" parents="58 18030 19335"/>
    </justification>
  </clause>

  <clause id="19337">
    <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(17669(a,1),15880(a,1,1))].">
      <j1 rule="para" parents="17669 15880"/>
    </justification>
  </clause>

  <clause id="19338">
    <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(15981(a,1),18036(a,1,1))].">
      <j1 rule="para" parents="15981 18036"/>
    </justification>
  </clause>

  <clause id="19340">
    <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(18913(a,1),19338(a,1,1))].">
      <j1 rule="para" parents="18913 19338"/>
    </justification>
  </clause>

  <clause id="19341">
    <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,18688,a(flip),b,19340,a)].">
      <j1 rule="hyper" parents="58 18688 19340"/>
    </justification>
  </clause>

  <clause id="19342">
    <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,18454,a,b,19341,a)].">
      <j1 rule="hyper" parents="58 18454 19341"/>
    </justification>
  </clause>

  <clause id="19344">
    <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(15572,a,19342,a)].">
      <j1 rule="hyper" parents="15572 19342"/>
    </justification>
  </clause>

  <clause id="19345">
    <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(16366,a,19344,a),flip(a)].">
      <j1 rule="hyper" parents="16366 19344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19346">
    <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(320,a,15553,a(flip),b,19345,a),flip(a)].">
      <j1 rule="hyper" parents="320 15553 19345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19347">
    <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(18035(a,1),19346(a,1,2))].">
      <j1 rule="para" parents="18035 19346"/>
    </justification>
  </clause>

  <clause id="19348">
    <literal><![CDATA[
      K(x,y * T(z,T(u / w,v5))) = K(x,y * T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(13916,a,19347,a)].">
      <j1 rule="hyper" parents="13916 19347"/>
    </justification>
  </clause>

  <clause id="19349">
    <literal><![CDATA[
      K(x,y * T(z,u \ w)) = K(x,y * T(z,w * u))
    ]]></literal>
    <justification jstring="[para(107(a,1),19348(a,1,2,2,2))].">
      <j1 rule="para" parents="107 19348"/>
    </justification>
  </clause>

  <clause id="19350">
    <literal><![CDATA[
      K(x,y * T(z,u \ (w \ v5))) = K(x,y * T(z,v5 * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(17668,a,19349,a)].">
      <j1 rule="hyper" parents="17668 19349"/>
    </justification>
  </clause>

  <clause id="19351">
    <literal><![CDATA[
      K(x,y * T(z,(u \ w) * v5)) = K(x,y * T(z,w * (v5 * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19349,a(flip),b,19350,a)].">
      <j1 rule="hyper" parents="58 19349 19350"/>
    </justification>
  </clause>

  <clause id="19352">
    <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,16511,a(flip),b,19351,a),flip(a)].">
      <j1 rule="hyper" parents="58 16511 19351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19353">
    <literal><![CDATA[
      K(x,T((y \ z) * T(u,z * (x * y)),w)) = K(T(x,w),u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(7679,a,19352,a)].">
      <j1 rule="hyper" parents="7679 19352"/>
    </justification>
  </clause>

  <clause id="19354">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(T(x,z * u),y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(15498,a,19353,a)].">
      <j1 rule="hyper" parents="15498 19353"/>
    </justification>
  </clause>

  <clause id="19355">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(x,T(y * (u \ z),z * u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7133,a(flip),b,19354,a),flip(a)].">
      <j1 rule="hyper" parents="320 7133 19354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19356">
    <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(19355(a,2),15499(a,1))].">
      <j1 rule="para" parents="19355 15499"/>
    </justification>
  </clause>

  <clause id="19357">
    <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(7683,a,19337,a)].">
      <j1 rule="hyper" parents="7683 19337"/>
    </justification>
  </clause>

  <clause id="19358">
    <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(16369,a,19357,a)].">
      <j1 rule="hyper" parents="16369 19357"/>
    </justification>
  </clause>

  <clause id="19360">
    <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),19358(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 19358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19361">
    <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(320,a,16332,a(flip),b,19360,a),flip(a)].">
      <j1 rule="hyper" parents="320 16332 19360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19364">
    <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(320,a,19275,a(flip),b,19361,a),flip(a)].">
      <j1 rule="hyper" parents="320 19275 19361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19365">
    <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(15763(a,1),19364(a,1,2))].">
      <j1 rule="para" parents="15763 19364"/>
    </justification>
  </clause>

  <clause id="19366">
    <literal><![CDATA[
      K(x,y * ((z * K(u,w)) * v5)) = K(x,y * (K(u,w) * (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(13916,a,19365,a)].">
      <j1 rule="hyper" parents="13916 19365"/>
    </justification>
  </clause>

  <clause id="19367">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((w * z) * v5))) = K(x,y * ((w * T(z,u)) * v5))
    ]]></literal>
    <justification jstring="[para(6086(a,1),19366(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6086 19366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19368">
    <literal><![CDATA[
      K(x,y * ((z * T(u,x)) * w)) = K(x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[hyper(17533,a,19367,a),flip(a)].">
      <j1 rule="hyper" parents="17533 19367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19369">
    <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,18162,a(flip),b,19368,a),flip(a)].">
      <j1 rule="hyper" parents="58 18162 19368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19370">
    <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),19369(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 19369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19371">
    <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,17576,a,b,19370,a),flip(a)].">
      <j1 rule="hyper" parents="58 17576 19370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19373">
    <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,17604,a(flip),b,19371,a),flip(a)].">
      <j1 rule="hyper" parents="58 17604 19371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19374">
    <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,18935,a(flip),b,19373,a)].">
      <j1 rule="hyper" parents="58 18935 19373"/>
    </justification>
  </clause>

  <clause id="19375">
    <literal><![CDATA[
      K(x,(y \ T(z,K(u,w) * v5)) * v6) = K(x,(y \ ((v5 * z) / v5)) * v6)
    ]]></literal>
    <justification jstring="[para(5095(a,1),19374(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5095 19374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19376">
    <literal><![CDATA[
      K(x,(y \ T(z,K(u,w) * v5)) * v6) = K(x,(y \ T(z,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(320,a,15372,a(flip),b,19375,a),flip(a)].">
      <j1 rule="hyper" parents="320 15372 19375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19377">
    <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,16559,a(flip),b,19376,a)].">
      <j1 rule="hyper" parents="58 16559 19376"/>
    </justification>
  </clause>

  <clause id="19379">
    <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(13775(a,1),18529(a,1,1,1))].">
      <j1 rule="para" parents="13775 18529"/>
    </justification>
  </clause>

  <clause id="19380">
    <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(13710(a,1),19379(a,1,1,2,3))].">
      <j1 rule="para" parents="13710 19379"/>
    </justification>
  </clause>

  <clause id="19381">
    <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(18258(a,1),19380(a,1,1,2))].">
      <j1 rule="para" parents="18258 19380"/>
    </justification>
  </clause>

  <clause id="19382">
    <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,18520,a(flip),b,19381,a)].">
      <j1 rule="hyper" parents="58 18520 19381"/>
    </justification>
  </clause>

  <clause id="19383">
    <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(320,a,18528,a(flip),b,19382,a),flip(a)].">
      <j1 rule="hyper" parents="320 18528 19382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19385">
    <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(17653(a,1),13949(a,1,1))].">
      <j1 rule="para" parents="17653 13949"/>
    </justification>
  </clause>

  <clause id="19386">
    <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,18688,a(flip),b,19385,a)].">
      <j1 rule="hyper" parents="58 18688 19385"/>
    </justification>
  </clause>

  <clause id="19387">
    <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(16619,a,19386,a)].">
      <j1 rule="hyper" parents="16619 19386"/>
    </justification>
  </clause>

  <clause id="19388">
    <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,17961,a(flip),b,19387,a)].">
      <j1 rule="hyper" parents="58 17961 19387"/>
    </justification>
  </clause>

  <clause id="19389">
    <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(16361,a,19388,a),flip(a)].">
      <j1 rule="hyper" parents="16361 19388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19391">
    <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(320,a,12222,a(flip),b,19389,a),flip(a)].">
      <j1 rule="hyper" parents="320 12222 19389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19392">
    <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(3950(a,1),19391(a,1,2))].">
      <j1 rule="para" parents="3950 19391"/>
    </justification>
  </clause>

  <clause id="19393">
    <literal><![CDATA[
      K(x,y * K(z \ (u * (w \ 1)),v5)) = K(x,y * K(v5,w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(13916,a,19392,a)].">
      <j1 rule="hyper" parents="13916 19392"/>
    </justification>
  </clause>

  <clause id="19394">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (1 / v5)))) = K(x,(y \ z) * K(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(15235,a,19393,a)].">
      <j1 rule="hyper" parents="15235 19393"/>
    </justification>
  </clause>

  <clause id="19395">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (1 / v5)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,13879,a(flip),b,19394,a),flip(a)].">
      <j1 rule="hyper" parents="320 13879 19394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19396">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (v5 \ 1)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[para(3749(a,1),19395(a,1,2,2))].">
      <j1 rule="para" parents="3749 19395"/>
    </justification>
  </clause>

  <clause id="19397">
    <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,18748,a(flip),b,19396,a)].">
      <j1 rule="hyper" parents="58 18748 19396"/>
    </justification>
  </clause>

  <clause id="19398">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w * (v5 \ 1)))) = K(x,y \ T(z,v5 * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,18767,a(flip),b,19397,a),flip(a)].">
      <j1 rule="hyper" parents="320 18767 19397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19399">
    <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,19036,a(flip),b,19398,a),flip(a)].">
      <j1 rule="hyper" parents="58 19036 19398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19400">
    <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(7679,a,19399,a)].">
      <j1 rule="hyper" parents="7679 19399"/>
    </justification>
  </clause>

  <clause id="19401">
    <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(15865,a,19400,a)].">
      <j1 rule="hyper" parents="15865 19400"/>
    </justification>
  </clause>

  <clause id="19402">
    <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(15500,a,19401,a)].">
      <j1 rule="hyper" parents="15500 19401"/>
    </justification>
  </clause>

  <clause id="19403">
    <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(320,a,7133,a(flip),b,19402,a),flip(a)].">
      <j1 rule="hyper" parents="320 7133 19402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19404">
    <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(16662(a,1),19403(a,2,2))].">
      <j1 rule="para" parents="16662 19403"/>
    </justification>
  </clause>

  <clause id="19405">
    <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(19404(a,2),15600(a,1))].">
      <j1 rule="para" parents="19404 15600"/>
    </justification>
  </clause>

  <clause id="19406">
    <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,16009,a(flip),b,18132,a)].">
      <j1 rule="hyper" parents="58 16009 18132"/>
    </justification>
  </clause>

  <clause id="19407">
    <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(17434,a,19406,a)].">
      <j1 rule="hyper" parents="17434 19406"/>
    </justification>
  </clause>

  <clause id="19408">
    <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,13824,a(flip),b,19407,a)].">
      <j1 rule="hyper" parents="58 13824 19407"/>
    </justification>
  </clause>

  <clause id="19409">
    <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(17844,a,19408,a)].">
      <j1 rule="hyper" parents="17844 19408"/>
    </justification>
  </clause>

  <clause id="19410">
    <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(16355,a,19409,a),flip(a)].">
      <j1 rule="hyper" parents="16355 19409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19411">
    <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(320,a,17190,a(flip),b,19410,a),flip(a)].">
      <j1 rule="hyper" parents="320 17190 19410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19412">
    <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(18131(a,1),19411(a,1,1,2))].">
      <j1 rule="para" parents="18131 19411"/>
    </justification>
  </clause>

  <clause id="19413">
    <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(2324(a,1),19412(a,1,2))].">
      <j1 rule="para" parents="2324 19412"/>
    </justification>
  </clause>

  <clause id="19414">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) / u) = K(x,L(y,z,z \ 1) / u)
    ]]></literal>
    <justification jstring="[hyper(6316,a,19413,a),flip(a)].">
      <j1 rule="hyper" parents="6316 19413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19416">
    <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,14809,a,b,19414,a)].">
      <j1 rule="hyper" parents="58 14809 19414"/>
    </justification>
  </clause>

  <clause id="19417">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / (u * (z \ 1))) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18395,a(flip),b,19416,a),flip(a)].">
      <j1 rule="hyper" parents="58 18395 19416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19418">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19308,a(flip),b,19417,a)].">
      <j1 rule="hyper" parents="58 19308 19417"/>
    </justification>
  </clause>

  <clause id="19419">
    <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,18433,a(flip),b,19417,a)].">
      <j1 rule="hyper" parents="58 18433 19417"/>
    </justification>
  </clause>

  <clause id="19420">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(320,a,17820,a,b,19418,a)].">
      <j1 rule="hyper" parents="320 17820 19418"/>
    </justification>
  </clause>

  <clause id="19422">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / ((z \ 1) * u)) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,16232,a(flip),b,19419,a),flip(a)].">
      <j1 rule="hyper" parents="320 16232 19419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19423">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19308,a(flip),b,19422,a)].">
      <j1 rule="hyper" parents="58 19308 19422"/>
    </justification>
  </clause>

  <clause id="19425">
    <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(19423(a,1),18801(a,1,2))].">
      <j1 rule="para" parents="19423 18801"/>
    </justification>
  </clause>

  <clause id="19426">
    <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(19423(a,1),19405(a,1))].">
      <j1 rule="para" parents="19423 19405"/>
    </justification>
  </clause>

  <clause id="19427">
    <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(18559(a,1),19425(a,1,2))].">
      <j1 rule="para" parents="18559 19425"/>
    </justification>
  </clause>

  <clause id="19428">
    <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(18932(a,1),19427(a,1,2))].">
      <j1 rule="para" parents="18932 19427"/>
    </justification>
  </clause>

  <clause id="19429">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18322,a(flip),b,19428,a)].">
      <j1 rule="hyper" parents="58 18322 19428"/>
    </justification>
  </clause>

  <clause id="19430">
    <literal><![CDATA[
      K(x,y / (z \ u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16231,a(flip),b,19429,a)].">
      <j1 rule="hyper" parents="58 16231 19429"/>
    </justification>
  </clause>

  <clause id="19431">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(x,((z \ 1) * u) \ y)
    ]]></literal>
    <justification jstring="[hyper(19426,a,19430,a),flip(a)].">
      <j1 rule="hyper" parents="19426 19430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19433">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19423,a,b,19430,a)].">
      <j1 rule="hyper" parents="58 19423 19430"/>
    </justification>
  </clause>

  <clause id="19434">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y * (T(z,u) \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19420,a(flip),b,19430,a)].">
      <j1 rule="hyper" parents="58 19420 19430"/>
    </justification>
  </clause>

  <clause id="19435">
    <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,19205,a(flip),b,19430,a),flip(a)].">
      <j1 rule="hyper" parents="58 19205 19430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19436">
    <literal><![CDATA[
      K(x,y * ((T(z,u) * y) \ u)) = K(x,y \ ((y * u) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19090,a(flip),b,19430,a),flip(a)].">
      <j1 rule="hyper" parents="58 19090 19430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19439">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ v5)) = a(x,y,K(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[para(19430(a,1),18210(a,1,3)),flip(a)].">
      <j1 rule="para" parents="19430 18210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19440">
    <literal><![CDATA[
      K(x,y * (z \ (u \ 1))) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5540,a(flip),b,19433,a),flip(a)].">
      <j1 rule="hyper" parents="58 5540 19433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19441">
    <literal><![CDATA[
      K(x,y * ((z / u) \ (w \ K(z,u)))) = K(x,y / (w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(18505,a,19440,a)].">
      <j1 rule="hyper" parents="18505 19440"/>
    </justification>
  </clause>

  <clause id="19442">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(320,a,15183,a(flip),b,19434,a),flip(a)].">
      <j1 rule="hyper" parents="320 15183 19434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19443">
    <literal><![CDATA[
      K(x,y / (z / u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19418,a(flip),b,19442,a)].">
      <j1 rule="hyper" parents="58 19418 19442"/>
    </justification>
  </clause>

  <clause id="19444">
    <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,18778,a,b,19443,a)].">
      <j1 rule="hyper" parents="58 18778 19443"/>
    </justification>
  </clause>

  <clause id="19446">
    <literal><![CDATA[
      K(x,y \ ((y * z) / u)) = K(x,(z / (y * u)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16237,a(flip),b,19436,a),flip(a)].">
      <j1 rule="hyper" parents="58 16237 19436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19447">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(19356,a,19431,a),flip(a)].">
      <j1 rule="hyper" parents="19356 19431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19448">
    <literal><![CDATA[
      K(x,(y \ z) \ u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,19327,a(flip),b,19447,a)].">
      <j1 rule="hyper" parents="58 19327 19447"/>
    </justification>
  </clause>

  <clause id="19449">
    <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,19238,a(flip),b,19448,a),flip(a)].">
      <j1 rule="hyper" parents="58 19238 19448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19450">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a(v5,u,K(w,(z \ y) * x))
    ]]></literal>
    <justification jstring="[para(19448(a,1),14234(a,2,3))].">
      <j1 rule="para" parents="19448 14234"/>
    </justification>
  </clause>

  <clause id="19451">
    <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(19448(a,1),14303(a,1,3))].">
      <j1 rule="para" parents="19448 14303"/>
    </justification>
  </clause>

  <clause id="19452">
    <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(19448(a,1),19234(a,1,1,3))].">
      <j1 rule="para" parents="19448 19234"/>
    </justification>
  </clause>

  <clause id="19453">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a(x * (z \ y),u,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,18219,a,b,19450,a),flip(a)].">
      <j1 rule="hyper" parents="320 18219 19450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19454">
    <literal><![CDATA[
      a((x * y) \ z,u,K(w,v5)) = a(y * (z \ x),u,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,14311,a,b,19453,a)].">
      <j1 rule="hyper" parents="58 14311 19453"/>
    </justification>
  </clause>

  <clause id="19455">
    <literal><![CDATA[
      a(x \ (y * z),u,K(w,v5)) = a(z * (x \ y),u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(14321,a,19454,a)].">
      <j1 rule="hyper" parents="14321 19454"/>
    </justification>
  </clause>

  <clause id="19456">
    <literal><![CDATA[
      a(x \ (y * z),u,K(w,v5)) = a((x \ y) * z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,18221,a,b,19455,a),flip(a)].">
      <j1 rule="hyper" parents="320 18221 19455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19457">
    <literal><![CDATA[
      a(x * (y \ 1),z,K(u,w)) = a(y \ x,z,K(u,w))
    ]]></literal>
    <justification jstring="[para(2(a,1),19455(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2 19455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19458">
    <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(19455(a,2),18239(a,1))].">
      <j1 rule="para" parents="19455 18239"/>
    </justification>
  </clause>

  <clause id="19459">
    <literal><![CDATA[
      a((x \ 1) * y,z,K(u,w)) = a(x \ y,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(18239,a,19457,a)].">
      <j1 rule="hyper" parents="18239 19457"/>
    </justification>
  </clause>

  <clause id="19460">
    <literal><![CDATA[
      a((x \ y) \ z,u,K(w,v5)) = a((y \ x) * z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,14312,a,b,19456,a)].">
      <j1 rule="hyper" parents="58 14312 19456"/>
    </justification>
  </clause>

  <clause id="19461">
    <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(19456(a,2),18239(a,1))].">
      <j1 rule="para" parents="19456 18239"/>
    </justification>
  </clause>

  <clause id="19462">
    <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),19460(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 19460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19463">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,(z \ y) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(320,a,19310,a(flip),b,19444,a),flip(a)].">
      <j1 rule="hyper" parents="320 19310 19444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19464">
    <literal><![CDATA[
      K(x,(y \ z) * (z \ (u * y))) = K(x,L(T(u,y),y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,17612,a(flip),b,19449,a)].">
      <j1 rule="hyper" parents="58 17612 19449"/>
    </justification>
  </clause>

  <clause id="19465">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,L(T(z,y),y,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,18982,a,b,19464,a)].">
      <j1 rule="hyper" parents="58 18982 19464"/>
    </justification>
  </clause>

  <clause id="19466">
    <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,19209,a(flip),b,19435,a)].">
      <j1 rule="hyper" parents="58 19209 19435"/>
    </justification>
  </clause>

  <clause id="19467">
    <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),19466(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5 19466"/>
    </justification>
  </clause>

  <clause id="19468">
    <literal><![CDATA[
      K(x,L(y / z,u,w) * (z / y)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[hyper(18099,a,19467,a)].">
      <j1 rule="hyper" parents="18099 19467"/>
    </justification>
  </clause>

  <clause id="19470">
    <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(19443(a,1),19452(a,1,2))].">
      <j1 rule="para" parents="19443 19452"/>
    </justification>
  </clause>

  <clause id="19471">
    <literal><![CDATA[
      K(x,y / (((z / u) \ 1) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,19383,a(flip),b,19470,a)].">
      <j1 rule="hyper" parents="58 19383 19470"/>
    </justification>
  </clause>

  <clause id="19472">
    <literal><![CDATA[
      K(x,y * (z / ((u / w) \ 1))) = K(x,y / ((w / u) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19443,a(flip),b,19471,a)].">
      <j1 rule="hyper" parents="58 19443 19471"/>
    </justification>
  </clause>

  <clause id="19473">
    <literal><![CDATA[
      K(x,y / ((z / u) / w)) = K(x,y * (w * (u / z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19310,a(flip),b,19472,a),flip(a)].">
      <j1 rule="hyper" parents="58 19310 19472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19474">
    <literal><![CDATA[
      K(x,y * (z / (u / w))) = K(x,y * (z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19443,a(flip),b,19473,a)].">
      <j1 rule="hyper" parents="58 19443 19473"/>
    </justification>
  </clause>

  <clause id="19475">
    <literal><![CDATA[
      K(x,y * (z * (u / T(y,u * z)))) = K(x,y \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18925,a(flip),b,19473,a),flip(a)].">
      <j1 rule="hyper" parents="58 18925 19473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19476">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) * (u / w))) = K(x,y * ((w / u) \ z))
    ]]></literal>
    <justification jstring="[hyper(18897,a,19474,a),flip(a)].">
      <j1 rule="hyper" parents="18897 19474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19477">
    <literal><![CDATA[
      K(x,y \ ((y * z) * u)) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,18088,a(flip),b,19475,a),flip(a)].">
      <j1 rule="hyper" parents="58 18088 19475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19478">
    <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,18019,a,b,19477,a)].">
      <j1 rule="hyper" parents="58 18019 19477"/>
    </justification>
  </clause>

  <clause id="19479">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) / u)) * u) = K(x,u \ ((u * y) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19328,a(flip),b,19477,a),flip(a)].">
      <j1 rule="hyper" parents="58 19328 19477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19480">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) / u)) * u) = K(x,(y / (u * z)) * u)
    ]]></literal>
    <justification jstring="[hyper(320,a,19446,a(flip),b,19479,a),flip(a)].">
      <j1 rule="hyper" parents="320 19446 19479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19481">
    <literal><![CDATA[
      K(x,y * ((z / u) \ w)) = K(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(18957,a,19476,a),flip(a)].">
      <j1 rule="hyper" parents="18957 19476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19482">
    <literal><![CDATA[
      K(x,y * ((z / u) * (w \ K(u,z)))) = K(x,y / (w * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19441,a(flip),b,19481,a),flip(a)].">
      <j1 rule="hyper" parents="58 19441 19481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19483">
    <literal><![CDATA[
      K(x,y / (z * (u \ w))) = K(x,y * ((w \ u) / z))
    ]]></literal>
    <justification jstring="[hyper(19314,a,19482,a),flip(a)].">
      <j1 rule="hyper" parents="19314 19482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19484">
    <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,19255,a(flip),b,19483,a),flip(a)].">
      <j1 rule="hyper" parents="58 19255 19483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19485">
    <literal><![CDATA[
      a(x,y \ z,K(u \ (y \ z),y)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19468,a(flip),b,19484,a)].">
      <j1 rule="hyper" parents="58 19468 19484"/>
    </justification>
  </clause>

  <clause id="19486">
    <literal><![CDATA[
      a(x,y \ z,K(u \ z,y)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(14371,a,19485,a)].">
      <j1 rule="hyper" parents="14371 19485"/>
    </justification>
  </clause>

  <clause id="19487">
    <literal><![CDATA[
      a(x,y,K(z \ y,u)) = a(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,14290,a(flip),b,19486,a)].">
      <j1 rule="hyper" parents="58 14290 19486"/>
    </justification>
  </clause>

  <clause id="19488">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19485,a(flip),b,19487,a),flip(a)].">
      <j1 rule="hyper" parents="58 19485 19487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19489">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = x * a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[para(19487(a,1),18841(a,2,2))].">
      <j1 rule="para" parents="19487 18841"/>
    </justification>
  </clause>

  <clause id="19490">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = y * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(19487(a,1),19018(a,2,2))].">
      <j1 rule="para" parents="19487 19018"/>
    </justification>
  </clause>

  <clause id="19491">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = L(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,14860,a(flip),b,19490,a),flip(a)].">
      <j1 rule="hyper" parents="320 14860 19490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19492">
    <literal><![CDATA[
      x * a(y,x,K(z,x \ u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19016,a(flip),b,19491,a)].">
      <j1 rule="hyper" parents="58 19016 19491"/>
    </justification>
  </clause>

  <clause id="19493">
    <literal><![CDATA[
      x * a(y,x,K(z,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(19488(a,1),19492(a,1,2))].">
      <j1 rule="para" parents="19488 19492"/>
    </justification>
  </clause>

  <clause id="19494">
    <literal><![CDATA[
      x * a(y,x,K(z,u)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(17362,a,19493,a)].">
      <j1 rule="hyper" parents="17362 19493"/>
    </justification>
  </clause>

  <clause id="19495">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(29,a,14863,a,b,19493,a)].">
      <j1 rule="hyper" parents="29 14863 19493"/>
    </justification>
  </clause>

  <clause id="19496">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(29,a,14860,a,b,19493,a)].">
      <j1 rule="hyper" parents="29 14860 19493"/>
    </justification>
  </clause>

  <clause id="19497">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(z,x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(29,a,14852,a,b,19493,a)].">
      <j1 rule="hyper" parents="29 14852 19493"/>
    </justification>
  </clause>

  <clause id="19498">
    <literal><![CDATA[
      a(x \ y,z,K(u,w)) = a(u,w,K(z,y \ x))
    ]]></literal>
    <justification jstring="[hyper(14321,a,19495,a)].">
      <j1 rule="hyper" parents="14321 19495"/>
    </justification>
  </clause>

  <clause id="19499">
    <literal><![CDATA[
      a(x,y,K(z,u \ 1)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(14309,a,19495,a),flip(a)].">
      <j1 rule="hyper" parents="14309 19495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19500">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,19495,a,b,14853,a)].">
      <j1 rule="hyper" parents="119 19495 14853"/>
    </justification>
  </clause>

  <clause id="19501">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(x,u)) = w
    ]]></literal>
    <justification jstring="[para(19495(a,1),14270(a,1))].">
      <j1 rule="para" parents="19495 14270"/>
    </justification>
  </clause>

  <clause id="19502">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u = L(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(19495(a,1),14861(a,1,1))].">
      <j1 rule="para" parents="19495 14861"/>
    </justification>
  </clause>

  <clause id="19503">
    <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(19495(a,1),18241(a,1))].">
      <j1 rule="para" parents="19495 18241"/>
    </justification>
  </clause>

  <clause id="19504">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,14195,a,b,19496,a)].">
      <j1 rule="hyper" parents="320 14195 19496"/>
    </justification>
  </clause>

  <clause id="19505">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(z,u,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,14195,a(flip),b,19496,a)].">
      <j1 rule="hyper" parents="320 14195 19496"/>
    </justification>
  </clause>

  <clause id="19506">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,v5)) = a(w,v5,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(18263,a,19496,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18263 19496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19507">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(19496(a,1),14270(a,1))].">
      <j1 rule="para" parents="19496 14270"/>
    </justification>
  </clause>

  <clause id="19508">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,u,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(19496(a,2),14270(a,1))].">
      <j1 rule="para" parents="19496 14270"/>
    </justification>
  </clause>

  <clause id="19509">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,u,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(19496(a,2),14307(a,1))].">
      <j1 rule="para" parents="19496 14307"/>
    </justification>
  </clause>

  <clause id="19510">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(19496(a,2),14249(a,1,2))].">
      <j1 rule="para" parents="19496 14249"/>
    </justification>
  </clause>

  <clause id="19511">
    <literal><![CDATA[
      a(x \ y,z,K(x,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14292,a(flip),b,19497,a),flip(a)].">
      <j1 rule="hyper" parents="320 14292 19497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19512">
    <literal><![CDATA[
      a(x,y,z) * a(y,z,K(x,u)) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,19497,a,b,18716,a)].">
      <j1 rule="hyper" parents="119 19497 18716"/>
    </justification>
  </clause>

  <clause id="19513">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,x,K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(19497(a,2),14307(a,1))].">
      <j1 rule="para" parents="19497 14307"/>
    </justification>
  </clause>

  <clause id="19514">
    <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(19497(a,2),18232(a,1))].">
      <j1 rule="para" parents="19497 18232"/>
    </justification>
  </clause>

  <clause id="19515">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a((z \ y) * x,v5,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(19451,a,19504,a)].">
      <j1 rule="hyper" parents="19451 19504"/>
    </justification>
  </clause>

  <clause id="19516">
    <literal><![CDATA[
      a(((x * y) \ x) * z,u,K(w,v5)) = a(u,v5,K(w,y \ z))
    ]]></literal>
    <justification jstring="[hyper(320,a,19462,a,b,19504,a)].">
      <j1 rule="hyper" parents="320 19462 19504"/>
    </justification>
  </clause>

  <clause id="19517">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) = a(y,x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14235,a,b,19504,a)].">
      <j1 rule="hyper" parents="320 14235 19504"/>
    </justification>
  </clause>

  <clause id="19518">
    <literal><![CDATA[
      a(x,y,K(z,(u \ 1) * w)) = a(u \ w,x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,19459,a(flip),b,19504,a),flip(a)].">
      <j1 rule="hyper" parents="320 19459 19504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19519">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(19504(a,2),14270(a,1))].">
      <j1 rule="para" parents="19504 14270"/>
    </justification>
  </clause>

  <clause id="19520">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,u,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(19504(a,1),14307(a,1))].">
      <j1 rule="para" parents="19504 14307"/>
    </justification>
  </clause>

  <clause id="19521">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w \ x) = w \ L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[para(19505(a,1),17241(a,1,1))].">
      <j1 rule="para" parents="19505 17241"/>
    </justification>
  </clause>

  <clause id="19522">
    <literal><![CDATA[
      x * (y * a(x,z,K(u,w))) = L(x,w,K(z,u)) * y
    ]]></literal>
    <justification jstring="[para(19505(a,1),17372(a,1,2,2))].">
      <j1 rule="para" parents="19505 17372"/>
    </justification>
  </clause>

  <clause id="19523">
    <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(17921(a,1),19505(a,1,3)),flip(a)].">
      <j1 rule="para" parents="17921 19505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19524">
    <literal><![CDATA[
      L(x,y,K(z,u)) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19493,a(flip),b,19494,a),flip(a)].">
      <j1 rule="hyper" parents="58 19493 19494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19525">
    <literal><![CDATA[
      L(x,y,K(z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(14857,a,19524,a),flip(a)].">
      <j1 rule="hyper" parents="14857 19524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19526">
    <literal><![CDATA[
      L(x,y,K(z * u,z)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(12675,a,19524,a)].">
      <j1 rule="hyper" parents="12675 19524"/>
    </justification>
  </clause>

  <clause id="19527">
    <literal><![CDATA[
      L(x,y * x,K(z,u)) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,18348,a(flip),b,19524,a),flip(a)].">
      <j1 rule="hyper" parents="320 18348 19524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19528">
    <literal><![CDATA[
      (K(x,y) * z) * L(u,x,K(y,z)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(119,a,19524,a,b,13,a(flip))].">
      <j1 rule="hyper" parents="119 19524 13"/>
    </justification>
  </clause>

  <clause id="19529">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),z,u) = L(x,z,T(u,y))
    ]]></literal>
    <justification jstring="[para(19524(a,1),14887(a,1,1))].">
      <j1 rule="para" parents="19524 14887"/>
    </justification>
  </clause>

  <clause id="19530">
    <literal><![CDATA[
      L(x,y,K(z,u)) / a(y,z,u) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(19524(a,1),14907(a,1,1))].">
      <j1 rule="para" parents="19524 14907"/>
    </justification>
  </clause>

  <clause id="19531">
    <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(320,a,2128,a,b,19525,a)].">
      <j1 rule="hyper" parents="320 2128 19525"/>
    </justification>
  </clause>

  <clause id="19532">
    <literal><![CDATA[
      L(x,y,K(z,u)) / a(y,z,u) = x / a(y,z,T(u,x))
    ]]></literal>
    <justification jstring="[para(19525(a,2),18719(a,1,1))].">
      <j1 rule="para" parents="19525 18719"/>
    </justification>
  </clause>

  <clause id="19533">
    <literal><![CDATA[
      T(x,x * (y \ L(y,z,u))) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(13340,a,19500,a)].">
      <j1 rule="hyper" parents="13340 19500"/>
    </justification>
  </clause>

  <clause id="19534">
    <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(19517(a,1),14266(a,1,1,1))].">
      <j1 rule="para" parents="19517 14266"/>
    </justification>
  </clause>

  <clause id="19535">
    <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(19517(a,1),14267(a,1,1,1))].">
      <j1 rule="para" parents="19517 14267"/>
    </justification>
  </clause>

  <clause id="19536">
    <literal><![CDATA[
      L(x,y,K(z,y * u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19524,a(flip),b,19526,a)].">
      <j1 rule="hyper" parents="58 19524 19526"/>
    </justification>
  </clause>

  <clause id="19537">
    <literal><![CDATA[
      L(R(x,y,z),y,K(z,u)) = R(x,y,T(z,y * u))
    ]]></literal>
    <justification jstring="[hyper(18253,a,19536,a),flip(a)].">
      <j1 rule="hyper" parents="18253 19536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19538">
    <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(19450(a,2),19513(a,1))].">
      <j1 rule="para" parents="19450 19513"/>
    </justification>
  </clause>

  <clause id="19539">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),z,u) = T(L(x,z,u) \ x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(320,a,15022,a,b,19529,a),flip(a)].">
      <j1 rule="hyper" parents="320 15022 19529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19540">
    <literal><![CDATA[
      a(x \ (y * z),u,K(w,v5)) = a(w,v5,K(u,z \ (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(14433,a,19498,a)].">
      <j1 rule="hyper" parents="14433 19498"/>
    </justification>
  </clause>

  <clause id="19541">
    <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,18273,a,b,19498,a)].">
      <j1 rule="hyper" parents="58 18273 19498"/>
    </justification>
  </clause>

  <clause id="19542">
    <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(19506(a,2),19509(a,1))].">
      <j1 rule="para" parents="19506 19509"/>
    </justification>
  </clause>

  <clause id="19543">
    <literal><![CDATA[
      K(x,L(y,z,u \ y)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(14417,a,19510,a)].">
      <j1 rule="hyper" parents="14417 19510"/>
    </justification>
  </clause>

  <clause id="19544">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(14275,a,19510,a)].">
      <j1 rule="hyper" parents="14275 19510"/>
    </justification>
  </clause>

  <clause id="19545">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = K(x,L(y,u,z * u))
    ]]></literal>
    <justification jstring="[hyper(14473,a,19543,a)].">
      <j1 rule="hyper" parents="14473 19543"/>
    </justification>
  </clause>

  <clause id="19546">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,L(T(z,y),u,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,19465,a,b,19544,a)].">
      <j1 rule="hyper" parents="58 19465 19544"/>
    </justification>
  </clause>

  <clause id="19547">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y)) = K(x,(z \ y) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19463,a(flip),b,19544,a),flip(a)].">
      <j1 rule="hyper" parents="58 19463 19544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19548">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ x)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19070,a,b,19533,a)].">
      <j1 rule="hyper" parents="58 19070 19533"/>
    </justification>
  </clause>

  <clause id="19549">
    <literal><![CDATA[
      K(x,L(y,z,u * z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19544,a(flip),b,19545,a),flip(a)].">
      <j1 rule="hyper" parents="58 19544 19545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19550">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y)) = K(x,z \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19336,a(flip),b,19549,a),flip(a)].">
      <j1 rule="hyper" parents="58 19336 19549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19551">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,u) / y) = x * K(z,L(T(u,y),x,y))
    ]]></literal>
    <justification jstring="[para(19549(a,1),18707(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19549 18707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19552">
    <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,13193,a,b,19548,a)].">
      <j1 rule="hyper" parents="58 13193 19548"/>
    </justification>
  </clause>

  <clause id="19553">
    <literal><![CDATA[
      a(x,y,z) * (a(y,z,K(x,u)) * w) = a(x,y,T(z,u)) * w
    ]]></literal>
    <justification jstring="[para(19512(a,1),17398(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19512 17398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19554">
    <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(19530(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="19530 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19555">
    <literal><![CDATA[
      R(x,y,T(z,y * x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7499,a(flip),b,19537,a),flip(a)].">
      <j1 rule="hyper" parents="58 7499 19537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19556">
    <literal><![CDATA[
      R(x,y,z) \ (z * (y * x)) = T(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(19555(a,1),12481(a,1,1))].">
      <j1 rule="para" parents="19555 12481"/>
    </justification>
  </clause>

  <clause id="19557">
    <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(19521(a,1),19223(a,2,2,1))].">
      <j1 rule="para" parents="19521 19223"/>
    </justification>
  </clause>

  <clause id="19558">
    <literal><![CDATA[
      x / a(y,z,T(u,x)) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,19530,a(flip),b,19532,a),flip(a)].">
      <j1 rule="hyper" parents="58 19530 19532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19559">
    <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(19558(a,1),2254(a,1,1))].">
      <j1 rule="para" parents="19558 2254"/>
    </justification>
  </clause>

  <clause id="19560">
    <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(5405(a,1),19542(a,1,1))].">
      <j1 rule="para" parents="5405 19542"/>
    </justification>
  </clause>

  <clause id="19561">
    <literal><![CDATA[
      K(x,y \ ((z * y) * u)) = K(x,(y \ z) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19547,a(flip),b,19550,a),flip(a)].">
      <j1 rule="hyper" parents="58 19547 19550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19562">
    <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,19478,a(flip),b,19561,a),flip(a)].">
      <j1 rule="hyper" parents="58 19478 19561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19563">
    <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(19556(a,1),14972(a,1,1,2))].">
      <j1 rule="para" parents="19556 14972"/>
    </justification>
  </clause>

  <clause id="19565">
    <literal><![CDATA[
      a(x \ (y \ (z \ u)),w,K(v5,v6)) = a(((u / z) \ y) * x,v6,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(18353,a,19515,a)].">
      <j1 rule="hyper" parents="18353 19515"/>
    </justification>
  </clause>

  <clause id="19566">
    <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(14304,a,19515,a),flip(a)].">
      <j1 rule="hyper" parents="14304 19515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19567">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a(z \ (y * x),v5,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,19456,a,b,19515,a),flip(a)].">
      <j1 rule="hyper" parents="320 19456 19515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19568">
    <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(19516(a,2),19513(a,1))].">
      <j1 rule="para" parents="19516 19513"/>
    </justification>
  </clause>

  <clause id="19569">
    <literal><![CDATA[
      a(x \ (y * (z \ 1)),u,K(w,v5)) = a(w,v5,K(u,z * (y \ x)))
    ]]></literal>
    <justification jstring="[para(13710(a,1),19540(a,2,3))].">
      <j1 rule="para" parents="13710 19540"/>
    </justification>
  </clause>

  <clause id="19570">
    <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(19540(a,2),14307(a,1))].">
      <j1 rule="para" parents="19540 14307"/>
    </justification>
  </clause>

  <clause id="19571">
    <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(19540(a,2),19519(a,1))].">
      <j1 rule="para" parents="19540 19519"/>
    </justification>
  </clause>

  <clause id="19572">
    <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(10332(a,1),19567(a,2,1,2))].">
      <j1 rule="para" parents="10332 19567"/>
    </justification>
  </clause>

  <clause id="19573">
    <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(19489(a,2),14902(a,1))].">
      <j1 rule="para" parents="19489 14902"/>
    </justification>
  </clause>

  <clause id="19574">
    <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,19553,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 19553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19575">
    <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(19222(a,2),19553(a,1,2))].">
      <j1 rule="para" parents="19222 19553"/>
    </justification>
  </clause>

  <clause id="19576">
    <literal><![CDATA[
      a(x \ (y * (z \ 1)),u,K(w,v5)) = a(z * (y \ x),v5,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14195,a(flip),b,19569,a),flip(a)].">
      <j1 rule="hyper" parents="320 14195 19569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19577">
    <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(19576(a,2),14270(a,1))].">
      <j1 rule="para" parents="19576 14270"/>
    </justification>
  </clause>

  <clause id="19578">
    <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,18351,a(flip),b,19541,a)].">
      <j1 rule="hyper" parents="58 18351 19541"/>
    </justification>
  </clause>

  <clause id="19579">
    <literal><![CDATA[
      T(x,y \ L(y,z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19071,a(flip),b,19552,a)].">
      <j1 rule="hyper" parents="58 19071 19552"/>
    </justification>
  </clause>

  <clause id="19580">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(13329,a,19579,a)].">
      <j1 rule="hyper" parents="13329 19579"/>
    </justification>
  </clause>

  <clause id="19582">
    <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(19580(a,2),14105(a,1))].">
      <j1 rule="para" parents="19580 14105"/>
    </justification>
  </clause>

  <clause id="19583">
    <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(18715(a,2),19582(a,1))].">
      <j1 rule="para" parents="18715 19582"/>
    </justification>
  </clause>

  <clause id="19584">
    <literal><![CDATA[
      a(x,y,L(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(19580(a,1),19583(a,1,3))].">
      <j1 rule="para" parents="19580 19583"/>
    </justification>
  </clause>

  <clause id="19585">
    <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(13456(a,1),19584(a,1))].">
      <j1 rule="para" parents="13456 19584"/>
    </justification>
  </clause>

  <clause id="19586">
    <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(13456(a,2),19585(a,1))].">
      <j1 rule="para" parents="13456 19585"/>
    </justification>
  </clause>

  <clause id="19587">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) * (y * u)) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,19377,a(flip),b,19562,a)].">
      <j1 rule="hyper" parents="58 19377 19562"/>
    </justification>
  </clause>

  <clause id="19588">
    <literal><![CDATA[
      K(x,(y * (z / u)) * u) = K(x,(y / u) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15396,a(flip),b,19587,a),flip(a)].">
      <j1 rule="hyper" parents="58 15396 19587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19589">
    <literal><![CDATA[
      K(x,(y / z) * (z * (u \ 1))) = K(x,(y / (z * u)) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,19480,a(flip),b,19588,a),flip(a)].">
      <j1 rule="hyper" parents="58 19480 19588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19590">
    <literal><![CDATA[
      K(x,(y / (z * u)) * z) = K(x,(y / z) * (z / u))
    ]]></literal>
    <justification jstring="[hyper(19313,a,19589,a),flip(a)].">
      <j1 rule="hyper" parents="19313 19589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19591">
    <literal><![CDATA[
      K(x,y \ ((y * z) / u)) = K(x,(z / y) * (y / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19446,a,b,19590,a)].">
      <j1 rule="hyper" parents="58 19446 19590"/>
    </justification>
  </clause>

  <clause id="19592">
    <literal><![CDATA[
      K(x,y \ ((y * (z * u)) / z)) = K(x,L(T(u,z),y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,19546,a(flip),b,19591,a),flip(a)].">
      <j1 rule="hyper" parents="320 19546 19591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19593">
    <literal><![CDATA[
      K(x,y / ((z * u) \ (u * y))) = K(x,L(T(z,u),y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19089,a,b,19592,a)].">
      <j1 rule="hyper" parents="58 19089 19592"/>
    </justification>
  </clause>

  <clause id="19594">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u)) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,19593,a(flip),b,19007,a(flip))].">
      <j1 rule="hyper" parents="119 19593 19007"/>
    </justification>
  </clause>

  <clause id="19595">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,u) / y) = (x * y) / (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19551,a,b,19594,a)].">
      <j1 rule="hyper" parents="58 19551 19594"/>
    </justification>
  </clause>

  <clause id="19596">
    <literal><![CDATA[
      (x * y) / (y * K(T(z,y),u)) = (x / (y \ 1)) * (y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18586,a(flip),b,19595,a),flip(a)].">
      <j1 rule="hyper" parents="58 18586 19595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19597">
    <literal><![CDATA[
      (x / (y \ 1)) * (y \ K(z,u)) = (x * y) / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(7123(a,1),19596(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7123 19596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19598">
    <literal><![CDATA[
      (x * (y / z)) / (K(u,y) * (y / z)) = (x / z) * (z * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(19144,a,19597,a),flip(a)].">
      <j1 rule="hyper" parents="19144 19597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19599">
    <literal><![CDATA[
      (x * (T(y,z) / u)) / (y / u) = (x / u) * (u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19171,a(flip),b,19598,a)].">
      <j1 rule="hyper" parents="58 19171 19598"/>
    </justification>
  </clause>

  <clause id="19600">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = L(x,K(u,z),y \ z)
    ]]></literal>
    <justification jstring="[para(19599(a,1),19185(a,1,1))].">
      <j1 rule="para" parents="19599 19185"/>
    </justification>
  </clause>

  <clause id="19601">
    <literal><![CDATA[
      L(x,K(y,z),u \ z) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(19573,a,19600,a),flip(a)].">
      <j1 rule="hyper" parents="19573 19600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19602">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,17749,a(flip),b,19601,a),flip(a)].">
      <j1 rule="hyper" parents="58 17749 19601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19603">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(12656,a,19602,a),flip(a)].">
      <j1 rule="hyper" parents="12656 19602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19604">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,19524,a(flip),b,19603,a),flip(a)].">
      <j1 rule="hyper" parents="320 19524 19603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19606">
    <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(19604(a,1),14181(a,1,1))].">
      <j1 rule="para" parents="19604 14181"/>
    </justification>
  </clause>

  <clause id="19607">
    <literal><![CDATA[
      a(((x / y) \ z) * u,w,K(v5,v6)) = a(((y \ x) \ z) * u,w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(19538,a,19565,a),flip(a)].">
      <j1 rule="hyper" parents="19538 19565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19608">
    <literal><![CDATA[
      a(x,y,K(z * (T(u,w) \ v5),v6)) = a(z * (u \ v5),v6,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(19542,a,19523,a),flip(a)].">
      <j1 rule="hyper" parents="19542 19523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19609">
    <literal><![CDATA[
      a((((x * y) / x) \ z) * u,w,K(v5,v6)) = a(u * (y \ z),v5,K(v6,w))
    ]]></literal>
    <justification jstring="[hyper(18275,a,19608,a)].">
      <j1 rule="hyper" parents="18275 19608"/>
    </justification>
  </clause>

  <clause id="19612">
    <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(19574(a,1),19575(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="19574 19575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19613">
    <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(5092(a,1),19572(a,1,1))].">
      <j1 rule="para" parents="5092 19572"/>
    </justification>
  </clause>

  <clause id="19614">
    <literal><![CDATA[
      a((x * (y * z)) \ u,w,K(v5,v6)) = a(u \ (x * (z * y)),v6,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(19542,a,19613,a)].">
      <j1 rule="hyper" parents="19542 19613"/>
    </justification>
  </clause>

  <clause id="19615">
    <literal><![CDATA[
      a((x * y) \ (z \ u),w,K(v5,v6)) = a(u \ (z * (y * x)),v6,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(14434,a,19614,a)].">
      <j1 rule="hyper" parents="14434 19614"/>
    </justification>
  </clause>

  <clause id="19617">
    <literal><![CDATA[
      a(x \ (y \ (z \ u)),w,K(v5,v6)) = a(u \ (z * (x * y)),v6,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(14434,a,19615,a)].">
      <j1 rule="hyper" parents="14434 19615"/>
    </justification>
  </clause>

  <clause id="19618">
    <literal><![CDATA[
      a(x \ (y * (z * u)),w,K(v5,v6)) = a(((y \ x) \ u) * z,w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(19538,a,19617,a),flip(a)].">
      <j1 rule="hyper" parents="19538 19617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19619">
    <literal><![CDATA[
      a(((x \ y) \ z) * u,w,K(v5,v6)) = a((y \ x) * (u * z),w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(19458,a,19618,a),flip(a)].">
      <j1 rule="hyper" parents="19458 19618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19620">
    <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,19607,a,b,19619,a)].">
      <j1 rule="hyper" parents="58 19607 19619"/>
    </justification>
  </clause>

  <clause id="19621">
    <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,19609,a(flip),b,19620,a),flip(a)].">
      <j1 rule="hyper" parents="58 19609 19620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19622">
    <literal><![CDATA[
      a(x \ (y * z),u,K(w,v5)) = a(y * (x \ z),w,K(v5,u))
    ]]></literal>
    <justification jstring="[hyper(19568,a,19621,a)].">
      <j1 rule="hyper" parents="19568 19621"/>
    </justification>
  </clause>

  <clause id="19623">
    <literal><![CDATA[
      a(x * (y \ (z \ 1)),u,K(w,v5)) = a(u,w,K(v5,z * (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(19577,a,19622,a),flip(a)].">
      <j1 rule="hyper" parents="19577 19622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19624">
    <literal><![CDATA[
      a(x * (y \ z),u,K(w,v5)) = a(v5,u,K(w,z \ (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(19571,a,19622,a),flip(a)].">
      <j1 rule="hyper" parents="19571 19622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19625">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a(y * (z \ x),w,K(u,v5))
    ]]></literal>
    <justification jstring="[hyper(19570,a,19622,a)].">
      <j1 rule="hyper" parents="19570 19622"/>
    </justification>
  </clause>

  <clause id="19626">
    <literal><![CDATA[
      a(x * (y \ z),u,K(w,v5)) = a(z * (y \ x),v5,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(19461,a,19622,a),flip(a)].">
      <j1 rule="hyper" parents="19461 19622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19627">
    <literal><![CDATA[
      a((x \ y) * z,u,K(w,v5)) = a(y * (x \ z),w,K(v5,u))
    ]]></literal>
    <justification jstring="[hyper(19458,a,19622,a)].">
      <j1 rule="hyper" parents="19458 19622"/>
    </justification>
  </clause>

  <clause id="19628">
    <literal><![CDATA[
      a(x * (y \ z),u,K(w,v5)) = a(u,v5,K(w,y \ (x * z)))
    ]]></literal>
    <justification jstring="[hyper(14270,a,19622,a),flip(a)].">
      <j1 rule="hyper" parents="14270 19622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19629">
    <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(19622(a,2),19520(a,1))].">
      <j1 rule="para" parents="19622 19520"/>
    </justification>
  </clause>

  <clause id="19630">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a(y * (z \ x),u,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,14195,a(flip),b,19624,a)].">
      <j1 rule="hyper" parents="320 14195 19624"/>
    </justification>
  </clause>

  <clause id="19631">
    <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),19624(a,2,3,2,2))].">
      <j1 rule="para" parents="4 19624"/>
    </justification>
  </clause>

  <clause id="19632">
    <literal><![CDATA[
      a(x * (y \ z),u,K(w,v5)) = a(w,u,K(v5,z * (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(19508,a,19626,a),flip(a)].">
      <j1 rule="hyper" parents="19508 19626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19633">
    <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(19626(a,2),19507(a,1))].">
      <j1 rule="para" parents="19626 19507"/>
    </justification>
  </clause>

  <clause id="19634">
    <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(19626(a,2),19520(a,1))].">
      <j1 rule="para" parents="19626 19520"/>
    </justification>
  </clause>

  <clause id="19635">
    <literal><![CDATA[
      a((x / y) * z,u,K(w,v5)) = a(x * (y \ z),w,K(v5,u))
    ]]></literal>
    <justification jstring="[hyper(19560,a,19627,a)].">
      <j1 rule="hyper" parents="19560 19627"/>
    </justification>
  </clause>

  <clause id="19636">
    <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),19628(a,2,3,2,2))].">
      <j1 rule="para" parents="5 19628"/>
    </justification>
  </clause>

  <clause id="19637">
    <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(19630(a,2),19520(a,1))].">
      <j1 rule="para" parents="19630 19520"/>
    </justification>
  </clause>

  <clause id="19638">
    <literal><![CDATA[
      a(x * (y \ (x \ z)),u,K(w,v5)) = a(w,u,K(v5,y \ z))
    ]]></literal>
    <justification jstring="[hyper(19520,a,19636,a)].">
      <j1 rule="hyper" parents="19520 19636"/>
    </justification>
  </clause>

  <clause id="19639">
    <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(19638(a,2),19501(a,1))].">
      <j1 rule="para" parents="19638 19501"/>
    </justification>
  </clause>

  <clause id="19640">
    <literal><![CDATA[
      a(x * (y \ (z \ 1)),u,K(w,v5)) = a(z * (x \ y),u,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,19504,a(flip),b,19623,a),flip(a)].">
      <j1 rule="hyper" parents="320 19504 19623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19641">
    <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(3559(a,1),19633(a,1,1,2))].">
      <j1 rule="para" parents="3559 19633"/>
    </justification>
  </clause>

  <clause id="19642">
    <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(18221(a,1),19634(a,1))].">
      <j1 rule="para" parents="18221 19634"/>
    </justification>
  </clause>

  <clause id="19643">
    <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,14998,a(flip),b,19563,a)].">
      <j1 rule="hyper" parents="58 14998 19563"/>
    </justification>
  </clause>

  <clause id="19644">
    <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(6168(a,2),19643(a,1,1,2))].">
      <j1 rule="para" parents="6168 19643"/>
    </justification>
  </clause>

  <clause id="19645">
    <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,14998,a(flip),b,19644,a)].">
      <j1 rule="hyper" parents="58 14998 19644"/>
    </justification>
  </clause>

  <clause id="19646">
    <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(19527(a,1),19606(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19527 19606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19647">
    <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(4167(a,1),19646(a,2,1))].">
      <j1 rule="para" parents="4167 19646"/>
    </justification>
  </clause>

  <clause id="19648">
    <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(320,a,13893,a(flip),b,19647,a),flip(a)].">
      <j1 rule="hyper" parents="320 13893 19647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19649">
    <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),19648(a,2,1))].">
      <j1 rule="para" parents="17 19648"/>
    </justification>
  </clause>

  <clause id="19650">
    <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(7852(a,1),19649(a,1,1,2,2))].">
      <j1 rule="para" parents="7852 19649"/>
    </justification>
  </clause>

  <clause id="19651">
    <literal><![CDATA[
      T(x * K(y,z * x),z) = T(x,z) * K(y,x * z)
    ]]></literal>
    <justification jstring="[para(12290(a,1),19650(a,1,1,2))].">
      <j1 rule="para" parents="12290 19650"/>
    </justification>
  </clause>

  <clause id="19652">
    <literal><![CDATA[
      x \ T(x * K(y,z * x),z) = K(y,x * z) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,19651,a,b,15597,a)].">
      <j1 rule="hyper" parents="116 19651 15597"/>
    </justification>
  </clause>

  <clause id="19653">
    <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(19651(a,2),19645(a,1,1,2,2,1))].">
      <j1 rule="para" parents="19651 19645"/>
    </justification>
  </clause>

  <clause id="19654">
    <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(19525(a,2),19531(a,1,1))].">
      <j1 rule="para" parents="19525 19531"/>
    </justification>
  </clause>

  <clause id="19655">
    <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(19525(a,2),19654(a,1,2,1,1))].">
      <j1 rule="para" parents="19525 19654"/>
    </justification>
  </clause>

  <clause id="19656">
    <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(19525(a,2),19655(a,1,2,1,2))].">
      <j1 rule="para" parents="19525 19655"/>
    </justification>
  </clause>

  <clause id="19657">
    <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(19640(a,1),19641(a,1))].">
      <j1 rule="para" parents="19640 19641"/>
    </justification>
  </clause>

  <clause id="19658">
    <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(19558(a,1),19559(a,1,2,2,1,2,1))].">
      <j1 rule="para" parents="19558 19559"/>
    </justification>
  </clause>

  <clause id="19659">
    <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(19612(a,1),19658(a,1,2))].">
      <j1 rule="para" parents="19612 19658"/>
    </justification>
  </clause>

  <clause id="19660">
    <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,13411,a(flip),b,19659,a)].">
      <j1 rule="hyper" parents="58 13411 19659"/>
    </justification>
  </clause>

  <clause id="19662">
    <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(19525(a,2),19660(a,1,1))].">
      <j1 rule="para" parents="19525 19660"/>
    </justification>
  </clause>

  <clause id="19663">
    <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(19525(a,2),19662(a,1,2,1,1))].">
      <j1 rule="para" parents="19525 19662"/>
    </justification>
  </clause>

  <clause id="19664">
    <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,19656,a(flip),b,19663,a)].">
      <j1 rule="hyper" parents="58 19656 19663"/>
    </justification>
  </clause>

  <clause id="19666">
    <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(320,a,19557,a,b,19664,a)].">
      <j1 rule="hyper" parents="320 19557 19664"/>
    </justification>
  </clause>

  <clause id="19667">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * L(w \ u,v5,v6)) = L(w * L(w \ u,v5,v6),x,K(z,y))
    ]]></literal>
    <justification jstring="[para(19495(a,1),19666(a,1,1))].">
      <j1 rule="para" parents="19495 19666"/>
    </justification>
  </clause>

  <clause id="19668">
    <literal><![CDATA[
      a(x,y,K(z,u * L(u \ w,v5,v6))) = a(z,x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(30,a,19502,a,b,19667,a)].">
      <j1 rule="hyper" parents="30 19502 19667"/>
    </justification>
  </clause>

  <clause id="19669">
    <literal><![CDATA[
      a(x,y,K(z,u * L(u \ w,v5,v6))) = a(w,x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,14195,a(flip),b,19668,a),flip(a)].">
      <j1 rule="hyper" parents="320 14195 19668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19670">
    <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(1689(a,1),19668(a,1,3,2))].">
      <j1 rule="para" parents="1689 19668"/>
    </justification>
  </clause>

  <clause id="19671">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5) * v6)) = a(u * v6,x,K(z,y))
    ]]></literal>
    <justification jstring="[para(633(a,1),19669(a,1,3,2))].">
      <j1 rule="para" parents="633 19669"/>
    </justification>
  </clause>

  <clause id="19672">
    <literal><![CDATA[
      a(x * L(y,z,u),w,K(v5,v6)) = a(y * x,w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(19514,a,19671,a)].">
      <j1 rule="hyper" parents="19514 19671"/>
    </justification>
  </clause>

  <clause id="19673">
    <literal><![CDATA[
      a(L(x,y,z) * u,w,K(v5,v6)) = a(x * u,v6,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(19507,a,19671,a)].">
      <j1 rule="hyper" parents="19507 19671"/>
    </justification>
  </clause>

  <clause id="19674">
    <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(19642,a,19672,a)].">
      <j1 rule="hyper" parents="19642 19672"/>
    </justification>
  </clause>

  <clause id="19675">
    <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(19673(a,1),19657(a,1))].">
      <j1 rule="para" parents="19673 19657"/>
    </justification>
  </clause>

  <clause id="19676">
    <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(19513,a,19670,a)].">
      <j1 rule="hyper" parents="19513 19670"/>
    </justification>
  </clause>

  <clause id="19677">
    <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(320,a,19626,a(flip),b,19674,a),flip(a)].">
      <j1 rule="hyper" parents="320 19626 19674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19678">
    <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(19676(a,1),19629(a,1))].">
      <j1 rule="para" parents="19676 19629"/>
    </justification>
  </clause>

  <clause id="19679">
    <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(19677(a,2),19634(a,1))].">
      <j1 rule="para" parents="19677 19634"/>
    </justification>
  </clause>

  <clause id="19680">
    <literal><![CDATA[
      a(x * (y \ L(x \ 1,z,u)),w,K(v5,v6)) = a(v5,v6,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(19678,a,19499,a)].">
      <j1 rule="hyper" parents="19678 19499"/>
    </justification>
  </clause>

  <clause id="19681">
    <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,19631,a(flip),b,19680,a)].">
      <j1 rule="hyper" parents="58 19631 19680"/>
    </justification>
  </clause>

  <clause id="19682">
    <literal><![CDATA[
      a(L(x \ 1,y,z) \ u,w,K(v5,v6)) = a(v6,v5,K(w,x * u))
    ]]></literal>
    <justification jstring="[hyper(14307,a,19681,a)].">
      <j1 rule="hyper" parents="14307 19681"/>
    </justification>
  </clause>

  <clause id="19683">
    <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,19578,a(flip),b,19682,a)].">
      <j1 rule="hyper" parents="58 19578 19682"/>
    </justification>
  </clause>

  <clause id="19684">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(w,v5,v6))) = a(w \ u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,19518,a(flip),b,19683,a),flip(a)].">
      <j1 rule="hyper" parents="320 19518 19683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19685">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(w,v5,v6))) = a(y,x,K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(13785(a,1),19683(a,2,3))].">
      <j1 rule="para" parents="13785 19683"/>
    </justification>
  </clause>

  <clause id="19686">
    <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(19684(a,2),19508(a,1))].">
      <j1 rule="para" parents="19684 19508"/>
    </justification>
  </clause>

  <clause id="19687">
    <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,19566,a,b,19685,a)].">
      <j1 rule="hyper" parents="58 19566 19685"/>
    </justification>
  </clause>

  <clause id="19689">
    <literal><![CDATA[
      a(((x * y) \ (x * z)) * u,w,K(v5,v6)) = a(v6,v5,K(w,u * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(320,a,19439,a(flip),b,19687,a),flip(a)].">
      <j1 rule="hyper" parents="320 19439 19687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19690">
    <literal><![CDATA[
      a(x,y,K(z,u * ((w * v5) \ (w * v6)))) = a(x,y,K(z,u * (v5 \ v6)))
    ]]></literal>
    <justification jstring="[hyper(19503,a,19689,a)].">
      <j1 rule="hyper" parents="19503 19689"/>
    </justification>
  </clause>

  <clause id="19691">
    <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(13971(a,1),19690(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="13971 19690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19692">
    <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(19675,a,19635,a)].">
      <j1 rule="hyper" parents="19675 19635"/>
    </justification>
  </clause>

  <clause id="19694">
    <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),19692(a,2,1))].">
      <j1 rule="para" parents="2 19692"/>
    </justification>
  </clause>

  <clause id="19695">
    <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(320,a,19625,a(flip),b,19694,a),flip(a)].">
      <j1 rule="hyper" parents="320 19625 19694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19696">
    <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),19695(a,2,1,2))].">
      <j1 rule="para" parents="61 19695"/>
    </justification>
  </clause>

  <clause id="19697">
    <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),19696(a,2,1))].">
      <j1 rule="para" parents="3 19696"/>
    </justification>
  </clause>

  <clause id="19699">
    <literal><![CDATA[
      a(x,y,K(z,u \ (L(u \ 1,w,v5) \ v6))) = a(v6,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(13785(a,1),19697(a,1,3))].">
      <j1 rule="para" parents="13785 19697"/>
    </justification>
  </clause>

  <clause id="19700">
    <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(19534(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="19534 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19701">
    <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(14248(a,1),19535(a,1,1))].">
      <j1 rule="para" parents="14248 19535"/>
    </justification>
  </clause>

  <clause id="19702">
    <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(19222(a,2),19701(a,1,1))].">
      <j1 rule="para" parents="19222 19701"/>
    </justification>
  </clause>

  <clause id="19703">
    <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(14862(a,1),19702(a,1,1,1))].">
      <j1 rule="para" parents="14862 19702"/>
    </justification>
  </clause>

  <clause id="19704">
    <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(5430,a,19703,a),flip(a)].">
      <j1 rule="hyper" parents="5430 19703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19706">
    <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,19539,a(flip),b,19704,a),flip(a)].">
      <j1 rule="hyper" parents="34 19539 19704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19707">
    <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(17154,a,19706,a)].">
      <j1 rule="hyper" parents="17154 19706"/>
    </justification>
  </clause>

  <clause id="19708">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (L(z,x,u) \ z) = T(L(z,x,u) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(19700,a,19707,a)].">
      <j1 rule="hyper" parents="19700 19707"/>
    </justification>
  </clause>

  <clause id="19709">
    <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(294,a,19708,a)].">
      <j1 rule="hyper" parents="294 19708"/>
    </justification>
  </clause>

  <clause id="19711">
    <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,17399,a,b,19709,a)].">
      <j1 rule="hyper" parents="58 17399 19709"/>
    </justification>
  </clause>

  <clause id="19712">
    <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(19511(a,2),19711(a,1,1,2))].">
      <j1 rule="para" parents="19511 19711"/>
    </justification>
  </clause>

  <clause id="19713">
    <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(14207(a,2),19712(a,1,1,2))].">
      <j1 rule="para" parents="14207 19712"/>
    </justification>
  </clause>

  <clause id="19714">
    <literal><![CDATA[
      T(L(x,y,z) \ x,x \ u) = T(L(x,y,z) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(6303,a,19713,a)].">
      <j1 rule="hyper" parents="6303 19713"/>
    </justification>
  </clause>

  <clause id="19715">
    <literal><![CDATA[
      T(L(x,y,z) \ x,x * u) = T(L(x,y,z) \ x,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),19714(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 19714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19716">
    <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(19714(a,1),11720(a,1))].">
      <j1 rule="para" parents="19714 11720"/>
    </justification>
  </clause>

  <clause id="19717">
    <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(13315(a,1),19716(a,1))].">
      <j1 rule="para" parents="13315 19716"/>
    </justification>
  </clause>

  <clause id="19719">
    <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(19715(a,1),19717(a,1))].">
      <j1 rule="para" parents="19715 19717"/>
    </justification>
  </clause>

  <clause id="19720">
    <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(13315(a,1),19719(a,1))].">
      <j1 rule="para" parents="13315 19719"/>
    </justification>
  </clause>

  <clause id="19721">
    <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(19720,a,6045,a)].">
      <j1 rule="hyper" parents="19720 6045"/>
    </justification>
  </clause>

  <clause id="19723">
    <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(11719(a,1),19721(a,1,1))].">
      <j1 rule="para" parents="11719 19721"/>
    </justification>
  </clause>

  <clause id="19724">
    <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(19723(a,1),19632(a,2,3,2,2))].">
      <j1 rule="para" parents="19723 19632"/>
    </justification>
  </clause>

  <clause id="19725">
    <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,19673,a(flip),b,19724,a)].">
      <j1 rule="hyper" parents="58 19673 19724"/>
    </justification>
  </clause>

  <clause id="19726">
    <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(19642,a,19725,a)].">
      <j1 rule="hyper" parents="19642 19725"/>
    </justification>
  </clause>

  <clause id="19728">
    <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),19726(a,1,1))].">
      <j1 rule="para" parents="2 19726"/>
    </justification>
  </clause>

  <clause id="19729">
    <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(19637,a,19728,a)].">
      <j1 rule="hyper" parents="19637 19728"/>
    </justification>
  </clause>

  <clause id="19730">
    <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(19679,a,19729,a)].">
      <j1 rule="hyper" parents="19679 19729"/>
    </justification>
  </clause>

  <clause id="19731">
    <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(19639,a,19730,a)].">
      <j1 rule="hyper" parents="19639 19730"/>
    </justification>
  </clause>

  <clause id="19733">
    <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(19686,a,19731,a)].">
      <j1 rule="hyper" parents="19686 19731"/>
    </justification>
  </clause>

  <clause id="19736">
    <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(14595(a,1),19733(a,1,3))].">
      <j1 rule="para" parents="14595 19733"/>
    </justification>
  </clause>

  <clause id="19737">
    <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,19699,a(flip),b,19736,a),flip(a)].">
      <j1 rule="hyper" parents="58 19699 19736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19739">
    <literal><![CDATA[
      a(x,y,K(z,u * a(w,v5,v6))) = a(u,x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,19691,a(flip),b,19737,a)].">
      <j1 rule="hyper" parents="58 19691 19737"/>
    </justification>
  </clause>

  <clause id="19740">
    <literal><![CDATA[
      a(a(x,y,z) * u,w,K(v5,v6)) = a(u,w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(19514,a,19739,a)].">
      <j1 rule="hyper" parents="19514 19739"/>
    </justification>
  </clause>

  <clause id="19742">
    <literal><![CDATA[
      a(x * (y \ a(z,u,w)),v5,K(v6,v7)) = a(y \ x,v7,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(19634,a,19740,a)].">
      <j1 rule="hyper" parents="19634 19740"/>
    </justification>
  </clause>

  <clause id="19743">
    <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),19740(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 19740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19745">
    <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(19742(a,1),14218(a,1,2,2))].">
      <j1 rule="para" parents="19742 14218"/>
    </justification>
  </clause>

  <clause id="19746">
    <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(19743(a,1),19745(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="19743 19745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19747">
    <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(320,a,19522,a(flip),b,19746,a),flip(a)].">
      <j1 rule="hyper" parents="320 19522 19746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19749">
    <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(19554,a,19747,a)].">
      <j1 rule="hyper" parents="19554 19747"/>
    </justification>
  </clause>

  <clause id="19750">
    <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(19749(a,2),476(a,1,2,2))].">
      <j1 rule="para" parents="19749 476"/>
    </justification>
  </clause>

  <clause id="19751">
    <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(19528(a,1),19750(a,1,2))].">
      <j1 rule="para" parents="19528 19750"/>
    </justification>
  </clause>

  <clause id="19752">
    <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(828,a,19751,a)].">
      <j1 rule="hyper" parents="828 19751"/>
    </justification>
  </clause>

  <clause id="19753">
    <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,13975,a(flip),b,19752,a),flip(a)].">
      <j1 rule="hyper" parents="58 13975 19752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19755">
    <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,19215,a(flip),b,19753,a)].">
      <j1 rule="hyper" parents="58 19215 19753"/>
    </justification>
  </clause>

  <clause id="19757">
    <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(19755(a,1),475(a,1,1,2,2))].">
      <j1 rule="para" parents="19755 475"/>
    </justification>
  </clause>

  <clause id="19758">
    <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,12067,a(flip),b,19757,a),flip(a)].">
      <j1 rule="hyper" parents="58 12067 19757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19759">
    <literal><![CDATA[
      a(K(x,y) * z,u,a(w,v5,v6)) = a(z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(19586,a,19758,a)].">
      <j1 rule="hyper" parents="19586 19758"/>
    </justification>
  </clause>

  <clause id="19762">
    <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,18831,a(flip),b,19759,a)].">
      <j1 rule="hyper" parents="58 18831 19759"/>
    </justification>
  </clause>

  <clause id="19763">
    <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,18819,a(flip),b,19759,a)].">
      <j1 rule="hyper" parents="58 18819 19759"/>
    </justification>
  </clause>

  <clause id="19764">
    <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,18816,a(flip),b,19759,a)].">
      <j1 rule="hyper" parents="58 18816 19759"/>
    </justification>
  </clause>

  <clause id="19765">
    <literal><![CDATA[
      a(T(x,y) \ z,u,a(w,v5,v6)) = a(x \ z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(5042(a,1),19759(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5042 19759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19766">
    <literal><![CDATA[
      a(x \ (y / z),u,a(w,v5,v6)) = a(x \ (z \ y),u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(13896(a,1),19762(a,1,1))].">
      <j1 rule="para" parents="13896 19762"/>
    </justification>
  </clause>

  <clause id="19767">
    <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,16742,a(flip),b,19764,a),flip(a)].">
      <j1 rule="hyper" parents="58 16742 19764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19769">
    <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,19766,a(flip),b,19767,a)].">
      <j1 rule="hyper" parents="58 19766 19767"/>
    </justification>
  </clause>

  <clause id="19770">
    <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(13655(a,1),19769(a,1,1,2,2))].">
      <j1 rule="para" parents="13655 19769"/>
    </justification>
  </clause>

  <clause id="19771">
    <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(5092(a,1),19770(a,1,1))].">
      <j1 rule="para" parents="5092 19770"/>
    </justification>
  </clause>

  <clause id="19772">
    <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,19759,a(flip),b,19771,a),flip(a)].">
      <j1 rule="hyper" parents="58 19759 19771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19774">
    <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,19653,a(flip),b,19772,a),flip(a)].">
      <j1 rule="hyper" parents="58 19653 19772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19776">
    <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(19652(a,1),19774(a,1,1,2))].">
      <j1 rule="para" parents="19652 19774"/>
    </justification>
  </clause>

  <clause id="19777">
    <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(6337(a,2),19776(a,1,1))].">
      <j1 rule="para" parents="6337 19776"/>
    </justification>
  </clause>

  <clause id="19778">
    <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,18818,a(flip),b,19777,a)].">
      <j1 rule="hyper" parents="58 18818 19777"/>
    </justification>
  </clause>

  <clause id="19779">
    <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,19763,a(flip),b,19778,a),flip(a)].">
      <j1 rule="hyper" parents="58 19763 19778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19781">
    <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(320,a,19765,a(flip),b,19779,a),flip(a)].">
      <j1 rule="hyper" parents="320 19765 19779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19783">
    <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(19781(a,1),14783(a,1,1))].">
      <j1 rule="para" parents="19781 14783"/>
    </justification>
  </clause>

  <clause id="19784">
    <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(207,a,19783,a),flip(a)].">
      <j1 rule="hyper" parents="207 19783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19787">
    <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(14748(a,1),19784(a,1,1))].">
      <j1 rule="para" parents="14748 19784"/>
    </justification>
  </clause>

  <clause id="19788">
    <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(320,a,18823,a(flip),b,19787,a),flip(a)].">
      <j1 rule="hyper" parents="320 18823 19787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19789">
    <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(15009(a,1),19788(a,1,1))].">
      <j1 rule="para" parents="15009 19788"/>
    </justification>
  </clause>

  <clause id="19790">
    <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(4023(a,1),19789(a,1,1))].">
      <j1 rule="para" parents="4023 19789"/>
    </justification>
  </clause>

  <clause id="19792">
    <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(320,a,14999,a(flip),b,19790,a),flip(a)].">
      <j1 rule="hyper" parents="320 14999 19790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19793">
    <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),19792(a,2,1))].">
      <j1 rule="para" parents="4 19792"/>
    </justification>
  </clause>

  <clause id="19795">
    <literal><![CDATA[
      a(x,a(y,z,a(u,w,v5)),v6) = a(y,z,a(u,w,v5)) \ a(y,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(19793(a,1),15474(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19793 15474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19796">
    <literal><![CDATA[
      a(x,a(y,z,a(u,w,v5)),v6) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,61,a(flip),b,19795,a),flip(a)].">
      <j1 rule="hyper" parents="320 61 19795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19797">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer("nil3 29, aa3-Nm")
    ]]></attribute>
    <justification jstring="[resolve(19796,a,59,a)].">
      <j1 rule="resolve" parents="19796 59"/>
    </justification>
  </clause>

</proof>

</proofs>
